Dynamics of the Vertically Restrained Rocking Column

Abstract

This paper investigates the rocking response of a slender column that is vertically restrained with an elastic tendon that passes through its centerline. Following a variational formulation, the nonlinear equation of motion is derived, in which the stiffness and the prestressing force of the tendon are treated separately. In this way, the post-uplift stiffness of the system can be anywhere from negative to positive depending on the axial stiffness of the vertical tendon. This paper shows that vertical tendons are effective in suppressing the response of smaller columns subjected to long-period excitations. As the size of the column or the frequency of the excitation increases, the effect of the vertical tendon becomes immaterial given that most of the seismic resistance of large rocking columns originates primarily from the mobilization of their rotational inertia.