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

Gusset plates are the critical connecting elements in braced frames, trusses, and lateral load-resisting systems. A single gusset plate must transfer brace forces into the beam-column joint while satisfying three distinct limit states: yielding/tension rupture on the Whitmore section, block shear rupture at the bolt group, and compressive buckling in the unsupported region.

In this guide: We design a gusset plate for a 45-degree diagonal brace carrying 120 kips (LRFD) using AISC 360-22. Every limit state is checked with real numbers and dimensions.

PRELIMINARY — NOT FOR CONSTRUCTION. All results discussed are for educational and reference use only. Must be independently verified by a licensed Professional Engineer or Structural Engineer before use in any project.

Design Problem Statement

Step 1: Whitmore Effective Width

The Whitmore section concept, introduced by R.E. Whitmore (1952), defines the effective width of gusset plate that resists axial force from the brace. It is determined by projecting 30-degree lines from the first fasteners (or start of weld) and measuring the total width at the last fasteners (or end of weld).

For a welded brace connection:

$$L_w = 2 \times L_{weld} \times \tan(30°) + g$$

Where:

• $L_{weld}$ = length of weld along the brace (12 in)
• $g$ = transverse spacing between welds (gage width of brace, say 6 in for an HSS 6x6)

$$L_w = 2 \times 12 \times 0.577 + 6 = 13.85 + 6 = 19.85\text{ in}$$

Check that the Whitmore width fits within the physical gusset plate (18 in wide). The projected width at the beam/column interface needs to be verified — the Whitmore width may be wider than the actual plate if not sized properly.

Tension yielding on Whitmore section:

$$R_n = F_y \times A_g = F_y \times (L_w \times t) = 50 \times (19.85 \times 0.50) = 50 \times 9.925 = 496.3\text{ kips}$$

$$\phi R_n = 0.90 \times 496.3 = \mathbf{446.7\text{ kips}} > P_u = 120\text{ kips}$$

D/C = 120 / 446.7 = 0.269. Tension yielding OK.

Tension rupture on Whitmore section:

$$R_n = F_u \times A_e = F_u \times (L_w \times t) = 65 \times 9.925 = 645.1\text{ kips}$$

$$\phi R_n = 0.75 \times 645.1 = \mathbf{483.8\text{ kips}} > 120\text{ kips}$$

D/C = 120 / 483.8 = 0.248. Tension rupture OK.

Step 2: Block Shear — AISC 360 Section J4.3

Block shear must be checked for the bolt group connecting the gusset to the beam and column. The critical block shear path depends on the bolt arrangement.

Bolt group: 4 bolts (2 rows x 2 columns), 3/4 in diameter, standard holes (13/16 in effective hole diameter).

Gusset-to-beam connection (load parallel to bolt rows):

Assume the force component transferred to the beam is $P_u \times \cos(45°) = 120 \times 0.707 = 84.9\text{ kips}$.

Block shear path: vertical shear plane through one column of bolts + horizontal tension plane through the outer row.

Gross shear area: $$A_{gv} = 2 \times (1.5 + 3.0) \times 0.50 = 2 \times 4.5 \times 0.50 = 4.50\text{ in}^2$$

Net shear area (subtract 1.5 holes in the shear path per shear plane): $$A_{nv} = 4.50 - 2 \times (1.5 \times 0.8125 \times 0.50) = 4.50 - 2 \times 0.609 = 4.50 - 1.219 = 3.281\text{ in}^2$$

Gross tension area: $$A_{gt} = (3.0) \times 0.50 = 1.50\text{ in}^2$$

Net tension area (one hole in tension plane): $$A_{nt} = 1.50 - 0.5 \times 0.8125 \times 0.50 = 1.50 - 0.203 = 1.297\text{ in}^2$$

Block shear strength: $$R_n = 0.60F_u A_{nv} + U_{bs}F_u A_{nt} \leq 0.60F_y A_{gv} + U_{bs}F_u A_{nt}$$

$$R_n = 0.60 \times 65 \times 3.281 + 1.0 \times 65 \times 1.297$$ $$R_n = 128.0 + 84.3 = 212.3\text{ kips}$$

Upper bound: $$R_n \leq 0.60 \times 50 \times 4.50 + 1.0 \times 65 \times 1.297 = 135.0 + 84.3 = 219.3\text{ kips}$$

$212.3 < 219.3$, so $R_n = \mathbf{212.3\text{ kips}}$.

$$\phi R_n = 0.75 \times 212.3 = \mathbf{159.2\text{ kips}} > 84.9\text{ kips}$$

D/C = 84.9 / 159.2 = 0.533. Block shear OK.

Step 3: Gusset Plate Buckling — AISC 360 Section J4.4

The unsupported portion of the gusset plate between the end of the brace connection and the beam/column interface acts as a short column in compression. Buckling in this region is a common failure mode in braced frame gussets.

Unsupported length (average of free edges):

The unsupported length $L_c$ is taken as the average of the three free edge lengths from the Whitmore section to the supported edges (beam and column interfaces). For a typical corner gusset:

$$L_c \approx 8\text{ in (measured from geometry)}$$

Effective length factor: $K = 0.65$ (for a plate with two edges supported by beam and column flanges, per the Dowswell and Roeder recommendations in AISC Design Guide 29).

Radius of gyration: $$r = \frac{t}{\sqrt{12}} = \frac{0.50}{\sqrt{12}} = 0.1443\text{ in}$$

Slenderness: $$\frac{KL_c}{r} = \frac{0.65 \times 8}{0.1443} = 36.0$$

Elastic buckling stress: $$F_e = \frac{\pi^2 E}{(KL_c/r)^2} = \frac{\pi^2 \times 29,000}{36.0^2} = \frac{286,180}{1296} = 220.8\text{ ksi}$$

Critical stress (AISC 360 E3): Since $KL_c/r = 36.0 \leq 4.71\sqrt{E/F_y} = 4.71 \times 24.08 = 113.4$, inelastic buckling applies:

$$F_{cr} = 0.658^{F_y/F_e} \times F_y = 0.658^{50/220.8} \times 50 = 0.658^{0.2264} \times 50 = 0.909 \times 50 = 45.44\text{ ksi}$$

Compressive strength on Whitmore section: $$R_n = F_{cr} \times A_g = 45.44 \times (19.85 \times 0.50) = 45.44 \times 9.925 = 450.9\text{ kips}$$

$$\phi R_n = 0.90 \times 450.9 = \mathbf{405.8\text{ kips}} > 120\text{ kips}$$

D/C = 120 / 405.8 = 0.296. Compressive buckling OK.

Step 4: Gusset-to-Beam and Gusset-to-Column Interface Checks

The gusset plate must also be checked for shear yielding and flexural yielding at the beam and column interfaces.

Shear Yielding at Interface

The vertical (or horizontal) force component at the interface:

$$V_u = P_u \times \sin(45°) = 120 \times 0.707 = 84.9\text{ kips}$$

Shear area (gusset width at beam interface ≈ 16 in):

$$A_g = 16 \times 0.50 = 8.0\text{ in}^2$$

$$V_n = 0.60 F_y A_g = 0.60 \times 50 \times 8.0 = 240\text{ kips}$$

$$\phi V_n = 0.90 \times 240 = \mathbf{216.0\text{ kips}} > 84.9\text{ kips}$$

D/C = 84.9 / 216.0 = 0.393. Interface shear OK.

Weld Strength — Brace to Gusset

Assuming a 1/4 in fillet weld, E70XX electrode, on both sides of the brace for 12 in:

Weld strength per inch (AISC 360 J2.4): $$R_n = 0.60 F_{EXX} \times 0.707 \times D = 0.60 \times 70 \times 0.707 \times 4 = 118.8\text{ kips/in}$$

Per inch: $R_n = 1.392 \times D\text{ (sixteenths)} = 1.392 \times 4 = 5.568\text{ kips/in}$

Total weld capacity: $5.568 \times 12 \times 2 = 133.6\text{ kips}$

$$\phi R_n = 0.75 \times 133.6 = \mathbf{100.2\text{ kips}}$$

Since the weld resists only the brace force component (120 kips), and we have 100.2 kips capacity, increase weld size to 5/16 in ($D = 5$):

Per inch: $1.392 \times 5 = 6.96\text{ kips/in}$

Total: $6.96 \times 24 = 167.0\text{ kips}$

$$\phi R_n = 0.75 \times 167.0 = \mathbf{125.3\text{ kips}} > 120\text{ kips}$$

D/C = 120 / 125.3 = 0.958. Use 5/16 in fillet weld.

Summary of Results — Corner Gusset, 120 kip Brace Force

All limit states are satisfied. The weld to the brace is the highest-demand element at D/C = 0.958.

Practical Application — Using Our Gusset Plate Calculator

Manual gusset plate design involves iterating through Whitmore section checks, block shear paths, and buckling calculations that change with every geometry adjustment. Our free Gusset Plate Calculator automates the full workflow:

• Gusset Plate Calculator — Enter brace force, angle, plate dimensions, and bolt/weld configuration. The calculator checks all AISC 360 limit states simultaneously and flags the governing check.

The calculator runs entirely in your browser with no signup required.

FAQ

What is the Whitmore section in gusset plate design?

The Whitmore section (Whitmore effective width) is the assumed width of the gusset plate that resists axial force from a brace. It is calculated by projecting 30-degree lines from the first row of bolts (or start of weld) outward, measuring the width where these lines intersect a line perpendicular to the brace axis at the last row of fasteners. The Whitmore width $L_w = 2 \times L_{weld} \times \tan(30°) + g$. This concept was introduced by R.E. Whitmore in 1952 and is codified in AISC 360 Section J4.

What is block shear and how is it checked in gusset plates?

Block shear is a limit state where a block of material tears out from the plate — combining shear rupture on one plane and tension rupture on the perpendicular plane. Per AISC 360 J4.3, $R_n = 0.60F_u A_{nv} + U_{bs} F_u A_{nt}$, capped at $0.60F_y A_{gv} + U_{bs} F_u A_{nt}$. Multiple block shear paths must be checked around bolt groups in gusset plates.

When does gusset plate buckling control the design?

Gusset plate buckling becomes the governing failure mode when the plate is thin relative to its unsupported length. AISC 360 provides guidance in Section J4.4 using an effective length factor $K$ and the plate radius of gyration $t/\sqrt{12}$. Corner gusset plates in concentrically braced frames with long unsupported edges are particularly susceptible.

Is this calculator a replacement for professional engineering judgment?

No — this is an educational reference only. All gusset plate designs must be independently verified by a licensed Professional Engineer before use in any project. Results are PRELIMINARY — NOT FOR CONSTRUCTION.

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