Ultimate Load Capacity of Multi-Story Steel Frame Structures with Geometrical Imperfections: A Comparative Study of Two Methods

This study presents two methods for analyzing the ultimate load capacity of a multi-story steel frame structure with geometric imperfections and material nonlinearities. The first method is in accordance with European standard (EC) for steel structures, based on which the initial geometrical imperfections (out-of-straightness and out-of-plumb) are determined. In the second method, the first order reliability method (FORM) is utilized in order to determine the ultimate design resistance. In this second approach, the initial geometrical imperfections are based on European standard for allowed manufacturer tolerances, and are considered as statistical parameters. Local bow-imperfection amplitudes of each column (in both directions), global sways of each floor (in two directions), as well as material elastic modulus and yield stress are considered as stochastic variables (together 80 random input parameters). Cumulative tolerances of each story position are monitored and random realizations which violate these tolerances are distinguished. The results of both methods are summarized and compared in the matter of the ultimate resistances: design value according to EC vs. 0.1% quantile of stochastic ultimate resistance out of the FORM method. Failure modes of the random realizations are discussed as well. Overall, both methods resulted in comparable values of the ultimate resistances, with the design value based on EC standard being slightly more conservative then the value based on the FORM method.