Introduction

In Chapter 9 we derive results that make it possible for us to calculate the mean value and the standard deviation of the response of a linear, time-invariant system if we know the load spectrum and the transfer function of the system. Even if such information can be important enough, it is in many cases of limited value. In connection with the design of a structure to withstand wave loads, it would be necessary to estimate the largest response and the associated stresses or strains in the structure over its specified lifetime. Such estimates cannot generally be calculated on the basis of the mean value and the standard deviation, or for that matter, on the basis of the response spectrum.

In this chapter, we provide an introduction to the calculation of extreme responses and response statistics. “Extreme” here means “the largest,” interpreted in a way that follows from the context. The background for this is that collapse of a structure, or part of a structure, is often assumed to take place either by first time exceedance of a capacity limit, or by fatigue, which is caused by accumulated damage due to repeated stress cycles at relatively moderate stress levels. We see that an important key to being able to handle these problems in practice lies in the calculation of the average number of times that the response process crosses a particular level during a given time interval.