Analytical and Numerical Reliability Analysis of Certain Pratt Steel Truss

Abstract

The main aim of this paper was to propose a new reliability index for steel structure assessment and to check it using the example of a popular Pratt truss girder. Structural analysis was completed in the finite element method system Autodesk ROBOT, and probabilistic analysis was implemented in the computer algebra software MAPLE. The stochastic finite element method (SFEM) was contrasted here with the Monte Carlo simulation and the girder span was selected as the input structural uncertainty source. Both methods were based on the same structural polynomial response functions determined for extreme deformation, for extreme stresses and also for the structural joint exhibiting the largest effort. These polynomials were statistically optimized during the additional least squares method experiments. The first four basic probabilistic characteristics of the structural responses, the first-order reliability method (FORM) index, and as the new proposition for this index were computed and presented. This new index formula follows the relative probabilistic entropy model proposed by Bhattacharyya. The computer analysis results presented here show a very strong coincidence of both probabilistic numerical techniques and confirms the applicability of the new reliability index for the input coefficient of variation not larger than 0.15. These studies should be continued for other engineering systems’ reliability and, particularly, for large-scale and multiscale computer simulations. The results presented in this paper may serve in different applied sciences, from biology through to econometrics, experimental physics and, of course, various branches of engineering.

Keywords

• reliability index
• Monte Carlo simulation
• stochastic perturbation method
• stochastic finite element method
• relative entropy