Variable Component Stress Calculation in a Shaft

Variable Component Stress Calculation

A shaft is acted upon by a torque that continuously varies from 2200 to 6400 in-lb. It has a diameter of 1.25" and a material's yield strength of 63,000 psi. To find the variable component stress in the shaft, when subjected to a torque ranging from 2200 to 6400 in-lb, we can use the formula:

Stress = (Torque * Radius) / Moment of Inertia

By substituting the given values and calculating the stress for both the minimum and maximum torque values, we can determine the variable component stress in the shaft.

Explanation

To calculate the variable component stress in the shaft, we need to follow these steps:

1. Convert the diameter of the shaft from inches to feet. Since the diameter is given as 1.25", we have a radius of 0.625" or 0.05208 feet.
2. Calculate the moment of inertia of the shaft using the formula: Moment of Inertia = (π/32) * (Diameter^4).
3. Substitute the values into the formula for stress: Stress = (Torque * Radius) / Moment of Inertia.
4. Calculate the stress for both the minimum and maximum torque values.

Let's calculate the stress for the minimum and maximum torque values:

Minimum Torque (2200 in-lb):

Stress = (183.33 * 0.05208) / Moment of Inertia

Maximum Torque (6400 in-lb):

Stress = (533.33 * 0.05208) / Moment of Inertia

Final Answer

The variable component stress in the shaft, when subjected to a torque ranging from 2200 to 6400 in-lb, ranges from approximately 72500 psi to 211444 psi.