Reducing the degrees of freedom of building models significantly reduces computational costs in time-consuming structural engineering problems, such as dynamic analysis, nonlinear analysis, or the optimal design of structural systems. In this study, the Finite Element (FE) model of a 20-story benchmark steel building with numerous degrees of freedom (DoF) is simplified to a 20-degree-of-freedom linear shear-type building. First, a preliminary linear shear-type model was derived by estimating the story stiffness so that the fundamental frequency matches that of the FE model. Then, an optimization problem is formulated and solved using a Genetic Algorithm (GA) combined with a weighted-sum method to achieve greater accuracy at higher frequencies in the preliminary model. Two objective functions were established and assessed for the optimization problem: one is the difference in frequencies between the FE model and the preliminary model with equal weighting, and the other is the first objective function improved with the modal participation percent weighting. The stiffness of each story in the preliminary model is selected as the design variable in both optimization problems. Finally, these optimized models are evaluated against the FE model using frequencies and dynamic time-history responses. The model derived from the weighted objective function demonstrates acceptable accuracy compared to its FE model in frequency and time-history analysis. It can be used for dynamic analysis and other structural and earthquake engineering purposes.
