A force-based macroelement for the nonlinear dynamic analysis of masonry buildings

This study presents a force-based macroelement formulation for the nonlinear analysis of masonry buildings, according to the equivalent frame model. The adopted 2-node beam macroelement consists of a central linear elastic part, two flexural hinges at the ends and a shear link arranged in series. To account for hysteresis and degradation under cyclic loads, the flexural hinges and the shear link are modelled through a classic Bouc-Wen formulation and a degrading Bouc-Wen model, respectively. The smooth transition between the elastic and plastic ranges, accounting for the progressive development of cracks in masonry structural elements, and the small set of parameters required to reproduce hysteresis loops with different shapes make this model accurate enough and relatively easy to implement. The macroelement formulation and the solution algorithm for the force-based element state determination are implemented in the code FEAP, used to perform the numerical analyses. Applications on simple piers subjected to cyclic loading show that the element is able to satisfactorily describe the experimental outcomes, reproducing the hysteresis loops and the strength/stiffness deterioration of masonry. At the same time, its computation burden is much lower than that of micro-or multi-scale models, making it suitable for the analysis of medium to large constructio.