Bracing Connection Calculator (Gusset Plate)

What it checks

A bracing connection transfers axial force from a brace member into a gusset plate and then into the frame. This calculator verifies the gusset plate in gross-section yielding and net-section rupture, the bolt group in shear and bearing, block tearing and tear-out, the weld to the supporting members, and the Whitmore section - the effective width of gusset that actually carries the brace force.

Bracing is an axial connection, so unlike a beam shear connection there is no eccentricity moment to resolve, but there are more ways for the plate to fail: a gusset can rupture on the net section, tear out a block of material around the bolt group, or buckle over the Whitmore width if the brace is in compression.

Net section, not gross section, governs

Running the tool on its defaults - a 120 by 400 by 10 mm S275 gusset with three M24 grade 8.8 bolts carrying 80 kN - gives:

Gusset, net-section rupture

291.0 kN, utilisation 0.275 - GOVERNS

Gusset, gross-section yielding

330.0 kN, utilisation 0.242

Bolt group

406.7 kN, utilisation 0.197

Weld

438.5 kN, utilisation 0.183

Whitmore section

582.1 kN, utilisation 0.137

Net-section rupture governs even though its resistance in kN is not the lowest number in a naive reading - the gross section yields at 330 kN and the net section ruptures at 291 kN, so the net section is the real limit. That is the usual outcome for a bolted gusset: drilling holes removes material exactly where the force is highest.

The consequence is that gusset design is driven by hole layout, not plate size. Staggering the bolts, or spreading them over more rows so the net width at any one section is larger, buys more capacity than making the plate wider or thicker.

The Whitmore section

The Whitmore section is the effective width of gusset that actually resists the brace force - conventionally taken by spreading 30 degrees each side from the first row of bolts to the last. Material outside that spread contributes little, so a very wide gusset does not help beyond the Whitmore width.

It matters most for a brace in compression, where the gusset can buckle over that effective width as a short column. With a tension brace the Whitmore check is usually comfortable - 582 kN against 291 kN net section in the example above - but a compression brace with a long unsupported gusset can make it the governing mode.

Formula reference

Gross-section yielding

$N_{pl,Rd} = \dfrac{A\,f_y}{\gamma_{M0}}$

Net-section rupture

$N_{u,Rd} = \dfrac{0.9\,A_{net}\,f_u}{\gamma_{M2}}$

Block tearing

$V_{eff,Rd} = \dfrac{f_u A_{nt}}{\gamma_{M2}} + \dfrac{f_y A_{nv}}{\sqrt3\,\gamma_{M0}}$

Bolt shear

$F_{v,Rd} = \dfrac{\alpha_v f_{ub} A_s}{\gamma_{M2}}$

Bearing

$F_{b,Rd} = \dfrac{k_1 \alpha_b f_u d t}{\gamma_{M2}}$

Whitmore effective width

$b_w = b + 2\,L\tan 30^\circ$

Design weld strength

$f_{vw,d} = \dfrac{f_u}{\beta_w\,\gamma_{M2}}$

Assumptions and limits

The brace force is assumed concentric with the bolt group, so no eccentricity moment is applied to the gusset. Where the brace centreline does not pass through the working point of the frame, the resulting moment is a real effect this tool does not model, and it can be significant on a shallow-angle brace.

Gusset buckling under a compression brace is addressed only through the Whitmore section check. A long, thin or unsupported gusset edge may need a proper stability check, and free-edge stiffening is a detailing decision the tool does not make.

The tool checks the gusset and its fasteners, not the brace member itself, not the beam or column it frames into, and not the frame action. Static persistent design situation; fatigue, fire and seismic detailing - including the capacity-design requirements that govern a seismic brace - are outside the scope.

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