Composite beam design ConSteel is capable of single as well as continuous span composite beam design in accordance with EN 199411:2010 (Eurocode 4). Partial and full shear connection can be also designed. Main features: Composite beam definition with profiled sheeting or with solid concrete slab Automatic calculation of effective width Cracked and uncracked analysis Option for moment redistribution Design resistance calculation for bending, shear, bending and shear interaction, shear buckling, shear stud, longitudinal shear, crushing of concrete flange Automatic calculation of the optimal number and layout of shear studs for partial shear (if possible) and also for full shear connection Clear and straightforward results using exactly the same symbols as in EuroCode GSS crosssection model for precise section properties and elastic stresses
EUROPEAN CONVENTION FOR CONSTRUCTIONAL STEELWORK CONVENTION EUROPEENNE DE LA CONSTRUCTION METALLIQUE EUROPAISCHE KONVENTION FUR STAHLBAU ECCS - Technical Committee 11 Composite Structures Composite Beams and Columns to Eurocode FIRST EDITION 1993 No72 All rights reserved No part of this publicationmay be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the Copyright owner : ECCS CECM EKS General Secretariat Avenue des Ombrages, 32136 bte 20 8-1200 BRUSSEL (Belgium) Tel 382-762 04 29 Fax 382-762 09 35 ECCS assumes no liability with respect to the use for any application of the material and information contained in this publication FOREWORD The Eurocodes are being prepared to harmonize design procedures between countries which are members of CEN (European Committee for Standardization) and have been published initially as ENV documents (European pre-standards - prospective European Standards for provisional application) The Eurocode for composite construction (referred to in this publication as EC4) is: ENV 1994-1-1: Eurocode Design of composite steel and concrete structures Part 1.1: General rules and rules for buildings The national authorities of the member states have issued National Application Documents (NAD) to make the Eurocodes operative whilst they have ENV-status This publication "Composite Beams and Columns to Eurocode 4" has been prepared by the ECCS-Technical Committee 11 to provide simplified guidance on composite beams and columns in supplement to EC4 and to facilitate the use of EC4 for the design of composite buildings during the ENV-period "Composite Beams and Columns to Eurocode 4" contains those rules from EC4 that are likely to be needed for daily practical design work It is a self-standing document and contains additional information as simplified guidance, design tables and examples References to EC4 are given in [ Any other text, tables or figures not quoted from EC4 are deemed to satisfy the rules specified in EC4 In case of doubt, when rules are missing (e.g for the design of composite slabs, etc.) or when more detailed rules are required, EC4 should be consulted in conjunction with the National Application Document for the country in which the building project is situated The working group of ECCS-TC 11, responsible for this publication is: The other members of ECCS-TC 1 are: Anderson, D Beguin, P Bode, H Brekelmans, J Falke, J Janss, J Lawson, R M Mutignani, F Arda, T.S Aribert, J.M Axhag, F Bossart, R Cederwall, K Lebet, J.P Leskela, M Schleich, J.B Stark, J.W.B Tschemmernegg, F United Kingdom France Germany (Chairman of TC11) Netherlands Germany Belgium United Kingdom Italy Turkey France Sweden Switzerland Sweden Switzerland Finland Luxembourg Netherlands Austria Particular thanks are given to those organisations who supported the work Besides ECCS itself and its members, specific contributions were made by: Bauberatung Stahl, Bundesvereinigung der Priifingenieure fur Baustatik, The Department of Trade and Industry British Steel (Sections, Plates & Commercial Steels) Germany Germany UK UK The text was prepared for publication by the Steel Construction Institute, UK Page ~ This publication presents useful information and worked examples on the design of composite beams and columns to Eurocode ‘Design of composite steel and concrete structures’ (ENV 1994-1-1) The information is given in the form of a concise guide on the relevant aspects of Eurocode that affect the design of composite beams and columns normally encountered in general building construction Each section of the publication reviews the design principles, gives design formulae and makes cross-reference to the clauses of Eurocode Information on the design of composite slabs is also given, although the publication concentrates on the influence of the slab on the design of the composite beam Pesign aids are also presented to assist in selecting the size of steel beams to be used in certain applications Worked examples cover the design of composite beams with full and partial shear connection, continuous beams, and composite columns Page I COMPOSITE BEAMS AND COLUMNS TO EUROCODE CONTENTS Page SUMMARY NOTATION PART 1: DESIGN GUIDE INTRODUCTION 1.1 1.2 1.3 Scope of Publication Cross-referencing Partial Safety Factors INITIAL DESIGN ACTIONS AND COMBINATION RULES FOR DESIGN 3.1 3.2 3.3 3.4 9 10 10 11 14 Fundamental Requirements Definitions and Classifications Design Requirements 14 14 15 3.3.1 General ‘3.3.2 Ultimate limit state 3.3.3 Serviceability limit state 15 15 16 Design of Steel Beams 17 MATERIALS AND CONSTRUCTION 18 4.1 Description of Forms of Construction 18 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 18 18 19 19 20 20 4.2 Types of columns Types of beams Types of slabs Types of Shear connectors Types of erection Types of connection Properties of Materials 22 4.2.1 Concrete 4.2.2 Reinforcing steel 4.2.3 Structural steel 22 23 23 Page 4.3 24 Partial Safety Factors for Resistance and Material Properties 24 COMPOSITE OR CONCRETE SLABS 5.1 5.2 5.3 5.4 5.5 4.2.4 Profiled steel decking for composite slabs 25 Introduction Initial Slab Design 25 26 5.2.1 5.2.2 5.2.3 5.2.4 26 27 27 28 Proportions of composite slabs Construction condition Composite action Deflections Influence of Decking on the Design of Composite Beams 28 5.3.1 Ribs transverse to beams 5.3.2 Ribs parallel to beam 29 29 Detailing Rules for Shear Connectors Welded Through Profiled Steel Decking 30 5.4.1 Welding and spacing of studs 5.4.2 Additional requirements for steel decking 30 31 Minimum Transverse Reinforcement 31 ULTIMATE LIMIT STATE: COMPOSITE BEAMS 33 Basis of Design of Composite Beams 33 6.1.1 General 6.1.2 Verification of composite beams 6.1.3 Effective width of the concrete flange 6.1.4 Classification of cross-sections 6.1.5 Distribution of internal forces and moments in continuous beams 33 33 34 35 40 Resistance of Cross Sections 42 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 42 42 44 45 45 6.1 6.2 General Positive moment resistance Negative moment resistance Vertical shear Momen t-shear interaction Page 6.3 Shear Connection 46 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 46 46 48 49 53 6.4 Partially Encased Beams 56 6.5 Lateral Torsional Buckling of Continuous Beams 57 SERVICEABILITY LIMIT STATE: COMPOSITE BEAMS 59 7.1 General Criteria 59 7.2 Calculation of Deflections 59 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 General Resistance of shear connectors Spacing of shear connectors Longitudinal shear force Transverse reinforcement Second moment of area Modular ratio Influence of partial shear connection Shrinkage-induced deflections Continuous beams 59 61 63 63 64 7.3 Vibration Checks 65 7.4 Crack Control 65 ULTIMATE LIMIT STATE: COMPOSITE COLUMNS 67 8.1 Introduction 67 8.2 Design Method 68 8.2.1 General 8.2.2 Design assumptions 8.2.3 Local buckling 8.2.4 Shear between the steel and concrete components 68 68 68 69 Simplified Method of Design of Composite Columns 70 8.3.1 Resistance of cross-sections to axial load 8.3.2 Resistance of members to axial load 8.3.3 Resistance of cross-sections to combined compression and uniaxial bending 8.3.4 Analysis for moments applied to columns 8.3.5 Resistance of members to combined compression and uniaxial bending 70 71 8.3 74 76 76 Page ~ ~ ~ 8.3.6 Limits of applicability of the simplified design method 78 FIRE RESISTANCE 80 10 CONSTRUCTION AND WORKMANSHIP 82 10.1 10.2 10.3 10.4 10.5 10.6 General Sequence of Construction Stability Accuracy during Construction and Quality Control Loads during Construction Stud Connectors Welded through Profiled Decking 82 82 82 82 83 83 11 REFERENCES 85 12 DESIGN TABLES AND GRAPHS FOR COMPOSITE BEAMS 86 12.1 Moment Resistance of Composite Beam Relative to Steel Beam 87 12.2 Second Moment of Area of Composite Beam Relative to Steel Beam 88 12.3 Design Tables for Composite Beams Subject to Uniform Loading 89 ANNEX DESIGN FORMULAE FOR COMPOSITE COLUMNS 94 PART 2: WORKED EXAMPLES 97 Simply Supported Composite Beam with Solid Slab and Full Shear Connection Simply Supported Composite Beam with Composite Slab and Partial Shear Connection Continuous Composite Beam with Solid Slab Composite Column with End Moments Page NOTATION Notation is not presented in detail here and reference should be made to Eurocode Part 1.1 However, the use of the following common symbols and subscripts is given to help understanding of this publication Symbols: A beff d E fck * fY F G h I L M N Q t V W YF Y x E X cross-sectional area effective width of slab diameter of shear connector; depth of web considered in shear area modulus of elasticity of steel characteristic compressive (cylinder) strength of concrete yield strength of steel force in element of cross-section; load (action) permanent loads (actions) depth of element second moment of area length or span moment (with subscripts as below) axial force variable loads (actions) thickness of element of cross-section shear force plastic section modulus partial safety factor for loads partial safety factor for materials (with subscripts as below) slenderness d ( f y /235) reduction factor on axial resistance due to imperfection Subscripts to symbols: a C k P S PP R S Rd Sd W structural steel concrete characteristic value profiled steel decking (sheeting) reinforcement plastic resistance (in bending, shear or compression) resistance (of member) internal force or moment design value of resistance design value of internal force or moment web of steel section Page Member axes: X Y along the axis of the member major axis bending minor axis bending Terminology: This publication adopts the terminology used in Eurocode Part 1.1 However, there are some important terms which may be defined to assist in understanding this document These are: Hogging moment Negative moment causing compression in the bottom flange of the beam Sagging moment Positive moment causing tension in the bottom flange of the beam Moment resistance Resistance of the steel or composite cross-section to bending actions Stud connector A particular form of shear connector comprising a steel bar and flat head that is welded automatically to the beam Decking Profiled steel sheet which may be embossed for composite action with the concrete slab Transverse reinforcement Reinforcement placed in the slab transversely (across) the steel beam Page TRANSVERSE REINFORCEMENT C6.3.51 Minimum transverse reinforcement for solid slab 0.002.4= 0.002~120~1000 = 240 m ' / m reinf bar m m / 200 m m - layers = &+Ab = 2-251.3 m ' / m Longitudinal shear in the slab Section a-a a) VR d = 2.5 \ v q-TR d +&.fskh,ls+vPd or b) VR d = - fck /yc +Vp d /d3 * s whichever is smaller, where ' I R ~= 0.30N / m ' (C?5/30) q=l (normal weight concrete) 4,,= ~ ~ O - ~ O=O120.10' O mm:/m Vpd =0 (contribution of the steel sheeting) and therefore 1.3.420/1.15)~10~' = 273.6 kN/m a) v R ~= (2.5.120.10'.1~0.~0+2~25 b) vRJ = (0.2.120*10'*1*25/1.5).10-3= 400 kN/m esample [Table 6.71 The longitudinal design shear is given by VSd = 98.0.1000/300 = 326.7 kN/m For each shear plane a-a vSd/2 = 326.7/2 = 163.3 < 273.6 kN/m and the verification is satisfied Section b-b Acv = (2-95+35).1000= 225.103 mtn’/m VRd = (2.5~225~1O3~1~0.3O+2~251.3~420/1.15)~1O3 = 352.3 kN/m VRd = 352.3 kN/m >vsd = 326.7 kN/in and the verification is satisfied SERVICEABILITY LIMIT STATE VERIFICATION 8.1 Calculation of maxiniuni deflection 8.1.1 Construction stage p1 = 10.80 kN/m 61 = 0.00542*p1*L4/(E.I,) = = 0.00542-10.80*10-3~1 200O1/(210*3374O*1O4) = = 17.1 inin 8.1.2 Composite stage example Page 18 mm' mm' rnm 13946.7 285 9880.0 mm 3974.8-1Oj mm' - 18.1 1673.6.10' 166.8 33740.0.10' rnm' mmJ 19478.1-10.' 21 151.7-10' 27495.6-10-1 1235.6.10-1 beff /n = 2400/20.65 = 116.2 mm e, = 3974.8.10'/23826.7 = 166.8 mm For simply supported beam and assuming full shear connection: Load considered for serviceability deflection = interior finishing, imposed load partition : and p2= 3.33+11.67+3.33= 18.33 kN/m = 22.5 mm Correction factor for support moment Mh C [7.2.5] = 0.6.0.7= 0.42 This correction factor c = 0.42 reduces the hogging bending moment in order to take account of the effects of cracking and yielding The value seems to be conservative Detailed analysis of stresses may show that cracking and/or yielding does not occur , 18.33 kN/m 13.33 C A 12000 I 12000 196.5 kNrn blh = 0.063.(18.33+3.33).122= 196.5 kNm Puse 19 1-0.42*M,/(p2.L2/8)=1-0.42*196.5/( 18.33.12*/8)= 0.75 6, = 0.75.22.5 = 16.9 tntn ,a, = = 17.1+16.9 = 34.0 inin equal to W353 < L/250 on:itcarenti- Minitnuin degree of shear connection N/Nf = 0.61 > 0.5 and the effects of incomplete interaction are ignored 8.2 CrackinP- of concrete Minimum reinforcement (for no control of crack widths): A, 0.002.3333.3.120 = 800 1nm2 Use bar diatn 12 mm/150 mm A, = 113.10 = 1130 mn2> 800 min2 The tnlliiinuin area of reinforcement required to ensure that the reinforcement remains elastic when cracking first occurs is given by: A, >k~k;f,,;A,/a,, = 0.8~0.7~3~180000/320 = 945 inin? where: z, = zg-h,/2 = 138.1-60 = 78.1 tntn zg = [b, ff.h’,/2+11.A, (11,/2+h~)]/(b, ff.h,+~i.A,) = = [ 1500~120’/2+6.88~9880(450/2+120)]/(1500~120+6.88~9880) = = 138.1 tntn k, = I/{1+[hC/(2z,,)1 1= = 1/{1+[120/(2.78.1)]}= 0.565 < 0.7 and then k, = 0.7 k = 0.8 A, = beff.lic= 1500.120 = 180000 Inin‘ fctc = N/mln’ us,= 320 N/mm2 (for crack width wk = 0.3 tnrn ) example Page 20 A, = 113.10 = 1130 mm2 > 945 mm2 where A, is referred to the effective width esimple Page WORKED EXAMPLE no.4 The example refers to a concrete encased composite column subject to compression load and uniaxial bending The length of the column is m The verification has been carried out according to the simplified method given in this publication No influence of shear forces has been considered 300 e.wple Page INDEX COMPOSITE COLUMN CHARACTERISTICS age p DESIGN VALUES OF ACTIONS 3 MATERIALS 3.1 Concrete 3.2 Reinforcing steel Structural steel 3.4 Partial safety factors 3 CROSS SECTION GEOMETRIC AND STATIC CHARACTERISTICS ULTIMATE LIMIT STATE CHECKS 5.1 Resistance of cross-section to axial compression 5.2 Effective elastic flexural stiffness of cross-section 5.3 Non-dimensional slenderness 5.4 Simplified method 4 esample COMPOSITE COLUMN CHARACTERISTICS Columnlength : L = 4000mm Type of construction = Steel profile = HEA200 concrete encased section DESIGN VALUES OF ACTION Design axial load for the column length - Maximum second-order design bending moment about axis y-y - Mvmas,Sd = 140 kNm Maximum design bending moment about axis z-z = M,max,Sd = MATERIALS 3.1 Concrete N,, =850kN kNm [4.2.1] Concrete strength class: 20/25 Characteristic strength: fCk= 20 N/mm2 Secant modulus of elasticity of short-term loading: E,, = 29.0 kN/mm2 Modular ratios: 3.2 Reinforcing steel [4.2.2] type of steel : S 420 steel grade : fsk = 420 N / m modulus of elasticity : E, = 210 kN/mm2 3.3 Structural steel [4.2.3] Nominal steel grade : Fe 510 nominal yield strength : fv= 5 N / m modulus of elasticity : E, esamplr -1 (t I 40 mm) = 10 kN/mm2 Page 3.4 Partial safety factors YM 3.4.1 Ultimate limit states structural steel Ya = 1.10 concrete Y C = steel reinforcement y , 1.50 = 1.15 CROSS SECTION GEOMETRIC AND STATIC CHARACTERISTICS c, CZ = (300-200)/2 = 50 IYKII = (300-190)/2 = 55 Reinforcement mm : 4412 bars A, = 452.4m.m' ULTIMATE LIMIT STATE CHECKS 5.1 Resistance of cross-section to axial compression 18.3.1J The plastic resistance to axial compression is given by Np1, Rd = & *fy/ya+&.(0.85*f,k/y, )+A,'fsk lys 5.2 Effective elastic flexural stiffness of cross-section Short term loading The flexural stiffness of cross-section about the main axes is (E.I), example = E,.I,+O.S.E,d.I,+E,.I, Page J about y-y (E*I), = E, *I, +O 8.E,d I,,+E, *Is = = E,~I,y+0.8~(E,m/y,)~I,y+E,~I,!, = = 10*3692*10+0.8.(29/1.3 5).(300'/12-3692*1P)+2 10.2.226.2.1152 = = 1.998.10" kN*mm2 about z-z (E.I), = E, *Iaz+O.8*E,d ICZ+Es*Isz= = E,~I,Z+0.8~(E,m/y,)I,,+Es*Isz= = 10*1336.102+0.8*(29/1 35).(3OOJ/12-1336.10')+2 10.2.226.2.115 = 1.543.10'O kN.m.m2 long term loading The eccentricity e of the normal force is defined by e = Mm as ,S dmS d in this case e, = 140/850 = 0.165 e, = e/d = 0.165/0.300 = 0.55 < where d is the overall depth of the cross section in the plane of bending considered The non-dimensional slenderness results h < 0.8(see 4.3) and therefore the influence of creep and shrinkage on the ultimate load need not to be considered 5.3 Non-dimensional slenderness The slenderness for the determination of the load bearing capacity of the column is given by e s m p i e -I Page where Npl,R = ~.f,+A,.(O.85.f,k)+As.f,L = = [5380.355+(3002-5380).(0.85.20)+452.4.420)]103 = = 3538 kN N,, 1, = (E*I)e.~2/12 = 4000 mm = 1, buckling length of the column N,.,! = (E*I)ey*7t2/Iy2 = 998*10'o*~2/4000' = 12320 kN Ncrz = (E.I),,.Ic~/~,~ = 1.54~.10'"*~'/4000' = 9520 kN and then - & = 0.536 - A, = 0.610 5.4 Simplified method C8.3.61 The conditions to be satisfied for the applicability of the method are: a) cross-section Izeometry The cross section of composite column (under examination) is double-symmetrical and uniform over the entire length b) steel contribution ratio = (b'fy/ya)/NpI , Rd = (5380~355.103/1.1)/2860= 0.607 0.2 < < 0.9 c) non-dimensional slenderness h ?,,,,,as = h, = 0.610 < d) concrete cover cy = 50 mm 40 mm < C, < 0.4.b = 0.4-200= 80 IIMII esample Page G cz = 55 mm 40mm < c, < 0.3ha = 57 mm e) longitudinal reinforcement 4 12 bars A, = 452.4 m Minimum reinforcement = 0.003.4= 0.003.(3002-5380) = 253.9< 452.4mm2 Maximum reinforcement that may be considered in calculations 0.04.4= 0.04*(300’-5380) = 3384.4> 452.4 mm2 5.4.1 Check of column axial compression resistance [8.3.2] The check is satisfied if for both axes where N,,,,, = 2860 k.N X = Q = 0.5.[l+a(h-0.2)+h2] = 0.786 a =0.49 I/[D+(Q’-~’)~~] = 0.780 b d on buckling about z-z curvec and then 850 < 0.780.2860= 2230 k.N 5.4.2 Resistance of cross-section in com bined compression and and uniaxial bending [8.3.3] Compressive resistance of the whole area of concrete: esample Page i Plastic bendine resistance MpI Rd plastic section modulus of reinforcement W,, =4*(122.~/4).112= 50.7.10jTI~P II Asn = 4-(12'-~/4)= 452.4 W' plastic modulus of structural steel plastic modulus of concrete part of section Wpc = b,~h,'/4-Wp,-W,, = 6269.1Oj W' position of neutral axis (in the web) h, = [ ~ ~ f c ~ - ~ , ~ ( ~ ~ f s ~ - f c ~ ) ] / [ ~ ~ b , ~ f c ~ ~ ~ ~ ~ , ( ~ ) ] where h, = [959000-452.4.(2.365.2-11.3)]/[2.300~ 11.3+2.6.j.(2.322.7-11.3)] (h, < h/2-t, = 19012-10 = 85 ITII~) = 42.1 mm W,,, = fw*h,'= 6.5.42.1' = 11537.0 W' Wpcn= bc.h,.,z-Wpan-Wpsn= 520944.0 mm3 - fyd.(Wpa-Wpan)+0.5.f~d.(Wpc-Wpcn)'fsJ.(Wps-W %l.Rd )= Psn = 322.7~(429000-11537)+0.5~11 3.(6269000-520944)+ +365.2.(50668-0)= 185.8 kXm M (kNm) example lZo Mpl,Rd 155.8 Puze 5.4.3 Resistance of member in combined compression and and uniaxial bending [8.3.4] where x= 0.780 Xd