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Building Design Using
Cold Formed Steel Sections
Structural Design to BS 5950-5:1998
Section Properties and
Load Tables
R M LAWSON BSc(Eng), PhD, ACGI, CEng MICE, MIStructE
K F CHUNG BEng, PhD, DIC, MIStructE, CEng, MHKIE
S O POPO-OLA BSc(Eng), MEng, PhD, DIC
SCI PUBLICATION P276
Published by:
The Steel Construction InstituteSilwood Park
AscotBerkshire SL5 7QN
Tel: 01344 623345Fax: 01344 622944
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2002 The Steel Construction Institute
Apart from any fair dealing for the purposes of research or
private study or criticism or review, as permittedunder the
Copyright Designs and Patents Act, 1988, this publication may not
be reproduced, stored ortransmitted, in any form or by any means,
without the prior permission in writing of the publishers, or in
thecase of reprographic reproduction only in accordance with the
terms of the licences issued by the UKCopyright Licensing Agency,
or in accordance with the terms of licences issued by the
appropriateReproduction Rights Organisation outside the UK.
Enquiries concerning reproduction outside the terms stated here
should be sent to the publishers, The SteelConstruction Institute,
at the address given on the title page.
Although care has been taken to ensure, to the best of our
knowledge, that all data and informationcontained herein are
accurate to the extent that they relate to either matters of fact
or accepted practice ormatters of opinion at the time of
publication, The Steel Construction Institute, the authors and the
reviewersassume no responsibility for any errors in or
misinterpretations of such data and/or information or any lossor
damage arising from or related to their use.
Publications supplied to the Members of the Institute at a
discount are not for resale by them.
Publication Number: SCI-P276
ISBN 1 85942 119 9
British Library Cataloguing-in-Publication Data.A catalogue
record for this book is available from the British Library.
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FOREWORD
The authors of this publication are Dr R M Lawson and Dr S O
Popo-Ola of The SteelConstruction Institute, and Dr K F Chung of
Hong Kong Polytechnic University.Dr Chung and Dr Popo-Ola were
responsible for preparation of the design tables. Thework was
funded by Corus Colors (formerly, British Steel Strip
Products).
This publication is a revised edition of the 1992 publication
Design of structures usingcold formed steel sections (SCI-P-089).
It gives general information on the design of coldformed steel
sections to BS 5950-5: 1998 (now revised from the 1985 version),
andincludes new design tables for a wide range of cold formed steel
sections used in generalbuilding construction.
The following individuals and organisations helped in the
preparation of this publication:
Mr R Colver Ayrshire Steel Framing
Mr V French Ayrshire Metal Products (Daventry) Ltd
Mr B Johnson Structural Sections Ltd
Mr I McCarthy Metsec Ltd
Mr T Harper Ward Building Components Ltd
Mr P Reid Hi-Span Ltd
Mr J Jones Albion Ltd
This publication is one of a general series on Building Design
using Cold Formed SteelSections. The series includes:
C Light Steel Framing in Residential Construction (P301,
2001)
C Durability of Light Steel Framing in Residential Buildings
(P262, 2000)
C Case Studies on Light Steel Framing (P176, 1997)
C Construction Detailing and Practice (P165, 1997)
C Architects Guide (P130, 1994)
C Fire Protection (P129, 1993)
C Acoustic Insulation (P128, 1993)
C Worked Examples (P125, 1993).
Other titles on light steel applications in modular construction
by the SCI are:
C Modular Construction using Light Steel Framing: Residential
Buildings (P302, 2001)
C Case Studies on Modular Construction (P271, 1999)
C Building Design Using Modular Construction: An Architects
Guide (P272,1991).
The section property data, member design tables and associated
information areintended to be used at the scheme design stage. For
more comprehensive dataconcerning particular sections and their
availability, the reader is advised tocontact manufacturers
directly. All sections that are included can be obtainedfrom the
manufacturers listed in the Appendix. For more information on
steelgrades and coatings, contact Corus directly (see
Appendix).
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CONTENTSPage No
SUMMARY vii
1 AIM OF THE PUBLICATION 11.1 Design tables 21.2 Limit state
design 2
2 INTRODUCTION TO USE OF COLD FORMED SECTIONS 32.1 Materials
32.2 Methods of forming 42.3 Methods of protection 52.4 Common
shapes of sections 52.5 Common applications 62.6 Fire protection
12
3 INTRODUCTION TO DESIGN OF COLD FORMED SECTIONS 133.1 Behaviour
of thin plates in compression 133.2 Behaviour of webs 173.3
Behaviour of members in bending 203.4 Behaviour of members in
compression 253.5 Serviceability limits 28
4 APPLICATION OF COLD FORMED SECTIONS IN BUILDING 294.1 Purlins
and side rails 294.2 Floor joists 304.3 Stud walling 324.4 Trusses
334.5 Structural Frames 344.6 Curtain walling and over-cladding
374.7 Housing 394.8 Modular construction 404.9 Frameless structures
404.10 Connections 41
5 SECTION PROPERTIES OF COLD FORMED SECTIONS 475.1 Notation used
in section property tables 515.2 Summary of assumptions in deriving
the section property tables 52
6 LOAD AND PERFORMANCE CHARACTERISTICS OF COLD FORMEDSECTIONS
546.1 Generic sections 546.2 Load capacity tables for beams 556.3
Load capacity tables for columns 556.4 Guidance on selection of
cold formed steel sections 576.5 Example of use of load-span tables
for beams 58
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7 REFERENCES 59
8 BIBLIOGRAHY 61
APPENDIX A: Contact Information 70
Yellow PagesSECTION PROPERTY TABLES A-1
C Sections A-3Z Sections A-35
Pink PagesLOAD CAPACITY TABLES FOR BEAMS - S280 B-1
Generic C Sections B-1Generic Z Sections B-21
LOAD CAPACITY TABLES FOR COLUMNS - S280 B-41Generic C Sections
B-41
Green PagesLOAD CAPACITY TABLES FOR BEAMS - S350 C-1
Generic C Sections C-1Generic Z Sections C-21
LOAD CAPACITY TABLES FOR COLUMNS - S350 C-41Generic C Sections
C-41
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SUMMARY
This publication reviews the design and application of cold
formed steelsections in building construction. The design of these
sections conforms toBS 5950-5: 1998: Code of practice for design of
cold formed thin gaugesections. Applications that are covered
relate to steel frames, trusses andsecondary members in commercial,
industrial and domestic buildings.
The main part of the publication presents design tables for
general use of coldformed sections. This data is tabulated in two
parts: section properties, andload tables. Section properties can
be used in general applications, whereasload tables can be used in
direct selection of beam and column sizes.
The cold formed steel sections listed in this publication can be
readily obtainedfrom manufacturers in the UK. Other references to
the use of cold formed steelare also given.
Berechnung von tragwerken aus kaltgeformten stahlprofilen
Zusammenfassung
Diese Verffentlichung gibt einen berblick ber die Bemessung
undAnwendung von kaltverformten Stahlprofilen im Bauwesen. Die
Bemessungdieser Profile entspricht BS 5950, Teil 5: Code of
practice for design of coldformed sections, Ausgabe 1998. Die
behandelten Anwendungsflle beziehensich auf Stahltragwerke,
Fachwerke und nichttragende Bauteile im Verwaltungs-, Industrie-
und Wohnungs-bau.
Der Hauptteil dieser Verffentlichung stellt Bemessungstabellen
fr denallgemeinen Gebrauch von kaltverformten Profilen vor. Dieses
Daten sind inzwei Teilen tabelliert: Querschnittsgr$en
Belastungstabellen. DieQuerschnittsgr$en knnen allgemein verwendet
werden, whrend dieBelastungstabellen der direkten wahl der Trger-
und Sttzenprofile dienen.
Die in dieser Verffentlichung enthaltenen, kaltverformten
Profile knnen vonHerstellern im Vereinigten Knigreich bezogen
werden. Andere Verweise zurAnwendung von kaltverformtem Stahl sind
ebenso enthalten.
Dimensionnement de structures en profils en acier form froid
Rsum
Cette publication passe en revue les mthodes de dimensionnement
et lesprincipales applications des profils en acier form froid dans
la construction.Le dimensionnement de ces profils est en accord
avec la BS 5950: Partie 5:1998 - Recommandations pour le calcul des
profils form froid. Lesapplications prsentes ont trait aux cadres
et portiques en acier ainsi quauxlments secondaires utiliss dans
les btiments industriels, commerciaux oupour habitation.
La partie principale de la publication prsente des tables de
dimensionnementpour les applications habituelles des profils form
froid. Ces informations sontrparties en deux catgories: les
proprits des sections et les tables donnant lescharges de
dimensionnement des lments. Les proprits gomtriques des
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sections peuvent tre utilises dans toutes les applications. Les
informationsrelatives au dimensionnement des lments permettent un
choix rapide desprofils utiliser en tant que poutres ou
colonnes.
Les profils en acier form froid repris dans la publication
peuvent treaisment obtenus prs des producteurs du
Royaume-University. Dautresrfrences relatives lutilisation des
profils en acier form froid sontgalement mentionnes.
Proyecto de estructuras usando secciones de acero conformado en
frio
Resumen
Esta publicacin revisa el proyecto y aplicacin de secciones de
aceroconformado en frio a la construccin de edificios. El proyecto
de estassecciones de acero se ajusta a la BS 5950: Parte 5: 1998:
Norma de buenaprctica para el proyecto de secciones de acero
conformadas en frio.
Las aplicaciones cubiertas se refieren a prticos de acero,
cerchas y piezassecundarias en edificios comerciales, industriales
y de habitacin.
La parte principal de la publicacin presenta tablas de diseo
para uso generalde secciones. Los datos se tabulan en dos partes:
propiedades de las seccionesy cargas de proyecto de piezas. Las
primeras son de uso general mientras quelas segundas pueden
utilizarse para la eleccin directa de las proporciones devigas y
columnas.
Las secciones de acero conformado un frio descritas en esta
publicacinpueden obtenerse fcilmente de los fabricantes del Reino
Unido. Tambin sedan otras referencias para el uso de secciones
conformadas en frio.
Progettazione di strutture realizzate con profili in acciaio
sagomati a freddo
Sommario
In questa pubblicazione viene presentato il dimensionamento e
lutilizzo diprofili in acciaio sagomati a freddo. La progettazione
di tali elementi in acciaiorisulta conforme alla normativa BS5950:
Parte 5, 1998, `Guida allaprogettazione di profili sagomati a
freddo. Le applicazioni che vengonopresentate sono relative a
strutture intelaiate, a travature reticolari ed elementisecondari
per strutture ad uso commerciale, civile ed industriale.
Nella parte principale di questa pubblicazione sono riportate le
tabelleprogettuali per differenti utilizzi dei profili sagomati a
freddo. Questi dati sonotabulati in due differenti parti: la prima
e relativa alle caratteristichegeometriche dei profili e la seconda
riporta i valori dei carichi di progetto deglielementi. Le
caratteristiche dei profili possono essere utilizzate in
applicazionidi carattere generale mentre una scelta diretta delle
dimensioni di travi ecolonne puo essere fatta sulla base delle
caratteristiche portanti degli elementi.
Le sezioni dei profili sagomati a freddo riportati in questa
pubblicazionepossono essere ottenute in brevi tempi da qualsiasi
stabilimento del regnoUnito. Vengono inoltre forniti diversi
riferimenti per lutilizzo dei profili inacciaio.
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NOTATION
A cross-sectional area of section
b plate width between corners or stiffeners
be effective plate width in compression
B width of the section
Cb coefficient representing variation of bending moment along a
member
D depth of web of section
E modulus of elasticity of steel (205 kN/mm2)
es eccentricity of line of application of axial force from
centroid of section
I second moment of area of section (subscript x or y indicates
major or minoraxis direction of bending)
K plate buckling coefficient
L length of member
Le effective length of member
Myelastic moment resistance of the section
N support width (mm)
py design strength of steel
pcr critical buckling stress in plate
po reduced stress in section determined by web properties
Q factor representing reduced performance of section in
compression
r corner radius
ry radius of gyration in y (minor) axis direction of bending
t net steel thickness
Us ultimate strength of steel
Ys yield stress of steel
" effective length factor including torsional flexural
buckling
8 slenderness of member
8y slenderness corresponding to B E/Ys
L Poissons ratio for steel (= 0.3)
Note: For notation used in section property tables, see Section
5.1.
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1 AIM OF THE PUBLICATION
This design guide is aimed at practitioners in the building
industry whomay have limited experience of the structural design of
light steel framingusing cold formed steel sections. The
publication presents an overview of thedesign principles for cold
formed steel sections in accordance withBS 5950-5:1998 [1] (revised
from the 1985 version). Cold formed steel sectionsare generally
produced by cold rolling from galvanized steel strip.
Most structural engineers are familiar with the application of
cold formed steelsections (also known as cold rolled sections) in
purlins and side-rails, which arehighly engineered products for
specific applications. The general use of coldformed sections as
primary members of light steel framing requires a moresimplified
design process appropriate to their applications as beams, floor
joists,columns, stud walling, members of roof trusses and
sub-frames.
A wide range of uses of cold formed sections and light steel
framing has beenrealised in recent years, and common applications
are in:
C housing
C medium-rise apartment buildings
C mezzanine floors
C roof trusses, including over-roofing in renovation
projects
C sub-frames for cladding, including over-cladding in renovation
projects
C framework of modular units
C separating and infill walls
C canopies.
This design guide concentrates on the general use of cold formed
steel sectionsin these structural applications. The information is
presented under three broadheadings:
1. An introduction to the design of cold formed sections. It is
appreciated thatthe design of these sections may appear to be more
complicated than thatof hot rolled sections. It is therefore
important to understand the designprinciples and also the practical
considerations of the structural use of thesesections.
2. A review of the application of cold formed sections in
buildings,concentrating on the main design features and details.
This also necessitatesa discussion on methods of cutting, joining
and attachment of othermembers and materials, which are fundamental
to the practical use of thesethinner sections.
3. A series of tables on section properties and loads for the
range of coldformed sections that are readily available for general
building use. Thesection properties have been calculated based on
first principles, inaccordance with BS 5950-5. The load tables
(also determined inaccordance with BS 5950-5) can be used to obtain
the required membersizes for specific applications.
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1.1 Design tablesSection properties are presented for the gross
and the effective sections on theyellow pages (i.e. as influenced
by local buckling under compression). Theseproperties may be used
by structural engineers when designing members forgeneral
application. Alternatively, designers may refer to the load-span
tablesfor beams or load-height tables for columns, which give the
member resistancesdirectly (see pink pages and green pages for
grades S280 and S350,respectively).
The tables in this design guide may be used for general
application of genericC and Z sections as floors and walls.
Manufacturers often design their sectionsfor specific uses, such as
purlins, and establish the member performance basedon test data
rather than calculations to BS 5950-5. This means thatmanufacturers
data may be more beneficial in certain cases.
Member resistance tables (in terms of working load capacity) are
presented forgeneric C or Z sections only. These load tables are
useful for selection ofmember sizes and are intended to be used for
initial or scheme design.However, for final design, the data
provided by the manufacturer of the selectedsections should be
used.
Manufacturers should be contacted directly with regard to
availability, cuttingto length, hole punching, etc. A list of UK
manufacturers and further sourcesof information are presented in
Appendix A.
1.2 Limit state designIn BS 5950-5[1], the loads to be used in
design are calculated from the workingloads multiplied by factors
of 1.6 for imposed load and 1.4 for dead loads(including self
weight). These factored loads are used to determine themoments and
forces in the members, which are then compared to the resistanceof
the members. Resistances may be as determined for all relevant
modes offailure, such as buckling, connection or local failure etc.
The methods ofdetermining the member resistance and load bearing
capacity of cold formedsections are presented in Section 3.
Additional checks on deflections are made for working loads
(i.e. for loadfactors of 1.0) in order to ensure adequate
performance in service. Light weightfloors should also be checked
for their vibration response to normal activities(see Section
6.1).
The methods in BS 5950 are not based on working load or
permissible stressdesign, although a global factor of safety of 1.6
may be used conservatively todetermine maximum working loads that
the structure can support.
The load capacity tables are presented in terms of working
loads.
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2 INTRODUCTION TO USE OF COLDFORMED SECTIONS
2.1 MaterialsSheet steel used in cold formed sections is
typically 0.9 to 3.2 mm thick(although thinner steels are used in
roofing and decking applications). It isusually supplied
pre-galvanized in accordance with European StandardEN 10147 (issued
by BSI in 1991 as BS EN 10147 [2] as a replacement forBS 2989 [3]).
Galvanizing gives adequate protection for internal
members,including those adjacent to the boundaries of building
envelopes, such aspurlins. The expected design life of galvanized
products in this environmentexceeds 60 years (see Section 2.3).
Steel strip is produced by cold reducing hot rolled coil steel
with furtherannealing processes to improve the ductility of the
material. It is a qualitycontrolled product with known and easily
tested properties. Grade S280 steel(formerly Z28) is a quality of
steel specified as having a guaranteed minimumyield strength of 280
N/mm2. Grades S280 and S350 steels are the mostcommonly specified
grades, although it is often found that the actual yieldstrength is
considerably higher than the specified minimum. Steel with
anon-guaranteed yield strength may be used in some applications,
provided thatthe strength of the material is determined by tensile
tests taken from the coilfrom which the material was cut.
During cold forming of a section, the increase in yield strength
of the steelincreases, due to cold working by the process of strain
hardening, asillustrated in Figure 2.1. The increase in yield
strength by cold working may besignificant (> 10%) for highly
stiffened sections with many bends. Strictly, theyield point is not
a clearly defined transition point, as it is for hot rolled
steels.The proof strength (at 0.2% strain) is often used as an
effective yield value.
due to cold working
Ultimate strength
Fracture
Str
ess
StrainLoss of ductility Ductility after cold working
Initial loading Further loadingafter cold working
Increase ofyield stressdue to strainhardening Yield point
after cold working
Figure 2.1 The influence of cold forming on the stress-strain
diagram ofstrip steel
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Ductility is defined on the basis of minimum elongation at
fracture over acertain gauge length. This is specified for S280
steel as a minimum of 20%elongation for a gauge length of 50 mm(2).
Ductility reduces with cold working.Cold working also has the
effect of reducing the ratio of the ultimate to the yieldstrength
of the material.
2.2 Methods of formingManufacturers purchase strip steel in
coils, normally of 1 m to 1.25 m width.The sheets are then cut
(slit) longitudinally to the correct width for the sectionbeing
produced and then fed into a series of roll formers. These rolls
are set inpairs moving in an opposite direction so that the sheet
is drawn through and itsshape is gradually modified along the line
of rolls. The number of rolls neededto form the finished shape
depends on the complexity of the section. Theoverall length of the
roll forming machinery can be over 30 m (see Figure 2.2).
Setting-up costs are high if special rolls are needed.
Adjustable rolls are oftenused, which permit a rapid change of
section depth or width. Roll forming istherefore most economic
where large quantities of the same section areproduced at one time.
The lengths of the members can be pre-programmed andcut accurately.
Holes for attachments and services can also be punched eitherbefore
or after forming.
An alternative method of cold forming is by press-braking. This
is normallyonly practicable for short lengths (up to 6 m, depending
on the size of themachine used) and for relatively simple shapes.
This method can beadvantageous for small production runs, because
of its lower setting-up costs.
Figure 2.2 Roll forms used for cold formed sections and
sheeting
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2.3 Methods of protectionHot dip galvanizing (zinc coating) of
preformed strip steel offers protection bysacrificial loss of the
zinc surface which occurs preferentially to corrosion of thesteel.
Guidance on thickness of galvanizing is given in Galvatite
TechnicalManual [4]. The specified sheet thickness includes
galvanizing. A zinc coatingof 275 g/m2 (total on both faces) is the
standard (G275) specification for internalenvironments, and
corresponds to a total zinc thickness of about 0.04 mm.G100 to G600
coatings can also be obtained but these are generallynon-standard.
The thicker coatings are used in applications where moisturemay be
present over a long period. Zinc coatings can also be applied by
hotdipping of the sections after manufacture.
Galvanized steel has good durability because, unlike paint,
scratches do notinitiate local corrosion of the steel. Similarly,
cut ends do not corrode, exceptwhere the rate of zinc loss on the
adjacent surfaces is high. In someapplications it may be necessary
to apply zinc-rich paint to the exposed steel.White rust or wet
storage stains [5] may occur if galvanized sections are storedin
bundles in moist conditions, but this does not normally affect
their long termperformance. Correct storage of bundles of sheets or
sections is thereforeimportant.
A recent SCI publication Durability of light steel framing in
residentialbuilding [6] shows that the design life of galvanized
steel in warm frameapplications is at least 200 years, provided
that the external envelope isproperly maintained.
Zinc-aluminium coatings also have high corrosion resistance and
are sometimesused in sheeting applications, but rarely on sections.
Organic coatings are notused for sections. Powder paint coatings,
in addition to galvanizing, are oftenused for specialist products
such as lintels.
2.4 Common shapes of sectionsCold formed sections are used in
many industries and are often specially shapedto suit particular
applications. In building applications, the most commonsections are
the C and the Z sections. There are a wide range of variants
ofthese basic shapes, including those with edge lips, internal
stiffeners and bendsin the webs.
Other sections are the top-hat section and the modified I
section. Thecommon range of cold formed sections that are marketed
is illustrated inFigure 2.3. The sections can also be joined
together back to back or toe to toeto form compound sections.
The reason for edge lips and internal stiffeners is because
unstiffened wide andthin plates are not able to resist significant
compression, and consequently thesections are structurally
inefficient. However, a highly stiffened section is lesseasy to
form and is often less practicable from the point of view of
connectionto other members. Therefore, a compromise between
structural efficiency andpracticability is often necessary.
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Compound sections
Z sections
ZetaLipped Z
Special sections
Modified sectionsTop hat Eaves beam
C sections
Plain Lipped Sigma
Figure 2.3 Examples of cold formed steel sections
2.5 Common applicationsCold formed steel sections are used
widely in building applications. Deckingis also used in composite
floors, and in flat roofs. Roof and wall sheeting arewell
established and are generally sold as colour-coated products with
variousforms of organic surface coatings.
The main advantages of using cold formed sections are:
C high load resistance for a given section depth
C long span capability (up to 10 m)
C dimensional accuracy
C long term durability in internal environments
C freedom from long term creep and shrinkage
C capability to be formed to a particular shape for specific
applications
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C lightness, which is particularly important for buildings in
poor groundconditions
C no wet trades, as a dry envelope is quickly achieved using
light steelframing
C ease of construction, as members are delivered to site cut to
length and withpre-punched holes, requiring no further
fabrication
C ability to be prefabricated into sub-frames as wall panels
etc;
C robustness, but sufficiently light for site handling
C connections are strong and easily made in factory or on
site.
Examples of the structural use of cold formed sections are as
follows:
Roof and wall members
A major use of cold formed steel in the UK is as purlins and
side rails to supportthe cladding in industrial-type buildings (see
Figure 2.4). Purlins are generallybased on the Z section (and its
variants), which facilitates incorporation ofsleeves and overlaps
to improve the structural efficiency of the members inmulti-span
applications.
Figure 2.4 Cold formed sections used as roof purlins
Light steel framing
An increasing market for cold formed steel sections is in
site-assembled framesand panels for walls and roofs, and for
stand-alone buildings. This approachhas been used in a wide range
of light industrial and commercial buildings andalso in mezzanine
floors of existing buildings (see Figure 2.5).
Housing
In modern house construction, storey-high wall panels are
factory-built andassembled on site by platform construction. The
panels are sufficiently lightto be handled on site. External
insulation is used in order to create a warmframe. Brickwork is
attached by wall ties in vertical tracks fixed through
theinsulation to the wall studs. Four light steel framing systems
are available in the
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housing sector in the UK. A major series of load tests has been
carried out toestablish the global action of light steel frames to
vertical and horizontal loads(see Figure 2.6).
Figure 2.5 Cold formed sections used in site-assembled
framing
Figure 2.6 Light steel framing for housing (Corus Framings
Surebuild system)
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Lintels
A significant market for cold-formed sections is for specially
shaped steel lintelsused over doors and windows inlow-rise masonry
walls. These products areoften powder-coated for extra corrosion
protection in cavity conditions.
Floor joists
Cold formed sections may be used as an alternative to timber
joists in floors ofmodest span in domestic and small commercial
buildings. Spans of up to 5 mcan be readily achieved for C or
sigma-shaped sections. Lattice joists may beused for longer
spanning applications.
Systems for commercial buildings
A prefabricated panel system using cold formed sections and
lattice joists hasbeen developed for use in buildings up to 4
storeys height (see Figure 2.7).Although primarily developed for
commercial buildings, this system has wideapplication in such as
educational and apartment buildings.
Roof trusses
Roof trusses may be manufactured using cold formed sections for
both newconstruction and renovation projects. They may be of the
traditional Fink orPratt truss form, or alternatively, they may be
designed as open roof trussesfor habitable use. Over-roofing of
existing flat roofs is also a large market forlong span trusses [7]
(see Figure 2.8).
Separating walls and partitions
Separating walls in framed buildings may be designed using C
sections andmultiple layers of plasterboard to provide a high level
of acoustic insulation andfire resistance.
Space trusses
A three-dimensional space truss based on a 3 m square module
using coldformed C sections is marketed in the UK by Spacedecks
Ltd..
Infill walling and over-cladding
A modern application of cold formed sections is in infill walls
to supportcladding to multi-storey steel buildings, and as mullions
and transoms instandard glazing systems. Over-cladding systems have
been developed for usein building renovation [8].
Prefabricated modular buildings
Prefabricated modular units are a new application of the use of
cold formedsections. The units are manufactured and fitted-out in
factory-controlledconditions. When installed on site with their
services and cladding, the unitsform whole or part buildings with a
high level of acoustic insulation andstructural integrity [9]. They
are also designed structurally for the stressesimposed during
lifting and transportation. Other applications are asprefabricated
toilet pod units in multi-storey buildings.
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10P:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002
Figure 2.7 Cold formed lattice joists and modular wall
panels
Figure 2.8 Roof truss used in over-roofing
Frameless steel buildings
Steel folded plates, barrel vaults and truncated pyramid roofs
are examples ofsystems that have been developed as so-called
frameless buildings (i.e. thosewithout beams and which rely partly
on stressed skin action).
Storage racking
Storage racking systems for use in warehouses and industrial
buildings are madefrom cold formed steel sections. Most have
special clip attachments, or boltedjoints engineered for easy
assembly, as shown in Figure 2.9.
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Composite decking
A major structural use of strip steel is in composite decking in
floors which aredesigned to act compositely with the in-situ
concrete placed on it. Compositedecking is usually designed to be
unpropped during construction, and typicalspans are 3 to 3.6 m.
This application, which is illustrated in Figure 2.10, iswell
covered in other publications [10] [11]. More recently, deep
decking has beendeveloped to achieve spans of 5 to 9 m in Slimdeck
construction.
Figure 2.9 Typical storage racking system
Figure 2.10 Steel decking used in composite slab
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Applications in general civil engineering include:
C Lighting and transmission towersThese towers are often made
from thin tubular or angle sections that may becold formed.
C Motorway crash barriersThese relatively thin steel members are
primarily designed for strength, butalso have properties of energy
absorbtion under impact by permitting grossdeformation.
C Silos for agricultural useSilo walls are often stiffened and
supported by cold formed steel sections.
C CulvertsCurved profiled sheets are often used as culverts and
storm pipes.
Other major non-structural applications in building include such
diverse usesas garage doors, and ducting for heating and
ventilating systems.
2.6 Fire protectionFire protection to cold formed sections in
planar floors or walls is usuallyprovided by special fire-resistant
gypsum plasterboards placed in one or twolayers to form the
finished surface. Fire resistance periods of 30 or 60 minutescan be
achieved by this simple method of protection provided joints
betweenthe boards are staggered.
Longer members such as beams and columns can also be boxed-out
usingstandard board protection, as in Figure 2.11. However, the
required thicknessof fire protection is usually greater than that
for hot rolled sections because thethinner steel elements heat up
more rapidly [12].
Figure 2.11 Box fire protection to columns using C sections
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3 INTRODUCTION TO DESIGN OF COLDFORMED SECTIONS
The main difference between the behaviour of cold formed
sections and hotrolled steel sections is that thin plate elements
tend to buckle locally undercompression. Cold formed cross-sections
are therefore usually classified asslender because they cannot
generally reach their full compression resistancebased on the
amount of material in the cross-section. Therefore,
effectivesection properties should be used in structural
calculations.
The benefits of cold forming on material properties may be taken
into account.A design formula for the increase in average yield
strength is presented inBS 5950-5, Clause 3.4, and this increase in
strength is typically 3 to 10%,depending on the number of bends in
the section. For S280 and S350 steelgrades, the design strength of
the steel, py is taken as the yield strength, Ys asmodified by
Clause 3.4.
3.1 Behaviour of thin plates in compression3.1.1 Elastic
bucklingThe full compression resistance of a perfectly flat plate
supported on twolongitudinal edges can be developed for a
width-to-thickness ratio of about 40.At greater widths, buckles
form elastically causing a loss in the overallcompressive
resistance of the plate. This is due to the inability of the
moreflexible central portion to resist as much compression as the
outer portionswhich are partly stabilised by the edge supports.
The critical compression stress at which elastic buckling of the
plate occurs isgiven by the expression:
pcr =K B2 E
12 (1 & v 2)tb
2
. 185 103 5 (t/b)2 N/mm2 (1)
where:b is the plate width, andt is the steel thickness.
The term 5, referred to as the buckling coefficient, represents
the influence ofthe boundary conditions and the stress pattern on
plate buckling. Normally,plates are considered to be infinitely
long but have various support conditionsalong their longitudinal
edges. The two common cases are, firstly, simplesupports along both
edges, and, secondly, one simple support and the other freeedge. In
the first case 5 is 4, whereas in the second, 5 reduces
dramatically to0.425. This indicates that plates with free edges do
not perform well underlocal buckling. These cases are illustrated
in Figure 3.1.
M. FIRDAUSHighlight
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14P:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002
Support
ed edge
cr
cr
Support
ed edge
cr
cr
Adequate lip No edge lip
Junction remainsstraight
Edge is freeto displace
Buckled shapeBuckled shape p
p p
p
Figure 3.1 Local buckling of plates with different boundary
conditions
The value of 5 may be enhanced considerably when the rotational
stiffnessprovided by the adjacent plates is included, or,
alternatively, when the loadingconditions do not result in uniform
compression. Different cases for sectionsin bending and pure
compression are given in Appendix B of BS 5950-5.
3.1.2 Post-critical behaviourPlate elements are not perfectly
flat, and therefore begin to deform out-of-planegradually with
increasing load, rather than buckle instantaneously at the
criticalbuckling stress. This means that the non-uniform stress
state exists throughoutthe loading regime, and tends to cause the
plate element to fail at loads lessthan the critical buckling
value. This is a dominant effect in the b/t range from30 to 60 (for
plates simply supported on both edges).
However, there are opposing effects for plate elements with
higher b/t ratios.Firstly, membrane or in-plane tensions are
generated which resist furtherbuckling, and secondly, the zone of
compression yielding extends from thelongitudinal supports to
encompass a greater width of the plate elements. Thesepost-critical
effects cause an increase in the load-carrying capacity of wide
plateelements (b/t > 60) relative to that given by Equation
(1).
The parameter which is used to express the behaviour of plate
elements incompression is the effective width. This is the notional
width which isassumed to act at the yield strength of the steel.
The remaining portion of theplate element is assumed not to
contribute to the compression resistance, asillustrated in Figure
3.2.
s s s
b
effb /2
effb /2
Actual stressdistribution
Simplifiedequivalentstresses
b YYY b
Figure 3.2 Illustration of effective width of compression
plate
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The effective width concept can be modified to take the above
factors intoaccount. A semi-empirical formula for the effective
width, beff, of a plateelement under compression is presented in BS
5950-5, Clause 4.3, as follows:
= (2)beffb
1 % 14fcpcr
1/2
& 0.35
4 &0.2
Where, fc is the compressive stress in the plate element, and
pcr is the criticalbuckling stress of the plate element, as defined
previously. fc is limited to avalue of Ys , which is the design
strength of the steel.
The relationship given by Equation (2) is plotted in Figure 3.3.
Also shown inthis figure is the equivalent elastic buckling curve
determined from Equation (1)and the corresponding AISI (American)
requirements [13] [14]. The fullcompression resistance of a real
(slightly non-flat) plate element supported ontwo longitudinal
edges can be developed at a b/t ratio of less thanapproximately 30,
and this therefore represents the most efficient spacingbetween
stiffeners or folds in a cross-section. Values of effective width
for plateelements of increasing b/t ratios are presented in Table
3.1 (taken fromBS 5950-5).
50 100 150 200 25000
0.2
0.4
0.6
0.8
b/t
eff
1.0
b b BS 5950:Part5
AISI/EC3 Part 1.3 Elastic Buckling
Figure 3.3 Ratio of effective width to flat width (Ys = 280
N/mm2) of
compression plate with simple edge supports
3.1.3 Influence of stiffenersThere are two types of stiffeners:
those at the edge of a plate element, and thoseinternally within a
plate element. They are known respectively as edge andintermediate
stiffeners, in the form of lips and folds, as illustrated in Figure
3.4.A rule of thumb is that edge stiffeners comprising a simple lip
or right anglebend should not be less in depth than one-fifth of
the width of adjacent plateelement, if they are to be fully
effective in providing longitudinal support.
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Table 3.1 Effective widths of compression plate elements
supported on twolongitudinal edges (Table 5 of BS 5950-5: 1998,
reproduced withthe permission of the British Standards
Institution)
b/t beff/b b/t beff/b b/t beff/b b/t beff/b
202122232425
1.0001.0001.0001.0000.9990.999
606162636465
0.6730.6620.6520.6410.6310.621
100105110115120125
0.4050.3870.3700.3550.3410.328
300305310315320325
0.1510.1490.1470.1450.1430.141
2627282930
0.9980.9970.9960.9940.992
6667686970
0.6120.6030.5940.5850.577
130135140145150
0.3160.3050.2950.2860.277
330335340345350
0.1390.1380.1360.1340.133
3132333435
0.9890.9850.9810.9760.969
7172737475
0.5690.5610.5530.5450.538
155160165170175
0.2690.2620.2540.2480.241
355360365370375
0.1310.1300.1280.1270.125
3637383940
0.9620.9550.9460.9360.926
7677787980
0.5310.5240.5170.5110.504
180185190195200
0.2350.2300.2240.2190.215
380385390395400
0.1240.1220.1210.1200.119
4142434445
0.9150.9030.8910.8780.865
8182838485
0.4980.4920.4860.4800.475
205210215220225
0.2100.2060.2010.1970.194
405410415420425
0.1170.1160.1150.1140.113
4647484950
0.8520.8380.8240.8110.797
8687888990
0.4690.4640.4590.4540.449
230235240245250
0.1900.1860.1830.1800.177
430435440445450
0.1120.1110.1090.1080.107
5152535455
0.7840.7710.7570.7450.732
9192939495
0.4440.4390.4350.4300.426
255260265270275
0.1740.1710.1680.1650.163
455460465470475
0.1060.1060.1050.1040.103
5657585960
0.7200.7080.6960.6840.673
96979899
100
0.4210.4170.4130.4090.405
280285290295300
0.1600.1580.1560.1530.151
480485490495500
0.1020.1010.1000.0990.098
NOTE: These effective widths are based on the limit state of
strength for steel with Ys = 280 N/mm2 and
having a buckling coefficient K = 4. For steels with other
values of Ys or sections having K 4, seeClause 4.4.1 of BS
5950-5.
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A simple formula for the minimum size of stiffener is given in
BS 5950-5. If thestiffener is adequate, the plate element may then
be treated as simply supportedalong both longitudinal edges, with a
5 value of 4. In BS 5950-5, edgestiffeners failing to meet this
limit are considered to be ineffective and aredisregarded, leading
to much reduced effective section properties.
Unstiffenedelement
Simplelip
Compoundlip
IntermediatestiffenerInternal
element
a) Section withunstiffened elements
b) Sections with elementsstiffened by lips
c) Section withintermediately
stiffened element
Figure 3.4 Types of element and stiffeners
Intermediate stiffeners are intended to reduce the flat width of
the plateelements so that the section operates more effectively.
They usually comprisefolds in the section. Again, a simple formula
for the minimum size of stiffeneris given in BS 5950-5, Clause
4.7.1. Because these stiffeners stabilise twoadjacent plate
elements, they have to be relatively robust (i.e. stiff).
Typically,a V shaped fold of height not less than one-fifth of the
width of the adjacentplate element on one side of the stiffener
will generally offer effective support.Thus, for a compression
flange of 150 mm width, a single intermediate fold of15 mm depth
should be satisfactory.
An additional problem with intermediate stiffeners is that the
stiffenedcompression plate element tends to buckle towards the
neutral axis of thesection in bending (a phenomenon known as flange
curling). This means thatthe effectiveness of very wide compression
elements with multi-stiffeners isreduced due to this deformation.
Account is taken of this effect in BS 5950-5,Clauses 4.7.2 and
4.7.3.
3.2 Behaviour of websWebs of cross-sections are subject to
shear, bending and local compression attheir supports. It is often
found that these local effects dominate the design ofcold formed
sections. In purlin design, for example, the sections are
supportedby cleats attached to the webs rather than sitting
directly on the supports whichmay reduce their effectiveness.
3.2.1 Web shearSlender webs normally fail in shear by shear
buckling. The buckling coefficient5 in Equation (1) for a simply
supported plate in pure shear tends to a value of5.35. This leads
to a critical shear stress qcr given by BS 5950-5, Clause
5.4.3as:
qcr = (3)106tD
2N/mm 2
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qcr is compared to the average shear stress acting across the
full web depth.Additionally, the average shear stress should not
exceed 0.6 Ys representing thelimiting stress at which shear
yielding occurs. In irregular sections, themaximum shear stress
should not exceed 0.7 Ys.
3.2.2 Web bendingWebs of sections in bending are subject to
varying compressive stress, reducingfrom a maximum at the junction
with the flange to zero at the elastic neutralaxis position. Very
deep webs can be influenced by local buckling incompression.
However, the varying stress in the web leads to a deeper
plateelement before buckling than for a plate element under pure
compression. Thisis reflected in the theoretical value of the
buckling coefficient 5 of 23.9 (ratherthan 4).
The effective width concept is also used to determine the
post-buckling bendingresistance of deep webs by considering two
separate zones adjacent to theneutral axis and to the compression
flange. This behaviour is illustrated inFigure 3.5(b).
c
Neutralaxis
c
Ys Ys
Y
effb /2 effb /2 effb /2 effb /2
Ys Ys
Y
effb /2 effb /2
Ys Ys
c
Neutralaxis
Y
effb /2 effb /2
po po
Y c
Ys
a) Effective width of compressionflange and fully effective
web
b) Effective width of webin compression
c) Reduced stress, pin fully effective web
d) Full yielding of web in tension(non-symmetric section)
o
Compression
Tension
Figure 3.5 Effective width models for cold formed sections in
bending
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In BS 5950-5, an alternative approach is used, whereby the
maximumcompressive stress in the web is determined. This is given
by the term pocalculated as in Clause 5.2.2.2 of BS 5950-5 (see
Figure 3.5(c)):
(4)p0 ' 1.13 & 0.0019Dwt
Ys280
py
where Dw is the depth of the web
3.2.3 Web crushingLocal failure at supports, or at locations of
point loads, can occur as shown inFigure 3.6. This reduces the
load-carrying resistance of the member. It is takeninto account by
an empirical formula representing the web crushing load.
Section A - A Use of cleat toavoid crushing
A
A
Cleat
Figure 3.6 Web crushing at a support
This effect is largely a function of the width of the support,
the thickness of thesteel, and the height/thickness ratio of the
section. The crushing load Pw (in kN)of a single vertical web with
stiffened flanges is given in BS 5950-5, Clause 5.3,as:
Pw = t2 k (1.33 ! 0.33 k)(1.15 ! 0.15 r/t)(2060 ! 3.8 D/t) (1 +
0.01 N/t) x 10!3
(5)where:
t is the steel thickness (mm)D is the section depthN is the
support widthr is the corner radius between the web and flange.k =
Ys /228.
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Equation (4) applies where the reaction (or point load) is
applied close to theend of the member and where the web is free to
move laterally. The equivalentvalue for an internal support
reaction or point load is approximately 50% higherthan that given
by this equation.
It follows that the support reaction or point load should not
exceed the webcrushing resistance. This can be best achieved by
increasing the width of thesupports or the thickness of the steel
section. Enhanced capacities are given fordouble C sections with
back to back webs, or webs with both flanges held inposition (see
Table 8 of BS 5950-5[1]).
Interaction between co-existent bending and web crushing may be
taken intoaccount using the relationship of the form indicated in
Figure 3.7. This meansthat the bending resistance of continuous
members may be reduced at internalsupports, unless wet crushing is
prevented by use of a stiffening element, e.g.an angle cleat.
1.0
0
0.4
1.00 0.45
Acceptable zone
max
w
MM
PP
Figure 3.7 Influence of combined moment, M and web reaction, P
fordouble C sections
3.3 Behaviour of members in bending3.3.1 Moment resistance of
sectionThe effective properties of sections in bending may be taken
into account fromfirst principles by considering the effective
widths of the compression elements,as illustrated in Figure 3.5.
The neutral axis of the section is determined bybalancing tension
and compression. The section modulus is then calculatedknowing the
elastic neutral axis position. The effective bending resistance
isobtained by multiplying the elastic section modulus by the design
strength ofthe steel. Both the neutral axis position and the
section modulus are thereforefunctions of the operating stress of
the compression flange.
For symmetric sections, the effective section modulus of the
compression plateis not greater than that in tension and therefore
compression yielding occurs
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first. However, for some non-symmetric sections, tension
yielding may occurfirst causing plastification in the tension
flange. This local yielding, asillustrated in Figure 3.5(d) is
permitted, provided the compression plate does notyield.
3.3.2 Influence of section shapeZ-shaped sections displace
laterally when loaded through their webs, becausethe principal axis
of bending is at an angle to the vertical axis through the
web.These sections are normally used as roof purlins, so that the
orientation of theprincipal axis counteracts that of the roof
slope, as in Figure 3.8(a). Somesections are specially formed to
reduce the angular difference between theprincipal and vertical
axes to about 5E. Fixing to rigid flooring or deep sheetingalso
assists in preventing lateral displacement.
Twisting aboutshear centre
Roof slo
pe
b) C sectionsa) Z sections as purlins
Principal axisof bendingclose to vertical
Load
Load
Shearcentre
Shearcentre
Figure 3.8 Behaviour of different sections under bending
C sections twist when loaded through their webs because the
shear centre of thesection is located outside the web (see Figure
3.8(b)). This is alleviated byplacing two sections back to back, or
by providing lateral restraints to bothflanges. Fixing to rigid
flooring also reduces twisting, depending on the locationand
spacing of the fixings. The shape of C sections can be modified to
a zetashape to bring the shear centre closer to the web.
Non-symmetric sections, as shown in Figure 3.5(d), may displace
laterally undermajor axis bending. These transverse bending
stresses should be considered inaddition to primary bending
stresses unless lateral movement is prevented.
3.3.3 Continuous membersFor simply-supported members, it is the
sagging (positive) moment conditionsthat determine the bending
resistance of the member. For members that arecontinuous over one
or more internal supports, moments are determinedelastically (i.e.
using moment distribution or other elastic methods). Plastichinge
analysis is not permitted because the slender sections are not able
tomaintain their full bending resistance when rotations exceed the
point at whichthe section reaches yield. There is, however, some
residual bending resistanceat large rotations as shown in Figure
3.9.
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Load
Support
Mom
ent
Rotation
Idealised behaviour
b) Moment - rotation characteristics of 'slender' sections
Moments followingredistribution
Actual behaviourof 'slender' section
Elasticmomentcapacity
Elastic moment
a) Redistribution of moments for 'plastic' sections
Figure 3.9 Illustration of influence of section type on
behaviour ofcontinuous beams
Design on the basis of elastic analysis means that the
conditions at the internalsupports of continuous members often
dominate the overall design (see therelationship between moment and
web crushing in Figure 3.7). In some cases,this can lead to the
conclusion that simply-supported members are stronger
thancontinuous members! Some purlin systems utilise the flexibility
of sleeved oroverlapping purlins at the supports in order to
achieve some elasticredistribution of moment, and hence to lead to
more efficient design of themembers (see Section 4.1). In order to
make an accurate prediction of theamount of redistribution that
will take place, it is necessary to know themoment-rotation
behaviour of the sleeved or overlapped section in hogging.This
should be determined by testing.
3.3.4 Lateral torsional bucklingThe above approach assumes that
the members are laterally restrained i.e. theycannot fail by
lateral buckling. This is the case where simply supportedmembers
are attached to floors etc. so that the compression flange is
preventedfrom displacing sideways (or laterally).
Where the lateral restraints are sufficiently wide apart,
lateral torsional bucklingmay occur. This effect is illustrated in
Figure 3.10. The elastic lateral bucklingresistance moment of an
equal flange I-section or a symmetrical C section bentin the plane
of the web is given in Clause 5.6.2.2 by the formula:
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23P:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002
ME = (6)B2 AED2 (LE/ry)
2Cb 1 %
120
LEry
tD
2 0.5
where:
LE is the distance between points of lateral restraintry is the
radius of gyration of the section in the lateral directionCb is the
factor representing the shape of the bending moment diagram
(unity
for constant moment).
u
f
Support
Loading
x
yz
Figure 3.10 Deformations u and N associated with
lateral-torsional buckling
Account may also be taken of the support conditions in modifying
the effectivelength LE. The ratio LE/ry defines the slenderness, 8
of the member. As theslenderness reduces, so ME increases, and
eventually the bending resistance, Mcof the section is reached.
Equation (5) may be converted to an effectiveslenderness, 8LT of
the beam according to the expression:
8LT = u v 8 (7)
where u is approximately equal to 0.9 for C or I sections,
v = (8)1 % 120
8tD
2 0.25
The effective slenderness may be non-dimensionalised to give the
modified
slenderness ratio, &8LT, by dividing by 8y where 8y = (see
Section 3.4.1).B E/Ys
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As the D/t ratio of these sections is very large, it follows
that v tends to unity.For a simply supported beam, its effective
slenderness 8LT may be taken as 0.98as a safe approximation. This
reflects the beneficial effects of non-uniform stressand torsional
stiffness on lateral torsional buckling of the section in
comparisonto a strut of slenderness 8.
The relationship between the modified slenderness ratio of the
member and thebending resistance, Mb of the section is shown in
Figure 3.11. This is based onthe Perry-Robertson approach, as
defined in BS 5950-5. The full bendingresistance of the section can
only be reached when 8 is less than 40 Cb.
00 0.5 1.0 1.5 2.0
s
1.2
1.0
0.8
0.6
0.4
0.2
ECCS TC7
Elastic lateraltorsional buckling
EC3 Part 1.3
BS 5950 - 1
BS 5950 - 5
Modulus of elasticity E = 205 kN/mmDesign strength Y = 280
N/mm
LTModified slenderness ratio ( )l
bc,
Rd
Mom
ent
ratio
(M
/M
)
Shape factor = 1.1
Figure 3.11 Design curves for cold formed sections used as
beams
Similar formulae may be developed for singly symmetric sections
such asC sections. However, in this case, the shear centre of a C
section does notcoincide with the plane of the web. Therefore loads
applied through the webcause twisting of the section (see Figure
3.8(b)). In principle, therefore, singleC sections should be
restrained against torsion if they are to be used effectively.If
not, then in-plane warping stresses due to torsion are created
which shouldbe added to bending stresses.
The hogging (negative) moment region of continuous members
requires specialconsideration, because it is usually more difficult
to restrain the lower flange ofthe section than the upper flange.
It is often assumed that the point of zeromoment may be considered
as a point of effective restraint, and that the part ofthe beam in
hogging may be treated as a member with a linear variation
ofmoment. If this gives a bending moment resistance less than the
appliedmoment, then additional lateral restraints are needed. It
should be noted,however, that treating the point of zero moment as
a point of effective restraintis only appropriate when adequate
torsional restraint is provided at the support(see Clause 5.5.5. of
BS 5950-1:2000). In purlin design, sag bars are generallyused to
provide restraint to the lower flange in wind uplift
conditions.
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3.4 Behaviour of members in compression3.4.1 Members in pure
compressionMembers in compression are typically columns loaded by
beams, or struts intrusses. Columns are usually only laterally
restrained at the beam-columnconnections, unless they are built
into a wall. The design of axially loadedsections may be treated as
a series of plates in compression. This leads to aneffective area
of the cross-section when the effective widths of all
thecompressive plate elements are combined, as shown in Figure
3.12. This ratioof the effective to the gross area of the section
is known as the Q factor andit represents the efficiency of the
section under axial compression.
Therefore, the compressive resistance of the section is:
PCS = Q A Ys (9)
where A is the gross (unreduced) cross-sectional area of the
column section.
Columns generally fail by buckling rather than pure compression,
as shown inFigure 3.13. Perfectly straight columns buckle
elastically at an Euler loadgiven by:
PE = = (10)B2 EIy
L2
E
B2EA
82
where 8 is the slenderness of the member between points of
lateral restraints(see Section 3.3.4), which is the effective
length Le divided by the radius ofgyration.
The modified slenderness ratio, &8 is defined as 8/8y, where
8y = inB E/Yswhich 8y corresponds to the slenderness of the
equivalent perfect strut whenacting at the yield strength, Ys.
Shearcentre
Eccentricity= A - B
A B
b) Reduced cross-sectionin compression
a) Axial load appliedthrough centroid
Centroid Modifiedcentroid
Figure 3.12 Analysis of restrained section in compression
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Torsional - flexuralbuckling mode
Section A - A
Floor
Floor
A A
Column Lateral bucklingmode
Figure 3.13 Buckling of column in compression between floors
Real columns are not perfectly straight; they fail before the
Euler buckling loadis reached. This is taken into account by a
Perry-Robertson type formula whichhas a solution of the form:
(11)Pc 'PE Pcs
N% N2&PE Pcs
where N = , Pc is the axial buckling resistance of thePcs % (1 %
0) PE
2column and 0 is an empirical factor accounting for the initial
imperfection of thecolumn, given in Clause 6.2.3 of by 0 = 0.002
(8-20). (Therefore, Pc = Pcs when8 # 20).
The variation of load ratio (Pc/Pcs) with slenderness ratio 8 is
presented inFigure 3.14.
3.4.2 Singly symmetric sectionsIn sections which are not doubly
symmetric about both axes (see Figure 3.12),the centroid of the
effective section (B) may be at a different location to thecentroid
of the gross section (A) through which axial forces are assumed to
act.This gives rise to combined bending and compression, which is
taken intoaccount by a modified value of PcN such that:
PcN = Mc Pc / (Mc + Pc es ) (12)
where Mc is the pure bending resistance of the section, and es
is the eccentricityof the applied load caused by the shift of
neutral axis from the gross section tothe effective section (see,
Clause 6.2.4).
3.4.3 Combined bending and axial loadingThe interaction between
bending and axial load may be taken into account bythe following
relationship for members which fail by lateral buckling:
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(13)Fc
Pc%
Mx
Mb%
My
Cb Mcy (1 & Fc/Pey)# 1
where Fc is the axial load applied to the column, and Mx and My
are the appliedmoments in the x and y (major and minor axis)
directions (see clause 6.4.3).
Mcx and Mcy are the design bending resistance based on an
independent analysisin the x and y directions. Cb takes into
account the variation of moment alongthe member (see Equation 6).
Pc is determined for an axially loaded member,as above, and PEY is
the compression resistance for buckling in the y direction(from
Equation 9).
This equation takes into account the potentially weakening
effects of thecombinations of different buckling modes.
3.4.4 Torsional flexural bucklingThin open cross-sections are
torsionally weak and may be more susceptible totorsional failure
than lateral buckling failure when loaded axially (as illustratedin
Figure 3.13). This is especially so for singly symmetric sections,
such asC sections, because of the separation of the centroid and
shear centre(representing the point about which the member
twists).
Analysis for torsional flexural buckling is quite complicated
and the approachin BS 5950-5 is to modify the effective length for
lateral buckling to take intoaccount the possibility of a lower
torsional flexural failure mode. This isachieved by the use of the
effective length multiplication factor, ". Appropriate" values for
a range of common sections are presented in Appendix C ofBS
5950-5(1).
1.2
1.0
0.8
0.6
0.4
0.2
00 0.5 1.0 1.5 2.0
Slenderness ratio
Load
rat
io
Elastic Eulerbuckling
EC3 Annex A
s
l
Modulus of elasticity E = 205 kN/mmDesign strength Y = 280
N/mm
BS 5950-5
BS 5950 - 1
Figure 3.14 Design curves for cold formed sections as
columns
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3.5 Serviceability limits3.5.1 Natural frequencyThe natural
frequency of light steel flooring systems should be calculated
inorder to avoid perceptible vibrations. According to current
SCIrecommendations, the natural frequency of these floors should
exceed 8 Hzwhen calculated for a load equal to the self weight plus
a permanent load of 0.3kN/m2. This is equivalent to a static
deflection of 5 mm under the same load.Assuming that the permanent
load is approximately 33% of the total serviceload, it follows that
the maximum deflection under total design loading shouldnot exceed
15 mm. This deflection limit is equivalent to that for
timberconstruction.
The natural frequency limit often controls for floor spans
greater than 5 m.
3.5.2 Deflection limitsDeflection limits are introduced for
floors in order that there is no serious riskof cracking of
partitions or other components supported by these floors,
orperceptible movement. Traditionally, an upper deflection limit of
span/360 isused for floors subject to imposed load, reducing to
span/250 when subject tototal loads. However, these limits may be
too relaxed for light steel floors,particularly in relation to
control of vibrations (see above). Because of this, it isproposed
that the limit on imposed load deflections should be reduced
tospan/450, and the limit on total deflection should be reduced to
span/350 (butnot exceeding 15 mm, as required for control of
vibrations).
Stricter limits are required for edge beams supporting cladding.
For brickwork,total deflection limit of span/500 is often used.
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4 APPLICATION OF COLD FORMEDSECTIONS IN BUILDING
The following Sections describe typical uses and potential
applications of coldformed steel sections in buildings. A common
use of these sections is in purlinsand side rails in industrial
buildings, but there are many new developments ofcold formed
sections as primary structural members in housing, light
industrialand commercial buildings.
4.1 Purlins and side railsPurlins are usually of Z shape, the
argument being that the principal axis ofbending of the section is
close to vertical when the section is orientated so thatthe upper
flange points up the roof for roof slopes of 10 to 15E, as shown
inFigure 3.8(a). This means that vertical roof loads do not cause
serious twistingof the sections. However, roof slopes in modern
industrial buildings can be aslow as 5E, and this has created the
need for modified section shapes. Theso-called Zeta section (see
Figure 2.3) is one attempt to provide a sectionshape more suitable
for shallow roofs.
C shaped sections and their derivatives have also been developed
for roof andwall applications. The web shape can be modified to a
sigma shape to reducethe twisting of the section by bringing the
shear centre of the section closer tothe web.
All purlins above a certain length are provided with sag rods
which are intendedto prevent twisting during erection and to
stabilise the lower flange against winduplift. The upper purlins
are usually tied at ridge level.
Lateral forces on the members can usually be transferred by
diaphragm orstressed skin action of the roof sheeting. The upper
flanges of the purlins areconsidered to be laterally restrained by
the sheeting.
The design of purlins has developed to an extent that empirical
methods basedon testing are often the only economic solution.
Purlins are usually designed tobe continuous in order to satisfy
deflection limits. However, elastic design ofcontinuous members can
be unduly onerous, when strictly interpreting therequirements of BS
5950-5 (see Section 3.3.3).
This factor has been recognised by the purlin manufacturers and
manyoverlapped and sleeved systems at the supports have been
developed. Themoment-rotation characteristics of these systems can
be matched to theperformance of the purlin, leading to optimum
design of the section. Thisbehaviour is illustrated in Figure 4.1.
Overlapping systems provide betterhogging bending resistance then
sleeved systems. Both provide double webthickness, improving the
shear resistance of the section at internal supports.
Shear forces are transferred to the supporting rafters by cleats
bolted to the websof the purlins. The cleats are designed so that
the lower flange of the purlin doesnot bear directly on the rafter,
and thus web crushing problems are avoided.The shear or bearing
strength of the connecting bolts provides the necessary
loadtransfer (see Section 4.10).
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Side rails are designed in a similar manner and are used in
walling applications.Vertical loads are resisted by the use of sag
rods or bracing members in theplane of the wall.
L
Sleeve or overlapJoint rotation
w
0.10wL
0.08wL
Redistribution momentsallowing for joint flexibility
Elastic moments
Figure 4.1 Redistribution of moments in sleeved or overlap
purlin system
4.2 Floor joistsSteel floor joists, usually of C section, may be
used to replace timber joists inhousing and other masonry
buildings. The joists may be built into walls orsupported on
traditional joist hangers (see Figure 4.2). Thicker cold
formedsections may also be used to replace lighter hot rolled
sections as secondarybeams in main frames.
Comparisons have been made of the design of cold formed sections
with thetraditional alternatives. These comparisons have been
characterised in terms offour typical applications that may be
encountered in domestic and commercialbuildings. The section sizes
and weights resulting from these designs arepresented in Table 4.1.
In practice, designs may be controlled by bendingresistance or
stiffness requirements.
In terms of equivalent bending resistance, a series of 175 mm 37
mm timberjoists may be replaced by 100 mm 40 mm 1.2 mm thick C
sections at thesame spacing. Other comparative performances may be
taken from Table 4.2.However, in practical applications, floor
joists should also be designed forrelatively strict deflection and
frequency limits which means that they are deeperthan for pure
bending resistance (see Section 3.5).
The cold formed sections can also be manufactured with punched
holes in theirwebs to allow passage of small diameter pipes and
other services. The depth ofthese holes is normally less than half
the member depth and has little effect onstructural performance.
Provision of these holes for services overcomes theproblem of
notching of timber joists. Attachment of the timber
floor-boardsincreases the stiffness of the light steel sections and
provides lateral restraint iffixed at regular intervals.
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Table 4.1 Comparison between section sizes for cold formed
steel, hot rolledsteel and timber for different applications
Section type
Domestic building Commercial building
Span = 4 mSpacing = 0.6 m
Span = 5 mSpacing = 0.6 m
Span = 5 mSpacing = 1.2 m
Span = 6 mSpacing = 1.2 m
PlainC section
150503W = 5.6
2No. 150503W = 11.0
2No. 150505W = 17.8
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LippedC section
165631.6W = 3.9
220631.8W = 4.9
2No. 220632.0W = 10.9
2No. 300652.0W = 15.0
Timber 25075W = 10.1
300 75W = 12.1
2No. 30075W = 24.2
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Hot Rolled Steel 10251 RSCW = 10.4
12776 UBW = 13.0
15289 UBW = 16.0
178102 UBW = 19.0
Imposed loading = 2.5 kN/m2 for domestic building= 3.5 kN/m2 for
office/commercial building
Dead loading = 1.0 kN/m2 in all casesW = weight in kg/mData
presented for S280 steel or standard timber grade.
Table 4.2 Structural equivalents of cold formed sections
Lipped C section Timber
D B t D B
70 40 1.2 150 37
100 40 1.2 175 37
100 40 1.5 175 50
100 65 1.6 200 50
120 65 1.6 225 50
127 65 1.6 225 63
165 65 2.0 250 75
Lipped C sections Hot rolled steel
D B t Designation
2 No. 220 65 2.0(12.5 kg/m)
127 76 UB(13.0 kg/m)
2 No. 300 65 2.4(17.9 kg/m)
178 102 UB(19.0 kg/m)
2 No. 300 65 3.0(21.0 kg/m)
203 133 UB(25.0 kg/m)
All dimensions in mm; S280 or grade S275 steel; Standard timber
grade.Based on equivalent bending resistance.
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Screw
C section
Bent plate as cleat
Screw
Truss connection
Joint hanger- connection to masonry
C section - C sectioncleat connection
Short C section
Figure 4.2 Examples of connections between C sections
4.3 Stud wallingStud walling using C sections of 50 to 100 mm
depth is a common form ofpartition construction in commercial
buildings. It is much lighter than traditionalblockwork and is
quicker and easier to construct. Importantly, it is a
dryconstruction and is easily removable..
Plasterboard or similar materials are attached by screws to the
stud walling toform the finished surfaces. This adds considerably
to the stiffness of the walls.An 80 mm thick stud wall can be used
to replace a 100 mm or 120 mmblockwork wall. A tall wall
constructed using C section studs is illustrated inFigure 4.3.
These walls may be assembled on site or pre-fabricated as
storey-high panels.
Separating walls between compartments and between apartments are
designedto achieve a high level of acoustic insulation and fire
resistance. This is achievedby using multiple layers of
fire-resistant plasterboard attached by resilient barsto the studs,
with insulation and quilt placed between the studs.
M. FIRDAUSHighlight
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An airborne sound reduction of over 53 dB and 60 minutes fire
resistance can beeasily achieved by this form of construction.
Improved acoustic insulation canbe achieved by using double stud
walls (usually the case in party walls, and inspecial applications,
such as cinemas).
Figure 4.3 Tall wall constructed using C section studs
4.4 TrussesPurpose-made steel trusses have been marketed for
many years. As shown inFigure 2.7, they comprise cold formed
sections as flanges with bent bars or tubesforming the bracing
elements welded to the flanges. These can be designed tospan
typically 5 m to 20 m (and up to 30 m in special applications) and
can beused as roof or floor joists.
Roof trusses for housing are rather different in shape, as the
roof pitch iscommonly in the range of 20 to 45E. The traditional
timber truss is of the Finktruss form and the truss spacing is
compatible with the size of tile battensnormally used. Various
steel truss systems have been developed.
Two generic forms of light steel roof truss may be used:
C Closely spaced roof trusses: the open roof truss uses bolted C
sections whichprovide for habitable roof space, as shown in Figure
4.4.
C Widely spaced roof trusses: the more traditional Fink trusses
may be spacedwider apart (3 to 5 m) and purlins may span between.
The space betweenthe trusses may be used for storage, etc.
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Both roof systems may be used in new-build and in renovation
projects by over-roofing. The Capella system, shown in Figure 4.5,
has been specificallydeveloped for over-roofing in renovation
applications. Generally, theconnections between the members are
bolted because of the relatively highforces that are transferred.
Over-roofing is covered in a recent SCI publicationOver-roofing of
existing buildings using light steel [7].
Figure 4.4 Open-roof truss for habitable use
Figure 4.5 Widely spaced roof trusses with purlins between the
trusses
4.5 Structural FramesCold formed sections can be used not only
as secondary members but also asbeams and columns in primary
structural frames. This has proved to besuccessful in light
commercial and industrial buildings and in mezzanine floors.Often
it is necessary to use C sections placed back to back in longer
spanapplications to increase their buckling resistance.
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Traditional C and Z sections can be made up into more complex
assemblies, asshown in Figure 4.6. The sections are thin enough to
facilitate connections byself-tapping screws. Alternatively, C
sections can be bolted together to form loadbearing frames, as
shown in Figure 4.7 for a school building. Bolted connectionscan be
made with autoform cleated ends and with pre-punched bolt holes.
Typical framing arrangements at junctions of floors and walls are
shown in Figure4.8. The transfer of vertical loads in the walls in
platform construction can beachieved by stiffening the ends of the
floor joists.
Figure 4.6 Use of C sections to form joists, stud columns, and
purlins
Figure 4.7 Load-bearing frames entirely composed of bolted C
sections
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Load bearingstud
Bottomtrack
Top track
Floor joist
Angleseat
Edgesupport
(a) Balloon construction
Load bearingstud
Floor joistTop track
Bottomtrack
Edgesupport
Webstiffener
Closuresection
(b) Platform construction
Figure 4.8 Typical framing arrangements at junctions of floors
and walls [15]
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The Swagebeam is a special form of C section that has been
developed toenhance the shear and bending resistance of bolted
connections between thesections. This is achieved via the bearing
action of indentations in the web of thesection and of embossments
in the web cleats. A typical swagebeam connectionin a mezzanine
floor is shown in Figure 4.9. This system has been used
inrectangular frames and in portal frames (up to 15 m span).
Figure 4.9 Swagebeam connection
4.6 Curtain walling and over-claddingCurtain walling to
multi-storey buildings consists of light frames which
supportglazing, aluminium or steel panels, or stone veneer. These
can be storey highpanels which are connected to the floor slabs.
Cold formed steel sections canbe used for the sub-frame components
to the cladding and there are a numberof recent examples of
buildings where this has been used successfully both innew
construction and in renovation (see Figure 4.10). A dry envelope is
erectedrapidly, which means that the internal fit-out can commence
without thecladding being on the critical path.
Over-cladding of existing buildings is an important market where
light steelsub-frames can be used to span directly between floors.
The sub-frames are alsodesigned to allow for adjustments due to
site tolerances (see Figure 4.11). Avariety of cladding materials
may be used, such as composite panels or cassettepanels. The design
requirements for over-cladding systems are reviewed in anSCI
publication Over-cladding of existing buildings using light steel
[8].
M. FIRDAUSHighlight
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Figure 4.10 Use of cold formed sections as curtain walling
Figure 4.11 Use of light steel framing as sub-frame in
over-cladding of existingbuildings
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4.7 HousingLight steel framing used in low-rise housing has been
successful in Australia,Japan, USA, Canada and now in the UK.
Currently, four light steel framingsystems are used in the housing
sector in the UK. Modern methods of light steelframing used in
housing may be considered to be of three basic forms:
C discrete members that are assembled on site to form to which
cladding isattached. These are similar to frame systems covered in
Section 4.5.
C wall panels, prefabricated in storey high units (platform
construction). Thisis a similar form of construction to that used
in timber framed housing. Thewall panels are insulated externally
to create a warm frame.
C complete house modules or modular components. Other more
sophisticatedsteel/concrete boxes have been developed for
applications in hotels orapartment blocks (see Section 4.8).
In wall panel systems, the individual panels are prefabricated
by self-piercingrivets, or welding, and the panels are lifted into
place, and bolted together on site(see Figure 4.12).
Figure 4.12 Erection of light steel framing for a two-storey
house
In the Surebuild system, steel floor joists sit on a Z shaped
trimmer sectionattached to the top of the lower storey wall panels,
and the upper panels areattached to the lower panels in so-called
platform construction. The steel studwall panels use 75 32 mm C
sections at 400 mm spacing. These are locatedon the warm internal
face of a 35 mm thick insulation board. The internalfinish is a
fire resistant plasterboard designed to give 30 minutes fire
resistance.Heavier or multiple board systems can provide 60 minutes
fire resistance.Brickwork is attached by wall ties located in a
vertical track which is screwedthrough the insulation to the wall
studs.
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The Metsec Gypframe system uses C sections attached by bolts in
countersunkholes. The Gypframe system is erected as two-storey high
wall panels and thefloor joists are bolted to the webs of the wall
studs. It is also constructed as awarm frame and insulation is
pre-attached to the panels.
The other housing systems that are available in the UK are by
Ayrshire SteelFraming and Forge Llewellyn Ltd.
4.8 Modular constructionModular or volumetric systems are
pre-assembled and generally fitted-out in thefactory, so that they
are delivered to site as units which are self-supporting andrequire
only minimal site work to complete the assembly of units. The
typicalframework of a pre-fabricated module is shown in Figure
4.13.
Figure 4.13 Modular construction using light steel framing
The units are generally less than 4.5 m wide and up to 12 m long
because of therequirements for transportation and lifting. The
framework of the modulescomprises cold formed C sections, often
supplemented by hot rolled sections atthe corner posts and bottom
beam supports. Some systems are corner supportedwhich means that
the braced walls act as deep beams. Others are continuouslyedge
supported.
Cladding and roofing is usually attached on-site to form the
completed building.Therefore, a variety of architectural features
can be achieved. Modular units canalso be used in refurbishment
[9].
4.9 Frameless structuresOver the last 20 years, there have been
important developments in framelessconstruction, where the members
and the cladding interact by stressed skinaction. The main
structural configurations that have been used are the foldedplate
roof [16], the truncated pyramid and the barrel vault.
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The folded plate roof behaves as a series of inclined beams
spanning betweenend frames. The fold-line members (cold formed
angles) absorb the axial thrustsand tensions, and the sheeted web
is in pure shear. From the point of view ofaesthetics and
structural performance the slope of the roof would normally
bebetween 30 and 45E (to the horizontal) and most efficient spans
are between15 m and 25 m.
The truncated pyramid roof, as shown in Figure 4.14, comprises a
compressionring and a tension ring with hip members transferring
the loads between. Theindividual sheeted panels are prefabricated
and they can be bolted together andlifted into place in a few
hours. Gutter outlets are placed along the valleys anddown the
hollow section columns.
Figure 4.14 Example of truncated pyramid roof using cold formed
steel sections
4.10 ConnectionsThe common types of fixing between cold formed
sections, and between sectionsand sheeting, are:
Type Usual Application
(a) Bolts Connecting cold formed sections.
(b) Self-tapping screws Fastening sheeting to sections (< 6
mm thick) orsheeting to sheeting at sidelaps.
(c) Blind rivets Fastening sheeting to sheeting at sidelaps.
(d) Powder actuated pins Fastening sheeting to members (>6 mm
thick).
(e) Spot welding Factory joining of thin steel.
(f) Puddle welding Site welding of sheeting to sections.
(g) Clinching Usually factory installed by press-joining.
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(h) Self-piercing rivets Usually factory installed.
(i) Nailing Site installed using special nails.
These different types of fixing are reviewed as follows:
(a) Bolts: Bolt holes can be punched in cold formed sections;
the connectionsbetween members are usually arranged so that the
bolts are loaded in shear.In almost all cases, the resistance of
the connection is determined by thebearing resistance of the
thinner steel section, rather than by shear of the bolt.
Countersunk bolts can be located in recessed holes punched into
thesections. In this way, the bolt head does not protrude and does
not affect thefixing of the plasterboard or other lining (see
Figure 4.15).
Figure 4.15 Countersunk bolts between wall elements
Autoform ends may also be formed during the cutting and punching
process;these facilitate bolting (see Figure 4.16).
Figure 4.16 Creation of autoform ends to C sections
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In BS 5950-5, Clause 8.2.5.2 the shear resistance of bolted
connections isgiven as:
Pu = 2.1 d t Ys for t # 1 mm (14)
or Pu = (1.65 + 0.45 t) d t Ys for 1 mm < t # 3 mm (15)
where:
d is the diameter of bolt (mm)Ys is the design strength of steel
in thinner plate (N/mm
2)t is the thickness of steel in thinner plate (mm)
These shear resistances assume that the bolt end distance is at
least 3d andthat washers are used under both the head and the nut.
The resistances aregreater than the equivalent values in BS 5950-1,
because of build up ofdeformed steel in front of the bolt as the
thinner section fails in bearing. Theyalso include a partial safety
factor, given by the ratio of the ultimate to theyield strength of
the steel (approximately 1.4).
(b) Self-tapping screws: Self-drilling self-tapping screws are
commonly used forconnecting thin steel components. A selection of
the screws and the drill thatmay be used is shown in Figure 4.17.
The drill part of the screw forms ahole in the steel plate and the
tapping part forms the thread. This is a singleoperation and gives
a relatively strong and stiff form of attachment.Thin-thick and
thin-thin attachments may be made depending on thelength of the
screw. The diameter of the screws is in the range of 4.2 to 8.0mm,
the most common size being about 6 mm for thin-thick
connections.The shear resistance (including partial safety factors)
may be obtained fromAppendix A of BS 5950-5.
Figure 4.17 Different forms of self-drilling self-tapping screws
and thestandard drill
M. FIRDAUSHighlight
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Typically, for a 6 mm diameter screw through 1 mm thick steel,
the shearresistance (including partial safety factors is 3.5 kN
(thin-thick fixings) and2.2 kN (thin-thin fixings). Premature
failure of a fixing by pull-out should beavoided by careful
detailing.
Fixings have also been developed for stand-off applications
where insulationmaterials or timber are to be attached (Figure
4.18).
Figure 4.18 Stand-off type fixing for soft insulation
materials
(c) Blind rivets can be in aluminium or alloyed metal (often
termed monel).They are fitted from one side into predrilled holes
and a mandrel is pulled bya special tool so that the rivet expands
into and around the hole. These rivetsare commonly of 2.4 to 6.3 mm
diameter (dependant on the hole diameter).It is a relatively firm
form of attachment with good pull out resistance and isuseful for
thin-thin attachments, e.g. seams in profiled decking.
Again,Appendix A of BS 5950-5 can be used to obtain the shear
resistance.
The huck bolt is a similar system, but is used for thicker
materials. As forthe blind rivet it is fitted from one side in a
pre-drilled hole. Tension isapplied to the stem of the bolt by a
special tool and a malleable ring ispushed to precompress the
plates to be attached. When the correct tensionhas been applied the
outer part of the stem break