(Solved): Question 2, 8-31 [20] A grooved shaft like the one shown below is machined from steel of 180Bhn an ...

Question 2, 8-31 [20] A grooved shaft like the one shown below is machined from steel of $$180\mathrm{Bhn}$$ and $${\mathrm{S}}_{\mathrm{y}}=65\mathrm{ksi}$$. Dimensions are $$D=1.1$$ in., $$d=1.0$$ in., and $$r=0.05$$ in. A commercial polish is given only to the surface of the groove. With a safety factor of 2, estimate the maximum value of torque $$T$$ that can be applied for infinite life when the fluctuating torsional load consist of (a) Completely reversed torsion, with the torque varying between $$+T$$ and $$?T$$, (b) A steady torque of $$\mathrm{T}$$ with superimposed alternating torque of $$2\mathrm{T}$$.