Shear stress on a curved surface 1

[itsdark]

Hi everyone,
I am trying to find an analytical approach to determine the shear stress induced on a curved surface. I had originally applied simple shear theory for beams but the shear stress distribution will not be uniform for a curved surface. More specifically I am trying to work out the shear stress at various points on a involute spline tooth but need alternative approaches to those addressed in the machinery handbook. Is anyone able to help at all?

 

[dinjin]

I do not see why the theory of stress for roller bearings cannot be applied to your problems.