Gusset Plate Design — Whitmore Section, Block Shear, and Buckling

Gusset plates connect diagonal braces to beam-column joints in braced frames. The gusset must transfer the brace force (tension or compression) into the beam and column through a combination of bolts and welds. Design involves checking the Whitmore section for tension yielding, the Thornton method for compression buckling, block shear rupture, and the gusset-to-frame interface forces.

Whitmore section — tension capacity

The Whitmore section is an effective width at the end of the connection that distributes the brace force across the gusset plate. It is defined by 30-degree lines drawn from the first bolt (or start of weld) to the last bolt in each outer line:

L_whitmore = s + 2 * l * tan(30°)

Where s = spacing between outer bolt lines (gage), l = connection length from first to last bolt. The tensile capacity on the Whitmore section:

phiRn = 0.90 * Fy * L_whitmore * tp    [yielding, AISC 360 Eq. J4-1]
phiRn = 0.75 * Fu * L_whitmore_net * tp [rupture, Eq. J4-2, if bolts cross the section]

Thornton method — compression buckling

When the brace is in compression, the gusset plate can buckle. The Thornton method treats the gusset as an equivalent column with length equal to the average of the three distances from the Whitmore section corners to the nearest gusset edge (L1, L2, L3):

L_avg = (L1 + L2 + L3) / 3
KL/r = K * L_avg / (tp / sqrt(12))

Where K = 0.65 (fixed-fixed, conservative) to 1.2 (AISC recommended for gussets), tp = gusset thickness, r = tp/sqrt(12) for a rectangular plate section. Then calculate Fcr from AISC 360 Chapter E column equations (Section E3) and: phiRn = 0.90 _ Fcr _ L_whitmore * tp.

Block shear rupture (AISC 360 Section J4.3)

Block shear on the gusset must be checked for the bolt pattern:

phiRn = 0.75 * (0.60*Fu*Anv + Ubs*Fu*Ant)
     <= 0.75 * (0.60*Fy*Agv + Ubs*Fu*Ant)    [Eq. J4-5]

Check block shear for all potential failure paths, including paths around the bolt group and paths to the gusset edge.

Interface forces — Uniform Force Method (AISC Manual Part 13)

The Uniform Force Method (UFM) distributes the brace force into the beam and column interfaces. The method finds the force distribution that produces uniform forces on the gusset edges, minimizing moments at the interfaces.

Key parameters: alpha (distance from beam-column work point to the gusset-to-beam connection centroid along the beam), beta (distance to the gusset-to-column connection centroid along the column), and r = sqrt((alpha + e_b)^2 + (beta + e_c)^2), where e_b and e_c are the eccentricities from the beam and column centroids to the gusset edge.

The beam interface carries: Hb = alphaP/r (horizontal) and Vb = e_bP/r (vertical). The column interface carries: Hc = e_cP/r (horizontal) and Vc = betaP/r (vertical).

Worked example — HSS6x6x3/8 brace, 200-kip tension

Given: HSS6x6x3/8 brace (Fy = 46 ksi, Fu = 58 ksi) carrying 200-kip factored tension, connected to a 1/2" A36 gusset plate (Fy = 36 ksi, Fu = 58 ksi) with 4 rows of 3/4" A325-N bolts at 3" spacing, 5.5" gage between outer bolt lines.

Step 1 — Whitmore section width: Connection length l = 3 rows of spacing = 3 _ 3 = 9 in. L_whitmore = 5.5 + 2 _ 9 _ tan(30°) = 5.5 + 2 _ 9 * 0.577 = 5.5 + 10.39 = 15.89 in.

Step 2 — Tension yielding on Whitmore section: phiRn = 0.90 _ 36 _ 15.89 * 0.50 = 257 kips > 200 kips. OK.

Step 3 — Tension rupture on Whitmore section: Net width = 15.89 - 2 _ (3/4 + 1/16 + 1/16) _ 0.50 = 15.89 - 0.875 = 15.01 in (two bolt holes cross the Whitmore section). phiRn = 0.75 _ 58 _ 15.01 * 0.50 = 326 kips > 200 kips. OK.

Step 4 — Thornton compression buckling: Average unbraced length from Whitmore corners to nearest gusset edge: L1 = 8.5 in, L2 = 10.2 in, L3 = 8.5 in. Lavg = 9.07 in. r = 0.50/sqrt(12) = 0.1443 in. KL/r = 1.2 * 9.07 / 0.1443 = 75.4. Fe = pi^2 _ 29000 / 75.4^2 = 50.3 ksi. Since 75.4 < 4.71sqrt(29000/36) = 134, use inelastic: Fcr = 0.658^(36/50.3) * 36 = 0.658^0.716 _ 36 = 0.736 _ 36 = 26.5 ksi. phiRn = 0.90 _ 26.5 _ 15.89 _ 0.50 = 189 kips < 200 kips. FAILS in compression. Increase gusset to 5/8": r = 0.1804 in, KL/r = 60.3, Fe = 78.7 ksi, Fcr = 30.4 ksi, phiRn = 0.90 _ 30.4 _ 15.89 _ 0.625 = 273 kips. OK.

Seismic gusset plate considerations (AISC 341)

For Special Concentrically Braced Frames (SCBF) per AISC 341 Section F2.6c:

2tp clearance: The gusset must accommodate brace buckling by providing a linear clearance zone of 2*tp perpendicular to the brace axis at the end of the brace connection. This allows plastic hinge formation without gusset fracture.
Elliptical clearance (alternate): An 8*tp elliptical clearance is an alternative to the linear 2tp zone per AISC 341 Section F2.6c(3).
Expected strength: Use R_y*Fy (expected yield, typically R_y = 1.1 for ASTM A36 plates, R_y = 1.4 for A500 Grade B HSS) for capacity calculations.

Multi-code comparison

AISC 360-22 (USA): Whitmore 30-degree spread, Thornton average-of-three-lengths compression model, block shear per Section J4.3, phi = 0.90 yielding / 0.75 rupture. Seismic gussets per AISC 341 Section F2.6c.

AS 4100-2020 (Australia): Similar Whitmore section concept used in practice (not explicitly codified). Compression buckling checked as a plate column per Section 6. Block shear per Clause 9.1.10. phi = 0.90 for yielding, 0.75 for fracture. No explicit 2tp clearance requirement — seismic detailing follows NZS 3404 in New Zealand or project-specific requirements.

EN 1993-1-8 (Europe): Gusset plate design follows Clause 3.12 for connection geometry and Clause 6.2 for resistance checks. Block tearing per Clause 3.10.2: Veff = FuAnt/gamma_M2 + FyAnv/(sqrt(3)*gamma_M0). Compression buckling of gusset plates is not explicitly addressed — designers use Annex B column buckling curves with an equivalent strut model. gamma_M0 = 1.00, gamma_M2 = 1.25.

CSA S16-19 (Canada): Whitmore section per Clause 13.11 commentary. Block shear per Clause 13.11: Tr = phi_u * (0.6AgvFy + AnFu) or phi_u * (0.6AnvFu + AgFy), whichever is less. phi_u = 0.75. Seismic gusset requirements in CSA S16 Clause 27 mirror AISC 341 with the 2tp clearance zone for ductile (Type D/MD) braced frames.

Common mistakes

Using K = 2.0 for gusset buckling. The cantilever assumption (K = 2.0) is overly conservative for gussets restrained by the beam and column. AISC research recommends K = 0.65 for compact gussets where all edges are connected, and K = 1.2 as a general-purpose value. Using K = 2.0 leads to unnecessarily thick plates.
Not checking the Whitmore section for net rupture on bolted connections. The Whitmore section may cross bolt holes. If it does, the net area rupture check (phi = 0.75) can govern over gross yielding, especially with large bolt diameters or tight gages.
Ignoring the gusset-to-frame interface design. The gusset edges must transfer horizontal and vertical force components to the beam flange and column flange via fillet welds or bolts. Under-designed interface welds are a frequent cause of brace connection failure — particularly the gusset-to-beam weld, which carries combined shear and axial force.
Omitting the 2tp clearance zone for seismic gussets. In SCBF systems, the brace buckles in compression at expected strength levels. Without the 2tp clearance, the gusset plate cannot accommodate the out-of-plane rotation, leading to fracture at the gusset-brace interface during cyclic loading.
Not checking the beam and column locally. The gusset forces impose concentrated loads on the beam web (local yielding per AISC 360 Section J10.2, web crippling per J10.3) and column web. These checks are often overlooked and can require web stiffeners or doubler plates.

Frequently asked questions

What is the Whitmore section? An effective width across the gusset plate defined by 30-degree spread lines from the connection. It determines the area available for tension yielding and compression buckling.

How do I size a gusset plate? Start with the brace force, estimate the Whitmore section width based on the connection geometry, and select a thickness that satisfies tension yielding, compression buckling (Thornton), and block shear. Then design the gusset-to-beam and gusset-to-column connections using the Uniform Force Method.

What is the Thornton method? A method for checking gusset plate compression buckling by treating the gusset as an equivalent column with an average unbraced length from the Whitmore section corners to the nearest free edge. It is documented in AISC Manual Part 13 and Engineering Journal papers by Thornton (1984).

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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, AISC 341 (seismic), and AISC Manual Part 13. The site operator disclaims liability for any loss arising from the use of this information.