Section Classification — Compact, Non-Compact & Slender
Section classification is the process of categorizing a steel cross-section based on its width-to-thickness (slenderness) ratios to determine its flexural capacity. It answers the fundamental question: can this section reach its full plastic moment before local buckling occurs?
λ = b/t (width-to-thickness ratio of each plate element)
If λ ≤ λp: Compact — section reaches and sustains Mp = Fy × Z
If λp < λ ≤ λr: Non-compact — section reaches My but not Mp
If λ > λr: Slender — local buckling before yield, Mn < My
PRELIMINARY — NOT FOR CONSTRUCTION. All content is for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.
Why Classification Matters
A compact W24x55 beam can reach its full plastic moment Mp = Fy × Zx and rotate substantially before local buckling. A slender plate girder with a thin web (h/tw > 137) will buckle locally before yielding — the beam fails at a stress below Fy, wasting the steel's strength. Classification prevents designing slender sections as if they were compact, and it guides selection: choose compact sections for moment frames requiring ductility, accept non-compact sections for simply-supported beams, and avoid slender sections unless buckling is explicitly accounted for.
AISC 360-22 Table B4.1b — Complete Limits
I-Shape Flanges (Flexure)
| Condition | λ = bf/(2×tf) | λp | λr (Fy=50 ksi) | Compact if |
|---|---|---|---|---|
| Flexure (compact flange criterion) | bf/(2×tf) | 0.38√(E/Fy) = 9.15 | 1.0√(E/Fy) = 24.1 | bf/(2×tf) ≤ 9.15 |
| Uniform compression | bf/(2×tf) | 0.56√(E/Fy) = 13.5 | 1.0√(E/Fy) = 24.1 | bf/(2×tf) ≤ 13.5 |
Physical meaning: For Fy = 50 ksi and E = 29,000 ksi, √(E/Fy) = 24.08. A flange with bf/(2×tf) = 6 (e.g., W14x48) is well within compact limits. A flange with bf/(2×tf) = 10 (e.g., W8x10) is non-compact — it will develop some yielding but cannot reach full Mp before the flange buckles locally.
I-Shape Webs (Flexure)
| Condition | λ = h/tw | λp | λr (Fy=50 ksi) | Compact if |
|---|---|---|---|---|
| Flexure (compact web criterion) | h/tw | 3.76√(E/Fy) = 90.5 | 5.70√(E/Fy) = 137 | h/tw ≤ 90.5 |
| Uniform compression | h/tw | 1.49√(E/Fy) = 35.9 | 1.49√(E/Fy) = 35.9 | h/tw ≤ 35.9 |
Web compactness is rarely the governing classification for standard rolled W-shapes. Most have h/tw ≤ 60, well below the 90.5 compact limit. Built-up plate girders with slender webs (h/tw > 137) require tension field action (AISC G2.2) or reduced effective section properties.
HSS Limits
| Element | λp | λr (Fy=50 ksi) |
|---|---|---|
| Rectangular flange (flexure) | 1.12√(E/Fy) = 27.0 | 1.40√(E/Fy) = 33.7 |
| Rectangular web (flexure) | 2.42√(E/Fy) = 58.3 | 5.70√(E/Fy) = 137 |
| Round HSS (flexure) | 0.07E/Fy = 40.6 | 0.31E/Fy = 180 |
HSS sections have different limits because the flange-to-web connection is continuous and the load path differs from open I-sections.
Flexural Strength by Classification
The classification determines which strength equation to use:
| Classification | Governing Equation | Example (W24x55, Fy=50 ksi) |
|---|---|---|
| Compact | Mn = Mp = Fy × Zx | Mn = 50 × 134 = 6,700 kip-in |
| Non-compact | Mn = Mp − (Mp − 0.7Fy×Sx) × (λ−λpf)/(λrf−λpf) | Linearly interpolated |
| Slender | Mn = 0.9 × E × kc × Sx / λ² (elastic LTB or FLB) | Buckling-controlled |
For a compact W24x55: bf/(2×tf) = 6.97 ≤ 9.15 ✓, h/tw = 54.6 ≤ 90.5 ✓. The section is fully compact and achieves Mp.
For a non-compact W8x10: bf/(2×tf) = 9.58 > 9.15. The flange is non-compact, so Mn is reduced below Mp using the linear interpolation formula. The member pays a capacity penalty for its thin flange.
EN 1993-1-1 — Class 1 to Class 4
Eurocode uses four classes instead of three:
| Class | Definition | Moment Capacity | Rotation Capacity |
|---|---|---|---|
| Class 1 | Cross-section can form a plastic hinge | Mp = Wpl × fy | Sufficient for plastic design |
| Class 2 | Can reach Mp but with limited rotation | Mp = Wpl × fy | Limited |
| Class 3 | Reaches yield at extreme fiber but not Mp | Mel = Wel × fy | None (elastic buckling limits yield) |
| Class 4 | Local buckling before yield is reached | Reduced Mel | None (effective width method) |
Limits for Class 1, 2, and 3 are given in EN 1993-1-1 Table 5.2, expressed as c/t limits that depend on stress distribution (α for webs, ψ for flanges). The most restrictive condition applies.
For S355, typical rolled I-sections: Class 1 flange limit ≈ 9ε where ε = √(235/fy) = √(235/355) = 0.81, so limit = 9×0.81 = 7.3. Compare to AISC λp = 9.15 for Fy=50 ksi (equivalent): EN 1993 is more conservative (stricter limits) for Class 1 than AISC is for compact.
AS 4100 — Plate Element Slenderness
AS 4100 uses plate element slenderness λe, defined differently from AISC:
λe = (b/t) × √(fy/250) (for flat plate elements)
| Classification | Criterion | Flexural Capacity |
|---|---|---|
| Compact | λe ≤ λep | Ms = fy × Ze (plastic) |
| Non-compact | λep < λe ≤ λey | Ms = fy × S (yield) |
| Slender | λe > λey | Ms = fy × Zeff (effective) |
For a Grade 300 HA flange: λep = 9, λey = 14. For Grade 350: λep = 10, λey = 15. The fy/250 normalization makes λe values directly comparable across steel grades.
Comparison Table — All Three Codes
| Condition | AISC 360 | EN 1993-1-1 | AS 4100 |
|---|---|---|---|
| Full plasticity OK | Compact (≤λp) | Class 1, 2 | Compact (≤λep) |
| Elastic yield only | Non-compact (≤λr) | Class 3 | Non-compact (≤λey) |
| Buckling before yield | Slender (>λr) | Class 4 | Slender (>λey) |
| Flange limit parameter | λ = bf/(2×tf) | c/t × ε | λe = (b/t)√(fy/250) |
| Web limit parameter | λ = h/tw | c/t × ε | λe = (d/t)√(fy/250) |
Frequently Asked Questions
What happens if my beam flange is compact but the web is slender? The section is classified as slender because the most unfavorable element governs. However, AISC 360 permits treating the web as compact for flexure if it satisfies the web compactness limit (h/tw ≤ 90.5 for flexure). If the web alone is slender, use the provisions of AISC Chapter G for plate girders, which account for post-buckling tension field action. The combined flange-web interaction is checked per AISC F4 and F5.
Why do the classification limits depend on Fy in AISC but on ε in EN 1993? Both depend on yield strength — the form differs. AISC expresses limits as constant × √(E/Fy) so that higher Fy (stronger steel) produces tighter (more restrictive) limits, because stronger steel is more susceptible to buckling relative to yield. EN 1993's ε = √(235/fy) accomplishes the same thing: as fy increases, ε decreases, and the c/tε limits tighten. The parameterization differs but the physics is identical.
Does section classification apply to tension members? No. Section classification only affects flexure and compression — limit states where local buckling can precipitate failure. Tension members are always "compact" in the sense that tension prevents local buckling (stretching stabilizes the cross-section). A tension-only member with an AISC-slender web can still reach its full tensile yield strength Fy×Ag.
Related Terms and Pages
- Compact Section — Lambda Limits & AISC Table B4.1
- Plastic Modulus — Definition & Formula
- Yield Strength (Fy) — Definition & Formula
- Lateral Torsional Buckling — LTB Explained
- Slenderness Ratio — Column Buckling
- Beam Capacity Calculator — Free Online Tool
- Section Properties Database
Educational reference only. Section classification must be verified per the governing design code for the project jurisdiction. All designs must be independently verified by a licensed Professional Engineer.
Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.