Linear dynamic analysis of multi-store tower buildings via an equivalent shear-shear torsional beam model

In this paper, an equivalent one-dimensional shear-shear-torsional beam model immersed in a three-dimensional space is proposed as an efficient tool for linear dynamic investigation. The formulation of the continuous model is derived in the framework of the direct 1D approach, while the constitutive visco-elastic law of the beam is drawn based on the equivalence of the elastic energy of the 3D-building generic cell with the elastic energy per unit length of the equivalent beam. The linear, fundamental problem, is written expanding the beam's equilibrium equations by introducing inertia. A suitable separation of variable, leads to a differential boundary value problem; the former, due to the boundary conditions, is satisfied by a 'trial' sinusoidal space-function. The algebraic problem is solved and natural frequencies and modes are evaluated for the undamped building. A comparison between frequencies coming from the coarse, homogeneized model and discrete one has been done; numerical results are shown for different layout of the colum.