Maximum Shear Stress At Outer Surface Given Diameter Of Shaft On Hollow Circular Shaft Calculator

Formula Used:

\[ \tau_{max} = \frac{16 \times d_{outer} \times T}{\pi \times (d_{outer}^4 - d_{inner}^4)} \]

Maximum Shear Stress on Shaft:

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1. What is Maximum Shear Stress on Shaft?

Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces. It represents the highest shear stress value experienced by the shaft material under torsional loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau_{max} = \frac{16 \times d_{outer} \times T}{\pi \times (d_{outer}^4 - d_{inner}^4)} \]

Where:

\( \tau_{max} \) — Maximum Shear Stress on Shaft (Pa)
\( d_{outer} \) — Outer Diameter of Shaft (m)
\( T \) — Turning Moment (N·m)
\( d_{inner} \) — Inner Diameter of Shaft (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the maximum shear stress at the outer surface of a hollow circular shaft subjected to torsional loading, considering both the outer and inner diameters.

3. Importance of Maximum Shear Stress Calculation

Details: Accurate calculation of maximum shear stress is crucial for shaft design, material selection, and ensuring structural integrity under torsional loads. It helps prevent shaft failure and ensures safe operation of mechanical systems.

4. Using the Calculator

Tips: Enter outer diameter and inner diameter in meters, turning moment in Newton-meters. All values must be valid (outer diameter > 0, turning moment > 0, inner diameter ≥ 0 and less than outer diameter).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the hollow shaft design?
A: Hollow shafts provide better strength-to-weight ratio compared to solid shafts, making them more efficient for many engineering applications while reducing material usage.

Q2: How does inner diameter affect maximum shear stress?
A: Increasing the inner diameter (making the shaft wall thinner) generally increases the maximum shear stress for the same applied torque, as there's less material to resist the torsional forces.

Q3: What are typical units for these calculations?
A: Diameters are typically in meters (m), turning moment in Newton-meters (N·m), and the resulting shear stress in Pascals (Pa).

Q4: When is this formula applicable?
A: This formula applies to hollow circular shafts made of homogeneous, isotropic materials experiencing pure torsion within the elastic range.

Q5: How does this compare to solid shaft calculations?
A: For solid shafts, set inner diameter to zero. The formula simplifies to \( \tau_{max} = \frac{16T}{\pi d^3} \) for solid circular shafts.