Abstract
The principal goal of this work is to investigate an application of the stochastic perturbation technique of the 10th order in coupled thermo-elasto-plastic analysis of tension of the steel elastic bar exposed to fire with thermally dependent material characteristics. An ambient temperature, calculated from the fire curve after ISO 834-1, equivalent to the fire exposure of the steel structure is treated here as the input Gaussian random variable. It is 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 considered all as highly temperature-dependent. Computational implementation known as the Stochastic Finite Element Method is carried out with the use of the FEM system ABAQUS and computer algebra system MAPLE. It uses both polynomial and non-polynomial local response functions of stresses and displacements. The basic probabilistic characteristics of time-dependent structural response are determined (expectations, coefficients of variation, skewness and kurtosis) and verified with classical Monte-Carlo simulation scheme and semi-analytical technique for input coefficient of variation not larger than 0.20. Finally, probabilistic convergence of all three methods versus increasing input uncertainty level is investigated.
Highlights
The influence of a fire on the behaviour of steel structures is always very interesting
We use the well-known Monte Carlo method, semi-analytical method and 10th order perturbation method implemented with the FEM originating from the Second Order Second Moment method [1]
Based on this computation we can say that the probability distribution of horizontal displacements ux under fire conditions is Gaussian if we narrow the range for the input coefficient of variation to Ts 0.05
Summary
The influence of a fire on the behaviour of steel structures is always very interesting. It is clear that the total time from a fire ignition up to its failure strongly depends on the basic structural materials as well as on the protection cover systems. The determination of this influence is very challenging. The basic probabilistic moments, as well as coefficients like skewness and kurtosis, are calculated by full symbolic expansion of integral definitions and partial differentiation of the nodal response functions with respect of gas temperature, which is a random input variable. We consider strength test of elasto-plastic steel cylindrical specimens subjected to fire known from literature In this case, all physical and mechanical material properties like Young modulus, yield strength, conductivity, heat capacity and linear, thermal elongation are temperature-dependent.
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