Stiffness of Rubber Bearings Considering Nonstandard Top and Bottom Boundary Conditions

Typical installations of seismic isolation assume flexurally rigid end conditions; however, in retrofit scenarios where bearings may be placed at the tops of columns or in bridges with tall piers, some rotation may occur at the boundaries. Very few experimental programs have explored the effects of these flexible boundary conditions; however, none have applied cyclic rotation at both top and bottom end plates in combination with cyclic horizontal demands, which is representative of potential loading with flexible boundary conditions. To address this gap, an experimental program on quarter-scale column-top mounted natural and lead-core rubber bearings was conducted. Rotations were applied at both the top and bottom bearing end-plates to investigate the impact of nonzero rotation boundary conditions on key design assumptions such as horizontal stiffness and rotational stiffness, and how these effects change with axial load beyond that for zero-rotation cases. Flexible boundary conditions reduce the horizontal stiffness, and the rotation-induced reduction in horizontal stiffness is dependent on the sum of the rotation at the ends, regardless of the rotation of one bearing end-plate with respect to the other. This rotation-induced decrease in stiffness is also dependent on axial load, with larger axial load leading to a higher dependency on rotation. Last, while it is known that the overlapping area method used for stability limits is conservative for rigid boundary conditions, this was shown to be true even for the bearing with a moderate shape factor ($S_1=19.6$) when supported by a flexible column. However, the overlapping area method was not conservative for the bearing tested with low shape factor ($S_1=7.9$), which exhibited a tangential stiffness of zero at an axial load less than the stability limit from this method.