A simplified inhomogeneous beam-like model for the dynamic analysis of multi-storey buildings

The analysis of multi-storey frames by means of simplified models, introduced in the last century, is still a subject of current interest since it allows drastically containing the required computational burden. Aiming at simulating the static and dynamic behaviour of entire buildings, beam-like models, equivalent to framed structures, have been formulated in recent researches. In the present study a performing beam-like model, suitable for the representation of buildings with non uniform mass and stiffness distribution along the height and within the floors, is proposed. Only shear and torsional deformability are considered in the proposed continuous beam thus leading to a simpler model, compared to those already presented in the literature taking into account also the flexural deformability. A Rayleigh-Ritz approach, based on a suitable number of modal shapes of the uniform shear-torsional beam models, allows to discretize the analysis and to evaluate the response in the generalized reduced space. Aiming at providing a numerical validation, the frequencies and modes of vibration of some reference multi-storey buildings, obtained by 3D FEM models, have been compared with those obtained considering the non-uniform beam-like model. The obtained results show a satisfactory correspondence with those provided by the detailed linear FEM simulation and proved the capability of the proposed equivalent non-uniform beam model to approximate the linear dynamic response of spatial asymmetric frames to seismic ground motion at a very low computational cost.