A method is presented that leads to accurate estimation of the cumulative fatigue damage incurred in a randomly loaded structural element when loading is given in the form of spectral density load, or stress, plots. The load plots are here approximated by a series of straight lines and a closed formula is obtained to yield the damage incurred by the load within each straight line segment. The method avoids the errors that result from human misjudgment in the commonly used curve-stepping approach. It is also adaptable for computer applications and can be incorporated in a stress calculation program to save on computation time. In comparison to curve stepping, five straight-line segments may give the same accuracy as a hundred curve steps. This contrast, however, depends on the degree of irregularity of the load curve.

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