An efficient Bouc & Wen approach for seismic analysis of masonry tower

The assessment of existing masonry towers under exceptional loads, such as earthquake loads, requires reliable, expedite and efficient methods of analysis. These approaches should take into account both the randomness that affect the masonry properties (in some cases the distribution of elastic parameters too) and the specific non-linear behavior (f.i. the small tensile strength). As an alternative to classical finite element technique approaches, in recent years several expeditious methods have been proposed to analyze the structural response of such structural systems. An approach based on the modal reduction (MO-RE) to analyze the response of slender masonry walls under turbulent wind was proposed in [1]: the material was assumed as no tensile resistant (NTR), but the mechanical properties were assumed as deterministic. To introduce randomness in material distribution an approach based on a Galerkin discretization was proposed in [2]: the material properties were assumed as a stochastic field. Other possible expeditious approaches may be based on perturbation methods, however the results of some preliminary analysis, seem to show that the use of a perturbation method does not allow, when the seismic action is assumed as a time history, to keep into account correctly the cracking and crushing phenomena that occur in masonry. Based on this background, and considering the need of simplified but effective methods to assess the seismic response of slender masonry tower, the paper aims to propose an efficient approach for seismic assessment of masonry towers assuming the material properties as a stochastic field. As a prototype of masonry towers a cantilever beam is analyzed assuming that the first modal shape governs the structural motion. With this hypothesis a non-linear hysteretic Bouc & Wen model [3] is employed to reproduce the system response which is eventually linearized to evaluate its bounds. The results of the simplified approach are compared with the results of FE model to show the effectiveness of the method.