A simple efficient algorithm based on compressive diagonal strength of unreinforced masonry walls is presented to determine capacity curve of unreinforced masonry building. The compressive strength is calculated based on a new close form solution. The new close form solution is determined based on predicted results using interface elements for modeling of mortar joints. Finite element method with two-noded linear elements is used for analyses. Different masonry structures, including low- and high-rise unreinforced masonry buildings, are analyzed using the new closed-form solution and the presented algorithm. A comparison of results of the present work with experimental data and other methods similar to the discrete element method show proper accuracy of the analyses in the present work. Consequently, the closed form solution with proposed algorithm can be used to satisfactorily analyze unreinforced masonry structures to predict the ultimate base shear force and the pushover curve. Hence, practicing engineers can determine the behavior of an URM building and its performance level with proper accuracy under seismic excitation using concepts described in the present work.

This paper presents the numerical implementation of a new proposed interface model for modeling the behavior of mortar joints in masonry walls. Its theoretical framework is fully based on the plasticity theory. The Von Mises criterion is used to simulate the behavior of brick and stone units. The interface laws for contact elements are formulated to simulate the softening behavior of mortar joints under tensile stress; a normal linear cap model is also used to limit compressive stress. The numerical predictions based on the proposed model for the behavior of interface elements correlate very highly with test data. A new explicit formula based on results of proposed interface model is also presented to estimate the strength of unreinforced masonry structures. The closed form solution predicts the ultimate lateral load of unreinforced masonry walls less error percentage than ATC and FEMA-307. Consequently, the proposed closed form solution can be used satisfactorily to analyze unreinforced masonry structures.