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.
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 FEd 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.
Check
Governing equation
Reference
Gusset gross yield
Fpl,Rd=γM0Agfy,p
EN 1993-1-1 §6.2.3
Gusset net rupture
Fu,Rd=γM20.9fu,pAnet
EN 1993-1-1 §6.2.3
Whitmore section
FRd=γM0befftpfy,p
Whitmore
Bolt group
FRd=nmin(Fv,Rd;Fb,Rd)
EN 1993-1-8 T3.4
Gusset weld
FRd=bp(Fw,T1+Fw,T2)
EN 1993-1-8 §4.5.3
Gusset plate in tension
The gusset plate is checked for the two classic tension modes: gross-section yielding, Fpl,Rd=Agfy,p/γM0, and net-section rupture through the bolt holes, Fu,Rd=0.9fu,pAnet/γM2. The plate tensile resistance is the smaller of the two and must exceed the brace force FEd.
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:
beff=w+2Ltan30∘
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.
where w is the connected brace width and L the length of the bolted joint. The gusset tensile resistance over this section is FRd=befftpfy,p/γM0. In compression the same section gives the gusset buckling resistance.
Bolt group and weld
The brace-to-gusset bolts are checked for shear, Fv,Rd=αvfubAs/γM2, and bearing on the gusset, Fb,Rd=k1αbfu,pdtp/γM2; 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 γ the effective throat is a=scos(γ/2), and the transverse resistance applies the factor K=3/(1+2cos2θ). The total weld resistance over the plate width is FRd=bp(Fw,T1+Fw,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 ≥1.2d0;
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
A bracing connection transfers the axial force of a diagonal bracing member - a steel rod, angle, hollow section or I-section - into the main frame, usually through a gusset plate welded to the beam and column and bolted (or welded) to the brace. Bracing carries the lateral loads (wind, seismic) of a steel frame, so its connections are designed for the brace axial force in tension and, for stiff braces, compression.
To Eurocode 3 (EN 1993-1-8) with SCI P358, every link in the load path is verified: the gusset plate in tension (gross-section yield and net-section rupture), the Whitmore effective-width section, the brace-to-gusset bolt group (shear and bearing), and the gusset-to-member fillet welds. Each design resistance must be at least the brace force F_Ed; SCI P358 also recommends allowing for the load eccentricity at congested gusset intersections.
The Whitmore section defines the width of the gusset plate that actually resists the brace force. The force spreads from the first bolt at 30 degrees to each side along the line of force, so the effective width at the last bolt is b_eff = w + 2 L tan30, where w is the connected brace width and L the bolted length. The gusset tensile resistance (and, in compression, the buckling resistance) is taken over this Whitmore width, not the full plate.
The gusset-to-member fillet welds run along the connected edges, often at an angle. For a weld run at an included angle gamma the effective throat is a = s cos(gamma/2), and the transverse resistance applies the directional factor K = sqrt(3/(1+2cos^2 theta)). The total weld resistance over the plate width is F_Rd = b_p (F_w,T1 + F_w,T2) summing the two runs. SCI P358 recommends designing the welds for at least the brace force, with an allowance for eccentricity.
A steel tension rod (often pre-tensioned through a turn-buckle) is welded to the gusset plate, either by a single flare-bevel-groove weld (Option 1) or by double-sided fillet welds (Option 2, preferred). The weld is designed to resist twice the rod tension (a robustness allowance), and a weldable mild steel rod such as S275 is recommended over high-tensile rod. For erection two bolts are preferred where a bolted detail is used.
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.
