Keywords: accidental eccentricity, uncertain mass, interval analysis, stochastic response.

Seismic assessment of structures is a public safety issue that nowadays still encompasses several uncertainties. In seismic engineering two types of parameter uncertainties need to be distinguished [1]. The first type arises from the random nature of the seismic action, while the second type is internal and it is related to the uncertainties of the structural parameters. As a result, the structural dynamic response is also uncertain. In this regard, it is mandatory to estimate the effect of these uncertainties on the structural dynamic response.

In the framework of the conventional structural analysis procedures, the internal uncertainties can be modelled as random variables or processes with a probability distribution function representing the distribution of the measured values. The probabilistic models lead to the evaluation of the random response of the structural systems considered. In the current literature there are four main strategies to evaluate the response of structural systems with random uncertainties, they are: (i) the Monte Carlo simulation method (ii) the perturbation methods, (iii) the stochastic finite element method [2,3]; (iv) the orthogonal series expansion method [2,4].

However in several structural problems, despite the success of the above probabilistic analysis, data on structural parameters are often absent or not sufficient to define the effective joint probability densities of the random variables or functions involved. In practice, only the bounds or the amplitude of uncertain parameters are often known. Therefore, to avoid invalid results, coherently the uncertainties should be modelled on the basis of alternative non-probabilistic conceptual frameworks.

In this paper, in the framework of the interval analysis [5], a method for evaluating the upper and lower bounds of the structural response of buildings with uncertain-but-bounded masses subject to deterministic and stochastic ground motion acceleration is proposed. The procedure requires the definition of a unique structural model so reducing the number analyses to be performed. Numerical results demonstrate the very good accuracy of the proposed procedure for all the cases considered.

1

R.A. Ibrahim, "Structural dynamics with parameter uncertainties", Applied Mechanics Reviews, 40(3), 309-328, 1987. doi:10.1115/1.3149532

2

R.G. Ghanem, P.D. Spanos, "Stochastic finite elements: a spectral approach", Springer Verlag; 1991.

3

M. Kleiber, H.D. Hien, "The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation", John-Wiley, 1992.

4

R.G. Ghanem, P.D. Spanos, "Polynomial chaos in stochastic finite elements", Journal of Applied Mechanics, 57(2), 197-202, 1990. doi:10.1115/1.2888303

5

Y. Ben-Haim, I. Elishakoff, "Convex Models of Uncertainty in Applied Mechanics", Elsevier Science Publishers, Amsterdam, 1990.

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