Bracing Connection Design Guide — AISC 341 Gusset Plates & Whitmore Section

Complete bracing connection design reference covering gusset plate design per AISC 341 Seismic Provisions, the Uniform Force Method (UFM) for connection force distribution, Whitmore section for effective width determination, gusset plate buckling checks using equivalent column strips, and the special requirements for Special Concentrically Braced Frames (SCBF) versus Ordinary Concentrically Braced Frames (OCBF).

PRELIMINARY — NOT FOR CONSTRUCTION. All results are 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.

Overview of Bracing Connection Design

Braced frames are the most efficient lateral force-resisting systems for low-to-mid-rise steel buildings, providing stiffness and strength through diagonal members that form vertical trusses. The connection between the brace and the beam-column joint is typically achieved through a gusset plate — a flat plate shop-welded to the beam and column and field-bolted or field-welded to the brace.

The bracing connection must perform three functions simultaneously: (1) transfer the full brace axial force into the beam and column through the gusset plate and its attachments; (2) accommodate the brace end rotation that occurs during buckling (for compression braces in seismic systems); and (3) provide a ductile load path that does not fracture before the brace yields or buckles. These competing demands make bracing connection design one of the more complex areas of steel connection engineering.

Gusset Plate Geometry and the Whitmore Section

The gusset plate is the central element in any bracing connection. Proper sizing begins with determining the effective width of the gusset that participates in force transfer — the Whitmore section.

Whitmore Section Determination: Per AISC Manual Part 9 (and originally developed by Whitmore in 1952), the effective width is measured at the end of the connection (the last row of fasteners or the end of the weld) as the width between two lines radiating outward at 30 degrees from each side of the first row of fasteners. This 30-degree spread angle has been validated by extensive physical testing and finite element analysis.

For a bolted gusset with a single vertical row of bolts: the Whitmore width at the last bolt = bolt gage + 2 × (L_bolt_group) × tan(30°), where L_bolt_group is the distance from the first to last bolt centerline. For a typical 4-bolt connection with 3-inch spacing and 4-inch gage: L = 3 × 3 = 9 inches, Whitmore width = 4 + 2 × 9 × 0.577 = 4 + 10.39 = 14.39 inches. The effective area = 14.39 × tg, where tg is the gusset plate thickness.

For welded gussets, the 30-degree lines start at the beginning of the weld and end at the end of the weld. The Whitmore width at the weld end controls the gusset tension capacity.

Design checks using the Whitmore section:

1. Tension yielding: φPn = 0.90 × Fy × Aw, where Aw = Whitmore width × tg
2. Tension rupture: φPn = 0.75 × Fu × An, considering any net section reductions at bolt holes
3. Compression buckling: treat the Whitmore strip as an equivalent column (see below)

Gusset Plate Buckling — Equivalent Column Method

Gusset plates loaded in compression (from the brace under compression loading) are susceptible to buckling out of the plane of the connection. The standard design approach treats a strip of Whitmore width as an equivalent column with an effective length determined from the geometry of the gusset edges.

Per AISC Manual Part 9 and validated by Thornton (1984), the buckling check proceeds as follows:

1. Determine the effective length Lc: Measure three distances from the centroid of the Whitmore section to the nearest supported edge: L1 (to the beam edge), L2 (to the column edge), L3 (to the brace edge). The average Lc = (L1 + L2 + L3) / 3.

2. Select the effective length factor K: For corner gussets (beam-to-column joint), K = 1.2 accounts for partial restraint at the supported edges. For gussets in a truss where both edges are beam- or column-supported, K = 0.65 may be used per AISC guidance.

3. Compute the radius of gyration: For a rectangular strip, r = tg / √12 = tg / 3.464. For a 3/8-inch plate, r = 0.375 / 3.464 = 0.108 inches.

4. Compute slenderness: KLc / r. If this exceeds 25 (as it usually does for gusset plates), use AISC 360 Chapter E column equations to compute the critical stress Fcr and buckling capacity φPn = φ × Fcr × Aw, with φ = 0.90.

Worked buckling check: Consider a gusset with tg = 3/8 inch, L1 = 10 inches, L2 = 12 inches, L3 = 8 inches. Average Lc = 10 inches. K = 1.2. KLc = 12 inches. r = 0.108 inches. KLc/r = 12 / 0.108 = 111. For A36 steel (Fy = 36 ksi): Fe = π²E / (KL/r)² = π² × 29000 / 111² = 23.2 ksi. Fy/Fe = 36/23.2 = 1.55. Since Fy/Fe > 2.25, use AISC Equation E3-3: Fcr = 0.877 × Fe = 0.877 × 23.2 = 20.3 ksi. Whitmore width = 14.39 inches, Aw = 14.39 × 0.375 = 5.40 in². φPn = 0.90 × 20.3 × 5.40 = 98.6 kips.

Note that gusset buckling capacity is highly sensitive to plate thickness — doubling the thickness reduces slenderness by half and can dramatically increase Fcr (moving from elastic buckling into inelastic or yield-limited capacity).

The Uniform Force Method (UFM)

The Uniform Force Method, described in AISC Manual Part 13, is the standard approach for distributing brace forces to the beam and column at a gusset plate connection. The key insight is that forces can be arranged such that no moments exist at the gusset-to-beam and gusset-to-column interfaces, simplifying both the connection design and the member design.

UFM Geometry: The work point (WP) is at the intersection of the beam, column, and brace centerlines. The distance from the work point to the gusset-to-beam connection centroid is α (horizontal), and to the gusset-to-column connection centroid is β (vertical). The brace force Pu is resolved into horizontal and vertical components at the gusset edge.

UFM Force Distribution: The forces at each interface are computed from equilibrium:

• At the gusset-to-beam interface: Hb = Pu × cosθ × ec / (α + β) and Vb = Pu × sinθ × ec / (α + β), with the couple arm R = √(α² + β²) for the connection forces.
• At the gusset-to-column interface: Hc = Pu × cosθ - Hb and Vc = Pu × sinθ - Vb.

For a typical diagonal brace at 45 degrees with Pu = 200 kips, α = β = 6 inches: Hb = 200 × 0.707 × 3 / 12 = 35.4 kips, Vb = 35.4 kips. Hc = 200 × 0.707 - 35.4 = 106.1 kips, Vc = 200 × 0.707 - 35.4 = 106.1 kips. The gusset-to-beam connection experiences 35.4 kips each of horizontal and vertical shear; the gusset-to-column connection carries the bulk of the load.

Special case — uniform force / no-moment distribution: When α and β are selected such that the gusset edge forces pass through the work point, the interface forces are purely axial (no shear). This is always preferred when geometry permits, as it eliminates combined loading on beam and column connections.

SCBF vs OCBF Gusset Plate Design

AISC 341 distinguishes between Special Concentrically Braced Frames (SCBF) for high-seismic applications (SDC D, E, F) and Ordinary Concentrically Braced Frames (OCBF) for moderate seismic (SDC B, C).

SCBF Requirements (AISC 341 Section F2):

• The gusset plate must accommodate brace end rotation during post-buckling behavior. This is achieved through a 2t clearance zone (where t is gusset thickness) between the end of the brace and the gusset-to-beam/column interface lines, or through a tapered gusset detail with an elliptical clearance.
• The brace-to-gusset connection must develop the expected brace tensile strength Ry × Fy × Ag and the expected brace compressive strength 1.14 × Fcre × Ag (where Fcre is the critical buckling stress at the brace slenderness).
• The gusset plate must resist the expected brace compressive strength without buckling. The Whitmore section buckling check uses the amplified load.
• The welds connecting the gusset to the beam and column must be sized for the expected brace strength, not just the factored load. This ensures the connection is stronger than the brace — a capacity-protected element.

OCBF Requirements (AISC 341 Section F1):

• The gusset is designed for the amplified seismic load Emh per ASCE 7 Chapter 12, which for OCBF is Ω₀ × QE (overstrength factor times the seismic effect).
• The 2t clearance detail is not formally required, but providing it is good practice to avoid tearing the gusset when the brace buckles.
• Brace-to-gusset welds may be sized for the amplified seismic force rather than the expected strength. The capacity-protected design philosophy is less rigorous for OCBF.
• Post-buckling residual strength of the brace (typically 0.3 times the compression capacity after buckling) should be considered for the connection design.

Weld Design for Gusset Plate Connections

Welds at the gusset-to-beam and gusset-to-column interfaces transfer the UFM-determined forces. For fillet welds, the design strength is checked using the elastic vector method for in-plane forces:

Direct shear stress: fv_direct = V / (2 × Lw) where V is the interface shear and Lw is weld length per side. Flexural stress (if UFM moments are not fully eliminated): fv_moment = M × c / Ip, where c is the distance from weld centroid to extreme fiber and Ip is the polar moment of inertia of the weld group treated as lines. Resultant stress: fv_resultant = √(fv_direct² + fv_moment²) ≤ φFw, where φFw = 0.75 × 0.60 × FEXX × (0.707 × w).

For the gusset-to-beam connection from the UFM example above (Hb = 35.4 kips, Vb = 35.4 kips, weld length Lw = 12 inches each side): Direct stress fv_direct = 35.4 / (2 × 12) = 1.48 kips/inch. If no moment, fv_resultant = 1.48 kips/inch ≈ φFw for 3/16 fillet = 4.18 kips/inch. Substantial excess capacity. Weld size is typically governed by the minimum per AISC Table J2.4.

Worked Example: SCBF Diagonal Brace Connection

Problem Statement: Design the gusset plate connection for an HSS 6×6×1/2 diagonal brace (A500 Gr C, Fy = 50 ksi, Ag = 9.74 in²) in an SCBF. Brace force Pu = 180 kips (tension), Pu_comp = 150 kips (compression, factored). Brace angle θ = 40 degrees from horizontal. Beam W18×50, column W14×90, both A992. Design per AISC 341 SCBF requirements.

Step 1 — Determine brace expected strength: Ry for A500 Gr C HSS = 1.4 per AISC 341 Table A3.1. Expected tensile strength: Ry × Fy × Ag = 1.4 × 50 × 9.74 = 681.8 kips. Expected compressive strength: use 1.14 × Fcre × Ag at the brace slenderness. Brace length = 18 ft (diagonal), HSS 6×6×1/2 rx = ry = 2.25 in. KL/r = 1.0 × 18 × 12 / 2.25 = 96. Fe = π² × 29000 / 96² = 31.0 ksi. Fy/Fe = 50/31 = 1.61. Use inelastic buckling (E3-2): Fcr = 0.658^(50/31) × 50 = 29.5 ksi. Expected compressive strength = 1.14 × 29.5 × 9.74 = 327.5 kips.

The gusset and its attachments must be designed for the expected strengths: 681.8 kips tension and 327.5 kips compression. These are capacity-protected design forces.

Step 2 — Gusset plate geometry: Select gusset plate thickness tg = 3/4 inch (A572 Gr 50, Fy = 50 ksi). Determine Whitmore width at the brace end. Brace-to-gusset connection: 4 rows of 7/8-inch A490-X bolts at 3-inch spacing. Bolt gage = 5 inches. Bolt group length = 3 × 3 = 9 inches. Whitmore width = 5 + 2 × 9 × tan(30) = 5 + 10.39 = 15.39 inches. Effective area Aw = 15.39 × 0.75 = 11.54 in².

Step 3 — Check gusset tension at Whitmore section: φPn_tension = 0.90 × 50 × 11.54 = 519.4 kips < 681.8 kips (expected tension). NOT ADEQUATE. Increase gusset to 1-inch thickness: Aw = 15.39 × 1.0 = 15.39 in². φPn_tension = 0.90 × 50 × 15.39 = 692.6 kips > 681.8 kips. OK.

Step 4 — Check gusset buckling: Average Lc from Whitmore centroid to supported edges: L1 (to beam) = 10 in, L2 (to column) = 12 in, L3 (to brace) = 8 in. Average Lc = 10 inches. K = 1.2 for SCBF corner gusset. KLc = 12 inches. r = 1.0 / √12 = 0.289 inches. KLc/r = 12 / 0.289 = 41.6. Fe = π² × 29000 / 41.6² = 165.3 ksi. Fy/Fe = 50/165.3 = 0.302 < 2.25, use E3-2: Fcr = 0.658^(50/165.3) × 50 = 49.1 ksi. φPn_comp = 0.90 × 49.1 × 15.39 = 680.4 kips > 327.5 kips. OK. Note that buckling capacity at the expected compression is non-governing; tension controls the design.

Step 5 — AISC 341 SCBF 2t clearance detail: Per F2.6c, provide an elliptical clearance zone between the end of the brace and the theoretical gusset fold lines. Clearance dimension = 2t = 2 × 1.0 = 2.0 inches from the end of the brace to the line connecting the gusset-to-beam and gusset-to-column interface points. This allows the gusset to buckle out-of-plane during brace compression buckling without the brace end gouging the gusset plate.

Step 6 — Check brace-to-gusset bolt capacity: 7/8-inch A490-X bolt single shear: φrn = 0.75 × 84 × 0.601 = 37.9 kips/bolt. For 4 bolts: 151.6 kips (single shear). Brace-to-gusset connection typically has double shear (gusset between splice plates), giving 2 × 151.6 = 303.2 kips.

Use 8 bolts in double shear: 8 × 37.9 × 2 = 606.4 kips. Check bearing on gusset (1-inch plate): φrn_bearing = 0.75 × 2.4 × 0.875 × 1.0 × 65 = 102.4 kips/bolt. Total = 819 kips > 681.8 kips. OK. Bearing check with expected strength.

Step 7 — UFM force distribution: Work point at beam-column-brace intersection. Select α = β = 6 inches. Brace force Pu = 681.8 kips at 40 degrees from horizontal. Eccentricity e = distance from WP to connection centroid. The UFM interface forces are computed from equilibrium equations per AISC Manual Part 13.

Step 8 — Gusset-to-beam and gusset-to-column welds: Design fillet welds for the UFM interface forces. Weld capacity must exceed the UFM force components with φ = 0.75.

Design Summary: Gusset plate PL 1 × 16 × 24 (A572 Gr 50), 8 rows of 7/8-inch A490-X bolts for brace-to-gusset, 2t = 2-inch elliptical clearance zone, fillet welds at gusset-to-beam and gusset-to-column per UFM. Thick gusset required to resist expected tension (692.6 kips design > 681.8 kips demand). Buckling non-governing at tg = 1 inch.

Engineering Best Practices

• For SCBF gussets, always check the expected brace strength — not the factored strength — for the capacity-protected design. Using factored loads instead of expected strengths is the single most common error in SCBF connection design.
• The elliptical clearance detail (2t zone) is mandatory for SCBF. Omitting it will cause the brace end to fracture the gusset during the first cycle of brace buckling.
• Gusset plate buckling is extremely sensitive to thickness (Pn ∝ tg × Fcr, and Fcr ∝ 1/(KLc/tg)²). A 1/4-inch increase in thickness can mean the difference between elastic buckling and yield-limited capacity.
• For the UFM, design the gusset geometry so that α and β produce an efficient force distribution. Unequal α and β force more load into one interface, potentially requiring thicker welds or stronger connections at that interface.
• The Whitmore width should be measured at the end of the weld or last bolt row — not at the start. The wider end captures the full stress distribution.
• Brace-to-gusset welds for SCBF must be CJP groove welds or fillet welds sized for the expected tensile strength. Fillet welds are rarely economical for SCBF brace connections given the Ry amplification.

References

• AISC 341-22 Section F2 — Special Concentrically Braced Frames
• AISC 360-22 Section J4.4 — Strength of Elements in Compression
• AISC Steel Construction Manual, 16th Edition — Part 9 (Gusset Plates) and Part 13 (Bracing Connections)
• AISC Design Guide 29 — Vertical Bracing Connections — Analysis and Design
• Thornton, W.A. (1984) — Bracing Connections for Heavy Construction, AISC Engineering Journal

Try Our Free Calculator

Try our free connection calculators to get instant AISC 360 and AISC 341 design checks for bolted and welded bracing connections. No signup required. Our browser-based tools check all limit states including Whitmore section tension, gusset buckling, UFM force distribution, and SCBF capacity-protected requirements.

Try it now: Check your bracing connection design with our free tools →