Full Yielding Torque For Hollow Shaft Calculator

Formula Used:

\[ T_f = \frac{2}{3} \pi r_2^3 \tau_0 \left(1 - \left(\frac{r_1}{r_2}\right)^3\right) \]

Outer Radius of Shaft (r₂):

Yield Stress in Shear (τ₀):

Inner Radius of Shaft (r₁):

Full Yielding Torque (T_f):

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1. What is Full Yielding Torque For Hollow Shaft?

Full Yielding Torque occurs when the torque is further increased beyond the elasto-plastic range, and the shaft will yield to the full depth of the cross section. It represents the maximum torque a hollow shaft can withstand before complete yielding.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_f = \frac{2}{3} \pi r_2^3 \tau_0 \left(1 - \left(\frac{r_1}{r_2}\right)^3\right) \]

Where:

\( T_f \) — Full Yielding Torque (N·m)
\( r_2 \) — Outer Radius of Shaft (m)
\( \tau_0 \) — Yield Stress in Shear (Pa)
\( r_1 \) — Inner Radius of Shaft (m)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the torque at which a hollow shaft completely yields, considering both the outer and inner radii and the material's yield stress in shear.

3. Importance of Full Yielding Torque Calculation

Details: Calculating the full yielding torque is crucial for designing safe and efficient hollow shafts in mechanical systems. It helps engineers determine the maximum torque capacity and prevent structural failure in applications such as automotive driveshafts, industrial machinery, and aerospace components.

4. Using the Calculator

Tips: Enter the outer radius and inner radius in meters, and yield stress in shear in Pascals. Ensure the inner radius is smaller than the outer radius, and all values are positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between yielding torque and ultimate torque?
A: Yielding torque is when the material begins to deform plastically, while ultimate torque is the maximum torque before fracture.

Q2: How does hollow shaft design affect torque capacity?
A: Hollow shafts can provide similar torque capacity with less weight compared to solid shafts, making them efficient for many applications.

Q3: What factors influence yield stress in shear?
A: Material composition, heat treatment, and manufacturing processes significantly affect the yield stress in shear.

Q4: Can this formula be used for solid shafts?
A: Yes, for solid shafts, set the inner radius (r₁) to zero, and the formula simplifies accordingly.

Q5: What safety factors should be considered in design?
A: Engineering designs typically incorporate safety factors to ensure the actual operating torque remains well below the full yielding torque.