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SCI PUBLICATION 169

Design of RHS Slimflor® Edge Beams

D L MULLETT CEng, MICE, MIMechE

Published by:

The Steel Construction InstituteSilwood ParkAscotBerkshire SL5 7QN

Tel: 01344 623345Fax: 01344 622944

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© 1997 The Steel Construction Institute

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

Enquiries concerning reproduction outside the terms stated here should be sent to the publishers,The Steel Construction Institute, at the address given on the title page.

Although care has been taken to ensure, to the best of our knowledge, that all data and informationcontained herein are accurate to the extent that they relate to either matters of fact or acceptedpractice or matters of opinion at the time of publication, The Steel Construction Institute, the authorsand the reviewers assume no responsibility for any errors in or misinterpretations of such data and/orinformation or any loss or damage arising from or related to their use.

Publications supplied to the Members of the Institute at a discount are not for resale by them.

Publication Number: SCI-P-169

ISBN 1 85942 055 9

British Library Cataloguing-in-Publication Data.A catalogue record for this book is available from the British Library.

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FOREWORD

This design guide describes the use of RHS Slimflor® edge beams in association with deepdeck composite slabs. Slimflor is a registered trademark of British Steel.

The publication refers to a new deep deck profile, SD 225, which is available from PrecisionMetal Forming Limited, Cheltenham, GL51 9LS.

A computer program on RHS Slimflor edge beams in the Windows environment, that iscomplementary to this publication is available from British Steel, Tubes & Pipes, Corby,NN19 1UA. The use of this software is explained in Appendix D.

The author of the publication is Mr D L Mullett of The Steel Construction Institute, assistedby consultant architect, Dr R G Ogden, Mr G M Newman, Dr C Bailey and Dr R MLawson of SCI.

The research leading to this publication was funded by British Steel, Tubes & Pipes. Theproject was initiated by Mr E F Hole of British Steel, Tubes & Pipes.

This publication is a companion to the SCI publication Design of Asymmetric Slimflor® BeamsUsing Deep Composite Decking.

GlossarySlimflor A registered trademark of British Steel that covers steel beams suitable for

floorings of limited depth; the first beam produced for this system was a steelUniversal Column section with a welded bottom plate that may be used withdeep deck composite slabs, or with precast concrete slabs.

Slimdek A registered trademark (applied for by British Steel) that covers the range offorms of slim floor construction, using deep deck composite slabs (currentlyincluding ASB, SFB and RH SFB).

ASB Asymmetric Slimflor Beam.

SFB Slimflor Fabricated Beam (as for Slimflor).

RH SFB Rectangular Hollow Slimflor Fabricated Beam, used primarily as an edge beam.

SD 225 New deep deck profile (225 mm deep).

CF 210 Former deep deck profile (210 mm deep).

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CONTENTSPage No.

FOREWORD iiiGlossary iii

SUMMARY vii

1 INTRODUCTION 11.1 Slim floor construction 11.2 The benefits of using slim floor construction 21.3 Edge beams in slim floor construction 21.4 The use of deep decking 3

2 FORM OF CONSTRUCTION 42.1 The RHS Slimflor edge beam 42.2 Composite slabs using deep decking 42.3 RHS Slimflor edge beams acting non-compositely

with floor slab 52.4 RHS Slimflor edge beams acting compositely with floor slab 62.5 RHS Slimflor edge beams and use of precast concrete slabs 7

3 CONSTRUCTION DETAILS 83.1 Beam to column connections 83.2 Support of cladding 10

4 DESIGN OF RHS SLIMFLOR EDGE BEAMS 174.1 Basis of design 174.2 Construction stage loading 184.3 Torsional effects on the RHS edge beam 184.4 Design of non-composite beams 194.5 Design of composite beams 254.6 Minimum natural frequency of the edge beam 31

5 FIRE RESISTANT DESIGN 335.1 General requirements of BS 5950: Part 8 335.2 Heating rate for RHS edge beams 345.3 Moment resistance of RHS edge beams in fire 355.4 Fire test at TNO in the Netherlands 355.5 Design tables for RHS edge beams 385.6 Additional fire protection 42

6 REFERENCES 44

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APPENDIX A Typical Worked Example for RHS Edge Beam 47

APPENDIX B Formulae for Plastic Moment Resistance of RHS EdgeBeam 65

APPENDIX C Design Tables for Initial Sizing 73

APPENDIX D Computer Screens and Output for RHS Slimflor Analysisand Design 81

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SUMMARY

Slim floor construction is a concept of integrating steel beams within the depth ofa floor slab. Slimflor is a system marketed by British Steel. This publicationpresents a method of design for the edge beams in Slimflor construction usingRectangular Hollow Sections (RHS). The beams are used in conjunction with steeldeep decking and in situ concrete which acts compositely with decking. Thecomposite slabs are supported by a plate welded to the underside of the RHS.

Design procedures in this publication are for simply supported beams subject touniformly distributed loading and are presented in accordance with BS 5950: Part 1and 3. Plastic analysis is adopted for design of the cross-section at ultimate limitstate, and elastic analysis at the serviceability limit state.

A worked example that illustrates the design procedures, and Design Tables withexplanatory notes for initial sizing of RHS Slimflor edge beams are given in theAppendices.

Dimensionnement des poutres de bordure en RHS pour planchers de type“Slimflor”

Résumé

La construction de planchers minces de type Slim floor est un concept structural oùles poutres en acier sont intégrées dans l’épaisseur du plancher. “Slimflor” est unsystème commercialisé par British Steel. Cette publication présente une méthode dedimensionnement des poutres de bordures, réalisées en profils creux rectangulaires(RHS), utilisées dans la construction “Slimflor”. Les poutres sont utilisées enconjonction avec une tôle profilée et du béton coulé sur place qui développe uneaction composite avec la tôle profilée. Les dalles composites ainsi réalisées sontsupportées par des plats soudés sur le profil RHS.

Les procédures de dimensionnement proposées dans cette publication sontapplicables aux poutres appuyées simplement et soumises à une charge uniforme.Elles sont en accord avec la norme BS 5950: Parties 1 et 3. Une analyse plastiqueest adoptée pour la vérification des sections, à l’état ultime. Par contre, les étatsde services sont analysés selon la méthode élastique.

Un exemple illustre les procédures de dimensionnement et des tableaux sont donnés,en annexe, pour faciliter le dimensionnement initial des poutres.

Proyecto de vigas de contorno RHS Slimflor

Resumen

La construcción de forjados esbeltos responde a la idea de integrar vigas de aceroen el canto de un forjado. El sistema de British Steel se comercializa con el nombrede Slimflor. Esta publicación presenta un método de proyecto para vigas decontorno en este tipo de construcción usando secciones rectangulares huecas (RHS).Las vigas se usan en conjunto con chapas plegadas de acero de gran canto yhormigón in-situ que actúa en forma de estructura mixta. Estas losas mixtas seapoyan en placas soldadas al ala inferior de la RHS.

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Los métodos de proyecto en esta publicación son aplicables a vigas simplementeapoyadas sometidas a carga repartida y se ajustan a la BS 5950: Partes 1 y 3.

Para proyectar la sección necesaria en estado límite último se utiliza el cálculoplástico, mientras que para los estados de servicio se recurre al cálculo elástico.

En los Apéndices se desarrolla un ejemplo del procedimiento de cálculo y seincluyen tablas con notas aclaratorias del predimensionado de vigas de contornoRHS Slimflor.

Berechnung von Rechteck-Hohlprofilen als Randträger von Flachdecken

Zusammenfassung

Beim Bau von Flachdecken werden die Stahlträger in die Decke integriert. DasSystem von British Steel wird als “Slimflor” vermarktet. Diese Veröffentlichungstellt eine Methode zur Berechnung von Randträgem in Flachdecken vor, unterVerwendung von Rechteck-Hohlprofilen (RHS). Die Träger werden in Verbindungmit einem hohen Stahltrapezblech und Ortbeton verwendet, der mit dem Trapezblechim Verbund wirkt. Die Verbunddecke wird von einer Stahlplatte getragen, die andie Unterseite des Hohlprofils geschweißt wird.

Das Berechnungsverfahren in dieser Veröffentlichung bezieht sich auf Einfeldträgermit Gleichstreckenlast und beruht auf BS 5950 Teil 1 und 3. Im Grenzzustand derTragfähigkert wind der Tragsicherheitsnachweis plastisch geführt, im Grenzzustandder Gebrauchsfähigkeit wird elastisch gerechnet.

Ein Berechnungsbeispiel welches die Berechnungsweise illustriert sowie Tabellen mitErläuterungen zur Vorbemessung von Randträgem aus Rechteck-Hohlprofilen inFlachdecken sind im Anhang zu finden.

Progettazioni di travi di bordo RHS slimflor

Sommario

I sistemi composti in spessore di solaio sono caratterizzati dalla trave metallicaposizionata all’interno della struttura orizzontale portante. Il sistema portantecomposto in spessore di solaio sviluppato dalla British Steel e’ stato denominato“Slimflor”.

Questa pubblicazione presenta un metodo per la progettazione di travi di bordo peril sistema Slimflor usando profili metallici rettangolari cavi (travi RHS).

Le travi in acciaio vengono utilizzate con lamiere grecate a alta nervatura econglomerato gettato in opera che realizza una soletta composta sorretta da unpiatto metallico saldato lateralmente alla trave RHS.

Le procedure progettuali riportate nella pubblicazione, riferite allo schema staticodi trave in semplice appoggio e con condizione di carico uniformemente distribuito,sono sviluppate in accordo alla normativa BS 5950: parti 1 e 3. Per il progettodelle sezioni trasversali allo stato limite ultimo viene adottato il calcolo plasticometre, per quanto riguarda lo stato limite di servizio si utilizza l’analisi elastica.

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Un esempio applicativo illustra la procedura di progetto e negli allegati sonoriportate tabelle progettuali corredate da esaustive note esplicative per ildimensionamento di travi bi bordo composte con profilo metallico di tipo RHS.

Dimensionering av RHS Slimflor kantbalkar

Sammanfattning

En Slim floor-konstruktion är ett koncept där bjälklagsbalken i stål integreras isjälva bjälklagskonstruktionen. British Steel marknadsför ett eget system på dettakoncept, “Slimflor”. Denna publikation presenterar en dimensioneringsmetod förkantbalkar av fyrkantiga konstrukionsrör (RHS) i ett Slimflor-system. Balkenanvänds tillsammans med en högprofil i stål och platsgjuten betong som samverkarmed den profilerade plåten. Samverkansbjälklaget ligger upplaggd på en plåtsvetsad till undersidan av RHS-profilen.

Dimensioneringsgången i denna publikation gäller för en enkelt upplagd balk medjämnt utbredd last, och presenteras enligt BS 5950: del 1 och 3. Plastisk analysutnyttjas vid dimensionering av tvärsnittet vid brottgränstillstånd och elasticitetsteorii bruksgränstillstånd.

Ett beräkningsexempel som illustrerar beräkningsgången, ochdimensioneringstabeller med förklaringar för en första preliminär bestämning avprofildimensioner, ges i ett appendix.

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Mesh

Bottom flange plate

'Slimflor' beam

End diaphragm

concreteIn situUC section

Cylindricalsleeve for duct

Reinforcement

Deep deck(CF210)

1 INTRODUCTION

1.1 Slim floor constructionSlim floor systems create a reduced total depth of floor by using beams integratedinto the floor structure. Downstand beams are thus avoided, and only the bottomflange of the slim floor beam is exposed.

In the UK, the Slimflor® concept was introduced in 1991. Slimfor is a RegisteredTrademark of British Steel plc. These beams comprise Universal Column (UC)sections with a welded bottom plate. This offers a form of construction of minimumdepth of typically 270 to 300 mm. Since its introduction, a large number ofimportant projects have been carried out using Slimflor construction, and the concepthas attracted worldwide attention.

Initially, Slimflor construction was used with precast concrete slabs spanningbetween the beams. Subsequently the system has been extended to include the useof deep decking, as shown in Figure 1.1.

Figure 1.1 Cut-away view of a Slimflor beam with CF210 deep decking,showing installation of service ducts

It is recognised that slim floor systems are slightly heavier compared to othercomposite floor systems, but this increase in steel weight is easily offset by thereductions in fire protection, cladding costs (because of the reduced overall heightof the building), and ease of servicing below the flat soffit. The slim floor methodof construction is specifically aimed at competing with reinforced concrete flat slabs.

The SCI has produced three publications covering slim floor construction:

C Slim floor design and construction(1).

C Slim floor construction using deep decking(2).

C Design of asymmetric Slimflor® beams using deep composite decking(3).

These publications present the basis of design, worked examples and design tables.

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The registered trademark Slimdek covers the range of products and applicationsgiven in the Glossary on page (iii).

1.2 The benefits of using slim floor constructionThe general benefits of Slimflor construction are:

C Floors have a flat or ribbed soffit. This offers unhindered passage for theservices.

C The overall floor construction depth is reduced. This has an influence on thecladding costs, i.e. the overall height of the building is reduced.

C Slimflor construction is rapid. It is comparable to other ‘fastrack’ methods inspeed of construction, in fact, the slim floor approach is now seen as a logicaldevelopment of normal composite construction.

C Good fire resistance. The concrete that surrounds the beam partially insulatesthe section, giving 60 minutes fire resistance. This can eliminate the need foradditional fire protection.

C The concrete that surrounds the beam increases its stiffness. This enhancementis helpful in reducing deflections.

C For local element instability, the concrete improves the load carryingcapabilities of the beam. For the future, this could prove an asset forcontinuous construction.

1.3 Edge beams in slim floor constructionThe first consideration for edge beam design is to determine the form of constructionthat is appropriate architecturally. The selected form of construction for the edgebeam will dictate the design concept. For example, if a downstand beam isacceptable with regard to the cladding details, a more traditional design approachcan be adopted. The decking can rest on the top flange of the beam and the verticalloads may be assumed to act through the shear centre of the beam.

In the past, this option has proved to be a popular method of construction becauseit has the advantage of eliminating the torsional effects on an open beam section.However, the use of downstand beams has the disadvantage of increasing theconstruction depth, which in turn can affect the architectural details and appearanceof the building.

The use of a conventional Slimflor beam for edge beams may give rise to someproblems, as the section is torsionally weak and flexible. The eccentric loads fromthe slab can lead to the use of relatively heavy sections to avoid excessive twist. Toprovide a more efficient solution for edge beams in this form of construction, theRHS Slimflor beam (sometimes referred to as RH SFB) has been developed, asshown in Figure 1.2. The good torsional properties of the RHS section ensure thatstresses and movements due to eccentric loads are minimised.

The RHS Slimflor beam can readily be used with RHS perimeter columns, leadingto more slender walls and, where the steel is exposed, to better appearance.

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The additional benefits of RHS Slimflor construction are:

C Good torsional properties of the edge beams.

C Smooth external face providing easier connections for brackets, cladding etc.

C Efficient member size, leading to reduced steel weights.

C Good fire resistance.

C Wide range of RHS section sizes and thicknesses.

Slimdek construction is now the generic title of Slimflor construction using deepdecking.

With the introduction of RHS edge beams in Slimdek construction, there is anopportunity to simplify cladding details and to offer an architecturally improveddesign in which the edge beam can be exposed. The provision for subsequentmovement between the frame and cladding may be reduced. This publication refersentirely to the use of RHS Slimflor sections as edge beams, although these sectionsmay be used in other applications where torsional forces predominate.

1.4 The use of deep deckingIn the UK, a new deep deck has been developed, which can span up to 6.5 m(unpropped) between beam centres, has a depth of 225 mm, and is trapezoidal incross-section. The steel deck reduces the dead weight of the floor in comparison toprecast concrete slabs and improves the robustness of the construction. Also, itlends itself to the accommodation of minor services within the slab depth betweenthe ribs of the deck by forming holes through the web of the beam. The new deck,designated as SD 225, will shortly replace the existing 210 mm (CF210) deep deck,which has been widely used to date in the UK, the Netherlands and Canada.

The descriptions and examples of the use of RHS Slimflor in this publication allrelate to their use with deep decking in Slimdek construction.

Figure 1.2 Cut-away view of an RHS Slimflor Edge Beam using SD 225deep decking

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2 FORM OF CONSTRUCTION

2.1 The RHS Slimflor edge beamThe RHS Slimflor edge beam uses a steel plate welded to the underside of a standardRHS section which are available in depths of up to 500 mm. The bottom plate is15 mm thick and it projects on one side, where it supports the floor slab, with a onlysmall projection on the other side, to facilitate fillet welding and the attachment ofcladding. A typical RHS Slimflor beam section is shown in Figure 2.1.

y

x x

Rectangularhollow section (RHS)

Fillet weld

Flange plate

y

Figure 2.1 Basic steel components of the RHS Slimflor beam

The RHS Slimflor beam is part of Slimdek construction. It is particularly welladapted to edge beam applications because of its good torsional properties andsmooth external appearance.

2.2 Composite slabs using deep deckingAs mentioned in Section 1.4, the new deep decking profile, SD 225, has been thesubject of extensive modifications to improve the spanning capability of the former210 mm deep profile. It is 225 mm deep and is manufactured from grade Fe E 350steel of 1.25 mm thickness. In addition, the deck configuration has been adaptedto readily accommodate the ceiling and services without the need to makeattachments into the concrete slab (see Figure 2.2).

During construction, the steel decking is designed to support the self weight of theconcrete and a construction load of 1.5 kN/m2 (as specified in BS 5950: Part 4(3)).Because the Code does not envisage the use of long span slabs, the construction loadfor unpropped cases is taken as 1.5 kN/m2 over the middle 3 m of the span, and0.75 kN/m2 elsewhere (as proposed in Eurocode 4: Part 1.1(4)). A construction loadof 1.5 kN/m2 is considered throughout for propped slabs.

Ponding of concrete, due to the deflection of the deck, is taken into account in theseconstruction loads provided the deflection of the deck after construction does notexceed span/180(3). The deck shape is highly stiffened to improve its bendingresistance, by reducing the effects of local buckling. Calculations and load testscarried out by British Steel (Welsh Technology Centre) have confirmed themaximum clear spans between supports during the construction stage to be:

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C 6.0 m (unpropped) for normal weight concrete slab (295 mm overall depth)

C 6.5 m (unpropped) for lightweight concrete slab (285 mm overall depth).

Dovetail

Dovetail

600 600

Rib reinforcement

600

SD 225 deckingMesh reinforcement

Outstand ofbottom flangeplate

Concrete slab

N.B. The re-entrant (dovetail) deck configurationcan be used to support ceiling and services

s

dD =225

D

15

Decking side lapstitched at600mm centres

Figure 2.2 Typical cross-section through the floor slab using SD 225decking

The difference in spanning capabilities is due to the difference in slab weight, theslab depth being also influenced by the fire resistance requirements (see Section 5).

The composite (or shear-bond) action of the slab with the steel decking is achievedby the use of vertical indentations in the webs of the decking. Also, the “dovetails”positioned in the crest and trough will enhance the composite action of the slab.Additional reinforcing bars are also necessary to provide fire resistance. However,these bars may also be included in the ‘normal’ design of the slab. It is generallyfound that the load-carrying capacity of the slab exceeds that required in mostapplications, provided spans are less than 8 m.

The reader should consult the supplier of the decking (Precision Metal Forming Ltd)for more detailed information and load-span tables.

When deep decking spans perpendicular to the Slimflor beam, end diaphragms areconnected to the bottom flange plate, which effectively provides a closure for theconcrete. The steel deck is placed on these diaphragms and connected using shotfired pins to the projecting bottom flange plate of the Slimflor beam. The in situconcrete is then poured or pumped onto the deck and levelled to a final finish.

2.3 RHS Slimflor edge beams actingnon-compositely with floor slab

RHS sections used in edge beam applications are typically 200 to 300 mm deep inthickness of 6.3 to 16 mm. Typical RHS sizes are 200 × 100, 250 × 150 and 300× 200. Grade S355 steel (formerly grade 50) is preferred. However, whereserviceability criteria control the design, use of grade S275 steel (formerly grade 43)is cost effective.

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Figure 2.3 shows typical details for a RHS Slimflor edge beam actingnon-compositely. In principle, the beams are designed to be unpropped duringconstruction, although there may be circumstances where propping is used toprovide the minimum steel beam size for a given span.

pD =225mm

60 min. (LWC)70 min. (NWC)

MeshConcrete slab

RHS Slimfloredge beam

End diaphragm

Cross-section through non-composite Slimflor RHS beam - Type A

Figure 2.3 Non-composite edge beam

Lightweight concrete is preferred in order to minimize the slab depth and weight.

2.4 RHS Slimflor edge beams acting compositelywith floor slab

Figure 2.4 shows typical details for a RHS Slimflor edge beam acting compositelywith the floor slab. Again, the beams are usually designed to be unpropped duringconstruction, and grade S355 steel and lightweight concrete are the preferredmaterials. Propping may be required for long span edge beams.

Mesh

t

D

t B

Be(effective width)

p

D

D p

s

Cross-section through composite Slimflor RHS beam - Type B

Shear studconnector

Angle supportstrap

Cold formedangle section

Transversereinforcement(U-bars)

Bp

SD 225deep deck

Figure 2.4 Composite edge beam

Although the bottom plate of the edge beam does not usually project much beyondthe web of the RHS, in composite applications it is often necessary for the slab toproject over the RHS in order to provide the required edge distance for the studshear connectors (i.e. 6 × stud diameter). Transverse reinforcement in the form ofU bars is required in the slab in this case.

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2.5 RHS Slimflor edge beams and use of precastconcrete slabs

RHS Slimflor sections may be used to support precast concrete (p.c.) slabs, providedthe following measures are adopted to ensure adequate performance of p.c.hollowcore slabs at the ultimate and fire limit states:

C Where hollowcore units are used, the span:depth ratio of the units and anyin situ concrete topping should not exceed 30.

C The minimum bearing length of the precast units should be 75 mm.

C For fire resistance periods of longer than 60 minutes:- the bottom flange should be fire protected;- reinforcement should be embedded in the voids of the hollowcore slabs,

and positively connected to the RHS section; and- an in situ concrete topping of at least 60 mm depth should be used.

The maximum span:depth ratio of the hollowcore units is adopted so that theinfluence of flexible supports on the shear resistance of the hollowcore units is notcritical to the design of the units. This limit may be relaxed if the manufacturertakes into account the influence of flexible supports in the design of the hollowcoreunits. An in situ concrete topping also reduces this effect considerably.

The reinforcing bars embedded in the hollowcore units should be a minimum of12 mm diameter, and two should be placed in every unit (but not less than everymetre). The bars may be attached to the RH SFB by a number of methods, such as:

C Welding to the section

C Bars looping around shear connectors

C L bars through the section, or angles welded to the section.

The RHS Slimflor bottom plate and fillet weld (minimum fillet weld size 8 mm)should be designed for the maximum shear force and torsional moment transferredby direct loading from the p.c. units. This approach is adopted irrespective of theuse of connecting reinforcing bars, detailed as above.

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3 CONSTRUCTION DETAILS

3.1 Beam to column connections 3.1.1 GeneralRHS edge beams are well suited to use with RHS columns. In the details presentedbelow, the perimeter columns are generally shown as RHS sections, althoughconnections can also be made to UC columns.

3.1.2 Non-composite edge beams Figure 3.1 shows typical structural details for non-composite RHS Slimflor edgebeams for the deck and slab orientations.

Figure 3.1(a) shows the case where the deck is orientated perpendicular to an RHSSlimflor edge beam. The edge beam has a 15 mm thick plate welded to theunderside that projects 100 mm from the face of the RHS. This 100 mm projectionacts as a suitable support to the decking.

If the bottom flange plate projects 100 mm from one side and, say, 10 mm from theother side, then the beam can be welded (flange plate to RHS) without the need forturning the section. However, this slight projection may affect the cladding detailsand therefore an alternative detail requiring welding to the underside may be used.

A full depth end plate that projects above and below the beam is welded to thesection. Conventional bolts may be used to connect the end plate to a UC column.This type of connection is effective in resisting torsional moments from the beam.

Flowdrill or Hollo-Bolt type bolting techniques are used to connect the edge beamto a RHS column. Adopting this form of fabrication provides a very neat solutionfor the beam to RHS column connection. However, due consideration must begiven to the erection tolerances, i.e. practical buildability of the system.

The tie member shown in Figure 3.1(a) is confined within the slab depth andprovides a support for the decking. This tie member can take the form of anysuitable structural section provided it can withstand part of the floor load in theconstruction stage, and will not deflect significantly between the columns. Thisarrangement would be suitable for buildings greater than four storeys and mustsatisfy code requirements for robustness. For reasons of cost and practicality, thetie member is likely to be fabricated from a structural Tee section.

Figure 3.1(b) shows the case where the decking runs parallel with the edge beam.Figure 3.1(c) shows an alternative tie detail for buildings up to four storeys high.The underside of the deck trough is supported by a separate plate welded to thecolumn. The main advantage of using this method of construction is that thedecking can be placed continuously at the column position and is not affected by thetie member.

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L RHS columnC

30

250

Cross-section through edge of building

100

225

60 or 70

'Flowdrill' typeconnection

L RHS columnC

Permanent tie

Elevation

15mm thickflange plate

(RHS or Tee section)

12mm thickend plate

SD225 deck250x150 RHS

(a) Decking placed perpendicular to edge beam

L RHS columnC

Temporary tie

600

Plate stop weldedto RHS column

(Any structural section)

L RHS columnC

Trimmer supportstrap

SD225 deck

Cold formedangle trimmer

200x100 RHS

(b) Decking placed parallel (c) Alternative tie detailto edge beam (up to 4 storeys only)

Figure 3.1 Typical structural details for the non-composite edge beams

Before the in situ concrete can be placed (normally by pumping), cold formed angleedge trimmers have to be connected to the RHS edge members. These edgetrimmers require support straps at approximately 400 mm centres. Also, barreinforcement (for fire resistance purposes) is placed in each trough and a layer ofmesh (A142) is positioned towards the surface of the slab with the minimum amountof cover.

Figure 3.2 shows an isometric projection of the details in Figure 3.1(b) in order tofurther illustrate the method of construction. The tie member between the columnsis not shown.

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Figure 3.2 Isometric projection of RHS edge beam and deep decking (tiemember omitted for clarity)

3.1.3 Composite edge beamsFigure 3.3 shows typical structural details for a composite RHS edge beam, wherethe decking is placed perpendicular to or parallel to the edge beam.

In this case, the basic construction details are similar to those shown in Figure 3.1,the main difference being the use of 19 mm diameter × 70 mm long shearconnectors (studs) welded to the upper surface of the RHS edge beam to achievecomposite action. In this case, the RHS wall thickness must be at least 8 mm,which is necessary to prevent burn through of the RHS.

In addition to the mesh reinforcement, transverse reinforcing bars (U bars) arerequired to ensure a smooth transfer of forces from the studs to the slab.

3.2 Support of cladding Cladding panels transmit lateral forces, arising from wind loading and other effects,to the building structure. Where cladding panels are connected to edge beams ofopen section, problems of transverse bending and torsion of the beam can arise.These are particularly severe when the top edge of a storey-height cladding panel isattached to the lower flange of the beam. Further information dealing with curtainwall connections can be obtained from the SCI Publication Curtain wall connectionsto steel frames(5).

Edge details in buildings often mean that it is difficult to avoid making connectionsto the lower flange of these open edge beams. Also, secondary steelwork may beneeded to provide lateral support to open sections; this can take various forms suchas wind restraint beams or diagonal struts connecting the lower flange of the beamsto the soffit of the floor slab. Both of these options have significant disadvantagesin terms of cost or installation time.

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L RHS columnC

85min

Mesh

60 min. (LWC) 70 min. (NWC)

200x100 RHS

a) Decking perpendicular to the edge beam

b) Decking parallel to the edge beam

L RHS columnC

End diaphragm

Mesh

11519 x 70 shear stud connectormin ∅

1005 thick plate

Tranverse reinforcement(U-bars)200x100 RHS

Cold formedangle trimmer

SD225 deck

Figure 3.3 Typical structural details for composite edge beams

For RHS edge beams it is unnecessary to stiffen the beams locally because, due totheir high torsional stiffness and strength, they are capable of resisting such actions.The RHS edge beam provides a structural solution that is simple, cost effective andarchitecturally pleasing.

3.2.1 Strongbacks and integral panelsStrongbacks

Stone veneer cladding and other thin materials, or materials with inadequatespanning capabilities, may be supported on frames known as strongbacks.Typically, these are aluminium, steel or stainless steel sub-frames, onto which panelsare screwed or bolted. One strongback may receive several cladding panels,enabling cladding such as stone to be used in relatively small, manageable sizes,appropriate to the structural properties of the veneer. Since the strongback resiststhe structural loads, it is usually possible to design panels to span from column tocolumn.

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Integral panels

Heavy reinforced concrete cladding panels, known as integral panels, are fixed tothe primary structure in a similar way to strongback panels. Integral panels may beeither top hung or bottom supported and typically bear onto the floor slab usingeither a boot (a projecting nib or ledge) or bolted on brackets (normally based uponan angle or series of angles).

Integral panels may be clad in other materials such as stone. The increased weightof these panels can lead to greater lateral loading of the edge beams, particularlywhere there is eccentric loading.

Supports

Support brackets for strongbacks or integral panels may be attached to columns, tothe floor edge, or to a combination of both. Panel head brackets may be fixeddirectly to channels or to other fixing points welded to the lower flange of the edgebeam.

Figure 3.4 shows a support arrangement for a typical strongback cladding panel.Top of slab brackets are cast into the floor, having been positioned using ‘chair’type brackets. The top of the fixing channels (or equivalent devices) is flush withthe top of the slab. Figure 3.5 shows the same detail in isometric view.

3.2.2 ‘Stick’ system‘Stick’ systems used in cladding comprise linear vertical and horizontal members.Vertical members (mullions) are nominally continuous, whilst horizontal members(transoms) are normally discontinuous. Conventionally, they are built in situ by thecladding contractor rather than the steelwork fabricator.

Stick systems are generally used for lighter cladding materials such as steel,aluminium and glass. The most common form of stick system comprises rectangularpanels restrained along four edges by extruded aluminium transoms and mullions.

Supports

Mullions in stick systems may be fixed either to columns or to edge beams. Thefixing arrangement will generally allow vertical movement due to deflection of thefloor, but must transmit lateral loads to the building structure.

RHS Slimflor edge beams will have better resistance to torsional bending than willconventional downstand edge beams. Brackets should be fixed directly to either thecolumns or the edge beams using channels welded to the outside face of thesteelwork, or other devices such as Flowdrill type connections.

Figure 3.6 shows the cross-section of an RHS attachment to a mullion andFigure 3.7 shows the same detail in isometric view.

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SD225 deck

Trimmersupport strap

SD225 deck

L RHS columnC

225

60 or 70

L RHS columnC

Note: Brackets have to fix to channels- these areeither welded to the underside of the steel plate (1)or cast flush with the concrete (2).a) Decking perpendicular to angle beam b) Decking parallel to edge beam

(2)

(1)

Figure 3.4 Alternative cladding attachment details

Figure 3.5 Strongback cladding system supported by RHS edge beams(isometric and plane views)

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CL RHS column

Mullion

Transom

Attachmentdetail

Figure 3.6 Detail of attachment of mullion

Figure 3.7 ‘Stick’ system cladding supported by composite RHS edgebeams (isometric and plan view)

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3.2.3 BrickworkBrickwork on multi-storey buildings has to be divided over its vertical height intoa series of structurally independent bands in order to reconcile the differentialmovement that can occur between the structure and the cladding. Brickworkexpands and contracts as a result of changes in temperature, experiences permanentmoisture expansion, and is susceptible to movement-related cracking.

Supports

In conventionally framed steel buildings, brickwork is supported off shelf angles.These stainless steel angles may be attached to the floor slab or to perimetersteelwork. Companies, such as Halfen, produce a comprehensive range of fittingsfor this purpose.

Fixing to the floor edge can be difficult to achieve when the slab is thin or wherethe brickwork is heavy (particularly where there is a large eccentricity in the shelfangle loading). Fixing to steelwork can be problematic in that the steel beam candeflect as the brickwork is erected, compromising structural integrity.

Shelf angles may be fixed to RHS members either by bolting them to fixing channelswelded to the face of the member, or using other devices such as Flow-drill typeconnections. RHS members are likely to have less tendency to deflect as a resultof heavy eccentric loading than are conventional steel edge beams.

Figure 3.8 shows the cross-section of an RHS attachment to a brickwork supportangle, and Figure 3.9 shows the same detail in isometric view.

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L RHS columnC

Brick supportangle(stainless steel)

Spacer bar

Figure 3.8 Detail of attachment of brickwork

Figure 3.9 Brickwork cladding support by composite RHS edge beam(isometric and plan view)

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4 DESIGN OF RHS SLIMFLOR EDGEBEAMS

4.1 Basis of designAs mentioned in Section 2, a RHS Slimflor beam used with deep decking, may bedesigned as either non-composite (see Figure 3.1), or composite (see Figure 3.3).Clearly, the different forms of construction give rise to different designconsiderations.

Both of these forms of construction may be used in cases where the decking isorientated, perpendicular or parallel, to the beam. The orientation of the deckingto the edge beam has an influence on how the loads are transmitted to the edgebeam.

It is normally preferable to select steel cross-sections that are plastic (Class 1) orcompact (Class 2). Semi-compact (Class 3) sections can be used, but they limit thedesign to the elastic moment resistance, which complicates the design proceduresand, more importantly, results in uneconomical use of the steel. In addition,BS 5950: Part 3(6) Clause 3.1 recommends the plastic design of cross-sections.

The general basis of design is normally applicable to:

(a) Unpropped simply supported beams, subject to uniformly distributed loading.

(b) Plastic or compact cross-sections.

(c) Plastic analysis of the cross-section is based on rectangular stress blocks.

(d) Moments and forces determined using factored loads.

(e) Serviceability checks determined using unfactored loads. To ensure thatirreversible deformation does not occur in the steel under normal service loads,the extreme fibre stress is limited to py. The in situ concrete stress is likewiselimited to 0.5 fcu.

This check is rarely critical, and is not required in hand calculations.However, it is included for completeness in the computer analysis.

(f) Deflections of edge beams that are normally limited to span/500 under imposedloads, and span/250 under total load. Pre-cambering should be consideredwhen the total deflection exceeds this limit. A further deflection limitation forcladding and imposed loads of span/360 should also be considered. More strictdeflection limits may be required for some forms of cladding.

(g) In the construction stage, the horizontal movement of the upper surface of theRHS is limited to span/500 in order to avoid possible problems with thecladding attachments. In addition, it is a requirement of BS 5950: Part 1(7) thatdue allowance should be made where deflections under serviceability loadscould impair the strength or efficiency of the structure or its components, orcause damage to the finishings.

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(h) The RHS Slimflor edge beam is considered to be laterally unrestrained at theconstruction stage, but restrained for the normal design.

On the above basis, design tables have been prepared and are presented inAppendix C (Design Tables C.1 to C.6). However, the design can be refined byusing computer software. Software for the design of RHS Slimflor edge beams canbe obtained from British Steel, Tubes & Pipes.

4.2 Construction stage loading During construction, the loading from the decking (chiefly the weight of the wetconcrete) produces out-of-balance (torsional) load effects on the edge beam. Also,a construction load of 0.5 kN/m2 over the total loaded area, in addition to the selfweight of the slab and beam, must be included when considering the design of theedge beam.

4.3 Torsional effects on the RHS edge beamAs stated previously, the edge beam is subjected to loads that can cause twisting ofthe beam. The design assumptions for the two methods of construction arepresented in the following sections:

4.3.1 Non-composite beamDeck orientated perpendicular to the edge beam

In the construction stage and in normal design, all floor loads (concrete, deck andconstruction load) are transmitted to the beam via the bottom flange plate. Claddingloads are assumed to be applied after the floor has been cast. The cladding loadspartially counteract the torsion from the floor loads.

Deck orientated parallel to the edge beam

In the construction stage and also in normal design, it is assumed that no loads aretransmitted to the bottom flange plate. It could be argued that there will be anominal load transmitted to the beam, but this is considered to be small and can beignored. The eccentric cladding loads are resisted by torsion and bending in theRHS edge beam.

4.3.2 Composite beamDeck oriented perpendicular to the edge beam

As for the non-composite beam, the construction loads (the weight of the concrete,decking and construction load) are transmitted to the beam via the bottom flangeplate. There is no cladding load at this stage

However, for the normal design, it is assumed that the imposed floor loading andcladding loads act concentrically on the edge beams, i.e. no torsional effects areconsidered. This is because the transverse reinforcement is looped around the shearconnectors welded to the section and out of balance moments are transferred directlyas bending in the slab.

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B

D

p

p

t

t

y

y

x x

d

B

b

Deck oriented parallel to the edge beam

As for the composite beam, it is assumed that no construction loads are applied tothe edge beam. With suitable transverse reinforcement, the cladding load isassumed to act concentrically to the edge beam and no imposed floor load is carriedby the edge beam.

4.4 Design of non-composite beams 4.4.1 Section classificationThe cross-section will normally be classified plastic or compact to BS 5950 (Class 1or 2 to EC3). The relevant dimensions are shown in Figure 4.1.

Figure 4.1 Section dimensions

The following width to thickness ratio limits are appropriate to a ‘compact’ section.

Internal element of the compression flange: b/t # 32,.

Web, generally: d/t # 98εα

where:

" =2yd

c

, = 1.0 for grade S275 steel

, = 0.88 for grade S355 steel

In most cases, the plastic neutral axis (pna) will be close to the bottom flange plate,which means that the section should be assumed as having compression throughoutthe web. From the above expression, it can be shown that, as yc . d, then " . 2.Thus from Table 7 of BS 5950: Part 1, the limiting classification check becomes:

d/t # 39, (this expression also applies to plastic and semi-compact sections).

This last expression is likely to govern the section classification of rectangularsections. However, for square sections, the internal element of the compressionflange (b/t # 32,) will, in the majority of cases, govern for a compact section.

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4.4.2 Lateral torsional buckling effectsLateral torsional buckling (LTB) of a closed section does not usually occur, becauseof the good torsional properties. Nevertheless, there is a check for LTB inAppendix B of BS 5950: Part 1(7) (Table 38). The limiting slenderness for boxsections is shown in Table 4.1.

Table 4.1 Limiting slenderness (8) for hollow sections of uniform wallthickness (BS 5950: Part 1, Table 38)

D/B 8

1 No limit

2 350 275y

×p

3 225 275y

×p

D, B are overall depth, width of section

respectively

4 170 275y

×p

Where the actual minor axis slenderness is less than 8 (as shown in the above

y

E

rL

table), no check for LTB is required and thus Mb = Mc = Sx py.

4.4.3 Biaxial stress effects in the flange plateFor the construction stage and normal design, it is assumed that all of the floor loadsare transferred to the edge beam via the bottom flange plate. Due to this loadingsystem, biaxial stresses will occur in the flange plate. The plate is subject tolongitudinal and transverse bending effects. The longitudinal stress due to overallbending of the section F1 has an influence in reducing the resistance of the platewhen also subject to a transverse bending stress, F2. This is irrespective of whetherthe stresses are plastic or elastic.

This action is illustrated in Figures 4.2 and 4.3.

RHS

Flangeplate

MX

Enlarged detail 'X'

Tensile stress due to overall bendingof the section

Figure 4.2 Diagrams showing how loads are applied to the bottom flangeplate

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t

t

t

c

c

(tension)σ 2

t (lever arm)

σ 2 (compression)

Plastic analysis

The effective transverse yield stress that may be resisted is reduced from py to F2

which, according to Von Mises yield criterion, is given by:

py2 = F2

2 - F1 F2 + F12

or F2 = ( )234

2/121

21 σσ −± yp

Figure 4.3 Plastic distribution through the flange plate

Using the above equations it can be shown that:

MM

cc pp y

= −212

2σ

where: c = (4py2 - 3F1

2)½

M is the maximum transverse moment applied to the plate (see Figure 4.2)

Mp is the moment resistance of the plate = t pp y

2

4tp is the plate thickness.

The graph shown in Figure 4.4 plots (M/Mp) on the vertical axis and (F1/py) on thehorizontal axis. This direct relationship between these two ratios gives a visualindication of the extent to which the longitudinal stress, F1, will influence thetransverse bending stress, F2.

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Plastic stresses1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.1 0.2 0.3 0.4 0.5 0.7 0.8 0.9 1.0

0.75

0.6

M/Mp

1 y /pσ

Figure 4.4 Graph showing the influence of the longitudinal stress on thetransverse bending stress for the plastic design

Example:

Say F1 = 0.6 py due to overall bending, then the plate transverse momentcapacity is . 0.75Mp

which equals per unit length of beam.34 4

316

22× = ×

t pt py

yp

p

This interaction between local transverse bending and longitudinal tension isincluded in the Worked Example given in Appendix A.

4.4.4 Out-of-balance floor loadingOut-of-balance loading is illustrated in Figure 4.5

PLAN

Edgebeam Deck

span

Typical cross-section throughthe edge beam

W

e

Figure 4.5 Typical plan layout showing edge beam arrangement

For the non-composite beam, it is assumed that all of the floor loads are eccentricto the edge beam. Where the decking is orientated perpendicular to the edge beam,the loads (W) are applied directly to the flange plate which, in turn, applies torsion

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to the beam. A rigorous method of analysis is used to combine the longitudinalbending effects with the torsion. This method of analysis is presented in the SCIpublication, Design of members subject to combined bending and torsion(8). It is notappropriate to fully illustrate its use here, but the fundamental equations are givenbelow. The worked example (Appendix A) fully demonstrates the methodology.Also, the rigorous approach covering this topic has been used for the computersoftware referred to in Appendix D.

There are two basic equations to be satisfied, as follows:

(i) Buckling check:

0.15.01byT ≤

+

++

b

x

y

w

b

x

MM

pMM σσ

where:

Mx is the applied moment in major axis of the beam

Mb is the lateral torsional buckling resistance moment, but generally willbe equal to Mc, plastic moment resistance.

FbyT = where: MyT = Mx NULS

M

ZyT

y

NULS is the angle of twist.

zy is the section modulus about the y-y axis

Fw is the warping stress (assumed to be zero for RHS).

(ii) Capacity check:

Fbx + FbyT + Fw # py

where:

Fbx is the longitudinal bending stress in the upper flange = MZ

x

x

zx is the section modulus about the x-x axis.

The other terms are explained above for the buckling check.

4.4.5 Moment resistance of non-composite beamFigure 4.6 shows the position of the plastic neutral axis (pna) in the web, at adistance yp below the centre line of the RHS. To analyse the moment resistancefrom this diagram would involve some tedious calculations. In order to simplify thecalculation, Figure 4.6 also illustrates a standard method of rearranging therectangular stress blocks.

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B

D

M

t

y

y

B

LC RHS

pna

2p

p

LC RHS

pna

Compression

Tensionp yp

y

yp

y

p

p

p

t

p

p (plate)yp (RHS)

p (RHS)y

s

y

pR pR

p

(a)

(b) (c)

Figure 4.6 Stress blocks for the non-composite beam

y p can be found by equating the tensile resistance of the plate Rp to the increasedcompressive zone in the web. Hence:

yp =R

p tp

y4

Moments are now taken about the mid-height of the RHS to determine the momentresistance Mc as follows:

Mc = Ms + Rp

−

+

y

ppp

4222 ptRRtD

ˆ Mc = Ms + ( )

−+

y

pp

p

ptR

tDR

42

where:

Ms = Sx py moment resistance of RHS section

Rp = Bp tp pyp and Bp and tp are the width and thickness of plate respectively.pyp is the design strength of the plates.

For other positions of the pna, Mc can be calculated using the formulae given inAppendix B.

The basic stress blocks are shown in Figure 4.6(a).

Addition of self-equilibrating stress blocks are shown cross-hatched as, inFigure 4.6(b), leading to the modified plastic analysis in Figure 4.6(c).

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4.4.6 Vertical shear capacityThe vertical shear capacity, Pv of the steel member is determined in accordance withBS 5950: Part 1, as follows:

PV = 0.6 py Av

where Av is the shear area taken as ABD

D

+

Vertical shear can influence the moment resistance of the beam. This occurs wherehigh shear and moment co-exist at the same position within the span. Simplysupported beams with one or two point loads are good examples of cases where thisoccurs. Point loads are not covered by this publication, as the scope of this designguide is restricted to simply supported edge beams with uniform loading only. Forthis condition, any influence the shear might have on the moment resistance isconsidered as minimal.

4.5 Design of composite beamsThe main assumptions and construction stage design are as for the non-compositebeam (see Section 4.4). For normal design it is assumed that the floor loads aretransferred to the composite section and not via the bottom flange plate, henceeliminating the torsion (out-of-balance loading).

4.5.1 Effective width of compression flangeThe effective width of slabs Be will vary at the ultimate and serviceability limit states

but a design value of for edge beams has been adopted for both cases in

+

28BL

BS 5950: Part 3: Section 3.1. The value of Be should not exceed the distancebetween beam centres, although this is not likely to occur in practice.

4.5.2 Modular ratioThe modular ratio is used for serviceability calculations and is the ratio of the elasticmoduli of steel and concrete. For buildings of normal usage, the modular ratioshould be assumed to be in the ratio of short term and long term values, reflectingthe influence of creep of concrete. This gives values of 10 and 15 for normal andlightweight concrete respectively for use in imposed load calculations.

4.5.3 Moment resistance of composite beamThe moment resistance of a composite RHS Slimflor edge beam is dependent on thedegree of shear connection acting between the concrete and steel beam.

Full shear connection

Full shear connection occurs where the number of shear connectors provided is atleast equal to that required to develop the full resistance of the concrete or the steelmember. This will generate the maximum moment capacity of the cross-section.

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Full shear connection exists when:

Rq $ Rc and Rq $ Rs + Rp

where:

Rq is given by the product of: number of shear connectors in the half span(between the positions of zero and maximum moments); the resistance of eachshear connector (determined from Table 5 of BS 5950: Part 3); a factor of 0.8;and for lightweight concrete by a further factor of 0.9. See Section 4.5.5 andTable 4.2 for the resistance of shear connectors.

Note: when yc = Ds, then Rq = Rc

The moment resistance for partial shear connection can be determined from otherpositions of plastic neutral axis, and formulae are given in Appendix B. In usingthese formulae:

Rc = Be (Dp + Ds - D) 0.45 fcu

Rp is as given in 4.4.5

Rs = A × py where A is the cross-sectional area of the RHS section.

Partial shear connection

Partial shear connection design may be used when there is an excess of momentresistance compared to the applied factored moment. In this situation, BS 5950:Part 3: Section 3.1 allows a reduction in the number of shear connectors that areneeded (to a maximum reduction of 40% for spans up to 10 m). For spans between10 and 16 m, the following relationship should be satisfied:

Na/Np $ (L - 6)/10 but Na/Np $ 0.4

where: Na/Np is the degree of shear connection, and L is the beam span (inmetres).

The principle is that the number of shear connectors may be reduced so that theforce transferred, Rq (see above), is sufficient to provide the required momentresistance. In this case, the force in the slab is Rq (not Rc) and the momentresistance may be determined from the stress blocks in Figure 4.7.

Position of plastic neutral axis (above mid-height of RHS):

yp =R R

p tq p

y

−×2 2

yp =R R

p tq p

y

−4

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B

D

y

D

D

M

a

b

p

ty

B

LC RHS

R

f

(R -R )

2ppna

p

e

p

q

cu

p

s

yp

y

y

p pq

R p

c

s

Bp

Figure 4.7 Typical cross-section through composite slab with partialshear connection

Taking moments about the mid height position of the RHS to find the momentresistance, Mc:

Mc = Ms + Rq a + Rp b + (Rq - Rp) yp/2

ˆ Mc = Ms + Rq a + Rp b - ( )

tpRR

y

2pq

8−

where:

Ms = Sx py

a = D DD y

s pc+ − −

2 2

yc =R

f Bq

cu e0 45.

b = 0.5 (D + tp)

4.5.4 DeflectionsTo provide general guidance on edge beam deflections is difficult because limitingdeflection will largely depend on the methods adopted for the edge beamconstruction as for the cladding design. The following recommendations areintended as a guide and apply to buildings of general usage using curtain walling ormasonry cladding. In this case the edge beam deflection is limited to span/500under imposed loads, and span/250 under total loads. A further deflection limitationfor cladding and imposed loads of span/360 should be considered.

In the construction stage, the horizontal movement of the top of the RHS is limitedto span/500. In addition, it is a requirement of BS 5950: Part 1 that due allowanceshould be made where deflections under serviceability loads could impair thestrength or efficiency of the structure or its components or cause damage to thefinishings. It may be necessary to adopt more severe limits for some forms ofcladding.

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Partial shear connection

As a consequence of the methods used for determining the moment capacity, anincrease in vertical deflection will have to be allowed for under serviceability loads.

Partial shear connection design results in a greater degree of slip occurring in theshear connectors which leads to an increase in vertical deflection. This is given bythe following expression for unpropped construction:

)(13.0 csp

ac N

N δδδδ −

−+=

where: *c is the deflection of the composite beam under imposed load

Na/Np is as given on page 26.

*s is the deflection for the steel beam acting alone under imposedload.

4.5.5 Shear connector designThe most popular size of shear connector available is the 19 mm diameter ×100 mm high (95 mm after welding). However, to keep the in situ concrete to aminimum thickness over the upper surface of the RHS, it is recommended to use the19 mm diameter × 75 mm high (70 mm after welding) stud. To prevent burnthrough, the diameter of the stud should not exceed 2.5 times the wall thickness ofthe RHS. Allowing for 15 mm cover, the minimum slab depth over the flangebecomes 85 mm. Any unnecessary increase in the concrete depth will obviously addfurther to the dead loads and produce greater construction depths.

The studs are generally welded to the upper surface of the RHS in the works priorto delivery to site. This procedure has the advantage over site welding in avoidingthe weather conditions that can interfere with the welding procedures.

Table 4.2 gives the characteristic resistance values for headed studs in normalweight concrete. For the use of lightweight concrete, the characteristic studresistances should be taken as 90% of the value given in Table 4.2. Where thedead loads are relatively high and deflections are to be kept to a minimum, the useof lightweight concrete may be a suitable alternative to normal weight concrete.

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Table 4.2 Characteristic resistances (kN) of headed stud shearconnectors (BS 5950: Part 3, Table 5)

Dimensions of stud shear connectors(mm)

Characteristic strength of concrete(N/mm2)

Diameter Nominalheight

As-weldedheight

25 30 35 $ 40

252219191613

100100100757565

959595707060

14611995827044

154236100877447

161132104917849

168139109968252

Notes:

1. For concrete of characteristic strength greater than 40 N/mm2 use the tabulated values for40 N/mm2

2. For connectors of height greater than tabulated, use the values for the greatest height tabulated.

3. Data provided is for normal weight concrete.

Shear connector spacing

The maximum longitudinal spacing between the shear connectors should not exceed600 mm, or four times the slab depth. In this instance, the slab depth is taken asthe smaller of the depth of in situ concrete above the upper surface of the RHS andthat above the deep decking. Figure 4.8 shows a plan of the RHS section with thelimiting dimensions for stud spacing.

5d

≥ 20

≥ 4ds

s≥≥ s3d

IN PAIRS STAGGEREDIN LINE

Edge of RHS Stud

Figure 4.8 Requirements for dimensional spacing of shear connectors

The minimum longitudinal spacing is five times the stud diameter, ds, and theminimum transverse spacing is four times the stud diameter (for studs in pairs),except when the studs are ‘staggered’.

4.5.6 Serviceability stressesStresses at the serviceability limit state are calculated to ensure that under workingloads no permanent deformations can occur in the steel member, leading to increaseddeflections.

The stress in the extreme fibre of the steel beam should not exceed the designstrength py and the stress in the concrete flange should not exceed 0.5 fcu.

The transverse moments in the bottom flange plate have to be combined with thelongitudinal stresses and compared to the design strength py of the steel member (seeSection 4.4.3 for further information).

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No account is taken of the effect of slip on these stresses and the associated forceson the shear connectors at the serviceability limit state.

Note, these stress checks do not control the design of non-composite beams and cangenerally be omitted. However it is included for completeness in the computersoftware (see Appendix D).

4.5.7 Transverse reinforcementTransverse reinforcement is used to ensure a smooth transfer of the longitudinalforce at the ultimate limit state (via the shear connectors) into the slab withoutsplitting the concrete. The potential shear failure plane (a-a) through the slab lieson only one side of the shear connectors, as shown in Figure 4.9.

The requirements of this section apply only to edge beams where the slab edge isless than 300 mm from the nearest row of shear connectors. In order to developtheir full resistance, the shear connectors must be less than 6ds from the slab edge.Additional transverse reinforcement should be placed in the form of U bars locatedbelow the top of the shear connectors. The diameter of the U bars should not beless than 0.5ds. Detailing rules are presented in Figure 4.9.

The shear resistance per unit length of each plane along the beam is given by:

vr = 0.7 Asv fy + 0.030 Acv fcu

but vr # 0 8. η A fcv cu

where:

fy is the yield strength of the reinforcement

fcu is the characteristic cube strength of the concrete in N/mm2, but not greaterthan 40 N/mm2

0 = 1.0 for normal weight concrete

0 = 0.8 for lightweight concrete

Acv is the average cross-sectional area, per unit length of the beam, of the concreteshear surface under consideration

Asv is the cross-sectional area per unit length of the beam of the combined top andbottom reinforcement crossing the shear surface, see Figure 4.9.

The longitudinal shear force per unit length, v, to be resisted, can be obtained fromthe spacing of the shear connectors.

v =NQs

where:

N is the number of shear connectors in a group

Q is the shear connector resistance for positive (sagging) moments

s is the longitudinal spacing of the shear connectors.

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This shear force to be resisted may be reduced according to the actual forcetransferred if more shear connectors are provided than required.

a

a

≥15

Mesh

Transversereinforcement

Cold formedangle trim

TYPICAL CROSS SECTION

s

s

s

Bar size φ

φ ≥

U-barss is the longitudinal spacing(centre-to-centre) of groupsof shear connectors

PLAN

SD225deep deck

0.5d

ds

s

Figure 4.9 Typical edge beam details and assumed shear failure planes atthe ultimate limit state

4.6 Minimum natural frequency of the edge beamThe design check on natural frequency is normally considered only for long spanbeams, but in view of the beam’s location at the edge of the slab, it would beprudent to check all edge beams, irrespective of the span.

For the purposes of design, a lower limit to the natural frequency of 4 Hz has beenfound to be adequate. The loading used for the calculation comprises all dead loads(including the cladding load), and 10% of the imposed load. In this instance,partitions are not included because they produce a dampening effect on the floorstructure.

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To determine the natural frequency of the floor beam, the following approximateexpression may be used:

fsw

= 18

δ

Where *sw is the deflection (in mm) of the beam (non-composite or composite,as appropriate) subject to the self weight of the floor including 10%of the imposed loads and cladding loads (but not including thepartition loads, see above). The effects of partial shear connectionneed not be calculated in this check.

Where a more exact design is required, reference should be made to the SCIpublication Design guide on the vibration of floors(9). Using that design guide, itmay be possible to justify the use of a lower value for the natural frequency.Normally this check is not required if the normal deflection limits for edge beamsare satisfied.

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5 FIRE RESISTANT DESIGN

Slimflor beams have inherently good fire resistance because they are partiallyencased within the floor slab. A fire resistance of up to 60 minutes can generallybe achieved without the need for applied fire protection. For longer periods of fireresistance, fire protection to the bottom plate is required.

A large number of fire tests have been carried out on Slimflor beams using deepcomposite slabs, leading to the design recommendations contained in SCI publicationSlim floor construction using deep decking(2). These recommendations may beextended to cover the design of rectangular hollow sections as Slimflor edge beams.The important parameter is the rate of heating of the RHS section, which has beenestablished by small-scale tests, and by a major full-scale fire test carried out atTNO in the Netherlands.

It is not intended to review the fire engineering method or the existing testinformation in detail, but rather to concentrate on the implications for RHS Slimfloredge beams.

5.1 General requirements of BS 5950: Part 8No specific requirements for slim floor construction are presented in BS 5950:Part 8(10). However, the strength reduction factors for structural steel and concreteat elevated temperatures are given. It is assumed that the strength reduction for steelcorresponding to 2% strain is appropriate for slim floor beams at the largedeformations experienced in fire.

Partial factors for loads are also defined in BS 5950: Part 8. A partial factor of 0.8may be used for variable imposed loads and 1.0 for all permanent loads at the firelimit state. The ratio of the applied loads at the fire limit state to the load resistanceof the member in normal conditions is generally in the range of 0.45 to 0.55 forpractical design cases.

The minimum depth of composite slabs required to satisfy the insulation criterionof BS476(11), the fire testing standard, is also given in BS 5950: Part 8. Fire testshave confirmed that these are applicable to slabs constructed using SD 225 decking.These values are presented in Table 5.1.

Table 5.1 Minimum slab depths to satisfy the insulation criterion forcomposite slabs with SD 225 deep decking

Fire Resistance(minutes)

Slab topping depth (mm) Total slab depths (mm)

NWC LWC NWC LWC

30 60 50 285 275

60 70 60 295 285

90 80 70 305 295

120 95 80 320 305

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The integrity criterion of BS 476 is satisfied by the presence of the steel deckingbeneath the slab and mesh reinforcement in the concrete topping. The momentresistance of a composite slab in fire is established from first principles using themethod described in BS 5950: Part 8, taking account of the reduced strength of allthe elements at elevated temperatures.

5.2 Heating rate for RHS edge beamsThe heating rate for conventional Slimflor beams is a function of the location of thesteel element within the concrete encasement. After 60 minutes exposure, thetemperature of the exposed bottom plate is typically 150EC below that of the fire.Furthermore, the temperature of the bottom flange is 60E to 80EC below that of thebottom plate, because of the thermal resistance of the slight air gap between theplate and flange.

The temperatures in the web of Slimflor beams reduce with the depth into theconcrete encasement, and at mid-height of the web the temperatures are such thatthe steel strength is unaffected.

However, the heating rate of a RHS Slimflor edge beam increases relative to aconventional Slimflor beam because:

C the bottom plate is not connected to the concrete over its full width

C the bottom flange of the hollow section is not connected to the concrete

C the inner web of the hollow section is only connected to the concrete on oneface

C the outer web of the hollow section is not connected to the concrete, althoughin general it will be insulated by its connection to the cladding, or by additionalfire protection on the outer face.

The heating rate has been established in a number of unloaded tests and in a loadedtest at TNO (see Section 5.4). The typical temperatures in a typical RHS sectionafter 60 minutes exposure are shown in Figure 5.1(a).

800800 850 820

250

400500

1.0

0.4

Plastic neutralaxis in fire

a) Temperatures in the steel

Insulation

b) Strength retention factors

0.1 0.08 0.1

0.8 0.97

0.23700

Figure 5.1 Temperatures and strength retentions in a RHS edge beam at60 minutes fire resistance

Provided the beam is of sufficient depth, it is possible to expose the top part of thebeam and still achieve the minimum slab depth. In this case, the upper exposed partof the RHS will experience a rise in temperature greater than the 140°C limitspecified in BS 476. Upper surface temperatures of between 200 and 300°C can be

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expected. This temperature rise is not acceptable and some form of insulation or shielding must be considered. It may be possible to detail a wall to cover the topof the section, or some form of non-combustible insulation should be applied.Approximately 20 mm of insulation will be required.

5.3 Moment resistance of RHS edge beams in fireThe reduced moment resistance of RHS edge beams at the fire limit state iscalculated on the following assumptions:

C the temperatures are determined by computer analysis, which has beencalibrated using data from fire tests

C composite action is developed with the concrete encasement for beams designedcompositely and incorporating shear connectors

C the strength reduction factors for steel are based on the 2% strain limit inBS 5950: Part 8

C for composite beams, concrete in compression is fully effective, but concretein tension is ignored

C partial factors for all materials are set to unity.

Typically the strength reduction factors (more correctly strength retention factors)in an RHS edge beam are illustrated in Figure 5.1(b). The plastic neutral axisdefines the level at which the residual tensile resistance of the section equals thecompressive capacity of the colder upper part of the section and the concrete slab.

The moment resistance of the section may be established by taking moments of thestress blocks of the various elements, acting at their reduced strength, about theplastic neutral axis. The maximum load ratio that can be sustained in fire conditionsis defined by:

Load ratio =Moment resistance in fire

Moment resistance at 20 C°

The moment resistance at 20°C is calculated assuming composite or non-compositesection properties as appropriate. Typically, the load ratio that can be sustained byan RHS slim floor edge beam is 0.5 at 60 minutes’ fire resistance.

The term load ratio is used in BS5950: Part 8. In the Eurocodes(14),(15) theequivalent term is load level, which is defined in the same way.

5.4 Fire test at TNO in the Netherlands5.4.1 Test dataA major fire test was carried out at TNO in the Netherlands in September 1996 aspart of an ECSC research project. The test consisted of a single span slab with twoRHS edge beams. The overall dimensions of the test specimen were 5.6 m long ×4.6 m wide, the beams spanning the shorter distance. The test load was typical ofnormal office loading. The slab depth in normal weight concrete was 290 mm. Theform of construction is shown in Figure 5.2, and the relevant test data are presentedin Table 5.2.

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The slab was unrestrained against thermal expansion, and the 200 mm × 100 mmRHS edge beams were torsionally restrained at both ends. The torsional momenton one beam was recorded during the test.

600

600

600

600

600

600

600

4200 4800

5500

A AB

B

250

290200

15

A192 mesh

75

210

25 Dia.6mm fillet

weld

210290

7525mm Dia.

Plan

Section A-A

Section B-B

Figure 5.2 Details of TNO fire test

The edge beams were designed to achieve at least 60 minutes fire resistance, and thecomposite slab was reinforced to achieve 120 minutes fire resistance. Therefore,in order to gain information on the fire resistance of the slab, the beam wasprevented from collapsing by blockwork plinths in the furnace, which werepositioned 200 mm below the beams.

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Table 5.2 Data from TNO fire test

Element Data

Beam span (m) 4.6

Slab span (m)(centre of bearing)

5.4

Test load (kN/m2) 3.55

Self weight (kN/m2) 3.1

Steel section (mm) RHS 200×100×10 thick

Steel plate (mm) 250 × 15

Steel strength (N/mm²)

409 (section)349 (plate)

Slab depth (mm) 290

Concrete strength(N/mm²)

49.5

Bar diameter (mm) 25

Axis distance (mm) 75

5.4.2 Test resultsThe RHS edge beam achieved a fire resistance of 90 minutes, and the composite slabachieved a fire resistance of 128 minutes. The test was terminated when the centraldeflection of the slab was 460 mm. The measured maximum deflection for the testis shown plotted against time in Figure 5.3.

0 20 40 60 80 100 120 1400

100

200

300

400

500

Time (mins)

Verti

cal d

ispl

acem

ent (

mm

)

Slab

Beam

Figure 5.3 Central slab deflection measured in TNO fire test

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The temperatures measured in the important elements of the cross-section aresummarised in Table 5.3.

Table 5.3 Temperatures in the important elements of the TNO test

ElementTemperature at time of

60 mins 90 mins Time at failure

Edge beamBottom plateBottom flangeTop flange

810687340

930880450

90 minutes

Composite slabBar ReinforcementSlab surface

32090

535110

128 minutes

Based on these temperatures, the calculated moment resistances after 90 minutes and120 minutes are compared to the applied moments in Table 5.4. For the beam,good correlation is obtained, but the calculated resistance of the slab is only 50%of the applied moment. This difference is thought to be due to in-plane membraneeffects in the slab, which could have been exaggerated by the physical size of thetest specimen. A smaller difference might have been expected if the beam span hadbeen greater.

Table 5.4 Applied moments and calculated resistances in the TNO test

Element

Moments (kNm)

Applied Calculated

Edge beam 53.151.2

(at 90 minutes)

Composite slab 12.56.23

(at 120 minutes)

Using the measured beam temperatures, the calculated load ratio that could beachieved after 60 minutes fire exposure was 0.52.

On the basis of this major fire test, it was concluded that the calculation method isconservative.

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5.5 Design tables for RHS edge beamsDesign tables for RHS edge beams have been prepared giving moment resistanceand load ratio at 60 minutes exposure, and are presented in Tables 5.5 and 5.6. Thetables cover both composite and non-composite beams using normal and lightweightconcrete with steel grade S355. For practical purposes the RHS depths have beenlimited to 350 mm.

The minimum slab depth for normal weight concrete is 295 mm, which is greaterthan the minimum slab depth for lightweight concrete of 285 mm. This differencehas no effect for non-composite construction, but can make up to 10% difference inmoment resistance for composite construction.

In the tables for non-composite beams (Table 5.5), the slab depth has been adjustedso that the minimum cover to the beam is 30 mm. Provided the beam is ofsufficient depth, it is possible to expose the top part of the beam and still achieve theminimum slab depth but then insulation must be provided to the top flange. Thiscase is not covered in the tables.

In the tables for composite beams, the effective width of the slab has been taken as3 × beam depth in order to be independent of the beam span.

Where the load ratio exceeds 0.5, the fire design case would probably not becritical. In practice, many Slimflor beams are designed to satisfy serviceabilitycriteria, in which case the required load ratio may be well below 0.5.

The tables are presented for the case in which the deep deck spans perpendicular tothe edge beam. For the case where the deck runs parallel to the edge beam themoment resistance in fire should be reduced by 5%. This is because the beam issubject to slightly greater exposure to fire in this condition. However, this case isunlikely to be critical because of the lower loading acting on these beams.

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Table 5.5 Design table for non-composite RHS edge beams(60 min fire resistance)

Size ofRHS section

Slab depth (mm) Moment resistance (kNm) Loadratio

NWC LWC Ultimate limitstate

Fire limit state

200x100x5 295 285 108.1 47.2 0.44

200x100x6.3 295 285 137.4 57.7 0.42

200x100x8 295 285 167.2 71.6 0.43

200x100x10 295 285 200.6 89.2 0.44

200x100x12.5 295 285 235.7 112.1 0.48

200x100x16 295 285 275.9 142.8 0.52

200x150x5 295 285 130.1 60.3 0.46

200x150x6.3 295 285 161.1 73.4 0.46

200x150x8 295 285 197.3 90.6 0.46

200x150x10 295 285 240.2 112.5 0.47

200x150x12.5 295 285 285.9 141.4 0.49

200x150x16 295 285 341.4 181.6 0.53

250x150x5 295 285 179.5 86.4 0.48

250x150x6.3 295 285 223.3 105.9 0.47

250x150x8 295 285 282.1 131.1 0.46

250x150x10 295 285 337.0 162.8 0.48

250x150x12.5 295 285 398.7 204.0 0.51

250x150x16 295 285 473.5 262.1 0.55

300x200x6.3 330 330 333.0 167.3 0.50

300x200x8 330 330 416.2 207.4 0.50

300x200x10 330 330 508.8 257.6 0.51

300x200x12.5 330 330 605.6 323.4 0.53

300x200x16 330 330 724.0 416.6 0.58

300x250x6.3 330 330 369.0 191.1 0.52

300x250x8 330 330 466.4 236.3 0.51

300x250x10 330 330 567.7 293.4 0.52

300x250x12.5 330 330 683.5 368.3 0.54

300x250x16 330 330 825.2 476.0 0.58

200x120x5 295 285 120.1 52.4 0.44

200x120x6 295 285 141.5 61.3 0.43

200x120x6.3 295 285 145.4 63.9 0.44

200x120x8 295 285 180.9 79.4 0.44

200x120x10 295 285 216.8 98.6 0.45

200x120x12.5 295 285 256.1 123.9 0.48

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Table 5.5 Continued

Size ofRHS section

Slab depth (mm) Moment resistance (kNm) Loadratio

NWC LWC Ultimate limitstate

Fire limit state

250x100x6.3 295 285 195.0 86.0 0.44

250x100x8 295 285 239.9 106.9 0.45

250x100x10 295 285 284.0 133.0 0.47

250x100x12.5 295 285 330.4 166.1 0.50

250x100x16 295 285 386.8 212.6 0.55

260x140x6.3 295 290 235.6 108.9 0.46

260x140x8 295 290 289.6 135.1 0.47

260x140x10 295 290 346.7 167.8 0.48

260x140x12.5 295 290 409.0 210.0 0.51

260x140x16 295 290 484.3 269.6 0.56

300x100x6.3 330 330 264.7 118.9 0.45

300x100x8 330 330 320.2 148.6 0.46

300x100x10 330 330 376.0 184.9 0.49

300x100x12.5 330 330 436.6 231.2 0.53

300x100x16 330 330 512.3 296.6 0.58

200x200x5 295 285 149.1 73.3 0.49

200x200x6.3 295 285 187.1 88.6 0.47

200x200x8 295 285 227.3 109.0 0.48

200x200x10 295 285 278.0 135.3 0.49

200x200x12.5 295 285 335.4 170.0 0.51

200x200x16 295 285 403.7 219.4 0.54

250x250x6.3 295 285 286.2 145.0 0.51

250x250x8 295 285 357.6 178.4 0.50

250x250x10 295 285 432.6 221.2 0.51

250x250x12.5 295 285 524.5 277.7 0.53

250x250x16 295 285 636.5 359.0 0.56

300x300x6.3 330 330 404.4 214.6 0.53

300x300x8 330 330 510.5 264.5 0.52

300x300x10 330 330 621.8 328.6 0.53

300x300x12.5 330 330 757.3 412.5 0.54

300x300x16 330 330 923.3 534.8 0.58

Note:1. Tabulated values are for decking perpendicular to edge beam. For the case where the deck runs

parallel to the edge beam the moment resistance in fire should be reduced by 5%.2. The moment resistance is based on grade S355 steel and that the Slimflor beam is constructed

using 15 mm plate. The plate is assumed to be 120 mm wider than the RHS section.3. The slab thicknesses are the minimum and are applicable to SD 225 steel deck.

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Table 5.6 Design table for composite RHS edge beams(60 min fire resistance)

Concrete Normal weight concrete Lightweight concrete

Section size (mm)

Slabdepth(mm)

Momentresistance (kNm)

Loadratio

Slabdepth(mm)

Momentresistance

(kNm)

Loadratio

Ultimatelimitstate

Firelimitstate

Ultimatelimitstate

Firelimitstate

200x100x8 295 265.5 136.4 0.51 285 248.0 124.4 0.50

200x100x10 295 293.2 157.1 0.54 285 276.4 144.5 0.52

200x100x12.5 295 322.6 182.6 0.57 285 306.3 169.4 0.55

200x100x16 295 358.7 216.5 0.60 285 342.0 202.8 0.59

200x150x8 295 301.5 153.5 0.51 285 285.5 142.0 0.50

200x150x10 295 339.0 178.5 0.53 285 321.0 166.5 0.52

200x150x12.5 295 380.7 210.4 0.55 285 362.9 197.9 0.55

200x150x16 295 429.6 254.6 0.59 285 412.6 240.5 0.58

250x150x8 335 453.0 228.7 0.50 335 453.0 228.7 0.50

250x150x10 335 499.1 267.7 0.54 335 499.1 267.7 0.54

250x150x12.5 335 550.8 315.9 0.57 335 550.8 315.9 0.57

250x150x16 335 616.3 381.3 0.62 335 616.3 381.3 0.62

200x120x8 295 280.7 143.2 0.51 285 262.6 131.7 0.50

200x120x10 295 311.4 165.8 0.53 285 295.0 153.2 0.52

200x120x12.5 295 346.5 194.2 0.56 285 329.4 181.0 0.55

250x100x8 335 400.9 209.6 0.52 335 400.9 209.6 0.52

250x100x10 335 435.5 242.8 0.56 335 435.5 242.8 0.56

250x100x12.5 335 474.7 283.0 0.60 335 474.7 283.0 0.60

250x100x16 335 525.7 336.5 0.64 335 525.7 336.5 0.64

260x140x8 345 480.8 244.6 0.51 345 480.8 244.6 0.51

260x140x10 345 525.3 285.8 0.54 345 525.3 285.8 0.54

260x140x12.5 345 578.0 335.7 0.58 345 578.0 335.7 0.58

260x140x16 345 644.3 404.5 0.63 345 644.3 404.5 0.63

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Table 5.6 Continued

Concrete Normal weight concrete Lightweight concrete

Section size (mm)

Slabdepth(mm)

Momentresistance (kNm)

Loadratio

Slabdepth(mm)

Momentresistance

(kNm)

Loadratio

Ultimatelimitstate

Firelimitstate

Ultimatelimitstate

Firelimitstate

200x200x8 295 330.7 170.0 0.51 285 312.8 159.1 0.51

200x200x10 295 379.6 199.8 0.53 285 356.9 187.9 0.53

200x200x12.5 295 433.6 237.4 0.55 285 415.8 225.6 0.54

200x200x16 295 497.5 290.8 0.58 285 480.2 277.5 0.58

250x250x8 335 537.7 266.4 0.50 335 537.7 266.4 0.50

250x250x10 335 609.2 316.3 0.52 335 609.2 316.3 0.52

250x250x12.5 335 690.3 379.1 0.55 335 690.3 379.1 0.55

250x250x16 335 791.4 469.1 0.59 335 791.4 469.1 0.59

Note:1. The table is based on 40% shear connection and can conservatively be used for higher degrees

of shear connection.2. Tabulated values are for decking perpendicular to edge beam. For the case where the deck runs

parallel to the edge beam the moment resistance in fire should be reduced by 5%.3. The moment resistance is based on grade S355 steel and that the Slimflor beam is constructed

using 15 mm plate. The plate is assumed to be 120 mm wider than the RHS section.4. The slab thicknesses are the minimum and are applicable to SD 225 steel deck.

5.6 Additional fire protectionThe procedures described in the previous Sections apply where the bottom plate ofthe RHS is unprotected, which is generally the case for 60 minutes fire resistance.For longer periods of fire resistance, the recommended design procedure is tomaintain a limiting temperature of not more than 700°C in the bottom plate by usingan appropriate thickness of fire protection. At this temperature, RHS Slimflor edgebeams will achieve a load ratio of at least 0.6.

This protection thickness can be conservatively calculated using a section factor of1/tp, where tp is the plate thickness in metres. For example, when tp is 15 mm, thesection factor is 67 m-1. Design tables for standard products are presented in theASFPCM/SCI publication Fire protection for structural steel in buildings(11).

Typically, a minimum of 12 mm of board or spray protection to the bottom plate isrequired for 90 minutes fire resistance, increasing to 20 mm for 120 minutes fireresistance. Intumescent coatings may also be used, and there is sufficient testinformation to demonstrate their performance for up to 90 minutes fire resistance.Some protection manufacturers have more accurate data and may be able to offerappreciably reduced thicknesses of protection for all types of slim floor beam.

The exposed side of the RHS should also be protected either by its attachment to thecladding material (such as blockwork or brickwork) or by a board or mineral woolmaterial. Any gap between the RHS and cladding should be “fire stopped” toprevent passage of smoke and hot gases.

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6 REFERENCES

1. MULLETT, D.L.Slim floor design and constructionThe Steel Construction Institute, 1992

2. MULLETT, D.L. and LAWSON, R.M.Slim floor construction using deep deckingThe Steel Construction Institute, 1993

3. LAWSON, R.M., MULLETT, D.L., and RACKHAM, J.W.Design of Asymmetric Slimflor® Beams using deep composite deckingSCI, 1997

4. BRITISH STANDARDS INSTITUTIONBS 5950: Structural use of steelwork in buildingPart 4: Code of practice for design of floors in profiled steel sheeting BSI, 1990

5. BRITISH STANDARDS INSTITUTIONDD ENV 1994-1-1: 1993 Eurocode 4: Design of composite steel and concretestructuresPart 1.1: General rules and rules for buildingsBSI, 1993

6. OGDEN, R.G.Curtain wall connections to steel framesThe Steel Construction Institute, 1992

7. BRITISH STANDARDS INSTITUTIONBS 5950: Structural use of steelwork in buildingPart 3: Codes of Practice for design in composite constructionSection 3.1: Design of simple and continuous composite beamsBSI, 1990

8. BRITISH STANDARDS INSTITUTIONBS 5950: Structural use of steelwork in buildingPart 1: Code of Practice for design in simple and continuousconstruction: hot rolled sectionsBSI, 1990

9. NETHERCOT, D.A., SALTER, P.R. & MALIK, A.S.Design of members subject to combined bending and torsionThe Steel Construction Institute, 1989

10. WYATT, T.A.Design guide on the vibration of floorsSCI in association with CIRIA, 1989

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11. BRITISH STANDARDS INSTITUTIONBS 5950: Structural use of steelwork in buildingPart 8: Code of Practice for fire resistant designBSI, 1991

12. BRITISH STANDARDS INSTITUTIONBS 476: Fire tests on building materials and structuresPart 20: Method of determination of the fire resistance of elements ofconstruction (general principles), and,Part 21: Method of determination of the fire resistance of load bearing elementsof constructionBSI, 1987

13. ASSOCIATION OF STRUCTURAL FIRE PROTECTIONMANUFACTURERS AND CONTRACTORSFire protection of structural steel in buildings (2nd Edition, revised)ASFPCM/SCI/FTSG, 1992 (Now ASFP)

14. BRITISH STANDARDS INSTITUTIONDD ENV 1993-1-2: Eurocode 3: Design of steel structuresPart 1.2: Structural fire design (including UK NAD)BSI, 1997 (expected)

15. BRITISH STANDARDS INSTITUTIONDD ENV 1994-1-2: Eurocode 4: Design of composite steel and concretestructuresPart 1.2: Structural fire design (including UK NAD)BSI, 1997 (expected)

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APPENDIX A Typical Worked Example for RHSEdge Beam

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In-situ concrete

100

BearingBrickwork50mm to 75mm

Mesh

The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 1 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

NON-COMPOSITE, RHS SLIMFLOR EDGE BEAM DESIGNPlan of building

B B

Deckspan

Cornercolumn

A

Axx

6m

6m

Beam to be designed is marked x-x

Section A-A

For the purposes of this design example,the minimum bearing length (50 mm)has been used.

The example uses SD225 deep decking.

Section B-

B

Coldformedangle

65

225

Data: Concrete: Lightweight (dry density = 1900 kg/m3)Steel: Section: 250 × 150 × 16 mm thick RHS in S355 steelPlate: 270mm wide × 15 mm thick in S355 steelDeck: Depth 225 mm, ribs at 600 mm centres, (SD225)Slab: Depth 290 mm

Slab & beam unpropped

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 2 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

DESIGN OF EDGE BEAM (see Section A-A)

LOADING

Dead Load

Steel beam: self-weight = 1.2 kN/m(including plate)

Concrete: slab-weight (LWC) = 2.44 kN/m2 (see PMF literature)

Decking = 0.2 kN/m2

Ceiling & Services = 0.5 kN/m2

Cladding = 8 kN/m

Imposed Load

Occupancy = 3.5 kN/m2

Partitions = 1.0 kN/m2

Other Loading

Construction load = 0.5 kN/m2

CONSTRUCTION STAGE

The design process for the construction stage is similar in approach to the ultimate limit state(ULS) conditions. This is because no composite action is assumed to occur with the concreteencasement at the ULS. This means that the assumed load path (all loads) to the beam is via the bottom flange plate welded to the RHS. Also, in the construction stage the RHS is notsubjected to lateral torsional buckling (LTB) as would be the case for an open section. Hence, the design example for this case will ignore the construction stage design.

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 3 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

ULTIMATE LIMIT STATE - NON-COMPOSITE SLIMFLOR BEAM

150 150

3

2

1

75

Loading Summary

1. Cladding = 1.4 × 8.0 × 6 = 67.2 kN2. Self weight = 1.4 × 1.2 × 6 = 10.1 kN3. Dead + Imposed = 1.4 × 18 × (0.2 + 2.44 + 0.5) × 18 + 1.6 × 4.5 × 18

= 208.7 kN

N.B. Load 3 is assumed to act at the centre of deck bearing, i.e. 100 - = 75 mm502

Stress Resultants

Torque = × 150 = 21.2 kNm1000

2.677.208 −

Bending moment = (67.2 + 10.1 + 208.7) × = 214.5 kNm68

CHECK TRANSVERSE BENDING IN PLATE FLANGE

Moment: M = = 15.7 kNm1000

757.208 ×

Mc(plate) = × 355 = 119.8 kNm6000 154 10

2

6

××

= = 0.131M

Mc (plate) 8.119

7.15

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 4 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

ˆ from Figure 4.4 (ref. 1): = 0.97σ 1

py

ˆ Maximum stress available for primary bending F1 = 344 N/mm2

CHECK FOR COMBINED BENDING AND TORSION

Section: 250 × 150 × 16 RHS: S355

Section dimensions

Major axis bending

B = 150 mmts = 16 mm

t s

C RHSL py

t p Bp

D

B

D = 250 mmBp = 270 mmtp = 15 mm

Design stresses: Section: py = 355 N/mm2 - S355 steelPlate: py = 344 N/mm2 - S355 steel

Section classification

By inspection, the section classification criterion is for the web in compression.

ˆ ε39td ≤

where:d d = D - 3ts = 250 - 3 × 16 = 202 mmt = 16 mm

, = = 0.882121

y 355

275

p

275

=

= 12.6 < 39 × 0.88 = 34.3dt s

= 20216

ˆ Section is plastic

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 5 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

Plastic moment of resistance, Mc

Plastic section modulus of RHS = 924 cm3

Ms = Sx py = 924 × 355 × 10-3 = 328 kNmRp = Bp tp pyp = 270 × 15 × 344 × 10-3 = 1393.2 kN

Position of plastic neutral axis, yp

yp = = = 61.3mmys

p

pt4

R

355164

102.1393 3

×××

Taking moments about the RHS centre line, plastic moment of resistance of the Slimflor beamis:

Mc = Ms + (D + tp) - Rp

Rp

2 2

yp

The derivation for Mc is given in Appendix B.

ˆ Mc = 328 +3102

2.1393

×( )

2

3.61

10

2.139315250

3×−+

= 469.9 kNm

Elastic section properties

(i) Major axis section properties

Position of elastic neutral axis, yex, below centre line of RHS:

yex =)AA(2

)tD(A

p

pp

+

+

where: Ap = 15 × 270 = 4050 mm2

A = 11700 mm2

ˆ yex = = 34.1 mm)117004050(2

)15250(4050

+

+

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 6 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

Second moment of area, Ixx

Ixx = IRHS +Ak12 + Apk2

2

where: k1 = yex = 34.1 mm

k2 = - yex2

t

2

D p+

= - 34.1 = 98.4 mm2

15

2

250 +

Ixx = 9089 × 104 + 11700 × 34.12 + 4050 × 98.42

ˆ Ixx = 144 × 106 mm4

Section modulus, Zt

Zt(compression) = where: yc = D/2 + yex =c

xx

y

I1.34

2

250 +

= 159.1 mm

=3

6

101.159

10144

××

= 905 cm3

Zb (tension) = Ixx/(D/2 + tp - ycx) = = 1360 cm3

144 102502

15 34 1

3×

+ −

.

(ii) Minor axis section properties

Position of elastic neutral axis, yey, from centre line of RHS

yey = [ (B/2 + p) - (Bp/2)] where p = plate projection = 100 mm )AA(

A

p

p

+

=117004050

4050

+( )

+

2

270100 150/2

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 7 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

= 10.3 mm

Iyy = Iy (RHS) + Ak12 + Iy (plate) + Apk2

2

Where : k1 = yey = 10.3 mm

k2 = B/2 + p - yey - Bp/2

k2 = + 100 - 10.3 - 270/2 = 29.7 mm2

150

Iy (plate) =12

Bt 3pp

= = 2460.4 cm4

12

27015 3×

Iyy = 3943 × 104 + 11700 × 10.32 +2460 × 104 + 4050 × 29.72

= 68.8 × 106 mm4

Zy = =y

I yy

3

6

107.164

108.68

××

= 417.7 cm3

St Venant torsion constant (J):

J = JRHS + a Bptp3 = 8863 × 104 + a × 270 × 153

= 88.9 × 106 mm4

Minor axis radius of gyration (ry)

ry = = 66.1 mm5.06

5.0

P

yy

15750

108.68

AA

I

×=

+

Slenderness:

8 = = = 90.8y

e

r

L

1.66

6000

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 8 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

As the section is closed, it is very stiff in torsion. Therefore, it is unlikely that lateral-torsionalbuckling should be checked. Nevertheless, the check for this case is in Appendix B ofBS 5950: Part I - Table 38 as follows:

D/B = 1.67 < 2.0

ˆ Limiting slenderness = = 271355

275350 ×

ˆ 8 < limiting slenderness of 271

Y no lateral-torsional buckling check is required and

Mb = Mc = 469.9 kNm

CAPACITY CHECKS - BENDING AND TORSION

Tq = 21.2 kNm

M̄x = 214.5 kNm (M̄x = mMx where m = 1.0)

Distribution of torsion along the beam:

ˆ Tave = = = 5.3 kNm4

Tq

4

2.21

Twist: NULS = =GJ

zTave

6

6

109.8879000

3000103.5

××××

= 0.0022 rads

Longitudinal bending stress in top flange:

Fbx = = = 237 N/mm2

x

x

Z

M3

6

10905

105.214

××

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 9 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

Transverse bending in top flange due to twisting:

MyT = M̄x NULS = 214.5 × 0.0022 = 0.47 kNm

ˆ stress: FbyT = = 1.13 N/mm2

3

6

107.417

1047.0

××

Warping stress (assumed to be zero for RHS)

ˆ Fw = 0

(i) Buckling Check

0.1M

M5.01

pM

M

b

x

y

wbyT

b

x ≤

+

++

σσ

ˆ = 0.46 # 1.0 ˆ OK

×+

++9.469

5.2145.01

355

013.1

9.469

5.214

(ii) Capacity check

Fbx + FbyT + Fw # py

ˆ 237 + 1.13 + 0 = 238.1 N/mm2 # 355 N/mm2 ˆ OK

Shear capacity of webs of RHS

Design requirement

Fv < 0.6 py Av

Av = A

+ BD

D

Av = 11700 = 7312.5 mm2

+ 150250

250

Fv = = 143.0 kN2

2.671.107.208 ++

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 10 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example of non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

0.6 py Av = = 1557.6 kN1000

5.73123556.0 ××

ˆ Fv < 0.6 py Av

Shear capacity is OK

ˆ Section satisfies all ULS criteria

SERVICEABILITY LIMIT STATE (SLS)

Elastic section properties (bare section)

250

AN

270

y

15

Ixx = 144 × 106 mm4

Ixx = 905 × 103 mm3

DEFLECTIONS

CONSTRUCTION STAGE - DEAD LOADING ONLY

Total self-weight loading = 1.0 × [18 × (0.20 + 2.44) + 1.2 × 6]

= 54.7 kN

Self-weight deflection * = =EI384

WL5 3

6

3

10144205384

60007.545

×××××

= 5.2mm

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 11 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

IMPOSED LOADING STAGE

Imposed = 3.5 × 18 = 63 kN

Partitions = 1.0 × 18 = 18 kN

Services = 0.5 × 18 = 9 kN

Cladding = 1.0 × 8.0 × 6 = 48 kN______

Total loading = 138 kN

Cladding and Imposed: * = = 13.2 mm6

3

10144205384

60001385

×××××

Limit = L/360 = 16.7 mm ˆ deflection is OK

Imposed only: * = = 8.6 mm6

3

10144205384

6000905

×××××

Limit = L/500 = 12.0 mm ˆ deflection is OK

Horizontal deflection in the construction stage: this occurs due to twisting at midspan.

Average torque at midspan = = Tave4

Tq

at SLS: Tave = = 1.78 kNm3104

1505.47

××

N = = 0.76 × 10-3 rads6

6

109.8879000

30001078.1

××××

Worst case: Assume shear centre is in bottom plate:

Deflection = rN where r = 265 mm

ˆ *H = 265 × 0.76 × 10-3 = 0.2 mm

The amount of horizontal deflection (0.2 mm) is negligible because an RHS is used, which istorsionally stiff.

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 12 of 17 Rev AJobTitle Design of RHS Slimflor edge beamsSubject Appendix A, Worked examples for non-composite edge

beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

STRESSES (AT SLS)

Self weight = 54.7 kN

Moment: Mx = = 41.0 kNm8

67.54 ×

Steel: Top: Ft = = = 45.3 N/mm2

t

x

Z

M3

6

10905

100.41

××

Bottom: Fb = = = 30.2 N/mm2

b

x

Z

M3

6

101360

100.41

××

Imposed loading and cladding = 138 kN

Moment: Mx = = 103.5 kNm8

6138 ×

Steel: Top: Ft = = 114.4 N/mm2

3

6

10905

105.103

××

Bottom: Fb = = 76.1 N/mm2

3

6

101360

105.103

××

COMBINING STRESSES AT S.L.S.

Steel: Ft = 45.3 + 114.4 = 159.7 N/mm2 < 355 N/mm2

Fb = 30.2 + 76.1 = 106.3 N/mm2 < 342 N/mm2

ˆ combined serviceability stresses OK. These checks show that serviceability stresses are rarelycritical for RHS Slimflor beams and are not required in practice.

DYNAMIC SENSITIVITY

Loading = Self weight + C&S + cladding + 10% imposed= 54.7 + 9 + 48 + 8.1= 119.8 kN

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 13 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

Instantaneous deflection due to these loads:

*f = = 11.4 mm

××××

6

3

10144205

60008.119

384

5

ˆ Natural frequency: f = = = 5.3 Hzf

18

δ 4.11

18

ˆ f > 4 Hz ˆ OK

Section satisfactory for serviceability conditions in office buildings

BEAM-COLUMN CONNECTION: DESIGN FOR SHEAR & TORSION

Elevation:

Plate

UC section (assume a 203x203 section)

250x150x16 RHS

C ColumnL

Section:

400

140

200

340

End plate (S275 steel)thickness = 10mm

RHS section (S355 Steel)

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61

r170

170

70

70

The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 14 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

Maximum vertical shear = = 143 kN2

2091067 ++

Four bolts used to resist shear:

ˆ Shear per bolt = = 35.8 kN4

143

Try four M20 grade 8.8 bolts

Plate bearing S275 steel = 20 × 10 × 310

460

= 92 kN > 35.8 kN ˆ OK

ˆ Use grade S275 steel for the 10 mm thick end-plate

Check on bolt forces due to combined bending and torsion

Polar inertia of bolt group using unit area method

Ioo = (702 + 1702) × 4 = 135200 mm4

r = = 183.8 mm22 17070 +

Modulus of bolt group =r

I

= 135200/183.8 = 735.6 mm3

Worst case for loading is the combination of imposed and cladding load (see sheet 3)

Torque = 21.2 kNm = Tq

Torsional moment on each end connection:

= = 10.6 kNm2

Tq

Vertical shear per connection: = 143 kN

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 15 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

Shear force per bolt = = 35.8 kN4

143

Component of bolt force due to torsion =6.735

106.10 3×

= 14.4 kN

Shear capacity, Ps

Ps = ps As (tensile stress area obtained from section tables)

= = 91.9kN310

245375×

r

43.0 kN35.8 kN

14.4 kN

43 kN < 91.9 kN (single shear capacity of M20 grade 8.8 bolt)

ˆ Use four M20 grade 8.8 bolts in conjunction with a 400 × 200 × 10 mm end-plate

RHS - PLATE WELD DESIGN

For symmetry, make both welds of the same throat thickness.

208.7 kN

Fillet weld

150 a=75

L=75

2520

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 16 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

The plate is assumed to behave as a propped cantilever.

RRHS CL A

208.7 kN = P

75 75 25

Analysis for the propped cantilever condition, RA

RA = P = 208.7 = 521.8 kN

+

L

a5.11

×+75

755.11

Load = 521.8/6 = 87 kN/m .......... (1)

1.4 P = 292 kN < RA ˆ OK (based on prying force analogy)

Note: When (L) is much greater than (a) the prying force will act closer to the weldthan 1.5 L. Hence the magnitude of the weld force will be larger than that givenby the simple expression:

P

+

L

a5.11

Plate tensile resistance (maximum): Rp = = 1437.8 kN1000

35515270 ××

Assume an elastic stress distribution for the transfer of longitudinal shear between the RHSand the plate.

1L /2

ˆ Maximum shear force/m length of beam is given by the formula:

= Rp2

LS

2

1 1××

ˆ Shear per weld, S = = 2

1

L

R4

1

p ×1

p

L

R2

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 17 of 17 Rev A

Job Title Design of RHS Slimflor edge beamsSubject Appendix A, Worked example for non-composite

edge beam

Client Made by DLM Date Apr 1997

BS Tubes & Pipes Checked by JWR Date May 1997

= = 479.3 kN/m ......... (2)6

8.14372 ×

Horizontal shear force (assume 6mm fillet weld):

10.5

75

208.7 kN

Horizontal force = = 1490.7 kN5.10

757.208 ×

Force/m = = 248.5 kN/m ......... (3)6

7.1490

Resultant of (1), (2) and (3)

Resultant force = (0.0872 + 0.47932 + 0.24852)½ = 0.55 kN/mm

6mm fillet weld strength = = 1.07 kN/mm1000

2557.06 ××

255 N/mm2 = Weld design strength using FE51 electrodes

ˆ Weld strength > resultant force

Use 6mm fillet welds for welding 15 mm flange plate to both sides of the RHS.

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APPENDIX B Formulae for Plastic MomentResistance of RHS Edge Beam

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 1 of 7 Rev

Job Title Design of RHS Slimflor edge beamsSubject Appendix B, Formulae for plastic moment

resistance

Client Made by DLM Date May 1996

BS (Tubes & Pipes) Checked by JWR Date May 1996

MOMENT RESISTANCE - STEEL SECTION

Case 1: Plastic neutral axis in the web

Applies when Rs - 2Rf > Rp

where: Rp = Bp tp pyp

and Rs = Apy

Rf = B ts py

L

B

D

p

B

p

t

t

pna

y2p

pyp

sM

Rp

yp

pRy p

C

yp =y

p

pt4

R

Ms = Sx py

Moment resistance, Mc

Moments about mid-height of RHS

Mc =2

yR

2

t

2

DRM p

pp

ps −

++

=

−++

ys

ppp

ps

pt4

R

2

R)tD(

2

RM

Mc = ( )

−++

ys

pp

ps

pt4

RtD

2

RM

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 2 of 7 Rev

Job Title Design of RHS Slimflor edge beamsSubject Appendix B, Formulae for plastic moment

resistance

Client Made by DLM Date May 1996

BS (Tubes & Pipes) Checked by JWR Date May 1996

Case 2: Plastic neutral axis in the bottom flange (RHS)

Applies when Rs > Rp > Rs - 2Rf

L

pna

p

yp

pR

yrR syp

C

s p(R -R )

yp =y

ps

pB2

RR −

Moment resistance, Mc

Moments about lower surface of flange plate

Mc =2

y)RR(

2

tR

2

DR p

psp

ps −−+

Mc =( )

y

2psp

psBp4

RR

2

tR

2

DR

−−+

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 3 of 7 Rev

Job Title Design of RHS Slimflor edge beamsSubject Appendix B, Formulae for plastic moment

resistance

Client Made by DLM Date May 1996

BS (Tubes & Pipes) Checked by JWR Date May 1996

Case 3: Plastic neutral axis in the plate

Applies when Rp > Rs

yp

Rpyr

R p

Rs

p2

pna

A

yp

Rp1 = Bp (tp - yp) pyp

Rp2 = Bp pyp yp

To find yp, equate forces above and below pna

Bp pyp yp = Rs + (tp - yp) Bp pyp

2 Bp pyp yp = Rs + Bp pyp tp

ˆ yp =tpB2

RR

ypp

ps +

Moment resistance, Mc

Take moments about plastic neutral axis in plate

but Rp2 = Rs + Rp12

yR)yt(

2

Ryt

2

DR p

p2ppp1

pps +−+

−+

= but Rp1 = (tp - yp) Bp pyp2

yRt

2

Ryt

2

DR p

spp1

pps ++

−+

=2

yR)yt(

2

Ryt

2

DR p

sppp

pps +−+

−+

ˆMc = ( )pppp

ps yt2

R

2

yt

2

DR −+

−+

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 4 of 7 Rev

Job Title Design of RHS Slimflor edge beamsSubject Appendix B, Formulae for plastic moment

resistance

Client Made by DLM Date May 1996

BS (Tubes & Pipes) Checked by JWR Date May 1996

COMPOSITE SECTION - FULL SHEAR CONNECTION (General Notes)

B

D

p

B e

R c

t p

st

D

D

s

B

Concrete ignored

Deep deck

y c

d

Effective breadth of concrete slab

Be =2

B

8

L +

yc is the maximum depth of concrete to be used for full shear connection.

when Dd > D, yc = Ds

Compression resistance of concrete slab

Rc = ycN 0.45 fcu

+

2

B

8

L

Tensile resistance of steel section = Rs + Rp

Full shear connection exists when:

Rq $ Rc and Rq $ Rs + Rp

where: Rq = longitudinal shear force transfer by the shear connectors betweenpoints of zero and maximum moment

Partial shear connection exists when:

Rq < Rc

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 5 of 7 Rev

Job Title Design of RHS Slimflor edge beamsSubject Appendix B, Formulae for plastic moment

resistance

Client Made by DLM Date May 1996

BS (Tubes & Pipes) Checked by JWR Date May 1996

PARTIAL SHEAR CONNECTION

Case 1: Plastic neutral axis in top flange of RHS

Applies when Rq < Rc and Rs + Rp > Rq > Rs - 2Rf + Rp

B

D

p

B e

B

t

t p

x

cuf

R ppyp

Ds

Dp

q R 2p ya

c

b

pna

R s

py

(R +R -R )p

yp

s q

x = depth of concrete in compression

a =2

xDDD sp −−+

b = Rs = A py2

D

c = Rp = Bp tp pyp2

tD p+

yp = x =y

qps

pB2

RRR −+

ecu

q

Bf45.0

R

Moment resistance of the composite section, Mc

Mc = Rq a + Rs b + Rp c + ( )

y

2qps

Bp4

RRR −+

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The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 6 of 7 Rev

Job Title Design of RHS Slimflor edge beamsSubject Appendix B, Formulae for plastic moment

resistance

Client Made by DLM Date May 1996

BS (Tubes & Pipes) Checked by JWR Date May 1996

PARTIAL SHEAR CONNECTION

Case 2: Plastic neutral axis in the web of the RHS

Applies when Rq < Rc

Rq + Rs > Rp +2Rf

Rq < Rs - 2Rf + Rp

LC RHS

R p

M s

pyp

y2p

yp

t pna

b(R -R )q p

q R

a

yp

x

To find position yp:

2(2 py ts yp) = (Rq - Rp) ˆ yp =tp4

RR

y

pq −

a = x =2

x

2

DDD ps −−+

ecu

q

Bf0.45

R

b = Ms = Sx py (Sx for RHS)2

t

2

D p+

Moment resistance of composite section, Mc

Mc = Ms + Rq a + Rp b ! (Rq ! Rp)2

y p

Mc = Ms + Rq a + Rp b ! ( )R R

p tq p

y s

−2

8

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Mc = Rq a+Rs b+Rp c ! y

2pqs

Bp4

)RRR( −+

The SteelConstructionInstitute

Silwood Park, Ascot, Berks SL5 7QNTelephone: (01344) 623345Fax: (01344) 622944

CALCULATION SHEET

Job No: BCB 585 Page 7 of 7 Rev

Job Title Design of RHS Slimflor edge beamsSubject Appendix B, Formulae for plastic moment

resistance

Client Made by DLM Date May 1996

BS (Tubes & Pipes) Checked by JWR Date May 1996

PARTIAL SHEAR CONNECTION

Case 3: Plastic neutral axis in lower part of the webApplies when Rq < Rc and Rq + Rs > Rp > Rq + Rs - 2Rf

LC RHS

pna

q R

a

b

R s

(R +R -R )q ps

Rpc=t /2p

x

y p

yp = x = Rs = Apy

R R R

Bps q p

y

+ −2 ecu

q

Bf0.45

R

Corrected Jan 2004

a = b = c =2

xDD ps −+ D

2

t p

2

Moment resistance of composite section, Mc

Mc = Rq a+Rs b+Rp c-(Rs+Rq-Rp)y p

2

Note: This case is unlikely to occur in practice.

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APPENDIX C Design Tables for Initial Sizing

Appendix C contains tables giving sizes of Rectangular Hollow Section (RHS) ingrade S355 steel for non-composite and composite RHS Slimflor edge beamconstruction.

These tables are intended to be used for the purposes of initial sizing. Where finaldesigns are required, the beam size should be verified by hand calculations or bycomputer software.

The following table gives the basic parameters covered by the initial sizing tables.

Table No. Method ofconstruction

Steel Grade Concretegrade and

type

Imposed loadkN/m2

C.1C.2C.3C.4C.5C.6

Non-compositeNon-compositeNon-composite

CompositeCompositeComposite

S355S355S355S355S355S355

30/LWC30/LWC30/NWC30/LWC30/LWC30/NWC

4.56.04.54.56.04.5

General Notes

(1) There are instances in Tables C.1 to C.6 where the normal limits fordeflection and vibration may be exceeded. It is the designer’s responsibilityto check that the calculated values are appropriate for the structure underconsideration.

(2) All decking spans and composite slab depths should be verified with the decksuppliers.

(3) Beam sizes highlighted with an asterisk are for a modified version of non-composite construction. Figure C.1 shows this revised form of construction,which reduces the concrete depth above the deck profile and leaves the topflange of the RHS exposed.

All of the design procedures given in Section 4 remain unaltered for thismodified form of construction.

(4) RHS section sizes shown for use with composite construction (Tables C.4 toC.6) have been restricted to avoid excessive depths of concrete above the deckprofile. For these practical reasons, the RHS depth has been limited to amaximum of 250 mm, or to 110 mm of concrete above the deck profile(whichever controls).

(5) The failure criterion is given (normally e or h). These criteria are also usedin the software.

e = normal stage: torsion check.

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(6) The tables are based on the following parameters:

Cladding load = 8 kN/mCladding eccentricity = 200 mm

h = normal stage: beam longitudinal bending check.

D =225

D =70s

d

Figure C.1 Modified version of non-composite construction

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Non-composite Construction

Imposed Load 4.5 kN/m2 Steel Grade S355 LWC Grade 30 Concrete, Density = 1900 kg/m3

Beam spacing (metres)

BeamSpan(m)

4.5 m 6.0 m 7.5 m

ConcreteDepth aboveDeck (mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

4.5 60 285 200 × 100 × 8 e 60 285 200 × 100 × 10 e 60 285 200 × 100 × 12.5 e

6.0 60 285 250 × 150 × 8 e 60 285 250 × 150 × 10 e 60 285 250 × 150 × 12.5 e

7.5 60 285 250 × 150 × 16 e 60 315 300 × 200 × 10* e 60 315 300 × 200 × 12.5* e

9.0 60 315 300 × 200 × 16* e 60 315 300 × 200 × 16* e 60 415 400 × 200 × 16* e

Notes:Design criterion e = Normal stage: torsion check

* = Beam projects above slab (see page 78).

Table C1 RHS Slimflor edge beams - Non-composite (LWC)

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Non-composite Construction

Imposed Load 6.0 kN/m2 Steel Grade S355 LWC Grade 30 Concrete, Density = 1900 kg/m3

Beam spacing (metres)

BeamSpan(m)

4.5 m 6.0 m 7.5 m

ConcreteDepth aboveDeck (mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

4.5 60 285 200 × 100 × 8 e 60 285 200 × 100 × 12.5 e 60 285 200 × 100 × 16 e

6.0 60 285 250 × 150 × 8 e 60 285 250 × 150 × 12.5 e 60 285 250 × 150 × 16 e

7.5 60 285 250 × 150 × 16 e 60 315 300 × 200 × 12.5* e 60 315 300 × 200 × 16* e

9.0 60 315 300 × 200 × 16* e 60 315 300 × 200 × 12.5* e 60 415 400 × 200 × 16* e

Notes:Design criterion e = Normal stage: torsion check

* = Beam projects above slab (see page 78).

Table C2 RHS Slimflor edge beams - Non-composite (LWC)

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Non-composite Construction

Imposed Load 4.5 kN/m2 Steel Grade S355 LWC Grade 30 Concrete, Density = 2350 kg/m3

Beam spacing (metres)

BeamSpan(m)

4.5 m 6.0 m 7.5 m

ConcreteDepth aboveDeck (mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

4.5 70 310 200 × 100 × 8 e 70 310 200 × 100 × 10 e 70 310 200 × 100 × 12.5 e

6.0 70 310 250 × 150 × 16 e 70 310 250 × 150 × 10 e 70 310 250 × 150 × 12.5 e

7.5 70 310 250 × 150 × 16 e 70 315 300 × 200 × 10* e 70 315 300 × 200 × 12.5* e

9.0 70 315 300 × 200 × 12.5* e 70 315 300 × 200 × 16* e 70 415 400 × 200 × 12.5* e

Notes:Design criterion e = Normal stage: torsion check

* = Beam projects above slab (see page 78).

Table C3 RHS Slimflor edge beams - Non-composite (NWC)

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Composite Construction

Imposed Load 4.5 kN/m2 Steel Grade S355 LWC Grade 30 Concrete, Density = 1900 kg/m3

Beam spacing (metres)

BeamSpan(m)

4.5 m 6.0 m 7.5 m

ConcreteDepth aboveDeck (mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

4.5 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h

6.0 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h

7.5 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h 110 350 250 × 150 × 8 h

9.0 60 300 200 × 100 × 8 h 110 350 250 × 150 × 8 h 110 350 250 × 150 × 16 h

Notes:Design criterion h = Normal stage: beam longitudinal bending check

Table C4 RHS Slimflor edge beams - Composite (LWC)

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Composite Construction

Imposed Load 6.0 kN/m2 Steel Grade S355 LWC Grade 30 Concrete, Density = 1900 kg/m3

Beam spacing (metres)

BeamSpan(m)

4.5 m 6.0 m 7.5 m

ConcreteDepth aboveDeck (mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

4.5 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h

6.0 60 300 200 × 150 × 8 h 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h

7.5 60 300 200 × 100 × 8 h 60 300 200 × 100 × 8 h 110 350 250 × 150 × 8 h

9.0 60 300 200 × 100 × 16 h 110 350 250 × 150 × 16 h 110 350 250 × 150 × 10 h

Notes:Design criterion h = Normal stage: beam longitudinal bending check

Table C5 RHS Slimflor edge beams - Composite (LWC)

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Composite Construction

Imposed Load 4.5 kN/m2 Steel Grade S355 LWC Grade 30 Concrete, Density = 2350 kg/m3

Beam spacing (metres)

BeamSpan(m)

4.5 m 6.0 m 7.5 m

ConcreteDepth aboveDeck (mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

ConcreteDepth

above Deck(mm)

TotalSlab

Depth(mm)

Section Sizemm

DesignCriterion

4.5 70 310 200 × 100 × 8 h 70 310 200 × 100 × 8 h 70 310 200 × 100 × 8 h

6.0 70 310 200 × 100 × 8 h 70 310 200 × 100 × 8 h 70 310 200 × 100 × 8 h

7.5 70 310 200 × 100 × 8 h 70 310 200 × 100 × 8 h 110 350 250 × 150 × 8 h

9.0 70 310 200 × 100 × 10 h 110 350 250 × 150 × 10 h 110 350 250 × 150 × 12.5 h

Notes:Design criterion h = Normal stage: beam longitudinal bending check

Table C6 RHS Slimflor edge beams - Composite (NWC)

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APPENDIX D Computer Screens and Outputfor RHS Slimflor Analysis andDesign

The input screens for the RHS Slimflor software are presented on the followingpages. The data common to a certain aspect of the design (such as steel data orloading) is input on a separate screen. Each screen can be accessed from the maindata screen.

The software has the facility for automatic design (i.e. all RHS sections arechecked) or beam check (i.e. one RHS section is checked). Summary output showsthe unity factors relative to the various design criteria, and the various componentdeflections (the user should decide if these deflections are acceptable). The fulloutput is presented in the form of design calculations and can be previewed orprinted. The data and output can be saved and accessed later.

The output calculations for the same design example are also presented in thisAppendix, following the input screens. The important unity factors are given oneach page of the output. The user should also refer to the deflections given onpage 5. The fire design on page 4 includes the intermediate calculations giving thestrength reduction of all the elements of the composite section. Stress checks at theserviceability limit state are included for completeness on page 6, but they are notrequired for hand analysis.

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General data

Floor plan data

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Fire details

Steel data

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enas

@ps

p.lt

on 1

5/11

/201

3

84

Concrete data

Loading details

Copy

right

ed m

ater

ial.

Lice

nsed

to b

enas

@ps

p.lt

on 1

5/11

/201

3

Copy

right

ed m

ater

ial.

Lice

nsed

to b

enas

@ps

p.lt

on 1

5/11

/201

3

Copy

right

ed m

ater

ial.

Lice

nsed

to b

enas

@ps

p.lt

on 1

5/11

/201

3

Copy

right

ed m

ater

ial.

Lice

nsed

to b

enas

@ps

p.lt

on 1

5/11

/201

3

Copyr

ight

ed m

ater

ial.

Lice

nsed

to b

enas

@ps

p.lt

on 1

5/11

/201

3