Abstract
A method of stochastic evaluation of the strength of structural members is developed by the bifurcation theory. Knowing that the strength of slender specimens/members is governed by the so-called hilltop bifurcation point, which implies the coincidental double critcal point of limit and bifurcation points, we derive a system of bifurcation equations for the local behavior at this special double critical point. On the basis of this system of equations, we formulate an imperfection sensitivity law and, in turn, the probability density function of critical loads, assuming that initial imperfections are subject to a multi-variate normal distribution. In addition, the associated formulas for a limit point are presented for comparison. The validity of the theoretical developments is assessed through its application to a simple truss structure, whereas the feasibility and capability of the proposed method is demonstrated for the data sets obtained in actual experiments and numerical simulations of structural members.
