Structural response to non‐stationary non‐white stochastic ground motions

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Abstract
A numerical procedure is presented for calculating the survival probability of a linear multidegree of freedom structure subjected to non‐stationary non‐white ground motions using the concept of qualified envelope crossings. The moment equations governing the covariances of the structural response and its Hillbert transform are derived, and efficient techniques for calculating various convolution integrals which appear in these equations are discussed. Numerical integration of the moment equations yields the statistics of the response and the response envelope, from which the survival probability can be estimated. Excellent agreement is found with published analytical results for the response variances of a three storey building, and it is shown that the method can readily deal with cases for which there is no analytical solution.

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