Shear Lag Factor U — AISC 360-22 Table D3.1, Complete Values and Examples

The shear lag factor U accounts for the uneven stress distribution in tension members when not all elements of the cross-section are connected to the gusset or splice plate. When a W-shape is connected only through its flanges, or a single angle is bolted 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. This page provides every case, worked examples, common shapes values, multi-code comparisons, and practical guidance.

Quick access:

• Why Shear Lag Matters
• When U = 1.0 vs U < 1.0
• Complete AISC Table D3.1 — All 8 Cases
• Shear Lag Factor Values for Common Shapes
• Connection Length L and Its Effect on U
• Worked Examples
• Multi-Code Comparison
• Common Mistakes
• Frequently Asked Questions

Why Shear Lag Matters

The effective net area of a tension member is:

Ae = An x U

where An = net area (gross area minus hole deductions) and U = shear lag factor (0 < U <= 1.0).

The tensile rupture capacity (limit state of fracture) is:

phiPn = 0.75 x Fu x Ae = 0.75 x Fu x An x U

where Fu = specified tensile strength and phi = 0.75 (AISC LRFD).

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 compared to a fully connected section.

Shear lag does not apply to the yielding limit state (phiPn = 0.90 x Fy x Ag), which uses the full gross area. It only applies to the rupture (fracture) limit state at the connection.

When U = 1.0 vs U < 1.0

U = 1.0 applies when:

• All cross-section elements are connected (Case 1)
• A plate has transverse welds across its full width
• Round HSS with a single concentric gusset and connection length L >= 1.3D
• Rectangular HSS with a single concentric gusset and L >= 1.3D (for sections loaded in the strong direction)

U < 1.0 applies when:

• Only some elements of the cross-section are connected (e.g., only flanges of a W-shape)
• Single angles connected through one leg
• Double angles connected through one leg of each angle
• HSS with slit connections or short gusset plates
• Plates connected by longitudinal welds only (less than 2w long)
• Tees connected through the web only

The key principle: if the load must transfer through an element that is not directly connected, shear lag occurs and U < 1.0.

Complete AISC 360-22 Table D3.1 — All 8 Cases

Case 1 — All Elements of the Cross-Section Connected

Description: Tension load is transmitted by transverse welds to all elements of the cross-section.

U = 1.0

Sketch: A W-shape with transverse welds across the full section (both flanges and web), or a round HSS with a full-perimeter weld to a gusset plate. The entire cross-section is engaged at the connection.

Case 2 — General Formula (Most Common Case)

Description: Tension load is transmitted by longitudinal welds or bolts to some, but not all, elements of the cross-section. This is the most frequently applied case.

U = 1 - x_bar / L

Where:

• x_bar = eccentricity of the connection (distance from the centroid of the connected elements to the plane of the connection, measured perpendicular to the load direction)
• L = connection length (distance between the outermost fasteners in the direction of loading, or the length of longitudinal weld)

Sketch: A W-shape connected only through its flanges. The centroid of the two flanges is offset from the neutral axis by x_bar. The connection length L runs from the first bolt row to the last bolt row.

This case applies to W-shapes, channels, tees, angles, and HSS connected through some elements. The longer the connection (larger L), the closer U approaches 1.0.

Case 3 — W-Shapes, M-Shapes, S-Shapes, and HP-Shapes (Flange Connections, 3+ Fasteners per Line)

Description: Tension load is transmitted only through the flanges of W, M, S, or HP shapes using bolts. The shape must have 3 or more fasteners per line in the direction of loading.

Where bf = flange width and d = overall depth of the shape.

Sketch: A W12x50 with flange plates bolted through both flanges, 3 or more bolts per line. For most standard W-shapes (bf/d >= 0.67), U = 0.90. Deep narrow shapes (e.g., W14x43) may fall below the 2/3 threshold and use U = 0.85.

Case 4 — W-Shapes, M-Shapes, S-Shapes, HP-Shapes, and Tees (Web Connections, 4+ Fasteners per Line)

Description: Tension load is transmitted only through the web (for W, M, S, HP shapes) or only through the stem (for tees). Requires 4 or more fasteners per line.

U = 0.90 (with 4+ fasteners per line)

Sketch: A WT section connected through its stem with a gusset plate bolted to the web. Four or more bolts per line are required to use this prescriptive value. With fewer fasteners, use the Case 2 general formula.

Case 5 — Single and Double Angles (Bolted Through One Leg)

Description: Single angles connected through one leg, or double angles (back-to-back) each connected through one leg. Loaded in tension.

Sketch: A single L4x4x3/8 connected through one leg to a gusset plate. The unconnected leg does not participate directly in load transfer. The tabulated U values are alternatives to the Case 2 formula; the designer may use the larger of Case 2 and Case 5.

Case 6 — Round and Rectangular HSS (Single Concentric Gusset)

Description: Round or rectangular HSS connected by a single concentric gusset plate through a slot in the HSS wall. Load is transmitted through longitudinal welds along the gusset.

Where D = outside diameter of round HSS, or the applicable cross-sectional dimension of rectangular HSS.

Sketch: A round HSS6.000x0.375 with a 3/8" gusset plate slotted into the middle and welded along both sides. When the weld length is at least 1.3 times the tube diameter, the full section is effectively engaged and U = 1.0.

Case 7 — Plates and Flat Bars (Longitudinal Welds Only)

Description: Flat plates or bars connected by longitudinal welds along both edges. No transverse weld is present.

Where l = length of longitudinal weld and w = plate width (distance between welds).

Sketch: A flat bar 6 inches wide with two longitudinal fillet welds of 14 inches along each edge. Since l/w = 14/6 = 2.33 >= 2.0, U = 1.0. If the welds were only 9 inches long, l/w = 9/6 = 1.5, and U would be 0.87.

For plates with transverse welds across the full width, U = 1.0 (Case 1 applies).

Case 8 — Rectangular HSS and Box Sections (Single Non-Concentric Gusset or Side Wall)

Description: Rectangular HSS or box sections connected through a single side wall, or connected with a non-concentric gusset plate. This case addresses the condition where the connection engages only one wall of the box section.

U = 1 - x_bar / L

Use the Case 2 general formula. The eccentricity x_bar is measured from the center of gravity of the HSS to the connected wall.

Sketch: A rectangular HSS6x4x3/8 connected through the 4-inch wall only. The centroid of the full section is offset from the connected wall, creating shear lag. This is distinct from Case 6, which applies only to concentric gusset connections.

Shear Lag Factor Values for Common Shapes

The table below provides typical U values for frequently used shapes. These are approximate prescriptive values; the general formula (Case 2) may yield higher values for long connections.

Connection Length L and Its Effect on U

The connection length L is the distance between the outermost fasteners measured in the direction of loading, or the length of longitudinal weld for welded connections. For the general formula U = 1 - x_bar/L:

• Longer L means higher U. As L increases, x_bar/L decreases and U approaches 1.0.
• Shorter L means lower U. Short connections (e.g., 2 bolts at 3" pitch, L = 3") produce higher x_bar/L ratios and lower U values.

Practical implications:

• Adding bolt rows increases L and U, but also adds cost and may increase the gusset plate size.
• For a W8x31 connected through both flanges (x_bar = 1.13 in.), a 3-bolt connection at 3" pitch (L = 6") gives U = 1 - 1.13/6 = 0.81. The same section under Case 3 prescriptive gives U = 0.90. Using the prescriptive value is advantageous here.
• For a single angle L4x4x3/8 (x_bar = 1.18 in.) with 2 bolts at 3" pitch (L = 3"), U = 1 - 1.18/3 = 0.61. This is worse than the Case 5 prescriptive values (which do not apply with only 2 bolts), so the general formula governs.
• Minimum L is determined by bolt spacing requirements (AISC Section J3.3) and edge distance requirements (AISC Table J3.4M/J3.4).

Worked Examples

Worked Example 1 — WT7x24 Tension Member Connected Through the Flange

Given: WT7x24 (cut from W14x48), connected through the flange to a gusset plate with 5 rows of 7/8" A325 bolts at 3" pitch (5 bolts per line). A992 steel (Fy = 50 ksi, Fu = 65 ksi).

Section properties: Ag = 7.08 in.^2, tf = 0.530 in., bf = 8.07 in.

Step 1 — Determine which case applies: The WT is connected through the flange only (not the stem). This matches Case 4 (tees connected through the web/flange with 4+ bolts per line).

Step 2 — Check Case 4 prescriptive value: With 5 bolts per line (>= 4), U = 0.90.

Step 3 — Check Case 2 general formula: x_bar = distance from the centroid of the flange to the neutral axis of the WT section. For a WT7x24, the centroid of the entire WT is approximately 1.56 in. from the outer face of the flange. The flange centroid is at tf/2 = 0.265 in. from the outer face. So x_bar = 1.56 - 0.265 = 1.30 in. (approximately; exact value from the AISC Manual tables).

Connection length L = (5 - 1) x 3" = 12" (distance from first to last bolt row).

U (Case 2) = 1 - 1.30/12 = 0.892.

Step 4 — Select the larger U: U = max(0.90, 0.892) = 0.90. The prescriptive Case 4 value governs.

Step 5 — Net area: Standard hole for 7/8" bolt: hole diameter = 7/8 + 1/16 = 15/16 in. Two bolt holes per row through the flange.

An = Ag - 2 x (15/16) x 0.530 = 7.08 - 0.994 = 6.09 in.^2

Step 6 — Effective net area: Ae = U x An = 0.90 x 6.09 = 5.48 in.^2

Step 7 — Rupture capacity: phiPn = 0.75 x 65 x 5.48 = 267 kips

Step 8 — Yielding capacity (for comparison): phiPn = 0.90 x 50 x 7.08 = 319 kips

Governing: Rupture at 267 kips controls.

Worked Example 2 — Single Angle L5x5x3/8 Connected by One Leg

Given: Single angle L5x5x3/8, connected through one leg to a gusset plate with 4 rows of 3/4" A325 bolts at 2-1/2" pitch (4 bolts per line). A36 steel (Fy = 36 ksi, Fu = 58 ksi).

Section properties: Ag = 3.61 in.^2, x_bar = 1.37 in. (distance from the back of the connected leg to the centroid of the full angle).

Step 1 — Check Case 5 prescriptive value: Single angle, 4 bolts per line. U = 0.80.

Step 2 — Check Case 2 general formula: L = (4 - 1) x 2.5" = 7.5".

U (Case 2) = 1 - 1.37/7.5 = 0.817.

Step 3 — Select the larger U: U = max(0.80, 0.817) = 0.817. The general formula provides a slightly higher value.

Step 4 — Net area: Standard hole for 3/4" bolt: hole diameter = 3/4 + 1/16 = 13/16 in. One hole through the connected leg per row.

An = Ag - (13/16) x 3/8 = 3.61 - 0.305 = 3.31 in.^2

Step 5 — Effective net area: Ae = U x An = 0.817 x 3.31 = 2.70 in.^2

Step 6 — Rupture capacity: phiPn = 0.75 x 58 x 2.70 = 117 kips

Step 7 — Yielding capacity: phiPn = 0.90 x 36 x 3.61 = 117 kips

Governing: Both limit states are approximately equal at 117 kips. This is an efficient design where yielding and rupture are balanced.

Worked Example 3 — Plate with Longitudinal Welds

Given: Plate 1/2" x 8" (A36 steel, Fy = 36 ksi, Fu = 58 ksi) connected by two longitudinal fillet welds, each 10 inches long, along both edges.

Step 1 — Determine the case: Plate with longitudinal welds only. Case 7 applies.

Step 2 — Calculate l/w ratio: l = 10 in. (weld length), w = 8 in. (plate width, distance between welds). l/w = 10/8 = 1.25.

Since w <= l < 1.5w (1.0 x 8 = 8 <= 10 < 1.5 x 8 = 12): U = 0.75

Step 3 — Net area (no bolt holes): An = Ag = 0.5 x 8 = 4.0 in.^2

Step 4 — Effective net area: Ae = 0.75 x 4.0 = 3.0 in.^2

Step 5 — Rupture capacity: phiPn = 0.75 x 58 x 3.0 = 131 kips

Note: If the welds were 16 inches long instead (l/w = 2.0), U would be 1.0 and phiPn would be 174 kips -- a 33% increase from simply lengthening the welds.

Multi-Code Comparison

Shear lag is addressed by structural steel design codes worldwide. The approaches differ in methodology but share the same fundamental principle.

AISC 360-22 (United States)

• Method: Tabulated U values in Table D3.1 for 8 specific cases, plus the general formula U = 1 - x_bar/L.
• Scope: Applies only to tension members (Chapter D).
• Key feature: Multiple prescriptive cases allow designers to avoid calculating x_bar for common configurations.

AS 4100-2020 (Australia)

• Method: AS 4100 Clause 7.3 applies a reduction factor to the net area for tension members with eccentric connections. For single angles connected through one leg, the effective area is reduced by a factor that depends on the connection geometry.
• Key provision: For a single angle connected by one leg with a single line of fasteners, the effective area in tension is taken as An x (a_c / (a_c + a_u)), where a_c and a_u are areas of the connected and unconnected legs respectively, modified by connection length factors. Alternatively, AS 4100 provides tabulated reduction factors similar in spirit to AISC Table D3.1.
• Comparison: The AS 4100 approach is generally more conservative than AISC for short single-angle connections but comparable for longer connections. The Australian code also explicitly requires checking for block shear (Clause 5.2.4) at the same location where shear lag is evaluated.

EN 1993-1-8 (Eurocode 3)

• Method: Eurocode 3 addresses shear lag through effective width concepts in Clause 3.2.2 of EN 1993-1-5 for wide flanges in bending, and through connection efficiency factors in EN 1993-1-8 for tension members.
• Key provision: For bolted tension connections, the effective area is calculated based on the distribution of fasteners and the stiffness of connected elements. The Eurocode does not use a single "U factor" but rather computes an effective net area based on the specific bolt layout and member geometry.
• Comparison: The Eurocode approach is more analytical and case-specific than the prescriptive AISC table. It tends to produce results within 5-10% of AISC for typical W-shape and angle connections, but can differ more significantly for HSS and plate connections. Eurocode also considers block tearing (analogous to block shear) separately from shear lag.

CSA S16-19 (Canada)

• Method: CSA S16 Clause 13.2 uses a conceptually similar approach to AISC, with reduction factors for eccentric connections. The Canadian standard provides tabulated values for common configurations.
• Comparison: CSA S16 values are generally similar to AISC Table D3.1, with minor differences in the prescriptive U values (typically within 0.02-0.05 of AISC values). Both standards use the x_bar/L formula as the general approach.

Summary Table

Common Mistakes

1. Using bolt diameter instead of hole diameter for net area. The hole deduction uses the hole diameter per AISC Table J3.3 (bolt diameter + 1/16 in. for standard holes), not the bolt diameter. For 3/4 in. bolts, the hole is 13/16 in., not 3/4 in.

2. Forgetting to check both Table D3.1 cases. When both the general formula (Case 2) and a specific prescriptive case (Cases 3-7) apply, AISC permits the designer to use the larger U value. Always check both.

3. Miscalculating x_bar for channels and tees. The eccentricity x_bar is measured from the centroid of the connected element(s) to the plane of the connection (the member neutral axis is not directly involved). For a WT connected through the flange, x_bar is the distance from the flange centroid to the overall WT centroid, not to the shear plane.

4. Using U = 1.0 for welded connections without justification. Welded connections can have shear lag too. A plate with only longitudinal welds that are shorter than 2w must use U < 1.0 per Case 7.

5. Applying shear lag to compression members. Shear lag factor U applies only to tension members (AISC Chapter D). Compression members use different effective area provisions in Chapter E.

6. Ignoring shear lag for short connections. A 2-bolt connection on a single angle can produce U as low as 0.50-0.60, which significantly reduces the fracture capacity. This is especially dangerous in bracing members with single-angle connections.

7. Confusing connection length L with member length. L is the distance between the outermost fasteners in the direction of loading (or the weld length for welded connections), not the total length of the member.

8. Not checking the 3-fastener minimum for Cases 3 and 4. The prescriptive values in Case 3 (3+ fasteners) and Case 4 (4+ fasteners) only apply when the minimum fastener count is met. With fewer fasteners, the designer must use the Case 2 general formula, which often produces a lower U.

Frequently Asked Questions

What is the shear lag factor U?

U is a reduction factor (0 < U <= 1.0) applied to the net area of a tension member to account for non-uniform stress distribution when not all cross-section elements are connected. The effective net area is Ae = An x U, and the fracture capacity is phiPn = 0.75 x Fu x Ae. Values range from approximately 0.60 (single angle with 3 bolts) to 1.0 (all elements connected).

When is U = 1.0?

U equals 1.0 when all elements of the cross-section are directly connected (Case 1), when a plate has transverse welds across its full width, or when round HSS has a single concentric gusset with connection length L >= 1.3D. In practice, U = 1.0 is common for fully welded end-plate connections and for members connected through all elements.

Does shear lag apply to both bolted and welded connections?

Yes. Shear lag occurs whenever the load path does not engage the full cross-section, regardless of fastener type. For bolted connections, Cases 2-6 apply. For welded connections, Cases 1, 2, 7, and 8 apply depending on the weld configuration. Longitudinal-only welds on plates (Case 7) are a common source of shear lag in welded connections.

How do I calculate x_bar for the general formula?

x_bar is the perpendicular distance from the plane of the connection (the face of the gusset plate) to the centroid of the connected portion of the cross-section. For a W-shape connected through both flanges, x_bar is the distance from the centroid of the two flanges to the neutral axis (which equals the distance from the neutral axis to the centerline of the flanges). For a single angle connected through one leg, x_bar is measured from the back of the connected leg to the centroid of the full angle (available in the AISC Manual part 1 properties tables).

Can I use both the prescriptive value and the general formula and pick the larger one?

Yes. AISC 360-22 permits the designer to calculate U using both the applicable prescriptive case (Cases 3-7) and the Case 2 general formula, and use the larger value. This is explicitly stated in the User Note in Section D3. For connections with long connection lengths, the general formula often gives a higher U than the prescriptive values.

What is the minimum value of U?

There is no explicit minimum U in AISC 360-22, but practical lower bounds are around 0.50-0.60 for short connections on highly eccentric sections. AS 4100 and some other codes impose a minimum effective area requirement. Extremely low U values (below 0.50) indicate a poor connection detail and should be redesigned with more fastener rows or a different connection configuration.

Does shear lag apply at all locations along a tension member?

No. Shear lag applies only at the connection location where the cross-section is partially engaged. Away from the connection, stress redistributes across the full section and U = 1.0 for the member away from connections. The AISC provisions evaluate shear lag only at the connection for the fracture limit state.

How does shear lag interact with block shear?

Shear lag and block shear are separate limit states that occur at the same connection location. Block shear (AISC Section J4.3) is a combined tension-and-shear tear-out failure mode, while shear lag is a stress distribution effect. Both must be checked independently. In some cases, block shear may govern over the shear-lag-reduced fracture capacity.

Run This Calculation

Use the Steel Calculator tools to run these checks on real sections:

• Bolted Connections Calculator — design and check bolted tension connections with automatic shear lag factor calculation
• Section Properties Database — look up Ag, An, x_bar, and other properties for any AISC shape

Related References

• Bolt Capacity Table — A325 and A490 bolt shear and tension values
• Bolt Hole Sizes — standard, oversized, and slotted hole dimensions per AISC Table J3.3M/J3.3
• Steel Fy and Fu Reference — yield and tensile strengths for A992, A36, A572, and other common steels
• Tension Member Design Reference — complete tension member design including yielding, fracture, and block shear
• Weld Capacity Table — fillet and groove weld strengths per AISC Chapter J
• Block Shear Strength — block shear rupture calculations per AISC Section J4.3
• Net Area Calculations — hole deductions, staggered holes, and net area determination
• How to Verify Calculations — step-by-step guide for hand-checking steel design calculations
• Connection Design Guide — practical guidance for designing tension connections

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 information presented here represents the author's interpretation of the AISC specification and may not cover all design situations. A licensed professional engineer must review and approve all structural designs. The site operator disclaims all liability for any loss, damage, or injury arising from the use of this information.