Cylindrical tanks with conical roof shells are utilized as oil storage tanks and for some containment vessels. It is known that conical roof shells and torispherical shells subjected to static internal pressure buckle into a displaced shape with circumferential waves caused by an instability condition commonly called bifurcation buckling. It can be important to obtain the dynamic bifurcation buckling load in designing conical roof shells. In this paper, the bifurcation buckling pressure is calculated for dynamic pressure during accident conditions as characterized by step pressure loading, ramp pressure loading and pulse pressure loading. The minimum bifurcation buckling pressure is shown to be a linear function of radius-to-thickness ratio $R/h$ of the shell in a linear fashion on a logarithmic scale. The minimum bifurcation buckling pressure is minimum for conical roof shells subjected to the step loading. The minimum dynamic bifurcation buckling pressure for step loading is about half of the static bifurcation buckling pressure.

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