Piping Stress Handbook

Piping Stress Handbook Second Edition -

-

Victor Helguero M.

Piping Stress Handbook Second Edition

Gulf Publishing Company Book Division Houston, London, Paris, Tokyo

Piping Second Library of

ISBN G87201_?03-6

Copyright @ 19_86 by Gulf publishing Company, Housron, Texas. All ngfts reserved. printed in the United Stabs;f

p-ar,b

ttrepf.

A;dca- itis book;; *itt out perJsio'i

may not be regoduced io a"y fo.rn

of the publisher.

$BN GE720r-nB{

.

.::

-i.j.

. -- ,,

Contents vlll

Preface

Chapter

1

Basic Theory of Pipe Stress and ANSI/ASME Codes 831.1, 831.3' ... . .. 1 831.4, and 831.8 Ptpe Stress Compliances . . . .

.

Pipe Stress Theory. Expansion Stresses. Cold Springing. ANSI 831.1 Fower Piping Code Stress Compliances (1983). ANSI 831.3 Chemical Plant and Petroleum Refinery Piping Code Stress Compliances (1984). ANSI B31.4 Liquid Fetroleum Transportation Piping Code Stress Compliances. DOT/B31.8 Gas Transmission and Distribution Piping Systems Stress Compliances. Standard Oudine for ANSI B3l Codes.

Chapter 2 Coefficients of Thermal

Expansion

,........17

Tables. Example Problem.

Chapter 3 Allowable Stress Range for ANSI/ASME Power Piping Code 831.1 ..... 38 (1e83)

.

Tables.

Chapter 4 Allowable Stress Range for ANSI/ASME Petroleum Piping Code 831.3 (19M) . Thbles.

.

... ....73

Chapter 5 Stress Intensification and Flexibility Factors

tlz

Definitions. Thbles.

Chapter 6 Rotational Nozzle Flexibilities for Cylindrical Vessels

.

......l?a

Thbles.

Chapter 7 hessure and Shess Ratioo

.

.......177

Thbles. Instructions and Examples. Branch Reinforcement. Sample Calcula_ tions for Branch Reinforcement.

Chapter 8 Ihsign Criteria for Allowable loads, Moment, and Stresses

........257

Design Criteria for Pumps with Steel Nozzles anit Casings. Design Criteria for Pumps with Cast Iron or Aluminum Nozzles and Casings. Design Criteria ior Tirbine Drivers wilh Steel Nozzles and Casings. Design Criteria for Thrbine Drivers with Cast Iron or Aluminum Nozdes and Casings. Design Criteria for Compressors with Steel Nozzles and Casings. Design Criteria for Cornpres_ sors with Cast Iron or Aluminum Nozzles and Casings. ApI Code 661 Design Criteria for Air-Cooled Heat Exchansers.

Chapter 9 Simptified Solutions for Pipe Stress

265

Example Problem 9-1. Thbles. Example Problem 9-2.

Chapter 10

PropertiesofPipe Definitions. Thbles.

.........292

Chapter

11

Components

Weight and Dimensions of Pipe and

..

. 299

Weight of Pipe and Components. Tables.

Chapter 12 Allowable Pipe Span Formulas and

Thbles

...... ... 314

Pipe-Span Stress Limits. Pipe-Span Deflection Limits. Piping Wind Loads.

Chapter 13 Pipe Support Selection and

Design

..,...,

.

34

Pipe Supports. Spring Supports. Insulated Pipe Supports and Anchors for Cryogenic Service. Thbles.

Chapter 14 Fundamentalsof

ExpansionJoints.

........351

Types of Joint Movements. Nomenclature and Symbols. Types of Expansion Joints. Anchors, Guides, and Supports. Forces and Moments' Cold Springing of Expansion Joints. Cycle Life Expectancy. Corrosion. Erosion. Calculating Thermal Expansion. Precompression. Application, Pipe Guides and Guiding. Iocation of Expansion Joints. End Connections. Covers. Sleeves.

..... ....

Glossary Index

.

368

.,..373

vtl

heface

Determining piping stresses for the design

of

petro_

. chemical and.power plant piping systems iniolves ^many

complex mathematical calculations. These calculationi cal be solved with the aid of any one of several computer programs available provided they have the required ca_ pacity and an acceptable input/output format. The most formidable task facing the engineer is compiling the ex_ tenslve amount ot data needed to run the program. These data include physical properties. allowable stiesses, valve weights and dimensions. stress intensification factorsthermal expansion coefficients. spring hangers and expanslon Jotnt selectlon, and piping wind loads.

This reference book provides formulas, technical data. and other pertinent design information not readilv avail_ able in a single source for the piping stress analyit in the petrochemical industry who often has difficulry co ecting the required data and solutions to complete a piping stresi

analysis. .Depending on the magnirude and complexity of the job, the data needed to complete a given tasi may be scattered throughout a host of sources. The author's aim is to bring together in a single reference all the above mate_ rial and present it in a convenient form. Much of the information included in this book was ob_ tained from the work of others; some was used in its orisi_ nal form. while some was rearranged for this applicatio-n.

The author wishes to acknowledge his indebtedness to

Mr. Robert Kingshill, Virender Shukla, and Timothv W. Calk. for their assisrance in preparing this handbooki and the American Society of Mechanical Ensineers which generously permitted the author to use sevlral eouations to develop tabulations contained in this handbook. Suggestions and criticism concerning errors that may .9.T]l spite_of all precautions will be greatly appri ciated. They will contribute to the further improvement of

this reference handbook.

Victor Helguero M. , PE.

viii

Basic Theory of Pipe Stress and ANSI/ASME Codes 831..1, 831.3, 83L.4, and 831.8 Pipe Stress Compliances

The bending stress due to temperature, weight of pipe, contents, insulation, snow and ice, wind or earthquake is calculated by the following equatron:

Pipe Stress Theory To understand the basic criteria of the ANSI+ pressure piping code, it will be useful to explain the way different stresses develop when a piping element is subjected to a

number of loading conditions. There are four main

piping element, as shown in Figure l1. The following gives the intensity of these stresses and the manner in which they may be combined: stresses that

affe.t

t,

: Vqgrr'lt*+l Z

a

where

: :

S5

Ii L

* For

reasons of space these codes will be designated ANSI codes riroughout the text of the book, Some readers may be mor€ familiar with the desisnation ANSI/ASME as indicated in the headings.

=

Mi M" Z

: : :

Bending stress

In-plane stress intensification factor Out-of-plane stress intensif ication factor In-plane moment, lb-in. Out-of-plane moment, lb-in. Section modulus of pipe, in.3

The direct longitudinal stress due to t€mperature and weisht is calculated as follows:

lJ\J"

.

: Fu :

where A s

t \o S, I

The longitudinal stress due to internal pressure is calculated as follows:

^PD

"P Sr

=

= S, = Ss = Sc

Longitudinal stress and the sum of three component parts (see Equation 1-1). Circumlerential stress Radial stress Shear stless

Figure 1-1. Stress-free-body diagram.

Metal pipe cross-sectional area, in.z Direct force, lb

4t'

where P D

= =

:

Internal pressure Outside diameter of pipe (see Chapter 10)

Pipe wall thickness (see Chapter 10)

S:

:

0 (shear)

2

Piping Stress Handbook

Both significant stresses act in the same direction; therefore the stresses are "additive," i.e.

: S6+\+Sa

S1

(1-l)

Nofe: Inngitudinal stresses due to temperature are excluded from the combination when doing code calculations.

Circumferential stress, S., is primarily due to internal

The preceding method is known as the maximum shear theory (Iresca) and is the preferred method of the ANSI Code. A second method, known as the distortion-energy theory (Von Mises), also provides good results but is not used by the Code:

"'3S-+J--T-+ STTT$"

pressufe:

S^:.q,D -2t Radial.stress, S., is primarily due to internal pressue, which is equal to P.

S.=P

The ANSI pressure piping code recognizes that stress

Shear sfiess, S", is the sum of two component parts: tortional stress and direct shear stress (the second stress is usually negligible). (This condition occurs in three-dimensional piping systems.)

ss: where

Expansion Stresses

T

+2.0&

n

A

SS:

T: F,:

Shear stress Torque, lb-in. Resultant shear force Cross-sectional area of pipe Section modulus of pipe

z: sr: T/22, tortional

due to thermal expansion tends to diminish with time as a

result of local yielding or creep. This reduction of stress will appear as a stress of opposite sign in the cold condition. This phenomenon is known as self springing. Cold springing is similar, and although the hot stresses tend to diminish with time, the sum of the hot and cold stresses for any one cycle will remain practically constant.. This sum is called the stress range, ard, the code for pressure piping defines this allowable expansion stress range established for thermal expansion in terms of hot and cold tabu-

lar S values

S.

stress

:

F (1.25 S"

where S,

While the ANSI pressure piping code considers stresses due to therrnal expansion separately from primary stresses due to pressure, weight, and external loadi_ngs,/it is obvious that when combined stresses formulas and a specific yield criterion existr/stresses from all loadings should be included to delermine the principal stresses before confirming them. Resultant principal stresses at the outside

as:

=

: Sr, : F: S"

+ 0.25 Sh)

Allowable expansion stress range

(see

Chapters 3 and 4)

Allowable stress for the cold condition (see Chapters 3 and 4) Allowable stress for the hot condition (see Chapters 3 and 4) Stress range reduction factor for the cyclic

condition

fiber are as follows:

Sr

. sz

=

:

l/2

|2

Ib calculate

[Sr

+ S. +..//4St+ (S'=TFf

[g + s"

- "v4trTre-.l]zr

the principal stresses use 51 or 52, whichever

is greater, or the following equation:

\4* + C;=TJ'

(r-2)

Tbtal No. of Cycles Over Expected Life 7,000 and less

1.0

14,000 and 22,000 and 45,000 and 100,000 and 250,000 and

0.9 0.8 o.7 0.6 0.5

less less less less less

Basic Theory of Pipe Stress and ANSI/ASME Codes The stress due to thermal expansion, which must not :rceed the allowable expansion range , is callel expansion .;-ess and is defined by the piping code as:

n,:(1 -znci(fJn &=cR

s"={SJ'?+4-(sF xe Equation 1-2, where Sp

:

0 and Sr

:

Ss

The piping code further states that the sum of the long; ,-idinal stresses due to pressure, weight, and other sus:ined external loadings shall not exceed $,. Ifthe longitu:jnal stress due to sustained loadings is less than S1, the

:ode permits the unused portion to be applied to extend range available for expansion effects. There-

-.1e stress

:ore, the code, in effect, permits a total equal to 1.25 S. * Sr,), for thermal expansion stress combined with suesses

from other sustained loadings.

n=[r-tn"El* ' I s" Er,l

These relationships apply only to two-anchor piping systems with no intermediate restraints (use whichever equation is greater) and with the further condition that

sn*E
no cold spring to one for lO0% cold

se=

E": Er' : R: Cold Springing

spring

Maximum computed expansion stress Modulus of elasticity in the cold condition Modulus of elasticity in the hot condition Range of reactions corresponding to the full expansion range based on E"

R" and R1 represent the maximum reactions estimated to

A piping system may be cold sprung, or prestressed, to :educe anchor forces and moments caused by thermal expansion or contraction. This is accomplished by shortenng or lengthening the overall length of pipe by any desired amount not in excess of the calculated expansion. The amount of cold spring (C. S.) is usually expressed as a percentage or fraction of the total expansion or contrac-

Ion. This procedure is recognized by the ANSI Code for pressure piping which states: The beneficial effect of judicious cold springing in assisting the system to attain its most favorable condition sooner is recognized. Inasmuch as dre life of a system under cyclic condition depends pdmarily on the stress range rather than the stress level at any one time, no credit for cold spring is warranted with regard to sresses. In calculating end trusts and moments acting on equipment containing moving or removable parts with close clearanc€s, the actual reactions at ally one time mther than their range are signifi-

calt, and credit accordingly is allowed for cold spring in

the

calculations of thrusts and moments.

The reactions (forces and moments) & and & il the hot and cold conditions, respectively, obtained as follows from the reactions, R, are derived from the flexibility calculations based on the modulus of elasticiw at room temperature, E.:

occur in the cold and hot conditions, respectively. Thus, the ANSI piping code does not allow any credit for cold springing in the cornputation of stress. For reactions in the hot condition credit may be taken for twothirds of the actual cold spring applied; however, the full amount of cold sping must be taken into account in computing reactions for the cold condition. To understand the effects of stress range, self springing, and cold springing, see Figure 1-2.

ANSI 831.1 Power Piping Code Stress Compliances (1983) The standard terms, used in the equations set forth in the ANSI code, are defined as follows:

i: Z: rm : D" : :

Stress intensification factor. The term (0.75i) shall never be taken as less than 1.0 Section modulus, tn.,Z: r^2t^ r Mean radius, in. Outside diametet in. Nominal wall thickness. in.

Piping Stress Handbook SELF.SPRING

-

26000 Psl

NO COLD SPRING

24000 Psl

I I

=20 o

5 (,1q a' t! Ir

6ro

ll

-ltt ol

t: !; ii t:

I

dls\

|\)

N

/ ,---'1. r It ,l .tl t\

Irt! ti

.It

a !

m

T

L --t

I

t

\,{

, I

dld \ II

t-

, I

I r--1

It ltI

I

I I

I

I

I

a )< aa

ul tr.^ a I

Figure 1-2. Stress-range curve with and without cold spring.

: : Mr : P M"

: K: K:

M"

S,o

:

q,:

$" : S"

=

_ * S" :

Sr,

Internal design pressure Resultant moment loading due to weight and other sustained loads, in.lbs Resultant moment loading due to occa-

sional loads, including earthquake loads, trusts from relief/safety valve loads, in.-lbs Range of resultant moments due to thermal expansion/contraction, in.-lbs 1.15 for occasional loads actinq less than l0% of the operation period 1.20 for occasional loads actins less than l7o of the operation period Longitudinal stress due to pressure, psr Iolgitudinal stress due to sustained loads,

S"

:

stresses.

S.

S"

=

:

f(1.25 S" + 0.25

Sh)

(see Chapter 4) Basic material allowable stress at minimum

temperature from allowable stress tables, psl

$, =

DSI

Basic material allowable stress at maximum temperature from allowable stress tables, psi Stress range reduction factor fot cyclic conditions for total number N of fuIl-temperature cycles over total number of years of system operation (see " Expansion Stresses")

Longitudinal stress due to occasional loads, psi Thermal expansion stress due to thermal 9xpansion and anchor displacements, psi Longitudinal stress due to sustained loads plus the thermal expansion stress, psi

Allowable stress range for expansion

Wall thickness, in. Coefficient having values as given in the

SE=

ANSI Code 831.1, Table tV.t.2(A) Maximum allowable stress in material due to internal pressure and joint efficiency at the design temperature

Basic Theory of Pipe Stress and ANSI/ASME

'

Pressure Design The rninimum wall thickness for straight pipe under internal pressure and temperatures not exceeding those for various materials listed in the allowable stress tables, including allowances for mechanical strength, should not be

less than that determined by this equation (Section 1M.1.2, Equation 3):

,_ ''' = [_

_ro"- * ol + Pn I

(see Chapter 7)

The design pressure should not exceed:

(t - A) (see Chapter 7) D"-2Y(t--A) where t- : minimum required wall thickness, in. (mm) If pipe

5

where M" is combined in the following manner:

M"

: (Ml

+My2 +M:)t2

For full size outlet connections the equation is:

Z: r where

th

rnztn

:

Nominal wall thickness of the run pipe

For reduced outlet branch connections the equation is (see

Figure 1-3):

[2(SE

P=

Codes

2SE

Z: r where

r5

q tb

th

r3t"

: : = :

Branch mean cross sectional radius, in.

Effective branch wall thickness. in. = lesser of t5 or (i) t5 Nominal branch wall thickness. in. Nominal thickness of run PiPe. in.

is ordered by its nominal thickness, the manufac-

turing tolerances must be taken into account. This minimum thickness must be increased to provide the increase of manufactured tolerance allowed by the applicable spec-

ification or required by the process. The next heavier commercial thickness should be selected.

External Pressure

Sustained Longitudinal Stress The sustained longitudinal stress, 56' is the algebraic summation of the longitudinal pressure stress and longitudinal sustained weight stress. Sh is calculated using the following Code equation (Section 1O4.8.1, Equation 11):

To determine wall thickness and stiffening requirements for straight pipe under external pressure, the procedures outlined in paragraphs UG-28, VG-29, and UG-30 of Section VIII , Division 1 of the ASME Boiler and Pressure Vessel Code should be followed.

Longitudinal Stress LEG 3

The internal pressure stress, by the followilg equation:

^''

S1o,

should be determined

PD.

4t,

Thermal Expansion Stress The thermal expansion stress is calculated using the following Code equation:

5" = 1iv./z)

Figure 1-3. Header and branch connections'

Piping Stress Handbook

sk =

I& 19'frll4t . 4t^ z

1.s51,

(see Chapter 3 for 56)

ANSI 831.3 Ghemical plant and Petroleum Refinery piping Code Stress Compliances (1984)

As can be seen from the equation, the longitudinal stress due to pressure. weight, and other sustainid loads should be less than or equal to the Sh for the rnaterial.

Pressure Stress The minimum allowed wall thickness is calculated by using the design pressure in the following equation:

Occasional Longitudinal Stress The occasional longitudinal stress, S1o, is the algebraic summation of the longitudinal sustained weight striss the , longitudinal pressure stress, and occasionai stresr. S," i. 9{cu,tatea using the following Code equation (Seciion 104.8.2, Equation 12):

PD" 0.75iM, " _ ".-+t,--z*'
(P) (o. D.)

where O.

0.75iMh

: SE : P

D. =

y:

As can be seen from the equation, the longitudinal stress due to occasional loads should be less than-or eoual to k sh.

.875

Allowable Thermal Expansion Stress The thermal expansion stress is calculated usins the fol_

lowing Code equation (Secrion 104.8.3 tA), Equation

+

2 (SE

:

A:

yP)

+A

(see Chapter 6)

Design pressure, psig

Actual pipe outside diameter, in. Maximum allowable stress in material due to internal pressure and joint efficrency

A coefficient having values as given in the ANSI Code, Tabte 304.1.1, A; normally 0.4 A factor used to account to the industy's 12.5% mill tolerance on finished_ wall thicknesses Allowance for corrosion, erosion, etc., in.

The allowed pressure is calculated by using:

13):

S" :

iM"/Z <

S"

+

f(Sh

-

S)(see Chapter 3 for S")

As can be_ seen from the equation, the thermal expan_ . sion stress should be less than or equal to S".

2 (SE) (r-

Puo*

-

A)

O.D.-2y(t^-A)

where

tm

SE

(see Chapter 6)

= .875 x wall thickness, in. : Maximum allowable stress of the material for internal pressure considering the joint efficiency

Sustained-Plus-Thermal-Expansion Stress

Expansion Stress

The sustained-plus-thermal-expansion stress, Sh + Se, is the algebraic summation of the longitudinal stress due to sustained loads and the thermal exDansion stress. S1, * S. is calculated using rhe following iquation: sr,

+ sE =

I&

+

o75iM"

4t"ZZ

+it" .

,r- *

a",

As can be seen from the equation, the sustained-plusthermal-expansion stress should be less than or eouil to the sum of S1 and S,.

The expansion stress is calculated using the Code equation (Section 319.4.4, Eqtation 17).

S":

(S52

+

where S" :

4sr2)r/2

Computed expansion stress, psi

56 = Resultant bending stress, psi S5 = [(i1M), +(t"M"r2]t/2lz S, : Torsional stress, psi, = Mtl2Z Mr = In-plane bending moment, in.Jb M" = Out-of-plane bending moment, in.Jb

Basic Theory of Pipe Stress and ANSI/ASME

Mr

=

Z: i:

Torsional moment on cross section, in.-lb Section modulus of pipe, in.l Stress intensification factor (see Chapter 5)

For branch connections, the resultant bending stress (56) is calculated using the Code equations (Section 319.4.4, Equations 19 and 20):

I

For the header (Legs

and 2 in Figure 1-3):

Z

Pressure Stress The minimum allowed walfthickness pressure stress is calculated by using the internal pressure in the equation:

:PD"+A 2S

where

For the branch (Leg 3):

A S

Z.

56

z"

=

:

fm

t"

= =

: 1.

lo

li

= = =

=

1.21.

Effective branch wall thickness, in., = lesser of t1 and (L) (tb) Thickness of pipe matching run of tee or header exclusive of reinforcing pad or saddle, in. Thickness of pipe matching branch, in. Out-of-plane stress intensification factor In-olane stress intensification factor

319.4.4, Equation 18):

Longitudinal Stress The longitudinal pressure stress is computed in accordance with the Code using the equation:

PD" \. "rP= -_: 4t where S1o : Longitudinal pressure stress, psi P = Internal pressure. psig t : Actual pipe wall thickness, in.

D" =

Nominal outside diameter of the pipe, in. MI

Resultant bending stress, psi

[(i'MJ2

^

Allowance for corrosion, erosion, etc., in. (0.72) (E) (SMYS), psi Specified minimum yield strength, psi, Thble 1-l Weld joint factor, Thble 1-2

Mean branch cross-sectional radius, in.

For elbows and miter bends, the resultant bending

:

E:

,.

stresses (S5) calculated using the Code equation (Section

Su

SMYS

Resultant bending stress, psi Effective section modulus for the branch,

in.3,

Pressure, psig Actual pipe outside diameter, in.

P

D"

+ (LM"lll" Sr= fti,Mif where

7

ANSI B31.4 Liquid Petroleum Transportation Piping Code Stress Compliances

[(iiM)' + (i"M"t]r/'?

-\:-

Codes

+ (i"M.l]'/2

'o=-_.v-

where ii

stress intensification factor Out-of-plane stress intensification factor In-plane bending bending moment, in.-lb

= In-plane

lo:

Mi:

M"=

Z:

(see Figure

14)

"'&.

Out-of-plane bending moment, in.-lb (see

Figure 1-4) Section modulus of pipe, in.3

A conservative equation generally utilized for the calcuiation of the allowable expansion stress range is given in the ANSI Code 831.3 Section 302.3.58d, Equation 1:

s"

:

f(1.25 s"

+

.25

Sh)

Gee Chapter 4)

^,,Qr Figure 1-4. ln-plane and out-of-plane bending ments.

mo-

Piping Stress Handbook Table 1-1 Tabulation of Examples of Allowable Stresses for Reterence Use in Liquid petroleum Transportation piping systems Allowablestless values (s) shown in this Table

of the pipe.

are

equal to 0-72 x

t

(weldjoint factor) x specified minimum yield strength

Allowable stressvalues shown are for neE pipe of known specification. Allowable strcss values for new pipe ofunknown specification, ASTM A 120 specification orused (reclaimed) fipe shalr be dete,-ined in accordance $/ith 402.3.1. some code computations, particularly with regard to bianch connections .. .-For Isee 404.3.1 (d) (3)] and expansion, flexibility, structural atlachments, supports, and restraints (Chapter II, Part 5), the weiojoint factorZ. need not be considercd. For specified mintnum yield strength of other grades in ipproved specifications, reter to that particular specification. Allowable slress value for cold worked pipe subsequently heated to 600 F or higher (welding excepted) shall be 75 percent of value listed in Table. Definitions for the various types of pipe are given in 400.2_ Specified

(s)

Min Yield Specification

Gmde

(E\

Strength

Weld

psi

Notes

Joint

Faclor

Allowable Stress Value -20 F to 250 F psl

Seamless

API 5L A-PI5L, ASTM A 53, ASTM A 106 API5L, ASTM A 53, ASTM A I06 ASTM A 106 ASTM A 524 ASTM A 524

API sLU API 5LU API sLX API 5LX API 5LX API 5LX API 5LX API sLX API 5LX

425 A B c I II u80 ul00 x42 x46 x52 x56 x60 x65 x70

Furnace Welded-8utt Wetded ASTM A 53

API 5L Class t & Class fi API 5L (Bessemer), ASTM A 53 (Bessemer) F!rnace Weided-Lap Welded 5L Class I API 5L Class II API 5L (Bessemer) API 5L Electric Furnace

Elecrric Resistance Wetded and Elecrric Flash Wetded A25

Reptuduced

(2) (2)

B

B

1.00 1.00

(1)

25,200

30,000

(l)

1.00

r.00

80,000 42,000 46,000 52,000

(4) (1) (4) (l) (2) (4) (l) (2) (4) (l) (2) (4)

21,600 57,600

56,000

(l) (4)

60,000 65,000 70,000

(1) (4) (l) (4) (1) (4)

2s,000

(t) (2,

100,000

{l)

x65

x70 u80

l.

r.00

72,000 30,250 33,100

37,450 40,300 43,200 46,800 50,400

0.60 0.60 0.60

r0,800

25,000 (1) (2) (6) 28,000 (1) (2) (6.) 30,000 (l) (2) (6) 2s,00o (1) (2) (6)

0.80 0.80 0.80 0.80

14,400

100,000

ul00

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

28,800

(2) (3) (2) (s)

56,000 60,000 65,000 70,000 80,000

x60

r8,000 21,600 25,200

(r') (2)

42,000 (l) (2) (4) 46,000 0) (2) (4) s2,000 (1) (2) (4)

x42 x46 x52 x56

1.00

r.00

40,000 35,000

25,000 (l) (7) 30,000 (2) 30,000 (l) 35,000 (2\ 3s,000 (l)

A

fron ANSI/ASME Code 831.4-1979, Tabte 402.3-

35,000

(l) (l)

2s,000 (l) 30,000 0)

A25

A-PI

API 5L API 5L, ASTM A 53, ASTM A I35 API 5L, API 5LS, ASTM A 53, ASTM A I35 API 5L, ASTM A 53, ASTM A I35 API 5L, API 5LS, ASTM A 53, ASTM A 135 API sLS, API 5LX ATI sLS, API 5LX API 5LS, API 5LX API 5LS, API sLX API sLS, API 5LX A}I 5LS, API 5LX API 5LS, API 5LX API 5LU API sLU

(l)

25,000

30,000

(l) 0) (l) (l)

(4) (4) (4) (4)

(1) (4) (l) (4)

Reprinted courtes!

1.00 0.85 1.00 0.85 1.00 1.00 1.00 1.00

r.00

10,800 12,950

t6,150 17,300 14,400 18,000 18,360 21,600

2l,420 25,200 30,250

33,r00 3',t,4SO

1.00

40,300 43,200 46,800 50,400

1.00

57600

1.00

'72,000

1.00

r.00

ofTh" e^"riron soi"ry of Munonirot rrxin"ug

Basic Theory of Pipe Stress and ANSI/ASME Codes Table 1-1 Continued (s)

Specified

(E)

Min Yield (iranorh

Weld

@o"

Specification

Notes

Joint

FactOr

Allowable S$ess Value -20 F to 250 F psi

Electric Fusion Welded ASTM A I34 ASTM A I39 ASTM A I39 ASTM A I55 ASTM A I55

A

A B x42 x46 x52 x56 x60 x65 x?0 u80 u100 Y35 v42 Y46 Y48 Y50 ]/52 Y60 Y65

API 5L, API 5IJ API 5L, API 5LS API 5LS, API sLX API 5LS, API 5LX API sLS, API 5LX API 5LS, API 5LX API 5LS, API 5LX API sLS, API sLX API sLS, API 5LX API 5LU API 5LU ASTM A 38I ASTM A 381 ASTM ASTM ASTM ASTM ASTM ASTM

A A A A A A

t'rooo

:

Submerged Arc Welded

38I 381

38I 38I 38I 38I

NOTES (l)Weld joint factor E

(1) (1) (2) (1)

30.000

0.80 0.80 0.80 0.90 1.00

(2) (2) (8) (8)

(l) (l)

1.00

21500 25,200

(2) (4) (r) (2) (4) (l) (2) (4)

1.00 1.00

r.00

30,000 35,000

(l)

42,000 46,000 52,000 56,000 60,000 65,000 70,000

(l) (l)

35,000 42,000 46,000 48,000 50,000 52,000 60,000 65,000

30,250 33,100 3',t,450

1.00 1.00 1.00

(4) (4)

(1) (4) (l) (4) (1) (4) (l) (4) (l) (2) (l) (2) (l) (2) (l) (2)

80,000 100,000

17,300 20,150

40,300 43,200 46,800 50,400

r.00 1.00

57,600

1.00 1.00

72,000 25,200 30,2s0

r.00 1.00 1.00 1.00 1.00

(l) (l) (l) (l)

33,100 34,550

36,000 37,450 43,200

1.00

1.00 1.00

,+6,800

(se€ Table 402.4.3) and allowable stress value a.e applicable to pipe manufactured after

1954.

(2)Weld joinr factor ,. (see Table 402.4.3) and allowabte stress value are applicable to pipe manuf.ctured befote l9 59.

(3)Class

It

produced under API sL 23rd Edition, 1968, or earlier has a specified minimum yield srrensth of

2a,OOO psi.

(4) Other Itades provided for in API sLS, API sLU, and API 5LX not precluded. (s)Manufacturewas discontinued and process deleted from API 5L in 1969(6)Manufacture was discontinued and process deleted ftom API 5L in 1962. (?) A25 is not produced in electric flash w€ld. (8)See applicable plate specification fo. yield point and r€fer to 402.3.1 for calculation

Allowable Longitudinal Stress The allowable stress value for by the Code in Section 419.6.4(c):

additive longitudinal

stresses is given

where SMYS

:

of(S).

Specified minimum yield strength, psi (see Thble 1- 17

Allowable Expansion Stress Range for Unrestrained Piping This is given by:

Sr

(allow)

where Su

:

= :

0.75

S"

The allowable expansion stress range, psi 0.72 SMYS

S"

:

0.72 (SMYS)

where SMYS

:

Specified minimum yield strength, psi (see Table l-lr

10

Piping Stress Handbook Table 1-2 Weld Joint Factor E Weld Joint

Specification Number

Pipe Mfrd. Before 1959

ASTM A 53

Seamless

1.00

Electric-Resistance-welded Furnace Lap-Welded Furnace Butt-Welded

Factort Pipe Mfrd.

Afler

0.85 (2) 0.80 0.60

1.00 1.00 0.80 0.60

1958

A

106

Seamless

1.00

1.00

ASTM A

I34

Electdc-Fusion (Arc)-Welded single or double pass

0.80

0.80

A

135

Electric-Resistance-Welded

0.85 (2)

1.00

A I39 ASTM A I55

Electric-Fusion-Welded single or double pass

0.80

0.80

0.90

1.00

ASTM A 381

Electric-Irusion-Welded, Double Submerged Arc-Welded

API 5L

Seamless

1.00 0.85 (2)

0.8s (2)

1.00 l 00 1.00 1.00

0.80 0.60

0.80 (3) 0.60

ASTM

ASTM ASTM

Electric-Fusion-Welded

Electric-Resistance-welded Electric-Flash-Welded

Electric-Induction-welded Submerged Arc-Welded Furnace Lapwelded Furnace Butt-Welded

API sLS

l-00

Electric-Resistance-welded Submerged Arc-Welded

API 5LX

1.00

t.00

Seamless

1.00 1.00 1.00

Electdc-Resistance-Welded Electdc-Flash-lvelded Electdc-Induction-Welded Submerged Arc-Welded

API

5LU

Known Unknown Unknown Unknown Unknown Unknown

1.00

1.00

Sean ess Electlic-Resistance-Welded Electdc-Flash-Welded Electric-lnduction-Welded Submerged Arc-Welded

-_ _ -

Known

(4)

Seamless

Electric-Resistance or F'lash-Wetded Electric-[jusion-Welded Furnace Lap-Welded or ovet 4lz" OD I:urnacc Butt-welded or 4%" OD and smaller

1.00 (6) 0.8s (6) 0.80 (6) 0.80 (7) 0.60 (8)

1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00

r.00 1.00

(5) 1.00 (6) 1.00 (5) 0.80 (6) 0.80 (7) 0.60 (8)

NOTES: (l) Definilions for the various pipe types (wetd joints) are given in 400.2, (2) A weld joint factor of I o may be used for electric-resistance-welded or etectric-flash-wetded pipe manufact ured prior to I 9 5 9 where (a) pipe furn ishe d un der this c tassifica ! ion has been su bj"" t"o to pp'r"'-"ni"i i""t"

and/or heat treatmenls as aFeed to by the supplier and the purchaser, and such sujplementat"u teits analor rreai treatment demonstrate the strength characteristics of the weld lo be equal to the rninimum tensite itrength for the pipe, or (b) pipe has been tested as requi.ed for a new pipetine in accordance with a3z.4.i ,^. speciried (r,| Il1anuracrure was discontinued and proeess deleted from AI,I SL in t 962. (4) Factors shown above for pipe manufactuled before r959 apply for new or used (rectaimed) pipe if pipe specification and pipe lvpe ate known and it is known that pile was manufacrured before r'9i9 ri.i r""*" whether manufactured after 19S8. ". (5) Factots shown above for pipe manufactured aft€r 1958 apply for new or used (rectaimed) pipe if pipe spec! ficarion and pip€ type are known and it is known rhar pip; was manufactured aiter 195s.(6) Factor apPlies for new or used pipe of unknown specific;tion and ASTM A t 20 if type of weld joint is known. (7) Factor applies fot new or used pipe of unknown specification and ASTM A l2o if iipe or *eta j"irr i" i"o*tl lo be furnace lap-wetded, or for pipe over 4% in. OD if type ofjoinr is unknown. (8) Factor applies for new or used pipe of unknown specification and ASTM A l20 if type of weld joint is known to be firrnace butt-welded, or for pipe 4% in. OD and smalter if type of joint is unknown.

Reproduced

from ANSI Code 831.419D,

Toble ,t02.4.3. Reprinad coutksy

of The Arncicai Sociey

oJ Mechanical Engineers.

Basic Theory of Pipe Stress and ANSI/ASME

M"

Longitudinal Expansion Stress for Restrained Piping

=

: ii :

Mt

For restrained piping, use the longitudinal expansion ANSI Code 831.4, Sec-

stress from the equation given in

tion 419.6.4

g: E= Sr.

Tr Tz

=

: :

Longitudinal compressive stress, psi Modulus of elasticity of steel, psi Hoop stress due to fluid pressure, psi Temperature at time of installation, 'F Maximum or minimum operating temper-

a=

ature, oF Linear coefficient of thermal expansion,

v:

Poisson's ratio

in./in./'F

= 0.3 for

The allowable stress value in shear is computed in accordance with the ANSI Code B31.4, Section 402.3.1 (e):

56 (allow)

=

(.45)

(S I,IYS)

The allowed internal pressure stress is S, where (0.72) (E) (SMYS), psi

S=

steel

DOT/831 .8 Gas Transmission and

Distribution Piping Systems Stress Compliances (1982)

0.90 (SMYS)

where SMYS

:

Allowable Internal Pressure Stress

This is calculated by using:

:

Bending moment out oi or transverse to, plane of member, in.Jbs Torsional moment, in.-lbs Stress intensification factor under bending in plane

Allowable Shear Stress

Allowable Expansion Stress Range for Restrained Piping

s"

11

ft):

Sr:E(a)(Tr-T1)-v(S) where

Codes

Pressure Stress

Specified minimum yield strength the pipe, psi (see Table l-1)

of

The design pressure for steel gas piping systems or the nominal wall thiclmess for a given pressure is determined by:

The expansion stress for unrestrained piping is calculated by using:

S.:

[56, + 4S,2]r2

where S" :

^.Z Sr

=

Mi =

2s' (F) (E) (T) D

(For limitations see Section

Computed expansion stress, psi

[(iiM), + (LI\AF]I"

:

P=

equivalent bending stress, psi MJ2Z torsional stress, psi Bending moment in plane of member (for

:

members having significant orientation, such as elbows or tees: for the latter the moments in the header and branch portions are to be considered separately), in.lbs

: S:

where P

D: F: E:

84l.l2l)

Design pressure, psig Specified minimum yield strength, psi (see Table 1-3). For special limitations on S see Section 841.121 (e) and (f). Nominal outside diameter of pipe, in. Nominal wall thickness, in. Construction-type design factor obtained from Table 14 I-ongitudinal joint factor obtained from Thble l-5 (see also Section 811.253 (d) Temperature derating factor obtained from Table 1-6

12

Piping Stress Handbook Table 1-3

specified Minimum Yield strength for steel and lron pipe commonly used in piping systems. Specilication

Tvpe

(l)

SMYS (psi)

A?I5L

BW, ERW, S

API5L

ERW, FW, S, DSA ERW FW, S, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERW, DSA ERw' FW, S, DSA ERW, FW, S, DSA ERW, FW, S, DSA ERW, FW, S, DSA ERw' FW, S, DSA ERW, FW, S, DSA ERW, Fw' S, DSA

API 5L

A?t 5LS (2) API API API API

5LS 5LS sLS 5LS A?I sLS

API SLS API sLS API sLS API SLX (2)

A?I sLX API 5LX API 5LX API sLX API5LX API5LX ASTM A53 ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM

A53 A53

ERW, ERW,

AI06

S

A106 AI 06

AI35 AI35

AI39 AI

B......... A.........

]9

A381

A38I ASTM A38I ASTM A38I ASTM A38I ASTM A381 ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM

c.........

Clas Y-35 .. cla$ Y 42 .. Clas

Y46

.

class Y-48 . clas. Y-50 . Cla\s Y-s2 .

. . . .

A38I

Class

Y-56

..

A381

Class

Y60

.

A38I

Class

Y-65 . .

AI34 AI55 A333 4333 4333 A333 4333 A333 4333 A559

I

3s,000 42,000 46,000 52,000 56,000

60,000 65,000 70,000

42,000 46,000 52,000 55,000 60,000 55,000

S

70,000 25,000 30,000 30,000

S

3s,000

BW BW

ASTM 453

25,000 30,000 35,000 30,000

10,000 35,000

s s ERW ERW EFW EFW DSA DSA DSA DSA DSA DSA DSA DSA DSA EFW EFW S, ERW S, ERW

40,000 30,000 35,000 30,000 35,000

3s,000 42,000 46,000 48,000 50,000

52,000 s6,000 60,000 55,000 (3) (3)

,7

S, ERW S, ERW

8

S, ERW

30,000 35,000 35,000 35,000 35,000 75,000

9

S, ERW

46,000

ERW

35,000

3

S

6

(l) Abbreviarions: BW Furnace butl-welded; ERW- Electric resistance weld€d; S-Seamtess: EFw - Electric fusion weldedi DSA- Double subme.led,a.c welded.

FW

-

Fhsh w€lded:

(i!) Intermediate

Brades ar€ available in API 5LS and 5LX. (3) S€€ applicabl€ plat€ specification for SMYS.

Note: This tablc is not conplete. R)r minimum specified yield strength of other grades and erades in approved specifications, rcfer to the particulor specification. Iron ANSI/ASME Code 831.8-1982, Appenn& D. Repdnted courvsy of me Americon Societt of Mechanicat Engineers.

Reproduced

Basic Theory of Pipe Stress and ANSI/ASME Codes

Expansion Stress

Table 1-4 Values of Design Factor F Conslruclion Type (Scc 841.151)

This is calculated by using the Code equation:

Design Factor

Type A Type B Typc (' Type D

F

S"

0.11 0.60

=

where

0.5 0

0.,10

Ul

Reproduced Irom ANSI/ASME Code 831.&1982, Table courtesy of The Ameicon Society of Mecha ical Engineers.

IC.

Repnntud

(S6'?

Fr.tol

C

:

tion, in.lbs Torsional moment on cross section, lbs Section modulus of piPe, in.3

Stress intensification factor (see ANSI Code B31.8, Appendix E)

1.00

Llcctric Resistancc Weldcd

.60

Furnrcc Bult Welded Scrmicss

AS IN{ A 134 AST}'1 A] 35 AST\'1 A1]9

lllcclric Irusion Art Wcldcd Llectric ResislLrnce Wclded

lllcclric Fusion wclded

00 .80 1.00 .30

ASTM A]55

Llcctric Ijusion Arc Wclded

L00

ASTM ,42I

Spiral WeLded Stccl PiPe Doublc Submergcd'AIc-welded

r.00

Sc:rmLess

l .00

I

ASTM A38I API 5L

Sermlcss

L00

Elcctric Rcsistirncc Wcldcd Llectric I:lash WcLded

L00

Submcrgcd Arc Weldcd

llectric

S"

.80

Rcsistancc Welded

1.00 1.00 r .00

Note: Definitions for the virious chsses of welded pipe given in 804.243 n"proa*"a.Iro^ ,tNSttlSME Code 831 8-1982, Thble UI

Tcmpcrrtulc 150 t or 300 350 F

This is computed by using:

lA

less

400 tl 450 F For intermediLite temperatures

-'' srn=-

Reprihted

where

for Steel Pipe

TelnPcrirrure Dtrating

|

Specified minimum yield strength, psi (see Table 1-3)

Nre

courtesj of me American Society of Mechanical Engineers

Degfccs Fahrcnhelt

:

Longitudinal Pressure Stress

*Manufactu.ewasdiscontinued and process deleted from API 5L in 1962.

I

0.72 (SMYS)

where SMYS

l.00

Subnergcd Arc Welded

Table 1-6 Temperature Derating Factor

=

1.00 .60 .80

Furnace llut l Welded *l:urnace L!p-Wcldcd

API 5LS

This is calculated by using:

L00

Llcctric Rcsistxncc weldcd Elcclric Flash Wcld.d

API 5I X

Allowable ExPansion Stress Range

l

AST}I A106

frffiiififi

:

L00

ASTIU A53

Note:

4S,2)r/2

Se = Computed expansion stress, PSi iM/Z Resultant bending stress, Psi psi Mtl2Z St= Torsional stress, Resultant bending moment on cross sec-

z= :-

Longitudinal Joint Factor E Pipe Clrss

+

Sr: M: M, :

Table 1-5 Spec. Number

13

l:!ctor f

4r

P : n:

Design pressure, psig Outside diameter of pipe, in. Pipe wall thickness, in.

The sum of the longitudinal pressure and longitudinal bending stresses due to external loads such as weight of pipe and contents, wind, etc., should not exceed'75% of owable stress in the hot condition. The allowable for the sum of the longitudinal stresses is given by:

thl a

r .000 0.967

0.9 31

0.900 0.867

51

intcrp(tl!te for derating

B3t E-1982, rabtc 84l 'qNs ASME code courtesy of The American Sociery of Mechanical Engi eers

PD"

lB

Reprinted

:

(allow)

:

0.7s (S) (F) (T)

where S = Specified minimum yield strength, psi E_ .l|_

Design factor obtained from Table 1-4 Temperature derating factor, Table 1-6

14

Piping Stress Handbook

Standard Outline for ANSI Bg1 Codes

ANS|Code 831.1: Power Piping Includes

l.

Power and auxiliary service piping systems for electric generating plants. 2. Industrial and institutional plants (also see ANSI

3. 4. 5. 6. 7

.

Code 831.9). Central and district heating plants (also see ANSI Code 831.9). All piping and cornponent parts within or part of plants as previously specified, unless specifically excluded. Boiler external piping which is covered under the ASME Code, Section I, stamping requirements. Geothermal steam and hot water piping. Oil or gas piping , downstream of meter, within plant

identified in l, 2. or 3, above. and hydraulic distribution syslems.

8. Air

2. 3.

Code.

4.

Gas gathering, transmission, and distribution sys-

5. 6.

tems covered by ANSI Code B31.8. LPG in the liquid state. Fuel gas-air mixtures in the combustible or flammable range.

ly'ore.' This Code will be withdrawn when the new issue of ANSI Code 7223.1 (which does not reference ANSI Code B31.2) is released. This service will be covered by ANSI Codes 831.9 and 2223.1.

ANSI Code B31.3: Chemical Plant and Petroleum Refinery Piping lncludes 1. All piping within the property limits of facilities engaged in the processing or handling of chemical or petroleum or related products.

Exctudes

1. Piping specifically covered by other ANSI/ASME sections. 2. Components covered by ASME B and pV Code. J. Fuel gas in industrial and institutional plants. 4. Building heating and distriburion sream piping for 15 psi (100 kPa) gauge or less or hot water systems for 30 psi (200 kPa) gauge or less. 5. Roof drains, floor drains, plumbing, sewer or fire protecflon systems. b. Piping for hydraulic or pneumatic tools. 7. Piping for nuclear power plants.

ANSI Code 831.2: Fuel Gas Piping Includes 1. Natural

Fuel gas piping covered by the ANSI Codes B3l . 1 , B31.3, 831.8, Z2l.3O, or ZtO6.l Pressure vessels covered by the ASME B and pV

Excludes

1. Nonhazardous fluid piping with

pressures between 0 and 15 psi (100 kPa) and temperatures ranging from

2. 3.

4.

5. 6.

-20'F (-29"C) to 366'F

(186"C). Piping covered by the ASME B and PV Code, Section I or ANSI Code B31 . 1, which requires Section I, Inspection and Stamping @.E.P. Piping). Pressure vessels, heat exchangers, pumps, etc., including internal piping and connections for external piping. Piping within the property limits which has been designated for design according to the ANSI Code 831.4 or 831.8 or to government regulation (pipeline rights-of-way). Plumbing or sewers. Piping for fire protection systems (covered by insurance underwriter's requirements).

gas.

2. Manufactured gas. 3. LPG-air mixtures above the combustible limit. 4. LPG-in the gaseous state.

lncludes

Excludes

1. Fuel gas piping where the metal temperature is above 450"F (232"C) or below

ANSI Code 831.4: Liquid Petroleum Transporiation Piping Systems

-20"F (-29.C\.

1. Piping transporting liquid petroleum and petroleum products between the producer's facilities and delivery and receiving points.

Basic Theory ol Pipe Stress and ANSI/ASME

1.

1. Water air, steam, lube oil, gas, and fuel piping.

3.

4.

Pressure vessels, heat exchangers, pumps' meters' etc., including internal piping and connecUons to ex-

ternal piping. Piping systems designed for internal pressures less than 15 psi (100 kPa). Piping systems designed for internal pressures

6. 7.

Pressure vessels and piping covered by the ASME B

and PV Code.

systems with metal temperatures above 450'F Q32'C) or below -20'F (-29"C). Piping in chemical plant or refinery property limits' natural gasoline extraction plans' etc. ' covered by

2. Piping 3.

ANSI Code 831.3.

greater than 15 psi (100 kPa) where the design temperature is below -2O"F (-29"C) or above 250"F

4. Atmospheric vent piping for waste gases. 5. Low pressure gas which is covered by ANSI Code

Casing, tubing, or pipe used in oil wells, wellhead assemblies, and piping connecting those assemblies' Piping covered by the ANSI Code B31.3 or B31.8. Ammonia reftigeration piping systems'

6. Wellhead assemblies. 7. Proprietary items of equipment.

831.4.

(120'C).

5.

15

Excludes

Excrudes

2.

Codes

ANSI Code 831.9: Building Services Piping ANSI Code 831.5: Refrigeration Piping

lncludes'

,ncrudes

1. Piping

systems

for building services for industrial,

commercial, public, institutional, and multi-unit res-

1. Refrigeration and brine piping systems down to

idential buildings.

-350'F (-

196"C) either erected on the premises or factory assembled, unless specifically excluded.

Examoles:

Excludes

reother laboratories. piping Water systems. Piping systems with internal or external pressure of tS psi ltOO kPa) or less.

1. Self-contained refrigeration systems covered by quirements of Underwriter's Laboratories or nationally recognized testing

2. 3.

ANSI Code 831 .8: Gas Transmission and Distribution Piping

A. B.

C. D.

E. F.

G.

Excludes 1. Pressure limit exclusions:

A.

Steam: 125 psi (860 kPa) Gauge B. Nontuel gas: 125 (860 kPa) Gauge C. Liquids: 300 (2,070 kPa) Gauge D. Full vacuum for all fluids

,ncrudes

1.

Gas transmission pipelines.

2. Gas compressor stations. 3. Gas metering and regulation stations. 4. Gas mains. 5. Service lines to oudet of customer's meter set' 6. Gas storage lines and storage equipment of closed-pipe type.

Dual+emperature water for heating and cooling' Chilled water. Condensing water. Hot water. Steam and condensate return Compressed air and other nonflammable gases. Fuel gas over 60 psi (415 kP-a) _(tuel.gas ulder 60 psi is covered by the new ANSI Code 2223'1)

the

*

(as per latest draft.)

16

Piping Stress Handbook

2. Other exclusions:

A. Piping systems covered by ANSI Code B3l . I

B. Sanitary, potable water, and storm drain piping

Excludes

l.

c. Fire protection systems D.

4c:tylene, hydrogen, oxygen and medical gas

Plpng E. Fuel oil piping

Vessels, heat exchangers, condensers, pumps, com-

pressors, expanders, scrubbers, ana

ment.

2.

, J.

b*rer

equlp_

rr'acuum

piping systems which supply insulating vacuum !o vacuum jackets of cryogenic piping syJtems. rtpmg sysrems specifically covered by ANSI Codas

831.5 or 831.3 lwording of draft).

ANSI Code 831.10: Cryogenic piping* lncludest 1. Liquid-solid mixtures (or slush), operating at tem_ qg-ra1u1ej-rgcinS ftom r2OK (_ 244"F, _ 153 "C) ro (-4^59"8 -273"C), either erected on the prem_ 9K

ANSI Gode 831.11: Slurry piping Systems

ises or factory assembled.

lncludes * (Io

be included io tuture ANSI Code 831.3)

r (as per latest draft.)

t. Initial coverage will be coal transported in water. 2. Future coverages will include slurries ofother solids transported in nonhazardous liquids.

Coeflicients of Thermal Expansion

This chapter contains tables of the coefficients of thermal expansion (Tbble 2-1) and other tables relating to the physical properties of piping materials (Tables 2-2 through 2-4).

17

18

Piping Stress Handbook Table 2-1

Coefticients of Thermal Expansion (in./100 ft) Carbon Steel Carbon-moly Temp, (F)

Low-chrome (Thru 3 Cr Mo)

-32t -?.370 -320 -2.344 -315 -2.313 -3r0 -2.292 -305 -2.?.66 -300 -2.240 -295 -2.214 -290 2. | 8 -?80 2.135 -275 -2. l r0 -210 -2.084 -265 -2.058 -260 -2.A32 -255 -2.006 -250 -r .980 -245 -t .954 -240 - 1.928 -230 -1.e76 -225 -r .850 -2?0 -1 . A22 -2l5 -l .794 -210 -l . 765 -205 -1.738 -200 -1. 710 -r 95 -l .589 -190 -l . 658 -t a0 -l . 606 -r 75 -i .5B0 -170 -r . 554 -r 60 -1 .500 -r 55 -1 .47 4 -r 50 -r .450 -145 -r . 420 -r40 -1.390 -t 35 -r .350 -r 30 -t .330 -125 -r .300 -120 -1.210 -1l5 -t .240 -t t0 -1.210 -r05 -1. r80 -r00 -1 .150 - 90 -r .090 - 35 -r .050 - 80 -1.030

Austenitic

MO Siainless Thru Steels 9CrMo 18Cr8Ni

5 CR

-) ,ri -2.I72

-J.t'5 -3.806

12 Cr

'17

Ct

27 Cl

-2.040

-2.016

-r .992

25 Cr 20

Ni

Monel

3t12

67 Ni 30 Cu

Nickel

-2.620 -z .595 -2

.572

-t .944

-2

.524

-t .920

-2.500

-2. t48

-2.124 -2. I00

-3.586 -2.052

-1.896

-2.234 -2.202 -2. 185 -2

.170

-2.150

-1 .87?

-2.452

-2.004

-3.498 -3.454

-l.848 -l .824

-2.404

-2.090

-l .980

-3.410

-l .80

-2.380 .356

-2.070 -2.048

-2

nua

-I al,

-J.lOO

-2

-1.752

-l .908 1.884

-3,234

-l .704

-t .850

-3.r9

-l .68

-l.312

-3. 146 -1 ln?

-r.836

-3.058 -1 ,7 64

-3.014

-1.715

-2.960 -2.914

-l -l

-l .230 -t

-l

-r .570

-t.800

-!.540

-1.46 -r .438 -1 .4r6

-2.500

-2.454 -2.40a

-l .394

-2. t56 -2.114

-1.024

-l

.780

-t .760 -1

.996 -1 .704

-1 .948

-t .924

-t

.648

-r .350

-1 .90

.620

-1

-t.305

.8;8 -t.355

1

-1

.592

.284 -1.262

-1.s34

-r.536 -r.50s

-1.3t2

.240

-1.214

-t.188 -1.162

-t. -2.0r

.840 -1.820

-1 .37?

-1

-2.218

t36

-1.480 -1.750 -1.710

-t .670 -r .630

-1.110

-l .084

-1

.548

-l

.420

-1 .390

-t.360 -'t.330 -1.298

-r.05t

-r.506

-t .802

-r .454

-l .234

-1.006

-1 .422

-1 .202

-1./)

-0. 98

-1 .380

-t

0

-t .052

-1 .860

-t .482

-t .906

-l .080

-t.920 -t.900 -t .830

-2.778

. 170 . 140

-'t.

21?

-2. I88 -2 ,164

-2.824

-1.258

-r.200

-1.960 -1 .940

-1

-1 .370

-r.286

260

-? -1.614

-1

-l.314

-2

-2.?36

-2.092 -2.068 -?.044

-t .524

-1.342

-t .982

-1.525 -1.504

.548

-t.50 4.474 -l .448

-2.0c4

-2.284

-2. 1 16

.520

-t .57:

-2.30B

-t .548

-2.870

-1.558 -1.644

-2. I 30

-1

.854

-t .700 -r.550

-0.954

-t.34

-1.600 -1.550

-0.902

-1.25

-1

-0.876

.30

-1

.255

.170

-t.138 -t.105

-r .074 -1 .042

Coelticients of Thermal Expansion Table 2-1 Continued

Austenitic

Carbon Sleel Carbon-moly Temp.

Low-chrome

(F)

Ohru 3 Cr Mo)

- 15 -l .000 - 70 -0.97 - 65 -0.94 - 60 -0.91 - 55 -0.88 - 50 -0.84 - 45 -0. AoC - 40 -0.716 - lJ -u. /.4{ - 30 -0.712

25 .20 - 15 - t0 - 5 -

-0.680 -0.542 -0. 604

MO Stainless Thru Steels 9CrMo 18Cr8Nl

5 CR

-0.940 -0. 910

-

-0.880 -0.850 -0.820

-1 ,29?

-0. 790

-1.240

-0.758 -0,7?6 -0.594 -0.662

-r.188

-0.630 -.0596

-0.980 -0.928 -0.875

-0.552

-0.528

{r. !26 -0.494

0

-0.49

-0.450

5

-0.455

't0

-0.555

-l .500 -l . 44A

-l .135 -l .084

-0. s24

4.772 -0.720

-0.59 -0.65

-0.48 -0.45

-0.460

4.232

-0.350 -0.310

50 55 60

-0.140

-0.13 -0.098 -u.uoo -0.034

-0.210 -0. r 58

70

c

a0

0.039 0.076

-0.602

-0. 6r

-0.534

-0.57

-0.5c -0.464

-0. s3

{.33

-0 .4?a

-0.392

-0.30

-0.41

-0.356

-0.370

-0. 3?0 -0.285 -0.252 -0.213

-0.24 -0.21 -0. 19 -0. l5

-0.302 -0.?34

-0- 184

4.12

-0.200

-0.r5

-0.I50

-0. I l3

-0.105 -0.054

-0.06

-0.100 -0.050

-0.038

0

0

0

0

0

0

0.037 0.074

0.056 0.112

0.053 0. 106

0.047 0.094 0.140

0.038 0.076

0.212

0.t85

0.1 l4 0. I52

c.l l4

0.lll

0.152

0. 148

0. 190

0.1 85

0.230

0.22

0. 158

0.22s 0.2&.

0.033 0,066 0.099 0.137

-0.268

0.t65

4.076

0.r90

0.200

0.320

0.28

0.23

0.294

0.340 0.396 0.452

0.264

0.424

0.375

0.296 0.328

0.475 0.528

0.306 0.344

0.370

0. 508 0. 564

0.520 0.876

0.350

0. 58

0.268 0.306 0.344 0.382

0.258

0.420 0.458 0.496 0.534

0.40

0.121 0.762

-0.51

-0.300

-0.250

0.510 0.648 0.685

-0.670

-0. 554

-0. I 64

0.572

-0.77 -0. 73

-0.364

-0.175

-0.840 -0.805

-0.57

-0.36

-0.2t2

-0.938

-0.77?

-u.oto

40 45

-1. r0 -l .06 I .02

-0.895 -0.812

-0. 600

-0. 396

-0.284

100 '105 I t0 I 15 120 t25 'i30 135 I 40 145 t50 I 55 r 60 t55 I70

-0.690 {,. OJU

.010

-.976 -.942 -.908 -.874

-l.t4

4.746

31h Nickel

-1

-i. t6

-0.824 -0.798

-n la

:c

90

Monel 25 Cr 20 Nl 67 Ni 30 Cu

-u.6:

-0 - 668

4.428

-0. 388 -0.354

-0.070

Cr

4.772

?0

-0. t05

12 Cr 17 Cl 27

0.435 0,472 0.508 0.544 0.580

u-oto

6 t1t

0. 394

0.424 0.472

0.42 0.458

0,664

0.496 0.534

0.712

0.572

u.oto

0.462

0.8'14

0.496

0.584 0.735 0.783

0.90

0.530

0. 84

0,594

0.798 0.846 0.894

0.942

0.552 0.688

I .068

0.626

0,892 0.944 0.996

0,724

1.124

u. 056

I . 048

0.956

t.012

u.j64

0.568

0.788

0.428

0.268

0.61

0.548

0.724 0.752

19

Piping Stress Handbook Table 2-1 Continued

Carbon Steel Carbon-moly Temp.

(D

t30 tdJ

r90 r95

Low-chrome (Thru 3 Cr Mo)

0.30 0.834 0.876 0.914

1.180 0.796 0.832

0.858 0.904

0.97

0.85 0.89d 0.928 0.962 0.995

'1.37

i.2?

1.01

r.2t0

1.130 1.750 1.170 1.806 1.210 I .862 I.918 I .250 I .974 I .290 1.330 2.030 2.038 I .368 ?.146 I .405 2.244 I .444 1.4A2 2-262 2.320 I .520 ?.318 I . s58 .596 2.435 2.444 ]. 534 1.672 2.552 2.610 t .710 2.568 1 .748 2.726 r .786 2.744 I .824 1.862 ?.842 2.900 1 .900 1.940 ' 2.960 3.020 I .980 2.020 3.080 2.060 3.140 3.200 2. 100 2.140 3.260 2.180 3.320 2.2?0 3.380 2.260 3.440 2.30 3.500 2.340 3.560 3.520 2.3& 2.420 3. 580 2.450 3.740 2.500 3.800 2.544 3.860 2.588 3.920 2.632 3.980 2.616 4.040

r.362 .400

250

1

t55 t60

1

.442 1.484 1.526

?.7 A

t75 130

1.568 1.610 1.652 1.694

290 295

1.778

300 305 310

t.s2 I .864

1.908 1.952

qq6

320

I

325

2.040

330 335

2.123

340 345

2.112

355 350

2. ?16

2.304

) )

16F 142

2.436 3B0

J6f, 390

2.480 2.524 2.558 2.612 2

.656

1t0

?.700 2.746 ?.79?

115 120

2.884

r00

1.054

1.092

1

0.89 0.93

I .182

1.015

.286

0.85

1.308

1.078 1 .122

I .324

0.81

1.038 I .086 1.134

0.826

2t0

240

c.99

1.404 1.518

.248

1.10

0.792

.978

1

0.724

Nickel

348

I

I .46

1

0.59

3112

Monel 25 Cr 20 Nl 67 Ni 30 Cu

1.204 1.256

.940

225 ?30

Cr

0.758

0. 990 034

l

12 CJ 17 Cr 27

,?92

1

200

??a

a="

Austenitic

MO Stainless Steels Thru 'l8Cr8Nl gCrMo

5 CR

l

424

.258

r

1.478 I .364

1 .54 .03 .594 t.c65 '1.102 I-748 1.138 1.802 I.174 L865 1.210 I .910 1 .964 1 .244 1.278 2.018 2.072 1.312 'I .345 2.126 'I .380 2.I80 'I .416 2.234 2.288 I .454 ?.342 I .490 2.396 I . 526 2.450 1 .55 l .596 2.504 2.558 I .532 I .558 ?.612 2.666 I .704 2.7? 1 .74 1.77A 2.174 I.816 2.828 2.8A2 I .854 l.892 ?.935 2.99 I .93 3.044 I .956 2.002 3.098 2.038 3.152 2.074 3.205 3.26 2. r I 2.148 3.314 2.I86 3.368 2.?24 3.422 2.262 3.476 2.30 3.530 2.340 3- 584 2.380 3.538 2.4?o 3.692 2.940 3.746 1

'1.13

1.17

1.586

I

r.09

.460

1

.

1.556 I .504

I

'I .750 'I . S10 1

.378

652

t.710 .860

1.910

210

.252 .294

r.508

'I 1

.420 .462

1

.504

1.545

']

588

1.950

t.630

2.010 2.060 2.110 2.160

I .714 1.756 1 .798

2.210

t.s4

2.302

?.348 2.394

I .956

.44 2.488

2.050

2

2.532

2.092 2.134 2.176 ?.218

2.680 2.728

2.176

2.26 2.302 2.344

'2,872

2.428

A?L

2.386

2.910

2.470

3.084

2.595 2.638

3.250 3.304

2.690

l-J!6

2.77 4

3.412

2.816

2

.732

Coefticients of Thermal Expansion Table 2-1 Continued

Carbon Steel Carbon-molY Temp.

(n

Low-chtome (Thru 3 Cr Mo)

2.930

2.976 140

3.068

145

4

3.

3.160 3.205 460

3.298 3.344

1 lqn 480 435 490

3.435 3. 432

495

500

3.620

510

3.668 3.716 3.812

525

540 545

3.860 3.910 3.960 4.010 4.060 4.110 4.158

560

4.206 4.254 4.302

5B0

4.350 4.400 4.450

590

4. 500 4. 550

500

4.600 4 -652

610 615 520

625 630 640

4.704

4.756 4.408 4.360 4. 910

4.950 5.010 5.060 5-110

5.214 663 570

Austenitlc

MO Stalnlesa Thru Steels gCrMo lSCrSNl

5 CR

4.100 2.72 ?.76? 4.162 2.804 4.224 2.345 4.286 2.888 4.348 2.930 4.410 2.972 4.470 4.530 3.0 t4 3.055 4.590 3.098 4.650 4.710 3. l40 3.182 4.770 3.224 4.830 3.256 4.850 3.308 4,920 3.350 5.010 3.395 5.010 3.442 5.130 3.488 5.190 3.534 5.250 3.580 s.310 3.524 5.372 3.658 5.434 1.712 5.495 3.756 5.558 3.800 5.620 3.844 5.582 3.888 5.144 3.932 5. SC5 3.976 5.858 4,020 5.930 4.054 5.992 4.108 6.058 6. t20 4.'t5Z 6. 182 4. ',t96

4.240 4.286 4.332 4.378 4.424 4.470 4.514 4.558 4.602 4.646 4.690 4,776 4.7A2 4.828 4.374

6.240 6.302

5.354

6.426 5.488 6.550 5.514 6. 678

6.742 6.306 6.370 6.932

6.995 7.057

7.'l19

12 Ct

l7 Cr 27 Cr

25 Ct 20

, qnn 2.538 t .7a 2.514 2-652

Nl

Monel 67 Nl 30 Cu

3.800

3.520

J'

6i'.

3.57 4

3.908

3.628 3.682 3.736

J.vo. 4.015

2.690 4.070 2.735 4.124 2.770 4.178 2.810 4.232 2.850 4.286 4.340 2.890 , q2q 4.394 2.966 4.448 3.004 4.502 3.042 4.555 3.0a0 4.510 3.120 4.664 4. 718 3. I 60 3.200 4.772. 3.2& 4.825 3.280 4.880 1 1?2 4,934 3.354 4.988 3.405 5.042 3.448 5.096 3.490 5. 50 3.530 5.204 3.570 5.258 3.610 5.312 3.550 5.365 3.690 5.420 3.732 5.474 3.774 5.528 3.815 5.582 3.858 5.535 3.900 5.590 5. 144 3. 940 3.980 5. i98 4.020 5.852 4.060 5.905 4.100 5.950 4.142 6.014 4.184 6.068 4.226 6.122 4.268 5.176 4.310 5.230 4-352 6.284 4.394 6.338 4.435 6.392 4.478 6.M6 ',l

31h Nlckel

2.910

?.954 2 qqR 3.042 3.086

3. BI,4

3.130 3.174

3.898

3.21 8

3.790

3.952

1ta?

4.006

3.306

4.050

3.350

4. 114

4.168 4.222 4.276

3.442 3.988

J.lJ'. 3.580

4. 386

4.442

3.626

4.498 4.554

3.tt6

4.610 4.658

3.810

4.126 4.7 84

3.164

3.902 3.948

qqA

4.842

1

4.900 4,958

4.040 4.086

5.UtO 5.074 5. tJ4

4.132 4.178 4.224

5. 180

4.270

<

4,316

4.362 14R

5.404

4.408 4.454

5. 518

4.500 4,458 4.596

5.634

4.644

5.460

4.692 4.7 40

5.810 5.870

4.788 4.836 4- 884

5.990

4.932

6.050

4.980 5.028 5.076

6. 108 6. 156

6.224

6.282

21

Piping Slress Handbook Table 2-1

Continued

l Calbon Steel Carbon.moly Temp. Low-chrome (D (Ihru 3 Cr Mo)

680

5.474 690

4.tJO 4.588

700 705 710

Austenltlc

MO Slalnless Thru Steels ICrMo 18Cr8Nl

5 CR

4.920 4.954

7. 180

5.008

7.308

5.052

7

q no6

720

5.738 5.792 5.946

t'?5

5.900

730

5,2U

7.628 7 .592

5.332 5. 380 5. 428

6.004

.

.372

7.500 7.554

t.

7

o. u50

745

6. 108

5.5n

750

6. 150 6.z',t4

5.620

5.524

.U0

7.886 7

740

760

.244

166

5. 140 5. 684

7

.952

8.0r8 8.084 8.150 8,21 4

o.z06

J/b

770

o.

775

6.430

780

5. 484

190

6,592

795 800 805 310

5.754

l.

t

6DU

ont

8.342 8.406 8.470 6.5JO

!.v5b

8.602

8.568

6.645

5.004 6.052

6.700

6.100

8.80

6.308

5. 148 6. 196

8.855

6.862

6.244

a

6.29?

9.064 9. r30

7.082

5.340 6.390 5.440

440

7.138

845

7.194

6. 490

6.754

820

6.916

825 830

6.970

8.734

ooq

q tot

a 1rq 9.394

350

9.460 6.538

960 7.4

t3

7.174 840 435 890 395

/.5U6 7 .542 7.698

900

7.754

6. 686

9.542

5.734 6.182

9.724

6.830 6.878

9.856

a

7qn

9.922 6.974

q

aea

7.0?Z

r0.054

7.810

7.070

9t0

/.doo 7 472

7.1r8

10. 120 10. 188

7. 156

tu.250

7.978 8.034

7.214

10. 324

920

ln

1q2

12 C. 77 Cr

27 C.

25 Cr 20

4.520 4.562 4.504 4,645 4,688 4.730 4.776 4.814 4.A55 4.898 4.940 4.984 5.028

5,0n 5. I fO

5.

150

5.204 5.248 5.292 t. JJD

6.500 6.554 6.508

6.662 5.716

5.170 6.824 6.878

6.932 6.985 7.040

7.094 7.148

7.702 t.Z)E

Nl

Monel

3t/.

67 Nl 30 Cu

Nlckel

5.340 5.400 6.460 6.520 6.580

5.220 5.354

5.412

5. 640

6. 700 6. 750

5.508

6.820 6.880

5.604

5.940 7 .002

5.700

7.064 7.126

5.796 5.844

t.

o5z

7. 188

,250

7. 310

7

7.364 7.418

7. 310 7

7.472 I .a.n

7.490

5.940 5.988 5.036 6.084 o. tJz

/.55U

6. 180

5,380 7.580 s.424 7.634 s.458 7.688 5.5"2 7.742 5.555 7.796 5.600 7.850 5.544 7.910 5.688 7.970 5.732 8.030 4.776 8.090 5.820 8.150 5.866 8.210 5.912 8.270 6.004 8.390 6.050 8.450 5.094 8.510 6,138 8.570 5. r82 8.630 6.225 8.690 6.270 8.750 6.314 8.810 6.358 8.870 6.402 8.930 6.445 3.990 6.490 9.050 6.534 9. n0 6.578 9.1 70 6.522 9.230 6.666 9.290

.370

7. 510

7.130 7.790

6.280 O. JIU 6.380

7.850

6.430 6.480

8.036

6.580

7 417 7.974

o.5lu o, oJu

8. 160

6.580 6.730

8.288

5. 780

8.416

6. S50

8.480 3.544 8.508 8.672

6.930 5.980 7.030 7.080 7. t30

6.830

8. 735

9.800 8.864 8.928

8.992

7. 180

7.230 7 .280 7.330 7.380

9. r20

7.430

9,248

7.480 7.530

f.i84 a ?t,

7.630

Coefficients ol Thermal Expansion Table 2-1

Continued

Carbon Steel Carbon-moly Temp.

(R

Austenllic

MO Stainless Thru Steels gCrMo 18Cr8Ni

5 CR

Low.chrome (Thru 3 Cr Mo)

7. 310

I0.460

8.t88

7.360 7.410

10.528 r 0. 596

940 945

8.242

7

950

8.350 8.404 8.458 s. 512 8.556

s.080 8.134

960

970 980 985 990

.460

7. 510

8.674

8.128 s.782

7.560 7.610 7.660

I0.554 1d 71' 10. 800 t 0. 858

10.936

1.710 7.760

I1.004

7. 810

II

7.360 7.910

r

11.012

.140

r .208

t't.344

s.835

7.950 8.010

000 1005 'r010 t 0l5 1020 1025 1030 1035 1040 1045 I050 LU:: 060 I065

8.390

8.060

l t .480

8.946 9.002

0 8. 160

1

1075 r 030 r 085 090 r 095 I 100 'r 05 r0 IIr5 1120 |25 I 130 1r 35 I140 l145 'lt 50 r I55 I t60 r 165 I I 70

r

r

8.

l1 .412 I .548

8.210 8.260

1t.584

l4

9- 170

8.300

I I

t.820

I

t.956

9.058 9- l

9.228

9.236 9. 344

9.402

8. 400 3- 450 a. 500

1

.888

1?.C24 12.094

I2.

9. 460

150

1?.228

f, tO

3. 600

9.634

3. 700

Aoa

3. 750

9.750

r2.500 t2.558 tz.0Jo

9.982

8.800 8.850 8.900 s.950 9.000

10.040

9.050

I2.840

', 9.575

o

9.408

9.866 9.9?9

r

8.650

12.296 12.364

12.704 12.712

I0.094

o

no6

12.908

10.144

9.142

12.976

t0.202

9. 188

13.044

10.255

9

.234

I3.112

9.280

13. r 80

r

0.310

10.362 10.414 10.466 10.518 10.570 10.622 10.574 10.126 10. 773

9.330 9.430 9.480 9.520 9.568 9.554

I3.248 r

3.316

13.384

I3.452 13. 538

13.724 13.79?

12 CJ

17 Cr 27

Cr

Monel 25 Cr 20 Ni 67 Ni 30 Cu

6.710 9.350 5.756 9.410 6.802 9.470 5.848 9.530 5.894 9.590 6.940 9,550 5.986 9.710 7,032 9.770 7.078 9.830 7.124 9.890 .170 9.950 1.215 l0.010 7.262 10.070 7.308 10.130 7.354 10.190 7.400 10.250 I0.310 7 .444 7.488 10.370 10.430 t' .532 | .576 I0.490 10.550 1 .620 7. 586 10. 610 7. t-52 10.570 7.818 10.730 7.884 10.790 7.950 10.350 7.996 10.910 8.042 10.970 8.088 I I .030 8.I34 il.090 8.180 11.150 8.205 l l .2'10 8.232 11 .270 8.258 1 .330 8.284 11 .390 8.310 l l.4s0 8.354 1l .516 8.398 1l.582 8.442 1l .548 8.486 l .714 8. 530 l1 . 780 8.576 I .345 9.622 ri.912 8.658 l1 .978 8.714 I2.044 8.760 l2.l l0 8.804 12.176 8.848 12 -292 8.892 I2. 308 8.936 12.374 7

,]

1

1

7.680 7.730

9.440 9.505

a

31h

Nicket

7.780

a72

9.638 9.704

7.830

9.170

7.930

9.834 9.399

7.880

7.978 3.026 8.074

10.026

8.122

10.090 10.156 10.222 10.288 10.354

8.170 8.218 8.266

10.420

8.410

I0.486 r0.552 10. 618 i 0. 686

10.750

I0. sl8 10. sa6

11.42? '11

.090

It-158 11

.226 .294

|.352 I I .430 11

.498

I1.555 1

t .702

r1.770

| .838 I1.905 ' .974 12.042 12.

1

l0

12.182 12-254

\2.3?6

1'

laA

12.470 12.538 12.605 12.57 4

12.742

8. 314

23

Piping Stress Handbook Table 2-l Continued

Carbon Steel

Austeni c

MO Slainless Thru Sleels 9CrMo lSCrgNl

Carbon-moly Temp, Low-chrome (D CIh.u 3 Cr Mo)

t't75 I180

5 CR

0.830

9, 750

13.850

10. 884

9.808

13.928

9.904

t 195

10.992 I I .046

14.054

9.952

14.'t32

1200

It.t00

10.000

r

lt95 lt90

ll oot

10.938

l2t0

I | .212

r

t22n

I1.268 I1.324

r0. r55 0.208

14.200 14.268 't4.335 i 4.404 14.472

.380

r0.260

1230

14. 540

I I .436

314

14.603

10.368 10.422

r4.676 14.7M

10.476

14.812

'10. 530

14.880

l2l5

rt.ltl

I 1240

r250

1

r0.052

.492

ir.598

'll .504 l I .660

r

0. 104

r0

I 0. 582

't4.948

0.634

I5.0r6

'tl .884

r0.738

15.084 IJ. IJZ

l0.

1285

.940 .946 12.052

1290

r2.

1295

12. r 64

1300 1305

'12.22

ll.7t5

l2 60

11.772

1270

I

I

r280

r

t.328

1

1 1

108

790

r

0. 952 I I .005

15.424

II

15.560 15.628 15.596

't0.898 r

.060 .108 .156

r3t0 l3l 5

12.276

|l

12.388

I

1320

12.444

11.2s2

r325

12.500

I I . 300 I I .350

1330

I I .450 'I | . 500

t 345 r

350

r2.780

350 J05

12.892 12.948

1370

13. 004

r I

1375 1380 1385

L204

'll.€0

I340

15.220 5.288

10.844

I

L550

15.492

'I

5. 754

15.832

l5, 900

't5.968 r 6.036 t 6.104 r 6.172 't5.240

I t . 600

'15.308

I1.650

16.375 16.444 I 6.512

11 . 1t .

700 750

3.060

l1 .800

t6

't390

13.112 13.228

I1.850 I1.900 I1.950

1395

13.284

12.000

r

1400

13.340

12.050

15. 920 lF ooa

1405 1410

l4l5 1420

1

r3.l

'|

5.580 't5.643 16. 7l 6

r6.784 6.852

17

.072

17.'t48 17.224

12 Cr

l7 Cr 27

C.

8.980

Monel 25 Cr 20 Nl 67 Nl 30 Cu

12. 440

1' a1'

12.810 12.878 12.946

12.638 12.704

13.014 13.082

9.200

12.770

9.244

12.836

I3.',I50 13.220

9.288 9.332 9.376

12.902

9.024 9.068 9.112 9,156

r

13.290 13.350 '13.430

3.034

9.420 3. t00 9.465 13.166 9.512 13.232 9.558 13.29S 9.504 13.364 9.650 t3.430 9.696 13.496 9.742 13.562 9.788 ',t3.628 9. S34 13.594 9.880 13. 760 9,926 t 3.826 9.972 13.892 10.0r8 13.958 t0.064 14.024 l0.l l0 14.090 r0,154 t4. t50 10.198 14.2t0 10.242 14.270 10.825 14.330 10.330 14,390 10.375 14.450 10.422 14.510 10.468 t4.570 10,514 14.530 10.550 14.540 r0.504 't0,648 14.750 14.810 r0.692 14.870 10.735 14.930 10.780 14.990 '10.826 r 5.050 r0.872 l5.l l0 't0.913 t5.170 r0.924 15.230 I I .010 15.290

13.500

1

13.544 r

3.788

13.360

r3.932 14.004 r 4.076 14. t 48

14.22 14.292 't4. 364

t4.435 14.508

r4.580 14,552 14.724 t 4.796 14.868 14,940 1

5, 084

15.300 t 5.444

lt.tlo r

5.588

I

t- 60u

15.732 15.804 15.876

15.948 I

5.020

31h Nickel

Coefficients of Thermal Expansion Table 2-1 Continued

Austenltlc

Catlon Steel

MO Stainless Thru Sleels 9ClMo 18Ct8Nl

12 CJ 17 Cr 27 C.

5 CR

Carbon-moly Temp. Low-chrgmo (D (Thru 3 Cr ilo)

Monel

25c|20 Nl 67 Nl 30Cu

3th Nickel

't7.300

1425 1430

1435 1440 1445

17.534

17.6i2

1450 1455 1460

17.690

t465

17

17.768 17.846

.924 I8.002

t470

18.080

1475 1480 1485 1490

r8. r58 18.235

I495

13.31 4 le 102

500

18.470

r

Temp.

(D

-32 5

-320

Alumlnum

-4.68 -4.636

-315 -310 -305

-4.592

-300 -295 -290

-4.46

-4.548 -4.504 -4.41 -4.36

-2Aq -280

-4.26

-275

-4.21

-270

-4.162 -4.1

l4

Gray lron Bronze Brass

Caal

-J. v6

-3.932 -3.884 -i e1f -3.788 -3.692 -3.644 -3.596 -3.548

70 Cu 30

Nl Ni.Fe.Cr

-J-66

-J.lt

-3.64

-2.87

-3.832 -3.094 -3.784 -3.038 -1 t16 -? aa? -3.688 -2.926 -3.592 -2.836 -3.544 -2.&2

-1.49D -a. t06 -1..t.t5 -a- I J4

-3.4s2 -3.352 -3.404 -3.304

-3.5 -3.40

-2.70 -2.666 -2.632

-3.308 -3.208

-2.564

-260 -255

-4.066 -4,018

-250 -245

-3.97

-3.26 -3.16

-2.53

-?40

-3. 366 -3.8',r4

-3.164 -3.068 -3.I t6 -3.022 -3.068 -2.976

-2.462 -2.428 -2.394

-235 -230

-3.2'12 -3.114 -2.496

'J.Va -210

-3.602 -3.548 -3.494

-a.tJ

_2. JO

-2.972 -2.884 -2.326 -2.924 -2.833 -2.292 -2.82A -2.746 -2.224

Ni-Cr.Fe

Ductile lron

25

Piping Stress Handbook Table 2-1

Continued Temp.

(D

Aluminum

Gray Csst lron

-2.78

-3.44 -3.384 -3.328

-2.732 -2.684

-2.654

-180

-3.216

-2. t66

-2.5

-175

-3.16

-2.54 -2.47 -2.494 -2.424 -2.448 -2.378 -2.402 -2.332

-200 -195 -190

-185

n70 -t

65

-160 -155

-3. 104

-3.048

-?.992 -2.936 -2.88

-r 45

-2.8i8

-140

-2,756 -2.694

-lJ5 -llu -125 - r20

nl5

-6t

-80 -75 -70 -65 -ou -55 -45 -40 -30 -25 -20

30 35

40 45

-t

.49

-l .45

-2.086

-t.J60

-2.052

-1

.4t

-i .362

-l .984

-l.314

-2.24

-1 .95

-2.144 -2.096

-1.908 -|.aroo -1 .824

-1 .29 -1 .264

1AJ

-?.27 -2.21 -2. 15 -2.09 -? i1

-t.ot -l .76

-t.ro

-1.53 n .49

-1 .04

'l.ll _l.OO

-l.OO4 -l.OlO

-1.97

-t .56 -1.52 -t.512 -1.474 -1.464 -1.42A -l.4t6 -1.382

n.91 -l .85 -t .79

-1

71

-r.ot

-l.6

-l .46 -1.39

-2.048

-1 .856

. 6',14

-l

,306

.236

-1.292 -l .182 -1.278 -t .128 -1.264 -1.074

.25

-1

-t.lt

- ,962 -0.866 -

.858 .804

-

.696

-.902

- .834 -.766 - .698 -

.56 .49 .42 .35

-t.o50

I

-l .16 -1.136 -1

-l

.l t2 .

c88

.45

-1.014 -.988

-1 .41

-,962

-l

-1.33

-l .29 -l.21 -1.13

-1

-1.32 -1.25

n.18

-'1.74

-1.698

-t.506

-1.212

-, . 160

-l .952 -l .904

-1.712

-t.233

-.91

-.882 -.854

-,826 -.798

-1 ,67

-.97

25

-2.31 26

-1

-1.064

0

20

-2. Z60

-r .5l

-2.148 b

-2. JaC

-2

-2.162

Ductile lron

-1 .572

-l .04

l0

|

-2.19

Ni.Cr.Fe

-l .808

- t5 - l0 -5 5

-2.608

Nl Ni.Fe.Cr

-2.00

-2.57 -2.51 -2.45

-tu5

-95 -90

-2.70

30

-2.21 -2.16 -2. 1 l -2.06 -2.01 -r .96 -t.9l -r .86

-110 -100

Z0 Cu

Eronze Brass

-',!

.02

-t. t3.t -.9vo -l .058 - .912

.714 .658 .602 .546 .49 .436 .382 .328 .274

-

.642

-1 .082

-.77

_.74

-.71 -0.986 -0.938

- .89 - .844 - .799 -.752 - .706 - .66 -.612 -.564

- .65

-.62 -.588 -.556

-.524 -4.9?

-.414

.588 .534

- .5',16 - .468

-.276

.48 .426 .372

-.374

-.212

.318

-

.282

-. 194 -. 176 -.158

.264

-.236

-.322

Coefficients of Thermal Expansion Table 2-1 Continued Temp.

(R

50 55 60

Alumlnum

-.28

- .21 - .14 0

ta

.3066 . J6JJ

'100

120

.616 .694 .772

125

.85

130 135 140 145

.926

5

165 170

.312 .346

.54

.414 .448

.72

,482

.84

.622

.08 .14

.542

2.00 ?.082 2.164

1.26 .764 70'l

.972

2.41

230

2.494 2.578

'L I

'I

.08 .118

I.i56 I .194

.232

2.7 46

1

250 255 260 265

2.43 2.912 ?.994

1.27

270

J. lc6

I

275

3.24

1.45 1.488

295

'I

.

.21

.246 .282 .318 .354

.472

.56

.52 .568

.664

.oto

.716

.oo+ .712

.612 -bbb

.

.76 .805

.7 .744

.57

.852

.798

.

.97

.898

1.02

.944

,832 .876

.684 .72?

.92 .966

.788

1.012

.826

.olz ,

768

.82 .87 .54

.07 .122 .174

.288

1.

. 175

346 404 462

,226

.278

.5b6

oa

.038 'I .086 1

't

.

]34

I.182

.39 .4?6 ..+Oa

.498

'1.058 'I

'I

.62

l.ott 1.74

1,8 1.86 1 .922

,902

1.342

2.294 2.356 ?.418

.4]4

2,8

2.542 2. 604

I .564

1.602

I .434

t./06

l.tJ6

1

.83

1.486

1

.59

2.14

2.232

'1.378

1.644 1.705

2.17

306

.

.94

2.046 2. t08

.984

2.666 2.728

o.to

.864

.',t04

'I

'1

1.86

2.202 L 914 2.264 1.968 2.326 2.022 2.388 2.076

2.512 2.574 2.698

.252

.196

| . JJ.t I .386

.288

1

.892 1 .644 ,954 I .698 2.C]6 1.752 2.078 I .806

'I

tJ+

.60s

l.Jo

225

290

1.

.14

.424

1.114

t.Jt' I .44

. 105

.51

uto

1.172

.035 .07

.46

,94 .998

'l

1

044

3.412 3.498 3.584

.41

| .76 .82 .88

I .32

.866

2.328

3.076

2

.0933

.35

.

|.

.0433 .0866 .13 .1 73 .216 .26 .304 .348 .392 .436 .48 .524

.25

.408 .466 .524 .582 .64

.96

220

280 285

.l15

.5',16

r.008

240 245

.1866

.48

2.246

2.35

.206 .258

1.386 I .464

1.698 1.776 1.854 1.932

205 210

.t4

.24 .J

.233 .291

.lla

.02

| .62

200

.12

.586

175

190 't95

.0466

'L 308

1

0

.05'16 .1033

.278

.14 .105 .07

-_.035

.0s83 .1166

.uo

.658 .694

-

0

.66

.002 .078 .154

180 '185

-

.?44

110

Ductile lron

Ni-FeCr

- ,21 - .105 q2E

.21

't05

Itt

.055

.035 .07 .105 .14

80

t3u

.165

0

.016

85 90

Nl

-

-.07

70

70 Cu 30

Gray Caal lron

2.184 2.238 2.346

'I

.012

']

048

I . 084

.438

I .49

'I

L.38

544

1

.426

t.t7

I .598

1

.472

1

'|

.

'I

.?1

.652

1.5i3

1.706

't

.564

1.75

'l

,5l

1

.658

.37

706

.41

802

.45 .49

1

1

'l

.8',t4

.868

1

922

']

.25 1.29

'1,754

1.976

1.

2.03 2.084 2.138 2.192 2.246

't

.85

I .898

I .568

1.946 I .994 2.O42

1

'|

.606

.644 I .682

28

Piping Stress Handbook Table 2-1

Continued Temp.

(D

Alumlnum

300 305

3.67

3i0

3. 838

Gray Casl lron

1

't

.64

.678 1.716

'1. 754

Bronze Brass

274 2.954 2.918 t oat 2.046

320

4.006

't.792

325

4.09 4.176 4.262

I.atj 1.87

3.',t I

r .91

3.234

1.95 I .99

3.296

3.4

330 340 345

4.348

4.434

350 355 360 365 370

4.52

4.864

2,03 2.068 2.106 2.144 2.182

375 380

4.95

4.606

4.692 4.778

3.1n

3,484 3.548

3.612 J.O/O

2.22

2'A

lAE

5.038

3.7 4 3. 802

5.126

2,3

3.864

390 395

5.2 14

2.34

400 405 410

5.39

5.302

s.478

2.42 2.46

5.566 5. 654

2.54 2.58

3.926 3.988 4.05

4.

4

4. 178 4.242 4.306

420

5.742

425 430

5.92

4.434

4.498 4.562 4.626

4.37

6.0i

2.704

440 445

6.1

2.7 46

450 455 460 465 470

6.28

2.788 2.83 2.87

4. 69

2.76

70 Cu 30

Nl NLFe-Cr

2.40

2.30 2.358

Nt-Cr-Fe

2.09

3.48

4.248

3.648

4. 314

3. 704

2.56 2.606 2.652 2.698 2.744

4.38 4.448

3,76

2.79

4,516

3.872 3,928

3.386 3.434

3.984

3.482

4.l l6 4.1e.

4.584 4.652

z.4to

2.474 ? q1,

2.648 2.706 2.764

2 e)t

2.136

2.182

2 2r9

2.2't4 2.368 2.416 2.464 2.512

2.8

2.56 2.508

J.UO

2

2.94 3.00 3. l2 3.

l8

2.4

2.95

3.0 3.05 3.098 3. 146 3. 194

2.91

4. 856

6.544 6.632

2.95

4. 882

4.094 4. 148

4.946

4.924 4.992

4.202 4.256

3.68

475

6.72

3.03

5.01

s.06

4.31

480 485 490 495

6.81

3. 78

5.074

6.9

3.072 3. 114

5.128 5. t96

+.

6.99

4.422

3. 156

7.08

l10a

5.202 5.266

3.828 3.876

5.264

4.472 4.534

3.924

.17 7.262 7.354

3.24 3.284 ? 1'A

5.394 5.458

4.59 4.646 4.702 4.758

5t5

7

520

7.538

.446

525

3.46

5.65

530 535

7.724 7.818

3.544

7.912

a. t61

s40

J. J6O

5. 848

545

8.006

3.628

5. 9',I4

5.

7',1

2.97 4 3. 04

G4

JOO

2.882 2.928

3.088 3. 63 3.',]84

3. 73

3.28 3.384 3.436

3.488

5.68

4. At4

4.02 4.07 4.12 4,17 4.22

5.75

4.87 4.929

4.27 4,32

3. /'6 3.806

5. 89

4.986 5.044

6.03

5. 102

4.42 4,47

3.898 3.944

5.54

5.522 3. 416

2.44 2.48

3.816

4.

5.40 5.47

2.05 ?.09

2.80 2.85

4.72

7

.97 2.01

,704 2.752

2.656

2,9

1to,

.804 .846 .888

2.13 2.176 2.222 2.268 2.314

4.788

500 505 510

.7?

2.824 2.456 2.838 2.512 a.taz 1, to6 3.016 2.624 3.08 2.68 3.146 2.736 3.212 2.792 3.278 2.848 3.344 2.904 3.41 2.96 3.474 3.015 3.538 3.072 3.602 3. 128 3,666 3. 184 3.73 3.24 3.794 3.296 3.858 3.352 3.922 3.408 3.986 3.464 4,05 3.52

4.754 4. Bl8

6.368 6.456

Duclile |ron

6

3.54 J. 0Z6

3.672

l./to

Coetficients of Thermal Expansion Table 2-1 Continued Temp, (F)

550

Aluminum

8.

Gray Casl

tlon

1

8. 192

3.

8.376

7l4

Bronze

Brass

5.98 6.046 6.112 6. I78 6.244

6.10

560 565 570

8.2U 8. 468

3.758 3.802 3.846

575 580 585 590 5q5

8. 56

3.89

8.654 8.748

3.934

b.l I b. J/b

8.842

4.022

b.

8.936

4.066

600 605 610 615

9.03

4.n

620 625 630 535 64C

645

4. 156 4.202

4.428 4.294 4.34 4.386

4.432 4.478 4.524

550 655 660 665 670

4.57

675 580 685 690 695

4.8

4.616

4.662 4.708 4.754 4.846 4.A92 4.938 4.984

700 705

5.076

7t0

5.122

715 720

5. I68

5.214

7?5

5.26 5.308

730 735

740 745 750 755 760 765

5.404

5.452 5.548 5.596 5. 644

770 775 780

785 790 795

5.7 4

5.788 5.884

5.932

6.442 !u6 o.l/+

70 Cu 30 Nl

Ni"Cr-Fe

5. 16

Ductile lron

3.99

4.32 4.57

4.036

4.62

4.082

6.31

5.218 5.276 5.334

6.38

5.392

4.7?

4.174

o. +J

5.45 s.496

4.77 L.82 4.87

4.2? 4.264 4.308

5.608 5.664

4.92

4. 352

6. 17

6.24

o.3z 6.59 0.00

o./J

6.64 6. 80 6.704 6.872 6.944 6. 768 7.016 6. 832 6.896 7.088 6.96 7 .16 7.234 7 .026 7.308 7 .092 7.158 7.382 7.224 7 .456 7.29 7.53 7.356 7.602 7.422 7.674 7.488 '1.7 46 7.554 7.818 7. 89 7 .62 7.686 7 .964 7.752 8.038 7.818 8.1 12 7.884 8.186 7.95 8.26 8.016 8.336 8.082 3.412 8.148 3.488 8.214 8.564 8.28 8.64 8.348 8.716 8.416 8.792 8.484 8.868 8.552 8.944 8.62 9.02 8.688 9.096 8.756 9.172 8.824 9.248 8.892 9.324 8.95 9.40 9.028 9.476 9.096 9.352 9.',164 9.628 9.232 9.704

4.128

1.97 4.44

3.72

4.484

5.778 5.1?

t.17

4.528 4.572

3.?2

4.616

6.01

5.27

4. 66

6. 068

5.322

4.708

6. 184

s.426

6.242

5.478

4.756 4.804 4.852

6.30

6.524

5.53 5.582 5.634 5.686 5.738

6.58 6.64

5.84?

5.836 5.894

(

oE,

6.126

6.355

6.412 6.468

4.9 4.948 4. 996

5.044 5.092

5.394 5.946 5.998

5.24

6.938

6.102

6.996 7.054

6. 154

5.432 5.474

6.206 6.258

5.558

6.362

5.60 5.65

6. 414

5.70

6.70 6.7 6

6. 88

7.112 7.17 7 .23 7 .29

7.35

5.34

5.75

7

.41

o.f,kt

7

.47

.528

7.586

6.57 6.6?4 6.678

5.85

7

.644

6.732

6.00

7

6.05

7.702

7.76 7.82 7.88 7,94 8.00

5.90

6. 84

6.t0

6.894

6. l5

6.948 7.002

6.20 5.25

5.30

29

Piping Stress Handbook Table 2-1

Continued Temp. (F)

Alumlnum

Gray lron Bronze Brass

Cast

.800

805 810 815 820

825

9.30

5.98 6.028

v,

6.124 6.172 6.22 6.27 6.32 6.37 6.42

850 855 860 865

6.47 6.52 6.57

870 875 880 885 890 895

5.72

900 905 910 915 9?0

6.97

6.77 6.87

7.022 7.O74

7.216 7.178

925 930

7.284 7.338

940 945

,392 7 .446

950 955 960 965

7.5

970

7.708

7

7

,604

7.656

975 980 985 990 995

7.812 7.864 7.916

'1000

8.02

't005

l0l0 i0r5

't020 1025 1030 1035 1040 1045

7.968

'10.4 10.96 1.038 10.47 t'l.lt6 10.54 l't .194 10.61 11.272 1

10.748 10.8't6 10.884 '10.952

11.02 I1.09 'l l.l6 11.23 'l l .3 11.37 'I r .438 1l

'I

I

.506 .574

11,642 l

t

.71

11.778 '11

.846 I I .982 l

l.9r4

12.05

12.12 '12.19

12.26 12.33 12.4

12.472 12.544 12.616 16.688

8. 06

y.556 9.936 10.014 10.092

'10.33

'10.68

Nl Ni_Fe_Cr

9.78

9.436 9.504 9.572 9,64 i0. I 7 9.71 10.25 9.78 10.33 9.85 10.41 9.92 10.49 9.99 10.57 10.06 10.648 10. 13 10.726 10.2 t0.804 10.27 10.882

5.076

830 835 840 845

Jo5

70 Cu 30

8.118

Ni_Cr_Fe

7

Ductlle lron

.10

8. I76

6.398 6.446

8.292

6.542

8.412

5,59 6.642

6.494

8.474

8.598

6. 694

o. /40 6. 798

8,66 6. 898

B,784 8.846

8.908 8.95 9.012 9.074 9.135 9.198

6. 946 6. 994

7.042 7. 09 7. 138

/. tt'0 .234 7 .282 7

1l .35 1

l

.43

11.51

ola

.59

I .44

1 1

II.57 11.75 11 .832 11 .914 11.996

12.078 12.

t6

12.242

12.324 12.402

9.5 9,622 9. 684

9.746

10.242 10.304 I

u. Joo

10.428 10. 49

t3.062

'10.

13.i44

10.614

13.226 13,308

't0.738

s52

10. 80

13,474

'10.862

13.558

10.924

13.642 13.726

7.772

7.9r

10.t8

',t3.39

7

9.87 a o?, 9.994

12.57 12.652

12.98

.64 .684 7.728 7

/.6tb

10.056 10.118

12.816 12.898

.466 .524 7 .582 7

1

9. 808

12.488

12.734

7.408

I0. '11

.

986 048

7. 86

8.01

8.06

8.rI 8. ',t s8

8.206 8.254 8.302

Coetficients ot Thermal Expansion

2-l Cofitlrued Table

Temp.

o

1050 1055

t060 1065 1070 '1075 r

080

1085 1090

t095 00 1105

l l t0 'n

l5

1120 1125 1130 1135 1 140

lt45 50 '1

155

Aluminum

Gray l;on

Cast

8r6nze Erass '

12.76 12.83 12.90 1?.97 '13.04

l3.l'l

r3.182 13.254

13.32 13.39 13.47

70 Cu 30

Nl Nl-Fe-cr

13.81

11.11

13.894 13.978 14.062 14.146

'11

14.23 14.314 14.398 14. 492

14.566

n.172 11.234 .296

'1t .3

58

11.42

1t.484 11.548 't1.612 l1 .676

l4.65

Il.74 r

1

.802

11 . 864

11.926 .988 12.05

't2,I16 12.182 12.248

12.3]4 12. 38

12.442

lt60 '1165

12. 504

l l70

12.628

'1175

12.69 tz. tao

1180 85

I190

|

2.500

12.&2 't

2. 888

'I195

12.954

r200

13.02 13.088 tJ. t50

't205 '1210

l2l5 1220 1225 '1230

13.292 IJ.JO

'13. 43

1235

1240 1245 1250 'I255

13.64 '13.

71

1260

13.776 13.842

1265 1270

13.974

1275 1280

't285 1290 1295

'13.908

14.04 '14. l '14.

l

l8

'14.25 14. 32

Nl-Cr-Fs

Ductlle llon

31

32

Piping Stress Handbook Table 2-1 Continued Temp.

o

300 i 305

Aluminum

Gray lron Bronze Erass

Casl

70 Cu 30

Nl Ni-Fe.Cr

l310

14.39 14.46 14.53

1320

14.67

1

't315

'I4. 60

14.7 4 1330 IJJ' 1340 1345 1350

14.812

'14.884

r5.028 '15. 10

tt.l06 I JOU I JOa

15.304

1370

15.372

375 I 380 'l 385 1390

15.44

r

't 1

5.584 5.656

15.278 1400

'1405 t

4l0

l4l

15,80

13.872 15.944

5

I 5.01 6

1420

16.088

1425

16.

1430 1435

16.234

't440 1445

l6

16.308 16.382 16.456

1450 1455 1460 1465

16.53

1470

16.81

1475

76.88

1480 1485 1490 r 495

17.029 17.102

'1500

17.25

16. 60 16.7 4

16. 954

17.176

Ni-Cr-Fe

Ductile Iron

lable 2-2 Modulus ot Elasticity-Ferrous Material Modulus ot Etasticity, psi (MultiPly Tabulated Values by

106)

oF

-325 -200 - 100

Iaterial

:--lrn :r::

70

300 400 500 600 700

200

800

9oo 1000 1r00 1200 1300 1400 1500

steels

content

l-r

or

\:=:.31/2 ..::.rr

30.0 29.5

29.0

27

.9

27

.7

27

.4

27 .O

26.4 25.7 24.8 23.4 18.5 15.4 13.0

steels

:'::

Coment i^rl ie

lr l

31.0 30.6 30.4 29.9 29.5 29.0 28.3 27.4

"c

26.'7 25.4 23.8

21.5 18.8 1s.0

11.2

23.0 20.4

15.6

--:':r-moly i---s. low -_:tme :--r'rgh

3

,- \to

,::

i -:,aOlarc

31.0 30.6

30.4 29.9 29.5 29.0 28.6 28.0 21.4 26.6 25

29.4 28.5

28.1

30.4 29.9

29.4 28.3 27.7

7

24.s

,:at:ne

;-.s "1, :-

(5 Cr

:_qh 9

-- \lo)

.

- i::lllc --:tI ' 1rK -' 1l?) r:-L-:: :-_

27.4

27

.1 26.8 26.4 26.0 2s.4 24.9 24.2 23.5 22.8 2r.9 20.8 19.5

27.1 26.6 26.1 25.4 24.8 24.r 23.4 223 22.0 21.3 20.7 r9.3

17 9

ChrO-

-ll

30.8 30.3 29.8 29.2 28.7 28.3 27.7 27.0 26.0 24.8 23.r 2r.r 18.6 15.6 r22

i- l:t

13.4 r3.2 12.9 12.6 r2.2 11.'l 11.0 10.2

aa "t . ;-:;

are

for infornation, and it is not implied that materials are suitable for all lhe tempefatures

shovrn.

Table 2-3 Materials Elasticity-Nonferrous Modulus of E = Modulus of Elasticity, psi (Multiply Tabulated values by TemDerature, "F

,,

18.1

:€

67 Ni-30 Cu) and

106)

26.8 26.6 26,4 26.0 26.0 26'0 25'8 25,6 25'4 24.7 2.31 2|.o 18.6 16.0 14.3 13.0 Cu-Al) r--e:-\ickel - J.r-30 Ni) 21.6 Zl.5 21.2 2O.9 20.6 20'3 20 O l9'7 l9'4 -. -::--.tm alloys 10.9 10.6 10.1 10.0 9.8 9.5 8.7 7 7 ll.3 ' rrr:.99.98% Cu) 17.0 16.7 16.5 16.0 15.8 15.6 15.4 15 1 14.7 14213.7 | :- e:cial bmss (66 Cu-34 Zn) 15.0 14.7 14.5 14.0 13.9 13.7 13.5 13.0 12.7 l2'2 lf '8 -ia:i: :in bronze 14.2 13.8 13.5 13.0 12.9 12.7 12.4 12.0 i1.7 11.3 10.9 rl :r-6 Sn-1.5 Pb-4.5 Zn) :c \l-29

' ,t :=:

erc

for infonation, and it is not implied lhat materials are suitable fot all lhe tenperotures shown'

Piping Stress Handbook Table 2-4 Propertles of Salurated Steam v-cs|E I T6Fhtw. ,s.ff

i

P'

0..|{, 0.45

I H6t or I L.6r H6r I To!.t H..t

.lll}''|

!h. Liquid

lofEvle4.lis

I

of

s44

,9c..i6. 77

Coelficients of Thermal Expansion Table 2-4 Continued

rdpa.*.

i

.#E:1".j"

l"tffiltl I 'St*.

v

6.5!{l 6.,t58

76.0

n.0 78.0

5,lll

5.055 5.001 4.948

101,0 102.0 103.0

r04.0

4.19.1

4.157

{,110

112.0 113.0

lt89.l 1189.{

{.015 3.981

rr89,5

3.9r4

1190.7

t.at

llqt.8

u90.9

3.61{

1191.9 1192.0 1192.1

3.110 3.147 3.264 3,712

la6.

to.

l$. 0 lag. 0

35

36

Piping Stress Handbook Table 2-4

Continued Hqr Tod Ha! .Her.f.. II dr-tdr! @uq@ Ei.po..rr@ I| of sr..E

:.134

2.67 |,9992

i.999 r.9183

Expansion

Coefficients of Thermal Step

ExamPle Problem Use Figure 2-1 to calculate the F factor for the

i

2.

move horizontally to the left to find the t€mper-

atue correction factor, F, which in this example is equal to 0.22.

: 660"F : l0 ft-O in. = lin. K : I (shrt fully insulated) 'F : Ambient temperature Tr : Average temperature

T I t

1.

Klt

vl

Enter the chart at the point along the botom line where kh/Ji. Then move up vertically to

the point where the curve intersects' Then

follow-

conditions:

sep

Step3. T1 Step

4. Td

: T-70'F:530'F.

:

F x Tr

:

O.22

x

530"F

:

116.6'F

or 117"F.

I x 10ft :-=IU

Steps.

T" =

Tur

* 70'F :

117"F + 70"F

r87"F.

1

l.o .9

.t .,

Temperature at top ot skkt (oD Av€raqe temperature of skirt (oD Height of skirt, ft

Thickness of sklrt, in. 1 lor skirt lully insulated 1.7 for skirt flreback insulaled 2.7 for skirl not insulated Temperature corrgcllon lactor

1.6 l

.5

I .3

37

Example (see Page 2)

.2 .t

t4

t6 t8 20 22

24

26

2A

---------1>

Flgure 2-1. Curve for determination of average skirt temperature.

30

32

3ll

:

Allowable Stress Range for ANSI/ASME Power Piping Code 831.1 (198t

This chapter contains allowable thermal stresses for petroleum piping. Values of Sh taken from ANSI/ASME Code 831.3-1980, Appendix A, Thble l. (Used courtesv of the American Society of Mechanical Engineers.)

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Stress Intensification and Flexibilitv trlactors

c Minimum radius. Tt'is dimension must not be less than .05 D65 except widr a branch diameter larger than 30 in. It need not exceed 1.50

The following is an explanation of the terms used in figuring flexibility and stress intensification factors. Refer to Tables 5-l through 5-3 for a tabular listing of the factors for different piping configurations. Figures 5-l and 5-2 illustrate these factors for widely spaced, two-weld and three-weld miter elbows, respectively.

t

.

i: T:

T: To: T.:

0:

Maximum radius, For outlet pipe sizes 8 inches nominal and larger, this dimension must not exc€€d 0.10 Dob + 0.50 in. For outlet pipe sizes less than 8 in. nominal, this dimension shall not be greater than 1.25 in.

When the external contour contains more than one radius, the radius of any arc sector of aF proximately 45" must meet the requirements for maximum and minimum of radii. o Machining must not be employed in order to meet the preceding requirements.

Definitions

h:

inches.

Flexibility characteristic Flexibility factor (never less than unity, factor for torsion equal to unity) Stress intensification factor (never less than unity, factor for torsion equal to unity) Nominal wall thickness of the fitting for elbows, and miter bends, in. Nominal wall thickness of the marching pipe for tees, in. Crotch thickness of tee, in. Pad or saddle thickness, when q is 1.5T, use h : 4Tlf . n. One-half angle between adjacent miter axes,

S = Miter spacing at centerline, in.

: Cr : C2 : D*

.

Closely spaced miter bend: S

o

Mdely

spaced miter bend:

(

12 (1 + tan 0) S >r2 (1 + tan 0)

O.D. of branch, in. Correction factor for curves with one end flanged, Cr : firre Correction factor for curves with both ends flanged, C2 : hr/3

deg

Rr:

Mean radius of matching pipe, in. Bend radius of welding elbow or pipe bend, in.

: S cot 0 /2 : [rz (1 * cot

o For closeV spaced miters Rr o For widely spaced miters Rr

0)lt2 Radius of curvature of the external contoured portion of the oudet measured in the plane containing the axis of the run and branch in inches. This is subjected to the following limitations:

The piping code does not speciff any particular distance from the end ofthe elbows arc or the centedine or a miter weld in which a flange will be effective in modiffing the K and i factors on these items. Until a better definition is published, the following rules can be applied: o Weld

elbows-Modifu the k and i factor when the butt weld of the flange is within one pipe diameter of the butt of the elbow. (Text continued on page 120.)

112

Stress Intensification and Flexibility Factors Table S1 Flexibility and Stress Intenslfication Factors Floxlbility

D.l6iprion

Outpl6n.

t

\lblding elbow

sirara lnt. F.ctorl'6

r.65

or pipe bend

Closely spaced miter bend s<12 (1 + tao 0)

F;t

Single miter bend or widely spaced

t.52

1.52

Fl.ribiliw Ch!r!ct!dnic h

li

'pz

0.9 'p;

tr'n

0.9

0.9

r;

314io + 114

(',)'

09

Cot 0

(")'

2

@#

l+coto r 2't

miter bend

s>/2 (1 + tan

-

ffi

lRt

0.9

0.75 'et

Skctch

d)

Weldins t€e

per -A.NSI 816.9

0.9

with

r,)I/a

D2

T

T"> 1.5 T

Reinforced fabricated

0.9

I

TE

I

TE

tee with pad or

314io+

ll4

saddle

UNeinforced fabricated tee

Extruded

welding tee

t

0.9

0.9

tt"=

3l1io+ rl4

3141o+ r14

T

(.f)f

T"<1.5 T Welded-in contour insert

r,)I/a

D2

0.9

1

t*

314

io+

T

ll4

T">1.5 T Branch weldedon finirg

0,9

0.9

(integra Y

3,3

T

-

reinforced)

ANSI/ASME 93l.3d-1984 Reproducedlfom ANSUASME Code 83l-3-1980, Appe dix D',lirble ical Engineers.

I. Repi

ted counesy ofThe At efican society of Mechatt-

113

rl 114

Piping Stress Handbook Table

+2

Str€ss Intensitication Factots for Branch Connections

40 80

f60 40 80

150 80

t20 160

xxs

'lt

1.00

1.00

I.OI 1.34

1.45

1.0 1.0

1.00 1.00

l.l0

0 0

1.00

2 0 0

t $

1.03 1.00 1.00 1.00 2.16 1.44 1.30

60 80

100 120 140 160

I .l

10 20 30

1.0 0 1.0 0 2.O4

1.84 1.60 1.36 L.20

t50 t0 20 ST 30 40

L.20

1.01

8

r.0

1.0

0

1.0 0

140

t60

40 50 80

100

L20

t.0 r I.0 0

1.0

0

l0

3.54

t.97 1.40

100

std

1.00 1.00

20 30

2.0 1.9

8 0

20 30 40

60 80

1.43

.250

30 40 60 80

100

0

r.0

0

4.39

1.0 2

1.00 4.0

0

2.90 8

1.10

stal

1.00

20 30 40

3.49

.250

1.00

.3r2 std 20 30 40

4.40 3.89 3.20

2.31 3.84

3.42 2.56 2.49 4.59

4.79 4.23 3.48 2.80 5.78

4.9

10

1.34

13

0I

4.64

4.42 IO

9

2.70

1.0

s!d

xs

l0

I.OI

4.0

stal

1.00

1.

1.49

10

2.54

1.00

r.

20

1.78

I.09

8

L.14 1.47

2.34

30 40 50 80

r.23

7.23

1.0

2.43

20

xs

1.88

100 120 140 150

1.10

140 160

t0

40

1.87 1.56

4 0

2.22

t

3.89

IO 20 30

1.0 1,0

1.00

2.09

1.0

2. a7

1.9

r.82

L20

2.40

1.00

2. r.0

80

I40 t60

0

2.59

100

I.00

1.0

0

60

r20

f.80 r. {8

1.00

r.0

xs

1.09 1.00

7

I.00

40

I.00 r.69 t.03

120 140

1.00

1.0

xs

l. l3

s9

1.45

std

L.O2

1.00

f.78

20 30

0

0

1.0

l.

I

I.0

r.22

1.0 L.0 1.0

rl

1.00

2.91

8

4.40

2.37 4.39 3.27 2.54

6.40 4.88 3.46

.

Slross Intensitication and Flexibility Factors

Table 5-2

Contlnued

40 80

160

1.00

d0 80

!.29

I50

{0 80

r20 r60

xxs {0 80 120 160

xxs

1.00

1.36

r.0 2.27 1.04 1.00

80

1.6

2.24 1.90

4

100

1.45

140

1. 16

160

1.05

30

{0 50 80

100

\20

l.l0

80

1.0

8

1.7

3

3.70 2.88

50

1.99

80 100

1.49

1.32

I00

IO

1.73

30 40

2.95 2.62

3.ss

60 s0 100 140 160

l0

!.L2

40 60 80

3.31

1.80

120 140 160

L.24

l0

5.66 4.86

std

4.39

20 10 20

30

s.36 4.11 3.91 3.34

1.08 s.80 4.24 3.6

4

7.0

3

3.41

140 10 20 30 40 60 80

I40

r00

t.4s

10 20 30 40

r60

100 120

1.70

1.49

r20

2.01

3.08

100 120 140 !.50

xs

40 50

2.5I

2.50

50

3.01

xs

30

40

xs

3.34

3, ?9

t.09

3.41 2.98

std.

sa

20

30

20

4.39

xs

140

t60

10

160

2.47

20

1.13

80

20 30 40

xxs

120 140

1.0

8

4.0 7

3.{9 3.09 2.09

t.52

6.08 5.36 4.39 3.34 7.82 s.96 4.A9

4.20 3.70

116

Piping Stress Handbook Table 5-2

Continued

f.70 0

1.00

1.58 1.30 1.04

1.40

L.0

40 80

L20 150

xxs

t.7

l.

4

41

l.14 t. 01

ll

1,00

1.83 1.70 1. 41

3,00

1.86

2

100 120 140

2.27

-t4

1.85 1.43

f0

2.64 2.Aa

xs 30 40 60 80

1.49

100 120 140 160

3,91

10

3.24

std

2.O 4

1. 41

I.29 4.74 3.06 2.85

2.O 4

I.7

4.23

f,49

3.7

7

3,0

7

1.22

.250

5.9

4

1.9

std 20 30 40

3.r7 2.44

2.60

10 s

3.82 3.32

4.75 3.9

r.50 r.25

20 30 40

3.68 3.20

4.57

.250

3.9

3

2.45 2.36

1.9I

5.3s,

tal

1.38 7.27

1.74

4.76

6.r7

8

2.O2

3,07 2.39

5.46

4.42

6.9I

6.01 5.31 4.69

10

3.38

2.38

5.99 4.56

6.34

0

4.35

20 30

2.94

1.,38

5.0

s.49

1.37

12

1.40

stil

1.28

t

1.54

2.03

.250

1.68

4

3.28

2.95 2.38

1.40 1.30

r.94

1,5r

4.0

7

t

l0

5.31

1.99

2.43

1.7

100

2.46

2.O7

1.94

10 20 30 40 60 80

3.28

20

2.Ar

7.12

1.29

20

2.69 1.6 7

2.00 I-7 4

1.20

3

5

3.09

100 120 140

3.49 3.0

3.'7

2.19

2.45

10 20 30 40 60 80

2.t9

1.68

1.37

4.94

6

3.45

40 60 80

140 160

1.20

2.a7

3,9

t20

1.23 20 30 40 50 80

7.52 f .35 1.25

XS

100

1.18

2.50 2.34

1.48 1.32

1.19

ST

I.20

1.31

rc

10 20 30

1,08 1.00

r.26

1.39

.3]-2 stal 20 30 40

6

5.78 4.'t

6

4.0

9

3.42 '7.89

6.80 6.00 4.9

5

3.44

4.25

6.8

r

8.75

5.9

0

5.24

6.66 5.4

8

4.72

*RXINFORCED FABRICATED TEE PAD THICKNESS EQUAI TO NOMINAT THICKNESS OF PIPE HEADER

.

Table

117

Stress Intensification and Flexibility Factors

.5F2

Continued

40 80

160 40 80

160

2.19

2-16 2.22 r.6 4

2.63

2.30 1.80

2,7

3.

r.88

7.34

3,90 3.03 2.50

xs

4.80 4.45

6.0?

4.57 3.34

2.10

2.41 10.44

1.76

2.Ol

8.0 8

4.61 4.31

5,49

r

4.21 3.64

2.07 2.02 4.71

4.2r

3.44

3.0 7

2,45 2.0

3

6.02 4.39 3.84 2.45

2.49 2.29

5. t4

4.60

4.9 5

2.80 2.43 6.85 4.25 3.?6

xs

4.0I 3.14 2,72 2.25

10 20 30 40

50 80

,94

4.61 3.9

4

3.39 3.0 3

2.24 9.09 4.14 3.17 3.24

2.59 2.37 't.69

4.78 a.40 3.30

9.60

2.70

2.44 r1.

?9

6. 8l 5.9 4

4.69

8.20

7.0

5

5.10

r0.73

6. r0

7.80

9.t2 8

10.44

1I.4

4

14.92

4.77 7.26 5.9

9.r2

6.92 6,04 5.36 4.45

8.89

3.18

3.9

6.81

1I.36 8.01

70.21

15.50 13.35

7.54 6.54 5.79

8,38 7.34

13.

f4

11.37 10.30

4.6 4 0

8.57 7.38

0

3.29

2.45

11. S2

8.0

11.8I

2,O9

9.'t5

10. s4

4.s3 2.94

l-2.46

8.30

9.9 0

6.40 5.54 4.92 4.44

7

3.0 2

2.40 10 20 30 40

4.58 3.92

3.68 2.76 2.33

2.98 2.67 2.35

120 140 160

30

2.79

3,4

r00

8.35

ST

l.8r

f.98

20 30 40 60 80

9.7!

10 20

4

2.07

t8

2.64

2.10

6.40

1I.82

17.f9

14.82 13.40

10.80 9.24 8.20

118

Piping Stress Handbook Table 5-3 Flanged Elbows-Flexibility Factors and Stress Intensiflcation Factors STZE

2.

I|ALL TIIICK

.154 .2La .436

2\ 2\ 2\ 2 tt" 2\ 2

.

083

,2"

3'

.120

.2I5 .300

3i

.600 .

3t" 3!"

on3

.1?o .314 .536 .0a3

.L20 .237 .337 .531 -674

'134 .258

.625 .750

50

.280

.432 .562 .718 .864 .148

3.2s 2.7r 2.24 L-74 7.73 L.44 1.32 l.03 1.00 1.00 I.00 1.o0 2.36 1.59

1.a3 1.24

I.OO

1.OO

l.0o 1.oo 3.54 2.95 2.74 2.24 2.7S I.48 1.38 I.15 1.01 l.OOj 1.00 1.00 3.85 3.21 2.97 2.47 r.88 I.56 L.44 L.20 1.O0 1.00

4.13 3.L9

3-44

r.22 L.04

1.Ol 1.00

2.66

I.OO l.O0

3.93 3.28 3.41 2.S4 2.13 l.?8 1.61 1.34 I.29 I.0o 1.07 1. o0 l.oo 1.00 4.41 3.68 1.65

1.3?

l.lo l.o0 1.00 1.00 5.20 4.34 4.23 3.52 2-92 2.44

.322

2.45 2.O4 2.06 t.72 r.77 r.47

.aL2 .875 .906

BqlC END FIANGED

i-

ii

.25O

.406 .500 .593 .718

8i

NOT A'JANGED

1.34 1.11 1.23 1.02 1.14 1.O0 r.11 l. o0

!2

1.42 1.lo t.25 I.O4 l.09 1.o0 1.00 1.00 l.o0 l.0o 1.20 1.06 r.00 I.OO

1.00 1.00 1.oo 1.00

1.73

1.49

1.2a I.06 1.12 1.OO 1.OO 1.00

1.00

1.00

1.64 1.36 I.30 1.08 r.I4 I.00 1.00 I.oo 1.93

1.61

1.16 1.0o l.os 1.00 1.00 1.oo 1.00 t.oo 1.88 1.57 1.76 1.46 1.38 1.16 1.20 1.OO I.09 1.O0 1.00 1.oo 1.OO 1.00

1.99 1.45 1.43 1.22 l.I0 r.o0 l.oo 2.16 I.96 1.57 1.49 1.36 1,18 1.11 l.06 l.ol l.oo

1.66

1.54

l.19 1.01

1.OO 1.OO

l.oo 1.81 1.63

qllE EI{D I:UINGED

it

2.35 1.78 r.47 1.20 1.00 I.OO 2.26 1.a5 L.3a 1.15 1.00 1.o0 2.52 1.50 1.00

iol 1.97

r.39 L.22

l.o0 t.oo l.OO

r.8A L.44

I.O8

l.oo

1.00 1.oo 2.09

I.25 1.oo

1.OO r.00

2.6e 2.23 2.20 1.83 1.28 r.07 L.00 1.00 2.S3 2.35 2.33 1.94 l.61 1.34 1.13 1.00 1.00 1.00 1.00 1.00 2.72 ?..27 2.45 2.O4 r..39 1.16 I.la I.00 1.O2 1.00 L.OO 1.00 2.96 2.47 1.ao 1.50 1.42 ].I8 1.05 1.00 1.OO 1.OO 3.35 2.80 2.88 2.39

1.31

!.24 1.14 1.0o

t.oo 1.o0

l.o0 l.oo

1.68 1.40 1.50 !.24 I.21 1.00 r.14 1.00 1.07 1.00 l.o5 1.OO

Note: l.o, iof, io2 are out-of,-p16ne intensifLcation factols i, 11r 12 are Ln plEne lntensiflcation factors

Stress Intensification and Flexibilitv Table 5-3 Continued

10" 10"

ro"

10" 10" Lo"

to" 10" 10"

ro" 10"

t2" 12" t2" 12"

.156 .180 .250 .330

12" L2"

.406 .500

12" t2"

5.23 4.55 3.4L 2.94

4.36 3.79

2.08

1.73

1.40 1.22 1.11

1. t7

5.26 4.'t9 3.8t 3.14 2.a7 2.7a 2.33

4.39

2.44

2.45

1.00 1.Oo

3.99 3.18 2.61

2.39 2.26 1.94

1.85 r.54 .443 1.000

1.39 1.16 1.27 r.06 r.12 1.o0

14" .250 l.4n .312 14" .375 14" .434 14" .500 14" .593 14" .750 14" .937 14" r.093 14" r.250 14" 1.406

3.90

3.25

2.92

2.44

16" ,250 16" .312 16" .375 16" .500 16" .556 16" .843 16" 1.O31 16" r".2IA t 6" 1.438

18n 18" la" 18" 18" la" 1am 18" 18" 18"

2.33 r.94 1.79

1.49

1.34 1.21 1.09

1.12 1.01

4-27 3.A1 3.23 2.63 2.17 1.81

3.55 3.18

1.o0

2.'7O

2.19 1.81 1.51

1.20 1.10

1.00 1.00

4.62 3.94

3.85 3.32

.475

.{34 .500 .352 .750

2.A7 2.39 2.63 2.t9

.93'l

1.82 1.56

1.52 1.30

1.23 1.11

1.00

t_.156

1.375 l-.562

t .78r

1.OO

2.r1 2.03 1.75 1.53 1.37 f.2a 1.19 1.12 t.o5 1.00 2.18 2.08 1.85 1.69 1.56 1.45 l.4t r.29 1.19 1.12 1.07 1.00

J..'t4 t.62 1.5? 1.45 1.38 1,27 1..17 f.10 1.05 1.00 r.96 1.83 1.71 1.54 1.40 r.2a f.18 1.11 1.04 1.03 2.O4 1.9O 1.78 1.69 1.61 1.54 L.39 1.28 t.r8 1.11 t.os l.oo

3.37

2.Af

2.44 2.18

2.O4

I.t4

1.69

r.40

1.0O

1.37

1.14

1.13 1.05

1.O0

3.16

2.63

1.41

2.30

l.9I

1.30

2.06 1.84

1.72 1.53

1.37 I.25 1.17 t.06

1.15 1.04

2.70 2.4r

2.25

1.84 L.t3

f.53 r.44

l.a1 1.69 1.45

r.2A

1.07

1.OO

1.00

1.oo

t.a2 1.73

r.54

1.2r 1.1? 1.04

1.00 t.Oo 1.00 1.00 1.45 1.35

r.3f 1.21 1.15 1.06

r.

r.73

1.42

1.00

r.44

1.O0

1.oo 2.0O

OO

o.92

L.oo

1.13 1.00 1.O4 1.00

1.64

2.9O 2.60 2.34 2.OL L.'74

2.41

1.35 1.23 l.l2

1.13 1.03

t.00 I.52 1.42

r.2a 1.r7 1.06

l.oo

L. oo

r.00 l-.00 r.7O 1.58

1.49 1.41 1.34

\.24 1.15 1.07 0.99

1.00 1.00

l.

oo

2.16 1.96

l.6a 1,45

1.00

r.05 1.00 3.07 2,56 2.75 2.29 2.51 2.O9 2.31 1.93 2.15 t.79 2.01 1.68 1.73 1.44 1.36 1.14 1.23 1.02 1.14 1.O0 1.05 l.o0

Note: i^, i^f i-2 are out-of-plane intensification factors i; jt; i2 ire in plane intensification facEors

Factors

119

120

Piping Stress Handbook Table 5-3 Continued

20" 20" 20" 20" 20" 20" 20" 20" 20" 20" 24" 24" 24" 24" 24" 24" 24" 24" 24" 24" 24n 30n 30" 30" 30"

I

t. t:l

.

.250 .375 .500 .593 .812 1.031 1.241 1.500 1.750 1.96A

.250 .375 .5OO

.562 .6A1

.968 1.21a

I.531 1.a12

2.062 2.343 .2so .375 .500 .625

4.91 3.77 3.0a

4.14 3.L4 2,5?

2.r8 r.82 1.a4 1.53 1.56 1.30 t.3a r.t5 L.22 t.02 1.11 1.OO 5.63 4.69 4.29 3.5'l 3.24 2-70 2.80 2-34 2.20 1.83 1.56 1.30 L.24 r.O3 1.12 1.00 5.63 4.97

4.69 4.L4

o8

2.57

Miter bends-Modify the K and i factor when the butt weld of the flange is located within one and one half pipe diameters of the nearest miter weld measured from the centerline of the pipe.

Although not specified by the Code, this will apply to both closely and widely spaced miters. Note: Large-diameter thin-wall piping elbows and miters are affected by internal line pressure. According to a *Batelle" report to dre AGA, the flexibility factors on these items are seriously impaired by internal pressure. To

correct the values from Table 5-1:

Divide K by: (P) (r)]" (Rt)t"

(1 + o 'E"tz

I2

2-L2 1.A4 'L.67

1.77 1.53

1.39

L.29 1.0? 1.19 1.00 1.11 1.OO 1.O5 1.00 1.O0 1.00 2.25 1.84 L.97 1.64 1.7a 1.48 r.71 L-42 1.59 1.32 1.30 l.oa t.oo l.r9 1.13 1.00 1.06 1.oo 1.OO 1.O0 2.43 2-O3 2-25 l-.84 1.93 1.61 1.7A 1.49

3.24 2.70 2.64 2.2O 2.26 r.a9 2.OA 1.73 r.75 1.46 1.54 r.28 1.36 1.13 1.24 1.03 1.13 1.OO l.05 t.o0 2-9L 2.51

2.42

4.76

1.46

2.O9

1.23 1.04 1.r5 r.00 1.06 1.00 3,24 2-A2 2.51

2

-70

2-34 2.O9

Factors and Characteristics h, k, and i

Butt-weld joint Reducer Weld-neck flange

Double-welded slipon flange Fillet-welded joint-single weld Socket-welded flange Single-welded slip-on flange Lap-joint flange (with ANSI Code

816.9 lap-joint stub) Screwed pipe joint or screwed flange Corrugated straight pipe or corrugated or creased bend.

1 I I I I I I I

| 5

1.0 1.0 1.0

l'.t 1.3 1.1

t.3 1.6

2.3 2.s

Divide i by:

(r+3.2s)9qq# Ecrr

Nate.' Factors shown apply to bending

for torsion equal to 0.9.

flexibility facrr

Stress Intensification and Flexibility Factors

121

Widely Spaced Miters D = Pipe

2-weld Miter

Size

(inJ 12 T4

16

l8 20 24 26

30 JZ

36

40 42 48 54 60 12

0.375 Wall 2-Weld

0.250 Wall

14.2 15.4 r7.3 l9.l 20.8 24.3 26.0 29.3 30.9 32.6 34.2 37 .3 38.9 43.5 48.0 52.4 61.0

Miter

5.4 5.7 6.3 6.8 7.3 8.3 8.7

10.1

4.1

10.9 12.2 13.5 14.8 t7 .3 18.5

4.4 4.8

9.6

11.'l

20.8 22.0 23.2 24.3 26.6

r2.0

27 .7

r3.2

31.0 34.2

10.0 10.4 10.9

r4.2 15.3 l7 .3

.3 43.5

37

Dimensions (in decimals ot teet) A 0.878 1.025

t.171

5.2

I .318

5.6 6.6

1.464 1.757 1.903

7.3

2.196

7.6

2.343 2.489

6.3

8.0 8.3 8.9 9.2 10.0

2.636 2.938 3.075

3.514

3.954 4.393

10.9 11.9 13.2

5.272

K = flexibility faaor

i. -

ii =

outof-plane stress intensificatian factor in plane stress inlensification Jbctor

Figure 5-1. Flexibility and stress intensification factors of two-weld miter elbows. Widely Spaced Miters D = Pipe

0.250 wall

Size

3-Weld

(in.)

Miter

12

t4 lo 18

20 24 26 30 34 36

40 48 54 60 72

ir=i"

i0.8 tt.1 13.1 14.5 15.9 18.5 19.8 22.3 23 .6 24.8 26.0 28.4 29.6 33.1 36.6 39.9 46.5

Wall 3-Weld Miter

0.375

4.3 7.7 4.6 8.3 5.1 9.3 5.5 10.3 5.9 lr.3 6.7 l3.l 7.0 1,4.1 7.7 1s.9 16.8 8. 1 8.4 17.6 8.'7 18.5 9.4 20.2 9.7 2r.1 10.6 23.6 11.5 26.0 12.3 28.4 13.9 33.1

lt =lo

3.3 0.696 0.401 3.5 0.812 0.468 3.8 0.928 0.535 4.2 .044 0.602 4.5 1.160 0.669 5.1 r.392 0.803 5.3 1.508 0.870 5.9 1.740 1.004 6.1 1.856 1.071 6.4 1.972 1.138 6.6 2.088 1.205 7.1 2.320 1.339 .4 2.436 1.406 8. l 2.784 r.607 8.7 3.132 1.808 9.4 3.480 2.009 10.6 4.176 2.411 1

7

K = fleribilitf factor

i" = it =

outof-plane

stress intensification

Dimensions (in decimals ot feet)

factor

in-plane strcss intensification factor

Figure 5-2. Flexibility and stress intensification factors of three-weld miter elbows.

Rotational Nozzle Flexibilities for Cylindrical Vessels

It is customary for piping stress analysts to model a piping system with rigid ends or anchors at the equipment

time and money on these changes, let's model the nozzh data points 5 ard 30 with flexible end conditions using the flexibility factors from Table 61. The table shows that fa exchanger E-l the in-plane rotational flexibility (R.F.) is .626 x 106 in.{bs/deg, and the out-of-plane R.F. is

nozzles. This assumption is acceptable when the system is flexible and the anchor loads are low. But anytime the system shows high loads and stress€s, the analyst must determine how reasonable the assumption in modeling the nozzles as rigid anchors was. The author has developed tables of rotational nozzle flexibilities for cylindrical vessels ranging in diameters from 2 ft to 20 ft and connecting nozzles ranging in diameters from 2

in.-lbs/deg. The new computer calculatior show that the highest stress is 12,015 psi and the new forces at anchor are:

in. to 48 in. sTD. thickness.*

To demonstrate how these flexibility facton really affect the accuracy of stress calculations for a simple piping system, an example where a l4-in. O.D. pipe from an exis shown in Figwe 6-1. changer E-l ties to a tower The computer stress calculation with rigid ends or anchors show a high stress of 33, 616 psi in the system and forces and moments at the nozzles as:

Tl

(}D. 5 30

Tl

lff .4Oi xltr

the in-plarc .209 x in.Jbs/deg. For the tower R.F. is 1.22 x lff in.-lbs/deg, and the outof-plane R.F. b

F,

(rb)

-il,113 l l.l l3

F,0b) -28,r4

28.182

n4 (ft-tb) 85,749

t49.174

Tb reduce these high forces and moments, we will have to modit the piping configwation with more elbows or an additional expansion joint. But before we spend more

D.P. 5 30

F.0b)

Fy

-2,tOO 2,100

-6,04

0b)

6,082

n4 (ft-rbo 3,3@

-20,741

These forces are obviously much lower ftan the frst assumption with rigid ends. Now we know tlnt the piprng system is not overstressed. The shell of the exchanger E-l or the tower T:-l needs to be checked for local stresses with the new loads. It is quite possible that they are acceptable to the exchanger and vessel designer and manufacturers. The following is a method for determining the spnng rate of nozzles attached to vessels or stubbed into larger piping. Only in- and out-of-plane rotational spring rat€s are included, since the radial flexibility is normally ignored. Nozde flexibilities sttould not be used if the nozde

122

Vessels

Rotational Nozzle Flexibilities for Cylindrical or pad diameter is greater than one third of the run or vessel diameter.

Nozde flexibilities were calculated in accordance with the phase report ORNL 115-3, Equation 8, page 6.

K:

c ws

DB

(-D/Wf"

WD

. MDBK o=-

(6-l)

(6-2)

EI

Spring Rate

:

EIPI

(6-3)

2160DBK

Solving Equation 6-2 tot (Ml?) and converting units to ftJbs/deg we have Equation 6-3.

where

C

c:

D: Ds: E= I: K: M: PI:

123

.09 for in-plane bending .27 for out-of-plane bending

Diameter of vessel or run, in. Diameter of branch, in. Modulus of elasticity, psi Moment of inertia of branch, in.a Flexibility factor Moment, in.{bs Circumference of a circle divided by the diameter

Angle of rotation, radiam e: of or run, in. Wall w: of branch, in. ws: Wall thickness thickness

vessel

In-plane bending refers to bngitudinnl bending in the run or vessel in the plane formed by the intersection of the branch and vessel or run centedines. Out-of-plane bendtngreferc to circumferentialbendng it a plane perpendicular to the vessel or run diameter.

PIPE:

MAT. -

C.S.

o.D. - 14"

THCK. - .375" TEMP, - 450'F EXCHANGER E.1:

MAT. -

C.S.

o.D. - 5'-0" THCK. TEMP,

- 1lz' - 45OOF

b I I I I

t

--TI

I

TOWER T-1:

MAT. -

o.D. THCK.

TEMP

C.S.

10'-o"

- %" - 450"F

I I I

Figure 6-1. An example diagram of a piping system where 14-in. O.D. pipe trom an exchanger ties to a tower'

124

Piping Stress Handbook Table 6-1 Rota Stiff calculation, Gyl. vessel ROIA 00.F1

vEss€L TCK,IN

2.000

.2 50

VESSEL

2.000 2.000 2.000 2.000 2.000 2.000 ?.000 2.000

.500 .6?5 J

1.?50 1.500 1.750 2.000

.250 .325 .500

2.C00

2.000 2.000 2.000 2.000 2.000 2.000

.000

.750 1 .000 1-250

2.OOO

1.500

.000 2.C00

2.000

2.000 2

2.00c 2.000 2.000 2.000

2 -OOr)

?-000

2.000 2.000 2.000 2.000 2.000 ?.000 ?.000 2.000 2

.000

.250 .375 .500

STI'F

CALCULATIOTI, CYL. VESSEL NO2 T

2.375 .375 .375

2 2

2.375 2.375 2.375 ? -375 2

.t75

?-375 2.3?5

.000 1.250 1.500 1

3.500 4.500 4.500 4. 500 4 -500

4

.500

4.500

6.625 6.625 6.625 6.625 6.625 5.625 6.625

2.500

.250

2.500

. t00

2.375 2.375 2.375 ?.3?5 2.375 2-375 2.375 2.375 2.3?5 2.375 3.500

2.50 2.50

.625

0

-750

0

2.500

1

.000

1.25(J

I .500 I .750

2.50 0 2 .500 2 .500

2.OfJO

2.500

.250

2.5C0

.37 5

2.500 2 .500 2 .500 2.500 2.500 2.50[r

.500

.625 .750 1.000 1-250 1.500 1.750

.154

.499 E +0 5 .871E+05

.4128r06 .8 47€r 06 .1 48 E+07

.233E+07 .343E+07 .479e +07 .394E+05

-216

.500 3 .500

3

6.625

.t75

.154

.2618+06

.1 50E r06

.22O8+07 .347 E+A7 . 510€+07 .712E +oz

3.500 3.500

2.OOO

.7 50

.154

.2438+05

3. 500

2.000 2.000 2.000 2.000

't

.154 .154 .154 .154

6

.6?5

6.6?5

.216 .216 .215 .216 .216 .237 .237

.237 .237 .237 .237 .237 .237 .?37 -280 .280 . ?80

.280

.280 .280 .280 .280 .280

.154 .151 .154 .154

.882Ef04

.265E+05 .729 Er 05

.223E+05 .389E+06

4.500 4.500 4.500

.7 50

-154

-216 -216

3.500 3.500

1.000 1-250

1.750 2.000 .250 .375 .500 .625

-154

.154 .216 .216

4.500

1. 500

CK,I

.500

3

-625

.7 50

ZLE ROT STIF IN.LB/DEG N INPLANE OUTPLAI.IE STD LOI,I6I CIRCU

r{ozzLE

OD,]N

.t0EE+06

.6'l4E+06

.126E+ C7

,520E|05 .143Er06 .294E+06 -514E+06

.81t8+06

.166E+07 .29'l E+Ol .459E+07 .67 4E107 .942E+07 .790E+05

.21EEf06 .4 478+ 06 .781E+06 .123E+07

.253E+07 .142E+A7

.697E+07 ,'102E+08 .143E+08

.1378+06 .28?E+06 .493 E +0 6 .7 78E+O 6 .114e+O7 .160E+07 -131E+05

.362E.05

.712E+o5

-130F+06 .205E+06 .420E+06 .733EtO 6

.1168+07

-170E+07 .2378+Q7

.l738+05 .478E+05

.981€+05 .1718+06 .27OE+D6

.555F+06 .9 69 E+06

.153E+07 -225t+O7 .314€+07 .263E+05 .726E+O5

.149E+06 .?608+06 .4118+06 .843E+06 .117e+A7 .232E+o7 .3428+07 .477E+47

-237E+05

.789E+O4 .217E+Os .446E+Q5

-154

.134E+06 .234E+06 .369E+06 .7 578+05 -132a+07 .2C9E+07

.154

.6528+05

.7798+05 .123E+O6

.2528+46 .4418+06 .695€+06

.'t 54

. 3C7E+ 07

.154

.128E+07 .552E+05

.1'l7E+O'

3.500 3.500

.216 .216 .216 .216

.970E+ 05

.323E+05

.199 E+06 .348 E +06

.56

.500

.?16

.5 49 Er 06

.183Ef06

.'113E+07 .197E+07

.376E+06

.3'10€+C7

-103E+07

5

3.500 3

.500

.216 .216 .216 .216

.456E+O?

-102Ef07

.143ErO7 4E

r0 5

-116etO6

.656Ef06 .152E +O7

20+ SSZL' 9O+3 L6L'

10+lS2t'

ZZ'

90+1299.

90+3tEt' 9O+3

L

90+l0t!' st]1rt08' S0+r06t' so+tzrL' to+1r 61' to+)6tL' 90+r9t6'

90+r 66S'

90+rttt' 9O+1L9

L'

90+:1901'

s0+3909'

s0+3952'

s0+rl.0l' 1.0+:0tl'

90rltt6'

90+35t9' 90+3?0t' 90+1052'

9Ot )Z I L' SO+) t, L'

90+ltor' S0+386t' t0+r0zl.'

tLtz'

l0+39t1' 9Crl0Zt' 90r10rz' 9A+tLtl' S0

+13Zr'

lar )z8g' to+ 12Lt' zo+ atgz' 10+108!'

20+lt0!' 90+ll0s' 90+l8tt'

Itz' tiz' z'

Lt

lt2'

L2' 9LZ' 9

tz' 9tz'

9

912' 9

LZ'

9C+rZ8l' !0+r968' s0+l tz t' lO+z L6r' z0+J082' to+ )o6L'

9LZ' 9LZ'

90+l169'

ts L' ,s L'

to+3lzL' 9O+a

Ltt' ,'

It

L2' 9A + 9O +1ZZ S0+3S65'

9tz'

t9 L' ts L' ts L'

ts ts

00s't 00E't 00s'?

00s't 005't

't 009' ,

005'

00s't 00s't

osz' 0c0'z

00('t

't 00s' t 00s't 00E' t 00E

00E't

00s't 009't 009't

stt'z slt'z glt'2

t' l'

,s L'

sLt'z

20+)r9S'

80+;1691'

g29'I

Lo+1s2?'

+3rz t' LO+1ZZS'

zzt' azt'

to+3rLt'

]166' 90+lE8r' 90+tg0t' 90+ 91+

f9lL.

80+3lzl'

20

20+)9' L' 90+3t26' 90+t6zs'

E0+r8E8'

90+ 1L92.

l0+SLzr' 101390t' lo+)eoz' L0+3ztl'

r. 10+i LL 6'

90+lllt.

9O+1'

S

l'

9O+3t9t'

90+rttz'

90+lttl'

s0+16t9' S0+39t2' lo+) L?z' l0+a LOZ' LO+) Lt l'

E0+rtt6' g0+rgZ

lo+39?9' 1.0+rg6t' L0 + )9 ZZ' L0

+

10L

t'

90+1669'

90]303t' 90+356t'. I0 +:l,l0l. 20+12' g'

/0+1t09'

90+1e98'

t0+30Lr. LC+ 10? Z.

90+ 39

20+36r

6i' 90+3ZrZ' 90+rEs l' s0+31.28'

SO+rlzr'

LO+

3

2LZ'

r.

9t+)SzL' 9C+109t' 90+lt9Z' 90+3 8Z

I'

90+lS9t' lo+1Ltg'

I9NO'] NJUI] I Nv-l dNI lNvldIn0 9rc/€'t'NI i Its 10u

sz9'

I

EZ9'8

sz9'a EZ9'

10+1662'

I

szg'8

zzt' zzt'

otiz' 082' 08 z' 08

z'

082' 03

z'

082' 082'

082' 082'

).tz'

Itz' 2t2'

lrz' Itz' Itz'

2t?' 9

L?'

09t'L 0c9'L 052't 000' I ost' szg' 00s'

09z' 000'z

00s't 09?'I 000' I

000'z OSL'L

009' I

osz'L 0c0' I os

L'

E29'S

a9

000

z' 'z

szg'9 szg'9 szg'9 szg'9 sz9'9 s z9'9 szg'9 szg'9 szg'9

as2'L o9s'L

oos't 00E't 00s't 00s -t 009't 005' t 00s't

OSL'L

00s't

l-tzz0N

-tJss3A'"llJ,NOllvlnllvl tlrls penu!luoc t-9 etqer

000't 000'5

0c0't 000't 000't 000'

t t

090'

5

000'

t

0c0'

t

0c0'

I t

00c'

000't 000't 000't 000'5

000't 000't 00c't 000'I

000'

sz9- 9

00E't 005'?

00c'l

009'

s29'8

t

000't

091'

szg' 00s'

008'

t I

000' 000'

000't 0c0't

E29'8 szg' I

(ls NI')]I

slassen lPcr.rpurdc Jof ssll!l!qrxell elzzoN leuollPlou

009't o9?' t 000'I r)s 2' szg'

00s

s0+39t?'

lo+lrot'

;

10+

osz't

000't 000't 0cs'z

cos 'z 00E' z

00s'z 009'z 009'z

00s' z

00s'z 00s'z c0g'z c35'Z

005'z oo3'z o09'z

'z

000' I 0Ez'

00E

00E'

00s'z 1xs'z 006'z 00s'z oos'z 00t' z

sz9'

09z' 000'z 00s' t osz'L

000't

0s2' sz9' 00s'

osz' 000'z

NI')JI -13 ss 3A v10u

00E'z oDs'z

00E' z

00E'z 005'

z

00E'z 00E'z

0cs'z 009'z 00s'z IJ'OO -l3sslA

126

Piping Stress Handbook Table 6-1 Continued ROIA STIfF CALCULAIIOII, CYL. VESSEL

OD,fT

3.000 3.000 3.U00

3.000

3.0c0 3.000 3.000 3.00c 3.000 3.000 3.000 3

.000

3.000 3.000

3.0c0 3.000 3.O00

3.000

L

l, l:i

l

t,

'

I

3

.000

3.000 3.000 3.000 5.000 5.000 5.000 3.000

3.000 3.000 3.000 3.000 3.0c0

VESSEL TC

K,IN

1.750 2.000 .z5g .375 .500 ,6 25 .7 50 1.000 1.250 'f . 500 1.750 2.000 .250 .375 . 500 .625 .750 I .000 t. ?50 1 .5s0 1.750 2.000 .250 .375 .500.625 .750 1.000 1.2r0 1.500 1.750 ?.000

3.500

3. 500

.250 .375 .500

1.500

.6?5 .7 50

.000 1.250 '|

f.500

3.5C0

1

.500

.750 2.000 .250 1

3.500 3

.50C

3.500 3.500 3.500 3-500 3.5C0

3.500

t.500

.500

.625 .750 1 .000 1.250 1.750 2-000

3.5C0

4.500 4-500

6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 8.625 4.625

. 500

.625 .7 5b

1.000

t.250

NOZZLE ROT STI f II{.LB/DE6 T

CK,I

SID

.280 .280 .280 .280 .280

.6458+05

.?15E+05

.2 E0

.?07E+07 .361E+07

10 -759 10 - 750

.l

78

E+

06

.365€+06

.638Ei06

.5938.05 .1228ro6 .2t3Er06

.569E+07

.2E0

.8t7E+07

280

.1'l7E+08

.389E+07

-853E+05 .235E+06

.284E+05

E.06

.161E+06

.135c+07 .?73E+07

.443E+06 .910E+06

.752e+07

.159E+07 .251E+O7 .569E+0 7

.280 .280 -

.32? .322 .322

.1018+07

.?56E+07

.3f,5E+06 .6888+06 .120E+07 .190E+07

-322 .322 -322

8.625 8.625 8.625 8.625 10.750 10.750 | 0.750 10.754 10.750

CIRCU . l84E +0 7

E.625 8 .625

8.625

OUTPLA}'IE

.551E +O7 .7 69 E+07

.237

.625

8

N INPLANE LONGI

.237

.322 .322 .322

4 92

.

.843Er06 .477Er07

-3?Z

.ttlE+08 .l 54Er 0E

.

-

t65

.365

.165 .36 5

107E+06

.279E+O7 .78

3

E.0 5

.e8l E+06

.51'E+O7 .358Ero5

.986Ei05 .?03Er06

.2968+06 .608E+06 .106E+07 .167a+07 .311E+07

.3548+06

.316E.07

.558E+06 -115E+07

.200E+07

10.750 10.750 10.750

- 565

.600E+07 .9 47 E+ E7

-365

.194Er08

2.375 2.375 2.375 2.375 2.375 2.375

.154

.2C0E+05 -551C+05

-154

2.375

.154

-640Er06 .112E+07

.154

.176E+07

.5888+06

-154

.259E+07 .362E+07

.1?1E+O7

.216 .216 .216 .216 .216 .216 .216

.298

2.37'

?.375 3.500 3.500 3.500 3.500 3.500 3,500 3.500 4

3.500

3.500 1.500 3.500

t{0zzLE OD,IN

VESSEL

.500

4.500 4.500 4,500 4.500 4.500 4.500

.365

.365

.t

54

.151 .154 .154

.154

. '139 E+0 8

.113Er06 .198Ff06 .312E{06

.659Er05 .1048+06

.213E+O6

.373Er06 .864Er06

.561E+05 .980E+05

.4648+O6

.952Ef06

.539Er07

.237 .237 .237

r04

.294E+ 06

.168Er06

-2'16

.2t7 .?t7

E

-184E105 .377E+Os

.99ZtrO4 .27iE+05

+C5

.166E+07 .?62E. 07

.237 .237

.6 67

.820E+05

E

.?16

.216

.464E+O7 .646 Er0 7

.386E+07

.155E+06 .317ErOo

.554E.06 .875E+06 .1?9e+O?

.1 80E+0 7 -t

.108€+06

.222Er06

31€r0

5

.361E+05 .741€+05

06

.i30E'06

.613 Ei 06

.204€+06

.389r

+

.126E+07 .2208+07

. 419 E+0 6

.733E+06

Rotational Nozzle Flexibilities for Cylindrical Table 6-l Continued ROTA STIFF CALCULATIONT

VESSEL NOZZLE ICKTIN 0D,Iil

VESSEL

0D,fI 3.5C0

1.500

1.500 3.500

'l

.7 50

2.000

.250

3.500 3.500 3.500 3.500 3.500 3.500 3.500

.500

.625

6.625 6.625

.7 50

t.00rJ 't

.250

1.500

3.50 0

.750 2.000 .250

5.500

.500 .625

.500

3

.625

6

1

3.500 3.5C0 .500 .500 3 .500 3 .500

3

3

3.5 00

3.500 3.500 3.500

E.625 E .625

.527E+C7

.2 80

.7 7 5E+ 07

.280

.1088+08 .790E+05 .218E+06

.4178+06 .780E+06 .123E+C7

10, 750

.500

1

0.750

.000

1

1.750

10 ,750

3

2

10

.500

3.500 3.500

.500 .625 .7 50

12 -750

.250

'12.?50

.0s0

.5C0

3.500 .500

.500

.500

2. 000

12.750 12.750 12.750

.500

2.375 2.375 2.375

.750

4.00 0 1, .000

4.000 .000

4.000 4.000 4.000 4 .00c

.000 .?50 .500

0

4.000 4.000 4.000 4.000 /,.000 4.000

2

4.rJ00

1

.000

?.375 ?.s75 2.375 2.375 2.375

.250

3. 500

.500

3. 500 3 .500

.75rJ

.000

3.500

3.500 3.900

.3'l0Er06

.637 E+O6

.1 'l1 E+07

.176E+07 .258E+07 _3617+07 .263E+0 5 .7?5E+O5

.149E+06 -260E+06 .410E+06

.23?E+07 ,34'l E+C 7

.11'3E+08

.47 6E+

.991E+05 .27 4E+06

.331E+0

.147E+07 07 5

.913€+05 .187E+06

.562E+06 .9838+06

.328E+06

SSEaOl

.517E+o6

.l

.106E+07 ,185E+07

,3 65

.877E+ 07

.292E+07

.365

.129 E+ 08 .180E+08

.6008+07

.750

12.750 1? .750 12.750 12.750

.549E+05 .113E+06

-696E+ 07

.3'l8E+07 .5568147

10.750

3.500 3.500

3.500

.365

.199E+05

,842€+05

.441E+C7

.50>

10.750

-1708 +O7

-?53E+C7

.102E+08

0. 750

.0c

.280

.625

1

/.

.2E0

.9318+o6 .191E+07 .3348+07

.3?2

a

1.250

4

.1978+06

.t55E+06

4.625

0, 750

3

.2 80

.338E+C6 .590E+06

.280

1.750 2.000 .250

r

3.500

.2E0

-t?2

-7 50

J

.237E+ol

.2a7

8.6?5

.?50 I .500

1-000

3

.1169+02

E

1

.500 3. 500

3

CIRCU

+07

.347

E -625 8 .625

.7 50

LOI1GI

,5108 +07 .7'l ?E + c7 .597e+ A5

.322

10.750 10.750

.500 3 .500

SID

8.625

.500

3

ZLE ROT STIF II{.LB/DE6 C(,I N II,IPLANE OU]PLANE

.280

3-500 3 .500

3,500

T

6.625 6.625 6.625 6.625 6.625 6.625

1.000

VESS€L

N02

4. 500

4.500 4.500 6.6?5

CYL'

.'l 20E+06

.375 .375 .375

.329 E+C6 .676E+ 06

.118E+07

.430E+A7 .399E+05

.1'l0Ef06

.225E+06 .394E+06

.i86E+07

.621 E+06 .'128F+07

.666E+07 .'1058+08

.223E+oz .351E+07

-375

.2168+08

.7?1E+O7

.15 4

- 187E+05

.624E+O4

.106Er06

.353Er05

.375 .375

. I 55 E+08

.154 .154 .154 .154 -'t 54

,154 .151

.'t54 .216 .2.16

.z't6 .2'16

.?16

.515E+05

.185E+06 .292E+06 -5999+06 .105E+07 . 't 65 E+ 07

-517 E+07

.172E+05 .61

6E +0 5

.972E+05 .200E+06 .349 E+ 06

.550E+06

.2438+07

.808E+06

.339E+O7 .2?8 € + 05 .7 67E+05

.928E+04 .256E+05

.157E+05 .27 5E+ 06 -454F+06 . 891

E+

06

.1'l3E+07 ,525Er05 .917E +O5

.1458+06 .29

7 E+O

6

Vessels

127

128

Piping Stress Handbook Table 6-1 Continued R0TA

vEssEL

VESSEL

4.000 4

.000

4.0c0 4.00 0 4.C00

1

1.750 2.000 .250 .375 .500 .6?5 .7 50

4. 500

1.000

4.C00

2.OOO

4.000 4.000 4.000 4.000 4

.000

/..000 4.000 4.000 4.000 4.000 4.000 4.000 /,

.00 0

4.000 4.000 4

.000

4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.0c0 4.000 4.000

1.000

.250 I .500 1.750 2.000 .250 1

.37 5

.500

a -625

.7 50

8.625 8.625 I .625

8.625

.625

1.0c0

.250 1 .500 1

1.759 2.000

E

.500

.625 .7 50

.000

.2 ro

.500

.750

2.000 .250

.t7

5

.500

1.500

1.750 2.000 .250 .375 .500 .625 1.000

1.250

.625

8.625 6.625

l0 .750 1

4.00 0

4.000 4.0c0 4.000 4.000

6.625 6.625 6.625 6.625 6.625 6.625 6.6?5 6.625 6.6?5 8.625

.7 50

t-000 1.254

4.00 0

4.500

.625

.625

4.000 4.000 4.000 4.000 4.000

4. 500

.37 5

4.0 00

4.000 4.000

4.500 4.500 4.500

.250

.000

4.000

.500 .500 4. 500

3 3

4.500 4.500 4.500

1.250 1.500 1.750

4

OD,IN

3.500 3.500

.250

1.500

4.000 4.000 4.000

4,000 4.000 4.000

i{0zz LE

ICKTIN

OD,fT

4.000 4.0c0 4.000 4.000 4.000

SfIFF CALCULATION, CYL. VESSEL

0

.750

10.750 't 0.7s0 10.750 10.750 I 0.750 10.750 r 0.750 10.750 12.750 12.750 12.750

NOZZLE ROT SII F IN.LB/DEG

TcKrIt{ INPLANE

STD

LONGI

0uTPLAt{E CIRCU

.216 .216 .216

.156E+A7

. 519

C7

E.06 .818E+06

-216

.361E+07 .504E+07

.1 208 +07 .l6E E+07

.237

.366

-123t+O5

-101Er06

.237 .?37 .237 .237 .237 .237 .237 .237

.215E

+

E+

05

.694

.324E+ 07 .477E +07

. 108E

.666E+07 ?80

.559Er05

.280 ,260

- 316E r 06

.

.2E0

.1 54E+06

.552E+C6

.?80 .280

.8718r06

.2E0

.312E+07

.280 .280 ,280

.t22

.322 -3?Z .322

.322 .322 .322

.179

*

A7

.493E+07 -7 ZsE+ 07

.1018+c8

.7398r05

.1218+06 .1 91 Ero6 -392E+06 .68

5

E+06

r07

.159E+0? .22?E+O7 .1E6E+05

.513E.05

.105E +06

.184E+06 .290 Er0 6

.5968+06 .104E+07 .164E+07 -2428+87

.t378 +47

.2o4E+06 .4'lEE+06

.246€+05 .678E+05 . 139 E+06

.730Ef06

. 243 E+0 6

.115€+07

.3848106

.236E

.78EE+06 .138E+07 .217 E+o7 .319E+O7 -416E+07

+

07

.413E+07

.322

.651E'07

-322

.958E+07

.365 .365

.930E+05 .256E+06

.134€r08 .526E+06

.365

.338 t +0 5 E+ 05

.2OaE+06 .363E+O6 .573E+06 . t 18E+07 .206E+07

.310Er05 .854Er05

.175E+06

.9'l9Er06

.306E|06

.145E+07

.4E5E+06

.296E+07

.992Ei06 .17

-365

.5208+07 .E208+07

.375

.112f+06

.565

.375

3E +07 .2738+O7

.121E+08 .168E+06

.40?Ero7

.3CEE+C6

.103E+06 .21 I E +06

.633r+06 .t118+07

.5618+07 .373€+05

.f68€+06

12.75O

.375

.750 't2.750 12.750 12.750

-375 .375

I 4.000

.37 5

.124E+06

.413Et05

.37 5

.311Er06

.114E+O6

.375

.700E+06 .122E+87

.233E+06 .40EE+06 .643E+06

1Z

.6258r07 .9E

6 E+

07

.145E|0E

.202Ef08

'12.750

14.000 1 4.000 I 4.000 14.000 1 4.000 14.000

.174E+07 .358E+07

.575

.193Er07 .396E+07 .692E+A7

.561 E+06 .119E+O7 .2O8E+87 -329E+07

.4838+o7

.675E+O7

-112E+O7

.?31E+Ol

Rotational Nozzle Flexibilities for Cylindrical Table 6-1 Continued ROlA

vEssEL lCK,lN

vEss€L OD,FT

4.000 4

.000

4.000 5

1.500

1.750 2.000

.000

5.000 5.000 5.000 5.080 5.000 5 .0c0 5.000 5-000 5.C0C

5.000 .00c 5,000 5.000 5.0c0

SIIfF

5

.000

5.000

.250 .5c0 .7 50

. t 65€+06 .261e+06

-154

.535E+06 .935E+06 .1 4EE+07 .217 E+ A7

-375 .375

4.500 /..500 4.500 4.500 /, ,500 4. 500 4 .500

.15 4 .1 54 .15 4

.154 .216

.3c3E+07

.820E+05

.386E+06 .797 E+ 06 .139E+07

- 129E+06

.2?OE+07

.7 32E+O6

-?16

.216 .216 .216 .216

.323E+07

I .625 I .625

1.?50 'l . 500

1.75n 2.000

8.625 8.625

8.625 10.750

.500

10 .750 10 .750

.? 50

1

10.750 0

.750

1

.000

10.750

't

.2 50

1

0

.750

.229E +O5

.469Er05 .?66a+06 -464Er46 .108E+07

-216

.451E+07

.150E+07

.329

-237

.907E+05 .186E+06 .325E+06

.110E+05 - 102€+05

.237 .237 .237

E

105

.105E+07

.351E+06 .613E+06 -967E+46 .'l42E+O7

.184€+07

.596t+ 07

.2t0

.500E+05 .138E+06 .283E+06

.2E0

.494E+ A6

.322 .3?2 .322

.32?

.322

.322 .322 -322 .365

.108E+06 .171E+

.?37 .280 .280

.2 E0

.6208+05

.5r3E+06

8.6?5

.000

.830E+C4

.216E+ A6

.500

a -625

-723E.O6 .10'18r07

-2't6

.250

.7 50 2. 000

.3',12E+O6

.492E+06

.?16

.280 .280 .280 .280 .280

.000 .250 .500

.176€+06

.2498 + 05 .686E+05 .141E+06

6.625 6.625 6.6?5 6.625 6.625 6.625 8.625

- 625 .7 50

.315E+05 .551E+05 .869E+05

.216

6 -625

/..500

.500

5.000

.154

.2908+A7 .427 E+07

.250

1

.154

-237

.500 ,750 2.000

5.C00

5.000 5.000 5.000 5.00c 5.000

.154

.500 3 .500 4 .500

.000

.000

5.000 5.000 5.000 5.000 5.000 5.000 5.000

2.375 2.375

3. 500

.250

5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.0c0

.'154Ei05

3

2. 000

5.0[0

5

.461E+05 .946E+05

.500 3. 500 3 .500

1.750

.7 50

5.000 5.000 5.000 5.000 5.000 5.000

2.375

3

,000

5

.7 47 ErOT

.7 50

1.500

.364F+07 .535E+07 .558E+04

.500 .6?5 .2 50

60E+ c8

.1 67E +05

3.500 3.500 3.500 3.500

1.000

1

.224€+08

2 z

2.000 .250

.500

.

.154 .154

2.375 2 .375

.000

5.000 5.000

.'109E+08

.000

4.000 14.000 2 .375

-7 50

5 - 000 5. 000

E ROT STI F IN.LBlDEG ICK,IN INPLANE 0UlPLAl'/t CIRCU STD LONGI

NO2 ZL

1

.500 -625

'|

r{022L€ 0Dr1N

't 4

5

5.000 5.000

CALCULATIOiIT CYL. VESS€L

.7

79

E

+a6

.160€+07 .279 E+47 .411F + 07

O

6

- 199E+07 .1 67 E+A 5

.459E+05 .943E+05 .165E+O6 .260E +o6

.53fE.106 .932E+06 .147E+O7

.618E+C7 .905E+07 .6618+ 05 . J82€+06

.216E+07 .3028+O7 .220E+05

.65!t+06

.2188+06

.37 4Elc6

.'103E+07

.607€+05 .125E +o6

.343E+06

A7

.7058+06

.369E+ 07 .533E+ 07 .856E + 07

.191E+07

.2't1E|

.'l

20E +0E

.832E+05 .?29 E+06

.471E +06

.E228+06

.130E'07 .2

07 .4 65E+07 66E+

.1?

3E

+

07

.285F +07 .399 E+o7

.277 E +O5 .7 64E+O5 .157E+06 .271E+o6

.4328t06

.887€106 .155E+o7

Vessels

129

130

Piping Stress Handbook Table 6-1 Conlinued nOTA VESSEL OD, FT

5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 ).UOU

5.000 5 .000 5.000 5.000 5.000 5.000 5.000 5.000 5 .000 5.000

5.000 5.000 5.00 0

5.000 5.000 5.000 5.000 5

.000

.750 ?.000 .250 .375 .500

.750

2.000

.t75 . 500

.625

.t50

6.000 6.000 6.000 6.000 6.000 6.000 6.00 c

'1.500

.750 2.000 1

.250

.375 .625 .750 1.000 1.250 I .500 1.750 2.000 .250

6.000 6.000

- 500

.625 .750

6.0 00 6.0 00

6.000 6.000

?50

'l

-000

1.?50

. t 44E +0E

.478E

.200E108 - t 288+06

.4?6E+O5

-000

.409 E +07 .715 € + 07 .113E+0E

16.00 0

.166E+ 0E

.231E+08

.145E+06

rE.000 r8.000 18.000 t 8.000 18.000 1 8.000 18.000 18.000

.151 .154 .154 .154 -154 .154 .?16

.216 .216 .216 .216 .216 -216

E+0 6

.1368+07 .2388+O7 .376E+O7

.552ErO7

.771Ero7 .483€+05 -273E+06 .4778+D6

.226E+07

.75

?8E+ 08

188€+08 .262E+08

2.375 2.375 2.375 2.375 2.375 ?.375 3.500 5.500 3.500 3.500 5.500 3.500 3.500

2.t75

.664

.14tE+07

.

.154 .154

.421E+06

.133Efo6

.810 E r 07

-154

.117E+06 .2 418+06

.8 20 s+ 06

.l .154

r07

.668 Ef07

.399E+06

.464Er 97

2.375 2.375 ?.375

.569E+05 .10?E+06 .209E+06

.619E+07 .976E+07

- 199 E+07

16.000 't 8.000 18.000

.4328+Ol .604Er07

.365E+06 .575E+06 .118E+07 .206E+07 .325E+07

.352Ef 06 .723E+06 .1268+07

6.000 6.000

. l07E+07

-1738+07 -351E+07

.109E+07

r6.000 16.000 't

.

08

.626Er06

16.000 16.000 16.000

1.500

1.000 1 .250

E +

. t 11 E+06

14 -000 14 -000

16 1

1.750 2.000 .250 .375 .500 .625

.2 94 E+0 7

.130Er08

.305E +06

I .000

1.250

.186e+07

.8 82 Er 07

14 -000

14.000 14.000 14.000

.245E+07 .359€+07

.559E+02

.3208f07

'11.000

CIRCU

.9e9E+06 .156E+07

.566Er06

14.000

OUTPLAI{E

.502Er07 .333Er05 .9'l9Er05 .189Er06 .J30Er06 .520Er06

.100E+06 .2?6e+06

.'l8l

.250 1.t00

1

LONGI

12 -750

14.000 14.000

1

STO

1?.750 12.750 1?.754 12.?50 12.750 12.750

.6?5

.750 1 .000

TCXTII{ INPLIN€

.151E+C8

1Z -750

.500

NOZZLE ROT SII F IiI-18/DEG

10.750 12.750 12.750

.500

1 1

VESSEL

.734E+07 .108E+08

I0.750

.625 .750 I .000 1 .250

cYL-

| 0.750

1.750 2.000 .250

6.000 6.000 5.00 0 6.00 0

0DrIl,l

TCKeIx

'1.500

CALCULATIONI

0zztE

VE SSEL

5.0 00

5.000 5.000 5.0c0 5.000 5.000 5.000

SlItr

.l

3E +0 6

.155E+O7 .278e rO7 -426E+O? .6?6E+O7 -E75 E+07

53E+05

.509€+04

.421Er05

.1 40E+05

.864Er05

.l5lE+06

.288E+05 .503E+05

.2388+06

.794E+05

4E9E+06

.1638+O6

-

.854E+06 .'155E{07 .198E+07 -276e+07 -227E+05 .626E+05 .129E+06 .225E+06

.285E+06 .449E+06 .660 E+06 -9228+gb

.757Er04 .209E +05

-428E+05

.749€r0

5

.5 54E+06

.ll6Er06

-727e+O6 .127Er 07

.423E+06

.242E+O6

Rotational Nozzle Flexibilities tor Cylindrical Table 6-1 Continued

sTltr CALCULATIONT CYL- VESSEL NOZ ZLE ROT STIF IN.LB/DEG VESSEL NOzZLE lCK,It{ INPLAxE 0UTPLANE TC(,II{ OD,IN CIRCU STD LONGI ROTA

VESSEL

OD,FT

6.000 6.000 6.000 6.000 6.000 6.000 6

-000

6.000 6.000 6.000 6.000 6.000 6.000 6.00

0

6.000 6.000 6.000 6.000 6.000 6.000 6.00 0

6.000

6.0c0 6.000 6.000 .).

1.500

1.750 2.000 .37

5

.500

.625 .750 '| .0c0 1.250 1.500 1.?50 2 .0c0 .250

1.750 2.000

6.r100

,000

6.000 6.000

2

.000

.250 .500

1

6,000 6.000 6.000 6.000 6.000 6.000

.000 6.00 0

6

6.000 6.000 6.000

6.00 0

6.000 6.000 6.000 6.000 6.000 6.0c0 6.000 6.000 6.000

.000

.411E+07

.1378+O7

.237

.3008105

.100Er05 .27 6E+O5

.?37

.82EE+05 . I 70 E+06

.237

.2t7

.

?80

.2 80

.280 .280

.280 .322

.322 .322 .32? .322 .37? -322

.365

10.75 0

1

.000

1.250 I .500

.750 2.000 1

.250

.500 .6?5 .?50

1.000

7.250 1.500 'l .750

2.000

0.750 10.750 10.750

10. 750

.365 .36 5

.365

10.750 10.750 r 0.750 10.750 1? .750

.625 .7 50

i.000

1.250 1.500

.468E+06

.961€r06 .168E+07 .265E+0?

.389E+07 .5

44e r

07

.4568+05 .126E+06 .2 58 E+ 06 .451E+06 .711E+06

.146Er07 .?558+07 .402E+07

.5928r47

.826E+ 07 . 603 E+05 . 166 E+ 06

.341E+06

.5968r06 .940E+06 .193E+07 -317e+O7

.532Er07 .782E+07

12.750 12.750 12.750 12 .7 50

4.000 14.000 14.000 14.000

t4-000 I 4.000 14.000 14.000

.320E+06 .5608+06 .883E+06 .130E+07 .181E+07 .152E+05 .4'19€+05

.8608+05

.l

508+06 .237 E+06 .487E+06

.850€+06 .131E+07 .197 EaOT .27 5E+07

.201E+05

.t14Er06 .199E+06 .513E+06

.643E+06 .112E+07 .1778+07 .261E+07 .364E+ 07

-253€r05

.4258+07

.698E+05 .143E+o6

.250Er06 .395Er06

.E10Er06 .142E+07

.670E+O7

.22i8+07

.984E+07

.328E+07

.517E+06

12 -750

.'l 568+06

.1098|08

12

.750

.566E+05 .989E105

.759E+05 .209E+06 .430E+06 .750E+06 .118E+07 .243E+47

1? .7 50

.902E+06

.4588+O7

.304Er05

.839E+05 .172E+06 .301E106

.375

.142Er07

.37 5 .37 5

.292E+07

.47 4E+O6 .97 4E+06

.510E{07

.170E+07

.375 .3?5

.EC5Er07

.2688+O7

.1188+08 . 16 5E +0t

.f95E+07 .551€+07

.101E+06 .279E+06 -57?E+06 .999 E+06

.33?E+05

.375

1

.500

.297E+ 06

.137E+08 .913E+05 .252E+O6

12.750 1?.750

-668€+06 .9828+06

.216

.280 .280 .?80 ,280 .280

4.625 a .625 I .625 10.750

.500

0

.2958+07

6.625 6.625 6.625 6 .625 6.625 6.6?5 6.625 6.625 6.625 6.625 4.625 8 .625 I .6?5 8.625 I .625

.200E{07

-216

.237 .237 .23?

4.500 4.500

'| . 500

.216

.500 4. 500 4

.000 1.250

.750

.500

4.500

1

0

6.0c0 6.000 6.000 6.000 6.000

4

.7 50

6.00

6

4.500 4.500 4.500

-oa>

0

.500

4. 500

.500

6.00c

6.000

3

.37 5

6.0c

6.00

3.500 3.500

.375 .3?5

.375 .315 .375

.158E+07 .323E. 07 .565E+07 .89'l E +07

.928€+05 .191E+06

.lf,3Ef06 .5258+06

.1 08 E+07

.188E+07 -297E+O7

Vessels

131

132

Piping Stress Handbook Table 6-1 Continued R0TA STIFF CALCULAII0tI, CYL- vESSEL v€ssEL

OD,FI

6.000 6.000 6.000 6.000 6.000 6.000 6.00

I

I I

lr

1.750

2.000

.250 .375 .500

.625 .750 .000

0

6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.0c0 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.0 00 6.0 00

6.000 6.000 6.0c

VESSEL ICX,IN

6.00c 6.000 6.000 6.000 6.000 7.000 7.000 7.000 7.000 7.000 7.000 7.00 0 7.0 00 7.0 00

7.000 7.000

7.0 00

7.000 7.000 7.000 7.000 7.000

6.00 0

CK,I

.375 .37 5

-375

.759 2.000 .250 . t75 .500 .625

.375 .375 .375 .375

t .000 1.250

18.000 18.000

.t7 5 .375

.250 .500

1

t.

500

1.750 2.000 .250 .37

5

.500

.625 .7 50 I .000

1.250 1.500

.750 2.000 1

.3?5 .500

6.000 6.000 6.000

T

16.000 1 6.000 16.000 16.000 't6.o00 18.000 1 8.000 18.000 18.000

0

6.0 00

NOZ

OD,IN

14.000 14.000 16.000 16.000 16.000 16.000 J

ZLE NOT STIf IN.LB/DEG N INPLANE OUIPLAT.IE LONGI CIRCU SID

NOZZLE

.625 .750 I .000 1 1 1

.250

.500

.750

?.000

.250 .375 .500 .625 .?50 I .000 1.250 I .5C0

.150 2.000 .250

1

.t75 .500

.625 .750 1 .000 1.250

18 .000

.37 5

.375 .375

.375 .375 .37 5

.375 .375

?.375 ".375 2.375 2.375 3. 500

1.500

.343E+07 .504E+07 .7 01E+o7

.44'lE+o5 .122E+06 .2t19E+06

.141E+07 .?47E+O7 -3a9E+07

.148Er06 .4088r06

.572c_+O7

.798 E+07 .493E+05 .'136€+05

.837E+06

.279E+06

.146E+O7

.487E+O6 .769 E+O6

.231E+07 .473E+07

. 1 92 E+08 +

06

.451Er06 .925E+06

.255E+07

.'t58E+07 .2768+47 .435E+07 .639E+o7 .893€+0? .545E+05 .

1

50 E+06

.308F+06 .519E+06

,850E+06 .17 4E+07

.375 .375

.523E+ a7

.3? 5

.1448+08

.305E+07 .481E+07

.212E+08 -?96E+06

.797p+O7

.9878+07

.141E+05 .390E+05

.471E+04

.800El05

.267E+05

.140E+06

.4 66 E+0 5

.375 .375 .154 .'t 54

.154 .15 4

.'l56 .154 .154 .154 .154

.'t54 .216 -216

.216

3. 500

.216 .216 .216

3.500

.217E+O7

.423E+ A7

.7 40t+07 .1178+08

.162Er07

3. 500

3.500

.'l2 4E+07

.436€+06 .687ErO6

. 164E

-37 5

.389E+05 ,107E+06 .220E+O6 -384E+06 .606E+06

-131E+07

.206E+07

.2688+08

22 .00 0 22 .000 22 .000

2.375 2.s75 2.375 2.375 2.375

.748E +06

.375 .375

22.000 22.d00

.2l l E+08

-375

22.000

22 .000

.1 51 E+08

.827E+07 . t 30 E+08

22 .000

22.000 22.000

.373E+07 .652E+A7 .103E+08

.172E+08 .239E+08

20.000 20.000

.610E+07

.3658+46

18.000 18.000

20.000 20.000 20.000 20.000 20.000 ?0.000 20.000

.437E+O7

.132E+O6

18-000

20.000

. 131 Er08

.1838+08 . t l7E+06 .3228+o6 .6608+06 .l l5E+07 .182E+07

-216

.914E+O7

.130E+05

.220E+O6

.735Ero5

.452E+06 .790E+06

.151E+06

.263E +06

.125e+07 .183E+07

.416E+06

.580E+05 .119E+06 .208E+06 .328E+06 .67 3E 106

. 195 E+0

.l1EE+07

.39?E+06

.256Er07 .?10E'05

.611E+o6 .E53E+06 .7018+O 4 5

.J97E+05 .693E+05 .109 E+06

.?248+06

Rotational Nozzle Flexibilities for Cylindrical Table 6-1 Continued R0TA vEssEl-

OD.Fl

STIFr CALCULATION, CYL. VESSEL

VESSEL lCKrIf{

NOZZLE

OD,IN

NOTZLE ROT SII F IN.LB/DE6

TCKTIN It'lPl-AllE

SID

LONGI

0UTPLANt CIRCU

.500

1.500

.216 .216

.186E+07

4.500

.381Er07

.237

.278E+05 .766E+05

.927e+04 .255E+05

.237 .237 .237 .237

.157E+06

.524E+O5

7.OOO

.250 .375 .500 .625 .7 to 1.000 1 .250

.618 E r0 6 -909E+06 .1278+O7

7.00 0

't

7.000 7-000 7.000 7.000 7.000 7.000 7.000 7.000 7.000

1

3-500 J .500

1-750 2.000

4

4.500 4.500

4. 500

4.500 4

4.500 4.500 6 .625

2.000

.250 .375 .500 .625 .750

7 .OOO

7.000 7.000 7.00 0

7.000 7.000 7.000 ?.000 7.000

7.00 c 7.00 0

7.000 7.OOC

.37

.7 50

I .000

1.000 1.250 1 .500

I .5C0

1.750 2

.000 .25D

.625

4.625 10 .750

10.750 10.750 10.750 10.750 10 .7 50 t 0.750

12.750 12.750 12.750 12.750 12.750 12.750 J4.000 14.000

.6?5

1

7.O0tJ

I .000

7.000

. 239E

+

06

.2AO

.4188+06

.260

- 659E+06

-280 .2E0

.135E+07

.

?80

.322 .322

.322 -322 -322

.62t

7 .OOA

1.250 1.500

.2E0

8 6

'14.000

7.000

.422t+05 .tJ6E+06

.322

. 500

.? 50

.280

4.625 4.6?5

7.00 0

7.000

.360E+07 .503E+07

.?36t+07

4.000 14.000 14.000 14.000 14.000

.365 .56 5

.365 .365

.870E +06

-179E+07 .3'l2E+ 0? .192E+07

.375 .375

.1648+O7 .337E+O7 -234E+O5

.398E+06

.133€+06

.695E+06

-232E+06

.194E +06

.110Er07 .225E+07 .393E+07 -911E+07

.646E+05

.565E+06 .750E+06 .131E+07 .207E+07 .3048+07 .424E+07

.2828|05

.777E+O5 -159 ErO6 .27aE+Q6 .439E +06

.13?ErO7 .271E+07 .4738+07

.902E+06

.7 45E+07

-24EE+O7

.l'l0E+08

.1 53E+0E - 936E+05 .752e +06

.529E+06 .9 25E+06

.146E+07 .2998

.375

.596E+06 .'l o 4E+o7

.101E+08 .703E+05

-E458+05 .23f,E+06 .4 78€ r06 .E35E+06

.375 .375

.105E+06 .184E+06 .290E+06

.241E+Ol

-375

.37 5

.183E+07 .?55E+ 07

.7 24E+ 07

.1278+08

-5at

.1f,9 E +06 -220E+O6 .4 5'l E+06 .78 7E +06

.1868+05

.365

.t75 -37'

.168E+07 .111E+05 .3EE€r05 .797E+Ot

E|05

5 5E

.620E+07

.37 5

.1208+O7

.124E+07

.365 .365

-36'

.518€+06 .817E+06

-3738+07

.5 48 E+07 .7 65E+0?

I .625

1? -750

1.000 1.250

-237

.245E+07

.154E+D6 .316E+06 -552E+06

-625

.7 50

.297E+O6

-

.500

.750 2.000

.7 41e+O6

.890E+06

.1558+07

.280

.916E+05

.4338+06

8.625

10.750 10.750 10.750 12.750 12.750 12.750

1

.2758r06

-217

.237 .237

.2 80

.500 .625

7.00 0

7.000 7.0c0 7.000 7.000 7.000 7.000 7.000 7.000

6.625 6.625

5

1.250 1.500 1.750 2.000 .250

-625

6 -625

.500

7.00 0

7.000 7.000 7.000 7.000 7.000 7.000 7.00c 7.000 7.000 7.000 7.000

6

1.750 2.000 .?50

7.00 0

7.000 7.000 7.000 7.00c

6.625 6 .625 6.625 6.625

I .000 1.250 1

.500

4. 500

.500

7.OOO

7.000 7.000 7.00c 7.000

.500

rAl

.'l

58 E+0 7

.365E+07 .510ErO7 .312E+05

.859E{05 .17 6E+06 .30EE+06

.4E68r06

.998E+06

.SZ3E+Oz

.17 4E+O7

.825E+07

.275e+07

Vessels

133

134

Piping Stress Handbook Table 6-1 Continued ROTA VESSEL OD, FT

7.00 0

7.000 7.0 00

7.000 7.000 7.000

7.00q 7.000 7.00 0

?.000

7.00 0

7.000 7.00

0

7.000 7.000

7.0 00

7.000 ?.000 7.000 7 -DOO

i

7.000 7.000 7.000 7.000 7-000

7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.00 0 7.00 0

7.000 7.000 7.000 7.0c0 7.000 7.000 7.0c0 7.000 7.0 00 7 .OOO

7.000 7.000 7.000 7.000

7.00 0

7.000 7.000 7.000 7.000 7.000 7.00c 7.000 7.000 7.0c0 7.000

SIIFF CALCULtII0NT CYL. VESSEL

VESSEL TCKTII{

1.759 2.000 .250 .375 .5rr0 .625 .750 I .000 1.250 I . 500 1.750 2.000 .250 .375 .500 .625 .750 1.000 1.250 1.500 1.750 2.000 .250 .375 . 500 .625 .750 1.000 I .250 1.500 1.750 2.000 .250 .375 .500 .6?5 .750 't .000 1.250 1.500 1 .750 2.000 .250 .375 .500 .625 .750 1.000 1 .250 1 .500 1.75A 2.000 .250 .375 .500 .625 .750 r.000 1 .250 1.500 1.750 2.000

ZLE ROT STtF IiI.LB/D€G N INPLANE OUTPLANE CIRCU STD LONGI

NOZZ L E

NOZ

OD'IN

ICKTI

.f218.08

14 -000

14.000 16.000 16.000 16.000 16.000 16.000 16.0c0 16.000 16.000 16.000 16.000

-375

.375 .375

.404E +O7

,loEE+06

.565E}07 .360Ef05

.298E+06 .611 E+06

.204€+06

.

t 69E+ 0E

.107Er07

.992E+O5

.3568rO6 .561E+06 .l l5E+07 .2018+07 .318E+07

.375 .375

.168E+07

.375

.9538+07 .140€+08 .1968+08

.375

.

.408 E+05

.346E+07

.604Er07

.467E+O7

.652e+07

18.000 18.000 18.000 18.000

.375

I 22 E+06 .338 E+06 .693E+06

.375

.121E+ 07

.113E+06 .23'l E+O 6 .4038+06

.191Er07

.636E+06

18.000 18.000

.375

.392E+07 .685E+07

.131E+07 .226E+07

.375

.1 C8 E+0E . 1 59E+ 0E

.360E+0 7 -529E+Oz

.222E+08

.739ErO7

.375

.1378+06

.457E+05 .126E+O6

.375 .375

.377E+06 .775E+06 .135E+07

1E.000

'18.000 1E.000

18.000 20.000 20.000 20.000 20.000 20.000 ?0 -000

20.000 20.000 20.000 20.000 22.000 22.000 22 -OOO

22.000 22.000 22.000

.375

.37 5 .37 5

.255E+O7

. 121E+08

.5058+05 . 139

.150E+07

.499E+06

.857€+06

.37 5

.236E +07

.s75

.485€+07 .847E+07

.16?E+a7 .?82ErO7

.134E+0E

.445E+O7 .654E+07 .914E+07

.37 5

.'l96E+08 .27 4erOE .166E+06

.375

.4578+06

.375

.259E+07 .531E+07

24.OOO

-375 -375

26 -OOO

E'06

.266Er06

.375

24.000

26.000 26.000 26,000 26.000 26.000 26.000 26.000

.5928r07 .626Er07

.417 E+06

.37 5

24.000 24.800 24.000 26.000 26.000

.4038+07

.151E+06

.938E+06 .1 648 + A7

24.OOO

.146E+07

.375

2?.ogo

24.000 24.000 24.000

.71?Ero6

.436E+07 .7 66a+07

.37 5

22.000 24-000

.451E+06

.2138+07

.178E+08 .248E+08

.3?5

22 -OOO

22.OOO

.258E+06

.9?7E+07 .1 46Er08 | 5E+08 .3 00E +08

.3 75

-2

-37 5 .37 5

.180Ei06

.375

.497ErO6

.375 .375 .375 .375 .375 .375 -375

.lcz€.07

.787E+O6

.5 53E+0 5

.152E+06 .313E+06 .546E+06

.862E+06 .177E+O7 .309 E +0 7 .488 E +0 7

.717E+07 .100€+08

.60',|Ef

.l

05

66Er0 6

.340E+06

.17EE+07

.594E+06 .9378 +06

.577E+07

.192E+07

.28'lEr07

.101 E+0E .'159E+08 .2 348 | 08

.3?7er08

.336€+0 7

.530Er07 .779E+O7

.109E+08

Rotational Nozzle Flexibilities for Cylindrical

Vessels

135

Table 6-1 Coniinued R0TA VESSEL

OD,FT

E

SS€L ICK,IN

VE

-00tJ

8.000

E.0c0 E.000 E.00 0

.375

?.375 2.375

.7 50

2

.000

1

1.250 1.500

1-750

E.000

2. 000

E.000

.37

.250

8.000 E.0c0 E.000

8.000 6.000

2.3?5 2.375 2 .375 2.375 3.500 .500 .500

.7 50

3. 500

.000 'l -250 't .500

3. 500 3 .500

5

.625

1

1.750 2.000

-250

8.0c c

.500

E.000

.750 I .000

6.000 8.000 8.000 8.000 8.000 8.0c0

2 -375

.500

[.0c0

8.000 8.000

.375

3 3

8.000 6.000

E.000 8 .000

NOzZL€

OO,IN

.500

8 .000 8.0c c E.0c0

6.000

STIFf CALCULAII0N, CYL. V€SSEL

.625

1.250 1.500

3.500 3.500

3.500 3. 500

4.500 4.500 4.500 4.500 4

.500

4.500 4.500 4

.500

/.. 500

.500

.000

4

.000

.500

E.000

.7 50

6.625 6.625 6,625 6.625

8

8.000

?

1

.000

8.000 8.000

1.250 1.500 1.750

8.CCC

2-AAO

E.000

8.000 3.000 8.000 6.000 8,000 8.000 t.000 8.000 8.000 6.000 1i .00c 8

8.000 E.0c0

6.000 8.000

tt.625

8

8.625

1.?50 .500

.500

.625 .7 50

.625

8.625 8.625

.750

1.750 2.000

-6?5

8.625

I .000 1

.6?5

6.625

8

I .625 8.625

10 . 750 10 . 750 10 .75 0

0. 750 1 0 .750 't

10.750

.000 1.?50

'10.750

't .

10

'I

500

8.CC0

E.000

6

.500

.000

.000 .000

6.625

.2 50

8.00c 3.000 E E

6.625

2. 000

.250

.750

10-750 't 0 .750 12.75t)

12,750

ZLE ROT STI f IN.LB/DEG N INPLANE OUTPLANE CIRCU LONCI STD NOZ

rCK,I

-154 54 .'154 .l54 -151 -154 .154 .154 -154 .154 .216 -2'.t6 .216 -216 .216 .z',t6 .216 .?16 .2'16 -2't6 .237 .?37 .237 -237 -237 .237 .23? .?37 .237 .237 .280 .280 .280 .280 .2 80 .280 .280 .280 .280 .280 .322 .322 -322 .32? .322 -3?Z -322 .322 .322 .3?? .365 .365 .365 .365 .365 .365 .365 .36, .365 .365 -3?5 .375

.1

. 132 €+0 5

.364€i05 .718E105 .',l31€+06 .2A6E+06 .423E+06 .7-19

E

+06

.117E+47

.171E+ol

.441E+04 -121ErO5

.2 49 E +O5

.436E+05 .687E+O5

.1418+06 .2{,68+O6 .389 E +06 .57?E+O6

.239E+O7

.7988+06

.197 t+Os .5 4ZE+05

.181F+05

.1118+06 .194F+06

.307Er06

.6 30€ +06

.1108+07 -17 4E+07

.255E+ol .356t+07

.260 E+ 0 5 .717E+05 .117E+O6

-?57 E+C6 .4058 +06 .832E+06

,1158+07

-2?9E.07 .3378+07 .4?18+07 .195F+A5 .109E+06 .?24E+46

. 391 E+ 06

.6r6E+06 .126E+07 .221E+ 07 .349E+O7 .5'12E+O7 .715E +O7

,656E+O4 .371E+05

.6488+05

.102Er06 .210Er06 .367E+O6

.578E+06 .8508+06 .119€+07 .8678+04

.27

L

7

E+O6

.4858+06 .7 64E+O6

.112E+07 ..|.57

E+

07

.132€+05 .363E+05 .745E+05

.130E+06 .2058+06 .422E+06 .7368+O6 .116E+O7 -'171

E+ 4 7

.238Ef07 -17 4E+05

-480E+05

.1 67 E +O7

.292E+47 .4618+O7

.9858+05 .17?E+46 .271E+06 .557 E+O6 .973E+06 .1548 +O7

- 677E+07

.2268+07

.9 45E+07 .658€+05

.315E+07 .219 E+45

.181E+06 .37?E+06 .650E+06 .',l03E+07 .2108+ 07

.6048+05 _124ErO6 .217E+o6 .3 42E+O6 .701E+06

.

3 68 E+

07

.580 €+07 .853E+07

.1198+08 -791E+05 .216E+06

(

i

.144E+46 .29 5 E f06 .e14E+06

\

.239E+05 .490E+05 .857E+05 .135E+06

.5228+05

.516Er06

l:

.1?3E+o7 .193E+07 .284E+17 .397 e+O7 .2 64e+ 0 5 -726E+OS

(

136

Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULATION, CYL. VESSEL VESSEL

VESSEL

OD,FT

ICK,'N

.500

8.00 0 8 .000

8.000 8.000 8.000

8.00 0

8-0cc 3.000 8.000 8.000 8.000

.7 50

I .000

1.250 1.500 .000

2

.2 50

E.000

8.000 6.000 E.000 8.0c0 6 .00c 6.000

.625

8.000 8.000 8.00

0

8.000 E.000

8.000 8.000

.75A I .000 1.25O 1 .500 1 .75A

2.000 .250

E.000

8.000 8.000 5.0 00 E.C00 3

.000

.0c0 8.000 6.000 8.000 8.000 8.000 E

8

.000 I .000 E.000 6

.000 8.000

E

E.000 E.000

6.000 6.000 6.000 8.000

.'136E+07

.230E+07

.489E+07

-163E+O7

.257 E+O7

.375

.7 72E+ 07 .113F+08

.1018+06

.337Ef05

.27EF+06

.9?8E+05

.375

.000

1 1

.500

.750

2.0 00

.250

.375 .500

.t91E+06

.999 r+06

.333E+06

.1588+07

.525Er06 .1088r07

.565E+07 .891E+07

.188E+07 .297E+07 .437E+C7

.131E.C8

.375

,163E+08

.64tE+06 .1?9E] 07

6.000

18.000 8

.000

20.000 20.000 20.000 20 .000

0.000

20 .000

20.000 20.000 20.000 20.000

.367E+d7 .641E+ 07

.375 .375 -375

.375 .315

22.000

1.250

.5?8E+o7

.572E+O6

.323Er07

22 .OOO

1

.378E+07

,610E+07

.377E+06 .595E+06 .122E+O7 .214E+O7

1

. ?50

.15EE +08

.113E+07

.7 5A

,500

.804€+05 .1658+06 .288a+06 .455F+06 .934E+06

.1058+06 .216E+06

2

.0c0

.292E+05

.316E+06

I

E.000 E.000

.875€+05 .241E+ 06

I E. 000

.625

.000

.342E+O7 .47 7 a +o7

.382E+05

.000 1 6 .000

1.250 I .500 1.750 2.000

-143E+08

.1 15E+06

18.000

.7 2. 0c0 'ti

E.C00 8

6.000 6.000 16.000 1 6.000 16.000 16.000 1 6.000 16.000 16.000 16.000

18.800 't E.000 1 E .000

1

oz

E+

.375

1 1

1E

.625

.4'l1E+O 6

.'l0f €r08

14 .000

1.000 1 .250 1.500

.000

8.000 E.0c0 8.000 8.000

.000

.149E+06 .260E+06 .E44E+06 .117E+O7 .232E+O7

.E65E+06

4

CIRCU

.123E+ A7

.697 -375

OUTPLANE

.253E+07

.4128+07

'|

.500

1

.731r+06

.000

1

.000

.4 47E+06

.495€.06

1

.500

TCK,IN INPLANE STO LONGI

11 .000

t .000 1-?54 'I .500

8.000 E

't2.750 I 4.000 I 4.000 4.000 1 4.000 1 4.000 14.000

E.000

NOZZLE ROT STI F It.I.LB/DEG

1?.750 12.750 12 .750 12.750 12.750 12.750 12.750

14

.7 50

.750 2.000 .250

t,000

0zzL€

OD,III

2? .OOO 22 .O00

22.000 22.000 22.000 22.000

.5f>

22 .OOO

22.000 24.000 24.000 24 .000

.37

5

.101E+08 .'149Er08 .207E+08

.1288+06 .355E+06 .725E+ 06 .127E+O?

.200E+o7 .410E+07

.7',16E +07

.337E+07 -495E+07 .691 E! 07 .427E+05 .118E+06 .Z 4ZE+O6

.122E.O6 ,6668+06 .137E107 .239E +O7

.1'13E+08 .166E+0E .212E+0E .112E+06 .390E+06 .E0'l E+06

.377E+07

.1 40E+07

,2218 + A7

.467E+O6 .736E+O6

.453E+07 .79?E+07

.264Er47

.1 25€+0E .184E108 .256E+0E

.155€+06 .428€+06 .8

7EE

'

o6

.55 4E+07 .7738+O7 .472E+O5

.130E.06 .267E+O6

.15'lE+07 -4'16E+07

.6128+O7

.855E+07 .517E+05

.143E+06

.293Er06

! Cylindrical Rotational Nozzle Flexibilities lor

Vessels

137

Table 6-1 Continued ROTI STITF CALGULATI0N' CYL'

VESSEL

NOZZLE ROT STI F ItI'LB/DEG.,

:::?i' Y:l:ih i8:ii' iii;io lii:l-' 8.000 8

.000

8.000 8 .000 8.000 8.000 8.0c0 8.000

E.000

8.000

.7 50

t .000

1.250 1.500 1.?50 2.000 .500

.000

.625

8.000 8.000

.0c0

8

.7 50

.2 50

E.000 8 -000

8.000 8.000 8.000 8.000 8.000 8.CC0

8.000 .000

6

8.000 8.000 8.000

.000 .000

8

6

8.000

.000 I .000

8

8.000 8

.000

8.000 8.000 8.000 8.00 0

.500 .7 50 2

.000

-250 .500

.625

.750 1.000 1 .250 1.500 1.75u 2.000 - 500

.750 I .000

1.250 1.500 1.150 2. 000

24.000 24.000 24.000 24.000 24

-000

24.000 24.000 26.000 26.000 26 .00 0

26.0c0 26.000 26.000 26.000 26.000 26.000 26.000 28 .000

28.000

28 - 000

28.000 28.000 28.000 28.000 28.000 28.000

28 .000

30 .00 0

30.000 30.000 30.c00 30.0c0 30.000 30.000 30-000

30.000 30.000

9.000 9.O00

t00 .625

.

.000

9

9.000 9.000 9.000

1

9

1

.000

9.000

9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9

.000

9.J00 9.000 9.000 9.000

.7 50

.000

.250 'r.500

1.750 2.000 .2 50

.500

2.175 2.375 ?.375 2 -375

2.375 2.375 2.375 3.500 3.500 3

.500

.7 50 1.O00

3'500 3.500 1.500 3.500 3.500

1.750

3

.000 .250

4

1.250 1.500 2

.500

3.500

.500

4.500

'i;i 'iti

'-1?i 'i;;

+07 -212F --istz'oz

-doee*oz . t:zt* oc

3!l:i^*' .E06E+06 7 ' 166E+o

.2q?!.91

'-1;t .zott+oa -456E+o7 '9!1,t-'9! .23'1E+0E 'Yl!:':' -375 'izi 'i;; '1;a

'.1it

1695+06 { 06 954g+06

- 465€

'5 621+o5

.155€+06

'3'l8Eio6

167E'07 '119!'96 ' :.. .E778+06 t A\F +o7 'it'. liioE'oz '.1?; i a31+ o7 '180E+67 '3\tq-+o^! 0E '1:9'-:Y' -375 .'l1et '-.ii -2196+08 '7298+o7 ':'-i an
:i;i;-o; :i+; '\zi 5ozF{06

.991!:95

167F +06

o7 '.314E+o6 .taOr*oz .600F+06 -28|E+oz '9 47 E+06 .igre. oz '1918+G7 . i ozr.oa '340F+07 .1615+08 '5368+07 .2 36g+oE .788E+07 .!366+oa '119:lo8 - 196E +06 '653F+05 sloE+c6 '180E+06 -l6eE+06 -ittt'oz --1s4E+o7 '9!28-+D6 3o5E+o? '102E+07 '-i?; -.iriE+07 '!9:!*07 16e5+08 '1!5.1-.ol .1i; '.;;;'17r8+08'1.6.1'.07 'i;i '8168+o7 'i545+08 ' z:le + o8 '-i?t

'iii 'i.;i 'i;4 'i|i '-i?t 'i;i 'iri, '.ir; ';;< 'i;. '|;i '.3;; 'i;.

-

163 6+

'118E+08

1at '-a;i ;;; '-;;i '.4;i

'-;ti

-'l25t+05 '416€+04 314t+ 05 ' 1 'l 5 +o s io5r+05 '235E+os5 :123E.06 ''le4E+06 ' 411E+o '6488+c5 -3eeE+o6 '111!'06 E

'.::: -lziiili ':l; ':l', ';'.; '.i;i rni '.tiz rie 'r;A

'.ia; ';;; ';;; '-i;; "r;i '.i;?

' i ))i ' )Jli,iz 'iz

aii

'.1":,i::"2 .53eF+06

-t5zE+o6

'618E+o/' os '170E+05 :5118 'os -105E.06 .35oEro5 -r

+

1E3F+06

-289F+06 -594E+06

'91.1E-+o5

'964E+05 .198E+06

16r,E+07 '119I'06 - 164E + 07 ' 51'55+06 .? L1E+o? .8 0 2 +06 +oz 3362+a? |z-tE+oL 't15E+05 "t '4768 +o5 +05 'E't7 '225F F

l,

Piping Stress Handbook Table 6-1 Continued

R0lA SllFr CALCULATI0NT CYL. VESSEL

OD,IT

VESSEL TCK,IN

9.000

9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9

.500

.625

.750 I .000 1.250 'l .500 ?.000 .250

.375 .500

.000

9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000

.7 50

1.000 I .250 I .500

1.750 2.000 .?50 .375 .625 .750 .000

.250 .500

9.0 00

9.000 9.000 9.000

9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.00c 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000

. 750

2.000 .500 .625

.750

I .000

1.250 '| .500 1.759 2.000 .250

.375 .500 .625 .750 I .000

1.250

NOZZL€

NO?ZLE

0DrIN

TCK,IN

4.500

4. 500 4 .500

4.500 4.500 4.500

.75C .000

.250 .500

.750 2.000 .250 .375 .5 00

.462e+o,

-2 42e+06

.808 E+05 .1?7E+O6 .262E+O6 .457E+O6 .7218+O6

.237 .237 .237 .237

.382Er06

.785E+06 .137E+O7

6.625 6.625

.148E+07

.2E0

.373E+05

.121ErO5 .3 4?E +0 5

6.62

.2E0 .2E0

-103€+06

.?118+06

.703€i05

.3688+C6

.123E+06 .194E+06

5

6.625 5.625

.237

6 -625

.280 .?80

6 -625

.280

6 -625

6.625 6.625 8.625 8.625 4.625

I .625 I .625

8.625 6.OZ)

.62> 8 .625

6

8.625 10.750 10.750 10.750 10 .750 10.750 10.750 r 0.750 10.750 10.750 10. 750

12.750 12.750 12.750 12.750 12.750 12.750 12 .750 '12.750

.625

. '1 39 Er 06

-237

.444E+07

2. 000

.500

.237

.216e+07 .318E+07

12.75D

.250

f IN.LB/DEG INPLANE OUTPLAI{E Lol,Gl CIRCU ROT STI

-237

,.. 500 4. 500

1

,500 t .750

slD

V€SSEL

14.000 '| 4.000 'r 4.000 14.000 't 4,000 14.000 14 .000

14.000 I 4.000 't4.000 16.000 16.000 16.000

.2 80

.280 -322 .32?

.58'l E+06 .1198+07 .208€+07 .329F+07 .433E+07

-1O6E+O7

.f,97E|06 -694E.06 .t10E+07 .161t+07

.67 4E. 07 .492E+05

.?25E+07 .164E+05 .452ErO5

.3ZZ

.279E+06

.92E E+0 5 -162E+O6

.322

.158E+07 .275E+87

.525Er06

.322 .3?2 .3?2

.322 .322

.365 .365 .365

.56 5

.365 .365

.136E+06

.437Fr06 .?68Ef06 -4348.07

.6388+07 .691E+07 .620€+05

.17'l

E+

06

.351E+06 .613E+06

.256E+06

.918E+06 .145E+07 .2138+O7

.297E+07 .207E+O5 -

5

70E+0 5

-117

E+O 6

.204E+06

.967Er06

-322E+O6

.'198Er07 .3 478+07 .5478+07 .804E+07

.661E106 .116E+07

.1'l2Er08

.1E2Er07 .2688+C7 .374E+07 .249E+05

.37 5

.746E+05 .205E+06

-375

.737E+06 -116E+07

.387Er06

.375

.239E+07

.795E+O6

.417 E+07 .657a+ A7

.219E+07

.375 .37 5

.175 .375

.422Er06

,685E'05 -141E+06

.246E+06 -'t 39 E+O7

.9 6?E+07

.322E+ol

.275Er05

-375

.135E+08 .825E+C5 .227E+06 .4 67 E+ 06

.815E+06

- 156E+06

.3? 5

-375

.129 E+07 .264E+07

.429E+O6 .880 E +06

.37 5

.4618+07 .728E107

.154E+O?

.37 5

.107E+08 .1 49€+ 08

.37 5 .37 5

.375

.375 .375

.953Er05 .263E+ 06

.375

.539 E+06

.450E+07

.758 E+05 .272E+O6

-243E+o? .357E+0?

.498€+07 .5

'13 g

r05

.875E+05

.lE0Ero6

Rotational Nozzle Flexibilities for Cylindrical

Vessels

139

Table 6-1 Continued ROTA VESSEL

OD,FT

9.0c0 .000

9

9.0c0 9.00

0

9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9 .0c0 9.000

9.000 9.000 9.0c0 9.000 9.00

.625 .750 1 .000 1.500 1.750 2 .000

.250 .500 .625 .7 50

9.000 9.000 .000

9

9.000 9 9

.000 .000

9.000 9.000 9.000 9

.060

9.000 9.000 9 .000 9 .000 9 -0 00

9

.000

9.000 9 9

.000 .000

9.000 9.000 9.000

.000

E. 000

1

18.000

t8.000

18.000 18.000

20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000

.500 .000

.2 50 1.5C0 't

1.750 2

16.000 16.000

.250

?. 000

1

16 - 000

18 .000

.000

'1E 1 '|

.00 0

8.000 8.000

18 .000

.?50

22 .000

.500 .6?5

22 .OOO 22 .00 0

.7 50

2

I .000

1.250 1.500 1.750 2.000 .?50

9.000 9.000 9.000

9.000 9.000 9.000 9-0c0 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000

16.000 16.000

.000 .25D .500 -750

0

.000

6, 000

1

16

9.000 9

VESSEL

VESSEL NOZILE NOZZLE ROT STIF IN'LB/OE6 TcK,IN TNPLANE oUTPLANE oo,rH ;;i;;N CIRCU LONGI STD

.000

9

SIIFF CALCULATION' CYL.

.500

.625 1.000 1.?50

t.500 1.750 2

.000 .250

.375 .500 .625 .?50 r .000

1.250 1.500 1-750 2.000 .250 .500

.625

22.000 2

.000

22.000 2? .OOO

22.000 ?2 .OOO

22.000 24 -000 21-OOO

.000 24-000 24

24.000 24.AOO

24.000 24.000 24.000 24.000 26.000 26.000 26.000 26.000 26.000 ?6.000 26,000 26.000 26.000

26 - 000 26 .00 0

28.000 2E

.000

28.000

.375 .375 .375 .375 .375 .375 .375 .375 .375 .3?5 .3?5 .3tS .3?5 .375 .3?5 .3?5 .375 -375 .375 .375 -3?5 .375 .375 .3?5 .375 .375 _37, .375 .375 .375 .3?5 .375 .3?5 .3?5 .375 .375 .3?5 _375 -37, .375 .3?5 .375 .375 .375 .375 .3?5 .375 .375 .375 .375 .375 .375 .375 -375 -375 .375 .375 -3?5 .375 -375 .375

,941E+06

.149Fr07

.3148+06 .495E+06

.305 E+07

.'l02Er07

.533E+07

.

.840E)07 . 1 24 E+ 08

1

78€ +07

-280E+0? .412E+O?

.172E+08

.5'58+07

.6118f06

.2L

.108E+06 .2988+06

.3,,0E+05 .9928+05

.1O7E+O7

.3568f06

.168E+02

.346Er07 .604E +O7

.953E+O7 .',|40E +08

.196E+08 . 121 E+06

4E

+46

.561 E+06 - 11

5

E+Ol

.201F+O7 .318E107 .467E+07

.652E+07

.403E+0t

.53fE+06

.1118+06

.683E+06 .119E+07

.3988}C6

.188 € + 07 .3FZa+O7

.228E +o 6

.628E+06 .129E+07

.675E+07

.2258+07

.1078+0E .157E+oE .219 Er 08 .1J4 €+06

.7 29 E+A7

.368E+06 .755€106 -132t +o7 .208E+07

- 427 6+O7 -7 47E+07

.,'166+06

.355E+07 .5??E+a7 .445C+05 .123E+06 .252E+06 -440E+06 .694E+06 .14?E+ 07

.?49E+07 -J93E+07

.173E+08 .2129+oE

.577 E+O7 .806E+07 .488E+05

.4639+06

.134E+06

.1A6t+46 .EZ8E+06 -1458+ 07

.228E+07 .468E+07

.27

6E

rO6

.482ErC6 .760E+06 - 15 a,E+07

.1908+0E

-273E+O7 .430E+07 -632E+o7

.438E+06 .900 E+ 06

.530E+05 .'116E+06 .300E+06

.'l57 E+O7 .2 482+07

.521E+06 .827E+O6

.889E107

.296e+o7

.8

18

E

+

07

.129Er08 .265E +08 .1 59E+06

.5098r07 - ',149E+08

.206E+08 .288E+08 .172E+o6 .4718+ C6 .972E+ 06 .170E +O7

.883E+07

.17oE+ol

.468Ei07 .68?E+07

.960E{07 .573Er05

.1588i06

.32 4E+o6 -566E+06

l,

140

Piping Stress Handbook Table 6-1 Continued ROTA STIFT CALCULATION,

EL TCK,IiI

VESSEL

VESS

OD,FI

9.000

9.000 9.0c0 9.000 9.000 9.000 9

.000

1.000

1.2rO 1.750 2. 000

.250

9.000

9.000 9.000 9.000 9.000 9.000 9.000 9.000 9.000 9

.000

9.000

.500

.625 I .000

1.250 1

9.000

.500 .625 .?50

9.00 0

9.000 9.000 9.000 9.000 9.000 9.000

t.000 t.250 1.500

.750 2.000 1

10.000

.250

r0.000 1

0.00 0

r0.000 10.000 10.000 10.000 10 .00 0

10.000 10.000 '| 0.000 't0.000 I 0.000 10.000 10.000 10.000 10.000 '10.000

10.000 10.000 10.000 10.000 10.000

. 500

-625

-750

I .000 1.?50 I .500 1.?50 2-000 .250 .37 5 - 500

.625 .750

I - 000 I .250 1 .500 1

10 .000

10.000 10.000 10.000 10.000 10.000 10.000 10.000

.750

2. 000

.250 .500

.625

10 .00 0

10.000

.500

1.750 2.000 .250

.750 1.000 1

.250

1.750 2.000 .250 .500

VE SS EL

NOZZLE

NOZ ZLE

ROT STI

OD,IN

TCK,IN

INPLANE

STD

LON

28.000 ?E.000 2E.000 ?E.000 28.C00

28.000 30.000 30.000 30.000 30.000 30.000 30.000 30.000 30 .000

30.000 30.000 5 2.000 32.000 52 .000

52.000

.000 .000 52 .000 3 2 3 ?

.375 .375

4. 500

4.500 4.500 4.500 4.500 4.500 4. 500

4.500

6.625 6.625 6.625

- 268

E

+07

.550E+07

.37 5

-31tE+0E

.375

.375 .375

.2 23E +08

.185f+06

.509E+06 .104E+07

.182Ei07 -375

.375 .375 .375

.268€+07 .591E+07 .103E+0E

.163E +08

.239E+08 .334E+06

OUIPLANE CIRCU

.E93E+06

.183€+07 .320E+07

.5058i07 .7 438+O7

.1048+0E .6158+05 .1 708+06 +06

- 348 f

.608 Er06

.959Er06 .197E+O7

.344ErO7 .543E+07 .7988+07 .1 'l I E+08

.375 .375 .375 .375

.197E+06 .544E+06 .1t2E+Oz

.l8J

.195E+o7

.37 5

.3088+07

.650E+06 .1of,E+07

.375

2.375 2.3?5 2.375 2.375 2.375 2.375 2.375 2.375 z .375 2.375 3.500 1.500 3.500 3.500 3.500 3.500 5.500 3.500 4.500 4.500

6I

.t75

.3?5 -375

-500

F It{.LB/DEG

.9 61e+07 - 1 52Er08

32.000 32.000 52.000

3

CYL.

-

632E+07

. 1 10E +08 - 174E+ 08

.658Er05

E+06 .372E+O6

.211E+o?

.3688+07

.5808r07

.375

.256€+0E .357E+08

.E538+07

.'t 54

.'tt8E+05

.594E+04

.326E+05

.109 F +0 5 .2?3e+O5

.1t4

.154 .754

.669€+05

-154

.1848+06

.151 .154 .154 .154 -154

.216 .216

-216 -216

.216 .216

.117E+06 .3?9E+06 .661E+06

.104E+07 .153E+07 "214E+07 .176E+05 .485E+05 .996E+05 .17 4E+06 .27 4E+ 06

.563E+06

.?16

.216

- 9 84 E+06 .155E+ O?

.z',t6

.2?88+o7

.216

.?37 .237 .?37 .237 -237

.319e+ 07

.119Er08

.390€+05 .6158+05 -126E+O6

.2208+06 .348€+06 .511E+06

.714Ero6 .587erO4 -162E+05

.332E+0 5

.580E+05

.915€+05 .18EE+06 -328E+06

.517Ei06

.7618+O6 .106E+07

.2338+05 .6418+05

-775E+O4

.132E+06 .230E+06

.439E+05 .766ErO5 .121E+06 -2488+06

.363€+06 .714E+06

.433Fr06

.237 .237 -237

-205E+07

-684E+06

-237 .2E0

.35fE+05

.140ErO7 .1'l8E+05

.97 4E+05

.325E+05

.280 .280

.130€+07

.2148+Os

.302E+07 .42'lE+07 .2C0

E+

06

.'101 E+07

.667Eros

Rotational Nozzle Flexibilities for Cylindrical Vessels

141

Table 6-1 Continued ROTA STTFF CALCULATION' CYL. VESSEL VESSEL

OD,FT

'l

0.000

1

0

VESS€L NOZZLE NOZTL€ RO] STIT IN'LB/D€G TCKu IN TNPLATJE oUIPLANE 0D,rN i;i;iN CIRCU STD LONGI 6.625 .7 50

.000

.000

10. 00 0

10.000 10.000 10.000

1.750

10 .0 0c

2

.2 50

.500 .000

.2 50

10.000 '| 0.000 10-600

.500

10.0c0 10.000 10.000 10.000

.7 50

'10.000

.000

,250

6.625 6.625 6.625 6.625 6.6?5

I .625 I .625

8.625 8.625 a a

.6?5 .625

a.625

.750 .2 50

10 .750

.000

2

10.000 't 0.000

.6?5

8 .625 a - 625

.500

't 0 .000 't 0.00 0

6

I .625

0

.500

10.000 10.000 10.000

10.750 10.750 10.750

.7 50

10 .7 50

1u.0

0

0.0 00 '10.000 1 0.00 0 10.00 0 10.00 0 1 0.00 0 1

1 1

.000

1

.500

.250

1.?50 2.000

.250 .37

5

10.750 10.750 10 .750 'ro.750

l0 . 750

1Z -750 '12 ,7 50

10.000

.500

1Z .750 12 .7 50

1C.000

.7 50

12.750

.625

10.0c0

10.000

t .000

'10.0c0

1.250

10-000

1

1

0.000

10-000

.500

1-750 2.000

.250

10.000 10.000 10.000

'10-000 1 ri . ti00 1 0. 00c

.625 .7 50 '|

.000

1.250 1.500

'10

2

10.000

10.000 10.000 10.000 10.000 10.000 1 0.000 I 0.000 10.cc0

'i0.c00

.250 .500 .625 .7 50 1

.000

1

.500

1,254

.000

.500

0

1

0.00

0

12 -750 1

4

.000

000

.t/,-000 I 4 .000 14.000

.00c 14.000 't 4.000 14

.000 14.000

16.000 16.00u 16.000 '16-000

16.000 16.000 16.000 16 .000

6.000 6.000 18.000 18.000 18.000 1 8.000

't

2.0c0

1

1Z -7 50

14

.000

10 .0c 0

10.c00 1 0.000

.750 12.750

12

11, -

.500

10.000 10.000 .00 0

'12.750

.2 50

1

.280 .2 80 .280 .280 .280 .280 ,280 .3zz -322 .32? -t?? .322 -32? -32? .3?2 .322 .322 .365 -565 -365 .365 -365 .365 .365 .355 .365 .365 .t75 .375 .375 .375 .375 .375 .375 -375 -375 .375 .375 .375 -375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .3ZS -375 .375 -375 .375 .375 .3?5 .375 .375 .3?5

.319 E. 06 .551E+06

.113E+al

.198E+02 -312E+a7 .458E+07

.6408+07 .467E+05 .129E+06

.116E+O6

.184E+06 .377 E+06 .659E+06 .104E+07

.153E+o7 .213E+47

.156E +05

.264E+ a6

.429E+05 -EE'l€+05

.46?E+06 .7 zEE+ 06

.243E+O6

- 1198+07

.261E +D7

.112E107 .606E+ 07

.846€+07 .538E+05

.162Et06 .533F+06 .5818+06

.'154€.06 .498€+06 .870E+06 .'t 37 E+47 .2629+O7 .282E+07

.1968+05 .540€+05 .194€+06

-329E+07

-7 63E+O7

.254E+07

.707E+0, .l95E+06

.2368+O5 .650E+05

06

E+

.'l88€+07 -519E +O7

.173E+Oi

. ',l06E+08

.355E +47

.400E+06 .699 €+ 06 .1,t 08+02

.l33E+06

.2?68.07 .395E+07 .6?48+07 .917E+07 .128E+0E .7E3€+05 .216E+46 .443E+06 .774E+06 .122E+O7 .251E +07 . 4 3EE +07

.690E+o7

.lClE+08 .',I12E+0E

.904E+05 06 .5J',l E+06 .Z 49

E+

.233E+06 .368E106 .754E+06 .132E+A7 -20EE+o7

-306E+07

.427E+07 .261F+05 .719Er05 .1488+O6 .2 5E E+0 6 -407E+06 .835E+06

.j

46E+O7

.23a8+o7 .338E+07 .4728+07 .30 | E+0 5 -830E+05 .120 E+ E 6

.893E+c6

.?9Et+O6

.2 89E + 07

.964Er06

.141E+Ol .5ArE+07 .797 E+07 .'117E+0E

.'164E+08 .102E+06 .ZEZE+46

.5f0E+06 .1c1.E

+

A7

I

.1'lIE+06 .306E+ 0 6 .62ZE+O6 .11OE+07

.917

I

.470E+06 .1688+O7

.266E+07 .391E+07 .545E+07 .31?t+O5 .911t+O5

-'l 938 +06 .338E+06

-l

142

Piping Stress Handbook Table 6-1 Continued ROTA

10.000 10.000 10.000 10.000 10.000 10.000 10.000 1 0.000 10.000 10.000 10.000 10.000 'r0.000 10.000 10.000 I 0.0 00

10.000 10.000 I I

NOZZLE

TCKrlftl

TCK,IN

1.250 1.500 1.750 2.000

1E.000

18.000 .000 .000 18 .000 1E.000

1.750 2.000 .250

20.000 20.000 ?0.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 22 .000

.37 5

22 .00 0

-375

.500

-625 -750

.000 1.250 1.500 'l

- 160E+ 07

.3?5

.573E+07 .904E+07

-533E+06 .1098+O7 .191E+O7

.13fE+08

.375 .375 .375

.lt5Er06

-t75

.375 .37 5 .37 5

.375 .375 -175

I 0.00 0 '10.0 0 0

22 .OOO

1.000

22.000 22.000 22.000

.37 5 .37 5 .3? 5

10.000 10-000 I 0.000 10.000 I 0.000 10.000

't0.000 10.000 10.000 10.000 10.000 10. c00

'10.000

0.000 10.000 10.000 10.000

'|

t 0 -000

10.000 10.000 't 0.000 10.0 0 0

10.000 10.000 10.000 10.000 10.000 10.000

.t75

.375

IRCU

.301E+07 .413E+07

.6'l8Ei07 .382E+05

.316E+O6

.105Ef06

.6488+06

,2168+06 .377E+86

-11tE+07

.179 E+07

.367E+07 .641E+o7 .101E+08 . 149€+0E

.247E+06 .127 E+ 06 .349 E+06 .7178+O6

- 59 5 €+06

.122E+47 .214E+07 .3378+47 .4958+07 .691E+O7 -422E+O5 t t 6E+06

.

.239

E+0 6 . 417E +06

07 -'l97E +87

.658E+06

.708 El07 .112E+06

.3728rO7

.125E

+

.405E+07

.135Er07 .236Ef07

22.OOE

.375

. 164E'08

2? .000

.37 5

24.000

.375

. ?29E+08 . 1398+C6

.7 64ErO7 .463E+05

24 .000

-375

.3838+06 .78tE+O6

.262E+O6

-375 .375

.1378+O7

.457Er06

.721E+96 .148E+07

-547E+O7

.f288r06

.625

.?59

I .000

24 .AOO 24 .000

.375

.216E+07 .441E+07

1.250 I .500 1.750 2.000

24.000

.375

.776E+O?

.259e+O7

-122E+08 .180E+08

.600E +07

.375 .500

.625 .750 1 .000 1.250 1.500 1.750 2.000 .250 .375 .500 .625 .7SO

I .000

10 -000

l0 -000

.375 .500 .6?5

I 0.00 0

.375

.186E+0E

C

21.000 24.000

.500

1.250 1.500 1.?50 2.000

10.000 10.s00 10.000

.328Er07

-375

.37 5

1.500 t .750 2 .000 .250

F I{.LB/DEG

.3 75

22.000 ?2.000

1.25C

ROT STI

OUTPLAI{E

.500 .625

10.000 10.000 10.000 10.000

VESSEL

STD

t8 1E

CYI.

I!IPLAN€ LOIIGI

'l0.000

t0.000

.l

CALCULATION,

VESSEL

1.000

I 0.00 0

x,

STIfF

. a>u

.7 50

24 .000

24.000 24

.000

26.000 26.000 26.000 26.000

.375 .375 .375 .37 5

26 -000

.375 -375

6.00 0 6.00 0

.375 .375

z

6.00 0

26.000 2 2

26.000 28 .000

28.000 28.000

30.00 0 3 0 .000

30.000

.784E+06

.483Ef07

. l6'l

.8448i07 .133E|08 .196E+08

E+0 7

.281E+O7

.141ErO7 .652E+07 .911E+07

.375 .375

.972E+O6

-307E+O6

.375

50.000

.497E+O6

.235E+07

.5438f05

0.00 0

3

.139E+06 .?85E+06

.163E+06 .449€ + 06

?8.000 ?8.000 28.000 2E.000

.854Ff06 .149Et07

.503€r05

.273€+08

.375 .375 .375 .375

28 -000

.416€+06

.8388+07

.t75

eE.000

28.000

.2 5l E +08 . 15'l E+06

.408Er07

.375 .3?5

.375 .375

.161E+07

.150E+06

.5378r06

.2 54F+07

.847r +06

.522E+07

.17 4E+07

.911e+ 07

.504E+07

.1 44 E+ 0E

.479E+O7

,211 E+0E .295 E+06 .175E+06 .483E+06 .991 E | 06

- 705

.273e+Oz

-910E+06

.l73E+07

Fl07

.984E+O7 .584E+05 - 1618+06

r0 5 -577E+O6

- 330E

Rotational Nozzle Flexibilities for Cylindrical

Vessels

143

Table 6-1 Continued ROTA VESSEL

0D,fT

10.000 .000

10

10.000 10.000 't0.000

STIff

I:i:ii il:ii' I .000 1-?50 1 .500

I .750 2.000

.00 0

'10

10.000 10.0

.500

0 0

0.000 0.030 10.006

.625

1 1

10. c0c '10.000 10

.000

10.000 10.000 10.000 10.000

CALCULATION'

.7 50 1

.000

1.250 1.500 2. 000

.250

30.000 30.000 30.000 50 .00 0

.375 . 51>

.375

.375

32.000 32.000 32.000

.37 5

32 .00 0

3 2 3 2

,000 .000

32.000 32 .00 0

32.000 32.000 36.000 3

10.000 'l0.000 10.000

.150 1.000 1.250

3 6.00 0 3 6 .000

1G.C00

1

36.0c0

-375 .37 5 .37 5

-375

.375

11 .0 00

.250

2-375

.154 .154

.500

2-375

.15 4

2 -375

.15 4

I

'l

'l

l .000

.000 11 .000 11.000 11

11.000 -000

11

11.000

1l.0c0

.000 11.000

'11

1',| .0 00

11.000 11.000

11.000 11.000 'l1.000 11.00c 11.000 11 .00 0 1

I .000

11 .00 0

11.000 11.000

.154

2.375

1.000

2.375

.15 4

.000

?.375 2.375 2 .375

.154

.250

3.50t1

.216

.500

3 3

.216

'r

.2 50

1

.500

1.750 2

1't.000 11.000 'l1 .000 11.000 11 .000

36 -000

.625

{10 0

.

11.000 11.000

.6?5 .7 50

I .000

1.250 1.5C0 1

.750

2

.000

.250 .500

.625 .7 50

I .000

1.250 I .500

1.750 2.000

.37t .500 .625

F IN'L8/DEG

INPLANE LONGT

OUTPLANE

CIRCU

.187E+a?

.560€+07 .979E+07

-326E+07 .51 5E+07

.154E+08 .227 E+08 .317E108

.7578+07 .106E+08

-624t+45

.1878+06

.172E+06 .353E+06

.1c6Er07

.195g+07

.617E+O6

.292E+07 .599E+07 .105E+08 .'t 65E+08 .213e+ 08

.200E+07 -349E+07 .S5oE+o7 .809E+07

.973E+06

.1t3E+08 .705Er05

. 339 E+0E

.399€+06

zc9E+07 .330E+07 -677E+07 .11E8+08

-697E+O6

+

: )j .r '!

.'1948106

o?

.1?OE

36.fjc0 36.000

2.375

ROT STI

.583E+06

1.750 2.000

11 .000

EL

V ESS

.Z1ZE+O6

10.000 10.000

1'l .000

L.

.516E+06

6. 000

36-000 3 6.000

.500

lli:li

30.000

.500

10 .000

CY

.

.110E+07

.226E+07

.394ar07 -622E+O7

.187E+CE .2 74 E+ 08

.911a+O7

-383Er0E

. '128E+08

.113Er05 .3'l 'l E+ 0 5

.37

6E

+04

.104E+05 E+0

.638 E+05

.21

.111Ei06

.372E+05

.176€+06 .361€+06

.586Er05

.1208.06

3

5

.210Er06

.154

.631E+06

.1 54

.146E+07

.487E+06

.995Er06

-332E+06

.154

.ZA4t+07

-68',|E+06

.1688i05

.559E+04

.500 .500

.216

.1548+05 .316€+05 .553Er05

3.500

.216 .216 .216 .216 .216

-462E+05 .949E+05 .1e6E+06 .2628+ 06 .537 er06 .938E+06

.872E+O5

.218f+07

.725E+ 06

f.500

3-500 3 .500

3.500 3.500 3.500 4.500 4.500 4. 500 4. 500

4.500 4.500 4.500 .500 .500 4 .500

4 4

6.625 6 -625

6.625 6.625

.?16

.2'16

.237 .?77 .23? .?37 .237 .237 .237 .237 .2 80

.280 .280 .280

.179t+O6

.3t3E+06

.148€+07

.493E+06

.3048+ 07 .222E+05 ,611 € +05 . 1?5€+06 .219E+46 .316E1C6 .? 10E+O6 .124E+07

.101€+07

. 739 Ei0 4

.204Er05 .4'165+05

.731E +o5 .1 'l 5Ei06 .237E+O6

.4'13€+06

o7

.6 5Z€+06

.293E+07 .AAZEiA7 .337E+05 .929E+05

-1348+07 -112e+o5

.19

6E +

.19t E+06 .333Er06

.958E+06 .310Er05

.636€r05 .1',|1 E+0 6

,.i t

.5 t,.

lt ,l t: \l

144

Piping Stress Handbook Table 6-1 Conlinued ROlA STIFF

VESSEL ICX,IN

VESSEL

OD,FT

11.000 t 1 .000 11

.000

.000 11.000 J1.000 I1

1

't

.000

.7 50 1

'| 1

6

.500 'l

10.750 10 -754

.000

2.000

't

.7 50

11 .0 00

t 1 .000

.000 11.000 11

.625 .750

11.000 11.000 11 .000 11 .000 11 .000

t1-00c

r 1 .0 00

11.000 t'l .000 11.000 1 1 .000 1't .000 11.000 1t - 000 1t .000

11.000 11.000 11-000 11.000

11.000 1t -c00 t 1 .000

11.000 11.000 11 .00 0

11.000 11.000

1 1

.000

.250 I .500 1 .750 2.000 -250 .500

.750

J.000 't

.2 50

.000

'ls -75Q

5

0.750 10.750 12.750

't2.750 12.750 12.750

12 -750

12.750 1?.750 12.750 12.750 12.750

?. 000

.3'l7E+06

.365 .365

.554E+06 -874E+06 .179 E+ 07 .31 1E+O7 .195E+07 .727E+O7 .102E+CE .67 4E+05

.375 .375 .375

.131E+07 .1928+O? .2 69 E +O7

.187E+05

.t06E+06 .1E5Elc6 .291E+O6

.5988+06 .105E+07 .1 65 E+o 7 .?42E+O7 .338E+07

.'186E+06 -3E2E+06 .666E+06

.619E+05

-t058+07

.3508+06

.216E+07 .377 E+07

.595E +a7

.87

1E + A7

.1 22E +08

-127E+ 06

.?2?E+0

6

.719 E+C6 .1?

6 t +O?

.1988+07 .291E+07 .4O7 E+07

.206E+06

.73EE+06

.2468+06

.239a+07

-'l16E+ 07

.388E+06 .79 6E+06

.417a+ A7

.139E+O7

.96EE+07 .135E+08 .862E+05

.323E+ o7

.237E+O6

.7 92 t+O 5 -162E1O6

4.000 4.000 14.000 'I 4.000 1 4.000

.4228+06

I

'I

4. 000

4.000

.658E+07

I 4.000

16-000 16 .000

t6-000 1 6.000 16.000

I 6.000 18.000 18 . J00

18.000 I 8 .000

.7 50

.1 558+06

.231E+06 .47 5E +06 . Ef 0Ef 06

't

16 .000

1.750

.2 49E+07

.393E+07 .5778+07 .806E+07 .56'tE+05

.147EtO6

.2 49E+o5 -686F+05

1.000 500

.113e+07

.17 5E+O6 .360E+06 .628E+06 .991E+06 .'l46E+O? -203E+07 .146E+05 .409E+05 .840E+05

.7468+05

.7 50

t.

-252E+06 .4 40E+06 .694E+06

OUTPLANT CIRCU

t4.000

16.000 16.000 't6.c00

'1.250

.365

't

14-000

't1.000 11.000 11.000 11

.750 10.750

1

.37

-3?2 -322 .32?

10

'l

.500 .625

.297E+a7

.437E+07 .6108+07 .4158+05 .1238+06

10 .-t 50

1.500

.750 2.000

.2E0

.322

10.750

.525E+ A6 .10E € +07 .1EEE+07

.280 .260 .322

-322

.500 .7 50

.280

8.625 t 0. 75r]

.3?5

TCK,IN STD LONGI 'NPLANE

.322

.250

VESSEL

NOZZLE ROT STI F IN.LB/DEG

-625

8

1-750 2.000

11.000 11

.625 8.625

.5A0

1

ULATION, CYL.

_625

.000

I .000 1 .25A t .500

'11.000

8 8

1-250

11.000 11.000 11.C00

-625

6.625

.000

r1.000

.500

E.625 8 .6?5

11 ,0 00 '| 1

6.625

-250

.000

11.000 11.000 'I1.000 11.000 11.000 11.000 11.000

OO,IN

1.750 2.000

11.000 1 I .000

LC

NO22LE

.000

1.250 't

CA

18.000

.4 87E + 06

.852E+06 - 1348+Oz

.27 6a+07

.482E+07

-375 .3?5

-

7

6OEr 07

.112E+08 .

1

56E+ 0E

.977E+05 .2 69 E+ 06

.553E+06

.9 66E +a6 .152E+ C7

.1 4'l E+O6

.219E+tl .450E+07 .287E+05

.284€+06

.4 48E+o6 .919E+06 .1618+O7 .?53E+O7 -3?2E+o7 -5?OE+07

.326E+05 .898 E+05

.184E+06 .322E+o6

. 508E +06

!

Rotational Nozzle Flexibilities for Cylindrical

Vessels

145

Table 6-1 Continued ROTA STTFF CALCULATION' CYL. VESSEL VESSEL

0DzFT

VESSEL NOZZLE TCKTIN OD,tN

NOZZLE

TCK'IN S

11.000

't.000 1.250 1.500

t l .000

2

11.000 1

.000

1

,1.000

18.000 .000 1 8 .000 't 8

1.750 .000

18.000 '18 -

000

1l.000

.2 50

20.000 20.000

.000

.500 .625

20 .000 20 .000

1't.000 11

11.000 11-000 11 .000

11.000 11.000

.750 I .000 1 .250 1 .500

.7tb

20.000 20.000 20.000 20 .000

2.000

11.000 't1.000

.250

20.000 20.000 22.000

11 .00 0

.500

22 -AOO 22 .00 0 22 .AAO

.000 11.000

11

11.000

l

.0 00

11

.000

'l

11.000

1

.7 50

1.000

22.000 22.000 22.000

t1.00c

1.250 't .5c0

0c

2.000

22 .COO

.37

Zr'.000

11.000 11 .0

11.000 11

.000

't1.000

l .000

't

11

.000

11.0CC

1't.000 't

'r

,000

11 .000 11 .0 00

5

.500 .? 50

.000 .25u .500 .7 50

2.000

.2 50

11.000 11.000

?? .ooo

22.O00

24.400 24.000 24.000 ?a.oao 24 -OOO

24.000 24.000 24 ,O00 24

-

000

26.000 26.000 26.000

'l 1

.500

'11.000

-7 50

26.000 26.000

. ?50

26.000

.000 11.000

.000

11.000 11 .00 0

11.000 1 1 .000

11.000 11.000 11.000

.500

.750 2.000

1'1

.00 0

11.000 11.000 11.000

11.000 't1.J00

28.000

.750 1 .000

23.0C0

1.250 'I

.5C0

1 -750 2 .OAO

.250

28.000 28.000 28.000 28.000 28.000

28.000 30.000 30.{.i00

11,000

,tic0

.500

11.0CC

-625

.7 50

11.000 '11.cti0

26.O00 26.000

.500

11,0C0 1'1

26.000

28.000

1'l .000

11.000

26.C00

1

,000

30.000 30.000 30,000 30.000

TD

.375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 -3?5 -375 .375 .375 .375 .375 .375 .375 -375 .375 .375 .375 .375 -375 -375 .375 .375 -375 .375 -375 -375 .375 .3'?5 .375 -375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 .375 -375 .375 .375 -375 -375 .375 .375 .375 .375 -375 -375

ROT STI

F IN.L8/DEG

INPLA!,IE LONGI -313E +07

-5 46E+07 -86?E+07 .127E+oE .1 77E+08 -',|09E+06 .30',1E +06 .6'l8E +06 .108E + 07

.170E+07 .3 50 E +07 .6'11€+07 .963E+ 07

.142E+08 . 198

E+

08

.1?1E+46 .333E+06 ,683E+06

.119E+07

OUTPLANE CIRCU

Jo4E+az .182E+07 -287E+07 ,422E+07 .590E+07

.364€105 .1008+06

.206€ +06

-360€+06 .568F+06 .117E+ 07

.204E+o7

.321€+07

.472E+O7

.6598+07 .4038+05

.t11E+06 .228E+06

.398F+06

07 .387E+O7 - 67 5E +47

.628E+06 .1?98+A7

.1578+OE

.522E+07

.219E+08 .132E+06 .365E+46 .719E+06 .'131E+07 .286E+A7

,729E+O7 .141E +O5

.138

E +

.1078+C8

.225E+07 .355E+07

.1?2E+A6

.250F+06 .436E+06

424E+A7

.688E+06 .141E+o7

.7loE+o7

.247 E+07

-

.117E+08 .1 72 E | 08

.?1OEr08 .1448+06 . 397E+ 06

.814E+06

.112E+o7 .224E+07

.4608+07 .EC4E+07 .127E+O8

.

187E+ 08

.260E+06 .1 55ErC6

.42E€+06 . E79 E+ 06

.154E+O7 .? 12E+ 07 .197E +47 -E69E+A7 . 137E+08

.202E+08 .281 E+ tl8 . 'l 67 F+ 06

.460E+06

.945€+06

.3t9E+07

.5?2e+87

.799E+07 .480E+05 .'l32E +06 .2 7'l E+o 6 .47 4E+06

.718E+06 .1538+O7 .2 68E +O7 .123E+07

.62?E +07

.868€+07 .518E+C5

,143€+06 .293E +0 6

.512E+06

.803E+06 .166E+07 ,29AE+O7

.457t+C7

.672E +a7

.938E+07 .557E+05 .153E+06 .315E+06

,165E+A7

.550€+06

.2 (OE + C7

.E68F+06

.534E+07

-'178E+07

1,,

t

146

Piping Stress Handbook Table 6-1 Continued

ROI^ STIFT CALCULAIIOI,, CYL.

SS€L ICKIIN

VESSEL

11.000 11.000 11.000

1

1'l .000

2. 000

11.000 11.000 11.000 t

.250

t .500 1

.750

.500

l .000

11.000 1t .000 1t .000 1t .000

NOZZLE

VE

OO,FT

.625 .7 5s

1.0c0 1.250 1.500

OO'IN

30.c00

12. 000

32.000

32 .OOO 32 .00 0 32 .000 32 .000

36.00 0

11.000

'11.000 11 .000

I I .000

.000 1J.000 '| 1

t1.000

1.000

1r .000 11.ADO

'r1.000 t I .000

-375 .500

40 .000

.7 50

t.000

1.250

t. t00

I .750 2.000

12.000 12.000

-250 .375

'12.000

12.C00

12.000 12.000 12.000

.500

.625 -7 50

I .000 I .250

1.500 1.750 2.0c0 .250

.500

12.AOO

12.000

t2.000 | 2.000

.625 .7 50

I .000

12.000 12.000 12,000

1.250 1 .500

12.000 12.000 12.00c 't 2.000

-250

t2.000

t2.000

36.00 0 36.00 0 4

11.0C0

't2.000 12.000 12.000 12.000 12.000

.000

.750 2.000

0.000

40.000 40.000

5

.375 -375

.375 -375 -375

.375 .375

.302Er08 .179E+06 - 49ZEr06

.164Er06

.101E+ 07

.337E+06 .588E+06

.1768+07 .278E+oz ,571E +07

-333E+O7

.2028+06

.672Ero5

.556E+06

.380E{06

.664E+06 .1058+07

.375

.375 .375 -3?5

.t7

5

.t75 .375

.113E+08

.178€+06

.2 61 E +08

.365E+08 .225E+06 . 619 E+ 06

.127e+87 .222E+07

-375

.1 26E+ 08

.375 .375

.291E+08

2.375 2.375 2.375 2.3?5 2.375 2.375 2.375 ?.375 2.375 2.375

.154

3.500

.216 .216 .216 .216

.500 .500 3-500 3 3

3.500 3.500 3.500 4-500 4 .500

4.500 4. 500 4-500

.185E+06

.199E+07 .314E+07 .645E+07

.375

3. 500

.77?E+O7 .108E+08

.375

40 .00 0 40 .00 0

.r25E+O?

.1 14E+07

40.000

40.000

.19AE +A7

.998E+07 .157E+08 .231E+08 .3 23E + 08

,3508+07 .719E+07

40.000

.92E€+06

.37 5

40 .00 0

1

.37

.375 .375

36 .000

36.000 36.000

11.0C0 t 1.000

t't .000

6.000

3 3 6

1.250 1.500 1.750 2.000

11.000

.311E+07

.722e+C7 .101 E+08 .595E+05

. >UU

.625 -750

CIRCU

.216E+08

0.000 3?.000 3

.37:

't'1.000

.934Er07

OUTPLANE

30 .000

1t.000 11.000

.37 5

N INPLANE LONGI

.191E +o7

r't.000 ,l

.250

r CK,I

STD

.147E+o8

52.000 3 2.000 32.000 56.000 36.000

1.000

NOZZLE ROT SII F IN.L8/DEG

30. 000

1.750 2.000

11.000

VESSEL

.1988+08 .4078+08

.215E+O7 -376E+07

-5938+07

.E71ErO7 .12?E+oB .749E+0 5 .2068+O6

.424E+06 -7 40E+O6

.117e +O7 -240E+07

.419E+07 .661E+O7

.971E+07 .136E+08

.106E+05 .298 E+05

.3608+04

-154

-f56Er05

.6llE+05

.15 4

.'t07E+06 .1689r 06

-992E+04 .204E+05

-154 .154

.346E+06 .604E+06

-561E+05 .115E+06 .201 E+06

.154

.154 .154 .154 .216

.216

.216 .216 .216 .237 .237 .237 .237 -237

.9528+96

.11OE+07

.195E+07

. t6lE+05 .443E+05 .909E+05 .159E+06 -250E+06

.317E+O6

.467E+O6 .652e+D6

.536E+o1 .14EE+05 .303E+05

.529E+05 .835E+0 5

.5'l4E+06

.1718r06

.898E+06

.2998+O6

.112E+oz

.472E+O6

.208€r07

.694E+06

.291E+07 .212t+ 05

.970 E+0 6 .706 E+04 .195E+05 .400 E+0 5 .700E+05

.585E+05 .120E+06 .210E | 06 .

J3t E+06

.1 10E +06

Rotational Nozzle Flexibilities for Cylindrical

Vessels

147

Table 6-1 Continued ROTA VESSEL

0D,ll

,090 12.000

12

't2,000 12.000 12.000 'l2.000 12.000 12.00c 1Z

1.000

1.250 1 .500 1.750 2. 000

.375

12.00c

1

.500

.000 12.000

2. 000

't2.000

12 .00 0

12.000 't 2.000 12.000 1?.000 12,000 '12.000

12.000 12.000 12.000 12.000 12.000 12

,000

12.000 't2.000 .000 12 .000

12

6.625 6.625 6.625 6.6?5 6.625 6.625 6.625 8.625 E.625

.250 .500

8.625

-f>u 1.000 1.250 I .500 1.750

8.625

8.625

2. 000 .37

5

.500

.625 -750

1.000 1.250 1.500

1.750 2.000 .250

12.000 12.000 12.000

.500

12.00 0

0. 750

10.750 10.750 1 0. 750 1 0 .750

t0.750 10. 750 't 0

.750

10.750 10

12 1?

.750

.750 .750

1?.7 50

.000 .500

1

.000

12.O00 1 2 .000

.500 -7 50 2

1

12.750 12.750 12.750 12.750 12.750 12.750 12.750

12.000

'tz.ou0 '| 2.000 12.000 12.000 't 2 .00! 12.000 12.000 12.000

6 -625

1.750

.290

.500

4.500 6.625 6.625

1.250

12.000 12. 00 c

4

.7 50

.000

12

4.500 4.500

.625 1

t?-000

,.. 500

.500

't2.000 t 2 .000

'14.000 14-000

4.000

14. 000 -7 50

.000 12 ,000

4.000 14.000 t 4.000

.500

12 . 000

.7 50 2. 000 .2 5A

't 4 14 ,l

12

12.000 12.000 12.C00 1? -004

12.000 12.000 12

.000

VESSEL

VESSEL NOZZLE NOZZLE ROl SIIf IN.L8/DE6 TCK,IN INPLANE OUTPLANE TCX,IN OD,IN CTRCU STD LONGI

.000

12 .OOO

Sttf F CALCULAITONT CYL.

.000

.500 - 1>U

I .000

1

.000 .000

4.000 1 6.000 't 6.000

'16.000 16 .000

16.000 I 6.000

.237 .237 .237 .237 .237 .280 .280 .280 .2 80 ,280 .2 80 .280 .280 .280 .?80 .322 .322 .322 .322 -322 -322 -32? .322 .322 .322 -365 .365 .36, .36' .365 .365 .365 .365 .365 -365 .375 .375 .375 .375 -375 .375 .375 .375 -375 -375 .375 -375 .375 -375 .375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 -3?5

.680E+06 .119E+O7

.187E.07

.275E+07 .384E+07 .3?3E+05 .889 E +05 .133 E+06 .319E+06

.5038+06 .1c3F+07

.l80E+07

.2n58+O7 .418E+07

.584E +47

.426E+05 .118E+06 .241E+O6

.4218+06

.665€t06

.22'l E+ O6 .396E+06 -621ErO6 .91EE+06

.'l28E+07 .108E+05 .?96E+05 .608E+05 .106E+06 . t d8E+06 44F +o 6

,t

.601 €+06 .949E+06 .139E+07 .195E+O7 .142E+05

t

.3

.3929+05 .804E+05 .140E+06 .?22E+o6

. 136E+07

.4558r06

.238E+o7

.79 5E+ O6 .125E+A7 .184E+O7

.37 6E+O7 .553E+07

.7728+ol

.?57E+o7

.537E+05 .14EE+06 .304E+C6

.l0lE+06

.531€+06 .837E+06 .172E+07 .300E+07

.47 4E.o7

.179E+05 ,493E+05

.177E +06 -279E+O6

.573E+06

.100E+07 .1 58 F+07

.696E+07

.232E+07

.972E+O7

.324E+O? .?15E+O5

.616E+05 .17E8+06 .3 6 5€| 06 .63E Ef 06

.1o1E+07 .2o7E+O7

.361E+07

.5938+05 .122Er 06 .2'l3E+O6 .3368+0 6 .689 E+06

.t20E+07

.569E+O7

.t90Er07

.E37E+07 . 1178 + 08 .715E+05 .197E+46 .404E+06

.279E+O7

.706E+ 06

.1't1E+O7

-zz9E+07

.l90E+07

.2399+05 .656E+05

-135Ef06 .235E+06 .371E+06 .762E+06

-4OOE+07

.133E+07

.6308+07

.21OE+07

.9?6E+ 07 .'l 29Er0E

.309E+07 .431E +O7

.825E+05 .2?7E+O6

.467 E+o6 .E15€+06 .129E+07 .261E+o7

.275E+05

.758Er05 .156E+06 .272E+O6

.4?9 E+06 .880E+06

t:

'i

ir\ I

il

it;

:l

iii

148

Piping Stress Handbook Table 6-1

Continued

SIIfF CALCULATIOII' CYL. VESSEL NOZ ZLE ROI STIF II].L8/DEG VESSEL NOZ2LE T CK,I N INPLANE ICKrIN 00rIN OUIPLANE STD LONGI CIRCU ROTA

v€ssEL 0D,FT

.000 12.000

1.250

12.000 12.000 12.000

2.000 .250

12

'12.000

t .500

1.750

r2.000

.500

.625

1Z-000 '12.000

1? .00 0

12.000

1

.000

16.000 16.000 | 6.000 16.000 .000 .000 18.000 18.000 18 18

't8.000 r 8.000

r8.000

.000

-375

18 .000

1.500

12 .00 0 12 .000

2. 000

18.000

12.4O0

.250 .375

12 .00 0

.500

20.000 20.000 20.000 20.000

2.000 '| 2.000 'r2.000 12.000 12.000 1?.000 12.000 12.00c 12.000

18

.625 1.0c0

1,250 1.500 'l

.7 50

2.000

20 .000

20.000 20.000 20.000 2

0

.37 5

.000

.?50

22.000

.00 0

22 .000

22 .00 0

12.000 1?.000 12.000 12.000

.500 2. 000

.375 .500 .625

12.000

12.000 12.000

12. 000

12.000 12.000 12.000 12.000

.750 I .000

1.250 1.500

.750 2.000 .250 1

12.C00

12.000 12.000 12.000 1?.000 12.000 72.DOO

12.000

.625

24.000 24.000 24.000 24.000 2 4

-000

.500

26.000 26

.000

28 .000

.000 2E.000 28

.625 I .000

1.250

26.000 28.000 28

.000

28.000

1 49E

+08

.936E+05 .2 5E€+06 .5 29 E+06 .9 248 +06 .146E+07

-37 5

.375

.486E{06

.105E+06 .288E106 .5928+06

.961El05

. l69E+08

.275E+o7 .564E+07 -3498+05 .197

E+o 6

.103E+07 .'163E+07

.3458+06

.585Er07

.195Er07

.3358+07

.544E+06 .1',\2e+07

.9228+07

.307E+07

.136E+08

- 452E+ O7

-631E+07 .386E+05

.116E+06 .319E+06 .654E+06 .114E+07

.106€+06 .2188+06

.370E+ 07

.123Er07

.647E+07

.216E+O7 .340E+O7

. 150E+08 . ?09t + 08

.381E+06

.6018+06

.5C0 E+07

.698E+07

06

.422E+O5

.319E+ 06

.116E+06

.717E+06

.239 E+O6 .417 E+O6

+

.125E+07 .1988+07 .4A5E+07 .706E+07 .112E+08 .164E+0E

.658E+06 .135E+07 .236E+O7

.372ErO7 .548E+07

.2?9E+ 08

.7 65E +07

.138E+06

.459E+05 .127E+O6

.441E+07 .7 7 0E+ 07

-375

.12't

.375 .375

.149Ef06

.375

.308E+06

- 404E+O7

.2'l5E+ol

.375

.E59E+05 .17 6E+O6

.121 E+08

.330E+06 .779 E+06 -136E+07

.375

.312Er05

.996 E +0 6 .17 4E+07

.523E+07 .825E+07

- 127E

.375

.3578107 .49aE+07

.299ri07

.175 .375 .3?5 .375

6.0 00

2 6.00 0 2 6 .000

.

.102E+08

.000

1.?50 1 .500

.243E+O7

-375

26.000 26.000 ?

.154E+O7

.72EE+07 .107E+08

.1808+07

24.OOA

26.000 26.000

't .7 50 2 .000

.37 5

21.OOO

.000

't

12.000 't2.000

24.000

.7 50 1

.250

12 .000 12 .00 0

24.OAO

26

12 .00 0

12.000 2.000

22.000 24.000 22.000 22.000 24.000

- 461Er07

.1898+08

22.000 22.000

12 .00 0

12.000

12.000

.373 .375

2?.OOO

.500

12.000

.37 5

20 .00 0

12.00 0

r2.000 12.000 12.000

.375 .375 .375 .375 .375

12.000 12.000

't

.375 .175 .375

E+ 0E

.179E]08

.2608+06 .4548+06 .716E+O6

.147E+07

.257t+07 .405E+O7

.249E+08

.595Ef 07 .8318+0? .496E+05

.4108+06

-137E+06

-842E+06

.2El E+06

.147E+07

.490E+06

.232E+O7 .47 6E+O7

. t 59E +0 7

.a32E+07

.773E+o6

.?77E+07

Rotational Nozzle Flexibilities for Cylindrical

Vessels

149

Table 6-1 Continued ROlA STIfF CALCULATION, CYL. VESSEL

OD,'T

VESSEL NOZZLE NOZZLE ROT STIF IN.L8lDE6 ]CKTIN INPLAN€ OUTPLANE TCK,IN ODU IN CIRCU STO LONGI

12 .00 0 12 .00 0

1.500

'12.000

-7 50

't

28 .000

.375

.1318+08

-37t

.269F+08 .160€+06

28.000 28.000

12.00c

2.000

.250

30 .000

12.000 12.000 12.000 't2.000

.500

30.00 0

't

2.00r1

3 0

'l

.000

30.000 50.000 30.000

.37

52 .000

12.040

2

.00

.500

1.750 .250

0

12.000 12.000 '12

.625

.0 00

12.000 12

.00

12

.000

0

12.000 .000

12.00c 12.000

5

.500

.500 .750 2.000

12.C00

.250

12.000 't2.000

.500

.000 t 2 .000 12 .000

.? 50

'12.00c

.625

12 .000 12 .000

12.O00 '1 2 ,000

1

,000

1

.250

1

.500

1,750 2. 000 .2 5A

I2.000

. 471E+ 06

.'157

2.00 0

.967E+06

.322E+O6

.266E+A7 .5 47 E+07 .956E+07

.1828+07 .3't 9 E+O7

ri

.502E+07 .739E+o7

lls

3

't3.000

13.000 13.000 'l3 .000

.500 .750 I .0c0

1.250 1.500 1.750 2

't3,000

.000

-2 50

13.000 13 .000

.500

13.000

. a>u

'13.000

13 .0 00

.169E +o7

32-000 32.000 32.000 J2.000 32.000 32.00c 32.000 36.000

.15'lE+08 .2728+O?.

.309€+08 .193E+06

6.00 0 36.00 0

.5f2E+06

36.0C0 36 -000

.301€+07

1

.000

,109E+07 .191E+07

36.000

6.000 36.000 36.000 3

3

6.00 0

,644E+0S .177 E+06 .364E+06

.6368+06 .100F+07 .568E+07 .834E+O?

.37 5

.349E+CE

.593E106 .213E+07 .33 jE107 .689E+07

.'l

.375

2.375

.'t54 .154

2 -375

.154

.500

.103E+08

.250E+06

4C.000 r.0.000

3

.563E+06 .888E+06

.1708+08

-122E+07

2.375 2 .375 3.500 3.500 3.500 3.500

6

.375

40 .000

2.375 2.375

E+ o

.?O6E+O7

,106E+08

.215E+46

2.375

.965E+O7 .5 70 E+0 5

- 618E+07

40.000

40.000 40.000

13.000 13 .000 13.000 13 .000 1 3 ,000 13 .000

.1718+07 .298E+a7 - 691e +O7

1.750 2.000

12.000 12.000

.470E+07

58E +07

.207E+08 .289E+0E .171E+06

.?50 1 .000

'12.000

.891E+ 07 . '1418+08

1

.37 5 .3? 5

12 .00 0

1.250 I .500

.2t9E+07 .5128+07

40.000 40.000 40.000 40.000

12.000 12.000

.898E+07

.375

.500

12.000

.137E+07 .64JE+07 .147 E+O6 .301 E+06 .527E+06 .831E+06

-441E+06 .

30.00 0

.00 0

12

.193F+0E

-904Er06

3

12

12.000

.375

.000

30.000 30.000

1.250

12

30.000

.750 1 .000

12.000 12.000

12.O04

VESSEL

?0E +08

.190E+08 .2798+0E .390E+08

.t04E+05 -286€+05 .587E+05 .103E+06

.15 4

.162E+ 06 .33?E+O6

.154

.580E+06 .915E+06

-154

.15 4

.1358+07

-'l54

.188E+07 .154E+05 .425E+05 .8 73 E+ 05 .1 53E+06 .?41E+06 .494E+06

.2'l6 .216 .216 .216 .2'16

.360€+07 .116E+08

.717F +05

.'198E+06 -406E+06 .709E106 .112E+O7

.230E+07 ,4018+07 .633E+07 .9308+07 .'l30E+08

.346Er04 .9Sj€+04 .196E+05 .342E+O5 .539E+05 .111E+05 .'193E+06 _305E+06

.4438+O6 .626E+O6

.515E+04 .142E+05

.2918+05 .509E+05 .802E+05 .165E+06

lx

it:

fl

150

Piping Stress Handbook Table 5-1 Continued

R0IA sTIfr CALCULAIIOI{r CYL.

VESSEL tIO2ZLE TOZZLE ROT STIF II{.LB/DEG ODrlN TCK,IN IiIPLANE 0UTPLAI{E rc(,Itl C IRCU STD LON6I

VESSEL

OD,FT

'13.000

13.000 13.000

13.000 13.000 't3.000 13.000 13.000 13 .0 00

13.0C0

13.000 13.000

13.000 13.0C0 l3 .000 13.000

13.000 '13

.750

1.500 3.500 3.500

.250

4

.500

4

1 -250

1.500 1

2.000

.625 .750 1.000 1.250 1 1

.500

.754 2.000 .500

.0 0c

13.000 13 .0 00

11.000 13.000 13.000 13 .000 l:i

1.000

1.250 I .500 1.750 2.000 .37

13.000 15.000 13.000 t 3 .000 13.000

13.000 13.000 13.000

'tf .000 13.000 13 - 000 13 .0 00

5

.500

.625 .750

't3.000

'13.000

13.000

.500 .500

4.500 4.500 4.500 4 .500 4.500 4

.500

6.6?5

6.625 6.625 6.625 6.625 6.625 6.625 6.625 6.625 8.62

5

4.625 a.625 8.625 a

.250

1. 500

.750 2.000

1

.375 .500

t .000

13 .000

4

1

13.C00

13.000 13.000

4.500

I .000

.625 .750 't .000 1 .250 I .500 1.750 2.000 .250 .375

13 .000 13 .00 0

.500

-625 E.625

13.000 13.000 13.000 13.000 13.000 13.000 13.000 13.000 13.000 15.000 13.000 't3.000 13.000 13.000 't3.000

3. 500

6.62t

15 .00 0 [:

VESSEL

.500

.625 1.250 1.500 1.?50 2.000

.250 .37 5

.500 .675 .7 50

1.000 I .?50

8

.625

8.625 a.625 8.625 10.750 10-750 10.750 10.750 10

-750

10.750 10.750 10. 750

10.750 10.750 1?.750 12.750 1?.750 12.750 12.750 12.750 't 2.750 12.750 12.?50 '12.750

14.000 14.000 '| 4.000 14.000 14.000 14.000 14.000

.?16 .216 -216 .216 .zt7 .237 .237 .237 -237 -237 -"37 -?37 -237 .?37 .280 .280 .280 .280 .2E0 -280 .280 -280 .280 .?80 -32? .3?Z -322 .322 -3?2 .322 .t2? .3?Z .322 .322 -565 .365 .365 .365 .365 .365 .365 .365 .365 .365 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 -37' -375 .375 .375

.863€ +06 . I l6E+07 .20081 07

.?79E+07 .204€+05

.562Ef05 .115Er06 .202Er06 .l'lEE+06

.288E+06 .454E+O6 .667e+ O6

.932Er06

.680E+04 .1 87Er05 .385€+05 -672ErO5

.1 06€ r0 6

.655€ +06

-2'l8Er06 .380Er06

.180€+07

.600E+06 -8828+06 .123E+Ol

.114er07 .265E+O7

.369E+O7 .310E+05 .854E+05 .17 5E+06 .

j06E+06

.103Er05 .285E+05

.5E5Ei05 .'102E+06

.483E+06 -992 E+06 -1?3E+07 .273E+07 .402E+o? .561E+07

.t61E+06

.113E+06

.376Er05

.4108+05

.331

E+0 6 . 578 Ef06

.911F+06 .134F+O7 .187 E+O7 .137E+05

.2328+06

.7738+O5

.40 5E+ 06 .639E+06

.213Eio6

.131E+07 .229E+a7

.361E+07

.135E+06 .437 E+O6 .7 63ErO6

.120E+07

.531E+O7 .7 42E+O7

.1778+O7

,516E+05 .142E+O6 .?92E+06

-172E.05

.247E+O7

.474E+05

.97iE+05

.510E+ 06

.170E+06

.804€106 .1658+07

.268E+06

.550E+06

. ?EEE+07

.96t E+06

.455E+07 .669 E+07 .934 E +07

.152E+O7 .223E+O7

.6 20E +05

.',l718+06 .351E106

.613€+06 .967E.O6 .199E+07 .317E+o7 .5 47E+O7 .aE4E+ 07

.1128+08

.687€ +05 .189E+06

.388E+06

.Jll

E+07

-2078+05 .570E+05

.1178+06 .2048+06

.662Er06 .116ErO7 .182E+O7 .268 E+07 .374E+07 .229E+O5

.631E+05 . 1 29 E+06

.679E+O6 -107E+O7

.226E+06

.384€ +07

.128E+07

.220E+07

.357E+O6

.732Er06

Rotational Nozzle Flexibilities for Cylindrical Vessels

151

Table 6-1 Continued ROIA STIFF CALCUIATI0Ne CYL. VESSEL

OD,TT

13.000

VESSEL TIOZZLE NOZZLE ROI STIF IN.L8/DEG TCK,IN INPLARE OUTPLANE TCK,IN OD,IN CIRCU LONGI STD .500

1

13.000 13 .000 13.000

1.750

11.000

.500

,000

2

-z>u

't3.000 13.000

.62 5 .7 50

13 - 000 13 .000

.000

'13.000 13

.500

.000

1f.000

.7 50

.000 .000 '| 3 .000 13 .000 13 .000 1J .000

2. 000

13.0C0 13.0 0 0

1

13

13

13 .00 0

13.000 13.000 13 .000 13

't 3

13.000 13 .000

13.000

1.250 I-500 2. 000

.500 .625 .7 50

,000 1.?50 1.500 1

1.7r0 2.000

.500

r3,000 '13.000

I .000

13 .000

1

.000 13.000

z

13.000 13 't

't4.000 't 6.000 16.000 'l6.000 16.000 16.000 1 6.000 't 6.000 16.000 I 6.000 't6.000 18.000 ,000 1E.000 8

I

13.000 13.000 .000

.000

.000

13 .000

15

4

.7 50

.000 .000

4.000

I

18.tto0 1 8.000

.625

.000

13.000 13.000

1

1

13.000 13

1.250 .500

1.750 .000

8

.000

8.000 18.000 18.000 16.000 20.000 20.000 20.000 20,000 20.000 20.000 20.000 20.000

't

20-000 20 .000

22.000 2 2.000 22.000 22.000 22 -OOO 22.OOO 22 .000

22.000 z2 -aoo

22.000

24 -OOO

3. 000

tt.000

.500

1f. 000

,625

24.000 24.000 24.000

.7 50

?4.AOO

.000

24

13.000

13.000

13.000 l3 .000 13.000 15.000 '13.000

1

't.250 I .500

1.750 2

13.000 11.000

.000 .500

t3.000 1J.000

.7 50

.000

13.0C0

1

.000 13.000

1-5C0

1.250

.000

24.000 24.000 21 .OOO

24.000 26

13.0C0

13

VESSEL

.000

26.000 26.000 26.000 26.000 26 .000

26.000 26.000

.375 .60 5E + 07 .375 .890 + 07 -375 ,124E+ 08 .375 .791E+05 .375 .218 E+06 .375 .448E+06 .375 .783E+06 .375 .1?4E +o7 .375 .?54E+O? .375 .4t 3E+07 .375 .699a+C7 .375 .103E+08 .375 . 143E]08 .375 .8998+05 .375 .? 4EE+06 -3?5 .508E+06 .375 .EE8E+06 .375 .1 40 F+ 07 .375 .288E+ 07 -375 .502E+07 .375 .793E+ 07 -375 .117E+0E .375 .1d3E+0E .375 .1008+06 .375 .?77E+06 .375 .569E+06 .375 .993€+06 .375 .157E+O7 '12?F +l\7 "7< -375 -562E+O7 .375 .8E6E+07 .375 .1 30 E+08 .375 .182E+08 .375 .1118+06 .375 .306E+06 .375 .629E +06 .375 . t 10Ei07 .375 .173E+ D7 -375 .3 56 E+07 .375 .621E+o7 .375 .980 E+0 7 .375 .',144E+08 .375 .201 E+oE .375 .122E+O6 .37t .3358+06 .375 .639Er06 .375 .120E+O7 .375 .190E+ol .375 .390E+07 ,375 .681E+07 .375 .107E+08 .375 .t 58E+08 .375 .220€+08 .375 .1328+06 .375 .3658+06 .375 .749E+O6 -375 .',131E+O7 .375 .206E+07 -375 .4248+07 .375 .7 40E+A7 .375 .117E+08 E

.?D2E+O7

.297E+Oz

.414E+Ol -2648+05

.728Er05 .149E+O6 .2 6'l E+ O6

.412E+0 6 .E46E+06 .148E+02 .233E+O7

,t

.343E+O7 .478E+O7

.300€+05 .8268+05 .169E+06 .296E+06 .467E+O6

.959E+06 .167 E+Of .2 64E+oz . f88E +07 -542E+07 .33 5E +0 5

,9 23E+o, .1 90E+06

.331E+06

.5?28.06

.107E+07 .1878+07

.295Ei07

.4348+D7

.606E+07 .370E+05 .102E+06 .210E+06 ,366E+06 .577E+06

.1 19 E +07

.?a7E+07 .3278+07 .480E+07 .67OE+07 .406E+05 -'l1?E+o6 .230E+06

.401E+06 -633E+06

.130E+07 -227E+O7

.358E+07 .526E+07 .735E+O7 -44JE+05

.122E+06 .250E+06 _436E]06 .688E+06

.141E+07 .217 E +07

.389E+07

i{

.,1

itr\

.,|\

|4

,)

itt

152

Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULATIOTI, CYL. VESS€L VESSEL

vE

OD,FT

TC

13

.000

13.000

ssEL

1.750 2.000

13 .0 00

13.000

.37 5

13 .0 c0

.500 .625

I

.7 50

'|

3.000

t.000

13.000

1-000

15.0C0

1.?50

13.000 13.000

1.750 2.000

13.000

t3.000

'1.500

.250

15.000 .500

13 .0 00

13.000 13.000 13.000

r3.000 13.C00

r3.000 13.000

.625

13

.000

13.000 't3.000

.5C0

.625 1.0c0

t.25D I .500 1.750 2 .000

.t75

.500

13.000

.625 .750

13.000

13.000

13.000 13.000

13.000 13.000 13.000 13.000 l3 .000 13 .0 00

13.000 13.000 13.000 13.000

13.000 13.000

I .000

1.250 1.500 1.750 2.000 .500

.625 .750 1.000 1 .250 1 .500 1.750 2-0c0 -?50 .37

13

5

.500

13.C00

.000

1.000

13 .000

'1

13.000

1t.0c0

28. 000

- 143E106

28.000 26.000 28.000 28.000

.7 50

. t00 1.750 2.000

OE

.240€+08

.t94e+O6

OUTPLA C

E

IRCU

.572E+O7

.799E+Ol .477E+05

.?238+07

.15',lE+06 .270E+O6 - 471ErO6 .743E+O6

.375 .s75

.153Ef07

.2668+O7 .4?OE+07

2E.000

.37t

.4 58E + 07 .799 E+07 .'126€+08

.00 0

-3? 5

.259E+0E

.

28 .000

28.000 28.000 2E

.375 .375

.!75

30.00 0

.375 .375 .375 .375

30.00 0

.375

30.000 30.000 30.000

.5r>

.375 .375 .375

30.00 0

32.000 32.000 32.000 32.000 32.000 32 .000

52.000

32 .00 0

32.O0D

32.000 3 6.000

36.00 0 36.00 0 36.00 0

36.000

.375 .375 .375 .375 .37 5 .37 5

.375 .37

36.000 36.000

.375

5

36.00 0 36.00 0

40.000 40.000 40.000

40 .00 0 40 - 000

40.000 40.000 40.000 40 .000

40.000

4E.00 0

4E.000

48.000 48.000 48.000 46.000 48.000 48.000 48.000

.809 Er 06

.141Er07

.lE5E+08 .

t 54E+06

.4?3E+06 .869 E r 06 .152e+O7 .239E+A7 -492E+07

.375 .375

.375

.s75 -375

.51?E+05

.141E+06 .2908+06 .506 E+06 .798E f06 .164E+O7

.286E+07

- 199 E+08

.664E+07 .927E+o?

.lf5E+08

.4 52 E+O7 .5 47E+0

5

.t5tE+06

06

.3'l0E+06

-1628+07 .?56E+07

.541E+06 .E53E+06

.9 29

E+

.5?6E +07

.91E8+07 .145E+08 .213E+08 .297 E+08 .185E+C6 .511E+06 .105E+07

.1838+07

.175Er07 .3068t07

.483E+07 .710 E+O7

.991Er07 .d18E+05 .170E+06

.350E+06 .611E+06

.289E+07

.9648+06

.591E+07 .1048+08

.t

.346Er07

- t 64E+0E .2 40E +0E

.545E+07

.336Er08

.112Er08

9EEr07

.E02€r07

.?07E+06

.6E9 E +05

.117 E+07

.190E+06 .390E+06

.570E+06 .2048+07 .3228+ 07 -662E+07 .

.375 .375

.618E+07 E63Ei07

.659E+07 .276E+08 -1648+C6 .453E+06

I6.000

4E.000

't5.000 't3.000 13.000

TCK.IN II'|PLANE STD LON6I .17?E

30.000 50.000 30.000

.375

NOZZLE ROT STl F IN.L8/DEG

6.000 26.000

1.250 1.500 1.750 2.000

1.000

N

2

30.000

13.000

15.000 13.000 15.000

OD,I

.7 50

13.0C0

13.000 13.000 13.000 13.000 13.000 15.000 13.000

0t z LE

K,I I,I

1 16

E+08

.68tE+06 .107E+07 .?21E+07 .385 E+0 7

.'l82E108

.608Er07

.268E+08 .374E+08 .249 E+ 06 .687E+06

.893E+07

.141E+07

.375

.246E+07 .389 a+07 .7988+ 07

.375

. 1J9E+08

.220E+08 .323E+ oE .451E+0E

.'l ?5E+08 .831E+0 5 .?29E+o5 .470E+06 .821E+06

.130E+07 .?668+O7 -4648107

.733E +07

.1088108 .1 508+08

Rotational Nozzle Flexibilities for Cylindrical Vessels Table 6-l Continued ROTA

0DrfT

VESSEL TC K,IN

.000

-250

VESSEL

14

4.000 14.000 14.000 't

14.0CC

14.000 14. 000

't4.000 't4.000 14.000 14.000 14.000 14.600 14.000 14,000 t 4 .000

14.000 '|

STIfF CALCULAIIOI'1, CYL.

4.O00

14.000 14.000 14.000 14.000 14.000 't4-000

.500 .625 1.000 1-258 1.5C0

1.750

z. 000

NOZZLE

0D,I

2.375

2.375 ?.375 z

.375

?.375 2.375 2.375 2.375 2.375 f.500 3

.500

.500

3.500

1

.000

3.500 1.500

't

.2 50

.625

3.500

2

3

.500

.000

14.000 't4.000 14.000 r4 14

.000 .000

14.000

.490Er05

.216 .216

.2328+O6 .176E+06 .E32€+06 .'131E+o7

.7738+05

.269

.8988+06

.216 .?16

.193€+07

E+ 07 . 'l97E+ 05

.281

E+0 5

.159E+06 .277a +O6 .437E+06 .643E+06 .655E+04

.28 0

.1678+07

.557E+06

.2638 + 07 .387E+0? .541E+07

.129 E+07

6.625

-2E0 - z6u .2E0

. I 09 E+06

.363E+05

.625

-322 -3?2

.322

.7 14 E+05 .'130E+06

8 -625

.223E+06 .390E+06 .615E106

1.250 1.500

8.625

.322

.2218+07

2.000

I .625

8.6?5 '| 0.750 10.750 10.750 1 0.750 10.750 10.750 10.750

.322 -322

.500 .500

6.625

6.625

.50b

6.6?5

6.525 6.625 6.625

1.000 1.250 1. 500 1

.750

2. 000

.375 .500

E

.62'

11

14

.117E+ 06

.9E48+05

.6?5

14-000

14.000 't4.000 14.000

. ?16

.137E+05

.27 4E+O5

4 4

4.000

.842E+05

.E23E+05 .169E+06 .295E+A6 .466E+06 .956E+06

2. 000

t

-?16

49 E+0 5

.4t08.05

.119E+O7 .996 E +04

1.750

.000 t 4 .000

I 4.000

.l

.2't6

.3568+07

14.000

14.000

-216

.?108+06

4.500

14.000 'r4.000 14.000 14.000

.181E+07

06

.629E+06 .1 10f+07 .173E+07 .255E+07

1.500

.0AA 14.0C0

.154

4E +

.237 .237 .237

4

14.000 14.000 14.000

.432E+0{i .6O3ErO6 .496E+O4

.500

.250

t4.000

.29

.130E+07

.154 .154 .154

.9888+05

.64E E +05 .102E +C6

'|

14.000 14.000 14.000

.EE?E+06

.154

.194E+06

14,C00 I 4.00 0

4.00 0

.156E+06 .320E+06 .559E+46

.9'18€+04 .189E+05 -329E+05 .5?0E+05 -107E+46 .1E6E+06

.237

4.500

'|

.15 4

.1818+05

4.500

.750

14.000 '| 4.000 14.000 14.000

.333E+04

.?76a+O5 .5668 | A5

.542F+05

1.000

14

.1 00E+05

.'t54

.237

.375 .500

14.000

.000

.154

4.500 4.500

4. 500 4 .500

14

ZLE ROT STIF IN.L8/DEG TCK,IN INPLANE OUIPLANE CIRCU STD LONGI

NOZ

-216

1.750 .000

N

VESSEL

1

.000

.250 .500 -625

t .000

1.250 1.500

1.750 2.000 .500

1

-237

.280 .280 .280 .280

.5 65 .3 65

.365

0. 750

10. 750

.306€+06

.299E+i5

.3958+05

.1268r07

.318E +07

.5'128+07 .715E+ 07

.497E+85

.'l37E+06 .281E+06 .491E+06 .7 7 5E+ A6

,365

10.750 12.750 1? .750

.1118+06

.159E+07 .?7EE+ol

.3 66E+

0

6

,5788+06 .850E106

.561Er05 .155E+06 .319Er06 .678€+06 .tE0E+07 .132E+0

5

.205E+06 .421 €+0 6 .736E+96 .116E+O7 .171E+07 .238E+07 .166E+05 .457 E+05 .937E+05 .164E+06 .258E+06 .530E+06 .926E+O6

.438E+07 .6 45E+07

.146E+07 .215E107

.596E+05 .165E+06 .336E+06

.199E+05

.9008+07

.375

.371E+Os

.300E+07 . 549€+0 5

-113E+06

154

Piping Stress Handbook Table 6-1 Continued ROTA VESSEL

OD'F1

14

.000

14.000 14.000 14.000 14.000 14.000 14.000

t4.000 14.000

14.0C0

14.000 | 4.00 0 I 4.00 0

14.000 14.000 14.000

14.000 14.000 14.000 14.000 I 1.000 t 4.000 t 4.000 14.000 14 .000

.625 .750 I .000 1.250 1

.500

1. ?50

2.000 -250 .625 .750 1.000

1.250 1.500 1.750 2.000

14

.000

| 4.000

14.000 14.000 'l4.000 I 4.000 14.000 14.000

14.000 t 4.000 14.000 14,000 14.000 14.000 't4.000 14.000 14.000 14.000 't 4.000 14.000

14.0C0

16

.625 1.000 1-?50 I .500

.000

1.250 1.500 1.750 2.000 .250 . 500

.625

.750 1.000 1

14.000 t 4.000 I 4.000 14.000 14.000 14.000

.500

.375

'1

14.000 14.000 14.000 14.000 14.000 11.000

t 4 .000

.2to

74.OOO 14 .000

12.750 12.750 12.750 12.750 12.750 12.750 1?.750 I 4.000

t 4 .000 16 .000

1.750 2.000 .250 .375 .500 .625 .750

14.000

CALCULATIOI,IT CYL. VESSEL

VESSEL NOZZ LE TCXTIN 0D,Itl

r4.000 14.000 14.000 14.000 14.000 14.000

14.000

STIfF

.250

I .500

1.750 2.000

.250

.375 .500 .625

.5918+06

.197E+O6

.932 E+06 .191E+O7

.311E+06 .638e+06

.375

.3J4€+07 .527E+07

-111E+07 .176E+O7

.375 .375 .375 .375 .t7 5

.37t

.375 -375

.375 .375 .375

.7

75E

+

07

.'l0E€+08 .662E+05 .182E+06 .3? 4E+06 .654E+06

. t 05E r07 .21?E+07

.370Ei07

.375 .375 .375

.000

.375

1E.000

.375 .375

'l 6

18.000 18.000

.608 Er05

.125E+06 -21EE+06

.3448r06 -706E+O6

.123E+O7

.194E+07 .?E6E+07

.7 558+06

.37 5

.221Ero5

.8 58 E+07 . t 20E+ 08 .764E+05

-375

.375

.258E+07 .361E+07

.583E+07

.2108+06 .432E+06

16.000 1 6.000 16.000 16.000 '| 6.000 I 6.000

IRCU

.375 .375

.37 5

.119E+07 .2 448+07

.399E+07 .255E+05 .70?E+05 -1418+46

.25?E+O 6

.397E+O6

.8'l5E+06

.427e+O7

.142E+O7

4E+07

.225E+O7

. (r7

.990E+07 .138E+08

.866Ei05

.239 t +06 .490E+06

.330Ero7

.461E+o7 .289E+05 .796 E+C 5 .163E+06 .2E5E+06

.37 5

.8t6E+06

.37 5

.135E+o? .277E+07

.16'l

18.000 18.000

.375

-484E+07 .7 64E+O7

.112€+08

16 -000 20 .000 20 .000

.37 5

.157E+08

.375

.96E

.375

.2c7a+ B6 .548E+06

.37 4E+07 .523E+O7 .3238+O5 .890E+05

IS-000 16.000 18.000 '18.000

20.000 20.000 20.000 2

0

.000

20.000 20.000 20.000 20.000

22.000 22.000

1.250 'l .50c 1-750 2.000

C

.375

.500

1.000

LON6I

000

-

2? .000 22 .000

.625

STD

16.000

-750

.37 5

I{OZZLE RO' STI F I}I.18/DEG ICK,I N INPLANE OUTPLANE

.37 5

.375 .375

E +

05

.957E+06 .151E+07 .310E+07 .5 41E+07 .854E+07 .126E | 08

.l

.375

22 - 000

22.000

.924E+O6 E+O?

.255E+07

.183E+06 .519E+06 .503E+06

-10f8+07

.180€+07 .265E+07 .41E E +0 7

?5E+08

.5848+07

107F106 .295E+06

.357E+05 .984E+05

06

.2OZE+Oa

.

.37 5

.450E|06

- 606E

+

.106E+07

.3538i06

.'l67E+07 .343E+07

-

5

56E+

06

.114E+07

22 -OOO

.37 5

.599Ei07

.?00Er07

22 .0C 0 22 .000

.37 5

.9 44E+ 07

.315E+O7

.375

.139E+08

.000

.375

22.000 24

24.000 2 4 2

.000

4.000

.37 5

.315

.t94E+0E .1 17 E+o6

.323€+06 .6648+e6 .116E+07

.463E+07 .616E+07 .5918+05 .108E+06 .221E+O6

.386E+06

Rotational Nozzle Flexibilities for Cylindrical

Vessels

155

Table 6-1

Conlinued ROTA STIFF CALCULATIONT OD,FT

VESSEL NOZZLE TCKrItl OD,IN

.000

.7 50

v€ssEL

14

14.000 14.0C0

4.000 14.000 14.000 14.000 I 4.000 14,000

1

1

.000

1.254 't.500 1.750 2. 000

.500

.625

14.000

14.000 14.000 14.000 14.000 't4.000 4.00 0 .000 'l 4 .000

'I

.7 50

1.000

1.250 1

.500

1.750 2. 000

14

14.000 14.000 14.000 t /, .000

14.000 't4.000 14.000 14

.500

.625 I .000 'l -?50

1 .500 1

.750

2.000

. ?50

.375

.000

14.000 '14.000

14.000 14-000 14 .000

14.000 t 4 .000

28 -000

2E.000 28 .000

28.000 28.000 28.000 28.000

30.00 0

30.000 30.000 30.000

30.000 30,000

30.00 0 30.00 0

.t75

f2.000

.500

.625

.500

1.750 2.000 .250

.375 .500 .6?5

'l

.750 .000

32.000 32.000 32.000 32.000 32.000 32.000 32.000 32.00c 32.000 36.000 36.000 3 6.000 36.000 36.00c 36 .00 0

2. 000

36.000 36.000 36.000 36.000

.500

40.000 40.000

.7 50

40.000

I .500

1.750

.000

'14,000

11.000

28.000

2. 000

1

14.000 t 4 .00c

.000

30 .00 0

14 .0 00

'l 4

28.000

1.250 1.500

I .000

'l .000 'I .2 50

14.000 14.000 14.000 14.000 14.000 14.000 't 4.000 14.0c0 t 4.000

26.U00

l0 .000

14.o00 14.000 14.000 14.000 14.000

I 4 .000

24.000 24.000 24.000 24.000 26.000 ?6.000 26.000 26.000 26.000 26.000 26.000 26.000 26.000

.7 50

t 4.000 I 4.000

14.000 14.000

24 .000

28

't4.000 't 4.000 14 .000

24.000

.64>

40 .000

40 .000

NOZZL€

TCK'IN STD

CYL.

VESSEL

ROT

STIF IN.L8/OEG

INPLANE LOTIGI

.1838+07 .37' .375 .375E+07 .375 .656E+0? .375 .'103E+08 -3?5 .152E+08 .375 .2',12E+08 .375 . 128E+06 .375 .551E+06 .375 -7?2Eta6 .375 .1?6E+O7 -375 .'1998+07 .375 .408[+07 .375 -7'l3E+O7 .375 . '1 12s+08 .3?5 -1659+08 .375 .231 E+08 .375 .13E€+06 .375 .380E+06 .375 .779E+O6 .375 .136E+07 .375 .2158ra7 .375 .4418+07 .3?5 .770E+47 .375 .1?2E+08 .3?5 .1798+08 -375 .249E+08 .375 .'l18E+06 .37t '408E+06 .375 .637E +06 .375 .146Et07 .375 .231E+O7 .375 .47 4E+A? .375 .AZ7E+Ol .3'15 .131E+08 .375 .192E+OB .3?5 .268E+0E 06 .375 .1 58E++06 .375 .4368 .3?5 .695E+06 07 .3?5 -'156E++O7 .3?5 .?47E -375 - 506Er07 .3?5 -8858t07 .375 .140E+08 .375 .205E+08 -375 .286E+08 .375 .179E+06 .375 .493E+06 .375 .101 E+07 .175 .177E+o7 .375 .279E+07 .375 .57?E+o7 .375 .999E+07 .375 .'t 5EE+ 08 .375 '232E+08 .3?5 .3 24E + 08 .375 .199€+06 .375 .549E+06 .373 .113E+07 .375 .197 s+o7 .375 .311E+07

OUTPLANE CIRCU

-610E+06

.125E +o? -219 E+07

.345E+07 .507E+07 .708E+07 .425E+05 -117E+06

.Z1j

E+O6

.420 E+0r5 .663E+06 .136E+0 7

.238€+07 .375ErO7 .551E+07 -7708+A7 .459E+05

.j27E+06

.260E +0 6 - 45 4E +O6

-7168+06

-14?E +O7

lir :t

t|j

{

ils

'{l

.ZS7E+47

.4o58+o7 .595E+07 .831E+07 .493E+05 .'1368+06

i!

.2798+06

.488E.06

.769 E +06 .

j

588 +02

-276E+O7 -435e+O7 -640E+O7

.89fE+07 .jAEE+05 .145€+06 .29EE+O6

,521F+06 .8228+06 .169E +Oz

.295E+07 .465E+07 -684E+07

.9558+07 .596E+05

.164€+06 .33?E+06 .589E+06 .929E+06 .19',l E+07 .

i33E+07

.525E+07 .772E+O7

.'t08€+08 ,664E+05 .'183E+06

.3t6E+86 .656E+06

.104E+07

,\

156

Piping Stress Handbook Table 6-1 Contlnued ROTA STTfF CALCULATION, CYL. VESSEL VESSFL

VESSEL

lcKrIN

OD,FI

1

14.000 14.000 I 4.000

1

t .500 1

2.000

14.000

.2 50 .37 5

.500

.625 .750 1.000 1.2t0 1.500

'15.000

.250

15.000 15 ir

lt 1

5.000

r5.000 15.000 1

5.000

15.000

5.000 I 5.000 't 5.000 15.000 't 5.000 15.000 15.000 1

tl

i

.500

.000

.625

I 5.000 't

F

.750

14.0C 0

14.000 't4.000 I 4.000 14.000 14.000 14.000 14.000 14.000

q;

.000

.250

15-000 t 5 .000

15.000 15.000 'l

I .000

1.250 I .500

.758 2.000 1

.375 .500 . ?50

1.000

1.250 1.500 2.000

.250 .375

5.00 0

15

.000

15.000 1 5.000 15.000 15.000 15.000 I 5.000 15.000 15.000 I 5.000 15.000 t 5.000 15.000 I 5.000 15.00 0

15.000 't5.000 I 5.000 I 5.000

15.000

.500

.625 1

.000

1.250 1.500 2.000

.250 .37 5

.500 .625 .7 50

1.000

1.250 1.500 1.750 2.000 .2 50

t 5 .000

15.000 15.000

N0zeLe

NOZZLE ROT STI F II{.LB/DEG

OD,IN

T

.638E+07

40 .000

40.000 40.000 40.000 40.000 48.000

- 11'l E+C8

48 .000

48.000 46.000 48.000

{8.000 48.000

.375

-?13E +O7

.3718+O?

.1?6E+08 .2 58Er 08

.586r+07

-21OE+06

.8 0l Er05

.662E+o5 .1f,6E+07 .237E+07

-221e+O6

.36'l E+08

.t7t

OUTPLAI{E CIRCU

.3? 4e+07 .7 69E+07

.861E107

.120Ef08

,4 53 E+0 6

.791E+O6

.125Er07 .256E+O7

.000

.375 .375

.212E+08

.706Er07

48 .00 0

.37 5

.311 E+08

.104E10E

48.000

.375

.435€+08

2.375 2.375 ?.375 2.375 2-375 2.375 2.375 ?.375 2.375 2.375 3.500

.151

.9 668+04

.3?2E+O4

3

.500 3 .500

.?16

5.500 3.500 5.500 3.500 3.500 3.500 3.500

-216

4E

4. 500 4

.500

4.500 4.500 4.500

4. 500

4.500

.500 4. 500 4-500 4

6.625

6.625 6.625 6.625 6 .625 6.625 6

-6?5

6.625 6.625 a.625 6

.625

CK,IN INPLANE STD LO}JGI

a

-62>

.625

.1 34E+08

-418E+O?

.'l

45

Fro8

.154

.?66E +05

.151

.546€r05

.887E+04 .1E28+05

.,t 54

.955E+05 .151E+06

.3t8E+05

.309E.06

.502E+05

.15 4

.154 .154

.540E+06 .8 52 E+ 06

-1808+06 .2848+06

.154

-1?5E+07

-

.154

.154 -2't6 .216

.175e+07

.479E+O4

.396€+ 05 .813E+05

.13?E+os

.1l?E+06

.473E+O5 .7 47E+05

06

.153E+06

.803E+06

.268E+06 .422E+06

.1278+ 07

.23? .237 .237 .237

. 460E

+

.1E6€+07

.8 67 E +06

. l908+05

.633E+04

-523E+05

.17 4E+A5 .358E+05

+

.107€+06 .l8EE+06 .296E+06 .60EE+06

. t06€+07 .1 67 E +O7 .2 468+07 .3 44E+ 07

.2898+05 .795r + 05

.2EO

.450 E+06

.1 63E+ 06

.285€+06 .924E+ 06

.2E0

.161E+07 .255E+07

.2 E0

.37 4E+07

.280 .322

.t22

,322 .3??

.621Er06

07

.260E

.280 .?80 .280 .280 .28 0

.271E+05

.2248+06

-716

.23? .237 .?3?

117E+O6

.583E+06

.144E+ 05

.216 .216 .216

.216 .216

.103E+06

.522e+07

.3E1€+05 .105E+06 .216E+06 .377 E+06

.626E+O5

.987E+05 .203E+06 .354E+06

,558Er06 .621E+06 .115e+O7 .9 62E+04 -265E+O5 .544E+O5

.951Er05

.150€+06 .308E+06 .538E+06 .848E+06 -125E+07 .174E+07 .127E+05 -350E+05 .719E+O5 .1?6E +06

Rotational Nozzle Flexibilities for Cylindrical Vessels

'157

Table 6-1 Continued ROTA STIFF VESSEL

OD,FT

VESSEI ICKTIN

15.000 15.000 15.000

15.000 15.000 15.000 15.000

NOZZLE

0D,IN

8

.625

8

.625

.500

a.625

8.625

.250

5.000 15.000 .000 .000 l5 .000

ALC

.750 .000

't

't 5 15

C

.7 50

.000

2

8.675 .750 10.750

.2 to

10

.500

1A.750

.62' ,7 50

10.750

'10.750

10.750

t5.000

.000 1.250 1.500 'l .750 2. 000

10

15.000

.250

'15.000

.500

.000

15

15 .000

I t .000

1

'15.000

15.000 15.000 J5.000 15.000 15.000

0 .750 I 0. 750 '1o.750

1

.750 12.750 12 .750 12.750 12 .750

.7 50

12 -750

1.500

'12.750

.0c0

1

12.750 12 .750

2. 000

12.750 12.750

15.000 15.000

.500

14.000 1/,.000

.000

.000 .250 .500

.000

15

15.000 15.008 15.000

1.750 .250

15.000 15.000 t 5.000 15.000

.7 50

.7 50

2-000

.0C0 '15.000

.250

15.000 1s-0c0

.500

15

15 't 5

.000

15.000 15.000 15

.? 50

.000

15.000

.000

1

.000

't.?50 1.500 1.750 2

'15.000

.000

.000 .000

.625 .7 50

15.000 15.000

1

.000

't5.0c0 t 5.000 15.000

1,258 1

.750

'l

2

.000

.000 1 5 .000 I 5 .000 15.000 15.000 15.000 5

'I

.500

.000

,000

14.000 I 4. 000

14.000 14.000 14.000 14.000 16

.000

16.000 16.000 I

6

.000

16.000 1 6.000 16.000 1 6.000 16.000 1 6.000

.000 18.0C0 1

15.000 15 15

4

1

'15.000 15

'14

8

t8-000 18.000 't 8.000 13 .000 16

.000

18.000 18.000 't 8.000 20.000 20 .000

.500 .750

20.000 20.o00 20 .008

ULATI0N'

CYL

VESSEL

'

NO?ZLE ROT STIf IN.LB/DEG

TCK,IN INPLANF LONGI STD

.322 .322 .322 -322 .322 .322 .365 -365 .36' .3 65 .365 .365 .365 .365 .365 .36 5 .375 .3?5 .375 .375 .375 -375 -375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 -375 .375 -375 .375 .375 -375 -375 -3_tj .375 .375 .375 -375 .375 -375 .375 .375 .3?5 .375 .375 .375 .375 .375 .3?5 .375 .375 .3tj .375

.595E+06 .1228 +O7 .213E+o7 .336E+07 .494E+07 .690E+07 .4 80E + 05 .13?E+O6

.272E+A6 .475E+ 06

.7 49E+O6 .154E+O7

.268E+07

.4248+07

-623E +O7

.869E+07 .578E+05 .159E+06 .32? E+ 06 .5?1E+ 06

.900E+06 .16

5 E+

07

.323E+a7 .5C9E+07

.7198+07 .105E+08 .639E+05 .17 6E+06

OUTPLANI CIRCU

.198E+06 .407F+06 .711E+O6

.1'l

?E+O 7

.'165E+07 .238E+O7

.160E+05 - 4 41E +O5

.906€+05

.'t5EE+06

.25OElo6 .512E

+

O6

.895E+06 .'11'lE+O7

.208E+07 .290E+07 .193E+05 .530E+05

.t09E+06

.190E+06 .300E+06 .616E+06 .108E+07

.250E+07 .34EE+07 .2't 3E+0 5 -587E+05 .1?1E+O6

.632E+06 .996E+06 .205E+07 .357E+07 -564E+07

.2'l1E+O6

.116E+08 .738 € + 05 -203E+06 .417 E+o6 .7 Z9E+O6

.115F+07 .236E+O7

.4138+07

.65'l

E+D?

-957E+07

.1J4E108

.837E+05 .231E+06 .4738+ 06

.827Ei 06 .130 E +0 7 .21EE+07

.332E+0 6

.682E+06

.119E +o?

.188E+07 .27 6E+07 .386E+07 -216E+O5

.678E+05 .119 E+06 .?43e+O6

.3838+06 .787E+06

.138€+07 .217 E+07

.319E+07 .4 4tE+01 -?79E+05 .769E+05 .158E+06 .?7 6E+o6 .435E+06

.893€]06

.738E+O7

.156E+07 -216E+07

.1oEE+08

.362E+O7

.4688+07 .

1

51E108

.505E+07

.936E+05 .258E+06 .529E+06

.t1?E+O5

.146E+07

.486€+06

.925!+06

,l

i: "l

t\

.170E +A7

.3 62 Ei 06

.829E+07

:

.859E+05 .17 6a+06 .308E+06

r{

I

158

Piping Stress Handbook Table 6-1 Continued R0TA SIIFF CALCULATIOIte CYL.

vEss€L

VESSEL

TC(rIN

0DrFT

15.000

r5.000 15

.000

15.000 15.000

t -000

.?50 1.500 1

1.750 2.000

15.000

.2 50 .37 5

15.000 15.000 15.000 15.000 15 .0

00

.500

.625 .7 50 1

.000

15.000 15.000

1.254 1 .500 1.750 ?.000 .250

5.00 0

.37 . 500 '

15.000 15.000 15.C00

r5.000 1

15.000 15.000 t 5.000 I 5.000 I 5.00 0

15.000 15.000 15.000 15.000

t5.000 1 5,000 15.000 I 5.000 15.000 15.000 15.000

15.000

t5.000 15.000 15.000 15.000 | 5.000 t 5 .000

'15.000 15 .000

15.000 15.000 15.000 15.000 ,| 5.000 15 .0

00

5.000 15.000 15.000 15.000 15.000 15.000 15.000 15.000 't

I 5.00 0

15.000 15.000 '15

.000

.625 .750

1

.000

1.250 I .500 1.750 2.000 . ?50

.500 -625

.7 50

1.000

.250 I .500 1.759 2.000 .250 1

.t75

.500

.625 .7 to 't .000 1.250 1.500 1.750 2.000 .250 .375 .625 .75A 1.000 1.250

t.5c0

1.750 2.000 .250 .375 .500 .625 .750 1.000

l{oztLE 0D,IN

20.000 20.000 20.000 20.000 20.000 22.000 ??.000

.ooo 22.000 22.000 z2-ooo z2

VESSEL

OZZL€ ROT STI F II{. LB/

lcKelt{ INPLANE STD LON6I .375 .375 .375 .375 .375 .375 .375 .375

.375 .375 .375

.299€+07 .52tE+ 07 .825 E+07 .1 2l E+08 .169 E+0E .103E+06 .285E+06 .565E+06 .102E+ 07

-37 5

.134E+08

22.OOO 24 .00 0 24.OOO

-375

, I E7E+ 0E

.375 .375

.312E+06

26 -OOO

26.000 28.000 28 .000

28.000 28.000 28.000 2E.000 2E .000 ?E.000

28.000 28,000 30.000 30 .00 0

30.000 30.000

30 .000

30.00 0

.3?5 .37 5

.375 .375 .3?5

.375

.37'

.375 .375 .37 5

.3?5 -375

.175 .375 .375

.375 .375 -375

.375 .37 5

.6348.07 .999E+07

.147Er08 - ?05 E+08

. 12f,Ef 05

.340€+06 .192E+O7 .39

4E +O7

.214E+O6 .373 E+06

.5E9Ef06 .721E+O7 . zl t E+q7 .333 E +07 .490E +07 .684E +07

.4llE+05 .t13Er06

.23OE+O7 -362E+O7

.1 60E+0E .2?3E+08 .133E+06

.532E+O7

.109Er08

.367E +06 .7538+ 06

.132E+07 .20EE+0? .426E+o? 44E+0?

.t75

.141El07

.173Ef06 .241E+A8

.375

.223E+07 .4588+07 .799E+07

.37 5 -375

-624E+O7

.578 E +0 5 . t 048+06

.689E+07

.394€+06

.000

.19f,E+07 .J04E+07 .447E+07

.232e+O5

.375 .375

.375 .375

.19 5e+06

.541Er06

.406E+06 .6408+05 .131E+07

. t 43E+ 06

-375

.950E+05

.122t+O7

-375

-375

-345E+05

.697E+06

.117E+08

.375 .375 .375 .375

32.000 5 2.000

.641 E+06 .112E+O7 .17?t+ 07 . 363 8.0 7

-375 -375

30.000 30.000 30.000 30.000 3 2.000 32.000 52.000 32

.1 13E+06

.?

.t75

.275E+07 .404ErO7 .565E+07

.538E+06

.5788+07 .9'l 2 E+ 07

24.000 24.000 24.000 2 4.000 24,000 24.000 24.000 2 4.000 2 6.000 26.000 26.000 26.000 26.000 26.000 26.000 26.000

r0 6

-110E+07

-375

.375

E

.17 4E+O7

.1 61 E+07

.375

22 .000

.998

.331e+O7

?2.000

22.OOO

DEG

0UTPLANE CIRCU

.809 E+06

.126E+0E .185E+06 .2 59E+ 08

.714E+07 .444E+05 .122e+O6 -251E+06 .438 E+06 .692E+06 .1 42E +0 7

.248e+o? .391E+07 .575e+07 .803 Er 0 7 .477E+O5 .131 Eio6

.270Er06

.4718+06 .743ErO6 .153E+07 .z66ErO7 .420

E+ 0

7

.618E+07 .863

€

+0 7

.J

.510Efo5

.421E+06 'f,E+06

.140E+06

.865Er06

.'l5l€+07

.238E+07 .489E+07

.28EE+06 .504E+06 -

7948r05 65Elo7

.t

Rotational Nozzle Flexibilities for Cylindrical Vessels

159

Table 6-1 Continued ROTr STTFF CALCULATION,

VESS€L TCK,IN

v€ssEL OD,FT

5.000 15.00c 15.000

.250

't

1

't

1.500 1.750 2.000

5. 000

.000 15.000 1 5 .000 'l 5 .000

15

.500 .7 50

.000

15.000 15.000 15.000 15.000 15.000 1 5.000 'l5 .00c 15.00c 15.000

-375

.855E+07 .135E+0E

32 .00 0

.375

.'198E+08 .27 7 E+ 08

.661E+07 .923E+07

.375 .51>

.'17 3E + 06

.37 5

.977E+A6

.576E+05 .159E+06 .326E+o6

32.000 .000 I6 -000

3 2

f6.000

36.000 36.000 36 .00 0

40.000 40.000 40.000

.500

.625 '|

.000

.000

1.250

40 ,000

40 .000

1

6.00

0

6.000 16.000 16.000 1 6.000 '| 6.000 16.000 1 6.000 16.000 16.000 t

't 6

.000

't6.000 '| 6.000 16.000 16.000 16.00 0

16.000 16.000 16.000 't6.000 1 6.000

1.000 1.250 1

.500

1.750 2

.000

1

.5C0 .7 50

.10/rEr08

.530E+06

.177E+o6 .363E+06

tl'l

.634€+06

"J

.5rt

,190F+07 .3008+07 .6168+Ol

.375

.108E+08

-319e+o7 .566E+O7 .832E+47

.192Ei06 .109

E+

07

.1708+08

.612E+O5

.100Er07 .?o5E+07

.438€+06

.2?9E+a7

.7 64E+O6

48.000 46 .000

.000

4E

.000

2.375 2.375 2.375 2.375 2.375 2-375 2.375 ?.175 2.375 2.375 3.500 3.500 3

.500

3-500 3.500 3.500 4.500 4.500 4.500 4.500

.2 50

.746E+O7

.1318+07

.000

4E

.500

2.000

.32?E+07 .50E8+07

.313E+08

.37 5

48.000

3.500 3.500

1.7t0

+06

.?13E+O6

.7 50

1.000 1.250

E

.897E+06 .184E+07

06

3-500

.500 .625

. 569

.7748+O5

1E

16.000

.449Er07

.?32E+O6

2. 000

.500

.9 658+07

-285E+07

48 .000

I 5 .000

16.000

.553E+07

IRCU

.250E+08 .348E+08

48.000 48.000

16.000 16.000

.171E +07 .2 69 Er A7 .152E+CE .221E + 08

40.000

1.750

.000

5

.4768+06

C

40 .000

15.000

15

.37

40 .000

,/.8.000

.000 .000

15.000

-375

.s75

15.000 15

32 .000

.500

1.500 1.750 2.000

OUTPLANE

LONGI

40.000 40.000

1. ?50

.000

TCKTIN INPLANE

2.000

1.000

5.000 15.000 15.000

NOZZLE ROT STI F IN.L8/DEG

6.000 36.000 36.000 3 6.000

. >uu

V€SSEL

STD

3

15-000

't 5 15

OD,IN

36.000

15.000 15.000 '| 5.000 t 5,c00

15 1

NOZILE

ClL.

4. 500

-5t>

.639

.375

.315 .15 4 .15 4

.154

.154

30E +08

.43?E +07

.205E+08 .301 E+08 .420E+08

.682E+Oz

.935E+04 .258E+05 .529E+05 .924E+05 .1 46E+06

.299E+06

.15 4

.5238+06 .8258+06 .121E+07 . t 69E+07

-154

.216 -2't6

.216 .216 .216 .216 .?16 -216

.?'t6

.237 .237 .237 .237

5;

.121E+07 .24EE+o7

+

.15 4

.154 .154

5r

07 .713E+ 07

-362E

.'l

.375

E+

.1168+08

.1008+08 . t 40E+08 .3'l2E+04 .859E+0rr .1 76E+05

.308E+05 .486E+05 .998E+05 .17 4E+o6 .275E+A6

.404E+06 .5 64E.

O

6

. 1l9E +05

.16LE+04

.3E3E+05

E0€+07

.128E+05 ,262 E+0 5 .45EE+05 .7?3E+05 .14EE+06 .259E+06 .409E+06 .601 E+0 6

.252E+07 .1E48+05 .507E+05 .104E+06 .'182E+06 .287E+06

.606E+05 .956E+05

.787E+05 .13EE+06 .217E+06 . 4 45 E+06 . 778 E+ 06 . t 25 E+ 07

-l

.840E+06 -6'l3E+04 .'l 69 E+0 5 .3478+05

ft

160

Piping Stress Handbook Table eFl

Continued ROTA V ESS

EL

OD,fT

VESSEL

TCK,IN

16.000 r 6.000 16.000 16.000

1.000

I 6.00 0

2. 000

16.000 16.000 16.000 16.000 16

.000

16.000 16.000 16.000 16.000 16.000 16.000

1.250 I .500 1.750 .250 .375 .500 .7 50

1.000 1.250 'l

.500

1.750 2.000 .?50

16.0 0 0

16.0c0

.500

16.000

-625

16.000 16.000

I .000

16.000

1.250 1.500

16.000

1

I 6.00 0

16.0C0

.750

2.000

16.000 16.000 16.000

16.000 16.000 16.000 16.000 't6.000 16.000 16.000 16.000 16.000 16.000 16.000 16.000 16.0c0 16.000 16.000 16.000 16.000

r6.000 'l6.000 16.000 16.000 16.000 16.000 16.000 16-000

-

z)u

.500

.625 .750 I .000 't

.2 50

1.500

1.750 2. 000

.250 .37 5

.500

.750 I .000

1.250 J.500 I .750 2. 000

.500 .625 1.000 1-250 1.500

1.750

16.000

1.000

2

.000 .37

5

.500

.625

vESSEL

NOZZLE NOZ2LE ROI STIF IN.L8/DEG ODEIIi TCK'IN INPLANE OUTPLAN€ CIRCU LONCI STD 4.500 4. 500 4. 500 4. 500

4.500 6.6?5

6.625 6.625 6.625 6.625 6.625 6.625 6.6?5 6.625 6.625

.?37 .237 .237 .237 .280 .280 .280 -280

.625

4.625 4.625 10.750 10 .750

10.750 10.750 10.750 10.750 10.750 10.750 10.750 10.750

-162e+07

.238r+07 .335E+07 .?79E+05 .770E+05

.145E+06 .298E+06

.280

.2 46E+ 07

.2E0

.506E+07 .369E+05

.280

.3?2

.322 .32? -322

.322

.156E +07

.362€+07

.t02E+06 .2C9

E

+06

.365E+06 .576E+06

.ll8E+07 .206E+07

.365

.3268+07 .479E+o7 -669Er07 .165E+05

.3 65

.1 28E+ 06 . 263E +06

.365

.460E+06 .7?5E+06

.3?Z

.322 .322 .365 .365 .365 .365

.36 5

.365 .365

.1 49 E+07

.37 5

.375

.179E+07 .3138+07

.3?5

-493E+Oz .7 25E +07

.000

1 4.00 0 1 1 1 1 4 .000

.339E+0 5 -696E+05

.1?2E+06

.192E}06 -394r+06

.688E +06 .109E f0 7

.160E+0? .223E+07 .155E+05 .4?7E+o5

.a77ErO5 .

l53Er06

.2128+06 .496E+O6

.316E+06 .551E+06 .8?2E+06

.13? E+07

.201E+g?

.28'lEr07 .185E+05

.291E+06 5968+06

-

.1048+07 .161E+07 -2428+O7 .337 E+O7

.375

.1018+06 .619E+05 .1 71 E+06 .350E+06

.2068+05

.175

.965E+06

.322E +o6

4.000 4.000 4.000

14.000 14.000 I 4.000 14.000 1 6.000 16.000 16.000 1 6.000 16.000 16.000

.123E+05

.5148+05 .1058+06 . 1 84 Ef06

.559Er05 .'154Er06

12.?50 12.?50 12.750 1Z .750

.121E+O7 .1 69 E+ 07

.867E+06

.375 .375 .3?5

.37'

.521Er06 .821E|06

.260E+07 .4108 +07 .603E+07 .8 428 +07

12.75A

12.750

.257E+O5

.280

.375

12 -750

.111E+07 .932E+04 .9?1E+05

12 .7 50

12.750

.795E+O6

.4368+06 .894Er 06

?80

.t2?

8

.343E+06 .5 4l Ei06

.276F,+O6

.

a .625

4.625 I .625 8.625 4.6?5

.196E+06

.1038+07

.527Ero5

.322

I .625

.589E+06

. 158E+05

.625

8

'14

16.000 16.00c 16.00c 16.000 16.000 16.000

t6.000

STrrF CALcULATIONT CYL.

.6'l2E+06

.375 .375

. 569 E+0 5

.1 l7E +06

.2848+06

.1988+07

.660€r06

.546Er07

.182E+07

.3 46E +07

.115€+07

.6c2E+07

. ?67E +o7

.1 'l ?E+08

.7'l5E+05

.373E+07

.2f8E+05 .656E.05

,375

.197E+06 .404E+06

.375

.706e+06 .111E+07

.371E+O6

.375

.229E+07

.7 62E+06

.135E+06

.235E+06

Rotational Nozzle Flexibilities for Cylindrical Vessels

161

Table 6-1 Continued ROIA STIFT CALCULATION, CYL. VESSEL

VE

OD,FT

TC

SSEL II

16.000

1-250

16.00 0

1.5C0

6.000 16.00c 16.000 16.000 't

.750 2.000 1

.250

.500

16.0 00

16.000 16.000 16.000 16.000 1

6. C00

16.000 16.000 't6.000 I 6.000 16.000 'l6.00

0

t6.000 t 6.000 16.000 16.00

0

16.000 16.0 0 0 'I 6.00 0

16.000 16.c00 16.000 16.000

.625

J

.000

OD,I

l6 ,000 't 6.000

-153E+06 -?67E+o6

E. 000

.259E+ 07 .4538 +07

.750 1 .000

6.00 0 16.0 0 0

'| -

1-?50

1.500

.711E+07 .105Er08

r

. 147E+0E

20 . c00

.906E+05 .250F+06

20 .000

.895€+06

20,G00

-'l 4'l

20 .000

20.000 20.000 20 ,000

22.aao 22.000 22.000 ?2.000 22.000 2a.000 22.000

.500

1

.7 50

24.OOO

16.0C 0

t6-000 16.000 t 6 .000

16.000 16.000

1

.000

.250 I .500 1 .750 1

2

.000 .250

.799E

.37 5

.117E+08 .164E+08 .1C0E+06

.375

16.!00 16.000

1

.375

.302E+06

16.000

7.25A 1.500

16.00

1

.1t0E+06 .62'l

E

+

o6

.375

26-000

.37 5

.42't e+o6 .864E+06 .151E+07

.?38E+o7

.3508f07 .4898r07

-3028+05 .832E+05 .'171E+06

.298E +06 .471E+ 0 6

.966E+06 -169E+07 .266E+O7 .391E+0? .547E+07 -134E+05 .920E+05 .189E+06

.330€+06 .5209+06 .107E+07 .'l87E+07 -29 4E+07

.433E+o7

.604E.07 .366E+05 .101E+06 .207E+06

.361E+06

.35'lE+07

.'117E+07 .2018+Oz

.570E+O6

.968E+07

.3238+07

.142E+08 .199E+08

.66?E.07

.1198+06 .329E+06

.6758+o6 .1'l6E+07 -375

.431F.D7

.108E+07 .1718 + 07 .613E +07

.000

26.000

.567E+06 .990E+06 .156F+ 07 .3?18+ 07 .560E+07 .883E+07

.s75

2,6.000

26

.000

1

07

.130E +0E .1 81 E +08

26.000 ?6.000

16.000

+

.?76E +06

24.000 24.000

24.000 24.000 26.000

07

.54>

26 -AOO

16.00 0

6.00 0 '16.000

24. ilo0

E+

.290E+07 .506€+07

22.OD1

16.000 16.000

6.000

.512€r06

20.000

24.000 24.000 24.000

16.000

.375

E. 000

22.000 22.000

16-000

.458€+06

1E.000

750 2. 000

1

.1298+08 .B l0Er05

.126E+07

18.000 'l

.3098+07

.801E+C6

8

20.000

| .000

.?1OE+o7

.000

18 .000

.580

.7 50

.131E+o7

.6J0E+07

.270E +O5 .7 44E+O5

.250

.500

.399E+07

,22fE+06

18.000

1

CTRCU

-375

t 8 .000

1

OUTPLAIIE

.9 26E+ 07

8.000 20.000

1.750 2,000 .250

ICK,IN INPLANE LONGI STD

.375

2. 000

1.250 1.500

NOZZL€ ROT SIIf IN.LB/DEG

'l6.000

18.000

1.750

N

16 .000

1.250 1.500

16.00 0

16.000 1 6.000

NOZZLE

X,I

VESSEL

.186E+07 .382E+07 .667E+07

.47 4E+07 .398E+05 .110E+06 -225E+06 .393E+06 .620E+06

.127E +07

.222E+07

26.OOO

.351E+47

.750

26.000

.'l05E+0E

16.000

2. 000

26.OOO

.216E+08

16.C00 16.0 0 0

-250

-'l29

06

.375

28.000 28.000

.7208+O7 .430E+05

.500 .6?5

28 .000 2E

.000

.355E+06 .729E+06 .127E+C7

.243E+06 .425E+C6

.000

.412e+ 07

.6705+06 .137E+a7

.7218+07

.240E+07

0

16.000 16.000 16.000 16.000

16.000

.750

I .000

1.250

28.000 2E

28.000

.t55E+08 E+

.201E+07

-516E+O7

.1'18 E+06

I {

it

I .l

162

Piping Slress Handbook Table 6-1 Contlnued

VESSEL

0DeFT

16.000 16.000 16.000 16.000

t6.000

16.000 16.000 16.000 16.000 16.000 16.000 16.00

0

6.000 16.000 16.000 16.000 16.000 1

f6.000 16.000 1

6.00 0

|

6

.000

16.00 0

16.000 16.000 t 6.000 16.000 16.000 16.000 16.000 16.000 16.000 16.C00

16.000 16.000 16.000 16.00c

r6.000 | 6.000 16.000 1 6.000 16.000 16.000 16

.00 0

16.000 16.000 16.000

t6.c0c t6-000

16.00c 16 .000

16.000 16 .00 0

16.000 17.000 17.00c 17.000 17.00n I 7.00 0

17.000

nOft STIFf CALCULATIONT CYL' VESSEL NOZ ZLE ROT STIF IN.LB/DEG NOZ Z LE VE SSEL IcKTIN It{PLAt{E 0UTPLANE 0DrIN TCk,ll{ CIRCU LONGI STD I . 500 1.750 2.000 .250 .375 .500 -625 .750 I .000 1.250 1.500 1.750 2.000 .250 .375 .500 -625 . ?50 I .000 1.250 1.500 1 .750 2.000 .250 .375 .500 .625 .750 1.000 1.250 I . t00 I .750 ?.000 .250 .375 .500 .625 .750 1.000 I .2 50 I . 500 1.750 2.000 .250 -375 .500 -625 -750 '| .000 't.250 1.500 1-750 2.000

.250 .375 . 500 .625 .750 1 .000

2E.000 2E.000 2E.000 30 -00 0 50.00 0

0.000 30.000 30.000

3

30.00 0 30.00 0 30.00 0

30.000 30.000 3 2.000 32.00

0

e.000 32.000 32.000 3 2.000 32.000 3

52.00 0

2.000 52.000 3 6.000 36-000 36.000 3 6.000 3

36.00

0

6.00 0 36.00 0

3

36.000 36.000 36.000 40.000 40.000 40.000 40.000 40.000 40.000 40.000 40.00 0

40.000 40.000 46.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 48.000 2.375 2.375 2.375

2.375 2.375 ?,375

.375 .375 .375 .375 .375 .375 .375 -375 .375 -375 -375 -375 .375 .375 .r7, -375 .375 -375 -175 -375 .375 .375 -375 .375 -375 -375 .t75 .375 .375 -375 .375 .375 .375 -315 -375 .375 .375 -375 -375 .375 .375 .375 .375 -375 .375 .37t .375 .375 .375 .375 .375 .375 .375 .154 .154 .154 .154 .151 -154

.1148+08

.3798+07

.167E+08 -235E+08

.778E+07

.138E+06 .

f,82E+06

.783E+06 .137E+07 .216E+o7 .4438+07 .774E+O? .1 22E+08

.'l80E+08 .251E+08

.1{EEr06 .408E+06

.8378+06 .1468+07 .231E+07 .47 4E+07

.828Ef07 . 131 E+06

.192Er08

.268E|08 .'l C7E+O6 .461E+06 .946E+06

.557 E+O7

.462E+05 .127E+06 .261 E+06

.4568+06 .719e+06

.148Er07 . ? 58

E+07

.407Er07 .598€+07 .636E+07 .493 E +0 5 -136E+06 .279E+O6

.488€+06 .769 E+06

.'l588+07

.27 6E+07 .435 E+0 7

.640€i07 .893Er07 .557E+05 .154E+06

.315Er06

.'l65E+07 .2618+07

.551 Er0 6

.535E+07

.17AE+07 -31?ErO7 .491E+O7

.9 35E+C7 -14?E+Oz .217E + 08

.303E+08 .186E+06 .514E+o6 . '105 E+ 07

. 1948+07

.291E+oz .596E+O7

.'l04E+08 .1648+08

.2 42 E+08 .337E+08 .225E+O6 .619E+06

.127t+O7 -22?ErO7

.350E+07

.8698f06

-7238+D7

.101E+0E .621E+05

.'l 71 E+06 .351Er06

.614E+06 .968E+06 .199E+07 .3478+O7

.548Er07 .805E+07 .112E+08

.7 498+OS .2068+06 .424E+O6 .740E+06 .117 E +07

- 291 E+08

.2408+07 .419E+07 .660F+07 .971E+07

.4078+08

.136€r0E

.907 E+04

.302E+04

.719e+O7

.1?6E+08 .'l9EE+08

.250€+05

.51fE+05 .8978+05

.1 r.1E+06 .290 E+ 06

.E338104 .171E+05

.299€+05 -471Er05

.968 E+0 5

Rotational Nozzle Flexibilities for Cylindrical

Vessels

163

Table 6-1 Continued ROTA STIf

VESS€L TCK,IN

VESSEL OD. FI

17.0

0

0

17.000 1 7.000 I 7.000 17,000 17.000 17.000 17.00c 17.000 't 7.000 17.00 c

17.000 17.000 17.000

1.250 I .500 1.750 2.000

1 1 1

0

17.000 17.000

17.000 '| 7.000 17.000 17.000 17.000 17.OOO

17.000

17.000 t 7.000 17.000 17.000 17.000 17.000 17.000 't7.000 17.000 17.000 t 7.000 .000 17.000 17.000 17.000 17

1

7.000

17.000

7.000 17.000 17.000 17.000 17.000 1

17.C00

ION,

.15 4 .15 4

.500

.675

4

.500

.500 4-500 /. .500

.1248 +05 .255E+05 .445E+05

.2'l0E+06

.701E+05

.432 €+06

.144E+O6

.,.500 4. 500

6.625 6.625 6.625 6.625

.250 .500

.6?5 .000

1.500

.375 .500 .625 .750 I .000 1.250 r.500

1

.000 .250

1.500 .250

.375 .500

.625 1.000

1.250

.33 6E +0 5 .588E+05

.27EE+ O6

.9?7E+ 05

E

+

07

.1758+07 .244E+07 .4928+05

.571E+06 .997F+ E6 .157 E+07

.231E+07

.190E+06 .332€+06 .524E+06 .771E+O6

-3?3E+07

.108E+07

.271t+05

.904E+04

.717E+05 .1538+06

.51',|E+05

.268E+06

.2 49E+05

.893E+05

.152E+07 .239E+O7

.797E+O6

6 -625

.280

.3518+07 .4918+07

- 1178+07

.625

.3?2 .3?2 -322

.625

8.625

I .625 I .625 8.625 10.750 10. 750 10 .750

750

I 0.750

,28 0

10-750 0. ?50

I 0. 750

12.750 12.750 12.750 1?.750 12.750 12 -750

12.750

.358E+05

.987Er05 .203E+06 .35 4E+O6

.164E+D7 .119E+05

.329€+05

.676e+O' .118Er06

.3?2 .3??

.5588+06

.1E6E+06

.1 15L+ 07

- 3E2E

.122

.Jt6E+07 .464E+ol

.105E+07 .1558+07

-322

.649E+07 .451E+45 .124E+06 .?55E+06

.t22 .32? .365 .365

.2oOE+ol

+06

.668E+06 .216E+07

.'l 50E+05 .414E+05

.851E.05

.1 49 E +06

.365

.4 468+06 .703€+06 .111e+07

.365

.25?E+ 07

.2348+06 .48'l E+ 06 .841E+06

.39E€+07

.133E+07

.365

.585E107 .E17E+07

.272E+A7

0. 750

'10. 750

.4236+06 .668€+06

.375

.542€+05 .149E+06

-375

.1958+07 -181Er05 .498E+05

.3078+06

.102Er06

.536E+06 .846E+06 .171E+07

.179E+06

.303€+07

1\

-t64E+05

.28 0

a

1

.101 E+ 06 .176E+06

.119

6 -625

8.625 8.625

'|

.178E+05

.252 E+06 -397E+06 .583E+06 .E15E+06 .595E+04

.755E+06

6.625

10 -

1

.280 .280 .280 .280

.133Er06

.4508+04

.'l41E+O6 .289 E+06 .505E+06

8

.375

-237

.'135E+05

.280 .?80

6.625

2.000

2.000

.237

.2EO

.7 50 1

-2't6

4

1.750 2.000

.592€+06

69 E+06 E + O6

.37 ?E + 05 .7 64e+05

-216 .?37 .237 .237 .237 .237

1.000 1.250 1.500

.1t8E+07

1

.?16

.216

4.500

.

.547 E+O6

J

.500

.507E+06

.'l64E+D7

.154

3.500

4

0UTPLANE CIRCU

.'t54 .216

.2',16

4.500

IN.LB/DEG

.267

3, q00 .500 4 .500

€L

.800E+06

.500

5.500

VE SS

ZLE ROI SIIF I NPL Allt STD LONGI

.500

.250

L.

TCXTIN

3

3.500

CY

NOZ

.000

.500 3 .500

.750

17.000 17.000 17.0C0

LCULAT

.216 .216 .2't6 .?'t6

17.OA0

t7.000 ,7.000

.500

5

2.00 0

7.00c 17.000

7.00

2.375 2.375 2.3?5

.500

1.750

r

't

OD,IN

3.500

17.000

17.000 17.000 't7.000

CA

NOZZL€

3

17.0 00

17.000

F

.?82E+O 6

.579€+06 .101E+07

!

164

Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCULAIION, CYL. VESSEL

v€ssEL

OD,fT

17.000 17.000 17.000 17.000 I 7.000 1

vE TC

1.500

I .750

?.000

.250

7.00 0

.625 .750

17-000

17.000 17.00c 17.000 17.000 17.000 17.000 17.O00

17.c00 17.000

I .000

1.250 I .500

1.750 2.000 .250 .37 5

17.C00

.500 .625

r7.000 17.000

I .000

17.AOO

1. 500

17.000 I,

i: "

'17.000

; I li ii

7.000 17.000 17.000 17.000 17.000

)rt

17.000 17.400 17.000 17.000

a:

l.

ssEL K,IT{

't

17-000

17 .00 0

1.250 1

.500 .625 .7 50

I .000 '| 't

17.0t/0

1

.37 5

't

14-000

14.000 14.000 14

.000

r6.000 16.000 I 6.000 1 6.000 1 6.000 16.000 16.000 16.000 16.000 16.000

.375

.375 .37 5

.375 .375

.000

.500

.625 .750

I .000

.250 1.500 1

1.750 2.000 .250

.375 . t00 .625

t7.oac

.7 50

I .000

1.250 1

1

8. 000

8.000 't8.000 18.000 18.000 1

.375 .37 5 .37 5

-375

.3 75

.375

.37 5

.5C0

.375

.000

.375 .375

20.000 20.000 20.000 2

0

.375 .37 5

?2 .000

22.000 ?2 .OOO 22 .00 0 22 .000

22.000 22.000 22.000 22.000 22 .000

.375

24

.000

24.000 24.000 21-OOO

.37 5

.192E +07

.336E+07 .529E+07

.375

24-OAO 24.OOO

.3? 5

.375

.200E+05 .552E+05 t 3E+ 06 E

+06

.312E+06 .640E+06 .112E+07

.176e+07

.7 78E+ a7 -109E+08 .693E+05 .191E+06 -39?E+06 .685E+06

.259 e+07

-222E+47 .388 E+07 .611E+A7 .E99E+07 .'125E+08

- 7t9E+O6

.362E+O7

.231

E+0 5

.6378+45 .13'lE+06 .??ae+o6 .360Er06 .1298+07 .204E+07 .300E+07 .418E+07

.786E+O' .2178+06 .445E+06

.26?E+O5 .722E+O5

.777E+06 .123E+ 07

.259E+06 .40EE+06

07

.838E+06

07 .69t8 + 07

.146e+O7

.102E+C8 .14?E+08

.340E+07 .47 4E+o?

.439E

+

.? 42E+ o6 .49?E+06 .868E+06

.137E+07 .281E+07 .491E+Oz

.l

488r06

.231E+O7

.293E+05 .607E+05 .'166E+06 .2 89

E

+06

.457 E+O6 .937f+O 6 .164E+Oz

.775E+ 07

.258E+07

.114E+08 .1 59E+0E .972E+05 .26E€+06

.380E+07

.550F+06

.5308+07

.3248+O' .895E+05

.183Ef06 .520€+06 .505E+06 . t 04 E+07

.5 4te+07

.lE1E+07

.857E+07 .'l26E+ 08 .176F+0E .106E+06

.286e+O7 .42OE+07 .586E+o7 .355E+05 .978 E+05

.2938+46 .6028+06 .105E+07

.000

24

.327E+O7

. 198

.311E+07

.37 5

.159E+07

.234E+o7

.593E+06 .936E+06

.151E+O7

21.OOO

CIRCU

.1

.960E+06

.37 5

OUTPLANE

.340€+06

.8 79E + 05

.000

20.000 20.000

.1 65 E+06

. ?5?E+

18.000 18.000 20.000 2 0.000 20.000 20

.478E+07 .703E+07 .982E+07 .6008+05

.108F+07

.37 5

1.250 1 .500 1.759 2.000 .250 .375

17.000 17.000 17.000 17.000 17.000 17.000 17.000

.375 .375

E.000

.7 50

7.000

17.000 17.000 17.000 17.000

-375

1

1

17.C00

4.000 14.000

.375 .375

.500

.525

'17.000

14 . C00 14 .000 14 -000

TCX,IN INPLANE STD LON6I

.375

,375 ,500

7.000

17.000 17.000 17.000 | 7.000 I 7.000 't 7.0c0

12.750 12.750 12.750 '| 4.000

NOZZLE ROT STI F IN.LE,/DEG

18 .000

t 7-000

t7.000

N

.2 50

1.750 2.000

I 7.000

17.O00

L E

OD,I

1E.000 .37 5

17.000 ,|

.750

2.000

t'l0zz

.166a+07 .341E+Ol .595E+07 .939E+07

-2O1E+O6

.351E+06 .553E+06

.114E+07 .'198E+Oz

.313E+O7

Rotational Nozzle Flexibilities lor Cylindrical Vessels

165

Table 6-1 Continued

SIIfF CALCULAIION, CYL. VESSEL NOZZLE ROT STIF IiI.LB/DEG VESSEL NOZZLE OUTPLANE T CK,I N INPLANE TC(,IN OD,II{ CIRCU STD LONGI ROTA

VESSEL

OD,FT

17,0 00

17.000 't

1.750 2

?.0 00

17.000

t 7.00 0

17.000 1 7.000 1 7.000

t 7-000

7.000 17.000 '| 7.000 17.000 1 7.000 17.000 17.000 17.000 17.000 17.000 17.000 1

-750

26.000

.150E+08 .2'l0E+0E

-500E+07 .698E+07

2.000

.500 1.0c0 1.?50 1-750 2.000 -z>tJ

.500 .000 .7 50 2. 000

.500 .6?5 .000

1.25O

1.500 1.750 2

.000

.500

1

.250

I .500

7.00 0

.500

17.000 t 7-000

17.000 17.000

.647

1.754 2

.000

.250 .375

I .000 't .2 59

't.500

E+

07

+06

.12ta+06

.417E+O5

28 .000

.345E+06 .7 Q7E+06

2E.000

.124E+07

.115E+06 .236E+06 .412E+06

28.000 28.000

.650E+06

28.000 28 .000

.195E+07 .400E+07

28.000 28.000 28 .000

.699E+07

.233E+o7

.375

.'110E+08 . t 62E+08

.36EE+07 .540E+07

28.000

.375

30 .00 0

-375

30.000 30.000 30.000 30.000 30.G00

30.000 30.000 30.000 30.000 .000

.375 -375

.375

.226E+08 .154E+06 , 370E+ 06

.760€+06 .133E+07 .2098+07 .430E+07 .751E+07 .'1188+06

.3?5

.375

.17

4E +

08

.243Er08 -144E+06

32.OOO

.396€+06

3 2

-E t 2E+06

.000

32.000 2.00 0

52.000 32.000 32.000 5

2.00

.375 .375

J2.000 56.000 3 6.000 36-000 56 .000 36

.000

36.000 3 6.000 J6.000 36.000 40.000

.375

40.000 40-000 40-000

40.000 40.000 40.000 40 -000

.375 -375 .375 .3?5

.375

.442t+O6 .698E+06 .1438+07 .?50E+o7 -395E+07

.5818+07 .8118+07 -479 E+05

.132€+06 .?7'l E +o6 .475E+06

.127E +08

.422E+O7

.26EE+07

.6218+07 .E67E+07 -541E+05

.4 47E+A6

.1tt9E+O6

.918E+06

.306E+06

. 160E+07

,534E+06

.253E+07

. E43E+06

.519

.'173E+07

E+

07

.907F+07 . t 43E+08 .2't0E+08 .29 4E+ 08 .181E+06

40 .000

.7518+07 .448E+05 .123E+06 .253E+06

.7 46E+06 .1538+a7

.16?E+06 -5()

.133E+O7

.142E+07 .224E+07 .460E+07 .803€+07 .'186E+08 .260E+0E

0

36.000

17.000 17.000 1 7.000 17.000 17.000 7.000

.37OE+ 07

26 ,000

3

't

.37 5

26.OBO

32

17-000

7.0C 0

- 601E

1

t . t)00

1

.1808+07 .1028+08

17.000 17.00c 17.000 17.000

1

.218E+06 .381E+06

?6 -OOO

17.OOO 17.OC0

't

.106€i06

.655E+06 .114E+07

.500

17.000 17.000 17.000 1 7.000 17.000 17.000 17.000 '17.000

.319E'06

1

7.000

7.0C 0

.37 5

.123E+07 .?16E+07 .340a+07

7.C00 17.O04 1

26 .000 26 . C00

.460E+07 .642E+o7 .386€+05

26 -OOO

'|

17.000 17.000

.193E+0E .116E+06

t .000 1-?50

17.C00 1

.138E*08

24.000

26.000 26.000 26.000

't

17.000 17.000 17.0c0 17.000

? 4 .OOO

.500

I 7.00 0

7.000 17.000

.000 -250

.302E+07 .4778+07 .7 0'l E.07 .979E+o7

-6038r05

.4988+06 .10?E+07 .179E+07

.166E+06 .341Ea06 .596E+06

.282E+07

.939

F+

C

6

07

.193€+07

.101E+08

.337E+O7

.579E

+

.1598+08 -234E+08

.551E+07 .78'lE+o7

rf

:l :

166

Piping Stross Handbook Table 6-1 Continued

R0lA STIFF CAI-CULATION, CYL. VESSEL VESSEL

OD,'T

17.000

ICK,IN

2.O00

17.000

.250 .315 . t00

I 7.00 0

-625

t 7.000 I 7.0 00

17.000 17.000 17.0 00

.7 50

1.000

1.250 I .500

48.000

18.000

.250 .375

2.375 2.375 2.375 2.375 ?.375 2.375 2.375 2.375 2 .375 2.375

.00 0

18.000 1E.000

tE.000 1

E.00 0

18.000

.500

.625 .750 1.000 1 .250 1

.250

.500

1E.000

18.000 18.000 18.0C0

16.000 18.000 't6.000 16.000 18.000

.500

1-750 2.000

I 8.0 00

iiI

4E.000 4 8 .000 48 .000

4E-000

t8.000

ir

40.000 48.000 48.000 48.000 48.000

1.750 ?.000

18.0c0 18.000 18.000

li

0zzLE OD,II{

17.000 17.000 17.000

18

i,:

vEssEL

.750 1.000 1.250 1.500 1.750 2.000 .250 .37 5

1E.C00

.500 .625

18.000 1E

.00 0

16.000 16.000 18.000 18.000 1E

.00 0

1E.000

.7 50

.000 1 -250 1

1.500 1 .?50 2.000

z>u .37 5

18.000

.

'tE.000 18.000 18 .0 18 .0

.500

.625

00 00

-7 50

18.000 't6.000

1

16.00 0

't

16.000 18.000 '16.000 18.0 0 0

'| 1

.000

3

.500

3.500 3.500 3. 500 3 .500 3 .500

3.500 3. 500 3.500 3.500 4. 500 4. 500

4. 500

4.500

4. 500 4 .500

4.500 4. 500

4.500 4.500 6-62> 6 .6?5

6.625 6-625 6.625 6-625

.250

6.625 6-625 6.6?5 6.625 4.625

500

8.625

.250

.500

.750

2. 000

I E.000

48.000

-

.625 .7 to

18.000 18.000 18.000

1

.000

18 .00 0 18 .00 0

1

.500

1.250

.6?5 8 .625

8

a

.625

a.625 4.625

NOZ2LE ROT SII f II{.LB/DEG OTJTPLANE T CK,I N IIIPLA E

SID

LOIIGT

CIRCU

.3278+08 .218E+06

.109E+08

.601E+06

.200E+06

.123E+ 07

.411E+O6

.3? 5 .37 5

.215e+07 .540E+07

.718E+06

-375

- 698E+07

-375

.'192E+08

.375 .375

.375

.375 .375

.'l22E+08 .283E+ 0E .395 E +08

.7?7e+Oj

.1138+07 .2t3E+O7 .406E+0? -641e+O7 .942E+D7 -'13

2

E

+08

-88?E+04

.2948+O4

54

.2438+05

.81 08 +0 4

-154 .154 .154

.499E+05 .871E+a5 .157E+06 .282E+06

-166Er05

.493E+06

-164E+06 .2 59 E+06 .381 €+06

.154

.t

.'154

.154 .154 .154 .154

.216 .216 .216 .216 .216 .216 .216 .216 .216 .216 .237 .237 .237 .237 .?37 .237 .217 .237 .280 .280 .28 0

.280 .280 .280 .280 .280 .280 .280

.322 .322

.778E+06 .111E+A7

.372 .322

.9418+05

60Er07

.sf,?E+06

.131E+05 .362E+05 .742E+05

.437E+O4

.130E+06

-43?E+O5

.t

.205E+06 .420E+06 .733E+06 .1 168+07 .170E+07 .237E+07 . l73E +05 .478 € + 05

.121E+05 .247E+O5 .682 €+0 5 .'140E+06 .z 44E+O6

.386E+06 -567Er06 .792E+O6 .

5 78E

+04

.159E+05

.9818+05 .1718+06 .2708+o6

.327E+O5

.555E+06 .969F+06

.22tE+97

-185E+06 .321E+06 .510E+06 .7 49E+06

.311E+07 .263E+05 -726e+Os ,|

.1 05E +07 .8 78 E+04

.2428+O5

49E+06

.497Er05

60E+ 06

.868E+05 .137 e +O6 - 2El E+06 .491E+06

.153E+07

. .

2

.411E+06

.843€+06 .147E+O7

.232e+07

. 571 E+0 5

.901E+05

.477E+Ol .348Er05

.774E+06 .114E+07 .159E+07 .1 l6E+05

.9 59E + 05

.320E+05

.342E+07

.197E+06

.322 .322 .3?2

.?90E105 .4 58 E+0 5

.314E +06

.543E+06 -111E+07

.195E+07 .307E+07

.657E +05

.1158+06 .18'l E+06 .371 E +06 .6 49 E +06

.102F+07

Rotational Nozzle Flexibilities for Cylindrical Vessels Table 6-1 Continued ROTA STIFF CAICULATION, CYL. VESSEL

vEssEL TC K,I I'I

VESSEL

00,fT

0zzLE OD,I N

NOZZLE

TCK,IN STD

0

1.750

18 .00 0

2,0 00

1E.00

18.000 1E.000 18.000

18.0

't

't

I C. 750

-ol>

10

.000

18 .00 0

'1

18.C00

1.750 2.000

. 500

1E . C00

18.00c

.375 .500

1E.000 1E.000 18 .000

18.000 '16.000

't8-000 1E.000

18.000 16.000

.750 1 1

18

16.000 1E.000 .000

18

?8.000 't8.000 1E.000 18-000

18.000 't I .000

.375 .500 .625 .750 .000

2. 000

.250 .37

5

.500 -750

1.000 1.250

t.500

-250

.7 50

r .000 't -250

?-000

-

000

18.000 18.0 00 18.0 0 0 1E.0 00 18 ,000 18 .0 00

18.000

12 -750

. 169F+07

12 .750 12 .7 50

11-OOO

.750

16 .00 0 18

.'l45E+06 .2968+06

14.000 1 4 .000 14 .000 1 4 .000

.500 .62

5

.750

1 .000 1.250 1.500 1,750

14

1

6

.375

.295E+07

.9E2E+06

1E

.000

1E .000 1E.000 1E .000 I E.000

18,000 20.000 20.000 20.000 20.000 20.000 20.000 20 .000

20.o00 20.000

+06

E

+

07

-515E+a7 .7 56E+ 07 .106E+08

-5ft

-375

.37 5

6

.155E+07 .22EE+Ol .318€+07 -195E+05 .536E+05 .110E+06 .192E+O6

.303E+06 .622E+O6 .1098+O? -1?2E+07 .?52E+O7

.352E+07 .619E+05

.666E+ A6 . 105E+07

.8738+07 .J?2E+08 .7 64E+05

.127E +O6 .222E +06

.350E+06 .719 E+O6 .126E+07

.'f98E+07 .291E+07 .106E+07 .2558+05

. 210E+ 06

.702E+O5

.432E+06

.144E+o6

,755€+06

.375

+O

.225E+O5

-594E+E7

-375

-5 62E

.186E+06 .3E1E+06

.377 E+07

.375

-27 4E+o6

.67 4E+05

.2168+07

18 ,000

18.000

.577t

.326E+07

.000

18.000 1 6.000

05

.3108+06 .1P'7

.000

t6-000 '| 6.000

+

.910E+06

.375

.9948+05 .'17 4E +0 6

.161E+06

16.000 16

-129E +07

.189E+07 -265E+07 .17 6E+Os .4E4E+05

.521E+06 -E22E+o6

.9 5 4E+07

.000

16.000 1 6.000 1 6.000 1 6.000 16.000

-468E+06 .817E+06

.527Er05

.750 12.750 12 .750 12.750 12

1

tE.000

1E.000

.79LE+07

12 -750

1.5C0

1.?50

1.500 1.?50

16 .00 0

I 0. 750

14.000 't 4.000 't 4.000

1

1E.000

18-000

.568E+07

12.750

-2288+06

.387E+ 07

10 . 750

- 5648

2. 000

t 6 .000

.245E+07

.375

1E.00 0

18.000 16.000

.365

I 4 .000

1-750

'18.000

10 .750

-114E+O6

.140r+07

.000 .250

2

.403€r05 ,827Er05

.24E8+06 .433E+06

.4658+07 .683E+07

18.0C0 1E.000

.146E+05

.375

.000 .000

.000

.438 E +05 .121E+06

.683 E+06

.750

-150E+07

.210E+0?

.365

0

CIRCU

.6J08+07

.750 10.750 't 0.750

I

OUTPLAT.IE

.1512+A?

'12.750

t8.000 r8.000 18.000 18.000

.000

F IN.L8/DE6

INPLANE LONGI

.250 1.500 1.750

1E.000

tE 't 8

0.750

.500

00

18.000

.322

10 . 750

18.000 18.000 1E.000

a.ol>

ROT STI

.119 E + O? .? 44E+07 .427E+07

-252E+06 .397E+06

.8'l5E+06 -142E+O?

-674t+e7

.225E+07

-99oE+07 .'138E+08

.330E+07

.235E+06 .483 E+06 .844E+06

.785E+05 .161E+06

. 1 33E +07

- 4 44E+06

.854€+05

.?738+A7 .477?+07 .753E+07

.11tE+08

- 461E+O7

.2858+05 .

z

8'l E+06

.9t'lE+06

.159E+07 .251E+o7

.369E+07

167

168

Piping Stress Handbook Table 6-1 Continued R0TA STIFF CALCULATI0NT CYL' 0DufT

VESSEL TI(TIN

3.00 0

2.000

VESSEL

1

2? -OOO

18.0 00

13.000

.500

18.000 1E,000

.750

18.C)00

18.000 18.00c 18 ,000

18.000 1b.000 18.000

OD,IN

20 .000 22 .00 0

.250

18.000

NOZ2LE

r.0c0 1.250

22.000 22.000 22.000 22.OOO

22.000

1.500 1.750

22 -000

.000

22 -OOO

2

22

.000

24.000 24.000 24.000 24.000

18.C00 18.0 00

.500

1E.000 1E.000

-750

24.DAO

1.000

1.2t0

18.000 18.00c

1.500 1.750

24.000 24.000 24.000 2/..000 2 6.000

'tE.0G0

18.000

2. 000

24 .000

1E.0 00

.250

18.000 1E.000 1E.000

5

?6.OAO

.500

26.000

- 750

I .000

26-000 26 ,000

18.000 18.00c 't8-000

1.250

.500 1.750

26.000 26.000 26.000

.000

2-000

1E-000

1E.000

1E

't3.000 18.000 18 .000 1E.000 18 .000 16.000 13.000 16.C0C

18.000 't8.000 18.C00 18.0U 0

16.000 18.000

.37

.625

1

.?50

28 .000

.500

E.000 28.000

.625

2E-000

.750

28 .000

.000 1 .250

28.000 2E.000

'I

1.500 'l ,7 50

?.000

.250

.375 .500

28.000 28.000 28.000 30.000 30.000 30.000 30-000

.750 .000 .250

50.000 30.000 30.000 30.000 30.000

2.000 .250

30.00 0

.500

32.000

18.000 18.000 16.000

18.000

18.000 18.00c 18.000 1E.000 18 .000

1

16 .00 0 18.00 0

1

t6.000

26.000 2

18.000

18.000 18.00c 16.000

26.OOO

1

.000 32 .000 3 2

.625

3? .OOO

.000

32 .000

.250

.500 1-750 2 .000

32.000

3 2.00 0 3 2 .00 i:J 3 2 .000

32 .000

VESSEL

f IN.L8'/DEG TCX,IN TNPLANE OUTPLANI CIRCU LONGI SID

NOZ2LE ROT STt

.375 .15 5E + 08 -375 -944E+05 -375 . ?60E+06 .375 .5348+06 .375 .933 +0 6 .375 .1478+O7 .3ZS .3OZE+07 .3?5 .528E+07 .3?5 .8 33E + 07 .375 .122E+08 .375 .171E+08 .375 .103Er06 .375 . 285 E+ 06 .375 .585E+06 .375 . 102E+07 .375 .161E+Ol .3?5 .331E+07 .375 - 578E+07 .375 .91?E +07 .375 .134E+08 0E -375 . 1872 E+ -375 .1t E+06 .375 .3',10E+06 .375 .636F+06 .375 -'l11Eto7 .375 -115E +O7 .3?5 -3608+07 .3?5 .629E+07 .375 -992a+O7 .375 .146€+08 .3?5 .204E+0E 06 .375 .122E++06 .375 .33 5E -375 .667E+06 .3?5 -12o8+oz .375 .139E+07 .375 .5898+07 -375 .1C7E+08 .375 '679E+Q7 .375 .1 58E +08 .375 .220E+03 .3?5 ' l31E+06 .375 .360E+06 6 .3?5 .7 3E Elo .375 .1298 +o7 -3?5 .204e +A7 .375 .4'l8 €+ 07 -375 .730 E+ 07 .3?5 .1 1 5E+08 .375 .169E+08 .375 .236E+08 .375 .1169 + 06 .375 .3R5€+06 .3?5 .790€+06 -375 - 133 5+0 7 .375 -?18E+O7 .375 -4t ?E+O7 .375 .760E+07 .37, .123E+08 .375 .181E+08 -375 .253E+o8 F

.515€+02 .3'l5E+05 .867E+05 .178E+06

.311Fr06 .491E+06 .101E+07 .17 6E+07

.2788+07 .408E+07 .570E+07

.345€+05 .950E+05

.'t95E+06 .3418+06 .53EE+06

.1'l0Ei07

.1938+07 .304E+07

.447E+07 .624E+O7

.3758+05 .103E+06 -212E+O6

.371E+06 .585E+06 -120E+07

.2'l0E+07 ,331E+o7

.486E+07 .679t+O7 .405E+05 .1128+O6 .229 E+06 .400E+06 .631E+06

.'l30 .22

E+0 7

6E + O7

.357E+07 .5?5e +o7 .733e+O7 .435E+05

.120E.06 -246E+06 .430E+06 .678E+06 , tJ9E+07 .243E+O7

.3E4Er07

.564Er07 .788e+07

.465E+05 .'128E+06 .263E+06

.460E+06 .7?5E+o6

.149Er07 .260E+D7

.4'l0E+07 .603€+07 .E12E+07

Vessels Rotational Nozzle Flexibilities for Cylindrical Table 6-1

Continued ROTA VESSEL

0D,rT 'tE.000 18.000 't

8

.000

18.0CC

1E.00c

tE.00ri 18.006 't 8.000 18.000 1E.000

18.000 18.000 18.000 1 8.000 18.000 18.000 16.000 't8.000 18 .00 0

15.C00

16.0c0 16.000

16.000 18,000 16.000 18.000 18 .000

18.000 16.000 18.000

STIf'

NO2ZLF

VE SSEL

OD,IN

TCK,IN

.250 .375 .500 .625 .? 50 1 .000 1 .250 1-500 1.750 2.000 .?50 .375 .500 .625 .75O 1.000 1.250 I .5OO 1 .7 50 2.000 .250 .375 . 500 .625 .750 't .000 1 .250 1.500 1 .750 2.000

CALCULATION'

36.000 36.000 36.00 0 36 - 000

6.000 6.000 36.000 36.000

3 3

36. ooo

6.000 40.000 /.0.000 40.000 40.000 40.00o 40.000 40.000 40.o0o

3

40 .000 40 -000

4E.ooo

48.000 48.000 48.000 48.000 48.000 48 .000

48.000 4E.000

48.000

CY

L.

VESSEL

NOZZLE

ROT STI

TCK,IN

INPTANE LONGI

slD

-375 -375 .375 -175 .375 .3?5 -375 -375 .375 .375 .37t .3?5 .375 .375 -375 -375 .375 -375 .3?5 -375 .375 .375 -3?5 .3?5 .375 -375 -375 .375 .3?5 .375

f

It{.LB/DEG

.158Er06 .434t+06 .892E+06 .156E+O7

.2468+07 .504E+07

.8El€+07 . 1f9 E+ 08

.204€+08 .285E+08

OUTPLANE

CIRCU

.525E+05

.115E+o6 _297E+O6 . 519 E+06 .819 E+06 . 168€ +07

-2948+07 .463E+07 .681E+O7 .951E r07

.176E+06

.586t+05

.484E+06 .99481 06 .17 4E+07

.f31E+06

.271E+07 -562E+O?

.9a2E+o7 .155E+08 .?28E+0E

.3135+08 .212E+06 .584E+06 "120E+07

.16',| E+06

.579F+06

.9.13E]06 -187E+o7

-327E+A7 .5168+O? -759'-+o7 .106E+08 .706E+05 -195E+O6

.209E+07

.399E+06 .698E+06 .'110E+07

.678E+07 .118E+08 .187E+08

.395Ef07

.330€i07

-226E+O7

-623E+O7

.383E+08

.9'l5E+07 .128€+06

.858E+04

.286E+04

.4t6Et05

.1628+05 .283F+05

.275€+08

rt,

2 -375

19.000

2 -375

19-CC0

19.000 19.000 't9.000 19 .000

19.000 19 .0

00

19.000 19.000 19.000 19.000 19.000 19.000 19.000 19

-

000

19.000

'19.000

19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000 19.000

.500 .625

2.375

.000 1.250 1.500

.500

2.375 ?.375 2.375 2.375 2.375 3.500 3.500 3.500

1.0c0

3.500

't

1.750 2.000

'l .250

.5c0 1-750 z-000

't

.250 - 500

3. 500

f.

500

3.500 3.500 3.500 4-500 4 .500 4. 500 4

.500

4.500 1

.000

1.250 1.500 1.750

4. 500

4.500 4. 500 4

.500

-154 -151 .'t54 .154 -154 .154 .154 -151 -154 -154 -216 -216 -216 -216 -z'16 .216 -216 -216 -216 -216 -23? -237 .237 -237 .237 .237 .237 .237 .237

-237E +o5

.78E E+04

.848E+05 .134 E + 06

-446E+0j

-275e+o6 .4808+06

.757E+ 06 - 1'l1E+o7

-155ErO7 . 128 E+05

-3528+05 -722E+O5

.915E+05 .160 E +06 -ZSZE+O6

-371E+O6

.5'188+06 .426F+O4

.117€+05

.241E+O5

.126E+06 .199E+06 -409E+06 -714E+o6

_42.1E+O5

- 166E+07

-5528+O6 -771E+o6 .563E+04

.113E+07 .231E+Oz

' 169E+05 .465E+05

.9 55 E+05

.167E+06

-2638r06

-6648+O5

.136E+06

.2388+06 .375E+O6

.155E+05

.318 E +0 5 .556E+05 -8778+O5

-

.180E+06

-119E+O7 -219E+O7

.196ErO6 .7292+o6

540€+06 -94f, E+ 06

.31 4E+06

Table 6-1 Continued RO]A STIFF CALCULATION, CYL.

VESSEL TCK,IN

vEss€L OD,FT

NOZZLE

NOIZLE

OD,!N

TCK,IN STD

19.000 19.00 0

19.000 19.000 19.000 19.000 19.000 't9.000 19.000 19.000 19 .00 0

19.000 19.00c 19.000 19.000 19.00 0

19-000

:l

2. 000

.250 .37

n

.750

19.000

19

10 .7 50 10 .750

5

1

.7 50 'l

1.750

2.000

.000

19.000 t 9 .000 19 . C00

19.000 19.000 19.000 19.000 9.00

.625 1 '1

19.000 19.000 19.000 19.000 19.ai00

.500

z. 000

.500 ,7 50 '|

.000

1.250 1.500

.3?2

.322 -3??

10.750 10.?50 12.750

12.750 12.750 12 .750 't2-750 12.750

.365

1

.5538+07 .5138+05

-375

.5i7E+o6 .800Ei06

.1648+ A7 .247E+07 .452E +07

.665E+C7

.9298+07 .568E+05 .157E+06

14

.32'l €+06 .561E+06 .885E+06 .132E+07 .317 E + A7 ,501E+07

.000

14.000

1

6.000

't

6. c00

16.000 6.000 1 6.000

t

.7 36e+07

.5 r>

.000

16.000

2. 000

.111E+A6 .290E+06

4.000 14.000 14.000 14.000 1 4.000 14.000

.7 50

1.500 1.750

.422E+06 .665E+06 .137 E+07 .?39E+07 .3768 +07

1

16.000 16.000

1.25A

t t8E+06

12 -750

c25

.000

.108E+07 .189E+07 .299E+07 -4398+07 .6118+07 .427E+05

-772t+Ol

12.750

16 .

.52EE+06

.241E +06

12 -750

.?50 .500

.934 E+05

.

0.750 10.750

t4-000

'l9.00 0 19 .000

.332E+07 .464E+07 .339E+05 .192E+06 . 3f5 E+06

't

1 4.00 0 1 6 .0C0

19.C00

.400E+06

.'143E+D7 .2 26E+ 07

10 .7 50

10 . 750

-855E+04 .236E+O5

.2E0

.322

.375

-375

.

NE

.1O?E+O7

.821Ei06

.322

A

CIRCU

.256E+Os

260

.280 .280 .280 .322

OUTPL

.3068+07 .7olE+C5 .145E+06 .253E+06

.280 .?80

0. 750

't -750

2. 000

9.000

19.000 19.000 19.000 19.000 19.000

.000

1.750

0

19.00 c

.280

'12.750 .500

19.0c c

1

.500

.600

19.000 19.000

'|

.000

1.250

19.000 19

8.625 8.625

.37

19

1

.6?5

3.625 'l0.750

.500

.000 't 9 .000

a

SII F IN.LB/DEG

INPLANE LOt./ GI

8.625

.000

.250

ROT

8 -625

t .0c0

.000

19 ,000

_

8.625

2

19.000 19.000

-625

6.625 6.625 6.625 a .625

.?50

19-C00

t9.0cc

.28 0

6

1.250 1.500 1.750 2.000

't.250 1.500 1.758

19.000 19.000

-625

6.625 6.6?5

.000

19.000 19.000 19.000 '19

-2E0

6

.75A 1

'19.000 'l

5

.500

4.500 6.625 6.625

VESSEL

tC3t+08

.484€+05 .845E+05 .133E+06 .27 4E+O6 .47EE+06 .7 51E +O 6 .111E +07 . 155E+07

.1t3E+05

.3'l l E+05 -

639E+0 5

-112F+06

.1 76E+06

.561E+06 -631E+06

.996E+06 .146E+C7 -204E+C7

.142ErO5

. 392 E+0 5

.805E+05 -141E+O6

.222E+06

.455E+06 .79

5 E+o 6 - 125E+O?

.'184E+oz

.257€+07 .17'l E +Os .171E+O5

.968Er05 -t69E+06 -267ErO6

.5 47 E+O6

.956E+06

.15t E+07

. ?22E+A7

.310E+07

.'189E+05 .522E+O5

.1078+06 .'l t 7E+o6 .295E+06 .606E+06

.106E+07 .1678tO7 .245E+07 .313E+07

.656E+05 .1E1E+06 .371E+06

.219E+05 -602E+05

6IEE + C6

.216E+O6

.102E+07 .21OE+07 .367 E+07

.341E+06

.850E+07

-2838+07

-

.578F107

.'l

19E+ 08

,'12

4 8+O

6

-699€+06 .122E+a7 .193E+O7 .39 6E+Ol

Rotational Nozzle Flexibilities for Cylindrical

Vessels

171

Table 6-1 Continued ROTA STtFF VESSEL

OD,fT

VESSEL I€KTIN

.375

19.C0C

1

.750 ,0c0

19.C00

'1

.?50

19.000 19.00c

1.750 2.0c0

19.000 19.000 19.000 19.000

.375

19 ,000

19. 000

E,000

18.000

-3?1E+07

.7 648+O5

20 .000

.229 g +O6 .470E+06

.25U

20.co0 20.000

.82'l E+06

.5O2E+07 .306E+05

19 .000

.500

22.000 ?2.000

.000

22 .OOO 24 .000

.520€+06 .9cBE+06

.173E +O6

.3038+06 -980E+06

2+ O7

.1718+87 -270E+O7

.3978+A7 .555E+07 .336E+05 .925s+05 .190E+06

.532E+06 -523E+06

.322E+07

.107E+07

.250 .500

24 -000 24 .000 2/, -000

.8E8E+02 .131E+08

.?9 6E 107

.7 50 2. 000

.500 -625

19.000 19.000 19.000

1

19 .00 0

't

.000

21 .OOO

26 .000

26.000 26.000 26.000 26.000 26.000 26

1.500 2

'19.000 19 .00 0

26.000 26.000

.608E+07

.109E+06 .302E+06 .619 E+ 06

.365Er05

.101 E+06

.'17'l E+o7

.569 E+06

.108Er07 .

j508+07

.6'l2E+O7

.965E+07

.206E+06 .3 61 E+06

J17E+A7

.204E +07

.322E+A7

.198E+08

.118Er06

.473E+07 .6618+o7 .394t+O5

.500

2E.000 28 .000

-326E+06 .669 E +06

.223E+06

.7 50

28.000

.0c0

28.000

.1 42€+08

28.O00

.117E+O7

2E.000 2E .000 28 .000

. 184€+07

1.750

28.600

.?50

30.00 0

.127E +06

'1

.435E+07

.'tE2€+08

-378E+07 .6 6'l € +07 - J 04 Er08 .1 53E+0E

1

.188E+07

26-000

.7 50

-250 .375

r9.000 19.000

.000

.563€+07

.000 .250

I .500

28.900

.2'l4E+08

I

.844E+05

.478Er06

-157

I I

.155E+07 .2448+07 .359E+07

-?94E+07 -514E+07 .811E+07 .119E+08 .'t 66E+08

?4.OOO 24 .000

*'l

E+06

. 143E+07

.10'l E+06 -ZtZE+46 .5708+06 .995E+06

24.000

7

24.O00

19 .00 B 19 .00 0

19.0 00

't

24.000

.000

19 .0C0

19.000 19.000 19.000 19.000 19.000

.

.7 50

19.000 19.000

19.000 19.000

22 -00 0 22 .000

1

0

19.000 19.000

.27qE+o6 ,432E+06

.108E+08 .150E+0E .919 E r 05 .253E+06

.2 50

19 .000

19.00

.157ErA6

20.000 2 0.000 22.000 22.000

20 .000

'I

.500

.449E +07 .277E+O5

.465E+ 07 .733E +07

-000

19.000 19.000 19.000

.219E+O7

20.0c0

22.000

250

.1 39E+0 7

.88

-?50 1 .000

-

.;93 E +06

30E+07 -2668+07

.625

2

.248E+05 .683E+05 .140E+06 .245e+O6

.9 61E+07

.ll5E+08 .831E'05

1.750

CIRCU

18.000

.000

19.O00

.421E+O6 .735E+O6

OUlPLANF

1t.000

.500

t9 -00c 19.000 19.000 19.000

.205Er 86

l8 .000 20.000 20.000

19.000

.0c0

.743E+05

.6568+07

.000

19.000

TCK,IN TNPLANE LONGI STD

.lE6E+06

t 8 .000

22 .000 22 .000

C

NOZZLE ROT STI T IN.LB/DEG

t 8 .800

-75n

19.000 19.000 19.000

VESSEL

.116e+D7 ,238E+07 .416E+Qz

18.000

20 .000

19 .0C

'| 9

1

1.000 J.250 1.500 1 .750 2.000

9.000

19

OD,III

ION' CYL'

'l .500

.500

.000

9

't

19

NOZ?LE

1E.000

19 .00 0

't

LCULAT

l8 .000

19.006 't9.000 19.000 'r9.000

19

CA

.109E+06 .390E+06 .615E+06 .126E+O7

.220F+07 .348 F+07

.5119+07 .714s+C7 .424E+Ot

It/

172

Piping Stress Handbook Table 6-1 Continued ROIA

VESSEL OD,FT

TCK,IN

00

19.000 19-000

19,000

r9.000 19.000 19.000 r9.000 19.000 19.000 19.000 19.000 t 9 .000

'19.00c

19.000 19.0c0

'19.000

19.000

t { il

'19.000

.500

30.000 30.000

.6?5

30.00 0

.750

I .000

1.25C

1,500

1.750 2.000 .250 .375 .500 .625 .750 1 .000 1.250 1-500

1.750 2.000 .2so

19.000 19.000 19.000 'r9.000 19.00c 19.000

't

19 .00 0

I .500

19.0C0 19 .00 0

19.000 19.000 J9.000 19.000 19.000

.37 5

.500 1

.000

.250

1.750 2.000 .3?5 .500 .6?5

19. 00 0

.000

J

-

9.C00

19.000 19.000 19 -000

19.000 19.000

.500

.750 2.000

19 .0 00

r9.000 19.000

.625 .7 50

'19.000

.000 .250 .500

19.000

t9.000 19.000 19.000 20.000 20.000 20.000 20.000 20.o00 20.000 29.000 20.0c0 ?0.000 20.000

250

.75A

2.000

.250

.375 .500

.625 . 750

I .0c0 1 -250

.750 2.000 1

.37 5

.375 -375

30 .00 0

.375

30 .00 0

-375

30.000 3

0.00 0

30-000

30.000 3?.000 32 .000

32.000

32 .00 0

32.000 32.000

52.00 0

f2 .0c0

52.00 0 32 .000

36.000 36.000

36.00 0 36 .00 0

.750

CtL. VESSEL NOZ ZLE ROT S'I' IN.L8/DEG TCK,I N I NE OUTPLAiIE '{PLA STD LONGI CIRCU

CAI-CULATl0lrlr

VESS€L

19.00c 19 .0

STIff

36.000 36.000

56 - 000

6.000 36-000 36.000 40.000 40.000 40.000 40.000 40.000 3

40

.000

40.000 40.000 4

0

.000

.375 .37 5

.375 .375 .375 .375 .375 .375 -375

.375 .375 .375 .375 .37 5

.375 .375 .375 -375 -375 .37 5

.375

.375 .375

40.000 4E.000 4E.000 48 .000

_37 5

4E.000

.5t>

48.000

48.000 4 8 .000 48 .000 4E -OOO 48 .000

2.375 2.375 ?.375 2.375 ?.375 2.375 2.375 2.3?5 2.375 2

.3?5

.350E+06 .7198+06 .1268+07 .198 E+07 .4O7E+07 .71Oa+07 . I 12E+08 .165E+08

.117E +O6 -24OE+06

./,19€+06 .660E+06 -136E+o7

.237E+07 .373E+07

.230E+08

.549E+O7 .767E+O7

-136E+O6

.453E+05

.374E+06 .7 69E+ 06

.134E+07 .21?E+07 .435E+07 .7598+ 07 .1 208+08 .17 6E+OE .2468+0E . t 55E+06

.42tE+O6 .66E

E+

06

-152E+07 -239E+07 .491e+ 07 .8 58 E +07 -135E+08 .'199E+0E .2?8E +08

-125E+06

.256E+06 .448E+06

.7068r06

.115E+O7

.253E+07 -399E+O7

.587E+O?

.820E+07

.5t1Er05

.141E+O6 .289 E+06

-505E+06

.797E+O6 -1648+O7 -Za6E+07 .451E+O7

.171E+06

.663e+07 .926E+07 .570E+05 .157E+o6

-967e+O6

-322E+O6

-267 E+O7 .5 47 a107

.889 E+06 .1828+O7

-171E+06

.169E+07 .956a+07 . 151E+08

.222E+08 .310€+08 .206E+06 .5688+06 -117E+Ol .204E+07 .321E+07 .660E+07 .115E+08

.5638+06

.3198ro7 .5038+07 .7398+O7 .103E +08

.687E+05 .1 89 E+06

.369 E+06 .679 ar06 -1O7E+07

.?67E+08

.220E+07 .384e+A7 .606E+07 .891E+07

-3?3e+DB

.124F-rOE

.1 54

. 837 E+ 04

.279E+O4

-154

.231e+O5 .473p+O5

. 768 €+04

.s75

.154 .154

.182E+08

.8278+05

.1 54

.130E+06

.154 .154 .154 .154 .154

.268€+06 .468 E+06 . 73E

E

.'108

E

+06 r 07

.1 5l E+07

.1 5E E+05 -276E+O5

.435E+05 .892E+05 - I 56E+06 -246E106

.362E+06 . 50 5Ef06

Rotatlonal Nozzle Flexibilities for Cylindrical Vessels

'173

Table 6-1

Continued ROTA STI f VESSEL

OO,FT

20. c0c

NOZZLE ODZIN

V€SSEL ICK,IN

.500

3.500

20-000

,500

3. 500

2C.000

-7 50

5. 500 3-500

20-000

.500 1-750

2C.000

.250

4.500

2C,000

.500 .6?5

4.500 4.500 4.500 4.500

?0.000 20.000 20.000 20.000 20.000

.000

20,000 20.000 2C-000 2C.000 2C

.000

2A.O00

20.000 20.000 20.000 20,000

4. 500

1

,000

't.250 .500 1-750

't

.500 4-500 4 .500 4

2.000

4.500

.500

6.6?5 6.6?5

,250

6 -625

-750 .000 .500

2C.000

2.000

26.000 20.000 20.000 20.000 u 0.000 20.000

.500 .500

3 3

.375

20 -0 00

20.060

3.500

3 -5AO

20.000 2C.000

3.500

2. 000

20,000 20.0c0

.7 50

6.6?5

6.625 6.625 6.625 6.625 8.625

.500 .750

E.625 I .625 E.625

- 000

.625

2C.C00

.250

20 .000

1.750 2.000 .250

10 . 750

- 500

'1o.750

20.000

20.000 20.000 20.0c0

8 8

- 500

20.c0i.J

20.000

a

.625 .625

8.625

'to.?50 1

0. 750

10 .750

20.000 20.000

.000

1

20.00iJ

.5C0 .7 50

19.750

20,000 20.000

20.000

2

.000

2C.000

.254

20 .000

.500

20.000 20.000 20.000 2C.000

20.000 ?0.000 20.000 2C.000

0.750

10 .750

1A.750 0. ?50

1

12.750

12 -750

.7 50

.000

't?.750 12 -750 12 -750

.500

12 ,750 12.750 12 .750

.2-50

14

.750 2-0c0

NOZZL€

TCK'IN STD

3

20.000

CALCULATION,

F

.000

CYL.

VESSEL

F IN.LB / DEG OUTPLANE INPLAN€ CIRCU LONGI ROT STI

.216 .1246+o5 .2'16 -3438+05 .2'16 .791'5+05 .?16 -123t+o6 .216 .19/+E+06 -216 .398E+06 .2'16 .696E+06 07 .216 - 'l 10 E++O7 .216 .161E .216 -?z5E+O7 .23? . 164E+05 .237 .153E+A5 -237 .9f l E+05 .237 .163E+06 ,237 .256E+06 .?37 .526t+O6 .237 .920€+06 -237 .145E+07 .?37 -?138+07 07 .237 .298 € ++C5 .25OE .?ttl .2E0 .689E+05 .280 .14'1E+O6 .280 -?47E+06 .280 .390E+o6 .280 .800E+06 -2E0 .140E+07 -280 -220E+07 .280 .3216+A7 .2EO .152E+07 -322 . j30E+05 .32? .910 E+ 05 .322 . t87E+06 .3ZZ .326E+06 _3ZZ .515 +06 .32? .106€+07 .32? . 185F+C7 .322 -291 E+o7 -3zZ .4288+C7 .3?z .598 E+07 .365 .416F-+O5 .36t .1 155+06 .365 .Zj5E+06 .365 .411E+06 .365 .643E+06 .365 -133E+Q7 .365 .233E+O7 .365 .367E+D7 .365 ,.539€+02 .365 .753E+07 .375 .,DgE+05 .325 ..t 38 E+06 .375 .?83Ef06 .375 .4E4E+O6 .375 .7S0E +06 -375 . 160E+07 .37, .280E+07 .375 -41'lE+O? .375 .648E+07 -375 .9 05 E+07 .375 .5 54 E+ 05 E

.4

15E+O4

.114E+05 .235E+05 .410E+05 .647E+05 .'133E+06 .23?E+O6

.366E+06 .538E+06 .751E+06 .548E+04

.'l5'l E+05 .f10E+05

i,i

.542E+05 .855E+05 _1ZSE+O6

.307E+06 .484E+06 -7118+O6

.993E+06

.6 33E +0 4

.230E+o, .171E+A5

.3239+05 .1 30E+0 6

.267 E+O6

.4666+O6 -735E+O6 . 108E+07

.1519+07 .110E+05 .303E+05

.62jE+05 .'l 09 E+06 .17 2E+o6

.3SZE+46 .616E+06 .971E+06

.143t+Oz

.199E+07

.139E+05 .3E2 E+0 5

-784E+05 .1378+O6 .216E+O6 .4 44E+o6 .7?SE+O6 -122E+O7

.180E+07 .251E+O7 .161E+D5 .459E+05 .943E+05

-1658+06 .260F+06 .533€+06 .932E+06 -147E+O7 -?16E+O7

.302E+O7 .185E+05

u

174

Piping Stress Handbook Table 6-1 Continued ROTA STIFF CALCUIATION, CYL. VESSEL V ESS

VESSEL ICK,II{

EL

OD,FT

20.000 20.000

.375 .500

20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000

.7 50

2C.000

20 -000

20.000 20.000 20.000 20.000 20.000 2

0.00

-625

t.000

1. ?50 'l .500 1

"750 2.000

.750 1 .000 1-250 1.500 1

-750

2. 000

.500

-750 2.08O

20.000

1.250 1.500

.625 .000 .25A

.500

- 500

.7SO 't

2C.000

20.000 20.000 2U.000

20.000 20.000 20.000 20.000 ?0.0c0 20.000 20.000 20.000 20.000 2C.000

20.000

.000

1.750 2.000 .250

2ri.00G

?0.000 20.000 20.000

NOZZLE ROT STIF IN.LB/DEG

TCK,IN IfuPLANE STD LONGI

14.000 14 .000 14 - 000

14.000 1 4.000 .000 14.C00 14

14.000 t 4 .000 16 .000

16.000 16.000 16.000 16.000 t 6 .000

16.000 1 6.000 16 -

.663E+06

-375

.309E+07 .4888+07

.375 .375 .375 .375

.37 5

.375

.500 .7 50

.000 1-250 1.500 1-750 2.000 't

.250 .500 .7 50

.000

18 1

.375

20.000

.587E+05 -121E+O6

.632E+06

.211e+06

.205E+07

.332€ +0 6 .6E2E+06

.357 E+07 .5 64 E+ 07

-137E+O6 .239 Et0 6 .377 E+06

.l'13€+07 .2328+O7

.405E.07 .639Er07 . 131€+08 .Et0€+05

4E

+

07

.'ltJ5E+08

.5078+06 .885E+c6 .140€+07

.'t 62F+08

.9t2E+C5

?4.LOO

.27OE+A6

24.OOO

.555F+06

24.000

.500

2. 000

24 ,000

24.000

26.000 z6.ooo

.37

5

.970E+06 .153E+07 .314E+07 .519E+Oz .E66E+07

,127Er08

.375

-313E+Cz -

437E+O7

.270E+05

,864€+06

-79OE+07

24 .000 24 -LAO

.135E+07 .213E+o7

.259E+ o?

.'116Fr08

24-000

.773E+O 6

.7 41E+ 05

.237E+07 .501E+07

22.000 22.000

.666F+05

-223E+06 .45E€+06 .601E+06

.247E+ A5

22 .000 ?2 -OCO

.386E+07

.410E+06

.E96E+05

22.000

-276E+O7

.242E+O5

.147€+08

22.OOO

.119E+07 .188E+07

.725E+05 .200E+06

.71

.375

E+0 7

.213€r05

6E + A6

.453:+07

?2.000 22.000 22.AOO 22.AOO

.17

.334

-3628rD6

.126E+07

.3-t5

.t03E+07

.100E+08 .639E105

-9 39E+47

.37 5

20 .000

20.000 20.000

z4 .ooo 24 -OOQ

.750

375

.000

20,000 ?0.800 20.000 20.000 20.000 20.000

-718E +07

.163E+07 .239e+07

. 716 E+06

.000

I .000

.590E+06

.ll6E+0E

-

.182Er06 .288E+06

07

7 E+

.629E+07

.000

I 6.000

.17

.996Er06

t 8 .000 1E

.547E+06

.375 .375

000

t 8 .000

. 508 €+0 5 . l04E+06

.313€+06

18.000 16.000 18

OUTPLANI CIRCU

.153E+06

I E.000

?0.000 20.000 20.000 20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000

20.0c0 20,000 20.000

OD,IN

'16.000 . 500

0

20.jco

NOZZL€

. 1 78E+ 0E .1o7E+A6 .291E+06

.153E+06 .2 6?E+06

-421E+o6

.1j'lE+07 .238E+07 .350€+07 4g9E+07 .299E+05 .323E+05

"

.169E+O6 - 295E+o6

.466E+06

.9t6E+06 -167E+o7 -263E+07

.387E+07 .5 4'l E+o7 .3?7E +o5 .902E+05 .'t 85E+06 .321E+06 .510E+06

.105E+07 .1E38+0 7 .289 E +O7

.424E+07 .592E+07 -356E+05

.980€+05

Rotational Nozzle Flexibilities for Cylindrical 'liable 6-1

Continued

SIITF CALCULATION, CYL. VESS€L NOZ ZLE ROT SlI f IN.L8/DEG VESSEL NOZZLE OUTPLANI TCK,IN INPLA}JE TCK,II'I OD,]N CINCU LONGI SID ROTA

VESSEL

0DrFT

2C.000

20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20 .00c 20.000 20.00c 20.000 20.0c0 20.000 20.0c0 20.000 20.000 20.000 ?0.000 20.000 20.0c0 20,0c0 20.000 20.c60 20.000 20.000 20.000 20,000 20.000 20.000 20.000 20.000 20.000 20.000 20.c00 20.000 2C.000

20.000 20.0c0 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000 2C.000

20.000 20.000 20.000 20.c00 20.000 20.00c 20-000

20.0!0

20.000 ? 0.000 20.000

26.000

.500

26.0C0

26.000 26-000

1-000

26.000 26.000 26.000 26.000

1.250 1- 500

1.750 2. 000

2E.000 2E.000

.375 .500

28.000 28-000 2E.000

.7 50

28.000

.000

28 .000

28.000 28.000 2E.000

2.000 .?50

10.000

.625 .750

30.000 30.000 30.000 30.000

30. 000 30.00 0

t .000

1.250 I .500 1.?50 2.000 .500 .6?5

1.000 1.250 1.?50 2.000 .250

50 .000 30. 000 30

.000

32.000 3 2 3

.000

2.000

32 .00 0

32 .00 0 32 .000

2.000 32.000 32.000 3

r2.000 56.000 36-000 6.

.500

3

.7 50

36-000

't.500 I .750

3 6 -000 36. 00 0 36 -000 3 6 .000

.625 1.000 I .250

2. 000

.250

.500 I .000

1.500 1 .750 2.000 .250 .37

5

.500

COo

56.000 36.000

40.000 40.000 40.000 40.000 40 .00 0 40 .000

40.000 40.c00 40.000 40.000 4E.000

48.000 48.000

.375 -375 .375 -375 -375 .375 .375 .375 .375 .375 .375 -375 -375 .375 -375 -375 .375 .375 .375 .375 .3?5 -375 .375 -3?5 .3?5 .375 -375 .375 .375 .375 .375 .375 .375 -375 .375 .375 .375 .3?3 .375 .375 .375 -375 .375 .375 .375 -375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375 .375

.604E+06

-201€+06

.166E+O7

.555ErC6 .'l11E+o7 .1998+07

.1658+07 .341E+07 .597 E+o7 .941E+O7 . 'l38E+08 -'t sf E+06 - 115

E

+06

.318E+06 .652E+06

.352E+06

.314E+O7 .461E+O7 .644E+O7

.384E+05 .'106Et06

.1148+o7

.217E+06 .380 E +0 6

.',|E0E+07

. 599 E+06

1F''f

.123t+o7

-644E+A7

.102E+08

.2152+07 .339E+07

.1 49E+08 .209€ +08

.696E+O7

z AA

E

.',1?4E+06

.341€+06

-498E+O7

.413E+05 .1148+06

.701E+06

.234E.06

- 12ZE+07 . ',l93E+ 07

-40E8+06 -644E+o6 .13? E+0 7

lOAc.a\7 -6928+07

.1098+08 . i 6iE+08 .224E+O8

.1328+06 .365E+06

.?3'l

E+O7

.364E+A7 .535E+07 .7 47E+O7 .441 €+05 .1?2E+O6

.719E+OC .13',1 E +07

.2 50E+06

-zo6E+07

.688E+06

.7 4OE+07

.217E+07 .389E+07 .57?E+07 .799E+07 .499E+05 .1378+06

.424t+07

.1178 +08 .17?E I oE .240E+08 . l50E+06 .112E+O6

.8 46 E+ 06

.118E+07 -233E+07 .479E+07 .E36E

r07

.132E+08

.'l948+0E .271E+O8 .1 67 E+ 06

.459E+06

.943E+06 .165E+O7

.436E+o6 .141e+O?

.282E+06 .4938+O6 .777s+O6 . t 608r07 .279 E+a7

.44OEr07 -646Er07 .90?€+07 .556E+05 .153E+06

.3148+06 .549E+06

.260E+O7

.E668+06

.533E+07

.'178E+A7

.9328+07 .147Er08 .2'l6E+08

.72OE+O7

.302E+08 .201E+06 .554E+06

.114Er07

.311E+o? .490E+A7

.101€.0E

.670 E+0 5

.185€+05 .379 E+06

Vessels

175

176

Piping Stress Handbook Table &1

Continued ROTA STIFF CALCULATION, VESSEL

OD, FT

20.000 20.0c0 20.000

20.0cc

20.000 20.0c0 20.000

vEssEL TCK,ll{ .625

ilozzLE

OD,Ill

48.000 .000 48 .000 48 .000 4E.000 4E.000 48

I .000 1

.250

1

.500

I .759

2.0c0

48.000

CYL.

VESSEL

ZLE RO' STIF IN.LB/D€G T{ INPLA'.IE OUIPLA}IE SID LOI{GI CIRCU

NOZ T

CK,I

.375 -375

- 199E+07

.313Er07 -643E+07

.1128+08

.177Er08 - 261

E

+08

.364E+08

-662E+O6

.1C4E+07 -214E+07

.3748+o7 .591E+07 .868 E+07 . 12t E+08

Pressure and Stress Ratios

By merely multiplying or dividing, P/S ratios may be used to readily determine: Ferritic Smls Temperature (Carbon and AlloYs

l.

Allowable working pressure 2. Working stress 3. Wall thickness required

900 950 1,000 1,050 1,100

This extreme simplicity arises because in the formulas devised to predict the stresses in a pipe under internal pressure, the P/S ratio may be equated to a quantity that is dependent only on the diameter and thickness of the pipe and the applicable allowance for threading, mechanical

D-2y(t -A)

.4 is known as the "modified lame" formula. In Sections 4 and 8 of ANSI 831 the Barlow formula is used, which is a special case of the general formula in which y 0. kr addition, Section 8 is based on nominal thickness rather than minimum thickness; the tabulated P/S ratios for y = 6 tut 6" placed on a nominal wall basis by mul-

:

as:

2(t.

:

tiplying by 8/7. Tables 7-1 through 7-4 give the precalculated values

=

t : A: D: y :

for

the right-hand side of the preceding general equation for each pipe size and weight based on a wall thickness 87Uz% of nominal and for values ofC varying from 0.0 to 100 in. in increments of .005 in. For any pipe size, wall thickness, and corrosion allowance the allowable working pressure is found merely by multiplying the P/S ratio by the allowable stress. Obviously, this relieves the designer from making annoying multiple arithmetical manipulations which might be subject to error.

lbs/

in.2

Ss

0.7

=

- A) D-2y(t.-A) where P : Maximum internal service pressure, P/S

o.7

The y value in the general formula reflects the effect of creep at high temperatures. In some ANSI Code sections that do not cover temperatures over 900'F, the y value of .4 is directly inserted in the formula; the formula with y

2SE(t--A)

This formula may be written

u.) 0.'l 0.7

strength, and/or corrosion. The general formula, adopted by the ASME Boiler Code in the section on power boilers and the ANSI Code for Pressure Piping is:

D_

0.4

Austenitic Steels (Cr-Ni stainless, such as Types 304, 316, and 347) 0.4 o.4 0.4 0.4 0.5 0.7

Allowable stress in material due to internal pressure Minimum pipe wall thickness, in. Allowance for threading, mechanical strengih. and/or corrosion, in. Outside diameter of pipe, in. Coefficient having values, as follows:

(Text continued on page 250.)

177

li

I

178

q o tl

(,

o

I -= io 'o 66

FE Fo o o

o

Ii al

o f o lt o

oa

I I

o.oF

o^to I lrtoF ourvl 10ur o ioco|.o'nr\l NArn a i(l|.r ... ...4 I

Piping Stress Handbook

2 I z,

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!1O !r |.t c'.O {! rrl .frorvo oo--

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Ratios 179

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rv J .rl o oo io3 < rr'r

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Pressure and Stress Ratios

249

250

Piping Stress Handbook

Tbbles are presented

y y y y

for four values of y:

: 0 @arlow) : 0.4 (Modified lame) = 0.5 (Average diameter) : 0.7 (Creep)

3. The following two solutions can be used to determine the maximum allowable working pressure perCtable

7-l)

(lable 7-2\ Clable 7-3)

missible.

r

(table 74)

Ushg the design formula from the ASME Code, Section VItr, Division 1, 1983, and the symbol definitions contained therein:

SEt

P: Instructions and Examples

Example 1: Determining Allowable Working Pressure Determine the maximum allowable working pressure in accordance with the ASME Boiler and Pressure Vessel Code, Section VIII Division |, 197'7 , for a 10-in. , schedule 80 steam line, A106 Grade B materials, operating at

750'F.

R + 0.6t

S

=

E

:

12,900 psi 1 .00 (See the 1983 ASME Code on joint efficiencies) t"r,, .518 in.

lnsloe

D-

(12,900) (1) (.518)

4.8s7 6 69.)

).lo/

Solulion.'

r 1. List known information about the pipe. Size:

Weight (or schedule no.): riy'all thickness

:Ze t

".:

Material: Code section:

Operating temperature: Corrosion allowance:

l0-in. nom. (10.750 o.D.) Schedule 80 .593 nom. (.518 rnin.) ,{106 Grade B ASME, Section VIII

Division 1, 1983 750'F 0 (The 1983 ASME Code formula does not include allowance for corrosion, therefore, it is the responsibility of the designer to adjust the wall thickness where corrosive conditions exrst.)

2.

=

12,900 psi

raOrUS

+

tnri "-'

(.6) (.s18)

: l.lv:

osl

A simplet quicker method is to obtain the applicable P/S ratio from the pressure/stress ratio table listing Y = 0.4 (Table 7-2). Nore: In the ASME Code, Section mula:

*:?-,* thus

P:

P/S

:

SEt R + 0.6r

Et R + 0.6t

E:1.0 P/S

: D" 2

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S

.. OrD" 2-

R:

P/S

:

-r+0.6t 2t

D"-2r+1.2t

VItr,

1983, for-

-w Pressure and Stress

pE:

D"

2t

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-

consrucuon

0.81

C

:

Ratios

251

0.5

thus, y in the basic ASME formula The foliowing two solutions can be used to find the stress or required yield strength.

P/S: 2(t -A) D-2y(t--A)

.

must equal 0.4

With the allowable stress(s) obtained from the ASME Code, Section VItr, Division 1, 1983,

therein:

(12,900 psi) and the P/S ratio obtained from Table

7-2

P: P:

?ST

P:---XFXEXT

(.r0M)

D

PD

^

SXP/S 12,900

Using the design formula from the ANSI Code 831.8, 1982, and the symbol definitions contained

2tFET

x.1004

=

l.295psi

Example 2t Determining Stress or Required Yield Strength

P

=

1,100

T1

-

1't 7<

11""*;

:

.562

F:.5 E:1.0 T : 1.0

Determine the stress or required yieid strength in accordance with the ANSI Code 831.8, 1982, on gas sion and distribution piping systems for a 12-in., schedule

transmis-

60, gas line, A106 Grade B materials, operating at 1,100 psi at 250"F.

s=

Solut'ons.'

s-

(1,100) (12.7s)

Q) (s62) (.5) (1) (1) 14'025 .562

=

24.955 psi

1. List known information about the pipe:

Size: 12 in. nom. Weight (or schedule

no.):

831.8,

t982 Operating temperature: 250"F

P:

1,100 psi

.

A simpler, quicker method is to obtain from Thble 7-1 where y = 0, the applicable P/S ratio, and then multiply to determine the stress or required yield strength.

Corrosion allowance: 0 P/S

2.

or required yield strength of

24,955 psi is less than the minimum yield strength of35,000 psi for A106 Grade B pipe, the pipe correctly meets Code requirements.

Schedule 60

section: ANSI Code

Operating pressure,

Since the stress

o.D.)

Wall thickness: .562 nom. Material: 4'106 Grade B Code

(12,750

ratio

:

.0771

Obtain from the Code section on gas transmission:

Minimum yield Y factor

strength : 35,000 psi =0

Because we are using a construction factor of .5 from the ANSI Code 83l .8 and because this Code is based on nominal wall, we must use the .5 fac-

Piping Stress Handbook

v:.4

tor and an 817 factor in the following formula along with our P/S ratio.

S: S:

A:0

P-P/S(8/7)(.s) 1,100

-

.0771 (8t7)

(.s)

:

(e00) (6.62s)

24,967 psj

2 tl3.000

<06?<

Example 3: Determining Wall Thickness Required

t^:'""-"

26,720

(900) (.4)]

.223

The nominal wall, T".-, is equal to .223 817 : .254. Because the ANSI

In accordance with the ANSI Code B31.1.0, 19g3, for power?iping, determine the pipe wall thickness required for a 6-in. steam line, A106 Grade B pipe, operating at 900 psi at 750'F at maximum allowable stress, with a iorrosion allowance of .050 in.

87lz% .223 x

Code B31 . 1 .0 design formula makes no allowance for corrosion and/or erosion, the corrosion allowance determined by the designer must be added to the nominal wall calculated. Therefore Tnon,,:

.254+.05O: .3M.

Sorutions.'

Then, refer to Chapter 10 "properties of pipe,' to determine the next thicker commercially available pipe. which is schedule 60, having a nominal

1. List known information about the pipe:

Size: Material: Code

wall thickness of .375.

6 in. (6.625 O.D.) A106 Grade B

.

section: ANSI Code B3l. 1.0, 1983

P: C:

:

Using Table 7-2 (where y 0.4) across from the 6-in. nominal pipe size under the column for .050 in. corrosion allowance, pick the pipe wall thickness having a P/S ratio equal to or greater than that just calculated. This value is .0869. Therefore, tno,o = .375 based on a P/S ratio of.0869 as

Obtain from the ANSI Code section on power piping (1983) the allowable srress:

S

=

=

y factor

A simpler, quicker method is to calculate the minimum required P/S ratio by dividing P by S:

P/S:900=13.000:.0692

Operating tempetature: 750.F Operating pressure, 900 psi Corrosion allowance, .050

2.

:

+

13,000 psi

0.4

shown in the table should be used.

The following two solutions can be used to find the

required wall thickness.

Note: Interpolation For values ofC and y intermediate to those shown in the tables, linear interpolation may be used.

.

Using the design formula from ANSI Code 831.1.0 and the symbol definitions contained therein:

PD^" 2(SE + Py)

L: ''' P

=900

D"

:

6.625

S = 13,000 E:1.0

+A

Note: Special calculations: Only the lhree most important uses for the P/S values have been illustrated. Those who would like to examine all of the uses are reminded that the tables may be employed to indicate the effect of operatmg temperature, corrosion allowance, material, and pipe size.

Branch Reinforcement The various ANSI piping codes give formulae for the reinforcement of nozzle openings in two respects:

Pressure and Stress Ratios 1.

The pressure area cut by the opening must be replaced by reinforcing the area within a prescribed

T = t :

zone around the opening.

which attach the reinforcement to the pipe must meet certain (essentialiy shear strenglh) requirements. The Petroleum Refinery Piping Code

2. The welds

831.3 (1980) gives detailed requirements in Section 304.3.3. The Power Piping Code B31.1 (1983) refers to Section 1O4.3.1 for a detailed description of this nozzle reinforcement design and calculation. For convenience, reprinted here is ANSI Code 831.3, Section 304.3.3 in Figure 7-1.

Nominal thickness of pipe, in. Pressure design thickness of pipe according to the appropriate wall thickness equation or procedure in 304.1 in. When the branch does not intersect the longitudinal weld of the run, the stress value for seamless pipe, of comparable grade, may be used in determining t for the purpose of reinforcement calculation only. When the branch does intersect the longitudinal weld of the run, the weld joint factor of the run shall enter the calculation. When the branch contains a weld, the weld joint factor of the branch shall enter the calculation.

Section 304.3.3 of the ANSI Code 831 .3-Reinforcement of Welded-Branch Connections Additional reinforcement is required when it is not provided inherendy in the components of the branch connection. This paragraph gives rules governing the pressure design of such branch connections for cases where the angle between the axes of the branch and of the run is between 45 and 90 degrees, inclusi.ve.

Required Area

-

The quantity (trdr) (2 sin B) is known as the required area; in the case of right-angle nozzles, the required area becomes t5d1 square inches. The branch connection must

be designed so that the reinforcement area defined in 304.3.3 (c) is not less than the required area.

Reinforcement Arca The reinforcement area shall be the sum of the followrng two areas.

Notation The notations described below are used in the pressure

design of branch connections. The notations are illustrated in Figure 7-2. Note the use of subscripts b for branch and h for run. Note also that Figure 7-1 does not indicate details for construction or weldins. B : Angle between axes of branch and run, degrees b = Subscript referring to branch : Corrosion allowance. in. c D" : Outside diameter of pipe, in. ,l : Actual corroded length removed from run pipe, in. : [D.o - 2(Tr - c)]/sin B : d1 or [T6 - c) + (Th - c) * dr/z] whichever is greater, but in any case not more than Dol : h Subscript referring to run or header L+ : Altitude of reinforcement zone outside of run pipe,1n. : 2.5 (Tr, - c) or 2.5 (Tb - c) + L, whichever is lesser : L Nominal thickness of reinforcing ring or saddle, in. T : Actual thickness ofpipe, in. @y actual measurement, or minimum thickness permissible under purchase specification)

1. The area lying within the reinforcement zone [defined in 304.3.3 (d)l resulting from any excess thickness available in the main run pipe wall and branch pipe wall over that required by the proper wall thickness equations, i.e., the thicknesses Tr - tn - c and T6 - to - c multiplied by appropriate lengths. Any line having a thickness greater than

2.

that required for corrosion allowance and for pressure and other loading considerations will occasionally be in service until the excess thickness is also corroded away. If this is the basis of the design, the excess thickness cannot be used for reinforcement of pipe+o-pipe branch connections. The area ofall other metal within the reinforcement zone (defined in Section 304.3.3 (d) provided by

weld and other reinforcement metal properly attached to the run of branch. In computing areas of weld metal deposits, the minimum dimensions required shall be used unless a definite procedure is employed to instruct the welder to provide specific larger dimensions, in which case lhe latter dimensions may be used in calculations. Fortions of the reinforcement area may be composed of materials other than those of the main run pipe, but if the allowable stress of these materials is less than that for the

254

Piping Stress Handbook

BRANCH REINFORCEMENT

DESIGNCONO|IONS:....... psig.......'F

Sfaigfn Pipo Und€r lr{om€l Pr€aslrg (a) For motallic pip6, thg inlornal prgssrro d6ign thicknoss 0) shall bs not legs than calculat€d by the lollowing Equalion 3, itt is loss han Do/4: 3O4.1 .2

HEADES

BRANCH

Nominal Siz6 Outside Oiameler

PY)

Dotr

Dob

T6

T6

S6

NominalWall Tabl6 304. t .l Values ot Y for Fenous Mato.ials

rempsraure

O€gr6o"F

Actual or min. Wall Matorial Spgc. ASTM

900&

115{, &

Below 950 lO00 1050 1100 Abovo

Ferritic

St€€ls Auslonidc

Sle€k

0.4 0.5 0.7 0.7 O.7

O-?

0.4 0.4 0.4 0.4 0.5

0.7

Allowabig Str€99

sh

Joint Elficiency

E6

Co€fliciont

Y6

Y6

Me
C6

eb

lhtorssc,iion Angl€

p

Y

REQUIREO THICKNESS OF HEAOEB AND BRANCHI PDoh

th=-= '' 2S6E6

2t.......x..,

+ 2YhP

2r.......x.. ..x....... . t 2x.,.....x..

.. +

PDcb

t 2Y6P 2t.......x...

2S6Ep

LIMITS OF REINFORCEMENT: Oqb

- 2(T6.C6)

... ...

.

-

2

r

(.......

-

.......)

sin P

(....... -.......) + (....... -.......) + 0.sx....... Sefecf farger ol lhe values, but not lo Exceed Ooh dZ = . .. ... , L4=2.5(th.Ch)=2.5(.......-.......)ot=2.5(lu-Co)+te=2.5(.......-.......)+.......

d2=d1

or

=

{Tb -

Cb) + Oh- Ch) + 0.S1 =

S€l€ct lossor of the valu69 (te = 0 if pad oi saddlg i9 not used) L4 = . . .

.

=

...

REOUIRED ANO AVAILABLE REINFORCEMENT AREA:

Ar€a =

...... . sq. in. required. (2x....... -....... ) (....... -.......

thdi = .... ... x... .... =

Ai =

(2d2 -

A2 =

214(Tb-tb.Cd =

A3 =

tf

dt)

(Th - th - Ch) =

= 1.......12

2r....... (....... -.....

-.......

- A3 =....... r....... +....... i..... AreaA-(At-Aa-Ad At + A2

A4 + 2 = sq. in. ol pad on €ach side ot nozzle =

sq. in. available. . . sq. in. ol area in pad requrred -

A4

+2-.......

Ac-2=L=.......* OEDusopadts

=.......

xL

=......,

Figure 7-1. Reproduction of ANSUASME Code 831.3, Section 304.3.3 giving detailed requirements for branch reinlorcemenl.

.

Pressure and Stress Ratios main run pipe, the corresponding calculated area must be reduced in the ratio of the allowable stress values before being counted toward the reinforcement area. No additional credit shall be taken for materials having higher allowable stress values than for the main run pipe.

Sample Calculations for Branch Reinforcement Example 7-l

Reinforcement Zone

The reinforcement zone is a parallelogram whose

length shall extend a distance d2 on each side of the centerline of the branch pipe and whose width shall start at the inside surface of the main run pipe (in its corroded condition) and extend to the distance La from the outside surface of the main run pipe measured perpendicular to this outside surface. (See Section 3M.3.3(c) (1)).

An NPS 8 run (header) in an oil piping system has an NPS 5 branch at right angles (Figure 7-3). Both pipes are Schedule 40 API 5L Grade A seamless. The design conditions are 300 psig at 400'F. The fillet welds at the crotch are minimum size in accordance with Section 327 .4'4. A corrosion allowance of 0.10 in. is specified. Is additional

reinforcement necessarv?

Figure 7-2. This figure illustrates the nomenclalure used in ANSI Code 831.3, Seciion 304.3.3, 1980. ll does not

inJicate complete w;lding details or a preferred melhod of construction. (Reprinted courtesy of the American Society of Mechanical Engineers.)

REINFORCEMENT ZON E

10.,*,".1 c=o'roin'

L4 = 0.268 in.

C

= 0.10 in.

4,286 in.

4.286-

Figure 7-3. Figure of branch reinforcement for use in Example

8.625 in. OO 7-1 '

7-

256

Piping Stress Handbook

t" : O.7 (0.237) = 0.166 in., or = 0.25, whichever is less : 0.166 in. t

Solution

SE:

Tr, =

Tr:

16.0 ksi. (0.322) (0.87t =,A.2{2

:

n.

(0.23? (0.87s) O.2U7 m. L'4 = 2.5(0.282-0.1) = 0.455 in., or 2.5(0.207 -O.l) + 0 0.268 in., whichever

:

t4 : dr: dz=

d,: tr, =

b:

is less 0.268 in.

I4.s -2(0.2s7 (0.207 2.432 4.286

-

in n.

-

0.l)l/sin (90') = 4.286 in.

0.1) + (0.282

-

o.D

+4':'6 z

or d1, whichever is grex er

+ (2) (0.4)

(300)

(300) (4.5m) (2) (16,000) + (2) (0.4) (300)

: :

0.080 in.

0.042 in.

:

0.166

o.1ut 0.235 in.

Thus, the required area, A1 (90)l 0.343 sq. in.

:

= (0.080) (4.28O t2 -

The rcinforcement area:

- I1l*o wall;

A.z

0.437 sq in.

:

In branch wall,

:

(300) (8.625) (2) (16,000)

Minimurn leg dimension of fillet weld

@.286) (0.282

A3

-0.08 -0.10)

sin

:

: (2) (0.268) l(0.207 -

0.042) - 0.101 0.035 sq in. In branch welds, Q) Q/2) (0.235)2 .

&:

ln. The total reinforc€ment area

:

:0.055

sq

0.527 sq in.

This is more than 0.343 sq in. so that no additional reinforcement is required to sustain the internal prcssure.

Design Criteria for Allowable Loads' Moments, and Stresses

Design Criteria for Pumps with Steel Nozzles and Casings

larger reactions. The vendor must submit comparable cri-

teria for pump cases constructed of cast hon. Suction and discharge nozzles should be designed to withstand forces and moments from the thermal expansion or contraction of prping. Piping reactions should be computed in conformance with ANSI Code B31 . or

API Code 610: Steel Pump Force, Moment, and Stress Limitations

I

The following criteria apply for pumps with 12-in. discharge nozzles or smaller. The forces contained herein are

considered minimum criteria and should be adjusted where the vendor has experimental or test data permitting

ANSI Code 831.3 for pressure piping and should be designed within the limiting criteria set by this standard. The modulus of elasticity must be adjusted for the operating temperature condition. Each nozzle should be capable of withstanding double the forces and amounts listed in Table 8-1 applied simulta-

Table 8-1 Nozzle Loadings

Fotce/

oment

Nomlnal Size ot Nozzle Flange (in.)

<

Each top nozzle E

160

F, (compression)

200

Fy (tension)

100

F,

130

Each side nozzle

R Fy

160 130

F,

200

Each end nozzle F" F

F,

200 130 160

Each nozzle

Mr

340 260 170

My

M" M= x=

Moneu Axis

Reprcduced

ft-h

parolzl to shaft

6810

2

240 300 150 200 240 2W 300 300 2W 240 700 530 350

320 400 2W 260 320 260 400 400 260 320 980 740 500

12

14b

'| 6D

530 700

1,000

1,500 1,800 920 1,200

560

850

1,200

1,500

4ffi

1,000 1,500

1,zffi

700

7W I,100

I ,800

1,600 1,900 2,000 2,3w 1,000 1,200 1,300 1,500 1,600 1,900 1,300 1,500 2,000 2,300

700

1,100

1,500

1,800

2,000

2,300

4@

700 850

1,000 1,200

r,2w

1,300 1,600

1,500

2,6N

3,700 2,800 1,800

4,500 3,400

4,7N 3,500

5,400 4,000

2,2W

2,300

2,7W

560 700 350 460

850 1,100

560 1,700 1,300

1,900 1,300

870

t,2N 1,500

750

1,500

I,900

J = Verticalgo" to shaft z = Hoizontalgo' to shaJt

from Centritugal Pumps for ceneral Refinery Services, Suth Edition,

Institute.

257

1981

, Standad 610 Table 2. Repinted courtes, of the Ameican Petroleum

25A

Piping Stress Handbook

neously to the pump through each nozzle, in addition to internal pressure, without causing an hternal rub or adversely affecting the operation of the pumps or seal. The baseplate and pedestal support assembly should be adequate to limit the shaft displacement, when measured at the coupling, to a maximum of 0.005 in. in any direction when subjected to the loads shown in Table 8-1. These loads represent the total effect of all external mechanical forces that may be applied to a fully grouted pump base. They are to be applied to the pump through the suction and/or discharge nozzle (see Figure 8-1): For purposes of evaluating computed piping-imposed external moments and forces, these forces be transferred from both suction and discharge flanges to the intersection of the X, Y, and Z axes. An algebraic surffnation should then be made for comparison with the moment limitation just given. The vendor should submit alternative criteria for pumps larger than 12 in. Because a particular nozzle on a pump will not always be subjected to the maximum allowable resultant force and moment simultaneously, an increase in either the resultant applied force or the resultant applied moment may be made if the following limitations can be satisfied at that nozzle:.

(F"iF.) + (M^/M.)

where C M"

: = =

<

2, F"/F,

<

2, and M"/M.

(

C

M. F, D

=

: :

=

forces and moments from Table 8-2 on both nozzles simultaneously, taken about a point defined by the intersection of the axis of the shaft and the centerline of the pedestals. For heavy-duty baseplates the total applied resultant forces and moments on the suction and discharge nozzles should not be more than twice the eouivalent of those given in Thble 8-1. For applied resultant forces and moments that are greater than these, allowable values shall be mutually agreed upon by the purchaser and the vendor.

Design Criteria for Pumps with Cast lron or Aluminum Nozzles and Casings

Aluminum Pump Force, Moment, and Stress Limitations

2, for nozzles 6 in. and smaller (D + 6)/D, for nozzles 8 in. and larger resultant applied moment at the nozzle, ft-

lb E

The resultant applied force or moment may be increased up to double the values in Table 8-2 if the maximum combined limit on the installed equipment is not exceeded. This limit is determined by the summation of the

resultant applied force at the nozzle, lb resultant moment (from Table 8-2), ft-lb resultant force (from Table 8-2) lb nominal diameter of nozzle flange. in.

The following criteria apply for pumps with 4-in. or smaller discharge nozzles (suction nozzles may be larger). The forces contained herein are considered minimum criteria and should be adjusted where the vendor has experimental or test data permitting larger reactions. Suction and discharge nozzles should be designed to withstand forces and moments from the thermal expan-

sion or contraction of piping. Piping reactions shall be computed in conformance with the petroleum refinery piping code for pressure piping ANSI Code 831.3, Section 319, and should be designed within the limiting criteria set by this standard. The modulus of elasticity should be adjusted for the operating temperature condition.

Table 8-2 Suggested Allowable Resullant Forces and Momenis (For Vendor's Standard Baseplates) E io^

-de..

Resultant Force/Moment F

Figure 8-1. Pump coordinate system.

M.

Nominal Size of Nozzle Flange (in.)

23

4

640

6

810

124

860 1,500 2,300 2,',700 2,900 690 1,400 2,000 3,500 5,200 6,600 8,200 430

Design Criteria for Allowable Loads, Moments, and Stresses Each nozde should be capable of withstanding forces from external piping determined by the following formuIas:

.

Limit tension and comDression forces to 500 lb

where F r X

Suction nozzles:

v z

F"(1.6w(50D r

w D d

Discharge nozzles:

F,6

(

S

(2w

F.,)

-

<

259

Force, lb Resultant of forces Axis parallel to shaft Vertical 90' to shaft Horizontal 90' to shaft Weight of pump only, lb Diameter, nominal diameter Discharge or exhaust Suction or intake

50D

o Top suction and top discharge nozzles are further limited by:

F. is the resultant shear force in the plane of any specific flange face.

and for suction nozzles

Each suction and discharge nozzle should be designed to withstand the forces described for the specific configuration. Unit stresses in each nozzle should be limited to: 4 one-third of the allowable hot stresses for pipe sizes

F*(1.3w(40D

in.; one-half of the allowable hot stresses for pipe sizes > 4 in.; as shown in ANSI Codes B31.1 and 831.3.

F.. and F,.a

:

(Fx2

+

Fz2)L/'z

(

(

1.2w Fr" (in compression) 25D Fr, (in tension)

( F",(w(35D

(

50D

The baseplate and pedestal support assembly on pumps

having a discharge nozzle of 4 in. should be adequate to limit the shaft displacement, when measured at the coupling, to a maximum of 0.005 in. in any direction when

and for discharge nozzles

F*a

(

(1.8w

r

F*) <

(

40D

t

(2w Fr") Fra (in compression) Fra (in tension) 0.5w < 25D

(

subjected to the following loads. These loads represent the forces tliat may be applied to a ful1y grouted pump base. They are to be ap-

tot;l effect of all externil mechanical

<

50D

nozzle.

F,a((wtF,,)<35D

o End suction and top discharge pumps are further limited by:

F":

G^'?+Fy.)-

and

F,6: (Fl and

+

M, :

3.0 W*

ftlb

: 2.0 wx ftlb = 1.5 W+ ft-lb M* : Moment in Y-Z plane My : Moment in X-Z Plane M, : Moment in X-Y plane W : Weight of pump only, lb Mv Mz

F"a'?)"'

For purpose of evaluating computed piping-imposed

for suction nozzles

external moments and forces, they should be transferred from both suction and discharge flanges to the intersection of the X, Y and Z axes. An algebraic summation should then be made for comparison with the moment limitation just given. The vendor must submit alternative criteria for pumps having a discharge flange of 4 in. NPS. It is suggested that these criteria be developed as a result of tests'

F".(1.2w(50D Fr.(0.6w(35D F.,< w(40D and

plied to the pump through the suction andior discharge

for discharge nozzles

F"a((1.8wtF*)<40D

(

Fra (in compression) 2w + Fy. Fra (in tension) 0.5w 25D

(

F.a((w1F".)935D

(

<

50D * Minimum W is 500 lb in tlpse

computations.

260

Piping Stress Handbook

D. :

Design Criteria for Turbine Drivers with Steel Nozzles and Casings Steel Turbines Force, Moment, and Stress Limitations At the operating temperature, using the hot modulus "E," resultant bending moments are permissible up to a value that would cause a bending stress of S5/4 in a connection having a section modulus equal to the connecting piping for the same size where the comection is 4 in. IpS or larger. On smaller size connections a stress of S"/3 is permitted. (56 is as defined by ANSI Code 83l . I or ANSI Code B31.3 (current issue) for the material of construcnon. ) The resultant shear force at the face of the flanee and any individual component may not exceed 2,000 lb. The resultant forces and individual components are limited

The combined resultants of the forces and moments

the centerlines of the exhaust connection and shaft must not exceed the following two conditions: (2s0 D.

F.

where

F, : M, : D. :

F(

F,<

( ( w(

F."

F

160D

'vr

F

Algebraic summation of F." Algebraic surnmation of Fo Algebraic summation of F,'

( ( (

F-r)'"

w

l.6w

(

2w

Use up to 100% cold spring and satisfl the operaring condition only. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the following:

(s0oD"

where

F : M:

-

Combined resultant

of inlet.

extraction.

and exhaust forces, lb

Combined resultant of inlet, extraction, and exhaust moments and moments resulting from forces, ftJb Diameter (in.) of a circular opening equal to the total areas of the inlet, extraction and exhaust openings up to a value of 9 in. in diameter. For values beyond this, use D. (i8 * equivalent diameter)/3 ln.

<

< <

50 D., 125 D., 100 D.,

M_

<250D, My. < 125D. M., < 125D.

1.6w

Combined resultant:

(F.*), + F.y, +

M.)

Components of these resultants should not exceed:

160D 130D

o Resultant components:

r

-

:

o Individual comDonents:

1.3w .6w

of

the inlets, extraction, and exlaust connections, resolved at

further as follows:

F-<

Pipe size of the connection (IpS) up to g in. in diameter. For sizes greater than this use Dc : (16 + IpS)/3 in.

M)

(lb), including pressure forces where unrestrained exoansion joints are used at the connection. except Resultant force

on vertical exhausts Resultant moment, ftlb

Vertical Exhaust Connection For installation of turbines with a vertical exhaust and an umestrained expansion joint at the exhaust, an additional amount of force caused by pressure loading is allowed. (The additional force referred to is perpendicular to the face of the exhaust flange and central.) For this type ofapplication, calculate the vertical force component on the exhaust connection, excluding pressure loading, and compare with the value of t/o the pressure loading on the exlaust. Use the larger of these two numbers for a vertical force component on exhaust connections in making the calculations just outlined. The force caused by the pressure loading on the exhaust is allowed in addition to the values established bv the Dreceding up to a maximum value of vertical force (ib) o; the exhaust connection (including pressure loading) of 151/: times the exhaust area (in.2). These values of allowable force and moment Dertain to

the turbine structure only. They do not pertain to the forces and moments in the cormecting piping, flange, and

Design Criteria for Allowable Loads, Moments, and Stresses flange bolting that should not exceed the allowable stress as defined by applicable codes and regulatory bodies. (See

Figure 8-2.)

261

resultant forces and individual components will be limited

further as follows: o Individual components:

F"(1.3w(40D Design Criteria for Turbine Drivers with Cast lron or Aluminum Nozzles and Casings Cast lron or Aluminum Turbine Force, Moment and Stress Limitations

Fr(.6w(35D F"< w(40D .

Resultant components:

Algebraic summation of F,* Algebraic summation of Fo Algebraic summation of F'"

.

( ( (

1.6w w 1.6w

Combined resultant:

At the operating temperature, using the hot modulus "8," resultant bending moments are permissible up to a

(F*2+F,r2+F''?),n<2w

value which would cause a bending stress of 56/4 in a connection having a section modulus equal to the connecting piping for the same size where the connection is 4 in. IPS or larger. On smaller size connections a stress of Sr,/3 is permitted. (56 is as defined by ANSI Code B3l. 1 or ANSI

Use cold spring, but comply to these limitations in both

Code 831.3 (current issue) for the material of constructlon.) The resultant shear force at the face of the flange and anv individual component should not exceed 500 lb. The

operating and installed conditions. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the following:

F< where

(s00D.

F

/

M)

= Resultant force (lb), including pressure forces where unrestrained expansion joints are used at the comection, except

RIGHT ANGLE TO

TURBINE SHAFT-

-

M: D":

on vertical exhausts Resultant moment, ft-lb Pipe size of the connection (IPS) up to an S-in. diameter. For sizes greater than this (16 + IPS)/3 in. use a D"

:

The combined resultants of the forces and moments of the inlet. extraction, and exhaust connections, resolved at the centerlines of the exhaust connections must not exceed the following two conditions.

l.F.<

(2s0

where F.

D.

:

M,: Figure 8-2. Turbine coordinate system.

-

M)

Combined resultant of inlet, extraction, and exhaust forces, lb Combined resultant of inlet, extraction, and exhaust moments and moments resulting from forces, ft-lb

262

Piping Stress Handbook

D.

:

Diameter (in.) of a circular opening equal to the total areas of the inlet, extraction, and exhaust openings up to a value of 9 in. in diameter. For

values beyond this, use D. (18 + equivalent diameter)/3 in. 2. Components

F*

o Combined resultant:

(F*2+Fry2+F.z;rnE2* Use 100% cold spring and satisf the operating condi tion only.

of these resultants should not exceed:

D., < M* < Fy. 125 D., < My. < F". 100 D,, < M". < 50

250 D. 125 D, 125 D,

The total resultant force ald total resultant moment imposed on the compressor at any comection must not exceed the following:

F< Design Criteria for Compressors with Steel Nozzles and Casings

where

F

= Resultant force (lb), including pressure forces where unrestrained expanston

M:

Centrifugal Steel Compressor Force, Moment, and Stress Limitations

value that would cause a bending stress of $,/4 in a connection having a section modulus equal to the comecting piping for the same size where the connection is 4 in. IPS or larger. On smaller-size comections a stress of S1/3 is permitted. (S1 is as defined by ANSI Code B31.1 or ANSI Code 831.3 (current issue) for the material of construc-

1.F.<

(463

where

D.

F. : MI:

( ( F" ( F,

1.3w .6w 1.0w

< < <

160D

l30D 160D

Resultant components:

Algebraic summation of Fo Algebraic summation of Fo Algebraic summation of F-

2. l.6w 1.6w

-

M.)

Combined resultant of suction, interstage and discharge forces, lb Combined resultant of suction, interstage and discharge moments result-

ing from forces, ftlb Diameter (in.) of a circular opening equal to the total areas of the suction, interstage, and discharge openings up to a value of 9 in. in diameter. For values beyond this, use D, = (18 + equivalent diamerer)/3 in.

Individual components:

F*

.

joints are used at the connection. Resultant moment, ftlb Pipe size of the connection (IPS) up to 8 inches in diameter. For sizes greater than this use D" : (16 + IPS)/3 in.

The combined resultants of the forces and moments of the suction interstage and discharge connections, resolved at the centerlines of the discharge comection must not exceed the followins two conditions.

tion.) The resultant shear force at the face of the flanee and any individual component should not exceed 2,60 lb. The resultant forces and individual components will be limited further as follows:

r

M)

J

D:

At the operating temperature, using the hot modulus "8," resultant bending moments are permissible up to a

-

(925D.

Components of these resultants should not exceed:

F," Fy.

F,,

< <

<

92 D.,

M_ <

230 D,, My.

460 D, 230 D,

r85 D,.

230 D,

< M. <

Design Criteria for Allowable Loads, Moments, and Stresses

Design Criteria for Compressors with Cast lron or Aluminum Nozzles and Casings

where

F :

(lb), including pressure forces where unrestrained e xpansion joints are used at the connection. except Resultant force

M= D"

:

Cast lron Compressor Force, Moment, and Stress Limitations At the operating temperature, using the hot modulus, "E," resultant bending moments are permissible up to a value that would cause a bending stress of S;/4 in a connection having a section modulus equal to tle connecting piping for the same size where the connection is 4 in. IPS or larger. On smaller-size connections a stress of 56/3 is permitted. (Sr is defined by ANSI Code 831.1 or ANSI Code 831.3 (current issue) for the material of construc-

:

The combined resultants of the forces and moments of the inlet, extraction, and exhaust connections, resoived at the centerlines of the exhaust connection must not exceed the followine two conditions.

1.F.<

(250

where

hon.) The resultant shear force at the face of the flange and any individual component shall not exceed 500 lb. The re-

.

-

MJ

Combined resultant

of suction, in-

terstage and discharge forces, lb

Combined resultant

of

suction, in-

terstage, and discharge forces, lb Diameter (in.) of a circular opening

eoual to the total areas of the suction, interstage, and discharge openings up to a vaiue of 9 in. in diameter. For values beyond this use D, = (18 + equivalent diameter)/3 in.

2.

ComDonents of these resultants should not exceed:

<

< 460 D. < 230 D, < F. < 185 D., M- < 230 D,

F."

F.y

Resultant components:

Algebraic summation of F* Algebraic summation of Fo Algebraic summation of F,"

F. : D, :

o Individual comDonents:

Fr(.6w(35D F"< w(40D

D.

M. =

sultant forces and individual components are limited further as follows :

F.(1.3w(40D

on vertical exhausts Resultant moment, ft-lb Pipe size of the connection (IPS) up to 8 in. in diameter. For sizes greater than this (16 + IPS)/3 in. use a D"

( ( <

92 D., M,230 D., M.y

1.6w 1.0w 1.6w

o Combined resultant:

(F*2+F.y2+F-'?)'n<2w

API Code 661 Design Criteria for Air-Cooled Heat Exchangers

Use cold spring, but comply to these limitations in both

operating and installed conditions. The total resultant force and total resultant moment imposed on the turbine at any connection must not exceed the followins:

F<

(s00D"

-

M)

Each nozzle in the corroded condition must be capable of withstanding the moments and forces defined in Table 8-3. The design of each fixed header, of the fixed header to sideframe connection, and of other support members should be such that no damage will occur due to the simul-

264

Piping Stress Handbook

taneous application of the following design iotal nozzle loadings on a single header:

For the direction of loads see Figure 8-3. The total of all nozzle loads on one multibundle bav should not exceed three times that allowed for a singli header.

Moments.

ftlb

Forces.

The maxirrum allowable moments and forces for floatirlg headers are a matter of agre€ment between the pur-

lb

F,FyF"

MM, IvI, 3,000 4,000 2,000

r,500 3,000

chaser and the vendor.

2,500

This recogrrizes that the application of th€s€ moments and forces will cause movement and that this movement will tend to reduce the actual lmds. Tabte

&3

Allowable External Forces and iloments tor Air-Cooled Heat Exchangers Nozzle

NPS Moments ft-lb Inches ilr lily M:

Slze,

lth 2

6 8 10

t2 14

50 70 50 70 120 70 200 300 2N 400 600 400

1,050 1,500 800 1,500 3,000 1,100

2,W0 2,5W

3,000

3,m0

1,250

3,000 1,500 3,500 1,750

Forces, lb

F,

F,,

F2

100 150 100 150 2ffi 150 300 250 300 500 400 500 600 750 750

850 2,000 1,000 2,000

1,200

1,500

1,250 2,W 2,000 1,500 2,500 2,500

Figure 8-3, The direction of the loads defined in Table & Exchangers for General Refinery Se/.v,bes, Second Edition, i978, Standard 661, Figure L Reprinted courtesy of the American Petroleum Instilute.

3. Reproduced lrcm Air-Cooled Heat

Simptified Solutions for Pipe Stress

These tables are developed as a tool for the piping stress

can readily be seen that the smaller expansion

engineer or the piping designer by which he can quickly evaluate a proposed layout before he proceeds with his deslgn worK. It is important for the reader to understand that the tables presented herein do not compose a rigorous solution to the pipe stress problem. Computer calculations must be made for borderline cases. The tables are approximate values onlv for two-anchor oroblems.

Example Problem 9-1 Consider the piping arrangement in Figure 9-1.

Size: 8 in. Schedule: Sch 40 Material:

O.D.:

=

F:

A-53 Grade B 8.625 in.

where

Temperature: 600'F Coefficient of thermal expansion: .046 in./ft

:

The expansion for the 20-ft leg is X .92 in., and the expansion for the 10-ft is X = .46 in. By inspection, it

will deflect

the longer leg more easily than the larger expansion will the shorter leg. To develop Tables 9-1 and 9-2, a guided cantilever formula has been used to calculate stresses. If we observe our Example Problem 9-1 for an expansion ofX -92 in., the required offset is about 13 ft for a stress of 15,000 psi (See Thble 9-1) and 23 ft for a stress of 5,000 psi (See Table 9-2). If Point A is attached to a piece of rotating equipment, you will need to have about 23 ft to make the system more flexible. If the system is attached to a piece of nonrotating equipment, a 13-ft offset will be sufficient. To find the thermal forces Table 9-3 is to be used, which shows forces for a unit reflection with various leneths of offset. Note that in identifuing pipe sizes the tables show wall thickness and moment of inertia as well as O.D. All forces are calculated from the formula:

6 Ell1728 L3 (guided cantilever)

F: E=

{:

Force, lb E O-.ton, t tn., Young's modulus of elasticity, (30 psi) Moment of inertia of pipe, in.a Length of the shorter leg, ft

I : L: I

I

Fys

=

F.B

x

106

434lb

=

Figure 9-1. Diagram for Example Problem

6,949lb.

9-1

.

(Text continued on page 291.)

265

256

Piping Stress Handbook

Table 9-1

Lengths ot Offset Required to Safely Absorb Various Expansions tor Piping Between Two Solld Anchors (Stress Limit is 15,000 pst)

Pipe O.D.

(in.) ol

1.3 1.9 2.3 4.5 6.6 l'.D

rs .7 74.9

16,S 18 .0

.g 24.5 2g

30 .s 36 .g

42,9

4A.S

54.9

1.5 2,6 3.5 3.3 4.2 5.1 5.3 5.7 5.1 6.4 7.9 7.8 9.3 tg .5

tength (ft)

Bequired to Absorb Expansion A (in.)

o.2

0.3

2.3

.8

3.4

3.0 5.2 5.9 6.6

l1,l

t4.l

I4.9

8.4

ro ,4

11.8 L3 .g

IS .1

14.3 16.3 L8 ,2

74.0

19 ,9 2g .8

L6 .O

l8 .0 26,0 24,9

3g .g 36 .S 42 .0

48,9

54.5

22.3 23.6

24.9

u.d

9.7

12.o 13.6 15.1 15 .5

l8 .9

2I.0

22.9 24 .T 27 .3

29.8

Jt.5

8.1 8.9 9.9 .5 11.1 10

tJ.o l4 .9

r6.l u.3

18.3

36.1 38,5

4r,s

9.9 10.9 13.4 L5.2 l5 .9 l8 .5 21.1 23 .5 25.6 26 .9 28.8 30.5 32.2 9.4 .2 .7 .9 a2.9

3

38.6 44.6 47 .3

5.1 6.7 7.4 8.4 9,4

5.il

tength (ft) Pipe O.D. (in.) -r-:3 2.9 2.5 1.3 1.9 2.3

3.9 4,3

4.6 5.2

4.3

7.6 8.1 8.5 9.1 9.9

0.4

43 a6 49

rg .2 16 .7

t2 ,2 12.a

t4.l

IE ?

17.3 18 .5

2L.I

0.5 3.6 4.4 4.8 6.5 5.8

9.4

10.5

IL.4 12 .g t2.a l4 .4

!7,6 2g ,8

0.6 4. 4.8 6.6 7.4 8.2 9.0 l0 .3 12,5

13.2 14

.l

14 .9

15.7 17 .3

l9 .3 2t .7

22.A

o.7 .3

5,2 ?1

8.5 8.9 11.1 L2.4 IJ.5

14.2 15.1 L7 .S

t8.5 2g

22

.8 .8

.4 28.0 26

23 .6

0.8 4.6

0.9 4.9

6.1 8.6 rs .4

lr.:t

l4 .5 .2 16.3 17.3 t8 .2 15

8.9 9.1 tg ,r

.3

1.1

1.2

6.2 5.9

5,4 6.5 7.2 8.9

6,8

t0.6

.l

9.3 10.5

12.2

I2 .8

7S

Lt.2

tl.l

lt.7

l4 .1

14.9 16.2

15.6

L7 .g

12,6 16.1

27 22 24 26 28 29

1.0

.r

23,6 .9 28.9

.4

25

.4 .2 .9

29 .9

18.2 l9 .3 26 .3 22 .3

24.9

29

,s

1',t t

14,9

14 .5

r7 .0

17.8

17.8 l8 .6

,2

2L .T

2S

23.4

22,3 24.4

26 .7

27 .3

33.1

34.5

28.6 39,9

JJ.5

Required to Absorb Expansion A (in.) 3,0 9.9 l0 .8 11.9 o.5 20 .2 .l

.r .l

23 za .6 28

29.5

38.6 43 .2 47 .3

51.1 54.7 5A.g

4.5 9,7 12.9 15.9

I8 .g 26 .g 2L .9 25 .0 27 .9

35,4 31.9 34.1

tg ,4

11.0

13.8

14 .6

17 ,g

2I.3 23

.4

29 .8 36 .4

36.1

38,5

JO.I

4g .7

4r .7 46 .7

51.1 55.2

59,1 62.6

5.9

44.6

49.9 54.7 53.1 67 .S

t3.3 78,5

26.5 24

.8

3r,5 34.4 36.1

ll.5

!4 .6 15 .4 t9 .6 2I .6 23 ,9 29 ,9

36,3 JU.I 4S

43.2

,'l

47 .3

45.6 49.9

58,6

51.1

67 .S

70.6 7 4,9

6.6 L2, 2g 22 25 27 31

23 ,6 26

.L

.3

4I.7

45.3

47 .3 49 .9

47.8

52 ,3

5 8.6 64.1 7

4.I

I7 .6

24.6

54.7

61.t

67,9

16.5 .2 22.5

18

39.9 41.4

43.5 46.5 49,3 52 ,S s5 .9

63.6

39 .4 43

.s

45,1 48.2

sl.1 53 .9

55,0 ?a I

8S

a2.6

7,0

28 ,2 34 .6 38 .S

4S

.6 42 .1

13 ,2 L6 .g

28 .6

34.9

66 ,O

7t.s

.0 .6 .g .4

16.9 29.8

6.5

,5

88.5

267

Simolified Solutions for Pipe Stress

Table 9-2 Lengths of Oftset Required to Safely Absorb Various Expansions tor Piping Connected to Rotating Equipment (Stress Limit is 5,000 psi)

Pipe O.D.

(in.) -6:i t.9 3,5

3.4

6,6 8.6

5.4 7.3

4.6

ro.7 8.r r2.7 8.9 74.s 9.3 L6.0 9,9 t8,0 I0,5 1t.r 28 .0 24 ,O 12.2 13,5 30 .o 36.s L4.9 42.A 15.1 48.0 L7 .3 54,6 18.3 Pipe O.D.

(in.) i.s 1.3 rl .0 1.9 13.3 2.3 14,6 3.5 18.0 4.5 29.5

8.6 24,3 ls.7 31.6 L2.7 34.4 14.0 36,L L6.0 3 8.5 18.0 4L.O 26.9 43.2 24.6 47 .3 30 ,0 52.9 5a.S 36 .0 42.O 62.6 48.5 67.0 54.9 7 r.g

Required to Absorb Expansion A (in')

Length (ft) o.2

4.9 4.8 6,6 7 .4 8.2 9,9 r0.3 12.5 t3,2 14.9 r7.3 19.3 21.1 22.8 24.4 25 ,9

0.3 4.9 5.9 8,9

9,r

t0.r

1r.1

12.6

15.4

16.r 18.3

27,r

23.6 25,9 28.9 29.9 31.7

Length (ft) 2.O

2.5

0.4

0.5

0.6 6.9 8.4

9,3 .5 11.7 12.8 14 .6 16.3 L7.8 18.6 19.9 2r ,r 22.3 24.4 27.3 29 .9 34.6 36 ,7 L6

70,4 1r .8 13.0

11 .4

14.3

15 .7

L2.9 14 .3

16 ,3

L8.2 19.9 2q .8

20 .0

2r .8

22.3

24.4

23.6 24.9

25 .9 27 ,3

27 ,3

0.5 33 .5

29.9

3

38.6 4L.0

36 .7

39.6 42 .3

44.9

o.7 7.5

0.8

rg .0

10 .7

74,0

8.0

r5,4

l6 .5

lo I

20

16.9

2r.6 24,7

r8.t

.7

26 .4

0., 8.t

76.1

1t .3

1.0 9.0 l0 .8 11,9 14.7

29.5

39.6

45 .7

48.5

11 .9

47 .A

43.2

44,9 48,5

47 ,3

55 ,g

58.0

6.q

7.9

17 .5

19.2

26.2 23

24.5 28 .g

.r

28,1 29.5

38.6

34,6 38.6

9,4

tr .4

1.2 9.8

.4 16 .1 r 9.4 29.2 24.2 25,3 29.5 36,8 32.3 30 .9 34.6 33 .l 3 8,5 37 .6 40.5 42,3 49.7 sl .9 56 .0 53 .6 57.3 59 .9 60,8 6 3.5

r4.0 t5 .8

28 .0 32 ,3

1.1

48.9

5I

.I

15

Required to Absorb Expansion A (in.) 3.0

15.6 16 .8 18.8 26 .3 15.9 18 .9 20 ,7 22,4 20.8 23.3 25,5 27 .6 23.6 26,4 29.s 31.3 29.2 32.0 3 4 .6 26 .L 28.6 32,0 4g.r 43.3 36,5 4q.8 44 .'t 48.3 44.5 48.'t 52.6 3 9,8 4r,7 46 .7 Fl I q( ' 44,6 49 ,9 54.7 59 .r 47.3 52.9 58 .0 62.6 49,9 5s.8 61, t 66.0 54.7 61.r 67 .0 72.3 61..1 68.4 74,9 8q.9 67.9 7 4.9 82 .S 88.6 72.3 89.9 88.6 95.7 77 .3 85.5 94 .7 r02.3 82.O 91.7 109.5 rsg.5

4,9 18 .0

29.5

4.5 23,g 25 ,4

5.0 20.L 33.0 37 ,4

37.9 49,5 46 .3

43,5

49.r 54,8 62.6 67 .0

61 ,0

70.6 86.5 L02.3

L09.4 116.0

77.0 74,9

4t .4 45.3

51.7

74.9 7 8.9 85,5

L00.5

ro5 .9

108.5

114 .4

rt6,g

123.1

28 .g

34.6 39.2

r22 .3 L29 .7

22,9 26.6

35,r 4t,0

43 .4 41 ,5

45.3

66 ,5

63.2 68.9 72.3

66.9 65.0

82 .0

9r.7

21.1

24.3

74.L 78,5 82,8

90.7

49 .7 56 ,7

22.9 27 .7

3t ,5 39.6

42 .7 49 .0

59.0

65.8

78.r

77 .3

80.5

85,5

96.0

94 ,7

98 .6

a2.g

23 .8 28 .8

88.6 93 .4

IO2 .3

I6L,4

10s.9

110 .3

]f

r2g ,o

125,3 134,0

130.5

135.4 L44.7

ItL.r

r36.1

1r5.0

I42.I

I2A .a 139 .5

L4't,9

4.4

r25.3

Piping Stress Handbook Table 9.3 Force (lb/ln.) ot Expansion tor L-Shaped pipe (No Etbow)

?.375

{IFF-

l. J/J

,,t65

FI i J 5 6

t I 7 LE

t.3ls 190 l,!li 5t3 :6? i52 9$ 5{ 45 J3 ?5

4!

19

l3

IE

t,

15 !l rfl

J.lt0 !.SS3

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t6!94: 5,5?t :!rtB t!98{ ,i2? 3t5 165

t8s 136

t9i ?n 6?

{t 45

E 31 7 t9 6 ?l 5 ts, 4t7

i0 12.;5 i .

4,5S9 5.563 ii,6:5 !.6?5 lS.;Ss l3,ig$ g,gs3 0.1t9 g.lr9 0,lg? Lt3{ 9.156 ?.8tt 6.?4t ll.84t ?6,{{t 6?.?6S t22.iAF Ig!586 99t457 t5{!!3? 344!?74 8l?r9fi9 l$.849 ?iigg? tf,7r5 tEi,BE1, ?4t,t3E i?f.lgg 1.573 l!!td7 t9,t8g 4Jtt34 19?,486 199:?t l

:!3,11 5!789 ?,87! ?!rfi{ 52,4?3 lS!!991 I.353 3,35t 5!7lz 1?!751 3g!5i6 t9,62? 853 ?! ltg .3,19i 9,F35 l9! t23 37,169 57? lr,ll3 7,418 :!17? lt,gu Z4Jrg {9t 993 l,i9l 3,778 8!997 17,{8F ftJ 724 l,?3{ :,;5,1 6!3:l l2r?{9 275 5{1 121 ?,989 {!9?8 9,578 169 4t9 714 11594 J.?96 7,378 t33 32t 55t I,I5{ 2!985 5,803 tE? ?64 45t l!fs{ ?!399 {.i{6 s7 4 3AA 816 l!t{t 3t717

7r i7 3gr 672 r.6tt 69 147 tst 561 t!t35 5i t?4 2l? 47i I,tIs 43

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sc!.i. 5s PIPE

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Simplitied Solutions for Pipe Stress Table 9-3 Contlnued

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UNES ARE O.D., WAIL T'IIICKNESS, AND MOMENT OF INERNA,

Piping Stress Handbook Tbble 9-3 Continued

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6! 3S 54

135 r:5 116

24

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221

712

Simplified Solutions for Pipe Stress Table 9.3

Contlnued

rt 0iF-

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4r

THICrjI/ESS, AND MOMENT OF INERTI,A-

Piping Stress Handbook Table 9-3 Continued

;t

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l4.gtg 16.tdd li,orf 9.t5J t.:50 8.286

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MICKNES& AND MOMENT OF INERTU.

Simplified Solutions for pipe Stsesg TEible 9-3 Contlnued

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Piping Stress Handbook Tbble 9-3 Continued

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3 UNFS ARE AD., WAIT TIIICKNESS, AND MOMENT OF NERTU.

Simplified Solutions for Pipe Stress Table 9-3

Continued

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UNES ANE O.D.

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TEICKNESS. AND MOMENT OF

NERTU.

276

Piping Stress Handbook Table

$3

Contlnued

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:,i?g i, 34:

WAIL TH]CKNESS, AND MOMENT OF INERNA.

16,864

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Simplified Solutions for Pipe Stress Table 9-3 Continued

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WAIL zIIICKNESS, AND MOMENT OF INERNA.

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Piping Stress Handbook Table 9-3 Continued

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3 UNES ARE AD., WAIL T'IIICKNESS, AND MOMENT OF NERNA,

Simplified Solutions for Pipe Stress Table 9-3

Continued

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1?4

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4.

FIRST 3 I.]NES ARE

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WAIL TIIICKNESS, AND MOMENT OF INERTU.

113,:94

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663,4Et

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Piping Stress Handbook Table 9-3 Continued

r.6?3 T!

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s.6:: ls. ist !:.75s L4.Nt 16,6S9 tg.E d ri.gsd 2a.686 t.Js6 0.55s t.36: S.591 0.656 9.7:, ,,Sl: S.?iS 85.i3t ilt. t5r 4fr8.429 55!.?t' 932,3:S 15i1,i;9 ??56.749 4{3:.it.J

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915.lBl 46u,573

2

t6i liI,763 !

i7 6,t4i 449,6?? 7l0,4it

t19 t4,368 1il. t95 2S3! 1{4 459.9t5 685. t57 43,1!l 8!.46S 114.398 l8t,&8{ 3t8, 154 45t, Ei 946.579 l:,iis :9.:86 :7,?16 gg! 345 l33r ??l :16!{l$ 3r?.4i6 664!S !. t4l 27,874 4l!716 5i!572 97,119 l57, ii5 :i5.$; 184,647 i.945 16! 388 31, i38 44,9i5 7?! 9.6 118,539 176,617 36{.1t1 5rl4t 12,7i1 t{,1J8 ll! l!6 56, tS3 ?t.305 $&!f49 tgg,467 4.ts? 19.s49 lE,t65 ?t,i6g 44!:95 7t,814 106,999 ??t,595 I,:69 4.046 15,:'il ?1.345 35,3t3 57, {i8 35.,r79 176,g2l z.,7ic 6,54? l?.159 17! 355 ?8,7i i' 16.74t 6?,611 143,599 t.:57 5.39t lS! 193 14,3tt 23!7!t tS,319 57,39? I l8! t?! 1,8tst 4,494 8,4tfi 1t!91? 19,759 3!.114 47,8,18 9E!64r 1,585 l!78E 7.15i lt, S43 16,653 i7r tsl 1S.lSE il.f$l i,343 3.:19 6.gEl 9t 339 14.1:9 t3,Sfi 34.?i3 ld.65t 1.153 :,7nF 3, ?14 7!lil llt liig 19,7:2 ?t.585 6trigl ??8 ?!;84 4r5t4 6,l:5 i9,187 l7! t36 !5!3d4 52!31; 22,977 15,:15l s68 ?,flt 3,?t7 5,5' ?! 121 I4, Sli 7,r87 l?,16t- i9 lil i?,S35 7rf l, 5 l,lig 4!gl4 669 1,5?l i,'iti 4,317 ;, ii?5 il.{ll 17!it5 ::.S5S :i: 1,4i3 !,069 ;1749 i,il5 !s,69s 19,845 ll t17 5:6 1.?5! :,1;j j,3ii 5,i2i a"i1j 13,1t: :i.3i4 47't tt ii! 2.1i9 :,9;6 4!t34 g.5i! lt.94l 31,6:i 4?l i,ifi!' i,lrg :, 6ttg 4,4?4 7! 1i,,- lS!;f9 :t,9;B 3,?r: 6,469 9,639 ti,r12 ai9 163 l.1ii l,,lrl 34t Bl8 I,545 !, 15t 1.597 5,844 8!797 l?,fiS 711 l!4t1d !,96,i t, ?6i 5.196 7,991 i6,:69 ll9 792 i74 l.l;J I,;87 ;. t64 .1,815 1|174 l,l.7tS !37 6i4 I, i6t l.6l$ 2,i97 4,190 nr3ll 13,456 :t5 56: 1, 561 1,4!d !.4;1 4,t14 3,981 l!,ili 5lg r7l 1.3i6 ?. ?,t3 3,685 5,4S3 il,lEl ir6 qts 5,i:9 10,18t : rit: l,lf: ItB ar4 i.:55 t, !17 3,1i3 4,i41 ?,5:B i5r 436 EII l, r5r l,;76 7i8i|! {. fi4 E!c3: 163 4i2 iig t, $i7 I,ii7 :.sbt 3! ?il S.17t Fs7 -q6 17? igl 1.517 i,,165 ;,67i ;,5;3 i44 :45 137 fls gs5 I,4r9 :.?S9 l!4ll 1,i12 l?6 s5s t3i

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3 UNES ARE O.D.. WAIL MICKNESS, AND MOMENT OF INERTA.

Simplified Solutions for Pip€ Str€ss Table $3 Contlnued

l.it5 T! l?,73 Ii{. stH. uS PIFE tiF-

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aii 419

17; t?4 9F

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s9g

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FIRST 3 UNES ARE

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TTIICKNESE, AND MOMENT OF INERTU.

Piping Stress Handbook Table 9-3 Continued

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?9S 1833.46t ?771.61S :67t.839

1i9.ii5 ?35!t4t 173,0:i t!, ?il 165.::l :6t, ?84 71,5t6 l:6,44i t9$,9S6

tt6, !t6 gl0,4i: :88.71F 5t0,tli

51,ifl 90.494 143.491 : l,l, 9l: {43, sgs 4l,4lJ tt,TrtJ l lS.5:4 167, I S.il.9gi 3?,tgg 54! 924 86.939 l ,4ll 169.9ii :$, $l! 43,5t5 6t,6fl lr5, 5 r15,ll I !l !It4 35, $St 5i.:S? 85.544 175, S:6 17,479 l9!4f6 46,6i8 ;g!496 !44,141 l4t57l ?4,316 38!t74 58t 764 l!6.15= n! ?76 ?t!6i3 3?t 748 49,504 lfl.t66. tg,43E t7. t6' :7.t45 4?! 99? 56,137 8,t49 t5!S:6 ?i,8?3 36.tgl ;3,8:: t73l l3,fi6 :9,6!3 ll, 175 il,796 6, ii4 rJl! 17.9J6 ?;, i14 55.,tS! 5.ESi 9tlqg 15,6t7 !-:! 7:9 49,559 7

:.1i9

s,713

t3.sls

4,591 7!;99 12,2?i 4,S7i 6,953 tS.!64 l,617 6,llt 9! 793 l,:61 5!4i7 F,7FS ?! 936 4,9t9 i, E3t :. s"? 4,4il 7,17 4 2,4i3- 4!S4l S,li l :.165 3.6i$ 5, 1,iE2 3,:5? 5!:t4 t!g?; 3!d,i5 4.85t S?B

1,67C ?.SS?

1,5i5 :.38? 1,4!l ?,37S l9 l,s3t 9b6 939 !,i0 7St 736 699

3t1ifr

!r rTJ

.j,'tcr

l.8Br t, i4g !!i!& 1,515 1,414 1,3:t l!:37 l. t6u

i.954 :! 771

t,287 r,Srt

l,l

4!4:4 ,1. $93

t,::o !.5i8 1,402

?.:4: :,596

lttS? 1,94t

?r,sg5

4?.73A

tE!,t77

37.

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Jl.

ill:

4?6

14,,158

36, d16

l3t

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t:I

91,{

1S.613 :t,88:

itl el1 s, t34 i.t4i t,

,

6,7J4

l9.El! 15,636

16.,14f

!5.!]3t

t]!

7Et

lss l?t ii3 :r 7fg i l, i64 5.?i? ig,i|i {,t67 9.969 4,511 9.? 4,139 g!3i:i l! 997 7,1i 3,631 ,411 l.lst i! 936 Ir 1ig 6!494 i! 966 6117g 6!

l

4

1

1 lrtl

q ,igl

3 UNES ARE O.D., WAIL THICKNESS, AND MOMENT OF INERTA.

Simplified Solutions for Pipe Stress Table 9-3 Contlnued

:.3;5 rS 1?,i5 li,l, slil. Bts PIFE

IFF-

t.375

:.59t

iEl

t. ?lg t,8rF

F.389

:t

ll,tsl :s,?0i 1i9,ll7 ;6!!i4? 5?7,::? 1.34i 15,0?{ 3i,t?s i9,149 l:6,?14 4t7!856 8lt.716? l,4ll i.3lr li,i4: li!i44 63,?SI i7t.f64 314.971 5tB.45S i?3 3,?4i 8,tfi9 l:,!?6 3l'74I 88!597 176,6;t 301,?8t ,119 1,S78 4!&35 l!968 19.5?; 5i!182 it?r?14 1t{.:56 3i{ l.iBl ?,9t9 6,!7i l?!ig7 3i!lt5 64!JrE id9'79t i77 79? l!955 4,?{5 8,239 ?1.5S8 43,1?l l3!i56 t:{ 55$ t!37J ?,954 3!7lA 13,ld6 39,?s6 5iii61 496 1,8c1 :!153 4,:18 llrFlz 2ztg18 $.661 tg 69 3t5 i5! 1,618 3' 161 8,174 16,58S !8'295 5?. ?35 579 1!?46 t,,141 6.3i3 l2t77i 11,794 4t Ig5 45S 9lt 1,9?6 l!91? 19!649 17t14? J63 ?85 1,537 4.gll 8!646 13,72: 13 l{8 ?97 618 l!t5t 3,:&3 t.542 1!,1:9 27 tln q9 :44 li6 1!g3i :,58? lrllt t.lts 72 l8 83 2$4 438 8t8 ?,:41 4.41{ ir6i6 76 1;2 3i9 i73 1!8Eg J!79! 6'{i8 16 lI 5? 146 3i4 6i5 1,6i3 3r?19 i,491 ;69 5?? 1,3?7 ltltr 4.;0u fl 51 l:5 ig 44 ls8 ?33 455 l.l8t itSg{ 41967 ,4 767 3l$ 1.s34 1,613 3,537 s 3r a2 177 34i 9S5 1,815 3!S95 7 ll 717 1,5?7 2,i24 71 156 lt5 7 it ri ?6 64 lJE 27* ;t5 l'4ll l!{ifl it7 l!!55 :, i4l 1f3 2$ it i 13 5 ?l 51 169 ?14 559 1,1:: t,9il t8 19? 35: !,St6 i!716 46 4 l8 452 955 1,144 88 lis 4 t7 4l lsa 40t Slg l'195 *t 3 15 J7 175 741 1ri64 7r t4l 3 l{ 34 j: lJ6 t7{ 1! 149 l:f 3l si i2 3s6 614 lrg4s 6E tl7 I 1l :8 s5 Li7 ?SS 562 ti8 15 : 10 515 u7t 95 ::7 5S r I t3 ,fl :J6 471 E7 4i 2 I :t g3 2t7 436 114 43 ? i 7fr 281 4t? 686 i7 i It 7 1S 3i2 6i5 71 ii6 36 2 7 t7 34 5g 112 145 383I 6 16 gt 169 3rg t46 Jl 1 6 15

; 4

5 6 7

t t LU

l? l3 l1 :s 1l

l9

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3

LTNES

ARE O.D.

,

WAIL TTIICKNESS, AND MOMEITT OF NETN'1.

Piping Stress Handbook Table 9-3 Contlnued

?,3;5

i;5

rFF.

?.

3iT

9.436

9T

i,ili:

2

T0

J,sSt 4.".J9fl 5,:63 6.6?5 !.61I S.itS0 9.b74 ,.73t 0.S64 9 giS 5.ttg i5.iEg lJ.6Jt i6.3t0 i6t.9git

UiY

78,921 ?l 1!q

4

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:67

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lt7

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r:1,911

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174

5d ,tg

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tl ll ti

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378

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11,495

32,95i

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ii?

5l

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ils :t3

i/'

it

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49.194

6, t 16,871 5! 191 17,{17 J.9t9 !t i65 3.1{5 7,6gi ?,518 d.l{t 2,847 5.106 t,687 4, tit l!416 3!{34 1, 1.35 :! 893 |,'tgi ?r,i6g F64 ?,!89 ;46 t,8?; r49 1.:85 5{8 I,3S7

It

t7

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:

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:t 4

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199 6,843 ?! 184 4, tr6 1.5?? J,5d4 1! 196 ?t 6li 9!l ?, i?B

?t4 i85 l5?

5i,?77 l:{!

4,642 lg!ill

6:

t63

iB,i?9

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gt3,;t6

l?1,7b1 34,7{4

t6l

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556

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103

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B.i!5 IR, Sti{. i:is FIFt

i35 1:6 ii6 lfit Lli'

iit

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3:5 4,19

42' 3?4

i6i 33J trEE

?84 261

:,i3

3 UNES ARE OD., WAIL T'HICKNESS, AND MOMENT OF INERNA.

Simplified Solutions for Pipe Stress Table $3 Contlnued

d.6i5 Tl ?4 iH.

,itt:!T

:;

s.6:5

g,5

i,J.

i5S

S.1r8

i2,75S S.443

iit.3?s :86.139 16l.65g

sCH. lEg PIFE

14.u6g 16,99t 13',Jrio 2g'fr88 :4'oti

r.937 l.g3t 1.156 l.:81

S?4.41{ lJ64.,l3t ?179'6SS

l3l5'ttS

1.5:l

e€:1.i?..

3

+

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7i :1

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157.467 46i,7t9 914 t 144 tgl. tt3 ?38,441 4S8,i4? 58.559 1:;,9BS ?7,J!854 16!t45 86,896 179'569

6g7r63g 397.5S7

659!99?

?59!375

41{,36t

?,157 :,111 !g! jil2 l{!?:5 I, B4l 4,145 S,:3f 1!,::l !,:it t!7?6 7.3iI lt!i35 I,lt3 1.3i3 ;. a i,:li IttgT ;,799 3!494 8,0i5 1,639 ?,43fi 4!!i9 ir S5l 914 :, rs6 4,?t: 6,?12 Edr l.lsg 3! i44 5!4?6 it? i,69i 3,3:9 4,SS6 64? I,514 2,?77 {:363 5?6 1,35t ?.s6: 3r !!? 3ts l!::? t,ltt 3,3?1 45S 1.164 z,lhi l! !8! 4?4 1! 6!if i,9ri4 ?,lu; 380 919 lt 795 2,ill st9 !!i!a ?,l9t ;i? 7iB I,,t89 ?! lg5 ;;? it5 095 i,365 :,,i93 lii iri i,::4 1tS41 :,i9 584 1,155 l,6ti :;f 341 1.,,6u l!5$5 :13 :8? 986 lr44g 191 ,i6, tl4 i 3,1? 1fl3 4t? 849 tli,li t

il FIFST

t$l.955

:4!693 58, 4 114.2i8 l!7!73? 277,513 445!{5S rzi.+lr -: 17,tJ6 4t,E!5 St! ?54 ll?:gg4 t94,?i4 3ll!455 473!6Bt 9it.Sl7 t?,63s :t.8s5 5S,5t5 gi,g7f r42.1?8 r?7. S5l 343rJl5 i13.7tB 9,495 ?!.393 43,956 64!322 196,?93 l7t,5B7 259,44S 5lg.??; 7!It1 i7,?4S Il!E5t 4?.699 93t ?59 lll!195 ll ?. aJs 413!t51 5!75? 13.166 ?4.619 39,SBl 64! S9t 103,146 l5?! 175 3:4! 969 4!656 ig! 8&? :1!lil il!?97 5lt7i6 BI!iq4 t?5,S41 169.lgl 1,745 8,83t 17,335 ?5,446 4?,1l? h7 t274 1g?,315 ztr,47t J,585 7,?7,1 14,:E4 :g! 946 i4.699 55,,11: s4.rt5 174.?18 ?!3?t 6,967 11,9dS 17.,lso ?8.939 4i! !14 7g,2g| 145, i7l

:1,17t

38,51?

zg,72t !7t766 t5,347

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7r:?l $,4i5

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164

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?:,1SS

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1$4,956

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tlg

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l9!64;

40.

11.515 16,343

17,144.

3s, ?6i

t!

319

t64 8.469 7!6!l 4,ii | {.:3t 6.1:9 3.953 6! 319 1,616 iri'ii 1,315 :t:96 It {;16 ,i, Ai6 ?.896 4,1g: 2!77t !, s6:

4J.

l

t?,!lg

5,

;,i9s i,;t6

5?! 6 3S.3{r

4.1:r

3,9!t 1,518

J,:94

3 UNES INN O.D., WAIL THICKNESS, AND MOMENT OF INERNA.

6t8

13,;3i !i! l:?

3?!:13

12,73?

:6.41,i :i! t5g

ll,igl

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Ig,33X:' ;1r;dl 9,&S9 l9,i6f

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f,

5,019 li! l:6

Piping Stress Handbook Table 9-g

Continued

4.i i0 l:.i5 I{. UiFSET

F1

2

;

I

1 a

I It l? i3

l5 l,: 17

ts

it 2g

?l :? :3 t5 ;b ?; !$

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tl i5

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FIPE

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l:1,

s4t

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115!

14,99? ?9!?7!

igl 7ig

a4t! 9tl 191,3!9

5,1:,lBt

I s9,746 ?is, i36 5?i.7ll ?t 443 4i!J4? lli,lll ??f. tEg 3t4, i?s 5!g?4 t!,4t9 23t 9?5 67,77{ 156,t59 3i?,445 i! 54t 7!9t3 15.SS6 4?,S8t 9S.465 l?4, Eit ?.371 5,t35 l0.tt3 ig! 59? 65, ?$4 lt$,547 l, &$i 1ttt77 7,989 ?fi!081 46,3?? 91rgE7 t,?15 :,6S6 5.16S 14,639 il,7;3 6,5,541' 3 t,014 3rg8l t0! 999 ?5,375 59,118 ;0J 1.551 t!t9t c.47? 19.545 lB,rdl

lg!

9J

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sti1,

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4t 17 34 31 ?i ?6 i,i t: 1fi 11 iu

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ga

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srt s? 75 6S 63 57 53 49 4i 1t lY

rr

J.JL

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l!531 1, ?6?

I

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i74 331

294 ?S3

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6,66J 15,3?3 5,115 l?.1t8 4!338 l$!997

1,374 It ?8t 2.:10 ?, ii4 I,EJd i,:Br

3S.4?3

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8.t45 16.JiA 6!87{ ll,6Fi 7!1 i1,461 4!9?4 9! 745 51

4r7ZZ

1,647 11175 3.17: 1, ?S3 2,17& 1.f59 ?! 443 937 3! 16! i44 661 6SS 54? 491 447 487 37: 141 il1 7AS t67 217 ?2i ?l?

8!l:5 7,;i? 6, i7; 5,494 1.435 4, ?79

t!71d 3,196 1.53? I,945 f! 355 I! i,li l!:31 :1476 1,134 ?,244 1,031 I,E4B 94S l!96g S5? i.;91 789 1,55t j74 i!43r 6i7 1,l2j; &!5 l!?18 ;,)t 1,1:i 5:g I,944 ,ifr 4t,

3 UNES ARE AD,, WAIL THICKNESS, AND MOMENT OF NERru.

Simplified Solutions for Pipe Stress Table 9-3 Contlnued

I,t 10 !4 il{. scll, 1i0

cFt-

iEI

l4.E9t ri.g00 lE'tlgg ig'g$n :4.d0, l.gt3 l.tlg l.3lt 1.-5Eg i.sl! 9ir.5:r' l:55.419

lsr.11: Il$,441

'J

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i3 t.l

249S.irgt 3;5{.13S 568,!34

l]?,819 !22,i32 :36!tsl 96,s:5 16?,S?? :oS! ?lB 7:,746 l?l 710 195t3{5 56,933 93!761 159,589 r

4{![7] 73,]{7 tl8!4{? J5!?96 59,i{6 94.83?

15

l6

76

1

gl5,t57

?93.gsl 6ii.l65

:?6.36i

4il

t77t996

379t987

!61?

l{?!514 ?i7,933 lt3!8A9 ?4t.49d

l2!978

5?,965

27,182

44t6i9

6i,p54

37,9J8

57,914 I lB! 839 48,8S? lSl!88?

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J?,5?7

19,455 17.495

?s,69S

15t

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7!958 13,3t7

:3

539,43S

lil,g58

95,473 ltg.9g9 79!597 155!S9g.

9!i9l

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77,19? 63!539

16!

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78?1'53S

28,6t9 48,967 ?3!619 3Yr33&

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l3?! 756

4?!2?6 3&.7?6 3?! 141 :8.r8€ 2:,0:8

83.01S 76.546 66! 999

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FIRST

PIFE

3

LINES ARE O.D.,

WAII TIIICriI{ESS,

5t,?6s

AND MOMENT OF NERNA.

Piping Stress Handbook Table 9-3 Continued

E,iir5 T0 iS. r'55 l:.75d d.El: L.t1g l. ltS

S,6?5

iiFF5EI

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9

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tt?r976

94,95r

r6r,gi?

il,7t4 zi,lt3 !l!7;r ts, i4i 15, sss iJ.t73

?t,9?6

!

19.

1,554

439,

195,595

it9

6l!

857,6;:i

i:5

54,344

17,r8?

130, I

4{r

63,330

19i,

7lg 3i,t3? iI,449

?6.71s

ri.965 4,{.6tt 37, ?38

,5!7

S05 ?9. s?8 lit,i4t 17,:?5 :4,418 8.7t4 15.i71 :i,lBi

,i{E 13! t6a tB, s;4 0,94! ll.7;c int iii4 i, Sgg lf,4l5 14, !rt5 5.436 tr ilg 11,:!, ,i.!i4 E,155 1i, r31 ji.la7 7,5:d li. tit i,96t 6. i93 9,518 3, it: e,l5r 8,7i5 l! ts5 ;.59i 7. t41 21977 5! l9{ 7,741 7.72L 4, itsi i,5;1 :,'i96 4,!i8 6! 669 ?,:91 l, t:] 1,1i1 ?: ll? :,.s: t 5,1]7 1,9"id J,:41 4,;4? l, s.4,1 t.59: 4,r-r? 1,6?? t,E6b 4.65i r:5:l !,661 3, i76 i

l

LNES ARE OD., WAIL THICKNESS. AND MOMENT OF INERTA.

l?

408,93t t?7.,1l9 i66, !S4

?09 t1t,i45

89.381

tB7,97A

75.?C6 l5,i, dsi

64,d:? :4,ECl t7.4i

i

11,:4S

t9: ll,;ii :e! iE4 l,l, ts4 :;,:10 :;,br,t 36,

18,i,i5

1ig,9E7 I

l!.3S5 97, citJ

!4..:,ii 73,

e4:

64,iri :7.:is 31,lli 15,0,15

4it. ?:7 36, a3S

1i,i64 ;t.!?: li.4Jl l?!:t9 1r 1;Z

lA )A.1 t, il; 0 tti

; ;;r

I s,l7l

6, gr

:7r1i5 :5, tgg

ii 1l

Eio tlaa

1t,;:;

l? 1?; ii :;: l!.1{C

14.

fii

13,

fl5

Simplilied Solutions for Pipe Stress Table 9-3 Continued

r.;i5 i0 1:.;5 I}{ Stii. !i-F-

i.3;5

5ai

t.l4i l.l5i

FT

l.5rs 4.5t0 3, ti: t.4:8 9.5;1 F. ElE 5.F3ii l:. i;i -l.l,sl,

l;i i-i, !l? l7?,;!-t 4,,iBi 19.441 3i,:fi ll.6id l, s9: !, tt: i6t 4,199 I l,!159 561 :,11S g,4cD :5i t.5lg 4. s38 !16 lrEl5 :.igt lg6 171 i,e?i i?1 5:5 r,l8? ti 3t4 1.039 lfi l$4 sfg t39 619 5i 5t4 44 i9l i6 !;5i 4tX 1.:6 lfg :ll 107 ?St !5 9E ::t !1 ii ii li:! 15 i6 itl ll 57 14! 19 iit ll

;

lg,

i t n

l B

I

ti

II

l!

1l

is

ii i1 IS

i?

!l

l! 4.1 I ld U14rf

1l i1

:i

ti9 6 6t4ri 7ll

:! !1 :i'j

:/

i i,+

lei}

!9 7l

:i it7

I

l1

ii

:t

:

!t3

i5

l: l,l

ar;l :irt

i:

4i FIPST

3

LINES ARE

i

FIFE

6.s;: g. E 5S.97i

8.

d:5

d.9tl6

li5.

USB

i0. r.

i:F ti;

ii. t5t

1.;i! 39t,t6fl ii1.l:!i

i5i ii7,llt

15.349 :!7,t?d

ti$ 95,995 :i9. ?t9 649,91: i39,:39 l::,75,! 6:r,9:g :5, r?: 4t, 114 eg,sio lt:,:67 576,7i9 11, St ?8.449 t6,3i9 lii 16? :i7:l:: 9! 119 17:?!E i1,99S Il,;5t sl,:t5 ii8.9!E o, ii9 ,1.:ts s,4ii 23,i94 3i,i57 i!l!Ji5 6.143 17. ?88 41,:9: S1,.rS7 I, l:a ::359 4,515 l?,9i3 31, ?51 5l,l3: F6! ts, sgs ?4,i?l I, EiB 3,355 17t ril6 lf. t32 t!424 :r7i6 7r86: :9,633 r, ?97 15.1:c ?,?-19 1, r4t i27 i, Elg :, t:9 i?!3t4 14, i99 7i4 1,5tt 4.:i9 It,155 rt,t65 6i7 I, ?59 3,3i7 8, {6s 16! i6: :3i 1, g5l ?,5$i 7, l: !1,951 456 3ti :,51! 6r ig{ l, i5; 18, i;1 .1$i ?! Lit 5, i!? i9l l,ti6 {.4ti t! i3b -ll9 6il i,{; iilb l,6lJ it4 -Jtl i,6ES 1.4 19 i,,ilt lii l,;is -1,!ii9 s.eui 444 i:i 5,:ig !, eii I, rf6 tg,i {! J:Y :!/ 7dr i. :58 1;8 ,i, ii,i rr: 57E :, ll: Lr9 1,:',t7 i.!95 is7 ld5 i4? i8, i,7t: .:';js t:s i:i 1,541 ;,':114 54$ ::9 lli !.:16 :,.;:l 589 :!;i irl5 :, i33 l,:69 9:; l: i6i ;' i6,t lJ 1:? 4Et 5i i/t j 1, t7t 14ri i,t58 st

43,

!

;17,

I

!

/' !

,1,

37,1

-.1't!

4td4b {!i1: 1 15 i13:5 :i?:: I 1i

t1

lYt,

l5,i

13

l-q

l*

i,r

ii 3i ti

;9 4:

i;i

t:l I

ll

! Ll{

ti

ur

4Ui .)iE l5l J.l_J lYl

''if 3t: ii;.l r:! /'Ji

|ii ::l

!5t it4

O.D., WALL THICKNESS, AND MOMENT OF INERTIA.

l,iY) i! /tJ r r c..o

-,'ilJ :,:ti

i,:;:' i, iEl

Piping Stress Handbook Table 9-3 Continued

14

:--' s

i !;j

14.i{$ i6. trt! 18.0i0 1.4s$ L5!3 f.igl I i lS.61d 1St3.5tt 3 9.?ot ::i! 1g: ls5,i4l 6t4t4tl 15?!i57 ?10.56r. 4ll,::u 6,31? 197,?4I tr 579

i9t 6i.ill

tt? I14, !{6 l4gl

97,

t:

;! :4 iil. 5ifi. :oi PttE

:t6,l1E 13frt4F

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5:,944 8r.771 143. 136 4?.J9t 7t, dti ll4!i43

lil l6

?3,t95 48,155 76,S$?

t:

l: i!

It :t

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441

s?3 {S,l4i JS,B i6,93S ?g! 757

93t

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64,S1,

19,945

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t49

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1.968 :,343 ?it t435.4tF

4:Ss.

iSlt Si3 $-i5.lst

477.6:6 9S4r?S? l5E,S48 it9.999

t76.4t4 fl7.19?

5r?,9!i

rii5? 14l,519

J59,9+3

l!$!

?49,16{ :FS,476

4{9,311

l74,

6t9 97 t?l]

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81.997

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14,541i :4.655 ;?,lt: t?::6t 21,295 33! 9$S

n9.6:i

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14,555 Ji. i6!

11.148

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FIRST 3 UNES ARE

.

if3

51,574 196,:3i

l! | 7-q8

594 li,att l9!

t;,5$9

6J, tt,i6

41,86S 4S,333

lb,47V

16,S31 t3,'J5i Siii lI, FiS

14,

11,:91

27,46

t"

i51 ?5. t6i I t. i4s :i.9t: t6,:17 ;lt1ll t,4i! Itt 445 t?,

E!764

s,d5?

ti,95s l6,6t4

i,4$l li, i9F 6! 9IS 14! tql ii! 'i47 ll.:?4 6, dn7 t:,389 5, siri ,:62 :r?4t td! Et9 ,i,9fli lf,l1t 4,tfro 9,487

O.D., WAIL TI/ICKNESS, AND MOMENT OF ]NERTA.

Simplified Solutions lor Pipe For the example shown in Figure 9-1, it will take 7,552 lb for a l-in. expansion for a 10-ft offset for Ax '9214 ex' oansion the force F- = 6,949 lb' For a 20-ft offset the iorce will tr-g44lb for a l-in. expansion. for Ay 46 in' 434 Ib. the force Fv

:

The nomograph in Figure 9-2 is used to size piping loops, depending on the size of the pipe and the thermal exoansion between anchors. This nomograph is conserva-

tivi for a refined design' An exact

calculation by com-

puter should be required.

What size piping loop will be required for a 300-ft straight pipeline under the following conditions: TbmDerature: 400"F O.D.: 12,750 Schedule: Sch 140 Materials: A-53 Grade B C.S. Use the nomograph in Figure 9-2, and join points A' B, and C. This will ihow a need of a 70-ft loop (L = 70 ft).

11

A

J&

;f

L = 2A+B

100

o

-c o

o <)

Tc)

-T

-o:i !x

o o

9+ <=* o-

E

;-

-o

o .9

^J

o-

oo

(d

'zo

291

Example Problem 9'2

B

l-t -]JL

Stress

o1000

IJJ

Flgure 9-2. Stress nomograph'

0)

10 Properties of Pipe

: Fifth power ofd, in.5 = DrlL2: outside pipe surface, ftrlft (ength) : dtr/12 : inside pipe surface, ff/ft Qength) : @2 - &)n 14 : metal area, in.2 : d'z rl4 : flow area, in.2 : 3.4A. = weight of pipe, lb/ft W* : 0.433 Ar : weight of water in pipe, lb/ft Rg : (UA)', : (V + &1*4 : radius of gyration. m. I : A.Rl : 0.0491 (Da - 6+; : moment of inertia, in.a Z : 2llD : 0.0982 (D4 - d4yD = section modulus : in.3 ds A" Ai A. & W

The following are the definitions of the tefms used in the table.

Definitions

D = Outside diameter of pipe, in. Sch : Pipe schedule, nondimensional t : tl6ll thickness, in. d : lnside diameter of pipe. in.

Table 10-1 Properties ot Pipe

T

Sch

D

losi

V8

40

sT 40s

D'.40S

80

xs

80s

Y4

40

sT {0si

D

-.540

3/s D

-.675

tosi

o

d"

Ao

A1

.105

.080

.049 .068 .095

.30? .269

.00141

tna

.215

.000{6

.108

.uoo .088

.410 .364

80 )
.u9

.302

.01159 .00639 .@251

.l4l

.u50 .107 .093

Am ,1qa

.314

.09?

.132

.330

,104

.42,5

.a .l9l

.04{xt8

.14:l

.q2st2

.124

.129

.lDrl

.423.

.01354

l0s

.oet .I09

.674 .546

.13909 :09310 .04852

r87

.46{;

nttoq

.2,94

.?s2

.00102

D -.840

160

.

)o(

.245

.t25 .I5:I

.i193

xs

.I215

.036

,54!i

Y2

.032 .025

.092

.09t

40s 80s

Rg

.186

.uoat

sT

Ww

.0?4 -u:tr

losl

40 80

l.l

.022

4osi 40 s{, xs €osi

sr

Af

$n

.l .05? .045

.48

.r0l

.568 .?39

.083

.06t

.5-fl .85t

,154

l1',

.tu

.ni

.l?8

.r97

.J:lrt

.163

.2.fi

3m

.304 .?'34

1.088

.t0l

.384

.l7r

1.304

.074

.504

.050

.no -no .ao

292

.l€ trt .uoo

.

t40

.t2,

I

z

.m09

.00{t

.0ol

.00s2

I

l{6 .mt2

.1694 .1628 .154? .2169 ,2090

.0028

.qxB .oqB

.0060

.01@ .0123 .0140

.01?r

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.269

.0143

.034t

.261

n!tt

.250

.020I

.244

.2t9

.02$

.0216

.02s5

.o.t{n .0478 .052?

.ofi

293

Properties of Pipe Table 10-1

Continued

)

e

3/t

t

Sch

l)

40

sT xsi

5.:

.uqt

losi

.08:l

.g?a .884

40s

.l t3

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-

1.050

-

1.315

l.6A)

1.900

D

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Lno .803

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.N

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.344

.230

.250

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.519 -Jbu

,344

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.0?t

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-uo!)

1.530

80

t60

xli

8{xi

xx

sT 40!i 80 xs 80s 160

80

xs

sT

t{o

.19l

2g

-uoit .109

.145

1.380

LnB 1.160

.478

1.404

,409 .374

.639

7tq

2.1t2

tta

.?54 .836

.m4

2.56{

.344

.15?

1.0?6

8.384

€!t

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5.UUit

434 434 434

-5t.(

434

13.46 10.82

497

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497

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t.770 1.682 1.610

.uoal

2.2+3

40s

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80s

xx 55

t0s

497

.506

.472

.3412

L.ZIJ

l.uo9

.649 .634 .623

.t58

.962 .882

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2-m t

naa

.?99

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2.7t4

1.068

l.$l

| 1et l.404

3.632 4.866 6.409

.@8

3.938 4.381

l.4l?

1.0?4

t.158 t.288

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13.74

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l.sql

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2.?09 2.635 2.45I)

t4s.9 91.8

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.491

1.669

2.761

5.6'14

I

.458

2.{0s

6.884

1.041

,442

2-0zs 2.190

?^240

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2.856

l.Tl4

9.q'0

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1.039

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3.531 5.?94

2.49€ 2.361

.753

5.45 4.79 4.68 4.24

1.812

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.568

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./ro

.lgq! .2t37 ,1253 .1934 .2346 -?s14 .3421

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.2& -cuat

.?10

.516 .654

.868

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.804 .738

1.102

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5.30

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1.Y50

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2.945

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3.6St

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oo?

1.605 2.638

.6?,,

.1811

l.ost

3.958 3.654 3.356

4.17

.148

t.2gt

t

.4t2

l-ttr5 t.750

D -3.50O

2.273

.588

O.lO

.lzs

1.498

.6?2

I

3.334 3.260 3.250

.648

.564 .550 .540

.6n

.zta

.t?a

.t?sz .l4os

46.59

.s24

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sll'ql

.534

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.622

.552

lt?t

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2.451

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1.885

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t.6l

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238

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49? 497

2.041

3 40si

.334 .304

.16-t .188

.tm 4{Xl

2.6r

€4 497

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3.409 2.100

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?.59 4.27

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l.lct

1.s00 1.33? 1.100

.200

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.

.382

40

8o 2.8?5

.234

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.064

.l?9

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D

2.441

.lgl

1

71i

.l4s

4os

2.3J5

I

.va

80 :c3 8{Et

xx t1l

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{o sT 40s

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160

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t.t4 t.93?

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t let

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z

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I

.49

1.09? 1.049

.1401

Rg

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t60 03

t94

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40

2

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t'f1

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5St

-

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D

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u-

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t11

tffi

n.

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x:E

ry4

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Ai

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.na

160

55

D

Ao

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x:<

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d"

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80

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d

4.51

?.58

3.61

l.gn

l.l2l

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iqo

t.l9{

3.49 3.32 3.20

1.186

2.t94

l.l6f

t a6t

l.D.to

3.018

t.724

l.8so

1.080

294

Piping Stress Handbook Table 10-1 Continued

t

Sch

D

(continuod)

3 D -3.500

.241 .254 80

xs

80s

160

55

-4.000

t oot t ot, 2.900

Ao

40 80

sT

xs

1A.'

244

.9t6 attl

3.834

88

1.04? 1.047

t.021 1.4&l

oa

1.047 1.04?

.970

r.047

.9,19

2.Al

10.94 10.78 r0.31

562 480

1.04?

2.680

t.04?

.929 ,900

oqo

3.€8 3.364

431

1.047

.881

.t.ol6

8.89

tz.sl

3.9st

9E t.Jo

13.€

3.?44

1.004 .984 .980

.134

3.732

AT'

.

t48

-

rtt6

3.?04 3.624

.tn t28

taz

3.548

,lta

.083

alt .r.t,

t20

69?

e ala

t.04? 269

4.334

1.04? 1.047 1.178

4.244

t371

1.178

t.1l

I.t?8

4.2t6

1358 1332

1.108 1.104

4.t24 4.090 4.026

1193 1144 1058

4.000

i024

3.900

3.500

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3.152

tno .t34

5,34S

$ sT 40s

5 D:5.563

80

xs

80s .438

t20

l@

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xx

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4.563 4.313 4.063

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l

L65l t.

tJo

-456 1.944 t

1.080

902

1.1?8

t.021

4.10

1.178

1.015 1.002

I t7q I t7e I l?a

ott

4.86

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5.59

I l?q

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1.178 4363

1.399

270a

t.456

t.272

ZJtaI

1.456 1.456

1.250

ll0?

1.456 1.456 1.4s6

l.38ri r.321

l.n7 l.l9{ I l2q

1.064

1.349

4.10

t.3!9 1.298

t ,ro

6.09 6.04

1.544

1.546

t.542

8.66 1.520

ta! 7c|

5.44

OA'

21.36

1.4.t4 1.425

4.O2

1.416

\t.Jtt

1.3?4

a tt

o

tt

t4.61

11.34

12.97

JO-JJ

2.81 J.JO 4.ZL

t.2{8

4.@

2.054

s.93

2-64 2.84

1.262 1.869

i.949

7.88

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4.27 10.42

9.ld

t't t, o.,t9

8.€

l5.l?

8.66 8.03

41Cr

t.928 1.920

9.70

4,925

4.02

1.464

27.04 32.9?

4.tn

8.?8 9.05

4.4t

23.95

3.33t

3.?0

4.78

7.9S

3.Ul

8.08 q i,t

19.00

?.4.74

2.394

z.atat

1.505 1.498 1.495

16.52

18.54 18.19 17.26

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1,664 2.050

', t1

I1.04 'tn 1l

t4-62

ata

r.sa

1.510

4.98

20.01

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1.461

1.534

14.99

u.43 a.o2

4.79

1.210

l.{8:i 1.4?

1.88 2.?S 4.30

7.04

3.04 it.,at

5.98

27.54

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1.368

1.549

9.28

2.74a

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.r.6t 3.19

2.?A4

2.78

1.489

7.80

1.962

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t.372

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13.46

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3.{3

3.42S

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1.455 1.4s6 1.456

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5.04 0.Ylt

4.67

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5.00

7.64

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l.l40

6.39

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3.9t

I1.80 I1.50

t. t?8

l.8o

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12.s7

94?

480

17.69

5.84 tt

3.34 3.60 3.74 ,l oa

1.047 1.036

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a crl 6.09

ota

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tcl

40

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3.10 3.04 2.90

l4{t

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55 losi

Z.5IJ

8.81 9.91

2.462 2.5S0

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40si

80s

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250

20s

Af

A1

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D

3.018

o

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tosi

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Properties of

Pipe

295

Table 10-1 Continued

D

S

t

ch lqs

.109 .134 .180 .188 .219

5

q

d 6.407

d"

Ao

Ai

10.80

1.734 1.734

t.6?7

10.38

9.82

I.734 r.?34

6.249

6.071 4{,

80

sT

xs

4osi 80si

:o( lnq

8.2t

.2.&

9.lol

.500

5.O25

.s62 .?18 .864

5.501

.109 .148 .158

8.407

4.897

5.04 ,t 7a

3.$

1.640 l. qlo 1.620

3.80

1.604 1.589

r.?34

t.588

I t.?34

t.440

4.41

J.5at

2.?'58

36.8

8.149 20

8

40

sT

.tTt 40tt

D-8.625 60

80

lm

xs

34.2

2.248

7.93?

1t<

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', otl

al ,

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7.875 7.813

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7.439

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xx

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10

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D = 10.750

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10.482 10.420 10.374

2.2€8 2.258

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2.133

2t.32 2237

cl a

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35.4

23.40

30.43

2.99

49.3

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47.9

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46.4 45.?

55.2 22.45

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2.81

2.74 2.73

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23.25 24.52

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140.6

32.60

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tt

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38.48

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14.30 \t.lJ

87.0

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84.5

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2.94

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23.44

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4.42

45.4

1a^ 8.40

6.83

2.246 2.248

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t8.gtl

3.94

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2.86 c.a

8.16

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10.344 10.310 10.250

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t0

ce t?

1.996 1.944

tn

v.o2

7

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2.089 2.O78

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2.2,58

to t lo.o

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15.64

2,180

2.045

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32.4

80s

120 140

35.4

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2.160

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9.29

13.28

2.201

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10.70

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q 1q7

31.?

8.40

J5.O

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18.78

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2.81 2.81

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80.7 79.4 ?8.9

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34.9 34.4

J.b9 3.68

I54-0

lAt

160.8

4.6

296

Piping Stress Handbook Table 10-1 Continued

n

?

Sch

(continurd)

..JYC

60

to D

-

10.750

xs

80s

80

l0o

.sll

12.85

?.55 2.54

16.t0

9.564

80.0

85.3

9.314

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2.81

2.50

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4'8

18.92

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tt.a

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68.1

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9.064 q ?q/t

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z,8l

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2.81

2.4

6.U

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30.63

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2-26

t.t2s

8,500

44.4

2.81

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298

t0s

.td)

12.390

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t?^344

82 u7

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12.312

2A3

8.625

40st

tlJw

t,J

?t.9

tt.2

xst 80s

32.3

3t.9

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172-5

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3.60 J.50 3.stt

244.9 ?€.8.2

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58.4

109.9

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3.52 3.4? 3.4It

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60.l

384.0

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3,l.Oa

56.?

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24.6

3.{il

399.4

?4.3

3.34 3.34 3.34

3.25 3.24

6.17

12t,5

2t.o

120.6

52.6 s2.2

8.(x!

1t9.7

4.45 4,44 4.44

1?9'4 140.5

3.el

24.2 27.2

3-n

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8.62 9.36 9.82

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t2.t92

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12.090

3.34 3.34

3.t8 3.I?

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269 zo:t 258

3.3{

r2.150

12.88

n4.8

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t2.062

it5!l

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I

249 242

3.16 3.14 3.13

I14.3

12.000

3.34 3.34 3.34

13.4t

.t' ID

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ttl o

4It.6 49.6 53.5

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88 n4

3.34 3,34 3.34

3.I I 3.08 3.04

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65.4 73.2

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103.9 101.6 96.1

80.9 88.5

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26.6 28.7

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212.7

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4.3!)

248.5

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4.39 4.38 4.3?

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47.1

4.36 4.3it {.31

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50.4 56.? 62.8

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144.4 143.6

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469 459 452

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26 24

32.3 34.8

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62.0 60.8

2S5

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4.86 4.84 4.82

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36.s 45.0

3nl

5:t.3

59.0 63.4 67.8

59.1

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4.80

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58.6 58.0

4.79

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80.3

55.3

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562 589

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13.188

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l3.l2s

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389 380

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13.0@ t2.814 t2.?50

40

xst 60

to2

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3?1

345

3:l?

2.98 2.90

taa

23.8t ?.6.&

118.3

15t.5

t9.2

a.o z4.l

I t.500 I t.s16

160

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23.56

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14.000

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9.960 9.?!t0 9.68?

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D-12-7fi

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140

t2

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31.5!l

10,29

3.53 3.50 3.47

10.80 IO.UJ

l4il.1 l4(,.s t3?.9

3.6? 3.67 3.67

3.45

17.34

136.6

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3.42

19.94

134.0

3.6? 3.6? 3.67

3.40

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132.?

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3.34

24.9A 26.26

84.9 89.3

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t3.44

tn.7

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242

lno o 116.4

84.1

Properties of

Pipe

297

Table 10-1

Continued

I

i

Sch

D

q

t

d

Ao

o

Al

Am

Rq

hI

I

z

I

I

(contiaucd)

.ooo .?50

80

I

t2.r?s

I00

l4 D-

1.093 1.250 1.344

120 140

14.000 160

.r

262

u.814 .t.ot

I1.500

1.406

I1.188

,I88

t5.624 I5.524

ott

4.19

902

4.

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15.500

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4.t9

842

4.19 4.19 4.19

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15.438

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15.124

30 ST

l6 D-

4()

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i

16.0@

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80

4.19 4.19 4.19 4.19 4.19

126.4 12,,.7

c.t I

614

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4.69

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38.4?

lr5-5

t30.8

50.0

4.63

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98.2 117.9

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4d32

109.6

150.7

3.0r

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47.5 4{i.0

4.58 4.53

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601

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4.19 4.19

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144.5

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t3.124 13.000

38!) rtll

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t2.at4

345

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16.750 16.562 16.500

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80 100

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120

15.250

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950

1.688

14.625

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13.94 17.36

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194.5

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136.8 143.3

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38.98

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132,5

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213.8

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2t0.6 m4.2

138.2 149.2

4.n 4.lr 3,99 3.89

{.876

t.?8t

4.?l

t?5.3 t

l.5m l.sg!

13.938

31.62

54.8

72.8

boc

t.4il8

tou

18.41

ct.5

684

I40

.?50 .812

184.1

14.688 14.625

459

60

t*r, ts.40 I6.92

,l ot

t3.56{

t8

t

4.19

t.218

40

too.

93.5

744

tm

xs

I

2t.4I

t.$r

ST

18.00O

15.062 15.000 14.938

808

.tt

l@

?n

D-

rf

Itc

.28 .2fi

!0

a

12.688 12.500

I

t,l'r

193.3 142.7

80.65

3.&t

86.{8

Itt6-u

3.?8

90.?3

tdt.?

lm.8

294.0 308.5

103.6

L1J

1

5.90

5.84 5.80

L

2908 3020

8I-A $!!.5 323.1

als.6

298

Piping Stress Handbook Table 10-1 Continued

Sch

D

t0

20 D

-

20

sT

30

xs

l9.s@

.sls

t9.3?5 r9.250 t9.124

.3t2

.4its .5tI,

40

.593

18.814

.62s

.8tz

I8.?50

6{'

tSIt

1.99

1.500

17.000

1.42

140

l.?50

16.500

l60

1.844 1.968

t.u

16.0€4

.?g

2t.s@

l0

st

:
.500

.?.&

sT

.312

4.?,fi

.€8

a.ps

.o{r,

D

-

23.000

.DOZ

22.876

.625

4.750 4.626 22.064

80

t.2r8

21.938 21.564

t0o

t.531

l.oall

I.812

140

2.0t2

160

2.188 ?-3+3

sa

xl;

20

ST

xll

.JI5

.500 ,312

20.938 20.376

r9.8?6 19.52s

r9.3t4

8.zfi

25.0q) 29.3?6

.438

2.9.t25

.500

29.000

tQ a.ra

8.zfi

30

42 42.000

23.500 23.376

.968

@

26.000

36.0@

2t.?so 21.0m

n.w

30

-

lo.Jl!t

.750

t0

D

17.€8

.irri'

.6Al

40

26

36

3.4

l?.938 l?.5@

tm

-

2.36

1.03t 1.2s0 1.28t

80

30

34.00O

5.11

2.N

5.24 5.24 3.24 5.24 5.24 5.24

2.02

xs

34

2.82 2.73 2.64 2.56 2.48

18.250

20

D-30.000

Ai

.EIO

l0

D:2{,000

Ao

2.to

D-2Co0

24

o

18.376 18.

20.000

22

D

19.000

.552

t6

-

.250

!e a?t

r00

D

)

t

ST

xs ST

xs ST

xli

-J/5

.s00 .r.rE

.5m II'E

.500

r.86 1.64

l.6t

5.24 5.24 5.24 5.24 5.24 5.24 5.24

5.Zt

5.0? 5.04

(nt

4.9? 4.94 4.93 4.91

4.8t 4.?8 4.?6 4.70 4.58

4.'r 4.4{t

t.t6

5.24 5.24

1.07

4.9 4.n

5.?A

4.21

4.59 4.3it 4.08

o.to

5.dl

c.,t0

7.r7

6.8

t.oo

o-15

Am

!9.36

ta t,

26.9 30.6 34.3 36.2 38.0 48.9 52.€ 54,3 61.4 J!t.o

?5.3 87.2

Af 298.6 294.8 291.0

?at.z 283.5

t29.8

lt 52.7

12s.3 LZt.O

t04.I

It6.8

t?0.4 l?8.7

6.48 5.4tt

4379

atl.at

6.4I

{586

?.69

t0l0

l -Dil

1490

209.0

Jilt.5

2,02.7

3?9.I

l?.r

363

58.1

120.4

ll{.8

lct.4

t787

35.tt

l4{i.?

o.l9

ucl 8.7

6.71

2&9

o.lo 6.72 6.64 6.63

2483

240.9 24a.3

32s!

325.1

tTn ztt.2 &[6 aa9.|

4217

Ett.6

it!9.5 42t.7 {3:1.9 4S8.8

9t.8

do.b

153.6

34ti

114.8

l5{r.0

?.@

I OCtl

434

l8?.8

8.4{)

185.8

t3t6

r09.6

at.Jat

l9{l

135.8 161.9

2249 2550

212.5

4ll

129.5 140.7

{ti.9

{06

5.92 5.89 5.78 5.74

50.3 54.8 70.0

442 398

l7l I

3A

J.O:l

5.48

a7.2 t08.1

C.JJ

126.3

5.20

s.t4

4N

l&!.8

d.,t:l

181.9 l TCt q

o.$t

156.0

l?8.0 i76.0

8.29 8.27

186.3

t72.2

238.1

loat.o

8.31

toiat

l3!i.4 171t.5

lgr.4

?a40

237.O 28S

a.?.2

3140 3420 or lu

8.ls 8.ts

46S3 4920

388

309

3?8

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lo.t.l

!50:|

296.4

8.07

36"?.4

t42.1

344 326 310

106.t t49.1

429.4 483.2

t4t.z

7.gI

134.3

?.?9

8630

?t9

302 293

509.? 542.0

t31.0

J.

tc

9-UO

149.9 159.4

7.70

9010 9455

?5t

30.2

501

102.5 136.2

216.8

9.06 9.02

2479

98.9

293.5 291.0

t0.50

3210 ,lta.,

2.69

6.8

10.26

o-61 5.81

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21.9

t?04

98.3 92.8 90.5

ll0.t

2.91

l5a4

6.88

2,€8,4

n.0

42'o

3.10

1624

104.1

415

3.5r

128.9

109.4

32.4 36.9 41.4

6.24 6.28 6.28 6.23 6.28

l4{i7

250.3 256.1

6.02 5.99

6.4

1289

6.90 6.88

208.9

6.2A 8.?A 8.2A

6.28

6.92

244.5 238.8

6.44

5.23 5.08 4.66 4.02

124.4

tu.8

ttt IIZ.J"

4?S

6.4 6.4

lu.4

261.6 259.8 252.7

27.8

o.l r

ll14

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6.28

126.0

129.3

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6.09 5.93

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938

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6.98 6.96 6.94

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tu.g

63.4 ?8.9 94.6

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6.28 8.24

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o.t.6 ?8.6 91.5

I00.3 t0s.2 I rl.5 25.5 33.8

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6.54

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tlt

E

4t0 4?3

6852

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t9l 250

2t.4

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7.69

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21.0 20.5

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138.0

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7.59

46.3 52.0

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286_0

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336

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195.1

28t,1

10.3!t

6230

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868

134.7 178.9

3?6.0 370.3

11.89 I l.ato

oo95

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142-7 189.6

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12.60

{16.6

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12.55

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488

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50€ 668

20.

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7.53

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39.

t

8.90

35.2s0 3:i.000

54.4 52.5

9.44 9.44

41.250 41.000

119.4 115.9

I

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I1.0

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10.80 10.13

39.6 5Z-O 42.O

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10.41

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{34

t4{xt?

L1 Weight and Dimensions o{ Pipe and ComPonents

Weight of PiPe and ComPonents

c

lhbight of iwulntion of the PiPe

I = Insulation density, 1b/ft3 T : Irsulation thiclness, in.

qnd compoWhen determining the weight of the pipe nents, several factois must be taken into consideration:

D=

Outside diameter of PiPe' in.

Weight of insulation Weipht of pipe : lJse the values for properties for carbon steej pipe as a standard. These values can be found in

o

Values

Chapiei tO. The relative weight factors for other mate-

Aluminum Brass Cast ircn Copper

Thermobestos

=

0'35

: l.l2 : 0'91 = l,l4 Fefrtic stainless steel : 0'95 Austenitic stainless steel = 1.@

{arbon

Depleted uanium

(D+f; = 67n

ll

lb/ft3

10

to 11 1b/ft3

11.53 lb/ft3

KAIJO

r9-2rlbltr

Super-X Foly-Urethane

?5tbltr 2.3rbltr

Amosite asbestos

16 lb/ft3 9 rb/ff 91b/ft3

Foamglas

Cellular glass

0.98

,

IT

Diatomaceous earth = 2rrbltr ?AIbItr High temperature

!

Wrbught

.0218

for insulati.on densitY:

Calcium silicate 85% magnesium

rials are:

:

,r)

Mineral wool

8lb/ff

Tables 11-1 Orough 11-10 give the weiglt of insulation and various pipe componens by size.

t

Wigtrt of water in pipe: See the proper.ties of pipe in Chapter 10.

The following pages are tables and figures showing fittings' valves, anct ptpe

standard dimensions of flanges, bends.

299

Piping Stress Handbook Table 11-l Weight of Insulation (lb/linear ft) Plpe Slze

Thickness of Insulation

21h" I

.72 .84

1.35

3

1.01 1.25

4 6

2.tl

t.62

3112"

1.94

2.',|6

| .71

2.52 2.53

3.47 3.48

2.08

3.01

4.O',l

2.5s

J.Ol 4.5'7

4.66 6.09

5.64

7.8s

t2 t4

3.28 4.13 5.20 6.04

.07

6.r6

16

6.90

8.38 9.33 10.4

8.45

11.6

8.93 10.5 10.7 12.0 13.3 14.6

t3.4

r7 .0

21.0

21.1 24.8

14.1

18.0 19.2

2r.9

26.0

23.4 25.0 26.5

27 .8

28.O

JJ. I

29.s

34.8 40.1

40.3

45.9

46.4

52.2

1.5

2

8

10

l8 20 24 26 28 30 J2

7

8.

10.0 10.4 11.2 I 1.9 12.7 13.4

36 42 * me tublc

15.

l3

I

16.1 t7

.l

t4.2

18.2 19.2

16.5

22.2

is based on calcium silicate at

I

20.5 21.7 23.0

t tb/ff

28.0

3.70 4.52 4.42 5.24 6.07 7 .60 9.48

5.59 6.65 7

11.5

t3.2 15. I

11.0 12.7 13.

l

15.8 t7 .5 19.3

14.6 16.3 l7 .7

29.5 31.3

34.0

and nust be adjutt"d 1o,

olnt

^ot"riol".

Table 11-2 Weight of Flanged Gate Valves (tb) Size

(inJ I 1.5

150# 300# JI

55

3

95

4

140

6

240

8

/100

t0 t2 t4 16

l8 20 24

900#

68 75 t4s 215 420 700

1500# 2500#

1,050 1,530 1,490 2,0w 1,150 2,170 2,410 1,580 2,800 3,500 630 830

1,910 3,720

136

115

194 270 530 940

330 720

256 460 610 1,410

1,220 |,560 2,600 1,880 2,350 2,630 35W

3,2W 4,680 4,230 6,500 7,2W

2,350

4,90

9,800

3,900

7

,380

I 1,800

CourEsy of Crane Co.

314 430 900

.4

20.4

1'7

18.

I

18.5

2t.3

20.5 22.6 24.6 28.7 30.2 32.2 JZ+. J

23.6 25.9

39.r

36.3

41.1

38.3

43.'7

rn" tort"

28.1

32.9 34.6 36.9

41.6 44.1 46.6

51.4

54.4 57 .5

49.1 51.7 59.2

iiuaiionaig *d-o*rin.

60.5

bJ-) 72.6 ."ighr.

(tb) Size

(in.) I

9l

16.0

Table 11-3

35

45

2

600#

9.10 11.5 13.8 15.5

weight ot wetd End cate valves

Rating 400#

.48

9.82

150# 300# 20

Ratlng 400#

1.5 29 55 245 60 380 120 4 120 170 220 6 210 360 460 8 340 590 830 l0 550 9r0 r,250 12 730 1,220 1,800 14 990 |,960 2,210 16 1,460 2,550 3,100 18 |,730 33N 3,76s 20 2,200 4,350 24 3,350 6,700 Courtesy of Crane Co.

600#

900#

25

80

70

125

80

155 270 &0

190

260 350 750

410 520 1,250

1,080 1,300 1,610 1,970 2,240 3,2N 3,000 4,350 4,030 6,000

1,910

6,760 8,950 10,500

. Weight and Dimensions of Pipe and Gomponents 301 Table 11-4 Welgtrt of Flanged Check (Swing) valves (tb)

Size

weight of wdd

3OO# 4OO# 600# 900# 1500# 2500#

160 70 23462 280 180 140 120 3 65 630 4 100 180 2W 260 3401,360 6 2N 330 395 530 640 8 390 620 680 900 1,180 2'100 l0 510 9m 9N 1,440 2'170 t2 775 r,2n 1,250 |,970 t4 1,200 1,650 16 1,450 2,050 2,420 18

.t

J

80

t40

6

250

8

a0

l0

598

t2

824

139 214 396

a8 686

14 16 18

20 24 Councst oI craie co.

zto

155

190 210 240 310 420 500 580 740 890 820 880

390 780 1,320

Counesy of Crane Co.

150# 300# 400#

4

100

2500#

130

18

Co.

79

900# 1500#

55

20 24

Table 11'7 End Globe \ralves weld tlreight of (tb)

slze

Ratlng

2

600#

1,015 1,150 r,200

t2 t4 t6

Table 1 1-6 vrteight of Flanged Globe \hlves (lb) Slze

47 80 130 zffi 510 760

1<

10

a^

Ctaw

Ratlng 400#

350 4 100 6 160 8 360

20

Courtesy of

(lb)

Size

Ratlng

(ln.) 150#

Table I l'5 End Check (Swing) l/alves

90 160

600# 115 191

233 476

318

820

1,2:U.

782

900# 1500#

2t5 46 4fi 490 65 920 1,890 215

2500#

Ratlng

(in.) 150# 3OO# 4OO# 600# 900# 1500# 2500#

234757897 3 75 115 130 L6 170 185 + 120 179 206 272 2N 285 6 220 332 401 656 630 680 8 363 530 900 1,100 1'1'+0 l'370

10 12

1,056 1,160

535

794

L4

l6 18

20 24 Courtesy of Cratv

C'a.

r,730

2,7N

3,850

2,400 3,024 4,lm0

Piping Stress Handbook

Table 11-B Wbight of Flanged Angle \hlves 0b) Ratng 150# 300# 400# 600# 900#

238 130 160 230 4 110 2N 235 280 370 6 zl0 370 385 675 1,000 8 360 634 685 985 10 552 1,130 1,950 12 r,720 3,100 2,350

14

lo 18

20

Counes! of Crune

Co.

Table 11-9 Weight of Weld End Angte Valves (tb) Rating

(inJ

r50# 300# 400# 600# 900# 15oo# 2soo#

2

70

3

8l

r70

4

155

490

o 8 10

530

330 880

t2

t4 16 18

20 24 Courtesy

ol Crane

Co.

r30

Table 11-10 Wbights ot Flanges (tnctuding Botts)

2WN 6 10 13 13 31 31 48 2SO 6 9 11 tl 32 32 48 2 BLD 5 10 12 12 31 31 49 3 WN 11 19 27 27 38 61 113 3SO 9 17 19 19 36 60 gg 3 BLD 10 20 24 24 38 61 105 4WN t7 29 4t 48 g 90 r77 4SO 15 26 32 43 6 90 158 4 BLD 19 31 39 47 67 90 164 6 WN 27 48 67 96 130 202 451 6 SO 22 45 54 95 r28 2U 396 6 BLD 29 56 71 101 133 197 418 8 WN 42 76 104 137 222 334 692 8 SO 33 67 82 135 207 3t9 60i 8 BLD 48 90 115 159 232 363 gg l0 wN 60 110 152 225 316 546 1,291 10 so 51 100 117 213 293 528 1.148 r0 BLD 78 146 t8l 267 338 5gg t.245 f2 wN 88 163 212 272 434 843 1.919 12 SO 72 140 1& 261 388 820 1,611 t2 BLD 118 209 26t 341 475 928 1,775 14 WN 11,3 217 277 406 642 1,241 14 SO 96 195 235 318 4@ 1,016 14 BLD r42 267 354 437 s74 16 WN 108 288 351 577 785 1,597 16 SO t85 262 310 42 559 1,297 16 BLD 160 349 455 @3 719 18 wN 140 355 430 652 1.074 2.069 l8 so 229 33t 380 s73 797 t,694 18 BLD 196 440 572 762 1,030 20 wN 43r 535 8lt 1.344 2.614 20 so 181 378 468 733 972 2,114 20 BLD 298 545 7tt 976 r,287 24 WN 295 632 777 1,157 2,450 4,153 24 SO 245 577 676 1,056 1,823 3,378 24 BLD 446 Ur 1.355 2.442 Courte\) of Crane Co.

303

Weight and Dimensions of Pipe and Components

Steel Butt-Welding Fittings (in.)

,."n a/rf-/..'t( '(tiiJ t!ng t.dlu.

t ilt

9Oo

llbow

on

aA T/f 4 LJJRodlu.

9Oo Shorr

:tbov,

on. lnd

.N -A/ > lons Rodlut Elbow "1.-J

45o

1 | | tl F\ i /i -t-:-L

I

5l..l9hl Cror!

r-l-T Ill t*tl _n Ll

/--*\-T / ,--\ \J

e]

tg":J-t l*G--!

c"P

,,--\

/ \ /ini\l \#l l+, l.-H- +l

B

6/s

r'/e

7/ra

lr/a'

I

1Yz

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1rh,

lr,

17/g

33/t 4r/z

I

lr/t 3r/r 4r/r

t'/2 5ta

tt/s l3/t

zYz

1rh

3 4

3Ve

1r/z 2

6

x

33/t

4Y8

9 l0s/a

3Yt

47/E

6

3.4

5'/t

E

8

133/t

l0

15

l0

t7

6U

t2

1t

t2

20rh

t '/2

8r/2 10

9

2l 16

24

t8 20

30 36

18 20 24

2

trk trh

2Yz

t'/z

lr/z

2ra,

2r/.

31h

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7

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31 6/re

53/ro

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4 5 6

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4a/t

6Yt

6

lr/a

67/ra t -/16

6

lr/t

8r/rs

tsh

8e/ro

t?/s 1r/z

113/t

2r/ta

4th

L'/16

5Vz 8 18

16 24

6r/t

\r/a

73/t

l0t/ta

95/te

12r/

9

40 4E

t

zYz 3 3r/z 3r/z

93/s

80

40 40 40

80 80 80 80

40 40 40 40

80 80 80

40 40

80

4

80 80 80

80

i

10n/s

8

2

t43/a

6

zoYs

tx|/a

2rh

t77/s

7

18%

248h

l5 t6ta tath

10 10

23/t

201/.

8

3r/t

22YB

13

l0

3r/z

24r/6 26yE 30r/a 34r/E

L4

JO

40

20

20 20

t0

28

60

8

6/re

44 4t) 40 4n

153/e

48 s4

toth

81/z

1Yt

Stror

l2E/rs 165/re

28

6

e

63/rs I -/L6

4r/s 43/t 51

Extr

S 2

4

L-/r6

7r/z 9

lrr/re 2 2r/z

lVs

30

6 6r/z

15'

2r/z

rt

t

llr/t t3rh.

lr

3 33/t

10

ll.

12r/2

M

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2Y1

r1h.

t'/2

t'/a

tL____J)

---r

H

I tta

6t/t

3r/z

s

lr6/ts

rYL

2Vz

[\

tl

F

D

s/t

lr/z

[_-\ l!--/-l k-

k

long Rodlur R.lurn B.nd

R.lnfor.lns

lYz

Shap!d Nlppl.!

20xlE'

w.ldlnr 5!ddl.

Yz

Dincnrion "T" it rhown in tobl. beloe; r.f.r lo lors. loblc for diln€nrion "E".

9oo Typ.

Stub End

R.turn a.nd

Size

R.ducinr Crott

ml url

t-M+l

Shorl Rodlur

M

R.du.lns T..

therein, to lhe American Standard, B r 6.q- r qi8; see page 2gr. Thickness: Stendard Fittings r z-inch and smaller ate made for use with Standard pipe (heaviest weight on 8, ro, and r zjinch sizes);sizes r4-inch and larger are made for use with O.D. pipe fu-inch thick, Exrra Strong Fittings rz-inch and smaller are made for use wilh Exlra Strong pipe; larger sizes are made for use with O.D. pipe \/2-inch Lhick. Schedule r60 Fittings are r''"'le for use with Schedule r6o pipe. Double Extra Strong Fittjngs are made for use with Double Extra Slrong pipe

Iong Tang.6t

Stroighl or

lll

l._E-*Ei

Arnerican Standard: These fittings conform, in sizes and types included

Lonr Rodl'rr

i

--r-'llf ill" T U- b .--ul

160,

ad Doubl. Exrro Strcns FitrinE. trov. tr|. ro,n. outdd. din.ttiott.

L__-r-'

1

T-/:

S.cndad, Exrrc st'ots. S.rrcduL

1

n

9oo

Courtesy of Crane Co.

F-c.---

F--A---l

30 36

40 48

x3 17r/t

20

304

Piping Stress Handbook

Forged Steel Flanges (in.) Courtesy of Crane Co.

150 ond 3oO-Pound

Slip-On W6lding Flqn!. 150 ond 30O-Pound

Class

Pipe Vz 3/t

3Vz

1/ts

31/8

I lr/t

4Y.

Yz e/rs

45/^

3A

2W

6 7

7r/t 3Y2 150

Pound E

8Vz 9

l3/s

2YE

r/-

lrr/ra

13/t

Y2

2 2y2

3Yg

I Vre

2TB

3A

35/e

%

rtl" I B/ts

l0

r,/rs

T1

I

l3Y2

lyE l3/rs

l6

150 ond 3O0-Pound

lyg

Tta

8

5/z

7Yz

E

5/e

t-/lB

8r/z

E

x/t

17/rs

9Vt

8

ll3/t

E

l3Aa 23/t

l6

27r/^

xqr/,

20 20

l3/e

Ls/e

11h

'rr

45/e

I

4YB

rr/ra

lr/z

6YA

t3/--

'/a

2

6th

2U

7V2

I

3

8Ut

lYs

%

l6

lrr/ra 3r/t 2 2,r/t

3W

27/8

4rh

37/e

4Y8

'/1

t3/t

f6 %

1rs/re 2r/r,

1

2Y2

4Y2

ru

lTAc 6.63 8.63

14.00 16.00

lr/t

3U,

6

24.O0

Y2

7/s

2r/ra

5/s

1

0.84 1.05

'/a

lr/rs

2r/e 27Aa

3/t

l3/ra 2rt/ta

4

rllc

3/t

6./e

8 8

ts/rel 3

,i\i,"l

3Ve 33/rs

1.90 2.38 2.88 3.50 4.00 4.50

5Y2

7V

E

"/a

7TE

8

lTg

33/s

l1

l3/s

75Ae 8r/z

9Y1

8

'/1 '/l

2

37/g

105/n

t2

3/"

2rAa

37/a

TE

27/te

43/s

I

x'/s

45/e

lr/s

27h

5Y8

3

55/e

6.63 8.63 10.75 12.75 14.00

l0

17Y2

t2

20Yz

2Vt

lo3/e

12t/t

1sY1

16

t7t/t

l5/rs

lY2

lrr/r, Lfa

77As

33/t

4

20

lVa

22W

20

lY.

3Y4

53/t

r6.00

4t/r

24t/e 27

x4

lr/e

3W

6r/t

1E.00

t'/a

24 24

lYa

33/t

6t/a 6./a

5V2

2

3Y2

20.00 24.00 4.50

l6

25W

xY1

l8

2E

23/e

21

20

30rh

2Yz

36

23/r,

27tA

l0

l3/e

6sAs t -/16

77/a

8

9ra

E

% %

to6/^

t2

7h

t2

I IYB lY4

ll

tr/z

12r/z

1s/*

8!z

17r/z

l1/B xYE

lo'/a l2t/e

loYz

2Yt

t73/a

l6 20 20 24 24

l5Y1

2s/p.

r6Yt 20r/t

16 18

25Yz 2a

2r/z

tgt/z

25/c

21

x0

3or/z

2r/t

36

3

77r/^

l3As

20r/a

16r/, lEYz

E

r3a

I

r.66 )

63/ts

l5/a l7/a 2

3Y" 37/re

lrAa

lr/t

t4c

l3/t

lYa 2rYre 5r/2 r E.00 lr3/rt lYe 27/8 5rr/te 20.00 4r/ra

l3/rs

t2r/,

te/,"

to-75 lr5/rt 2t/re

9

6 8

l0

xl/rs

I

s/e

s%

3 3Y2

3r/z

E

3./a

rY1 2r3/rs

0.84 '/e 1.05 "/a 1.32 rr/re txt 1.66 1.90 % 2.38 1 2.88 lY8 3.50 13/,, 4.00 4.50 t -/16

l0

l4

40O, 600, 9O0, 1500, ond 2soo-Pound

5/s

6 7

223/t

33/e

l,

W.ldins No
5lz

5 5r/z 6sAs / -/16 ar/z los/a

2T

u

5

Pound

4Yg

lrr/ra

t4

400

21/re 2Y2

27Yz

lrh

W!ldlng N.Gk Flans.

I

l8Y2

18 20 24

Pound

%

l7/re le/ra

l6

3Y2 4

^/2

x3r/z

lr/r

21

tL/-^ 23/re

-/a

18./t 2lY4

19

l4

2r/ra

4r/.

t6rL

17,

l7/e

'/a

37/8

13/,

150 ond 3oo-Pound

H

|3/.-

4

l4Yt t7

10

300

Yz

E

r/

3t/c

123/t

C.oh.l.p Flong.

Cron.lop Fl.nso 4OO, 600, 900, | 500, o.d 250o-Poqnd

Bolts

D

Siie

1r/z 2

Scr6v.d Flon9. 400, 600, 9O0, 1500, ond 2500-Pou.e

5lip-On !Y.ldi.s Fldns! 400. 600, 9O0, ond l5o0-Pound

21Yz 2434 27

lr/" z\g

6 2

zrh

2r/t 4t/," 2rrAe

6.63

2V,

E.63

rr/rs

27/B

47/B

r0.75

4

3YB

53/e

lr/t 3sle

12.75

4V.

57/a

l3/s 3rr/rs t./E 31h

6 6Y2

lr/z

6E/a

14.00 16.00 18.00 20.00 24.00

t3a

4r/,

67/*

53/s

5t/t

Weight and Dimensions of Pipe and

Forged Steel Flanges (in.) Continued. Courtesy of Crane Co. Class

Pipe Size

rY1

5r/t

r3/,"

2 2r/2

lYz

6Yg

7/e

x7/8

2

z\z

6Y2 7r/z

IYB

3

81/^

lYt

lo3/t

lr/z

63/ra

13

l3/e lr/p.

t -/16

I

Y2

'/e '/a

31h.

'/L

0.84

xr/t

1.05

1r/rs rYa

21/ra

l|/t

23/t 27h 3Y8 3r/^

L5/e

8

-/B

t/t

6s/e,

3A

lr3/rc

8r/z

8 8 8

11/ta l5/e

1/B

2r/B

loYz

I

gYz

rrv

8 11

I

1,5/^

45/e

lo5/s

t33A

t2

lYg

J

5Y1

33/s

6 6Yg 6Vz

Lr/^

l4

10

20

2r/,

123/a

t7

l6

lr/t

20

lY4

233/L

2r/e X3/t

19Y1

l4

16r/a

X03/a

z0

3rr/ts

l8Y2

233/e

20

l3/t lr/z

18

29Yt

2.53/t

20

l5/e

46/a

7 7\/a 7Yz

l7/a

$t/z

E

3Yz 9Yz 133/t 15

900

t

23/e

ll

lra

8rh

11,y,

t2

rVa

33/e

5r/z

12

l3/e l3/e l3/e

4Yz

4V

7Yt

6.63 8.63 10.75

4V8

77/a

12.7 5

5s/s

83/a

14.00

6Va

24

3YB

t6rh

22

l6

X73/t

33/t 3r/z

lSYz

2Ar/q

27Vt

l6 20 20

3Y6 63/e

11/z

r'/a

t'/a

81/z

r6.00

6Y2

l7/s 2

6

9

6V

93/t

35r/z

xo

ZYz

E

llr/z

18.00 20.00 24.00

/ '/2

29U

20 20 20

x7

l3/s

3Y4

lY1

23/e

9r/e

I

"/a

'/1

lrr/rs

3Y2

-/A

l3/e

23/a

I

57/g

lr/s

2

7/E

lt/e

27/B

lY1

6r/r,

rVR

2r/z

43/z

4

1/"

F/a

27/e

lYz

7 8r/z

lr/n lYz

x7/e

47/s

I

lr/a

3V

35/e

6r/,

E

%

2V

96/e

l5/s l7/e

4YB

7r/z

d

I

21/z

4Y8

t0rh

E

E

rYa

lxr/t

zYB

9Y2

8

143/t

27/B

63Aa TsAs

llYz

rv

27h.

E

lr/z

6

t5y,

3r/^

8r/,

12r/2

tz

8

19

35/a

t05/B 123/t

tx l4

4r/t 47h

3e/ts

47/e

4.50

3e/re

4Y8

6Ys

l3/a

4rr/ts

63/t

4rrA,

rsYz

l6/t

5'/a

83/s

6.63 8.63

l9

6V

16

l7/8 2

l6

'),r/^

22\/2

5Y4

lB/ra

l3/e

3Y2

ta

sw 6V

Ita

lrr/te

33/t

3/a

I

13/e

7r/

lV2

4r/a 5Va

%

lr,

2 2r/z

8

ls/t

27/s

534

4

2

33/e

63/t

E

I

23/e

zYl

4r/s

734 9

8

IYB

E

8

ev

2Y2

lor/z

3

tt

l5/a

4s/a

l6r/t

lYz

lx/s

2Yt

5r/t

2

0.84 1.05

8r/t

t0v lYl

1.66 1.90 2.38 2.88 3.50

26Yz 29r/2

Yz t/a

5r/z 6 6Yz 2Ys

25r/^

l0

4s/s

14.00 16.00 18.00 20.00 24.00 3.50

t4

3

3

4.50

l5t/2 l8Y2

2W

43/a

4Yz

lx"/o

2

6.63 8.63 10.75

2e/t 3Yg

1o7s

%

zY8 L"/e

lYa

73/t

4t/t

--)

8 8

2Y2

5r/z

lr3/r'

9r/t

23Ae

4l

rv

lTAa ls/e

2Y8

75/ra

4Ya

tv"

7/B

2

133/t

1.66 1.90 7.38 2.88 3.50 4.50

8

5 63/ra

t8t/z 2lYz

18 20 24 r/z

1

lr/ra

'/2

lY2 t3/t

l0

E

43Ae

L'/A

28r/z

27r/t

I/s

2Yra

l6t/z

3 3r/a

H

I

5 4YE

G 7h

E

llY2

Pound

rt/ts

lr

Dia.

6

3

2500

4Y2

47h

20 24

1500

3r/z

I

27

Pound

t./a 3r/t

41/s

t2

Pound

l3/e Yre

3x/e

-/1

600

Pound

D

lz

116 '/a

Bolts

c

B

t4 l6Yz

3

63/ra

lo3/t

35/e

123/t

t

l9

41A

l4r/,

E

r/t

t2

13/t

IYz

4YB

t0.75 lrYB t2.75 10

55/a

7

8%

tt3/a

14.00

9r/"

27/8

0.84 1.05

lsAe

r'/t6 lLYra

3Ys

I

1I/s 2rAa

3r/z 3t/^

lYs

23/s

1r%o

t.32

tlA 2rAa

43/e

1.66 1.90 2.3E

2./t

3Y8

5'/e

2.88

3Y8

lVt

35/e

6r/e

lVz

4V

7Yz

4.50

4Yl

5VE

9

6

tosa

5th

8

2lt/t

5

t -/t5 8Yz lo5/s

10

26y.

6rh

123/t

2trh

2r/z

9

l6Yz

1o.75

9

t2

30

7Yt

t5

243/e

2.4

t0

l8r/t

12.75

l0

5 6

17

2

l1Y2

2

6.63 8.63

Components

305

Piping Stress Handbook

Cast Steel Wedge Gate Valves 150- to 1500-Pound Dimensions Courtesy of Crane Co.

E-T FEh ltf JIK D

E-T l-E$r--l ,-t

|tI

I

I

JIL D fltt ory" ./-i\ |

I

Ylf i*

I

_5=a r- I

T-

/- i\

I I I

T--T--T -=] fi=-l='il1 r-i--l l-c----l

I

-1 I -t- -l-

f---r-l F-A----l

Bun-W.lding

Dimensions, in Incher Cless

Size of

B

Valve

6r/t

t'/2

zrh 3r/z 4 5 6

1S0-Pound

734

8

8

8Y2 9

c

D

E

Er/z

Lt'/l 16Yz

8 8

201/.

9

grh

llVt

25.4

l0

3r/z 4

B

c

D

E

\rYz

llYz

l3

l3

l8r/+ 22r/t

6 9

t4

l4

253/a

10

32

l5 t7

t7

20 22

20

6 8

26

3l

363/t

14 14 16

423/t

20

52Y1

24 27

3lr/z

10

l5

30%

157/e

JnYa

t4

8

tlr/z

t6r/z

4

l6

10

13 14

18 193/t

52Yz

IE

l0

ffir/z

l8

t2

70

7or/t

27

14

77r/t

30 30

l4 l6

79s/t

l8

97Y1

27 30

20

trh

z0

32

ll23/t

30

163/t

8

7

IE

8

2r/z

l9

3 5

7r/z 8Y2

E9

15

27r/t 3tr/2

4

18

t2

t2

28r/t

l0

15

15 t57/e

33r/z

t7

l0

38r/z

14

t2

3E

l6 16

4oY2 44r/z

30

30

7s%

l6 IE

33 36

9lr/z

30

20

39

993/t

45

36 39 45

t2oy2

36 36

l6

16

303/a

18 19r/z 23r/z

1E

26Y2 30 32Y2

1E

22

900-Pound

20

6

24

E

29

I lr/t

20

38 40Y2

44r/z

10

l0

ll

11

l6

423/t

20

52\h

24 27 30 30

62V1 73r/z

77r/t

a5t/t

l6t/z

t2

11

10

9

l4r/z

22YB

l0

263/E

12

16r/z

l6Y2

Itrh

l8Y2

11

4

2lY2

ttr/z

5

26Yz

3t3/t

6 8

273/a

26rh 27%

323/t

323/t

i'5

t9r/z

40r/t 5or/z

20

26r/z 30 32r/z J5'/2

593/t

67./t

74

74t/.

27

8 8

l4r/2

L'/2

73Yz

t4

363/t

3

1500-Pound

t2

2

1t./-

8l

14 16

36

126

11

t4

l4 l6

t04r/z

23r/t

l9t/t

10

47

llr/z

IE

t

20

llYE

t9./t

6

43

8 9

47 56Y2 64Y1

39

62V

l8

9th

l6Yz

31

833/t 933/t

8Yz 9Y2

r6Yz IE

l0

39

7 8 9

Ls% 8

600-Pound

l6

24 26 28

18

400-Pound

Valve 2rh

9

t2

Size of

l0Y2

t2

300-Pound

Class

'A

l4 16

20

Weight and Dimensions of Pipe and Components

Cast Steel Globe and Angle Valves Courtesy of Crane Co.

Claes

Butt-Welding

Flanged

2

z\z 150

Pou

r

t500

Pound

E

16r/2

11Y2

t93/a

rrlh

t9t/t

53/a

173/e

14

23

l6

2ot/e 7.134 X3r/z

E

8 9 9

lTYt

10 10

x4Y2 26

l9t/z

24r/z 26

7 8 93/t

loYz

173/t

Sr/a

173/e

t9

53/a

19

2oY2

6Y4

xo\2

9 10 10

65/s

22r/z

tx

7

24t/t

t4

7Ye

x6v

l6

293/e

36lz

IE x4

12Y2

xoYz 22r/z

121/2

14

l2Y2

l3x/t

91h

ttth

l3t/r.

HIK

4t/t 4t/t

t9

3r/z

Flaneed or

All alves

Butt-W€ldingt

t4t/2 t6r/z

173/t

243/t

14

243/.

11

16

5 6

t53/t t7r/2

26rh 293/.

t7r/z

293/t

E

22

36U

L2

36y2

834 l1

l6

25Y1

16

8

xSYa

l4

28Y2

It

x1t/r

18

28Y2 3lV1

9

28Y2

1E

93/a

31r/n

20

38r/a

ll3/a

38t/t

x7

23Yz

6Yz 7 7Y2

2tr/1 23rh

z7r/z

8Yz

27rh

r8

l0

303/a

x0

191/z

3lr/t

191/z

E

23r/z

3ara

23r/z

2 zYz

llY2 l3 l4

l9

1lY2

21r/e

t7

27r/2

20 22

303/t

x3Yz

t4

20

l5 18

29Y2

IE

37t/a

6

303/e

22

3

2

l4lrz

25V8

l4Y2

2r/2 3

r6yz

28r/s

18r/z

33Y2

t6t/z l8t/2

10

t9

2lr/t

3Y2

b

900

133/t

$Yz

rrrh

Pound

Pound

I

l4Y2

t0r/2

400

Pound

t33/t

8 8V2 9Yz 10r/z

2U Pound

600

JJ

2 +J

300

K

K

19rh

8

Screwed

HH

HH

l4 l6

5 6

Angle Valves

Globe Valves

Size

t2

l4

II

24

24 29r/2

7Y2

9

24 791/z

373/t

t2

37 3/a

20

l4 28r/a 331/2

IE

308

Piping Stress Handbook

Cast Steel Swing Check Valves Courtesy of Crane Co. Weighlr cnd Dimension:

Js I P F+ T'---'-'T t--N

Prea-

Size

Class

Pounds, Each Valves

,r.l

2V2

3rh r50

5

Pound

5

50

30

Flanged or Butt-Welding

P

E

l0

100

100

140 200

120

390 510

360

5

8

slz

!

$rh 9r/t roYz

1rh

5

rlYz

300

Pound

400

Pound

80

100

120

l2YE

27Yz

133/a

on 39 60 80

9rh lo3/t

63/t

torh

6t/t

E

ll3/t

llr/z

E

EYl

l2Yz

130

l4

g3/t

153/t

t03/t

6

260

lTVz

t\3/"

8

620

510

2l

t4

l0

920

760

12

1290

1015

24t/z 2a

200 270

190

16

l0

IE

t2

6

310

19r/z

8

6E0

l0

900

580 820

13Yz 26r/z

t2S0

I150

30

38

32 40 70

l3

100

14

4

260 400 530

17 20

6

170 300 420

E

900

l0

1440

740 880

t2

1970

1200

180

6

340 640

t

I lE0

l4Yz

t$r/t

63/t

llY2

70

J

l5 I

6V 9Yz

140

900

500

t0r/t

240

2r/z

t

lgYz 24th

180

2

Pound

8 9

250 330

lr/t

Pound

13

160

4

1Y2

600

6 6Yz

ltr/z

1200 1450

40 70

P

8

12

2 zYz

M

$rh 9rh

94 96

M

N

u 40 50

Screwed

Valves Weldinp Valves

FD&SF

Inches 2

Dimeneions, in Inches

Butt-

$r/t

I

tor/r 123/.

tir/t 31

t8t/t 2lr/z

15

Ith ll

240

l8

500 890

29

t6r/, EY1

t0r/z

t33/t

trh

ll0

EO

2 2r/z

160

130

t2 t4rh

245

t70

l6V2

2E0

210

l8Vz

ttut

630 950

Ltr/z

l3r/t

1360

390 480 780

26r/2 273/t

t51/t

2100

1320

3

Pound 6 8

93/t

rsv

Weight and Dimensions ot Pipe and Compononts

Miter Welding

30"

Siz.

6o'

45"

+v2

3/4 15/r 6

5ta

7la

6

I

c

R

r-3/8

r- r

5/16

3/4 15t16

6

1-5l16

I 1-0

t3/a 1-13/16

1-1/8

I,13/r 6

2-1t2

10

1.1t16

2.114

3rl8

12

r

2.5la

3-11/16

l-6

+1n6

1-9

2-1lA

+5la

2-O

35/16

11/16

11la

lA

2.7

2.11A

35/16

18

2.7 t16

r3l4

20

2.11t16

+1ta

t6

22 26

71116

i6

4 13^6

1-7 7-7

| 16

3a

t1l16

.t0

5.3/8

t2

5-An

8,11/16

6,7/16 1.1/4

9,15/

"q 1)

5/8

lA

1r

-3/16

'|

-

o-1/16

1

-

2.r5/16

7 15t16

t

911/16

8-1t/16 s 15/r6 11,Vt6

r-05/16 1

,2.1116

1-

3-r3/16 5'9/r 6 7 5/16

-

3-O

5

1

-

2-15/16

9-1t4 9- | 3/16

103/8 1l I t -9/',t6

l6

1,G7t16

8,3/16

63/8

&5/8

4-5116

4-t5l16

1-7t16

1r-91/16

8-1/16

+9/r6

r

r

tr3/r6

34

3/16 1G9/16

r-11/16

5,3/8

- 0-t/8 1- r7ta

1-

+1tA

'|

-

5-318

2

7.1ft 8 5/r6

1I2

7.7t4 9-1/a

8-lt/16

2,2.1t4

6-0 6-9 7-6

915/16 113/16

2

9-O

1

3-6 3-9 40 4-3 4-6 4-9 5-0

r

r ,3-9/16 r

-

8-13/16

Source: Tclas Pipe Bending Co., btc., Houston' Texas'

5,3/8 5-13/16

1

6-3/16

6-5/8

1

1-v16

1

1.7 | 16

1

-

0-7/16

2-15t16

10-3/8 11,5/8

GT/A

8-3/4

-

-

22-

to.tla o-S/A 2.31a 4-1/A

2-5714

2 7-5tA 2 - 9-3ft 2- 11-1tA 3-O.7lA

43

- 9-S/16 3- 1-1t4

3

6-5/t6

5

0-7116

!t/2

4.r

9-15/16

1-9/ 16

r

6-r5/16 1.1/2

1-7/16

1

I-

5

3 r/8

10-3/ 16

I

+1lA 4.5t16

6

2.114

5

5.1t4 8- r

2.5rc

3.3t4

3-314

2-9

+9/r

32

v2

3.

2-

3-3/16

4

2-5la

t8

5-3t4

2-15lr6

6

E

5-1t4 6-7 lA

2-1t2

2.t14

3-3t4

63/r6 6sta

30

't-7

3

6-3/16 11-7/A

4.314

5-3114

11-

2 2

11,1/8 2-1t2

5.7la

2-9-1/A

- 2-15lt6 r - 5-3/8 1-7 7/a I - 10.3/8

2

0.1t4

r/t6

11.5/8

1,

t-14

1-

21ta 45tA

1

- 0-7116 2 3-5t16 1 - 6,3/16 2 5-13t16 1-1.13116 3 - 3-13/16 1 - I,S/16 3-7.1 6 2 8-5/16 1- 11.3/t6 2 - 10-13/16 3 - 10-7lr6 2- O-1ta 3 - 1-114 4,1-5/8 4-5 2 - 4-1/a 3 6-114 4 - 8-3/8 2 - 5-1ta 3 a-3t4 4 - 11,5/8 2- 7-1t2 3 - 11.1/4 5-3 4- 1-11/16 2 - 9.r/16 5 - 6-5/16 2 - tor3/16 4 - 4.3116 5 - 9-9/16 3 - 3-314 4 - r I,5/8 3 - 8'3/4 5 -7.11A 7 - 5-1t2 a, 3.7t16 6 - 2,9/16 4- 1-11/16 4,11.94 I - 1t-3/8 3

309

310

Piping Stress Handbook

Miter Welding Dimensions

K

H

13/r6

3.5/16

3.1n6

2-1116

1-7 /16

1-5/8

+Aa

4.1116

3-3/16

1t8

2-1/16

6 9/16

69/ l6

4-13/16

r.l5/ r 6 3-rlr6

l/8

33/r

8,13/t 6

8.11/',r6

6-7lr6

ll

lG15/16

8-1/16

9.58

6 t/4

1t2

l-

6

1.7116

I

M

11/16 +13/ t6

t7 la 2-1/a 2.7

/16

5.5/8 6.7

/16

1.1/4

1-

1-3/16

1

1

3-3/8

r

5-9/16 7-314

211/t6 81/r6 2.15/16

8, t

3/16

3-3/16

$5/8 10.7

t16

3.3/4

11-114

4

1

+5/16

1-O.7la

+gfi6

1

-

1-

5.51A

- 4.7t4 - 7.5t16 1 - 9-1r/16 2 - O.1lA

6.7116

7.1t4

8-1/r6

1

'|

Source: Texas

G3/16 2.3t4

r

2

+9t16

2

2-

6.3t4

2 -

2

-

11.1|a

1.11/16

5 3/8

4-1116

-

2

0-1/16

413/16 1-2-7/16 5.r/16 1 - 3.114

l-3 t-51/8 1 - 7.5/16 - 9.1t16

3,9/t6

3 7.15/t 6 3 - 1(}t/8 4- +t1t16 4- t1-5/16 5-5-7tA

6-7

'|

3 7tA

t1-9/16

1

-

1C1t2

-

a.1la

2

-

O.1/8

2

-

rG5/r6

2

-

1,

3 3 -

3

0-7116

29/16 4- 1tlt 6 6-7tA

3-9 4- 3.1t16 4-9.7lA

5 4,3/8 6-51/4

PW Bending Co., Inc., Houston, Tlxas

22 2 22 3 3-

4

7la

23tA

l1l16

3

1-114

3 9/16

r0 1rlr6

-

Gr5/16 t-7 /8

-

+1/A

t1t16

3-5/16

+15t16 6.9/16 4.1/a S-3t4

2-9t16

73ta 0-1t4

4-10

- 8-7/16 - 9-3/8 1- 1O1/? 2- 1-111t6 2- 4-7 tA 2- 8-1/8 3 - 2.3t4 1

r

4.13/

5 3/16

11-13/16

1

t-3116

4 3/16

9-9/16

1

&5la

1- r

7-1/2

1

7ta

3/a

1ll16

8-5/8

2-1t16

- 4-ll16 r - 5lr/16 1 - 7.5t16 1 A-7 la

2 3

3

1t-114

1-O7lA

s

N

3/16

l6

7.3/16 9-5/A

I -O

T

29/16

t

3-114

4-15/16 6-1/2

8-1/16

3

-13/ 16

23t8 9/r6 43/4 515/16 7 3t16

11/16 1-.1/2

2.3/1C 3

3.13/16

q.iirrc 9.1rl16 - 2-1t16 t.3/8 4,3/16 1 - 4.13t16 11.1t8 8 3/8 s.slu '| 7-114 t.s/16 4-3t4 r - 0-r1/16 I9/',t6 6.7/ 16 l.r3lr6 5-3/8 1 I5/8 1 - 2 3t4 10-3/4 7,rta 2 515/16 2- 0-1/16 r 1-15/r6 t.'ts,1c 2-3t16 6-3/t6 2 - 2-7t16 1- 5.112 1,11t4 q 914 2.3/a 7-3/t6 2 - 4.13/16 1 ,7.1t16 \- 2:9t16 , e:9/16 2.9t16 7.3/4 2 - 7.1t4 | 8,5/8 1 - 3.112 lo 3,/8 2.13n6 8.3/8 2 S-a/a I 10,5/16 t 1:1/l6 3 8-15/16 3 - Or/16 1- 11-1t8 1 - 5.1t4 11.7tB 3,3/16 I9/16 3 - 2-1116 2 - 1-112 1 - 7.1/a 1 0.3/4 1G r/8 1- 1.9/1C 3-3/8 3 - 4-7/a 1 8,5/16 1G3/4 1 9- 12 3-9/16 3- 7 1t4 2 - 4-5/A 1-23!a I t-5116 3-3t4 I - 10.11/r6 1 - 3.3/1€ 11- 15/16 4, G1/16 2 7.71A 4 1- 11-l ta r - 3.7/6 4 3/16 1 -O.112 4 2.1/2 2 - g-7 t16 2- 1-11t6 1 1111. 4.3/4 4- 9,11/16 2 - 4-5ta l-71l',8 1 - 4-1/8 5 - 4-7la 5-3/8 3-7 2 A 1t4 1-9.1/2 6.15/16 1 - 5-718 6 - 0-1/8 3 - 11-5/8 2 - 11.3t4 I - I1.7,t 7.3/16 1 -9.1/2 7 -2-1/2 4 - 9-3/8 2, 45ie 3-1 1

a_

Weight and Dimensions of Pipe and Components

L€ngth of Pipe in Bends Courtesy of Crane Co.

Radius of Pip€ Bends

-'l

f*.9\ |
90" Bends

|

180' Bends

the length of prpe in d bend having a radius not qiven above. add together the Iength of pipe in bends whose combined radii equal the required radius.

ro nna

270' B€nds

540' Bends

length of pipe in 90'bend of 5'9'radius. Ersmolcr ' Find Lenetli of prpA r; o0" bend of 5 radius = o+ra' Lengrh of prpc rn 90'beno of a' ,adius = W Then, l€ngth of pipe in 90" bend of 5' 9' radius

=

109rl'

311

312

Piping Stress Handbook

Calculation ot Pipe Bends Courtesy of Crane Co.

4i'

Eromple No.

8-Given A,

9o

:

sin

B, C, D,

R

tH : lllc K:tanlH L:A-K P: B _K N:F*2K

E : D -A _B F :YE'+ E

zc

x

R

Exornple No. I

B:

3.414

2.828 0.828

t+A--E

,

l.-s1

Eromple No.

E:D_A-B F:2N_C e :11o"+

$:

tan

r'

zH

K:14c

Exomple No.

E=D-A-B e -tVl-lT" " =

=

stn

ltJ

z,

tso

x x

x

^R

R

l--€ivcn R ond 45o Angler T = T ans.ent

Length oipipe in bend

R

9.425

x R +27

:

-

9-Given A,

M

B, C' D,

R

:llK'-n,

{:sinzN lP :90" *

to:r4tP

ZH

- tN

S:tanlOxR

lO-Givan A, B, C, D,

otf

l2-Given A,

P:2D C:A-2R n _tl,op,, r--, E:D-n F :2E

R

tH:tltc K=rantHxR v =A-K \. _ R .K ':-"-

Erornple No.

Exomple No.

C:%B

D=R+C

E = A -2R F =l/D'+E'

R

C/2R:

sin

tG

lH:90'+ lG lK = 180'-2 tG

l3-Given A,

EiF = sin lG H =%F x = 1ln-' K/H : sin lL

n'

B,

R

tJ[:tG-tL

lN = r80'+2lM t?==s2o; +

trI

Weight and Dimensions of Pipe and Components

313

Galculation of PiPe Bends Courtesy of Crane Co.

Exomple No.

D:B-C F =ll I

Ii = H: --l

aA

Sln

Exomole No.

l--Given A, B, C, R

zr F lS: tP * tG tK : 9O" - tS tL : t4 tS_ M = rar] lL xt( N:H+M O:B_C-M = stn

E,

Zu

llr;-

n'

4-Givsn A,

E:V a'+ D'

€xonple No.

2--Given A, B, C, N fxomple No.

D: B -C E:A -R F

:lo,

+ o'

E

F=s:nz\l H

:

lr'- n'

D:B -C

E:la'+a A

E --'-'

-A

c

:y

S-Given A,

(2R)"

R (1

- B'

lp:

sin

tD

R

7:sinlP t8:zP+tG lS lK:9O' lL : 1/2 lSM=tanlLY,R N:H+M _M O :B -C

Exomole No. 3---Given

R

LU:sinzF H:tanlG Xft tG:y2tF P:C -H

D:B-C

B =2R

B, C'

A, B, C,

fxomole No.

C:thB D: t4A

tG:%tF H:tanlGxR P :C -H

D

E --'--

E:IC'+ U

G

Exomple No.

R

E

=D

6-Given A,

=%E

B

lH:90" - tF A, + R1 -' 4A | _ rtl

Z-Given A, B, C, D,

G/H:sinlK

-A-B F:R-C t':lzH G:n+F H=lE+ G" rI:V L'-R'

R

IIlL=sintN to :90' - tK , t\ 7p =/2 tO S:tan IPXR

12 Allowable Pipe Span trlormulas and Tables

Pipe-Span Stress Limits

^M -Z

5

WL' 42

In order to have a workable set ofpipe-span tables or to

find an allowable span that will require a minimum of manual calculations, the limit for dead load stresses is set at S1/2. This eliminates the need for checkins the sum of

'=!@

the longitudinal pressure stresses plus dead load stress. (Sr, allowable stress at maximum temperature. ASA

:

Code 831.1 and 831.3.) The formula used to determine the maximum soans in the tables (Thbles 12-l through l2-9) is a mean berween a uniformly loaded beam simply supported at both ends and a uniformly loaded beam with both ends fixed. This mean formula most nearly depicts the conditions actually existing in a refinery. (See Figure 12-1.) By inspection, if the two moment diagrams in Figure 12-1 are superimposed, the point of the maximum bending moment will still be at mid-span.

Mean=

M:vz(Y.y-)

A safety factor of 1.25 is required because of the discrepancy between theoretical assumption ald the actual field situation.

M:wL'xl 124

Pipe-Span Deflection Limits Maximum allowable pipe deflection between supports must not exceed 1 in. or ll2 the nominal pipe diameter. whichever is the smaller. This is the basic piping practice: however,.it is subject to compliance with the customer,s specfrcanon. The formula used to determine the deflections in Thbles 12-1 through 12-9 is a mean between a uniformly loaded beam simply supported at both ends and a uniforn r loaded beam with both ends fixed. (See Figure l2-2.) In order to maintain homogeneous units, "Lt' must be in in. and "W" must be in lbs/in. , however, for ease of handling we wish to have "L" in ft and "W" in lb/ft, whicL we must now convert to inch units. The preceding equation becomes:

5 WL2 48

In order to maintain homogeneous units, "L" must be in lb/in.; however, for ease of handling we wish to have "L" in feet and 'W" in lb/ft, which we musr now converr to

.

wL4 I28EI

^

13.5WL4

inch units. Thus the preceding equation becomes:

M =-

5WI

-

48

2

60

wL,

5 WL2

48

l3.5WL4 EI

EI (Text continued on Dase 3:0

314

a Allowable Pipe Span Formulas and

Tables

Fixed Ends

simply Supported

frrnT 1_,-N

Load

I Shear

t uoment

2-l

z-l--

uJf Fixed Ends

Simply Supporled WL ., V =-

., "-

"'-=Y

rvrl -

2

,., -

WL 2

WL, ;;

by figuring the and a uniformly both ends at supported mean between a uniformly loaded beam loaded beam with both ends {ixed.

Figure 12-1. Diagram showing how stress limits are determined

!

r,

Fixed Ends

Simply Supported 5WL4

WL4

384E1

384E1

Mean: =

A1 +A2

3WL4 384E1

WL4 128E1

by figuring and a uniboth ends al supported the mean between a unitormly loaded beam fixed. formlv loaded beam with both ends

Figure 12-2, Diagram showing how deflection limits are determined

t

315

316

Piping Stress Handbook Table 12-1 Piping Spans Based on the Following carbon steel Materials: seamless A53 Gr. A, A106 Gr. A, Apt 5L Gr. A; Wetded A53 cr. B, Apt 5L Gr. B, A155 C55 Ctass 2 >200.F wilh Water,

(L =

No Insulation

7,650 psi)

201'F-600.F wilh Commodity

(f. =

6,175 psi)

=

Wetghi ot Waler, Minimum Insutation

Maximum

'

Exceeds maximum dettecrion. Courtesy of Po$,er Piping Company.

Tabte 12-2 Piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A312 Tp316, Ag12 TP317, 4430 FP316H, A376 TP317 >200"F with Warer, No Insutarion

(L =

Pipe

Size

'

SCH.

9,375 psi)

Maximum Span

Exce€ds maxiftum deflection,

Co nesy of Power Piping Conpany.

201'F-600oF with Commodity

(L =

8,550 psi)

Maximum Span

=

Weight ot Water, Minimum tnsularion

Recommended

Allowable Pipe Span Formulas and

Tables

Table 12-3

TP304L' A312 Piping spans Based on the Following stainless steel Pipe Materials: seamless A213 FP304H A430 TP304, A376 TP3o4L, 201.F-600.F with commodity

>2OO'F with Waler, No Insulation (1, = 7,550 psi)

(r3

=

5'800 ps4

weight ol water, Minihum Insulation

Becommended

Maximum

'

=

Exceeds ma)(imum dellection. Courtesy of Power Piping ConPanY.

Table 12-4

piping Spans Based on the Following Stainless Steel Pipe Materials: Seamless A213 TP304L' A312 TP3O4L >2Oo"F with W.ler, No Insulaiion (1, = 7,650 Psi)

Maximum Span

'

Exceeds maximum delleclion. Courtesy of Power PiPing Compan

Becommended

201.F-600.F wirh commodity

{L =

a,500 Psi)

Maximum Span

=

weigh! ol water, Minimum Insulallon

Recommended

317

318

Piping Stress Handbook Table 12-5 Piping Spans Based on the Following Nickel pipe Material: Seamless 8161 Annealed >200'F with Water,

(L =

No Insulation

4,ooo psi)

Maximum

201dF-450cF wlth Codmodity 1,000 psl)

[. =

Recommended

=

Weight of Waier, Mtnlmum Insutation

Maximum

Courtesy of Po,,er Piping Company.

Table 12-6 Piping spans Based on the Following Aluminum pipe Material: seamless B24l Gr.3oo3 H112 >200'F wlth Wbter, No Insutation (1. = 4,000 psi) Maximum

Cowteq of Power Piping Compaat

Recommended

201'F-400.F wilh Commodity

(r. =

1,7s0 psl)

Maximum

=

Wetght ot Warer, Mtnimuh tnsstation

Recommended

Allowable Pipe Span Formulas and

Tables

319

Table 12-7

PipingspansBasedontheFo||owingA|uminumPip"M"tg'iM >2oooF with water, No Insulation (1. = 3,000 Psi)

Pipe Size

'

scH,

201.F-4O0dF with Commoclily d- 2.ooo Dsi)

=

=

Weight ol Waier, Minimum lnsutalion

Recommended SPan

Maximum Span

Maximum Span

Exc€eds maximum dell€ction. CourresJ of Power PiPing Comqany

Table 12-8 8235 Piping spans Based on the Following Aluminum Pipe Materials: seamless B21O' 9'234' and H18 Gr. 3003 Gr. 6061 T4, 8241 >200'F with Waler, No Insulatlon (1. = 4,500 psi) Maximum

'

Exceeds maxlmum dellectlon.

CouneE of Power Piping ComPant

Recommenaled

201.F-6OO.F with Commodity (t! 9s0 psi)

=

Maximum

=

welght o, water, Minimum Insulation

Becommended

320

Piping Stress Handbook Table 12-9 Piping spans Based on the Following Red Brass pipe Materiar: seamress B43 >200"F wilh Waler, No Insulatton

(l =

tot

1,500 psi)

Maximum

u:o'o:offn

il.

=

weisht ot warer' Minimum Insuration

""""oditv

Fecommended

Courkq of Power Piping Conpany.

: : W:

where SB

L E I Z f

=

: : : :

Longitudinal bending stress, psi Maximum deflection, in. Weight of pipe, including commodity and insulation if any, lb/ft Length of span, ft Hot modulus of elasticity of pipe, psi Moment of inertia of pipe, in.t Section modulus of pipe, in.3 Unit stress = Sr/2, psi. 56 per ASA Code 831.3

To solve for an allowable pipe span with a known __ llectlon, use the foliowing lormula:

.

4i EIA Y 13.5W

de_

Piping Wind Loads Wind Loads Tables 12-10 through 12-12 can be used to calculate wind loads. The wind pressure (P) in lb/ff on a flat surface normal to the direction the wind for any given velocity (V) in miles/hr is given quite accurately by the formuli

P

:

0.004v,

Table 12-11 gives the pressure per square foot on a flat surface normal to the direction of the wind for different velocities as calculated by the preceding formula. The design wind pressure at the location of a given pipeline should be applied ro the projected area ofthiout-

I

l

Allowable Pipe Span Formulas and Tables side of the pipe (or insulation) to determine a uniformly distributed load as follows:

w_ where

(P) (c") (D)

The design wind pressure depends on the location of the vessel or stack. The U.S.A. Standard Building Code Requirements for Minimum Design Loads, in Buildings and Other Structures, A58.1-1972, and the Uniform Building

Code include a table showirg wind pressure at various

t44

P: C": D: W:

I

heights, and a map where these values apply.

Design wind pressure, 1b/ft2 Shape factor (See T};ble 12-12)

Outside diameter of pipe (or insulation)' in. Wind load 0b/in) pounds per linear foot of plpe

More tables have been developed according to wind velocity in miles/hr, wind pressure lb/ft2, wilh reference to a pipe outside diameter. These tables are very usefirl for computer data input to model uniform wind load on pip-

ins.

Table 12-12 Shape Factors

Table 12-10

Ofticial Designations of Winds

Shape Less than

Calm

Ito

Light wind

1

Cylinder

/

8to12

Gentle wind Moderate wind Fresh wind Strong wind Gale Whole gale Hurricane

Factor

General Use

13 to 18 19 to 24 zf, to J6

Octagon Sphere

Flat

39 ts 54 55 to 75 Above 75

* Beoufon Wind kole, U.S. Weather Burca-.

Towers, stacks, drums, tanks, exchangers, prping, etc. Piers for towers and drums

0.6

Tbnks

0.60

Open signs Solid signs Closed buildings, framing, and com. parts Frames, open-type structure

1.60

0.80

1.40 1.30

1.60 Open plan

0.80 Sec. plan 0.00 other Plan

Table 12-11 Pressure per Sq Ft on a Flat Surface Normal to the Direction of the Wlnd Corespondlng Pressule Velocity

(miles/hr)

(lbflrl

To

10

0.4

Gende wind

20

1.6

30

3.6

Fresh wind Strong wind

40

6.4

)U

10.0

60

t4.4

80 100

25.6 40.0

Gale Gale

Whole gale Hurricane Violent hurricanes

322

Piping Stress Handbook Table 12- l3 Wind Load (lb/in.)

t5

rb/tt2 lil

il

0

40

45

50

55

9l

to0

105

lt2

117

85

.r4 .2t

.19

.24

.29

,29

.35

.43

.51

.25

.31

.41

.50

.58

.37

.,t5

.56

.65

.75

.69

.81

.68

.42

.89

.

.4r

rl5

.55

8.625

r0.750

.67

.89

12.7 50

,79

t.06

I4

35

80

4.500

5.525

30

7! es,/ti R

2.375

4.0

20

l.tl

.39

.49

.58

.55 .83

.84

.93

.92

1.04

1 t5

L.27

.96

1.10

1.23

1,38

1.51

r.0?

1.25

I.44

I.61

1.34

1.56

2,r2

t.38

1.32

2.01

.47 r -15

1.45

1.75

2.04

2.3

3

2.61

1.00 r.33

1.66

2.00

2.3

3

2.67

2,99

l8

t.r2

1.87

3.35

20

t.25

22

r,37 1.83

24

1.50 1.99

t,62

1.4

9

2a

r.7

30

r.87 2.49

5

2.62

3.00

2,50

2,9I

3.34

2.75

3.20

2.49

3.00

3.45

4.00

2.70

3.25

1.79

4,34

4.85

2.9t

3.50

4.0

8

4.61

.12

4.75

4.31

s.01 5.3

2.08

2.13

3

2.00 2.56

3.32

4.00

4.66

34

2.t2 2,83

3.53

4.25

4.95

35

2.25

2,99

3.7

4

'1.50

5.21

38

2.17

3.r6

3.95

4.75

40

2.50

3.33

4.16

5.00

12

2.62

3.49

{.35

5.25

44

2,75

3.56

4

46

2.al 3.83

t ,74

48

3.0 0

3.99

4.99

50

3.r2

4

.16

5.20 5.40

I.9l 2.39

1.46 2,92

2.9r 4 -1,2

a,16

4.58

rt

4.58

5.0r1

4.48

4.99

5.45

5.45

5.9S

4.

6.41 5.51

5.8?

5.9 8

6.65

7.33

6.35

7 -08

7 .7A

5.0I

6.?3

7,49

8,24

-34

7.10

7.91

8.?0

6.68

7,48

8.3 3

9.15

8.?4

9.62

6

5.83

.9t

4

.01

7.85

6.4I

7.34

8.22

9.r5 10.0I

5,75

6.70

7.68

8.60

9.58 10.s3

6.0

0

6.99

8.01

s.97

9.99 l0 .99

6.25

7 .29

8,35

9.35

10.41 I1.45

8.68

9.t2

10.83

,57

4.33

.80

.71

7

rl.9I

5{

3.37

4.49

s.6t

6.75

55

3,50

4.66

5.82

?.00

8.

58

3,52

4.83

1.25

60

3,75

4

6.24

7.50

4.14

10.02 Ll.22

t2.49

1.3

3.87

5.16

6

.44

7.75

9.03

10.35

tr.59

12.9t

14.20

.99

54

4.00

5.33

6.5

56

4.12

5.49

5.

9.01 10.09

1t.24 \2.X7

r5

9.3 5 10.47

1r.66 !2.42

4.45

9.58 10.84

12.08 13.28

7

.87

5

.008

10.68 1r.95

g5

8.25

1I.02 12,34

.7 4

14.66 13.74

15.12

Table 12'13 Uniform Wind Loads (lb/ln.)

.59

1.02

.9{ 4.00 /t.500 5

1.00

l.l2

8.625

r0.750

I4 18 20

1.08

2.15 2.58

1.3r

1.2r t,?

"525

.79

.84

1.09

l.16

r.23

r..25

1.33

r.

.54

1.40

9

2.69

2.33

2.34

2,47

3.05

2.91 3.45

1.33

/t.50

4.8?

5.00

5.41

1.3I

r./15

2.14

1.78

r.87

2.62

2.76

3.41

3,59

4.03

t.25

t.17

4.78

5.02

3.99

1.21

l.5r

1.37

.4.56

{.95

1.65

5.00

5.33

5.83

6.25

?.08 8,25

8.?0

9.00

9.49

9.20

9.7 5

10.29

9.91

10.50

r1.08

t.08

4.00

.98

1.66

1.49 2.20

.94

r.50

!11

3.80

3.50

.89

5.54 5.00

5.99

22

5.50

5.95

6.41

6

.87

7.79

21

6.00

5.49

7 .OO

?.50

8.49

25

6.50

8.56

?.54 7.58

8.15

?.91

10.83

2S

7.00

30

?.50

32

8.00

r0.00

r0.56

11.33

8,50

r0.62

11.33

12.03

13.45

r4.16

L2.7 4

L1.24

15.0

15.04

15.83

34 36

40

9.00

10.0

9.99

9.20 4

10.50

r0.29

II.OE

9.7

10.83 L2.23

a2

ta

II.O 12.45

45 !t5

14.00

r2.0 12.5

13.54

13,0

t{.08

5a

r3.tl

L4.62

15.75

15.70

16.9t

54

t5,0

12.00

13.45

14.25

13.3

1{.1

rt.00

13.12

13.99

14.87

13.75

t{.66

15.00

16.5

17.4I r8.20

19.16

16,99

r 8.00

18.99

20,00

17.?0

18.?

5

19.79

20.83

16.25

17.33

t8.al r9.50

20.58

16.87

17.99

19.12

20.25

2!.37

17.50

18.56

r9.82

21.00

r 8,75

15.78

19.37

20.55

17.33

20.00 20.52

2L.21

2a.!.6

22,50

23 .7 4

25.00

23.25

24.53

25.83 25.66

24.00 23.27

22.50 23.22

2L.75

18.12

\5.24

0

17.50

15.28

14.37

19.99

!7 .A7

rt .8?

2

12,50

r1.87

14.58

14.0

50

11.99

10.5

24.75

25.L2

27.50

13 Pipe Support Selection and Design

Pipe Supports

t Because piping is aflected by thermal expansion. supports in a piping system move thermally in different directions. Weight is supported by two kinds of supports-rigid

tions are critical (very expensive). They have been use
and flexible.

c Rigid supports are supports in a piping system which stay fixed. They generally move thermally in two directions-horizontally and laterally, but not vertically. The weight at this point is usually supported by shoe supports, bracket supports, dummy legs, or a rigid hanger. There are hundreds of ways these supports can be designed and every company seems to have its own way. (See Figure 13- 1.)

c Flexible supports move in all three directions. Weight is supported in this application by use of spring supports.

Spring Supports The types of springs offered for industrial support applications can be segregated into three classifications: are the springs most commonly used in the petrochemical industry for supporting loads. They are used almost exclusively in the construction of pre-engineered and calibrated variable- and constant-support spring hangers. They are also used in less expensrve forms in the construction of hold downs, field supports, and vibration dampeners. c Disc spings (BeIlviIIe springs) are seldom used in the construction of variable- or constant-support spring hansers, but are available if desired when space limita-

o CoiI spings

Variable Spring SuPPorts The word "variable" in this description refers to the fact that the load-carrying capacity of the spring varies considerably as the spring is compressed or extended from a fixed reference point. In other words, as the pipe moves up, the spring is extended and the load that it exerts is decreased. The opposite effect is experienced when the pipe moves down. In either case, the force exerted must not vary when extended or compressed by more than 25 % (maximum) from the calculated load. Manufacturers offer a large variety of variable-load spring hangers with standard and nonstandard scales. (See Figure 13-2.) The scale is attached to the spring support

frame and indicates the vendor's recommendation for range of load. Normally, a safety scale is provided above and below the scale. Beyond these points the unit either loses all load carrying capacity or it reaches its fully compressed position, therefore prohibiting frrther displacement. In every case, an attempt should be made to select a spring so that the calculated load falls in the center of the spring-scale range. The maximum deflection, which will compute to be not more than a 25% variability, can be found by dividing the full range of the spring scale, in inches, by a factor of 2.5. Where the equipment loading is sensitive or critical, larger-range scales may be beneficial in reducing the variability percentage. Typical applications are shown in the next pages along with an explanation on how to size and how to determine the type of spring to be used. Dimensions for variable {Texl conlinued on Page 327

324

E

\

"'l

J

.,|

",1

\tf\ET

" , 'S+

I

x

;

e

!4

t

E

F.l

t6 t

HI

I

1

g

o.l

FI

|

-.ll

tlsstA

trTli |t /

ill $

tl

E

Ie

ol

;l

ll.l tl

u_!J

lP

l+

Pipe Support Selection and

I _l

r.

fl

J

o RI

c)l

.{l

.i

a

Design

o

f

oo-

6 o l

o (9

o

.9 lt

325

326

Piping Stress Handbook

Type A

Typr A

Typo B

!t

T=

I

m

T

,t

Special variable spring hangers can be fabricated for

.d\ V

i|fr

l|\ Typc C

fi

lo D.Lrnio. Type: The type of variable sorine hanger to be used depends upon the physical ihari acteristic-s_ reqlired by the suspension problem; i,e., amount,9f head room, whether pipe is to be supported above the spring or below the spring, etc. Conslderation _should be given to the seven standard types of-

Typr

How

fered (see line cuts of types ,,A', througlr',,6"r, unusual conditions.

How io Dctcrminc Sire: Conplete sizing infornation is given above the hanger selection chart This information is applicable to sizing hangers of all series.

It will be noted

on the hanger selection charts that

the total spring deflection in the casing leaves a leserve above and below the recommended working

D

load mnge.

Trovol Stop: lrrtr-l PICCEI

lrnev:L

f

i LrIrTl

sroP

PtEqg

Typr F

Typc

F

Wirh Roller

L--,1 rH

The functional design of the pre-compressed variable spring hanger pereits the incorpo.ation of a two-piece travel stop that locks the hanger spring against up-

Type E

Typr

G

ward or downward movement for temporary conditions of underload or overload, The complete travel stop, the up litnit stop only for cold set purposes or the down limit stop only which rnay be ernployed during erection, hydrostatic test or chenical cleanout will be fumished only when specified. The travel stop is painted red and is installed at the fsctory with a red ..cautio!,' tag attached calling attention that the device rnust be removed before the pipe line is put in service.

Figu.e 13-2. variable supports. (courtesy support rechnology and piping Technology products,

Inc_)

Pipe Support Selection and springs are generally the same for all the malufacturers. That is why loading tables and dimensions that can be used for application in supporting piping have been included.

Constant Spring SuPPorts The word "constant" in this description implies that the spring will exert the same lifting effort as the pipe moves up and down. Actually, the spring rate in most cases rs minimized by transferring the load through a series of levers so that the elongation or compression of the spring is

negligible. Constant-support spring hangers are considerably more expensive than variables and are therefore used sparingly. They are used in conjunction with large deflections where variability becomes a problem, large loads where erren small variabilities are a problem, and at strain-sensitive equipment. (See Figure 13-3.) Manufacturers offer a wide variety of load ranges, deflection ranges, and frames for their constant-support springs. Loading tables given in Thbles 13-1 through 13-5 and in Figures 13-3 through 13-6, generally are the same for all the manufacturers, but dimensions are different and should be obtained from each manufacturer. (See Figure 13-7 for typical arangements of constant supports.)'

Travel Stops

All hangers have built-in stops to limit the travel at the top and bottom to a small percentage beyond the specified range. In addition, temporary stop pins are provided at the initial travel position for the purpose of hydrostatic testing and to facilitate erection. All stops are of rugged construction to withstand appreciable overloads. It should be remembered, however, that hangers will function only when temporary stops are removed and the hangers load-rods are adjusted properly to enable the hanger to operate within the specified range oftravel. An arrow traveling on a scale readily indicates the travel posi-

tion at all times. Load Ad justment

All

hangers are equipped with a load-adjusting nut that permits up to a 10Vo increase or a 10% decrease in loadcarrying capacity. However, since all hangers are carefully tested ald preset in the factory to specified loads, it is recommended that no field load adjusfinent be made until it is accurately determined that a change is necessary.

Otherwise, the proper distribution of pipe stresses in the system may be disturbed.

Design

327

Standard Hangets Load-travel data, physical design features, and dimensions are shown on the following pages, for convenience in selecting the proper type and size hangers for any specific requirement. Since the load-supporting capacity of a given size is inversely proportional to the travel function, excessive overfavel when specified may require a larger and more costly hanger size than actually needed.

Sway Brace Support This type of support is also a spring, but is not used to take care of the weight effect. It is recommended for controlling vibration, absorbing shock loading, guiding or re-

straining thermal expansion, and bracing a pipe line against sway. Figure 13-8 shows different sway braces and tables for loading and sizes.

Insulated Pipe Supports and Anchors for Cryogenic Service Gryogenic Pipe Supports and Hangers The design of supports for piping used in cryogenic service diffbrs from those designs used for standard piping. In this application the support is designed to avoid metal-to-metal contact of the support with the pipe. Such contact would create a heat sink whereby heat would be transferred from the ambient environmental conditions to the cold pipe through the metai support. To avoid this metal-to-metal contact, a support is manufactured from rigid polyurethane foam. Polyurethane offers both the insulating properties necessary to maintain the cryogenic temperature, and also the high strength necessary to support the pipe. Figure 13-9 illustrates a typical cryogenic support. The insulated support is normally furnished with the foam, vapor barrier, protection shield, and a galvanized cradle. These components are all adhered together into a unit that is easily installed. The saddle as ihown in this figure may be removed and replaced with other types of supports such as a pipe clamp for use with rigid and spring hangers, or with graphite teflon slide Dlates.

The design of the polyurethane support includes the following considerations: . Required insulation property (K-factor). o Thickness ofthe insulation on the remainder ofthe pip(Text conlinued ofl page 3,15.)

324

Piping Stress Handbook Table 13-1 Load Table for Variable Spring Supports for Selection ot Hanger Size

Lood Toblc in Poundrr lor Sclection of llonger

site

0

3

3

1

6

I 6

2

hir

I

21/.

sp.in, S.dl.

- lb, p.r i.,

Courtes! of Support Technolog, Products, Inc., and Piping Technolog)t Products, Inc.

il'

Pipe Support Selection and Design

Figure 2680

TY PE -8.

TYPE-A

329

TYPE-C

-

Type B and C opringe are furnished with one ot two luge ae ehown, welded to tlre toP cap of epring'

Typc A rpringc are furnirhed with r threedcrl buchirg in the toP Platc, providing for a rimplc rod attachment for the upper connection. ugt naiad

ha|t9al !12a

load

tb

20 3'o

00 124

v, c

713

tu9

cadn0

crdng

thd lgth

holc

lengtn

dlan

c

3l2a

v2

th

813/rs gqa

5 27 29

Vr

950

6

1Ol/s

1235

3/t

6

12Vs

62

t/.

1615

1\h 11/1

1

79

1Vs

7

th

a4 100 124

11h

7

1

lU!

7

1V2

154

14t

5130

16o 7125 170 q5fl0 18o 12645 19o 1680s 200 22325

21o 29688 19591

l.ngth

6

lt

x

R

s

T

tht

1Y2

101/rs 1013/re

1Ua

7h

1V2

301

2

3,18

2U1

456 528 684

21/,

2!e

I

1Ya

a

I I

t0 10 11

2% 27/a

3Ys

9154e 1oe/r o

85/6

8% 8%

131/ro 131316

1/a

1U4

t/s

V4

1V2

121/^

11/a

7/e

V4

125h

1313/,e 14s/ro 1sYa

11/2

1Ua

121/B

15

11/2

12 13%

1Ua

1st/g

16%

11/2

137/s

14rh

167/a

'|

11/2

14V2

11/4

1U4

1

1V2

1Sla

1U4

11/^

16la

17Y2 18Ya

''|

2

147/a

1Ya

15%

177e

15%s

11/2

187/rs

1V2

2171rc

187ls

11/2

1515he 1815/rs 181s/rs

qa

2131le 2471rc

23111le 261s/ro

tt tt

19t 3

2V2

2811rc

3 3 4

41/2

313i ro

23tr

129a

4Y2

35rrAa

265/r s

12qa 1zEa

41/2

3813/rs 45r1/16

2U,

3

U1

263lta

as's 12Ve 12Ya

2Vt 2Y.

115/,0

,2

1rb

1/2

%

2011ha 2 2315h6 2Y2

't%

181/a

32%

6

1V2

1V2

18V^

n

115

7/a

1lz

ash

1sqa 161/rs

10,/rs Va

11/4

!,t

13Ys 13U1

lk

x mtn

lUr

,lr

6% 6% 8% 8% 8% ask

1l/a

lenglh

nelS

1013/rs 115/rs

4

1O1/.

2850

15o

ptn

ash

146 3aoo

13o

ihlck-

d.plrr

op€n|n9

Ss/r s

Ya

120 2134

d6vl3

pln9

5s/rs

5 5

l5

61

snrF

ol

't1h

8s/,e

loedod

h.i9hl

thrlrd

5

V2

14

399 532

R.H.

V2

166 29C

1lo

tb

't

4o

6o 7g 80 9o 10o

alza

7

0o 1o

PFO

6rn

rd

187ll.^

2#l'a

C^

26rri,e

27/s

Ya

31h 33h

le

28sh6 31r46 311'/re 3431rc 363/,c

3811/,4

3%

1

395/15

4113/r o

37/a

1

463/rs

48rr/16

Figure 13€, Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products, Inc')

330

Piping Stress Handbook

TYPE-D

Figure 2680

TYPT-T

EJ

TY PE-F

--,

c=_: .-- rl

Type D spring permits adjustment from the top, by lurning lhe nuls on the hanger rod against a piece ot tubing. The tubing is securely welded to the spring cap. Type D spring is set above the supporting steet_ Type E permits rod adjustment from either above or below the spring. Type F spring assembly is designed to suppofi piping lrom below, direclly lrom the tloor Adjustment is made by inserting a bar into holes in the load column. and turning the load column as a jack screw The base plate is welded to the case and has lour holes for fastening.

type F csBlng

Lnglh a

0o

6r1/,0

cr3lng

!hipplng l.ngth K

4

10

M

9'3/,6

3Vs

8s/,a

50

8%

4

3Ys

5s/16

5s/,6

60

%

80

5/s

90

tto

7h

813/,6

6%

11/2

6s/s

1Y2

1O1/a

67a

-lY2

101h

8s

1

9'si,^

150 160

8%

1t/a

3

12'h6 131r/i6

15rr/rs

13v4 13Y.

'|

I37s

13'/16

8% 8

2Y2

16Ya

2Y)

8% a%

3

169r

31/2

19'/i6

4

21VE

1qa

181/6

85/s

1AY6

12Ya

21A

201h 235h

124b

5

23%

123/a

5e/,s

265h

123/4

61/t

295/,6

32

1211$ 137/,0

16th

2

3

107l*

155h

12151,^

21Vs

3 3 3 3 3 3 3 3 3

3 3

AY. AY. eY.

t{

Y.

a%

Y.

U.

Y.

Y.

1orh

Y.

+t

107 101

Y.

I

13//s

+t

AY.

I 1(F/16

16}t

3

161{

10'

13Y2

131/.

121/B

14Ya

1@/16

18%

14rr/16

16!r^

13U. 13U. 13U.

1@1.

16V2

1@/'6 1G/r6 15%

16h

5

15r^6

171116

179!

19%

13Y. 13Y.

25%

197/,n

2t,t,e

131/.

25r1/,5

191^6 2151'6

21\lt6

17Y.

197a

2gqe 3231,a 35e/i

6

295116

127e

lG6

17U.

15,1/.

17U.

159t 15Y.

l7U. 17U.

Figure 13-3. Continued.

10'/!6

1g/.

6,a 161, r

6V16

Y. U2

8U.

a%

Y.

aU. Y.

Y2

AY.

%

v,

AY.

16'4

aU. Y.

16Y2

\,

A1/.

Y2

AY.

,2

AY.

tt

12\t

%

7l

12y2

Y.

td

't2h

12V2

-2

2

3i3 5U.

1Ak

1V,

15r3/,6 183/a

tt

AY.

71h

3

21h

21/a

121/a

111/e

18o 190

21/2

101/a

1431a

2

fian96

7r.

3 3

131k 151h

bolta

7Y2

131/a

170

200 21o 220

10'5/,6

9s/16

141/a

8%

16th6

7 7

3

8%

13y4

7

7Vz

123/a

10,/15 131/4

1251o 13

1j/a

9Ya

'l2Ys

100

8is/,s

11r/i6

nrng.

nan9.

7|h 7\k

1211h6

107h6 11/a

nrngo

9r^6

T

thlck-

fr6n9.

L

ranglh

.l

1011/ro

20 3o

120 130 140

lenglh

h.ighl

tt

12\t

6

Pipe Support Selection and Design

i80

Figure 2680

ROO

SrZ€ A',

--

l

L

z

N\

-c Type G trapeze type spring assemb,y is formed by welding lwo standard spring assemblies to the ends of

a pair ot channels. Type G assembly is especially adaptable tor use where headroom is limited, lo avoid interference, or lo accommodate unusually heavy loads. The assembly can be furnished wiih center to center dimensions, as specified by purchaser. When ordering Type G, divlde the total pipe load in half to select the proper spring size. Ihe travel range of the springs remain unchanged-

r F

hanger

.alod load

(appror)

!tza

tb

each, lb

0o

138

1o

200

20 3o 40 5o 6o

256

70

8o 9o 10o 110

12o 130 140 150 160

170 18o 190

200

21o 22o

rod

caslng

lenglh

79142

min thread cngegornonr

channtla

V2

6rr/re

1/z

Y2

38 39 63

8s/'"

4 4 4

,b

Ya Ya

5e/ro 7151rc

3/a

V2

a5h

Ya

sh 5k

813/15

6s/a

2 2

th

1

2

7/o

1U.

3 3 3

7/e

123

la

107/a

8E4

137

Ua

'lzYs

87a

125 't37 175

1/g 1

10,/re

1Ya

131/s

183

1Va

13Y4

224 270 326 630

1U4

13/a

8% 8%

11/g

11/z

161/re

gVa

231rc

2Va

13/a

lAYs

Bsh

271rc

21/e

91s/rs

2

18Y.

2U4

20

2V,

2316

3

at6

Ya

1

10v4

11/re

%

lt 1

6% 6%

V2

1V2

2

Ya

Y2

1V2 1Y2

5h

1/a

1b

933 1137 1436

z

P

28 29 30

v2

446 598 798 1064 1426 1900 2470 3230 4276 5700 7600 '| 0260 14250 19000 25290 33610 44650

caslng dlamater

1Ya

11/a

11/4

1

1Y2

t/a

1

11/2

12Ya 12Ea

2651rc

12/a 12!a

32%

1zCa

1lz 2

2131rc

2%

4

3r^6

2sh

4

3s/rs

27/a

3e/'a

3rr/ro

3Vs

4

Figure 13-3, Continued.

31t

4

3il

l

332

Piping Stress Handbook

Figure 980 TY PE-B

TYPE-C

--I-

RiS

rElh r

rll

I

stzE'A'

Type A springs are furnished with a threaded bushing in the top plate, providing for a sjmple rod attachment for the uDoer connection. Type B and C springs are unfurnished with one or two iugs as shown, welded to the top cap of spring. These types are designed for use where headroom is limited, as these springs can be attached direc y to building steel by a pair of angles, eye rod or a single plate.

rypr

B Aa,c o,Ec oo

lo

20 30 40

].t

lt

tt +t

170

,h

U.

4

lu.

rh

U.

tY.

r6lt

5r/rr

th th llt

ld'/rr

6tr

18tl

651

I

i9.

lh lh th

6tt

2Al

851

r8U.

a9i

lr

lgrt

811

1Y.

2411

8tl 8tl

1}|

24h

1U.

25Y.

6l

th

'lx

v

81r 8St

131

L

,A

I

ltt

t40 ltl

150 160

1Y.

149t 1srh

llt

18,o 2 190 2Y.

no

2U

21o

2*

220 3

4h

't

1lt

lt

llt 2

3

37U. 41U.

12Y.

2L

4h

l€'h

1?g.

lg.

Y.

1Y. 1Y.

,h

'lY.

ri

'|

h

2rr

3lt

th

1

3tt

5

1

13

t3

20

255^.

197/l

t5

15

2O.l$

2*h. r stt

l7+f

m

19

22tl$

16?h

1At/.

23 25

1AU.

20L

26rt

't81r

*f

21

20"'

25tr

?31h

2a%

m'l16

21V.

261n

73th

2A?h

2-lU.

211he 26r/'e

23Y.

2lt.h. 26i'hl 241'h. 29irl! 21Y. AV. 2qh. a,t$ 27'h. 24'h. 263h1 2ovr

A.h.

yr 2631rr 315/r6

a\

38 46

21

39

6l

69 72

58

u

t(X

9a

?f''ltr 2Ahl

149

147

342

t8a

27

1|:|4

273

544

3|14

38lt

381r

,€1t

€r

311rr 33pir

37tr 42y 37.ht 12'l|. 46'r/,r

1aV.

SiVr 3Flr

25S

n3

34th. 3€rA!

482 570

147

772

693

57,t

61lt 66% 4Sl^ 75'h. &)r/r 62

2.1

t29 t37

U.

7111L

140

189

L

En.

127 '187

213 285

8Y.

3tr

126

134 171 174

8Y.

4$i. 54. ! 38'/r $!rnr 57'tt 629nr

67 't(B

124 94 134

5t 57

87

28'lr

30r!nr 3511,r 263ha

26rVl 3r,rn. 3131r 36t/r3 26ttt 2A'hl

43

2 37 45 49

28tt l9i3/rr 211't 2411hl 29rr/'l 211h. 23tlt

39

33 37

39Y.

$ 1

t9

171.1

8%

t{

2h

'tl

15'V,l

2.t$ 2Vlft .

{ch

D,E

16U.

t43 r58 204

tt

*t

23\'l

La.c 'tl

14Y.

23.h

l8%

21'lr.

tl

s 1

aw

H

1k

6

2111$ 18u/r6

18'/,r ?35 Y.

2h 2h a

0r

,^

2

2tt

1g

h

1U.

1U. 1V. 1Y.

161/,3

15..

th 1tl th

lx

3(|lt

1Y. 1U.

is3

(rppror) lb,

tP.

a,c

I

l1

81i

100

lhlct

th th th

?0'h.

1lo

R

hg a

,^

1

15Y.

6o 70 80 9o

r.ltht

Llgll H

12rl

t4

5O

120 't3 0

||,!

A, C

\l

520 594

n7

3o:l

936 I

l7t

1573

51l,t

9r0

015

842

196

64

210

t1t0

1154

2506

Figure 13-4, Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,

Inc.)

Pipe Support Selection and Design

Figure 980

***-ffj

___l_

T-ffi-r I FC-t I

xllE

llrll Ll-l-L---i TYPE-D

TY

T YPE -G

TYPE-F

PE-I

!

0o 'lo 20 30 10

50 80 70

19%

2.Y.

1Y. 1U. 1Y.

2OY.

1U.

22 23v.

1Y.

21lt

23\'tr th 25Y.

80

5h 5\t 5\t

1Y.

5h

29h

O

25Y.

120

27Y. 32Y.

130 140 150

1.900

AYa

tl

1.9m 1.9m

7V2

8Y.

Y.

vh

a%

71h

AY.

7Vr

7

1\'

90 100

th

Yr

7 7

8Y.

7'h

7V2

I

1oth

8

107h 1Ot/.

13U

16V,

13rl

16v.

stt

2h 2h

13% 13' 13U.

10e/,.

16v2

l0'/,.

16Y. 16v, 16v,

13u.

3S'

70

13h

5v,

13U

160 190

48tl

l5Y.

5ra

'|

200 210 220

35'1. m+t

13%

Y.

,l

ti li

3.50 3.50 3.50

53/r. 9Vt

8U. 8u.

v.

1Y. 1Y. 1U.

h

4.50 4.50

aU.

9U.

h h

th th

4.50

AV.

4.50 4.50 4.50

a%

2Vr

al

12/t

17v.

l5V.

llUa

r

5?r

22

2

U.

*

It

Figure 13-4. Continued.

2h

8Vt

5.563 5.56:]

51{

h

2\l

5.563

6Y.

2

2

l2v.

{ 4

lVa

AY.

lsya

5!t

h

4.50

5 563

1th

V.

12v. 12v. 12v,

sV,r

I I

4.50 4.50

qt

'ty'

Ua

Y.

5.563

Y.

Y.

5Y. 5Y.

V.

Ua

th

5U.

15Y.

17Y. 17U. 17U.

6n

lt lt

16v, 16v.

l0'/t

t60

3Yr

2.875 2.475 2.475

'16Y7

13U.

2Y.

AY.

2'h

3}t

3ti

1

{ a 1

a 1

333

334

Piping Stress Handbook

Figure 820

TYPE-A III' ROD S|ZE

"A"

TYPE-C

TYPE-B

r-l-t

- --_<,1

__JH

I

B

__t

ROD SIZE

"A"

Type A springs are lurnished wilh a threaded bushing in the top plate, providing lor a simple rod attachmenl for the uooer connection. Type B and C springs qre unlurnished with one or two lugs as shown, welded to the top cap of spring. These types are designed for use where headroom is limited, as these springs can be attached directly lo building steel by a pair of angles, eye rod or a single plate.

S

r.rqhl {lp9ror)

lug in9

c

\E,C o,E

f

00 20

10 10

25

6

'

27

17

29

t8

31

tl

I I t0

19

32

8

17

t8

45

8V.

8%

m

19

51

8%

8tk

21

m

45

12

6r3i

85/,6

r

1O'/,6

8'/rs

30

5',

6J^G

50 6o 70

6% 7th

80 9o r00

91/,6

8

9r/,6 gvz

BV2

10

8Y.

1OV.

9'/r6 10j/,0

11%

2

130

3

r5o

3

16()

3 ?

3 3

r90 16 1T

3

131

14y1

3

2

200

127/.

2

16

16% 18Y. 2O1t$

20 2111

133i,6

23

24!.

13$/i6

1913i,e

2lllt6 26\ t\5

2651'a

6 7

s

ro

91/?

9'1

171

12rs/,r

26'/,0 2O5116

5

gv,

1215h6 15?/ro 103^5 15ir/,s 1011$

97/r6

2

7

61h

lOYa

12tlt

120

61/2

13r16

105/ro

1to

220

4

8j/re s'g/i6

210

..ch

h.bhr

B A.A,C

180

rb,

29eltt

288/re 30r^6

18

19

33'3/ro 35r/re

22r.

23v.

52

a€

45

41

4a 59 62

43

25

53

68

't6 117 101

08

112

71

134

55

8l

139

71

65

86

88

T7 91

112

zla

256

196 218

210 245

488 539

32()

zi2

314

3o9

318

&7

40r

it13

1006

460

$

172

m2

Figure 13-5. Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,

Inc.)

Pipe Support Selection and Design

Figure 820

ROD & NUT NOT

FURNISI]ED LENGTH TO SUIT CUSTOMER

TYPE-E

TYPE.t) r-r--

--

ROD SIZE

.

LOAO FLANGE NOT FUFNISHED

\\\ INDICATOF

00 10

20 30 40

7v,

7 7 7

AYa

7Ya

9Yt

ala

1 900

2.475 2.875 2 475

AYa

50 70 80 90

9

I

9

8

1Ot/r

I I

1oth 1O7/.

13Y. 13%

16v2

13%

161/,

120

13V.

16V.

130

13%

16V,

13U.

16Y2 16Y2

't6Vz

100 110

2

13% 13V. 5

25

%

h

16V,

3

3i3/,e 3r3^6

1

I

1.9m 8%

50

140 150 160 170 180 190 200 210 2.O

1.9m YB

16v2

l5Y.

22

17U

15Y. 15V.

22 22

17Y. 17Y.

157. t 5Y.

22 22

v,

3.50 3.50 3.50

5% 5%

I

5Va

1

1

I

65/,6

1

4.50 4.50 4.50

41.,a

2 2 2 2

S1/.

1Y. 1V.

2 2

4.5!o

8%

1V,

4.50

1V. 3

4.fi

8V. a%

1Y2

3

450

aV.

21h

1

4.50 4.50

8% 8th

2v.

2 2

5.563 5 563 5.563

Figure 1&5. Continued.

8Va

v,

214

12V2

2%

121h

2rt

121h

27/.

12V, 12V.

3th 3%

v,

1

335

336

Piping Stress Handbook

2Il2"8H

SERVICE: Recommended for light loads where vertiCal movement does not exceed 1% inches. APPROVALS: Compties with Federal Soecification WW-H-171D (Type a9) and Manufacturers Standardization Society SP-69 (Type 4B). INSTALLATION: Designed tor attachment to its supporting member by screwing a rod into the top cap of the hanger the full depth of the caD.

THO,

4'FN. TIiD

LIGHT DUTY SPRING HANGER Corbon Steel Spring Coil ond Coge The Light Duiy Spring Honger is used for the support of rniscelloneous lield run piping systems subiect to slight (up to l,/4") verticol displocement. lt is designed for incorporotion in rod hongers with o lood coupling provided for spring Iooding. lhe unit does not hove o lood scole ond trovel indicotor. Amount of spring looding con be opproximoied by reloting "8" dimension with spring deflecfron role.

Selection of correcl spring size is normolly done by opproximoie methods toking into occount weight o{ pipe, covering, contents ond mojor fittings. Ordering: Order by port number ond spring size nurnber,

DIMENSION5 IN INCHES Sl1in e

a

c

No. %

l)

D

E

Def

6/,

2

6'/.

l'/1

7)/.

t1

81"

6'/^

I0'/s

Lood

1,/, 2

V/"

Spr in o

Defle

oio

w n

sighr Lbs.

per 100

52

26

160

266

66 87 152

00

200

238 287 350 680

600

210

982

5 3',/,

6t/,

6

ledion

,4

Figure 1$6. Spring supports. (Courtesy Support Technology Products, Inc. and Piping Technology Products,

Inc.)

Pipe Support Selection and Design

I

f

L. T +

T

----'l

.[w7-.,

-es.;-

Figure 13-7. Typical arrangements oi constant supports. (Courtesy of Elcen Metal Products Company.)

Piping Stress Handbook Table 13-2 Load Table for Constant Spring Supports (lb for total fuavel in in.) hango. 3lzo

load in oounda for lolal truvel in lnche3

Pipe Support Selection and Design Table 13-3 Load Table for Constant Spring Supports (lb tor total travel in in.) losds in Dound3 lor lotal trevel in inchas

340

Piping Stress Handbook Table 13-4 Load Table for Constant Spring Supports (lb for total travel in in.) load In pound! lor total lraval In Inchca

mn0aa

trzc

65

a

aV.

19225

t

201m

17049 17866

22064

19615

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7V2

i

1l431

10986

53AO

13982

16080

!4618

2816 13400

I1486

17654

16049

14711

12370 13580

10253 10720

12610

1

I

I

aY.

9613 10050 r 1094

9047 9459 10385

8544 8SKl3

th

10

10v,

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8094 8463

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73?3

6990

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7657

7308

6991

a8c7 9613

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1926

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11635

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13733

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32835 34764

29186 30s04

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21889

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17512 18542

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14593

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3825 14639

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23880 25286

14634 15450 16418

11054 11707 12360

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16311

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19400

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17244

16336

15520

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172.1

18380

15580

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14,25

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1a955 15788

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48888

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40000

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2s883

24444

23157

32858

30666

24750

270f0

25555

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21903

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23816

r9129 20@0 21390 22741

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41819

3a332

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52400

44728 47€!7

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29111

24210 25494 27574

55400

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34625

32589

30777

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27t@

26079

25179

24085

44921 47?32

41715

38032

385m

34354

32444

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38375

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99236

2796

26894

25562

fi771

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30736 32315

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31426 35045

29997

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319S

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5749 10416 44135

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550m

51165 54990

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20500

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61331

56617

52572

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43295

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67164 73500

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57573

53732

5G75

47413

44777

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6784 8

58799

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51884

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4t665

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61344 63888

58156 60525

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53909

51666

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71666 74444

57500 59750 620@ 64500

61423

58G31

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67000 6S500

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m96 ws1

720m

64566

87500

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75716 78930

70665 73665

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6q)53

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71a75

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82665 85998

875&

77500 80625 8i]750 86875

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6235s 66@2 67649 70296

78826 81767 84708

87500

110

1$m

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107

11939

13244 13940

19573

i5819 600m

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s

I

0756 103(n

25a5 m972

584m

9.

921

!t611 10179 10747

a5m0

1

8o1l

10042 11235

11149

52500

5111

/u,

9043

3299

57500

tt

aaTa

231f7

s8

91

9808

t2

13907 14680

87

90

1769

'fl 1{

v21

70524

38378

[email protected]

cx30

Stgla

71351

62604 65430 68250

6ta1,l

743t 1 77265

71c62

dJ122

80946

739€

70831

84469

80628

v125

73914

875m

83992

80342

a7446

s3646

770m m183

875m

86050

830

8@@

73156 75787

83610 47221

79210

75250

71661

43176 65444 68402

82629

785m

74756

67500

86050

81750

n851

87500

850@ 87500

66185

64708

Pipe Support Selection and

Design

Table 13-5 Load Table for Constant Spting Supports (lb for total travel in in.) load In pound3 ior

nangJ aLa no.

l2V.

13v2

14

14Ya

't5

5696

5492

5303

5126

4961

4a06

42

5544

5359

518 7

5025

1SV2

16

64

6152

5915

65

6432

6184

66

7062

67$

6538

6304

6087

5884

5694

5617

67

7@0

7394

7120

6966

6629

6408

620 r

m0a

6a

8320

sm

7m3

7428

7172

6933

6709

65@

8843

8503

8188

7895

7623

7365)

7131

6909

9005

8671

8361

8073

7804

7552

7317

a m

57

lotll tievol 15Y2

In

inchc

17

llth

t8

1AV2

le

19h

m

71

9888

9507

9155

8428

8523

8239

7973

n25

72

10507

10103

9724

cts

9057

8755

4473

82G

73

11126

10697

10301

9932

9590

9270

8971

8692

74

11714

1

t292

r0873

10484

10123

9786

9470

9175

12416

1r

ct8

11496

11084

10703

10346

10012

9700

76

1$88

12544

12118

11584

11282

10906

10554

10225

77

!3760

13230

12740

122€4

11861

1

1466

11096

10750

78

14507

1399

13432

12951

12505

12088

11698

|l34

79

15254

r4666

t

4123

13618

13149

12710

12300

11917

&)

16000

153€4

14814

fi2€4

13792

12902

125.O

81

16m0

r6153

15555

14S8

14482

14m0

1354 7

13125

8it

't7€o0

'16922

16295

15712

15171

1465s

14r92

13750

83

18400

17602

17(B6

16427

15861

15332

14lX)7

14375

19680

18522

142.1

1756S

16364

16398

15859

r5375

20960

20153

19406

1A712

18068

17465

16902

16375

86

22160

213o7

m517

19783

19102

18465

17869

173r3

87

23:t60

?2461

21628

20855

20't36

19465

18A37

18250

88

24560

23614

2739

21C26

21171

20465

't9805

19188

89

25384

2757

219e8

21288

20625

2€3o7

24413 2725a

23569

m

26400 29440

26283

25377

24331

23740

23000

g1

3?210

31@0

29&50

a7a2

27791

26864

25998

25188

g2

35280

as22

32665

31496

301r I

29397

28449

27563

3aan0

37g)E

35944

34639

33446

32330

31247

3)313

12!00 40788

39257

37853

$549

3530

34t90

33125 321 19

31175

3@45

29442

2fl647

27494

27179

26500

442@

42494

40g24

39460

381m

36830

35642

34531

33482

32498

31570

30691

29863

29078

28332

27625

4amo

44ZiO

42590

41067

39652

38330

370€3

35938

34445

32856

31941

31080

30262

29486

?€750

47800

,r5960

44257

42873

41204

39829

39545

37344

35209

43822 35r 45

3r'141

3l}191

32295

31448

30640

?3875

4SOO

47690

45023

4428[

42755

41329

4m00

38750

37572

36468

35/27

34441

33511

32631

31794

310m

99

51600

49613

47n5

46066

44479

429S6

41609

40313

39087

37939

36855

3584t0

3/,862

3:}946

33076

32250

tm

$6m

51536

49627

47451

46203

44662

43221

41A75

406m

39r09

38284

37219

36214

35a62

34358

335m

u

s 91

95

98

tol

55800

53459

51479

49637

47927

46329

44434

43434

42117

40880

39712

34607

37565

36578

35640

34750

102

57600

56382

5330

5142 4S51

47995

4&47

450m

4S32

42350

41141

39996

38916

37894

36922

38000

1(x,

802m

5788e

55738

53744

51892

50r 62

44544

47031

456(P

44262

429S

41801

40673

39604

385€8

37625

104

62800

60382

58

54r 34

52324

50640

49063

47571

$174

44455

43607

42429

41315

&255

39250

105

65400

62882

m552

58346

56375

54495

5e737

51094

49541

4€085

46712

45412

44196

€025

11921

40875

106

68000

65382

62960

60707

58616

56661

54834

53125

51510

5mm

48569

47214

45943

44736

435€8

42500

107

700m

6€228

657m

63350

5116€

59127

572m

55438

53752

52r 73

506a3

49273

47942

46683

454 85

44350

t0a

7"3920

68441

65992

63719

61594

59607

57750

55994

54350

52797

51328

49942

€6i]0

47343

a6200

109

70960

7to14 74m0

71255

6530

u127

62059

60125

58297

5459

53439

5200

50€30

49331

48rm

1t0

80000

76920

74070

68706 71120

64960

66€60

64510

62500

60600

57140

55550

54050

52630

51280

5m00

r45

58820

341

342

Piping Stress Handbook

Figure 550

VIBRATION COIIIROl AND SWAY BRACT

The FIG 550 vibrotion conlrol ond swoy broce presents o neol, conpoci oppeqronce

Sire Ronge: For pipe sizes 2 through 24 inch. Service: Recommended for conttolling vibration; absorbing shock loadings; guidittg or restraining the movement of pipe resulting from thermal expansioni bracing a pipe line against sway. Instollotion: Shipped ready foi installation

Adiustment The sway brace should be in the neutral position when the system is Hot and operating, a: which time the tension test collar should be hani tight, If it is not, the sway brace should be adjusted to the neutral position by use of the loai coupling. The screws in the tension test colla: need not be loosened, since they serve o[ly to secure it to the load coupling. Feotures:

rVibration is opposed with an ilstantaneous counter foice bringing the pipe back to normal position. rA single energr-absorbing pre-loaded spring provides two way action.

Cut.owoy section shows simplicity

of exclusive .single spring

design

o

One spring saves space and simplifies design.

o

Spting has 3-inch travel in either direction.

r Accurate neutral adjustment assured.

oEnclosed spring excludes ditt and gives a clear. compact aPpeaaance.

Speci{icotions: Fulfills the requirements of the ASi Code for Pressure Piping as to fabrication details and materials.

Deflection of single spring occurs when thrust exceeds pre.compress ion

Tension couses dellection of sin. glo spring in opposite direction

Figure 13-8, Vibration control and sway braces. (Courtesy Support Technology and Piping Technology

Produc:-.

Inc.) Fi

Pipe Support Selection and Design

lmportont: Rod lengths should be cut and final tension adjustments made for the hot or operating position of the pipe. If, with the pipe in its hot position, the

Siue Selection: The vibration control and sway btace

gives full deflection forces from 200 to 1800

pounds

initial precomptessed spring forces from 50 to 450 pounds to dampen vibrations, oppose pipe sway and has

tension test collar can not be turned by hand or if it tums very freely, loosen the jam nut adjacent to the rod coupling and rotate the coupling until the coliar

and absorb shock forces.

The exact amount of energy needed to control piping should be in proportion to the 6ass, amplitude of movement, and nature of disturbing forces acting on the pipe. When it is possible to calculate the exact restraining force required, the size of the vibration control and sway brace capable of providing this force

can just be turned by hand. Retighten the jam nut.

When correct tension adjustments are completed, the btace exerts no force on the pipe in its operating

position. Undei shut-down conditions, the brace allows the pipe to assume its cold position. It exerts a nominal cold strain force equal to the pre.load force plus the amount of travel from the hot to cold position, times the spring scale of the particular size of the vjbratron control €nd sway brace.

should be selected.

To simplify the selection of size, engineets have designed the vibration control and sway brace in three sizes that are readily related to nominal pipe size. For pipe sizes 3%-inch and smaller, the small size is recommended; for 4 to 8-ioch, the medium size; and for 10-inch and larger, the large srze. Instollotion: The vibration control and sway brace is shipped ready for installation. The rod coupling rotates with slight resistance and the tension test collar can be rotated by hand while holding the rod coupling statiorla!y,

vibrqtion control crnd sway brrrce END

El'lD

PLATE

PLATE

SPR]NG PLATE

rN SIO

343

-.

SPRING PLATE

,-ROD

COUPLTNG

STD. JAIV NUTT

JAM NIJT,'

E E

loads

.

L

FtG 550

weights

o

FtG 555

dimensions (inches)

FtG.550 preload

1

2 3

21o

spring

weight

to

(approx) each. lb

4to I

50 150

10 to 16 18 to 24

450 900

31/,

5 6

1350

1800

ID

200 600 1800 3600 5400 7200

rod size,

trkeoul

3ize,

E '11/z

22 1

36

plpe

1

11/a

2 2 2

79 95

212

41/z

135/o 14TB

41,'

1 1

3/a

1

11/2

'|

1Yz

11/2

'lrz

Y2

11/z

6tb

15/B

177/s 185/s

173/4

15/s

22

17

21/a

141.h

21/a

2011

2lt

13/B

23r3/ro

6Ys

1 ,1

87/a

1

13

63/q

lYz

111i2

63/a

112 112

13 15

63/a

11/a

95/a 11/a

1

r3i, o

FrG. 555 spfing ror pipe size

l 2 3

4 5

6

2lo 4lo

tb 31/2

8 16

10 to 18 to 24

50

150 450 900 1350 1800

A As specified by customer.

Figure 13-8. Continued.

pipe size,

weight (3ppror,

rod M,

each, lb

E

200 600

23 26

11/?

1

1

2

1

1800

38

1

2

1

3600 5400 7200

1v2

2 2vz

'| Y2

a2

11/2

6s/s

98

1t'2

21/2

1\',2

65/s

3/a

11/a

41i2 3/a

1Y2

65/e

20

24Va

77/a

I

2O3/a

25

77/a

1

241/s

283/B

7?/3

1

2451.o 6s/rs 2513/, o 6'g/,s 2713 rc 6'g/,s

31Ya 33Ls

295/B

g'/a 91/a

11,, 11.,

9Ya

1)ta

93i r6 91si, e

135/,s 12

13lz 15Yz

11/a

1l/a

344

Piping Stress Handbook

FIG 550 A **il:"1iu *ll *

FIG 555 A dimension

i! 2It 0 in

recornmended when W dimension is

or les!

2

lt

0

in, o! lo38,

-

FIG 555

FIG 55OB recommended when W dim€nson is 2

Il I in.

B

recomm€nded when W dimeBion is 2 lt

or rnot€

I in.

or more

-r.

_

PIPE

olAp

-

tl!alqace

corior oI plpa noDLnol plpa

drs

rwoy broce

!l:e

2

2% 3

I

6% 2

I

l4 l8 20 24

7 8,,16

sX" r0%

l0 t2

s% s% sr\e 8Xe

3% 4 5 6

lo olltlld6 stud ol ptD6 cloEp

3

rr%

t2tlft r3,\"

I4tXc rs% r7%

Dimenaions lor ssgemblies lor lsrger pip€ sizes dvdilobl€ on opplicalion. psrogroph "How lo sir6 qsBemblios" obove.

S€€

Figu.e 13-8, Continued.

t

-a-

\

Pipe Support Selection and

Design

Molded rigid polyurethane foam supports may also be to support other types of piping systems where the medium being transferred in the pipe is to be maintained at a high temperature and protected from a cold environment. This type of application is typical of a pipeline pumping oil at a design temperature of 180'F through a cold environment at approximately -50"F. The insulating properties of the polyurethane foam are necessary to keep oil in a low viscous state for pumping over long distances. The supports for this type of application are designed in the same manner as those for cryogenic appli-

ing system. The thickness of the polyurethane support should match that of the line pipe. . Support load, o Environmental conditions-The exposed cradle may require special coatings or galvanizing. From these design conditions, a suitable foam density is selected for the supports. Thbles 13-6 through 13-11 include some typical properties of molded rigid polyurethane foam used to fabricate supports. Examining these tables, it is apparent that as the foam density at ambient temperature is increased, both the thermal conductivity factor and the compressive strength also increase. At cryogenic temperatures, however, higher density rigid polyurethane foam has approximately the same thermal conductivity factor as lower density foam. This results from the fluorocarbon within the foam cells becorning a liquid at the cryogenic temperature, thus creating a partial vacuum. Thus the normal support design procedure involves first determining the required K factor to insulate the piping based upon the thickness of the matching pipe insulation. Secondly, the foam density needed to produce the required K factor is selected. Lastly, the length of the support needed to

used

cations.

lnsulated Anchors For special designs where it is necessary to anchor the piping system, it is also necessary to avoid the metal-tometal contact for the conditions already stated. Anchors are fabricated for this application by foaming between an actual piece ofthe line pipe and an outerjacket. See Figure 13- 10.

support the pipe is determined using the selected density.

P0WERFoAM/P0WEBSLIDE Beference Guide

POLYUBETNANE FOAM

sEcTloN "B.s'

AOLTEO PLATE TO STR1JCTUBE

l-g-

*..o.o

"*r.

ro

"t"r"tu".

Al ligure numbers ir lhis section

are ava lable in any POWEFFOAM thickness, sin91e, double

or lriple layefing lo conform to the line

Figure 13-9. POWERFOAM/POWERSLIDE"

345

reference guides. (Courtesy of Power Piping Company.)

346

Piping Stress Handbook

POWERF0AM lnsulated Pipe Anchor Stainless, copper and alumanum pipe can be made

into PowERFoAM anchors.

ULTRA HIGH DENSITY POWERFOAM STEEL PIPE EXACT DUPLICATE OF LINE PIPE TO BE WELDEO TO LINE PIPE

ON/CONTRACTION

Figure 13-10. POWERFOAM" insulated pipe anchor. (Courtesy of Power Piping Company.)

Pipe Support Selection and Design

347

Table 13-6 POWERFOAM- Thermal Properties

oella "T"/2 ll. lb./cu.ll. 10 10 14 14

160.0

20 20

320.0 320.0

Cou

Hol Face

Kq./cu. m,

+43 5 +42.9 +41.6 +42.4 +44.3 138.7

160.0 224.O 224.O

esy of Power

cold

Hol Face

Cold Face 1S3 7

I

162 193.4 159 6 193.4 157 6

l.

''K" Faclor Blu. ln. Hr. Fl.2

264

88.7

0 0213

o 141

0.0219 0.0241 o.0244 0.0297

0.r52 0167 0169

110 3 109 2 106

-3I6.7

103.2

-261 2

760

232

792

-316.1

104 6

-58 4

109

986 860

-746

111 7

102.2

357

-59 4

101 7

-255.3 ,316.1 251 7

24.9 25.2

750

31 8

121 7 108 6

1

Conduclivity

Blu/Hr.

Face

-15 1 -60 0 -75 9

I

Apparent Thermal

Power Input amount ol Energy Pow€r Loss To Malntain

TemDeralure in Fahrenheil

Temperalurein Cenligraale

Powerloam Den3ilier

"F

0.206 o.223

0 0321

PipW ConpanJ.

Table 13-7 POWERFOAM* Physical Properties Engineering Oata Slrenglh Compressive

At Yield with a Safety Faclor

Ske.glh

Srrenglh

Or 5:1

Densilies Kq.

t0

160 0 160.0

10

224.0 224.O

320.0

20 20

320 0

-256 -318 -256 -318 -256

160 194.5 160

60

194.5

,318

194 5

6.0 6.0 6.0

r60

60 60

152 152 152 152

152 152

5900 4500 9200 9200 r 4600 18000

2625

I191

2550

3575

1157 1667

2800

1270

4204 3900

1905 1315

PSI

PSI

PSI

PSI

2676 2441 4173 4173 6522 8165

534 408 833 833 1322

38 29 59 59 93

1630

115

234 231 333

17

2.8 1.9

23

3.1

3.2

254 380 354

PSI

27

32

25

4.8

19500 22104 27200 27004 40000 34900

1371 1483 1912

1898

2812 2453

106.8 81.6 166.6 166.6 264.4 326.0

5.74 11.71 11.71 1€.59

22.92

ar Yrerd

Courtesy of Power Piping Conpan!.

"o*',l'-?;ly ST?31'.':Tf;",:"':$f3$'j1".'#ij::l'.'h Table 13-8 POWERFOAM" Temperature Range

lrsrimum (Hol)

Temperalure

Temperelure

Den3illes lb./cu.

Kg./cu. m.

10 14

160 0 224 0 320 0

20

Minlmum (cryogenic) seflice

Servace

'c +275

135

425

+275

r35

-425

-245 ,254

,275

135

-425

-254

Data is all based on tests performed on POWERFOAIiI made with our tormula and molding techniques. Independent testing laboratory corroborating iesl data available upon request.

Courtesy of Power Piping Compant

SUPPORT CONTACT 30" each side of vertical center line.

60"

-

SUSTAINABLE LOAD FORMULA:

/n'D'L I lc\ Sustainaute Loao \ 6 l\ t = C = Compressive strength with safety lactor O = Ouier diameter in inches L = Length in inches

Piping Stress Handbook Table 13-9 Engineering Data

IEIGHI

OF PIPE, WATEi {PEe Footl

r'rl|sutaTtol{ 1J2

22 2.052

i5 192.01

I 5

402.n

'u

f .375 t "r^"",1 PIPE I

t7912 39.59 23

1323.,15

'.62

257.&A 751"O

r3233 9

i

"Are

nol regular p pe

sz6

*"SUSTAINABLE

LOADS OF INSULATED PIPE SUPPORTS

2 fb./cu. tl. 32 Kg./cu. n. COMPaESSIVE STRENGTH = 5.8 pst (.40774 Ks./Cm.t W|TH 5:1 SAFETY FACTOR

-

'rrBased on ioam .c,mpresston (with

a S:1 salery

Courtes! of Power Pipin| Company.

tacroi,

tengrh ot slpports and pipe sizes.

FOAM BY AMBIENT TEMP

-it

Pipe Support Selection and Design Table 13-10 Engineering Data

*-SUSTAINABLE LOADS OF INSULATED PIPE SUPPORTS 4 lb./cu. tt. - & Kg./cu. d. 13 PSI ( 9139 KS /Cm, WITH 5:1 SAFETY FACTOR

COMPAESSIVE STRENGTH =

*rBased on loam compression (with

a

AMBIENT TEMP,

5l

saietv laclor) length ol supporb and pipe srzes

96 Kg./cu. m' 6 lb./cu. fi. COMPBESSIVE STRENGTH ='I6 PSI (1.1248 KS./CM.4 WITH 5:1 SAFETY FACTOB (NON-MOLDEO FOAM AY OTHEFS AMBIENT TEMP

-

"'Based

on road compression (wnh a 5:1 salely lacior). length oi supports and pipe s[es

Courtesy of Power Piping Conpany.

Piping Stress Handbook Table 13-1 1 Engineering Data

-*SUSTAINABLE LOADS OF INSULATED PIPE SUPPORTS t tbJcu. fi. - 128 Kg./cu. m. COiIPRESSIVE STRENGIII = ZI PSt (1.5466 Kg./Cm.,) WITHi:1 SAFETY FACTOR lt{ON-MoLDEo

FoAM ay

OTHERS AMBIEXT TEMP.

ot supporrs and pipe si:es.

fi'8as.d

on foam densirios (wnh a

""Comprossive strength ol

5r

salety lacto4, iength ot supporls and pip€ sizos.

POWERFOAM onty.

Counesy of Power Piping Conpan!.

J

t4 Fundamentals of ExPansion Joints

Thermal movements in pipelines and ducting result from variations in temperature of the flowing medium or from variations in ambient temperature where piping is exposed to weather. If not compensated for in system design, these movements may cause high stresses, possibly resulting in failure of the piping or connected equipment. Compensation for thermal movement in a piping system . can be achieved by three basic methods:

Nomenclature and SYmbols Standard nomenclature used in discussing expansion joints and the symbols used in applications drawings are presented in Figure 14-2.

Types of Expansion Joints

1. Designing a flexible piping system that utilizes

2. 3.

-

changes of direction to absorb movement. Using pipe loops or bends to absorb the movement. Using expansion devices, such as expansion joints, swivel joints, ball joints, ard flexible hose.

There are two general categories of expansion jointsthe slip type and packless (or bellows) type. The packless, corrugated metal expansion joint is most frequently used in modern piping applications. It does not require maintenance, and its hherent flexibility to absorb thermal movements in several planes permits greater freedom in piping design. The slip joint, a pair of telescoping sleeves made pressure tight by a packing gland, can absorb a greater amount of axial movement than a comparable bellowstype joint. However, it requires periodic maintenance and is restricted to axial movement only.

Types of Joint Movements

The type of expansion joint used depends on the qpe movement to which it will be subiected.

of

Single Expansion Joint This is the simplest type of expansion joint . As its name

implies, it is constructed with one bellows and is used mostly to absorb axial movements. A single joint can also be used to absorb angular ald lateral movements, as well as a combination of these three basic movements. Figure 14-3 typifies good practice in the use of a single expansion joint to absorb axial movement. Note that the expansion joint is placed between two main anchors (MA) and that it is located near one of the anchors. Q'{otice also that the first alignment guide (GD is placed close to the joint. The second guide (G2) is close to the frst, and intermediate alignment guides (G) are provided along the balance of the line.

Expansion joints installed in piping systems are subject to thee types of movement-axial movement, angular rotation, and lateral deflection. These movements can occur individually or in combinations. The four examples in Figure l4-1 show how single and universal expansion ioints absorb these movements.

Double Expansion Joint This consists of two single joints joined by a common connector that is anchored to a rigid part of the structure by means of an anchor support base. Double expansion

351

Piping Stress Handbook

I r*F AESORPTION

OF AXTAL

I

MOVEMEIiT

(SINGLE JOTNT)

ABSORPTION

OF ANGULAR ROTATION (SINGLE.'OINT)

--I -t-' 1+

-

-li rl

L EGEND

- X: +X: 9: Y:

ABSORPTION OF LATERAL DEFLECTION AND AXIAL MOVEMENT (UNIVERSAL.JOINT)

COMPRESSION

EXTENSION ANGLE OF ROTATTON L

ATERAL DEFLEcTIoN

Figure 14-1. Expansion joint movements. (Courtesy of Badger Expansion Joint Company.) joints are supplied with or without an anchor support base depending on the customer's preference. See Figure 14-4. A double joint is used when the axial movement to be absorbed is too large to be handled by a single joint. The intermediate anchor on the center nipple divides this movement so that each bellows of the double joint is usually located in the center of a pipe run: so both ends are subjected to the same movements and have the same num-

ber of corrusations.

Universal Expansion Joint This consists of two bellows joined by a common connector which is not anchored to the structure. This per-

mits the universal expansion joint to absorb any combinaand angular-where these movements are too sreat to be handled by a single joint. Universal joints usually have tie rods with stops that distribute the movement between the bellows and siabilize the corrunon connector. The joints find increasing use in steam and hot-water distribution systems because there

tion of three basic movements-axial, lateral.

are impressive cost savings for the large amounts of movement they can absorb with a minimum of guiding and anchoring.

Figure 14-5 illustrates a universal expansion joint used to absorb lateral deflection in a single plan Z bend. Both anchors are intermediate anchors because the pressure loading is absorbed by the tie rods. Only directional guid-

Fundamentals of ExDansion

T

MAIN ANcHoR

Xf--f

T

Ft DMA l2\-------------1

mmr

F__x--? IA

.

-ffi-

Joints

353

sTNGLE E*PANSToN JorNT

DTREcnoNAL

DOUBLE EXPANSION JOINT

MA|N ANcHoR

WITH INTERI\4EDIATE ANCHOR

INTERMEDIATE ANCHOR PRESSURE BALANCEO

T

EXPANSION JOINT

I

t

\DIRECTIONAL INTERMEDIATE

m7f DIA

'ANcHoR wtrH

GUTDE

SINGLE EXPANSION JOINT

l----

PrPE ALTGNMENT GUTDE

WITH TIE RODS

rr---r l

'" lfi:11 tEt mmm sroE vrEw

UNIVERSAL EXPANSION JOINT

END VIEW

WITH OVERALL TIE RODS

PLANAR PIPE ALIGNMENT GUIOE

ra*/L 't

t

c-------E-------

)

sPRrNc suPPoRr

UNIV€RSAL EXPANSION IOINT WITH SHORT TIE RODS

+

P,PE REDU.ER

GUSSET

UNIVERSAL PRESSURE EALANCED EXPANSION JOINT

l--'-4

-Ff

HTNGED EXPANSToN

rorNr

GIIvIBAL EXPANSION JOINT

Figure 1'l-2. Expansion loint symbols. (Courtosy ol Badger Expansion Joint Company.)

Piping Stress Handbook

di

'1il-

l|l Figure 14-3. Single expansion joint. (Courtesy of Badger Expansion Joint Company.)

Figure 14-4. Double expansion joint. (Courtesy ot Badger Expansion Joint Company.)

fI

-LATERAL

MOVEMENT HOT

Figure 14-5. Universal expansion joint. (Courtesy of Badger Expansion Joint Company.) ing, if any, is required because the compressive load on the pipe consiss onJy of the force necessary to deflect the expansion joint.

Where dimensionally feasible, the expansion joint

should be designed to fill the entire offset les so th;t its expansion is absorbed within the tie rods as ixial movement.

Pressure Balanced Expansion Joint This is a combination of single joints that oppose each other in the same way the internal pressure loads oppose the other. This prevents excessive loading due to presiure thrust from being transmitted to pipe anchors, turbines, or

Figure 14-6. Pressure balance expansion joint. (Courtesy of Badger Expansion Joint Company.) process equipment. The compressive forces of the two bellows are additive, but these are usually negligible in comparison with the pressure forces. This type ofjoint is used where a pipeline changes direction. It absorbs axial or a combination of axial and lateral movements. _ Figure 14-6 shows a tlpical application of a pressurebalanced expansion joint for combined axial movement and lateral deflection. The anchor on the piping run and that on the turbine are intermediate anchors, and onlv directional guiding is required. By proper design. the guide directly above the turbine can be made to absorb the axial movement forces of the expansion joint without transmitting these to the turbine. The only force imposed on the turbine is that which is required to deflect the expansion ioint laterallv.

Fundamentals of Expansion Joints Hor

Hinged Expansion Joint This is a single expansionjoint designed to permit angular rotation in one plane only by use of a pair of pins through hinge plates attached to the expansion joint ends. Hinged jo-ints are used in sets of two or three to absorb pipe movement in one or more directions in a single plane piping system. Each individual joint in the system is restricted to pure angular rotation by its hinges. However, each pair of hinged joints, separated by a section of piping, will act together to absorb lateral deflection in much the same manner as a universal expansionjoint in a singleplane - application. Expaniion joint hinges are designed to transmit the fu1l pressure thrust of the expansion joint and, in addition' may be designed to support the weight of piping and

----------.1

rA(:

HEJ:

Hings Expansion Joint

PG:

Planar Guide

equipment, and absorb thermal loads, wind loads, and other external forces. A hinged system permits large movements to be absorbed with the minimal anchor forces.

Figure 14-7 illustrates a two-hinge expansion joint system. In this application the expansion joints absorb only the differential vertical growth between the vessel and pipe riser. Any horizontal movement due to piping elpqiion, vibration, wind loads, etc. will be absorbed by bending of the vertical pipe leg. A planar guide may be installed near the top of the vessel to protect the hinged joints from wind loads at right angles to the plane of the piping.

Figure 14-7. Hinged expansion joint. (Courtesy Badger Expansion Joint ComPanY.)

Gimbal Expansion Joint This is a single expaqsion joint designed to permit angular rotation in any plane by the use of two pairs of hinges affixed to a cornmon floating gimbal ring' Unlike the hinged joint which can absorb angular rotation in a single plane ofun the gimbal joint can absorb angular rotation in any plane. The ability of the gimbal expansion joint to atsorb angular rotation in any plane is most often applied by

using two gimbal joints which act together to absorb movement. Gimbals, like hinges, are designed to transmit the pressure thrust and are used in pairs, or in conjunction with a hinged joint. Figure 14-8 illustrates a gimbal-joint application. Because pressure loading is absorbed by the gimbal structure, only intermediate anchors are required. Planar zuides are provided to restrict the movement of each piping leg. Ai in a hinged-joint installation, the location of pipe suppo.t. is simplified by the load-carrying ability of the simbal.

Figure 14-8. Gimbal expansion joint. (Courtesy Badger Expansion Joint Company.)

of

Piping Stress Handbook

Anchors, Guides and Supports Pipe Anchors The.function of pipe anchors is to divide a pipeline into individual expanding sections. Since thermaj movement cannot be restrained, it is the function of pipe anchors to limit and control the movement that expansion joints, lo_ cated in the line between the anchors, must abiorb. In some applications, major pieces of connected equip_

ment such as turbines, pumps, compressors. and reaciors, lI desrgned to wlthstand the forces acting upon them. can

function as anchors. Additional pipe ichors are com_ monly located at valves, at changeJ in pipe direction, at blind ends of pipe and, at major branchionnections. ix_ pansion devices must be installed in each of the pipe sec_ tions to provide flexibility.

Pipe Guides A pipe guide is a sleeve or frame fastened to a risid structure that permits the pipeline to move onJy along-its 9wn lxls: The guide is needed to prevent the pipeline from buckling due to the pressure thiust or ftelbiiity of

the expansion joint-or both. planar pipe guide is a pipe guide modified to permit .. A limited movement in one direction other than loneitudi_

nal. It is used in

"L" or "2"

Cold Springing of Expansion Joints "Cold springing" means prestraining the elements of a piping system at the time of installation so that thermal stresses occun'ing when the piping is hot are appreciably reduced. The purposes of cold-springing expaniion joints may be considerably different, although the mechanics are basically the same. Cold springing is generally applied to expansionjoints absorbing only lateral deflection or angular rotation. Cold springing should not be confused with ..orecompressing" or "presetting" an expansion joint. Tire laner terms apply to adjusting an expansion joint in an axial direction to allow for specified amounts of axial compression or extension without physical interference between the corrugations or overextending the corrugations, yhich mighl damage them. If deshed, cold springing can be done at the factory before shipment to facilitate installation. The endurance or cyclic life of an expansion joint is dependent on the maximum mnge of stress to which the bellows is subjected, the numerical maximum stress value being a far less significant factor. Cold springing an expansion joint to reduce the maximum numerical stress would not result in any great improvement in cyclic life. There are, however, a number of other reasons for coldspringing exparsion joints as foliows:

piping configurations (see

figurg J+j) where rhe expansion idints ar6 subiected to lateral deflection or angular rotatton. Pipe guides should be located and spaced carefullv in a piping system. (See Figure l4-9.) A pipe support carries the dead weight ofthe insulation, . piping. and its contents. Pipe supports are not pipe guides. supports do not lim.it the free movement of piping or con_ tribute to guiding it in any way. The recommendations for pipe anchors and guides given in this chapter represent the mlrxmum requrements tor controlling pipelines contain_ ing expansiotr joints. However, standard piping practice usually requires additional pipe supports b;twe;n guides.

Forces and Moments To calculate the loads on piping, supports, and equipment, the forces and moments to move an expansion joint must be known. The expansion joint manufacturer will provide axial, lateral, and angular spring rates.

Force Reduction

Il

a wide range of applications, the force required to deflect an expansion joint is significant. Where the expansion joint is used to relieve the loading on sensitive equip-

ment, where anchor structures are limited to extremely small loads, and in other similar cases, cold-springing the expansion joint at installation can cut the maximum deflection force in half. In some cases, a 100% cold spring will reduce deflection forces to a minimum at extremely high operating temperatures.

Stability Figure l4-1 shows the movements ofbellows due to angular rotation and/or lateral deflection. In both cases, one side of the bellows is extended and the other compressed. so the bellows may become distorted when subjected to

Fundamentals of ExPansion Joints MAXll,4UM RECOMMENDED SPACING FOR TNTERMEDIATE PIPE GUIDES AXIAL MOVEMENT ONLY (VALUES BASED ON STANDARD WEIGHT CAREON STEEL PIPE

400

357

)

400

350

350

300

300 250

200

200 r80

t80

r60

t60

r40

r40 r20

6

roo

=a^

feo r..r 70

e lao

(9 -k--

6

>40 CE

F

z-30

toL

400

250 MAXIMUM PRESSURE-PSIG NOTE: I.ADOIIIONAL PIPE SUPPORTS ARE USUAILY iEOUIREO A€TW€EI'I GIIIDES II{ ACCORDANCE WITH STANOARO PRACTIC€. 2 ARROWS REF€R TO EXAMPLE GIVE^I IN TEXI

Figure 14-9. Spacing for guides with expansion joint. (courtesy of Badger Expansion Joint company.) internal pressure. Reducing either the internal pressure or the displacement of the corrugations will improve the stability of the expansion joint. By cold springing the expansion joint 50% at installation, the maximum displacement per corrugation is cut in half and the exparsion joint is far more stable. For this reason, where expansion joints are subjected to large lateral deflections, or where operating pressures are high, it is good practice to install the joint in a 50% cold-sprung condition.

Component Clearances Where an expansion joint is furnished with internal sleeves, external covers, or tie devices spanning the be1-

lows, these components must have enough clearance to accornrnodate the lateral deflection or angular rotation of the joint. The required clearance can be reduced to a minimum if the joint is cold sprung 50%. By this means, hter-

358

Piping Stress Handbook

nal sleeves of maximum diameter can be furnished, the overall diameter of an expansion joint incorporating external covers or tie devices minimized, and the desien of external structures simplffi ed.

Use of Internal Sleeves in Expansion

Joints

. I?"r:lJ

sleeves should be specified in expansion joints

ln me Iollowlnq cases:

l.

transmitted through the flange bolts to the mating ange and then to the connecting pipe.

In some instances cold springing is recommended to keep tie rods closer to the bellows. thereby minimizing moments. When ordering, advise if joints are to be insul lated. If so, speci$ the insulation thickness, because this will affect the hardware desien. . Consideration must also be-given to the crushing of piping. Attachments must be designed to distribute -the l-oid as much as possible.

to

When smooth flow and/or minimum friction losses are desired.

2. Where flow velocities are hish. 3. Where there is a danger of pitting or erosion. 4. In high-temperature applications. 5. When copper bellows are used and the application

is

for high-pressure drip, super-heated steam, hot water^or condensate, or where there is any possibility of flashins.

In some

increase the thickness

cases

it becomes necessary

of the pipe wall and/or

the lengths of the pipe nipples in orderlo distribute the load. Proper design of attachments is extremely important. parJicularly for critical applications with high piessures and temperatures. In such cases, hardware-cai cost as much as or mrcre than the expansion joints. For greater systgm rgliab_ilrry, it is important that emphasis be put on engineerirg design rather than price. Upon receipt of per_ unent apptlcatron data. sp€cial requirements can be deter_ mlneo,

Internal sleeves should not be used where tars or other

il;;;;;t-";;;;

Calculation of Forces and Loads highly viscous fluids are nowing. 'jplcking up," "coking," or "caking" and result in joint failure..If purging will prwent these conditions, sleeves The forces or loads to be calculated for tie rods, hinges should be used in conjunction with purging

comections.

Tie Rods, Hinges, and Similar Accessories In a piping system with expansion joints, it is often impractical to provide main anchors to absorb pressure thrusts. In these cases. tie rods. hinges, or gimbals may solve the problem as long as their attachments are designed to transmit the forces imposed by pressure in the expansion joint.

Method of Attachment

and attachments are: 1. Pressure thrust. 2. Force to extend or compress the expansion joint due to thermal growth within its tied lensth. .'- Weight of joint. 4. Unsupported weight of prptng and insulation between a pair of bellows. 5. Weight of fluid carried in the joint and unsupported piping. In large joints, consideration should be eiven to the weight o[ water used in hydro testing.

6. Wind loading effects, if

present.

In addition, effects of temperature and flow conditions must be accounted for.

Tie rods, hinges, and gimbals are attached in two basic ways:

1. By a structure whose function is to transmit the loads to the pipe or equipment. This concentrated loading may introduce high localized stresses into the prping in addition to the stresses due to internal pressufe.

2. By direct attachment to

flanges, which then carry the loads on the rods or hinges in addition to their normal flange load. In this method the total load is

Cycle Life Expectancy The cycle life expectancy of an expansion joint is affected by various factors in physical Construction. These are:

1. Operating

pressure.

2. Operating temperature. 3. Bellows material.

Fundamentals of Expansion

4. 5. 6. 7.

The movement per corrugation. The thickness of the bellows. The center-to-center distance of the corrugations. Depth and shape of the corrugation.

Any change in these factors will result in a change in the life of the expansion joht. The life expectancy is defined as the total number of complete cycles that can be expected from the expansion joint based on data tabulated from tests performed at room temperature under simulated operating conditions. A cycle is one complete movement from the full-open to the fi.rll-closed to the full-open position. It should be noted, however, that laboratory tests rarely if ever duplicate actual service conditions. Cycle life is only one factor in the design of an expansion joint and may be tle least important. Many life cycle tests have been conducted and expansion joints can be manufactured to meet any specification. However, experience has shown that few applications have a real need for high cycle-life design, which adds unnecessary costs to the expansion joint.

Joints

359

prevented by covering the bellows and using an antispatter compound when welding. External conditions should also be considered. External corrosion can result from fumes or sprays that may contact the bellows or in tunnel and manhole installations where water is allowed to collect. Direct application of insulation to the expansion-joint bellows and direct burial in the ground are not recommended. Many corrosion problems encountered in the field can be reduced, if not completely eliminated. Where corrosion problems are complex, consult a qualified corrosion engineer.

Erosion This is the mechanical wearing away of the metal surfaces in a joint. It usually results from the irnpact of solid particles entrained in the flowing medium. Where there is a possibility of severe erosion, such as in lines carrying abrasive media, heavy liners should be used to protect the bellows of the expansion joint.

Corrosion Corrosion can significantly reduce the service life of an expansion joint. The design and operating characteristics of expansion joints are such that they may be exposed to corrosive attack under conditions that do not affect piping and fittings of similar materials. Types of corrosion most frequendy experienced in expansion-joint applications are as follows:

1. Stress-corrosion (a cracking of the material as the

2. 3. 4. 5. 6.

result of a combination of stress and corrosive environment). Intergranular-corrosion, characterized by a preferential attack along the grain boundaries in metals. Pitting, which is a localized attack on metals. General corrosion or the gradual eating away of the metals in a system. Impingement and corrosion erosion, associated with the impact of a liquid or gas medium on the surface of the material under attack. Elevated temperature oxidation, most comrnonly encountered in hot ak and exhaust lines.

Calculating Thermal Expansion Metallic, packless expansion joints are normally designed to move in axial compression only, and unless otherwise specified, the minimum and installation temp€ratures are assumed to be 60'F. Here is how to determine the amount of thermal expansion in a piping system:

Example Assume a 10-in. steam line fabricated from carbon steel is carrying superheated steam at 300 psig and the distance

between pipeanchors is 1,10 ft-O in. The minimum ambi ent temperature is 70"F and the maximum operating temperature is 460'F.

Sorution The corrosion resistance of stainless steel depends on the formation of a thin, unbroken, chromic oxide surface, which will form slowly in the atmosphere on clean stainless steel. Particles of steel from welding spatter should be

From Chapter 2, Table 2-1, we find that the expansion of carbon steel pipe at 460'F is 3.25 in. per l0O ft, and at 70'F the expansion per 100 ft is 0 in.

Piping Stress Handbook Total expansion:

(r4O ft) (3.2s

in.)

-

100

0 in.

Example

:

4.55 in.

Therefore, we find that we should select an exDansion joint that will absorb ar least 4.55 in. of axial

"o*o."._

slon.

Assume that the installation temperature will be 70"F. The required precompression is then calculated as follows:

6(70.F P_ (460"F

Precompression

- 0.F) _ - 0.F)

0.913 in.

Note: If the amount of precompression is very small (Va in. per corrugation or less), it may be neglected. When precompression is required, remember to deduct the amount of this precompression from the normal overall length dimensions.

If the minimum operating temperature is lower than the qggput d installation temperature, the expansion joint will be subjected to both enension and compression-dur_ ing^operation. Because most expansion jointjare designed to runcuon rn compression only. any expansion joint used rn lyclr an apphcatlon must be precompressed (prior to in_ stallatton) to prevent extension of the expansion joint beyond its original. overall length. If advised of the minimum. maximum, and installation temperalures when the order is placed. the expansionjoint wlll be tactory precompressed and may be installed as re_ ceived. In the case of expansion joints specified for low-temperature service only, the installation and maximum temoeratures are normally the same. so thejoints function eniirely in extension. Where such service conditions are clearly specified, the expansion joint will always be factory precompressed, ready for installation.

Where it is not possible to anticipate the installation temlerature, the expansion joint may be precompressed in the field. The amount of precompression is determined as follows:

-4(Tz-Tr) (Ts - Tr) D-

Application Pipe Anchors The first step is to determine the tentative locations of pipe anchors. By proper location, any piping system can be reduced to a number of individual eipanding pipe sections having relatively simple configurations. The number and location of pipe anchors will depend upon piping configuration, amount of thermal expansion, the proximiry of structural members suitable for-use as anchors, and-the location ofpipe fittings, connected equipment, and branch connections.

. Start out with the assumption that single expansion joints in straight axial compression will provide the simplest and most economical layout. Wherever possible, the distance between anchors and amount ofexpansion should be kept uniform so rhat the expansion joinis used will be interchangeable. Ib minimize the number of exDansion joints adjust the distance between alchors so thai exoansion joints having a maximum number of corrugations in each bellows (consistent with stabilitv) can be ised.

Total amount of precompression, in. Total rated axial movement of the expan-

Galculation of Forces Acting on Main Pipe Anchors

Installation temperature determined by actual temperatue reading of adjacent piping. Do not use the ambient atmospheric temperature for this purpose.

A main pipe anchor must be designed to withstand the forces and moments imposed upon it by each of the pipe sections to which it is attached. In the case of the installation illustrated in Figure 14-10, the force acting on the main anchor consists of the full line thrust due to pressure , -the the force required to deflect the expansion joint, rated

sion joint, in. Minimum temperature

Maximum temDerature

Fundamentals of Exoansion Joints

'1 0z

I

Figure 14-10, Diagram illustrating the forces that act upon the main

anchor.

Figure 14-11. Diagram illustrating the forces that act upon the main anchor in applications involving straight pipe selections and in applications involving anchors at pipe bends and elbows.

movement, and the frictional force due to the pipe align-

where

ment guides. Formulas for calculating anchor forces in various applications follow. The steps for calculating the main anchor forces for applications involving straight pipe sections (see the center anchor in Figure

14-ll)

are:

: F, : F. : F,nn

Fg :

I 2.

t

Static thrust due to internal pressure' lb Force (ftom data sheet) required to extend or compress the expansion joint, lb Frictional force due to pipe alignment guides. Note: This can be obtained from the manufacturer of the

1. Calculate the firll line thrust:

F":AP where F, : A: P:

Force on main ancho! lb

guides. Static thrust due to internal pressure,

lb Effective pressure thrust area (in.2) taken from data she€t Maximum pressure (p6i) based on the most severe conditions whether design, operational or test

Assuming that the weight of the pipeline and its contents are carried by supports. To calculate the total by any one force imposed on the main anchor pipe section use the following equation:

(F)

F':F"+F.+F"

To determine the net load on the anchor, it is necessary to add vectorially the forces imposed upon it by

each

of the three pipe

sections

to which it is at-

tached.

To calculate the main anchor forces for applications involving straight pipe sections containing expansion joints ofdifferent diameters (see center anchor in Figure 14-12), use the following equation:

4:(Ar-&)P

Piping Stress Handbook

Figure 14-12. Diagram illustrating the torces that act upon the main anchor in applications involving straight pipe selections containing expansion joints of ditferent diameters.

where

A1 :

Effective area, corresponding to the mean diameter of the corrugations of the expansion joint in the larger pipe section,

,q.2

:

P :

m.' Effective area, corresponding to the mean diameter of the expansion joint in the smaller pipe section, in.2 Maximum pressure (psi), based on the most severe conditions, whether design, operational, or test.

Here again, it is necessary to consider the differences in the forces required to extend or compress the expansion joints and the differences in the frictional forces due to pipe alignment guides and supports. Thus, the total force on the center anchor

will

be:

F,":F"+F-r+Fgr-Fgz where F.1

=

F- : Fr1 Fez

: :

Force (from data sheet) required to extend or compress the expaniion joint in the larger pipe section, lb Force (from data sheet) required to extend or compress the expansion joint in the small pipe section, lb

Frictional force (from guide manufacturer) due to pipe alignment guides in the larger pipe section, lb

Frictional force (from guide manufacturer) due to pipe alignment guides in the smaller pipe section, lb

To calculation the main anchor forces for applications involving anchors at pipe bends and elbows (see Figure 14-10) the following calculation must be used. In the case of an anchor located at a pipe bend or elbow, it is necessary to consider the forces imposed by the pipe sections on both sides of the anchor. Thus, assuming that each section contains an expansion joint, the line thrust due to pressure (F" : AP) and the forces F- and F", explained previously, become biaxial components and-must be added vectorially. In addition, the effect at the elbow of

the centrifugal thrust (Fo) due to flow, must be considered. Fo may be calculated as follows:

rp:

2ADV2

0

: Internal where A-slnD e

o

: : : :

ff

area of pipe, DensiU of fluid, lb/ft3 Velocity of flow, ft/sec Acceleration due to gravity, 32.2 fllsec2 Angle of pipe bend

Calculation of Intermediate Pipe Anchor Forces An intermediate pipe anchor must be designed to withstand the force and moments imposed upon it by each of the pipe sections attached to it. However, an intermediate anchor does not have to be designed to withstand the full line pressure thrust, because this force is always absorbed by main anchors or by devices on the expansion joint. such as limit rods, tie rods, gimbals, or hinges. Assuming that the weight of the pipeline and its contents is caffied by supports, the following calculation will determine the forces acting on an intermediate pipe anchor in a pipe section containing expansion joints (see Figure 14-13):

Fre : F.r * where F^1

Frr

Fno

=

: :

Fr1

*

Fn2

*

Fgz

The force (ftom the data sheet) required to extend or compress expansion joinr

EIl

shown in Figure 14-13.

The total force due to friction of all the

pipe alignment guides installed on the pipe section to the right of the intermediate anchor in Figure 14-13. The force required to extend or compress expansion joint EI2 shown in Figure 14-

tJ-

-Fundamentals of Expansion Joints

363

Figure 14-13. Diagram illustrating theJorcesthat act upon an intermediate pipe anchor in a pipe section containing expansion joints.

Fgz

=

The total force due to friction of all tlte pipe alignment guides installed on the pipe section to the left of the intermediate anchor in Figure l4-13.

Nore: The frictional force due to pipe alignment guides can be obtained from the manufacturer of the guides.

If the pipe is the same diameter on both sides of the intermediate anchor, and if the guides on both pipe sections are similar in number and design to F,,z and Fgr, respectively, but opposite in sign, F1a will be equal to zero. However, it is possible that the pipeline may heat up gradually from one end, thereby causing one of the pipe sgctions to expand before the other. It is therefore considered good practice to design the htermediate anchor to resist the forces exerted by one of the two pipe sections (i.e., F1a : F*1 *Fgr).

used only in applications involving lateral deflection or angular rotation resulting from L- or Z-shaped pipe configurations . Proper alignment is very important in the installation of all expansion joints. Expansion joints will not function properly unless the pipeline in which they are installed is securely anchored and guided.

Spacing of Pipe Guides Where an expansion joint is located close to an anchor, the first pipe guide should be located no more than four pipe diameters ftom the moving end. The second should be located no more than fourteen pipe diameters from the first. The recommended spacing for intermediate guides along the balance of the pipeline can be determined from Figure 14-9. For any known pressure and pipe size, the guide spacing can be determined by locating the pressure on the scale at the bottom of Figue 14-9. Follow the pressure line vertically until it intersects the diagonal line for

Pipe Guides and Guiding A pipe alignment guide is a sleeve or frame fastened to some rigid structure that permits the pipeline to move freely along its own axis and limits it to this type of motion. A roller support, U bolt, or pipe hanger, which orily supports the weight ofthe pipe, cannot be substituted for a pipe guide. Pipe guides are required to prevent buckling ofthe pipeline. Buckling is caused by compressive loading on the pipe due to the internal pressure thrust and the flexibility of the expansion joint which causes the pipe to act like a column with end loading. In axial movement applications, avoid using a single pipe-alignment guide because such a guide may act as a fulcrum, which might impose lateral deflection or angular rotation on the expansion joint due to movement of the piping in a dhection other than axial. Planar pipe guides are modified to permit limited movement and/or bending of the piping in one plane. These are

pipe size. From this intersection, follow across horizontally to the guide spacing column (left to right) and read the recommended spacing. For example, the recommended intermediate guide spacing for a 6-in. pipeline containing an expansion joint under a pressure of 125 psig is 43 feet. The first guide should be no more than 24 in. from the expansion joint, and the second pipe guide 84 in.

from the first.

Location of Expansion Joints Wherever possible, an exparsion

joint should be lo-

cated irnmediately adjacent to a pipe anchor. If it is not possible to locate the expansion joint near a pipe anchol pipe guides should be used on both sides of the expansion joint ir accordance with the instructions given in the precedhg paragraphs under "Spacing of Pipe Guides."

Piping Stress Handbook

Figure 14-10 shows the preferred practice in the use of a single expansion joint (EI) to absorb axial pipeline expansion. Note the use of one expansion joint between two main anchors (MA) , the nearness of the expansion joint to an anchor, the closeness of the fimt alignment guide (G1), the spacing between the fint alignment guide and the second alignment guide (Gr), and the spacing of intermediate guides (G) along the balance of the line. Expansion joints should not be located immediately

downstream from turbulence-pnrducing devices (such as butterfly valves). plug valveJ, and su-dden increases in pipe size, mitered elbows, etc. If it is impossible to locate

joint an adequate distanceiway from tubulence producers. the joint slould be equipped with a heavy sleeve. Figures 14-14 and 14-15 show the information required for standard and special expansion joints specification sheets. the expansion

End Connections The type of end connections selected depends upon the operating conditions and the customer's re.guirements. See Figure l4-16 for illustrations. The following is a briefdescription of the various g?es available.

Fixed Flanges (Type SF) The flanges are welded directly to the bellows material without the use of intermediate pipe nipples. In this construction the flanges are in direct contact with the flowins medium.

Fixed Flanges (Type F) The flanges are welded to pipe nipples, thereby provid-

ing greater overall length. In this construction bbth the pipe nipple,s and flanges are in direct contact with the flowing medium.

Combination Ends Expansion joints can be supplied with one weld end and one flanged end to meet installation requirements.

Covers Covers protect expansion joints from mechanical damage and serve as a base for insulation.

Van Stoned Flanges (Type V) The flanges are slipped over the ends ofthe bellows and the bellows material is flared out or "Van Stoned" over the faces of the flanges. The \r'an Stones are roughly equivalent to the raised faces on standard forged steel flanges. The flanges are loose and free to rotate, thus permitting easy alignment with the mating pipeline flanges. This construction is generally used in applications involving product purity or corrosion, because the only material in contact with the flowing medium is the corrosionresistant bellows matefial.

Sleeves Sleeves minimize pressure drop and also streamline the

flow of gas or fluid through an expansion joint, thereby reducing friction losses and turbulence. They are recommended for all expansion joints, except in applications

where high-viscosity fluids such as tar are involved. Sleeves are required whenever the velocity of flow exceeds the following values:

Welding Ends (Type W) The ends of the expansion joint are supplied with pipe suitably beveled for welding to connecting equipment or piping. Standard joints are supplied with carbon steel weld ends. See individual data sheets for grade and type. Other thicknesses, lengths, and grades of carbon steel weld ends are available on order. Where alloy pipe is used, it may be advantageous to use weld ends that are shorter and thinner than carbon steel standards. Consult the factory for recommendations when alloy pipe is used.

Nominal

Size 3 to 6 in. ) 6 in. 3 to 6 in. > 6 in. Pipe

Medium in Pipe

Steam Steam Air (other gases) Air (other gases)

Velocity

of trlow 1,000 ft/min/in. dia 6,000 ff:/min 250 ft/min/in. dia 1,500 fl:/min

Fundamentals ol Exoansion

For additional data use the sheet for supplemental information for special expansion joints. Customer

Inquiry/Job No.

Project

1. Item No.

2. Quantrty 3. Size 4. Flowing Medium+ 5. Flow Velocity 6. Int. Design Pressure, psig 7. Int. Text Pressure, psig 8. Maximum Temperature, "F 9. Minimum Temperature, oF

10. Installation Temperature, oF 11. Axial compression, in.

12. Axial

extension, in.

13. Lateral deflection, in. 14. Angular rotation, deg. 15. Pipe specification 16. Weld end specification 17. Flange specification 18. Type or catalog number 19. Internal sleeves 20. External covers 21. Anchor base 22. Limit rods Use manufacturer's standard unless otherwise specified by purchaser.

23. Bellows material 24. Equalizing ring material 25. Total corrugations 26. Lenglh limitation

If flowing medium is corrosive,

erosive, or viscous explain in detail.

Figure 14-14. Standard expansion joint specification sheet.

Joints

365

366

Piping Stress Handbook

Customer

Project

hquiry/Job No.

1. Item No.

2. External design pressure, psig 3. External test pressure, psig 4. Pipe purge, instr. connection 5. Vibration amplitude 6. Vibration frequency Special Flange Design

7. Material 8. Facing 9. O.D. 10. I.D.

ll.

12. 13. 14. 15.

Thiclness

B.C. diameter No. holes Size holes

Hole orientation

Design Restrictions

16. 17. 18. 19.

Length Maximum O.D. Minimum I.D. Axial force 2O. LatercJ force (Shear) 21. End moment 22. Cychc design life 23. ASME Code partial Data forms required 24. Applicable codes and specifications

Figure 14-15. Supplemental information for special expansion joints, to be used with the standard expansion ioint specitication sheet.

Fundamentals of Expansion Joints

Figure 14-16. End connections.

15 Glossarv .,/

Aging-The term originally applied to the process or sometimes to the effects of allowing a metal to remain at ordinary temperatures. H;at treatment ar temperatures above room temperature for the purpose of accelerating changes of the type that might take place during aging at ordinary temperature is called artificial aging. The changes taking place

during artificial aging are due to the precipitation treatment. Aging is an approach to the attaitment of equilibrium from an unstable condition induced by a prior operation. The fundamental reaction involved is generally one of precipitation, sometimes submicroscopic. The method employed to bring about aging consists of exposure to a favorable temperature subsequent to (1) a relatively rapid cooling from some elevated temperature (quench aging) or (2) a limited degree of cold work (strain aging). Alclad-The common name for a type of clad-wrought aluminum product with coatings of high purity aluminum; or an aluminum alloy different from the core alloy in composition. Alloy-A metallic substance consisting of two or more elements, of which at least one is metal, and in which all elements are miscible in the molten state and do not separate when solid. Alloying elements-Chemical elements constitutins an alloy. In steel. usually rhe elements added to mo?ify the properties of the steel. Annealing-A heating and controlled operation to impart specific desirable properties generally concerned with subsequent fabrication of the alloy, such as softness and ductility. When annealing follows cold working for the purposes of stress removal, it is called stress annealing. Arc welding-Welding accomplished by using an electric arc formed between a metallic or carbon electrode and the metal being welded, between two separate electrodes, or between two separate pieces being welded (also called fusion welding). 368

Austenite-A solid solution in which

gamma iron is the

solvent, having a face-centered cubic crystal structure. Austenitic steel-Steel, which due to its comoosition has a stable structure at normal lroom) timperatures; as for example: the 18-8 types. It is not hardened by thermal treatrnent. Bend test-A test commonly used to determine relativ! ductility of a sample by bending it over a given radius and through a given angle. BilIet-A semi-finished rolled ingot of rectangular or nearly rectangular cross section. Brass-A copper-base alloy in which zinc is the principal added element. Brazing-Joining metals by fusion of nonferrous alloys with melting points above 800"F but below the melring point of the metals being joined. Brinell hardness-A hardness number determined br applying a known load to the surface of the mareriil to be tested through a hardened steel ball of known diameter. Note: Not suitable for measurins the hardness of strip and sheet because of insulfic-ient thick. ness.

Brittleness-A tendency to fracture without appreciable deformation. Carbon steel-Steel in which carbon provides the properties without substantial amounts of other alloyins elements.

Carburizing-Diffusing carbon into the surface of ironbase alloys by heating in the presence of carbonaceous materials.

Case hardening-Carburizing, nitriding, or cyanidinr

and subsequent hardening by suitable heat trearment, if necessary, all or part ofthe surface portion: of a section of iron-base alloy. Casting-Fouring molten metal into a mold or a meta. object so produced.

Cementite-An iron-carbon compound with the chem;cal formula Fe3C often called iron carbide.

--

Glossary Charpy test-A pendulum-q pe impact tesr in which

a

notched specimen, supported ar both ends as a simple beam, is broken by the impact of the falling pendulum. The energy absorbed in breaking the specimen, as determined by the deireased rise of the pendulum, is a measure of the impacr strength of the

metal. Chemical analysis-Separating an allor. into its component elements and identi! in-e them. In quantitative analysis, the proportion of each element is determined. Chromium-A hard crystalline metal used as an alloying element to give resistalce to heat. corrosion, and wear and increase strength and hardenability. Cold working-Permanent deformadon of a metal below its recrystallization temperature. Also defined as plastic deformation of a metal at a temperature low enough to ensure strain hardening. Mechanical properties, such as tensile strength, hardness, and ductility, are also altered. Compressive strength-The ability to withstand compressrve stresses.

, Compressive stress-Stress caused by a compressive load or in fibers compressed by a bending. Cooling stresses-Stresses caused by uneven contraction, external restraint, or localized plastic deformation during cooling. Corrosion-Gradual chemical or electrochemical attack on a metal by atmosphere, moisture, or other elements.

Corrosion embrittlement-Embrittlement in certain al- loys caused by exposure to a corrosive environment. Corrosion fatigue-Combined action of corrosion and fatigue in which local corroded areas act as stress concentrators, causing failure at the point of stress concentration and exposing new metal surfaces to corrosion. The failure is progressive and rapid. Creep-Plastic flow of metal, usually occurring at high temperatures, subject to stress appreciably less than its yield strength. It progresses through first, second, and third stages to fracture or results in stress relaxation. Cyaniding-A process of case hardening a ferrous alloy by heating in a molten cyanide salt bath, thus causing the alloy to absorb carbon and nitrogen simultaneously. Cyaniding is usually followed by quenching to produce a hard case. Ductility-That property of metal which allows the metal to be permanently deformed before final rupture. Elastic limit (limit of elasticity)-Maximum stress to which a metal can be subjected without permanent deformation at the point of stress. Electrochemical corrosion-Localized corrosion that results from exposure of an assembly of dissimilar

349

metals in contact with or coupled with one aa'drc: or of a metal containing microscopic areas di-isr::-

lar in composition or structure. The dissimilar er:ments form short-circuited electrodes. The corr.--

sive medium is the electrolyte, and an electrlc current is induced. which results in the disolution of the electrode that has the more anodic solution potential, while the other is unattacked.

Elongation-The amount of permanent extension in

the

tensile test, usualll' expressed as a percentage of the original gage lengrh. (e.g. , 25 percent in 2 inches). It may also refer to the amount of extension at any stage in any process which continuously elongates a

body, as in rolling. Endurance limit-A limir of stress below which metal will withstand stress without fracture; a specified large number of applications of such stress. Eutectoid steel-A carbon steel containine 0.80% carbon that becomes a solid solution ar anitemoerature in the austenite temperarure range between i ,333.F and 2,500"F.

Fatigue-The tendency of a metal to fracture under conditions of repeated cyclic stressing below the ultimate tensile strength but above the yield strength. Ferrite-A solid solution in which alphas iron is the solvent and having a body-cenrered iubic crystal structure.

Ferritic steel-Steel which, due to its composition, is not hardenable by heat trearmenr. Such stainless types as 405, 430, and 448 are essentially ferritic steels.

Free machining-The property of steel imparted by additions of sulphur, selenium, or phosphorus which promote chip breakage and permit increased ma-

chining speeds. Additions of sulphur or selenium also help to decrease friction between the chips and the tool face.

Galling-The damaging ofone or both rnetallic

surfaces

by removal of particles from localized areas during sliding friction. Galvanic corrosion-Corrosive action occurrins when two dissimilar metals are in contact and arJioined by a solution capable of conducting an electric current, a condition which causes a flow of electric current and corrosion of the more anodic of the f$.o metals. (Also see Electrochemical Conosion.) Gas welding-Welding in which heat is supplied b1' a manually or automatically controlled torch flame of oxyacetylene or oxyhydrogen (also called fusion welding). Grains-Individual crystals in metal. Hardenability-In a ferrous alloy, the propern that determines the depth and distribution of hardness ilduced by heat treating and quenching.

37O

Piping Stress HandbooK

Hardness-Resistance to indentation by standard balls. diamonds, etc.. under standard loais. Also, the degree of cold working. Heading-An upsetting process used to form rivet, screw, and bolt heads in making these products from wire or rod. Heat treatable-Refers to an alloy that may be hardened by heat treatment. Heat treatment-A combination of heating and cooling operations timed and applied to metal or alloy to produce desired properties. Homogenizing-A process of heat treatment at high temperature to eliminate or decrease chemical segregation by diffusion. Attainment of austenite that has a uniform distribution of carbon. Hooke's Law-Stress is proportional to strain in the elastic region. Hot forming-Working operations performed on metals heated to temperatures above room temperature. Hot working-Hot forming above the recrystallization rcmperature.

Hydrogen embrittlement-A brittleness sometimes engendered by contact with plating and pickling solution acid due to absorption of hydrogen by the

metal. The embrittlement is more evident in hardened parts, and can be removed by aging or heating the steel for a prescribed period. Hypereutectoid steels-Steels containing from 0.80% to above 2.0% carbon. Hypoeutectoid steels-Carbon steels containing less than 0.80% carbon. Impact test-A test designed to determine the energy absorbed in fracturing a test bar at high velocity. The usual impact test specimen is a standard size square bar with a V or keyhole type notch. (See Charpy test and Izod test.) Intergranular corrosion-Corrosion that tends to localize at grain boundaries, usually under conditions of prolonged stress and certain environments, and in association with poor heat reating or welding practice that has caused the precipitation of a more easily attacked constituent at these boundaries. Izod test-A pendulum-type of notched-bar impact test in which the specimen is supported at one end as a cantilever beam and the energy required to break off the free end is used as a measure of impact strength. Machinability-The rate and ease with which a metal can be machined. Magnetic particle testing-This method of inspection consists in suitably magnetizing the material and applying a prepared magnetic powder which adheres along lines of flux leakage. On properly magnetized material, flux leakage develops along surface nonuniformities. This method is not applicable to high

manganese or austenitic stainless steels and nonfer-

rous alloys, which are nonmagnetic.

Martensite-An unstable constituent in quenched steel, the hardest of the transformation products of austenite.

Martensitic steel-Steel which, due to its composition, has martensite as its chief constituent after cooling.

The hardenable stainless types are all martensite ste€ls.

Mechanical prop€rties-Those pfoperties that reveal the reaction, elastic or plastic, ofa material to an applied stress or that involves the relationship between stress and strain; for example, Young's modulus, tensile strength, fatigue limit. These properties have often been designated as physical properties, but the term mechanical properties is technically more accurate and therefore preferred. Modulus of rigidity-The ratio of the unit shear stress to the unit angular strain in the elastic range.

Nitriding-A

process of surface hardening in which a ferrous alloy is heated in an atmosphere of cracked ammonia gas or other suitable nitrogenous material thus allowing nitrogen to diffuse into the surfaca metal. Nitriding is conducted at temperatures below the critical temperature range and produces surface hardening of the metal without quenching.

Normalizing-A

process in which steel is heated to a suitable temperature above the transformation range and is subsequently cooled in still air at room teiperature. This operation is used for grain refining or to develop specified mechanical properties.

Notch sensitivity-The reduction caused in nominal strength, impact or static, by the presence of a stress concentration, usually expressed as the ratio of the notched to the unnotched strength.

Permeability-Magnetic permeability is the ratio of the magnetic induction to the intensity of the magnetizing field. Physical properties-Those properties familiarly discussed in physics, exclusive of those described under Mechanical Properties; for example, density, electrical conductivity; coefficient for thermal expansion. The term has often been used to describe mechanical properties, but such usage is not recommended. Pickling-Immersion in dilute acid or other suitable media for the removal of oxide scale from hot-rolled or otherwise sealed surfaces. Plasticity-The ability of a metal to be deformed exten-

sively without rupture. Plating-Deposition of a thin film of a metal or alloy on a different base metal from a solution containins ions of the plating metal.

G Glossary Poisson's ratio-Ratio expressing the relation of strain normal to the applied load as a proportion of direct strain within the elastic limit. Also relates moduli of elasticity ard rigidity. hecipitation hardening-Hardening of metallic alloys, by aging, which results from the precipitation of a constituent from a supersaturated solid solution, usually nonferrous alloys. Also termed as hardening. (See ,{grng.) Process annealing-An annealing operation carried out at a constant temperature just below the critical transformation temperature (also referred to as sub-

critical annealing) . Proof stress-In a test, stress that will cause a specified permanent set in a material, usually 17o or less. Proportional limit-The highest stress at which the material still follows Hooke's Law, similar to elastic

limit. Quenching-A process of rapid cooling from an

ele-

vated temperature.

Radiography-The use of X-rays or gamma radiation to detect internal structural defects in metal objects. . Reduction of area-In a tensile test, the difference between the original cross-sectional area and that of the smallest area ofthe point ofrupture. It is usually stated as a percentage of the original area. Also called contraction of area, it is not applicable to the mechanical testing of sheet and strip. It is also a measure of cold work. Refractory metals-Metals such as tungsten, columbium, tantalum, and molybdenum, which have rela- tively high melting temperatures. Residual stress-Stresses locked in a metal after the completion of nonuniform heating or cooling, working, etc. due to expansion, contraction, phase changes, and other phenomena.

Resistance

welding-A welding

process

in which the

work pieces are heated by the passage of an electric current through the contact area, combined with pressure causing joining by fusion. Rockwell hardness test-This test consists of forcins a cone shaped diamond or hardened steel ball int6 a metal specimen to determine the degree of penetration and. hence. the hardness. Rupture stress-The true stress given by dividing the load at the moment of incipient fracture by the area supporting that load. Salt spray tesl-An accelerated corrosion test in which the metal specimens are exposed to a fine mist of salt water solution. Scaling-Surface oxidation caused by heating in an oxidizing atmosphere. Seam welding-Resistance welding that consists of a series of overlapping spots forming a continuous weld .

37'l

Shear-Plastic deformation in which parallel planes of metal crystals slide so as to retain their parallel relationship. Also called angular elastic strain. Shear stress-Stress acting on a shear plane. Solution treating-A condition of complete solubility resulting in a single phase for compositions of two or more alloying elements at temperatures lower than the solids. Solid solutions may be limited in extent with respect to range of alloy composition or can be continuous, extending throughout an alloy series.

Specific gravity-A numerical value representing rhe weight of a given substance compared with the weight of an equal volume of water. Spot welding-A resistance-welding process in which the fusion is limited to a small circular or oval area. Stabilization-Prevention of the formation of carbides at the grain boundaries of austenitic stainless steels. Dimensional control of nonferrous castines. Strain-Deformation expressed in units pe-r unit of length produced by strain. Strain aging-Load per unit of area. Stress concentrator or stress raiser-Any notch, scratch, sharp change of contour, slot groove, hole, defect, or other discontinuity in an engineering material that has the effect of concentratins the stresses applied to the material or generated in-it by heating or cooling. Stress corrosion-Corrosive action induced and accelerated by the presence of stresses.

rupture-A test to destruction at elevated temperature, by which it is possible to determine the stress that causes failure at a given temperature and with the lapse of a given period of time.

Stress

Temper-A condition produced in a metal or alloy by mechanical or thermal treatment and havins chancteristic structure and mechanical propertiei. Temper brittleness-Brittleness that results when certain steels are held within or slowly cooled throug! a certain range of temperature below the transformation range. The brittleness is revealed by a notchedbar impact test at room temperature or lower temperatufes. Tempering-The process of reheating quench hardened or normalized steel lo a temperature belo*. t}le rars-

formation range and then coolhg at an) rare desired. This operation is frequently called sress relieving. "Drawing" is synonymous xith temperhg. but the latter is the preferred usage. Tensile strength-The maximum load il pou_n& ger square inch, based on the origiml cro=.-^.e.-tibn. which may be developed in rensile resrilg. isee a.L:o Uhimate Strength.)

372

Piping Stress Handbook

Thermal stresses-Stresses in metal, resulting from nonuniform temperature distribution.

Through-hardening-Thermal description of alloys that harden completely, so the center of a hardened section exhibits hardness similar to the surface. Torsion-Strain created in an object by a twisting action or the stresses created by such an action. Toughnesl-Ability to absorb considerable energy before fracture, usually represented by the area under a stress-strain curve and therefore involvins both ductility and strength. [Jltimate strength-The maximum strength or stress before complete failure or fracture occurs.

Vacuum melting-A process by which alloys are melted rn a near pertect vacuum to prevent contamination

by atmospheric elements. Vickers hardness test-An indentation hardness test utilizing a diamond pyrarnid and useful over the entire range of common metals.

process of joining metals whereby partial melting of the parent metals occurs except in the case of pressure welding when heating is only sufficient to cause recrystallization across the interface.

Welding-A

Yield point-The load per unit or original cross section at which a marked increase in deformation occurs without increase in load. In stainless and heat-resisting steels, this occurs only in the martensitic and ferritic chromium types. In the austenitic stainless and heat-resisting steels, the yield point is the stress corresponding to some definite and arbitrary total deformation, permanent deformation, or slope of the load deformation curve; this is more properly termed the yield strength.

Yield strength-Stress corresponding to some fixed permanent deformation such as 0.1 or 0.2% offset from the modulus slooe.

aa

Index

Air-cooled heat ex changerc, 263-264 Allowable expansion stress range, 2, 8-9, 11, 13 Allowable external forces and moments (tables), 264

Allowable internal pressure stress,

1l Allowable loads, 257 -264 Allowable longitudinal stress, 9 Allowable momenlq 257 -264 Allowable pipe deflection, 314 Alowable pipe span, 314 Allowable resultant forces and moments (table), 258 Allowable shear stress, 11

Disffibution Piping), 11, 13, 15, 251

ANSI/ASME Code 831.9 (Building Services Piping), 15 ANSI/ASME Code 831.10 (Cryogenic Piping), 16

ANSI/ASME Code B31.11 (Slurry Piping), 16 ANSI/ASME Code for Pressure Piping, 177 API Code 610, (steel pump force, moment, and stress limitations), 257 -258 API Code 661 (design criteria for

air-cooled heat exchangers),

263-2&

Allowable span, 314 Allowable stress(es), 8-11, 257 -264

ASME Boiler Code, 177

-

Barlow formula, 177 Baseplate support, 258-259 Bellows, 356

range (tables), 38-111 Allowable working pressure, 177,

250-251 Anchor(s), 122, 345, 356, 360-363 forces and moments, 3 intermediate, 362-363

main, 360-362 Angle valves cast steel, 307

flanged,302 ANSI/ASME Code 816.9, 120 ANSI/ASME Code B31.1 (Power Piping), 3-6, 14, 257 , 260 allowable stress range (tables),

38-'72 ANSI/ASME Code 831.2 (Fuel Gas

Piping),

14

ANSI/ASME Code 831.3 (Chemical Plant and ktroleum Refinery Piping), 6-7, 14, 25'l -260 allowable stress range (tables),

73-111 ANSI/ASME Code 831.4 (Liquid Petroleum Transportation Piping

, 9, 11, 14-15 ANSI/ASME Code 831.5 (Refrigeration Piping), 15 ANSI/ASME (DOT) 831.8 Code Systems),

7

(Gas Transmission and

Bellville (disc) springs, 324 Bending, 123 maximum, 314 stress, 1, 260 Bends, 120, 3ll-323, 350 Boiler external piping, ,14 Bracket supports, 324 Branch connections , ll4, 253-255 Branch reinforcement, 252-256 Buckling, 356, 363

Building Services Piping Code (ANSr/ASME 831.9), 15

Coil springs, 324 Cold springing, 2-3, 356-358 Combination ends, 364 Compliance codes, 3- l6 Components of pipe, 299-313

clearances,357 Compressors, 262-263 Connections

branch, 114, 253-254 end,364 purging, 358 vertical exhaust, 260-261 Cons^TLlt sprjng supports. 327,

load table, 338-341 Corrosion,359 Covers, of expansion joints, 364 Creep, 2, 177 Cryogenic hargers, 327 , 345, 349 Cryogenic Piping Code

(ANSr/ASME 831.10), 16 Cycle life expectancy, 2, 358-359 Cylindrical vessels, 122- 176

Deflection, 324, 329 lirnits of, 314-315 Design criteria air-cooled heat exchansers.

263-264 compressors, 262-263

pipe suPports, 324-350

pumps,257-259 turbine drivers, 260-262

Butt-welded fittings, 303

Design factor

Caking,358 Centrifugal steel compressor, 262

Direct longitudinal sness. I Direct shear stress, 2 Disc (Bellville) springs. 3?4

Chemical Plant and Petroleum Refinery Piping Code (ANSI 831 .3) , 6-7 , 14 , 257 -258 allowable stress range (tables),

73-111 Circumferential bendhg, 123 Circumferential stress, 2 Coefficients of thermal expansion

(tables),2-32

373

F,

13

Discharge nozzles. 257 -259 Distortion energy (von Mis€sl theory, 2 DOT Code B31.8. 13. 15. 51 Double expansion joim- 15l-351 Dummy legs, 324

ll.

Elbows, 112, 118-lll Electric generadng pla s. l-t

374

Piping Stress Handbook

End connections, 364 Ends, 121, 364

i

loops, 351

Erosion,359

factor (table), 120 Industrial plants, 14 Insulated anchors, 345 Insulated pipe supports, 348-350 Insulation of pipe, 299-300 Intermediate pipe anchor, 362-363

spans,314-320 rypes of, 325-329

Expansion devices, 351 Expansion forces, (tables), 278-290 Expansion joints, 351-367

anchors,356 application, 360-363 cold springing, 356 corrosion, 359

Internal sleeve, 358

k factor (table), 120, 327

erosion,359

Load adjustment, 327

265-291

't2

specified rninimum yield strength,

forces and moments, 356 guides, 356, 363-364 precompression, 360 thermal expansion calculations,

Loading, sustained external, Loads,257-2&, 326,357 Leaf springs, 324

359-360 types,351-355

Piping Systems Code (ANSUASME 831.4), 7-1r Longitudinal joint factor t, 13 Longitudinal stress, 1-3, 5,7,9,

Factors, k, h, i (table), 120 Flanged elbows, 118 Flanged valves, weight of (tables)

angle,302 check (swing), 301 gate,300

globe,30l Flanges

fixed, 364 forged steel, 303-305 weight (tabl€), 302

Flexibility, 122 Flexibility factors,

1

12

flanged elbows, 118- 119 miter elbows, 120-121

Flexible piping, 351 Flexible support, 324 Force reduction, 356 Forces and moments,3, 122,

257,26/.,356,358 Fuel Gas Piping Code (ANSI/ASME

83r.2),

14

Gas Transmission and Distribution

Piping Code (ANSI/ASME (DOT) 831.8), 11- 15, 2s1 Gimbals, 355, 358 Globe valves, 307 Guides, 356, 363

stress, l-2, 5-7 compliance codes, 3-16 simplified solutions (tables),

Joint movements, 351

cycle life expectancy, 358-359 end connections, 364-367

Expansions, offset lensths reouired (tables), 266-267' Expansion stresses, 2-3, 6, 13 range, 8-9, 11 External mechanical forces, 258 External pressure, 5

materials, properties (tables), 33 properties (table), 292 -298

3

Liquid ktroleum Transportation

tl,

13

Machining, 112 Main pipe anchors, 360-362 Maximum allowed wall thickness, 6 Maximum allowable resultant forces

supports. See a/so Supports. tor cryogenic service, 329, 345 design and selection, 324-350 flexible, 324, 356 insulated, 348-350 nsid, 324 Piping restrained, 11 three-dimension, 2 two-anchor, 3

unrestrained,9 Piping codes, 3-16 Piping wind loads, 320-323

(tzble),324-325

Planar piDe euide. 356. 363 POWER,FOAMTM, 345-347

and moments, 258 Maximum bending, 314 Maximum def lection, 324

Fower Piping Code (ANSI/ASME 831.1), 3-6, 14, 257 , 260 Precompression, 356, 360

Maximum radius, 112 Maximum shear (Tresca) theory, 2 Mechanical forces, 258-259 Minimum radius, 112 Minimum thickness, 177 Miter(s)

Pressure

bends, 120 elbows, 120-121 spactng, 112, 120-121

welding,308-309 "Modified lame" formula, 177 Modulus of elasticity (table), 33,257

external, 5

working, 176, 250-251 Pressure-balance expansion, 354 Pressure design, 5 Pressure stress, 6-7, 11

rutios,

177

, 250-256

(tables), 178-249 Prestressing,3 Pumps, 256-258 Purging connections, 358

Moments. See Forces and moments

Nominal wall thickness, 11, 111, 177

Nozzles, 122-123

flexibilities, 122-

176

loadings (table), 257 snction, 257 -259 Occasional longitudinal stress, 6 Offset lengths required (tables),

266-267

Oil piping,

14

Radial flexibility, 122 Radial stress, 2 Refrigeration Piping Code

(ANSr/ASME 831.5),

15

Reinforcement area, 253, 255 Reinforcement zone, 255 Required area for branch connections,253 Required yield strength, 350-351 Restrained piping, 1l Resultant applied forces and

moments, 258 Pedestal support, 258-259 Pipe(s)

Hangers, 324, 327, 345, 349 Heat exchangers, 263-264 Heating plants, 14 h factor (table), 120 Hinged expansion joint, 355, 358

anchors, 356, 360-363

Hot \pater piping, 14

insulation, 299-300

Resultant bending stress, 6-7 Resultant shear force, 259

deflection, 314

Right Rigid Rigid Rigid

guides,356,363

Rotational nozzle flexibilities

bends,311-323,351 components, 299 -313, 357

angle nozzles, 253 ends, 122 hanger, 324 support, 324

(tzbles), 122-176

-

{d ---r

Index {Is Saturated sream. properties

(tables). 3-l-36 -

Self sprineins.

l

Shaft displaciment

of

. 258-259

Shape factors. 321 Shoe suppon. 3!-1 Shear strissSingle expansion ioint, 351

l

Sleeve.356.358,364

Slurry Piping Code (ANSt/ASME 831.11). t6 Spans, allouable, 313. See also ptpe sPans.

Specified rninimum yield stren eth (SMYS.,, 9, Spring rate of nozzles, 122 spnng suppons, 324_341

ll

Stabiliry,356

Standard hangers, 327

standard terms, 3_4

Stress(es). .te€ aho piDe stress.

allowable. 8-l l. 38--l I t, 257_264 deadload, 314 intensificarion factors, l. I12. I L4-121

limits,314-315 pressure/stress r atios,

prtmary, 2

lj 7 _256

range, 2 shear,

ll

Structuraj supports, 325

suctron nozzles, 257_259 Supports. 324-325, 327, 342. 356. Slee a/so Pip€(s) supports. baseplare. 258-259 pedasral, 258-259

-'

Support load, 345 Sustained longitudinal stress. 5 )usralned-pIus_thermal expansion stress, 6 Sway brace support, 327. 342 Swing check v-aives, 30gTemperature derating factor terms, standard. 3_4

Thermaf expansion, 2-3,

359-360

f,

l.]

5-6. 324,

_.coefficienrs of (tabtes), 2_32 r nerma movements, 351 Three-dimension pipine. 2 Three-weld-miter elbo;s. 12 I tte roos, JJ6 Torsional stress, 2 Travel stops, 327 Tresca (miximum shear) theory, 2 rwo-anchor Ptplng systems, 3

turbines,260-267

Thrbulence-producing device, 364

Uni{orm Building Code, J2l unrtorm wind loads, 323

U.S.A. Standard Buildins Code R^equirements for Deiign Loads. Universal expansion joint, 352_J54 unrestratned ptplng, g

rtical exhaust connecrion. 160_16 l vrbratron control, 342_ J4.t Von Mises (distortion energr r l.betrrVe.

2-'

Wall thickness pressure stress, 7. 251

wall thlckness

maxrmum allowable. 6

nominal, l l, l12, required, 177 Weather,35l

177

Wedge gate valves. 306 Weld elbows, l12 Weld-end valves (tables)

angle,302 check (swing), gate,300 globe,301

301

Welding ends, 363 Weld joint factor E,

l0

Wind loads, 320-321 (table),322-323 Wind pressure, 320

Working stress, 172

y values (tables), 177_250 y : Q Garlowy, 178-195, 250

y=

Van Stoned flanges. 3& Variable spring iupports, 324_327 load tabte, 328

y

U.4 (modified lame). 196_214,250 = 0.5 (average diameter).

y

:

2t4_231, t50

0.7 (creep), 232_250