Structural Design to BS 5950-51998 Section Properties and Load Tables.pdf

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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 Institute Silwood Park Ascot Berkshire SL5 7QN Tel: 01344 623345

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Apart from any fair dealing for the purposes of research or private study or criticism or review, as permitted under the Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the UK Copyright Licensing Agency, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organisation outside the UK.

Enquiries concerning reproduction outside the terms stated here should be sent to the publishers, The Steel Construction 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 information contained herein are accurate to the extent that they relate to either matters of fact or accepted practice or matters of opinion at the time of publication, The Steel Construction Institute, the authors and the reviewers assume no responsibility for any errors in or misinterpretations of such data and/or information or any loss or 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.

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FOREWORD

The authors of this publication are Dr R M Lawson and Dr S O Popo-Ola of The Steel Construction 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. The work was funded by Corus Colors (formerly, British Steel Strip Products).

This publication is a revised edition of the 1992 publication Design of structures using cold formed steel sections (SCI-P-089). It gives general information on the design of cold formed steel sections to BS 5950-5: 1998 (now revised from the 1985 version), and includes new design tables for a wide range of cold formed steel sections used in general building 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 Steel Sections’. 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 Architect’s Guide (P272,

1991).

The section property data, member design tables and associated information are

intended to be used at the scheme design stage. For more comprehensive data

concerning particular sections and their availability, the reader is advised to

contact manufacturers directly. All sections that are included can be obtained

from the manufacturers listed in the Appendix. For more information on steel

grades and coatings, contact Corus directly (see Appendix).

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SUMMARY

This publication reviews the design and application of cold formed steel sections in building construction. The design of these sections conforms to BS 5950-5: 1998: Code of practice for design of cold formed thin gauge sections. Applications that are covered relate to steel frames, trusses and secondary members in commercial, industrial and domestic buildings. The main part of the publication presents design tables for general use of cold formed sections. This data is tabulated in two parts: section properties, and load tables. Section properties can be used in general applications, whereas load tables can be used in direct selection of beam and column sizes.

The cold formed steel sections listed in this publication can be readily obtained from manufacturers in the UK. Other references to the use of cold formed steel are also given.

Berechnung von tragwerken aus kaltgeformten stahlprofilen Zusammenfassung

Diese Veröffentlichung gibt einen Überblick über die Bemessung und Anwendung von kaltverformten Stahlprofilen im Bauwesen. Die Bemessung dieser Profile entspricht BS 5950, Teil 5: “Code of practice for design of cold formed sections”, Ausgabe 1998. Die behandelten Anwendungsfälle beziehen sich auf Stahltragwerke, Fachwerke und nichttragende Bauteile im Verwaltungs-, Industrie- und Wohnungs-bau.

Der Hauptteil dieser Veröffentlichung stellt Bemessungstabellen für den allgemeinen Gebrauch von kaltverformten Profilen vor. Dieses Daten sind in zwei Teilen tabelliert: Querschnittsgrö$en Belastungstabellen. Die Querschnittsgrö$en können allgemein verwendet werden, während die Belastungstabellen der direkten wahl der Träger- und Stützenprofile dienen. Die in dieser Veröffentlichung enthaltenen, kaltverformten Profile können von Herstellern im Vereinigten Königreich bezogen werden. Andere Verweise zur Anwendung von kaltverformtem Stahl sind ebenso enthalten.

Dimensionnement de structures en profils en acier formé á froid Résumé

Cette publication passe en revue les méthodes de dimensionnement et les principales applications des profils en acier formé á 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 formé à froid. Les applications présentées ont trait aux cadres et portiques en acier ainsi qu’aux éléments secondaires utilisés dans les bâtiments industriels, commerciaux ou pour habitation.

La partie principale de la publication présente des tables de dimensionnement pour les applications habituelles des profils formé à froid. Ces informations sont réparties en deux catégories: les propriétés des sections et les tables donnant les

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sections peuvent être utilisées dans toutes les applications. Les informations relatives au dimensionnement des éléments permettent un choix rapide des profils à utiliser en tant que poutres ou colonnes.

Les profils en acier formé á froid repris dans la publication peuvent être aisément obtenus prés des producteurs du Royaume-University. D’autres références relatives à l’utilisation des profils en acier formé á froid sont également mentionnées.

Proyecto de estructuras usando secciones de acero conformado en frio Resumen

Esta publicación revisa el proyecto y aplicación de secciones de acero conformado en frio a la construcción de edificios. El proyecto de estas secciones de acero se ajusta a la BS 5950: Parte 5: 1998: “Norma de buena práctica para el proyecto de secciones de acero conformadas en frio”.

Las aplicaciones cubiertas se refieren a pórticos de acero, cerchas y piezas secundarias en edificios comerciales, industriales y de habitación.

La parte principal de la publicación presenta tablas de diseño para uso general de secciones. Los datos se tabulan en dos partes: propiedades de las secciones y cargas de proyecto de piezas. Las primeras son de uso general mientras que las segundas pueden utilizarse para la elección directa de las proporciones de vigas y columnas.

Las secciones de acero conformado un frio descritas en esta publicación pueden obtenerse fácilmente de los fabricantes del Reino Unido. También se dan 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 l’utilizzo di profili in acciaio sagomati a freddo. La progettazione di tali elementi in acciaio risulta conforme alla normativa BS5950: Parte 5, 1998, `Guida alla progettazione di profili sagomati a freddo’. Le applicazioni che vengono presentate sono relative a strutture intelaiate, a travature reticolari ed elementi secondari per strutture ad uso commerciale, civile ed industriale.

Nella parte principale di questa pubblicazione sono riportate le tabelle progettuali per differenti utilizzi dei profili sagomati a freddo. Questi dati sono tabulati in due differenti parti: la prima e’ relativa alle caratteristiche geometriche dei profili e la seconda riporta i valori dei carichi di progetto degli elementi. Le caratteristiche dei profili possono essere utilizzate in applicazioni di carattere generale mentre una scelta diretta delle dimensioni di travi e colonne puo’ essere fatta sulla base delle caratteristiche portanti degli elementi. Le sezioni dei profili sagomati a freddo riportati in questa pubblicazione possono essere ottenute in brevi tempi da qualsiasi stabilimento del regno Unito. Vengono inoltre forniti diversi riferimenti per l’utilizzo dei profili in acciaio.

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NOTATION

A cross-sectional area of section

b plate width between corners or stiffeners b_e effective plate width in compression B width of the section

C_bcoefficient representing variation of bending moment along a member D depth of web of section

E modulus of elasticity of steel (205 kN/mm2)

e_s 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 minor

axis direction of bending) K plate buckling coefficient L length of member

L_e effective length of member

M_yelastic moment resistance of the section N support width (mm)

py design strength of steel

p_crcritical buckling stress in plate

p_o reduced stress in section determined by web properties

Q factor representing reduced performance of section in compression r corner radius

r_y radius of gyration in y (minor) axis direction of bending t net steel thickness

U_sultimate strength of steel Y_s yield stress of steel

" effective length factor including torsional flexural buckling 8 slenderness of member

8_y slenderness corresponding to B E/Y_s L Poisson’s ratio for steel (= 0.3)

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1 AIM OF THE PUBLICATION

This design guide is aimed at practitioners in the building industry who may have limited experience of the structural design of light steel framing using cold formed steel sections. The publication presents an overview of the design principles for ‘cold formed’ steel sections in accordance with BS 5950-5:1998[1] (revised from the 1985 version). Cold formed steel sections are generally produced by cold rolling from galvanized steel strip.

Most structural engineers are familiar with the application of cold formed steel sections (also known as cold rolled sections) in purlins and side-rails, which are highly engineered products for specific applications. The general use of cold formed sections as primary members of light steel framing requires a more simplified 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 been realised 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 sections in these structural applications. The information is presented under three broad headings:

1. An introduction to the design of cold formed sections. It is appreciated that the design of these sections may appear to be more complicated than that of hot rolled sections. It is therefore important to understand the design principles and also the practical considerations of the structural use of these sections.

2. A review of the application of cold formed sections in buildings, concentrating on the main design features and details. This also necessitates a discussion on methods of cutting, joining and attachment of other members and materials, which are fundamental to the practical use of these thinner sections.

3. A series of tables on section properties and loads for the range of cold formed sections that are readily available for general building use. The section properties have been calculated based on first principles, in accordance with BS 5950-5. The load tables (also determined in accordance with BS 5950-5) can be used to obtain the required member sizes for specific applications.

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1.1 Design tables

Section properties are presented for the gross and the effective sections on the yellow pages (i.e. as influenced by local buckling under compression). These properties may be used by structural engineers when designing members for general application. Alternatively, designers may refer to the load-span tables for beams or load-height tables for columns, which give the member resistances directly (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 generic C and Z sections as floors and walls. Manufacturers often design their sections for specific uses, such as purlins, and establish the member performance based on test data rather than calculations to BS 5950-5. This means that manufacturers’ data may be more beneficial in certain cases.

Member resistance tables (in terms of working load capacity) are presented for generic C or Z sections only. These load tables are useful for selection of member sizes and are intended to be used for initial or scheme design. However, for final design, the data provided by the manufacturer of the selected sections should be used.

Manufacturers should be contacted directly with regard to availability, cutting to length, hole punching, etc. A list of UK manufacturers and further sources of information are presented in Appendix A.

1.2 Limit state design

In BS 5950-5[1], the loads to be used in design are calculated from the working loads 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 the moments and forces in the members, which are then compared to the resistance of the members. Resistances may be as determined for all relevant modes of failure, such as buckling, connection or local failure etc. The methods of determining the member resistance and load bearing capacity of cold formed sections are presented in Section 3.

Additional checks on deflections are made for working loads (i.e. for load factors of 1.0) in order to ensure adequate performance in service. Light weight floors 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 stress design, although a global factor of safety of 1.6 may be used conservatively to determine maximum working loads that the structure can support.

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2 INTRODUCTION TO USE OF COLD

FORMED SECTIONS

2.1 Materials

Sheet 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 is usually supplied pre-galvanized in accordance with European Standard EN 10147 (issued by BSI in 1991 as BS EN 10147[2] as a replacement for BS 2989[3]). Galvanizing gives adequate protection for internal members, including those adjacent to the boundaries of building envelopes, such as purlins. The expected design life of galvanized products in this environment exceeds 60 years (see Section 2.3).

Steel strip is produced by cold reducing hot rolled coil steel with further annealing processes to improve the ductility of the material. It is a quality controlled product with known and easily tested properties. Grade S280 steel (formerly Z28) is a quality of steel specified as having a guaranteed minimum yield strength of 280 N/mm2. Grades S280 and S350 steels are the most commonly specified grades, although it is often found that the actual yield strength is considerably higher than the specified minimum. Steel with a non-guaranteed yield strength may be used in some applications, provided that the strength of the material is determined by tensile tests taken from the coil from which the material was cut.

During ‘cold forming’ of a section, the increase in yield strength of the steel increases, due to cold working by the process of “strain hardening”, as illustrated in Figure 2.1. The increase in yield strength by cold working may be significant (> 10%) for highly stiffened sections with many bends. Strictly, the yield 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

Stress

Strain Loss of ductility Ductility after cold working

Initial loading Further loading after cold working Increase of

yield stress due to strain

hardening Yield point

after cold working

Figure 2.1 The influence of cold forming on the stress-strain diagram of strip steel

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Ductility is defined on the basis of minimum elongation at fracture over a certain 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 yield strength of the material.

2.2 Methods of forming

Manufacturers 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 section being produced and then fed into a series of roll formers. These rolls are set in pairs moving in an opposite direction so that the sheet is drawn through and its shape is gradually modified along the line of rolls. The number of rolls needed to form the finished shape depends on the complexity of the section. The overall 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 often used, which permit a rapid change of section depth or width. Roll forming is therefore most economic where large quantities of the same section are produced at one time. The lengths of the members can be pre-programmed and cut accurately. Holes for attachments and services can also be punched either before or after forming.

An alternative method of cold forming is by press-braking. This is normally only practicable for short lengths (up to 6 m, depending on the size of the machine used) and for relatively simple shapes. This method can be advantageous for small production runs, because of its lower setting-up costs.

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2.3 Methods of protection

Hot dip galvanizing (zinc coating) of preformed strip steel offers protection by sacrificial loss of the zinc surface which occurs preferentially to corrosion of the steel. Guidance on thickness of galvanizing is given in Galvatite Technical Manual [4]. The specified sheet thickness includes galvanizing. A zinc coating of 275 g/m2 (total on both faces) is the standard (G275) specification for internal environments, and corresponds to a total zinc thickness of about 0.04 mm. G100 to G600 coatings can also be obtained but these are generally non-standard. The thicker coatings are used in applications where moisture may be present over a long period. Zinc coatings can also be applied by hot dipping of the sections after manufacture.

Galvanized steel has good durability because, unlike paint, scratches do not initiate local corrosion of the steel. Similarly, cut ends do not corrode, except where the rate of zinc loss on the adjacent surfaces is high. In some applications 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 stored}

in bundles in moist conditions, but this does not normally affect their long term performance. Correct storage of bundles of sheets or sections is therefore important.

A recent SCI publication Durability of light steel framing in residential building[6]_{shows that the design life of galvanized steel in ‘warm frame’}

applications is at least 200 years, provided that the external envelope is properly maintained.

Zinc-aluminium coatings also have high corrosion resistance and are sometimes used in sheeting applications, but rarely on sections. Organic coatings are not used for sections. Powder paint coatings, in addition to galvanizing, are often used for specialist products such as lintels.

2.4 Common shapes of sections

Cold formed sections are used in many industries and are often specially shaped to suit particular applications. In building applications, the most common sections are the C and the Z sections. There are a wide range of variants of these basic shapes, including those with edge lips, internal stiffeners and bends in the webs.

Other sections are the ‘top-hat’ section and the modified I section. The common range of cold formed sections that are marketed is illustrated in Figure 2.3. The sections can also be joined together back to back or toe to toe to form compound sections.

The reason for edge lips and internal stiffeners is because unstiffened wide and thin plates are not able to resist significant compression, and consequently the sections are structurally inefficient. However, a highly stiffened section is less easy to form and is often less practicable from the point of view of connection to other members. Therefore, a compromise between structural efficiency and practicability is often necessary.

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Compound sections Z sections Zeta Lipped Z Special sections Modified sections

Top hat Eaves beam

C sections

Plain Lipped Sigma

Figure 2.3 Examples of cold formed steel sections

2.5 Common applications

Cold formed steel sections are used widely in building applications. Decking is also used in composite floors, and in flat roofs. Roof and wall sheeting are well established and are generally sold as colour-coated products with various forms 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

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C lightness, which is particularly important for buildings in poor ground conditions

C no wet trades, as a ‘dry envelope’ is quickly achieved using light steel framing

C ease of construction, as members are delivered to site cut to length and with pre-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 support the cladding in industrial-type buildings (see Figure 2.4). Purlins are generally based on the Z section (and its variants), which facilitates incorporation of sleeves and overlaps to improve the structural efficiency of the members in multi-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 frames and panels for walls and roofs, and for stand-alone buildings. This approach has been used in a wide range of light industrial and commercial buildings and also in mezzanine floors of existing buildings (see Figure 2.5).

Housing

In modern house construction, storey-high wall panels are factory-built and assembled on site by ‘platform’ construction. The panels are sufficiently light to be handled on site. External insulation is used in order to create a ‘warm frame’. Brickwork is attached by wall ties in vertical tracks fixed through the

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housing sector in the UK. A major series of load tests has been carried out to establish 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

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Lintels

A significant market for cold-formed sections is for specially shaped steel lintels used over doors and windows inlow-rise masonry walls. These products are often 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 of modest span in domestic and small commercial buildings. Spans of up to 5 m can be readily achieved for C or sigma-shaped sections. Lattice joists may be used for longer spanning applications.

Systems for commercial buildings

A prefabricated panel system using cold formed sections and lattice joists has been developed for use in buildings up to 4 storeys height (see Figure 2.7). Although primarily developed for commercial buildings, this system has wide application in such as educational and apartment buildings.

Roof trusses

Roof trusses may be manufactured using cold formed sections for both new construction and renovation projects. They may be of the traditional ‘Fink’ or ‘Pratt’ truss form, or alternatively, they may be designed as ‘open’ roof trusses for habitable use. ‘Over-roofing’ of existing flat roofs is also a large market for long span trusses[7] (see Figure 2.8).

Separating walls and partitions

Separating walls in framed buildings may be designed using C sections and multiple layers of plasterboard to provide a high level of acoustic insulation and fire resistance.

Space trusses

A three-dimensional space truss based on a 3 m square module using cold formed 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 support cladding to multi-storey steel buildings, and as mullions and transoms in standard glazing systems. ‘Over-cladding’ systems have been developed for use in building renovation[8].

Prefabricated modular buildings

Prefabricated modular units are a new application of the use of cold formed sections. The units are manufactured and fitted-out in factory-controlled conditions. When installed on site with their services and cladding, the units form whole or part buildings with a high level of acoustic insulation and structural integrity[9]. They are also designed structurally for the stresses imposed during lifting and transportation. Other applications are as prefabricated ‘toilet pod’ units in multi-storey buildings.

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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 of systems that have been developed as so-called frameless buildings (i.e. those without beams and which rely partly on stressed skin action).

Storage racking

Storage racking systems for use in warehouses and industrial buildings are made from cold formed steel sections. Most have special clip attachments, or bolted joints 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 are designed to act compositely with the in-situ concrete placed on it. Composite decking is usually designed to be unpropped during construction, and typical spans are 3 to 3.6 m. This application, which is illustrated in Figure 2.10, is well covered in other publications[10] [11]. More recently, deep decking has been developed to achieve spans of 5 to 9 m in Slimdeck construction.

Figure 2.9 Typical storage racking system

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Applications in general civil engineering include: C Lighting and transmission towers

These towers are often made from thin tubular or angle sections that may be cold formed.

C Motorway crash barriers

These relatively thin steel members are primarily designed for strength, but also have properties of energy absorbtion under impact by permitting gross deformation.

C Silos for agricultural use

Silo walls are often stiffened and supported by cold formed steel sections. C Culverts

Curved profiled sheets are often used as culverts and storm pipes.

Other major non-structural applications in building include such diverse uses as garage doors, and ducting for heating and ventilating systems.

2.6 Fire protection

Fire protection to cold formed sections in planar floors or walls is usually provided by special fire-resistant gypsum plasterboards placed in one or two layers to form the finished surface. Fire resistance periods of 30 or 60 minutes can be achieved by this simple method of protection provided joints between the boards are staggered.

Longer members such as beams and columns can also be “boxed-out” using standard board protection, as in Figure 2.11. However, the required thickness of fire protection is usually greater than that for hot rolled sections because the thinner steel elements heat up more rapidly[12].

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3 INTRODUCTION TO DESIGN OF COLD

FORMED SECTIONS

The main difference between the behaviour of cold formed sections and hot rolled steel sections is that thin plate elements tend to buckle locally under compression. Cold formed cross-sections are therefore usually classified as ‘slender’ because they cannot generally reach their full compression resistance based on the amount of material in the cross-section. Therefore, effective section 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 in BS 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 steel grades, the design strength of the steel, p_y is taken as the yield strength, Y_s as modified by Clause 3.4.

3.1 Behaviour of thin plates in compression

3.1.1 Elastic buckling

The full compression resistance of a perfectly flat plate supported on two longitudinal edges can be developed for a width-to-thickness ratio of about 40. At greater widths, buckles form elastically causing a loss in the overall compressive resistance of the plate. This is due to the inability of the more flexible central portion to resist as much compression as the outer portions which are partly stabilised by the edge supports.

The critical compression stress at which elastic buckling of the plate occurs is given by the expression:

pcr = K B 2 _E 12 (1 & v2₎ t b 2 . 185 × 103_{5 (t/b)}2_N/mm2 ₍₁₎ where:

b is the plate width, and t is the steel thickness.

The term 5, referred to as the buckling coefficient, represents the influence of the boundary conditions and the stress pattern on plate buckling. Normally, plates are considered to be infinitely long but have various support conditions along their longitudinal edges. The two common cases are, firstly, simple supports along both edges, and, secondly, one simple support and the other free edge. In the first case 5 is 4, whereas in the second, 5 reduces dramatically to 0.425. This indicates that plates with free edges do not perform well under local buckling. These cases are illustrated in Figure 3.1.

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Supported edge cr cr Supported edge cr cr

Adequate lip No edge lip

Junction remains

straight Edge is freeto displace

Buckled shape

Buckled 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 stiffness provided by the adjacent plates is included, or, alternatively, when the loading conditions do not result in uniform compression. Different cases for sections in bending and pure compression are given in Appendix B of BS 5950-5.

3.1.2 Post-critical behaviour

Plate elements are not perfectly flat, and therefore begin to deform out-of-plane gradually with increasing load, rather than buckle instantaneously at the critical buckling stress. This means that the non-uniform stress state exists throughout the loading regime, and tends to cause the plate element to fail at loads less than the critical buckling value. This is a dominant effect in the b/t range from 30 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 further buckling, and secondly, the zone of compression yielding extends from the longitudinal supports to encompass a greater width of the plate elements. These post-critical effects cause an increase in the load-carrying capacity of wide plate elements (b/t > 60) relative to that given by Equation (1).

The parameter which is used to express the behaviour of plate elements in compression is the “effective width”. This is the notional width which is assumed to act at the yield strength of the steel. The remaining portion of the plate element is assumed not to contribute to the compression resistance, as illustrated in Figure 3.2. s s s b eff b /2 eff b /2 Actual stress distribution Simplified equivalent stresses ≈ ≈ b Y Y Y b

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The effective width concept can be modified to take the above factors into account. A semi-empirical formula for the effective width, b_eff, of a plate element under compression is presented in BS 5950-5, Clause 4.3, as follows:

= (2) b_eff b 1 % 14 f_c p_cr 1/2 & 0.35 4 &0.2

Where, f_c is the compressive stress in the plate element, and p_cr is the critical buckling stress of the plate element, as defined previously. f_c is limited to a value of Y_s , which is the design strength of the steel.

The relationship given by Equation (2) is plotted in Figure 3.3. Also shown in this figure is the equivalent elastic buckling curve determined from Equation (1) and the corresponding AISI (American) requirements[13] [14]. The full compression resistance of a real (slightly non-flat) plate element supported on two longitudinal edges can be developed at a b/t ratio of less than approximately 30, and this therefore represents the most efficient spacing between stiffeners or folds in a cross-section. Values of effective width for plate elements of increasing b/t ratios are presented in Table 3.1 (taken from BS 5950-5). 50 100 150 200 250 0 0 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 (Y_s = 280 N/mm2) of compression plate with simple edge supports

3.1.3 Influence of stiffeners

There are two types of stiffeners: those at the edge of a plate element, and those internally within a plate element. They are known respectively as ‘edge’ and ‘intermediate’ 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 angle bend should not be less in depth than one-fifth of the width of adjacent plate element, 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 two longitudinal edges (Table 5 of BS 5950-5: 1998, reproduced with the permission of the British Standards Institution)

b/t b_eff/b b/t b_eff/b b/t b_eff/b b/t b_eff/b 20 21 22 23 24 25 1.000 1.000 1.000 1.000 0.999 0.999 60 61 62 63 64 65 0.673 0.662 0.652 0.641 0.631 0.621 100 105 110 115 120 125 0.405 0.387 0.370 0.355 0.341 0.328 300 305 310 315 320 325 0.151 0.149 0.147 0.145 0.143 0.141 26 27 28 29 30 0.998 0.997 0.996 0.994 0.992 66 67 68 69 70 0.612 0.603 0.594 0.585 0.577 130 135 140 145 150 0.316 0.305 0.295 0.286 0.277 330 335 340 345 350 0.139 0.138 0.136 0.134 0.133 31 32 33 34 35 0.989 0.985 0.981 0.976 0.969 71 72 73 74 75 0.569 0.561 0.553 0.545 0.538 155 160 165 170 175 0.269 0.262 0.254 0.248 0.241 355 360 365 370 375 0.131 0.130 0.128 0.127 0.125 36 37 38 39 40 0.962 0.955 0.946 0.936 0.926 76 77 78 79 80 0.531 0.524 0.517 0.511 0.504 180 185 190 195 200 0.235 0.230 0.224 0.219 0.215 380 385 390 395 400 0.124 0.122 0.121 0.120 0.119 41 42 43 44 45 0.915 0.903 0.891 0.878 0.865 81 82 83 84 85 0.498 0.492 0.486 0.480 0.475 205 210 215 220 225 0.210 0.206 0.201 0.197 0.194 405 410 415 420 425 0.117 0.116 0.115 0.114 0.113 46 47 48 49 50 0.852 0.838 0.824 0.811 0.797 86 87 88 89 90 0.469 0.464 0.459 0.454 0.449 230 235 240 245 250 0.190 0.186 0.183 0.180 0.177 430 435 440 445 450 0.112 0.111 0.109 0.108 0.107 51 52 53 54 55 0.784 0.771 0.757 0.745 0.732 91 92 93 94 95 0.444 0.439 0.435 0.430 0.426 255 260 265 270 275 0.174 0.171 0.168 0.165 0.163 455 460 465 470 475 0.106 0.106 0.105 0.104 0.103 56 57 58 59 60 0.720 0.708 0.696 0.684 0.673 96 97 98 99 100 0.421 0.417 0.413 0.409 0.405 280 285 290 295 300 0.160 0.158 0.156 0.153 0.151 480 485 490 495 500 0.102 0.101 0.100 0.099 0.098 NOTE: These effective widths are based on the limit state of strength for steel with Y_s = 280 N/mm2_and having a buckling coefficient K = 4. For steels with other values of Y_s or sections having K … 4, see Clause 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 the stiffener is adequate, the plate element may then be treated as simply supported along both longitudinal edges, with a 5 value of 4. In BS 5950-5, edge stiffeners failing to meet this limit are considered to be ineffective and are disregarded, leading to much reduced effective section properties.

Unstiffened element Simple lip Compound lip Intermediate stiffener Internal element a) Section with

unstiffened 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 plate elements so that the section operates more effectively. They usually comprise folds in the section. Again, a simple formula for the minimum size of stiffener is given in BS 5950-5, Clause 4.7.1. Because these stiffeners stabilise two adjacent 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 adjacent plate 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 of 15 mm depth should be satisfactory.

An additional problem with intermediate stiffeners is that the stiffened compression plate element tends to buckle towards the neutral axis of the section in bending (a phenomenon known as flange curling). This means that the effectiveness of very wide compression elements with multi-stiffeners is reduced 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 webs

Webs of cross-sections are subject to shear, bending and local compression at their supports. It is often found that these local effects dominate the design of cold formed sections. In purlin design, for example, the sections are supported by cleats attached to the webs rather than sitting directly on the supports which may reduce their effectiveness.

3.2.1 Web shear

Slender webs normally fail in shear by shear buckling. The buckling coefficient 5 in Equation (1) for a simply supported plate in pure shear tends to a value of 5.35. This leads to a critical shear stress q_cr given by BS 5950-5, Clause 5.4.3 as:

qcr = 106 t (3)

D 2

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q_cr is compared to the average shear stress acting across the full web depth. Additionally, the average shear stress should not exceed 0.6 Y_s representing the limiting stress at which shear yielding occurs. In irregular sections, the maximum shear stress should not exceed 0.7 Y_s.

3.2.2 Web bending

Webs of sections in bending are subject to varying compressive stress, reducing from a maximum at the junction with the flange to zero at the elastic neutral axis position. Very deep webs can be influenced by local buckling in compression. However, the varying stress in the web leads to a deeper plate element before buckling than for a plate element under pure compression. This is reflected in the theoretical value of the buckling coefficient 5 of 23.9 (rather than 4).

The effective width concept is also used to determine the post-buckling bending resistance of deep webs by considering two separate zones adjacent to the neutral axis and to the compression flange. This behaviour is illustrated in Figure 3.5(b). c Neutral axis c Y_s Y_s Y eff

b /2 b /2eff b /2eff b /2eff

Y_s Y_s Y eff b /2 b /2eff Y_s Y_s c Neutral axis Y eff b /2 b /2eff p_o p_o Y _c Y_s a) Effective width of compression

flange and fully effective web b) Effective width of webin compression

c) Reduced stress, p

in fully effective webo d) Full yielding of web in tension(non-symmetric section) Compression

Tension

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In BS 5950-5, an alternative approach is used, whereby the maximum compressive stress in the web is determined. This is given by the term p_o calculated as in Clause 5.2.2.2 of BS 5950-5 (see Figure 3.5(c)):

(4) p₀ ' 1.13 & 0.0019 Dw t Y_s 280 ½ p_y where D_w is the depth of the web

3.2.3 Web crushing

Local failure at supports, or at locations of point loads, can occur as shown in Figure 3.6. This reduces the load-carrying resistance of the member. It is taken into account by an empirical formula representing the web crushing load.

Section A - A Use of cleat to

avoid 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 the steel, and the height/thickness ratio of the section. The crushing load P_w (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 depth N is the support width

r is the corner radius between the web and flange.

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Equation (4) applies where the reaction (or point load) is applied close to the end of the member and where the web is free to move laterally. The equivalent value for an internal support reaction or point load is approximately 50% higher than that given by this equation.

It follows that the support reaction or point load should not exceed the web crushing resistance. This can be best achieved by increasing the width of the supports or the thickness of the steel section. Enhanced capacities are given for double C sections with back to back webs, or webs with both flanges held in position (see Table 8 of BS 5950-5[1]_).

Interaction between co-existent bending and web crushing may be taken into account using the relationship of the form indicated in Figure 3.7. This means that the bending resistance of continuous members may be reduced at internal supports, unless wet crushing is prevented by use of a stiffening element, e.g. an angle cleat. 1.0 0 0.4 1.0 0 0.45 Acceptable zone max w M M P P

Figure 3.7 Influence of combined moment, M and web reaction, P for double C sections

3.3 Behaviour of members in bending

3.3.1 Moment resistance of section

The effective properties of sections in bending may be taken into account from first principles by considering the effective widths of the compression elements, as illustrated in Figure 3.5. The neutral axis of the section is determined by balancing tension and compression. The section modulus is then calculated knowing the elastic neutral axis position. The effective bending resistance is obtained by multiplying the elastic section modulus by the design strength of the steel. Both the neutral axis position and the section modulus are therefore functions of the operating stress of the compression flange.

For symmetric sections, the effective section modulus of the compression plate is 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 occur first causing plastification in the tension flange. This local yielding, as illustrated in Figure 3.5(d) is permitted, provided the compression plate does not yield.

3.3.2 Influence of section shape

Z-shaped sections displace laterally when loaded through their webs, because the 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 the principal axis counteracts that of the roof slope, as in Figure 3.8(a). Some sections are specially formed to reduce the angular difference between the principal and vertical axes to about 5E. Fixing to rigid flooring or deep sheeting also assists in preventing lateral displacement.

Twisting about shear centre Roof slope b) C sections a) Z sections as purlins Principal axis of bending close to vertical Load Load Shear centre Shear centre

Figure 3.8 Behaviour of different sections under bending

C sections twist when loaded through their webs because the shear centre of the section is located outside the web (see Figure 3.8(b)). This is alleviated by placing two sections back to back, or by providing lateral restraints to both flanges. Fixing to rigid flooring also reduces twisting, depending on the location and spacing of the fixings. The shape of C sections can be modified to a zeta shape to bring the shear centre closer to the web.

Non-symmetric sections, as shown in Figure 3.5(d), may displace laterally under major axis bending. These transverse bending stresses should be considered in addition to primary bending stresses unless lateral movement is prevented.

3.3.3 Continuous members

For simply-supported members, it is the sagging (positive) moment conditions that determine the bending resistance of the member. For members that are continuous over one or more internal supports, moments are determined elastically (i.e. using moment distribution or other elastic methods). Plastic hinge analysis is not permitted because the ‘slender’ sections are not able to maintain their full bending resistance when rotations exceed the point at which the section reaches yield. There is, however, some residual bending resistance at large rotations as shown in Figure 3.9.

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Load

Support

Moment

Rotation Idealised behaviour

b) Moment - rotation characteristics of 'slender' sections Moments following redistribution Actual behaviour of 'slender' section Elastic moment capacity Elastic moment

a) Redistribution of moments for 'plastic' sections

Figure 3.9 Illustration of influence of section type on behaviour of continuous beams

Design on the basis of elastic analysis means that the conditions at the internal supports of continuous members often dominate the overall design (see the relationship between moment and web crushing in Figure 3.7). In some cases, this can lead to the conclusion that simply-supported members are stronger than continuous members! Some purlin systems utilise the flexibility of sleeved or overlapping purlins at the supports in order to achieve some ‘elastic’ redistribution of moment, and hence to lead to more efficient design of the members (see Section 4.1). In order to make an accurate prediction of the amount of redistribution that will take place, it is necessary to know the moment-rotation behaviour of the sleeved or overlapped section in hogging. This should be determined by testing.

3.3.4 Lateral torsional buckling

The above approach assumes that the members are laterally restrained i.e. they cannot fail by lateral buckling. This is the case where simply supported members are attached to floors etc. so that the compression flange is prevented from displacing sideways (or laterally).

Where the lateral restraints are sufficiently wide apart, lateral torsional buckling may occur. This effect is illustrated in Figure 3.10. The elastic lateral buckling resistance moment of an equal flange I-section or a symmetrical C section bent in the plane of the web is given in Clause 5.6.2.2 by the formula:

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ME= B (6) 2 _AED 2 (L_E/r_y)2 Cb 1 % 1₂₀ L_E r_y × tD 2 0.5 where:

L_E is the distance between points of lateral restraint

r_y is the radius of gyration of the section in the lateral direction

C_b is the factor representing the shape of the bending moment diagram (unity for constant moment).

u

φ

Support Loading x y z

Figure 3.10 Deformations u and N associated with lateral-torsional buckling Account may also be taken of the support conditions in modifying the effective length L_E. The ratio L_E/r_y defines the slenderness, 8 of the member. As the slenderness reduces, so M_E increases, and eventually the bending resistance, M_c of the section is reached. Equation (5) may be converted to an effective slenderness, 8_LT of the beam according to the expression:

8_LT= u v 8 (7)

where u is approximately equal to 0.9 for C or I sections,

v = 1 % 1 (8)

20 8 tD

2 0.25

The effective slenderness may be non-dimensionalised to give the modified slenderness ratio, &8_LT, by dividing by 8_y where 8_y = B E/Y_s (see Section 3.4.1).

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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 8_LT may be taken as 0.98 as a safe approximation. This reflects the beneficial effects of non-uniform stress and torsional stiffness on lateral torsional buckling of the section in comparison to a strut of slenderness 8.

The relationship between the modified slenderness ratio of the member and the bending resistance, M_b of the section is shown in Figure 3.11. This is based on the Perry-Robertson approach, as defined in BS 5950-5. The full bending resistance of the section can only be reached when 8 is less than 40 C_b.

0 0 0.5 1.0 1.5 2.0 s 1.2 1.0 0.8 0.6 0.4 0.2 ECCS TC7 Elastic lateral torsional buckling EC3 Part 1.3 BS 5950 - 1 BS 5950 - 5 Modulus of elasticity E = 205 kN/mm² Design strength Y = 280 N/mm² LT Modified slenderness ratio ( )λ

b

c,Rd

Moment 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 as C sections. However, in this case, the shear centre of a C section does not coincide with the plane of the web. Therefore loads applied through the web cause twisting of the section (see Figure 3.8(b)). In principle, therefore, single C 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 should be added to bending stresses.

The hogging (negative) moment region of continuous members requires special consideration, because it is usually more difficult to restrain the lower flange of the section than the upper flange. It is often assumed that the point of zero moment may be considered as a point of effective restraint, and that the part of the beam in hogging may be treated as a member with a linear variation of moment. If this gives a bending moment resistance less than the applied moment, then additional lateral restraints are needed. It should be noted, however, that treating the point of zero moment as a point of effective restraint is 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 generally used to provide restraint to the lower flange in wind uplift conditions.

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3.4 Behaviour of members in compression

3.4.1 Members in pure compression

Members in compression are typically columns loaded by beams, or struts in trusses. Columns are usually only laterally restrained at the beam-column connections, unless they are built into a wall. The design of axially loaded sections may be treated as a series of plates in compression. This leads to an effective area of the cross-section when the effective widths of all the compressive plate elements are combined, as shown in Figure 3.12. This ratio of the effective to the gross area of the section is known as the “Q factor” and it represents the efficiency of the section under axial compression.

Therefore, the compressive resistance of the section is:

P_CS = Q A Y_s (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 in Figure 3.13. Perfectly straight columns buckle elastically at an “Euler load” given by: P_E = B = (10) 2 _EI y L_E2 B2 EA 82

where 8 is the slenderness of the member between points of lateral restraints (see Section 3.3.4), which is the effective length L_e divided by the radius of gyration.

The modified slenderness ratio, &8 is defined as 8/8_y, where 8_y = B E/Y_s in which 8_y corresponds to the slenderness of the equivalent perfect strut when acting at the yield strength, Y_s.

Shear

centre Eccentricity_{= A - B}

A B

b) Reduced cross-section in compression a) Axial load applied

through centroid

Centroid _Modified

centroid

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Torsional - flexural buckling mode Section A - A Floor Floor A A

Column _{Lateral buckling}

mode

Figure 3.13 Buckling of column in compression between floors

Real columns are not perfectly straight; they fail before the Euler buckling load is reached. This is taken into account by a Perry-Robertson type formula which has a solution of the form:

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P_c ' PE Pcs

N% N2&_P

E Pcs

where N = Pcs , P_c is the axial buckling resistance of the % _{(1 % 0) P}

E 2

column and 0 is an empirical factor accounting for the initial imperfection of the column, given in Clause 6.2.3 of by 0 = 0.002 (8-20). (Therefore, P_c = P_cs when 8 # 20).

The variation of load ratio (P_c/P_cs) with slenderness ratio 8 is presented in Figure 3.14.

3.4.2 Singly symmetric sections

In 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 the centroid of the gross section (A) through which axial forces are assumed to act. This gives rise to combined bending and compression, which is taken into account by a modified value of P_cN such that:

P_cN = M_c P_c / (M_c + P_c e_s ) (12)

where M_c is the pure bending resistance of the section, and e_s is the eccentricity of the applied load caused by the shift of neutral axis from the gross section to the effective section (see, Clause 6.2.4).

3.4.3 Combined bending and axial loading

The interaction between bending and axial load may be taken into account by the following relationship for members which fail by lateral buckling:

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(13) F_c P_c % Mx M_b % My C_b M_cy (1 & F_c/P_ey) # 1

where F_c is the axial load applied to the column, and M_x and M_y are the applied moments in the x and y (major and minor axis) directions (see clause 6.4.3). M_cx and M_cy are the design bending resistance based on an independent analysis in the x and y directions. C_b takes into account the variation of moment along the member (see Equation 6). P_c is determined for an axially loaded member, as above, and P_EY is the compression resistance for buckling in the y direction (from Equation 9).

This equation takes into account the potentially weakening effects of the combinations of different buckling modes.

3.4.4 Torsional flexural buckling

Thin open cross-sections are torsionally weak and may be more susceptible to torsional failure than lateral buckling failure when loaded axially (as illustrated in Figure 3.13). This is especially so for singly symmetric sections, such as C 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 approach in BS 5950-5 is to modify the effective length for lateral buckling to take into account the possibility of a lower torsional flexural failure mode. This is achieved by the use of the effective length multiplication factor, ". Appropriate " values for a range of common sections are presented in Appendix C of BS 5950-5(1). 1.2 1.0 0.8 0.6 0.4 0.2 0 0 0.5 1.0 1.5 2.0 Slenderness ratio Load ratio Elastic Euler buckling EC3 Annex A s λ Modulus of elasticity E = 205 kN/mm² Design strength Y = 280 N/mm² BS 5950-5 BS 5950 - 1

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3.5 Serviceability limits

3.5.1 Natural frequency

The natural frequency of light steel flooring systems should be calculated in order to avoid perceptible vibrations. According to current SCI recommendations, the natural frequency of these floors should exceed 8 Hz when calculated for a load equal to the self weight plus a permanent load of 0.3 kN/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 service load, it follows that the maximum deflection under total design loading should not exceed 15 mm. This deflection limit is equivalent to that for timber construction.

The natural frequency limit often controls for floor spans greater than 5 m.

3.5.2 Deflection limits

Deflection limits are introduced for floors in order that there is no serious risk of cracking of partitions or other components supported by these floors, or perceptible movement. Traditionally, an upper deflection limit of span/360 is used for floors subject to imposed load, reducing to span/250 when subject to total 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 is proposed that the limit on imposed load deflections should be reduced to span/450, and the limit on total deflection should be reduced to span/350 (but not 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 FORMED

SECTIONS IN BUILDING

The following Sections describe typical uses and potential applications of cold formed steel sections in buildings. A common use of these sections is in purlins and side rails in industrial buildings, but there are many new developments of cold formed sections as primary structural members in housing, light industrial and commercial buildings.

4.1 Purlins and side rails

Purlins are usually of Z shape, the argument being that the principal axis of bending of the section is close to vertical when the section is orientated so that the upper flange points up the roof for roof slopes of 10 to 15E, as shown in Figure 3.8(a). This means that vertical roof loads do not cause serious twisting of the sections. However, roof slopes in modern industrial buildings can be as low as 5E, and this has created the need for modified section shapes. The so-called “Zeta” section (see Figure 2.3) is one attempt to provide a section shape more suitable for shallow roofs.

C shaped sections and their derivatives have also been developed for roof and wall applications. The web shape can be modified to a sigma shape to reduce the twisting of the section by bringing the shear centre of the section closer to the web.

All purlins above a certain length are provided with sag rods which are intended to prevent twisting during erection and to stabilise the lower flange against wind uplift. The upper purlins are usually tied at ridge level.

Lateral forces on the members can usually be transferred by ‘diaphragm’ or ‘stressed skin’ action of the roof sheeting. The upper flanges of the purlins are considered to be laterally restrained by the sheeting.

The design of purlins has developed to an extent that empirical methods based on testing are often the only economic solution. Purlins are usually designed to be continuous in order to satisfy deflection limits. However, elastic design of continuous members can be unduly onerous, when strictly interpreting the requirements of BS 5950-5 (see Section 3.3.3).

This factor has been recognised by the purlin manufacturers and many overlapped and sleeved systems at the supports have been developed. The moment-rotation characteristics of these systems can be “matched” to the performance of the purlin, leading to optimum design of the section. This behaviour is illustrated in Figure 4.1. Overlapping systems provide better hogging bending resistance then sleeved systems. Both provide double web thickness, improving the shear resistance of the section at internal supports. Shear forces are transferred to the supporting rafters by cleats bolted to the webs of the purlins. The cleats are designed so that the lower flange of the purlin does not bear directly on the rafter, and thus web crushing problems are avoided. The shear or bearing strength of the connecting bolts provides the necessary load transfer (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 the plane of the wall.

L

Sleeve or overlap Joint rotation

w

0.10wL² 0.08wL²

Redistribution moments allowing for joint flexibility

Elastic moments

Figure 4.1 Redistribution of moments in sleeved or overlap purlin system

4.2 Floor joists

Steel floor joists, usually of C section, may be used to replace timber joists in housing and other masonry buildings. The joists may be built into walls or supported on traditional joist hangers (see Figure 4.2). Thicker cold formed sections may also be used to replace lighter hot rolled sections as secondary beams in main frames.

Comparisons have been made of the design of cold formed sections with the traditional alternatives. These comparisons have been characterised in terms of four typical applications that may be encountered in domestic and commercial buildings. The section sizes and weights resulting from these designs are presented in Table 4.1. In practice, designs may be controlled by bending resistance or stiffness requirements.

In terms of equivalent bending resistance, a series of 175 mm × 37 mm timber joists may be replaced by 100 mm × 40 mm × 1.2 mm thick C sections at the same spacing. Other comparative performances may be taken from Table 4.2. However, in practical applications, floor joists should also be designed for relatively strict deflection and frequency limits which means that they are deeper than for pure bending resistance (see Section 3.5).

The cold formed sections can also be manufactured with punched holes in their webs to allow passage of small diameter pipes and other services. The depth of these holes is normally less than half the member depth and has little effect on structural performance. Provision of these holes for services overcomes the problem of notching of timber joists. Attachment of the timber floor-boards increases the stiffness of the light steel sections and provides lateral restraint if fixed at regular intervals.

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Table 4.1 Comparison between section sizes for cold formed steel, hot rolled steel and timber for different applications

Section type

Domestic building Commercial building Span = 4 m

Spacing = 0.6 m Span = 5 mSpacing = 0.6 m Span = 5 mSpacing = 1.2 m Span = 6 mSpacing = 1.2 m Plain

C section 150×50×3W = 5.6 2No. 150×50×3W = 11.0 2No. 150×50×5W = 17.8 -Lipped C section 165×63×1.6W = 3.9 220×63×1.8W = 4.9 2No. 220×63×2.0 W = 10.9 2No. 300×65×2.0 W = 15.0 Timber 250×75_{W = 10.1} 300 ×75_{W = 12.1} 2No. 300×75_{W = 24.2}

-Hot Rolled Steel 102×51 RSC_{W = 10.4} 127×76 UB_{W = 13.0} 152×89 UB_{W = 16.0} 178×102 UB_{W = 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 cases}

W = weight in kg/m

Data 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.

Structural Design to BS 5950-51998 Section Properties and Load Tables.pdf

Building Design Using

Cold Formed Steel Sections