Sectional Shape Functions for a Box Beam Under Flexure

The sectional shape functions of a box beam subjected to a flexural load are derived in this chapter using a procedure similar to that presented in Chaps. 4–6. (Other approaches may be found in Ferradi and Cespedes (2014) and Bebiano et al. (2015)). As in the cases for torsional or extensional loads, three types of deformable section modes are considered in addition to rigid-body section modes: (1) warping modes {Wk}k=1,2,…, (2) unconstrained distortion modes {χk}k=1,2,…, and (3) constrained distortion modes {η¯k,η^k}k=1,2,…. The warping mode W_k has the z-directional shape function ψzWk(s) only, which depicts the wall-membrane deformations of a beam section. On the other hand, the unconstrained distortion mode χ_k has both the s-directional shape function ψsχk(s) representing wall-membrane deformation and the n-directional shape function ψnχk(s) representing wall-bending deformation. The constrained distortional modes η¯_k and η^_k have only the n-directional shape functions ψnη¯k(s) and ψnη^k(s), respectively, representing wall-bending deformations. The shape functions ψsχk(s) and ψzWk(s) representing wall-membrane deformations are derived in Sect. 7.2 while ψnχk(s), ψnη¯k(s) and ψnη^k(s) representing wall-bending deformations are derived in Sects. 7.3–7.5. Section 7.6 presents numerical results using the derived modes.