Steel Buildings in Europe

Part 4: Detailed Design of Portal Frames 4 - 73 APPENDIX B Calculation of  cr,est B.1 General EN 1993-1-1 § 5.2.1 (4) B gives:              H,Ed Ed Ed cr   h V H However, this can only be applied when the axial load in the rafter is not significant. Note 2B of § 5.2.1(4)B describes significant as when Ed y 0,3 N Af   , which may be rearranged to indicate that the axial load is not significant when cr Ed 0,09 N N  Where: N cr is the elastic critical buckling load for the complete span of the rafter pair, i.e. 2 2 cr L EI π N  L is the developed length of the rafter pair from column to column, taken as span/Cos θ ( θ is the roof slope). If the axial load in the rafter exceeds this limit, the expression in EN 1993-1-1 cannot be used. An alternative expression, accounting for the axial force in the rafter, has been developed by J. Lim and C. King [6] and is detailed below. For frames with pitched rafters:  cr,est = min   cr,r,est cr,s,est ;   where:  cr,s,est is the estimate of  cr for sway buckling mode  cr,r,est is the estimate of  cr for rafter snap-through buckling mode. This mode need only be checked when there are three or more spans, or if the rafter is horizontal, or when the columns are not vertical. B.2 Factor  cr,s,est The parameters required to calculate  cr,s,est for a portal frame are shown in Figure B.1.  NHF is the lateral deflection at the top of each column when subjected to a notional lateral force H NHF . (The magnitude of the total lateral force is arbitrary, as it is simply used to calculate the sway stiffness). The horizontal force applied at the top of each column should be proportional to the vertical reaction.