Drawing Capcity Spectrum and Determining of Target Displacement without Control Point For Horizontally Curved Bridges

Nonlinear Static pushover (NSP) analysis has become a popular tool for the seismic assessment of buildings and bridges. One of the well-known methods to determine the target displacement during NSP is Capacity Spectrum Method (CSM).In the Conventional CSM, capacity spectrum is drawn based on the location of control point to determine the target displacement. Because of dependency of displacement capacity spectrum on the location of control point, determination of displacement capacity spectrum needs further evaluation and can be time consuming specially for complicated structures. Previous studies have been proposed different choices for location of control point in the bridges such as the point with the maximum displacement or the top point of critical pier. In this paper the CSM has been developed for drawing capacity spectrum. The proposed method is based on determination of displacement capacity spectrum from pushover analysis of MDOF system without selection of any control point. The proposed method is based on derivation of frequency of SDOF system based on current situation of MDOF system for each mode and step. Moreover, nonlinear behavior of MDOF system is considered in frequency of SDOF system step by step. After derivation of frequency of SDOF system, displacement capacity spectrum of SDOF system at each mode and step is determined based on the current frequency and current acceleration capacity spectrum. In this paper for both of the proposed and conventional methods, demand curve is obtained by time history analysis of a SDOF system and specifications of bilinear capacity spectrum. In the proposed method, determination of displacement for each point is based on NSP step that SDOF bilinear capacity curve intersect to demand curve. For evaluation of proposed and conventional methods a horizontally curved bridge have been selected and critical pier and earthquake corresponding to displacement capacity of bridge is determined through Incremental Dynamic Analysis(IDA). Then the proposed and conventional methods in the horizontally curved bridge are applied during NSP with force distribution based on first transverse mode shape. Assessing the result reveals that displacement from proposed and conventional method are different because of different formulations and dependency of proposed method to displacement vector,force vector and mass matrix of structures during NSP while the conventional method depends only to displacement of one point. Another feature that distinguishes proposed from conventional method and causes different results is the way that target displacement is determined from target spectrum displacement for top of critical pier. Finally comparison of top displacement of critical pier from proposed and conventional methods with those derived from (IDA) shows the efficiency of proposed method to reduce difference between the NSP and IDA results.