Comparative Study of First Order Reliability Method Based on Steepest Descent Search Directions for Reliability Analysis of Steel Structures

The reliability assessment of structures under uncertainties in external loads including blast, gravity and lateral loads and also material properties change, is important to determine the reliable levels of structures. Therefore, the reliability analysis can be provided a suitable management from the reliable levels subjected to the increasing the loads and decreasing the resistance of structures. In this paper, three algorithms of first order reliability method (FORM) using steepest descent search direction are applied to evaluate the failure probabilities of structural steel problems which are designed by the Iranian National Building code. The FORM formula is modified based on a dynamic step size which is dynamically adjusted based on the merit functions between 0 and 1.5 named as modified Hasofer-Lind and Rackwitz-Fiessler (MHL-RF) method. The convergence performances for both robustness and efficiency of the gradient method, HL-RF and  proposed MHL-RF were compared through four steel examples including a bar structure under tensile capacity, a multi-span beam under bending capacity, a connection under tension load and a column under axial force. The results illustrated that the all structural reliability methods-based steepest descent search direction are robustly converged, but the MHL-RF method is more efficient than the HL-RF and gradient method. The designed steel components by the Iranian National Building code where shown a good confidence levels with the reliability index in the range from 2.5 to 3.0.