Calculator Inputs
Formula Used
For a hollow circular section, the second moment of area is:
I = π/64 × (D4 − d4)
The elastic section modulus is:
Z = I / (D/2) = π × (D4 − d4) / (32D)
For a solid circular section, set d = 0. Bending stress is estimated from σ = M / Z.
How to Use This Calculator
- Select hollow pipe or solid circular bar.
- Choose the geometry input method and preferred units.
- Enter outer diameter and either inner diameter or wall thickness.
- Add a bending moment to estimate elastic bending stress.
- Enter allowable stress to evaluate moment capacity and safety factor.
- Press Calculate to show results above the form and graph below.
Example Data Table
| Case | Outer Diameter (mm) | Inner Diameter (mm) | Section Modulus (mm³) | Moment of Inertia (mm⁴) |
|---|---|---|---|---|
| Light pipe | 114.3 | 102.3 | 52,530.46 | 3,002,115.96 |
| Medium pipe | 168.3 | 154.1 | 139,059.58 | 11,701,863.63 |
| Heavy pipe | 219.1 | 193.7 | 401,810.67 | 44,018,358.97 |
FAQs
1. What does pipe section modulus measure?
It measures elastic bending strength for a cross-section. A larger section modulus means lower bending stress for the same applied moment.
2. Is section modulus the same as moment of inertia?
No. Moment of inertia describes stiffness against bending, while section modulus converts that geometry into bending stress capacity at the outer fiber.
3. Can I use wall thickness instead of inner diameter?
Yes. This calculator supports both entry styles. It converts wall thickness into inner diameter automatically for hollow sections.
4. What formula is used for a hollow pipe?
The calculator uses I = π/64 × (D⁴ − d⁴) and Z = I ÷ (D/2). These formulas apply to circular hollow sections.
5. Why does bending stress decrease with larger diameter?
Increasing outer diameter raises section modulus sharply because diameter is raised to the fourth power in inertia calculations. That reduces stress for the same moment.
6. What is the D/t ratio shown in results?
D/t compares outer diameter with wall thickness. It helps describe whether the pipe behaves more like a thick or thin-walled member.
7. Does this calculator handle solid circular bars?
Yes. Choose the solid option and the tool sets inner diameter to zero. The same bending relationships then apply to the solid section.
8. Can I export the results for reports?
Yes. Use the CSV button for spreadsheet work or the PDF button for a formatted report snapshot of the calculated values.