Calculated Result
The result appears above the form, directly below the header, as requested.
2,313.96 mm
5,391.30 mm
300.00 kN-m
Inelastic lateral-torsional buckling
Compact (λf = 6.250)
Compact (λw = 26.800)
1.00 applied from governing class Compact
Beam Moment Capacity Form
Capacity Curve
Example Data Table
| Case | Fy | Zx | Lb | Cb | Governing Class | Capacity | Status |
|---|---|---|---|---|---|---|---|
| WF Beam A | 350.00 | 1,850,000 | 2,000 | 1.20 | Compact | 582.75 kN-m | Within capacity |
| WF Beam B | 345.00 | 2,400,000 | 4,200 | 1.00 | Compact | 622.76 kN-m | Within capacity |
| WF Beam C | 250.00 | 3,100,000 | 5,500 | 1.10 | Compact | 444.43 kN-m | Over capacity |
Formula Used
Plastic moment:
Mp = Fy × Zx
Yield moment:
My = Fy × Sx
Limiting laterally braced lengths:
Lp = 1.76 × ry × √(E / Fy)
Lr = 1.95 × rts × (E / 0.7Fy) × √[(Jc / Sxho) + √((Jc / Sxho)² + 6.76(0.7Fy / E)²)]
Nominal flexural strength, Mn:
- If
Lb ≤ Lp, thenMn = Mp - If
Lp < Lb ≤ Lr, inelastic lateral-torsional buckling interpolation is used - If
Lb > Lr, elastic lateral-torsional buckling governs throughFcr
Local buckling check:
Flange slenderness λf = bf / 2tf
Web slenderness λw = h / tw
This page reports flange and web classes using compact, noncompact, and slender limits.
A transparent modifier is then applied to the LTB result:
1.00 for compact, 0.90 for noncompact, and 0.75 for slender.
Design strength:
LRFD Capacity = φMnASD Capacity = Mn / Ωb
These equations are useful for estimation and preliminary checking. Exact design provisions vary by code edition, shape type, local buckling rules, and project requirements.
How to Use This Calculator
- Select the unit system and design method.
- Enter steel material properties such as Fy and E.
- Input section properties, including Zx, Sx, J, ry, rts, and ho.
- Enter geometric values for flange and web compactness checks.
- Provide the unbraced length and moment gradient factor Cb.
- Enter the applied design moment to compare demand with capacity.
- Press Calculate Capacity to show the result above the form.
- Review the capacity card, the chart, the governing limit state, and the local-buckling classification.
- Use the CSV or PDF buttons to export the result summary.
Frequently Asked Questions
1) What does this calculator estimate?
It estimates steel beam flexural capacity using section properties, bracing length, and design factors. It compares yielding and buckling behavior and shows whether the applied moment stays within the estimated limit.
2) Is the result suitable for final design approval?
No. It is best for preliminary design, checking alternatives, and fast what-if studies. Final approval should follow the governing steel code, project load combinations, and qualified engineering review.
3) Why are Zx and Sx both needed?
Zx gives plastic moment strength, while Sx gives elastic yield strength and helps with buckling formulas. Using both values allows the calculator to evaluate several flexural limit states more realistically.
4) What does Cb do in the calculation?
Cb adjusts lateral-torsional buckling strength for moment gradient effects. A favorable bending pattern often increases available flexural capacity compared with uniform moment along the unbraced segment.
5) Why does capacity drop as unbraced length increases?
Longer unbraced lengths make the compression flange easier to twist and buckle laterally. That reduces the moment the beam can resist before instability controls the response.
6) What is the difference between compact, noncompact, and slender?
These classes describe how likely flange or web elements are to buckle locally before full plastic strength develops. Compact sections can usually reach higher flexural strength than slender ones.
7) Can I use imperial units?
Yes. Switch the unit system to imperial and enter values consistently in ksi, inches, cubic inches, and fourth-power inches. The displayed moment capacity will then appear in kip-ft.
8) What do the export buttons save?
The CSV export saves a clean summary of the main result values. The PDF export creates a compact report with the calculated capacity, limit state, classification, and utilization.