Force reduction factor for out-of-plane simple mechanisms of masonry structures

The dynamic behaviour of existing masonry buildings mainly depends on the out-of-plane response of the vertical walls. A proper evaluation of their response can be analytically performed considering the dynamic equation of motion of the rigid body, in the framework of rigid in compression no tension material. The above equation is numerically solved with increasing magnitude of the seismic action, until the collapse condition of the wall, due to a lack of equilibrium, is reached. In the paper two local collapse mechanisms are considered, the two sided and the one sided rocking. The influence of considering a simplified trilinear moment-rotation law is also discussed. For each mechanism, the force-reduction factor, defined as the ratio between the seismic acceleration value causing the collapse of the masonry element and the one corresponding to the activation of the rocking motion, is evaluated. The dependence of this factor on the main parameters of the model is deeply investigated by means of numerical analyses, varying the geometrical characteristics of the panel, the energy dissipation model and the features of the seismic input. A power function law between an effective force reduction factor, defined as the ratio of the force reduction factor multiplied for the gravitational acceleration to the peak ground acceleration, and the Housner Spectrum Intensity is identified for both the examined models. These laws allow accounting for the so-called scale effect within a force-based framework. Eventually, novel formulations for evaluating the force reduction factor of two and one sided rocking systems are here proposed. Their effectiveness has been also highlighted considering both spectrum-compatible accelerograms and natural records.