This paper uses the lognormal probability function to modify deterministic design equations into probabilistic design, thereby transforming the traditional safety factor into a reliability factor. The reliability factor is related to the coefficients of variation (covs) of design parameters and a failure probability. An approximation of the reliability factor for initial sizing is defined as probabilistic design factor. The serviceability design model parameters are treated as random variables characterized by mean values and covs. The cov of the design model is obtained by using first order Taylor series expansion. Multiple serviceability criteria such as bending strength, lateral torsional stability, transverse deflection, and fillet weld strength are considered.
The results from this study compare favorably with previous ones and sometimes give solutions with lower weight. In the first example, the solution in the present approach deviates on the conservative side from the previous one by 2.6% for 99.9% reliability and 3.8% for 99.997% reliability. These results are practically the same, suggesting that the method presented is reasonable and accurate. In the second example, the beam in the new solution has 23.65% lower volume or weight and the weld bead volume is lower by 8.4%. This suggests possible substantial cost reductions. From the sizes of the beam and weld bead, it can be concluded that the “factor of reliability” approach of this study and the stochastic Monte Carlo simulation method used previously are in good agreement.
Due to the very good results from the examples considered, it seems reasonable to say that the “factor of reliability” method presented is a satisfactory model. The approach has the advantage of being much less computationally intensive and requires no specialized software or skills. These features can lead to cost savings in design projects. Design sizes from this method may be used to create solid models which can be optimized using FEM (Finite Element Method). In addition, and from an instructional perspective, the method could be used to introduce undergraduate engineering students to probabilistic design approaches.