| Abstract: | Design for a specific ductile failure mode is assuming a rǒle of increasing importance for earthquake-resistant structures. This necessitates an accurate assessment of the distribution of overstrength in the structure, in order that the predefined failure mode can be realized. Consequently, the variability of the response for a given variability in the salient material properties, such as yield strength for steel structures, should be assessed and accounted for. In this paper an analytical method is proposed for the evaluation of the probability density function of the response of a single-degree-of-freedom hysteretic system with random parameters subject to a variable amplitude cyclic load history. A simple algorithm is derived which may be used to obtain the system response as a function of the system parameters. This response function may then be used to evaluate the displacement response probability density function when given the probability density function of the system parameters. Results derived from this procedure are verified against Monte Carlo simulation. It is shown that accurate response statistics are obtained at a fraction of the computing cost of simulation techniques. |
