Structural reliability and Monte Carlo simulation

Using elementary engineering mechanics, a simple boom structure is analysed and its reliability is assessed. It is assumed that four of the structural variables are random with a known joint probability distribution function. From the structural analysis, an explicit expression for failure is obtained. The reliability of the structure is computed analytically from first principles of probability theory. Additionally, it is shown that Monte-Carlo simulation can be implemented more readily with results that compare favourably to the theoretical calculations. Thus, the power and utility of Monte-Carlo simulation are demonstrated. Specifically, the boom is analysed for different probability distribution functions for the underlying components. The analytical and numerical analysis contained in this application are appropriate for any upper level undergraduate course in applied mathematics, scientific computation or engineering reliability where the Monte-Carlo method is being studied.