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Shear stress on a curved surface

Shear stress on a curved surface

Shear stress on a curved surface

(OP)
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?

RE: Shear stress on a curved surface

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

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