Compact Section Limits — AISC 360 Table B4.1b Width-Thickness Ratios

Section compactness determines whether a steel member can develop its full plastic moment capacity (Mp) or is limited by local buckling. AISC 360-22 Table B4.1b classifies flexural members as compact, noncompact, or slender based on width-to-thickness ratios. This classification directly affects available flexural strength.

Why compactness matters

• Compact sections develop the full plastic moment Mp = Fy*Zx. Local buckling does not occur before the full cross-section yields. Most standard rolled W-shapes with Fy <= 50 ksi are compact.
• Noncompact sections develop partial yielding but local buckling limits capacity to between My (= Fy*Sx) and Mp. Strength varies linearly based on the width-thickness ratio.
• Slender sections buckle locally before yielding initiates. Capacity is significantly less than My. Uncommon in hot-rolled W-shapes but occurs in built-up sections and HSS.

AISC 360-22 Table B4.1b — flexural members

Flanges of rolled I-shapes and channels

Width-thickness ratio lambda = bf/(2*tf):

Most standard W-shapes satisfy this (e.g., W16x40 has bf/(2tf) = 6.93). The lightest W-shapes approach the noncompact limit.

Webs of doubly symmetric I-shapes in flexure

Width-thickness ratio lambda = h/tw:

All standard rolled W-shapes have compact webs for Fy <= 50 ksi. Web compactness only becomes an issue for built-up plate girders or high-strength steel.

Flanges of rectangular HSS

Width-thickness ratio lambda = b/t (flat width to wall thickness):

Round HSS (pipes)

Width-thickness ratio lambda = D/t:

Summary table — lambda_p and lambda_r

*HSS Fy = 46 ksi standard. **Round HSS Fy = 42 ksi.

Checking compactness — step by step

Example: W21x44, Fy = 50 ksi. bf = 6.50 in, tf = 0.450 in, h/tw = 53.6.

Flange: lambda = 6.50/(20.450) = 7.22 < 9.15 -- COMPACT. Web: lambda = 53.6 < 90.6 -- COMPACT. W21x44 can develop full Mp = FyZx.

Example: HSS 12x6x1/4, Fy = 46 ksi. b/t = 22.8 (short wall), h/t = 46.5 (long wall). Short wall: 22.8 < 28.1 -- COMPACT. Long wall: 46.5 < 60.8 (web limit for rect. HSS) -- COMPACT.

W-Shapes Near the Compact/Noncompact Boundary (Fy = 50 ksi)

The flange compact limit at Fy = 50 ksi is lambda_p = 9.15. The following W-shapes have flange slenderness ratios close to or exceeding this limit:

Only 4 sections out of 148 standard W-shapes are noncompact at Fy = 50 ksi: W6x8.5, W6x9, W8x10, and W10x12. The capacity reduction for these sections is 1-3% below Mp, so the practical impact is minimal. For Fy = 65 ksi (lambda_p = 8.03), several additional light sections become noncompact.

All standard rolled W-shapes have compact webs at Fy = 50 ksi. The highest web slenderness ratio in the AISC Manual is approximately 60, well below the compact limit of 90.6.

AS 4100:2020 — Plate Element Slenderness

AS 4100 uses a different approach with plate element slenderness (lambda_e) and yield slenderness limits (lambda_ey, lambda_ep):

Section constant alpha_s = (lambda_ep/lambda_e)^2 for noncompact, limited to 1.0 for compact.

Key difference: AS 4100 limits are numerically similar but derived differently. AS 4100 uses a separate section constant alpha_s in the member capacity calculation rather than modifying Mn directly.

EN 1993-1-1 — Cross-Section Classification

EN 1993 classifies cross-sections into four classes:

Classification limits for I-section flanges (EN 1993-1-1 Table 5.2)

Where c = (bf - tw - 2r) / 2 (outstand of compression flange) and epsilon = sqrt(235/fy).

Key difference: EN 1993 separates the plastic hinge case (Class 1) from the plastic moment case (Class 2). AISC treats both as compact. EN 1993 Class 1 is needed for plastic analysis (moment redistribution), while Class 2 is sufficient for simply using Mp in elastic analysis.

High-strength steel considerations

For Fy >= 65 ksi, compact limits tighten significantly. I-shape flange lambda_p drops from 9.15 (Fy=50) to 8.03 (Fy=65). Several light W-shapes become noncompact at higher grades. Always verify compactness when using A913 Gr. 65 or A709 Gr. 70 steel.

Effect on flexural capacity

AISC Table B4.1b — Complete Limits Table for All Element Types

AISC 360-22 Table B4.1b provides width-to-thickness ratio limits for compression elements of members in flexure. The complete table covers all element types encountered in practice:

Flanges of I-Shapes in Flexure (Case 10)

For Fy = 50 ksi: lambda_p = 0.38 x sqrt(29000/50) = 0.38 x 24.08 = 9.15 For Fy = 65 ksi: lambda_p = 0.38 x sqrt(29000/65) = 0.38 x 21.13 = 8.03

Webs of Doubly Symmetric I-Shapes in Flexure (Case 15)

For Fy = 50 ksi: lambda_p = 3.76 x 24.08 = 90.6, lambda_r = 5.70 x 24.08 = 137.3

Flanges of Rectangular HSS in Flexure (Case 17)

For Fy = 46 ksi: lambda_p = 1.12 x sqrt(29000/46) = 1.12 x 25.10 = 28.1

Webs of Rectangular HSS in Flexure (Case 17)

For Fy = 46 ksi: lambda_p = 2.42 x 25.10 = 60.7, lambda_r = 5.70 x 25.10 = 143.1

Round HSS in Flexure (Case 20)

For Fy = 42 ksi: lambda_p = 0.07 x 29000/42 = 48.3, lambda_r = 0.31 x 29000/42 = 214.1

Flanges of Tees in Flexure (Case 12)

Compression Elements in Axial Compression (Table B4.1a)

For members in pure compression (columns), Table B4.1a provides separate limits:

Elements exceeding lambda_r in compression are classified as slender, and the effective area is reduced per AISC Section E7.

Compact/Noncompact/Slender Classification Examples for Popular W-Shapes

Complete Classification for Common Beam Sizes (Fy = 50 ksi)

Sections Near the Compact/Noncompact Boundary

HSS Compact Limits — Detailed Classification

Rectangular HSS Classification (Fy = 46 ksi, A500 Gr.C)

Flat width calculation: b_flat = outside dimension - 2(corner radius). Per AISC, corner radius is approximately 3t for rectangular HSS, so b_flat = B - 3t (short wall) or H - 3t (long wall).

Thin-wall HSS sections (3/16" wall) are frequently noncompact or slender in the long wall direction. This reduces their flexural capacity below Mp.

Round HSS Classification (Fy = 42 ksi, A500 Gr.B)

Large-diameter thin-wall pipes are frequently noncompact. The lambda_r = 214 limit is very generous for round HSS; few standard sections exceed it.

Flange and Web Check Procedures

Step-by-Step Procedure for Checking Compactness

1. Identify the steel grade and Fy. For A992 W-shapes: Fy = 50 ksi. For A500 Gr.C HSS: Fy = 46 ksi.

2. Determine the applicable element type from AISC Table B4.1b (flange, web, HSS wall, etc.).

3. Calculate the width-to-thickness ratio lambda. Use the correct formula for the element type (e.g., b_f/(2t_f) for I-shape flanges, h/t_w for I-shape webs).

4. Look up lambda_p and lambda_r for the given Fy from Table B4.1b.

5. Classify the element:

   • lambda <= lambda_p: Compact
   • lambda_p < lambda <= lambda_r: Noncompact
   • lambda > lambda_r: Slender

6. Classify the section by its most limiting element. A section with a compact web but noncompact flange is classified as noncompact overall.

7. Apply the appropriate design equation based on classification:

   • Compact: Mn = Mp = Fy x Zx (AISC Eq. F2-1)
   • Noncompact flange: Mn per Eq. F3-1 (linear interpolation)
   • Slender flange: Mn per Eq. F3-2 (elastic local buckling)
   • Slender web: Use AISC Chapter F4 or F5 (plate girder provisions)

Example: Complete Check for W21x44 (Fy = 50 ksi)

Step 1: Fy = 50 ksi (A992). lambda_p (flange) = 9.15, lambda_r (flange) = 24.1. lambda_p (web) = 90.6, lambda_r (web) = 137.3.

Step 2: Flange: b_f/(2t_f) = 6.50/(2 x 0.450) = 6.50/0.90 = 7.22. 7.22 < 9.15. Compact.

Step 3: Web: h/t_w = (d - 2t_f)/t_w = (20.7 - 2 x 0.450)/0.350 = 19.80/0.350 = 56.6. 56.6 < 90.6. Compact.

Step 4: Overall classification: Compact. Full plastic moment Mp = Fy x Zx = 50 x 95.4 = 4,770 kip-in = 397.5 kip-ft.

How Limits Affect Design — Plastic Moment vs Elastic vs Effective

The section classification directly determines which design strength equation applies:

Capacity Comparison for W8x10 at Various Fy Values

The W8x10 loses 13% of its plastic moment capacity when Fy increases from 36 to 65 ksi, because the higher Fy tightens the compact limit. This illustrates why compactness must always be checked for the specified Fy.

Common mistakes

1. Assuming all rolled W-shapes are compact. Nearly all are for Fy = 50 ksi, but a few very light sections (W6x8.5, W8x10) are noncompact. Always verify.

2. Using wrong lambda formula for HSS. Rectangular HSS uses flat width b/t, not full outside dimension. Flat width = outside - 3*t.

3. Forgetting to check both flange and web. A section is classified by its most limiting element.

4. Applying compact equations to built-up sections. Plate girders with slender webs require AISC Chapter F4/F5.

5. Not adjusting for actual Fy. Higher actual Fy tightens compact limits. Use specified minimum Fy for design.

Frequently asked questions

What does compact mean for a steel section? A compact section has flanges and web stocky enough to develop Mp = Fy*Zx before local buckling occurs. All compression elements must have width-thickness ratios below limits in AISC 360 Table B4.1b.

Are all W-shapes compact? Nearly all for Fy = 50 ksi. The vast majority of standard rolled W-shapes in the AISC Manual are compact. No standard rolled W-shape has a slender web at Fy = 50 ksi.

What happens if my section is noncompact? Flexural capacity is reduced below Mp but remains above 0.7FySx. Use AISC Eq. F3-1 to interpolate.

How do I check compactness for HSS sections? For rectangular HSS: flat width = outside dimension minus approximately 3t (accounts for corner radius). Compare b/t and h/t against the lambda_p and lambda_r limits. Many thin-wall HSS sections (e.g., HSS 8x4x1/4) are slender in the long wall direction. For round HSS: compare D/t against 48.3 (Fy=42 ksi).

What is the difference between AISC compact and EN 1993 Class 1? AISC "compact" allows Mp to develop. EN 1993 Class 1 allows Mp to develop AND requires sufficient rotation capacity for plastic hinge formation (moment redistribution). EN 1993 Class 2 allows Mp but not redistribution. AISC does not separate these two cases.

Does compactness affect column capacity? For compression members, AISC uses a single lambda_r limit (Table B4.1a) to determine whether local buckling reduces the effective area. Compact columns use the full cross-section area. Slender columns use a reduced effective area. Most standard W-shapes are non-slender in compression.

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This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against AISC 360-22 Table B4.1b for the specific section and steel grade. The site operator disclaims liability for any loss arising from the use of this information.