(Solved): A circular shaft with a keyway can be approximated by the section shown. The ...

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A circular shaft with a keyway can be approximated by the section shown. The keyway is represented by the boundary equation \( r=\mathrm{b} \) while the shaft has a boundary relation \( r=2 a \cos \theta \). (a) Suggest a stress function for the problem and find stresses \( \tau_{\mathrm{xz}} \) and \( \tau_{\mathrm{zy}} \). (b) Find stress components at the point with coordinates of \( r=b \) and \( \theta=0 \). (Note the fundamental property of stress function is its vanishing magnitude along the boundary.)