Plastic buckling of unanchored roofed tanks under dynamic loads

Cylindrical tanks that are not anchored effectively to their foundations often rock during seismic loading. Vertical compressive forces in the tank wall that are required to resist seismic overturning moments then tend to be concentrated over a small portion of the circumference of the tank. where the tank wall remains in contact with the foundation. This together with the effect of internal pressures often leads to plastic buckling of the tank wall at the base or the so-called elephant foot bulge. This paper aims at predicting not only whether elephant foot bulging will occur, but also the extent of elephant foot bulging. This is done by means of a nonlinear dynamic time history analysis on a simplified rigid cylinder model, in which equivalent springs are used to represent elastic tank deformations, as well as nonlinear effects including geometric and plastic shortening of the tank wall caused by elephant foot bulging, and the resistance to uplift provided by the hold-down action of the floor plate. A physically based approach is provided to calculate the properties and location of the equivalent springs using finite-element analyses of the tank that can be performed with minimal computational effort. This leads to a simplified model for which key aspects of the behavior (dynamic as well as static) match that of the real tank. The approach is applied to a tank that was damaged during the 1977 San Juan earthquake. Although field measurements of the amount of elephant foot bulging are not available, photographs taken after the earthquake show an amount of bulging that is consistent with the predictions.