Page 66 - Aircraft Stuctures for Engineering Student

Torsion of solid sections

The elasticity solution of the torsion problem for bars of arbitrary but uniform cross-
section is accomplished by the semi-inverse method (Section 2.3) in which assump-
tions are made regarding either stress or displacement components. The former
method owes its derivation to Prandtl, the latter to St. Venant. Both methods are
presented in this chapter, together with the useful membrane analogy introduced
by Prandtl.

Consider the straight bar of uniform cross-section shown in Fig. 3.1. It is subjected to
equal but opposite torques T at each end, both of which are assumed to be free from
restraint so that warping displacements w, that is displacements of cross-sections
normal to and out of their original planes, are unrestrained. Further, we make the
reasonable assumptions that since no direct loads are applied to the bar
a, = a), = az = 0

Fig. 3.1 Torsion of a bar of uniform, arbitrary cross-section.