Out of plane behaviour of a vertical spanning unreinforced masonry strip wall restrained by a flexible diaphragm

Abstract

Out-of-plane response is one of the most debated topics in last decade about the performance of existing unreinforced masonry building. The response of parapet walls and vertical spanning strip wall, with rigid top support, has been studied to a large extent. Here, the vertical spanning strip wall is assumed and with a flexible top restraint, representing the diaphragm. Hence, the system has two degrees of freedom. The cracked wall is considered undergoing four different patterns. Due to the finite thickness of the wall, each pattern consists of two cases according to orientation of blocks described by angular displacement. Some transitions from a pattern to another are associated to energy dissipation due to impact of the top wall segment with the bottom one, or between bottom segment and foundation. The base hypothesis is that one impact at time can occur at a specific snapshot, either with the base or between the blocks. Some other transitions are due of sudden change in ground motion, involving the opening of the base or intermediate crack. A Matlab code has been developed to solve the highly non-linear second order differential equations of the rocking wall subjected to earthquake ground motion. The analytical model has been compared with existing experimental data and analytical models, for both free and forced vibrations, and for all the patterns for which references are available. The analytical model has been calibrated to improve the agreement with existing tests. The proposed model has been used to perform a parametric study, investigating the influence on the wall performance of the relevant parameters: aspect ratio and size of the wall, crack position, diaphragm characteristic, ground motion.