Issue 29

L. Facchini et alii, Frattura ed Integrità Strutturale, 29 (2014) 139-149; DOI: 10.3221/IGF-ESIS.29.13 140 In the following, a masonry cantilever beam, as a prototype of masonry towers, is analyzed assuming that the first modal shape governs the structural motion. With this hypothesis the nonlinear hysteretic Bouc & Wen model is employed to reproduce the system response, which is subsequently employed to evaluate the bounds of the structural response through a perturbation approach. The results of the proposed approach are compared with the results of a finite element (FE) model to show the effectiveness of the method. I DENTIFICATION OF B OUC &W EN MODEL FOR THE TOWER he Bouc [4] & Wen [5, 6] model (in the following BW for short) has been extensively employed to model the dynamic behavior of hysteretic systems. As masonry is a no-tensile resistant material, it may on occasion exhibit such kind of behavior. To assess the employability of the BW model as an efficient approach for seismic analysis of masonry towers the paper analyzes the clarifying example of a masonry cantilever beam. To identify the BW model parameters several methods have been proposed. Herein the tuning of the BW parameters is performed by comparing the behavior of the BW model with the response of the masonry cantilever beam acted upon by a static transversal force as evaluated through a FE analysis. Figure 1: The curve “applied force – computed displacement” (ANSYS analysis under cyclic loading). Numerical FE modeling As a reference case the structural behavior of a cantilever masonry beam with dimensions 10 (length) × 40 (height) × 1 (thickness) m was investigated by the ANSYS FE code [9]. The behavior of the masonry tower under seismic loads was analyzed by means of both static nonlinear pushover analysis and dynamic nonlinear analysis. To model with the ANSYS code the nonlinear behavior of masonry, a proper combination of two failure domains was employed. On the one hand the Drucker-Prager (DP) plasticity criterion [10], originally proposed for geo-materials, was employed. The material parameters required to define the plasticity model, the cohesion c and the internal angle of friction φ, were introduced in such a way that the circular cone yield surface of the DP model corresponds to the outer vertex of the hexagonal Mohr-Coulomb yield surface. The DP criterion was combined with the Willam and Warnke (WW) failure criterion, originally proposed for concrete [11], which accounts for both cracking and crushing failure modes through a smeared model. With these assumptions the masonry is modeled as an isotropic continuous medium capable to exhibit plastic deformation, to crack by traction and to crush by compression. The assignment of the mechanical parameters required by the DP and WW criterion requires a careful calibration [12, 13], especially if a macro-element approach is used. In the present study, being the analyses aimed to assess the effectiveness of a disordered BW system, these parameters were assumed on the basis of available literature results for stone masonry walls [14]. The final three-dimensional model consisted of 902 joints and 400 solid elements corresponding to 2,640 degrees of freedom (dofs). The nonlinear system of equations was solved by an incremental Newton-Raphson method. Details of the T