Stability of nonlinear masonry members under combined load

Under examination is the post buckling of unreinforced load-bearing masonry walls or piers subject to a combined load consisting of a uniformly distributed axial load and a concentrated eccentric load at the top end. Fixed free-ended prismatic columns are examined, taking into consideration no-tension material with a parabolic stress–strain law. The integro-differential problem has been formulated extremely carefully and solved numerically with the finite difference method (FDM). Depending on eccentric load intensity, on the height-depth ratio, on the intensity of the distributed axial load and the initial eccentricity of the concentrated load, a column can fail owing to elastic instability or because the masonry has reached, or exceeded, its allowable compressive stress. It is shown that the load distributed along the axis, in the case of a centred top load or one with slight eccentricity, always produces a reduction of the limit load. Whereas in the case of a top load applied with strong eccentricity the distributed load has a stabilizing effect at low values of its intensity and produces a reduction of the limit load at high values instead. Finally the accuracy of the finite difference results is assessed by comparison with the results obtained by the use of the 4th-order Runge–Kutta Method and the Collocation Method.