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The Steel Construction Institute
S Design of Structural Steelwork
Lattice Framed Industrial Building (Revised Edition)
mit deutscher Zusammenfassung _______________________
avec résumé français — =
___________ This document con resumen español ___________ contains 100 pages
con sommario italiano -
Institut de a Construction Métallique Institut für Stahlbau Istituto di Costruzioni in Acciaio Instituto de Ia ConstrucciOn Metálica
/
is The Steel Construction Institute. Its aim is to promote the proper and effective use of steel in construction. = =
Membership is open to all organisations and individuals that are concerned with the use of steel in construction, and members include designers, contractors, suppliers, fabricators, academics and government departments in the United Kingdom, elsewhere in Europe and in countries around the world. SC! is financed by subscriptions from its members, by revenue from research contracts and consultancy services and by the sales of publications.
SCI's work is initiated and guided through the involvement of its members on advisory groups and technical committees. A specialist advisory and consultancy service is available free to members on the use of steel in construction.
SC! 's research and development activities cover many aspects of steel construction
including multi-storey construction, industrial buildings, use of steel in housing, development of design guidance on the use of stainless steel and cold formed steel, behaviour of steel in fire, fire engineering, use of steel in barrage and tunnel schemes, bridge engineering, offshore engineering, and development of structural analysis systems.
Further information is given in the SC! prospectus available free on request from: The Membership Secretary, The Steel Construction Institute, Silwood Park, Ascot, Berkshire, SL5 7QN. Telephone: (0344) 23345, Fax: (0344) 22944.
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.
© The Steel Construction !nstitute 1993
Instituut voor Staalbouwconstructie Institut de la Construction Métallique Staalkonstruktion !nstitut Institut für Stahlbau Instituto da Construcao Metálica !stituto di Costruzioni in Acciaio !voriroisro Yuipó.v iccxraaicevó.v Instituto de Ia Construcción Metálica
SCI PUBLICATION 028
Design of Structural Steelwork Lattice Framed Industrial Building (Revised Edition)
Entwurf elnes Stah/bau-Gebãudes - G/tterahmen /ndustriegebãude
Dimensionnement d'/mmeubles a structure meta/llque - bétiment industriel en cadre et tre I/I/s
Progettazione dl Ed/f/cl in Accialo: Ed/f/cl Industrial! Inte/alat/ a Tra/lcclo
Pro yecto de Ed/f/c/os con Estructura de Acero. Ed/f/do /ndustr/al en Ce/os/a
C SOUTHCOMBE BSc(Eng), MSc(Eng), CEng, MICE
ISBN 1 870004 83 3
British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library
© The Steel Construction Institute 1993
The Steel Construction Institute Silwood Park Ascot Berkshire SL5 7QN Telephone: 0344 23345 Fax: 0344 22944
FOREWORD
This publication is a revised edition of the original text written by Mr W Bates and first published in 1983.
Its purpose is to aid the education of undergraduate students in Engineering by providing sample calculations for a typical industrial building capable of future extension.
The revision was made necessary by changes in design Codes and current practice over the past decade.
For their helpful contributions regarding design, fabrication and the erection process, the author is indebted to:
Mr. A. Curnow (Blight and White Limited, Plymouth) Mr. R. Fox (F. Parkin and Son Ltd., Exeter) Mr. P. Marozinski (Conder Limited, Winchester)
11
CONTENTS Page
FOREWORD U
SUMMARY v
1. INTRODUCTION 1
2. SCOPE 2
3. STANDARDS AND CODES OF PRACTICE 4
3.1 British Standard 5950 - Structural use of steelwork in building 4 3.2 BS 5502 - Buildings and structures for agriculture 4 3.3 BS 6399: Part 1: 1 984 - Design Loading for Buildings 4 3.4 BS 6399: Part 3: 1 988 - Code of practice for imposed roof loads 4 3.5 CP3: Chapter V: Part 2: 1972- Wind Loads 4 3.6 Statutory regulations 5 3.7 National structural steelwork specification for building construction
(2nd Edition) 5 3.8 Quality assurance 5
4. BUILDING FORM 6
4.1 General 6 4.2 Low pitch roofs 6
5. LATTICE FRAMED ROOFS 8
5.1 Simple forms 8 5.2 More complex forms 10 5.3 Cladding 1 2 5.4 Purlins 13 5.5 Side rails 14
6. CONCEPTUAL DESIGN 16
7. PRINCIPLES OF DESIGN 19
7.1 Purlins and side rails 19 7.2 Lattice framed roof girders 19 7.3 Stanchions 1 9 7.4 Bracing 21 7.5 Connections 21
111
CONTENTS - Continued Page
8. EXAMPLE - DESIGN BRIEF AND APPROACH 24
8.1 Brief 24 8.2 Cladding 24
9. DESIGN OF STEELWORK 27
9.1 Loading 27 9.2 Assessment of roof load 27 9.3 Assessment of wind load on structure 28 9.4 Design of purlins 31 9.5 Design of main roof frame 36 9.6 Preliminary calculations 37 9.7 Loading Cases (for characteristic loads) 40 9.8 Analyses 40
10. FINAL DESIGN 49
10.1 Top boom 49 10.2 Bottom boom 51
10.3 Internal members 53 10.4 Comparison of member sizes 54 10.5 Column design - members 1 to 4 and 5 55 10.6 Gable steelwork 61 10.7 Bracing 67 10.8 Column Base (Reference 1. Clause 4.13) 70 10.9 Foundation 73
11. ALTERNATIVE FRAME ANALYSIS 75
12. JOINT DESIGN 78
1 2.1 Application limit check list 78 12.2 Joint welds 81
13. FINAL FRAME LAYOUT 84
REFERENCES 87
BIBLIOGRAPHY 89
iv
SUMMARY
Design of structural steelwork - Lattice framed industrial building
The designer of single storey buildings for commercial and industrial use will consider a number of possible solutions. A decision has to be made regarding cladding, structural form and material. This publication illustrates for the benefit of students, the many factors which influence the final choice of a suitable design.
Consideration is given to a variety of building forms as well as to the choice of cladding and its supporting element at the conceptual design stage; other factors influencing the design are related to fabrication, transport and erection.
A structural steelwork frame incorporating solid web beams for columns and a latticed structure for the roof, is chosen and full design details worked out.
The detailed design of a building 30 m wide, 48 m long x 6 m to eaves is provided as an illustration.
The solution considers the main loading calculations and members initially. A detailed
analysis is carried out and checks are made of all members, the latticed roof being formed of rectangular hollow section. Typical joints and the foundation are designed.
Entwurf eines Stahlbau-Gebäudes - Gitterahmen Industriegebäude
Zusammenfassung
Der Konstrukteuer eines eingeschossigen Handels - oder Industrie-Gebaudes wird eine Reihe moglicher LOsungen in Berracht ziehen. Entscheidungen mQssen getroffen werden hinsichteich Verkleidung, Formgebung und zu verwendender Werkstoffe. Diese Veroffentlichung illustriert zum Nutzen von Studenten die vielen Faktoren, die die endgtlltige Wahi eines geeigneten Entwurfs beeinflussen.
Bei der Konzeptentwickiung werden verschiedene Gebäude-Formen als auch eine Auswahl von Verkleidungen und ihre Befestigungs - Elemente betrachiet; andere Fakioren, die den Entwuif beeinflussen, betreffen ilerstellung, Transport und Errichtung.
Em Stahlbaurahmen mit soliden Ste gträgern fir die Stlitzen und etne GitterstrukiurftJr das Dach wird gewahit, wozu alle Entwurfs-Einzelheiten ausgearbeiter wurden.
Als illustration 1st der detaillierte Enlwurfeines Gebäudes mit 30 m Breite und 48 m Lange, sowie 6 m bis zur Unterkante des Daches dargesteilt.
Bel der LOsung wurden die wesentlichen Lastberechnungen der Glieder im Ausgangszustand beracksichtigt. Eine deraillicerte Analyse wurde durchgefilhrr sowie alle Glieder aberprtlft; das Rahmendach wird aus rechteckigen Hohlquerschnirren gebildet. Typische Verbindungen und die Grtindung sind dargesrelir.
V
Dimensionnement d'immeubles a structure métallique - bãtiment industriel en cadre et treitlis
Résumé
Le projeteur d 'immeubles, a un seul niveau, pour usage industriel et commercial peut envisager de nombreuses solutions constructives, une decision doit être prise concernant la forme structurale, les parios et le matériau.
Cette publication discute, a 1 'intention des étudiants, les nombreuxfacteurs qui influencent le choix d 'un bon dimensionnement.
On considère une grande variétE de formes de bãtiments ainsi que le choix des parois et des éléments qui les supportent, dans le cadre de I 'etape de conception du bãtiment. D 'autres
facteurs qui influencent le dimensionnement et qui sont relatfs a la fabrication, au transport et au montage, sont egalement discutés.
Une structure en acier comportant des colonnes en prof/s et une toiture en treillis, est choisie et étudiée en detail.
Le dimensionnement détaillC d 'un bâtiment de 30 m de large, 48 m de long et 6 m sous la toiture est donnC comme illustration.
La solution comporte une analyse détai!lée et une verfi cation de tous les Cléments, le treillis de toiture étant rCalisC en profils creux rectangulaires; certains assemblages ainsi que les
fondations sont egalement étudiés.
Progettazione di Edilici in Acciaio: Edifici Industriali Intelaiati a Traliccio
Sommario
Nella pro gettazione di edfici monopiano ad uso commerciale e industriale devono essere esaminate dirvese possibili so! uzioni. E' necessario operare Ia scelta del rivestimento, della struttura portante e del materiale. Questa pubblicazione presenta, a beneficio degli studenti, tutti quei fattori che infiuenzano la scelta finale in vista di una adeguata pro gettazione.
Per la fase preliminare di progettazione viene presa in considerazione la varieta' delle
tipologie strutturali, !a scelta del rivestimento e dci suoi elementi di collegamento, a/tn fattori che influenzano ii pro getto sono que/li relativi alla lavorazione, a! trasporto ed al montaggio.
Si il/ustra in particolare, sviluppando tutti i dettagli relativi al pro getto, un edfici intelaiato in acciaio, formato da colonne ad anima piena e da elementi di copertura realizzati con una struttura a traliccio.
A titolo di esempio viene presentata la pro gettazione dettagliata di un edficio alto 6 metri con dimensioni in pianta di 30 metri di larghezza e 48 metni di lunghezza. Sono presentati I
principali calcoli relativi ai carichi ed al predimensionamento. L 'analisi dettagliata e' seguita dalla verfica di tutti gli elementi portanti. In particolare Ia struttura a traliccio onizzontale e' formata da sezioni rettangolari cave. Vengono inollre progettati alcuni giunti tipici e le
fondazioni.
vi
Proyecto de Edificios con Estructura de Acero. Edificlo Industrial en Celosia
Resumen
El proyectista de edficios de una planta para usos comerciales o industriales dispone de dferentes posibles soluciones. Para la selecciOn deben tomarse decisiones sobre revestimientos, materiales y fonna de la estructura. Esta publicaciOn aclara para los estudiantes todos losfactores que infiuyen en Ia eiección final de un proyecto adecuado.
Se analizan dferenres formas de ed/lcios as! como la elecciOn de revestimiento y sus elementos de soporte a nivel de diseflo conceptual. Se tratan ademds otrosfactores influyentes relacionados con la fabricaciOn, transporte y montaje.
Se escoge como modelo una estructura aporticada de acero formada por perfiles de alma ilena en los pilares y una celosta para la cubierta, desarroiidndose completamente todos los detalles del proyecro.
Como ilustraciOn se incluye ci ca/cub dew//ado de un edficio de 30 m. de anchura, 48 m de ion gitud y 6 m. de altura. La soluciOn comienza considerando las cargas principales sobre las barras. A continuaciOn se 1/eva a cabo un análisis dew//ado as( como la comprobaciOn de todas las barras (la celos(a de cubierta estd formada por tubos rectangulares). Tamb(en se proyectan los nudos y zapatas t(picos.
vii
1. INTRODUCTION
In general the basic brief for the design of the majority of single storey buildings for industrial and commercial use is to provide, for the client, a structure which has no internal columns. If some columns are essential the number should be limited. Thus, in principle, the requirement is for the construction of four walls and a roof for a single or multi bay structure. The walls can be formed of different materials e.g. steel columns with cladding which may be of profiled or plain sheet, precast concrete, or masonry load bearing walls etc. The designer will generally consider for the roof a system of beams or latticed frameworks in structural steel to support the roof cladding. Solid web beams will make use of universal beam sections.
The use of light latticed frameworks for the roof of an industrial building provides a neat, efficient structure which frequently satisfies architectural requirements. The design of the steelwork is simple. Modern fabrication systems and erection procedures make these structural forms economic.
This is particularly apparent when it is appreciated how many industrial buildings today employ latticed roof framing and how many makers of standard buildings, as well as suppliers of industrialised building systems, make use of this type of framing in preference to solid web beam construction.
The purpose of this publication is to discuss the many factors which can influence the decision making process and can lead to adopting latticed framework construction. Alternative design solutions are then illustrated by means of a practical example.
1
2. SCOPE
The scope of the publication is mainly restricted to plane frame structures. Other forms, such as space frames, are not considered in detail.
Various types of steel sections are used in the construction of the components for this type of structure, viz, hot rolled structural shapes such as universal beams, universal columns, angles, structural hollow sections and cold formed sections, etc.
Important factors which must be considered at the conceptual stage of the design process are the questions of workshop facilities - including size - and transportation between workshop and site. Whilst long girders or large sections may appear to be desirable, in order to reduce the number of site connections, this can reduce the number of fabricators who could tender for a given project.
In the United Kingdom, road transport is normally used and loads up to 2.9 m width, 18.3 m
long and 76,200 kg weight may be moved without any problems. Above these dimensions the Police need to be notified of "Abnormal Indivisible Loads" and indemnity to Highway and
Bridge Authorities is required. Where the dimensions exceed width 6.1 m, length 27.4 m, or weight 152,400 kg a Department of Transport Special Order is required. (Reference 'Abnormal Indivisible Loads', "Aide Memoire for Requirements as to Notice and Authorisation when not complying with Construction and Use Regulations", Source: Director (Transport), Departments of the Environment and Transport).
It should be noted that the various police authorities have different periods when abnormal loads are allowed to move through their districts. If neighbouring "times" are significantly out of phase and general traffic hold-ups cause disruption to the movement of abnormal loads it is possible for the latter to be delayed by up to 24 hours. If one or more cranes and associated erection staff are held up by these enforced delays, the additional costs can be very significant.
Certain towns and cities place length restrictions on materials which can be moved by road
e.g. certain areas of London restrict lengths to 12 m.
Girders can be fabricated and despatched lying flat, the overall height of the load is dependent upon the route travelled and the clear height of any bridges likely to he encountered. Rail
transport can accommodate long pieces, but width and height are more restricted.
One solution to limit the length and height of units being transported is to use a system as illustrated in Figure 1. The two external sections are shop welded and the central section is site or shop assembled; the whole being bolted together on site. The completed rafter can be craned into position.
For export where shipment is involved, pieces up to the same dimensions as for road transport may be accommodated but it should be appreciated that shipping charges are often based on volume rather than weight. Often there are relatively severe restrictions on the length of a
piece that can be carried in the hold of a ship. The ship's engineer may refuse to carry the steelwork as deck cargo. It may be found more economical to despatch the steel piece-small for subsequent assembly on site. Care must then be taken to ensure that the site work is
satisfactory.
Other factors of importance which can influence the economics of this type of construction are the facilities available for fabrication and for erection on site.
2
Many fabrication shops now have equipment which can cut and hole steelwork in a semi-automatic manner thus reducing direct labour costs. Jigs can also be used for the rapid assembly of components. All these tend to make lattice construction more attractive. On site the lighter overall weight of individual components can result in the use of simple lifting equipment; site costs rise appreciably if heavy cranes have to be installed for erection purposes.
For the design example in this publication it is assumed that the building is for the home market and that a well equipped fabricator will manufacture and erect the steelwork. It follows that the design must be in accordance with the appropriate British Standards, codes and regulations. Brief explanatory notes on these publications are given in Section 3.
External Central section section
7,7,7 Z7rr
Figure 1 Sectioned girder
3
3. STANDARDS AND CODES OF PRACTICE
3.1 British Standard 5950 - Structural use of steelwork in building This document' is in nine parts combining codes of practice to cover the design, construction and fire protection of steel structures and specifications for materials, workmanship and erection.
The relevant parts incorporated into this publication are Parts 1 and 5.
3.1.1 BS 5950: Part 1: 1990 Code of practice for design in simple and continuous construction: hot rolled sections
This limit state specification provides limiting values for strength and deformation for various elements which form part of structures, and for whole systems. The document' covers aspects related to hot rolled sections i.e. UBs, UCs, angles, channels, hollow sections, etc.
3.1.2 BS 5950: Part 5: 1987 Code of practice for design of cold formed sections
This specification2, using limit state philosophy, provides limiting values for strength and deformation and identifies full design procedures and empirical methods. Within this publication, it is used in the design of purlins and side sheeting rails.
3.2 BS 5502 - Buildings and structures for agriculture Various parts which cover materials, design, construction and loadings3.
3.3 BS 6399: Part 1: 1984 - Design Loading for Buildings This is a "Code of practice for dead and imposed loads" for use in designing buildings(4 (this is provided as a revision to CP3 Chapter V Part 1: 1967 which it supercedes).
3.4 BS 6399: Part 3: 1988 - Code of practice for imposed roof loads
This is a "Code of practice for imposed roof loads" and in particular suggests methods of considering snow loads for various buildings5. The loads can be used for permissible stress design or where factored loads are adopted.
This code recognises the variation in snow loading throughout the United Kingdom and the effect of variable snow loads on a roof due to drifting effects.
3.5 CP3: Chapter V: Part 2: 1972 - Wind Loads
The effect of wind on a building has been found to be very complex and dependent upon many factors such as the geographical location, the shape of the building and its relationship, to other buildings and natural features. The various rules for calculating the design wind loads on a structure and its cladding are given in this code of practice6, supplemented by a guide published by the Building Research Establishment7.
4
This code will be replaced by BS 6399: Part 2.
3.6 Statutory regulations In addition to the above the buildings must comply with the requirements of the Building Regulations, which apply in England and Wales, and where appropriate with the special variations or equivalent regulations applicable throughout the UK. Particular thermal and sound insulation requirements of the cladding must also be met. For buildings outside the United Kingdom the local regulations must be observed. Whilst many places accept structures designed to British Standards care must be taken to consider any unusual features such as typhoons or earthquakes.
3.7 National structural steelwork specification for building construction (2nd Edition)
The object of this publication8 by BCSA and SCI is to achieve greater uniformity in contract specifications issued with tender and contract documents.
3.8 Quality assurance
BSI Handbook provides a comprehensive document of the relevant standards associated with this topic. Of particular interest to the designer/fabricator/erector is BS 5750 : 1987'° which provides a three level specification of QA requirements in the contractual situation.
5
4. BUILDING FORM
4.1 General
Before proceeding to the detailed design of a lattice framed roof it is desirable to consider the alternatives available.
At the outset is must be appreciated that if an industrial building is to be warm during the winter and cool during the summer some form of heating and ventilation is required in addition to the thermal insulation called for by the Thermal Insulation (Industrial Buildings) Regulations. The roof space, which will be heated with the rest of the building unless cut off completely by a horizontal ceiling, is a constant charge on running costs without contributing to the work space. There are, therefore, financial advantages in keeping the roof space to a minimum bearing in mind that services can be accommodated in this space. This can be achieved by keeping the roof space as shallow as possible, commensurate with economy of initial cost and efficiency of the cladding.
A flat roof, or a roof with only a nominal camber, can reduce the roof space to the minimum but may be expensive to build since the roof cladding will have to be of a more sophisticated nature to ensure adequate weather protection. Again, with a flat roof of any reasonable span, deflection of the structure or girders becomes important and extra steelwork may be required merely to reduce it. A portal frame design helps to reduce the deflection but it does not reduce the cost of the cladding and the provision of the necessary rigid joints is an added cost on the structure.
Probably the most economical form of roof construction is one of low pitch (say 50 which is the preferred minimum) on which a simple form of cladding can be used with success and which at the same time reduces deflection whilst maintaining reasonable heating costs. However care is required in the selection of the type of sheet, the type of fixing and the sealing of end laps (which should be avoided, if possible). Special care is required where translucent sheets are required (see section 5.3 on cladding). For other than raised seam roofing 7½ ° is the preferred minimum slope.
4.2 Low pitch roofs
Such low pitch roofs can be supported by either solid web beams, castellated beams or lattice frames. Each has advantages and disadvantages which must he examined before a decision can be made.
4.2.1 Solid web beam
This is the heaviest form though relatively simple and cheap to make. However, the depth of section satisfactory for structural purposes may be too shallow for the penetration of service ducting. A monorail or underslung crane can be supported at any position but local stiffening of the section may then be required.
4.2.2 Castellated beam
This is a method of increasing the sectional properties of a beam without materially increasing the weight. The roof space increases but some services can be accommodated in the castellations. Monorails can be located as required but it may be necessary to fill in local castellations and stiffen the flange to carry the load. Castellated beams increase the bending strength and flexural stiffness quite significantly. Enhanced shear capacity at points of high shear can be accommodated by filling the castellations in that region.
6
4.2.3 Lattice frame
Figure 2 shows three different types of rafter and indicates the facilities for services and monorails. It also illustrates that, notwithstanding its extra depth, the lattice frame has a distinct advantage where services have to be carried in the roof. In addition, the reduction in weight of the girder can result in economy in the supporting structure and foundations.
This is the lightest form of construction though it requires more fabrication. The roof space increases but services can usually be accommodated within the depth of the girder. Monorails supported at the panel points cause little problem, but if they are located between them some local stiffening may be required.
The latticed girder will have a much larger second moment of area and section modulus (about XX axis) than a corresponding solid web beam of a similar weight. Therefore there will be enhanced strength and stiffness.
Type (c)
Figure 2 Typical roof girders
Monorail
7
Solid web beam
Type (a)
Type (b)
5. LATTICE FRAMED ROOFS
5.1 Simple forms
Depending on the overall dimensions of the building, the lattice framed roof can take many forms, some of which are examined below:
5.1.1 Single bay low pitch roof
Economically spans up to 30m are often fabricated using standard UB, UC section portals. Above this span lighter rafters are provided by latticed girders, as shown in Figures 1 and 3. The advantage of the horizontal boom is that designing for the "kick out" effect, Figure 4, is removed. Columns are then only designed for axial load and moment (due to the eccentricity of the load) from the roof, in addition to wind load on the vertical cladding. A factor to be considered is the possible lengthening of the bottom boom due to tensile strain.
5.1.2 Multi-bay low pitch roof
Eaves displacement
The single low pitch roof can be extended into a series of similar bays (Figure 5). Alternate stanchions in the valley can be omitted, the intermediate roof frames being carried on a longitudinal valley girder, spanning two longitudinal bays, as indicated.
5.1.3 Single bay monopitch roof
When the slope of the roof is low it is sometimes advantageous to use a monopitch roof (Figure 6). The extra roof space can be compensated for by the saving in drainage since a gutter is required only along one edge and not two. Monopitch roofs are mainly used for
relatively small spans.
8
Figure 3 Single bay low pitch roof
— — —
/
Figure 4 "Kick out "effect
Figure 6 Single bay monopitch roof
5.1.4 Multi-bay roof
In combining frames to obtain a multi-bay system alternate stanchions can be omitted
(Figure 7). The roof is supported at the apex and the valley by girders spanning two
longitudinal bays. Alternatively a multi-bay frame can be provided using a multi-monopitch roof arrangement (Figure 8.)
It is preferable to ensure that a valley gutter is wide enough for an erector or maintenance
operative to stand in.
In the alternative case using mono pitch roofs (Figure 8) the lattice frames all slope in the same direction. Extra gutters are required but advantage can be taken to introduce lights above the valley gutters. This system is particularly useful if direct sunlight into a building is to be avoided. The glazing can then be provided in the north facing slope of the saw-toothed roof.
Eaves gutter
Ridge Cladding
Side cladding
Figure 5 Multi-bay pitch roof
flashing
Side claddi
bolts
Side Ridge flashing
Longitudinal girders
Stanchions at alternate frames
Figure 7 Alternative multi-bay pitch roof
9
5.2 More complex forms
North light Cladding
Where large internal areas are to be relatively free of stanchions, a double latticed system can be adopted. Here, secondary frames in one direction are supported by primary frames
spanning in the other direction between widely spaced stanchions.
These notes on lattice framed construction would not be complete without some reference to more complicated forms built up of lattice frames or lattice girders and trusses and of space frames.
5.2.1 Umbrella roof
In this form of construction light trusses are slung either side of main lattice girders (Figure 9). The pitch of the roof must be sufficient to accommodate the main girders which
in turn should be of sufficient depth to avoid excessive flexibility, bearing in mind the incidental application of imposed and wind loading. Care needs to be taken to ensure
adequate provision for drainage of rainwater.
The trusses act as cantilevers with the bottom chord in compression from imposed loading but
wind loading may cause a reversal of stress. Since these compression members are not
laterally restrained (in normal truss construction the rafters are the main compression members
and they are restrained by the purlins etc.) a system of inclined or horizontal bracing is
required.
Eaves Ridge
cladding
Figure 9 Umbrella roof
10
Figure 8 Alternative form of multi-bay using monopitch roof
Roof
— Stanchion
— Cantilever trusses
Floor, level
5.2.2 Space frames
When large areas need to be covered by a roof, with minimum use of internal columns, a possible solution is to use a space frame. Generally these are formed of tetrahedrons as shown in Figure 10. In principle, parallel series of lattice booms (top and bottom) are connected by a system of diagonal members to form a latticed 2-way spanning plate of significant stiffness.
Angle section upper ch
bars
11
Tubular
Secondary tie bars
Space deck module
Figure 10 Typical space frame
5.2.3 Butterfly roof
The butterfly roof (Figure 11) is unlikely to have the drainage problem of the umbrella roof. Since the lattice girders do not directly govern the slope, the roof can be flatter. The lattice
girders being placed in the valleys do, however, call for increased roof space.
5.2.4 General comment
These various forms, and indeed many others, are frequently adopted to suit the requirements of a particular project, but it must be remembered that they can increase the unit cost of a structure compared with the more simple forms.
Side cladding
Figure 1 1 Butterfly roof
5.3 Cladding Cladding to a building (roof and walls) has to be provided to satisfy aesthetic and functional criteria and to satisfy the economics of the project.
A satisfactory appearance is accomplished by selecting the appropriate colour and shape to blend in with the remainder of the building and neighbouring structures.
A useful "Product Selector" for "Roofing and Cladding in Steel" has been produced by BSC
Strip Mills Products' '. This provides details of about 70 different products.
Functionally, the system has to provide resistance to atmospheric conditions, sound
transmission, and light reflection. It is essential to ensure that both roof and walls are
watertight under all conditions, wind causes no damage to either cladding or structure, and
adequate insulation is provided against heat and cold. Structurally, cladding has to be of adequate strength and stiffness to resist induced stresses and excessive deformation. Profiled
sheeting is commonly used since it satisfies these requirements and is additionally light, durable and easy to erect quickly.
Coated steel sheets are extensively used for cladding all types of industrial buildings. They are available in a wide range of profiles (rib depths) and colours. Many proprietary cladding products provide integral insulation systems, making use of expanded polystyrene or similar insulation material. Double skin metal systems are available and are considered by some
designers to be the best type of cladding. Clearly where composite cladding systems are used there is only one operation for the erectors.
12
Roof Eaves ci
H.D. bolts
In general a single skin is used for stores where heat retention is not a significant factor e.g. timber stores etc. In factories and offices where the envelope is dependent on the "U' value, double skin cladding is a sensible solution. However, lining sheets may be a critical factor in the design for wind suction.
Sheets, supported by purlins (Figure 12), are available in long lengths. Where possible, sheets are lifted into position by cranes to provide better safety conditions for the fixer. Hence the number of laps should be minimised in order to reduce the possibility of water ingress, particularly on shallow slopes. It is possible to vary the spacing of supports for cladding depending upon the thickness and shape of the profile. Three factors generally control the spacing. The first is purlin size and the second is the limitations of lining supports. Often the length of the inverted 'T' sections used to support lining panels is limited to about 1.8 m, consequently purlin centres are restricted to that dimension. Finally purlins are often used to provide lateral restraint to the rafters or frames. All of these factors need to be considered to determine the most economical solution to the roofing system.
Aluminium sheeting is similar to steel sheeting, although it tends to be lighter. The aluminium coating may provide better resistance to industrial atmospheres, greater solar heat reflection and brighter appearance.
Natural lighting can be provided by the introduction of translucent sheets (which structurally can be very weak), or stretches of patent glazing. The latter is clearly more expensive and is often limited to slopes greater than 12°. Translucent sheets can be moulded to the profile of the main cladding and would use similar fixings.
Care must be taken in positioning roof lights. It is generally necessary to have a metal or similar main cladding sheet at the top and bottom of the roof light in order to provide adequate strength to the system. When lights are placed near to the eaves and/or ridge there may be inadequate support.
Cladding can be fixed by the use of self tapping screws or hook bolts. Self tapping screws may have recommended torques. An aspect to be carefully considered is the thickness of the purlin. It is essential to ensure there is sufficient thickness of metal to accommodate self tapping screws. If there is any doubt it is advisable to check with the cladding and purlin manufacturers of the adequacy and safety of the composite system.
Screw sizes vary and their strengths are dependent on their "pull-out" capacity. In checking these the screw manufacturer has to take into account the high "local" wind suction effects.
Often gutters are placed inside at eaves level to provide enhanced appearance. However, this advantage needs to be weighed against the difficulties which may be encountered in the repair and maintenance of the gutter. With this system the use of overflow weirs should be considered to allow for blocked pipes and freak storms.
5.4 Purlins
Purlins are required to support any of the types of cladding available. Cold formed sections have been developed to provide elements of adequate strength and stiffness which also allow maximum speed of erection.
If the design criteria is such that cold formed sections are inappropriate then use can be made of hot rolled sections.
13
For frame spacings between 6.0 m and 10.0 m a propped purlin system can be adopted constructed from either light angle, tee or channel sections or structural hollow sections, as shown in Figure 12. For even wider frame spacing the use of lattice purlins should be considered. They can be made up in many ways, e.g. using flats with rod lacing or small structural hollow sections. (Cold formed lattice purlins are also available). Castellated beams have been used on occasions.
It should be noted that both propped and lattice purlins can be useful for providing restraint to the bottom of the main supporting frames.
As indicated in Section 5.3 on cladding it may be necessary to limit the purlin centres to 1.8 m (generally fabricators prefer 1.7 m to 1.9 m).
Of particular consideration is the location of the purlins relative to the node positions of the lattice frame. If they coincide with the nodes then the top boom would only transmit axial loads. If they are located between nodes then bending is induced in the boom member in addition to axial forces.
The span of purlins may be controlled by a fixed specification for the main frame centres.
Alternatively frame centres can be determined by selecting specific purlins which may have limiting spans. Cold formed sections are normally available in lengths up to 10 m and depths from 120 mm to 300 mm. Normally spans are of the order of 4.5 - 6 m. To enhance the lateral stiffness of the purlins it is sometimes necessary to use anti-sag bars - Figure 16. This, however, can increase labour costs and therefore their use should be weighed against larger purlins or closer frame centres.
An aspect to be considered concerns the design for snow loads. Cold formed purlins have generally been developed on the basis of tests carried out using uniformly distributed loads. Snow loading may be trapezoidal and care is required in the interpretation of the manufacturers' literature.
A further design criteria which has implications on purlin size is the incorporation of a dominant opening in the side of a building. This can significantly increase the uplift due to wind.
Purlins are often used to provide lateral restraint to the compression flange of the main supporting frames, and to transmit wind loads to the bracing system. If this is the case combined loading needs to be considered when selecting the appropriate purlin i.e. it could be subjected to the maximum dead plus superimposed (snow) loads, which induce bending, and additionally axial load from wind effects.
Eaves purlins are also available which have a sloping top flange. Various types of purlins are shown in Figure 12.
5.5 Side rails
In general the comments provided in the previous Section on purlins are applicable to side rails. The loads acting on these will be different since vertical forces are induced by the self weight of the cladding which acts perpendicular to the wind loads. Sheeting rails are often fixed at about 1.8 m. Generally, a limit of 2 m is placed on their centres. Anti-sag rods are more easily fixed to stiffen these elements.
14
Asbestos cement sheets
Self tapping screws
Steel sheets i 5°)L
S%iRaft:):;;:ul:tion Cold formed Z (Anti-sag bars required for spans over 4.5 m)
'Structural hollow section (circular or rectangular)
Propped angle purlin
Sheeting and insulation
Lattice purlin —
Roof girder
Figure 12 Types of purl/n
15
Purlin
Lattice girder
Purlin stays
Hook bolts Hook
Sheeting
Rafter
Angle
Insulation
Rafter
Roof girder
Props to bottom of roof girder
6. CONCEPTUAL DESIGN
Before consideration is given to the method of analysis and design to be adopted certain decisions have to be taken, which may later be modified as the design progresses. The effect of any modifications clearly can alter the detailed design and alterations to calculations would ensue.
There are four principal components of a light industrial building i.e. the cladding, the cladding supports, the main frame and the foundations.
Early decisions are required on type(s) of cladding and type of purlin and sheeting rails. Since these are all supported by the main frame.
If the frame is considered as a simple portal, Figure 13, it is necessary to decide on the type(s) of fixity to be provided at the base, eaves and ridge. Generally, the columns to the frame will be of I or H section, unless the building incorporates a high capacity overhead travelling crane when a composite column might be required.
If the rafters are to be latticed structural steelwork it is possible to use different layouts of the internal members, Figure 14. However, since the diagonals are likely to be subject to stress reversal, due to wind effect, the warren type truss is generally preferred. In selecting the layout it is necessary to decide on the position of purlins. If these are located at node points then local bending in individual top boom members are avoided. In principle, forces in all of the members are either direct tensile or compressive, with bending and shear effects being secondary, as a result of deformation of the truss.
Analysis of the framework can be carried out by hand calculation, drawing or computer. In the first two methods, it is essential to assume that all joints are pinned and preferably end support conditions to the rafters are such that the truss is statically determinate.
When a software package is used there are a number of options, three of these are:
(i) assume all joints of the truss and the connections to the columns are pinned;
(ii) assume full rigidity of all joints;
(iii) assume the internal bracing members are pinned to the booms which are considered to be continuous and therefore rigid.
In adopting (i) or (iii) it is necessary to consider the possible effect of secondary stresses caused by:
(a) loads applied between the truss nodes;
(b) moments resulting from the actual rigid joints and truss deflections.
Additionally, in all cases care needs to be taken in member layout, since secondary stresses can be induced by eccentricity at the connections. (Specific reference should be made to BS 5950: Part 1, Clause 4.l0' and Structural Steel Design'2 by Dowling, Knowles and Owens), Dowling et al suggest secondary stresses should be calculated for heavy trusses used in industrial buildings (e.g. those supporting overhead cranes) and bridges. It is traditionally recognised (e.g. in British Steel Publication, Design of SHS Welded Joints' 3)) and Dowl ing et al also suggest that latticed structures are assumed, for design purposes, to have pinned joints. This may lead to higher defiections than those induced in a rigid jointed truss, but in practice
16
this is unlikely to be significant with the exception of girders supporting crane beams.
The design example illustrated uses a package hut initial hand calculations are used to ascertain member sizes. These are useful for the software data input.
Generally a decision will be taken early during the conceptual design process on the type(s) of member(s) to be used for the latticed frame. There are many options:
(a) Hollow sections - circular or rectangular. (b) Traditional sections - angles, tees, channels, UCs. (c) Combination of (a) and (b).
The selected truss should reflect the need not only to produce the lightest frame but also to minimize the cost of fabrication and erection.
Rigid
Pinned Pinned
Pinned
Rigid
Fully rigid
Pinned
Figure 13 Basic arrangement for portal frames
'Pratt' or 'n' truss
'Warren' truss
Figure 14 Typical arrangement for latticed girders
17
Rigid Rigid
An example of composite form is shown in Figure 15 where the booms are of UC section and
the internal members RHS. The UCs enable easy connection of services to the truss and easy connection to columns. Also bracing in the plane of the roof can be provided using simple in
plane members and simple connections, or by using the relative stiffness of an I or H section.
When hollow sections are used with welded joints reference should be made to the British Steel Publications, listed in Section 7.5. It is essential to ensure that it is possible to make a full weld. Difficulties can arise where large booms and small internal members are used which may require joint stiffeners. These may be expensive and it is likely to be prudent to increase the member size. The designer must be aware of problems which can arise in the detail design at the joints.
The specific advantages of hollow sections (and tubes) when compared with traditional sections (UBs, UCs, Channels, Angles etc.) are the high strength to weight ratio, maximum
efficiency in tension, efficiency as struts, good torsional properties, appearance and
maintenance. In deciding to use CHS or RHS the designer should remember that some fabricators are not fully equipped to use circular hollow section.
Their main disadvantages can be the higher cost of connections especially at nodes involving overlapped CHS bracings and chords, the relative difficulties of making on site connections for services (electrical etc.) and higher basic costs than traditional sections on a tonnage basis (overall, however, lighter weight frames are produced).
Relevant to the design code BS 5950: Part 1(1) is the consideration of section classification (Fable 7 of the code). Tees cut from UBs are generally slender, hence a reduced yield stress has to be used. Tees cut from UCs are not affected in the same manner.
In designing the joint it is necessary to examine whether high local stresses will be induced by the selected arrangement and member sizes. These high local stresses may even occur when member axes intersect.
The relative slopes of the internal members are relevant to the detailing for the fabrication
process. If they are parallel to each other then the angle of cut at each end is identical for all members.
The final decision on the type(s) of member(s) to be used may be influenced by aesthetics and not cost.
CHS UC UC RHS
OHS RHS RHS RHS
CHS UC UC RHS
Figure 15 Alternative lattice girder layouts
18
7. PRINCIPLES OF DESIGN
The design of all the steelwork for low rise lattice framed buildings should satisfy the "aims of economical structural design" and "limit state" philosophies outlined in the appropriate Codes of Practice.
Basic design assumptions are made as to the behaviour of the various units which make up the structure.
7.1 Purlins and side rails
Purlins and side rails can be designed to satisfy the strength and deformation requirements of the appropriate codes or they can be designed using empirical rules given in Clause 4.12 of BS 5950: Part 1' and Section 9 of BS 5950: Part 5(2)
It is of note that the empirical rules are based on unfactored loads and also that the tables of section properties (A checklist for designers'6 published by the SCI) do not list plastic moduli for angles.
Purlins are generally designed as continuous members, over two or more spans, supporting uniformly distributed loads. In this case connections have to be made to transmit shear and bending.
Cold formed sections can be selected from manufacturers' catalogues where it is guaranteed that the carrying capacity of the various systems is based on the results of extensive research and development.
Continuity is obtained by the use of sleeves, and the effective length of purlins are reduced by the use of anti-sag bars (Figure 16).
When applied loads are not uniformly distributed e.g. trapezoidal snow loading or when purlins are used to support ventilation systems etc. then original calculations are required. These will make use of BS 5950: Part 5 and section properties for cold formed purlins provided in manufacturers' catalogues.
7.2 Lattice framed roof girders As indicated in Section 6 the design will be based on the assumption that joints are pinned, rigid or a combination of the two.
The girder will support vertically applied dead and superimposed loads plus wind loads. The latter is likely to induce stress reversal in the members. The rafter will also transmit the horizontal wind loads from the vertical cladding and may act to transmit wind loads in the plane of the roof. Typical load directions are shown in Figure 17.
7.3 Stanchions
When pinned bases are adopted then moment fixity is required at the column head. The column will be designed for axial and shear forces only at the bottom but for axial, shear and
bending in the upper length. Use of fixed bases enables the stanchions to be designed as propped cantilevers, although it should be noted that simply linking the top of the stanchions with the roof trusses does not provide a fully rigid propped system. The column heads and
19
girders can all move together. It is of note that the relative stiffness of the rafter and column are significantly different (possibly of the order of 4 to 1). Also changes in the overall depth of the rafter can significantly increase or decrease the stiffness of that member.
The stanchion size is controlled by its effective length, which is likely to differ about
orthogonal axes. Care is required in the selection of end and intermediate fixity conditions.
Reversible wind loads
Figure 17 Frame loads
20
rail
Cleat (behind)
rafter
Figure 16 Sleeved purlln system
I I
\
Dead & I Vertical imposed loads
Reversible wind loads
I
Vertical cladding (dead) load
7.4 Bracing
Bracing must be provided to accommodate wind loads on the gable columns. This can be used to facilitate plumbing and squaring the building during erection. It can also provide essential stability to the steelwork during erection.
Bracing normally consists of diagonal members between columns and trusses both in the walls and plane of the roof. The bracing can be single diagonal or cross members (Figure 18). If the former system is adopted the members are designed to support compressive and tensile loads. When cross members are used only the members in tension are assumed to be effective, those in compression are designed to satisfy the slenderness criteria, Clause 4.7.3.2 of BS 5950: Part 1: 199O'.
When masonry is used as all or part of the vertical cladding, it is feasible to use that element as part of the bracing system.
/\NN/7NNNN Single diagonal roof bracing
>< >< x >< Cross member roof bracing
Figure 18 Roof bracing
7.5 Connections A very important aspect of design using any material is the design of connections. Structural members are designed to carry axial loads, shear force, bending moment and torsion. Consequently connections must be designed to transmit these forces from one element to another without inducing excessive stresses or deformations.
To produce a good design of a complete structural assembly it is essential for the designer to clearly state at an early stage the basic methods by which various members are to be joined.
Sophisticated methods of analysis are now available to determine to a good degree of accuracy the forces and deformations throughout both simple and complex structures. This degree of sophistication is not however generally available in connection design. The stresses induced by connections are often indeterminate and their distribution throughout a joint is not always consistent even in identical conditions. Stress is always a function of deformation and the latter can vary with the irregularities of the properties of the members being connected, the type of fasteners, the quality of workmanship in making the connection and "built in" stresses in the parent members.
21
Most connection design is, at present, only approximate. The essential aim is to provide the type of connection stipulated by the designer which is efficient, economical and aesthetically pleasing. The latter is not always essential. Use will be made principally of the basic laws of statics i.e.:
EX =EY =EZ =0 = EM = EM = 0
i.e. all joint behaviour will be considered to be statically determinate. The distribution of internal forces in a connection has to be assumed and either elastic or limit state design may be appropriate.
The fabrication of connections is particularly labour intensive and therefore in order to keep overall costs down it is necessary to try to produce simple but efficient methods of joining members, by welding or bolting.
In general the design of connections will follow the recommendations given in BS 5950: Part 1: 1990, Section Six. Connections.
In the case of the following design example using hollow section the design is carried out using as references the following publications produced by British Steel viz:
Design of SHS Welded Joints TD 338' Jointing TD 325 Welding ID 328' Hot finished structural hollow sections; sizes, properties and technical data TD 167
Useful reading in the first instance is TD 325 which provides an indication of the wide spectrum of application of RHS.
Publication TD 338 provides a clear method of Designing SHS Welded Joints. As indicated in Section Six of BS 5950: Part 1, it is common practice to carry out the analysis on the basis of pin-jointed frames with members in direct compression or tension and the centre lines of members intersecting at the nodes, as shown in Figure 19. Often it is necessary to provide a gap or overlap as shown in Figure 20. Joints may take a variety of geometric forms as shown in Figure 21. TD 338 details the method of establishing the joint's design capacity in limit state terms, compatible with BS 5950 and Eurocode 3.
It should be noted that fillet welds generally provide the most economic method of connecting members in structures subject to static load. Clearly one exception is the case of end to end connections where butt welds can be provided to develop the full strength of the sections connected. In this case with RHS sections internal backing members are provided, which are formed from strips 20-25 mm wide and 3-6 mm thick.
Of note is the recommendation in a paper by N Yeomans, New Developments in the use of Structural Hollow Sections17:
"Because of the influence of member and joint geometry on the joint behaviour, it is important that engineers design the joints when determining member sizes; with SHS design this job should not be left to the detailer".
22
Figure 19 Noding joints
a) Gap joint with positive eccentricity
Figure 20 Definition of eccentricity
b) 100% overlap joint with negative eccentricity
X joints I and Y joints /
/ N and K joints with gap N and K joints with overlap
I / oy[1%e2 -* -
/
Figure 21 Joint geometries
23
a
/ ,es
—Y-------k-
8. EXAMPLE - DESIGN BRIEF AND APPROACH
8.1 Brief
The client requires a single storey, single bay industrial building to be used as a light machine
shop. It is to be sited on an industrial estate on the outskirts of Leicester.
Main dimensions - 30 m wide x 48 m long x 6.7 m to eaves
Cladding - Colour coated steel sheets to roof, sides and ends with 20% natural lighting provided by translucent sheet inserts.
Insulation - A lining system to be provided to wall and roof sheeting.
Access - A roller shutter door 4 m X 4 m is to be provided in both gable ends with personnel doors 1 m x 2 m adjacent and along the side walls.
Note: The possibility that the roller shutter doors would be open during a severe storm was discussed with the client. The final decision was that the design should be based on the assumption that both doors would be closed during a severe storm.
Services - Allowance was to be made to support set-vices from the roof structure. Mechanical handling was not required.
General - It was agreed that:
(a) The roof pitch would be set at 50
(b) The roof to be of hot rolled hollow section latticed framework.
(c) Hot rolled I sections would be used for the columns.
The outline of the building based on the above brief is shown in Figure 22.
Selection of RHS for the roof structure is based on its enhanced efficiency and the cost effectiveness of joints which will, in general, be quite simple. The girders will be shop fabricated in two halves, approximately 15 m in length and 1.2 m deep.
Hollow sections can be used in simple, semi-rigid and rigid design and can adequately carry axial (tensile and compressive) loads, bending, shear and torsion.
8.2 Cladding Since the decision has already been made to use colour coated steel sheets with insulation
lining and translucent sheet inserts, it is only necessary to settle upon the most suitable thickness and profile of sheet to be adopted. This need not be the same for both roof and sides and they are therefore considered separately.
24
5° pitch
Cross section
Roller shutter door
/
E 0
/
I
I
0
(5.; 4, >. (5
co
/
30.Om
Plan - Centre lines of frames
End elevation
Figure 22 General layout of building
25
8.2.1 Roof sheeting The span of the roof is 30 m and with a 5° pitch the length of one slope is marginally over 15 m. Not all manufacturers produce sheeting of such length and it may be necessary to use, say, 2/8 m sheets lapped at the centre. The laps should be bedded in sealant because of the low rise.
A suitable spacing for the purlins will be 1.85 m, which on a slope length of about 15 m, divides the rafter of the roof frame into eight panels. A typical sheeting system would be the "Warmclad 1000R", with lining, manufactured as a BSC Profile (Reference 6), this is suitable for roof and walls.
8.2.2 Wall sheeting The height from the floor to the eaves is 6 m hence sheeting rails can be spaced at 1.5 m c/c. To achieve a different architectural effect to the building either a different sheet and/or an alternative colour could be adopted.
Figure 23 shows a cross section of the building.
6.0 m
0.7m
,1
Figure 23 Cross section
26
Lined roof cladding and translucent sheets Ridge tie
Lined wall cladding
'Weathering curb
ground level
15.0 m Half span
9. DESIGN OF STEELWORK
9.1 Loading The loading for which the steelwork must be designed is in four parts:
(1) Dead load - from cladding and structure, assessed from the mass/unit of the various items (Reference 4).
(2) Imposed load - (Reference 5).
(3) Service load - allowance for trunking etc. required by client.
(4) Wind load - (Reference 6).
The first three loading conditions can be calculated as the design proceeds but the assessment of the wind load requires consideration of the complete structure at the outset.
9.1.1 Load factors
Table 2 of BS 5950: Part iW
.yf
Dead load 1.4
Dead load restraining uplift or overturning 1.0
Dead load acting with wind and imposed loads 1.2
Imposed load 1.6
Imposed load acting with wind load 1.2
Wind load 1.4
Wind load acting with imposed load 1.2
Forces due to temperature effects 1.2
9.2 Assessment of roof load
BS 6399: Part 3 : 1988 provides the detailed method of evaluating minimum imposed roof loads (Clause 4). With no roof access the load is taken as the greater of:
(a) the uniformly distributed snow load.
In this case Figure 1 in the code provides the "basic snow load on the ground", say 0.6 kN/m2 = s0.
The roof snow load Sd = j s where 0.8 (Figure 4 in the code).
Hence Sd = 0.48 kN/m2
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(b) a uniformly distributed load (u.d.1.) of 0.6 kN/m2
For simplicity in this example drifting has been ignored and the roof snow load is therefore taken as 0.6 kN/m2.
9.3 Assessment of wind load on structure
CP3 : Chapter V : Part 2 : 1972(6) gives a detailed method of calculating the design wind loads on a structure. The code was prepared following extensive investigation at the Building Research Establishment.
The dynamic pressure q exerted by the wind is found in the formula:
q = kV2 N/rn2
where: q = dynamic pressure k = constant having a value of 0.613 V design wind speed
= V x S1 x S2 x S3
where V = basic wind speed for geographical location
S1 = topography factor, usually taken as unity (except where conditions are abnormal)
= ground roughness, building size and height above ground factor
S3 = building life factor, usually taken as unity.
S3 is a factor inserted in the formula to enable account to be taken of any special circumstances which may justify a variation in the design wind speed.
For a factory located in the Midlands the basic wind speed V, from the map in the code, is 44 rn/sec. Then, if unity is accepted for S1 and S2 the design wind speed, V V x S2.
A wide range of values for 2 are given in Table 3 of the code. These are divided into four
groups related to the surroundings of the building under consideration, and each group is divided into three classes relating to cladding or structure and its size. The value of 2 also
varies with the height above ground level, stepped at intervals.
The building in this example is located on an industrial estate where it will be surrounded by other buildings. Group 3 is thus applicable, with Class A factors for the cladding and, since none of the main dimensions exceeds 50 m, Class B factors for the structure.
Table 3 gives values of S2 at heights of 3, 5 and 10 m above ground. As the overall height from ground level to ridge is say 8 m the value of S7 for the structure at that height may be obtained by interpolation between the tabulated values at 5 m and at 10 m and this results in a value of 0.70. The values of S2 are therefore as shown in Figure 24. (For more detailed information on the values of S, reference should be made to Wind loading handbook published by BRE7).
28
Figure 24 Values of coefficient S2
Using these values for 2' the design wind speeds and dynamic pressures over the two height ranges are as tabulated below:
Table 1 Wind speeds and dynamic pressures
Height range
m
Cladding Structure
S2 V q rn/s N/rn2
S2 V, q rn/s N/rn2
(a) Oto3
(b) 3 to 8
0.64 28.16 486
0.75 33.00 668
0.60 26.40 427
0.70 30.80 582
The design wind loads on either the cladding or the structure are found by multiplying the dynamic pressure, q, by the area applicable and by a further coefficient C, in the case of externally applied forces and C for the internal effects i.e. internal pressure or suction which depend on the permeability of the building shell.
Values for the external pressure co-efficient, C , are related to the shape and dimensions of the building and are given in Tables 7 and B orc3 : Chapter V: Part 2: 1972(6).
For the building under consideration the relevant information is:
Width of building, w = 30.0 m Length of building, 1 = 48.0 m Height to eaves, h = 6.7 m
Then hiw = 6.7/30 = 0.22 < 0.5 and 11w = 48.0/30
= 1.6 i.e. between 1.5 and 4.
From Tables 7 and 8 of the code the values of C are:
(a) wind on side of building
Windward side = +0.7 Leeward side = -0.25 Windward roof slope (5°) = -0.9 Leeward roof slope (50) = -0.4 Either gable end = -0.6
(b) Wind on end of building
Windward gable = +0.7 Leeward gable = -0.1 Both roof slopes = -0.8 maximum Either side = —0.5
The following calculations are based on the assumption that the doors will be closed during a severe storm, which has validity and also simplifies the design process for this example. Hence C is taken as the more onerous of +0.2 and -0.3.
29
However, it should be noted, as stated in Appendix E to CP3: Chapter V: Part 2: 1972, that the value taken for the internal pressure coefficient, must be related to the permeability of the cladding and the presence or otherwise of large openings. It is necessary to ensure the correct decision is taken concerning the permeability of a building which is constructed with one or more large doors. It is often, quite incorrectly, assumed that the door(s) will always be closed during a severe storm. In reaching this decision no account is taken of loadings which will arise during the construction period when it is very likely the door will not be in
position. Nor does it take into account the use of the building which, during its lifetime, is
likely to be such that the door will be unavoidably opened. An argument also put forward is that in the event of the door being open during a severe storm, the sheeting would probably "blow out" before damage to the structure occurred.
The various coefficients to be used to determine wind loads on sides and roof of the structure only are shown diagrammatically in Figure 25.
As far as general stability i.e. overturning, is concerned internal pressure has no effect since the horizontal forces on the sides and horizontal components of the forces on the roof all cancel each other. For the design of individual members and for deciding on the minimum
anchorage required, the most adverse conditions are taken from (e), (f), (g) and (h) of Figure 25.
0.7f}225 o[_'b}.5 Wind on side Values of c1 Wind on end
Pressure Values of c,, Suction
0.5 4TfO.45 0. 0.7
(C) - ( 0.2) (C,,) - ( 0.2)
1.0 TIj..o.os 0.
(C) - (— 0.3) (C) - C— 0.3)
Figure 25 Evaluation of total pressure coefficients (Cpe and C,,1)
30
The following calculations are made using the values of q applicable to the structure. The cladding and its fixings must be capable of resisting the higher values shown in Table 1, adjusted by the values of C and Cr1. The areas adjacent to the eaves, ridge and verges, and the corners of the building are designed using the local coefficients in Tables 7 and 8 of the code, which are aimed at avoiding local damage. These local coefficients for the fixing of claddings are significantly different to those shown for the structure, but these are not included within the scope of this publication. This is information which would be required by the manufacturers of cladding and fixings.
9.4 Design of purlins These may be either cold rolled or hot rolled sections and both a cold rolled zed section and a hot rolled angle are designed for comparison.
The purlins have a span of 6 m and are spaced at 1.85 m centres.
9.4.1 Cold rolled Z purlin
Normally a cold rolled purlin can be selected from a manufacturers' catalogue (e.g. Metsec'8) where safe distributed loads are given for various sizes and shapes. No further design checks are necessary if these have been designed to BS 5950: Part 5: 1987(2).
Dead load, sheeting and lining, say 0.19 kNIm2
Imposed load QQ kN/m
Total dead and imposed loads 0.79 kNIm2
Self weight, say kN/m2
Total load 0.82 kNIm2
Using a load factor of 1.6 the design load due to dead and imposed is 1.6 x 0.79 = 1.27 kN/m2. Purlin design is based on a normal load acting on the member. The dead and imposed loads are gravitational. However the difference between gravitational and normal loads for a low pitch roof is not significant.
From a manufacturer's catalogue a 202 x 65 x 60 x 1.8 mm thick Z purl in (Figure 26) will
carry an allowable (unfactored) load of 1.29 kN/m2 (excluding putlin self weight of 5.01 kg/rn).
The maximum wind uplift on the roof will be 0.582 x 1.1 = 0.64 kN/m2 (see Table 1 and Figure 25(e)).
In selecting an appropriate purlin it is necessary to consider the effect of using the purlin as part of the bracing to transmit wind loads in the plane of the roof. See Section 10.7.1.
Gross uplift on a purlin spanning 6 m at 1.85 m centres = (0.64 - 0.22) x 6 x 1.85 = 4.44 kN. With a factor of 1.4 the design wind uplift = 4.44 x 1.4 = 6.3 kN.
According to the manufacturer's catalogue the Z purlin selected is capable of resisting a wind load of 9.2 15 kN. To support this load no anti-sag bars are required.
Use 202 x65 x6Ox 1.8
31
H 65b 1 ______
—1.8
Figure 26 Z purlin
9.4.2 Hot rolled purlins (I) Anti sag rods
Purlins (and rails) can be designed in accordance with Clause 4.2' i.e. as beams, or empirically (as in this example) using the rules detailed in Clause 4. 12.4'. The elements are designed assuming the cladding provides lateral restraint to the section. Clearly the cladding and fixings have to be capable of providing the necessary support (in particular care is needed in areas of high local wind effects).
Anti-sag rods may not be required when hot rolled sections are used for purlins spanning less than 6 m. They may however be used to provide stability during erection. This will reduce deflections in the plane of the cladding.
(ii) Angle purlins (Figure 27)
Rafters @ 6 m c/c
Dead + imposed load = 0.8 kN/ir? (refer to Section 9.4.1)
However the minimum imposed load (Reference 1 Clause 4.12.4.3) should be taken as 0.75 kN/m2. Hence load/purlin = 0.95 x 1.85 = 1.76 kNIm.
32
wp
wp
Figure 27 Loading on purlins
For self weight first consider:
= 6000 = 133 45 45
B L6000_100 6O Minimum section to satisfy D and B would be 200x lOOx 10 angle.
This weighs 23 kg/rn.
Total load = Wp/m = 1.76 + 0.23 = 1.99 kN/m.
Hence W, = 1.99 x 6 = 12.0 kN (note - unfactored loads are used).
WL 12x6000 Therefore Z 1800 1800
40 cm3
This will be satisfied by the 200x100x10x23 kg/rn angle (Z = 93.2cm3).
(ii!) RHS Purlins
The limiting factors in this case are:
WL 1800 say 40 as before
� 600040
Minimum section to satisfy D and B is a 100x50x6.3 RHS, this weighs 13.4 kg/rn and Z = 40.5 cm3, or consider lOOx6Ox5x 11.7 kg/rn RHS, Z, = 38.5 cm3.
Thus W, = (1.76 + 0.12)6 = 11.3 kN.
zi 11.3 x 6000 37.7 cm3 1800
Section is satisfactory.
Of note is the significant difference in weights of the cold formed Z section (5.01 kg/rn), the hot rolled angle section (23 kg/rn) and the hot rolled R}IS (11.7 kg/rn).
Unless special conditions dictate it is highly unlikely that other than a cold rolled section will be used for purlins.
Of note is the possibility that tubes with open ends may be subject to internal corrosion. It is recom,nended that hollow sections are sealed.
33
9.4.3 Design of side rails
These may be cold or hot rolled. Side rails span of 6 m horizontally and are at 1.5 m c/c
vertically. From Figures 25(f) and (g) and Table 1 the characteristic wind loads are:
Pressure 1.0 x 0.582 = 0.582 kN/m2 Factored pressure = 1.4 x 0.582 = 0.815 kN/m2
Suction 0.7 x 0.582 = 0.407 kN/m2 Factored suction = 0.570 kN/m2
(I) Cold rolled Z rail
From manufacturer's catalogue a suitable section is 142 x 54 x 49 x 1.8 mm thick Zed sleeved system, using one row of side rail supports.
(ii) Hot rolled angle rail (BS 5950: Part 1, Clause 4.12.4)
Using weight of sheeting and lining of 0.2 kN/m2, the vertical load on a rail = 0.2 x 6 x 1.5 = 1.8 kN. Allow for self weight of 0.2 kN/m. Hence W1 = 1.8 + (6 x 0.2) = 3.0 kN (Figure 28).
W2 = 3.0 kN
1 W1=5.24kN
— — -Y
Figure 28 Side rail arrangement
W1L (0.582 x 1.5 x 6) x 6000 - 5.24 x 6000 — 17 5 cm2 1800 1800
—
1800 —
where W1 is the unfactored horizontal load
Z, 17.5 cm3
W2L 3x6000 3 1200 1200
15cm
L 6000 D — 134mm
B 6000100mm
A 150x 150x 10x23 kg/rn angle satisfies (Z = 56.9, Z, = 56.9 cm3). Check D since Z1 provided is greater than minimum Z1 required from Table 30 and Clause 4. 12.4.4(d)(').
34
6000 17.5 D'.. = __ x—=41 tmi 45 56.9
ButD B hence check a 120x120x8x14.7 kg/rn angle (Z1 = Z2 = 29.1 cm3)
In this case the controlling factors are Z1 = 17.5 cm3 and Z2 = 15 cm3, which are satisfied.
Check D x = 80 mm, which is satisfied.
Use 120 x 120 x 8 x 14.7 kg/rn angle.
(iii) Hot rolled RHS
Z1 17.5 cm2 Z2 15 cm3.
O857
B
A 100x60x3.6x8.59 kg/rn RHS would satisfy. Adjustment can be made for D i.e.
6000 17.5 — D1.. x___—52 70 29.3
In this case there is no available lighter section, a thicker walled section might be preferable.
Use 142 x54 x49 x 1.8 Zed sleeved system with one row of anti-sag bars.
9.4.4 Eaves detail
At the eaves a possible solution when using a Zed purlin system is to use a cold formed eaves beam. A typical section is shown in Figure 29.
Figure 29 Special eaves purl/n
35
9.4.5 Design of gable rails
These will be of different size to the side rails since, although the vertical spacing will be set at 1.5 m c/c, the spans are 7.5 m. Consideration could be given to maintaining the spans at 6 m. Side rails would then be of the same size throughout.
The loading is the same as the side rails i.e. pressure 0.582 kN/m2 and suction 0.407 kN/m2.
From manufacturer's catalogue a suitable section is 202 x 60 x 60 x 1.6 mm thick Zed single span system, using 2 rows of side rail support. It should be noted the gable rails are single span, whereas the side rails are sleeved. The latter are used providing there are two or more
spans. The gable end is broken by the provision of the large roller shutter doors. Use 202 x60 x6Ox 1.6 Z.
9.4.6 Typical system
Typical arrangements for a building which incorporates Z purlins and Z side rails are shown in Figure 16.
9.5 Design of main roof frame
In order to design the members it is necessary to decide on the method(s) of analysis to be used to obtain member actions (forces, moments etc) and deformations. In this example it is
initially assumed, in order to determine preliminary member sizes, that the frame is a portal as shown in Figure 30, where:
(a) the columns are pinned at the base;
(b) the girder is initially treated as a "beam with partial restraints at the end". The bending moment and deflection at the centre can then be evaluated;
(c) Having deduced the bending moment in the girder the joints of the latticed truss are assumed to be pinned (this complies with Clause 4. lOW).
Figure 30 Lattice girder/pinned portal analogy
9.5.1 Preliminary design - joints of latticed truss pinned
Span 30 m; spacing 6 m.
To proceed with the design it is necessary to estimate the self weight of the girder. Initially assume that the self weight will approximate to 50% of the weight of the cladding.
36
The frame adopted is a lattice girder (beam). As such there are two main design criteria to be considered namely strength and deflection.
In the case of strength, assuming use is made of Grade 43 steel, the maximum yield stress allowed is 275 N/mm2 (Table 6(1)). Allowance has to be made for slenderness and member classification in order to determine the design strength (p for struts (Tables 7 and 27(1)). The reduction can vary from 2% to 75% of the full member compressive capacity.
Generally the smaller the member cross section the larger the percentage reduction.
With respect to deflection limitations are not specified, in fact Table (1) particularly excludes pitched roofs. However experience has shown that a deflection limit of span/200 is a useful guide for such a shallow pitch.
If the girder is assumed to be subject to a uniformly distributed load (as distinct from 17 No. purlin loads) then, say, deflection limit is
384 El 200
where W (kN) is the unfactored imposed load and L is in metres. (Note: deflection for a
simply supported beam supporting a udl (14') is 5WL31384 El and for a fixed ended beam it is IVL3/384 El. Hence for partial restraint assume deflection is 214L3/384 El).
Taking E = 205 kN/mm2 and re-arranging the required I = 0.51 WL2 cm4.
Preliminary calculations are thus carried out assuming the self weight of the girder approximates to 50% of the weight of the cladding, the compressive stress in the boom is 250 N/mm2, in the diagonal strut 220 N/mm2 and I required is 0.51 yp2 cm4.
9.6 Preliminary calculations
9.6.1 Loading (excluding wind) - based on full sheeting width say 30.6 m
kN
Dead load (characteristic) Sheets and lining 30.6 x 6 x 0.2 = 36.8 Purlins 18 No. x 6 x 0.04 = 4.3 Self weight of girder, say = 18.4 Services load, say = 1L Total = 71.0
Imposed load (characteristic) 30.6 x 6 xO.6 110 kN
Design load (Table 2 of BS 5950: Part 1)
F=(1.4x71)+(1.6x 110)=276kN.
37
9.6.2 Initial member size
(i) Main booms
a) Assume maximum bending moment (BM) in the girder =
WL = 276 x 30 = 5l8kNm 16 16
The assumed BM of WL/16 takes into account the partial restraint produced on the whole girder by the connection to the columns i.e. BM at the centre lies between WLI8
for a simply supported beam and WL/24 for a fixed ended beam (both subjected to a udl of WkN).
b) Since the girder depth (d) is 1.2 m the approximate force in the top and bottom boom members is 518/1.2 = 432 kN.
c) Using an assumed compressive stress for the top boom, of say 250 N/mm2 the area
required =
432x10 2 ______ = 17.3cm. 250
d) The designer may chose to incorporate the slenderness criteria provided in
Clause 4.10(1). These limitations have not been brought into this design since it is considered that secondary stresses in this "lightly loaded" truss will not be significant. (This is checked in Section 11.0).
Use a 120x80x5.0X 18.4 kg/rn RHS (A = 18.9 cm2) for top boom.
Whilst the bottom boom will be subject to tension and compression (the latter at the
support) select its preliminary size on the basis of a tensile force of 432 kN, at the centre.
For bottom tie area required
= 432 x 10 = 15.7 cm2 275
Use a 120x60x5x 13.3 kg/rn. (A = 16.9 cm2) for bottom boom.
e) Deflection
Requiredl=0.51 x 110x302=5.0X
Considering area of top and bottom booms as 16.9 cm2.
I provided is approximately equal to 2A (d/2)2 = 0.5Ad2.
= 0.5 x 16.9 x 1202 = 12.2 x cm4, which is satisfactory (and indicates that deflection will not be critical).
38 -
(ii) Diagonals
Total load = 276 kN.
Hence shear in end panel = say 138 kN.
The diagonal slopes at an angle approximately tan'(1.2/0.925) = 52.4° and has a length of 1.52 m.
Force in diagonal = 138/sin 52.4 = 175 kN (tension and compression). Hence area of strut = 175 x 10/220 = 8.0cm2.
Use 60x40x5x6.97 kg/rn RHS. (A = 8.88 cm2) for diagonal struts.
Area of tie = 175 x 10/275 = 6.4 cm2.
Use 60x40x4x5.72 kg/rn (A = 7.28 cm2) for diagonal ties.
Ciii) Check Self Weight
Self weight = 30.6 (14.8 + 13.3) + 16 x 1.52 (5.72 + 6.97) = 1169 kg
11.7kN
(compared with the assumed value of 18.4 kN). Hence figure used in the final calculation could be reduced. Say self weight = 13.4 kN (i.e. reduction of 5 kN).
(iv) Final loads, excluding wind
Dead,say =66kN Imposed = 110 kN.
(v) Columns (preliminary sizing)
The columns which have pinned bases are subject to axial load, bending moments and shear. The combination of axial load and bending affects are assessed using the equations given in Clause 4.8 of BS 5950: Part 1. Consequently a simplified approach, based on axial loads and moments, is much more difficult to define. A useful guide to the size of the column is to
consider the second moment of area 'F. The ratio of 'girder: 'column normally lies between 4:1 to 1:1. A further guide is to use the relationship 'c"g = 3h/2L.
Hence 1c = 'g X 3 X 6.7/(2 x 30)
i.e. say = Jg/3.
Since 'g = 12.2 x i04 cm4 then assume Ic = 4 x i0 cm4. A suitable section for the column would be 457 x 191 x 89 UB = 4.1 X i0 cm4).
(vi) Preliminary member sizes
The preliminary member sizing is assumed to be as calculated and the relevant section
properties have been incorporated into the computer analysis.
39
9.7 Loading Cases (for characteristic loads) DEAD (see 9.6.1 (iv))
Dead load on girder = 66.0 kN Load/purlin = 66/16 = 4.13 kN
IMPOSED
Imposed load on girder = 110 kN Load/purlin = 110/16 = 6.87 kN.
WIND CASE I (refer to Figure 25(e)).
Slope area of sheeting = 6 x 15.4 = 92.4 m2.
Load/purlin, left hand slope = 1.1 x 0.582 x 92.4/8 = 7.4 kN (uplift). Load/purlin, right hand slope = 0.6 x 0.582 x 92.4/8 = 4.04 kN (uplift).
Load on left hand column (rail area = 1.5 x 6 = 9 m2), allowance needs to be made for say 300 mm sheeting overhang to top and bottom rails i.e. area supported = 6 x 1.05 = 6.3 m2.
Lower rails = (0.5 x 0.427 x 9)
Upper rails = (0.5 x 0.582 x 9)
Load on right hand column
Lower rails = (0.45 x 0.427 x 9)
Upper rails = (0.45 x 0.582 x 9)
= 1.92 kN (pressure)
= 2.62 kN (pressure).
1.73 kN (suction).
= 2.36 kN (suction).
WIND CASE II (Refer to Figure 25 (fT))
Load/purlin, both sides Lower rails, both columns Upper rails, both columns
= 6.72 kN (uplift) = 2.69 kN (suction) = 3.67 kN (suction)
WIND CASE Ill (refer to Figure 25 (g))
Load/purlin, left hand slope Load/purlin, right hand slope Lower rails, left hand side Upper rails, left hand side Lower rails, right hand side Upper rails, right hand side
9.8 Analyses
= 4.04 kN (uplift) = 0.67 kN (uplift) = 3.84 kN (pressure) = 5.24 kN (pressure) = 0.19 kN (pressure) = 0.26 kN (pressure)
The general frame layout is shown in Figure 31.
For "hand" analysis the sizes of respective members do not effect the calculations of pin-jointed frames.
40
C'1
vi
Fig
ure
31
Gen
eral
layo
ut o
f fra
me
\ (59)
- M
embe
r num
ber
2
28 -
Join
t nu
mbe
r
Pin
ned
base
J 3O
.
For the computer analysis the properties of the following member sizes are used:
Top boom 120x80x5 RHS Bottom boom 120x60x5 RHS Diagonals - struts 60x40x5 RHS
-ties 60x40x4 RHS Columns 457x191x89 UB
For the computer analysis the columns are assumed to have pinned bases and are continuous from base to eaves e.g. joints 2, 3, 4, and 5 are rigid. The joints of the lattice girder are assumed to be pinned including the connections to the columns at joints 5, 6, 39 and 40. The girder acts as a brace to the two pinned columns. The respective tension and compression in the top and bottom booms provide an effective moment at the top of the column providing an analogous pinned portal, as shown in Figure 30. This is Frame Type No. 1. In Section 11
alternative frame analyses are considered.
The positioning of the purlins at node points removes the effect of local bending between joints in the case of the pin-jointed truss. In practice it is possible the number of panels would have been reduced from 8 to say 6. In this case bending would be induced in the rafters. Design could then have been in accordance with Clause 4.10(c) of BS 5950: Part 1, incorporating a BM of WLI6 with the axial forces or using bending moments obtained from the computer analysis.
Typical loading diagrams are shown in Figures 32 and 33. These were used in the respective computer analyses. The results of the analyses are listed in Tables 2-5.
42
In
2.22
kN
Impo
sed
3.fi
kN
15
x 4.
44 k
N
15
x 6.
87 k
N
D
(58)
(5
q)
2.22
kN
(3)
3.44
kN
I—
.1
30. O
m
I
Fig
ure
32
Ver
tical
load
ing
due
to d
ead
and
impo
sed
load
s on
gird
er
It,
U,
In 0
7 x
1.
kN
0.
3.7
,. 2.
02
c'J 0
(56)
c
7 x
4.04
kN
(60)
(6
1)
(62)
(6
5)
(66)
2.02
kN
(61)
30.O
m
1.3S
kN
1.13
kN
2.36
kN
2.05
Ic
N
1.13
kN
0.81
kN
Fig
ure
33 L
oadi
ng o
n co
lum
ns a
nd g
irder
due
to
win
d ca
se 1
I, I
Table 2 Axial forces (kN) and bending moments (kNm) in columns
F M F M F M F M
Notes: —ye BM indicates tension on inside of column face. —ye Force indicates compression. +ve Force indicates tension. Wind Case Ill has not been tabulated - examination of computer print-out indicated that the loads were not significant.
* * Members highlighted by two asterisks are critical members for subsequent design.
45
MEMBER DEAD IMPOSED WIND I WIND II
1 -33.0 0 -55.0 0 +50.4 0 +54.6 0
2 -33.0 28.5 -55.0 47.4 +50.4 -51.6 +56.6 -38.9
3 -33.0 57.0 -55.0 94.9 +50.4 -100.3 +54.6 -81.8
* * -33.0 85.5 -55.0 142.3 + 50.4 -145.6 + 54.6 -129.5
* * -23.8 104.6 -39.5 173.9 +35.6 -173.3 +39.4 -164.3
73 —23.8 104.6 —39.5 173.9 +26.4 -116.0 +39.4 -164.3
74 -33.0 85.5 -55.0 142.3 +37.2 -91.7 +54.6 -129.5
75 -33.0 57.0 -55.0 94.9 + 37.2 -58.2 + 54.6 —81.8
76 -33.0 28.5 -55.0 47.4 + 37.2 -27.8 + 54.6 -38.9
77 -33.0 0 -55.0 0 +37.2 0 +54.6 0
Table 3 Axial forces (kN) in top boom
Truss Members Pin Jointed
MEMBER DEAD IMPOSED WIND I WIND II
6 +64.9 + 107.3 -107.8 -98.7
7 +21.8 +36.2 -37.3 -30.1
8 -14.5 -24.1 +21.6 +27.9
9 -44.3 -73.7 + 68.8 + 75.3
10 -67.6 -112.5 +104.4 +112.2
11 -84.4 -140.4 ÷128.2 +138.5
12 -94.8 -157.7 +140.5 +154.2
* -98.7 -164.1 + 141.1 +154.2
14 -98.7 -164.1 + 135.0 + 159.3
15 -94.8 -157.7 +124.8 +154.2
16 -84.4 -140.4 +108.3 +138.5
17 -76.6 -112.5 +85.3 +112.3
18 -44.3 -73.3 +56.0 +75.5
19 -14.5 -24.1 +20.4 +28.1
20 +21.8 -36.2 -21.7 -29.9
21 * ÷64.9 -107.3 -70.1 -98.4
Notes: —ye BM indicates tension on inside of column face. —ye Force indicates compression. + ye Force indicates tension. Wind Case III has not been tabulated - examination of computer print-out indicated that the loads were not significant.
* * Members highlighted by two asterisks are critical members for subsequent design.
46
Table 4 Axial forces (kN) in internal boom members
Truss Members Pin Jointed
MEMBER DEAD IMPOSED WIND I WIND II
* 22 * *23 *
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44 45
46
47
48
49
50
51
52
53
54
+ 35.6
-38.8
÷ 30.6
-33.3
+ 25.6
-27.9
+ 20.6
-22.4 + 15.6
-16.9 ÷ 10.5
-11.5 +5.5 -6.0 +0.5 -0.5
+ 13.9
-0.5 + 0.5
-6.0 +5.5
-11.5 + 10.5
-16.9
+ 15.6
-22.4 + 20.6
-27.9 + 25.6
-33.3 + 30.6
-38.8 + 35.6
+ 59.3
-64.6
+ 50.9
-55.5
+ 42.6
-46.4 + 34.2
-37.3 + 25.9
-28.2 + 17.5
-19.1
+9.2 -10.0 +0.8 -0.9
+ 23.1
-0.9 + 0.8
-10.0 + 9.2
-19.1
+ 17.5
-28.2
+ 25.9
-37.3 + 34.2
-46.4 + 42.6
-55.5 + 50.9
-65.5 + 59.3
-58.6
+ 63.9
-49.6
+ 54.0
-40.6 + 44.2
-31.6 + 34.4
-22.5 + 24.5
-13.5
+ 14.7
-4.5
+ 4.9
+ 4.6
-5.0 -18.9 +5.6 -5.2
+ 11.0
-10.1
+ 16.4
-15.0 + 21.7
-20.0 + 27.1
-24.9 + 32.5
-29.8 + 37.9
-34.8 + 43.2
-39.7
-56.8
+ 61.8
-48.6 + 52.9
-40.4 +44.0
-32.2
+ 35.1
-24.0 + 26.2
-15.8 + 17.2
-7.6 +8.3
+0.6
-0.6
-20.0 -0.7
+0.6 +8.3 -7.6
+ 17.2
-15.8 + 26.1
-24.0
+ 35.0
-32.2
+44.0 -40.4
+ 52.9
-48.6 + 61.9
-56.8
Notes: —ye BM indicates tension on inside of column face. —ye Force indicates compression. +ve Force indicates tension. Wind Case III has not been tabulated - examination of computer print-out indicated that the loads were not significant.
* * Members highlighted by two asterisks are critical members for subsequent design.
47
Table 5 Axial forces (kN) in bottom boom members
Truss Members Pin Jointed
Notes: —ye BM indicates tension on inside of column face. —ye Force indicates compression. +ve Force indicates tension. Wind Case Ill has not been tabulated - examination of computer print-out indicated that the loads were not significant.
* * Members highlighted by two asterisks are critical members for subsequent design.
48
MEMBER DEAD IMPOSED WIND I WIND II
*55* -106.6 -177.2 +170.8 +175.2
* 56 * 60.6 -100.8 +95.2 + 101.9
57 -21.1 -35.1 +31.1 +39.2
58 +12.0 +19.9 -21.2 -13.0
59 +38.5 +64.0 -62.0 -54.5
60 +58.6 +97.4 -91.0 -85.5
61 +72.2 +120.0 -108.5 -105.9
*62* +79.3 +131.8 -114.2 -115.7
* 63 * + 79.3 + 132.9 -108.4 -115.0
* 64 * +79.9 + 132.9 -108.4 -115.0
*65* +79.3 +131.9 -101.7 -115.7
66 +72.2 +120.0 -88.7 -106.0
67 +58.6 +97.4 -69.3 -85.6
68 +38.5 +64.0 -43.6 -54.7
69 +12.0 +19.9 -11.4 -13.1
70 -21.1 -35.1 +27.1 +39.0
71 -60.6 -100.8 +71.9 +101.6
72 106.6 -177.2 +123.2 +174.9
10. FINAL DESIGN
Use Grade 43C steel throughout.
10.1 Top boom
From the tabulation of forces it is noted that members 6 and 13 are the most heavily loaded elements.
Maximum axial loads (to 3 significant figures) (Table 3)
Member 6 Member 13
Dead 65 kN (T) 99 kN (C) Imposed 107 kN (T) 164 kN (C) Wind 108 kN (C) 159 kN (T)
Maximum compression due to dead and imposed loads (member 13).
F = (1.4x99)+(1.6x164)=4OlkN(C)
Maximum tension due to dead and Imposed loads (which is significantly greater than the compression due to dead and wind), (member 6).
FT = (1.4 x 65) + (1.6 x 107) = 263 kN (T)
Effective length (BS 5950: Part 1, Clause 4.10(e)) = 1.85 m
Referring to the preliminary design it is appropriate to try a 120 x 80 x 5 RHS
D = 120 mm B = 80 mm t = 5.0 mm A = 18.9 cm2 r = 4.43 cm ry = 3.21 cm
Design strength (Table 6, Reference 1), p, 275 N/mm2 since t < 16.0 mm.
Design as a Compression Member in accordance with Clause 4.7 (Reference 1).
Section classification (Clause 3.5)
= = 1 (Table 7, Reference 1) py
From Figure 3 (Reference 1)
The possible effect of secondary stresses in the section can be reduced by placing the 80 mm side in the vertical plane, as shown in Figure 34.
Hence x,' 0.85 185 = 40 < 180 < 50
(Clauses 4.7.3.2
and 4.10 of Reference 1).
=J8! =42<180 4.43
49
This is also a better way for the section when considering connections to the internal bracing members and purlin support cleats.
b 120-3x5 b = B — 3t therefore — = __________ = 21.0 t 5
d = D — 3t therefore d = 80 — 3 x = 13.0 r 5
Hence from Table 7 (Reference 1)
< . < 39 section is NOT SLENDER t t
i.e. section capacity will not be reduced by local buckling (Clause 3.6, Reference 1).
120
— -
fxs 80
Figure 34 Section through top boom
Compressive strength
= AgPc where, according to Table 25 (Reference l) is obtained from Table 27(a).
For p, = 275 N/mm2 and X = 49 (say)
= 252 N/mm2 (Note this is an 8% reduction).
Hence = 18.9 x 252 = 476 kN > 401 kN 10
SECTION IS SATISFACTORY IN COMPRESSION.
Check for tension Clause 4.6.1
Tension capacity P = A Py
Since Ae = A then
= 18.9 x 275 = 520 > 263 kN 10
SECTION IS SATISFACTORY IN TENSION AND IN FACT THIS SHOULD BE OBVIOUS SINCE p, > p and F> F1.
50
As an alternative to the above detailed calculation use the SC! publication "Steelwork Design Guide to BS 5950 Vol. 1, Section properties member capacities
For a 120x80x5 RI-IS this shows P, 446 kN when Le' 2.0 i.e. > 1.85 m and P = 520 k/V.
lop boom use 120 x 80 x5 RHS, 80 mm size vertical (the reader should check to determine whether a lighter section would be satisfactory).
10.2 Bottom boom
Examination of the force analysis tables and considering member, and therefore effective lengths, it is clear that there are several members in the bottom boom which need to be considered.
(a) Members 62 and 63
Maximum axial loads (Table 5):
Member Member 63 62
Dead 80 kN (T) 80 kN (T) Imposed 132 kN (T) 133 kN (T) Wind (Case II) ll6kN(C) 115 kN (C)
Maximum tension due to dead plus imposed loads
FT = (1.4 x 80) + (1.6 x 133) = 325 kN (1').
Compression effects are low in comparison with members adjacent to the column.
(b) Members 55 and 56
Maximum axial loads
Member 55 Member 56
Dead 107 kN (C) 61 kN (C) Imposed 177 kN (C) 101 kN (C) Wind (Case II) 175 kN (T) 102 kN (I)
Maximum compression in member 55
= (1.4 x 107) + (1.6 x 177) = 433 kN.
Maximum compression in member 56
= (1.4 x 61) + (1.6 x 101) = 247 kN
From the above the controlling load is 433 kN (C) in member 55. Since the maximum tensile load in the boom (325 kN) is smaller than the maximum compressive load (433 kN) the bottom boom has only to be designed for compression.
51
Try the assumed size of 120 x60x5 RHS.
D = 120 mm B = 60 mm t = 5.0 mm A = 16.9 cm2 r = 4.24 cm ry = 2.43 cm.
Provide a purlin brace from joint 8 as shown in Figure 12.
Also place 60 mm side vertically.
Check section classification
b = 120—(3x5) = 21 d = 45 = - 5 t 5
then < . < 2&, hence section is plastic (Table 7, Reference 1).
Hence r' = r = 2.43 cm
r' = r = 4.24 cm
Lex1 = 92.5 cm Ley' 185 cm
= . x 0.85 = 33 < 50 2.43
= --- = 44 4.24
Hence p = 257 N/mm2 (Table 27a, Reference 1).
= 257 x 16.9 = 434 kN > 433 kN. 10
Hence section is satisfactory.
The purlin brace, at an angle of 45° would be approximately 1.2 = 1.7 m long. Load in the brace is 2½% of load in the boom (Clause 4.3.2') i.e. 43.3kN. Assuming an effective
length of 1.7 m a suitable brace would he a 40x40x3 RHS (Reference 19).
Use of sheeting brace. Occasionally it may he advantageous to brace node 7 of the bottom boom to the sheeting rail. In that case Ley'
= 92.5 cm. The reader should check the effect
of the bracing.
Bottom boom use 120 x60x5 RHS (60 side vertical), braced to nurlin at node 8 using 40x40x3 RHS.
52
10.3 Internal members
Diagonal bracing - Members 22 and 23
Note - Member 22 is a tie and Member 23 is a strut.
Maximum axial loads (Table 4):
Tie (22) Strut (23)
Dead 36 kN (T) 39 kN (C) Imposed 59 kN (T) 65 kN (C) Wind 59 kN (C) 64 kN (1)
10.3.1 Tie design (22)
Maximum tension due to dead + imposed load
= (1.4x36)+(1.6x59)
= 145kN(T)
Maximum compression due to dead plus wind
(1.0x36)-(1.4x59)=47kN(C).
Member length = 1.59 m
Selecting member size for tensile force, hence area required =
145 x 10 = 5.3 cm2. 275
Try6Ox4Ox3RHS
A = 5.60 cm2 = 1.59 cm
Check for compressive strength.
Xy = x 0.85 = 81 (See Reference 1, Clause 4.10 allow for some end fixity).
p = 201 N/mm2 (Table 27a of Reference 1)
= 201 x 5.6 = 113 kN > 45 kN C 10
Diagonal ties 60x40x3 RHS
53
10.3.2 Strut design (23)
Maximum compression due to dead + imposed load
= (1.4 x 39) + (1.6 x 65) = 159 kN (C).
Maximum tension due to dead + wind
= -(1.0 x 39) + (1.4 x 65) = 52 kN (T)
Clearly compression design will control.
Try 80 x 40 x 5 RHS
A = 10.9 cm2 r = 1.55 cm
X. =ix0.85=84 1.55
= 194 N/mm2 (Table 27a Reference 4)
= 194 xlO.9 = 211 kN > 159kN
Diagonal struts 80 x 40 X S RHS
10.4 Comparison of member sizes
It is perhaps useful to compare the assumed sizes of the girder members used in the analysis and the calculated values of the RHS sections.
Member Assumed section Designed section
Top boom 120x80x5 120x80x5
Bottom boom 120x60x5 120x60x5
Diagonals:
Struts 60x40x5 80x40X5
Ties 60x40x4 60x40x3
i.e. The basis for assumed section sizes is basically justified. Note: Using the top and bottom boom with the 120 mm horizontal side is convenient for welding the diagonal strut.
The reader could easily check the possibility of using a 90x50x3.6 RHS (Reference 19) which is lighter and which could be a suitable member.
In Section 9.6.2 (e) it was stated that deflection would not be critical. From the computer analysis the maximum deflections in the girder occurs at joint 23.
Dead load deflection = 35.3 mm
Imposed load deflection = 58.8 mm
Ratio of imposed load deflection/span = 58.8/30000 = 1/5 10, which is satisfactory.
54
10.5 Column design - members 1 to 4 and 5
Axial loads and moments (Refer to Table 2)
Member 1 to 4
Maximum axial loads Maximum BM
Dead 33 kN (C) 86 kNm Imposed 55 kN (C) 142 kNm Wind 1 50 kN (C) -146 kNm Wind 2 55 kN (1') -129 kNm
Design load: dead + imposed
= (1.4 x 33) + (1.6 x 55) = 134 kN (C)
Dead BM: dead + imposed
= (1.4 X 86) + (1.6 x 142) = 348 kNm
Design load: dead + wind I
= (1.0 x 33) - (1.4 x 50) = 37 kN (T)
Design BM: dead + wind I
= (1.0 x 86) -(146 x 1.4) = 118 kN.m.
Hence worst effect in column is due to dead and imposed load effects.
Selection of the effective length for the column provides an interesting problem. About the XX axis member 1 to 5 is restrained in position at the base but not in direction. At the top it is partially restrained in position and direction. This condition does not relate to any of the standard cases in Table 24 or Appendix D of BS 5950: Part 1. Reference to the computer frame analysis provides the horizontal and rotational movements. The figures for the separate dead and wind load conditions indicate points of contraflexure in the column occur between
joints 3 and 4. Assume contraflexure occurs at joint 4 which is 4 m above the base. Then the corresponding effective length of an analogous pin-ended strut would be 8 m. As a ratio of the member length, this provides an effective length factor of 8/5.5 = 1.45. Figure 17 of BS 5950: Part 1 indicates Lex = 1 .5L for a fixed base. However, the connection effect of the latticed girder is clearly stiffer than that provided by the roof connection shown, but the (partial) fixity provided at the base is not the same as that used in Figure 19 of BS 5950: Part 1.
The above discussion indicates the careful consideration which must be given to the selection of an appropriate effective length factor. When in doubt it is essential to use a conservative value i.e. in this case 2.OL = 2.0 x 5.5 = 11 m.
About the YY axis the base is restrained in position and direction and the head of the column is restrained in position, but not direction (by the eaves rafter and first rafter purlin). Hence as in Figure 17, (Reference 1) assume Ley
= 0.85L = 0.85 x 6.7 = 5.7 m.
Lex = 11 m, Ley = 5.7 m.
55
In selecting a column size a useful starting point is item (v) of Section 9.6.2 i.e. try the 457x191x89 UB.
D = 463.6 mm B = 192.0 mm t = 10.6 mm T = 17.7 mm d = 407.9 mm
bIT = 5.42 dIr = 38.5
41000 cm4 r = 19.0 cm r = 4.28 cm = 1770 cm3 S, = 2010 cm3
A =114cm2 x =28.3
Since 40 > T> 16 mm then = 265 N/mm2 (Table 6(1))
Hence:
= s/275/265 = 1.02
Section Classification (Table 7 and Clause 3.5.4W).
Examine the "outstand of the compression flange" and "web generally".
For the flange bIT = 5.42 < 8.5E, hence flange is plastic. The web is in combined axial and flexural compression (Figure 35). Determine the position of the neutral axis and check footnote to Table 7(1)
192.0
Figure 35 Stress diagram
Check section classification for "web generally".
Length of web subjected to direct axial load = '< 47.7 mm
From Figure 35 the plastic neutral axis is (47.7/2) = 23.85 say = 23.9 mm from the XX axis.
The footnote to Table 7(1) indicates that a = d
In this case y = (463.6/2) + 23.9 = 256 mm
a = 2 x 256/407.9 = 1.26
56
'—I cv,I
(0 (V) (0 1
t*17.7 yc
— - 3.854 x—
79 = 79 x 1.02 = 70 > = 38.5 0.4 + 0.6a 0.4 + (0.6 x 1.26) t
Hence web and flange are plastic. Two checks are required for the design: Local capacity and overall buckling.
(a) Local capacity (Clause 4.8.3.1')
F M M __ +__ +_L�i AgPy M M
NowM = 0
For plastic section
= S,p = 2010 x 265 x i0 532.7 kNm or l.2p,,i' = 1.2 x 1770 x 265 x i0 = 562.9 kNm
Hence 134 x 10 + 348 = 0.044 + 0.653 = 0.697 < 1.0 114 x 265 532.7
Section satisfies local capacity check.
If use is made of the relationship:
M M +
Mrx M thenZ1 = 2.0 = 1.0 and M = 0.
i.e.
M2 __f_ �i M
Now Mrx = Srx Jy
where S, = K! — K2 (n)2 (Reference 19).
n = F/A .p, = 134 x 10/(1 14 x 265) = 0.044
K1 = 201f K2 = 3070
Srx = 2010 - 3070 x ØØ442 = 2004 cm3.
Mrx = 2004 x 265/1000 = 531 kNm.
M2 = =0.43
531
This provides a much more conservative answer than 0.697 obtained above.
57
(b) Overall buckling (Clause 4.8.3.3.1")
F mM mM ____ + + _2 � 1
AgPc Mb
Compressive strength, p >x
= Lex/rx = 1100/19.0 = 58 =
Lc,/r,, = 570/4.28 = 133
From Tables 25, 27a and 27b Reference 1, i' = 234 or 90 N/mm2.
Usep = 90 N/mm2
Buckling resistance moment Mb. Use the conservative approach (Clause 4•37•7(1))•
From Table 10 (Reference 1) on the basis that the base is restrained laterally and torsionally and the top of the column has a lateral restraint to the "tension flange", assume:
Le = 0.7L and m = 1.0
Take n = 0.94 (Table 20w).
X = 0.7 x 550 x 0.94/4.28 = 85
Whenx = 28.3 and X = 85
= 184 N/mm2 (Table l9a')
Mb = S,(p = 2010 x 184/1000 = 370 kNm.
The interaction expression
134 x 10 — l.Ox34.8 = 0.131 + 0.941 > 1.0
Therefore, lower section of column is not satisfactory if the simplified approach is used.
There are four options:
(i) use full calculation to obtain Mb (see Clause 4.3.7 Reference 1)
(ii) increase size of column
(iii) provide a restraint to the compression flange from the sheeting rail, say at joint 4.
(iv) use the more exact approach (Clause 4.8.3.3.2(1)) i.e. check the interaction equation
58
mM —�1 M
where M is taken as the lesser of:
Pcx
or Mb (1 — F/P) 0.5F 1+
Pcx
= 265 x 2010/1000 = 533 kNm (Clause 4.25').
F = 134 kN P = Ag = 114 x 234/10 = 2668 kN
Mb = 370 kNm = Agp 114 x 90/10 = 1026kN.
Hence
M = 533 x — (134/2668)] = 494 kNm
[1+(0.5 x 134/2668)]
or
= 370 (1 — (134/1026)) = 322 kNm
Hence M = 322 kNm.
To obtain 'm' use Table 18 of Reference 1 = 0, since the moment at the base of the column is zero. Hence m = 0.57.
Therefore
?nM = 0.57 x 348 = 0.62 < 1
322
The more exact approach appears to indicate that the column can adequately support the applied load and bending moment. However the footnote to Clause 4.8.3.3.2 states "In cases where M or M approaches zero the more exact approach may be more conservative than the simplified approach. In such situations the values using the simplified approach y (should?) be used". Clause 4.8.3.3.2 probably should only be used for bi-axial conditions. In this solution provide a column/rail restraint.
Check member 5.
Maximum effects due to dead and imposed loads (Table 2)
Axial load = (1.4 x 24) + (1.6 x 40) = 98 kN
Bending moment = (1.4 x 105) + (1.6 x 174) = 425 kNm
59
Checking local capacity.
98 x 10 + 425 = 0.032 + 0.8 = 0.832 < 1.0. 114 x 265 532.7
A check is also made on the overall buckling capacity of member 1-5, using the more exact method.
= 533 kNm F = 98 kN M = 425 kNm = 2668 kN i.e. using the value determined for the column section 1-4.
Mb is evaluated for X over the full height of column. i.e. X = 0.7 x 670 x 0.94/4.28 = 103.
Hencep = 154 N/mm2 (Table 19a' for x = 30).
Mb = 2010 x 154/1000 = 310 kNm.
is evaluated for = 0.85 L/r (Table 24'). i.e. = 0.85 x 670/4.28 = 133.
Hence p = 90N/mm2 (Table 27b').
= 90 x 114/10 = 1026 kN (Note it is coincidental that this is the same value as that evaluated for the column length 1-4).
Hence M = 533 x (1—(98.2668)) = 504 kNm. (1 + (0.5 x 98/2668)
or = 310 (1 - (98/1026)) = 280 kNm.
Hence M = 280 kNm.
mM 087 x 425 Therefore ____ . 0.87 < 1.
M 280
Hence overall buckling of column length 1-5 is satisfied.
Check horizontal deflection
Deflection at Deflection at Joint 4 Joint 39
mm mm
Dead -5.0 +1.5 Imposed -8.2 +2.5 Wind 1 +11.9 +3.5 Wind 2 +7.3 +3.4
Maximum deflection at joint 4, due to dead and imposed loads
= 5.0 + 8.2 = 13.2 mm 13.2/4000
= 1/303
60
Maximum deflection at eaves
= 1.5 + 2.5 + 3.5 = 7.5 mm
= 7.5/6700 = 1/893
BS 5950: Part 1 does not provide guidance for portal frame, however Table 8.1 in Reference 20 specifies a limiting deflection of height/100 at the eaves, which is satisfied.
The selected section satisfies all design criteria. The interaction equations, for local and overall buckling, clearly show the main design criteria are bending effects. This justifies the use of a universal beam section.
Use 457x 191 x89 UB for column.
10.6 Gable steelwork
There are a number of alternative methods of design of the gable steelwork.
Gable columns can be considered as pinned or fixed at the base. Normally they will be designed as pinned at the top being supported in this position by the gable rafter and/or "wallbracing" and purlins and/or roof bracing. Consequently gable columns are designed as propped cantilevers or simply supported beams. Figure 18 shows typical roof bracing arrangements. It should be noted that the props at the head of propped cantilever gable columns are not fully rigid. The wall and roof bracing can be single diagonal members or cross diagonals. In the former the members need to be designed to transmit direct tension and compression (normally due to wind loads). With cross bracing the members in compression are ignored, the members in tension are assumed to transmit all of the load (to the foundations in the case of wall bracing and into the roof in the case of roof bracing). In the following design single bracing is used. Purlins need to be checked for the additional axial load since they are providing the propping reaction.
10.6.1 Gable rafters
These are simply supported on a span of 7.5 m between stanchions. They are held in place and loaded by the purlins at 1.875 m c/c (Figure 36). The loads will be dead, imposed and wind (uplift) loads on the roof together with some end sheeting vertical load.
W/2 W W W/2
4 x 1.875 = 7.5 m
Figure 36 Gable rafter loading
61
Loading (see Section 9.7) Load/purlin
Dead 4.13/2 = 2.07 kN
Imposed 6.87/2 = 3.44 kN
Wind (Uplift) 7.4/2 = 3.70 kN
Vertical Sheeting, say 0.2 x 1.88 x 1.5/2 = 0.3 kN
Maximum downward load (W) = 1.4 (2.07 + 0.3) + 1.6 (3.44) = 8.8kN
Hence reaction = 8.8 x 2 = 17.6 kN
Maximum uplift = 1.0 (2.37) - 1.4 (3.7) = -2.8kN.
Maximum bending moment at C due to 'W' 1.5W x 3.76 - W X 1.88 = 3.76W.
Max. BM = 3.76 x 8.8 = 33.1 kNm.
Allowing for self weight, design say for 34 kNm.
The rafter should be designed as a laterally restrained beam, clearly with low shear.
(Clause 4.2.5').
Try 203x102x23 UB
= 5.46 = 32.6 T = 9.3 mm t t
r = 2.37 cm S, = 232 cm3 x = 22.6 = 206 cm3
= 2090 cm4 p, = 275 N/mm2 From Table 7 (Reference 1) section is plastic.
Moment capacity M = S p, 232 x 275 x i0 = 63.8 kNm < 1.2 Z > 34kNm
Buckling resistance, using the conservative approach (Clause 4.3.7.lW).
Mb=pbSX m=1.0
As an approximation assume n = 1.0
X = Leiry 188/2.37 = 79
"Rounding up" to assume X = 80, x = 25 then Pb = 201 N/mm2 (Table l9bW).
Mb = 201 x 232 x i0 = 47 kNm > 34 kNm
Note: Reference 19 indicated that Pb 46 kNm for n = 1.0 and Le = 2m. This is
satisfactory.
62
The reference also states section is "plastic".
Clearly wind uplift will not create a critical situation.
Deflection check.
Assume total imposed load of 6.88 kN acts as a central point load then central deflection is wi. 3/48E1.
= 6.88 x 753 X i05 = 14.1 mm C 48x205x2090
This provides a deflection/span ratio of 14.1/7500 = 1/532. Hence showing that deflection is not significant, even when the loads are considered as a single central point load.
Use 203 x 102 x23 UB for gable rafter.
10.6.2 Gable columns
These support the gable rafters, which induce vertical load, and gable rails which transmit the wind load, as shown in Figure 37.
Assume gable columns are tixed at the base and pinned at the top therefore consider as a
propped cantilever. The central column is say 8 m high.
Sheeting Load from load gable rafters
______ Roof bracing acts as prop
Assume uniform wind load 8 m
I//I Figure 37 Loads on gable columns
Dead plus imposed load reactions = 2 x 17.6 = 35.2 kN.
Sheeting self weight (Section 9.4.3) = 0.2 kN/m2.
Rail weight = 0.2 kN/m (5 No. at 7.5 m long).
Total weight from sheeting and rails = (0.2 x 7.5 x 8) + (0.2 X 5 X 7.5) = 19.5 kN.
Design vertical load = 35.2 + (1.4 x 19.5) = 62.5 kN say 65 kN, allowing for self weight.
63
Wind load (Section 9.3) and Table 1.
On end = (Cpe
— C) = 1.0.
As a conservative design assume wind load over the full height of the gable is 0.582 kN/m2.
Total design load from wind = 1.4 x 1.0 x 0.582 x 8 x 7.5 = 49 kN.
Maximum bending moment in a propped cantilever occurs at the base and equals WL/8.
Max. BM due to wind = 49 x 8/8 = 49 kNm.
Ignoring wind uplift, design the gable column for vertical load of 65 kN and BM of 49 kNm. It will be noted that bending is the controlling applied action.
The reaction at the pinned end of a propped cantilever is:
W=x49 = 18.4kN 8 8
This will be the load transmitted to the wind (root) bracing.
In considering buckling effects:
For axial load design the slenderness should be limited to 180 (Clause 4.7.3.2')
Lex 0.85L = 0.85 x 8 = 6.8 m (propped cantilever Table 24(1))
Ley = 0.85 x 8 = 6.8 m (Appendix D').
For lateral torsional buckling design, the effective length is again problematical. Consider the deflected shape for a propped cantilever subject to a uniformly distributed load. Zero slope occurs at a point 0.42 15 L from the free end i.e. column head. Allowing for some movement of the prop it is appropriate to suggest Le = 2 x (0.5L) = 1 .OL. Hence LE = L = 1.0 x 8 = 8 m (Table 9(1))
In designing for buckling use is made of Table 19 and Clause 43•77(1)
To initially assume a section size either use Reference 19 (Axial Load and Bending Tables) or assume a value for Pb For low loads and moments with L = 8 m the use of Reference 19 is not applicable. Hence assume a value for Pb = 150 N/mm2.
Then S = M/p = 49 x 10/150 327 cm3
Also if X < 180 then r < 680/180 = 3.78 cm.
Try 305 x 165 x 40 UB.
D = 303.8mm B = 165.1 mm t = 6.1mm T = 10.2mm bIT = 8.09 d/t = 43.6
= 8520 cm4 r = 12.9 cm = 3.85 cm = 561 cm3 3 S, = 624 cm x = 31.1 A = 51.5 cm
Note: dit = 43.6 > 39€ (Table 7(1))
64
However the latter is used for webs subject to compression throughout. Whilst this is the situation when considering dead plus imposed loads it does not apply when the bending due to wind effects are present. As will be seen the axial effects on the column are small and therefore a reduced value of p (Clause 3.6(1)) has not been considered.
Since T < 16 mm then p = 275 N/mm2.
Using the approach outlined in Section 10.5 it will be deduced that the section classification is
plastic. çFable 7(1))
Local capacity check (Clause 4.8.3.1(1)). Whilst it is suggested the relationship:
M M + __2. should be checked for plastic sections, use is made of:
M,.),
F M M AgPy
+ M
+
being a simplified (conservative) approach in this case.
= 0
= = 624 x 275 x 1O = 172 kNm (Check Reference 19)
F + M 65x10 + AgPy M 51.5 x 275 172
= 0.041 + 0.285 = 0.326 < 1
Section satisfies local capacity
Overall buckling check (Clause 4.8.3.3.1(1)).
Compressive strength, p > = 680/12.9 = 53 k, = 680/3.85 = 177 < 180
From Tables 25, 27a and 27b (Reference 1)
p = 55 N/mm2.
Buckling resistance moment Mb
X = 800/3.85 = 208.
From Table 19(1) Pb = 75 N/mm2 (say).
Mb=SJb=624 x75 x 103=46.8kNm <M=49kNm.
Hence buckling is not satisfied using the simplified approach.
65
The critical condition has been induced by the high slenderness value, when considering buckling. The option used in this case is to examine the exact approach Clause 4.8.3.3.2(1).
mM i.e. � 1
M where M is the maximum buckling moment about the major axis in the presence of axial load and is taken as the lesser of:
________ F or Mb 1 - - 0.5F 1+—_ Pcx
In this case the moment at the top of the column is zero hence = 0 (Table 18(1)), therefore m = 0.57, M = 172 kNm.
For X = 53 then = 248 N/mm2 (Table 27a').
= 248 x 51.5 = 1278kN. 10
For = 177 then p, 55 N/mm2 (as before)
= 55 x 51.5 = 283 kN. 10
1- 65 1278
= 172 _______________ = 159 kNm
0.5F 10.5x65 1+__c_
1278
Mb 1 - -L 46.8 1 - = 36.1 kNm 283
Hence take M = 36.1 kNm.
mM = 0.57 x 46.8 = M 36.1
i.e. section is satisfactory.
The significant difference between the simplified and exact analysis is due to the reduction in the applied design bending moment i.e. the effect of 'm'.
Use 305x 165 x40 UB for gable columns.
66
10.7 Bracing
10.7.1 Roof bracing (at both ends of building)
Figure 38 Use of cross bracing
The wind load at the top of the central column = 18.4 kN. At the top of the intermediate columns = 18.4 x 7.35/8 = 16.9 kN. (i.e. in proportion to column height).
At the top of the corner columns = 18.4 x 6.71(8 x 2) = 7.7 kN.
If cross bracing, Figure 38, is used the members in tension are assumed to carry all of the load; compression members need only satisfy the slenderness criteria (Clause 4.7.3.2(1)). i.e. � 350 where member length is 9.6 m. For ease of construction single bracing is used, Figure 39.
33.8 33.8 kN
1 /N ¶ ¶ I I
16.9 18.4 16.9 7.7 kN
Figure 39 Use of single or tension bracing
Maximum tension occurs in member (a) = (33.8 — 7.7) x 9.6/6 = 42 kN.
Since single bracing is used the member will be designed for compression forces, noting the load will be smaller since it is only necessary to design for suction pressure coefficients
(Cpe —
Cr1) = (—0.6 — (+ 0.2)) —0.8 (see Section 9.3), instead of 1.0.
33.8 33.8 kN
1'
7.7 16.9 18.4 16.9 7.7 kN
6m1
1 I, 4x7.5m
67
Design load = 0.8 x 42 = 34 kN and slenderness criteria = 250 (Clause 4.7.3.2').
Using circular hollow section, required area of section = 34 x 10/275 = 1 .24 cm2.
Required radius of gyration � 960/250 3.84 cm.
Try 114.3 x 5 CHS A = 17.2 cm2 r = 3.87 cm I = 257 cm4 S = 59.8 cm3 Dit = 114.3/5 23 < 40 (Table 7(1)) hence section is plastic.
Need to satisfy P = Ag P
X = 960/3.87 = 248 < 250.
1 '1' Hencep = 31 N/mm (Tables 25, 27a' ').
P = 17.2 x 31/10 = 53 kN > 34 kN.
Note a check needs to be made on the self weight deflection (Clause 4.7.3.2(1)).
Self weight deflection = 5WL31384E1 = 5 x 0.135 x 9.6 x 10/(384 x 205 x 257) = 28.3 mm.
Since this is greater than L/1000 = 9.6 mm the effect of bending must be considered.
(Clause 4.8.3).
Self weight bending moment = = 0.135 x 9.62/8 = 1.6 kNm.
MCX = p S (Clause 4.2.5) = 275 x 59.8/10 = 16.5 kNm.
In the interaction equation
F + M 34 x 10 + = 0.07 + 0.1
AgPy M 17.2 x 275 16.5
= 0.17 < 1
i.e. local capacity is satisfied
Check overall buckling.
Buckling resistance Mb = = 16.5 kNm.
In the interaction equation
F mM 34 16 __ + X+....064+010074<1 AgPy Mb 53 16.5
Hence bending criteria is satisfied.
68
The disadvantage of having to use a larger member for the single bracing system (as compared to smaller members for cross bracing) is outweighed by the savings in connections and erection costs.
Use 114.3 x5 CHS for roof bracing in plane of top chord.
Check also the end purlin for the effect of transmitting axial load (gable column reaction) of 18.4 kN.
From Section 9.4.1 it is noted the proposed 202x65x60x1.8 mm thick Z purlin will support a factored load of 1.29 kN/m2. The applied total factored load is 1.27 kN/m2. Hence there is little reserve for the axial load effect.
It would be necessary to check with the manufacturer on the effect of axial load plus bending, since their literature does not normally consider combined loading. It is also noted that generally the load tables listed by manufacturers for their cold rolled sections were obtained by testing. A possibility will be to use a thicker section for the end bays only.
10.7.2 Gable bracing (at both ends of the building)
6.7 m
Member (a) is 10.lm long (Figure 40) and has to resist a wind load say,
F = [Yj (Cpe
- C ) q A/2J where (C — Cr1)
= 1.0, q = 0.582 kN/m2 (see Section 10.6.2) andA = 3 x 6.1= 20.1 m2.
F = (1.4 x 1.0 x 0.582 x 20.1)/2 = 8.2 kN
Force in member (a) 8.2 x 10.1/7.5 = 11.1 kN.
Radius of gyration 1010/250 = 4.04 cm
Use 139.7 x5 CHS for gable brace (Reference 19)
10.7.3 Longitudinal side wall bracing (at both ends of the building) Member (b) is 9 m long (Figure 41). The wind force at the eaves level is 33.8 kN (Figure 39) Hence force in (b) = 9/6 x 33.8 = 50.7 kN.
Radius of gyration 900/250 = 3.6 cm.
Use 114.3 x5 CHS (Reference 19).
69
Figure 40 Gable bracing
7.5m
Figure 41 Longitudinal side wall bracing
10.8 Column Base (Reference 1. Clause 4.13)
The basic assumption in the frame analysis was that the connection at the column base would be pinned. The connection has to be capable of transmitting axial compression, shear and
uplift as shown in Figure 42.
Axial compressive force
F = 135 kN Axial tensile force (uplift) F = 44 kN Shear F = 80 kN
457 x 191 x 89 UB
t = 20mm
bleed holes
Concrete grade 20
Length of holding down bolts will depend on type used
o e.g. expansion bolt or bolt set in clearance holes which are grouted (using mortar or epoxy)
Bolt edge distance is satisfied (Cl. 6.2)
Figure 42 Baseplate details
A simple slab baseplate will be used, welded to the column.
To comply with current safety requirements it is necessary to provide four bolts to ensure
stability of the columns during erection. These 4 bolts can be positioned closely together, as shown in Figure 42. Keeping the bolts close to the axis of the column will ensure that any moment restraint effect will be kept to a minimum.
70
6.7 m
71111/ 7i,i1/i YiJ/ k 6m 6m
— I 'I —I
8
/
a /
Loading (Fable 2) Unfactored loads (kN)
Maximum vertical dead load = 33
Minimum vertical imposed load = 55
Maximum wind uplift = 55
Shear in conjunction with the loads (computer analysis)
Dead =19
Imposed = 32
Wind, with max uplift = 26
Vertical design loads
Due to dead + imposed = (1.4 x 33) + (1.6 x 55) = 135
Due to dead + wind = (1.0 x 33) - (1.4 x 55) = -44 uplift
Shear design loads due to dead and imposed = (1.4 x 19) + (1.6 x 33) = 80
Shear design loads due to dead and wind = (1.4 x 19) + (1.4 x 26) = 63
10.8.1 Baseplate
Only the design of the main frame baseplate and plate are detailed within this text. These being designed to resist vertical load and shear only.
For the gable post bases reference should be made to Reference 21, Steelwork Design Guide to BS 5950: Part I . 1990 Volume 2 "Worked Examples". This details the baseplate design for shear, vertical load and moment.
Assume concrete to base to have a 28 day cube crushing strength (f) of 20 N/mm2. Use an allowable bearing stress of 0.4f. = 270 N/mm2 (Clause 4.13.2.2(1)).
135x Hence area required = __________ 0.4 x 20
Minimum size = 16,875 mm2
This is impracticable for the size of column. Try a baseplate 600 x 400 mm, area 240,000 mm2.
Hence actual baseplate pressure = 135 X 10 = 0.57 N/mm2 600 x 400
71
Due to a concentric force the minimum baseplate thickness (Clause 4.l3.2.2W)
t = . w (a — 0.3b2) pyp
In this case a = (400 - 192)/2 = 104 b = (600 - 463.6)12 = 68 mm
t = x 0.57(1042 — 0.3 x 682)]
= 7.1mm
This is again impracticable. Match the base plate, approximately to the flange thickness
(T = 17.7 mm) i.e. use 20 mm base plate. (Clause 4.13.2.2').
Baseplate 600x400x2Omm.
10.8.2 Holding down bolts
These bolts (4 No.) are to be designed to resist the tension due to uplift and accompanying shear (Clause 6.3.6.3) and positioned to satisfy Table 3l'. Assume bolts are M20 where tensile stress area = 245 mm2, Grade 4.6.
Shear capacity (Clause 6.3.2).
=
= 160 N/mm2 (Table 32W).
(Reference 19, Bolt Capacities).
= 4 x 160 x 245 x i0 = 157 kN.
Tensile capacity (Clause 6.3.6)
= pA1 = 4 x 195 x 245 x i0 = 197 kN.
Combined shear and tension (Clause 6.3.6.3).
F F + — � 1.4
PS P1
+ = 0.63 < 1.4 157 197
Hence use 4 No. M20 Grade 4.6 holding down bolts.
72
10.8.2 Welds (Reference 1, Clause 6.6) It is likely that a fillet weld would be provided around the full perimeter of the UB to avoid the formation of corrosion pockets between the column and base plate. Weld strength = 215 N/mm2 (Table 36'). It is suggested that for practical purposes the weld should be at least 6 mm leg length.
Total perimeter is approximately (2 xd) + (4 x 7) = (2 x407.9) + (4 X 192) = 1584 mm.
The shear capacity of say a 6 mm fillet weld is 0.7 x 6 x 215 x i0 = 0.903 kN/mm. (See Reference 19).
Hence shear strength of weld
= 0.903 x 1584 = 1430 kN
which is far in excess of any forces to be transmitted.
Generally it is recommended, web weld 0.5t and flange weld 0.5T.
However, it should be noted the cross-sectional area (and therefore relevant cost) of welds is proportional to the square of the leg length.
Hence use 6 mm f.w. for web and 8mm f.w. for flange.
10.9 Foundation
The foundation has to be capable of transmitting the vertical and horizontal loads to the supporting soil and to resist uplift (Figure 43).
Maximum vertical load = 135 kN and uplift = 44 kN (both factored)
135 kN
52 kN
450 55O 900
Figure 43 Mass concrete foundation
73
1500 7/ 1500
To prevent uplift isolated foundation pad needs to weigh at least 44 kN. Using a concrete
weight of 24 kN/m2 then volume of concrete = 1.84 m3. A base 0.9 m thick and 1.5 m
square will be adequate.
This size needs checking against magnitude and distribution of ground pressure under
serviceability load conditions.
Vertical service load = (33 + 55 + self weight) = 137 kN Horizontal service load = 52 kN
Taking moments about a bottom corner of the foundation, position of resultant vertical load is at (137 x 0.75 - 52 x 0.9)/137 = 0.408 m, hence eccentricity = 1.5/2 — 0.408 = 0.342 m.
As this falls outside the middle third the linear distribution of ground pressure is triangular on a base of (3 x 0.408) = 1.224 m.
Maximum ground pressure = 2 x 137 = 149 kN/m2 for which the soil must be 1.224 x 1.5
adequate to sustain.
Factor of safety against overturning:
Overturning moment = 52 x 0.9 = 46.8 kNm Restoring moment = 137 x 0.75 = 102.8 kNm
Hence factor of safety against overturning
102.8 . . = 46 8
= 2.2 which is satisfactory.
A check should be also required for the factor of safety against sliding.
Use foundation 1.5 m square x 0.9 m deep. Grade 20 concrete.
74
11. ALTERNATIVE FRAME ANALYSIS
As indicated in Section 9.8 two alternative systems were to be considered for the frame analysis:
(a) assuming base is pinned and all joints of the latticed truss are pinned (Frame Type 1).
(b) assuming base is pinned and all joints of the latticed frame are rigid (Frame Type 2).
Two members of the top chord are checked for these two frame systems.
Frame Type 1 was used for the design in Section 10.
MEMBER 6
Load Type
FRAME TYPE
Number I Number 2
Max. axial load (kN) Max. axial load (kN) Max. BM (kNm)
Dead 65 (1') 64 (T) 0.70
Imposed 107 (1') 107 (T) 1.16
Wind 108 (C) 107 (C) 1.15
It is noted the ("rounded off") axial loads are identical for this member, Frame Type No. 2 includes a small bending moment. Consider the effects of this bending moment.
Design tensile load (dead + imposed) = (1.4 x 64) + (1.6 x 107) = 261 kN(T)
= (1.4 x 0.70) + (1.6 x 1.16) = 2.84 kNm
= (1.0 x 64) - (1.4 x 107) = -86 kN(C) = (1.0 x 0.70) + (1.4 x 1.16) = 2.32 kNm.
Design bending moment (dead + imposed)
Design compression load (dead + wind)
Design bending moment
75
MEMBER 13
Load Type
FRAME TYPE
Number I Number 2
Max. axial load (kN) Max. axial load (kN) Max. BM (kNm)
Dead 99 (C) 99 (C) 0.35
Imposed 164 (C) 164 (C) 0.58
Wind 159 (T) 159 (T) 1.55
Design compressive load = (1.4 X 99) + (1.6 X 164) = 401 kN
Design bending moment = (1.4 x 0.35) + (1.6 X 0.58) = 1.42 kNm
Comparing the forces and moments of the two members a check is made on the compressive capacity of Member 13 and then on the tensile capacity of Member 6.
Check Member 13, 120 x 80 x5 RHS, for axial compression and moments, considering local
capacity and overall buckling. (Clause 4.8.3').
Local Capacity Check
The clause indicates the use, for plastic sections, of the relationship:
M
Mrx
where Mrx is the reduced moment capacity in the presence of axial loads obtained from
published tables. These values are not generally available for RHS hence use is made of:
F M ____ + _..L where F = 401 kN M = 1.42 kNm AgPy M X
is obtained from Clause 4.2.5 i.e. M, = S but � 1.2 pZ where S = 75.4 cm3 Z = 61.7 cm3. However 5,7 = 1.21 i.e. > 1.2.
From footnote to Clause 4.2.5 it is noted that the value 1.2 is replaced by Factored Load/U nfactored Load ratio = say 1.4.
i.e. = 275 x 75.4 x i0 = 20.7 kNm or = 1.4 x 275 x 61.7 x i0 = 23.8 kNm i.e. Use = 20.7 kNm (See Reference 19).
Hence in the interaction equation
401 X 10 + = 0.77 + 0.07 = 0.84 < 1
18.9 x 275 20.7
Local capacity is satisfied (notice the effect of the moment is relatively small).
76
Overall buckling check (Clause 4.8.3.3W).
Simplified approach
F +mMx�1 AgPc Mb
In considering the buckling resistance moment Mb reference is made to Appendix The footnote indicates that if X =
Le/ry < co (for DIB taken as 1) then lateral torsional buckling need not be checked.
PbPy andMb=SXpY=20.7kNm
Hence, p = 476 kN (as in Section 10.1).
In the interaction equation assume m = 1.0. Clearly for secondary moment design 'm' will be less than unity and a value from Table 18' could be used with advantage.
401 + = 0.842+0.069 = 0.911 < 1
Satisfactory. Again the effect of the moment is small.
Check Member 6 for the axial tensile load and moments (Clause 4.8.2).
F M _____ + where F = 263 kN, M = 2.84 kNm. AePY M X
263 x 10 + = 0.51 + 0.14 18.9 x 275 20.7
= 0.64 < 1
This is satisfactory.
Similar checks can be made on other members of the framework.
It is apparent that the basic assumption to use pinned joints in the analysis and rigid joints in the built structure for the lattice truss is justified. The use of pinned joints for the analysis and design process leads to a simpler and therefore quicker solution to the problem. It is of note that relative to the slenderness limitation of 50 stipulated in Clause 10(1) that members 55 and 72 are significantly below that value. It is suggested that the reader checks these members for the secondary stress effects.
77
12. JOINT DESIGN
A useful guide for the arrangements of connections is the British Steel/CIDECT Publication Construction with Hollow Steel Sections22.
A check is made of joint 8 (Figure 44) following the method given in design example No 3 (p 52) in TD 338'.
Figure 44 Joint 8 (K gap)
Member
6
7
78
23
24
Dead
65kNcI') 22 kN (T)
39 kN (C)
3lkN(T)
Imposed
107 kN (T)
36 kN (T)
65 kN (C)
51 kN (T)
— 80 = 0.67 ) i.e. all satisfactory -i
b0 — 120
to —
5 = 24.0 � 35
Member 7
kN
80mm
Total (Factored)
262 kN (T)
88 kN (1')
159 kN (C)
125 kN (1')
Member 6
172 kN
80 x 40 15
104 Member 23
x 3 RHS
Member 24
A
bracings,and b0 > h0 hence refer to Table 11 of This is a K-Gap Joint with RHS Chords and Reference 13.
12.1 Application limit check list
H1
b1
h2 —
b2 —
60
= =0.5 ) �0.5
=0.67 ) �2.0
Bracing angles O = 02 = 52.3° � 90°, � 30°.
=- = 16�35 5
= = 0.67 �0.35 120
= = 0.5�0.35 120
= = 0.33 < 0.35 120
Member 6
172 kN
104 kN
Member 7
58kN
0mm
x 40 x 3 RHS
Figure 45 Joint 8 (overlap)
As above
h h1 h2 0.5 � _, —, — � 2.0 b0 b1 b2
Bracing angles 900 � 02 � 30°.
b1 = 80
b0 120 = 0.67 � 0.25
79
to
b1
b2
b0
b0
Hence this criteria is not satisfied using a gap joint.
Note: The 90x50x3.6 RHS suggested as an alternative in Section 10.4 would satisfy the criteria for a gap joint.
For the 80x40x5 RHS try an overlap K joint, Table 13(13) (Figure 45) where:
0.55 h0 � e � 0.25 h0.
80 x 40 x 5 RH
mber 23
82 kN
4
b2 = 60 = 0.5 � 0.25
= h = 40 = 0.33 � 0.25
Chord
h0 = 80 = 16�40
b0 — 120 = 24�40
RHS bracing in compression (p = 275) (E = 205 kN/mm2)
b1 = 80 = 16 � 30 where 30 = 1.1 /E/p1
RHS bracing in tension
b2 = 60 = 16�35
All limits are satisfied.
Use of tabulated allowable loads
Pyo = Pyi = Py2 (i.e. chords and bracings have same design strength).
b1 80 BracingsO.8< — = 133> 125
Hence use following equation:
Allow 30 mm actual overlap.
= Actual overlap sin 0 < Then percentage overlap Chord h
= 30 sin 52.3° ________ x 100 = 59% 40
Hence overlap 50 < 59 > 80%
80
Therefore the allowable joint capacity is given by:
1 + sin(0 + 0,) N =
pyj ti (2h1 —
4t1 + be + be(ov)) 2 sin (0 + 02)
inn p .t where b = .
° . b b01t0 p,1 .
and
— 10.0 Pyj.tj OV h/t , I jj Pyi I
Note - suffix 'ov' refers to overlapped member
Therefore b = 10 x 80 x 275 x 5 x 5 = 333 e 120x275x5
— 10x275x5x80x5 — 50 be(ov) —
80 x 275 x 5 —
N1 = 275x5 [2x40)-4 x 5)+33.3+50)] x [(1+sin 104.6)1(2 sinlO4.6)J x i0 N1 =200kN.
Since N1 = 200 kN > bracing compression load (104 kN) the joint is satisfactory.
The reader should carry out checks on other joints, as considered necessary. It is feasible that bottom boom joints might not be satisfactory. These calculations have indicated the effect of the member size and orientation.
12.2 Joint welds
Design of welds to lattice girder is carried Out using limit state design and Reference 15, SHS Welding.
Note: use is made of an Amendment to Reference 15 - Revised Text for Pages 26 and 27.
The minimum fillet weld throat size is taken as the larger value of:
(i) a = Applied factored load pw x s
or
(ii) a = ffl) X f(w) x t
81
Where:
pw = weld design strength (Table on page 24') and equals 215 N/mm2 for Grade 43 steel.
s = intersection length (Table 2B'5).
t = thickness of branch member andf(7) is a function equal to the higher value of:-
Actual applied factored load Member tension capacity
or
Actual applied factored load Joint capacity
The functionf(w) is the ratio of material strength to weld strength.
For Grade 43 steel:
f(w) = 275/215 = 1.28.
Design of weld for member 23.
This is a single 'T' joint, at 52.3°.
When the fusion faces at the toe of the branch member is, at 127.7°, greater than 1200 it is necessary to prepare and make the bracing toe connection as a butt weld, as shown in
Figure 46.
/•.
/'\ = 30°to6O°
Figure 46 Preparation of bracing member
Bracing member is a 80x40x5 RHS carrying a factored load of 159 kN (Section 10.3.2).
The factored tension capacity of the brace = AePy
10.9 x 275 x 10 = 300 kN.
The chord is a 120x80x5 RHS with an unfactored joint capacity (Section 12.1) of 200 kN. Assume a load factor of 1.5 then design joint capacity = 200 x 1.5 = 300 kN.
Total intersection length for 52.3° angle, s = 283mm. (Table 2B)5, b1 = 80 mm.
82
Hence:
(1) a = 159 x 10 = 2.6 mm 215 x 282
or
(ii) a = f(7) X f(w) x t
f(7) = 159/300 = 0.53
or
f(l) = 159/300 = 0.53
Hence usef(1) = 0.53
Thus a = 0.53 x 1.28 x 5 = 3.4 mm.
Therefore the minimum throat size = 3.4 > 2.6 mm.
Hence the minimum leg length = 3.4/0.7 = 4.9 mm.
Use a 5 mm fillet weld.
83
•0
q)
(I)
ci'
N
0, U-
13. FINAL FRAME LAYOUT
Layout of the building steelwork is shown in Figures 47 to 50.
Finally a check must be made of the self weight of the girder, as estimated against actual. The designer may need to decide whether a new analysis is required.
4-.
E E
a,
I U) x
Eo gco .Q X a.O o c'1 I-'--
U 4-. •0. 0 In
(I) I Em ox
(0 x 0 C.,'
U,
)< 0 (0 'C In CD
'C c'l 0 C'IN
U) I IC)
'C 0 x
1
C w— e 4-. 0;
CO
OC .C 0 <a,
V C.- '4- C o o D o b
.0 C C w 0
04-
U)
'C 0) 1 'C
U) 'C—
a, C
•0 V 0
U)
0) U) 'C I- 0)
x
U) > a,
C
U,
U.
wgL'wgL W 9. W 8
0 V
84
3O'x 165 x UB .— gable column
Figure 48 P/an of roof stee/work
/ 0 CD
/ 0 (0
/ 0 CD
/ 0 CO
/ 0 CO
0 CD
/ 0 CD
/
85
r Om
F' 7 / -7 0 CO
J-I
457 x 191 x 89 UB / Column Lattice roof truss .4
/ E co
/
114.3x 5 CHS Wind girder in plane of top chord
142x54x49x 1.8 Z side rail
Wind girder in plane of top chord
\ 18 lines of 202 x 65 x 60 x 1.8 Z purlins at 1.85 m c/c
/ 11
4.3
x 5
CH
S
Win
d br
ace
142
x 54
x 49
xl.
8 si
de ra
il
457
x 19
1 x
89 U
B
Mai
n co
lum
n
139.
7 x
5 br
acin
g
457
x 19
1 x
89
UB
col
umn
Ant
i-sag
bar
s
7,
___
I, I
N
7,
N T
\
—
.N.
I I
N
I
203
x 10
2 x
23 U
B
gabl
e ra
fter
305
x 16
5 x
40
gabl
e co
lum
n
Fig
ure
49 E
nd e
leva
tion;
gen
eral
arr
ange
men
t of s
teel
wor
k
gabl
e br
ace
202
x 60
x 6
0 x
1.6
rail
nti-s
ag b
ars
REFERENCES
1. BRITISH STANDARDS INSTITUTION BS 5950: Structural use of steelwork in building Part 1: Code of practice for design in simple and continuous construction: hot rolled sections BSI, 1990
2. BRITISH STANDARDS INSTITUTION BS 5950: The structural use of steelwork in building Part 5: Code of practice for design of cold formed sections BSI, 1987
3. BRITISH STANDARDS INSTITUTION BS 5502: Building and structures for agriculture Various parts
4. BRITISH STANDARDS INSTITUTION BS 6399: Loading for buildings Part 1: Code of practice for dead and imposed loads BSI, 1984
5. BRITISH STANDARDS INSTITUTION BS 6399: Loading for buildings Part 3: Code of practice for imposed roof loads BSI, 1988
6. BRITISH STANDARDS INSTITUTION CP3: Chapter V: Loading Part 2: Wind loads (This will be superseded by BS 6399: Part 2) BSI, 1972
7. BUILDING RESEARCH ESTABLISHMENT The designer's guide to wind loading of building structures Part 1; Butterworths, 1985 Part 2; Butterworths, 1990
8. THE BRITISH CONSTRUCTIONAL STEELWORK ASSOCIATION / SC! National steelwork specification for building construction (2nd Edition) BCSA/SCI, 1991
9. BRITISH STANDARDS INSTITUTION Handbook 22: Quality assurance BSI, 1990
10. BRITISH STANDARDS INSTITUTION BS 5750: Quallty systems Parts 0 to 3
BSI, 1987
11. BRITISH STEEL STRIP PRODUCTS Roofing and cladding in steel - Product selector BS Strip Products, 1987
87
12. BRITISH STANDARDS INSTITUTION BS 4360: Specification for weldable structural steels BSI, 1990
13. BRITISH STEEL TECHNICAL MANUAL TD 338/5E/91R Design of SHS welded joints BS Welded Tubes, 1991
14. BRITISH STEEL TECHNICAL MANUAL TD 325/1OE/89 Jointing BS Welded Tubes, 1989
15. BRITISH STEEL TECHNICAL MANUAL TD 328/10/90 Welding BS Welded Tubes, 1990
16. THE STEEL CONSTRUCTION INSTITUTE A check list for designers SC!, 1987
17. YEOMANS, N. New developments in the use of structural hollow sections SCllBritish Steel Conference, December 1989
18. METAL SECTIONS LIMITED Zed purlins technical manual to BS 5950: Part 5 Metsec, 1988
19. THE STEEL CONSTRUCTION INSTITUTE Steelwork design guide to BS 5950: Part 1: 1990 Volume 1: Section properties and member capacities SCI, 1992
20. THE STEEL CONSTRUCTION INSTITUTE Steetwork design guide to BS 5950 Volume 4: Essential design data for designers SC!, 1991
21. THE STEEL CONSTRUCTION INSTITUTE Steelwork design guide to BS 5950: Part 1: 1990 (Revised Edition) Volume 2: Worked examples SCI, 1991
22. BRITISH STEEL GENERAL STEELS WELDED TUBES In conjunction with CIDECT Construction with hollow steel sections First edition 1984
88
BIBLIOGRAPHY
In addition to the publications listed in the text, reference has been made to catalogues produced by:
METAL SECTIONS LIMITED Building products Birmingham Road, Oldbury Warley West Midlands B69 4HE
SPACE DECKS LIMiTED Chard Somerset TA2O 2AA
Reference has also been made to:
BRITISH STEEL TECHNICAL MANUAL TD 16716E192 Hot finished structural hollow sections; sizes, properties and technical data BS Welded Tubes, 1992
89
RECENT SCI PUBLICATIONS:
P062 Steel Designers' Manual - 5th Edition Sc, & Blackwell Scientific Publications Ltd
P079 Steel Construction Yearbook - 1993 Thomas Telford Directories / SC!
P083 Design of Composite Trusses Skidmore 0 wings Merrill / SC!
P101 Curtain Wall Connections to Steel Frames - Interfaces A G Ogden
P114 Steelwork Design Guide to Eurocode 3: Part 1.1 -
Introducing Eurocode 3 J C Taylor, N R Baddoo, A W Morrow & C Gibbons
P118 Design of Stub Girders R M Lawson & R McConnel
P119 Design of Stainless Steel Fixings and Ancillary Components N R Baddoo
P120 Technical Report - Slim Floor Construction using Deep Decking 0 L Mu/lett & A M Lawson
P123 Concise Guide to the Structural Design of Stainless Steel B A Burgan
P124 Technical Report - The Fire Resistance of Web-Infilled Steel Columns G M Newman
P205 Joints in Simple Construction Volume 1: Design Methods (2nd Edition) SC! & BCSA
P206 Joints in Simple Construction Volume 2: Practical Applications BCSA & SC!
For further information please contact:
The Publications Department, The Steel Construction Institute, Silwood Park, Ascot, Berkshire, SL5 7QN. Telephone: 0344 23345 Fax: 0344 22944
cto
Typeset and page make-up by The Steel Construction Institute, Ascot, Berks. Printed and bound by Burgess Science Press, Basmgstoke, Hampshire. 1500/3-1993
o&.
