What is the uniform force method for gusset plate design?

The uniform force method (also called the Thornton method) is the AISC-recommended approach for distributing brace axial force to beam and column interfaces in gusset plate connections. It assumes uniform stress distribution along each interface and resolves the brace force P into horizontal and vertical components. The horizontal force on the beam is Hb = P × cosθ × (ec / (eb + ec)), and the vertical force on the beam is Vb = P × sinθ × (eb / (eb + ec)), where eb and ec are the distances from beam and column centerlines to the gusset centroid. The column forces are Hc = P × cosθ − Hb and Vc = P × sinθ − Vb. The method ensures force equilibrium at the work point (theoretical intersection of brace, beam, and column axes) and produces uniform interface forces for efficient connection design.

What is the Whitmore section and how is it checked?

The Whitmore section defines the effective width of a gusset plate at the end of the brace connection for tension and compression resistance. The effective width lw is constructed by projecting 30° lines from the outermost fasteners in the connection to the end of the connection: lw = l + 2 × ltan × tan 30°, where l is the distance between outermost bolt rows and ltan is the distance from the last bolt row to the plate end. Three Whitmore section checks are required: tension yielding (φ × Fy × lw × t ≥ Pu), tension rupture (φ × Fu × (lw − bolt holes) × t ≥ Pu), and compression buckling (φ × Fcr × lw × t ≥ Pu). The buckling length for compression is taken from the brace end to the last bolt row projected perpendicular to the Whitmore section. This check ensures the gusset plate can transfer the full brace force into the beam and column.

What is the 2t linear offset rule for SCBF gusset plates?

The 2t linear offset rule is a seismic detailing requirement for SCBF gusset plates per AISC 341. The rule requires holding the end of the brace a distance of 2 times the gusset plate thickness (2t) away from the theoretical restraint line — the line where the gusset plate bends to accommodate brace buckling. This clearance creates an elliptical plastic hinge in the gusset plate during brace buckling, preventing fracture at the connection. Without the 2t offset, the gusset plate would be too stiff and the brace would fracture at the connection before developing its full compressive buckling capacity. The offset creates a controlled yielding zone in the gusset that allows multiple inelastic buckling cycles without connection failure, which is essential for SCBF seismic performance in SDC D and above.

What limit states must be checked in gusset plate design?

Gusset plate design requires checking eight limit states per AISC 360. For the gusset plate itself: tension yielding (φ × Fy × Ag per J4.1), tension rupture (φ × Fu × Ae per J4.2), shear yielding (φ × 0.6 × Fy × Agv per J4.3), shear rupture (φ × 0.6 × Fu × Anv per J4.3), block shear rupture combining shear yield/rupture with tension rupture per J4.3, and compression buckling (φ × Fcr × Ag per Chapter E). For the bolted connection to the brace: bolt bearing (φ × 2.4 × d × t × Fu per J3.10) and bolt tearout (φ × 1.2 × lc × t × Fu per J3.10). The brace itself must also be checked for tension yielding of the gross section, tension rupture of the net section at bolt holes, and compression buckling. Minimum gusset thickness ranges from 3/8 inch for light bracing (under 50 kips) to 1 inch for very heavy bracing (400-600 kips).

How do K-brace, V-brace, and X-brace configurations differ?

The four common braced frame configurations differ in brace geometry and force distribution. X-bracing places two diagonal braces crossing at mid-bay; under lateral load, one brace acts in tension while the other buckles in compression. The tension-only design approach (R=3) is economical but limited to low-seismic regions. V-bracing (chevron) connects both braces to the beam at mid-span from below; the beam must be designed for the unbalanced vertical force when the compression brace buckles, equal to Ry × Fy × Ag × sinθ from the tension brace. Inverted V-bracing (inverted chevron) is identical but braces meet from above, commonly used where headroom below is needed. K-bracing connects braces to a column mid-height and is the least common — AISC 341 prohibits K-bracing in SCBF because column plastic hinging at the brace-colum intersection is difficult to control. Single-diagonal bracing is simplest but accumulates forces in one direction only, used mainly for light retrofit applications.

Brace Connection Design — Gusset Plates & Forces

Brace connections transfer axial forces from diagonal braces into beams and columns through gusset plates. The gusset plate is the critical element, and its design requires checking multiple limit states. This page covers the uniform force method, gusset geometry, and design procedure per AISC.

Braced Frame Types

Type	Configuration	Brace Force Pattern	Typical Application
X-brace	Diagonals cross at center	One brace in tension per load	Light lateral systems
V-brace	Braces meet beam from below	Both braces active	Chevron bracing
Inverted V	Braces meet beam from above	Both braces active	Inverted chevron
K-brace	Braces meet column mid-height	Shorter braces	Limited use (seismic)
Single diagonal	One brace per bay	Tension or compression	Light retrofit

Gusset Plate Geometry

Key Dimensions

Dimension	Definition	Typical Range
Gusset length	Along beam or column connection	12 to 48 in
Gusset height	Perpendicular to connected member	6 to 24 in
Gusset thickness	Plate thickness	3/8 to 1 in
Edge distance	From bolt center to plate edge	1.5 to 2 in minimum
Clip angle	Angle between gusset edge and brace axis	15-30° for free edge

Minimum Gusset Thickness

Gusset plate thickness is selected based on the brace force and connection geometry:

Brace Force (kips)	Typical Thickness (in)	Remarks
0 - 50	3/8	Light bracing
50 - 100	1/2	Moderate bracing
100 - 200	5/8	Heavy bracing
200 - 400	3/4	Very heavy bracing
400 - 600	1	Special design

Uniform Force Method (Thornton Method)

The uniform force method is the AISC-recommended approach for distributing brace forces at gusset plate connections. It assumes uniform stress distribution along each interface.

Force Resolution

The brace force P is resolved into components at the beam and column interfaces:

Horizontal component on beam: H_b = P × cos θ × (e_c / (e_b + e_c))

Vertical component on beam: V_b = P × sin θ × (e_b / (e_b + e_c))

Horizontal component on column: H_c = P × cos θ - H_b

Vertical component on column: V_c = P × sin θ - V_b

where θ = brace angle from horizontal, e_b = eccentricity to beam, e_c = eccentricity to column.

Work Point and Eccentricities

Parameter	Definition	Significance
Work point (WP)	Theoretical intersection of member axes	Force resolution point
e_b	Distance from beam C.L. to gusset centroid	Beam eccentricity
e_c	Distance from column C.L. to gusset centroid	Column eccentricity
r	Gusset connection length	Controls force split

When the work point is at the beam-column intersection (concentric connection), the force distribution depends solely on the geometry of the gusset plate attachment.

Whitmore Section

The Whitmore section defines the effective width of the gusset plate at the end of the brace connection. It determines the area available for tension or compression resistance.

Whitmore Effective Width

The effective width (l_w) is constructed by drawing 30° lines from the outermost bolts in each row of the connection to the end of the connection:

l_w = l + 2 × l_tan × tan 30°

where l = distance between outermost bolt rows, l_tan = distance from last bolt row to plate end.

Whitmore Section Checks

Tension yielding: φ × Fy × l_w × t ≥ P_u
Tension rupture: φ × Fu × (l_w - bolt holes) × t ≥ P_u
Compression buckling: φ × Fcr × l_w × t ≥ P_u (for compression braces)

The buckling length for the Whitmore section is taken from the end of the brace to the last row of bolts, projected perpendicular to the Whitmore section.

Gusset Plate Limit States

Every gusset plate connection must be checked for these limit states:

Gusset Plate Checks

Limit State	Formula Basis	AISC Section
Tension yielding (gross)	φ × Fy × Ag	J4.1
Tension rupture (net)	φ × Fu × Ae	J4.2
Shear yielding	φ × 0.6 × Fy × Agv	J4.3
Shear rupture	φ × 0.6 × Fu × Anv	J4.3
Block shear	φ × (0.6Fy×Agv + Fu×Ant)	J4.3
Compression buckling	φ × Fcr × Ag	E3
Bolt bearing	φ × 2.4 × d × t × Fu	J3.10
Bolt tearout	φ × 1.2 × lc × t × Fu	J3.10

Brace Checks

Limit State	Formula Basis	AISC Section
Brace tension yielding	φ × Fy × Ag	J4.1
Brace tension rupture	φ × Fu × Ae (net area)	J4.2
Brace compression	φ × Fcr × Ag	E3

Interface Checks (Beam and Column)

Limit State	Applies To
Weld shear (gusset to beam)	Beam interface
Weld shear (gusset to column)	Column interface
Beam web yielding	Localized force
Beam web crippling	Transverse force
Column flange bending	Transverse force

Gusset Edge Distance and Free Edge Stability

Free Edge Buckling

The unsupported (free) edge of the gusset plate must be checked for buckling under compression:

If the free edge is not stiffened, the maximum l/t ratio (length/thickness) should be limited
AISC recommends: l/t ≤ 340 / √Fy for unstiffened edges
For A36: l/t ≤ 57; for A572 Gr 50: l/t ≤ 48

If the free edge exceeds this limit, add an edge stiffener (angle or plate) or increase the gusset thickness.

2t Rule for Brace Buckling (SCBF)

For Special Concentric Braced Frames (seismic), the gusset must allow brace buckling out of plane. The "2t rule" requires:

The end of the brace is held back 2t from the restraint line (where gusset meets beam/column)
This allows the gusset to bend plastically when the brace buckles
The gusset must be detailed with a clear flexural yield zone

Worked Example — Chevron Brace Gusset

Given: HSS6x6x3/8 brace at 45°, Pu = 150 kips (LRFD, tension). W18×50 beam, W14×68 column. A500 Gr B (Fy = 46 ksi). Gusset PL 5/8 in A36.

Step 1: Whitmore Section Assume 3 rows of 7/8 in bolts at 3 in spacing: l_w = 6 + 2 × 3 × tan 30° = 6 + 3.46 = 9.46 in A_w = 9.46 × 0.625 = 5.91 in²

Step 2: Tension yielding of Whitmore section φRn = 0.9 × 36 × 5.91 = 191.5 kips > 150 → OK

Step 3: Gusset tension yielding (brace direction) Assume brace connection length = 12 in: A_g = 12 × 0.625 = 7.5 in² φRn = 0.9 × 36 × 7.5 = 243 kips > 150 → OK

Step 4: Block shear (bolt group) Assume 3 bolts per row, 2 rows (6 bolts total): Gross shear area = 2 × (6 + 1.5) × 0.625 = 9.375 in² Net shear area = 9.375 - 2 × 2 × 0.9375 × 0.625 = 9.375 - 2.34 = 7.03 in² Net tension area = (3 - 1) × 0.9375 × 0.625 = 1.17 in² (approximate)

φRn = 0.75 × [0.6 × 58 × 7.03 + 58 × 1.17] = 0.75 × [244.6 + 67.9] = 234.4 kips > 150 → OK

Step 5: Check free edge stability Free edge length ≈ 18 in, t = 0.625 in l/t = 18 / 0.625 = 28.8 < 57 (A36 limit) → OK

Frequently Asked Questions

What is the uniform force method? The uniform force method (Thornton method) distributes the brace force to the beam and column interfaces based on the gusset geometry and eccentricities. It assumes uniform stress along each interface. It is the method recommended by AISC for designing gusset plate connections.

What is the Whitmore section? The Whitmore section is an effective width at the end of a gusset plate connection, constructed by projecting 30° lines from the outermost bolts. It defines the area of the gusset plate that resists the concentrated brace force in tension or compression.

How thick should a gusset plate be? Gusset plate thickness depends on the brace force. Typical ranges: 3/8 in for forces under 50 kips, 1/2 in for 50-100 kips, 5/8 in for 100-200 kips, and 3/4 in for 200-400 kips. The thickness must satisfy all limit states (yielding, rupture, block shear, buckling).

What is the 2t rule in brace connections? The 2t rule is a seismic detailing requirement (SCBF) where the end of the brace is held back a distance of 2 times the gusset plate thickness from the beam or column face. This creates a flexible zone in the gusset that allows the brace to buckle out-of-plane without fracturing the connection.

Connection Types Explained — All connection types
HSS Connection Design — AISC Chapter K
Seismic Connections — AISC 341 requirements
Bolted Connections — Bolt capacity calculator
Welded Connections — Weld capacity calculator

Disclaimer

This is a calculation tool, not a substitute for professional engineering certification. All results must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in construction, fabrication, or permit documents. The user is responsible for the accuracy of all inputs and the verification of all outputs.