GALCIT Colloquium

The nonlinear dynamic analysis of the highly complex problem of  rocking (overturning) instablity of free–standing statues on the top of ancient multispondyle columns under horizontal ground motion is thoroughly discussed. Attention is focused on the minimum ground acceleration leading to the rocking instability of the statue, by including the translational and rotational inertia of its mass. Instability criteria for the overturning of the statue with or without impact are presented comprehensively. It is shown that an exact analysis of the problem is impossible due to insurmountable computational difficulties in evaluating the loss of energy between spondyles in connection with the extremely large number of highly nonlinear differential equations of motion. For the solution of the problem a viscoelastic monolithic (slender) column with loss of energy equivalent to that of the multispondyle column is proposed. The solution and uniqueness of such a monolithic column problem are properly established. The work presented, which is based on an analytic energy approach supplemented by experimental data, gives the best approximate solution for this problem which has not been solved for more than half a century.