The analytical approach is used for checking the stability of laterally unrestrained bisymmetric beams.The stability equations for simply supported beams are solved approximately using the Bubnov-Galerkin method [4]. The lateral buckling moment depends on bending distribution and on the load height effect. Each of applied concentrated and distributed loads, may have arbitrary direction and optional coordinate for the applied force along the cross section's height. Derived equations allow for simple, yet fast control of lateral buckling moment estimated by FEM [15].

Deriving the formulas for strain components, we are assuming, that cross-section of a rod being rotated in space during deformation does not need to be perpendicular to deformed centroid line. This not a quite intuitive assumption allows for more compact and easier formulas for strain tensor or equilibrium equations. Derived transformations between actual and initial coordinate system, components of strain tensor and virtual works principle for investigated spatially curved beams of bisym metric cross-section are shown in Ibis paper.Conformity with other models fi·om referenced literature is also shown.

The paper presents a computational analysis of the effect constructional details of coped connections, assumed to be a fork support in calculations, on the critical LTB moment values. On the basis of analytical formulas by Lindner [1], a formula, having a simple form, was derived for the reduction factor rn for the critical LTB moment. The parameters for the formula were presented in a tabular form, taking into account the beam section (IPE/HEA), the type of beam to end-plate connection (Types 1-3), the load type (q / P) and the way the load is applied (top / bottom flange). The correctness of the derived formula was validated on the basis of the analytical results and the Finite Element Method results obtained with the Abaqus/CAE software. In the program, the beam geometric dimensions and connections were represented as volumetric finite elements. Additionally, the dimensions of the end-plate for IPE and HEA section series were arranged in a systematic manner following the British catalogue.

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