Direct approach to elastic deformations and stability of thin-walled rods of open profile

A new geometrically nonlinear theory of thin-walled rods of open profile accounting for warping and bi-moment is developed. The direct approach we employ is based on the principles of Lagrangean mechanics. Linear equations for small deformations in the vicinity of a pre-stressed state are derived. These equations can be used in particular for stability analysis. Stability of a beam subjected to axial or transversal loading is considered as an example. Solutions with coupled bending and twisting mode of buckling are compared with the classical Euler's solution, existing results for thin-walled rods and numerical solutions for a shell model.