On sequentially coupled thermo-elastic stochastic finite element analysis of the steel skeletal towers exposed to fire

Abstract

This work demonstrates an application of the stochastic perturbation technique and the corresponding Stochastic Finite Element Method (SFEM) in numerical analysis of the temperatures, stresses and deformations for the spatial steel tower structure exposed to a fire. This approach is based on the 10th order Taylor expansion of all input random parameters, the resulting state functions and, independently, on the Least Squares Method (LSM) determination of the structural responses in addition to the input random parameters. An initial temperature equivalent to the fire exposure of the tower structure is adopted as the input Gaussian random variable and applied at the bottom structural members, where material parameters of the steel as Young modulus, heat conductivity and capacity as well as thermal elongation are considered all as highly temperature-dependent. We explore various algebraic forms of the response functions as polynomial bases and, additionally, power, exponential, hyperbolic to make our results totally independent of this choice. This study is an example of a hybrid usage of the Finite Element Method (FEM) system ABAQUS and the computer algebra system MAPLE in stochastic transient sequentially coupled thermo-elastic 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.