Out-of-plane load–displacement model for two-way spanning masonry walls

Abstract

This paper describes a methodology for modelling the nonlinear, inelastic load–displacement behaviour of two-way spanning unreinforced masonry walls subjected to out-of-plane loading. The model utilises a simplified macroblock approach that starts with the assumption of a collapse mechanism based on the wall’s boundary conditions. It then treats the wall as having zero tensile strength and assumes that the resistance comes entirety from two gravity-based resistance components: elastic rigid block rocking, and inelastic friction, with the total load resistance of the wall taken as the sum of these individual components. Analytical expressions for calculating the load and displacement capacities of the elastic rocking component of response are derived from the principles of statics using an integration approach well suited for the treatment of two-way mechanisms. Expressions for the associated frictional capacity component are obtained using the virtual work method. Comparison of the theoretical load–displacement response with experimentally measured data is favourable as demonstrated using data obtained via quasistatic cyclic tests on two-way spanning walls; the model is shown to provide an acceptable lower bound estimate of actual behaviour. The developed approach could be used to construct pushover curves for a range of different collapse mechanisms and therefore has the potential to be assimilated into a simplified displacement-based seismic design/assessment technique for two-way spanning walls against out-of-plane collapse.