International Journal of Bridge Engineering (IJBE), Vol. 2, No. 3, (2014), pp. 67-75 THE DYNAMICS OF A VERTICALY RESTRAINED ROCKING BRIDGE Nicos Makris 1 and Michalis F. Vassiliou 2 1 Dept. of Civil Engineering, Division of Structures, University of Patras, GR-26500, Greece 2 Institute of Structural Engineering (IBK), ETH Zürich, Switzerland, Formerly: PhD Student, Dept. of Civil Engineering, University of Patras, Greece e-mail: nmakris@upatras.gr, mfvassiliou@gmail.com ABSTRACT: This paper investigates the rocking response and stability analysis of an array of slender columns caped with a rigid beam which are vertically restrained. This simplified system describes models a rocking bridge. The nonlinear equation of motion is formulated in which the stiffness and the prestressing force of the tendons are treated separately. In this way, the post- uplift stiffness of the vertically restrained rocking bridge can be anywhere from negative to positive depending on the axial stiffness of the vertical tendons. The paper shows that the tendons are effective in suppressing the response of rocking bridges with small columns subjected to long period excitations. As the size of the columns, the frequency of the excitation or the weight of the cap- beam increases, the vertical tendons become immaterial. KEY WORDS: Rocking, uplifting, negative stiffness, earthquake engineering 1 THE DYNAMICS OF THE VERTICALLY RESTRAINED ROCKING FRAME The main motivation for this study is to establish the dynamics of the vertically restrained rocking frame which emerges as a most promising alternative design concept for tall bridges [1]. Our analysis goes beyond the one bay configuration introduced in [1], which essentially represents the transverse motion of the bridge system as shown in Figure 1 (top left) and examines the planar rocking response of an array of N identical vertically restrained columns capped with a rigid beam that is clamped with the vertical restrainers. This configuration, shown in Figure 1, idealizes the longitudinal motion of a multi-span bridge. When the elasticity, EA, of the restrainer is small compared to the weight of the rocking columns, m c g, upon uplifting the lateral stiffness of the systems remains negative as in the free rocking case. As the elasticity, EA, of the restrainer increases, the lateral stiffness of the rocking frame increases gradually from negative to positive as shown in Figure 1 (bottom-left).