Analytical model for the out-of-plane response of vertically spanning unreinforced masonry walls

An analytical model describing the flexural response of vertically spanning out-of-plane loaded unreinforced masonry walls is presented in this paper. The model is based on the second-order Euler-Bernoulli beam theory and captures important characteristics of the out-of-plane response of masonry walls that have been observed in experimental tests and from numerical studies but for which an analytical solution was still lacking: the onset and the evolution of cracking, the peak strength of the out-of-plane loaded walls, and the softening of the response due to P−Δ effects. The model is validated against experimental results, and the comparison shows that the model captures both the prepeak and postpeak response of the walls. From the analytical model of the force-displacement curve, a formula for the maximum out-of-plane strength of the walls is derived, which can be directly applied in engineering practice.