What is gusset plate design in structural steel design?

Gusset Plate Design is a key concept in structural steel engineering governed by international design standards including AISC 360, EN 1993, AS 4100, and CSA S16. This reference page provides definitions, formulas, values, and worked examples.

How do you calculate gusset plate design?

The calculation method depends on the governing design code and loading condition. Refer to the formulas and worked examples on this page. For automated calculation, use the free tools linked in the calculator CTA section below.

Where can I find official gusset plate design values and tables?

Official values are published in the AISC Steel Construction Manual (US), EN 1993 standards (Europe), AS 4100 (Australia), and CSA S16 (Canada). The AISC Shapes Database v16.0 provides tabulated values for all standard sections. This reference page summarizes commonly used values for quick lookup.

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).

Uniform Force Method — step-by-step procedure

The Uniform Force Method (UFM), documented in AISC Manual Part 13 and the AISC Steel Construction Manual 15th Ed. Chapter 13, is the standard method for distributing brace forces to the gusset-to-beam and gusset-to-column interfaces. The UFM finds the distribution that minimizes moments at the interfaces by placing the resultant force at specific locations on the gusset edges.

Step 1 — Establish geometry

Define the following dimensions from the beam-column work point to the gusset edge:

alpha (a): Horizontal distance from the beam-column work point to the centroid of the gusset-to-beam weld group.
beta (b): Vertical distance from the beam-column work point to the centroid of the gusset-to-column weld group.
e_b: Eccentricity from the beam centroid to the gusset-to-beam connection surface (typically the distance from beam centerline to beam flange outer face).
e_c: Eccentricity from the column centroid to the gusset-to-column connection surface (typically the distance from column centerline to column flange outer face).

Step 2 — Calculate the normalized distance

r = sqrt( (alpha + e_b)^2 + (beta + e_c)^2 )

This is the diagonal distance from the intersection of the beam and column centerlines to the theoretical centroid of force on the gusset.

Step 3 — Distribute the brace force

For a brace force P (positive in tension, negative in compression):

Beam interface forces:

Hb = alpha * P / r     (horizontal force on beam, parallel to beam axis)
Vb = e_b * P / r       (vertical force on beam, perpendicular to beam axis)
Mb = 0                  (no moment — this is the key advantage of UFM)

Column interface forces:

Hc = e_c * P / r       (horizontal force on column, perpendicular to column axis)
Vc = beta * P / r       (vertical force on column, parallel to column axis)
Mc = 0                  (no moment at column interface)

Step 4 — Verify equilibrium

Check that the interface forces are consistent with the brace force:

Horizontal equilibrium:  Hb + Hc = P * cos(theta)
Vertical equilibrium:    Vb + Vc = P * sin(theta)

Where theta is the angle of the brace from horizontal. If equilibrium is not satisfied, check the geometry definitions and recalculate.

Step 5 — Design interface connections

For the gusset-to-beam connection: Design welds or bolts for combined Hb (shear) and Vb (axial). The resultant force per unit length on the weld is:

f_weld = sqrt( (Hb / L_beam_weld)^2 + (Vb / L_beam_weld)^2 )

For the gusset-to-column connection: Design for combined Hc (axial) and Vc (shear) using the same approach.

Selecting alpha and beta

The designer has freedom to choose alpha and beta, subject to the geometric constraint that the gusset must fit within the available space. Common guidelines:

Set alpha such that the gusset-to-beam connection centroid aligns with the beam flange to minimize eccentricity.
Set beta such that the gusset-to-column connection centroid aligns with the column flange.
A starting point: alpha = e_b and beta = e_c (symmetric distribution), then adjust based on the connection layout.
If the brace angle is close to 45 degrees, alpha and beta will be approximately equal. For shallow brace angles (under 30 degrees), alpha will be much larger than beta.

Whitmore section — detailed evaluation

The Whitmore section is the effective cross-section of the gusset plate that resists the brace force. It was first proposed by Whitmore (1952) and is now the standard method for checking gusset plate tension and compression capacity.

Whitmore width calculation

The Whitmore width L_w is defined by two 30-degree lines emanating from the first and last bolts (or weld start/end points) in the outermost lines of the connection:

L_w = s + 2 * L_connection * tan(30 deg)
L_w = s + 2 * L_connection * 0.577

Where s = horizontal distance between outer bolt lines (gage), L_connection = length from first to last bolt center.

Whitmore section location and checks

The Whitmore section is located at the end of the connection farthest from the brace. Two checks are required:

Tension yielding on the gross Whitmore section: phi*Rn = 0.90 * Fy _ L_w _ t_p This check ensures the gusset does not yield across the effective width.
Tension rupture on the net Whitmore section (if bolt holes cross the section): phiRn = 0.75 * Fu * (L_w - nd_hole*t_p) * t_p Where n = number of bolt holes crossing the Whitmore section, d_hole = hole diameter + 1/16" (damage allowance).
Compression buckling (Thornton method): Treat the gusset as a column with the Whitmore section as the cross-section and an effective length from the Whitmore section to the nearest free edge. See the Thornton method section above.

Whitmore width for different connection geometries

Connection Geometry	Gage (s)	Connection Length (L)	Whitmore Width L_w	Notes
2 bolt lines, 3 rows at 3" c/c	5.5"	6"	12.4"	Typical HSS brace connection
2 bolt lines, 4 rows at 3" c/c	5.5"	9"	15.9"	Longer connection, wider Whitmore
2 bolt lines, 5 rows at 3" c/c	5.5"	12"	19.3"	Heavy brace, many bolts
Single bolt line, 4 bolts at 3"	N/A	9"	290.577 = 10.4"	Single line — s=0, spread from one line
Welded connection, 10" length	N/A	10"	2100.577 = 11.5"	Spread from weld start to weld end

Block shear per AISC J4.3 — detailed procedure

Block shear is a limit state where a block of material tears out of the gusset plate along a path combining shear and tension failure surfaces. AISC 360 Section J4.3 provides the block shear resistance equations.

Block shear resistance equations

phi*Rn = 0.75 * (0.60 * Fu * A_nv + Ubs * Fu * A_nt)         [rupture governs]
phi*Rn = 0.75 * (0.60 * Fy * A_gv + Ubs * Fu * A_nt)         [yielding governs]

Use the lesser of the two expressions.

Where:

A_gv = gross area in shear (along the shear failure path)
A_nv = net area in shear (gross minus bolt holes in the shear path)
A_nt = net area in tension (across the tension failure path)
Ubs = 1.0 for uniform tension stress (typical for symmetric bolt patterns); 0.5 for non-uniform tension stress
phi = 0.75

Shear and tension areas for a typical gusset bolt pattern

For a gusset with n_bolt_rows rows of bolts at spacing s, edge distance L_ev (vertical), and n_bolt_cols columns at spacing g, edge distance L_eh (horizontal):

Shear area (along two vertical lines of bolts):

A_gv = 2 * t_p * (n_bolt_rows * s + L_ev - d_hole/2)   ... wait, let me correct
A_gv = 2 * t_p * (n_bolt_rows * s + L_ev)
A_nv = A_gv - n_bolt_rows * d_hole * t_p * 2             ... subtract holes in both lines

Actually, more precisely:

A_gv = 2 * t_p * [ (n_bolt_rows - 1) * s + L_ev ]
A_nv = A_gv - 2 * n_bolt_rows * (d_hole + 1/16) * t_p

Tension area (across the top between the two bolt lines):

A_nt = t_p * ( g - d_hole )    ... for one bolt hole in the tension path
A_gt = t_p * g                  ... gross tension area

Worked example — HSS6x6 brace gusset with full UFM procedure

Given: A diagonal brace connection in a braced frame. HSS6x6x3/8 brace (Fy = 46 ksi, Fu = 58 ksi) at 45 degrees from horizontal, carrying a factored compression force P = 180 kips. The gusset plate is 5/8" thick A36 (Fy = 36 ksi, Fu = 58 ksi). The brace is bolted to the gusset with 4 rows of 3/4" A325-N bolts at 3" spacing, 5.5" gage between outer bolt lines.

The gusset is welded to a W18x50 beam (d = 17.99", tf = 0.570", tw = 0.355") and a W14x68 column (d = 14.04", tf = 0.720", tw = 0.415"). Beam e_b = 17.99/2 = 9.0 in. Column e_c = 14.04/2 = 7.0 in. Selected alpha = 12.0 in., beta = 9.0 in.

Step 1 — Whitmore section

Connection length Lconn = 3 * 3 = 9 in. Lw = 5.5 + 2 * 9 * tan(30) = 5.5 + 10.39 = 15.89 in.

Step 2 — Compression buckling (Thornton)

Measured distances from Whitmore corners to nearest free gusset edge: L1 = 7.5 in., L2 = 9.0 in., L3 = 7.5 in. Lavg = (7.5 + 9.0 + 7.5) / 3 = 8.0 in. r = t_p / sqrt(12) = 0.625 / 3.464 = 0.1804 in. KL/r = 0.65 * 8.0 / 0.1804 = 28.8 (using K = 0.65, edges connected) Fe = pi^2 _ 29000 / 28.8^2 = 345 ksi Fcr = 0.658^(36/345) _ 36 = 0.658^0.104 _ 36 = 0.959 * 36 = 34.5 ksi phiRn (compression) = 0.90 _ 34.5 _ 15.89 * 0.625 = 308 kips > 180 kips. OK.

Step 3 — Block shear

Bolt hole diameter d_h = 3/4 + 1/8 = 7/8" = 0.875 in.

Shear paths (two lines, 4 bolt holes each): Agv = 2 * 0.625 _ (33 + 1.5) = 2 * 0.625 _ 10.5 = 13.13 in^2 A*nv = 13.13 - 2 * 4 _ 0.875 _ 0.625 = 13.13 - 4.38 = 8.75 in^2

Tension path (between outer bolt lines, single bolt hole): A*nt = 0.625 * (5.5 - 0.875) = 0.625 _ 4.625 = 2.89 in^2 Ubs = 1.0 (symmetric pattern)

Rupture expression: 0.75 _ (0.60 _ 58 _ 8.75 + 1.0 _ 58 _ 2.89) = 0.75 _ (304.5 + 167.6) = 0.75 _ 472.1 = 354 kips Yielding expression: 0.75 _ (0.60 _ 36 _ 13.13 + 1.0 _ 58 _ 2.89) = 0.75 _ (283.6 + 167.6) = 0.75 _ 451.2 = 338 kips

Block shear capacity = 338 kips (yielding expression governs) > 180 kips. OK.

Step 4 — Uniform Force Method distribution

r = sqrt( (12.0 + 9.0)^2 + (9.0 + 7.0)^2 ) = sqrt(441 + 256) = sqrt(697) = 26.4 in.

Beam interface: Hb = 12.0 _ 180 / 26.4 = 81.8 kips (horizontal shear on beam flange) Vb = 9.0 _ 180 / 26.4 = 61.4 kips (vertical force on beam flange)

Column interface: Hc = 7.0 _ 180 / 26.4 = 47.7 kips (horizontal force on column flange) Vc = 9.0 _ 180 / 26.4 = 61.4 kips (vertical shear on column flange)

Verification: Hb + Hc = 81.8 + 47.7 = 129.5 kips. Pcos(45) = 1800.707 = 127.3 kips. Close (difference due to rounding). Vb + Vc = 61.4 + 61.4 = 122.8 kips. P*sin(45) = 127.3 kips. Close.

Step 5 — Interface weld design

Gusset-to-beam weld: Combined force per inch on a 15-in. long weld: f = sqrt( (81.8/15)^2 + (61.4/15)^2 ) = sqrt(29.8 + 16.8) = sqrt(46.6) = 6.82 kip/in. Required weld size: w = 6.82 / (0.75 _ 0.60 _ 70 * 0.707) = 6.82 / 22.3 = 0.306 in. Use 5/16" fillet weld.

Gusset-to-column weld: Combined force per inch on a 14-in. long weld: f = sqrt( (47.7/14)^2 + (61.4/14)^2 ) = sqrt(11.6 + 19.2) = sqrt(30.8) = 5.55 kip/in. Required weld size: w = 5.55 / 22.3 = 0.249 in. Use 1/4" fillet weld (minimum per AISC Table J2.4 for 5/8" gusset plate is 5/16"; use 5/16" fillet weld to satisfy minimum weld size).

Step 6 — Summary

Check	Capacity	Demand	D/C Ratio	Status
Whitmore tension yielding	322 kips	180 kips	0.56	OK
Thornton compression buckling	308 kips	180 kips	0.58	OK
Block shear	338 kips	180 kips	0.53	OK
Beam interface weld	6.82 kip/in	6.82 kip/in	1.00	OK (5/16")
Column interface weld	5.55 kip/in	5.55 kip/in	1.00	OK (5/16")

All checks pass. The 5/8" A36 gusset plate is adequate for the 180-kip brace force.

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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.

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