Calculated Results
Results appear here after submission and stay above the form for quick review.
Beam Input Form
Example Data Table
| Case | Section | Span | Load | Max Moment | Bending Stress | Von Mises | FoS at 250 MPa |
|---|---|---|---|---|---|---|---|
| Simply supported UDL | Rectangular 150 × 300 mm | 5.0 m | 12 kN/m + 20 kN axial | 37.50 kN·m | 16.67 MPa | 17.20 MPa | 14.53 |
| Simply supported point load | Solid circular 180 mm | 4.0 m | 40 kN center load | 40.00 kN·m | 69.86 MPa | 69.89 MPa | 3.58 |
| Cantilever point load | I-section 200/20/12/300 mm | 2.5 m | 18 kN end load | 45.00 kN·m | 38.65 MPa | 39.89 MPa | 6.27 |
Formula Used
Maximum moment and shear by load case
- Simply supported with center point load: M = PL / 4, V = P / 2
- Simply supported with full UDL: M = wL² / 8, V = wL / 2
- Cantilever with end point load: M = PL, V = P
- Cantilever with full UDL: M = wL² / 2, V = wL
- Custom mode accepts direct maximum moment and shear inputs.
Stress equations
- Bending stress: σb = M / Z = Mc / I
- Axial stress: σa = P / A
- Worst-case combined normal stress: σcombined = |σb| + |σa|
- Rectangular shear: τ = 1.5V / A
- Solid circular shear: τ = 4V / 3A
- I-section web shear at the neutral axis: τ = VQ / Itw
- Equivalent stress: σvm = √(σcombined² + 3τ²)
- Factor of safety: FoS = σy / σvm
A is area, I is second moment of area, Z is section modulus, c is extreme fiber distance, Q is first moment of area, and σy is yield strength.
How to Use This Calculator
- Choose the beam load case that best matches your structure.
- Select the section type or choose custom properties.
- Pick the length, force, load, and stress output units.
- Enter span and load details, or enter custom moment and shear.
- Add section dimensions, axial force, and optional material yield strength.
- Press Calculate Beam Stress to show results above the form.
- Review bending, shear, combined, and von Mises stresses.
- Use the CSV or PDF buttons to export the result table.
FAQs
1. What does this beam stress calculator estimate?
It estimates maximum bending moment, shear force, bending stress, axial stress, combined normal stress, von Mises stress, and factor of safety for common beam cases.
2. Which beam load cases are included?
It covers simply supported beams with center point loads or full uniform loads, cantilever beams with end loads or full uniform loads, and a custom mode.
3. Which section shapes can I analyze?
You can analyze rectangular, solid circular, hollow circular, symmetric I-sections, or any custom shape when you already know area and section modulus.
4. Why is section modulus important?
Section modulus links geometry to bending strength. A larger value reduces bending stress for the same moment, which usually improves structural efficiency.
5. Does the calculator include axial force?
Yes. It adds axial stress from the entered force and combines it with bending stress using a conservative worst-case extreme-fiber approach.
6. How is shear stress handled for different sections?
Rectangular and solid circular shapes use common closed-form maximum shear formulas. I-sections use web shear at the neutral axis, while custom and hollow sections use approximations.
7. When should I use the factor of safety result?
Use it for preliminary design screening. Final engineering checks should also consider deflection, buckling, fatigue, support details, connection behavior, and code requirements.
8. Can I export the results?
Yes. After calculation, use the CSV button for spreadsheet work or the PDF button for a clean summary you can share or archive.