Application Of Equivalent Linearization Method In The Seismic Design Based On Displacement And Energy

In the seismic design based on displacement and energy, the accurate assessment of structure elasto-plastic response under rarely occured earthquake is an important part of their theoretical research, and the equivalent linearization method as a simplified and practical method for calculating the responses of elasto-plastic structures, has the characteristics of clear concept and wide range of application, which has been received the widespread attention in the study of structural seismic design.The equivalent linearization model is established by adjusting the period and the damping of linear elastic calculation model, the seismic response of elastic-plastic structures is solved by this approximation, so the reasonable establishment of equivalent linearization model is the key to ensure the accurate evaluation of the elastic-plastic response of the structure.At present, researchers around the world proposed a variety of equivalent linearization methods based on the different equivalence principles, i.e. the AASHTO specification, Japanese Bridge aseismic design codes JPWRI, the California CALTRANS specification, the experimental method by Gulkan and Sozen, and the empirical formula method by Iwan. In this paper, five equivalent linearization methods are discussed, which are applicated in the seismic design based on the direct displacement and energy.The above five kinds of equivalent linearization method is applied to seismic design based on directly displacement, then comparing the base shear respectively. The results showed that G&S method to calculate the base shear design value is the most conservative and the rest of the four kinds of methods calculation results is close to each other. Considering the influence of the equivalent parameters of each method and the structural parameters on the calculation results, the equivalent period formula of each equivalent linearization methods had little effect on structure design, the effect of yield stiffness coefficient on structural design is small, and the effect of ductility factor on structural design is great. Finally, a numerical example is used to analyze the strength value of the structural design under the application of the equivalent linearization methods, and the results are consistent with the theoretical analysis.The application of equivalent linearization methods in solving the energy spectrum of seismic input based on energy design is analyzed, compares computational accuracy and applicable range of these methods, and analyzes and discusses the influence of various structural parameters on the calculation error of equivalent linearization methods at the same time. The results indicated that the prediction error of the input energy spectrum for short period structures under the selected four equivalent linearization methods is bigger, Caltrans' or Iwan's methods are relatively stable with an error below 10%,while the computation error of short period range is very large, which mainly due to the short period is overestimated. In general, the influence of ductility coefficient for short period range structure energy spectrum estimation accuracy is bigger, and with the ductility coefficient increases computational error increases, post yield stiffness coefficient of energy spectrum estimation accuracy is not obvious, the initial damping only in the long period range of calculations have an impact, and with the increase of the initial damping ratio, the calculation error of the energy spectrum reduce.Based on the evaluation results of above approximate calculation of earthquake input energy spectrum, obviously, the equivalent linearization method is not suitable for the approximate estimation of short period structures,but for medium and long period structures, the accuracy of approximate results by Iwan is higher. Therefore, this paper uses the genetic algorithm to optimize computing the equivalent period formula for Iwan method in short period range, by fitting the optimal parameter solution, the equivalent period fitting formula of short period structure is obtained, and comparing with the exact elastic-plastic seismic input energy spectra calculated by nonlinear time history analysis, the evaluation result shows the fitting formula is reasonable.