Compact Section — Definition, Slenderness Limits & Code Comparison
A compact section is a structural steel cross-section whose constituent plate elements (flanges and web) have width-to-thickness ratios sufficiently low to prevent local buckling before the section reaches its full plastic moment capacity. Compact sections can develop and sustain the plastic moment Mp = Fy * Z through large rotations, making them the most ductile and efficient sections for moment-resisting frames and plastic design.
The compactness classification is the first step in determining a section's flexural design strength under AISC 360, AS 4100, EN 1993, and CSA S16. A section that is not compact cannot reach Mp and must be designed for a reduced moment capacity.
Classification Hierarchy
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| Classification | Criterion | Flexural Capacity | Local Buckling Before Yield? | Plastic Hinge Rotation |
|---|---|---|---|---|
| Compact | lambda <= lambda_p | Mn = Mp = Fy * Z | No | Yes — sufficient for plastic design |
| Non-compact | lambda_p < lambda <= lambda_r | Mp > Mn >= My = Fy * S | Yes — after partial yielding | Limited |
| Slender | lambda > lambda_r | Mn < My | Yes — before yield | None — elastic buckling governs |
Where lambda is the width-to-thickness ratio of the element, lambda_p is the compactness limit, and lambda_r is the non-compact limit (onset of elastic buckling).
AISC 360-22 Table B4.1b — Width-to-Thickness Limits
Flange Limits (I-Shapes in Flexure)
| Element | lambda | lambda_p | lambda_r (Fy=50 ksi) | Compact if |
|---|---|---|---|---|
| Flange (flexure) | bf/(2*tf) | 0.38*sqrt(E/Fy) = 9.15 | 1.0*sqrt(E/Fy) = 24.1 | bf/(2*tf) <= 9.15 |
| Flange (uniform compression) | bf/(2*tf) | 0.56*sqrt(E/Fy) = 13.5 | 1.0*sqrt(E/Fy) = 24.1 | bf/(2*tf) <= 13.5 |
Web Limits (I-Shapes in Flexure)
| Element | lambda | lambda_p | lambda_r (Fy=50 ksi) | Compact if |
|---|---|---|---|---|
| Web (flexure) | h/tw | 3.76*sqrt(E/Fy) = 90.5 | 5.70*sqrt(E/Fy) = 137 | h/tw <= 90.5 |
| Web (uniform compression) | h/tw | 1.49*sqrt(E/Fy) = 35.9 | 1.49*sqrt(E/Fy) = 35.9 | h/tw <= 35.9 |
For Fy = 50 ksi, sqrt(E/Fy) = sqrt(29000/50) = 24.08.
HSS Limits
| Element | lambda_p | lambda_r (Fy=50 ksi) |
|---|---|---|
| HSS Rectangular (flange, flexure) | 1.12*sqrt(E/Fy) = 27.0 | 1.40*sqrt(E/Fy) = 33.7 |
| HSS Rectangular (web, flexure) | 2.42*sqrt(E/Fy) = 58.3 | 5.70*sqrt(E/Fy) = 137 |
| HSS Round (flexure) | 0.07*E/Fy = 40.6 | 0.31*E/Fy = 180 |
Compactness of Common W-Shapes (Fy = 50 ksi)
| Section | bf/(2*tf) | Compact Flange? (<= 9.15) | h/tw | Compact Web? (<= 90.5) | Fully Compact? |
|---|---|---|---|---|---|
| W8x10 | 9.58 | No — non-compact (9.58 > 9.15) | 32.3 | Yes | No |
| W8x31 | 6.30 | Yes | 22.7 | Yes | Yes |
| W10x26 | 6.90 | Yes | 42.1 | Yes | Yes |
| W12x26 | 8.55 | Yes | 47.6 | Yes | Yes |
| W14x22 | 4.73 | Yes | 56.0 | Yes | Yes |
| W14x48 | 6.75 | Yes | 33.6 | Yes | Yes |
| W18x55 | 5.90 | Yes | 47.4 | Yes | Yes |
| W21x44 | 7.22 | Yes | 53.4 | Yes | Yes |
| W24x55 | 6.97 | Yes | 54.6 | Yes | Yes |
| W30x99 | 7.85 | Yes | 48.7 | Yes | Yes |
| W36x135 | 7.56 | Yes | 53.4 | Yes | Yes |
| W10x45 | 6.47 | Yes | 19.3 | Yes | Yes |
| W12x14 | 9.63 | No — non-compact | 32.3 | Yes | No |
Observation: Nearly all commonly used W-shapes (W8x31 and above) have compact flanges and webs for flexure at Fy = 50 ksi. Only very light sections (W8x10, W12x14) may have non-compact flanges. Web compactness is rarely the limiting factor.
AS 4100 — Plate Slenderness Limits
AS 4100 uses a different approach based on plate element slenderness lambda_e:
| Element | Yield Limit lambda_ey | Plastic Limit lambda_ep |
|---|---|---|
| Flat flange (HA, Grade 300) | 14 | 9 |
| Flat flange (HA, Grade 350) | 15 | 10 |
| Web (bending) | 82 | 45 (approx.) |
| Web (compression) | 35 | 30 (approx.) |
Sections are classified as Compact, Non-compact, or Slender based on lambda_e compared to lambda_ep and lambda_ey.
EN 1993-1-1 — Cross-Section Classification (Classes 1-4)
| Class | Description | Capacity | AS 4100 Analog | AISC Analog |
|---|---|---|---|---|
| Class 1 | Plastic — can form plastic hinges | Mp, full rotation | Compact | Compact |
| Class 2 | Compact — can reach Mp with limited rotation | Mp, limited rotation | Compact | Compact |
| Class 3 | Semi-compact — reaches yield but not Mp | My = Fy * S | Non-compact | Non-compact |
| Class 4 | Slender — local buckling before yield | Reduced My | Slender | Slender |
EN 1993 classification limits are given in Table 5.2 and depend on the stress distribution (uniform compression, bending, or combined).
Seismic Compactness — AISC 341
For seismic applications, AISC 341 imposes stricter width-to-thickness limits ("seismically compact"):
| Element | AISC 360 lambda_pd | AISC 341 (highly ductile) | Extra reduction |
|---|---|---|---|
| I-shape flange | 0.38*sqrt(E/Fy) = 9.15 | 0.30*sqrt(E/Fy) = 7.22 | 21% stricter |
| I-shape web (flexure) | 3.76*sqrt(E/Fy) = 90.5 | 2.45*sqrt(E/Fy) = 59.0 | 35% stricter |
Many standard W-shapes that are compact per AISC 360 may not satisfy AISC 341 highly ductile limits. For example, W24x55 with bf/(2*tf) = 6.97 is compact per AISC 360 (6.97 < 9.15) AND seismically compact per AISC 341 (6.97 < 7.22).
Design Significance
The compactness classification directly controls the nominal flexural strength Mn:
- Compact: Mn = Mp = Fy * Zx (full plastic capacity)
- Non-compact flange: Mn = Mp - (Mp - 0.7FySx) * (lambda - lambda_pf) / (lambda_rf - lambda_pf)
- Slender flange: Mn = 0.9 _ E _ kc * Sx / lambda^2 (elastic buckling)
- Non-compact web: Similar interpolation for web local buckling
Checking compactness is therefore the first step in computing beam flexural capacity.
Frequently Asked Questions
What makes a steel section compact? A section is compact if all its plate elements (flanges and web) have width-to-thickness ratios less than or equal to lambda_p per AISC 360 Table B4.1b. This ensures the section can reach and sustain its full plastic moment without local buckling.
What is the difference between compact and non-compact sections? Compact sections can reach Mp = Fy * Z (full plastic moment) and sustain it through large rotations. Non-compact sections have one or more elements with lambda between lambda_p and lambda_r — they can reach yield but not full plasticity before local buckling occurs, so capacity is reduced per AISC 360 F3 or F4.
Are all W-shapes compact? Most standard W-shapes (W8x31 and heavier) are compact for flexure at Fy = 50 ksi. Very light sections like W8x10, W12x14, and W14x22 may have non-compact flanges. At higher yield strengths (65 or 70 ksi), lambda_p decreases, and more sections become non-compact.
How do AS 4100 and EN 1993 define compact sections differently? AS 4100 uses plate element slenderness lambda_e compared to yield and plastic limits. EN 1993-1-1 uses Classes 1-4 (Class 1 = plastic, Class 2 = compact, Class 3 = semi-compact, Class 4 = slender). Both produce similar classifications to AISC 360 but with different limit values and calculation approaches.
Related Terms and Pages
- Plastic Modulus — Definition & Formula
- Elastic Section Modulus — Definition & Formula
- Lateral Torsional Buckling — LTB Explained
- Web Crippling — Definition & Design Check
- Block Shear — Definition & Failure Mode
- Beam Capacity Calculator — Free Online Tool
- Compact Section Limits — AISC 360 Reference
- Section Properties Database
Educational reference only. Compactness must be verified per the governing design code (AISC 360 Table B4.1, AS 4100 Table 5.2, EN 1993-1-1 Table 5.2) by a licensed Professional Engineer for all construction applications.
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.