This study presents a simplified estimation method on the rocking behavior of the unanchored cylindrical liquid storage tank of which baseplate uplifts partially from its soil foundation and of which shell plate distorts its circular cross-section due to the horizontal seismic loads. Since the vertical reaction force distribution along the bottom end of shell plate, which yields resistant moment against the overturning moment due to the horizontal seismic load, deflects from sinusoidal when its baseplate uplifts partially. The out-of-plane deformation is induced in the shell plate of tank due to the axial force in the shell plate of higher harmonic number than the sinusoidal mode because of the partially uplifting of the base plate. This feature brings the vertical displacement along the bottom of shell plate redistribution, and it affects the buckling strength at the compression side of the shell plate and the bending strength at the uplifting side of the joint between the cylindrical shell plate and the baseplate. To take such a rocking behavior into account, the vertical reaction force distribution acting on the bottom of the shell plate is expanded with Fourier series and the out-of-plane deformation of shell plate is derived by the membrane theory of shell for each coefficient of Fourier series. Numerical results of tank deformations calculated by the present method are compared with those obtained by a commercial FEM code.

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