Structural Engineer’s Pocket Book
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Structural Engineer’s Pocket Book Fiona Cobb
AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO
Elsevier Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 200 Wheeler Rd, Burlington, MA 01803 First published 2004 Copyright ª 2004, Fiona Cobb. All rights reserved The right of Fiona Cobb to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1T 4LP. Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publisher Permissions may be sought directly from Elsevier’s Science and Technology Rights Department in Oxford, UK: phone: (þ44) (0) 1865 843830; fax: (þ44) (0) 1865 853333; e-mail:
[email protected]. You may also complete your request on-line via the Elsevier homepage (http://www.elsevier.com), by selecting ‘Customer Support’ and then ‘Obtaining Permissions’ British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress ISBN 0 7506 5638 7
For information on all Elsevier Butterworth-Heinemann publications visit our website at http://books.elsevier.com Typeset by Integra Software Services Pvt. Ltd, Pondicherry, India www.integra-india.com Printed and bound in Great Britain
Contents Preface
ix
Acknowledgements
xi
1
2
3
General Information Metric system Typical metric units for UK structural engineering Imperial units Conversion factors Measurement of angles Construction documentation and procurement Drawing conventions Common arrangement of work sections Summary of ACE conditions of engagement
3 4 5 6 8 10 11
Statutory Authorities and Permissions Planning Building regulations and standards Listed buildings Conservation areas and Tree preservation orders Archaeology and ancient monuments Party Wall etc. Act CDM
13 14 17 18 19 21 24
Design Data Design data checklist Structural form, stability and robustness Structural movement joints Fire resistance periods for structural elements Typical building tolerances Historical use of building materials Typical weights of building materials Minimum imposed floor loads Typical unit floor and roof loadings Wind loading Barrier and handrail loadings
25 26 29 30 31 32 34 38 41 43 44
1 2
vi
4
5
6
Contents
Selection of materials Selection of floor construction Transportation Temporary works toolkit
46 47 48 52
Basic and Shortcut Tools for Structural Analysis Load factors and limit states Geometric section properties Parallel axis theorem and Composite sections Material properties Coefficients of linear thermal expansion Coefficients of friction Sign conventions Beam bending theory Deflection limits Beam bending and deflection formulae Clapeyron’s equations of three moments Continuous beam bending formulae Struts Rigid frames under lateral loads Plates Torsion Taut wires, cables and chains Vibration
55 56 60 61 64 65 66 67 68 69 76 78 79 81 84 88 89 91
Geotechnics Geotechnics Selection of foundations and retaining walls Site investigation Soil classification Typical soil properties Preliminary sizing Trees and shallow foundations Contamined land
92 93 94 95 96 100 109 113
Timber and Plywood Timber Timber section sizes Laminated timber products Durability and fire resistance Preliminary sizing of timber elements
117 119 120 122 125
Contents
7
8
9
vii
Timber design to BS 5268 Timber joints
127 135
Masonry Masonry Geometry and arrangement Durability and fire resistance Preliminary sizing of masonry elements Masonry design to BS 5628 Masonry design to CP111 Lintel design to BS 5977 Masonry accessories
141 143 147 148 152 166 168 170
Reinforced Concrete Reinforced concrete Concrete mixes Durability and fire resistance Preliminary sizing of concrete elements Reinforcement Concrete design to BS 8110 Reinforcement bar bending to BS 8666 Reinforcement estimates
175 177 179 180 182 185 205 207
Structural Steel Structural steel Mild steel section sizes and tolerances Slenderness Durability and fire resistance Preliminary sizing of steel elements Steel design to BS 5950 Steel design to BS 449 Stainless steel to BS 5950
208 210 239 242 246 249 261 269
10 Composite Steel and Concrete Composite steel and concrete Preliminary sizing of composite elements Composite design to BS 5950
275 277 281
11 Structural Glass Structural glass Typical glass section sizes and thicknesses Durability and fire resistance Typical glass sizes for common applications Structural glass design Connections
284 287 288 289 291 293
viii
Contents
12
Building Elements, Materials, Fixings and Fastenings Waterproofing Basement waterproofing Screeds Precast concrete hollowcore slabs Bi-metallic corrosion Structural adhesives Fixings and fastenings Cold weather working Effect of fire on construction materials Aluminium
295 296 299 300 301 302 304 307 308 310
Useful Mathematics
314
13
Useful Addresses
320
Further Reading
331
Sources
336
Index
339
Preface As a student or graduate engineer it is difficult to source basic design data. Having been unable to find a compact book containing this information, I decided to compile my own after seeing a pocket book for architects. I realised that a Structural Engineer’s Pocket Book might be useful for other engineers and construction industry professionals. My aim has been to gather useful facts and figures for use in preliminary design in the office, on site or in the IStructE Part 3 exam, based on UK conventions. The book is not intended as a textbook; there are no worked examples and the information is not prescriptive. Design methods from British Standards have been included and summarized, but obviously these are not the only way of proving structural adequacy. Preliminary sizing and shortcuts are intended to give the engineer a ’feel’ for the structure before beginning design calculations. All of the data should be used in context, using engineering judgement and current good practice. Where no reference is given, the information has been compiled from several different sources. Despite my best efforts, there may be some errors and omissions. I would be interested to receive any comments, corrections or suggestions on the content of the book by email at
[email protected]. Obviously, it has been difficult to decide what information can be included and still keep the book a compact size. Therefore any proposals for additional material should be accompanied by a proposal for an omission of roughly the same size – the reader should then appreciate the many dilemmas that I have had during the preparation of the book! If there is an opportunity for a second edition, I will attempt to accommodate any suggestions which are sent to me and I hope that you find the Structural Engineer’s Pocket Book useful. Fiona Cobb
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Acknowledgements Thanks to the following people and organizations: Price & Myers for giving me varied and interesting work, without which this book would not have been possible! Paul Batty, David Derby, Sarah Fawcus, Step Haiselden, Simon Jewell, Chris Morrisey, Mark Peldmanis, Sam Price, Helen Remordina, Harry Stocks and Paul Toplis for their comments and help reviewing chapters. Colin Ferguson, Derek Fordyce, Phil Gee, Alex Hollingsworth, Paul Johnson, Deri Jones, Robert Myers, Dave Rayment and Andy Toohey for their help, ideas, support, advice and/or inspiration at various points in the preparation of the book. Renata Corbani, Rebecca Rue and Sarah Hunt at Elsevier. The technical and marketing representatives of the organizations mentioned in the book. Last but not least, thanks to Jim Cobb, Elaine Cobb, Iain Chapman for his support and the loan of his computer and Jean Cobb for her help with typing and proof reading.
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3 Design Data Design data checklist The following design data checklist is a useful reminder of all of the limiting criteria which should be considered when selecting an appropriate structural form:
. . . . . . . . . . . . .
Description/building use Client brief and requirements Site constraints Loadings Structural form: load transfer, stability and robustness Materials Movement joints Durability Fire resistance Performance criteria: deflection, vibration, etc. Temporary works and construction issues Soil conditions, foundations and ground slab Miscellaneous issues
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Structural Engineer’s Pocket Book
Structural form, stability and robustness Structural form It is worth trying to remember the different structural forms when developing a scheme design. A particular structural form might fit the vision for the form of the building. Force or moment diagrams might suggest a building shape. The following diagrams of structural form are intended as useful reminders:
TRUSSES
Couple
Tied rafter
Howe (>10 m steel/ timber)
Double howe (8–15 m steel/ timber)
Bowshing
Thrust
Northlight (>5 m steel)
Bowshing (20–40 m steel)
King post
Northlight (5–15 m steel)
Queen post
Fink (>10 m steel/ timber)
Double fink (5–14 m timber) (8–13 m steel)
Scissor (6–10 m steel/ timber)
Double scissor (10–13 m steel/ timber)
Fan (8–15 m steel)
French truss (12–20 m steel)
Umbrella (~13 m steel)
Saw tooth (~5 m steel)
Pratt
Warren
Modified warren
Howe
Fink
Modified fink
GIRDERS
Double lattice
Vierendeel
Design Data
PORTAL FRAMES
All fixed
2 pin
2 pin mansard
3 pin
ARCHES
Thrust
Tied
3 pin
SUSPENSION
Cable stay
Suspension
Closed suspension
WALLS Solid
Piers
Chevron
Diaphragm
TIMBER
Ply/ply stressed skin
Ply web
Ply/timber stressed skin
Flitched
RETAINING WALLS
Embedded
Cantilever
Gravity or reinforced earth
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Structural Engineer’s Pocket Book
Stability Stability of a structure must be achieved in two orthogonal directions. Circular structures should also be checked for rotational failure. The positions of movement and/or acoustic joints should be considered and each part of the structure should be designed to be independently stable and robust. Lateral loads can be transferred across the structure and/or down to the foundations by using any of the following methods:
. Cross bracing which carries the lateral forces as axial load in diagonal members. . Diaphragm action of floors or walls which carry the forces by panel/plate/shear action. . Frame action with ‘fixed’ connections between members and ‘pinned’ connections at the supports.
. Vertical cantilever columns with ‘fixed’ connections at the foundations. . Buttressing with diaphragm, chevron or fin walls. Stability members must be located on the plan so that their shear centre is aligned with the resultant of the overturning forces. If an eccentricity cannot be avoided, the stability members should be designed to resist the resulting torsion across the plan.
Robustness and disproportionate collapse All structural elements should be effectively tied together in each of the two orthogonal directions, both horizontally and vertically. This is generally achieved by specifying connections in steel buildings as being of certain minimum size, by ensuring that reinforced concrete junctions contain a minimum area of steel bars and by using steel straps to connect walls and floors in masonry structures. It is important to consider robustness requirements early in the design process. The Building Regulations require buildings of five or more storeys (excluding the roof) to be designed for disproportionate collapse. This is intended to ensure that accidental damage to elements of the building structure cannot cause the collapse of a disproportionately large area of a building. The disproportionate collapse requirement for public buildings with a roof span of more than 9 m appears to have been removed from the regulations. Typically the Building Regulations require that any collapse caused by the failure of a single structural element should be limited to an area of 70 m2 or 15% of any storey area (whichever is the lesser). Alternatively the designer can strengthen the structure to withstand the ‘failure’ of certain structural supports in order to prevent disproportionate collapse. In some circumstances the structure cannot be arranged to avoid the occurrence of ‘key elements’, which support disproportionately large areas of the building. These ‘key elements’ must be designed as protected members (to the code of practice for the relevant structural material) to provide extra robustness and damage resistance.
Design Data
29
Structural movement joints Joints should be provided to control temperature, moisture, acoustic and ground movements. Movement joints can be difficult to waterproof and detail and therefore should be kept to a minimum. The positions of movement joints should be considered for their effect on the overall stability of the structure.
Primary movement joints Primary movement joints are required to prevent cracking where buildings (or parts of buildings) are large, where a building spans different ground conditions, changes height considerably or where the shape suggests a point of natural weakness. Without detailed calculation, joints should be detailed to permit 15–25 mm movement. Advice on joint spacing for different building types can be variable and conflicting. The following figures are some approximate guidelines based on the building type:
Concrete
25 m (e.g. for roofs with large thermal differentials)– 50 m c /c.
Steel industrial buildings
100 m typical–150 m maximum c /c.
Steel commercial buildings
50 m typical–100 m maximum c /c.
Masonry
40 m–50 m c /c.
Secondary movement joints Secondary movement joints are used to divide structural elements into smaller elements to deal with the local effects of temperature and moisture content. Typical joint spacings are: Clay bricks
Up to 12 m c/c on plan (6 m from corners) and 9 m vertically or every three storeys if the building is greater than 12 m or four storeys tall.
Concrete blocks
3 m–7 m c/c.
Hardstanding
70 m c/c.
Steel roof sheeting
20 m c/c down the slope, no limit along the slope.
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Structural Engineer’s Pocket Book
Fire resistance periods for structural elements Fire resistance of structure is required to maintain structural integrity to allow time for the building to be evacuated. Generally, roofs do not require protection. Architects typically specify fire protection in consultation with the engineer. Building types
Minimum period of fire resistance minutes Basement storey including floor over
Ground or upper storey
Depth of a lowest basement
Height of top floor above ground, in a building or separated part of a building
>10 m <10 m >5 m
<18 m <30 m <120 m
301
602
902
301
301
603
n/a
60
301
60
90
1205
90 60
60 60
301 301
60 301
90 60
X 1205
not sprinklered sprinklered
90 60
60 60
60 301
60 60
90 60
X 1205
Assembly & recreation
not sprinklered sprinklered
90 60
60 60
60 301
60 60
90 60
X 1205
Industrial
not sprinklered 120 sprinklered 90
90 60
60 301
90 60
120 90
X 1205
Storage and other nonresidential
not sprinklered 120 sprinklered 90
90 60
60 301
90 60
120 90
X 1205
n/a 60
151 301
151 60
Residential flats and maisonettes
90
60
Residential houses
n/a
Institutional residential4
90
Office
not sprinklered sprinklered
Shops & commercial
Car park for open sided light vehicles all others
n/a 90
151 90
1202 n/a
60 1205
NOTES: X Not permitted 1. Increased to 60 minutes for compartment walls with other fire compartments or 30 minutes for elements protecting a means of escape. 2. Reduced to 30 minutes for a floor in a maisonette not contributing to the support of the building. 3. To be 30 minutes in the case of three storey houses and 60 minutes for compartment walls separating buildings. 4. NHS hospitals should have a minimum of 60 minutes. 5. Reduced to 90 minutes for non-structural elements. 6. Should comply with Building Regulations: B3 section 12.
Source: Building Regulations Approved Document B (1991).
Design Data
Typical building tolerances SPACE BETWEEN WALLS Brickwork ± 20 mm Blockwork ± 21 ± 32 Timber
Steel Timber
WALL VERTICALITY
COLUMN VERTICALITY
10 mm 10 17 11
Maximum
Steel 6 mm Timber 10 In situ concrete 12 Precast concrete 10
Maximum
VERTICAL POSITION OF BEAMS
Steel Timber In situ concrete Precast concrete
± 12 mm ± 12
In situ concrete ± 18 Precast concrete ± 13
In situ concrete ± 24 Precast concrete ± 18
Brickwork Blockwork In situ concrete Precast concrete
SPACE BETWEEN COLUMNS
± 20 mm ± 20 ± 22 ± 23
PLAN POSITION
VERTICAL POSITION OF FLOORS
In situ concrete ± 15 mm Precast concrete ± 15
FLATNESS OF FLOORS 3 m straight edge max
Brickwork Steel Timber In situ concrete Precast concrete Source: BS 5606: 1990.
± 10 mm ± 10 ± 10 ± 12 ± 10
In situ concrete Floor screed
5 mm 5
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Structural Engineer’s Pocket Book
Historical use of building materials
1714
1800
1837
1901
Post Wars
Inter Wars
Edwardian
Victorian
Georgian including William IV
Masonry and timber
1919
1945
MASONRY Bonding timbers Non hydraulic lime mortar 84
Mathematical tiles 50s
Hydraulic lime mortar
30s 90s
96
60s
Clinker concrete blocks 00s
Cavity walls
50
10
51
Pressed bricks
70s
Flettons
20
Concrete bricks
50s
Dense concrete blocks 20s
Sand line bricks
20s
Stretcher bond
40s
Mild steel cavity wall ties
45s
60s
Galvanised steel cavity wall ties
80s 65
Stainless steel cavity well ties
53 60s
Aerated concrete blocks
TIMBER Trussed timber girders
33
King + queen post trusses
50
92 50s
50
Wrought iron flitched beams Belfast trusses
10s
70 60
40s 50s
Trussed rafters
60s
Ply stressed skin pannels Mild steel flitched beams
Source: Richardson, C. (2000).
40s
80s
Design Data
33
1714
1800
1837
1901
1919
Post Wars
Inter Wars
Edwardian
Victorian
William IV
including
Georgian
Concrete and steel
1945
CONCRETE Limecrete/Roman cement
96
Jack arch floors
96
80s 62 24
Portland cement
51
30 30s
70s
Filler joists
80
Clinker concrete 54
RC framed buildings
30 97 20s
RC shells + arches
25
Hollow pot slabs 00s
Flat slabs
80
31 32
Lightweight concrete
50 50
Precast concrete floors Composite metal deck slabs
52
64
Woodwool permanent shutters
69
90s
Waffle/coffered stabs
60s
Composite steel + concrete floors with shear keys
70s
CAST IRON (CI) + WROUGHT IRON (WI) CI columns CI beams WI rods + flats WI roof trusses WI built up beams WI rolled sections
20s
92
30s
96
65 10s
80
37 40 50s 90s
‘Cast steel’ columns
10s
MILD STEEL 80
Plates + rods
90s
Riveted sections Hot rolled sections Roof trusses Steel framed buildings
60
83 90s 96
55
Welds
38
Castellated beams
50
High strength friction grip bolts (HSFG)
60
Hollow sections
13
STAINLESS STEEL Bolts, straps, lintels, shelf angles, etc.
Source: Richardson, C. (2000).
70s
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Structural Engineer’s Pocket Book
Typical weights of building materials Material
Aggregate Aluminium Aluminium bronze Asphalt Ballast Balsa wood Bituminous felt roofing Bitumen Blockboard Blockwork Books Brass Brickwork
Bronze Cast stone Cement Concrete
Coal Chalk Chipboard Chippings Clay Copper
Description
Cast alloy Longstrip roofing
Thickness/ quantity of unit
Unit load kN/m2
Bulk density kN/m3 16 27
0.8 mm
0.022 76
Roofing – 2 layers Paving
25 mm
0.58 21
see Gravel 1 3 layers and vapour barrier
0.11 11–13
Sheet Lightweight – dense On shelves Bulk Cast Blue Engineering Fletton London stock Sand lime Cast
18 mm
0.11 10–20 7 8–11 85 24 22 18 19 21 83 23 15 10 18 24 9 22 7
Aerated Lightweight aggregate Normal reinforced Loose lump
Flat roof finish Undisturbed Cast Longstrip roofing
1 layer
0.05 19 87
0.6 mm
0.05
Design Data
Cork Double decker bus Elephants Felt Glass Glass wool Gold Gravel Hardboard Hardcore Hardwood
Hollow clay pot slabs
Granulated see Vehicles Adult group Roofing underlay Insulating Crushed/refuse Clear float Quilt
1
50 mm
3.2 0.015 0.05
16 25 100 mm
0.01 194 16 21
Loose Undisturbed
Greenheart Oak Iroko, teak Mahogany Including ribs and mortar but excluding topping
6–8 19 10 8 7 6 12
300 mm thick overall
100 mm thick overall Iron Ivory Lead
Lime
Linoleum Macadam Magnesium MDF Mercury Mortar Mud Partitions
15
Cast Wrought Cast Sheet 1.8 mm Sheet 3.2 mm Hydrate (bags) Lump/quick (powder) Mortar (putty) Sheet 3.2 mm Paving Alloys Sheet
Plastered brick Medium dense plastered block Plaster board on timber stud
6
72 77 19 114 0.21 0.36 6 10 18 0.05 21 18 8 136 17–18 17–20
102 þ 2 13 mm 100 þ 2 13 mm
2.6 2.0
21 16
100 þ 2 13 mm
0.35
3
35
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Structural Engineer’s Pocket Book
Typical weights of building materials – continued Material
Description
Patent glazing Pavement lights Perspex Plaster
Single glazed Double glazed Cast iron or concrete framed Corrugated sheets Lightweight Wallboard and skim coat Lath and plaster Traditional lime plaster Sheet Expanded sheet
Plywood Polystyrene Potatoes Precast concrete planks
Quarry tiles
Roofing tiles
Sand Screed Shingle Slate Snow
Thickness/ quantity of unit
Unit load kN/m2
Bulk density kN/m3 25
100 mm
0.26–0.3 0.52 1.5
13 mm 13 mm
0.05 0.11 0.12
12 9
19 mm
0.25 20 7 2 7
Beam and block plus 50 mm topping Hollowcore plank Hollowcore plank Solid plank and 50 mm topping
150–225 mm
1.8–3.3
150 mm 200 mm 75–300 mm
2.4 2.7 3.7–7.4
Including mortar bedding Clay – plain Clay pantile Concrete Slate Dry, loose Wet, compact Sand/cement Coarse, graded, dry Slab Fresh Wet, compacted
12.5 mm
0.32
0.77 0.42 0.51 0.30
minimum 0.6 minimum 0.6
Softwood
Soils
Battens for slating and tiling 25 mm tongued and grooved boards on 100 50 timber joists at 400 c/c 25 mm tongued and grooved boards on 250 50 timber joists at 400 c/c Loose sand and gravels Dense sand and gravels Soft /firm clays and silts Stiff clays and silts
19 19 24 28 16 19 22 19 28 1 3 6
0.03 0.23
0.33
16 22 18 21
Design Data
Stainless steel roofing Steel Stone Granite Limestone
Marble Sandstone
Slate Terracotta Terrazzo Thatch Timber
Longstrip
0.4 mm
0.05
78
Mild
78
Cornish (Cornwall) Rublislaw (Grampian) Bath (Wiltshire) Mansfield (Nottinghamshire) Portland (Dorset) Italian Bramley Fell (West Yorkshire) Forest of Dean (Gloucestershire) Darley Dale or Kerridge (Derbyshire) Welsh
26 25 21 22 22 27 22 24 23–25 28
Paving Including battens see Hardwood or Softwood
20 mm 305 mm
Vehicles
London bus New Mini Cooper Rolls Royce Volvo estate
73.6 kN 11.4 kN 28.0 kN 17.8 kN
Water
Fresh Salt
0.43 0.45
Cast Longstrip roofing
18 22
10 10–12 6
Woodwool slabs Zinc
37
72 0.8 mm
0.06
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Structural Engineer’s Pocket Book
Minimum imposed floor loads The following table from BS 6399: Part 1 gives the normally accepted minimum floor loadings. Clients can consider sensible reductions in these loads if it will not compromise future flexibility. A survey by Arup found that office loadings very rarely even exceed the values quoted for domestic properties. The gross live load on columns and/or foundations from sections A to D in the table, can be reduced in relation to the number of floors or floor area carried to BS 6399: Part 1. Live load reductions are not permitted for loads from storage and/or plant, or where exact live loadings have been calculated. Type of activity/occupancy for part of the building or structure
Examples of specific use
UDL kN/m2
Point load kN
A Domestic and residential activities (also see category C )
All usages within self-contained dwelling units. Communal areas (including kitchens) in blocks of flats with limited use (see Note 1) (for communal areas in other blocks of flats, see C3 and below)
1.5
1.4
Bedrooms and dormitories except those in hotels and motels
1.5
1.8
Bedrooms in hotels and motels Hospital wards Toilet areas
2.0
1.8
Billiard rooms
2.0
2.7
Communal kitchens except in flats covered by Note 1
3.0
4.5
Balconies
Single dwelling units and communal areas in blocks of flats with limited use (see Note 1)
1.5
1.4
Guest houses, residential clubs and communal areas in blocks of flats except as covered by Note 1
Same as rooms to which they give access but with a minimum of 3.0
1.5/m run concentrated at the outer edge
Hotels and motels
Same as rooms to which they give access but with a minimum of 4.0
1.5/m run concentrated at the outer edge
B Offices and work areas not covered elsewhere
Operating theatres, X-ray rooms, utility rooms
2.0
4.5
Work rooms (light industrial) without storage
2.5
1.8
Offices for general use
2.5
2.7
Banking halls
3.0
2.7
Kitchens, laundries, laboratories
3.0
4.5
Rooms with mainframe computers or similar equipment
3.5
4.5
Machinery halls, circulation spaces therein
4.0
4.5
Projection rooms
5.0
Determine loads for specific use
Factories, workshops and similar buildings (general industrial)
5.0
4.5
Foundries
20.0
Determine loads for specific use
Catwalks
–
1.0 at 1 m c/c
Balconies
Same adjacent rooms but with a minimum of 4.0
1.5 kN/m run concentrated at the outer edge
Fly galleries (load to be distributed uniformly over width)
4.5 kN/m run
–
Ladders
–
1.5 rung load
Design Data C Areas where people may congregate
Public, institutional and communal dining rooms and lounges, cafes and restaurants (see Note 2)
C1 Areas with tables
Reading rooms with no book storage
2.5
4.5
Classrooms
3.0
2.7
Assembly areas with fixed seating (see Note 3)
4.0
3.6
Places of worship
3.0
2.7
Corridors, hallways, aisles, etc. (foot traffic only)
3.0
4.5
Stairs and landings (foot traffic only)
3.0
4.0
Corridors, hallways, aisles, etc. (foot traffic only)
4.0
4.5
Corridors, hallways, aisles, etc., subject to wheeled vehicles, trolleys, etc.
5.0
4.5
C2 Areas with fixed seats
C3 Areas without obstacles for moving people
Corridors, hallways, aisles, stairs, landings, etc. in institutional type buildings (not subject to crowds or wheeled vehicles), hostels, guest houses, residential clubs, and communal areas in blocks of flats not covered by Note 1. (For communal areas in blocks of flats covered by Note 1, see A) Corridors, hallways, aisles, stairs, landings, etc. in all other buildings including hotels and motels and institutional buildings
Stairs and landings (foot traffic only) Industrial walkways (light duty) Industrial walkways (general duty) Industrial walkways (heavy duty)
2.0
2.7
4.0
4.0
3.0 5.0 7.5
4.5 4.5 4.5
Museum floors and art galleries for exhibition purposes
4.0 (see Note 4)
4.5
Balconies (except as specified in A)
Same as adjacent rooms but with a minimum of 4.0
1.5/m run concentrated at the outer edge
Fly galleries
4.5 kN/m run distributed uniformly over width
–
C4 Areas with possible physical activities (see clause 9)
Dance halls and studios, gymnasia, stages
5.0
3.6
Drill halls and drill rooms
5.0
9.0
C5 Areas susceptible to overcrowding (see clause 9)
Assembly areas without fixed seating, concert halls, bars, places of worship and grandstands
5.0
3.6
Stages in public assembly areas
7.5
4.5
D Shopping areas
Shop floors for the sale and display of merchandise
4.0
3.6
39
40
Structural Engineer’s Pocket Book
Minimum imposed floor loads – continued Type of activity/ occupancy for part of the building or structure
Examples of specific use
UDL kN/m2
Point load kN
E Warehousing and storage areas. Areas subject to accumulation of goods. Areas for equipment and plant
General areas for static equipment not specified elsewhere (institutional and public buildings)
2.0
1.8
Reading rooms with book storage, e.g. libraries
4.0
4.5
General storage other than those specified
2.4 per metre of storage height
7.0
File rooms, filing and storage space (offices)
5.0
4.5
F
G
Stack rooms (books)
2.4 per metre of storage height (6.5 kN/m2 min)
7.0
Paper storage for printing plants and stationery stores
4.0 per metre of storage height
9.0
Dense mobile stacking (books) on mobile trolleys, in public and institutional buildings
4.8 per metre of storage height (9.6 kN/m2 min)
7.0
Dense mobile stacking (books) on mobile trucks, in warehouses Cold storage
4.8 per metre of storage height (15 kN/m2 min) 5.0 per metre of storage height (15 kN/m2 min)
7.0
Plant rooms, boiler rooms, fan rooms, etc., including weight of machinery
7.5
4.5
Ladders
–
1.5 rung load
Parking for cars, light vans, etc. not exceeding 2500 kg gross mass, including garages, driveways and ramps
2.5
9.0
Vehicles exceeding 2500 kg. Driveways, ramps, repair workshops, footpaths with vehicle access, and car parking
To be determined for specific use
9.0
NOTES: 1. Communal areas in blocks of flats with limited use refers to blocks of flats not more than three storeys in height and with not more than four selfcontained dwelling units per floor accessible from one staircase. 2. Where these same areas may be subjected to loads due to physical activities or overcrowding, e.g. a hotel dining room used as a dance floor, imposed loads should be based on occupancy C4 or C% as appropriate. Reference should also be made to Clause 9. 3. Fixed seating is seating where its removal and use of the space for other purposes is improbable. 4. Museums, galleries and exhibition spaces often need more capacity than this, sometimes up to 10 kN/m2.
Source: BS 6399: Part 1: 1996.
Design Data
41
Typical unit floor and roof loadings Permanent partitions shown on the floor plans should be considered as dead load. Flexible partitions which may be movable should be allowed for in imposed loads, with a minimum of 1 kN/m2. 1.5/2.5 kN/m2 (1.0) 0.15 0.2 0.15 Domestic/ 2.0/4.0 kN/m2 office totals
Timber floor
Live loading: domestic/office (Office partitions) Timber boards/plywood Timber joists Ceiling and services
Timber flat roof
Snow and access Asphalt waterproofing Timber joists and insulation Ceiling and services
0.75 kN/m2 0.45 0.2 0.15 Total 1.55 kN/m2
Timber pitched roof
Snow Slates, timber battens and felt Timber rafters and insulation Ceiling and services
0.6 kN/m2 0.55 0.2 0.15 Total 1.5 kN/m2
Internal RC slab
Live loading: office/ classroom/corridors, etc. Partitions 50 screed/75 screed/raised floor Solid reinforced concrete slab Ceiling and services
t
External RC slab
t
Metal deck roofing
Live loading: snow and access/office/bar Slabs/paving Asphalt waterproofing and insulation 50 screed Solid reinforced concrete slab Ceiling and services
Live loading: snow/wind uplift Outer covering, insulation and metal deck liner Purlins – 150 deep at 1.5 m c/c Services Primary steelwork: light beams/trusses
2.5/3.0/4.0 kN/m2 1.0 (minimum) 1.2/1.8/0.4 24t 0.15 Total – kN/m2 0.75/2.5/5.0 kN/m2 0.95 0.45 1.2 24t 0.15 Total – kN/m2 0.6/1.0 kN/m2 0.4 0.3 0.1 0.5–0.8/0.7–2.4 Total – kN/m2
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Structural Engineer’s Pocket Book
Typical ‘all up’ loads For very rough assessments of the loads on foundations, ‘all up’ loads can be useful. The best way is to ‘weigh’ the particular building, but very general values for small-scale buildings might be: Steel clad steel frame
5–10 kN /m2
Masonry clad timber frame
10–15 kN/m2
Masonry walls and precast concrete floor slabs
15–20 kN/m2
Masonry clad steel frame
15–20 kN/m2
Masonry clad concrete frame
20–25 kN/m2
Design Data
43
Wind loading BS 6399: Part 2 gives methods for determining the peak gust wind loads on buildings and their components. Structures susceptible to dynamic excitation fall outside the scope of the guidelines. While BS 6399 in theory allows for a very site-specific study of the many design parameters, it does mean that grossly conservative values can be calculated if the ‘path of least resistance’ is taken through the code. Unless the engineer is prepared to work hard and has a preferred ‘end result’ to aim for, the values from BS 6399 tend to be larger than those obtained from the now withdrawn wind code CP3: Chapter V: Part 2. As wind loading relates to the size and shape of the building, the size and spacing of surrounding structures, altitude and proximity to the sea or open stretches of country, it is difficult to summarize the design methods. The following dynamic pressure values have been calculated (on a whole building basis) for an imaginary building 20 m 20 m in plan and 10 m tall (with equal exposure conditions and no dominant openings) in different UK locations. The following values should not be taken as prescriptive, but as an idea of an ‘end result’ to aim for. Taller structures will tend to have slightly higher values and where buildings are close together, funnelling should be considered. Small buildings located near the bases of significantly taller buildings are unlikely to be sheltered as the wind speeds around the bases of tall buildings tends to increase.
Typical values of dynamic pressure, q in kN/m2 Building location
Maximum q for prevailing south westerly wind kN/m2
Minimum q for north easterly wind kN/m2
Arithmetic mean q kN/m2
Scottish mountain-top Dover cliff-top Rural Scotland Coastal Scottish town City of London high rise Rural northern England Suburban South-East England Urban Northern Ireland Rural Northern Ireland Rural upland Wales Coastal Welsh town Conservative quick scheme value for most UK buildings
3.40 1.69 1.14 1.07 1.03 1.02 0.53 0.88 0.83 1.37 0.94 –
1.81 0.90 0.61 0.57 0.55 0.54 0.28 0.56 0.54 0.72 0.40 –
2.60 1.30 0.87 0.82 0.80 0.78 0.45 0.72 0.74 1.05 0.67 1.20
NOTE: These are typical values which do not account for specific exposure or topographical conditions.
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Structural Engineer’s Pocket Book
Barrier and handrail loadings Minimum horizontal imposed loads for barriers, parapets, and balustrades, etc. Type of occupancy for part of the building or structure
Examples of specific use
Line load kN/m
UDL on infill kN/m2
Point load on infill kN
A Domestic and residential activities
(a) All areas within or serving exclusively one dwelling including stairs, landings, etc. but excluding external balconies and edges of roofs (see C3 ix)
0.36
0.5
0.25
(b) Other residential (but also see C)
0.74
1.0
0.5
(c) Light access stairs and gangways not more than 600 mm wide
0.22
n/a
n/a
(d) Light pedestrian traffic routes in industrial and storage buildings except designated escape routes
0.36
0.5
0.25
(e) Areas not susceptible to overcrowding in office and institutional buildings. Also industrial and storage buildings except as given above
0.74
1.0
0.5
C Areas where people may congregate: C1/C2 areas with tables or fixed seating
(f) Areas having fixed seating within 530 mm of the barrier, balustrade or parapet
1.5
1.5
1.5
(g) Restaurants and bars
1.5
1.5
1.5
C3 Areas without obstacles for moving people and not susceptible to overcrowding
(h) Stairs, landings, corridors, ramps
0.74
1.0
0.5
(i) External balconies and edges of roofs. Footways and pavements within building curtilage adjacent to basement/sunken areas
0.74
1.0
0.5
C5 Areas susceptible to overcrowding
(j) Footways or pavements less than 3 m wide adjacent to sunken areas
1.5
1.5
1.5
(k) Theatres, cinemas, discotheques, bars, auditoria, shopping malls, assembly areas, studios. Footways or pavements greater than 3 m wide adjacent to sunken areas
3.0
1.5
1.5
B and E Offices and work areas not included elsewhere including storage areas
(l) Designated stadia*
See requirements of the appropriate certifying authority
D Retail areas
(m) All retail areas including public areas of banks/building societies or betting shops. For areas where overcrowding may occur, see C5
1.5
1.5
1.5
F/G Vehicular
(n) Pedestrian areas in car parks including stairs, landings, ramps, edges or internal floors, footways, edges of roofs
1.5
1.5
1.5
(o) Horizontal loads imposed by vehicles
See clause 11. (Generally F 5 150 kN)
* Designated stadia are those requiring a safety certificate under the Safety of Sports Ground Act 1975
Source: BS 6399: Part 1: 1996.
Design Data
45
Minimum barrier heights Use
Position
Single family dwelling
(a) Barriers in front of a window (b) Stairs, landings, ramps, edges of internal floors (c) External balconies, edges of roofs
All other uses
(d) Barrier in front of a window (e) Stairs (f) Balconies and stands, etc. having fixed seating within 530 mm of the barrier (g) Other positions
*Site lines should be considered as set out in clause 6.8 of BS 6180.
Source: BS 6180: 1999.
Height mm 800 900 1100 800 900 800* 1100
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Structural Engineer’s Pocket Book
Selection of materials Material
Advantage
Disadvantage
Aluminium
Good strength to dead weight ratio for long spans Good corrosion resistance Often from recycled sources
Cannot be used where stiffness is critical Stiffness is a third of that of steel About two to three times the price of steel
Concrete
Design is tolerant to small, late alterations Integral fire protection Integral corrosion protection Provides thermal mass if left exposed Client pays as the site work progresses: ‘pay as you pour’
Dead load limits scope Greater foundation costs Greater drawing office and detailing costs Only precasting can accelerate site work Difficult to post-strengthen elements Fair faced finish needs very skilled contractors and carefully designed joints
Masonry
Steelwork
Provides thermal mass The structure is also the cladding Can be decorative by using a varied selection of bricks Economical for low rise buildings Inherent sound, fire and thermal properties Easy repair and maintenance Light construction reduces foundation costs Intolerant to late design changes Fast site programme Members can be strengthened easily Ideal for long spans and transfer structures
Timber
Traditional/low-tech option Sustainable material Cheap and quick with simple connections Skilled labour not an absolute requirement Easily handled
Skilled site labour required Long construction period Less economical for high rise Large openings can be difficult Regular movements joints Uniform appearance can be difficult to achieve Design needs to be fixed early Needs applied insulation, fire protection and corrosion protection Skilled workforce required Early financial commitment required from client to order construction materials Long lead-ins Vibrations can govern design Limited to 4–5 storeys maximum construction height Requires fire protection Not good for sound insulation Must be protected against insects and moisture Connections can carry relatively small loads
Selection of floor construction 800
5
700
6
Depth (m)
600
11
500
2
400 1
300
9 8
7 3
200 100 0
4 10 2
4
6
8
10
12
14
16
18
20
Span (m) Timber joists at 400 c/c Stressed skin ply panel One way reinforced concrete slab Precast prestressed concrete plank Precast double tee beams Coffered concrete slab
7. 8. 9. 10. 11.
Beam + block floor Reinforced concrete flat slab Post tensioned flat slab Concrete metal deck slab Composite steel beams 47
1. 2. 3. 4. 5. 6.
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Structural Engineer’s Pocket Book
Transportation Although the transport of components is not usually the final responsibility of the design engineer, it is important to consider the limitations of the available modes of transport early in the design process using Department for Transport (DfT) information. Specific cargo handlers should be consulted for comment on sea and air transport, but a typical shipping container is 2.4 m wide, 2.4–2.9 m high and can be 6 m, 9 m, 12 m or 13.7 m in length. Transportation of items which are likely to exceed 20 m by 4 m should be very carefully investigated. Private estates may have additional and more onerous limitations on deliveries and transportation. Typical road and rail limitations are listed below as the most common form of UK transport, but the relevant authorities should be contacted to confirm the requirements for specific projects.
Rail transportation Railtrack can carry freight in shipping containers or on flat bed wagons. The maximum load on a four axle flat wagon is 66 tonnes. The maximum height of a load is 3.9 m above the rails and wagons are generally between 1.4 and 1.8 m high. All special requirements should be discussed with Railtrack Freight or Network Rail.
Road transport The four main elements of legislation which cover the statutory controls on length, width, marking, lighting and police notification for large loads are the Motor Vehicles (Construction & Use) Regulations 1986; the Motor Vehicles (Authorization of Special Types) General Order 1979, the Road Vehicles Lighting Regulations 1989 and the Road Traffic Act 1972. A summary of the requirements is set out below.
Height of load There is no statutory limit governing the overall height of a load; however, where possible it should not exceed 4.95 m from the road surface to maximize use of the motorway and trunk road network (where the average truck flat bed is about 1.7 m). Local highway authorities should be contacted for guidance on proposed routes avoiding head height restrictions on minor roads for heights exceeding 3.0 m–3.6 m.
Weight of vehicle or load Gross weight of vehicle, W kg
Notification requirements
44 000 < W 80 000 or has any axle weight greater than permitted by the Construction & Use Regulations
2 days’ clear notice with indemnity to the Highway and Bridge Authorities
80 000 < W 150 000
2 days’ clear notice to the police and 5 days’ clear notice with Indemnity to the Highway and Bridge Authorities
W > 150 000
DfT Special Order BE16 (allow 10 weeks for application processing) plus 5 days’ clear notice to the police and 5 days’ clear notice with indemnity to the Highway and Bridge Authorities
Design Data
49
Width of load Total loaded width*, B m
Notification requirements
B 2.9
No requirement to notify police
2.9 < B 5.0
2 days’ clear notice to police
5.0 < B 6.1
DfT permission VR1 (allow 10 days for application processing) and 2 days’ clear notice to police
B > 6.1
DfT Special Order BE16 (allow 8 weeks for application processing) and 5 days’ clear notice to police and 5 days’ clear notice with indemnity to Highway and Bridge Authorities
* A load may project over one or both sides by up to 0.305 m, but the overall width is still limited as above.
Loads with a width of over 2.9 m or with loads projecting more than 0.305 m on either side of the vehicle must be marked to comply with the requirements of the Road Vehicles Lighting Regulations 1989.
Length of load Total loaded length, L m
Notification requirements
L < 18.75
No requirement to notify police
18.75 L <27.4
Rigid or articulated vehicles*. 2 days’ clear notice to police
(rigid vehicle) L > 27.4
DfT Special Order BE16 (allow 8 weeks for application processing) and 5 days’ clear notice to police and 5 days’ clear notice with indemnity to Highway and Bridge Authorities
(all other trailers) L > 25.9
All other trailer combinations carrying the load. 2 days’ clear notice to police
* The length of the front of an articulated motor vehicle is excluded if the load does not project over the front of the motor vehicle.
Projection of overhanging loads Overhang position
Overhang length, L m
Rear
L < 1.0
No special requirement
1.0 < L < 2.0
Load must be made clearly visible
2.0 < L < 3.05
Standard end marker boards are required
L > 3.05
Standard end marker boards are required plus police notification and an attendant is required
Front
Notification requirements
L < 1.83
No special requirement
2.0 < L < 3.05
Standard end marker boards are required plus the driver is required to be accompanied by an attendant
L > 3.05
Standard end marker boards are required plus police notification and the driver is required to be accompanied by an attendant
50
Typical vehicle sizes and weights Vehicle type
Weight, W kg
3.5 tonne van
3500
7.5 tonne van
Length, L m
Width, B m
Height, H m
Turning circle m
5.5
2.1
2.6
13.0
7500
6.7
2.5
3.2
14.5
Single decker bus
16 260
11.6
2.5
3.0
20.0
Refuse truck
16 260
8.0
2.4
3.4
17.0
2 axle tipper
16 260
6.4
2.5
2.6
15.0
Van (up to 16.3 tonnes)
16 260
8.1
2.5
3.6
17.5
Skiploader
16 260
6.5
2.5
3.7
14.0
Fire engine
16 260
7.0
2.4
3.4
15.0
Bendy bus
17 500
18.0
2.6
3.1
23.0
51
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Structural Engineer’s Pocket Book
Temporary works toolkit Steel trench prop load capacities Better known as ‘Acrow’ props, these adjustable props should conform to BS 4704 or BS EN 1065. Verticality of the loads greatly affects the prop capacity and fork heads can be used to eliminate eccentricities. Props exhibiting any of the following defects should not be used:
. . . . .
A tube with a bend, crease or noticeable lack of straightness. A tube with more than superficial corrosion. A bent head or base plate. An incorrect or damaged pin. A pin not properly attached to the prop by the correct chain or wire.
Steel trench ‘acrow’ prop sizes and reference numbers to BS 4074 Prop size/reference*
0 1 2 3 4
Height range Minimum m
Maximum m
1.07 1.75 1.98 2.59 3.20
1.82 3.12 3.35 3.96 4.87
*The props are normally identified by their length.
Steel trench prop load capacities A prop will carry its maximum safe load when it is plumb and concentrically loaded as shown in the charts in BS 4074. A reduced safe working load should be used for concentric loading with an eccentricity, e 1.5 out of plumb as follows:
Capacity of props with e 1.5 (KN) Height m
£2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75
Prop size 0, 1, 2 and 3
17
16
13
11
10
–
–
–
–
Prop size 4
–
–
17
14
11
10
9
8
7
53
Design Data
Soldiers Slim soldiers, also known as slimshors, can be used horizontally and vertically and have more load capacity than steel trench props. Lengths of 0.36 m, 0.54 m, 0.72 m, 0.9 m, 1.8 m, 2.7 m or 3.6 m are available. Longer units can be made by joining smaller sections together. A connection between units with four M12 bolts will have a working moment capacity of about 12 kNm, which can be increased to 20 kNm if stiffeners are used.
Slimshor section properties Area cm2
Ixx cm4
Iyy cm4
Zxx cm3
Zyy cm3
rx cm
ry cm
Mmax kNm
19.64
1916
658
161
61
9.69
5.70
38
x
Slimshor compression capacity m 5m =2 m , e 8m xis = 3 xa ,e xxis xa x-
m 5m =2 m , e 8m xis = 3 ya ,e yxis ya y-
Allowable load (kN)
150 140 120 100 80 60 40 20 0 2
4
6
8
10
Allowable bending moment (kNm)
Effective length (m) e = eccentricity of load Factor of safety = 2.0
50 40 30 Use hi-load waler plate
20 10 0 20
40
60
80
100
120
140
160
Allowable axial load (kN) Factor of safety = 1.8
Mmax kNm 7.5
y
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Structural Engineer’s Pocket Book
Slimshor moment capacity Source: RMD Kwikform (2002).
Ladder beams Used to span horizontally in scaffolding or platforms, ladder beams are made in 48.3f 3.2 CHS, 305 mm deep, with rungs at 305 mm centres. All junctions are saddle welded. Ladder beams can be fully integrated with scaffold fittings. Bracing of both the top and bottom chords is required to prevent buckling. Standard lengths are 3.353 m (110 ), 4.877 m (160 ) and 6.400 m (210 ). Manufacturers should be contacted for loading information. However, if the tension chord is tied at 1.5 m centres and the compression chord is braced at 1.8 m centres the moment capacity for working loads is about 8.5 kNm. If the compression chord bracing is reduced to 1.5 m centres, the moment capacity will be increased to about 12.5 kNm. The maximum allowable shear is about 12 kN.
Unit beams Unit beams are normally about 615 mm deep, are about 2Z.5 times stronger than ladder beams and are arranged in a similar way to a warren girder. Loads should only be applied at the node points. May be used to span between scaffolding towers or as a framework for temporary buildings. As with ladder beams, bracing of both the top and bottom chords is required to prevent buckling, but diagonal plan bracing should be provided to the compression flange. Units can be joined together with M24 bolts to make longer length beams. Standard lengths are 1.8 m (60 ), 2.7 m (90 ) and 3.6 m (120 ) Manufacturers should be contacted for loading information. However, if the tension chord is tied at 3.6 m centres and the compression chord is braced at 2.4 m centres the moment capacity for working loads is about 13.5 kNm. If the compression bracing is reduced to 1.2 m centres, the moment capacity will be increased to about 27.5 kNm. The maximum allowable shear is about 14 kN.
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t
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1.3 d = 125 (mm) d = 150 d = 175 d = 200 d = 225 d = 250 d = 300 d = 400
Shear capacity,Vc (N/mm2)
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3
0
0.5
1.0
1.5
2.0 2.5 100As % bd
3.0
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2.0
Modification factor for tension reinforcement F2
1.9 1.8 1.7
M = 0.5 bd 2
1.6 1.5
0.75
1.4
1.0
1.3 1.2
1.5
1.1
2.0
1.0 3.0
0.9
4.0 5.0 6.0
0.8 100
120
140
160
180
200
Service stress, fs =
2fyAs req 3As prov
220
(N/mm2)
240
260
280
Modification factor for compression reinforcement, F3
1.6
1.5
1.4
1.3
1.2
1.1
1.0 0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
100As′ bd
# >
#
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$
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$
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$ = } "##=' ` #' #
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KU
M FU = Me
KL + KU + 0.5KB
KU
W kN/m
M FL = Me
Total factored load WT kN/m
Unfactored dead load WD kN/m KB1
KB KL
KU
KL KL + KU + 0.5KB
KU M FU = Mes KL + KU + 0.5K1 + 0.5K2
KB2 KL
KL M FL = Mes KL + KU + 0.5K1 + 0.5K2
Stiffness, k = I L Me = Fixed end beam moment Mes =Total out of balance fixed end moment
#
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1.8 e
1.6
b
h = 20
d = 0.95 h Asc 2
1.4 1. pf y =u Fc
1.2
Bars included in calculating Asc
h d
Bars excluded
Asc
4
2
p=
Asc bh
2
1. 0
1. 0.
N bhFcu
1.0 8
0.8
6
0.
0.6 4
0. 2
0.
0.4 0
0.
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0.2
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0.4
0.5
0.6
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1.6
b
h = 20
d = 0.85 h Asc 2
1.4
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1.2
Bars excluded Asc 2
=
cu
pf y
F
Bars included in calculating Asc
p=
Asc bh
2
1. 0
1.
1.0 N bhFcu 0.8
8
0. 6
0. 4
0.
0.6 2
0.
0.4 0
0.
0.2 Design as a beam 0
0.1
0.2
0.3
0.4 m bh 2Fcu
$ = %==%
0.5
0.6
0.7
1.8
b
h = 0 e 2
1.6 1.4
Bars included in calculating Asc Bars excluded
h d Asc 2
1.2 pf y
p=
Asc bh
=
u
Fc
4
1.
1.0
2
1. 1.
0.8
0
N bhFcu
d = 0.75 h
Asc 2
8
0. 6
0. 4
0.
0.6 0
0.
2
0.
0.4 0.2
Design as a beam 0
0.1
0.3
0.4 m bh 2Fcu
0.5
0.6
#
$ = %==%
0.2
%==
Q `[ }[
e= h 20
1.4 1.2
hs = 0.9 h
h hs
pf
1.0
F
y =1 cu
p=
1. 1. 2 0 0. 8
0.8 0.6
0. 4
6
0.
0.
0.4
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N bhFcu
0.
2
0
0.2 Design as a beam 0
0.1
0.2
0.3 M bh2Fcu
$ = %==%
0.4
4Asc πh 2
\
1.4 e h = 20
1.2
hs = 0.8 h
h hs
pf y
1.0
p=
=
u
4
1.
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0
6
8
0.
0. 4
0.
0.
0.4
2
1.
1.
N 0.8 bhFcu 0.6
2
0 0.
0.2
Design as a beam 0
0.1
0.2
0.3 M bh2Fcu
$ = %==%
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4Asc πh 2
%=#
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1.4 1.2
u
4 1.
1. 2 0 8
=
Fc 1.
p=
0. 4
0.
6
0.
0.
0.4
hs
pf y
1.0 0.8 N bhFcu 0.6
hs = 0.7 h
h
0.
2
0
0.2 Design as a beam 0
0.1
0.2
0.3 M bhFcu
$ = %==%
0.4
4Asc πh 2
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R
A A
(B ) L = A + (B ) – r/ – d 2
L=A (C)
(B ) L = A + (B ) – R/ – d 2
A B
A L = A + 0.57B + (C ) – 1.57 d A
A
B
(C )
L = A + (C ) B
B
C
A
(E)
C L = A + B + C + (D ) – 3r/ – 3d 2
A L = A + B + (C )
(C)
A B
A
D B
C L = A + B + C + D + (E ) – 2r – 4d C
E B D
C L = A + 2B + C + (E )
A
B
D
C L = A + B + C + D + (E ) – 2r – 4d A
D
B
L = 2 (A + B + C ) – 5r – 5d /2
C = no. of turns
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E
(E )
B
A L = Cπ(A-d)
(D)
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D
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B L = A + B + (C ) – r – 2D
(C )
D
L = 2A + 3B + 17d A B D
A
L=A
R
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9 Structural Steel The method of heating iron ore in a charcoal fire determines the amount of carbon in the iron alloy. The following three iron ore products contain differing amounts of carbon: cast iron, wrought iron and steel. Cast iron involves the heat treatment of iron castings and was developed as part of the industrial revolution between 1800 and 1900. It has a high carbon content and is therefore quite brittle which means that it has a much greater strength in compression than in tension. Typical allowable working stresses were 23 N/mm2 tension, 123 N/mm2 compression and 30 N/mm2 shear. Wrought iron has relatively uniform properties and, between the 1840s and 1900, wrought iron took over from cast iron for structural use, until it was in turn superseded by mild steel. Typical allowable working stresses were 81 N/mm2 tension, 61 N/mm2 compression and 77 N/mm2 shear. ’Steel’ can cover many different alloys of iron, carbon and other alloying elements to alter the properties of the alloys. The steel can be formed into structural sections by casting, hot rolling or cold rolling. Mild steel which is now mostly used for structural work was first introduced in the mid-nineteenth century.
Types of steel products Cast steel Castings are generally used for complex or non-standard structural components. The casting shape and moulding process must be carefully controlled to limit residual stresses. Sand casting is a very common method, but the lost wax method is generally used where a very fine surface finish is required.
Cold rolled Cold rolling is commonly used for lightweight sections, such as purlins and wind posts, etc. Work hardening and residual stresses caused by the cold working cause an increase in the yield strength but this is at the expense of ductility and toughness. Cold rolled steel cannot be designed using the same method as hot rolled steel and design methods are given in BS 5950: Part 5.
Hot rolled steel Most steel in the UK is produced by continuous casting where ingots or slabs are pre-heated to about 1300 C and the working temperatures fall as processing continues through the intermediate stages. The total amount of rolling work and the finishing temperatures are controlled to keep the steel grain size fine – which gives a good combination of strength and toughness. Although hollow sections (RHS, CHS and SHS) are often cold bent into shape, they tend to be hot finished and are considered ‘hot rolled’ for design purposes. This pocket book deals only with hot rolled steel.
Structural Steel
Summary of hot rolled steel material properties Density
78.5 kN/m3
Tensile strength
275–460 N/mm2 yield stress and 430–550 N /mm2 ultimate strength
Poisson’s ratio
0.3
Modulus of elasticity, E
205 kN/mm2
Modulus of rigidity, G
80 kN/mm2
Linear coefficient of thermal expansion
12 106/ C
209
210
Structural Engineer’s Pocket Book
Mild steel section sizes and tolerances Fabrication tolerances BS 4 covers the dimensions of many of the hot rolled sections produced by Corus. Selected rolling tolerances for different sections are covered by the following standards: UB and UC sections: BS EN 10034 Section height (mm)
h 180
180 < h 400
400 < h 700
700 < h
Tolerance (mm)
þ3/2
þ4/2
þ5/3
5
Flange width (mm)
b 110
110 < b 210
210 < b 325
325 < b
Tolerance (mm)
þ4/1
þ4/ 2
4
þ6/5
Out of squareness for flange width (mm)
b 110
110 < b
Tolerance (mm)
1.5
2% of b up to max 6.5 mm
Straightness for section height (mm)
80 < h 180
180 < h 360
360 < h
Tolerance on section length (mm)
0.003L
0.0015L
0.001L
RSA sections: BS EN 10056–2 Leg length (mm)
h 50
50 < h 100
100 < h 150
150 < h 200
200 h
Tolerance (mm)
1
2
3
4
þ6/4
Straightness for section height
h 150
h 200
200 < h
Tolerance along section length (mm)
0.004L
0.002L
0.001L
PFC sections: BS EN 10279 Section height (mm)
h 65
65 < h 200
200 < h 400
400 < h
Tolerance (mm)
1.5
2
3
4
Out of squareness for flange width
b 100
100 < b
Tolerance (mm)
1.5
2.5% of b
Straightness for section height
h 150
150 < h 300
300 < h
Tolerance along section length (mm)
0.005L
0.003L
0.002L
Hot finished RHS, SHS and CHS sections: BS EN 10210 Straightness:
0.2%L
Depth, breadth of diameter:
1% (min 0.5 mm and max 10 mm)
Squareness of side for SHS and RHS:
90 1
Twist for SHS and RHS:
2 mm þ 0.5 mm per m maximum
Structural Steel
211
Examples of minimum bend radii for selected steel sections The minimum radius to which any section can be curved depends on its metallurgical properties, particularly its ductility, cross sectional geometry and end use (the latter determines the standard required for the appearance of the work). It is therefore not realistic to provide a definitive list of the radii to which every section can be curved due to the wide number of end uses, but a selection of examples is possible. Normal bending tolerances are about 8 mm on the radius. In cold rolling the steel is deformed in the yield stress range and therefore becomes work hardened and displays different mechanical properties (notably a loss of ductility). However, if the section is designed to be working in the elastic range there is generally no significant difference to its performance.
Section
Typical bend radius for S275 steel m
610 305 UB 238 533 210 UB 122 305 165 UB 40 250 150 12.5 RHS 305 305 UC 118 300 100 PFC 46 150 150 12.5 SHS 254 203 RSJ 82 191 229 TEE 49 152 152 UC 37 125 65 PFC 15 152 127 RSJ 37
40.0 30.0 15.0 9.0 5.5 4.6 3.0 2.4 1.5 1.5 1.0 0.8
Source: Angle Ring Company Limited (2002).
212
Structural Engineer’s Pocket Book
Hot rolled section tables Universal beams – dimensions and properties
UB designation
Mass Depth Width Thickness Root Depth Ratios for Second moment h/t per of of radius between local buckling of area better metre section section fillets known Flange Web Axis x–x Axis y–y in Web Flange BS449 as h b s t r d b/2t d/s Ix Iy D/T kg/m
mm
mm
mm
mm
mm
mm
y
486.6 436.9 392.7 349.4 314.3 272.3 248.7 222
1036.1 1025.9 1016 1008.1 1000 990.1 980.2 970.3
308.5 305.4 303 302 300 300 300 300
30 26.9 24.4 21.1 19.1 16.5 16.5 16
54.1 49 43.9 40 35.9 31 26 21.1
30 30 30 30 30 30 30 30
867.9 867.9 868.2 868.1 868.2 868.1 868.2 868.1
2.85 3.12 3.45 3.77 4.18 4.84 5.77 7.11
28.9 32.3 35.6 41.1 45.5 52.6 52.6 54.3
914 419 388 914 419 343
388 343.3
921 911.8
420.5 418.5
21.4 19.4
36.6 32
24.1 24.1
799.6 799.6
5.74 6.54
914 305 289 914 305 253 914 305 224 914 305 201
289.1 253.4 224.2 200.9
926.6 918.4 910.4 903
307.7 305.5 304.1 303.3
19.5 17.3 15.9 15.1
32 27.9 23.9 20.2
19.1 19.1 19.1 19.1
824.4 824.4 824.4 824.4
838 292 226 838 292 194 838 292 176
226.5 193.8 175.9
850.9 840.7 834.9
293.8 292.4 291.7
16.1 14.7 14
26.8 21.7 18.8
17.8 17.8 17.8
762 267 197 762 267 173 762 267 147 762 267 134
196.8 173 146.9 133.9
769.8 762.2 754 750
268 266.7 265.2 264.4
15.6 14.3 12.8 12
25.4 21.6 17.5 15.5
686 254 170 686 254 152 686 254 140 686 254 125
170.2 152.4 140.1 125.2
692.9 687.5 683.5 677.9
255.8 254.5 253.7 253
14.5 13.2 12.4 11.7
610 305 238 610 305 179 610 305 149
238.1 179 149.2
635.8 620.2 612.4
311.4 307.1 304.8
610 229 140 610 229 125 610 229 113 610 229 101
139.9 125.1 113 101.2
617.2 612.2 607.6 602.6
533 210 122 533 210 109 533 210 101 533 210 92 533 210 82
122 109 101 92.14 82.2
457 191 98 457 191 89 457 191 82 457 191 74 457 191 67
98.3 89.3 82 74.3 67.1
y y y y y y y
1016 305 487 1016 305 437 1016 305 393 1016 305 349 1016 305 314 1016 305 272 1016 305 249 1016 305 222
cm4
cm4
cm
1021400 909900 807700 723100 644200 554000 481300 408000
26720 23450 20500 18460 16230 14000 11750 9546
19 21 23 25 28 32 38 46
37.4 41.2
719600 45440 625800 39160
25 28
4.81 5.47 6.36 7.51
42.3 47.7 51.8 54.6
504200 15600 436300 13300 376400 11240 325300 9423
29 33 38 45
761.7 761.7 761.7
5.48 6.74 7.76
47.3 51.8 54.4
339700 11360 279200 9066 246000 7799
32 39 44
16.5 16.5 16.5 16.5
686 686 686 686
5.28 6.17 7.58 8.53
44 48 53.6 57.2
240000 205300 168500 150700
8175 6850 5455 4788
30 35 43 48
23.7 21 19 16.2
15.2 15.2 15.2 15.2
615.1 615.1 615.1 615.1
5.4 6.06 6.68 7.81
42.4 46.6 49.6 52.6
170300 150400 136300 118000
6630 5784 5183 4383
29 33 36 42
18.4 14.1 11.8
31.4 23.6 19.7
16.5 16.5 16.5
540 540 540
4.96 6.51 7.74
29.3 38.3 45.8
209500 15840 153000 11410 125900 9308
20 26 31
230.2 229 228.2 227.6
13.1 11.9 11.1 10.5
22.1 19.6 17.3 14.8
12.7 12.7 12.7 12.7
547.6 547.6 547.6 547.6
5.21 5.84 6.6 7.69
41.8 46 49.3 52.2
111800 98610 87320 75780
4505 3932 3434 2915
28 31 35 41
544.5 539.5 536.7 533.1 528.3
211.9 210.8 210 209.3 208.8
12.7 11.6 10.8 10.1 9.6
21.3 18.8 17.4 15.6 13.2
12.7 12.7 12.7 12.7 12.7
476.5 476.5 476.5 476.5 476.5
4.97 5.61 6.03 6.71 7.91
37.5 41.1 44.1 47.2 49.6
76040 66820 61520 55230 47540
3388 2943 2692 2389 2007
26 29 31 34 40
467.2 463.4 460 457 453.4
192.8 191.9 191.3 190.4 189.9
11.4 10.5 9.9 9 8.5
19.6 17.7 16 14.5 12.7
10.2 10.2 10.2 10.2 10.2
407.6 407.6 407.6 407.6 407.6
4.92 5.42 5.98 6.57 7.48
35.8 38.8 41.2 45.3 48
45730 41020 37050 33320 29380
2347 2089 1871 1671 1452
24 26 29 32 36
Structural Steel
b
s h d r t
Radius of gyration
Elastic modulus
Plastic modulus
Buckling Torsional Warping Torsional Area of parameter index constant constant section
Axis x–x Axis y–y Axis x–x Axis y–y Axis x–x Axis y–y rx ry Zx Zy Sx Sy u
H
J
A
dm6
cm4
cm2
21.1 23.1 25.5 27.9 30.7 35 39.9 45.7
64.4 55.9 48.4 43.3 37.7 32.2 26.8 21.5
4299 3185 2330 1718 1264 835 582 390
620 557 500 445 400 347 317 283
0.885 0.883
26.7 30.1
88.9 75.8
1734 1193
494 437
1601 1371 1163 982
0.867 0.866 0.861 0.854
31.9 36.2 41.3 46.8
31.2 26.4 22.1 18.4
926 626 422 291
368 323 286 256
9155 7640 6808
1212 974 842
0.87 0.862 0.856
35 41.6 46.5
19.3 15.2 13
514 306 221
289 247 224
610 514 411 362
7167 6198 5156 4644
959 807 647 570
0.869 0.864 0.858 0.854
33.2 38.1 45.2 49.8
11.3 9.39 7.4 6.46
404 267 159 119
251 220 187 171
4916 4374 3987 3481
518 455 409 346
5631 5000 4558 3994
811 710 638 542
0.872 0.871 0.868 0.862
31.8 35.5 38.7 43.9
7.42 6.42 5.72 4.8
308 220 169 116
217 194 178 159
7.23 7.07 7
6589 4935 4111
1017 743 611
7486 5547 4594
1574 1144 937
0.886 0.886 0.886
21.3 27.7 32.7
14.5 10.2 8.17
785 340 200
303 228 190
25 24.9 24.6 24.2
5.03 4.97 4.88 4.75
3622 3221 2874 2515
391 343 301 256
4142 3676 3281 2881
611 535 469 400
0.875 0.873 0.87 0.864
30.6 34.1 38 43.1
3.99 3.45 2.99 2.52
216 154 111 77
178 159 144 129
22.1 21.9 21.9 21.7 21.3
4.67 4.6 4.57 4.51 4.38
2793 2477 2292 2072 1800
320 279 256 228 192
3196 2828 2612 2360 2059
500 436 399 356 300
0.877 0.875 0.874 0.872 0.864
27.6 30.9 33.2 36.5 41.6
2.32 1.99 1.81 1.6 1.33
178 126 101 75.7 51.5
155 139 129 117 105
19.1 19 18.8 18.8 18.5
4.33 4.29 4.23 4.2 4.12
1957 1770 1611 1458 1296
243 218 196 176 153
2232 2014 1831 1653 1471
379 338 304 272 237
0.881 0.88 0.877 0.877 0.872
25.7 28.3 30.9 33.9 37.9
1.18 1.04 0.922 0.818 0.705
121 90.7 69.2 51.8 37.1
125 114 104 94.6 85.5
cm
cm
cm3
cm3
cm3
cm3
40.6 40.4 40.2 40.3 40.1 40 39 38
6.57 6.49 6.4 6.44 6.37 6.35 6.09 5.81
19720 17740 15900 14350 12880 11190 9821 8409
1732 1535 1353 1223 1082 934 784 636
23200 20760 18540 16590 14850 12830 11350 9807
2800 2469 2168 1941 1713 1470 1245 1020
0.867 0.868 0.868 0.872 0.872 0.873 0.861 0.85
38.2 37.8
9.59 9.46
15630 13730
2161 1871
17670 15480
3341 2890
37 36.8 36.3 35.7
6.51 6.42 6.27 6.07
10880 9501 8269 7204
1014 871 739 621
12570 10940 9535 8351
34.3 33.6 33.1
6.27 6.06 5.9
7985 6641 5893
773 620 535
30.9 30.5 30 29.7
5.71 5.58 5.4 5.3
6234 5387 4470 4018
28 27.8 27.6 27.2
5.53 5.46 5.39 5.24
26.3 25.9 25.7
x
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
213
214
Structural Engineer’s Pocket Book
Universal beams – dimensions and properties
UB designation
Mass Depth Width Thickness Root Depth Ratios for per of of radius between local buckling metre section section fillets Web Flange Flange Web
h
b
s
t
r
d
kg/m
mm
mm
mm
mm
mm
mm
457 152 60 457 152 52
59.8 52.3
454.6 449.8
152.9 152.4
8.1 7.6
13.3 10.9
10.2 10.2
406 178 74 406 178 67 406 178 60 406 78 54
74.2 67.1 60.1 54.1
412.8 409.4 406.4 402.6
179.5 178.8 177.9 177.7
9.5 8.8 7.9 7.7
16 14.3 12.8 10.9
406 140 46 406 140 39
46 39
403.2 398
142.2 141.8
6.8 6.4
356 171 67 356 171 57 356 171 51 356 171 45
67.1 57 51 45
363.4 358 355 351.4
173.2 172.2 171.5 171.1
356 127 39 356 127 33
39.1 33.1
353.4 349
305 165 54 305 165 46 305 165 40
54 46.1 40.3
305 127 48 305 127 42 305 127 37
Second moment of area
h/t better known Axis x–x Axis y–y in BS449 as D/T Ix Iy
b/2t
d/s
407.6 407.6
5.75 6.99
50.3 53.6
25500 21370
795 645
34 41
10.2 10.2 10.2 10.2
360.4 360.4 360.4 360.4
5.61 6.25 6.95 8.15
37.9 41 45.6 46.8
27310 24330 21600 18720
1545 1365 1203 1021
26 29 32 37
11.2 8.6
10.2 10.2
360.4 360.4
6.35 8.24
53 56.3
15690 12510
538 410
36 46
9.1 8.1 7.4 7
15.7 13 11.5 9.7
10.2 10.2 10.2 10.2
311.6 311.6 311.6 311.6
5.52 6.62 7.46 8.82
34.2 38.5 42.1 44.5
19460 16040 14140 12070
1362 1108 968 811
23 28 31 36
126 125.4
6.6 6
10.7 8.5
10.2 10.2
311.6 311.6
5.89 7.38
47.2 51.9
10170 8249
358 280
33 41
310.4 306.6 303.4
166.9 165.7 165
7.9 6.7 6
13.7 11.8 10.2
8.9 8.9 8.9
265.2 265.2 265.2
6.09 7.02 8.09
33.6 39.6 44.2
11700 9899 8503
1063 896 764
23 26 30
48.1 41.9 37
311 307.2 304.4
125.3 124.3 123.4
9 8 7.1
14 12.1 10.7
8.9 8.9 8.9
265.2 265.2 265.2
4.47 5.14 5.77
29.5 33.1 37.4
9575 8196 7171
461 389 336
22 25 28
305 102 33 305 102 28 305 102 25
32.8 28.2 24.8
312.7 308.7 305.1
102.4 101.8 101.6
6.6 6 5.8
10.8 8.8 7
7.6 7.6 7.6
275.9 275.9 275.9
4.74 5.78 7.26
41.8 46 47.6
6501 5366 4455
194 155 123
29 35 44
254 146 43 254 146 37 254 146 31
43 37 31.1
259.6 256 251.4
147.3 146.4 146.1
7.2 6.3 6
12.7 10.9 8.6
7.6 7.6 7.6
219 219 219
5.8 6.72 8.49
30.4 34.8 36.5
6544 5537 4413
677 571 448
20 23 29
254 102 28 254 102 25 254 102 22
28.3 25.2 22
260.4 257.2 254
102.2 101.9 101.6
6.3 6 5.7
10 8.4 6.8
7.6 7.6 7.6
225.2 225.2 225.2
5.11 6.07 7.47
35.7 37.5 39.5
4005 3415 2841
179 149 119
26 31 37
203 133 30 203 133 25
30 25.1
206.8 203.2
133.9 133.2
6.4 5.7
9.6 7.8
7.6 7.6
172.4 172.4
6.97 8.54
26.9 30.2
2896 2340
385 308
22 26
203 102 23
23.1
203.2
101.8
5.4
9.3
7.6
169.4
5.47
31.4
2105
164
22
178 102 19
19
177.8
101.2
4.8
7.9
7.6
146.8
6.41
30.6
1356
137
23
152 89 16
16
152.4
88.7
4.5
7.7
7.6
121.8
5.76
27.1
834
89.8
20
127 76 13
13
127
76
4
7.6
7.6
96.6
5
24.1
473
55.7
17
yAdditional sizes to BS4 available in UK.
cm4
cm4
215
Structural Steel
b
s h d r t
Radius of gyration
Elastic modulus
Plastic modulus
Axis x–x Axis y–y
Axis x–x
Axis y–y
Axis x–x
Axis y–y
Buckling parameter
Torsional index
Warping constant
Torsional constant
Area of section
u
x
H
J
A
dm6
cm4
cm2
rx
ry
Zx
Zy
Sx
Sy
cm
cm
cm3
cm3
cm3
cm3
18.3 17.9
3.23 3.11
1122 950
104 84.6
1287 1096
163 133
0.868 0.859
37.5 43.9
0.387 0.311
33.8 21.4
76.2 66.6
17 16.9 16.8 16.5
4.04 3.99 3.97 3.85
1323 1189 1063 930
172 153 135 115
1501 1346 1199 1055
267 237 209 178
0.882 0.88 0.88 0.871
27.6 30.5 33.8 38.3
0.608 0.533 0.466 0.392
62.8 46.1 33.3 23.1
94.5 85.5 76.5 69
16.4 15.9
3.03 2.87
778 629
75.7 57.8
888 724
118 90.8
0.871 0.858
38.9 47.5
0.207 0.155
19 10.7
58.6 49.7
15.1 14.9 14.8 14.5
3.99 3.91 3.86 3.76
1071 896 796 687
157 129 113 94.8
1211 1010 896 775
243 199 174 147
0.886 0.882 0.881 0.874
24.4 28.8 32.1 36.8
0.412 0.33 0.286 0.237
55.7 33.4 23.8 15.8
85.5 72.6 64.9 57.3
14.3 14
2.68 2.58
576 473
56.8 44.7
659 543
0.871 0.863
35.2 42.2
0.105 0.081
15.1 8.79
49.8 42.1
13 13 12.9
3.93 3.9 3.86
754 646 560
127 108 92.6
846 720 623
196 166 142
0.889 0.891 0.889
23.6 27.1 31
0.234 0.195 0.164
34.8 22.2 14.7
68.8 58.7 51.3
12.5 12.4 12.3
2.74 2.7 2.67
616 534 471
73.6 62.6 54.5
711 614 539
116 98.4 85.4
0.873 0.872 0.872
23.3 26.5 29.7
0.102 0.085 0.072
31.8 21.1 14.8
61.2 53.4 47.2
12.5 12.2 11.9
2.15 2.08 1.97
416 348 292
37.9 30.5 24.2
481 403 342
60 48.5 38.8
0.866 0.859 0.846
31.6 37.4 43.4
0.044 0.035 0.027
12.2 7.4 4.77
41.8 35.9 31.6
10.9 10.8 10.1
3.52 3.48 3.36
504 433 351
92 78 61.3
566 483 393
141 119 94.1
0.891 0.89 0.88
21.2 24.3 29.6
0.103 0.086 0.066
23.9 15.3 8.55
54.8 47.2 39.7
10.5 10.3 10.1
2.22 2.15 2.06
308 266 224
34.9 29.2 23.5
353 306 259
54.8 46 37.3
0.874 0.866 0.856
27.5 31.5 36.4
0.028 0.023 0.018
9.57 6.42 4.15
36.1 32 28
8.71 8.56
3.17 3.1
280 230
57.5 46.2
314 258
88.2 70.9
0.881 0.877
21.5 25.6
0.037 0.029
10.3 5.96
38.2 32
8.46
2.36
207
32.2
234
49.8
0.888
22.5
0.015
7.02
29.4
7.48
2.37
153
27
171
41.6
0.888
22.6
0.01
4.41
24.3
6.41
2.1
109
20.2
123
31.2
0.89
19.6
0.005
3.56
20.3
5.35
1.84
22.6
0.895
16.3
0.002
2.85
16.5
74.6
14.7
84.2
89.1 70.3
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
216
Structural Engineer’s Pocket Book
Universal columns – dimensions and properties
UC designation
Mass Depth Width Thickness Root Depth Ratios for per of of radius between local buckling metre section section fillets Web Flange Flange Web
Second moment of area
h/t better known in BS449 as
Axis x–x Ix
Axis y–y Iy
cm4
cm4
6.1 6.89 8.11 9.48 10.9 12.8 15.8
274800 226900 183000 146600 122500 99880 79080
98130 82670 67830 55370 46850 38680 30990
6 7 8 9 9 11 13
6.94 7.83 8.95 10.5
17.6 20.2 23.6 27.9
66260 57120 48590 40250
23690 20530 17550 14610
14 15 17 20
246.7 246.7 246.7 246.7 246.7 246.7 246.7
3.65 4.22 5.01 6.22 7.12 8.22 9.91
9.21 10.7 12.9 15.6 17.9 20.6 24.9
78870 64200 50900 38750 32810 27670 22250
24630 20310 16300 12570 10700 9059 7308
8 9 11 13 15 17 20
12.7 12.7 12.7 12.7 12.7
200.3 200.3 200.3 200.3 200.3
4.18 5.16 6.31 7.41 8.96
10.4 13.1 15.6 19.4 23.3
30000 22530 17510 14270 11410
9870 7531 5928 4857 3908
9 11 13 15 18
20.5 17.3 14.2 12.5 11
10.2 10.2 10.2 10.2 10.2
160.8 160.8 160.8 160.8 160.8
5.1 5.97 7.25 8.17 9.25
12.7 16.1 17.1 20.4 22.3
9449 7618 6125 5259 4568
3127 2537 2065 1778 1548
11 12 15 16 18
8 11.5 6.5 9.4 5.8 6.8
7.6 7.6 7.6
123.6 123.6 123.6
6.71 8.13 11.2
15.5 19 21.3
2210 1748 1250
706 560 400
14 17 22
h
b
s
t
r
d
b/2t
kg/m
mm
mm
mm
mm
mm
mm
356 406 634 356 406 551 356 406 467 356 406 393 356 406 340 356 406 287 356 406 235
633.9 551 467 393 339.9 287.1 235.1
474.6 455.6 436.6 419 406.4 393.6 381
424 418.5 412.2 407 403 399 394.8
47.6 42.1 35.8 30.6 26.6 22.6 18.4
77 67.5 58 49.2 42.9 36.5 30.2
15.2 15.2 15.2 15.2 15.2 15.2 15.2
290.2 290.2 290.2 290.2 290.2 290.2 290.2
2.75 3.1 3.55 4.14 4.7 5.47 6.54
356 368 202 356 368 177 356 368 153 356 368 129
201.9 177 152.9 129
374.6 368.2 362 355.6
374.7 372.6 370.5 368.6
16.5 14.4 12.3 10.4
27 23.8 20.7 17.5
15.2 15.2 15.2 15.2
290.2 290.2 290.2 290.2
305 305 283 305 305 240 305 305 198 305 305 158 305 305 137 305 305 118 305 305 97
282.9 240 198.1 158.1 136.9 117.9 96.9
365.3 352.5 339.9 327.1 320.5 314.5 307.9
322.2 318.4 314.5 311.2 309.2 307.4 305.3
26.8 23 19.1 15.8 13.8 12 9.9
44.1 37.7 31.4 25 21.7 18.7 15.4
15.2 15.2 15.2 15.2 15.2 15.2 15.2
254 254 167 254 254 132 254 254 107 254 254 89 254 254 73
167.1 132 107.1 88.9 73.1
289.1 276.3 266.7 260.3 254.1
265.2 261.3 258.8 256.3 254.6
19.2 15.3 12.8 10.3 8.6
31.7 25.3 20.5 17.3 14.2
203 203 86 203 203 71 203 203 60 203 203 52 203 203 46
86.1 71 60 52 46.1
222.2 215.8 209.6 206.2 203.2
209.1 206.4 205.8 204.3 203.6
12.7 10 9.4 7.9 7.2
152 152 37 152 152 30 152 152 23
37 30 23
161.8 157.6 152.4
154.4 152.9 152.2
d/s
D/T
217
Structural Steel b
s h d r t
Radius of gyration
Elastic modulus
Plastic modulus
Buckling parameter
Torsional index
u
x
Axis x–x rx
Axis y–y ry
Axis x–x Zx
Axis y–y Zy
Axis x–x Sx
Axis y–y Sy
cm
cm
cm3
cm3
cm3
cm3
18.4 18 17.5 17.1 16.8 16.5 16.3
11 10.9 10.7 10.5 10.4 10.3 10.2
11580 9962 8383 6998 6031 5075 4151
4629 3951 3291 2721 2325 1939 1570
14240 12080 10000 8222 6999 5812 4687
7108 6058 5034 4154 3544 2949 2383
0.843 0.841 0.839 0.837 0.836 0.835 0.834
Warping constant
Torsional Area of constant section
H
J
A
dm6
cm4
cm2
5.46 6.05 6.86 7.86 8.85 10.2 12.1
38.8 31.1 24.3 18.9 15.5 12.3 9.54
13720 9240 5809 3545 2343 1441 812
808 702 595 501 433 366 299
16.1 15.9 15.8 15.6
9.6 9.54 9.49 9.43
3538 3103 2684 2264
1264 1102 948 793
3972 3455 2965 2479
1920 1671 1435 1199
0.844 0.844 0.844 0.844
13.4 15 17 19.9
7.16 6.09 5.11 4.18
558 381 251 153
257 226 195 164
14.8 14.5 14.2 13.9 13.7 13.6 13.4
8.27 8.15 8.04 7.9 7.83 7.77 7.69
4318 3643 2995 2369 2048 1760 1445
1529 1276 1037 808 692 589 479
5105 4247 3440 2680 2297 1958 1592
2342 1951 1581 1230 1053 895 726
0.855 0.854 0.854 0.851 0.851 0.85 0.85
7.65 8.74 10.2 12.5 14.2 16.2 19.3
6.35 5.03 3.88 2.87 2.39 1.98 1.56
2034 1271 734 378 249 161 91.2
360 306 252 201 174 150 123
11.9 11.6 11.3 11.2 11.1
6.81 6.69 6.59 6.55 6.48
2075 1631 1313 1096 898
744 576 458 379 307
2424 1869 1484 1224 992
1137 878 697 575 465
0.851 0.85 0.848 0.85 0.849
8.49 10.3 12.4 14.5 17.3
1.63 1.19 0.898 0.717 0.562
626 319 172 102 57.6
213 168 136 113 93.1
9.28 9.18 8.96 8.91 8.82
5.34 5.3 5.2 5.18 5.13
850 706 584 510 450
299 246 201 174 152
977 799 656 567 497
456 374 305 264 231
0.85 0.853 0.846 0.848 0.847
10.2 11.9 14.1 15.8 17.7
0.318 0.25 0.197 0.167 0.143
137 80.2 47.2 31.8 22.2
110 90.4 76.4 66.3 58.7
6.85 6.76 6.54
3.87 3.83 3.7
273 222 164
309 248 182
140 0.848 112 0.849 80.2 0.84
13.3 16 20.7
0.04 0.031 0.021
91.5 73.3 52.6
19.2 10.5 4.63
47.1 38.3 29.2
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
218
Structural Engineer’s Pocket Book
Rolled steel joists – dimensions and properties
Inside slope ¼ 8o RSJ designation
254 203 82 203 152 52 152 127 37 127 114 29 127 114 27 102 102 23 102 44 7 89 89 19 76 76 13
Mass Depth Width Thickness Radius Depth Ratios for per of of between local buckling metre section section fillets Web Flange Root Toe Flange Web
h
b
s
kg/m
mm
mm
mm mm
t
mm
82 52.3 37.3 29.3 26.9 23 7.5 19.5 12.8
254 203.2 152.4 127 127 101.6 101.6 88.9 76.2
203.2 152.4 127 114.3 114.3 101.6 44.5 88.9 76.2
10.2 8.9 10.4 10.2 7.4 9.5 4.3 9.5 5.1
19.6 15.5 13.5 9.9 9.9 11.1 6.9 11.1 9.4
19.9 16.5 13.2 11.5 11.4 10.3 6.1 9.9 8.4
r1
r2
d
b/2t
d/s
mm 9.7 166.6 7.6 133.2 6.6 94.3 4.8 79.5 5 79.5 3.2 55.2 3.3 74.6 3.2 44.2 4.6 38.1
5.11 4.62 4.81 4.97 5.01 4.93 3.65 4.49 4.54
16.3 15 9.07 7.79 10.7 5.81 17.3 4.65 7.47
Second moment of area Axis x–x
Axis y–y
Ix
Iy
cm4
cm4
12020 4798 1818 979 946 486 153 307 158
2280 816 378 242 236 154 7.82 101 51.8
h/t better known in BS449 as
D/T
13 12 12 11 11 10 17 9 9
219
Structural Steel
b
98°
r1 h d
t
Radius of gyration Axis x–x
Elastic modulus Axis y–y
Plastic modulus
Axis x–x
Axis y–y
Axis x–x
Axis y–y
3
3
3
cm3
cm
cm
cm
10.7 8.49 6.19 5.12 5.26 4.07 4.01 3.51 3.12
4.67 3.5 2.82 2.54 2.63 2.29 0.907 2.02 1.79
947 472 239 154 149 95.6 30.1 69 41.5
cm
224 107 59.6 42.3 41.3 30.3 3.51 22.8 13.6
cm
1077 541 279 181 172 113 35.4 82.7 48.7
371 176 99.8 70.8 68.2 50.6 6.03 38 22.4
Buckling parameter
Torsional index
Warping constant
Torsional constant
u
x
H
J
A
dm6
cm4
cm2
0.312 0.0711 0.0183 0.00807 0.00788 0.00321 0.000178 0.00158 0.000595
152 64.8 33.9 20.8 16.9 14.2 1.25 11.5 4.59
105 66.6 47.5 37.4 34.2 29.3 9.5 24.9 16.2
0.89 0.891 0.866 0.853 0.868 0.836 0.872 0.83 0.852
11 10.7 9.33 8.76 9.32 7.43 14.9 6.57 7.22
Area of section
220
Structural Engineer’s Pocket Book
Parallel flange channels – dimensions and properties
PFC designation
Mass Depth Width Thickness Per of of metre section section
D kg/m
B
Root Depth Ratios for local radius between buckling
Web Flange t T r
nd
Flange b/t
Web d/t
Second moment of area
h/t better known in BS449 as
Axis x–x
Axis y–y
D/T
4
cm4
mm
mm
mm
mm
mm
mm
cm
430 100 64 64.4
430
100
11
19
15
362
5.26
32.9
21940
722
380 100 54 54.0
380
100
9.5
17.5
15
315
5.71
33.2
15030
643
22
300 100 46 45.5 300 90 41 41.4
300 300
100 90
9 9
16.5 15.5
15 12
237 245
6.06 5.81
26.3 27.2
8229 7218
568 404
18 19
260 90 35 260 75 28
34.8 27.6
260 260
90 75
8 7
14 12
12 12
208 212
6.43 6.25
26 30.3
4728 3619
353 185
19 22
230 90 32 230 75 26
32.2 25.7
230 230
90 75
7.5 6.5
14 12.5
12 12
178 181
6.43 6
23.7 27.8
3518 2748
334 181
16 18
200 90 30 200 75 23
29.7 23.4
200 200
90 75
7 6
14 12.5
12 12
148 151
6.43 6
21.1 25.2
2523 1963
314 170
14 16
180 90 26 180 75 20
26.1 20.3
180 180
90 75
6.5 6
12.5 10.5
12 12
131 135
7.2 7.14
20.2 22.5
1817 1370
277 146
14 17
150 90 24 150 75 18
23.9 17.9
150 150
90 75
6.5 5.5
12 10
12 12
102 106
7.5 7.5
15.7 19.3
1162 861
253 131
13 15
125 65 15
14.8
125
65
5.5
9.5
12
82
6.84
14.9
483
80
13
100 50 10
10.2
100
50
5
8.5
9
65
5.88
13
208
32.3
12
23
221
Structural Steel
b
r1 s d
h
t
Radius of gyration
Elastic modulus
Elastic NA
Axis x–x
Axis y–y
Axis x–x
Axis y–y
cy
Axis x–x
Axis y–y
kg/m
mm
mm
mm
mm
mm
mm
16.3
2.97
1020
97.9
2.62
1222
176
0.954
14.8
3.06
791
89.2
2.79
933
161
0.904
0.932
21.2
0.15
45.7
68.7
11.9 11.7
3.13 2.77
549 481
81.7 63.1
3.05 2.6
641 568
148 114
1.31 0.879
0.944 0.934
17 18.4
0.081 0.058
36.8 28.8
58 52.7
10.3 10.1
2.82 2.3
364 278
56.3 34.4
2.74 2.1
425 328
102 62
1.14 0.676
0.942 0.932
17.2 20.5
0.038 0.02
20.6 11.7
44.4 35.1
9.27 9.17
2.86 2.35
306 239
55 34.8
2.92 2.3
355 278
98.9 63.2
1.69 1.03
0.95 0.947
15.1 17.3
0.028 0.015
19.3 11.8
41 32.7
8.16 8.11
2.88 2.39
252 196
53.4 33.8
3.12 2.48
291 227
94.5 60.6
2.24 1.53
0.954 0.956
12.9 14.8
0.02 0.011
18.3 11.1
37.9 29.9
7.4 7.27
2.89 2.38
202 152
47.4 28.8
3.17 2.41
232 176
83.5 51.8
2.36 1.34
0.949 0.946
12.8 15.3
0.014 0.008
13.3 7.34
33.2 25.9
6.18 6.15
2.89 2.4
155 115
44.4 26.6
3.3 2.58
179 132
76.9 47.2
2.66 1.81
0.936 0.946
10.8 13.1
0.009 0.005
11.8 6.1
30.4 22.8
5.07
2.06
77.3
18.8
2.25
89.9
33.2
1.55
0.942
11.1
0.002
4.72
18.8
4
1.58
41.5
1.73
48.9
17.5
1.18
0.942
10
0
2.53
13
9.89
Plastic modulus
Plastic NA
Buckling parameter
Torsional index
Warping constant
Torsional constant
Area of section
ceq
u
x
H
J
A
cm4
cm4
22.5
0.219
63
82.1
0.917
cm
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
222
y
a
v t x
Rolled steel equal angles – dimensions and properties RSA designation
Mass per metre
DBT
u
Root radius
Toe radius
Distance of centre of gravity
Second moment of area
Radius of gyration
r1
r2
Cx & Cy
Axis x–x, y-y
Axis u–u
Axis v–v
Axis x–x, y–y
Axis u–u
Axis v–v
Axis x–x, y–y
kg/m
mm
mm
cm
cm4
cm4
cm4
cm
cm
cm
cm3
200 200 24 200 200 20 200 200 18 200 200 16
71.3 60.1 54.4 48.7
18 18 18 18
4.8 4.8 4.8 4.8
5.85 5.7 5.62 5.54
3356 2877 2627 2369
5322 4569 4174 3765
1391 1185 1080 973
6.08 6.13 6.15 6.18
7.65 7.72 7.76 7.79
3.91 3.93 3.95 3.96
237 201 183 164
150 150 18 150 150 15 150 150 12 150 150 10
40.2 33.9 27.5 23.1
16 16 16 16
4.8 4.8 4.8 4.8
4.38 4.26 4.14 4.06
1060 909 748 635
1680 1442 1187 1008
440 375 308 262
4.55 4.59 4.62 4.64
5.73 5.78 5.82 5.85
2.93 2.95 2.97 2.98
120 120 15 120 120 12 120 120 10 120 120 8
26.7 21.7 18.3 14.8
13 13 13 13
4.8 4.8 4.8 4.8
3.52 3.41 3.32 3.24
448 371 316 259
710 588 502 411
186 153 130 107
3.63 3.66 3.69 3.71
4.57 4.62 4.64 4.67
100 100 15 100 100 12 100 100 10 100 100 8
21.9 17.9 15.1 12.2
12 12 12 12
4.8 4.8 4.8 4.8
3.02 2.91 2.83 2.75
250 208 178 146
395 330 283 232
105 86.4 73.7 60.5
2.99 3.02 3.05 3.07
90 90 12 90 90 10 90 90 8 90 90 7 90 90 6
16 13.5 10.9 9.6 8.3
11 11 11 11 11
4.8 4.8 4.8 4.8 4.8
2.66 2.58 2.5 2.46 2.41
149 128 105 93.2 81
235 202 167 148 128
62 52.9 43.4 38.6 33.6
þ
11.9 9.7 7.4
11 11 11
4.8 4.8 4.8
2.33 2.25 2.16
87.7 72.4 56
139 115 88.7
36.5 30.1 23.3
þ
80 80 10 80 80 8 80 80 6
r2
c y a
Elastic modulus
mm mm mm
þ
u r1
c
x
t v
Area of section
D/T
A cm2
8 10 11 13
90.8 76.6 69.4 62
99.8 84.6 68.9 58
8 10 13 15
51.2 43.2 35 29.5
2.34 2.35 2.37 2.38
52.8 43.1 36.4 29.5
8 10 12 15
34 27.6 23.3 18.8
3.76 3.81 3.84 3.86
1.94 1.95 1.96 1.97
35.8 29.3 24.8 20.2
7 8 10 13
28 22.8 19.2 15.6
2.7 2.73 2.75 2.76 2.76
3.4 3.43 3.46 3.47 3.48
1.75 1.76 1.77 1.77 1.78
23.5 19.9 16.2 14.2 12.3
8 9 11 13 15
20.3 17.2 13.9 12.3 10.6
2.4 2.42 2.44
3.03 3.05 3.07
1.55 1.56 1.58
15.5 12.6 9.6
8 10 13
15.2 12.3 9.4
þ
70 70 10 70 70 8 70 70 6
10.3 8.4 6.4
11 11 11
4.8 4.8 4.8
2.08 2 1.92
57.1 47.4 36.8
90.3 75 58.2
24 19.7 15.4
2.08 2.1 2.12
2.62 2.65 2.67
1.35 1.36 1.37
11.6 9.49 7.24
7 9 12
13.2 10.7 8.2
60 60 10 60 60 8 60 60 6 þ 60 60 5
8.8 7.2 5.5 4.6
11 11 11 11
4.8 4.8 4.8 4.8
1.84 1.76 1.67 1.62
34.7 28.9 22.6 19.2
54.7 45.7 35.7 30.2
14.7 12.1 9.45 8.06
1.76 1.78 1.8 1.8
2.21 2.24 2.26 2.26
1.15 1.15 1.16 1.17
8.33 6.82 5.21 4.37
6 8 10 12
11.2 9.12 7 5.91
þ
50 50 8 50 50 6 50 50 5 þ 50 50 4 þ 50 50 3
5.9 4.6 3.9 3.1 2.4
11 11 11 11 11
4.8 4.8 4.8 4.8 4.8
1.51 1.42 1.37 1.32 1.25
16 12.6 10.7 8.72 6.6
25.3 19.9 16.9 13.7 10.3
6.78 5.28 4.51 3.71 2.88
1.46 1.47 1.48 1.48 1.47
1.83 1.85 1.86 1.85 1.83
0.949 0.954 0.958 0.963 0.968
4.59 3.52 2.95 2.37 1.76
6 8 10 13 17
7.52 5.8 4.91 4 3.07
þ
45 45 6 45 45 5 45 45 4 þ 45 45 3
4.1 3.5 2.8 2.2
11 11 11 11
4.8 4.8 4.8 4.8
1.3 1.25 1.2 1.13
8.95 7.63 6.22 4.71
14.1 12 9.79 7.37
3.76 3.21 2.65 2.05
1.31 1.32 1.31 1.3
1.65 1.65 1.65 1.63
0.851 0.853 0.857 0.86
2.8 2.35 1.88 1.4
8 9 11 15
5.2 4.41 3.6 2.77
þ
3.6 3.1 2.5 1.9
11 11 11 11
4.8 4.8 4.8 4.8
1.18 1.13 1.08 1.01
6.1 5.21 4.25 3.22
9.63 8.22 6.7 5.04
2.57 2.19 1.8 1.4
1.15 1.15 1.15 1.14
1.45 1.45 1.45 1.43
0.747 0.748 0.75 0.752
2.16 1.81 1.45 1.08
7 8 10 13
4.6 3.91 3.2 2.47
2.3 1.9 1.5
11 11 11
4.8 4.8 4.8
0.89 0.84 0.78
2.02 1.65 1.25
3.19 2.61 1.96
0.846 0.691 0.53
0.832 0.829 0.816
1.05 1.04 1.02
0.539 0.536 0.532
0.956 0.764 0.561
6 8 10
2.91 2.4 1.87
1.9 1.6 1.2
11 11 11
4.8 4.8 4.8
0.78 0.73 0.67
1.09 0.894 0.672
1.72 1.42 1.06
0.462 0.372 0.281
0.673 0.668 0.654
0.846 0.841 0.823
0.438 0.431 0.423
0.634 0.504 0.367
5 6 8
2.41 2 1.57
þ þ þ þ þ
þ þ
þ þ
40 40 6 40 40 5 40 40 4 þ 40 40 3 þ þ
þ
30 30 5 30 30 4 30 30 3
þ þ þ
25 25 5 25 25 4 25 25 3
þ þ
+British Standard sections not produced by Corus. Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
223
224
Structural Engineer’s Pocket Book
Rolled steel unequal angles – dimensions and properties
RSA designation
Mass per metre
DBT
Root radius
Toe radius
Distance of centre of gravity
Distance of centre of gravity
Angle x–x to u–u axis
Second moment of area
r1
r2
Cx
Cy
Tan a
Axis x-x
Axis y–y
mm mm mm
kg/m
mm
mm
cm
cm
cm4
cm4
200 150 18 200 150 15 200 150 12 200 100 15 200 100 12 200 100 10
47.2 39.7 32.1 33.9 27.4 23.1
15 15 15 15 15 15
4.8 4.8 4.8 4.8 4.8 4.8
6.34 6.22 6.1 7.17 7.04 6.95
3.86 3.75 3.63 2.23 2.11 2.03
0.549 0.551 0.553 0.26 0.263 0.265
2390 2037 1667 1772 1454 1233
1155 989 812 303 251 215
150 90 15 150 90 12 150 90 10
26.7 21.6 18.2
12 12 12
4.8 4.8 4.8
5.21 5.09 5
2.24 2.12 2.04
0.354 0.359 0.361
764 630 536
207 172 147
150 75 15 150 75 12 150 75 10
24.9 20.2 17
11 11 11
4.8 4.8 4.8
5.53 5.41 5.32
1.81 1.7 1.62
0.254 0.259 0.262
715 591 503
120 100 86.3
125 75 12 125 75 10 125 75 8
17.8 15 12.2
11 11 11
4.8 4.8 4.8
4.31 4.23 4.14
1.84 1.76 1.68
0.354 0.358 0.36
355 303 249
96 82.5 68.1
100 75 12 100 75 10 100 75 8
15.4 13 10.6
10 10 10
4.8 4.8 4.8
3.27 3.19 3.1
2.03 1.95 1.87
0.54 0.544 0.547
189 162 133
90.3 77.7 64.2
100 65 10 100 65 8 100 65 7
12.3 10 8.8
10 10 10
4.8 4.8 4.8
3.36 3.28 3.23
1.63 1.56 1.51
0.41 0.414 0.415
154 127 113
51.1 42.3 37.7
8.3 7.3 6.3
8 8 8
4.8 4.8 4.8
2.55 2.5 2.46
1.56 1.52 1.48
0.544 0.545 0.546
65.8 58.5 50.9
31.5 28.1 24.5
7.4 5.7
7 7
2.4 2.4
2.53 2.44
1.29 1.21
0.43 0.436
52.4 40.9
18.6 14.6
6.8 5.2 4.4
6 6 6
2.4 2.4 2.4
2.12 2.04 2
1.37 1.3 1.26
0.569 0.575 0.577
34.9 27.4 23.3
17.8 14.1 12
4 3.4
6 6
2.4 2.4
2.2 2.16
0.72 0.68
0.252 0.256
18.3 15.7
1.9
4
2.4
1.36
0.62
0.38
þ
80 60 8 80 60 7 80 60 6
þ þ þ
75 50 8 75 50 6
þ þ
65 50 8 65 50 6 65 50 5
þ þ þ
60 30 6 60 30 5
þ þ
40 25 4
3.86
3.05 2.64 1.15
225
Structural Steel
r2 u v
t x
x R1
cx t
t
U
v
cy
Second moment of area
Radius of gyration
Elastic modulus
Area of section
Axis u–u
Axis v–v
Axis x–x
Axis y–y
Axis u–u
Axis v–v
Axis x–x
Axis y–y
cm4
cm4
cm
cm
cm
cm
cm3
cm3
2922 2495 2044 1879 1544 1310
623 531 435 197 162 138
6.3 6.34 6.38 6.41 6.45 6.48
4.38 4.42 4.45 2.65 2.68 2.7
6.97 7.02 7.07 6.6 6.65 6.68
3.22 3.24 3.26 2.13 2.15 2.17
175 148 120 138 112 94.5
104 87.8 71.4 39 31.9 26.9
11 13 17 13 17 20
60.1 50.6 40.9 43.1 34.9 29.4
844 698 595
127 104 89.1
4.74 4.78 4.81
2.47 2.5 2.52
4.99 5.03 5.06
1.93 1.95 1.96
78 63.6 53.6
30.6 25 21.2
10 13 15
34 27.6 23.2
756 626 534
79.2 65.2 55.7
4.75 4.79 4.82
1.95 1.98 2
4.89 4.93 4.96
1.58 1.59 1.6
75.5 61.6 52
21.1 17.3 14.7
10 13 10
31.7 25.7 21.7
392 336 275
58.8 50.2 41.2
3.95 3.98 4
2.06 2.08 2.09
4.16 4.18 4.21
1.61 1.62 1.63
43.4 36.7 29.7
17 14.4 11.7
10 13 16
22.7 19.2 15.5
230 197 163
49.5 42.2 34.7
3.1 3.12 3.14
2.14 2.16 2.18
3.42 3.45 3.48
1.59 1.59 1.61
28.1 23.8 19.3
16.5 14 11.4
8 10 13
19.7 16.6 13.5
175 144 128
30.2 24.9 22.1
3.14 3.17 3.18
1.81 1.83 1.84
3.35 3.38 3.39
1.39 1.4 1.41
23.2 18.9 16.6
10.5 8.56 7.56
10 13 14
15.6 12.7 11.2
80.2 71.4 62.2
17.1 15.2 13.2
2.49 2.5 2.51
1.72 1.73 1.74
2.75 2.76 2.77
1.27 1.27 1.28
12.1 10.6 9.19
7.09 6.26 5.41
10 11 13
10.6 9.35 8.08
60.1 47.1
10.9 8.48
2.36 2.38
1.4 1.42
2.52 2.55
1.07 1.08
10.5 8.1
5 3.86
9 13
9.44 7.22
43.1 34 29
9.62 7.49 6.38
2.01 2.04 2.05
1.44 1.46 1.47
2.24 2.27 2.28
1.06 1.07 1.07
7.97 6.14 5.18
4.92 3.8 3.21
8 11 13
8.61 6.59 5.55
19.3 16.6
2.01 1.72
1.9 1.91
0.774 0.783
1.95 1.96
0.629 0.632
4.82 4.08
1.34 1.14
10 12
5.09 4.3
0.692
1.26
0.685
1.33
0.532
1.46
0.612
10
2.45
4.32
þBritish
D/T
A cm2
Standard sections not produced by Corus.
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
226
B Y
D X
X t
Hot finished rectangular hollow sections – dimensions and properties RHS designation
Size
Thickness
Mass per metre
Area of section
A
Radius of gyration
Y
Ratios for local buckling
Second moment of area
Elastic modulus
Flange
Web
Axis x–x
Axis y–y
Axis x–x
b/t
d/t
Ix
Iy
rx
cm4
cm4
cm 1.79 1.77 1.76 1.74 1.72 1.67
1.19 1.17 1.16 1.14 1.13 1.08
4.73 5.43 5.68 6.16 6.6 7.49
3.48 3.96 4.13 4.45 4.72 5.26
5.92 6.88 7.25 7.94 8.59 10
4.11 4.76 5 5.46 5.88 6.8
11.7 13.5 14.2 15.4 16.6 19
5.73 6.51 6.8 7.31 7.77 8.67
Axis y–y
Plastic modulus
Torsional constants
Axis x–x
Axis y–y
Axis x–x
Axis y–y
ry
Zx
Zy
Sx
Sy
J
cm
cm3
cm3
cm3
cm3
cm4
Surface area of section
Approx length per tonne
m2/m
m
0.154 0.152 0.152 0.151 0.15 0.147
346 293 277 250 228 189
C
DB
T
mmmm
mm
50 30 50 30 50 30 50 30 50 30 50 30
2.5 3 3.2 3.6 4 5
2.89 3.41 3.61 4.01 4.39 5.28
3.68 4.34 4.6 5.1 5.59 6.73
9 7 6.37 5.33 4.5 3
17 13.7 12.6 10.9 9.5 7
11.8 13.6 14.2 15.4 16.5 18.7
60 40 60 40 60 40 60 40 60 40 60 40 60 40 60 40
2.5 3 3.2 3.6 4 5 6 6.3
3.68 4.35 4.62 5.14 5.64 6.85 7.99 8.31
4.68 5.54 5.88 6.54 7.19 8.73 10.2 10.6
13 10.3 9.5 8.11 7 5 3.67 3.35
21 17 15.7 13.7 12 9 7 6.52
22.8 26.5 27.8 30.4 32.8 38.1 42.3 43.4
12.1 13.9 14.6 15.9 17 19.5 21.4 21.9
2.21 2.18 2.18 2.16 2.14 2.09 2.04 2.02
1.6 1.58 1.57 1.56 1.54 1.5 1.45 1.44
7.61 8.82 9.27 10.1 10.9 12.7 14.1 14.5
6.03 6.95 7.29 7.93 8.52 9.77 10.7 11
9.32 10.9 11.5 12.7 13.8 16.4 18.6 19.2
7.02 8.19 8.64 9.5 10.3 12.2 13.7 14.2
25.1 29.2 30.8 33.8 36.7 43 48.2 49.5
9.73 11.2 11.7 12.8 13.7 15.7 17.3 17.6
0.194 0.192 0.192 0.191 0.19 0.187 0.185 0.184
272 230 217 195 177 146 125 120
80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40
3 3.2 3.6 4 5 6 6.3 8
5.29 5.62 6.27 6.9 8.42 9.87 10.3 12.5
6.74 7.16 7.98 8.79 10.7 12.6 13.1 16
10.3 9.5 8.11 7 5 3.67 3.35 2
23.7 22 19.2 17 13 10.3 9.7 7
54.2 57.2 62.8 68.2 80.3 90.5 93.3 106
18 18.9 20.6 22.2 25.7 28.5 29.2 32.1
2.84 2.83 2.81 2.79 2.74 2.68 2.67 2.58
1.63 1.63 1.61 1.59 1.55 1.5 1.49 1.42
13.6 14.3 15.7 17.1 20.1 22.6 23.3 26.5
9 9.46 10.3 11.1 12.9 14.2 14.6 16.1
17.1 18 20 21.8 26.1 30 31.1 36.5
10.4 11 12.1 13.2 15.7 17.8 18.4 21.2
43.8 46.2 50.8 55.2 65.1 73.4 75.6 85.8
15.3 16.1 17.5 18.9 21.9 24.2 24.8 27.4
0.232 0.232 0.231 0.23 0.227 0.225 0.224 0.219
189 178 160 145 119 101 97.2 79.9
kg/m
cm2
5.22 5.94 6.2 6.67 7.08 7.89
cm3
76.250.8 76.250.8 76.250.8 76.250.8 76.250.8 76.250.8 76.250.8 76.250.8
3 3.2 3.6 4 5 6 6.3 8
5.62 5.97 6.66 7.34 8.97 10.5 11 13.4
7.16 7.61 8.49 9.35 11.4 13.4 14 17.1
13.9 12.9 11.1 9.7 7.16 5.47 5.06 3.35
22.4 20.8 18.2 16.1 12.2 9.7 9.1 6.53
56.7 59.8 65.8 71.5 84.4 95.6 98.6 113
30 31.6 34.6 37.5 43.9 49.2 50.6 57
2.81 2.8 2.78 2.77 2.72 2.67 2.66 2.57
2.05 2.04 2.02 2 1.96 1.91 1.9 1.83
14.9 15.7 17.3 18.8 22.2 25.1 25.9 29.6
11.8 12.4 13.6 14.8 17.3 19.4 19.9 22.4
18.2 19.2 21.3 23.3 28 32.2 33.4 39.4
13.7 14.5 16 17.5 20.9 23.9 24.8 29
62.1 65.7 72.5 79.1 94.2 108 111 129
19.1 20.1 22 23.8 27.8 31.2 32 36.1
0.246 0.246 0.245 0.244 0.241 0.239 0.238 0.233
178 167 150 136 111 95 91.1 74.6
9050 9050 9050 9050 9050 9050 9050 9050
3 3.2 3.6 4 5 6 6.3 8
6.24 6.63 7.4 8.15 9.99 11.8 12.3 15
7.94 8.44 9.42 10.4 12.7 15 15.6 19.2
13.7 12.6 10.9 9.5 7 5.33 4.94 3.25
27 25.1 22 19.5 15 12 11.3 8.25
84.4 89.1 98.3 107 127 145 150 174
33.5 35.3 38.7 41.9 49.2 55.4 57 64.6
3.26 3.25 3.23 3.21 3.16 3.11 3.1 3.01
2.05 2.04 2.03 2.01 1.97 1.92 1.91 1.84
18.8 19.8 21.8 23.8 28.3 32.2 33.3 38.6
13.4 14.1 15.5 16.8 19.7 22.1 22.8 25.8
23.2 24.6 27.2 29.8 36 41.6 43.2 51.4
15.3 16.2 18 19.6 23.5 27 28 32.9
76.5 80.9 89.4 97.5 116 133 138 160
22.4 23.6 25.9 28 32.9 37 38.1 43.2
0.272 0.272 0.271 0.27 0.267 0.265 0.264 0.259
160 151 135 123 100 85.1 81.5 66.5
10050 10050 10050 10050 10050 10050 10050 10050
3 3.2 3.6 4 5 6 6.3 8
6.71 7.13 7.96 8.78 10.8 12.7 13.3 16.3
8.54 9.08 10.1 11.2 13.7 16.2 16.9 20.8
13.7 12.6 10.9 9.5 7 5.33 4.94 3.25
30.3 28.3 24.8 22 17 13.7 12.9 9.5
110 116 128 140 167 190 197 230
36.8 38.8 42.6 46.2 54.3 61.2 63 71.7
3.58 3.57 3.55 3.53 3.48 3.43 3.42 3.33
2.08 2.07 2.05 2.03 1.99 1.95 1.93 1.86
21.9 23.2 25.6 27.9 33.3 38.1 39.4 46
14.7 15.5 17 18.5 21.7 24.5 25.2 28.7
27.3 28.9 32.1 35.2 42.6 49.4 51.3 61.4
16.8 17.7 19.6 21.5 25.8 29.7 30.8 36.3
88.4 93.4 103 113 135 154 160 186
25 26.4 29 31.4 36.9 41.6 42.9 48.9
0.292 0.292 0.291 0.29 0.287 0.285 0.284 0.279
149 140 126 114 92.8 78.8 75.4 61.4
10060 10060 10060 10060 10060 10060 10060 10060
3 3.2 3.6 4 5 6 6.3 8
7.18 7.63 8.53 9.41 11.6 13.6 14.2 17.5
9.14 9.72 10.9 12 14.7 17.4 18.1 22.4
17 15.7 13.7 12 9 7 6.52 4.5
30.3 28.3 24.8 22 17 13.7 12.9 9.5
124 131 145 158 189 217 225 264
55.7 58.8 64.8 70.5 83.6 95 98.1 113
3.68 3.67 3.65 3.63 3.58 3.53 3.52 3.44
2.47 2.46 2.44 2.43 2.38 2.34 2.33 2.25
24.7 26.2 28.9 31.6 37.8 43.4 45 52.8
18.6 19.6 21.6 23.5 27.9 31.7 32.7 37.8
30.2 32 35.6 39.1 47.4 55.1 57.3 68.7
21.2 22.4 24.9 27.3 32.9 38.1 39.5 47.1
121 129 142 156 188 216 224 265
30.7 32.4 35.6 38.7 45.9 52.1 53.8 62.2
0.312 0.312 0.311 0.31 0.307 0.305 0.304 0.299
139 131 117 106 86.5 73.3 70.2 57
12060 12060 12060 12060 12060 12060
3.6 4 5 6 6.3 8
9.66 10.7 13.1 15.5 16.2 20.1
12.3 13.6 16.7 19.8 20.7 25.6
13.7 12 9 7 6.52 4.5
30.3 27 21 17 16 12
227 249 299 345 358 425
76.3 83.1 98.8 113 116 135
4.3 4.28 4.23 4.18 4.16 4.08
2.49 2.47 2.43 2.39 2.37 2.3
37.9 41.5 49.9 57.5 59.7 70.8
25.4 27.7 32.9 37.5 38.8 45
47.2 51.9 63.1 73.6 76.7 92.7
28.9 31.7 38.4 44.5 46.3 55.4
183 201 242 279 290 344
43.3 47.1 56 63.8 65.9 76.6
0.351 0.35 0.347 0.345 0.344 0.339
104 93.7 76.1 64.4 61.6 49.9
227
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
228
B Y
D X
X t
Hot finished rectangular hollow sections – dimensions and properties RHS designation
Size
Thickness
DB
T
mm mm
mm 3.6 4 5 6 6.3
Mass per metre
Radius of gyration
Y
Area of section
Ratios for local buckling
Second moment of area
Elastic modulus
Plastic modulus
Torsional constants
Flange
Web
A
b/t
d/t
Axis x–x Ix
Axis y–y Iy
Axis x–x rx
Axis y–y ry
Axis x–x Zx
Axis y–y Zy
Axis x–x Sx
Axis y–y Sy
J
cm4
cm4
cm
cm
cm3
cm3
cm3
cm3
cm4
cm2 13.7 15.2 18.7 22.2 23.2 28.8 34.9
19.2 17 13 10.3 9.7 7 5
30.3 27 21 17 16 12 9
276 303 365 423 440 525 609
147 161 193 222 230 273 313
4.48 4.46 4.42 4.37 4.36 4.27 4.18
3.27 3.25 3.21 3.17 3.15 3.08 2.99
46 50.4 60.9 70.6 73.3 87.5 102
36.7 40.2 48.2 55.6 57.6 68.1 78.1
55.6 61.2 74.6 87.3 91 111 131
42 46.1 56.1 65.5 68.2 82.6 97.3
301 330 401 468 487 587 688
8 10
10.8 11.9 14.7 17.4 18.2 22.6 27.4
150 100 150 100 150 100 150 100 150 100 150 100 150 100 150 100
4 5 6 6.3 8 10 12 12.5
15.1 18.6 22.1 23.1 28.9 35.3 41.4 42.8
19.2 23.7 28.2 29.5 36.8 44.9 52.7 54.6
22 17 13.7 12.9 9.5 7 5.33 5
34.5 27 22 20.8 15.8 12 9.5 9
607 739 862 898 1087 1282 1450 1488
324 392 456 474 569 665 745 763
5.63 5.58 5.53 5.52 5.44 5.34 5.25 5.22
4.11 4.07 4.02 4.01 3.94 3.85 3.76 3.74
81 98.5 115 120 145 171 193 198
64.8 78.5 91.2 94.8 114 133 149 153
97.4 119 141 147 180 216 249 256
73.6 90.1 106 110 135 161 185 190
160 80 160 80 160 80 160 80 160 80 160 80 160 80 160 80
4 5 6 6.3 8 10 12 12.5
14.4 17.8 21.2 22.2 27.6 33.7 39.5 40.9
18.4 22.7 27 28.2 35.2 42.9 50.3 52.1
17 13 10.3 9.7 7 5 3.67 3.4
37 29 23.7 22.4 17 13 10.3 9.8
612 744 868 903 1091 1284 1449 1485
207 249 288 299 356 411 455 465
5.77 5.72 5.67 5.66 5.57 5.47 5.37 5.34
3.35 3.31 3.27 3.26 3.18 3.1 3.01 2.99
76.5 93 108 113 136 161 181 186
51.7 62.3 72 74.8 89 103 114 116
94.7 116 136 142 175 209 240 247
58.3 71.1 83.3 86.8 106 125 142 146
Approx length per tonne
C
kg/m
12080 120 80 120 80 120 80 120 80 120 80 120 80
Surface area of section
cm3
m2/m
m
59.5 65 77.9 89.6 92.9 110 126
0.391 0.39 0.387 0.385 0.384 0.379 0.374
92.7 83.9 68 57.5 54.9 44.3 36.5
660 807 946 986 1203 1432 1633 1679
105 127 147 153 183 214 240 246
0.49 0.487 0.485 0.484 0.479 0.474 0.469 0.468
66.4 53.7 45.2 43.2 34.7 28.4 24.2 23.3
493 600 701 730 883 1041 1175 1204
88.1 106 122 127 151 175 194 198
0.47 0.467 0.465 0.464 0.459 0.454 0.449 0.448
69.3 56 47.2 45.1 36.2 29.7 25.3 24.5
5 6 6.3 8 10 12 12.5
22.6 26.8 28.1 35.1 43.1 50.8 52.7
28.7 34.2 35.8 44.8 54.9 64.7 67.1
17 13.7 12.9 9.5 7 5.33 5
37 30.3 28.7 22 17 13.7 13
1495 1754 1829 2234 2664 3047 3136
505 589 613 739 869 979 1004
7.21 7.16 7.15 7.06 6.96 6.86 6.84
4.19 4.15 4.14 4.06 3.90 3.89 3.87
149 175 183 223 266 305 314
101 118 123 148 174 196 201
185 218 228 282 341 395 408
114 134 140 172 206 237 245
1204 1414 1475 1804 2156 2469 2541
172 200 208 251 295 333 341
0.587 0.585 0.584 0.579 0.574 0.569 0.568
44.3 37.3 35.6 28.5 23.2 19.7 19
250 150 250 150 250 150 250 150 250 150 250 150 250 150 250 150
5 6 6.3 8 10 12 12.5 16
30.4 36.2 38 47.7 58.8 69.6 72.3 90.3
38.7 46.2 48.4 60.8 74.9 88.7 92.1 115
27 22 20.8 15.8 12 9.5 9 6.38
47 38.7 36.7 28.3 22 17.8 17 12.6
3360 3965 4143 5111 6174 7154 7387 8879
1527 1796 1874 2298 2755 3168 3265 3873
9.31 9.27 9.25 9.17 9.08 8.98 8.96 8.79
6.28 6.24 6.22 6.15 6.06 5.98 5.96 5.8
269 317 331 409 494 572 591 710
204 239 250 306 367 422 435 516
324 385 402 501 611 715 740 906
228 270 283 350 426 497 514 625
3278 3877 4054 5021 6090 7088 7326 8868
337 396 413 506 605 695 717 849
0.787 0.785 0.784 0.779 0.774 0.769 0.768 0.759
32.9 27.6 26.3 21 17 14.4 13.8 11.1
300 200 300 200 300 200 300 200 300 200 300 200 300 200 300 200
5 6 6.3 8 10 12 12.5 16
38.3 45.7 47.9 60.3 74.5 88.5 91.9 115
48.7 58.2 61 76.8 94.9 113 117 147
37 30.3 28.7 22 17 13.7 13 9.5
57 47 44.6 34.5 27 22 21 15.8
6322 7486 7829 9717 11820 13800 14270 17390
3396 4013 4193 5184 6278 7294 7537 9109
11.4 11.3 11.3 11.3 11.2 11.1 11 10.9
8.35 8.31 8.29 8.22 8.13 8.05 8.02 7.87
421 499 522 648 788 920 952 1159
340 401 419 518 628 729 754 911
501 596 624 779 956 1124 1165 1441
380 451 472 589 721 847 877 1080
6824 8100 8476 10560 12910 15140 15680 19250
552 651 681 840 1015 1178 1217 1468
0.987 0.985 0.984 0.979 0.974 0.969 0.968 0.959
26.1 21.9 20.9 16.6 13.4 11.3 10.9 8.67
400 200 400 200 400 200 400 200 400 200 400 200 400 200
6 6.3 8 10 12 12.5 16
55.1 57.8 72.8 90.2 107 112 141
70.2 73.6 92.8 115 137 142 179
30.3 28.7 22 17 13.7 13 9.5
63.7 60.5 47 37 30.3 29 22
15000 15700 19560 23910 28060 29060 35740
5142 5376 6660 8084 9418 9738 11820
14.6 14.6 14.5 14.4 14.3 14.3 14.1
8.56 8.55 8.47 8.39 8.3 8.28 8.13
750 785 978 1196 1403 1453 1787
514 538 666 808 942 974 1182
917 960 1203 1480 1748 1813 2256
568 594 743 911 1072 1111 1374
12050 12610 15730 19260 22620 23440 28870
877 917 1135 1376 1602 1656 2010
1.18 1.18 1.18 1.17 1.17 1.17 1.16
18.2 17.3 13.7 11.1 9.32 8.97 7.12
450 250 450 250 450 250 450 250 450 250
8 10 12 12.5 16
85.4 106 126 131 166
109 135 161 167 211
28.3 22 17.8 17 12.6
53.3 42 34.5 33 25.1
30080 36890 43430 45030 55710
12140 14820 17360 17970 22040
16.6 16.5 16.4 16.4 16.2
10.6 10.5 10.4 10.4 10.2
1337 1640 1930 2001 2476
971 1185 1389 1438 1763
1622 2000 2367 2458 3070
1081 1331 1572 1631 2029
27080 33280 39260 40720 50550
1629 1986 2324 2406 2947
1.38 1.37 1.37 1.37 1.36
11.7 9.44 7.93 7.62 6.04
500 300 500 300 500 300 500 300 500 300
8 10 12 12.5 16
97.9 122 145 151 191
125 155 185 192 243
34.5 27 22 21 15.8
59.5 47 38.7 37 28.3
43730 53760 63450 65810 81780
19950 24440 28740 29780 36770
18.7 18.6 18.5 18.5 18.3
12.6 12.6 12.5 12.5 12.3
1749 2150 2538 2633 3271
1330 1629 1916 1985 2451
2100 2595 3077 3196 4005
1480 1826 2161 2244 2804
42560 52450 62040 64390 80330
2203 2696 3167 3281 4044
1.58 1.57 1.57 1.57 1.56
10.2 8.22 6.9 6.63 5.24
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
229
200 100 200 100 200 100 200 100 200 100 200 100 200 100
230
Structural Engineer’s Pocket Book
D Y
D X
X t Y
Hot finished square hollow sections – dimensions and properties SHS designation
Size DB mm mm
Mass Area of Ratios for per section local buckling metre
Thickness T mm kg/m
A cm2
Flange b/t
Second Radius moment of of area gyration
Web d/t I cm4
Elastic Plastic modulus modulus
Torsional constants
r cm
Z cm3
J cm4
S cm3
C cm3
Surface Approx area of length section per tonne
m2/m
m
0.154 0.152 0.152 0.151 0.15 0.147
346 293 277 250 228 189
40 40 40 40 40 40 40 40 40 40 40 40
2.5 3 3.2 3.6 4 5
2.89 3.41 3.61 4.01 4.39 5.28
3.68 4.34 4.6 5.1 5.59 6.73
13 10.3 9.5 8.11 7 5
13 10.3 9.5 8.11 7 5
8.54 9.78 40.2 11.1 11.8 13.4
1.52 1.5 1.49 1.47 1.45 1.41
4.27 4.89 5.11 5.54 5.91 6.68
5.14 5.97 6.28 6.88 7.44 8.66
13.6 15.7 16.5 18.1 19.5 22.5
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50
2.5 3 3.2 3.6 4 5 6 6.3
3.68 4.35 4.62 5.14 5.64 6.85 7.99 8.31
4.68 5.54 5.88 6.54 7.19 8.73 40.2 10.6
17 13.7 12.6 10.9 9.5 7 5.33 4.94
17 13.7 12.6 10.9 9.5 7 5.33 4.94
17.5 20.2 21.2 23.2 25 28.9 32 32.8
1.93 1.91 1.9 1.88 1.86 1.82 1.77 1.76
6.99 8.08 8.49 9.27 9.99 11.6 12.8 13.1
8.29 9.7 10.2 11.3 12.3 14.5 16.5 17
27.5 32.1 33.8 37.2 40.4 47.6 53.6 55.2
10.2 11.8 12.4 13.5 14.5 16.7 18.4 18.8
0.194 0.192 0.192 0.191 0.19 0.187 0.185 0.184
272 230 217 195 177 146 125 120
60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
3 3.2 3.6 4 5 6 6.3 8
5.29 5.62 6.27 6.9 8.42 9.87 10.3 12.5
6.74 7.16 7.98 8.79 10.7 12.6 13.1 16
17 15.7 13.7 12 9 7 6.52 4.5
17 15.7 13.7 12 9 7 6.52 4.5
36.2 38.2 41.9 45.4 53.3 59.9 61.6 69.7
2.32 2.31 2.29 2.27 2.23 2.18 2.17 2.09
12.1 12.7 14 15.1 17.8 20 20.5 23.2
14.3 15.2 16.8 18.3 21.9 25.1 26 30.4
56.9 60.2 66.5 72.5 86.4 98.6 102 118
17.7 18.6 20.4 22 25.7 28.8 29.6 33.4
0.232 0.232 0.231 0.23 0.227 0.225 0.224 0.219
189 178 160 145 119 101 97.2 79.9
70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70
3 3.2 3.6 4 5 6 6.3 8
6.24 6.63 7.4 8.15 9.99 11.8 12.3 15
7.94 8.44 9.42 10.4 12.7 15 15.6 19.2
20.3 18.9 16.4 14.5 11 8.67 8.11 5.75
20.3 18.9 16.4 14.5 11 8.67 8.11 5.75
59 62.3 68.6 74.7 88.5 401 104 120
2.73 2.72 2.7 2.68 2.64 2.59 2.58 2.5
16.9 17.8 19.6 21.3 25.3 28.7 29.7 34.2
19.9 21 23.3 25.5 30.8 35.5 36.9 43.8
92.2 97.6 108 118 142 163 169 200
24.8 26.1 28.7 31.2 36.8 41.6 42.9 49.2
0.272 0.272 0.271 0.27 0.267 0.265 0.264 0.259
160 151 135 123 400 85.1 81.5 66.5
80 80 80 80 80 80 80 80 80 80 80 80 80 80
3.2 3.6 4 5 6 6.3 8
7.63 8.53 9.41 11.6 13.6 14.2 17.5
9.72 10.9 12 14.7 17.4 18.1 22.4
22 19.2 17 13 10.3 9.7 7
22 19.2 17 13 10.3 9.7 7
95 105 114 137 156 162 189
3.13 3.11 3.09 3.05 3 2.99 2.91
23.7 26.2 28.6 34.2 39.1 40.5 47.3
27.9 31 34 41.1 47.8 49.7 59.5
148 164 180 217 252 262 312
34.9 38.5 41.9 49.8 56.8 58.7 68.3
0.312 0.311 0.31 0.307 0.305 0.304 0.299
131 117 406 86.5 73.3 70.2 57
90 90 90 90 90 90 90 90 90 90 90 90
3.6 4 5 6 6.3 8
9.66 10.7 13.1 15.5 16.2 20.1
12.3 13.6 16.7 19.8 20.7 25.6
22 19.5 15 12 11.3 8.25
22 19.5 15 12 11.3 8.25
152 166 200 230 238 281
3.52 3.5 3.45 3.41 3.4 3.32
33.8 37 44.4 51.1 53 62.6
39.7 43.6 53 61.8 64.3 77.6
237 260 316 367 382 459
49.7 54.2 64.8 74.3 77 90.5
0.351 0.35 0.347 0.345 0.344 0.339
104 93.7 76.1 64.4 61.6 49.9
10.8 11.9 14.7 17.4 18.2 22.6 27.4
13.7 15.2 18.7 22.2 23.2 28.8 34.9
24.8 22 17 13.7 12.9 9.5 7
24.8 22 17 13.7 12.9 9.5 7
212 232 279 323 336 400 462
3.92 3.91 3.86 3.82 3.8 3.73 3.64
42.3 46.4 55.9 64.6 67.1 79.9 92.4
49.5 54.4 66.4 77.6 80.9 98.2 116
328 361 439 513 534 646 761
62.3 68.2 81.8 94.3 97.8 116 133
0.391 0.39 0.387 0.385 0.384 0.379 0.374
92.7 83.9 68 57.5 54.9 44.3 36.5
100 100 3.6 100 100 4 100 100 5 100 100 6 100 100 6.3 100 100 8 100 100 10
6.22 7.1 7.42 8.01 8.54 9.6
231
Structural Steel
D Y
D X
X t Y
SHS designation
Size DB mm mm
Mass Area of Ratios for Second Radius Elastic Plastic Torsional per section local buckling moment of modulus modulus constants metre of area gyration
Thickness T A mm kg/m cm2
Flange b/t
Web d/t
I cm4
Surface Approx area of length section per tonne
r cm
Z cm3
S cm3
J cm4
C cm3 m2/m
m
120 120 4 120 120 5 120 120 6 120 120 6.3 120 120 8 120 120 10 120 120 12 120 120 12.5
14.4 47.8 21.2 22.2 27.6 33.7 39.5 40.9
18.4 22.7 27 28.2 35.2 42.9 50.3 52.1
27 21 17 16 12 9 7 6.6
27 21 17 16 12 9 7 6.6
410 498 579 603 726 852 958 982
4.72 4.68 4.63 4.62 4.55 4.46 4.36 4.34
68.4 83 96.6 100 121 142 160 164
79.7 97.6 115 120 146 175 201 207
635 777 911 950 1160 1382 1578 1623
101 122 141 147 176 206 230 236
0.47 0.467 0.465 0.464 0.459 0.454 0.449 0.448
69.3 56 47.2 45.1 36.2 29.7 25.3 24.5
140 140 5 140 140 6 140 140 6.3 140 140 8 140 140 10 140 140 12 140 140 12.5
21 24.9 26.1 32.6 40 47 48.7
26.7 31.8 33.3 41.6 50.9 59.9 62.1
25 20.3 19.2 14.5 11 8.67 8.2
25 20.3 19.2 14.5 11 8.67 8.2
807 944 984 1195 1416 1609 1653
5.5 5.45 5.44 5.36 5.27 5.18 5.16
115 135 141 171 202 230 236
135 159 166 204 246 284 293
1253 1475 1540 1892 2272 2616 2696
170 198 206 249 294 333 342
0.547 0.545 0.544 0.539 0.534 0.529 0.528
47.7 40.1 38.3 30.7 25 21.3 20.5
150 150 5 150 150 6 150 150 6.3 150 150 8 150 150 10 150 150 12 150 150 12.5
22.6 26.8 28.1 35.1 43.1 50.8 52.7
28.7 34.2 35.8 44.8 54.9 64.7 67.1
27 22 20.8 15.8 12 9.5 9
27 22 20.8 15.8 12 9.5 9
1002 1174 1223 1491 1773 2023 2080
5.9 5.86 5.85 5.77 5.68 5.59 5.57
134 156 163 199 236 270 277
156 184 192 237 286 331 342
1550 1828 1909 2351 2832 3272 3375
197 230 240 291 344 391 402
0.587 0.585 0.584 0.579 0.574 0.569 0.568
44.3 37.3 35.6 28.5 23.2 19.7 19
160 160 160 160 160 160 160 160 160 160 160 160 160 160 160 160
5 6 6.3 8 10 12 12.5 16
24.1 28.7 30.1 37.6 46.3 54.6 56.6 70.2
30.7 36.6 38.3 48 58.9 69.5 72.1 89.4
29 23.7 22.4 17 13 10.3 9.8 7
29 23.7 22.4 17 13 10.3 9.8 7
1225 1437 1499 1831 2186 2502 2576 3028
6.31 6.27 6.26 6.18 6.09 6 5.98 5.82
153 180 187 229 273 313 322 379
178 210 220 272 329 382 395 476
1892 2233 2333 2880 3478 4028 4158 4988
226 264 275 335 398 454 467 546
0.627 0.625 0.624 0.619 0.614 0.609 0.608 0.599
41.5 34.8 33.3 26.6 21.6 18.3 17.7 14.2
180 180 180 180 180 180 180 180 180 180 180 180 180 180 180180
5 6 6.3 8 10 12 12.5 16
27.3 32.5 34 42.7 52.5 62.1 64.4 80.2
34.7 41.4 43.3 54.4 66.9 79.1 82.1 102
33 27 25.6 19.5 15 12 11.4 8.25
33 27 25.6 19.5 15 12 11.4 8.25
1765 2077 2168 2661 3193 3677 3790 4504
7.13 7.09 7.07 7 6.91 6.82 6.8 6.64
196 231 241 296 355 409 421 500
227 269 281 349 424 494 511 621
2718 3215 3361 4162 5048 5873 6070 7343
290 340 355 434 518 595 613 724
0.707 0.705 0.704 0.699 0.694 0.689 0.688 0.679
36.7 30.8 29.4 23.4 19 16.1 15.5 12.5
232
Structural Engineer’s Pocket Book
D Y
D X
X t Y
Hot finished square hollow sections – dimensions and properties – continued SHS designation
Mass Area of Ratios for Second Radius Elastic Plastic Torsional per section local buckling moment of modulus modulus constants metre of area gyration
Size DB mm mm
Thickness T A mm kg/m cm2
Flange b/t
Web d/t
200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
5 6 6.3 8 10 12 12.5 16
30.4 38.7 36.2 46.2 38 48.4 47.7 60.8 58.8 74.9 69.6 88.7 72.3 92.1 90.3 115
37 30.3 28.7 22 17 13.7 13 9.5
37 30.3 28.7 22 17 13.7 13 9.5
250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
5 6 6.3 8 10 12 12.5 16
38.3 48.7 45.7 58.2 47.9 61 60.3 76.8 74.5 94.9 88.5 113 91.9 117 115 147
47 38.7 36.7 28.3 22 17.8 17 12.6
300 300 300 300 300 300 300 300 300 300 300 300 300 300
6 6.3 8 10 12 12.5 16
55.1 57.8 72.8 90.2 107 112 141
70.2 73.6 92.8 115 137 142 179
350 350 350 350 350 350 350 350 350 350
8 10 12 12.5 16
85.4 106 126 131 166
400 400 400 400 400 400 400 400 400 400
8 10 12 12.5 16
97.9 122 145 151 191
I cm4
Surface Approx area of length section per tonne
r cm
Z cm3
S cm3
J cm4
C cm3 m2/m
m
2445 2883 3011 3709 4471 5171 5336 6394
7.95 7.9 7.89 7.81 7.72 7.64 7.61 7.46
245 288 301 371 447 517 534 639
283 335 350 436 531 621 643 785
3756 4449 4653 5778 7031 8208 8491 10340
362 426 444 545 655 754 778 927
0.787 0.785 0.784 0.779 0.774 0.769 0.768 0.759
32.9 27.6 26.3 21 17 14.4 13.8 11.1
47 38.7 36.7 28.3 22 17.8 17 12.6
4861 5752 6014 7455 9055 10560 10920 13270
9.99 9.94 9.93 9.86 9.77 9.68 9.66 9.5
389 460 481 596 724 844 873 1061
447 531 556 694 851 1000 1037 1280
7430 8825 9238 11530 14110 16570 17160 21140
577 681 712 880 1065 1237 1279 1546
0.987 0.985 0.984 0.979 0.974 0.969 0.968 0.959
46.1 21.9 20.9 16.6 13.4 11.3 10.9 8.67
47 44.6 34.5 27 22 21 15.8
47 44.6 34.5 27 22 21 15.8
10080 10550 13130 16030 18780 19440 23850
12 12 11.9 11.8 11.7 11.7 11.5
672 703 875 1068 1252 1296 1590
772 809 1013 1246 1470 1525 1895
15410 16140 20190 24810 29250 30330 37620
997 1043 1294 1575 1840 1904 2325
1.18 1.18 1.18 1.17 1.17 1.17 1.16
18.2 17.3 13.7 11.1 9.32 8.97 7.12
109 135 161 167 211
40.8 32 26.2 25 18.9
40.8 32 26.2 25 18.9
21130 25880 30430 31540 38940
13.9 13.9 13.8 13.7 13.6
1207 1479 1739 1802 2225
1392 1715 2030 2107 2630
32380 39890 47150 48930 60990
1789 2185 2563 2654 3264
1.38 1.37 1.37 1.37 1.36
11.7 9.44 7.93 7.62 6.04
125 155 185 192 243
47 37 30.3 29 22
47 37 30.3 29 22
31860 39130 46130 47840 59340
16 15.9 15.8 15.8 15.6
1593 1956 2306 2392 2967
1830 2260 2679 2782 3484
48690 60090 71180 73910 92440
2363 2895 3405 3530 4362
1.58 1.57 1.57 1.57 1.56
10.2 8.22 6.9 6.63 5.24
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
233
Structural Steel
D Y
X
X t Y
Hot finished circular hollow sections – dimensions and properties CHS designation
Mass Area of Ratio for Second Radius of Elastic Plastic Torsional per section local moment gyration modulus modulus constants metre buckling of area
Outside Thickness diameter D t
A kg/m
D/t
cm2
mm
mm
21.3 26.9
3.2 3.2
1.43 1.87
1.82 2.38
6.7 8.4
33.7 33.7 33.7 33.7
3 3.2 3.6 4
2.27 2.41 2.67 2.93
2.89 3.07 3.4 3.73
42.4 42.4 42.4 42.4
3 3.2 3.6 4
2.91 3.09 3.44 3.79
48.3 48.3 48.3 48.3 48.3 48.3
2.5 3 3.2 3.6 4 5
60.3 60.3 60.3 60.3 60.3 60.3
2.5 3 3.2 3.6 4 5
76.1 76.1 76.1 76.1 76.1 76.1 76.1 76.1
I
r
Z
S
J
cm4
cm
cm3
cm3
cm4
Surface Approx area of length Per section tonne
C cm3
m2/m
m
0.768 0.65 1.7 0.846
0.722 1.27
1.06 1.81
1.54 3.41
1.44 0.067 2.53 0.085
700 535
11.2 10.5 9.4 8.4
3.44 3.6 3.91 4.19
1.09 1.08 1.07 1.06
2.04 2.14 2.32 2.49
2.84 2.99 3.28 3.55
6.88 7.21 7.82 8.38
4.08 4.28 4.64 4.97
0.106 0.106 0.106 0.106
440 415 374 341
3.71 3.94 4.39 4.83
14.1 13.3 11.8 10.6
7.25 7.62 8.33 8.99
1.4 1.39 1.38 1.36
3.42 3.59 3.93 4.24
4.67 4.93 5.44 5.92
14.5 15.2 16.7 18
6.84 7.19 7.86 8.48
0.133 0.133 0.133 0.133
343 323 290 264
2.82 3.35 3.56 3.97 4.37 5.34
3.6 4.27 4.53 5.06 5.57 6.8
19.3 16.1 15.1 13.4 12.1 9.7
9.46 11 11.6 12.7 13.8 16.2
1.62 1.61 1.6 1.59 1.57 1.54
3.92 4.55 4.8 5.26 5.7 6.69
5.25 6.17 6.52 7.21 7.87 9.42
18.9 22 23.2 25.4 27.5 32.3
7.83 9.11 9.59 10.5 11.4 13.4
0.152 0.152 0.152 0.152 0.152 0.152
354 298 281 252 229 187
3.56 4.24 4.51 5.03 5.55 6.82
4.54 5.4 5.74 6.41 7.07 8.69
24.1 20.1 18.8 16.8 15.1 12.1
19 22.2 23.5 25.9 28.2 33.5
2.05 2.03 2.02 2.01 2 1.96
6.3 7.37 7.78 8.58 9.34 11.1
8.36 9.86 10.4 11.6 12.7 15.3
38 44.4 46.9 51.7 56.3 67
12.6 14.7 15.6 17.2 18.7 22.2
0.189 0.189 0.189 0.189 0.189 0.189
281 236 222 199 180 147
2.52 3 3.2 3.6 4 5 6 6.3
4.54 5.78 5.41 6.89 5.75 7.33 6.44 8.2 7.11 9.06 8.77 11.2 10.4 13.2 10.8 13.8
30.4 25.4 23.8 21.1 19 15.2 12.7 12.1
39.2 46.1 48.8 54 59.1 70.9 81.8 84.8
2.6 2.59 2.58 2.57 2.55 2.52 2.49 2.48
10.3 12.1 12.8 14.2 15.5 18.6 21.5 22.3
13.5 16 17 18.9 20.8 25.3 29.6 30.8
78.4 92.2 97.6 108 118 142 164 170
20.6 24.2 25.6 28.4 31 37.3 43 44.6
0.239 0.239 0.239 0.239 0.239 0.239 0.239 0.239
220 185 174 155 141 114 96.4 92.2
88.9 88.9 88.9 88.9 88.9 88.9 88.9 88.9
2.5 3 3.2 3.6 4 5 6 6.3
5.33 6.36 6.76 7.57 8.38 10.3 12.3 12.8
6.79 8.1 8.62 9.65 10.7 13.2 15.6 16.3
35.6 29.6 27.8 24.7 22.2 17.8 14.8 14.1
63.4 74.8 79.2 87.9 96.3 116 135 140
3.06 3.04 3.03 3.02 3 2.97 2.94 2.93
14.3 16.8 17.8 19.8 21.7 26.2 30.4 31.5
18.7 22.1 23.5 26.2 28.9 35.2 41.3 43.1
127 150 158 176 193 233 270 280
28.5 33.6 35.6 39.5 43.3 52.4 60.7 63.1
0.279 0.279 0.279 0.279 0.279 0.279 0.279 0.279
188 157 148 132 119 96.7 81.5 77.9
114.3 114.3 114.3 114.3 114.3 114.3 114.3
3 3.2 3.6 4 5 6 6.3
8.23 8.77 9.83 10.9 13.5 16 16.8
10.5 11.2 12.5 13.9 17.2 20.4 21.4
38.1 35.7 31.8 28.6 22.9 19.1 18.1
163 172 192 211 257 300 313
3.94 3.93 3.92 3.9 3.87 3.83 3.82
28.4 30.2 33.6 36.9 45 52.5 54.7
37.2 39.5 44.1 48.7 59.8 70.4 73.6
325 345 384 422 514 600 625
56.9 60.4 67.2 73.9 89.9 105 109
0.359 0.359 0.359 0.359 0.359 0.359 0.359
121 114 102 91.9 74.2 62.4 59.6
234
Structural Engineer’s Pocket Book
D Y
X
X t Y
Hot finished circular hollow sections – dimensions and properties – continued DHS designation
Mass Area of Ratio for Second Radius of Elastic Plastic Torsional per section local moment gyration modulus modulus constants metre buckling of area
Outside Thickness diameter D t
A
D/t
Surface Approx area of length per section tonne
I
r
Z
S
J
cm4
cm
cm3
cm3
cm4 cm3
m2/m
m
320 357 393 481 564 589 720 862
4.83 4.81 4.8 4.77 4.73 4.72 4.66 4.6
45.8 51.1 56.2 68.8 80.8 84.3 103 123
59.6 66.7 73.7 90.8 107 112 139 169
640 713 786 961 1129 1177 1441 1724
91.6 102 112 138 162 169 206 247
0.439 0.439 0.439 0.439 0.439 0.439 0.439 0.439
92.8 82.8 74.7 60.2 50.5 48.2 38.5 31.3
52.6 46.8 42.1 33.7 28.1 26.7 21 16.8 14 13.5
566 632 697 856 1009 1053 1297 1564 1810 1868
5.84 5.82 5.81 5.78 5.74 5.73 5.67 5.61 5.54 5.53
67.2 75.1 82.8 102 120 125 154 186 215 222
87.2 97.7 108 133 158 165 206 251 294 304
1131 1264 1394 1712 2017 2107 2595 3128 3620 3737
134 150 166 203 240 250 308 372 430 444
0.529 0.529 0.529 0.529 0.529 0.529 0.529 0.529 0.529 0.529
76.8 68.4 61.7 49.7 41.6 39.7 31.6 25.6 21.6 20.8
29.6 35.4 37.1 46.7 57.7 68.5 71.2
38.7 32.3 30.7 24.2 19.4 16.1 15.5
1320 1560 1630 2016 2442 2839 2934
6.67 6.64 6.63 6.57 6.5 6.44 4.42
136 161 168 208 252 293 303
178 211 221 276 338 397 411
2640 3119 3260 4031 4883 5678 5869
273 322 337 416 504 586 606
0.609 0.609 0.609 0.609 0.609 0.609 0.609
43 36 34.3 27.3 22.1 18.6 17.9
26.4 31.5 33.1 41.6 51.6 61.3 63.7 80.1
33.6 40.2 42.1 53.1 65.7 78.1 81.1 102
43.8 36.5 34.8 27.4 21.9 18.3 17.5 13.7
1928 2282 2386 2960 3598 4200 4345 5297
7.57 7.54 7.53 7.47 7.4 7.33 7.32 7.2
176 208 218 270 328 383 397 483
229 273 285 357 438 515 534 661
3856 4564 4772 5919 7197 8400 8689 10590
352 417 436 540 657 767 793 967
0.688 0.688 0.688 0.688 0.688 0.688 0.688 0.688
37.9 31.7 30.2 24 19.4 16.3 15.7 12.5
29.5 35.3 37 46.7 57.8 68.8 71.5 90.2
37.6 45 47.1 59.4 73.7 87.7 91.1 115
48.9 40.8 38.8 30.6 24.5 20.4 19.6 15.3
2699 3199 3346 4160 5073 5938 6147 7533
8.47 8.43 8.42 8.37 8.3 8.23 8.21 8.1
221 262 274 340 415 486 503 616
287 341 358 448 550 649 673 837
5397 6397 6692 8321 10150 11880 12290 15070
441 523 547 681 830 972 1006 1232
0.768 0.768 0.768 0.768 0.768 0.768 0.768 0.768
33.9 28.3 27 21.4 17.3 14.5 14 11.1
mm
mm
kg/m cm2
139.7 139.7 139.7 139.7 139.7 139.7 139.7 139.7
3.2 3.6 4 5 6 6.3 8 10
10.8 12.1 13.4 16.6 19.8 20.7 26 32
13.7 15.4 17.1 21.2 25.2 26.4 33.1 40.7
43.7 38.8 34.9 27.9 23.3 22.2 17.5 14
168.3 168.3 168.3 168.3 168.3 168.3 168.3 168.3 168.3 168.3
3.2 3.6 4 5 6 6.3 8 10 12 12.5
13 14.6 16.2 20.1 24 25.2 31.6 39 46.3 48
16.6 18.6 20.6 25.7 30.6 32.1 40.3 49.7 58.9 61.2
193.7 193.7 193.7 193.7 193.7 193.7 193.7
5 6 6.3 8 10 12 12.5
23.3 27.8 29.1 36.6 45.3 53.8 55.9
219.1 219.1 219.1 219.1 219.1 219.1 219.1 219.1
5 6 6.3 8 10 12 12.5 16
244.5 244.5 244.5 244.5 244.5 244.5 244.5 244.5
5 6 6.3 8 10 12 12.5 16
C
235
Structural Steel
D Y
X
X t Y
DHS designation
Mass Area of Ratio for Second Radius of Elastic Plastic Torsional per section local moment gyration modulus modulus constants metre buckling of area
Outside Thickness diameter D t
A
D/t
Surface Approx area of length per section tonne
I
r
Z
S
J
cm4
cm
cm3
cm3
cm4 cm3
m2/m
m
9.48 9.44 9.43 9.37 9.31 9.24 9.22 9.1
277 329 344 429 524 615 637 784
359 428 448 562 692 818 849 1058
7562 8974 9392 11700 14310 16790 17390 21410
554 657 688 857 1048 1230 1274 1569
0.858 0.858 0.858 0.858 0.858 0.858 0.858 0.858
40.3 25.3 24.1 19.1 15.4 12.9 12.5 9.86
11.3 11.2 11.2 11.2 11.1 11 11 10.9
393 468 490 612 751 884 917 1136
509 606 636 799 986 1168 1213 1518
12740 15140 15860 19820 24320 28640 29690 36780
787 935 979 1224 1501 1768 1833 2271
1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02
25.4 21.3 20.3 16 12.9 10.8 10.4 8.23
10550 13200 16220 19140 19850 24660
12.4 12.3 12.2 12.2 12.1 12
593 742 912 1076 1117 1387
769 967 1195 1417 1472 1847
21090 26400 32450 38280 39700 49330
1186 1485 1825 2153 2233 2774
1.12 1.12 1.12 1.12 1.12 1.12
18.4 14.6 11.7 9.83 9.45 7.46
64.5 50.8 40.6 33.9 32.5 25.4
15850 19870 24480 28940 30030 37450
14.1 14.1 14 14 13.9 13.8
780 978 1205 1424 1478 1843
1009 1270 1572 1867 1940 2440
31700 39750 48950 57870 60060 74900
1560 1956 2409 2848 2956 3686
1.28 1.28 1.28 1.28 1.28 1.28
16.1 12.7 10.2 8.57 8.24 6.49
89.2 113 140 168 175 222
72.5 57.1 45.7 38.1 36.6 28.6
22650 28450 35090 41560 43140 53960
15.9 15.9 15.8 15.7 15.7 15.6
991 1245 1536 1819 1888 2361
1280 1613 1998 2377 2470 3113
45310 56890 70180 83110 86290 107900
1983 2490 3071 3637 3776 4723
1.44 1.44 1.44 1.44 1.44 1.44
14.3 11.3 9.07 7.59 7.3 5.75
99.3 126 156 187 195 247
80.6 63.5 50.8 42.3 40.6 31.8
31250 39280 48520 57540 59760 74910
17.7 17.7 17.6 17.5 17.5 17.4
1230 1546 1910 2265 2353 2949
1586 2000 2480 2953 3070 3874
62490 78560 97040 115100 119500 149800
2460 3093 3820 4530 4705 5898
1.6 1.6 1.6 1.6 1.6 1.6
12.8 10.1 8.14 6.81 6.55 5.15
kg/m cm2
mm
mm
273 273 273 273 273 273 273 273
5 6 6.3 8 10 12 12.5 16
33 39.5 41.4 52.3 64.9 77.2 80.3 101
42.1 50.3 52.8 66.6 82.6 98.4 102 129
54.6 45.5 43.3 34.1 27.3 22.8 21.8 17.1
3781 4487 4696 5852 7154 8396 8697 10710
323.9 323.9 323.9 323.9 323.9 323.9 323.9 323.9
5 6 6.3 8 10 12 12.5 16
39.3 47 49.3 62.3 77.4 92.3 96 121
50.1 59.9 62.9 79.4 98.6 118 122 155
64.8 54 51.4 40.5 32.4 27 25.9 20.2
6369 7572 7929 9910 12160 14320 14850 18390
355.6 355.6 355.6 355.6 355.6 355.6
6.3 8 10 12 12.5 16
54.3 68.6 85.2 102 106 134
69.1 87.4 109 130 135 171
56.4 44.5 35.6 29.6 28.4 22.2
406.4 406.4 406.4 406.4 406.4 406.4
6.3 8 10 12 12.5 16
62.2 78.6 97.8 117 121 154
79.2 100 125 149 155 196
457 457 457 457 457 457
6.3 8 10 12 12.5 16
70 88.6 110 132 137 174
508 508 508 508 508 508
6.3 8 10 12 12.5 16
77.9 98.6 123 147 153 194
C
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind permission of Corus UK Ltd.
236
Structural Engineer’s Pocket Book
Mild steel rounds typically available Weight Bar diameter kg/m mm
Weight Bar Weight Bar Weight Bar diameter kg/m diameter kg/m diameter kg/m mm mm mm
6 8 10 12
16 20 25 32
0.22 0.39 0.62 0.89
1.58 2.47 3.85 6.31
40 45 50 60
9.86 12.5 15.4 22.2
65 75 90 100
26.0 34.7 49.9 61.6
Mild steel square bars typically available Bar size mm
Weight kg/m
Bar size mm
Weight kg/m
Bar size mm
Weight kg/m
8 10 12.5 16 20
0.50 0.79 1.22 2.01 3.14
25 30 32 40 45
4.91 7.07 8.04 12.60 15.90
50 60 75 90 100
19.60 28.30 44.20 63.60 78.50
Structural Steel
237
Mild steel flats typically available Bar
Weight Bar
Weight Bar
Weight Bar
Weight Bar
Weight
size mm
kg/m
size mm
kg/m
kg/m
size mm
kg/m
size mm
kg/m
13 3 13 6 16 3 20 3 20 5 20 6
0.307 0.611 0.378 0.466 0.785 0.940
45 6 45 8 45 10 45 12 45 15 45 20
2.120 2.830 3.530 4.240 5.295 7.070
65 40 20.40 70 8 4.40 70 10 5.50 70 12 6.59 70 20 11.0 70 25 13.70
100 15 100 20 100 25 100 30 100 40 100 50
11.80 15.70 19.60 23.60 31.40 39.30
160 10 160 12 160 15 160 20 180 6 180 10
12.60 15.10 18.80 25.20 8.50 14.14
20 10 25 3 25 5 25 6 25 8 25 10
1.570 0.589 0.981 1.18 1.570 1.960
45 25 50 3 50 5 50 6 50 8 50 10
8.830 1.180 1.960 2.360 3.140 3.93
75 6 3.54 75 8 4.71 75 10 5.90 75 12 7.07 75 15 8.84 75 20 11.78
110 6 5.18 110 10 8.64 110 12 10.40 110 20 17.30 110 50 43.20 120 6 5.65
180 12 180 15 180 20 180 25 200 6 200 10
17.00 21.20 28.30 35.30 9.90 15.70
25 12 30 3 30 5 30 6 30 8 30 10 30 12
2.360 0.707 1.180 1.410 1.880 2.360 2.830
50 12 50 15 50 20 50 25 50 30 50 40 55 10
4.71 5.89 7.85 9.81 11.80 15.70 4.56
75 25 14.72 75 30 17.68 80 6 3.77 80 8 5.02 80 10 6.28 80 12 7.54 80 15 9.42
120 10 120 12 120 15 120 20 120 25 130 6 130 8
9.42 11.30 14.10 18.80 23.60 6.10 8.16
200 12 200 x 15 200 20 200 25 200 30 220 10 220 15
18.80 23.60 31.40 39.20 47.20 17.25 25.87
30 20 35 6 35 10 35 12 35 20 40 3
4.710 1.650 2.750 3.300 5.500 0.942
60 8 60 10 60 12 60 15 60 20 60 25
3.77 4.71 5.65 7.07 9.42 11.80
80 20 80 25 80 30 80 40 80 50 90 6
12.60 15.70 18.80 25.10 31.40 4.24
130 10 130 12 130 15 130 20 130 25 140 6
10.20 12.20 15.30 20.40 25.50 6.60
220 20 220 25 250 10 250 12 250 15 250 20
34.50 43.20 19.60 23.60 29.40 39.20
40 5 40 6 40 8 40 10 40 12 40 15 40 20
1.570 1.880 2.510 3.140 3.770 4.710 6.280
60 30 65 5 65 6 65 8 65 10 65 12 65 15
14.14 2.55 3.06 4.05 5.10 6.12 7.65
90 10 7.07 90 12 8.48 90 15 10.60 90 20 14.10 90 25 17.70 100 5 3.93 100 6 4.71
140 10 140 12 140 20 150 6 150 8 150 10 150 12
11.00 13.20 22.00 7.06 9.42 11.80 14.10
250 25 250 40 250 50 280 12.5 300 10 300 12 300 15
49.10 78.40 98.10 27.48 23.55 28.30 35.30
40 25 40 30 45 3
7.850 9.420 1.060
65 20 65 25 65 30
10.20 12.80 15.30
100 8 100 10 100 12
150 15 17.70 150 20 23.60 150 25 29.40
300 20 300 25 300 40
47.10 58.80 94.20
size mm
6.28 7.85 9.42
238
Structural Engineer’s Pocket Book
Hot rolled mild steel plates typically available Thick-
Weight
ness
Thick-
Weight
ness
mm
kg/m2
mm
3
23.55
10
3.2
25.12
12.5
4
31.40
5 6 8
Thick-
Weight
ness kg/m2
Thick-
Weight
ness
Thick-
Weight
ness
mm
kg/m2
mm
kg/m2
78.50
30
235.50
55
431.75
90
98.12
32
251.20
60
471.00
100
785.00
15
117.75
35
274.75
65
510.25
110
863.50
39.25
20
157.00
40
314.00
70
549.50
120
942.00
47.10
22.5
176.62
45
353.25
75
588.75
130
1050.50
62.80
25
196.25
50
392.50
80
628.00
150
1177.50
mm
kg/m2 706.50
Durbar mild steel floor plates typically available Basic size mm
Weight kg/m2
Basic size mm
Weight kg/m2
2500 1250 3 3000 1500 3
26.19
3000 1500 8 3700 1830 8 4000 1750 8 6100 1830 8
65.44
2000 1000 4.5 2500 1250 4.5 3000 1250 4.5 3700 1830 4.5 4000 1750 4.5
37.97
2000 1000 10 2500 1250 10 3000 1500 10 3700 1830 10
81.14
2000 1000 6 2500 1250 6 3000 1500 6 3700 1830 6 4000 1750 6
49.74
2000 1000 12.5 2500 1250 12.5 3000 1500 12.5 3700 1830 12.5 4000 1750 12.5
2000 1000 8 2500 1250 8
65.44
The depth of pattern ranges from 1.9 to 2.4 mm.
100.77
Structural Steel
239
Slenderness Slenderness and elastic buckling The slenderness () of a structural element indicates how much load the element can carry in compression. Short stocky elements have low values of slenderness and are likely to fail by crushing, while elements with high slenderness values will fail by elastic (reversible) buckling. Slender columns will buckle when the axial compression reaches the critical load. Slender beams will buckle when the compressive stress causes the compression flange to buckle and twist sideways. This is called Lateral Torsional Buckling and it can be avoided (and the load capacity of the beam increased) by restraining the compression flange at intervals or over its full length. Full lateral restraint can be assumed if the construction fixed to the compression flange is capable of resisting a force of not less than 2.5% of the maximum force in that flange distributed uniformly along its length.
Slenderness limits Slenderness, ¼ Le =r where Le is the effective length and r is the radius of gyration – generally about the weaker axis. For robustness, members should be selected so that their slenderness does not exceed the following limits: Members resisting load other than wind
180
Members resisting self-weight and wind only
250
Members normally acting as ties but subject to load reversal due to wind
350
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Effective length for different restraint conditions Effective length of beams – end restraint Conditions of restraint at the ends of the beams
Effective length Normal loading
Destabilizing loading
Compression flange laterally restrained; beam fully restrained against torsion (rotation about the longitudinal axis)
Both flanges fully restrained against rotation on plan
0.70L
0.85L
Compression flange fully restrained against rotation on plan
0.75L
0.90L
Both flanges partially restrained against rotation on plan
0.80L
0.95L
Compression flange partially restrained against rotation on plan
0.85L
1.00L
Both flanges free to rotate on plan
1.00L
1.20L
Partial torsional restraint against rotation about the longitudinal axis provided by connection of bottom flange to supports
1.0L þ 2D
1.2L þ 2D
1.2L þ 2D Partial torsional restraint against rotation about the longitudinal axis provided only by the pressure of the bottom flange bearing onto the supports
1.4L þ 2D
Compression flange laterally unrestrained; both flanges free to rotate on plan
NOTE: The illustrated connections are not the only methods of providing the restraints noted in the table.
Source: BS 5950: Part 1: 2000.
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Effective length of cantilevers Conditions of restraint
Effective length
Support
Cantilever tip
Continuous with lateral restraint to top flange
Free
3.0L
7.5L
Top flange laterally restrained
2.7L
7.5L
Torsional restraint
2.4L
4.5L
Lateral and torsional restraint
2.1L
3.6L
Free
2.0L
5.0L
Top flange laterally restrained
1.8L
5.0L
Torsional restraint
1.6L
3.0L
Lateral and torsional restraint
1.4L
2.4L 2.5L
Continuous with partial torsional restraint
Continuous with lateral and torsional restraint
Restrained laterally, torsionally and against rotation on plan
Normal loading
Destabilizing loading
Free
1.0L
Top flange laterally restrained
0.9L
2.5L
Torsional restraint
0.8L
1.5L
Lateral and torsional restraint
0.7L
1.2L
Free
0.8L
1.4L
Top flange laterally restrained
0.7L
1.4L
Torsional restraint
0.6L
0.6L
Lateral and torsional restraint
0.5L
0.5L
Cantilever tip restraint conditions Free
Top flange laterally restrained
Torsional Restraint
Lateral and torsional restraint
Source: BS 5950: Part 1: 2000.
Effective length of braced columns – restraint provided by cross bracing or shear wall Conditions of restraint at the ends of the columns
Effective length
Effectively held in position at both ends
0.70L 0.85L 0.85L 1.00L
Effectively restrained in direction at both ends Partially restrained in direction at both ends Restrained in direction at one end Not restrained in direction at either end
Effective length of unbraced columns – restraint provided by sway of columns Conditions of restraint at the ends of the columns
Effective length
Effectively held in position and restrained in direction at one end
1.20L 1.50L 2.00L
Other end effectively restrained in direction Other end partially restrained in direction Other end not restrained in direction
Source: BS 5950: Part 1: 2000.
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Durability and fire resistance Corrosion mechanism and protection 4Fe þ 3O2 þ 2H2O ¼ 2Fe2O3 . H2O Iron/Steel þ Oxygen þ Water ¼ Rust For corrosion of steel to take place, oxygen and water must both be present. The corrosion rate is affected by the atmospheric pollution and the length of time the steelwork remains wet. Sulphates (typically from industrial pollution) and chlorides (typically in marine environments – coastal is considered to be a 2 km strip around the coast in the UK) can accelerate the corrosion rate. All corrosion occurs at the anode (ve where electrons are lost) and the products of corrosion are deposited at the cathode (þve where the electrons are gained). Both anodic and cathodic areas can be present on a steel surface. The following factors should be considered in relation to the durability of a structure: the environment, degree of exposure, shape of the members, structural detailing, protective measures and whether inspection and maintenance are possible. Bi-metallic corrosion should also be considered in damp conditions.
Durability exposure conditions Corrosive environments are classified by BS EN ISO 12944: Part 2 and ISO 9223, and the corrosivity of the environment must be assessed for each project. Corrosivity category and risk
Examples of typical environments in a temperate climate* Exterior
Interior
C1 – Very low
–
Heated buildings with clean atmospheres, e.g. offices, shops, schools, hotels, etc. (theoretically no protection is needed)
C2 – Low
Atmospheres with low levels of pollution. Mostly rural areas
Unheated buildings where condensation may occur, e.g. depots and sports halls
C3 – Medium
Urban and industrial atmospheres with moderate sulphur dioxide pollution. Coastal areas with low salinity
Production rooms with high humidity and some air pollution, e.g. food processing plants, laundries, breweries, dairies, etc.
C4 – High
Industrial areas and coastal areas with moderate salinity
Chemical plants, swimming pools, coastal ship and boatyards
C5I – Very high (industrial)
Industrial areas with high humidity and aggressive atmosphere
Buildings or areas with almost permanent condensation and high pollution
C5M – Very high (marine)
Coastal and offshore areas with high salinity
Buildings or areas with almost permanent condensation and high pollution
* A hot and humid climate increases the corrosion rate and steel will require additional protection than in a temperate climate.
BS EN ISO 12944: Part 3 gives advice on steelwork detailing to avoid crevices where moisture and dirt can be caught and accelerate corrosion. Some acidic timbers should be isolated from steelwork. Get advice for each project: Corus can give advice on all steelwork coatings. The Galvanizers’ Association, Metal Sprayers Association and paint manufacturers also give advice on system specifications.
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Methods of corrosion protection A corrosion protection system should consist of good surface preparation and application of a suitable coating with the required durability and minimum cost.
Mild steel surface preparation to BS EN ISO 8501 Hot rolled structural steelwork (in mild steel) leaves the last rolling process at about 1000 C. As it cools, its surface reacts with the air to form a blue-grey coating called mill scale, which is unstable, will allow rusting of the steel and will cause problems with the adhesion of protective coatings. The steel must be degreased to ensure that any contaminants which might affect the coatings are removed. The mill scale can then be removed by abrasive blast cleaning. Typical blast cleaning surface grades are: Sa 1 Sa 2 Sa 21/2 Sa 3
Light blast cleaning Thorough blast cleaning Very thorough blast cleaning Blast cleaning to visually clean steel
Sa 21/2 is used for most structural steel. Sa 3 is often used for surface preparation for metal spray coatings. Metallic and non-metallic particles can be used to blast clean the steel surface. Chilled angular metallic grit (usually grade G24) provides a rougher surface than round metallic shot, so that the coatings have better adhesion to the steel surface. Acid pickling is often used after blast cleaning to Sa 21/2 to remove final traces of mill scale before galvanizing. Coatings must be applied very quickly after the surface preparation to avoid rust reforming and the requirement for reblasting.
Paint coatings for structural steel Paint provides a barrier coating to prevent corrosion and is made up of pigment (for colour and protection), binder (for formation of the coating film) and solvent (to allow application of the paint before it evaporates and the paint hardens). When first applied, the paint forms a wet film thickness which can be measured and the dry film thickness (DFT – which is normally the specified element) can be predicted when the percentage volume of solids in the paint is known. Primers are normally classified on their protective pigment (e.g. zinc phosphate primer). Intermediate (which build the coating thickness) and finish coats are usually classified on their binders (e.g. epoxies, vinyls, urethanes, etc.). Shop primers (with a DFT of 15–25 mm) can be applied before fabrication but these only provide a couple of weeks’ worth of protection. Zinc rich primers generally perform best. Application of paint can be by brush, roller, air spray and airless spray – the latter is the most common in the UK. Application can be done on site or in the shop and where the steel is to be exposed, the method of application should be chosen for practicality and the surface finish. Shop applied coatings tend to need touching up on site if they are damaged in transit.
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Metallic coatings for structural steel De-greased, blast cleaned (generally Sa 21/2) and then acid pickled steel is dipped into a flux agent and then into a bath of molten zinc. The zinc reacts with the surface of the steel, forming alloys and as the steel is lifted out a layer of pure zinc is deposited on outer surface of the alloys. The zinc coating is chemically bonded to the steel and is sacrificial. The Galvanizers’ Association can provide details of galvanizing baths around the country, but the average bath size is about 10 m long 1.2 m wide 2 m deep. The largest baths available in 2002 in the UK are 21 m 1.5 m 2.4 m and 7.6 m 2.1 m 3 m. The heat can cause distortions in fabricated, asymmetric or welded elements. Galvanizing is typically 85–140 mm thick and should be carried out to BS EN ISO 1461 and 14713. Paint coatings can be applied on top of the galvanizing for aesthetic or durability reasons and an etch primer is normally required to ensure that the paint properly adheres to the galvanizing.
Hot dip galvanizing
Thermal spray
Degreased and blast cleaned (generally Sa 3) steel is sprayed with molten particles of aluminium or zinc. The coating is particulate and the pores normally need to be sealed with an organic sealant in order to prevent rust staining. Metal sprayed coatings are mechanically bonded to the steel and work partly by anodic protection and partly by barrier protection. There are no limits on the size of elements which can be coated and there are no distortion problems. Thermal spray is typically 150–200 mm thick in aluminium, 100–150 mm thick in zinc and should be carried out to BS EN 22063 and BS EN ISO 14713. Paint coatings can be applied for aesthetic or durability reasons. Bi-metallic corrosion issues should be considered when selecting fixings for aluminium sprayed elements in damp or external environments.
Weathering steel Weathering steels are high strength, low alloy, weldable structural steels which form a protective rust coating in air that reaches a critical level within 2–5 years and prevents further corrosion. Cor-ten is the Corus proprietary brand of weathering steel, which has material properties comparable to S355, but the relevant material standard is BS EN 10 155. To optimize the use of weathering steel, avoid contact with absorbent surfaces (e.g. concrete), prolonged wetting (e.g. north faces of buildings in the UK), burial in soils, contact with dissimilar metals and exposure to aggressive environments. Even if these conditions are met, rust staining can still affect adjacent materials during the first few years. Weathering bolts (ASTM A325, Type 3 or Cor-ten X) must be used for bolted connections. Standard black bolts should not be used as the zinc coating will be quickly consumed and the fastener corroded. Normal welding techniques can be used.
Stainless steel Stainless steel is the most corrosion resistant of all the steels due to the presence of chromium in its alloys. The surface of the steel forms a self-healing invisible oxide layer which prevents ongoing corrosion and so the surface must be kept clean and exposed to provide the oxygen required to maintain the corrosion resistance. Stainless steel is resistant to most things, but special precautions should be taken in chlorinated environments. Alloying elements are added in different percentages to alter the durability properties: SS 304
18% Cr, 10% Ni
Used for general cladding, brick support angles, etc.
SS 409
11% Cr
Sometimes used for lintels
SS 316
17% Cr, 12% Ni, 2.5% Mo
Used in medium marine/aggressive environments
SS Duplex 2205
22% Cr, 5.5% Ni, 3% Mo
Used in extreme marine and industrial environments
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Summary of methods of fire protection System
Typical thickness2 for 60 mins protection
Advantages
Disadvantages
Boards Up to 4 hours’ protection. Most popular system in the UK
25–30 mm
Clean ‘boxed in’ appearance; dry application; factory quality boards; needs no steel surface preparation
High cost; complex fitting around details; slow to apply
Vermiculite concrete spray Up to 4 hours’ protection. Second most popular system in the UK
20 mm
Cheap; easy on complex junctions; needs no steel surface preparation; often boards used on columns, with spray on the beams
Poor appearance; messy application needs screening; the wet trade will affect following trades; compatibility with corrosion protection needs to be checked
Intumescent paint Maximum 2 hours’ protection. Charring starts at 200–250 C
1–4 mm1
Good aesthetic; shows off form of steel; easy to cover complex details; can be applied in shop or on site
High cost; not suited to all environments; short periods of resistance; soft, thick, easily damaged coatings; difficult to get a really high quality finish; compatibility with corrosion protection needs to be checked
Flexible blanket Cheap alternative to sprays
20–30 mm
Low cost; dry fixing
Not good aesthetics
Concrete encasement Generally only used when durability is a requirement
25–50 mm
Provides resistance to abrasion, impact, corrosion and weather exposure
Expensive; time consuming; heavy; large thickness required
Concrete filled columns Used for up to 2 hoursprotection or to reduce intumescent paint thickness on hollow sections
–
Takes up less plan area; acts as permanent shutter; good durability
No data for CHS posts; minimum section size which can be protected 140 140SHS; expensive
Water filled columns Columns interconnected to allow convection cooling. Only used if no other option
–
Long periods of fire resistance
Expensive; lots of maintenance required to control water purity and chemical content
Block filled column webs Up to 30 minutes protection
–
Reduced cost; less plan area; good durability
Limited protection times; not advised for steel in partition walls
NOTES: 1. Coating thickness specified on the basis of the sections’ dimensions and the number of sides that will be exposed to fire. 2. Castellated beams need about 20% more fire protection than is calculated for the basic parent material.
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Preliminary sizing of steel elements Typical span/depth ratios Element
Typical span (L) m
Beam depth
Primary beams/trusses (heavy point loads) Secondary beams/trusses (distributed loads) Transfer beams/trusses carrying floors Castellated beams Plate girders Vierendeel girders
4–12 4–20 6–30 4–12 10–30 6–18
L/10–15 L/15–25 L/10 L/10–15 L/10–12 L/8–10
Parallel chord roof trusses Pitched roof trusses Light roof beams Conventional lattice roof girders Space frames (allow for l/250 pre-camber)
10–100 8–20 6–60 5–20 10–100
L/12–20 L/5–10 L/18–30 L/12–15 L/15–30
Hot rolled universal column
single storey 2–8 multi-storey 2–4 single storey 2–8 multi-storey 2–4 4–10 9–60
L/20–25 L/7–18 L/20–35 L/7– 28 L/20–25 L/35–40
Hollow section column Lattice column Portal leg and rafter (haunch depth <0.11)
Preliminary sizing Beams There are no shortcuts. Deflection will tend to govern long spans, while shear will govern short spans with heavy loading. Plate girders or trusses are used when the loading is beyond the capacity of rolled sections.
Columns – typical maximum column section size for braced frames 203 UC
Buildings 2 to 3 storeys high and spans up to 7 m.
254 UC
Buildings up to 5 storeys high.
305 UC
Buildings up to 8 storeys high or supports for low rise buildings with long spans.
354 UC
Buildings from 8 to 12 storeys high.
Columns – enhanced loads for preliminary axial design An enhanced axial load for columns subject to out of balance loads can be used for preliminary design: Top storey: Intermediate storey:
Total axial load þ 4Y Y þ 2X X Total axial load þ 2Y Y þ X X
Where XX and YY are the net axial load differences in each direction.
Trusses with parallel chord
Axial force in chord, F ¼ Mapplied =d where d is the distance between the chord centroids. P Ac d2=4 where Ac is the area of each chord.
Itruss ¼
For equal chords this can be simplified to Itruss ¼ Ac d2=2:
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Portal frames The Institution of Structural Engineers’ Grey Book for steel design gives the following preliminary method for sizing plastic portal frames with the following assumptions: . Plastic hinges are formed at the eaves (in the stanchion) and near the apex, therefore . . . .
Class 1 sections as defined in BS 5950 should be used. Moment at the end of the haunch is 0.87Mp. Wind loading does not control the design. Stability of the frame should be checked separately. Load, W ¼ vertical rafter load per metre run.
r
h
L
Horizontal base reaction, H ¼ HFRWL
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
0.20
2.0
1.5
1.0
Span/eaves height (L/h)
Rise/span (r/L)
0.15
0.10
0.05
0 0.06
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.76
HFR Horizontal force factor for stanchion base
Design moment for rafter, Mp rafter ¼ MPRWL2 Also consider the high axial force which will be in the rafter and design for combined axial and bending!
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1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
10.0 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.7 5.5 5.0
Span/eaves height (L/h) 0.20
Rise/span (r /L)
0.15
0.10
0.05
0 0.015
0.020
0.025
0.030
0.035
0.040
0.045
MPR rafter ratio
Design moment for stanchion, Mp
2 stanchion ¼ MPLWL
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5
10.0
Span/eaves height (L /h) 0.20
Rise/span (r /L)
0.15
0.10
0.05
0 0.03
0.04
0.05
0.06
MPL stanchion ratio
Source: IStructE (2002).
0.07
0.08
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Steel design to BS 5950 BS 5950: Part 1 was written to allow designers to reduce conservatism in steel design. The resulting choice and complication of the available design methods has meant that sections are mainly designed using software or the SCI Blue Book. As the code is very detailed, the information about BS 5950 has been significantly summarized – covering only grade S275 steelwork and using the code’s conservative design methods.
Partial safety factors Load combination
Load type Dead
Imposed
Dead and imposed
1.4 or 1.0
1.6
Dead and wind
1.4 or 1.0
–
Dead and wind and imposed
1.2
1.2
Dead and crane loads
1.4
–
Dead and imposed and crane loads
1.2
Crane V ¼ 1.4
Wind
Crane loads
Earth and water pressures
–
–
1.4
1.4
–
–
1.2
–
–
–
V ¼ 1.6 H ¼ 1.6 V and H ¼ 1.4 V ¼ 1.4 H ¼ 1.2 V and H ¼ 1.4
–
Crane H ¼ 1.2 Dead and wind and crane loads
1.2
–
1.2
1.2
–
Forces due to temperature change
–
1.2
–
–
–
Exceptional snow load due to drifting
–
1.05
–
–
–
Source: BS 5950: Part 1: 2000.
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Selected mild steel design strengths Steel grade
Steel thickness less than or equal to mm
Design strength, py N/mm2
S275
16 40 63
275 265 255
S355
16 40 63
355 345 335
Generally it is more economic to use S275 where it is required in small quantities (less than 40 tonnes), where deflection instead of strength limits design, or for members such as nominal ties where the extra strength is not required. In other cases it is more economical to consider S355.
Ductility and steel grading In addition to the strength of the material, steel must be specified for a suitable ductility to avoid brittle fracture, which is controlled by the minimum service temperature, the thickness of steel, the steel grade, the type of detail and the stress and strain levels. Ductility is measured by the Charpy V notch test. In the UK the minimum service temperature expected to occur over the design life of the structure should be taken as 5 C for internal steelwork or 15 C for external steelwork. For steelwork in cold stores or cold climates appropriate lower temperatures should be selected. Tables 4, 5, 6 and 7 in BS 5950 give the detailed method for selection of the appropriate steel grade. Steel grading has become more important now that the UK construction industry is using more imported steel. The latest British Standard has revised the notation used to describe the grades of steel. The equivalent grades are set out below:
Current grading references BS 5950: Part 1: 2000 and BS EN 100 25: 1993 Grade
Charpy test temperature C
Steel use
Superseded grading references* BS 5950: Part 1: 1990 and BS 4360: 1990 Max steel thickness mm
Grade
Charpy test temperature C
Steel use
Max steel thickness mm <100 >100 N/mm2 N/mm2
S275
Untested
Internal only
25
43 A
Untested
Internal
50
25
External
30
15
Internal
50
25
S275 JR Room temp. 20 C
Internal only
30
43 B
Room temp. 20 C
External
30
15
S275 J0 0 C
Internal External
65 54
43 C
0 C
Internal External
n/a 80
60 40
S275 J2 20 C
Internal External
94 78
43 D
20 C
Internal External
n/a n/a
n/a 90
* Where the superseded equivalent for grades S355 and S460 are Grades 50 and 55 respectively.
Source: BS 5950: Part 1: 2000.
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Section classification and local buckling Sections are classified by BS 5950 depending on how their cross section behaves under compressive load. Structural sections in thinner plate will tend to buckle locally and this reduces the overall compressive strength of the section and means that the section cannot achieve its full plastic moment capacity. Sections with tall webs tend to be slender under axial compression, while cross sections with wide out-stand flanges tend to be slender in bending. Combined bending and compression can change the classification of a cross section to slender, when that cross section might not be slender under either bending or compression when applied independently. For plastic design, the designer must therefore establish the classification of a section (for the given loading conditions) in order to select the appropriate design method from those available in BS 5950. For calculations without capacity tables or computer packages, this can mean many design iterations. BS 5950 has four types of section classification: Class 1: Class 2: Class 3: Class 4:
Plastic Cross sections with plastic hinge rotation capacity. Compact Cross sections with plastic moment capacity. Semi-compact Cross sections in which the stress at the extreme compression fibre can reach the design strength, but the plastic moment capacity cannot be developed. Slender Cross sections in which it is necessary to make explicit allowance for the effects of local buckling.
Tables 11 and 12 in BS 5950 classify different hot rolled and fabricated sections based on the limiting width to thickness ratios for each section class. None of the UB, UC, RSJ or PFC sections are slender in pure bending. Under pure axial compression, none of the UC, RSJ or PFC sections are slender, but some UB and hollow sections can be: UB SHS amd RHS (hot rolled) CHS Where D ¼ overall depth, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e ¼ 275=Py .
Slender if d/t > 40e Slender if d/t > 40e Slender if D/t > 80e2 t ¼ plate thickness, d ¼ web depth, py ¼ design strength,
For simplicity only design methods for Class 1 and 2 sections are covered in this book. Source: BS 5950: Part 1: 2000.
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Tension members Bolted connections: Pt ¼ (Ae 0.5a2) py Welded connections: Pt ¼ (Ae 0.3a2) py If a2 ¼ Ag a1 where Ag is the gross section area, Ae is the effective area (which is the net area multiplied by 1.2 for S275 steel, 1.1 for S355 or 1.0 for S460) and a1 is the area of the connected part (web or flange, etc.).
Flexural members Shear capacity, Pv Pv ¼ 0.6py Av
Where Av is the shear area, which should be taken as: tD AD=ðD þ BÞ t (D T ) 0.6A 0.9A
for rolled I sections (loaded parallel to the web) and rolled T sections for rectangular hollow sections for welded T sections for circular hollow sections solid bars and plates
t ¼ web thickness, A ¼ cross sectional area, D ¼ overall depth, B ¼ overall breadth, T ¼ flange thickness. If d=t > 70 for a rolled section, or >62 for a welded section, shear buckling must be allowed for (see BS 5950: clause 4.4.5). Source: BS 5950: Part 1: 2000.
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Moment capacity MC
The basic moment capacity (Mc) depends on the provision of full lateral restraint and the interaction of shear and bending stresses. Mc is limited to 1.2py Z to avoid irreversible deformation under serviceability loads. Full lateral restraint can be assumed if the construction fixed to the compression flange is capable of resisting not less than 2.5% of the maximum compression force in the flange, distributed uniformly along the length of the flange. Moment capacity (Mc) is generally the controlling capacity for class 1 and 2 sections in the following cases: . . . .
Bending about the minor axis. CHS, SHS or small solid circular or square bars. RHS in some cases given in clause 4.3.6.1 of BS 5950. UB, UC, RSJ, PFC, SHS or RHS if < 34 for S275 steel and < 30 for S355 steel in Class 1 and 2 sections, where ¼ LE =r
Low shear (Fv < 0.6Pv)
Mc ¼ pyS
High shear (Fv > 0.6P 2 v) Mc ¼ py (S rSn) Where ¼ 2 PFvv 1 and Sv ¼ the plastic modulus of the shear area used to calculate Pv.
Lateral torsional buckling capacity Mb
Lateral torsional buckling (LTB) occurs in tall sections or long beams in bending if not enough restraint is provided to the compression flange. Instability of the compression flange results in buckling of the beam, preventing the section from developing its full plastic capacity, Mc. The reduced bending moment capacity, Mb, depends on the slenderness of the section, LT. For Class 1 and 2 sections, LT ¼ . A simplified and conservative method of calculating Mb for rolled sections uses D=T and LT to determine an ultimate bending stress pb (from the following graph) where Mb ¼ pbSx for Class 1 and 2 sections. Source: BS 5950: Part 1: 2000.
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Ultimate bending strengths for rolled sections, pb
270 260 250 240 230 220 Ultimate bending stress, pb (N/mm2)
210 200 190
D = 5 T
180 170 160 150 140 10
130 120 110 100
15
90 80
20
70
25
60
30 35 40 45 50
50 40 25
50
75
100
125
150
175
Slenderness (Le/ry)
200
225
250
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Compression members The compression capacity of Class 1 and 2 sections can be calculated as Pc ¼ Agpc, where Ag is the gross area of the section and pc can be estimated depending on the expected buckling axis and the section type for steel of 40 mm thickness.
Type of section
Strut curve for value of pc Axis of buckling x–x
y–y
Hot finished structural hollow section
a
a
Rolled I section
a
b
Rolled H section
b
c
Round, square or flat bar
b
b
Rolled angle, channel or T section/paired rolled sections/compound rolled sections
Any axis: c
Ultimate compression stresses for rolled sections, pc
Ultimate compression stresses for rolled sections, pc
280 260 240
Ultimate compressive stress, pc (N/mm2)
220 200 c
180
b
a Strut curve
160 140 120 100 80 60 40 20 0 50
100
150 200 250 Slenderness (Le/ry)
300
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Combined bending and compression Although each section should have its classification checked for combined bending and axial compression, the capacities from the previous tables can be checked against the following simplified relationship for section Classes 1 and 2:
My F Mx þ < 1:0 þ P Mcx or Mb Mcy
Section 4.8 in BS 5950 should be referred to in detail for all the relevant checks.
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Connections Welded connections
W
W
The resultant 2of combined longitudinal and transverse forces should be checked: FL 2 FT þ < 1:0 : PL PT
Ultimate fillet weld capacities for S275 elements joined at 90 Leg length s mm
Throat thickness a ¼ 0.7s mm
Longitudinal capacity* PL ¼ pw kN/mm
Transverse capacity* L ¼ pwaK kN/mm
4 6 8 12
2.8 4.2 5.6 8.4
0.616 0.924 1.232 1.848
0.770 1.155 1.540 2.310
* Based on values for S275, pw ¼ 220 N/mm2 and K ¼ 1.25.
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Bolted connections Limiting bolt spacings 1.25D
2.5D 1.25D 2.5D 1.25D
Rolled, machine cut or flame cut, sawn or planed edge.
Direct shear W
W Single shear
W
W Double shear
Simple moment connection bolt groups e P F1 F2 F3
X4 X3
X2 X1
F4
X3
X2
X1
X4
P Mcap ¼ no. rowsx1 of bolts Pt x2i V ¼ Pnt xn Fn ¼ Pt xn1
Where x1 ¼ max xi and xi ¼ depth from point of rotation to centre of bolt being considered, Pt is the tension capacity of the bolts, n is the number of bolts, V is the shear on each bolt and F is the tension in each bolt. This is a simplified analysis which assumes that the bolt furthest from the point of rotation carries the most load. As the connection elements are likely to be flexible, this is unlikely to be the case; however, more complicated analysis requires a computer or standard tables.
Bolt capacity checks
For bolts in shear or tension see the following tabulated values. For bolts in shear and tension check: ðFv =Pv Þ þ ðFt =Pt Þ 1:4 where F indicates the factored design load and P indicates the ultimate bolt capacity.
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Selected ultimate bolt capacities for non-pre-loaded ordinary bolts in S275 steel Diameter of bolt, f mm
Tensile Tension Shear stress capacity capacity area kN Single Double mm2 kN kN
Grade 4.6 6 20.1 8 36.6 10 58 12 84.3 16 157 20 245 24 353 30 561
3.9 7.0 11.1 16.2 30.1 47.0 67.8 107.7
3.2 5.9 9.3 13.5 25.1 39.2 56.5 89.8
Grade 8.8 6 20.1 8 36.6 10 58 12 84.3 16 157 20 245 24 353 30 561
9.0 16.4 26.0 37.8 70.3 109.8 158.1 251.3
7.5 13.7 21.8 31.6 58.9 91.9 132.4 210.4
Bearing capacity for end distance ¼ 2f kN Thickness of steel passed through mm 5
6
6.4 11.7 18.6 27.0 50.2 78.4 113.0 179.5
13.8 18.4 23.0 27.6 36.8 46.0 55.2 69.0
15.1 27.5 43.5 63.2 117.8 183.8 264.8 420.8
13.8 18.4 23.0 27.6 36.8 46.0 55.2 69.0
8
10
12
15
20
16.6 22.1 27.6 33.1 22.1 29.4 36.8 44.2 27.6 36.8 46.0 55.2 33.1 44.2 55.2 66.2 44.2 58.9 73.6 88.3 55.2 73.6 92.0 110.4 66.2 88.3 110.4 132.5 82.8 110.4 138.0 165.6
41.4 55.2 69.0 82.8 110.4 138.0 165.6 207.0
55.2 73.6 92.0 110.4 147.2 184.0 220.8 276.0
6.6 22.1 27.6 33.1 22.1 29.4 36.8 44.2 27.6 36.8 46.0 55.2 33.1 44.2 55.2 66.2 44.2 58.9 73.6 88.3 55.2 73.6 92.0 110.4 66.2 88.3 110.4 132.5 82.8 110.4 138.0 165.6
41.4 55.2 69.0 82.8 110.4 138.0 165.6 207.0
55.2 73.6 92.0 110.4 147.2 184.0 220.8 276.0
NOTES: 2 mm clearance holes for f < 24 or 3 mm clearance holes for f < 24. . Tabulated tension capacities are nominal tension capacity ¼ 0.8A p which accounts for prying forces. t t . Bearing values shown in bold are less than the single shear capacity of the bolt. . Bearing values shown in italic are less than the double shear capacity of the bolt. . Multiply tabulated bearing values by 0.7 if oversized or short slotted holes are used. .
. .
Multiply tabulated bearing values by 0.5 if kidney shaped or long slotted holes are used. Shear capacity should be reduced for large packing, grip lengths or long joints.
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Selected ultimate bolt capacities for non-pre-loaded countersunk bolts in S275 steel Diameter of bolt, f mm
Tensile Tension Shear stress capacity capacity area kN Single Double mm2 kN kN
Grade 4.6 6 20.1 8 36.6 10 58 12 84.3 16 157 20 245 24 353
3.9 7.0 11.1 16.2 30.1 47.0 67.8
3.2 5.9 9.3 13.5 25.1 39.2 56.5
Grade 8.8 6 20.1 8 36.6 10 58 12 84.3 16 157 20 245 24 353
9.0 16.4 26.0 37.8 70.3 109.8 158.1
7.5 13.7 21.8 31.6 58.9 91.9 132.4
Bearing capacity for end distance ¼ 2f kN Thickness of steel passed through (mm) 5
6
8
10
12
15
20
6.4 11.7 18.6 27.0 50.2 78.4 113.0
8.6 – – – – – –
11.3 12.9 – – – – –
16.8 20.2 21.9 – – – –
22.4 27.6 31.1 34.5 – – –
27.9 35.0 40.3 45.5 55.2 62.1 –
36.2 46.0 54.1 62.1 77.3 89.7 85.6
50.0 64.4 77.1 89.7 114.1 135.7 140.8
15.1 27.5 43.5 63.2 117.8 183.8 264.8
8.6 – – – – – –
11.3 12.9 – – – – –
16.8 20.2 21.9 – – – –
22.4 27.6 31.1 34.5 – – –
27.9 35.0 40.3 45.5 55.2 62.1 –
36.2 46.0 54.1 62.1 77.3 89.7 85.6
50.0 64.4 77.1 89.7 114.1 135.7 140.8
NOTES: . Values are omitted from the table where the bolt head is too deep to be countersunk into the thickness of the plate. . 2 mm clearance holes for f <24 or 3 mm clearance holes for f <24. . Tabulated tension capacities are nominal tension capacity ¼ 0.8A p which accounts for prying forces. t t . Bearing values shown in bold are less than the single shear capacity of the bolt. . Bearing values shown in italic are less than the double shear capacity of the bolt. . . .
Multiply tabulated bearing values by 0.7 if oversized or short slotted holes are used. Multiply tabulated bearing values by 0.5 if kidney shaped or long slotted holes are used. Shear capacity should be reduced for large packing, grip lengths or long joints.
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Steel design to BS 449 BS 449: Part 2 is the ‘old’ steel design code issued in 1969 but it is (with amendments) still current. The code is based on elastic bending and working stresses and is very simple to use. It is therefore invaluable for preliminary design, for simple steel elements and for checking existing structures. It is normal to compare the applied and allowable stresses. BS 449 refers to the old steel grades where Grade 43 is S275, Grade 50 is S355 and Grade 55 is S460.
Notation for BS 449: Part 2 Symbols f P l/r D t
Stress subscripts Applied stress Permissible stress Slenderness ratio Overall section depth Flange thickness
c or bc t or bt q b e
Compression or bending compression Tension or bending tension Shear Bearing Equivalent
Allowable stresses The allowable stresses may be exceeded by 25% where the member has to resist an increase in stress which is solely due to wind forces – provided that the stresses in the section before considering wind are within the basic allowable limits. Applied stresses are calculated using the gross elastic properties of the section, Z or A, where appropriate.
Allowable stress in axial tension Pt Form
Steel grade
Thickness of steel mm
Sections, bars, plates, wide flats and hollow sections
43 (S275)
t 40
170
40 < t 100
155
Source: BS 449: Part 2: 1969.
Pt N/mm2
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Maximum allowable bending stresses Pbc or Pbt Form
Steel grade
Thickness of steel mm
Pbc or Pbt N/mm2
Sections, bars, plates, wide flats and hollow sections Compound beams – hot rolled sections with additional plates Double channel sections acting as an I beam
43 (S275)
t 40
180
40 < t 100
165
Plate girders
43 (S275)
t 40 40 < t 100
170 155
Slab bases
All steels
185
Upstand webs or flanges in compression have a reduced capacity and need to be checked in accordance with clause 20, BS 449. These tabulated values of Pbc can be used only where full lateral restraint is provided, where bending is about the minor axis or for hollow sections in bending. Source: BS 449: Part 2: Table 2: 1969.
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263
Allowable compressive bending stresses The maximum allowable bending stress is reduced as the slenderness increases, to allow for the effects of buckling. The reduced allowable bending stress, Pbc, can be obtained from the following graph from the ratio of depth of section to thickness of flange (D/T ) and the slenderness ð ¼ Le =rÞ:
180 170 160
Allowable compressive bending stress, P bc (N/mm2)
150 140 D =5 T
130 120 110 100
10
90 80 15
70 20
60
25
50
30
40
35 40 45 50
30 25 50
75 100 125 150 175 200 225 250 275 Slenderness (le /ry)
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Allowable compressive stresses For uncased compression members, allowable compressive stresses must be reduced by 10% for thick steel sections: if t > 40 mm for Grade 43 (S275), t > 63 mm for Grade 50 (S355) and t > 25 mm for Grade 55 (S460). The allowable axial stress, Pc, reduces as the slenderness of the element increases as shown in the following chart:
180
160
140
Allowable compressive stress, Pc (N/mm2)
120
100
80
60
40
20
0 50
100
150
200
250
300
350
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265
Allowable average shear stress Pv in unstiffened webs Form
Steel grade
Thickness mm
Pv* N/mm2
Sections, bars, plates, wide flats and hollow sections
43 (S275)
d 40 40 < d 100 d 63 63 < d 100 d 25
110 100 140 130 170
50 (S355) 55 (S460)
* See Table 12 in BS 449: Part 2 for allowable average shear stress in stiffened webs.
Section capacity checks Combined bending and axial load Compression:
Tension:
fbc fc fbcx þ þ y 1:0 Pc Pbcx Pbcy
ft fbt þ
1:0 Pt Pbt
and
fbc fbcx þ y 1:0 Pbcx Pbcy
Combined bending and shear
2 p 2 p 2 fe ¼ ðfbt þ 3fq2 Þ or fe ¼ ðfbc þ 3fq2 Þ and fe < Pe and ðfbc =Po Þ2 þ fq0 =P0q 1:25
Where fe is the equivalent stress, fq0 is the average shear stress in the web, Po is defined in BS 449 subclause 20 item 2b iii and Pq0 is defined in clause 23. From BS 449: Table 1, the allowable equivalent stress Pe ¼ 250 N/mm2 for Grade 43 (S275) steel < 40 mm thick.
Combined bending, shear and bearing p 2 p 2 fe ¼ ðfbt þ fb2 þ fbt fb þ 3fq2 Þ or fe ¼ ðfbc þ fb2 þ fbc fb þ 3fq2 Þ and 2 0 0 2 fbc =Po þ fq =Pq þ fcw =Pcw 1:25 Source: BS 449: Part 2: 1969.
fe < Pe and
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Structural Engineer’s Pocket Book
Connections Selected fillet weld capacities for Grade 43 (S275) steel Leg length s mm
Throat thickness a = 0.7s mm
Weld capacity* kN/mm
4 6 8 12
2.8 4.2 5.6 8.4
0.32 0.48 0.64 0.97
* When a weld is subject to a combination of stresses, the combined effect should be checked using the same checks as used for combined loads on sections to BS 449.
Selected full penetration butt weld capacities for Grade 43 (S275) steel Thickness mm
Shear capacity kN/mm
Tension or compression capacity* kN/mm
6 15 20 30
0.60 1.50 2.00 3.00
0.93 2.33 3.10 4.65
* When a weld is subject to a combination of stresses, the combined effect should be checked using the same checks as used for combined loads on sections to BS 449. Source: BS 449: Part 2: 1969.
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Allowable stresses in non-pre-loaded bolts Description
Bolt grade
Axial tension N/mm2
Shear N/mm2
Bearing N/mm2
Close tolerance and turned bolts
4.6 8.8
120 280
100 230
300 350
Bolts in clearance holes
4.6 8.8
120 280
80 187
250 350
Allowable stresses on connected parts of bolted connections (N/mm2) Description
Allowable stresses on connected parts for different steel grades N/mm2 43 (S275)
50 (S355)
55 (S460)
Close tolerance and turned bolts
300
420
480
Bolts in clearance holes
250
350
400
Source: BS 449: Part 2: 1969.
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Selected working load bolt capacities for non-pre-loaded ordinary bolts in grade 43 (S275) steel Tensile Tension Shear stress capacity capacity area kN Single Double mm2 kN kN
Bearing capacity for end distance ¼ 2f kN
5
6
8
10
12
6 8 10 12 16 20 24
20.1 36.6 58 84.3 157 245 353
1.9 3.5 5.6 8.1 15.1 23.5 33.9
1.6 2.9 4.6 6.7 12.6 19.6 28.2
3.2 5.9 9.3 13.5 25.1 39.2 56.5
7.5 10.0 12.5 15.0 20.0 25.0 30.0
9.0 12.0 15.0 18.0 24.0 30.0 36.0
12.0 16.0 20.0 24.0 32.0 40.0 48.0
15.0 20.0 25.0 30.0 40.0 50.0 60.0
18.0 24.0 30.0 36.0 48.0 60.0 72.0
30
561
53.9
44.9
89.8
37.5 45.0 60.0 75.0 90.0 112.5 150.0
6 8 10 12 16 20
20.1 36.6 58 84.3 157 245
4.5 8.2 13.0 18.9 35.2 54.9
3.8 6.8 10.8 15.8 29.4 45.8
7.5 13.7 21.7 31.5 58.7 91.6
7.5 10.0 12.5 15.0 20.0 25.0
24 30
353 561
79.1 125.7
66.0 104.9
132.0 209.8
Diameter of bolt, f mm
Thickness of steel passed through 15
20
Grade 4.6 22.5 30.0 30.0 40.0 37.5 50.0 45.0 60.0 60.0 80.0 75.0 100.0 90.0 120.0
Grade 8.8 9.0 12.0 15.0 18.0 24.0 30.0
12.0 16.0 20.0 24.0 32.0 40.0
15.0 20.0 25.0 30.0 40.0 50.0
18.0 24.0 30.0 36.0 48.0 60.0
22.5 30.0 30.0 40.0 37.5 50.0 45.0 60.0 60.0 80.0 75.0 100.0
30.0 36.0 48.0 60.0 72.0 90.0 120.0 37.5 45.0 60.0 75.0 90.0 112.5 150.0
NOTES: . 2 mm clearance holes for f < 24 or 3 mm clearance holes for f < 24. . Bearing values shown in bold are less than the single shear capacity of the bolt. . Bearing values shown in italic are less than the double shear capacity of the bolt. . Multiply tabulated bearing values by 0.7 if oversized or short slotted holes are used. . Multiply tabulated bearing values by 0.5 if kidney shaped or long slotted holes are used. .
Shear capacity should be reduced for large packing, grip lengths or long joints.
Bolted connection capacity check for combined tension and shear f t fs þ 1:4 Pt Ps
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Stainless steel to BS 5950 Stainless steels are a family of corrosion and heat resistant steels containing a minimum of 10.5% chromium which results in the formation of a very thin self-healing transparent skin of chromium oxide – which is described as a passive layer. Alloy proportions can be varied to produce different grades of material with differing strength and corrosion properties. The stability of the passive layer depends on the alloy composition. There are five basic groups: austenitic, ferritic, duplex, martensitic and precipitation hardened. Of these, only austenitic and Duplex are really suitable for structural use.
Austenitic Austenitic is the most widely used for structural applications and contains 17–18% chromium, 8–11% nickel and sometimes molybdenum. Austenitic stainless steel has good corrosion resistance, high ductility and can be readily cold formed or welded. Commonly used alloys are 304L (European grade 1.4301) and 316L (European grade 1.4401).
Duplex Duplex stainless steels are so named because they share the strength and corrosion resistance properties of both the austenitic and ferritic grades. They typically contain 21–26% chromium, 4–8% nickel and 0.1–4.5% molybdenum. These steels are readily weldable but are not so easily cold rolled. Duplex stainless steel is normally used where an element is under high stress in a severely corrosive environment. A commonly used alloy is Duplex 2205 (European grade 1.44062).
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Material properties The material properties vary between cast, hot rolled and cold rolled elements. Density
78–80 kN/m3
Tensile strength
200–450 N/mm2 0.2% proof stress depending on grade.
Poisson’s ratio
0.3
Modulus of elasticity
E varies with the stress in the section and the direction of the stresses. As the stress increases, the stiffness decreases and therefore deflection calculations must be done on the basis of the secant modulus.
Shear modulus
76.9 kN/mm2
Linear coefficient of thermal expansion
17 106/ C for 304L (1.4301) 16.5 106/ C for 316L (1.4401) 13 106/ C for Duplex 2205 (1.4462)
Ductility
Stainless steel is much tougher than mild steel and so BS 5950 does not apply any limit on the thickness of stainless steel sections as it does for mild steel.
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271
Elastic properties of stainless steel alloys for design The secant modulus, Es ¼ Esi ¼ E m 1þk
ðEs1 þ Es2 Þ , where 2
f1 or 2 Py
where i = 1 or 2, k ¼ 0:002E=Py and m is a constant. Values of the secant modulus are calculated below for different stress ratios ðfi =Py Þ
Values of secant modulus for selected stainless steel alloys for structural design Stress Secant modulus ratio* fi Py
kN/mm2 304L
316L
Duplex 2205
Longitudinal Transverse Longitudinal Transverse Longitudinal Transverse 0.0
200
200
190
195
200
205
0.2
200
200
190
195
200
205
0.3
199
200
190
195
199
204
0.4
197
200
188
195
196
200
0.5
191
198
184
193
189
194
0.6
176
191
174
189
179
183
0.7
152
173
154
174
165
168
* Where i ¼ 1 or 2 for the applied stress in the tension and compression flanges respectively.
Typical stock stainless steel sections There is no UK-based manufacturer of stainless steel and so all stainless steel sections are imported. Two importers who will send out information on the sections they produce are Valbruna and IMS Group. The sections available are limited. IMS has a larger range including hot rolled equal angles (from 20 20 3 up to 100 100 10), unequal angles (20 10 3 up to 200 100 13), I beams (80 46 up to 400 180), H beams (50 50 up to 300 300), channels (20 10 up to 400 110) and tees (20 20 3 up to 120 120 13) in 1.4301 and 1.4571. Valbruna has a smaller selection of plate, bars and angles in 1.4301 and 1.4404. Source: Nickel Development Institute (1994).
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Structural Engineer’s Pocket Book
Durability and fire resistance Suggested grades of stainless steel for different atmospheric conditions Stainless steel grade
Location Rural
Urban
Industrial
Marine
Low Med High Low Med High Low Med High Low Med High 304L
3
3
3
3
3
(3)
(3)
(3)
X
3
(3)
X
O
O
O
O
3
3
3
3
(3)
3
3
(3)
O
O
O
O
O
O
O
O
3
O
O
3
(1.4301) 316L (1.4401) Duplex 2205 (1.4462)
Where: 3 ¼ optimum specification, (3) ¼ may require additional protection, X ¼ unsuitable, O ¼ overspecified.
Note that this table does not apply to chlorinated environments which are very corrosive to stainless steel. Grade 304L (1.4301) can tarnish and is generally only used where aesthetics are not important; however, marine Grade 316L (1.4401) will maintain a shiny surface finish.
Corrosion mechanisms Durability can be reduced by heat treatment and welding. The surface of the steel forms a self-healing invisible oxide layer which prevents ongoing corrosion and so the surface must be kept clean and exposed to provide the oxygen required to maintain the corrosion resistance. Pitting Mostly results in the staining of architectural components and is not normally a structural problem. However, chloride attack can cause pitting which can cause cracking and eventual failure. Alloys rich in molybdenum should be used to resist chloride attack. Crevice corrosion nuts and washers.
Chloride attack and lack of oxygen in small crevices, e.g. between
Bi-metallic effects The larger the cathode, the greater the rate of attack. Mild steel bolts in a stainless steel assembly would be subject to very aggressive attack. Austenitic grades typically only react with copper to produce an unsightly white powder, with little structural effect. Prevent bi-metallic contact by using paint or tape to exclude water as well as using isolation gaskets, nylon/Teflon bushes and washers.
Fire resistance Stainless steels retain more of their strength and stiffness than mild steels in fire conditions, but typically as stainless steel structure is normally exposed, its fire resistance generally needs to be calculated as part of a fire engineered scheme. Source: Nickel Development Institute (1994).
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273
Preliminary sizing Assume a reduced Young’s modulus depending on how heavily stressed the section will be and assume an approximate value of maximum bending stress for working loads of 130 N/mm2. A section size can then be selected for checking to BS 5950.
Stainless steel design to BS 5950: Part 1 The design is based on ultimate loads calculated on the same partial safety factors as for mild steel.
Ultimate mechanical properties for stainless steel design to BS 5950 Alloy type
Steel
European
Minimum
Ultimate
Minimum
desig-
grade
0.2%
tensile
elongation
nation
(UK grade)
proof
strength
after
stress
N/mm2
fracture
N/mm2 1
Basic austenitic
X5CrNi
304L
18-9
(1.4301)
Molybdenum
X2CrNiMo
316L
austenitic2
17-12-2
(1.4401)
Duplex
X2CrNi
Duplex
MoN
2205
22-5-3
(1.4462)
%
210
520–720
45
220
520–670
40
460
640–840
20
NOTES: 1. Most commonly used for structural purposes. 2. Widely used in more corrosive situations. The alloys listed in the table above are low carbon alloys which provide good corrosion resistance after welding and fabrication. As for mild steel, the element cross section must be classified to BS 5950: Part 1 in order to establish the appropriate design method. Generally this method is as given for mild steels; however, as there are few standard section shapes, the classification and design methods can be laborious. Source: Nickel Development Institute (1994).
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Structural Engineer’s Pocket Book
Connections Bolted and welded connections can be used. Design data for fillet and butt welds requires detailed information about which particular welding method is to be used. The information about bolted connections is more general.
Bolted connections Requirements for stainless steel fasteners are set out in BS EN ISO 3506 which split fixings into three groups: A = Austenitic, F = Ferritic and C = Martensitic. Grade A fasteners are normally used for structural applications. Grade A2 is equivalent to Grade 304L (1.4301) with a 0.2% proof stress of 210 N/mm2 and Grade A4 is equivalent to Grade 316L (1.4401) with a 0.2% proof stress of 450 N/mm2. There are three further property classes within Grade A: 50, 70 and 80 to BS EN ISO 3506. An approximate ultimate bearing strength for connected parts can be taken as 460 N/mm2 for preliminary sizing.
Ultimate stress values for bolted connection design Grade A property class Shear strength* Bearing strength* Tensile strength* N/mm2 N/mm2 N/mm2 50
140
70 (most common) 80
510
210
310
820
450
380
1000
560
* These values are appropriate with bolt diameters less than M24 and bolts less than 8 diameters long. Sources: Nickel Development Institute (1994).
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