Strength reduction factor for out-of-plane failure mechanisms of masonry walls

The analysis of the dynamic problem of a rocking element acquires fundamental importance in order to define a realistic “seismic strength reduction factor” which takes account of the ultimate inelastic response of a masonry structure. A proper evaluation of the dynamic response of such elements can be analytically done considering the dynamic equation of the rigid body not resistant to tensile stresses. In this work, the dynamic equations corresponding to different out-of-plane failure mechanisms are presented and—for each considered mechanism—the strength reduction factor is evaluated. The analytical model addresses the rocking motion of a rigid block subjected to a seismic acceleration time history: the displacement capacity is numerically evaluated solving the differential equations of motion associated to the kinematic mechanism. In the case of squat walls, the motion is defined by a single equation and the collapse is achieved by loss of equilibrium. For slender masonry walls, also the elastic flexural stiffness of the element is considered and the motion is defined by a system of two differential equations. In the work the results of an extensive numerical investigation are reported. The outcomes show a dependence of the strength reduction factor on various parameters as the block geometry, the rocking mechanisms and the seismic input features.