Issue 29

L. Facchini et alii, Frattura ed Integrità Strutturale, 29 (2014) 139-149; DOI: 10.3221/IGF-ESIS.29.13 139 Focussed on: Computational Mechanics and Mechanics of Materials in Italy An efficient Bouc & Wen approach for seismic analysis of masonry tower Luca Facchini, Michele Betti Department of Civil and Environmental Engineering (DICEA), University of Florence luca.facchini@unifi.it , mbetti@dicea.unifi.it A BSTRACT . 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 affects the masonry properties (in some cases also the distribution of the elastic parameters) and, of course, the nonlinear behavior of masonry. Considering the need of simplified but effective methods to assess the seismic response of such structures, the paper proposes 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 nonlinear hysteretic Bouc & Wen model is employed to reproduce the system response which is subsequently employed to evaluate the response bounds. The results of the simplified approach are compared with the results of a finite element model to show the effectiveness of the method. K EYWORDS . Bouc & Wen model; Masonry towers; Nonlinear dynamics; Perturbation methods. I NTRODUCTION he analysis of the structural response of slender masonry towers, especially in case of seismic loading, should take into account both the randomness that affects the masonry material (even the elastic parameters distribution along the height of the beam) and the specific nonlinear masonry behavior (the small tensile strength). Several methods have been proposed in recent years to analyze the structural response of such structural systems. Betti et al . [1] analyzed the response of a slender masonry wall under turbulent wind proposing an approach based on the modal reduction (MORE: Modal Reduction). The material was assumed as no tensile resistant (NTR), but the mechanical properties were assumed as deterministic. An analysis method to solve this typology of mechanical problems, assuming the properties of the material as a stochastic field, was further proposed by Facchini et al . [2] based on a Galerkin approach. Additional possible approaches are the perturbation methods, originally proposed by Liu et al . [3]. To offers an insight on this background, the paper proposes an expeditious and effective method to assess the seismic response of slender masonry towers where the masonry is assumed as a random material by means of an approach based on a nonlinear hysteretic Bouc [4] & Wen [5, 6] model. The Bouc & Wen hysteretic model has been found great interest in nonlinear stochastic dynamics being a smooth and multipurpose hysteresis model that allows for explicit form calculation of the linearization terms. The versatility of the Bouc & Wen model is also demonstrated by the large number of applications reported in the scientific literature concerning, f.i., steel and concrete [7] and wood structures [8]. Despite the spreading of the model only few case studies, to the authors’ knowledge, are reported concerning applications with masonry structures. T