Ultimate Instability of Earthquake Structures

The parametric motions considered are very general and may be due to mechanical vibrations or horizontal and vertical components of earthquakes. A computer program has been developed for the nonlinear dynamic response of structural systems which are formulated in incremental form based on the displacement method and numerical integrations. Numerical examples are provided from which one may observe that the structure becomes dynamically unstable when a certain frequency of vertical motion is present and that the growth of the vibrating amplitude may possibly cause lateral collapse of the system. Although no definite relationship between vertical earthquake frequencies and the lateral natural frequencies exists for an earthquake structure, the vertical earthquake motions can excite some structures having certain natural frequencies becoming dynamically unstable due to large deflections. The vertical force may not always be critical to dynamic response and can actually cause certain structures to have smaller deflections than that of the associated systems without the influence of the axial force.