structural design to bs 5950-51998 section properties and load tables.pdf

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

iiP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

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.

iiiP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

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).

ivP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

vP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

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

viP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

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

viiP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

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

viiiP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

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.

ixP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

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.

xP:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

1P:\CMP\Cmp657\pubs\P276\P276-Final.wpd 18 April 2002

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.


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.


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

M. FIRDAUSHighlight

M. FIRDAUSHighlight


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


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.


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

M. FIRDAUSHighlight

M. FIRDAUSHighlight


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


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)


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.


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.


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


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


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


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


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.


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.


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


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


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.


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


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.


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:


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


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.


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


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:


(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


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.


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).


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.


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




PlainC section

150503W = 5.6

2No. 150503W = 11.0

2No. 150505W = 17.8

-

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

-

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.


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


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.


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.


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


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]


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


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


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.


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.


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.


(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


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


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

structural design to bs 5950-51998 section properties and load tables.pdf

Documents

publication data

time of publication

publication number

building design

steel sections scip

british steel strip

c light steel framing

dr chung