A review of problems related to sensitivity analysis of thin walled members with open monosymmetric or bisymmetric cross-section is presented. The restraints imposed on angle of cross-section rotation, transverse displacement and cross-section warping are taken into account. The consideration is based upon the classical theory of thin-walled beams with nondeformable cross-section. The first variations of state variables due to a change of the design variable are investigated. Arbitrary displacement, internal force or reaction of the member subject to static load, critical buckling load, frequency and mode of torsional vibration are assumed to be the state variables. The dimensions of the cross-section, the material constants, the restraints stiffness, and their locations, position of the member ends are taken as the design variables. Accuracy of the approximate changes of the state variables achieved by sensitivity analysis is also discussed.

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Sensitivity analysis of thin-walled members, problems and applications

The paper deals with the load carrying capacity probabilistic variance-based sensitivity analysis of thin-walled box-section girders subjected to pure bending. The lower- and upper-bound load capacity estimation is performed using two different analytical methods. The sensitivity analysis performed is based on the methodology of the Monte-Carlo method. The analysis is carried out using the polynomial decomposition and multi-dimensional linear regression. The sample results obtained are presented in diagrams and pie charts showing the sensitivity of load capacity to different random input variables (material properties and geometrical parameters). The variance-based analysis (Anova) of lower-bound and upper-bound load capacity estimation is carried out, from which some conclusions are derived, if (and how) assumed changes in standard deviations of input variables influence the magnitude of the load capacity and differences in upper-bound and lower-bound load capacity estimations. The results of Anova tests are shown in sample histograms. Some final conclusions concerning the efficiency of the applied models and the statistically significant influence of input random variables (yield stress, wall thickness, height and length of the beam) upon the upper-bound and lower bound estimation of the load capacity as well as the difference of these two estimations, are presented.

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Load capacity probabilistic sensitivity analysis of thin walled beams

Sensitivity analysis of critical loads of I-columns

The sensitivity analysis of the critical load of torsional buckling of thin-walled I-columns resting on a Winkler-type elastic foundation is presented. The column behaviour is described according to the theory of a thin-walled beam with non-deformable cross-section. The first-order variation of the critical load due to the design variable variations is derived. The cross-section dimensions, except for the web height, the column material constants and the foundation stiffness, are assumed to be the design variables. The single eigenvalues are only discussed. Finally, a numerical example dealing with a simply supported I-column is presented. The accuracy of the approximation of the critical load change, caused by the design variable variations by means of its first-order variation, is also investigated.

Czesa̵w Szymczak

Papers

Sensitivity analysis of critical torsional buckling load of thin-walled I-columns resting on elastic foundation