Calculator Inputs
Example Data Table
| Case | OD (mm) | t (mm) | CLR (mm) | Moment (N·mm) | Pressure (MPa) | SIF | Bending Stress (MPa) | Von Mises (MPa) |
|---|---|---|---|---|---|---|---|---|
| Light utility line | 60.3 | 3.91 | 180 | 450000 | 1.2 | 1.10 | 53.95 | 54.46 |
| Process pipe bend | 114.3 | 6.02 | 457.2 | 1500000 | 2.5 | 1.15 | 32.75 | 38.10 |
| Heavier service bend | 168.3 | 7.11 | 650 | 3200000 | 4.0 | 1.20 | 27.58 | 47.99 |
These rows are sample engineering cases for comparison only. Final design checks should follow your project code, loading envelope, and fabrication rules.
Formula Used
M = F × L or use direct input moment
Di = Do − 2t
I = π/64 × (Do4 − Di4)
Z = I / (Do/2)
σb = SIF × M / Z
σax,p = P × Dm / 4t
σh = P × Dm / 2t
where Dm = Do − t
σax,total = σb + σax,p
σvm = √(σax,total2 + σh2 − σax,totalσh)
σallow = Yield Strength / Safety Factor
Utilization = σvm / σallow
Outer Fiber Strain = (Do/2) / R
How to Use This Calculator
- Choose whether your loading is entered as force and lever arm or as a direct bending moment.
- Enter outer diameter, wall thickness, and bend radius using consistent millimeter values.
- Provide internal pressure if pressure effects should be included. Leave it at zero when not needed.
- Enter the stress intensification factor if your fitting or bend geometry increases local stress.
- Fill in material properties: Young’s modulus, yield strength, and the design safety factor.
- Press Calculate Stress to show results above the form, download options, and the stress chart.
- Review utilization ratio and status first. Values above 1.0 indicate the case exceeds the selected allowable limit.
Frequently Asked Questions
1) What does this calculator estimate?
It estimates bending stress, pressure-related axial stress, hoop stress, von Mises stress, strain, allowable stress, and utilization for a bent pipe section.
2) Why is wall thickness important?
Wall thickness strongly affects the inner diameter, second moment of area, and section modulus. Thicker walls usually reduce bending stress for the same moment.
3) What is the stress intensification factor?
It adjusts nominal bending stress to reflect local geometric effects near bends, fittings, or discontinuities. A higher value increases calculated bending stress.
4) Why include internal pressure?
Pressure adds longitudinal and hoop stress. Those stresses can raise the equivalent stress level, even when bending alone looks acceptable.
5) What does utilization ratio mean?
Utilization is equivalent stress divided by allowable stress. A value below 1.0 is within the chosen allowable. Above 1.0 means the case exceeds it.
6) Is bend radius the same as pipe length?
No. Bend radius describes curvature of the bend centerline. Pipe length is the physical run length. Smaller bend radius usually increases strain demand.
7) Can I use direct moment instead of force?
Yes. Select the direct moment mode when the bending moment is already known from analysis, testing, or another structural model.
8) Is this enough for final code compliance?
No. It is a practical screening tool. Final acceptance should follow the project’s governing piping code, stress combination rules, load cases, and fabrication tolerances.