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torsion slit

Torsion of annular rod with longitudinal slit

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I have a question regarding simple torsion of a circular shaft with a uniform cross section. Given a hollow circular shaft with inner radius R1 and outer radius R2, length L, shear modulus G, fixed-free boundary conditions and applied torque T about the central axis, the equation for the rotation angle at the end of the beam is

 phi = T*L/(J*G)

where J = pi/4*(R2^4-R1^4)

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