Effect of out-of-roundness on the dynamic response of liquid storage tanks

Abstract

The objective of this study is to examine the possible effects that an initial out-of-roundness could produce in the radial displacement response of liquid storage tanks subjected to earthquake ground motions. Theory predicts that such structures vibrate in modes proportional to cos when excited laterally. Model tests conducted recently indicated that the radial response was dominated by functions proportional to cos 3 and cos 4. It was these unpredicted results that inspired the study given here. Two possible response mechanisms are considered. An out-of-roundness could produce higher order cos pressures which in turn produce higher order deflections. This analysis was shown to be deficient in explaining the magnitudes of the experimental results. The other mechanism considered is that filling an initially out-of-round tank removes a portion of its magnitude and that dynamic pressures can cause conditions such that the removed portion is partially recovered. This analysis shows that a high order of initial out-of-roundness such as cos 8 or greater is significantly removed when the tank is filled with water. This is the result of hoop forces which tend to stretch the tank wall, thus removing a portion of the irregularity. Under dynamic excitation, the hydrodynamic pressures are dominated by a function proportional to cos 8. In the region where the hydrostatic pressure is relieved, there is an accompanying reduction in the hoop force which allows the recovery of a portion of that which was removed initially. The experimenters were then most likely measuring this partial recovery for their response function. Due to the small number of radial sensors used in the test, this high order complex response was then erroneously interpreted to be cos 3 and cos 4 dominant. The results of this analysis are of a magnitude comparable to the experimental results indicating that the proper response mechanism was chosen.