A contemporary of Le Corbusier and onetime employee of Frank Lloyd Wright, R.M. Schindler was architect of (amongst much else of note) the Lovell Beach House in California, acknowledged to be one of the key modernist buildings of the 1920s. This book, a reappraisal of Schindlers thought and works, presents plans, line drawings and photographs of buildings and furniture. A selection of Schindlers own writings is included, alongside articles by many scholars of the architects works that trace Schindlers career on both sides of the Atlantic, from his early days in Vienna studying under Wagner, to his later life in America, where his talents found full expression
STEEL BUILDINGS IN EUROPE Multi-Storey Steel Buildings Part 5: Joint Design Multi-Storey Steel Buildings Part 5: Joint Design - ii Part 5: Joint Design FOREWORD This publication is part five of a design guide, Multi-Storey Steel Buildings The 10 parts in the Multi-Storey Steel Buildings guide are: Part 1: Part 2: Part 3: Part 4: Part 5: Part 6: Part 7: Part 8: Part 9: Part 10: Architect’s guide Concept design Actions Detailed design Joint design Fire Engineering Model construction specification Design software – section capacity Design software – simple connections Software specification for composite beams Multi-Storey Steel Buildings is one of two design guides The second design guide is Single Storey Steel Buildings The two design guides have been produced in the framework of the European project “Facilitating the market development for sections in industrial halls and low rise buildings (SECHALO) RFS2-CT-2008-0030” The design guides have been prepared under the direction of Arcelor Mittal, Peiner Träger and Corus The technical content has been prepared by CTICM and SCI, collaborating as the Steel Alliance - iii Part 5: Joint Design - iv Part 5: Joint Design Contents Page No FOREWORD III SUMMARY VII INTRODUCTION 1.1 About this design guide 1.2 Joint behaviour 1.3 Standardised joints 1.4 Tying resistance 1.5 Design guidance in this publication 1.6 Symbols PARTIAL DEPTH END PLATE 2.1 Recommended details 2.2 Checks for vertical shear 2.3 Checks for tying 2.4 Worked Example – Partial depth end plate 5 12 14 FIN PLATE 3.1 Recommended details 3.2 Checks for vertical shear 3.3 Checks for tying 3.4 Worked Example: Fin Plate 21 21 22 33 38 DOUBLE ANGLE WEB CLEATS 4.1 Recommended details 4.2 Checks for vertical shear 4.3 Checks for tying 4.4 Worked Example: Angle Web Cleats 51 51 52 63 68 COLUMN SPLICES (BEARING TYPE) 5.1 Recommended details 5.2 Checks for tension 5.3 Check for horizontal shear 5.4 Checks for vertical tying 5.5 Worked Example – Column Splice 83 83 86 91 91 93 COLUMN BASES 6.1 Base plate size 6.2 Calculation of c 6.3 Base plate thickness 6.4 Base plate welds 6.5 Worked Example – Column base 101 101 102 103 104 105 APPENDIX A LATERAL TORSIONAL BUCKLING STRENGTH REFERENCES 1 3 108 109 5-v Part 5: Joint Design - vi Part 5: Joint Design SUMMARY This design guide gives the design procedure for simple joints in multi-storey buildings according to the Eurocodes The guide covers different types of joints: Beam-to-beam and beam-to-column joints Partial depth flexible end plate Fin plate Double angle web cleats Column splices Column bases Each design procedure is illustrated by a worked example, using the recommended values given in the Eurocodes - vii Part 5: Joint Design - viii 5.4 Title Worked Example – Column Splice of Web cleats Use 90908 angles to accommodate M20 bolts in opposite positions on adjoining legs 0,5huc Length Packs, tpa = = 0,5 260 = 130 mm t w,lc t w, uc = 11, 10 = 0,8 mm 5.2 Checks for vertical shear 5.2.1 Net tension Say 150 mm, OK Say mm, OK 5.2.1.1 Net tension effects Basic requirement for no net tension: MEd ≤ N Ed,G h = MEd N Ed,G h 760 260 10 3 = 99 kNm = 110 kNm > 99 kNm Net tension does occur and the flange cover plates and their fastenings must be checked for a tensile force FEd FEd = M Ed N Ed,G 110 760 = = 43 kN 3 h 260 10 5.2.1.2 Tension resistance of the flange cover plate Basic requirement: FEd ≤ Nt,Rd Where Nt,Rd = N pl,Rd ; N u,Rd ; N bt,Rd Tension resistance of gross section Npl,Rd = M0 Gross area, Npl,Rd = EN 1993-1-1 § 6.2.3(2) Afp f y,p Afp = 26012 = 3120 mm2 3120 275 10 3 = 858 kN 1,0 Tension resistance of net section Nu,Rd = Net area, Nu,Rd = EN 1993-1-1 § 6.2.3(2) , Afp,net f u,p M2 Afp,net = 26012 – 22212 = 2592 mm2 , 2592 430 10 3 = 802 kN 1, 25 Thus Nu,Rd = 802 kN – 95 Title 5.4 Worked Example – Column Splice of Block tearing resistance For concentrically loaded bolt group: Nbt,Rd = Veff,1,Rd 2e2 = 255 = 110 mm p2 = 150 ≤ 2e2 § 3.10.2(3) Hence Afp,nt = tp( 2e2 – d0 ) = 12 (255 – 22) = 1056 mm2 Afp,nv = 2tp ( e1+(n1 – 1)p1 – (n1 – 0,5)d0 ) = 212 (40 + (2 – 1)160 – (2 – 0,5)22) = 4008 mm2 430 1056 275 4008 10 3 = 1000 kN Veff,1,Rd = 1, 1, 25 Nbt,Rd = 1000 kN Nt,Rd = min(858; 802; 1000) = 802 kN FEd = 43 kN ≤ 802 kN, OK Check for the suitability of ordinary bolts (It is sufficiently accurate to base this calculation on the gross area of the flange) FEd 43 10 = = 0,04 < 0,1 12 , 260 355 t f,uc b f,uc f y,uc There is no significant net tension in the column flange and the use of ordinary bolts in clearance holes is satisfactory 5.2.1.3 Bolt group resistance e1 = 40 p1 = 160 e = 55 p2 =150 Flange cover plate Shear and bearing resistance of the flange cover plate Basic requirement: FEd ≤ FRd – 96 Ref [4] 5.4 Title Worked Example – Column Splice § 3.7 The design resistance of the bolt group, FRd,fp: max of FRd ΣFb,Rd if F b, Rd FRd nfp (Fb, Rd ) if ( F b, Rd ) F v,Rd ( F b, Rd ) max FRd nfp Fv,Rd if F v,Rd F b, Rd F v,Rd Shear resistance of bolts The shear resistance of a single bolt, Fv,Rd = v f ub A M2 A factor to account for the long joint effect must be introduced if Lj > 15d 15d = 1520 = 300 mm Lj = 160 mm, < 15d Table 3.4 § 3.8 Therefore there is no long joint effect Total thickness of flange pack, tpa = 30mm > d , mm Therefore Fv,Rd must be multiplied by a reduction factor βp βp = 20 9d = = 0,72 20 30 d t pa For M20 8.8 bolts, Fv,Rd = , 72 , 800 245 ×10-3 = 68 kN 1, 25 Bearing resistance Bearing resistance, Fb,Rd = For edge bolts, k1 k 1 b f u,p dt p Table 3.4 M2 55 e = min 2,8 1,7; 2,5 = min 2,8 1,7; 2,5 22 d0 = 5,3; 2,5 = 2,5 For end bolts αb e f 800 40 = min ; ub ; 1,0 = min ; ; 1,0 3d 22 430 f u,p = 0,61; 1,86; 1,0 = 0,61 For inner bolts, αb p f = min 0,25; ub ; 1,0 3d f u,p 800 160 = min 0,25; ; 1,0 430 22 = 2,17; 1,86; 1,0 = 1,0 – 97 5.4 Title End bolts, Worked Example – Column Splice Fb,Rd,end = Fb,Rd = , , 61 430 20 12 10 3 1, 25 = , 1, 430 20 12 10 3 1, 25 of = 126 kN Inner bolts, Fb,Rd,inner = Fb,Rd max = 206 kN Thus Fv,Rd < Fb,Rd FRd = nfp Fv,Rd = 468 = 272 kN FEd = 43 kN ≤ 272 kN, OK 5.2.2 Check for horizontal shear For a bearing type splice, any horizontal shear VEd is assumed to be resisted by friction across the splice interface Ref [4] Basic requirement: VEd ≤ shear resistance of splice interface Vertical load with coexistent shear M Ed N Ed,G 110 10 760 = = 803 kN h 260 Shear resistance of splice interface: 8030,2 = 161kN VEd = 60 kN ≤ 161 kN, OK 5.3 Structural integrity 5.3.1 Tying force Check 4.2.1.2 and 4.2.1.3 should be carried out with: Ftie FEd = Ftie = FEd 43 = 86 kN 5.3.2 Tensile resistance of the flange cover plate Basic requirement: Ftie ≤ Nt,Rd Where Nt,Rd = N pl,Rd ; N u,Rd ; N bt,Rd 5.3.2.1 Tension resistance of the gross area Npl,Rd = EN 1993-1-1 § 6.2.3(2) Afp f u,p Mu Gross area, Afp = 26012 = 3120 mm2 Npl,Rd = 3120 430 10 3 = 1220 kN 1, – 98 5.4 Title Worked Example – Column Splice of 5.3.2.2 Tension resistance of the net area Nu,Rd = EN 1993-1-1 § 6.2.3(2) , Afp,net f u,p Mu Net area, Afp,net = 26012 – 22212 = 2592 mm2 Nu,Rd = , 2592 430 10 3 = 912 kN 1, Thus Nu,Rd = 912 kN 5.3.2.3 Block tearing resistance Table 3.4 For concentrically loaded bolt group: Nbt,Rd = Veff,1,Rd 2e2 = 255 = 110 mm p2 = 150 ≤ 2e2 Hence Afp,nt = tp( 2e2 – d0 ) = 12 (255 – 22) = 1056 mm2 Afp,nv = 2tp ( e1+(n1 – 1)p1 – (n1 – 0,5)d0 ) = 212 [40 + (2 – 1)160 – (2 – 0,5)22] = 4008 mm2 430 1056 275 4008 10 3 = 1049 kN Veff,1,Rd = ,1 1, Nbt,Rd = 1049 kN Nt,Rd = min(1220; 912; 1049) = 802 kN Ftie = 86 kN ≤ 912 kN, OK 5.3.2.4 Bolt group resistance Shear and bearing resistance of the flange cover plate Basic requirement: Ftie ≤ FRd § 3.7 The design resistance of the bolt group, FRd,fp: FRd ΣFb,Rd if Fb,Rd max Fv,Rd FRd n fp ( Fb,Rd ) if ( Fb,Rd ) F v,Rd ( Fb,Rd ) max FRd n fp F v,Rd if F v,Rd Fb,Rd min Shear resistance of bolts The shear resistance of a single bolt, Fv,Rd = v f ub A Mu A factor to account for the long joint effect must be introduced if Lj > 15d 15d = 1520 = 300 mm Lj = 160 mm, < 15d – 99 Table 3.4 5.4 Title Worked Example – Column Splice of Therefore there is no long joint effect Total thickness of flange pack, tpa = 30mm > d , mm Therefore Fv,Rd must be multiplied by a reduction factor βp βp = 20 9d = = 0,72 d t pa 20 30 For M20 8.8 bolts, Fv,Rd = , 72 , 800 245 10 3 = 77 kN 1,1 Bearing resistance k 1 b f u,p dt p Bearing resistance, Fb,Rd = For edge bolts, k1 55 e = min 2,8 1,7; 2,5 = min 2,8 1,7; 2,5 22 d0 Mu = 5,3; 2,5 = 2,5 For end bolts e f 800 40 = min ; ub ; 1,0 = min ; ; 1,0 3d 22 430 f u,p αb = 0,61; 1,86; 1,0 = 0,61 p f = min 0,25; ub ; 1,0 3d f u,p For inner bolts, αb 800 160 0,25; ; 1,0 = min 430 22 = 2,17; 1,86; 1,0 = 1,0 End bolts, Fb,Rd,end = Fb, Rd min = , , 61 430 20 12 10 3 ,1 = 143kN Inner bolts, Fb,Rd,inner = Fb,Rd max = , 1, 430 20 12 10 3 1, = 235 kN Thus Fv,Rd < Fb,Rd FRd = nfp Fv,Rd = 477 = 308 kN Ftie = 86 kN ≤ 308 kN, OK – 100 Table 3.4 Part 5: Joint Design COLUMN BASES This design method applied to fixed bases of I section columns transmitting an axial compressive force, and a shear force (i.e a nominally pinned column base) The rectangular base plate is welded to the column section in a symmetrically position so that it has projections beyond the column flange outer edges on all sides 6.1 Base plate size b bp bf h hp hf Basic requirement: Ap Areq Ap [Reference 4] = area of base plate = hpbp for rectangular plates Areq = required area of base plate fjd = F Ed f jd = fcd where: df = max h p , b p , eh h p e ,1 b bp , [Reference 3] If some dimensions are unknown, a value of = 1,5 is generally appropriate hp is the length of the base plate bp is the width of the base plate df is the depth of the concrete foundation hf is the length of the concrete foundation – 101 Part 5: Joint Design bf is the width of the concrete foundation tf is the flange thickness of the column eb is the additional width outside of the base plate = bf b t f / eh is the additional depth outside of the base plate = hf h t f / 6.2 f ck = cc fcd [EN 1992-1-1, §3.1.6(1)] c αcc is a coefficient that takes into account long term effects on the compressive strength and of unfavorable effects resulting from the way the load is applied [13] c is the material factor for concrete from EN 1992-1-1, §2.4.2.4[13] Concrete class C20/25 C25/30 C30/37 C35/45 Cylinder strength, fck (N/mm2) 20 25 30 35 Cube strength, fck,cube (N/mm2) 25 30 37 45 Calculation of c hp c bp A eff 2c + tf Projection, c tf = flange thickness tw = web thickness Basic requirement: Areq = Aeff If 2c ≤ h t f , then there is no overlap Thus c may be calculated from the following equations for I and H sections: Aeff ≈ 4c2 + Percolc + Acol where: Acol is the cross sectional area of the column Percol is the column perimeter If 2c > h t f , then there is an overlap Thus c may be calculated from the following equations for I and H sections: Aeff ≈ 4c2 + 2(h + b)c + h b – 102 Part 5: Joint Design To ensure that the effective area fits on the base plate: h + 2c < hp b + 2c < bp 6.3 Base plate thickness c A eff 2c + tf Basic requirement: ≥ tp,min tp,min =c f jd M0 [Reference 3] f yp where: fyp is the yield strength of the base plate fjd = fcd = cc fcd f ck c , αcc, c, fck, and c are as defined previously – 103 Part 5: Joint Design 6.4 Base plate welds NEd VEd Basic requirement: For shear: VEd Fw,Rd ℓweld,shear [Reference 4] For axial load: This check is only necessary when the contact faces of the column and base plate are not in tight bearing See Reference [4] for more details FEd Fw,Rd ℓweld,axial where: Fw,Rd is the resistance of the fillet weld per unit length = fvw,d a fu fvw,d = [EN 1993-1-8 §4.5.3.3(3)] fu is ultimate tensile strength of the weaker part joined w = 0,8 for S235 steel w M2 = 0,85 for S275 steel = 0,9 for S355 steel = 1,0 for S460 steel a is the weld throat ℓweld,shear is total effective length of the welds in the direction of shear ℓweld,shear = l s l (for IPE, HE, HD sections) is the weld length in the direction of shear ℓweld,axial is the total effective length of the welds to the column flange for rolled sections M2 is the partial factor for welds from EN 1993-1-8 The leg length is defined as follows: s a – 104 6.5 Worked Example – Column base Made by Calculation sheet of CZT Checked by ENM Date 06/2009 Date 07/2009 Column base Details and data Unless noted otherwise, all references are to EN 1993-1-8 HD 320 x 127 S355 N Ed = 4300kN 50 V Ed = 100kN 600 f ck= 30N/mm 100 600 600 600 50 Base plate S275 mm fillet welds M24 grade 4.6 holding down bolts Contact faces of the column and the base plate are in direct bearing – 105 6.5 Title 6.1 Worked Example – Column base of Base plate size Basic requirement: Ap Areq Area of base plate: Ap = hp bp = 600 600 = 360000 mm2 fcd from f ck Design strength of the concrete: fcd = cc Area required: Areq Ref [3] 30 = 1, 1, c N Ed 4300 10 = = f jd 1, 20 Ap = 360000 mm2 > 215000 mm2 6.2 Calculation of c EN 1992-1-1 §3.1.6(1) = 20 N/mm = 215000 mm OK tf tw b t w +2c b+2 c bp h Aeff h+2 c hp Basic requirement: Aeff = Areq To calculate the effective area, assume first that there is no overlap ≈ 4c2 + Percolc + Acol Column perimeter Percol = 1771 mm Area of column Acol ≈ 4c2 + 1771c + 16130 Aeff = 16130 mm2 = 215000 = Areq c = 93 mm To ensure that there is no overlap, c has to be less than half the depth between flanges: h 2t f = αcc from EN 1992-1-1 §3.1.6(1) C from EN 1992-1-1 Table 2.1N t f + 2c Aeff 320 20 , = 139,5 mm > 93 mm Therefore the assumption that there is no overlap is correct – 106 6.5 Title Worked Example – Column base of To check that the effective area fits on the base plate: h + 2c = 320 93 = 506 mm < 600 mm b + 2c = 300 93 = 486 mm < 600 mm Therefore the calculated value of c is valid (otherwise recalculate c) 6.3 Base plate thickness tp,min =c fjd = Ref (3) f jd M0 f y,p 2 f cd 1,5 20 = 20 N/mm2 3 Yield strength of the 50 mm plate, fy,p = 255 N/mm2 20 1, = 45 mm 255 tp,min = 93 = 50 mm > 45 mm 6.4 Base plate welds (Shear resistance of column-tobase weld) Basic requirement: VEd OK F w,Rd l eff,shear Ref [4] Ultimate tensile strength of the 50 mm plate, fu,p = 410 N/mm2 Fw,Rd = f vw,d a = fu w M2 a = 410 , = 1248 N/mm , 85 1, 25 ℓeff,shear = (l – 2s) = 100 = 168 mm Fw,Rdℓeff,shear = 1248 168 10 3 = 210 kN VEd = 100 kN ≤ 210 kN OK – 107 Fw,Rd from § 4.5.3.3(3) Part 5: Joint Design APPENDIX A Lateral torsional buckling strength Lateral torsional buckling strength taken from BS 5950-1 Table 17[10] Lateral torsional buckling strength (N/mm2) Steel grade LT 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 210 220 230 240 250 235 235 235 235 224 206 190 175 162 150 139 130 126 122 118 114 110 106 101 96 90 85 80 75 71 67 64 60 57 54 52 49 47 45 43 41 39 36 33 31 28 26 245 245 245 245 231 212 196 180 167 154 142 135 131 127 123 118 113 109 104 97 91 86 81 76 72 68 64 61 58 55 52 50 47 45 43 41 39 36 33 31 29 27 S275 255 255 255 255 237 218 201 185 171 158 146 140 136 131 127 122 117 112 106 99 93 87 82 77 73 69 65 62 59 56 53 50 48 46 44 42 40 37 34 31 29 27 265 265 265 265 244 224 207 190 176 162 150 145 141 136 131 125 120 115 107 101 94 89 83 78 74 70 66 62 59 56 53 51 48 46 44 42 40 37 34 31 29 27 – 108 275 275 275 272 250 230 212 195 180 166 155 151 146 140 135 129 123 117 109 102 96 90 84 79 75 71 67 63 60 57 54 51 49 46 44 42 40 37 34 31 29 27 315 315 315 300 276 253 233 214 197 183 177 170 163 156 149 142 132 123 115 107 100 94 88 83 78 73 69 65 62 59 56 53 50 48 46 43 42 38 35 32 30 28 325 325 325 307 282 259 238 219 201 188 182 175 168 160 152 144 134 125 116 108 101 95 89 83 78 74 70 66 62 59 56 53 51 48 46 44 42 38 35 32 30 28 S355 335 335 335 314 288 265 243 223 205 194 187 179 172 164 156 146 136 126 117 109 102 96 90 84 79 74 70 66 63 59 56 53 51 48 46 44 42 38 35 33 30 28 345 345 345 321 295 270 248 227 209 199 192 184 176 167 159 148 137 128 119 110 103 96 90 85 80 75 71 67 63 60 57 54 51 49 46 44 42 39 35 33 30 28 355 355 355 328 301 276 253 232 212 204 196 188 179 171 162 150 139 129 120 111 104 97 91 85 80 75 71 67 63 60 57 54 51 49 47 44 42 39 36 33 30 28 Part 5: Joint Design REFERENCES EN 1993-1-8:2005: Eurocode Design of steel structures Design of joints EN 1991-1-7: 2006: Eurocode Actions on structures General actions Accidental actions Detailed European design guides to the Eurocode (http://www.access-steel.com) Joints in steel construction: Simple connections Steel Construction Institute, 2002 CHENG, J J R and YURA, J A Journal of the Structural Division, ASCE, October 1986 Local web buckling of coped beams CHENG, J J R, YURA, J A and JOHNSON C P Department of Civil Engineering, University of Texas at Austin Design and behaviour of coped beams PMFSEL Report No 841, July 1984 JARRETT, N D Tests on beam/column web side plate connections BRE Client Report CR 54/90 Building Research Establishment, Watford, September 1990 JASPART, J.-P., DEMONCEAU, J.-F.,.RENKIN, S., and GUILLAUME, M L European recommendation for the design of simple joints in steel structures Publication n°126, First edition, ECCS, 2009 RENKIN, S Development of a European process for the design of simple structural joint in steel frames (in French): Diploma work, University of Liege, June 2003 10 BS 5950-1:2000 Structural use of steelwork in building Code of practice for design Rolled and welded sections BSI, 2000 11 YURA, J A., HANSEN, M A and FRANK, K H Bolted splice connections with undeveloped fillers Journal of the Structural Division ASCE, December 1982 12 EN 1090-2:2008: Execution of steel structures and aluminium structures Technical requirements for the execution of steel structures 13 EN 1992-1-1:2004: Eurocode Design of concrete structures General rules and rules for buildings Flow charts Flow charts for End plate, Fin plate and Column bases are available on the Access Steel web site (http://www.access-steel.com) The document references for these joint types are as follows: Partial depth end plate SF008a Fin plate SF009a Column bases SF010a – 109