Question: A hollow circular tube A (outer diameter dA, wall thickness tA) fits over the end of a circular tube B (dB, tB), as shown in

A hollow circular tube A (outer diameter dA, wall thickness tA) fits over the end of a circular tube B (dB, tB), as shown in the figure. The far ends of both tubes are fixed. Initially, a hole through tube B makes an angle ( with a line through two holes in tube A. Then tube B is twisted until the holes are aligned, and a pin (diameter dp) is placed through the holes. When tube B is released, the system returns to equilibrium. Assume that G is constant.
(a) Use superposition to find the reactive torques TA and TB at the supports.
(b) Find an expression for the maximum value of ( if the shear stress in the pin, Tp, cannot exceed Tp,allow.
(c) Find an expression for the maximum value of ( if the shear stress in the tubes, Tt, cannot exceed Tt,allow.
(d) Find an expression for the maximum value of if the bearing stress in the pin at C cannot exceed Tb,allow.

PA T, TB Tube B Pin,at C Tube A Tube B Cross-section at C

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