Mechanical model for cylindrical flexible concrete tanks undergoing lateral excitation

In this paper, a mechanical model is developed for evaluating the seismic response of flexible concrete cylindrical tanks under horizontal ground motion. For obtaining the parameters of the liquid-shell interaction of this model, a semi-analytical approach is employed using the Rayleigh-Ritz method. In the developed analytical approach, the vibration modes of a deformable open-top clamped-bottom shell are considered. The shell is assumed to be thin and the first-approximation theory is applied. Based on the analytical approach, a simple yet sufficiently accurate mechanical model, in which effects of the liquid and the tank wall considered separately, is proposed for tanks completely or partially filled with liquid. Parameters of this model are illustrated in charts easy to use for design purposes. In this model, only the first circumferential and vertical modes are considered. Also, the time history of sloshing wave height and its maximum are obtained. Finally, the base shear and the overturning moment, calculated by the analytical method and proposed mechanical model, are compared with those suggested by ACI 350.3-06. The results demonstrate that the proposed mechanical model is very successful in predicting the base shear and overturning moment, but ACI 350.3-06 overestimates or underestimates the responses case by case. Therefore, this model can be utilized with confidence for estimation of the design seismic loads of concrete cylindrical tanks.