Shear Lag Factor U — AISC 360 Table D3.1 Reference
The shear lag factor U accounts for the uneven stress distribution in tension members when not all elements of the cross-section are connected. When a W-shape is connected only through its flanges, or an angle is connected only through one leg, the stress in the unconnected elements lags behind the stress at the connection. AISC 360-22 Section D3 and Table D3.1 define U for different member and connection configurations.
Why shear lag matters
The effective net area of a tension member is Ae = An _ U, where An = net area (gross area minus hole deductions) and U = shear lag factor (0 < U <= 1.0). The tensile rupture capacity is phiPn = 0.75 _ Fu _ Ae = 0.75 _ Fu _ An _ U. When U < 1.0, the effective area is reduced, meaning the member's fracture capacity is lower than if the entire cross-section were fully connected. For many practical connections, U ranges from 0.60 to 0.90, representing a 10-40% capacity reduction.
AISC 360-22 Table D3.1 — shear lag factors
Case 1: All elements connected
When every element of the cross-section is connected (e.g., a W-shape connected through both flanges and web): U = 1.0.
Case 2: General formula (most common)
For tension members where load is transmitted through some but not all elements:
U = 1 - x_bar / L
Where x_bar = connection eccentricity (distance from the centroid of the connected elements to the connection face) and L = connection length (distance between first and last fasteners in a line, or weld length). This is the most frequently used case and applies to W-shapes, channels, tees, angles, and HSS connected through some elements.
Case 3: W-shapes, M-shapes, S-shapes, HP-shapes (flanges with 3+ bolts per line)
| Condition | U |
|---|---|
| bf >= 2/3 * d | 0.90 |
| bf < 2/3 * d | 0.85 |
Where bf = flange width and d = overall depth.
Case 4: W-shapes, tees — connected through web only
U = 0.90 with 4+ bolts per line.
Case 5: Single angles
| Condition | U |
|---|---|
| 4+ bolts per line | 0.80 |
| 3 bolts per line | 0.60 |
| 2 bolts per line | Use Case 2 formula |
Case 6: HSS (round and rectangular)
For HSS connected with a single concentric gusset plate: when L >= 1.3D (round HSS), U = 1.0. For shorter connections, U = 1 - x_bar/L.
Case 7: Plates and flat bars (longitudinal welds only)
| l/w Ratio | U |
|---|---|
| l >= 2w | 1.00 |
| 2w > l >= 1.5w | 0.87 |
| 1.5w > l >= w | 0.75 |
Where l = weld length, w = plate width. For plates with transverse welds across the full width: U = 1.0.
Worked example — W10x49 flange connection
Given: W10x49 tension member, connected through both flanges with 4 rows of 3/4" A325 bolts at 3" pitch (3 bolts per line). Ag = 14.4 in^2, bf = 10.0 in, d = 10.0 in, tf = 0.560 in.
Step 1 — Check Case 3: bf/d = 10.0/10.0 = 1.0 > 2/3. With 3 bolts per line in flanges, U = 0.90.
Step 2 — Net area: Hole deduction = 13/16" + 1/16" = 7/8" per hole. 4 holes total. An = 14.4 - 4*(7/8*0.560) = 14.4 - 1.96 = 12.44 in^2.
Step 3 — Effective net area: Ae = 0.90 * 12.44 = 11.20 in^2.
Step 4 — Tensile rupture: phiPn = 0.75 _ 65 _ 11.20 = 546 kips (A992 steel).
Step 5 — Yielding: phiPn = 0.90 _ 50 _ 14.4 = 648 kips.
Governing: Rupture = 546 kips controls.
Worked example — single L4x4x3/8 angle
Given: L4x4x3/8, 3 bolts in a single line at 3" spacing, connected through one leg. Ag = 2.86 in^2, x_bar = 1.18 in.
Case 2: L = 2*3" = 6". U = 1 - 1.18/6 = 0.80.
Case 5: 3 bolts per line: U = 0.60.
AISC permits the larger value: U = max(0.80, 0.60) = 0.80. This nuance -- that you take the larger of the general formula and the tabulated value -- is an important detail many designers miss.
Common mistakes
Using bolt diameter instead of hole diameter for net area. The hole deduction uses the hole diameter (per Table J3.3) plus 1/16" for damage allowance, not the bolt diameter.
Forgetting to check both Table D3.1 cases. When both the general formula (Case 2) and a specific case apply, use the larger U value.
Miscalculating x_bar for channels and tees. The eccentricity x_bar is measured from the centroid of the connected elements to the shear plane, not the centroid of the entire cross-section.
Using U = 1.0 for welded connections without checking. Even welded connections can have shear lag if not all elements are welded.
Applying shear lag to compression members. Shear lag factor U applies only to tension members (Chapter D).
Frequently asked questions
What is the shear lag factor? U is a reduction factor applied to the net area of a tension member to account for non-uniform stress distribution when not all cross-section elements are connected. Ae = An * U. Values range from 0.60 to 1.0.
When is U = 1.0? When all elements are directly connected, when a plate has transverse welds across its full width, or when round HSS has a connection length >= 1.3D.
Does shear lag apply to bolted and welded connections? Yes. Shear lag occurs whenever the load path does not engage the full cross-section, regardless of fastener type.
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Related references
- Bolt Capacity Table
- Bolt Hole Sizes
- Steel Fy and Fu Reference
- How to Verify Calculations
- tension member design reference
- Tension Member
Disclaimer
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 D3.1 and the governing project specification. The site operator disclaims liability for any loss arising from the use of this information.