Simplified Seismic Analysis of Disordered Masonry Towers

The structural assessment of existing masonry towers under exceptional loads, such as earthquake loads, requires reliable and expedite methods of analysis. These approaches should take into account both the specific nonlinear behavior of the material (for instance, the small tensile strength) and the randomness that affect the masonry material’s properties (in some cases the distribution of the elastic parameters too). Considering the need of simplified but effective methods to assess the seismic response of such a class of structures, the paper proposes an expeditious approach based on an equivalent Bouc and Wen model. As a prototype of masonry towers, a cantilever masonry beam is analyzed assuming that the first mode shape governs the dynamic behavior. With this hypothesis, the nonlinear Bouc and Wen model is employed to reproduce the system hysteretic response. Subsequently, assuming the material properties as random variables, stochastic linearization and the perturbative approach are employed to evaluate the bounds of the seismic response. The results of the simplified approach are compared with the results of finite-element models to show the effectiveness of the method.