Theory of Composite Arches and Beams

A first-order-shear-deformation-theories formulation is presented to model composite beams with variable curvature in curvilinear coordinates, considering general and classic Timoshenko-theory-based approaches for planar arches. The governing equations are derived from those associated with the rectangular plate and with singly-curved translational shells. In particular, the two-dimensional shell structure is condensed along its depth, and therefore the number of variables is reduced. The first-order kinematic model is established with unified formulation, and classical theories are also derived. Finally, the fundamental equations for a straight beam are obtained by removing the curvature effects.