Deterministic and stochastic seismic analysis of buildings with uncertain-but-bounded mass distribution

The actual and the computed seismic response of buildings are in general different due to the unavoidable uncertainties involved in the definition of the mass and stiffness distributions as well as in the estimation of the ground motion spatial variability. The discrepancies are accounted for by building codes through the so-called accidental eccentricity, which defines the bounds of the actual position of the centre of mass for each floor. Therefore, the seismic analysis problem is posed as the finding of the response of a structural system with uncertain-but-bounded parameters forced by deterministic or stochastic loads. In this paper, in the framework of the interval perturbation method, a procedure for determining upper and lower bounds of the dynamic response of structures with uncertain-but-bounded mass distribution vibrating under either deterministic or stochastic input is proposed. The procedure requires the definition of a unique structural model so reducing the number of analyses to be performed. Moreover, by the proposed approach all the possible permutations are implicitly considered so to include the worst condition. Numerical results showed a very good accuracy of the proposed procedure for all the cases analyzed.