Steel Buildings in Europe

Title APPENDIX D Worked Example: Design of portal frame using elastic analysis 27 of 44 4 - 108  1 = y f E  = 355 210000  = 76,4 EN 1993-1-1 §6.3.1.3 z  = z 1 cr 1  i L = 76, 4 1 41, 2 1700  = 0,540  z =     2 z z z 0,2 0,51        z =     2 0,51 0,34 0,540 0,2 0,540    = 0,704 EN 1993-1-1 §6.3.1.2  z = 2 z 2 z z 1      = 2 2 0,540 0, 704 0, 704 1   = 0,865 N b,z,Rd = M1 z y   Af = 3 10 1, 0 355 9880 0,865     = 3034 kN N Ed = 127 kN < 3034 kN OK Lateral-torsional buckling resistance for bending, M b,Rd In this zone, lateral-torsional buckling is checked between restraints, which are the purlins. For equally spaced purlins, the critical length is at the point of maximum bending moment. In order to determine the critical moment of the rafter, the C 1 factor takes account of the shape of the bending moment diagram. In this case the bending moment diagram is nearly constant along the segment in consideration, so   1,0. Therefore:  1 1  C ,0 Appendix C of this document M cr = z 2 t 2 z w 2 z 2 1 EI L GI I I L EI C    = 2 4 2 1700 10 1676 210000 1, 0      4 2 4 2 4 9 10 1676 210000 66,9 10 81000 1700 10 1676 791 10            M cr = 2733  10 6 Nmm Appendix C of this document LT   cr pl,y y M f W = 6 3 10 2733 355 10 1702    = 0,470 EN 1993-1-1 §6.3.2.2     2 LT LT,0 LT LT LT 0,51          EN 1993-1-1 §6.3.2.3