Equivalent-Frame Modeling of Two Shaking Table Tests of Masonry Buildings Accounting for Their Out-Of-Plane Response

Equivalent frame models are an effective tool for the seismic assessment of existing masonry structures. Due to their simplicity, these models can be used to perform multiple nonlinear dynamic analyses, accounting explicitly for different sources of modeling and input uncertainty. In the past, equivalent frame models have been used to effectively estimate the global response of buildings whose behavior is dominated by in-plane failure modes of piers and spandrels. The recent development of a three-dimensional macroelement formulation for modeling both the in-plane and out-of-plane response extends the use of equivalent frame models to the additional study of local out-of-plane mechanisms of a building. This work applies the newly developed formulation, implemented in OpenSEES (McKenna et al., 2000), to the modeling of two shaking table tests on a stone masonry building and on a modern mixed concrete-unreinforced masonry structure. Since the approach explicitly accounts for the quality of connections in the building (i.e., wall-to-wall and floor-to-wall connections), specific elements and material models were developed for modeling these connections in an equivalent frame idealization of the three-dimensional structure. Through comparison with the experimental results, the performance of the modeling approach is discussed, and the sensitivity of the response to the major sources of modeling uncertainty (quality of connections, damping model) is assessed. The comparisons show that these new equivalent frame models can capture the onset of out-of-plane failure for historical structures with poor floor-to-wall connections and for modern URM buildings with stiff RC slabs, where the slab can uplift from the URM wall, which leads to changing static and kinematic boundary conditions of the out-of-plane loaded wall. The results further show that 1-2% of damping leads to good agreements with the experimental results if initial stiffness proportional Rayleigh damping is used.