Beam Bending Stress Calculator Form
Overall page sections remain in a single vertical stack. The input area below uses a responsive three, two, and one column grid.
Formula Used
The calculator uses the flexure formula σ = M × c / I = M / S,
where σ is bending stress, M is maximum bending moment,
c is extreme fiber distance, I is second moment of area,
and S is section modulus.
- Simply supported, center point load:
M = P × L / 4 - Simply supported, point load at distance:
M = P × a × (L - a) / L - Simply supported, full span UDL:
M = w × L² / 8 - Cantilever, end point load:
M = P × L - Cantilever, point load at distance:
M = P × a - Cantilever, full length UDL:
M = w × L² / 2 - Rectangular section:
I = b × h³ / 12,S = b × h² / 6 - Solid circular section:
I = π × d⁴ / 64,S = π × d³ / 32 - Hollow circular section:
I = π × (Do⁴ - Di⁴) / 64,S = I / (Do / 2) - Symmetric I section:
I = [Bf × H³ - (Bf - Tw) × (H - 2Tf)³] / 12 - Allowable stress:
σallow = fy / FS - Safety margin:
Margin = σallow - σ
Inputs are handled in kN, m, mm, and MPa so the resulting bending stress is reported directly in MPa.
How to Use This Calculator
- Select the beam load case that best matches your site condition.
- Enter span, point load, distance, uniform load, or custom moment as needed.
- Choose the section type and provide the matching dimensions in millimeters.
- Enter material yield strength and your intended factor of safety.
- Submit the form to view bending moment, stress, utilization, margin, and status.
- Review the Plotly stress graph to understand extreme fiber demand.
- Use the CSV and PDF buttons to export the current result summary.
- Compare your output with the example table below before final design checks.
Example Data Table
| Scenario | Inputs | Section | Mmax | Stress |
|---|---|---|---|---|
| Simply supported, center point load | L = 6 m, P = 20 kN | Rectangular 200 × 300 mm | 30.000 kN·m | 10.000 MPa |
| Simply supported, full span UDL | L = 5 m, w = 12 kN/m | Rectangular 150 × 300 mm | 37.500 kN·m | 16.667 MPa |
| Cantilever, end point load | L = 2.5 m, P = 8 kN | Solid circular d = 180 mm | 20.000 kN·m | 34.931 MPa |
| Cantilever, full length UDL | L = 3 m, w = 5 kN/m | I section H300, B150, Tf20, Tw10 | 22.500 kN·m | 25.482 MPa |
These examples help verify the setup. Actual project checks should still follow the relevant construction code and detailing requirements.
FAQs
1. What is beam bending stress?
Beam bending stress is the internal normal stress caused by bending moment. It is largest at the extreme fibers and zero at the neutral axis.
2. Which units does this calculator use?
The calculator uses beam loads in kN, beam length in meters, section dimensions in millimeters, and reports bending stress in MPa.
3. Why does section modulus matter?
Section modulus measures bending efficiency. A larger section modulus lowers bending stress for the same moment, which usually improves safety and performance.
4. When should I use custom moment input?
Use custom moment when maximum bending moment already comes from another structural analysis, code table, or frame model and you only need stress checking.
5. Does this calculator include shear, axial force, or deflection?
No. This page focuses on bending stress only. Shear stress, axial load effects, local buckling, bearing, and deflection should be checked separately.
6. Why can two beams carry the same load differently?
Support condition, load position, and section shape all affect maximum moment and section modulus. That changes the final bending stress result significantly.
7. What does the safety margin show?
Safety margin is allowable stress minus calculated stress. A positive margin means reserve capacity remains. A negative margin means the section is overstressed.
8. Can I use a custom section modulus from a manufacturer table?
Yes. Select the custom section modulus option, enter the tabulated modulus, add the overall depth, and the calculator will estimate bending stress.