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:
- Step 1: Calculate the torque (T) using T = 63,025*HP/n.
- Step 2: Determine the polar moment of inertia (J) using the formula J = π*(d^4)/32.
- 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.