Transient failure analysis of liquid-filled shells PART II: Applications

In this paper, applications of the theory developed in the companion paper by Liu and Uras [1] are presented. The effects of various types of ground motion on the dynamic stability of the fluid-structure system are analyzed. The stability criteria of liquid-filled shells subjected to horizontal and rocking excitation, shear loading, bending/shear combined loading, and vertically applied load are established. The resulting instability regions and stability charts are given in tables and in ω-ε{lunate} plots. Under horizontal and rocking motion, modal coupling in the circumferential direction as well as in the axial direction is observed. The possible buckling modes for a tall tank can be identified as cos2θ, cos3θ and cos4θ under horizontal and rocking motion, and cos5θ and cos6θ, under vertically applied load. For a broad tank two sets of instability modes are found: cos6θ through cos9θ, and cos12θ through cos14θ under horizontal and rocking motion. When subjected to vertically applied load, the failure modes of a broad tank shift to cos10θ through cos12θ, and cos14θ through cos15θ. The effect of shear load on a broad tank appears to be important only if damping is relatively small. Under bending/shear combined loading, the bending forces dominate the stability of the fluid-filled shells.