ABSTRACT
For boundary conditions, assume that the lateral boundaries of the member are unloaded. The stress-traction relation already implies that τx=0 and τy=0 on the lateral boundary S. For traction τz to vanish, we require that
τz=nxSxz+nySyz=0 on S. (14.8)
Upon examining Figure 14.2, it can be seen that nx=dy/ds and ny=−dx/ds, in which s is the arc length along the boundary at z. Consequently,
(14.9)
Now, on and therefore ψ is a constant, which can, in general, be taken as zero. We next consider the total torque on the member. Figure 14.3 depicts the cross section
at z. The torque on the element at x and y is given by
