Stochastic Combination of Load Effects

Risk-informed condition assessment of civil infrastructure: state of practice and research issues

“…Many structural loads that arise from infrequent operating or environmental events such as overloads, accidental impact, earthquakes, and tornadoes, are short in duration and occupy a negligible fraction of a structure's service life. Such loads can be modeled stochastically as a sequence of short-duration load pulses, the occurrence of which is described by a Poisson process, with the mean (stationary) rate of occurrence, l, random intensity, S j , and duration, t (Pearce and Wen 1984). (If the load process is intermittent and the duration of each load pulse has an exponential distribution, the probability that the load process is nonzero at any arbitrary time is lt.) Taking into account the randomness in the number of loads and the times at which they occur as well as initial strength, the reliability function becomes, approximately ,…”

Time-Variant Reliability

“…Taking the mean over the resistance introduces some level of dependency in the upcrossing rate, thus making the Poisson assumption in Equation 18.1 less appropriate. The EUR approximation consists of approximating the arrival rate of upcrossings through a random barrier by the ensemble average of upcrossings [24]. Typically, this leads to an overestimation of the failure probability [25].…”

Reliability-based condition assessment of steel containment and liners

“…Such loads can be modeled as a sequence of shortduration load pulses occumng randomly in time. One of the simplest pulse process models is illustrated by the sample function in Figure 4.la The occurrence in time of the loads (impulses) is described by a Poisson process, with mean (stationary) rate of occurrence, A, random intensity Sj and duration z (Pearce and Wen, 1985). The number of events, N(t), to occur during service life, t, is described by the probability mass function, P[N(t) = n] = (A t)" exp (-At)h!…”