Theory of anisotropic thin-walled beams

Asymptotically correct, linear theory is presented for thin-walled prismati c beams made of generally anisotropic materials. Consistent used of small p arameters that are intrinsic to the problem permits a natural description o f all thin-walled beams within a common framework, regardless of whether cr oss-sectional geometry is open, closed, or strip-like, Four "classical" one -dimensional variables associated with extension, twist, and bending in two orthogonal directions are employed. Analytical formulas are obtained for t he resulting 4 X 4 cross-sectional stiffness matrix (which, in general, is fully populated and includes all elastic couplings) as well as for the stra in field, Prior to this work no analytical theories for beams with closed c ross sections were able to consistently include shell bending strain measur es. Corrections stemming from those measures are shown to be important for certain cases. Contrary to widespread belief, it is demonstrated that for s uch "classical" theories, a cross section is not rigid in its own plane. Vl asov's correction is shown to be unimportant for closed sections, while for open cross sections asymptotically correct formulas for this effect are pr ovided. The latter result is an extension to a general contour of a result for I-beams previously published by the authors.