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

In this paper, an efficient computational solution technique based on the energy balance equations is presented for 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 which is 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 accuracy in comparison with other techniques, but is not only faster compared with modal analysis but also does not require adjusting and calibrating the stability parameter as compared with a method of time integration like the Newmark method.