Novel technique for dynamic analysis of shear frames based on energy balance equations

Abstract

In this paper, an effcient computational solution technique based on the energy balance equations is presented to perform the dynamic analysis of shear frames, as an example of a multi-degree-of-freedom system. After deriving the dynamic energy balance equations for these systems, a new mathematical solution technique called elimination of discontinuous velocities is proposed to solve a set of coupled quadratic algebraic equations. The method will be illustrated for the free vibration of a two-story structure. Subsequently, the damped dynamic response of a three-story shear frame, which is subjected to harmonic loading, is considered. Finally, the analysis of a three-story shear building under horizontal earthquake load, as one of the most common problems in earthquake engineering, is studied. The results show that this method has acceptable and greater accuracy than other techniques; it is faster than modal analysis and does not require adjusting and calibrating the stability parameter as compared to a time integration method like the Newmark method.