The excessive uplifting displacement of the base plate of an unanchored liquid storage tank usually causes a plastic hinge to develop in the connection between the base plate and the shell. Table (5.8) shows the response of the unanchored tanks to El Centro and Northridge earthquakes, respectively, taking into consideration the possibility of the formation of this plastic hinge and the large deflection effect. The tank base plate was considered supported on a tensionless elastic foundation of a uniform stiffness of 1000 lb/in/in2 in compression.
The lateral stiffness of the unanchored tank shell may be divided into two components: a vertical stiffness and a horizontal stiffness. The vertical stiffness is caused by the cantilever effect which depends mainly on the rotational stiffness provided from the connection between the base plate and the tank shell. The horizontal stiffness is caused by the hoop effect due to the horizontal curvature of the shell. The formation of the plastic hinge decreases the vertical stiffness of the tank shell leading to a longer period for its lateral vibration. As a result, the hydrodynamic forces on the tank wall are less than those exerted when the plasticity was ignored. In addition, formation of the plastic hinge increased the uplift displacements of the base plate and decreased the contact area of the base plate with the foundation.