Analytical modelling of out-of-plane flexural response of unreinforced and strengthened masonry walls

Abstract

The available literature on out-of-plane bending of masonry walls identifies two distinct phases – pre-cracking and post-cracking, in the force-displacement response. Accordingly, a semi-empirical model for out-of-plane behaviour of unreinforced and strengthened masonry walls is developed, which considers the overall load-displacement response in two phases. The pre-cracking phase model predicts the peak strength of the masonry, whereas the post-cracking model provides a hysteresis envelope (back-bone curve). A tri-linear displacement-based model is developed for one-way bending walls subjected to uniformly distributed lateral load, using a database of 38 experiments available in the literature. Analytical expressions for maximum lateral force and instability displacement are derived using the kinematic approach. Using the experimental database, two factors, λ1 and λ2 are estimated to calibrate the analytical results. The calibrated analytical model shows a good agreement with the experimental results. An analytical method for predicting the two-way out-of-plane flexural capacity in the pre-cracking phase of unreinforced and strengthened masonry walls using crackline method is also developed. This model shows reasonably good results, even with the assumption of an idealized crack pattern. However, the force-displacement parameters for obtaining two-way bending back-bone curve in the post-cracking phase show large scatter indicating that the available test results are not adequate to develop an empirically calibrated model.