--------- | ----------------------------- | ----------------------------- | --------------------- | | X-brace | Diagonals cross at center | One brace in tension per load | Light lateral systems | | V-brace | Braces meet beam from below | Both braces active | Chevron bracing | | Inverted V | Braces meet beam from above | Both braces active | Inverted chevron | | K-brace | Braces meet column mid-height | Shorter braces | Limited use (seismic) | | Single diagonal | One brace per bay | Tension or compression | Light retrofit |

Gusset Plate Geometry

Key Dimensions

Minimum Gusset Thickness

Gusset plate thickness is selected based on the brace force and connection geometry:

Uniform Force Method (Thornton Method)

The uniform force method is the AISC-recommended approach for distributing brace forces at gusset plate connections. It assumes uniform stress distribution along each interface.

Force Resolution

The brace force P is resolved into components at the beam and column interfaces:

Horizontal component on beam: H_b = P × cos θ × (e_c / (e_b + e_c))

Vertical component on beam: V_b = P × sin θ × (e_b / (e_b + e_c))

Horizontal component on column: H_c = P × cos θ - H_b

Vertical component on column: V_c = P × sin θ - V_b

where θ = brace angle from horizontal, e_b = eccentricity to beam, e_c = eccentricity to column.

Work Point and Eccentricities

When the work point is at the beam-column intersection (concentric connection), the force distribution depends solely on the geometry of the gusset plate attachment.

Whitmore Section

The Whitmore section defines the effective width of the gusset plate at the end of the brace connection. It determines the area available for tension or compression resistance.

Whitmore Effective Width

The effective width (l_w) is constructed by drawing 30° lines from the outermost bolts in each row of the connection to the end of the connection:

l_w = l + 2 × l_tan × tan 30°

where l = distance between outermost bolt rows, l_tan = distance from last bolt row to plate end.

Whitmore Section Checks

1. Tension yielding: φ × Fy × l_w × t ≥ P_u
2. Tension rupture: φ × Fu × (l_w - bolt holes) × t ≥ P_u
3. Compression buckling: φ × Fcr × l_w × t ≥ P_u (for compression braces)

The buckling length for the Whitmore section is taken from the end of the brace to the last row of bolts, projected perpendicular to the Whitmore section.

Gusset Plate Limit States

Every gusset plate connection must be checked for these limit states:

Gusset Plate Checks

Brace Checks

Interface Checks (Beam and Column)

Gusset Edge Distance and Free Edge Stability

Free Edge Buckling

The unsupported (free) edge of the gusset plate must be checked for buckling under compression:

• If the free edge is not stiffened, the maximum l/t ratio (length/thickness) should be limited
• AISC recommends: l/t ≤ 340 / √Fy for unstiffened edges
• For A36: l/t ≤ 57; for A572 Gr 50: l/t ≤ 48

If the free edge exceeds this limit, add an edge stiffener (angle or plate) or increase the gusset thickness.

2t Rule for Brace Buckling (SCBF)

For Special Concentric Braced Frames (seismic), the gusset must allow brace buckling out of plane. The "2t rule" requires:

• The end of the brace is held back 2t from the restraint line (where gusset meets beam/column)
• This allows the gusset to bend plastically when the brace buckles
• The gusset must be detailed with a clear flexural yield zone

Worked Example — Chevron Brace Gusset

Given: HSS6x6x3/8 brace at 45°, Pu = 150 kips (LRFD, tension). W18×50 beam, W14×68 column. A500 Gr B (Fy = 46 ksi). Gusset PL 5/8 in A36.

Step 1: Whitmore Section Assume 3 rows of 7/8 in bolts at 3 in spacing: l_w = 6 + 2 × 3 × tan 30° = 6 + 3.46 = 9.46 in A_w = 9.46 × 0.625 = 5.91 in²

Step 2: Tension yielding of Whitmore section φRn = 0.9 × 36 × 5.91 = 191.5 kips > 150 → OK

Step 3: Gusset tension yielding (brace direction) Assume brace connection length = 12 in: A_g = 12 × 0.625 = 7.5 in² φRn = 0.9 × 36 × 7.5 = 243 kips > 150 → OK

Step 4: Block shear (bolt group) Assume 3 bolts per row, 2 rows (6 bolts total): Gross shear area = 2 × (6 + 1.5) × 0.625 = 9.375 in² Net shear area = 9.375 - 2 × 2 × 0.9375 × 0.625 = 9.375 - 2.34 = 7.03 in² Net tension area = (3 - 1) × 0.9375 × 0.625 = 1.17 in² (approximate)

φRn = 0.75 × [0.6 × 58 × 7.03 + 58 × 1.17] = 0.75 × [244.6 + 67.9] = 234.4 kips > 150 → OK

Step 5: Check free edge stability Free edge length ≈ 18 in, t = 0.625 in l/t = 18 / 0.625 = 28.8 < 57 (A36 limit) → OK

Frequently Asked Questions

What is the uniform force method? The uniform force method (Thornton method) distributes the brace force to the beam and column interfaces based on the gusset geometry and eccentricities. It assumes uniform stress along each interface. It is the method recommended by AISC for designing gusset plate connections.

What is the Whitmore section? The Whitmore section is an effective width at the end of a gusset plate connection, constructed by projecting 30° lines from the outermost bolts. It defines the area of the gusset plate that resists the concentrated brace force in tension or compression.

How thick should a gusset plate be? Gusset plate thickness depends on the brace force. Typical ranges: 3/8 in for forces under 50 kips, 1/2 in for 50-100 kips, 5/8 in for 100-200 kips, and 3/4 in for 200-400 kips. The thickness must satisfy all limit states (yielding, rupture, block shear, buckling).

What is the 2t rule in brace connections? The 2t rule is a seismic detailing requirement (SCBF) where the end of the brace is held back a distance of 2 times the gusset plate thickness from the beam or column face. This creates a flexible zone in the gusset that allows the brace to buckle out-of-plane without fracturing the connection.

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Related Pages

• Connection Types Explained — All connection types
• HSS Connection Design — AISC Chapter K
• Seismic Connections — AISC 341 requirements
• Bolted Connections — Bolt capacity calculator
• Welded Connections — Weld capacity calculator

Disclaimer

This is a calculation tool, not a substitute for professional engineering certification. All results must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in construction, fabrication, or permit documents. The user is responsible for the accuracy of all inputs and the verification of all outputs.

Design Resources

Calculator tools

• Bolted Connection Calculator
• Weld Capacity Calculator
• End Plate Moment Connection Calculator
• Fin Plate Shear Connection Calculator
• Gusset Plate Calculator

Design guides

• Bolted Connection Worked Example
• Bolted Connection Checklist
• Steel Connection Calculator Guide
• Weld Design Checklist
• EN 1993-1-8 Bolted Connection Worked Example

Reference pages

• Shear Tab