Dynamical collapse of masonry arches under sequences of impulses of horizontal acceleration

A new formulation of the seismic response of the masonry arch hit by sequences of impulses of horizontal acceleration, of assigned intensity and duration, is the subject of the paper. After a preliminary evaluation of the static limit acceleration intensity AL, under which the arch starts to move, the central point of the paper is the determination of the equation of the motion of the arch, considering the gradual changes of mechanism's geometry. It is shown that the arch, under the hammering sequence of impulses of suitable intensity and duration, can reach, without oscillations, a resonance condition with a consequent build-up of progressively accumulating deformation up to the configuration of zero strength and the consequent dynamic failure. The ratio qN = AN/AL - between the impulse collapse acceleration AN and the limit static acceleration AL - is achieved by considering the gradual increase in the impulse number N of the sequences. The minimum value of the collapse acceleration ratios qN, which is the real behavior factor q, is then obtained by considering the PGA and the period TE of the expected earthquake. A discussion on the differences existing between the static and the dynamic collapse of the arch, with the development of many examples, concludes the paper.