Sectional Shape Functions for a Box Beam Under Extension

In this chapter, we will derive the sectional shape functions for a box beam subjected to an extensional (or axial) load using a recursive and hierarchical method similar to that used to derive sectional shape functions for a box beam under torsion, as presented in Chaps. 4 and 5. In this chapter, the shape functions (ψzW, ψsχ) corresponding to the wall-membrane field and those (ψnχ, ψnη¯, ψnη^ ) corresponding to the wall-bending field will be derived altogether. Although the applied load type considered in this chapter differs from the torsional loads considered in Chaps. 4 and 5, the characteristics of the sectional shape functions derived for extensional loads are identical to those derived for torsional loads. Therefore, the derivation procedures for both sets of shape functions are nearly identical. Accordingly, we will not present the details of the procedure used to derive the shape functions needed to deal with extensional loads.