Beam Input Form
Enter section properties in N, mm, MPa, and kN·m units. The calculator assumes a doubly symmetric steel I-beam and uses an elastic critical moment approach for lateral-torsional buckling.
Example Data Table
| Beam | E (MPa) | Fy (MPa) | Lb (mm) | Cb | Iy (mm⁴) | J (mm⁴) | Cw (mm⁶) | Sx (mm³) | Zx (mm³) | Mu (kN·m) |
|---|---|---|---|---|---|---|---|---|---|---|
| Sample Rolled Beam | 200000 | 345 | 4500 | 1.14 | 84,000,000 | 950,000 | 3,800,000,000,000 | 1,080,000 | 1,220,000 | 180 |
| Warehouse Girder | 200000 | 250 | 6000 | 1.00 | 61,500,000 | 630,000 | 2,100,000,000,000 | 820,000 | 910,000 | 145 |
These values are illustrative. Actual results depend on the exact member properties, load pattern, end restraint, and code assumptions used in design.
Formulas Used
Elastic critical moment
Mcr = Cb × (π / Lb) × √[ E × Iy × ( G × J + (π² × E × Cw / Lb²) ) ]
Reference moments
My = Fy × Sx
Mp = Fy × Zx
Non-dimensional slenderness and reduction
λ̄LT = √(Mp / Mcr)
φ = 0.5 × [1 + αLT × (λ̄LT − 0.2) + λ̄LT²]
χLT = 1 / [φ + √(φ² − λ̄LT²)]
Nominal and design strength
Mn = min(Mp, χLT × Mp, Mcr)
LRFD capacity = φb × Mn
ASD capacity = Mn / Ωb
Demand ratio = Mu / Design capacity
This calculator is intended for preliminary checking. It assumes a doubly symmetric beam, consistent units, and a user-supplied Cb factor. Final design should follow the governing project code and verified section-property data.
How to Use This Calculator
- Enter the beam name for your report.
- Select LRFD, ASD, or nominal strength mode.
- Fill in steel material values E, G, and Fy.
- Enter the unbraced length Lb and chosen Cb factor.
- Input Iy, J, Cw, Sx, and Zx from section data.
- Enter the applied major-axis moment Mu in kN·m.
- Review the result block above the form after submission.
- Use the CSV or PDF buttons to download the report.
FAQs
1) What does this calculator check?
It checks whether a steel beam’s applied moment exceeds its estimated lateral-torsional buckling resistance. It also reports critical moment, reduced capacity, utilization, and pass or fail status for quick design screening.
2) Which beam shape is this best for?
It is best suited to doubly symmetric steel I-beams where section properties are known. Use caution for mono-symmetric, channel, tapered, composite, or unusual built-up members because their behavior may differ materially.
3) Why is Cb important?
Cb adjusts the elastic critical moment for the moment gradient along the unbraced segment. A favorable gradient can increase buckling resistance, while a uniform or severe pattern may reduce the benefit.
4) What units should I use?
Use MPa for stresses and moduli, millimeters for lengths, mm³ for section modulus, mm⁴ for inertia, mm⁶ for warping constant, and kN·m for applied moment. Keep all entries consistent.
5) What does λ̄LT represent?
It is a non-dimensional slenderness indicator comparing plastic capacity to elastic buckling resistance. Lower values generally mean stronger buckling performance, while higher values indicate greater susceptibility to lateral-torsional instability.
6) Why can the beam fail even below Mp?
A beam may buckle laterally before reaching full plastic bending resistance. Long unbraced lengths, weak torsional stiffness, low warping restraint, or unfavorable moment gradients can lower usable flexural capacity substantially.
7) Is this suitable for final code design?
It is useful for advanced preliminary evaluation and comparison. Final design still requires the exact governing code equations, correct section database values, restraint verification, load combinations, and engineering judgment.
8) What do the CSV and PDF downloads contain?
They include the beam name, selected design method, applied moment, critical and nominal moments, design capacity, utilization, reduction factor, slenderness classification, governing mode, and pass or fail status.