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The dynamic analysis of the out-of-plane response of masonry walls, with different reinforcing systems and hit by sequences of pulses alternating in sign, representative of the seismic action, is the aim of the paper. The analysis is done in the context of the Heyman model of the no tension masonry structures. We consider the wall of the last story of a simple masonry house, commonly reinforced at its head by a ring beam, usually in a reinforced concrete. It has also been considered the retrofitting of the wall by applying, on both its sides, vertical bands in FRP, or similar. The dynamics of the wall, activated by sequences of pulses, is analyzed in detail, considering the change of geometry occurring in the mechanism during the motion. The corresponding differential equation is integrated in a closed form. It is shown that, under the alternating sequence of shocks, the dynamical collapse of the wall takes place immediately after the occurrence of an accumulation of out-of-plane deformation of the wall that drags it into the configuration of zero strength, where any resistance, due to the weight, has been lost. The collapse takes place right after when the subsequent incoming pulse pushes the wall to go further beyond this configuration. The check of the seismic safety of the masonry wall concludes the paper. The smallest limit static strength of the wall required in order the wall, having pulsation p, could be able to sustain, at the limit of the dynamical collapse, the action of the asymptotic pulse sequence with acceleration intensity PGA and specific duration p TE/2 of the expected earthquake. It is shown that the wall, reinforced by a top ring beam, with the addition of vertical bands of glass or similar, of suitable length, pasted with lime mortar, can reach the required level of seismic safety. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]