Canadian Gusset Plate Design — CSA S16 Whitmore Section Method

Complete reference for gusset plate design per CSA S16-19 for Canadian braced frame connections. Covers the Whitmore section method for tension and compression, block shear verification, weld and bolt group design at interfaces, and a step-by-step worked example.

Quick access: Brace connection → | Shear tab → | Weld capacity →

CSA S16 Gusset Plate Framework

Per CSA S16-19 Clause 13.2 and the CISC Handbook, gusset plates must be checked for:

Tension yielding on gross section (Whitmore width)
Tension fracture on net section
Compression buckling (plate out-of-plane stability)
Block shear at bolt lines
Interface welds/bolts to beam and column
Bearing at bolt holes

Whitmore Section Width

The Whitmore section width is: L_w = 2 × L_b × tan(30°) + w_g

Where:

L_b = distance from the last bolt row to the first bolt row along the brace axis (or the distance from the last bolt to the end of the plate)
w_g = width of the bolt group perpendicular to the load direction
tan(30°) = 0.577

The Whitmore section distributes the brace force at a 30° angle from the outermost bolts through the gusset plate.

Tension Checks

Gross Section Yielding

Per CSA S16 Clause 13.2(a)(i):

Tr_gross = phi × A_g × Fy

Where A_g = L_w × t_plate (gross area of Whitmore section).

Net Section Fracture

Per CSA S16 Clause 13.2(a)(ii):

Tr_net = phi_u × A_n × Fu

Where A_n = net area of Whitmore section through the bolt holes (gross minus holes along the critical chain).

Compression Buckling

Per CSA S16 Clause 13.3, the gusset plate compression capacity is checked using an effective length factor K = 1.2 (for the gusset plate free edge) and the radius of gyration for plate bending about its weak axis:

r_plate = t_plate / sqrt(12) ≈ 0.289 × t_plate

The slenderness ratio: KL/r = K × L_free / (0.289 × t_plate)

Where L_free = the longest unsupported edge of the gusset plate (typically the free edge between beam and column connections).

Critical Buckling Stress

The compressive resistance is:

Cr_gusset = phi × A_g × Fy × (1 + lambda^(2n))^(-1/n)

Where:

n = 1.34 (same as W-shapes for plate buckling)
lambda = KL/r × sqrt(Fy / (pi^2 × E))

Gusset Plate Thickness

Practical gusset plate thicknesses:

Brace Force (kN)	Min t (350W)	Typical t	Bolt Dia
< 300	8 mm	10 mm	M16-M20
300-600	10 mm	12-16 mm	M20
600-1000	12 mm	16-20 mm	M22-M24
1000-1500	16 mm	20-25 mm	M24-M27
> 1500	20 mm	25-32 mm	M27-M30

Interface Connection Design

The gusset plate-to-beam and gusset plate-to-column connections (welded or bolted) must be designed for force components per CSA S16 Clause 27 for seismic connections:

Force Distribution

The brace force is resolved into horizontal and vertical components at the gusset interfaces:

H = P × cos(theta) (horizontal component at beam or column) V = P × sin(theta) (vertical component)

Where theta = brace angle from horizontal (typically 30-60°).

Weld Design at Interfaces

For a gusset welded to beam flange and column flange:

The weld at each interface must resist the direct force plus moment from eccentricity
Per CSA S16, use the uniform force method (UFM) or Kline's method for interface force distribution
For seismic connections, weld must develop 1.25 × P_brace (overstrength factor per Clause 27.5)

Worked Example — Concentric Brace Gusset Plate

Given: HSS 178×178×8 brace at 45°. Brace force Cf = 500 kN (factored compression). Gusset plate 350W steel. Bolted connection: 6-M20 A325M bolts in two rows of 3.

Step 1 — Gusset Geometry: Bolt layout: 2 rows of 3, at 70 mm horizontal spacing, 75 mm vertical. Distance from last bolt to plate end along brace: L_b = 200 mm. Whitmore width: L_w = 2 × 200 × tan(30°) + 2 × 70 = 2 × 200 × 0.577 + 140 = 231 + 140 = 371 mm.

Step 2 — Try 12 mm gusset plate: Gross area (Whitmore): Ag = 371 × 12 = 4,452 mm^2 Tr_gross = 0.90 × 4,452 × 350 / 1000 = 1,402 kN ≥ 500 kN. OK.

Step 3 — Net Section Fracture: Net width through 2 bolt holes: 371 - 2 × 22 = 327 mm An = 327 × 12 = 3,924 mm^2 Tr_net = 0.75 × 3,924 × 450 / 1000 = 1,324 kN ≥ 500 kN. OK.

Step 4 — Compression Buckling: Free edge length (unbraced): L_free = 350 mm (from free edge of gusset) rp = 0.289 × 12 = 3.47 mm KL/r = 1.2 × 350 / 3.47 = 121 lambda = 121 × sqrt(350 / (pi^2 × 200,000)) = 121 × 0.01332 = 1.61 lambda^(2n) = 1.61^(2.68) = 1.61^2.68 = 3.75 Cr = 0.90 × 4,452 × 350 × (1 + 3.75)^(-0.746) = 1,402,380 × 0.230 = 323 kN

Compression check: Cf = 500 > Cr = 323 kN. NOT OK.

Increase plate to 16 mm: Ag = 371 × 16 = 5,936 mm^2 rp = 0.289 × 16 = 4.62 mm KL/r = 1.2 × 350 / 4.62 = 90.9 lambda = 90.9 × 0.01332 = 1.21 lambda^(2.68) = 1.21^2.68 = 1.59 Cr = 0.90 × 5,936 × 350 × (1 + 1.59)^(-0.746) = 1,869,840 × 0.370 = 692 kN ≥ 500 kN. OK.

Step 5 — Bolt Check: 6-M20 A325M AA: Vr = 6 × 81.3 = 487.8 kN < 500 kN. Not OK. Try 8-M20 A325M AA: Vr = 8 × 81.3 = 650.4 kN ≥ 500 kN. OK.

Result: 16 mm gusset plate (350W), 8-M20 A325M AA bolts, Whitmore width = 371 mm, free edge length = 350 mm. Compression governs — plate thickness driven by buckling capacity.

Seismic Design Considerations

Per CSA S16 Clause 27.5 for moderately ductile (MD) braces:

Gusset plate must accommodate brace end rotation at yield: Provide 2 × tp (2 × plate thickness) clearance from the brace end to the beam/column face
The Whitmore section must be checked for 1.25 × brace factored force (overstrength)
Interface connections must develop the brace overstrength force
Gusset plate buckling capacity must exceed 1.25 × brace compression capacity

Frequently Asked Questions

What is the Whitmore section method? The Whitmore section (also called the Whitmore effective width) assumes the brace force spreads through the gusset plate at a 30° angle from the outermost bolts or weld ends. The effective width L_w = 2 × L_b × tan(30°) + w_g. The gross area of this section (L_w × t) is used for tension yielding checks. For compression, the same width is used with plate buckling capacity.

How is gusset plate buckling checked per CSA S16? Gusset plate buckling is checked per CSA S16 Clause 13.3 using the plate's weak-axis radius of gyration (rp = t/sqrt(12)) and the unbraced free edge length. K = 1.2 is typically used for the free edge. The Cr follows the standard column curve for W-shapes (n = 1.34). Buckling often governs for thin gusset plates (t ≤ 12 mm) with large free edge lengths.

What is the minimum gusset plate thickness in Canadian practice? CSA S16 does not specify an explicit minimum, but practical minimums are 8 mm for light bracing and 10 mm for standard braces in buildings. For seismic braces (MD or LD braces), 12-16 mm is typical. The CISC Handbook suggests tp ≥ 0.5 × d_bolt for bolted connections. For welded connections, the minimum is governed by weld heat input (CSA W59 minimum weld sizes).

How are gusset plate interface forces distributed? The uniform force method (UFM) distributes brace force components to the beam and column interfaces such that no moment is induced at the connections. The horizontal component goes primarily to the beam (if the gusset is on the beam) and the vertical to the column. For gusset plates connecting to both beam and column, the UFM provides interface forces that are statically equivalent with zero moment at the work point.

This page is for educational reference. Gusset plate design per CSA S16-19. Verify Whitmore section and buckling capacity for the specific brace angle and connection geometry. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.

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