A hollow steel (G = 77.5 GPa) torsion bar has a circular cross section with outer diameter...

A hollow steel (G = 77.5 GPa) torsion bar has a circular cross section with outer diameter of 55 mm, inner diameter of 45 mm. and wall thickness t. The mean diameter is D = 50 mm and t/D = 0.10. The length of the bar is 1.50 m. The shear stress at the mean diameter is τ = 40 MPa. Determine the applied torque and the angle of twist of one end relative to the other end

a. by means of Eqs. 6.66 and 6.67

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b. by elasticity theory.

 (6.66)

 (6.67)