Advanced Analysis of Space Steel Frames

This chapter presents advanced analysis methods for space steel frames which consider both geometric and material nonlinearities. The geometric nonlinearities come from second-order P   and P   effects (see Fig. 1.) as well as geometric imperfections, while the material nonlinearities are due to gradual yielding associated with residual stresses and flexure. The P   effect results from the axial force acting through the relative displacement of the ends of the member, so it is referred to as a member chord rotation effect. The P   effect is accounted in the second-order analysis by updating the configuration of the structure during the analysis process. The P   effect is caused by the axial force acting through the lateral displacement of the member relative to its chord, so it is referred to as a member curvature effect. The P   effect can be captured by using stability functions. Since the stability functions are derived from the closed-form solution of a beam-column subjected to end forces, they can accurately capture the P   effect by using only one element per member. Another way to capture the P   effect without using stability functions is to divide the member into many elements, and consequently, the P   effect is transformed to the P   effect.