Diameter Of Shaft Given Bending Stress Pure Bending Calculator

Formula Used:

\[ d = \left( \frac{32 \cdot M_b}{\pi \cdot \sigma_b} \right)^{1/3} \]

Diameter of Shaft on Strength Basis (d):

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1. What is the Diameter of Shaft Given Bending Stress Pure Bending?

This calculator determines the required diameter of a shaft based on bending stress under pure bending conditions. It ensures the shaft can withstand applied bending moments without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d = \left( \frac{32 \cdot M_b}{\pi \cdot \sigma_b} \right)^{1/3} \]

Where:

\( d \) — Diameter of shaft (m)
\( M_b \) — Bending moment (N·m)
\( \sigma_b \) — Bending stress (Pa)
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: The formula calculates the minimum shaft diameter required to withstand a given bending moment while keeping the bending stress within acceptable limits.

3. Importance of Shaft Diameter Calculation

Details: Proper shaft sizing is crucial for mechanical design to ensure structural integrity, prevent failure, and optimize material usage in rotating machinery and transmission systems.

4. Using the Calculator

Tips: Enter bending moment in N·m and bending stress in Pa. Both values must be positive numbers. The calculator will compute the required shaft diameter in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is pure bending?
A: Pure bending occurs when a structural element is subjected to bending moments only, without any axial or torsional loads.

Q2: What are typical bending stress values for shaft materials?
A: Bending stress limits vary by material. Common values range from 50-200 MPa for steel shafts, depending on the specific alloy and safety factors.

Q3: Does this formula account for safety factors?
A: No, this formula calculates the theoretical minimum diameter. Engineers should apply appropriate safety factors based on application requirements.

Q4: Can this be used for hollow shafts?
A: No, this formula is specifically for solid circular shafts. Different formulas apply for hollow shafts or other cross-sections.

Q5: What if the shaft experiences combined loading?
A: For shafts under combined bending and torsion, more complex formulas (like the maximum shear stress theory or distortion energy theory) should be used.