A SIMPLE APPROXIMATE FORMULATION FOR THE FIRST TWO FREQUENCIES OF ASYMMETRIC WALL–FRAME MULTI-STOREY BUILDING STRUCTURES

A simple approximate method is presented to estimate the first two coupled natural frequencies of uniform asymmetric wall–frame multi-storey buildings. Firstly, the fundamental uncoupled torsional-to-lateral frequency ratio is determined by using the maximum structural static deflection resulting from the gravity load acting horizontally. Secondly, the concept of equivalent eccentricity is proposed and determined by means of the frequency ratio of the second to the fundamental mode in the same direction of a building structure. Finally, a combination of the fundamental uncoupled torsional-to-lateral frequency ratio and the equivalent eccentricity is used to extend the simple formulae, which are limited to coupled natural frequencies of proportionate structural systems, to estimate the first two coupled natural frequencies of asymmetric wall–frame buildings. Numerical examples show that a good agreement between results from the proposed method and FEM has been achieved.