FEM and Analytical Solutions for Buckling of Nonlinear Masonry Members

Abstract

The numerical analysis of slender cracked and uncracked masonry members—including nonlinear stress-strain relationship, self-weight, and vertical and lateral concentrated and distributed loads—is carried out. Analytical solutions of the stability problem are also provided for large cracked members (large eccentricity in each cross section) by neglecting the self-weight. A finite-element method (FEM) approach, using the Galerkin weighted residuals approach, is developed to study the stability problem for any stress-strain relationship and any load condition of the masonry member. The reliability and the convergence of the proposed nonlinear FEM is evaluated by the comparison of the solutions with available analytical ones and with those obtained by means of another numerical technique. It is shown that the self-weight has a stabilizing effect for large eccentricities of the vertical load, but an unstabilizing effect for small eccentricities. The unstabilizing effect is more marked for nonlinear stress-strain relationships. Dimensionless graphs allowing the resolution of similar practical problems are reported.