The Slender Rigid Block: Archetype for the Seismic Analysis of Masonry Structures

The elasto-plastic oscillator, representing the basic model for reinforced concrete and steel structures, shows its inadequacy when dealing with masonry structures. The column, resting on a rigid plane with friction, is shown to be particularly appropriate to model the dynamic behaviour of masonry structures. At this aim, this paper investigates the motion of a slender rigid block (SRB), initially resting in its vertical configuration and hit by a seismic input, represented through a single impulse constituted by a rectangular or sinusoidal half-wave or a simplified sequence of horizontal acceleration pulses, having rectangular or sinusoidal shapes. An accumulation of the rotation of the SRB exists under the action of sequences of opposite acceleration pulses. The dynamic collapse is shown to take place when the column is led to its critical configuration - where the restoring moment of the weight is lost - so that the last pulse can further increase the rotation of the column. Expressing the behaviour of the SRB by means of the force reduction factor, the ratio between the magnitude of the collapse horizontal acceleration and the static strength of the column, the difference between the responses of the column decreases with increasing the number of the pulses of the sequence. A simple definition of the asymptotic failure domain can be obtained with a good approximation with a limited number of pulses. It is possible to evaluate the minimum collapse acceleration intensity of seismic sequences of pulses of any assigned duration able to produce the collapse of the rigid block, representing the seismic strength of the SRB. Finally, the results obtained in the theoretical analysis are compared with the outcomes of more accurate and time-consuming non-linear dynamic or incremental analyses (IDA).