Dynamic analysis of a sdof model of a masonry lintel and peers system

The dynamic behaviour of a block-like masonry system consisting of a lintel supported by two peers standing free on their foundation is examined. A single-degree-of-freedom model is assumed, the lintel being the rigid block where the mass is concentrated and the peers being the “semi-rigid” blocks with mass neglected. The shear resistance of the peers is calculated by defining inelastic strut elements inside the blocks which involve plastic deformations during the oscillation of the system. The features of these resistant elements are assumed to depend on both the normal forces acting on the peers and their eccentricity. A non-linear elastic model, characterised by a tri-linear shear-displacement relationship for the peers and neglecting impact between blocks and hysteresis loops, is therefore defined. Firstly the free vibration of the model is herein investigated by means of a standard explicit time-history algorithm. The numerical results show that, mostly for thick peers subjected to large normal compressions, a simplified shear-displacement law and the shear resistance independent of the horizontal displacement can be adopted. It involves the concept of very large stiffness of the peers so that the eccentricity of the normal forces jumps discontinuously from one side to the other. Although the free vibrations are represented by a periodic motion, the natural frequency of the model depends on the initial conditions, owing to the non-linearity of the shear-displacement relationship. This non-uniqueness of the natural frequency involves difficulties in the analysis of the seismic response. Nevertheless, when analysing free vibrations only, an equivalent linear elastic single-degree-of-freedom system can be defined for each choice of initial conditions. Finally, some issues regarding the forced vibration are discussed.