Design of a composite beam using the failure probability-safety factor method

The paper shows the practical importance of the failure probability-safety factor method for designing engineering works. The method provides an automatic design tool by optimizing an objective function subject to the standard geometric and code constraints, and two more sets of constraints, that guarantee some given safety factors and failure probability bounds, associated with a given set of failure modes. Since a direct solution of the optimization problem is not possible, the method proceeds as a sequence of three steps: (a) an optimal classical design, based on given safety factors, is done, (b) failure probabilities or bounds of all failure modes are calculated, and (c) safety factors bounds are adjusted. This implies a double safety check that leads to safer structures and designs less prone to wrong or unrealistic probability assumptions, and to excessively small (unsafe) or large (costly) safety factors. Finally, the actual global or combined probabilities of the different failure modes and their correlation are calculated using a Monte Carlo simulation. In addition, a sensitivity analysis is performed. To this end, the optimization problems are transformed into another equivalent ones, in which the data parameters are converted into artificial variables. In this way, some variables of the dual associated problems become the desired sensitivities. The method is illustrated by its application to the design of a composite beam