A simplified method for calculation of the natural frequencies of wall–frame buildings

Abstract A simple hand method is presented for the three-dimensional frequency analysis of buildings braced by frameworks, coupled shear walls, shear walls and cores. Lateral vibration is characterised by three types of deformation: the full-height ‘local’ bending of the individual columns/wall sections/shear walls/cores, the full-height ‘global’ bending of the frameworks/coupled shear walls, which is associated with the axial deformations of the columns/wall sections, and the shear deformation of the frameworks/coupled shear walls. Based on the stiffnesses associated with these three types of deformation, a closed formula is derived for calculation of the lateral frequencies. An analogy between bending and torsion is used to carry out the pure torsional frequency analysis. The coupling of the lateral and pure torsional modes is taken into account. The results of a comprehensive accuracy analysis covering 144 multi-storey structures demonstrate good agreement with the finite element solution, the maximum difference being 7%. A worked example with step-by-step instructions shows the easy use of the method.