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This work demonstrates an application of the generalized stochastic perturbation technique and the corresponding Stochastic Finite Element Method in numerical analysis of the stresses for the steel structural element subjected to higher temperatures. This approach is based on higher order Taylor expansion of the input random parameters and of the resulting state functions and, independently, on the Least Squares Method determination of the structural responses to the input random parameters. An initial temperature equivalent to the fire exposure of the steel structure is taken as the input Gaussian random variable and uniquely defined by the constant mean value at outer surfaces of this element, where material parameters of the steel as Young modulus, yield strength, heat conductivity, capacity and thermal elongation are all considered as highly temperature-dependent. These functions are adopted according to the experimental evidence provided in the literature. We adopt various degree of polynomial functions to verify an influence of the response function choice upon the resulting probabilistic characteristics. This study is an example of a hybrid usage of the FEM system ABAQUS and the computer algebra system MAPLE in stochastic transient fully coupled thermo-mechanical analysis, where up to the fourth order probabilistic characteristics of the temperatures, displacements and stresses may be directly used in fire reliability analysis of the civil engineering structures with the temperature both independent and dependent material characteristics. The results obtained in this study may serve directly in the stochastic reliability analysis of the steel structures subjected to a fire according to both First and Second Order Reliability Methods (FORM and SORM).

ON FULLY COUPLED THERMO-ELASTO-PLASTIC STOCHASTIC FINITE ELEMENT ANALYSIS OF STEEL STRUCTURES