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Abstract

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].
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Abstract

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 bisymmetric cross-section are shown in this paper. Conformity with other models from referenced literature is also shown.
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