TABLE OF CONTENTS In the previous section, thin-walled beams that can be constructed from an assembly of thin strips were analyzed. In this section, a more general approach is presented, and an asymptotically correct, linear theory for thin-walled prismatic beams made of generally anisotropic materials is derived. So, rather than focusing on I-beams as the previous section, here we make consistent use of small parameters that are intrinsic to the problem. This permits a natural description of all thin-walled beams within a common framework, regardless of whether the crosssectional geometry is open, closed, or strip-like. The four classical one-dimensional variables associated with extension, twist, and bending in two orthogonal directions are again employed. Analytical formulae are obtained for the resulting 4 4 cross-sectional stiffness matrix, which is in general fully populated and includes all elastic couplings, as well as for the strain field. Moreover, results of this theory are contained in closed-form expressions for the stiffness matrices of single- and double-celled composite thin-walled beams. The procedure is outlined for dealing with multi-celled composite beams. Finally, the importance of the approach s generality is demonstrated by several examples.
Prior to this work there were no analytical theories for beams with closed crosssections that consistently included the effects of shell bending strain measures. Corrections stemming from those measures are shown in Sec. II.E, this chapter, to be important for certain closed-cell configurations. Contrary to widespread belief, it is demonstrated that for such classical theories a cross-section is not rigid...
