How to Design a Fillet Weld to EN 1993-1-8 — Directional Method Explained

The strength of a fillet weld is governed by its effective throat dimension a, not its leg size s. For a standard 45° fillet the throat factor is 0.7, so a = 0.7 s. A 10 mm leg fillet has an effective throat of only 7 mm — the perpendicular distance from the root to the face. The throat is the critical section because it is the minimum cross-section the full force resultant must cross. Specifying a minimum throat size is therefore the first design decision: EN 1993-1-8 Table 4.3 gives minimum throat sizes as a function of the thicker plate, and AWS D1.1 Table 4.5 gives similar prequalified minimums.

The throat section is idealised as a thin strip of length equal to the weld run length L and width equal to the throat a. For a single weld line the throat area is Aw = a·L and the section modulus for in-plane bending is Ww = a·L²/6. These are the cross-section properties used to convert the applied forces and moments into stress components on the throat plane.

The directional method of EN 1993-1-8 §4.5.3.2 distinguishes three stress components on the throat cross-section. A stress normal to the throat plane is σ_⊥; a shear stress perpendicular to the weld axis (in the throat plane) is τ_⊥; and a shear stress parallel to the weld axis (along the weld run) is τ_∥. For a fillet weld under transverse load (bending), the resultant throat stress p = M/Ww is equally split between σ_⊥ and τ_⊥ because the 45° throat is at 45° to both the load and the weld axis — each component equals p/√2. For a direct (in-plane) shear force, the load runs parallel to the weld axis and appears only as τ_∥ = F/Aw. For torsion, the resultant torsional shear at the farthest weld point is T·r/Jw, which also contributes to τ_⊥.

The three components are combined into a von Mises equivalent stress for the weld throat, and the result must satisfy two independent conditions: the equivalent stress must not exceed the directional resistance f_weld, and the normal stress σ_⊥ alone must not exceed a second limit of 0.9·fu/γ_M2. The governing utilisation is the maximum of the two checks, and the safety factor is its reciprocal.

The directional design resistance f_weld = fu / (βw · γ_Mw) contains the correlation factor βw, which reflects the fact that weld metal and the heat-affected zone are not as strong as the nominal parent plate. EN 1993-1-8 Table 4.1 tabulates βw from 0.80 for S235 to 1.00 for S420 and S460. A higher-strength steel has a higher βw, because the weld deposit can be formulated closer to matching the parent strength. The factor appears in the denominator: a higher βw gives a lower (more demanding) f_weld relative to fu, so the standard correctly penalises designers who assume the weld is as strong as the parent plate.

The equivalent shear resistance per unit throat area is f_vw = fu/(√3 · βw · γ_Mw). For direct-shear load cases the utilisation is τ_∥/f_vw, and this is usually less critical than the von Mises condition 1 check — but the calculator evaluates all three utilisation ratios and reports the governing one.

When the connection carries both a direct shear force and a bending moment, the stresses are computed from the throat-section properties and combined on the throat plane. For a single weld line of length L with throat a: throat area Aw = a·L (used for direct shear); section modulus Ww = a·L²/6 (used for bending); polar moment Jw = a·L³/12 and farthest-point radius r = L/2 (used for torsion). For two parallel weld lines separated by a clear gap b: Aw = 2·a·L; Ww = a·L²/3; Jw = a·L·(3b² + L²)/6 and r = √((b/2)² + (L/2)²). These weld-line properties follow Shigley Tables 9-1/9-2 and are consistent with Blodgett's Design of Welded Structures.

After computing σ_⊥, τ_⊥ and τ_∥ from the throat-section properties and the applied loads, the von Mises formula collapses to simpler special cases: for pure direct shear σ_eq = √3 · τ_∥; for pure bending on a fillet σ_eq = 2 · σ_⊥ (because σ_⊥ = τ_⊥ = p/√2 and √(σ_⊥² + 3·τ_⊥²) = 2·σ_⊥). These identities are useful sanity checks when verifying a calculation by hand.