Bi-directional Seismic Analysis and Design of Bridge Steel Truss Piers Allowing a Controlled Rocking Response

4-legged bridge steel truss piers provide support for gravity, transverse, and longitudinal lateral loads of bridges. Allowing a controlled rocking response for seismic resistance of 4-legged truss piers requires the development of design equations considering ground motions in two horizontal directions and vertical excitation. First, the static kinematic and hysteretic bi-directional behavior of controlled rocking 4-legged piers, relevant for design, is developed analytically and some of the design rules are established. The seismic response of a 4-legged pier to 3 components of ground excitation is then investigated using inelastic, dynamic time history analyses. Introduction Roadway and railway bridges supported on steel truss piers have a number of 2-legged piers primarily designed to support gravity loads that also resist transverse lateral loads but do not provide any significant resistance to longitudinal lateral loads. When 4-legged piers provide support for gravity loads, transverse loads, and are the primary elements for resisting longitudinal lateral loads together with the abutments in some instances. The controlled rocking approach to seismic resistance allows uplifting of pier legs at the foundation while displacement-based steel yielding devices (buckling-restrained braces) are implemented at the uplifting location to control the rocking response. Allowing uplift effectively increases the pier’s period of vibration, partially isolating the pier. The controlled rocking system has an inherent restoring force that allows for pier self-centering following a seismic event. This approach to seismic resistance has been investigated for 2-legged (2D) piers in Pollino and Bruneau (2004). The design of 4-legged piers must consider the bi-directional response of the controlled rocking piers along with the effects of vertical excitation. The kinematic and hysteretic behavior are _____________________________ Graduate Research Assistant, University at Buffalo, 212 Ketter Hall, Buffalo, NY 14260, E-mail: 1 [email protected] Director, Multidisciplinary Center for Earthquake Engineering Research, and Professor, Dept. of Civil, Structural and 2 Environmental Engineering. University at Buffalo, 212 Ketter Hall, Buffalo, NY 14260, E-mail: [email protected] Paper No. 1954 developed such that simple design rules can be developed. Capacity design principles, considering a number of dynamic effects that occur during uplifting and impact of pier legs, are applied to the existing pier and bridge deck such that they remain elastic. Maximum displacements are determined using the capacity spectrum method of analysis. Directional and modal combination rules are used to predict maximum developed displacements and forces. A set of pier and device properties are then used in an example to illustrate the concepts presented and to compare the results of nonlinear, time history analyses and the design rules. Seven sets (x, y, and z) of synthetically generated acceleration histories are used in the time history analyses. Kinematic and Hysteretic Behavior of 4-legged Pier Considering Bi-directional Response A typical 4-legged truss pier is shown in Fig. 1. along with a defined coordinate system. Also shown is a directional vector that lies in the x-y plane at an angle α from the x-axis that will be used throughout this paper. The cyclic hysteretic curve for a 2-legged pier was developed “step-by-step” and shown to not be path dependent beyond the 2 cycle in Pollino and Bruneau (2004). The primary difference nd between the hysteretic behavior of controlled rocking 2-legged piers and the uni-directional response (α=nπ/2 rad., n=0,1,2,...) of 4-legged piers is the use of four energy dissipating devices (one at the base of each leg). However, when a 4-legged pier is free to move in the entire x-y plane, the hysteretic curve is path dependent and therefore is only defined for the path considered. Thus, the kinematic and hysteretic behavior of 4-legged piers, considering bi-directional response, is investigated to provide recommendations for design to account for the uncertainty in the hysteretic path. Compatibility, equilibrium, and force-deformation relationships for a 4-legged pier are developed below to assist in the design of controlled rocking piers. For earthquake excitation in 2 horizontal directions, it is possible for the pier to uplift such that it is supported vertically on one of its legs. In that case, 3 of the energy dissipating devices located at the base of the pier could yield depending on the magnitude of the respective uplifting displacement. Assuming that rotation of the pier about a vertical axis does not occur (i.e. neglecting torsional response), the top of parallel frames undergo the same horizontal deformations. In other words, using the notation illustrated in Fig. 1, the top of frames 1-1 and 2-2 experience the same horizontal displacements while frames 3-3 and Figure 1. Typical 4-legged pier and defined coordinate system