Probabilistic Linear Time-Dependent Stress Beam Analysis and Its Stress-Strength Reliability

Abstract

Based on the principal stress values generated by the bending beam, the material’s strength required at 10^6 cycles is determined depending on time. To determine the stress/strength reliability (R(t)), the stress distribution is determined directly from the range of the principal stresses values, and the strength distribution is determined based on the reduced tensile strength (S0e) and fatigue strength (Se) range. Therefore, based on the time-dependent stress and the material’s strength, a step-by-step method to determine the reliability R(t) of the structural element at 10^6 cycles is provided. The R(t) index is used to select the best among the feasible beam alternatives of the static/elastic and plastic methodologies. The method’s efficiency is based on the time-dependent stress analysis performed by using the elastic modulus, and corresponding strain as time dependence variables. Because the time-dependent stress is related to the changes of the bending deflection through time, it is determined based on the addressed equivalent stress at 10^6 cycles.