Abstract
In probabilistic structural design some actions on structures can be well described by renewal processes with intermittencies. The expected number of renewals for a given time interval and the probability of “on“-state at an arbitrary point in time are of a main interest when estimating the structural reliability level related to the observed period. It appears that the expected number of renewals follows the Poisson distribution. The initial probability of “on”-state is derived assuming random initial conditions. Based on a two-state Markov process, the probability of “on”-state at an arbitrary point in time then proves to be a time-invariant quantity under random initial conditions. The results are numerically verified by Monte Carlo simulations. It is anticipated that the proposed load effect model will become a useful tool in probabilistic structural design. The aims of future research are outlined in the conclusions of the paper.
Highlights
Actions on structures are often of a time-variant nature
It is indicated that the cumulative distribution function FT0(t) of the first renewal T0 obtained in the paper can suitably be used to simulate random initial conditions of the renewal process
The expected number of renewals E[N(0, T)] of the renewal process considered here is shown to be independent of the initial conditions
Summary
Actions on structures are often of a time-variant nature. Special attention is in particular required when a combination of time-variant loads needs to be considered. Approaches to probabilistic structural design based on different load combination models are indicated by JCSS [1] It appears that an advanced load effect model based on renewal processes can be suitably used to describe random load fluctuations in time, enabling sufficiently accurate estimates of the reliability level in practical applications. A formula for the expected number of renewals E[N(0,T)] is verified Both the basic properties of the renewal process are investigated under random as well as given initial conditions. A two-state Markov process developed by Madsen and Ditlevsen [7] is adopted to derive the probability of „on“-state pon(t) at an arbitrary point in time It appears that pon(t) is a time-invariant quantity under random initial conditions.
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