Stresses and rate of twist in single-cell thin-walled beams with anisotropic walls

The classical theory of elastic thin-walled beams of (assumedly) nondeformable cross section, familiar to aerospace structures engineers, is generalized to the case in which the walls are anisotropic. The assumed anisotropy is such as to allow coupling between cross-sectional shear flow and longitudinal strain and, reciprocally, between shear strain and longitudinal stress. The theory and several illustrative applications show that anisotropy of the walls can, as expected, lead to coupling phenomena not present in the classical theory, e.g., twist due to bending mements, bending due to torque, twist due to tension, and extension due to torque, thus confirming the well-known possibility of tailoring elastic behavior through the use of laminated composites. It is also shown that anisotropy of the walls can lead to a nonconstant rate of twist in uniform beams even if the cross-sectional torque and shears are constant. Another interesting outcome of the present theory is its prediction that the shear flows are independent of the coupling constant in the constitutive equations, i.e., the constant that defines the longitudinal strain due to shear flow and the shear strain due to longitudinal stress, and also independent of the elastic constant relating shear strain to shear flow.