An equivalent beam model to estimate the three-dimensional response of tall buildings to random loads is proposed in this paper. The model fully describes coupling between bending and torsion. In particular, bending behavior is described using the Timoshenko beam, while free warping is used to model torsional behavior. The beam dynamic characteristics (natural frequencies and modal shapes) are determined solving the coupled differential equations that rule the problem by means of the state variable approach. The main advantage of using such an equivalent beam is the use of a reduced-order model to estimate the response to random loads. Indeed, the proposed model can be used to reduce the computational time needed to estimate the three-dimensional elastic response of tall buildings to random loads. The influence of the mechanical characteristics of the beam on the calibration procedure and the influence of the eccentricity between centroid and center of mass on both natural frequencies and modal shapes are assessed and shown. Finally, the proposed approach is used to estimate the stochastic response of a tall building with a nonsymmetric plant to earthquake and wind loads.
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