The study presents the results of theoretical investigations into lateral torsional buckling (LTB) of bi-symmetric I-beams, elastically restrained against warping at supports. Beam loading schemes commonly used in practice are taken into account. The whole range of stiffness of the support joints, from free warping to warping fully restrained, is considered. To determine the critical moment, the energy method is used. The function of the beam twist angle is described with power polynomials that have simple physical interpretation. Computer programs written in symbolic language for numerical analysis are developed. General approximation formulas are devised.Detailed calculations are performed for beams with end-plate joints. Critical moments determined with programs and approximation formulas are compared with the results obtained by other researchers and with those produced by FEM. Very good accuracy of results is obtained.

The study shows the results of theoretical investigations into lateral torsional buckling of bisymmetric I-beams elastically restrained against warping and against rotation in the plane of lateral torsional buckling (i.e., against lateral rotation) at the support nodes. The analysis accounted for the whole variation range of node stiffnesses, from complete warping freedom to full restraint, and from complete lateral rotation freedom to full restraint. It was assumed the beams are simply supported against bending about the major axis of the section. To determine the critical moment, the energy method was used. Both the twist angle function and the lateral deflection function of the beam were described using power polynomials with simple physical interpretation. Computer programmes were developed to make numerical and symbolic “computations”. General approximation formulas for the critical moment for lateral torsional buckling were derived. The formulas covered the basic and most frequently found loading diagrams. Detailed computations were performed for different values of the index of fixity against warping and against rotation in the plane of lateral torsional buckling. The critical moments determined using the programmes devised and approximation formulas were compared with the values obtained with LTBeam software (FEM). A very good congruence of results was found.

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1Thin-walled bars currently applied in metal construction engineering belong to a group of members, the cross section res i stance of which is affected by the phenomena of I ocal or distortional stability loss. This results from the fact that the cross-section of such a bar consists of slender-plate elements. The study presents the method of calculating the res i stance of the cross-section susceptible to local bucki ing which is based on the loss of stability of the weakest plate (wali). The "Critical Plate" (CP) was identified by comparing critical stress in cross-section component plates under a given stress condition. Then, the CP showing the lowest critical stress was modelled, depending on boundary conditions, as an interna( or cantilever element elastically restrained in the restraining plate (RP). Longitudinal stress distribution was accounted for by means of a constant, linear or non-linear (acc. the second degree parabola) fu nction. For the critical buckling stress, as calculated above, the ]ocal critical resistance of the cross-section was determined, which sets a limit on the validity of the Vlasov theory. In order to determine the design ultimate resistance of the cross-section, the effective width theory was applied, while taking inio consideration the assumptions specified in the study. The application of the Critical Plate Method (CPM) was presented in the examples. Analytical calculation results were compared with selected experimental f i ndings.lt was demonstraled that taking into consideration the CP elastic restrainl and longitudinal stress variation results in amore accurate representation ofthin-walled element behaviour in the engineering computational model.

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