$4-4$ An engineer is forced by geometric considerations to apply the torque on the spring

of Problem $4-3$ at the location $x=0\mathrm{.}4l.$ For a uniform$-$diameter spring, this would

cause one leg of the span to be underutilized when both legs have the same diameter.

For optimal design the diameter of each leg should be designed such that the maximum

shear stress in each leg is the same. This problem is to redesign the spring of part $($b$)$

of Problem $4-3.$ Using $x=0\mathrm{.}4l,l=10in,T=1500lbf*in,$ and $G=11\mathrm{.}5M,$

design the spring such that the maximum shear stresses in each leg are equal and the

spring has the same spring rate $($angle of twist$)$ as part $($b$)$ of Problem $4-3.$ Specify

$d_1,d_2,$ the spring rate $k,$ and the torque and the maximum shear stress in each leg.