A tapered bar AB of solid circular cross section is twisted by torques T = 36,000 lb-in. (see figure). The diameter of the bar varies linearly from dA at the left-hand end to dB at the right-hand end. The bar has length L = 4.0 ft and is made of an aluminum alloy having shear modulus of elasticity G = 3.9 ( 106 psi. The allowable shear stress in the bar is 15,000 psi and the allowable angle of twist is 3.0°.
If the diameter at end B is 1.5 times the diameter at end A, what is the minimum required diameter dA at end A? (Hint: Use the results of Example 3-5).