Reliability of Randomly Imperfect Beam‐Columns

Abstract

A stochastic finite element method is developed for reliability studies of problems such as beam‐columns under axial loading with random geometric imperfections, uncertain material properties, and uncertain moduli of elastic foundations. The random geometric imperfections are described by an explicit form of autocorrelation function or a given initial displacement function with amplitude described as a random variable. The effects of random initial geometric imperfections are treated as a set of equivalent random initial forces. This concept enables the direct employment of existing stochastic finite element methods developed for treating random forces. This formulation can be straightforwardly used to study the reliability of practical beam‐column problems with complex loadings, realistic boundary conditions, arbitrary geometries, and imperfections, for which analytical solutions are difficult to obtain. To establish the validity of the present formulation, a series of examples including random loadings and uncertain material properties were solved. Since existing alternative solutions are limited, analytical solutions are also obtained for comparison. The last of the series of examples is a simply supported beam‐column with four simultaneous uncertain parameters: geometric imperfection, modulus of elasticity, moment of inertia, and modulus of elastic foundation. All the four parameters cover ranges of values with practical significance.