Steel Buildings in Europe

Title APPENDIX D Worked Example: Design of portal frame using elastic analysis 22 of 44 4 - 103 Firstly individual checks are carried out for flexural buckling alone and lateral-torsional buckling alone. Then the interaction expression for in-plane buckling is applied to verify that the combination of axial force and bending moment does not cause excessive buckling on the columns. 7.6.1. Flexural buckling resistance about the mayor axis, N b,y,Rd b h  200 500  2,5 t f  16 mm buckling about y-y axis:  Curve a for hot rolled I sections   y  0,21 EN 1993-1-1 Table 6.2 Table 6.1 The buckling length is the system length, which is the distance between nodes (i.e. the length of the column), L = 6000 mm.  1 = y f E  = 355 210000  = 76,4 EN 1993-1-1 §6.3.1.3 y  = y 1 cr 1  i L = 76, 4 1 204 6000  = 0,385  y =     2 y y y 0,2 0,51       =     2 0,51 0,21 0,385 0,2 0,385    = 0,594 EN 1993-1-1 §6.3.1.2  y = 2 2 1      = 2 2 0,385 0,594 0,594 1   = 0,956 EN 1993-1-1 §6.3.1.2 N b,y,Rd = M1 y y   Af = 3 10 1, 0 355 11600 0,956     = 3937 kN N Ed = 168 kN < 3937 kN OK 7.6.2. Lateral-torsional buckling resistance, M b,Rd M b,Rd is the least buckling moment resistance of those calculated previously. M b,Rd =   min 779; 640 M b,Rd = 640 kNm 7.6.3. Interaction of axial force and bending moment – in-plane buckling In-plane buckling due to the interaction of axial force and bending moment is verified by satisfying the following expression: 1, 0 b,Rd y,Ed yy b,y,Rd Ed   M M k N N