OPTIMAL ESTIMATION OF LINEAR SHEAR-TYPE MODELS FOR BENCHMARK STEEL STRUCTURES IN DYNAMIC ANALYSIS

Reducing the degree of freedoms of building models significantly decreases the computational costs in time consuming structural engineering problems like dynamic analysis of structures, nonlinear analysis or any optimal design of structural systems. In this study, the finite element models of 3- and 9-story benchmark steel buildings with numerous degrees of freedoms are simplified to 3- and 9-degree-of-freedom linear shear-type buildings and reduced to just 3- and 9-degree of freedom buildings, respectively. First, initial linear shear-type models were derived by estimating the stiffness of the stories, ensuring that their fundamental frequency matches the corresponding frequencies of the finite element models. Then, an optimization problem is defined and solved using a Genetic Algorithm (GA) to achieve more significant accuracy in the higher frequencies of the initial linear shear-type models. Two objective functions were established and assessed for the optimization problem: one is the difference in frequencies between the finite element models and the initial linear shear-type models with equal weighting, and the other is the first objective function improved with the modal participation percent weighting. The stiffness of the stories in the shear models are selected as the design variables in both optimization problems. Finally, the models are subjected to four benchmark earthquake excitations and different structural responses are compared with those of finite element models to evaluate the accuracy of optimal linear shear-type models based on the time responses of buildings under natural ground motions. The Root Mean Square (RMS) and peak of the displacement, velocity, and absolute acceleration of the building's roofs have been selected and compared as the performance criteria of the proposed objective functions. The results show that the model derived from the weighted objective function outperformed the objective function with equal weighting. Moreover, by comparing the proposed optimal 3- and 9-story models with those of available in the literature, it can be shown that the proposed optimal linear shear-type models are significantly more accurate both in frequency and time-history analysis.