Page 29 - Dynamic Loading and Design of Structures

Page 16

Figure 1.6 Schematic representation of damage accumulation problem.

It is evident from the above remarks that the best approach for solving a time-dependent
reliability problem would depend on a number of considerations, including the time frame of
interest, the nature of the load and resistance processes involved, their correlation properties
in time, and the confidence required in the probability estimates. All these issues may be
important in determining the appropriate idealizations and approximations.

1.4.2 Transformation to time independent formulations

Although time variations are likely to be present in most structural reliability problems, the
methods outlined in Section 1.2 have gained wide acceptance, partly due to the fact that, in
many cases, it is possible to transform a time-dependent failure mode into a corresponding
time independent mode. This is especially so in the case of overload failure, where individual
time-varying actions, which are essentially random processes, p(t), can be modelled by the
distribution of the maximum value within a given reference period T (i.e. X=max {p(t)})
T
rather than the point in time distribution. For continuous processes, the probability
distribution of the maximum value (i.e. the largest extreme) is often approximated by one of
the asymptotic extreme value distributions. Hence, for structures subjected to a single time-
varying action, a random process model is replaced by a random variable model and the
principles and methods given previously may be applied.
The theory of stochastic load combination is used in situations where a structure is
subjected to two or more time-varying actions acting simultaneously. When these actions are
independent, perhaps the most important observation is that it is highly unlikely that each
action will reach its peak lifetime value at the same moment in time. Thus, considering two
t
time varying load processes P (t),p (t),0≤≤T, acting simultaneously, for which their
1
2
combined effect may be expressed as a linear combination p1(t)+p2(t), the random variable of