Structural reliability analysis of optimsed steel structures

Abstract

Designing a structure essentially comes down to making decisions in light of economy and uncertainty. Optimisation is one such tool were economy is pushed to its limits. The significance of optimisation in structural engineering is limited, if the inherent nature of uncertainty in these structures is not considered. A Level 2 optimisation study, which aims at minimising structural weight, is conducted in order to directly account for the uncertainty in resistance and loading variables while an optimal point is sought. A component and system reliability approach using First order Reliability Methods (FORM) and Second Order Reliability Method (SORM) is carried out to eventually be able to calculate the design point values for a Level 2 optimisation study, in which the variables used are described statistically. The statistical description of steel yield stress is found from data gathered about locally imported 8275 steel beams and is described using a normal distribution. These Level 2 design points are used to analyse the relevance of Level 1 design points investigated in light of safety. Level 1 optimisation procedures are carried out on a portal frame using plastic analysis. The optimisation procedure makes use of a graphical approach, where the objective function is defined using Foulkes' Theorem. This study is carried out on a total of thirty-two frames which vary in geometry and cladding material, and based on the presumption that failure is due to plastic collapse. In most cases, it can be seen that the limit state approach defined using Level 1 optimisation studies are reliable in view of uncertainty. Furthermore, the Level 2 optimisation studies result in frames with a lesser structural weight than those obtained from Level 1 optimisation studies. This depicts the fact that the "true" optimal point is not actually attained when Level 1 optimisation study is carried out in these scenarios.