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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
Sulla modellazione termomeccanica delle attività di una caldera: deformazioni e fratturazioni allo stato eruttivo ed applicazioni al bradisismo flegreo
Dynamical assessment of the performance factor "Q" for the masonry wall under the out of plane seismic action
The non-linear out of plane dynamical response of the masonry wall, suitably reinforced at the top and hit by sequences of acceleration pulses, alternating in sign and with different intensity and duration, is the subject of the paper. The wall moves out of its plane with a gradually changing failure mechanism and two relevant aspects characterize this motion: the occurrence of a rotational build up under the action of the pulse sequence, in spite of their alternating in sign and the occurrence of the dynamical collapse. This last takes place when, under the second last pulse of the sequence, the increasing mechanism has reached the critical configuration in which all resistance of the wall is lost. The arriving of the last pulse, pushing the wall to further increase its rotation, yields the collapse. The ratio between the dynamical and the statical collapse accelerations – the so-called strength reduction or performance factors – is thus directly determined following the dynamical response of the wall to the pulse sequences. The paper, which is part of an ongoing research (Coccia et al. 2022) reveals how the wall, so vulnerable under the out of plane seismic actions, can mobilize collapse mechanisms capable of defending it by the destructive action of the quakes
Out-of-plane dynamical strength of masonry walls under seismic actions
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 T-E/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
Ricerca teorico-sperimentale sullo svergolamento nel piano e fuori del piano dei profilati in presenza di tensioni residue
Ricerca teorico-sperimentale sullo svergolamento nel piano e fuori del piano dei profilati in presenza di tensioni residue
Rocking of cracked masonry walls under constant impulse acceleration
Multi-storey walls with openings, composed by wall piers and spandrels, represent the main resistant structural components of a masonry building. The in-plane seismic forces are countered by means of their weights, which oppose to the action of the horizontal forces. The behaviour of masonry constructions results to be very far from the one characterizing ductile structures, because of the lack of energy dissipation during the deformation. Masonry constructions endeavour in fact to elude the seismic action, activating a rocking motion rather than deforming with doubtful dissipating mechanisms. A strength resource of masonry structures, properly reinforced in order to avoid early local failures, consists in exhibiting rocking behaviour, until a failure condition is attained. Aim of the paper is to investigate the dynamic behaviour of masonry multi-storey walls, according to Housner's studies and properly introducing the effect of diagonal cracks, shown by typical post-earthquake cracking patterns. Cracks start from the toe of the wall piers, developing along a diagonal direction and identifying a masonry volume that remains ineffective during the development of the mechanism, without taking part with its weight to the opposing action against the overturning. Starting from the evaluation of the incipient rocking acceleration of the system, in presence of cracking of the masonry wall piers, the free and forced motions of the wall are examined. A simple constant horizontal acceleration impulse of given duration has been considered to represent schematically the seismic action. An ad hoc energy dissipation model is also specifically implemented, according to the classical Housner's approach
Influenza della deformabilità sulla risposta dinamica di elementi in muratura sollecitati fuori dal piano
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