Inner Diameter Of Hollow Circular Shape In Bending Stress Calculator

Formula Used:

\[ d_i = \left( d_o^4 - \frac{32 \times Z \times d_o}{\pi} \right)^{1/4} \]

Inner Diameter of Shaft (dᵢ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Inner Diameter Calculation Formula?

The formula calculates the inner diameter of a hollow circular shaft under bending stress, considering the outer diameter and section modulus. This is essential in mechanical engineering for designing shafts that can withstand bending moments.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_i = \left( d_o^4 - \frac{32 \times Z \times d_o}{\pi} \right)^{1/4} \]

Where:

\( d_i \) — Inner diameter of shaft (mm)
\( d_o \) — Outer diameter of shaft (mm)
\( Z \) — Section modulus (m³)
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: The formula derives from the relationship between bending stress, section modulus, and the geometric properties of a hollow circular cross-section.

3. Importance of Inner Diameter Calculation

Details: Accurate calculation of inner diameter is crucial for designing efficient and safe hollow shafts in various mechanical applications, ensuring proper strength-to-weight ratio and material optimization.

4. Using the Calculator

Tips: Enter outer diameter in millimeters, section modulus in cubic meters. Both values must be positive numbers. The calculator will compute the corresponding inner diameter.

5. Frequently Asked Questions (FAQ)

Q1: What is section modulus?
A: Section modulus is a geometric property that measures a cross-section's resistance to bending. It's calculated based on the shape and dimensions of the cross-section.

Q2: Why use hollow shafts instead of solid ones?
A: Hollow shafts provide better strength-to-weight ratio, reducing material usage while maintaining structural integrity, which is particularly important in rotating machinery.

Q3: What are typical applications of this calculation?
A: This calculation is used in designing drive shafts, axles, and other structural components in automotive, aerospace, and mechanical engineering applications.

Q4: Are there limitations to this formula?
A: This formula assumes uniform material properties, perfect circular geometry, and applies specifically to bending stress calculations for hollow circular sections.

Q5: How does inner diameter affect bending strength?
A: Increasing inner diameter (while maintaining outer diameter) reduces material and weight but also decreases bending strength. There's an optimal balance for each application.