Calculating Torsional Shear Stress in a Solid Circular Shaft

How to compute the torsional shear stress in a solid circular shaft with specific parameters?

Answer:

The torsional shear stress in a solid circular shaft that is transmitting 110 hp at a speed of 560 rpm with a diameter of 1.25 in is approximately 5085 psi.

Understanding Torsional Shear Stress Calculation

Torsional shear stress is a critical consideration in designing components that transmit rotational power, such as shafts.

Formula for Torsional Shear Stress:

The formula to calculate torsional shear stress (τ) in a solid circular shaft is τ = T*r / J.

  • T: Torque
  • r: Radius of the shaft
  • J: Polar moment of inertia of the shaft

Calculation Steps:

  1. Step 1: Calculate the torque (T) using T = 63,025*HP/n.
  2. Step 2: Determine the polar moment of inertia (J) using the formula J = π*(d^4)/32.
  3. Step 3: Substitute the values of T, r, and J into the shear stress formula τ = T*r / J.

By performing the calculations based on the given data:

  • Torque (T) = 1,246.39 lb-in
  • Polar moment of inertia (J) = 0.153 in^4

Substituting these values yields a torsional shear stress of approximately 5085 psi in the solid circular shaft.

Conclusion:

Understanding and accurately calculating torsional shear stress is crucial for ensuring the structural integrity and performance of mechanical components subjected to torque.

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