A circular shaft with a keyway can be approximated by the section shown in the following figure. The keyway is represented by the boundary equation r = b, while the shaft has the boundary relation r = 2a cos θ. Using the technique of Section 9.4, a trial stress function is suggested of the form:

where K is a constant to be determined. Show that this form will solve the problem and determine the constant K. Compute the two shear stress components τ,_xz andτ,_yz.

Transcribed Image Text:

4 = K (b 1) ( 2a cos 0 r