In‐Plane Vibrations of X‐Braced Frames

Abstract

In resisting lateral forces, X‐bracings are considered very effective for high‐rise frames. As an extension of earlier work of vibration of X‐braced portal frames, in‐plane vibrations of N‐story X‐braced frames are investigated. The elements of such a frame are made of elastic continuum undergoing transverse as well as axial vibrations. Comparing this approach with other numerical methods such as the finite element method, for dynamic analysis of elastic frames, the present method is simpler in formulations and better in results since the solutions obtained are exact in the framework of small‐vibration theory. The characteristics of X‐braced frames are investigated by six sets of numerical examples including free and forced vibrations, and dynamic responses of ground motion. The effectiveness of X‐bracings is also examined by comparing an X‐braced frame with an unbraced rectangular frame.