Bracing Connection Design Theory (Gusset Plate)

The theory behind this bracing calculator: how a brace member bolted to a gusset plate welded to the main member is verified to Eurocode 3 (EN 1993-1-8) with SCI P358. We cover the gusset plate in tension (gross yield and net rupture), the Whitmore effective-width section that sets the gusset tensile/buckling section, the brace-to-gusset bolt group (shear and bearing), and the gusset-to-member fillet welds at their connection angles.

Run this method in the free calculator and export the result to Excel (.xlsx) or PDF.

A bracing connection transfers the axial force of a diagonal bracing member - a steel rod, an angle, a hollow section or an I-section - into the main frame. The most common arrangement is a gusset plate welded to the main members (a beam and a column, or a beam-column intersection) with the brace bolted to the plate. This page explains the mechanics and every formula behind the checks this calculator performs to Eurocode 3 (EN 1993-1-8) with SCI Publication P358.

A gusset plate welded into the beam-column corner, with a diagonal brace bolted to it. The brace axial force is carried by the bolts, the gusset and the welds.

The verification framework

The axial force $F_{Ed}$ in the brace flows through the bolts into the gusset plate and out through the welds into the main members. Every link is verified - the gusset plate in tension, the Whitmore section, the bolt group and the welds - with the utilisation kept at or below 1.0.

Gusset plate in tension

The gusset plate is checked for the two classic tension modes: gross-section yielding, $F_{pl,Rd} = A_g f_{y,p}/\gamma_{M0}$, and net-section rupture through the bolt holes, $F_{u,Rd} = 0.9 f_{u,p} A_{net}/\gamma_{M2}$. The plate tensile resistance is the smaller of the two and must exceed the brace force $F_{Ed}$.

Block shear and tear-out

Beyond a clean tension rupture across the net section, a bolt group can tear a whole block of gusset out - it ruptures on the tension face across the end bolts and shears along the plane(s) parallel to the force. Eurocode 3 (EN 1993-1-8 §3.10.2) sizes this as the sum of a tension term on the net tension area $A_{nt}$ and a shear term on the net shear area $A_{nv}$:

For a concentric bolt group the full tension term applies; a group loaded with in-plane eccentricity (a single offset line) takes a reduced tension term, $V_{eff,2,Rd} = 0.5 f_u A_{nt}/\gamma_{M2} + f_y A_{nv}/(\sqrt{3}\gamma_{M0})$. This tool models a single bolt line loaded axially, where the tear-out is bounded by the two checks it already performs: net-section rupture (the tension plane) andbolt bearing, whose end-distance term $\alpha_b = e_1/3d_0$ is exactly the gusset shearing out ahead of the end bolt. A separate block-shear check becomes the governing requirement for a multi-line bolt pattern, where a genuine two-dimensional block can form - keep the end distance $e_1$ generous so the shear planes stay long.

The Whitmore section

The bolted force does not act on the full gusset width - it spreads from the first bolt at 30 degrees to each side along the line of force. The width of the gusset at the last bolt row over which the force is effective is the Whitmore effective width:

The Whitmore section: the force spreads 30 degrees from the first fastener; b_eff is the width across the spread at the last fastener. It sets the gusset's tensile (and, in compression, buckling) section.

The gusset tensile resistance over this Whitmore section is $F_{Rd} = b_{eff} t_p f_{y,p}/\gamma_{M0}$; in compression the same section sets the gusset buckling resistance, since a Whitmore width that is also long and thin can buckle before it yields.

Bolt group and weld

The brace-to-gusset bolts are checked for shear, $F_{v,Rd} = \alpha_v f_{ub} A_s/\gamma_{M2}$, and bearing on the gusset, $F_{b,Rd} = k_1\alpha_b f_{u,p} d t_p/\gamma_{M2}$; the group resistance is the number of bolts times the smaller. The gusset-to-member fillet welds run at the angles of the connected edges; for a run at angle $\gamma$ the effective throat is $a = s\cos(\gamma/2)$, and the transverse resistance applies the factor $K = \sqrt{3/(1+2\cos^{2}\theta)}$. The total weld resistance over the plate width is $F_{Rd} = b_p(F_{w,T1} + F_{w,T2})$.

Detailing notes

• design the gusset-to-member welds for at least the brace force (SCI P358 recommends an allowance for eccentricity);
• keep edge and end distances $\ge 1.2 d_0$;
• for a steel-rod brace via a turn-buckle, use a weldable mild steel rod (S275) and design the weld for twice the rod tension;
• allow for load eccentricity at congested beam-column gusset intersections.

Frequently asked questions

Ready to check your connection? Run the full EN 1993-1-8 / SCI P358 verification for a gusset-plate bracing connection in 3D, with step-by-step derivations for every check.