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------------------------------------------------ Using an allowable shearing stress of 6.2 ksi, design a solid steel shaft to transmit 12 hp at a speed of 1200 rpm.

Hint: Calculate torque first, then use the stress equation to calculate the radius.

a) 1.64 inches
b) 2.05 inches
c) 3.12 inches
d) 4.28 inches

Correct option is A) To design a solid steel shaft to transmit power, first calculate torque and then determine the radius using the allowable shearing stress. The correct answer among the options provided is 1.64 inches.

Explanation:

The torque can be calculated first to design the solid steel shaft to transmit power. Given the power and speed, torque can be found using the formula: Torque (lb-ft) = (Power (hp) * 5252) / Speed (rpm). Next, the radius of the shaft can be determined using the allowable shearing stress and the torque. The stress equation is Shear Stress = (Torque * radius) / (Polar Moment of Inertia), where the Polar Moment of Inertia for a solid shaft is (pi * radius^4) / 2.

By calculating the torque and then rearranging the stress equation to solve for the radius, the correct radius for the solid steel shaft should be 1.64 inches (Option a).