05 Eurocodes Steel Workshop SIMOES

1 Design of MembersRui Sim esDepartment of Civil Engineering University of CoimbraEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 Contents Introduction Design of columns Design of beams Design of beam columnsEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 INTRODUCTIONMain internal forces and combinationsCompression+Bending+ShearBen ding+ShearTension/CompressionTorsion less commonBuilding master example (Cardington - UK) Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 INTRODUCTIONM ember design: i) resistance of cross sections; ii) member buckling resistance. Clause of Eurocode 3, part differentapproaches, depending of cross section shape, cross sectionclass and type of internal forces (N, M+V, N+M+V,..): elastic criteria (clause (5));MyGVz NEd My,Ed RESISTANCE OF CROSS SECTIONS Cross section classification -Class 1; Class 2; Class 3 and Class ,0,20,20, MyEdMyEdzMyEdxMyEdzMyEdxfffff Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 INTRODUCTIONMEMBER buckling RESISTANCE buckling resistance(clause of Eurocode 3,part ) must be checked in all memberssubmitted to compressive stresses, which are: members under axial compression N; members under bending moment M; or under a combination of both (M+N).

2 1,,,, RdzEdzRdyEdyRdEdMMMMNN Section properties gross section, net section(deduction for holes) or effective section (class 4 or shearlag effects)(clause of EC3-1-1). linear summation of the utilization ratios class 1/2/3 (clause (7)); nonlinear interaction formulas class 1/2 (clause (6)). Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNSC olumn cross sections and applications Rolled open or closed sections, welded sections or built-up sections Theobjective is to maximize the second moment of area in the relevant bucklingplan in order tomaximize the buckling Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNSC ompression resistance (clause of EC3-1-1)Aeff- effective , RdcEdNN0,MyRdcfAN 0,MyeffRdcfAN (class 1, 2 or 3)(class 4)i) Plastic resistanceii) buckling resistance Nb,Rd,in general the flexural bucklingresistance, which is analysed the design value of the axial compression.

3 Nc,Rdis the design resistance to axial compression, given by the minimum of:NEd fyA Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNSy(x)Ny(x) L Ny x N0 Ncr(z)022 yNdxydIE22 LIENcr Column buckling Flexural bucklingis in general the buckling mode, which govern the design ofa member in pure compression. For this mode in a pinned column, theelasticcritical loadNcr,defined as the maximum load supported by the column, freefrom any type of imperfections, is given by the well known Euler s formula:E I Bending stiffnessL buckling length(LEfor other support conditions) buckling in a bending mode In specific cases ( members with cruciform cross sections) buckling mayoccur in other modes:torsional buckling or flexural-torsional Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNS22 E AN iLE yfE 1yf cryNAf 1 2222 ELAIEEcr iLE AIi Critical stressyycrfEfE 1212 SlendernessEuler s curveNon-dimensional slendernessRadius of gyrationColumn Buckling22 EcrLIEN curvesEuler yf or real columns (geometrical imperfections and material imperfections).

4 Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF (Class 1, 2 or 3)(Class 4)221 but is the reduction factor for the relevant buckling crEdNNNeglect buckling if:orBuckling Resistance(clause of EC3-1-1)Theoretical behaviourEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNS11 iLNfAcrcry 1 AAiLNfAeffcrcryeff (Class 1, 2 or 3)(Class 4) yfEyf 235 cryTNfA cryeffTNfA Torsional or flexural-torsional buckling - buckling in flexural buckling mode about z axis (Class 1, 2 or 3)(Class 4)Flexural bucklingBuckling Resistance(clause of EC3-1-1) Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNSS afety verification of a column member of the building represented in master exampleEXAMPLE 1B A C D E F 1 2 3 4 m m m m 2b 2a A C E mi)The inner column E-3 represented in the figure, at base level, is selected.

5 This member hasa length of m and is composed by a section HEB 340 in Steel S this column the bending moments (and the shear force) may be neglected; thedesignaxial force(compression) obtained from the previous analysis is given byNEd= Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNSii) Cross section classification section HEB 340 in pure characteristics:A= cm2,b= 300 mm,h= 340 mm,tf= mm,tw= 12 mm,r= 27 mm,Iy= 36660 cm4,iy= cm,Iz= 9690 cm4,iz= properties of the Steel :fy= 355 MPa andE= 210 ) ( tcWeb in compression (Table of EC3-1-1)Flange in compression (Table of EC3-1-1)HEB 340 cross section, Steel S 355, in pure compression is class 1(class 1)(class 1)cEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNSiii) Cross section verification - class 1 in pure ,kNfANNMyRdcEd iv) buckling EzLBuckling lengths Assuming that the design forces were obtained by a second orderstructural analysis, the buckling lengths areconsidered (conservatively) equal to the reallengths (mid-distance between floors), given by.

6 buckling in the plan x-y (around z) -Determination of the slenderness yEyyiL zEzziL zzBuckling in the plan x-z (around y) -EXAMPLE 1 Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNSyzCalculation of the reduction factor ftand). () ( yz Asbcurveccurve andzmin EXAMPLE 1 HEB 340300340 Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF COLUMNSEXAMPLE 1v) Safety , MyzRdbfAN , RdbEdNNAs,safety is verified with the cross section HEB 340 in S 355 z z z zmin Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSHot-rolled sections (IPE, HEA or HEB, RHS,..) Welded sections Welded sections in non-uniform beams Castellated beams A beam may be defined as a member subjectedessentially to bending and shear cross sections and applicationsEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF Class 1 or 2 Class 3 Class 4 Uniaxial bending(clause of EC3-1-1)Cross section.

7 ,, RdzplEdzRdyplEdyMMMMBi-axial bending (clause of )n5;2 2 6 1 butbutIor HCHSRHSRdplEdNNn, Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSC ross section resistancey GVEdz Av , RdcEdVVPLASTIC RESISTANCE (clause of EC3-1-1)ELASTIC RESISTANCE MyEdf tISVEdEd Av Shear area(obtained from (3) of EC3-1-1 orfrom tables of profiles). Shear stresses - Shear buckling for webs without stiffeners should be verified in accordance with EC3-1-5, if: 72 wwthhwandtware the height and thickness of the web and is inaccordance with /yf 3yf 3yfEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSRdplEdVV,%50 RdplEdVV,%50 yyrff 1 RdplEdVV RdcyMywwyplRdVyMftAWM,,02,.,4 wwWthA NO REDUCTIONREDUCED MOMENTForI and H cross sections of equal flanges,withbendingaboutthemajoraxisy,th ebending moment resistanceMy,V,Rdis given by (clause of EC3-1-1):Bending and Shear Interaction (clause of EC3-1-1)tw My fyr fyr (Vz) (My) Vz hmzy+ fy fyMy, section resistanceEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSL ateral-Torsional buckling Instability phenomenon characterized by the occurrence of large transversaldisplacements and rotation about the member axis, under bending momentabout the major axis (y axis).

8 This instability phenomenon involves lateral bending (about z axis) and torsion ofcross Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSL ateral-Torsional buckling TWzTEcrIGLIEIEIGLM221 In the study of lateral-torsional buckling of beams, theElastic Critical MomentMcrplays a fundamental role; this quantity is defined as the maximum value of bendingmoment supported by a beam, free from any type of imperfections. For a simple supported beam with a double symmetric section, with supports preventlateral displacements and rotation around member axis (twist rotations), but allowingwarping and rotations around cross section axis (y and z), submitted to a uniformbending momentMy( standard case ), theelastic critical momentis given by:Which depend mainly of:Loading and support conditions;Length between lateral braced sections (L);Lateral bending stiffness (E Iz); Torsional stiffness (G IT);Warping stiffness (E Iw).

9 L zz My x xMya) Elevation A BCEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSy z C Gy z GC sagzzz yAsjIdAzzyzz critical momentMcr PCMcr,2<Mcr PCPMcr,1>Mcr C- applicable to member with symmetric and mono-symmetric cross sections, - include the effects of the loading applied below or above the shear centre;- several degrees of restriction to lateral bending (kz) and warping (kw);- several shapes of bending moment diagram (C1, C2and C3 in the next tables).Lateral-Torsional BucklingEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSL ateral-Torsional BucklingElastic critical moment- LTBeam Publication n 119 do ECCS (Boissonnade et al. 2006). Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSL ateral-Torsional BucklingLateral-torsional buckling resistance (clause of EC3-1-1) Wy= 1 and 2;Wy= 3;Wy= 4.

10 LTis the reduction factor for lateral-torsional buckling , which can be calculated by one of two methods, depending of member cross Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSL ateral-Torsional Bucklingi) General method LT Mcr-Elastic critical momentTa b l e 6 . 4 - Eurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSii) Alternative method (rolled sections or equivalent welded sections) 20, , LT (may be specified in National Annexes of Eurocode 3)Lateral-Torsional BucklingTa b l e 6 . 5 -Mcr-Elastic critical momentEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSfLTLT mod, , LT f0,LTLT 20,LTcrEdMM Neglect LTB if:Lateral-Torsional BucklingEurocodes Design of Steel buildings with worked examplesBrussels, 16 17 October 2014 DESIGN OF BEAMSEXAMPLE 2 Safety check of a beam of the building illustrated in the figure (along line E).