Outer Diameter Of Hollow Shaft Given Bending Stress Of Hollow Shaft Calculator

Formula Used:

\[ d_o = \left( \frac{32 \cdot M_{b_h}}{\pi \cdot \sigma_{b_h} \cdot (1 - C^4)} \right)^{1/3} \]

Bending Moment in Hollow Shaft (M_{b_h}):

N·m

Bending Stress in Hollow Shaft (σ_{b_h}):

Ratio of Inner to Outer Diameter (C):

(dimensionless)

Outer Diameter of Hollow Shaft (d_o):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Outer Diameter of Hollow Shaft Calculation?

This calculation determines the outer diameter of a hollow shaft required to withstand a given bending moment while keeping the bending stress within acceptable limits, considering the ratio of inner to outer diameter.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_o = \left( \frac{32 \cdot M_{b_h}}{\pi \cdot \sigma_{b_h} \cdot (1 - C^4)} \right)^{1/3} \]

Where:

\( d_o \) — Outer diameter of hollow shaft (m)
\( M_{b_h} \) — Bending moment in hollow shaft (N·m)
\( \sigma_{b_h} \) — Bending stress in hollow shaft (Pa)
\( C \) — Ratio of inner to outer diameter of hollow shaft
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: This formula derives from the bending stress equation for hollow circular shafts, considering the moment of inertia for hollow sections.

3. Importance of Outer Diameter Calculation

Details: Accurate calculation of outer diameter is crucial for designing hollow shafts that can withstand specified bending loads while maintaining structural integrity and minimizing material usage.

4. Using the Calculator

Tips: Enter bending moment in N·m, bending stress in Pa, and the diameter ratio (0 ≤ C < 1). All values must be positive, and the ratio must be less than 1.

5. Frequently Asked Questions (FAQ)

Q1: Why is the ratio C limited to values less than 1?
A: The inner diameter cannot exceed the outer diameter, so C must be between 0 (solid shaft) and values approaching 1 (very thin-walled shaft).

Q2: What are typical values for bending stress in shaft design?
A: Bending stress limits depend on the material. For steel shafts, typical allowable bending stresses range from 50-200 MPa, depending on the application and safety factors.

Q3: How does hollow shaft design compare to solid shaft design?
A: Hollow shafts provide better strength-to-weight ratio, reducing material usage while maintaining similar bending strength compared to solid shafts.

Q4: What are the limitations of this formula?
A: This formula assumes pure bending, homogeneous material, and circular cross-section. It may not account for combined loading, fatigue, or dynamic effects.

Q5: Can this calculator be used for other cross-sectional shapes?
A: No, this formula is specifically derived for hollow circular shafts. Other shapes require different bending stress equations.