Brace Connection — Engineering Reference

Whitmore section, block shear, net section fracture, UFM interface forces, and AISC 341 SCBF gusset requirements with an interactive check.

Overview

Brace connections transfer axial force from a diagonal bracing member into the beam-column joint through a gusset plate. The design must address the gusset plate itself (Whitmore section tension, Thornton compression buckling, block shear), the gusset-to-beam and gusset-to-column interfaces (bolts or welds transferring the resolved brace force components), and the beam and column at the joint (web yielding, web crippling, panel zone). For seismic applications (SCBF per AISC 341), additional requirements for overstrength, ductile behavior, and gusset plate hinging must also be satisfied.

The two primary analysis methods for distributing gusset interface forces are the Uniform Force Method (UFM) from AISC Manual Part 13 and the parallel force method. The UFM produces a set of forces at the gusset-to-beam and gusset-to-column interfaces that are statically consistent with the brace force without introducing additional moments on the interfaces. This simplifies the interface connection design.

Whitmore section — gusset tension capacity

The Whitmore effective width defines how much of the gusset plate participates in resisting the brace tension force:

W_w = 2 x L_w x tan(30) + s_g

where L_w is the length from the first bolt row to the last bolt row along the brace axis, and s_g is the bolt gage perpendicular to the brace axis. The tension capacity is:

phi x P_n = 0.90 x F_y x W_w x t_g (yielding) or 0.75 x F_u x W_n x t_g (net rupture)

where W_n = W_w minus hole deductions and t_g is the gusset plate thickness.

Thornton method — gusset compression buckling

When the brace is in compression, the gusset plate can buckle. The Thornton method models the gusset as an equivalent column with an effective length determined by the geometry:

1. Identify the three distances from the Whitmore section corners (two corners and the midpoint) perpendicular to the nearest gusset edge (beam flange, column flange, or free edge).
2. The effective length L_eff is the average of these three distances.
3. The radius of gyration r = t_g / sqrt(12).
4. The slenderness ratio KL/r = K x L_eff / r, where K = 0.65 for a gusset restrained by framing on two edges.
5. Calculate F_cr from AISC E3 and phi x P_n = 0.90 x F_cr x W_w x t_g.

Uniform Force Method (UFM)

The UFM distributes the brace force P into horizontal (H) and vertical (V) components at each interface without eccentricity moments:

• alpha = e_b x tan(theta) - e_c + (distance to beam interface centroid)
• beta = e_c x cot(theta) - e_b + (distance to column interface centroid)

where e_b and e_c are the half-depths of the beam and column at the work point, and theta is the brace angle. When alpha and beta satisfy the UFM equilibrium equations, the gusset-to-beam interface carries H_b and V_b, and the gusset-to-column interface carries H_c and V_c, with no additional moment.

Worked example — HSS 6x6x3/8 brace to corner gusset

Given: HSS 6x6x3/8 brace (A500 Gr C, A = 7.58 in^2, F_y = 46 ksi, F_u = 62 ksi), brace angle theta = 45 degrees, P_u = 200 kip (tension), gusset plate 1/2 in. A36, four 3/4 in. A325-N bolts in a single line at 3 in. spacing on the brace.

1. Whitmore width: L_w = 3 x 3 = 9.0 in. (4 bolts). W_w = 2 x 9.0 x tan(30) + 0 = 2 x 9.0 x 0.577 = 10.4 in. (single line, gage = 0).
2. Gusset tension yielding: phi x P_n = 0.90 x 36 x 10.4 x 0.50 = 168.5 kip < 200. NG.** Increase to 5/8 in. plate: phi x P_n = 0.90 x 36 x 10.4 x 0.625 = **210.6 kip > 200. OK.
3. Gusset net rupture (5/8 in. plate): W_n = 10.4 - 1 x (13/16 + 1/16) = 9.525 in. phi x P_n = 0.75 x 58 x 9.525 x 0.625 = 258.9 kip. OK.
4. Bolt shear: 4 bolts x 17.9 kip = 71.6 kip < 200. NG. Need bolts in double shear or larger bolts. With 7/8 in. A325-N: phi x r_n = 0.75 x 54 x 0.6013 = 24.4 kip. 8 bolts (double line of 4): 8 x 24.4 = 195 kip. Still marginal — use 7/8 in. A490-N: phi x r_n = 0.75 x 68 x 0.6013 = 30.7 kip. 8 bolts = 245 kip. OK.

SCBF seismic requirements (AISC 341 F2.6)

For Special Concentrically Braced Frames, gusset plate connections must satisfy additional requirements:

• Design force: The connection must resist the expected brace capacity in tension: R_y x F_y x A_g = 1.30 x 46 x 7.58 = 453 kip (for HSS A500 Gr C). This is much larger than the code-level force.
• Compression design: The connection must also resist 1.14 x F_cre x A_g (expected compression capacity) without buckling.
• Gusset plate hinging: The gusset must be detailed to allow the brace to buckle out-of-plane. The standard detail provides a 2t_g linear clearance (clear distance of twice the gusset thickness) between the end of the brace and the beam/column re-entrant corner. This clearance allows a yield line to form in the gusset plate during brace buckling.
• Net section reinforcement: If the brace connects with a slotted gusset, the reduced net section through the slot must develop the expected brace capacity. Reinforcing plates may be required at the slot.

Code comparison — brace connections

Common mistakes to avoid

• Designing the gusset for the code-level brace force instead of the expected capacity — in SCBF, the connection must resist R_y x F_y x A_g, which is typically 2-3 times the code-level seismic force. Under-designed gusset plates are the most common failure in braced frames during earthquakes.
• Ignoring the Thornton compression check — a gusset plate that is adequate in tension can buckle in compression if it is too thin relative to its unbraced length. The Thornton method must be checked for all braces that carry compression.
• Not providing the 2t clearance for SCBF — the standard SCBF gusset detail requires a straight line free distance of 2t_g from the brace end to the nearest restraint (beam flange/column flange re-entrant). This allows the gusset to form a ductile yield line during brace out-of-plane buckling. Without this clearance, the gusset may fracture instead of yielding.
• Omitting the beam-to-column interface check — the UFM distributes forces to both the gusset-to-beam and gusset-to-column interfaces. The beam web must be checked for the vertical and horizontal components at the gusset, and the column must be checked for any additional axial or shear demand from the gusset connection.
• Not checking the beam for the "frame action" forces — in a chevron braced frame, the beam at the brace intersection must resist an unbalanced vertical force when one brace yields and the other buckles. This force can be very large and may govern beam sizing.

Run this calculation

• Gusset Plate Calculator
• Section Properties Database

Related references

• Steel Connection Design
• Bolt Capacity Table
• How to Verify Calculations
• base plate design
• SCBF and OCBF systems
• gusset plate design reference
• steel connection capacity calculator
• weld capacity for connection design
• Bolt Pattern
• Girder-to-column connections

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.