Advanced Structural Analysis/Part I - Theory/Failure Modes/Fatigue/Crack Initiation/Loading/Load Spectra/Miner-Palmgren rule

Load histories in real applications are often complex and irregular. The total fatigue effect of such loads can be estimated by the Miner-Palmgren rule, see the equation below. Fatigue failure is assumed to occur when the Miner-Palmgren equation is true.

$$D = \sum{\frac{n_i}{N_i}}$$

Where: $$D=$$ a constant, often ranging between 0.33 and 3 $$n_i=$$ the number of occurrences of a specific load cycle progression, $$i$$ $$N_i=$$ the fatigue life of a specific load cycle progression, $$i$$

Shortcomings of Miner's rule
The Miner-Palmgren rule is rather rough and neglects several important qualities of a general load history. Among these properties are the order and shape of the individual cycles.