Unified theory for analysis of curved thin-walled girders with open and closed cross section through HSA method

The behaviour of thin-walled structures is deeply influenced by non-uniform torsion and cross section distortion. In this paper the extension of the Hamiltonian Structural Analysis (HSA) Method to thin-walled straight and curved beams is presented. The proposed method solves the structural elastic problem of thin-walled beams through the definition of a Hamiltonian system composed of 1st order differential equations. The method allows engineers to solve the elastic problem by introducing the degrees of freedom and the corresponding compatibility equations, founding equilibrium equations in the variational form. The methodology is explained in the framework of the so-called Generalized Beam Theory, considering beams on elastic foundation and thin-walled structures with non-uniform torsion and distortion in a unified theory for open and closed cross section considering the shear deformability of the wall midline. The exact solution is found for straight and horizontally curved beams and distortion of box section is directly solved avoiding the analysis through the Beam on Elastic Foundation (BEF) analogy. Numerical applications are given in order to show the wide range of applicability of the proposed method and to validate it through comparisons with literature data.