This study presents a mathematical model for analyzing the dynamic response of two-dimensional (2D) frame structures subjected to dynamic loads such as wind and seismic forces, due to their significant impact on structural safety and performance. The main objective is to develop a numerical framework to investigate the behavior of these structures when modeled as multi-degree-of-freedom (MDOF) systems. The governing equations of motion are solved numerically using the fourth-order Runge–Kutta method in MATLAB to compute the time-history displacement response, which is evaluated at both peak and steady-state conditions. In addition, linear regression is used to examine the relationship between applied load and displacement. The results of the coefficient of determination (R²) indicate a strong correlation between the variables. The findings demonstrate the effectiveness and accuracy of the proposed model in capturing structural behavior under dynamic excitations. This approach provides an efficient and practical tool for estimating structural response while reducing computational effort, making it suitable for preliminary analysis and engineering design applications.
Keywords
Coefficient of Determination (R²)Equations of MotionDynamic AnalysisLinear RegressionMulti-Degree-of-Freedom (MDOF)Runge–Kutta methodStructural Response
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