Peak Factor and Random Fatigue
This second chapter on random vibration is devoted to the analysis of the statistics of the random response in order to assess the reliability of the structure; two important failure mechanisms are examined: the failure by threshold crossing and fatigue. The first part of this chapter is devoted to the peak factor, that is the statistics of the extreme value of the random process during a given observation period. Approximate formulae are derived. The relationship between the peak factor and the so-called Response Spectrum traditionally used in earthquake engineering is elucidated. The second part of this chapter is devoted to random fatigue according to the linear damage theory (Miner). Classical results of uniaxial Gaussian stresses with zero mean are reviewed first; the case of biaxial loading is also addressed, by the definition of a special uniaxial equivalent von Mises stress; the finite element formulation of the method is outlined. A set of problems is proposed at the end of the chapter.