Equivalent models of pure conical tanks under vertical ground excitation

Elevated water tanks are commonly built with superstructure vessels that have a truncated conical shape. As a result of the inclination of the vessel's walls, the axisymmetric hydrodynamic pressure that is associated with vertical ground accelerations develops hoop and axial meridional stresses. The purpose of the current study is to establish a simple procedure that can be used to estimate the seismic forces acting on a conical tank subjected to vertical ground accelerations. The study is conducted using a numerical model that is based on a coupled finite-boundary element formulation previously developed for the analysis of this fluid-structure interaction problem. First, the numerical model is used to develop charts that can be used to identify the fundamental frequency of the axisymmetric vibrations of conical tanks. Then, an equivalent mechanical model in which the fluid mass is simulated as rigid and flexible mass components is developed. The parameters of the mechanical model are presented in chart form. An example that estimates the forces acting on a conical tank subjected to the vertical component of real prerecorded earthquake motion is presented to illustrate the procedure.