Steel Buildings in Europe

Title APPENDIX D Worked Example: Design of portal frame using elastic analysis 39 of 44 4 - 120 8.2.2. Compression resistance The compression resistance of cross-section No.1: N c,Rd = M0 y  A f = 3 10 1, 0 355 15045    = 5341 kN N Ed = 129 kN < 5341 kN OK EN 1993-1-1 §6.2.4 Bending and axial force interaction: When axial force and bending moment act simultaneously on a cross-section, the total stress,  x,Ed , must be less than the allowable stress.  x,Ed =  N +  M  M = y Ed I M z  = 4 6 10 200500 501, 6 661 10    = 165 N/mm 2  x,Ed =  N +  M = 8,57 + 165 = 174 N/mm 2 EN 1993-1-1 §6.2.9.2 The maximum allowable stress is:  max = M0 y  f = 1, 0 355 = 355 N/mm 2  x,Ed = 174 N/mm 2 < 355 N/mm 2 OK A similar calculation must be carried out for the remaining cross-sections. The table below summarize compression resistance verification for the haunched member: Table 4 Compression verification for cross-sections 1 to 5 Cross- section (i) N Ed (kN) A (mm 2 ) N c,Rd (kN) N Ed  N c.Rd Bending and axial interaction 1 129 15045 5341 Yes No 2 129 13870 4924 Yes No 3 128 12686 4504 Yes No 4 127 11501 4083 Yes No 5 127 9880 3507 Yes No 8.2.3. Bending moment resistance The bending moment resistance of cross-section No.1 is: M c,y,Rd = M el,y,Rd = M0 el,min y  f W = 6 3 10 1, 0 355 10 4055     = 1440 kNm M y,Ed = 661 kNm < 1440 kNm OK EN 1993-1-1 §6.2.5(2) A similar calculation must be carried out for the remaining cross-sections. The table below summarizes bending moment resistance verification for the haunched member.