For the keyway section of Exercise 9.23, show that resultant stresses on the shaft and keyway boundaries are given by:

Determine the maximum values of these stresses, and show that for b the maximum keyway stress is approximately twice that of the shaft stress. Finally, make a plot
of the stress concentration factor:

versus the ratio b/a over the range 0 ≤ b=a ≤1: Note that τ,_{max(solid shaft)} is the maximum shear
stress for solid shaft of circular section and can be determined from Example 9.1 or strength of
materials theory. Show that the stress concentration plot gives:

Data from exercise 9.23

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.

Data from example

Transcribed Image Text:

Tage = yeona (2004-1), shaft paa cos Tkeyway = a(2a cos 0 - b)