Rocking instability under ground motion of large statues freely standing atop elastically supported cantilevers

Abstract

The rocking (overturning) instability of freely standing large statues atop the capital of elastically supported cantilevers subjected to ground motion is thoroughly discussed. The present analytical solution deals with a monolithic slender cantilever carrying a freely standing rigid block (simulating the statue) instead of the actual multi-drum cantilever of ancient columns that exhibit the loss of energy due to impact and sliding between drums. Hence, owing to the omission of the dissipation of energy, the results of this analysis based on a monolithic cantilever are quite conservative. Attention is focused on establishing the minimum-amplitude ground acceleration causing overturning of the rigid block with or without impact. Rocking instability criteria for determining such a minimum amplitude, which leads through the vanishing of the angular velocity to an escaped motion in the phase-plane portrait, are properly established by including the effect of time-dependent initial conditions. Closed-form solutions confirmed via numerical simulation bring to light important findings regarding the individual and combined effect of various parameters on the rocking instability of the rigid block.