Flexibility of superstructures and supports in the seismic analysis of simple bridges

Abstract

SUMMARYThis paper addresses the elastic dynamic response of simply supported bridges to ground motion in their transverse direction. The interaction between superstructure and support #exibilities is studied in a systematic manner for symmetric spans. The bridges are modelled as beams with uniformly distributed mass and elasticity, simply supported at the ends by elastic springs. It is shown that a dimensionless sti!ness index, which re#ects the relative sti!ness of the superstructure compared to the sti!ness of the substructure, completely de"nes the dynamic mode shapes of the model. Useful closed-form expressions, based on approximate shape functions, are derived for the dynamic parameters of the "rst mode, and their accuracy is assessed. The e!ect of the sti!ness index on these dynamic parameters is investigated. Numerical case studies are presented to illustrate the use of proposed equations in the seismic analysis of bridges.

Displacement limits and performance displacement profiles in support of direct displacement‐based seismic assessment of bridges

“…Adopting a RDT( R ) pattern, minimal efforts are needed to define the PDP of the bridge, because the amplitude of the PDP is controlled by the pier/abutment‐deck subsystem with the lowest displacement limit at the selected PL; For bridges with up to two internal expansion joints in the superstructure, recent studies show that a linear displacement pattern can be adopted (Figure (c)–(d)); For bridges with ‘flexible’ continuous deck (refer to Eq. ) and neoprene pads on abutments, that feature a balanced mass and stiffness configuration, the PDP of the bridge can be evaluated based on the approximate expression of the first mode shape (Figure (e)) proposed in : with where EJ is the flexural stiffness of the deck, K e is the abutment bearing‐line stiffness (elastic or secant, depending on the selected PL) and L is the total bridge length; For symmetric bridges with ‘flexible’ continuous deck and monolithic pier‐deck connections, reference to approximate expressions of the first‐mode shape can be made. For pinned abutment and regular or valley pier configurations (see Figure (f)), for instance, the following deformed shape can be adopted : where L d is the length of the deck.…”

“…(ii) For bridges with up to two internal expansion joints in the superstructure, recent studies [36] show that a linear displacement pattern can be adopted ( Figure 6(c)-(d)); (iii) For bridges with 'flexible' continuous deck (refer to Eq. (25)) and neoprene pads on abutments, that feature a balanced mass and stiffness configuration, the PDP of the bridge can be evaluated based on the approximate expression of the first mode shape ( Figure 6(e)) proposed in [37]:…”

Supplemental system retrofit considerations for braced steel bridge piers

“…Equation (20) can be thought of as the result for two springs in series, in which the springs represent the non-linear shear displacement dependent device, and the linear overturning. This is the same concept as used for the development of local versus global ductility demands for simple bridges as derived in Reference [3]. However, there the relationship derived was not for a system subject to large overturning displacements, but for a fuse element and a protected element.…”