Keywords: frame, sensitivity, imperfection, material, structural, variance.

The sensitivity analysis is used for the determination to assess what degree the imperfections of a steel plane frame influence the frame static ultimate load, i.e. how sensitive is the system response to a change in the input parameter. In general, all components of imperfections (material a geometrical) are random quantities. Therefore a purely deterministic approach when determining their influence on the structure response cannot be considered to be perfect. The influence of the variance of initial imperfections on the variance of the load-carrying capacity studied was calculated using stochastic sensitivity analysis.

The coherent concept of stochastic sensitivity analysis enabling an analysis of the influence of arbitrary subgroups of input factors (doubles, triples, etc.) on the monitored output was worked out by the Russian mathematician Ilja M. Sobol [1,2,3] and extended in [4]. The Sobol's variance decomposition is used for investigation of first-order effects, second-order effects due to interactions.

The computation model is based on a non-linear finite element method, the steel plane frame being modelled by means of beam elements. The frame geometry was meshed by beam elements with initial curvature in form of a parabola of the third degree. The load-carrying capacity was solved by the nonlinear Euler incremental method and combined with the Newton-Raphson method.

All input imperfections were considered to be random quantities. In the numerical Monte Carlo simulation method, the random effect of initial imperfections on a frame load-carrying capacity can be simulated. The system imperfection was considered according to the first buckling mode. Material and geometrical characteristics of steel members from the IPE series (European parallel flange beams) were considered to be random quantities the histograms of which were obtained from experiments [5].

Imperfections that have a dominant influence on the load-carrying capacity are identified. The sensitivity analysis results are used as bases for decision making on modification of technological procedures for manufacturing the hot-rolled beams, and for the work of designers, making possible the amelioration of the reliability of designed manufactured structures and elements [6].

1

Sobol' I., "Multidimensional Quadrature Formulas and Haar Functions", Nauka, Moscow, 1969. (in Russian)

2

Sobol' I., "Sensitivity Estimates for Nonlinear Mathematical Models", Matematicheskoe Modelirovanie 2, pp.112-118, 1990. (in Russian, translated in English in Sobol' 1993)

3

Sobol' I., "On 'freezing' Unessential Variables", Vestnik Mosk. Univ. Ser. Mat., 6, pp. 92-94, 1996.

4

Saltelli A., Ratto M., Andress T., Campolongo F., Cariboni J., Gatelli D., Saisana M., Tarantola S., "Global Sensitivity Analysis Guiding the Worth of Scientific Models", New York: John Wiley and Sons, 2007.

5

Melcher J., Kala Z., Holický M., Fajkus M., Rozlívka L., "Design Characteristics of Structural Steels Based on Statistical Analysis of Metallurgical Products", Journal of Constructional Steel Research, 60, pp. 795-808, 2004. doi:10.1016/S0143-974X(03)00144-5

6

Kala Z., "Sensitivity Analysis of the Stability Problems of Thin-walled Structures", Journal of Constructional Steel Research, 61, pp. 415-422, 2005. doi:10.1016/j.jcsr.2004.08.005

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