On the least squares stochastic finite element analysis of the steel skeletal towers exposed to fire

Abstract

The main issue in this paper is an application of the generalized stochastic perturbation technique to thermal stresses and deformations analysis for the spatial steel tower structure exposed to a fire. This approach is based on the given order Taylor expansion of all random parameters and state functions around their mean values as well as on the Least Squares Technique to determine the analytical functions in-between design parameters and structural responses. A distribution of the temperature in the model is considered for a simplicity as the set of constant values for all structural members. The temperature equivalent to the fire exposure in the analyzed structure is taken as the input Gaussian random variable, where basic material parameters are considered as temperature-dependent and this is the basis to calculate up to the fourth probabilistic moments and characteristics of the stresses and deformations. This study is an example of a hybrid usage of the FEM engineering system ROBOT and the computer algebra system MAPLE in stochastic analysis, where thermal stresses and strains may be straightforwardly used in fire reliability analysis of the civil engineering structures with both temperature-independent and dependent material characteristics.