Weld Design to Eurocode 3 - Throat, Stresses & EN 1993-1-8 Methods
The theory behind the Eurocode 3 mode of this weld calculator: the effective throat, the normal and shear stresses on it, the two EN 1993-1-8 routes - the directional and simplified methods - the correlation factor β_w, and butt (groove) welds.
A fillet weld is checked not on its visible leg but on its effective throat - the narrowest plane through the weld, where failure is assumed to occur. For an equal-leg fillet of leg size s the throat is
a=2s≈0.707s
Fillet weld - leg size s and effective throat a = s/√2
All design stresses act over the throat area Aw=aLeff, where Leffis the effective length (the full length for a continuous run; doubled for a double-sided fillet). The throat - not the leg - is the quantity that sets the weld's capacity.
Stresses on the throat
The applied force is resolved into three components on the throat plane: the normal stress σ⊥, the transverse shear τ⊥ (perpendicular to the weld axis) and the longitudinal shearτ∥ (along the weld axis). A force perpendicular to the weld at 45° to the throat producesσ⊥=τ⊥.
Stresses on the throat plane: σ⊥ (normal), τ⊥ (transverse shear), τ∥ (longitudinal shear)
Directional method (EN 1993-1-8 §4.5.3.2)
The directional method combines the throat stresses and checks two conditions against the design weld strengthfvw,d:
σ⊥2+3(τ⊥2+τ∥2)≤fvw,d=βwγM2fu
σ⊥≤γM20.9fu
where fu is the ultimate strength of the weaker connected part, γM2=1.25 andβw is the correlation factor. This method rewards welds loaded along their length and is generally less conservative.
Simplified method (§4.5.3.3)
The simplified method ignores direction: the resultant design force per unit length Fw,Ed must not exceed the design resistance per unit length, Fw,Rd=fvw,da. It is faster and always at least as safe as the directional method.
Fw,Ed≤Fw,Rd=fvw,da
The correlation factor β_w
The correlation factor βw (EN 1993-1-8 Table 4.1) depends on the steel grade:
Steel grade
β_w
S235
0.80
S275
0.85
S355
0.90
S420 / S460
1.00
Butt (groove) welds (§4.7)
A full-penetration butt weld made with matching consumables develops the weaker parent metal - no separate weld check is needed; verify the parent (von Mises against fy/γM0). A partial-penetrationbutt weld is treated as a deep-penetration fillet on its effective throat aeff.
Weld groups - the "weld as a line" method
When a pattern of welds (a box, a C-shape, two lines) resists an in-plane force and a torsion moment, the classic approach treats the weld as a line of unit throat. Compute the group length L, its centroid and the polar moment of the weld line Ip=Iy+Iz. The direct force per unit length isfdir=F/L; torsion adds ftor=Mrmax/Ip at the farthest point. The two combine as vectors at the worst corner to give the peak resultant per unit length, divided by the real throat to a stress checked against the same code limit:
fres=fdir+ftor,τ=afres
Select a weld pattern in the calculator's Weld group tab and enter the box size and the in-plane actions to get the governing utilisation.
Frequently asked questions
To EN 1993-1-8 the fillet weld is checked on its effective throat. First find the throat a = s/√2 from the leg size s, then the throat area A_w = a·L. Resolve the applied forces into the normal stress σ⊥, the transverse shear τ⊥ and the longitudinal shear τ∥ on the throat. The directional method requires √(σ⊥² + 3(τ⊥² + τ∥²)) ≤ f_u/(β_w·γ_M2) and σ⊥ ≤ 0.9·f_u/γ_M2. This calculator evaluates both conditions plus the simplified method automatically.
The effective throat a is the shortest distance from the root to the face of the weld - the plane on which the weld is assumed to fail. For an equal-leg 90° fillet of leg size s it is a = s/√2 ≈ 0.707·s. All Eurocode fillet-weld stresses act on this throat area, not on the leg face, so the throat is the key dimension in any weld strength calculation.
Both are given in EN 1993-1-8 §4.5.3. The directional method resolves the force into components normal and parallel to the throat and combines them with √(σ⊥² + 3(τ⊥² + τ∥²)) ≤ f_vw,d - it is less conservative and rewards welds loaded along their length. The simplified method ignores direction and simply requires the resultant force per unit length F_w,Ed ≤ F_w,Rd = f_vw,d·a - it is quicker and always safe. This tool reports both.
β_w is the fillet-weld correlation factor from EN 1993-1-8 Table 4.1. It accounts for the weld metal being matched to the parent steel and reduces the design weld strength f_vw,d = f_u/(β_w·γ_M2). It depends on the steel grade: 0.80 for S235, 0.85 for S275, 0.90 for S355 and 1.00 for S420/S460. A larger β_w (higher grade) gives a lower design weld strength relative to f_u.
Size the weld so the governing utilisation is ≤ 1.0. Increase the leg size s (which raises the throat a and the capacity) or the weld length L until the directional and simplified checks both pass. Practical minimums also apply (often a minimum leg of about 3 mm, and a leg not exceeding the thinner connected part). Enter trial values in the calculator and read the utilisation directly.
Ready to check a weld to Eurocode 3? Enter the leg size, length and forces to get the throat stresses, capacity and PASS/FAIL.
