Closed form solution for predicting the horizontal capacity of masonry portal frames through limit analysis and comparison with experimental test results

Abstract The paper deals with the problem of evaluating the in-plane seismic capacity of unreinforced masonry portal frame, which can be considered the basic structural element in historical buildings. In particular, the Limit Analysis approach is used to provide simplified “closed form” expressions of the horizontal collapse multiplier, also taking into account the eventual contribution of steel tie rods. Both sliding shear and shear diagonal cracking are also considered in order to take into account the shear failure modes of the pier walls. The proposed formulations have been used for performing an extensive parametric analysis, with the aim of studying the effect of both geometry and vertical/horizontal loading distributions on the portal horizontal strength. Furthermore, the influence of the steel tie-rods has been addressed in order to understand their effectiveness on the portal seismic capacity. A comparison with the results of experimental tests on full-scale portal frames is also provided in terms of in-plane collapse multiplier and failure mechanism aimed to validate the proposed “closed form” expressions. Major outcome of this study is a simple rule of thumb, which can be used for the straightforward assessment of the horizontal strength of simple masonry structures, and for verifying the results of more complex structural analyses such as the nonlinear static analysis.