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www.onlinecivil.tk
www.onlinecivil.tk
Structural Engineer’s
Pocket Book
www.onlinecivil.tk
This Page Intentionally Left Blank
www.onlinecivil.tk
Structural Engineer’s
Pocket Book
Fiona Cobb
AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD
PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO
www.onlinecivil.tk
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
www.onlinecivil.tk
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
www.onlinecivil.tk
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
www.onlinecivil.tk
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
www.onlinecivil.tk
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
www.onlinecivil.tk
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
www.onlinecivil.tk
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www.onlinecivil.tk
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
www.onlinecivil.tk
26
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
www.onlinecivil.tk
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
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Cantilever
Gravity or
reinforced earth
27
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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.
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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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30
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.
Minimum period of fire resistance
minutes
Building types
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).
www.onlinecivil.tk
Design Data
Typical building tolerances
SPACE BETWEEN WALLS
Brickwork ± 20 mm
Blockwork ± 21
Timber
± 32
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.
www.onlinecivil.tk
± 10 mm
± 10
± 10
± 12
± 10
In situ concrete
Floor screed
5 mm
5
31
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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).
www.onlinecivil.tk
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
80
10s
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).
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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
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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
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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
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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
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
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
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78
Mild
Paving
Including battens
see Hardwood or
Softwood
Zinc
37
72
0.8 mm
0.06
38
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
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
B Offices and work areas
not covered elsewhere
Fly galleries (load to be distributed
uniformly over width)
4.5 kN/m run
–
Ladders
–
1.5 rung load
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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)
2.0
2.7
4.0
4.0
Industrial walkways (light duty)
Industrial walkways (general duty)
Industrial walkways (heavy duty)
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
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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)
Plant rooms, boiler rooms, fan
rooms, etc., including weight of
machinery
7.5
4.5
7.0
9.0
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
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.
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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
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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
42
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
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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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44
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.
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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.
www.onlinecivil.tk
Height
mm
800
900
1100
800
900
800*
1100
46
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
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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
www.onlinecivil.tk
1.
2.
3.
4.
5.
6.
48
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
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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
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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
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
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Length, L
m
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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52
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
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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
x-
m
5m
=2 m
, e 8m
xis = 3
xa ,e
xis
xa
Allowable load (kN)
x-
m
5m
=2 m
, e 8m
xis = 3
ya ,e
xis
ya
y-
y-
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
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Mmax
kNm
7.5
y
54
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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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.
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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 10
www.onlinecivil.tk
6 / 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:
Twist for SHS and RHS:
www.onlinecivil.tk
90 1
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).
www.onlinecivil.tk
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
fillets
known
metre section section
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
www.onlinecivil.tk
Structural Steel
b
s
h d
r
Radius of
gyration
Elastic
modulus
Plastic
modulus
t
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.
www.onlinecivil.tk
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
fillets
metre section section
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
cm4
cm4
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.
www.onlinecivil.tk
215
Structural Steel
b
s
h d
r
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
u
x
t
Torsional
constant
Area of
section
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.
www.onlinecivil.tk
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
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
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
www.onlinecivil.tk
Second moment
of area
b/2t
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.
www.onlinecivil.tk
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
Radius
Depth
Mass Depth Width Thickness
Ratios for
between local buckling
per
of
of
fillets
metre section section
Web Flange Root Toe
Flange Web
h
b
s
kg/m
mm
mm
mm mm
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
www.onlinecivil.tk
t
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
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
www.onlinecivil.tk
Plastic
modulus
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
mm
B
Root
Depth
Ratios for local
radius between buckling
Web Flange
t
T
r
nd
mm
mm
mm
mm
mm
11
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
cm
430 100 64 64.4
430
100
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
www.onlinecivil.tk
23
221
Structural Steel
b
r1
s
d
h
t
Radius of
gyration
Elastic
modulus
Elastic
NA
Plastic NA
Buckling
parameter
Torsional
index
Warping
constant
Torsional
constant
Area of
section
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
ceq
u
x
H
J
A
cm4
cm4
16.3
2.97
1020
97.9
2.62
1222
176
0.954
0.917
22.5
0.219
63
82.1
14.8
3.06
791
89.2
2.79
933
161
11.9
11.7
3.13
2.77
549
481
81.7
63.1
3.05
2.6
641
568
148
114
0.904
0.932
21.2
0.15
45.7
68.7
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
4
1.58
41.5
18.8
2.25
89.9
33.2
1.55
0.942
11.1
0.002
4.72
18.8
1.73
48.9
17.5
1.18
0.942
10
0
2.53
13
9.89
Plastic
modulus
cm
Source: Corus Construction (2002). Copyright Corus UK Ltd – reproduced with the kind
permission of Corus UK Ltd.
www.onlinecivil.tk
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
www.onlinecivil.tk
c
y
a
Elastic
modulus
mm mm mm
þ
u
r1
c
t
v
r2
x
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
40 40 6
40 40 5
40 40 4
þ
40 40 3
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
þ
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
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
www.onlinecivil.tk
224
Structural Engineer’s Pocket Book
Rolled steel unequal angles – dimensions and properties
RSA
designation
Mass
per
metre
DBT
mm mm mm
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
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
þ
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
þ
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
40 25 4
www.onlinecivil.tk
3.86
3.05
2.64
1.15
225
Structural Steel
r2
u
v
t
x
x
R1
t
U
cx
t
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.
www.onlinecivil.tk
226
B
Y
D X
X
t
Hot finished rectangular hollow sections – dimensions and properties
RHS designation
Mass
per
metre
Area
of
section
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
Torsional
constants
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
ry
Zx
Zy
Sx
Sy
J
cm
cm3
cm3
cm3
cm3
cm4
m
346
293
277
250
228
189
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
www.onlinecivil.tk
Axis
y–y
0.154
0.152
0.152
0.151
0.15
0.147
T
mmmm
5.22
5.94
6.2
6.67
7.08
7.89
Axis
x–x
m2/m
DB
cm2
Axis
y–y
Approx
length
per
tonne
Thickness
A
Axis
x–x
Surface
area of
section
Size
kg/m
Axis
y–y
Plastic
modulus
C
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.
www.onlinecivil.tk
228
B
Y
D X
X
t
Hot finished rectangular hollow sections – dimensions and properties
RHS designation
Size
Thickness
DB
T
mm mm
mm
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
8
10
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
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
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
3.6
4
5
6
6.3
www.onlinecivil.tk
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
www.onlinecivil.tk
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
Mass Area of Ratios for
per
section local buckling
metre
SHS
designation
Size
DB
mm mm
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
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
www.onlinecivil.tk
6.22
7.1
7.42
8.01
8.54
9.6
Surface Approx
area of length
section per
tonne
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
www.onlinecivil.tk
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.
www.onlinecivil.tk
233
Structural Steel
D
Y
X
X
Y
t
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
t
D
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
www.onlinecivil.tk
234
Structural Engineer’s Pocket Book
D
Y
X
X
Y
t
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
www.onlinecivil.tk
C
235
Structural Steel
D
Y
X
X
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
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.
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236
Structural Engineer’s Pocket Book
Mild steel rounds typically available
Bar
Weight
diameter kg/m
mm
Bar
Weight Bar
Weight Bar
Weight
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
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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
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
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
20 10
25 3
25 5
25 6
25 8
25 10
25 12
30 3
30 5
30 6
30 8
30 10
30 12
30 20
35 6
35 10
35 12
35 20
40 3
40 5
40 6
40 8
40 10
40 12
40 15
40 20
40 25
40 30
45 3
1.570
0.589
0.981
1.18
1.570
1.960
2.360
0.707
1.180
1.410
1.880
2.360
2.830
4.710
1.650
2.750
3.300
5.500
0.942
1.570
1.880
2.510
3.140
3.770
4.710
6.280
7.850
9.420
1.060
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45 25
50 3
50 5
50 6
50 8
50 10
50 12
50 15
50 20
50 25
50 30
50 40
55 10
2.120
2.830
3.530
4.240
5.295
7.070
8.830
1.180
1.960
2.360
3.140
3.93
4.71
5.89
7.85
9.81
11.80
15.70
4.56
60 8
60 10
60 12
60 15
60 20
60 25
3.77
4.71
5.65
7.07
9.42
11.80
65 20
65 25
65 30
10.20
12.80
15.30
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
size
mm
65 40 20.40
70 8
4.40
70 10 5.50
70 12 6.59
70 20 11.0
70 25 13.70
75 6
3.54
75 8
4.71
75 10 5.90
75 12 7.07
75 15 8.84
75 20 11.78
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
80 20
80 25
80 30
80 40
80 50
90 6
12.60
15.70
18.80
25.10
31.40
4.24
100 8
100 10
100 12
6.28
7.85
9.42
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
110 6
5.18
110 10 8.64
110 12 10.40
110 20 17.30
110 50 43.20
120 6
5.65
130 10
130 12
130 15
130 20
130 25
140 6
140 10
140 12
140 20
150 6
150 8
150 10
150 12
10.20
12.20
15.30
20.40
25.50
6.60
11.00
13.20
22.00
7.06
9.42
11.80
14.10
150 15 17.70
150 20 23.60
150 25 29.40
180 12
180 15
180 20
180 25
200 6
200 10
200 12
200 x 15
200 20
200 25
200 30
220 10
220 15
220 20
220 25
250 10
250 12
250 15
250 20
250 25
250 40
250 50
280 12.5
300 10
300 12
300 15
300 20
300 25
300 40
17.00
21.20
28.30
35.30
9.90
15.70
18.80
23.60
31.40
39.20
47.20
17.25
25.87
34.50
43.20
19.60
23.60
29.40
39.20
49.10
78.40
98.10
27.48
23.55
28.30
35.30
47.10
58.80
94.20
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
39.25
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
706.50
98.12
32
251.20
60
471.00
100
785.00
15
117.75
35
274.75
65
510.25
110
863.50
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
Durbar mild steel floor plates typically available
Basic size
mm
Weight
kg/m2
Basic size
mm
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.
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Weight
kg/m2
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
Members resisting self-weight and wind only
Members normally acting as ties but subject to
load reversal due to wind
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350
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Structural Engineer’s Pocket Book
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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Structural Steel
241
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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242
Structural Engineer’s Pocket Book
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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Structural Steel
243
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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Structural Engineer’s Pocket Book
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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Structural Steel
245
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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Structural Engineer’s Pocket Book
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
Total axial load þ 2Y
Y þ 2X X
YþX X
Where X X and Y Y 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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Structural Steel
247
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).
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0.07
0.08
Structural Steel
249
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
S275 JR Room
temp.
20 C
Internal
only
30
43 B
Room
temp.
20 C
S275 J0 0 C
Internal
External
65
54
43 C
0 C
Internal
External
94
78
43 D
S275 J2
20 C
20 C
Internal
50
25
External
30
15
Internal
50
25
External
30
15
Internal
External
n/a
80
60
40
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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Structural Steel
251
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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Structural Steel
253
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
v) Mc ¼ py (S
Where ¼ 2 PFvv
Pv.
1
2
rSn)
and Sv ¼ the plastic modulus of the shear area used to calculate
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)
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200
225
250
Structural Steel
255
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.
Strut curve for value of pc
Type of
section
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
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100
150
200
250
Slenderness (Le/ry)
300
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Structural Engineer’s Pocket Book
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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Structural Steel
257
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
Fn ¼ Pt xnxn 1
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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Structural Steel
259
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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Structural Steel
261
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
Stress subscripts
Symbols
f
P
l/r
D
t
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
Sections, bars, plates,
wide flats and hollow sections
43 (S275)
Source: BS 449: Part 2: 1969.
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Thickness of
steel
mm
Pt
N/mm2
t 40
170
40 < t 100
155
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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)
170
155
Slab bases
All steels
t 40
40 < t 100
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
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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
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100
150
200
250
300
350
Structural Steel
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 y 1:0
þ
Pc Pbcx Pbcy
ft fbt
1:0
þ
Pt Pbt
and
fbc
fbcx
þ y 1:0
Pbcx Pbcy
Combined bending and shear
2
p 2
p 2
þ 3fq2 Þ or fe ¼ ðfbc
fe ¼ ðfbt
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.
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fe < Pe and
266
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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Structural Steel
267
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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Structural Engineer’s Pocket Book
Selected working load bolt capacities for non-pre-loaded ordinary
bolts in grade 43 (S275) steel
Diameter
of bolt, f
mm
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
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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Structural Steel
269
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 10 6/ C for 304L (1.4301)
16.5 10 6/ C for 316L (1.4401)
13 10 6/ C for Duplex 2205 (1.4462)
Ductility
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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.
Structural Steel
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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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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Structural Steel
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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274
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).
www.onlinecivil.tk
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