Seismic Fragility Analysis And Optimization Of Steel Frame Structure Based On Force Analogy Method

Rational and quantitative description of two types of damage named the first transcendental failure and the cumulative damage under the earthquake action is the key to the analysis of structural seismic vulnerability.The selected quantitative indicators need to reflect the structural failure mechanism reasonably while taking account of the high efficiency and convenience of the calculation process.The force analogy method(FAM)is an efficient and stable analytical tool with formulation where the nonlinear stiffness force is represented by a change in displacement instead of a change in stiffness.Meanwhile,the hysteretic energy distribution of the steel frame structure can be directly obtained by using FAM.Considering the above factors,the main contents of this article are as follows:(1)Introduce formulas using static condensation to reduce the size of the matrix for nonlinear static analysis of a multi degree of freedom system.Then,the state space method is used to complete the dynamic nonlinear analysis of the structure.Finally,the force analogy method is applied to the seismic energy response analysis of the steel frame structure to derive the energy equation and the expression of the input energy,the damping energy,the strain energy,the kinetic energy,the plastic energy of each plastic hinge and the whole plastic energy dissipation of the structure.(2)Establish comprehensive damage index of steel frame structure by combining maximum interlayer displacement angle and plastic energy consumption which composed by the weighted combination of component damage.Based on this index,seismic fragility analysis is carried out for numerical examples.(3)Optimize the structure based on the genetic algorithm with comprehensive damage index as the objective function and the section type of components as optimization variable,according to the results of seismic vulnerability analysis.The results show that the exceedance probability of the structure under earthquake is reduced to a certain extent,and the seismic performance of the structure is improved.