A review of field measurements on bridges under traffic showed that a family of Rayleigh probability-density curves can represent the frequency of occurrence of stress ranges of different magnitudes in actual bridges. A particular histogram for a bridge can be approximated by a particular curve from the family. Each curve is defined by: (1)The modal stress range, Srm; and (2)a parameter Srd, which is a measure of the width of the probability-density curve. Different combinations of Srm and Srd were included. The variable-amplitude data can be related to the constant-amplitude data by using an effective stress range to represent the variable-amplitude spectrum. The effective stress range is the constant-amplitude stress range that would result in the same fatigue life as the variable-amplitude spectrum, and may be taken as the root-mean-square stress range of the spectrum or calculated from Miner's law.
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Schilling et al. (1977) studied this question.