Unanchored Liquid Storage Tanks under Dynamic Loads

Marwan  A. BKAILY

The objective of this work is to study the plastic buckling of unanchored liquid storage tanks with roof under the influence of bi‑directional seismic excitation that leads to elephant foot bulging. To do that, a simple mechanical model is presented that predicts not only the inception but also the extent of elephant foot bulging of unanchored liquid storage tanks.

 In the following chapter, a brief review of the relevant literature is introduced where mainly the theoretical studies about the behavior of liquid storage tanks are highlighted. Special emphasis is drawn to the different mechanical and structural models that appear in the literature in order to show the difference and the similarity between the model presented in this work and other models.

 In the third chapter, geometrically and materially nonlinear axisymmetric collapse analysis is carried out for all conceivable values of the geometry and material parameters of the cylindrical shell to determine the local force‑deflection relation needed for the mechanical model. Equations fitting the results of the axisymmetric collapse analyses are developed; and their application in a simplified analysis for unanchored tanks under lateral loads is illustrated by an example to predict not only the inception, but also the extent of elephant foot bulging. The applicability of the moderate deflection theory is also investigated.

 The fourth chapter is devoted to provide the purpose and description of the mechanical model presented here to study the dynamic behavior of unanchored liquid storage tanks. More specifically, the phenomena that the model represents are discussed in detail with the modifications needed to incorporate them here in a simple manner.

 The fifth chapter demonstrates the validity of the mechanical model by studying the dynamic behavior of two tanks under a given earthquake excitation. Firstly, a brief description is presented about the chosen earthquake that causes damage to many tanks in that region (All these tanks suffer from elephant foot bulging). Secondly, the preliminary analyses needed and the programs used to prepare some of the variables for the model are discussed for the two chosen tanks. Thirdly, the dynamic analysis of these two tanks is performed and the predicted damage by the mechanical model is compared with the actual damage caused by the earthquake.

 In the last chapter, results are obtained for plastic buckling in unanchored liquid storage tanks. The entire parameter space which is covered by the provided force-deflection relations is specified and the type of simplified analysis that can incorporate these relations to study elephant foot bulging phenomena is emphasized. Then, the results of the dynamic analysis are presented which shows that the model proposed here can predict collapse of unanchored tanks. At the end, some issues are highlighted that deserve further investigation.