---------------------- | ------------------- | ------------------- | ------------------------ | ----------------- | | Whitmore section yielding | J4.1 (phi=0.90) | Cl 7.2 (phi=0.9) | Cl 6.2.3 | Cl 13.2 (phi=0.9) | | Net section rupture | J4.2 (phi=0.75) | Cl 7.2 (phi=0.9) | Cl 6.2.3 (gamma_M2=1.25) | Cl 13.2 (phi=0.9) | | Block shear | J4.3 (phi=0.75) | Cl 9.1.6 (phi=0.75) | Cl 3.10.2 | Cl 13.11 | | Plate buckling | DG29, E3 (phi=0.90) | Cl 6.3 (phi=0.9) | Cl 6.3.1 (chi) | Cl 13.3 | | Bolt group | J3 | Cl 9.2 | Cl 3.6-3.8 | Cl 13.12 | | Weld interface | J2 | Cl 9.7 | Cl 4.5 | Cl 13.13 |

Key difference: AISC uses K = 0.5 for the Thornton buckling length when two or more gusset edges are restrained. AS 4100 does not prescribe the Thornton method specifically but uses general compression member provisions (Cl 6.3) with the designer selecting an appropriate effective length. EN 1993-1-8 uses the buckling curve approach with the plate treated as a compression element.

Step-by-Step Example

Problem: Check a 1/2-inch A36 gusset plate for a 150-kip tension brace force. Bolted connection with 4 rows of 3/4-inch A325-N bolts at 3-inch spacing, single-line (gage = 0). Edge distance = 1.5 in.

Step 1 -- Whitmore section width: Lc = (4 - 1) rows × 3 in spacing = 9 in (first to last bolt). w_Whitmore = 0 + 2 × 9 × tan(30°) = 2 × 9 × 0.5774 = 10.39 in.

Step 2 -- Gross yielding: Ag = 10.39 × 0.50 = 5.20 in^2. phi × Rn = 0.90 × 36 × 5.20 = 168.5 kips > 150 kips. OK (utilization = 0.89).

Step 3 -- Net section rupture: One bolt hole across the Whitmore section. dh = 3/4 + 1/8 = 7/8 = 0.875 in. An = (10.39 - 1 × 0.875) × 0.50 = 4.76 in^2. phi × Rn = 0.75 × 58 × 4.76 = 207.0 kips > 150 kips. OK (utilization = 0.72).

Step 4 -- Block shear (two shear planes along bolt line, one tension plane at end): Assume transverse edge distance = 1.5 in on each side. Shear length per plane = 1.5 + (4 - 1) × 3 = 10.5 in. Agv = 2 × 10.5 × 0.50 = 10.5 in^2. Holes per shear plane = 4 - 0.5 = 3.5. Anv = 10.5 - 2 × 3.5 × 0.875 × 0.50 = 10.5 - 3.06 = 7.44 in^2. Tension plane width = 2 × 1.5 = 3.0 in (single column, both transverse edges). Ant = (3.0 - 1 × 0.875) × 0.50 = 1.06 in^2. phi × Rn = 0.75 × (0.6 × 58 × 7.44 + 1.0 × 58 × 1.06) = 0.75 × (258.9 + 61.5) = 240.3 kips > 150 kips. OK.

Step 5 -- Bolt shear: 4 bolts, single shear. phi × rn per bolt = 0.75 × 54 × 0.4418 = 17.9 kips. Total = 4 × 17.9 = 71.6 kips < 150 kips. FAILS. Need 9 bolts minimum (150/17.9 = 8.4).

Result: Bolt shear controls. Revise to 10 bolts (2 columns of 5) or use 7/8-inch bolts (phi × rn = 24.3 kips, need 7 bolts). Gusset plate itself is adequate for yielding (0.89 utilization) with the revised bolt pattern.

Common Design Mistakes

• Using the wrong spread angle for the Whitmore section: The standard is 30 degrees from each side of the connection, not 30 degrees total. Using 15 degrees per side underestimates the Whitmore width by 42%.
• Ignoring buckling for compression braces: Gusset plates in braced frames carry compression when the brace is loaded in compression. The Thornton buckling check often governs for thin, long gussets and is the most commonly missed limit state.
• Not checking the gusset-to-beam and gusset-to-column interfaces: Even if the gusset plate itself is adequate, the interface welds or bolts to the beam and column must transfer the full brace force components. Undersized interface welds are a common fabrication error.
• Assuming the Uniform Force Method always produces zero interface moments: UFM produces zero moments only when the gusset geometry satisfies the ideal geometric condition. For most real connections, the geometry deviates from the ideal and moment couples must be added to the interface forces.
• Using K = 1.0 for gusset buckling: AISC Design Guide 29 demonstrates that K = 0.5 is appropriate when at least two gusset edges are restrained by the beam and column. Using K = 1.0 doubles the effective length and can quadruple the required plate thickness for buckling.
• Not accounting for the brace angle in the interface force distribution: The horizontal and vertical components of the brace force that pass through the gusset to the beam and column depend on the brace angle. A 45-degree brace splits the force equally; a shallow brace sends most force horizontally. Wrong angle assumptions propagate errors to every interface check.

Frequently Asked Questions

How is the Whitmore section width calculated, and why is a 30-degree spread angle used? The Whitmore effective width is determined by projecting lines at 30 degrees from each side of the first bolt in the connection (or the start of the weld) to the last fastener row, measured along the axis of the brace force. The total Whitmore width is the perpendicular distance between the two 30-degree lines at the last fastener. The 30-degree angle comes from experimental and analytical work by Richard Whitmore in 1952 and has since been validated as a reasonable approximation of the stress spread through the plate; it is now codified in AISC design guides as the standard method for evaluating gross yielding, net section rupture, and plate buckling on the Whitmore section.

What are the two failure modes in block shear, and how are they combined? Block shear is a combined failure where a block of material tears out along two surfaces simultaneously. Shear yielding acts along the shear planes parallel to the applied force, while tensile fracture (rupture) occurs on the tension plane perpendicular to the force at the end of the bolt group. The nominal block shear strength is the sum of the shear yielding capacity (0.6Fy × gross shear area) plus the tensile fracture capacity (Fu × net tension area), or the shear fracture capacity (0.6Fu × net shear area) plus the tensile yielding capacity (Fy × gross tension area) — whichever combination is smaller. The controlling combination depends on the relative areas and material properties.

How is gusset plate buckling checked, and what effective length is used? Gusset plate buckling is checked by treating the plate as a column on the Whitmore section, with an effective length equal to the average of three distances measured perpendicular to the brace axis from the Whitmore section to the nearest gusset edge or beam/column face — a method attributed to Thornton. The slenderness ratio L/t (effective length divided by plate thickness) is then used with column curve expressions to determine the plate’s compressive resistance. Plates in compression with high L/t ratios can buckle at loads well below the Whitmore gross yielding capacity, making buckling the controlling limit state for thin plates with long free lengths.

What is the Uniform Force Method (UFM) for gusset plate design? The Uniform Force Method distributes the brace force to the beam and column connections in a way that produces only direct forces (no moments) at the gusset-to-beam and gusset-to-column interfaces, simplifying the interface weld or bolt design. It achieves moment-free interfaces by selecting specific values of the horizontal and vertical setback distances that satisfy a geometric relationship involving the gusset centroid. When the actual geometry deviates from the UFM ideal geometry, moment couples must be added to the interface forces — the resulting "modified UFM" is required when field conditions constrain the gusset placement.

What minimum plate thickness is required to prevent local buckling of the gusset free edge? Gusset plates with long unsupported free edges can buckle locally under compressive brace loads before the Whitmore section capacity is reached. AISC guidance limits the free-edge slenderness: the unsupported edge length divided by the plate thickness should generally not exceed approximately 0.75√(E/Fy) for the plate to remain non-slender. For A36 plate (Fy = 36 ksi), this limit is roughly 12.7, and for A572 Grade 50 it is approximately 10.8. Stiffening the free edge with an angle or bent plate returns the plate to compact behavior and eliminates the local buckling penalty.

How does a welded gusset differ from a bolted gusset in terms of critical failure modes? In a bolted gusset, net section rupture through the bolt hole pattern is often the controlling limit state, because holes reduce the gross area by 15–25% depending on bolt diameter and spacing. Block shear is also more prominent in bolted configurations due to defined shear and tension planes along the bolt rows. In a welded gusset, there are no holes, so gross yielding on the Whitmore section and plate buckling tend to govern; the critical check shifts to the weld throat capacity along the gusset-to-brace interface and the gusset-to-frame interfaces, which must be sized to transfer the full brace force.

Related pages

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