An Application of Relative Entropy in Structural Safety Analysis of Elastoplastic Beam under Fire Conditions

The main aim of this work is to propose a new algorithm of reliability assessment for steel civil engineering structures subjected to fire temperatures. This new algorithm is based upon the relative probabilistic entropy concept elaborated by Bhattacharyya, and this probabilistic distance is sought in-between extreme and admissible deformations of some structural beam subjected to higher temperatures. Similar to the First Order Reliability Method, this approach uses the first two probabilistic characteristics of the structural response, when structural output may be modelled with the use of Gaussian distribution. The probabilistic structural response is found here using hybrid computational technique–the Finite Element Method system ABAQUS with its fully coupled thermo-elastic analysis with 3D solid elements and probabilistic modules implemented in the computer algebra system MAPLE. The probabilistic response is determined via a triple stochastic analysis, which is based on the classical Monte-Carlo simulation, iterative generalized stochastic perturbation technique, and also using semi-analytical probabilistic calculus. Final determination of the relative entropy in the Serviceability Limit State of the given structure and its comparison with the results obtained using the FORM analysis enables to calibrate this new technique to numerical values proposed in the engineering designing codes. Hence, a more accurate probabilistic method may use some experimental-based admissible values included in the existing design of legal provisions.