Theory and Application of Naturally Curved and Twisted Beams with Closed Thin-Walled Cross Sections

A novel theory for analyzing naturally curved and twisted beams with closed thin-walled cross sections is presented based on the small displacement theory. By introducing the eigenwarping functions and expanding axial displacements or axial stress distribution in a series of eigenwarpings, the differential equation for determining generalized warping coordinate and the expression for eigenvalues call be derived from the principle of minimum potential energy. In the derivation procedure, the effects of the initial torsion and small initial curvature of the beams arc, accurately taken into account. The non-classical influences relevant to the beams are transverse shear and torsion-related warping deformations. Improved solutions call be obtained by adding a series expansion in terms of eigenwarpings to the uncorrected solution. The present theory is used to investigate the stresses and displacements of a cantilevered, rectangular box curved beam subjected to a uniformly distributed load. It is observed that the numerical results obtained agree well with the data from FEM. (C) 2009 Journal of Mechanical Engineering. All rights reserved.