Imperfection sensitivity and probabilistic variation of tensile strength of steel members

Elastic stability theory is applied to description of tensile strength variation in steel members due to variation of initial imperfections, despite criticism on the occurrence of unloading due to plastic instability. In numerical simulation of such members, the maximum load is attained at a limit point or a hilltop bifurcation point. This load is not much different for either type of point; hence, little attention has been paid to the type of points up to now. Yet it is noteworthy that these two types of points follow different imperfection sensitivity laws within the framework of elastic stability theory. Numerical experiments on steel members undergoing plastic deformation are conducted to ensure that empirical imperfection sensitivities for these members agree well with those sensitivity laws. This assesses applicability of elastic stability theory to description of plastic instability behaviors of steel members. Moreover, empirical histograms of steel members obtained through Monte-Carlo simulations are compared with theoretical probabilities of maximum loads, which are a normal distribution for the limit point and a Weibull-like one for the hilltop point. Therefore, elastic stability theory is useful to describe tensile strength variation of steel members.