Dynamic Response of a Rigid Slab Supported by Four Rigid Cylindrical Rocking and Wobbling Columns

Abstract

Letting columns uplift has been proposed as an earthquake response modification strategy for bridges and other large structures. Uplift could be allowed along solely one di-rection of the structure or along both directions. In order for the latter approach to be imple-mented, the 3d behavior of systems allowed to uplift, rock and wobble should be studied. This paper studies the dynamic response of a rigid slab supported on 4 rigid cylindrical rocking and wobbling columns. The columns are constrained not to roll out of their initial position, which is a necessity for the system to be resilient. This system is the simplest 3d extension of the 2d rocking frame system.The equations of motion are derived analytically and directly numerically integrated. Since the system has only 2DOFs it is computationally inexpensive and allows for extensive para-metric analysis. Similar to the 2d rocking frame, it is found that the addition of the slab makes the investigated frame more stable than the individual columns.