Fatigue Load Equivalent to Distribution of Loads From the US Population

In seeking to simplify fatigue life calculations for components of fitness equipment, this paper develops a general expression for the user weight L_e which, in N_T cycles, generates the same fatigue damage as a set of user weights {L_i} described by a probability density function f_i = N_i/N_T, where each L_i gets applied for N_i cycles and Σ N_i = N_T. The derivation of the method goes beyond the textbook development of equivalent load by retaining geometric, material, and loading parameters throughout the derivation. The expression allows exploration of the effect of the geometry of the mechanical component, material properties, and loading on the value of the user weight L_e which simulates the set of user weights {L_i}. The paper explores a range of stress-life exponent b typical of common steels. The paper explores the complete range of stress ratio R ∈ (-1, 1). The paper explores the combined effect of the component’s ultimate tensile strength and the ratio between applied load and stress. These last two parameters determine the user weight L_b which causes single-cycle fracture of the component. The results indicate a strong dependence of L_e on stress ratio R, stress-life exponent b, and on breaking weight L_b. The paper proposes guidelines for assignment of L_e in the special case where the {L_i} arise from body weights of the US population.