Nonlinear Dynamic Analysis of Multistory Structures Using Runge-Kutta Integration
Keywords:
Nonlinear Structural Dynamics; Runge-Kutta Integration; Multistory Buildings; Seismic Response Analysis; Structural Engineering; Time-Dependent Differential Equations; Numerical Methods in Civil Engineering; Inter-Story Drift; Dynamic Load Modeling; Structural Response Prediction.Abstract
In the field of structural dynamics, the accurate analysis of nonlinear behavior in multistory structures under seismic and wind-induced loading has become increasingly crucial. This study presents a robust numerical framework for the nonlinear dynamic analysis of multistory buildings using the classical fourth-order Runge-Kutta integration technique. Unlike linear assumptions which often oversimplify real-world responses, nonlinear dynamic modeling provides a more precise depiction of structural behavior under large displacements and varying stiffness. The integration of the Runge-Kutta method enables the step-by-step resolution of the system’s differential equations governing nonlinear time-dependent responses, capturing both geometric and material nonlinearities. A set of real-world structural data from the Pacific Earthquake Engineering Research (PEER) Center database is used to validate the model. Results demonstrate significant differences in displacement and inter-story drift when nonlinear effects are considered, highlighting the necessity of advanced integration schemes in structural analysis. This research contributes a mathematically rigorous and computationally efficient methodology, bridging the gap between theoretical mechanics and practical structural engineering applications, especially in seismic-prone urban infrastructures.
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