EN 1993-1-8 Weld Design Guide — Fillet Welds, Directional Method, βw

Quick Reference: This comprehensive guide covers EN 1993-1-8 fillet weld design: the directional method (Cl. 4.5.3.2) with stress components σ⊥, τ⊥, and τ∥; the simplified method (Cl. 4.5.3.1); the βw correlation factor by steel grade; effective throat thickness a; minimum and maximum weld sizes; and a full worked example with a double fillet welded bracket connection. Use the free welded connection calculator for instant EN 1993-1-8 checks.

PRELIMINARY — NOT FOR CONSTRUCTION. All calculations are illustrative educational examples. Results must be verified by a licensed Professional Engineer before use in any design project.

Weld Types per EN 1993-1-8

EN 1993-1-8 covers three main weld types:

Fillet welds are the most common in building structures, accounting for ~85% of structural welds.

Effective Throat Thickness a

For a conventional fillet weld with equal legs of size s:

a = s / √2 = s × cos(45°) ≈ 0.707 × s

For deep-penetration fillet welds where proven by procedure qualification testing, the effective throat may be larger than the theoretical value. EN 1993-1-8 permits up to a = s for welds with proven penetration.

The βw Correlation Factor (Table 4.1)

The βw factor relates weld metal strength to base metal strength. It accounts for the fact that the matching filler metal may be stronger or weaker relative to different steel grades.

Note: S420 has βw = 0.88 while S355 has βw = 0.90 — the S420 weld is stronger per unit throat despite the lower βw. The interaction between fu and βw means the unit design strength for a fillet weld is:

fvw,d = fu / (√3 × βw × γM2)

Comparative unit strengths (γM2 = 1.25):

Simplified Method (Cl. 4.5.3.1)

The design resistance per unit length of fillet weld:

Fw,Rd = fvw,d × a

where fvw,d = fu / (√3 × βw × γM2)

This method assumes the weld is loaded in shear on the throat plane and is independent of the direction of the applied force. It is conservative for transverse fillet welds because the directional method shows transverse fillet welds are approximately 22% stronger than longitudinal fillet welds.

Fw,Rd per mm of weld = a × fu / (√3 × βw × γM2)

For S275, 6 mm fillet (a = 4.24 mm): Fw,Rd = 4.24 × 223.4 = 947 N/mm = 0.95 kN/mm

Directional Method (Cl. 4.5.3.2)

The directional method resolves the applied force into stress components on the throat plane:

• σ⊥ = normal stress perpendicular to the throat
• τ⊥ = shear stress perpendicular to the weld axis (on the throat plane)
• τ∥ = shear stress parallel to the weld axis (on the throat plane)

Two checks are required:

Check 1 — Combined Stress Criterion

√[σ⊥² + 3(τ⊥² + τ∥²)] ≤ fu / (βw × γM2)

This is a von Mises equivalent stress check on the throat plane.

Check 2 — Normal Stress Criterion

σ⊥ ≤ 0.9 × fu / γM2

This limits the direct normal stress to prevent brittle fracture from excessive triaxiality.

For a fillet weld loaded in pure transverse tension (σ⊥ ≠ 0, τ⊥ = τ∥ = 0), Check 1 reduces to:

σ⊥ ≤ fu / (βw × γM2)

While for pure longitudinal shear (τ∥ ≠ 0, σ⊥ = τ⊥ = 0):

τ∥ ≤ fu / (√3 × βw × γM2)

Comparing transverse to longitudinal: the transverse strength is √3 ≈ 1.732 times the longitudinal strength. This is why the simplified method (which uses the longitudinal value for all load directions) is conservative for transversely loaded welds.

Full Worked Example — Double Fillet Welded Bracket

Design Data

Step 1: Determine Weld Group Forces

The eccentric shear produces both direct shear and torsional moment on the weld group:

Direct shear per unit length: v∥,d = VEd / Σl = 120,000 / (2 × 150) = 400 N/mm

Torsional moment: MEd = PEd × e = 120,000 × 100 = 12.0 × 10⁶ N·mm

Polar moment of inertia of the weld group (two parallel 150 mm lines 200 mm apart):

Ipx = 2 × (150 × 100²) = 2 × 1,500,000 = 3,000,000 mm³ (approximate method)

Maximum force per unit length from torsion (at the weld ends):

fT = MEd × rmax / Ipx where rmax = √(100² + 75²) = 125 mm, but for parallel welds:

fT = MEd × (200/2) / (2 × 150 × 100² + 2 × 150³/12) — simplified to:

For two parallel welds spaced s = 200 mm apart:

x-direction component: fx,E = MEd × (s/2) / Ipc = relies on full calculation

For a quick design approach, resolve the eccentric moment as a force couple:

FEd = MEd / s = 12.0 × 10⁶ / 200 = 60,000 N = 60 kN

This acts as an additional shear on each weld side perpendicular to the weld axis.

Step 2: Simplified Method Check

Resultant force per unit length (vector sum of direct shear + moment-induced shear):

fv,Ed = √(400² + (60,000/150)²) = √(160,000 + 160,000) = √(320,000) = 566 N/mm

Weld resistance per unit length (simplified method):

Fw,Rd = fvw,d × a = 223.4 × 5.66 = 1264 N/mm = 1.26 kN/mm

fv,Ed/Fw,Rd = 0.566/1.264 = 0.448 → OK ✓

Step 3: Directional Method Check

The resultant stress is at an angle θ = tan⁻¹(400/400) = 45° to the weld axis.

The throat stress components for a fillet weld loaded at angle θ to its axis:

The force per unit length Fw,Ed at 45°: vertical = 400 N/mm, horizontal = 400 N/mm

Resultant = 566 N/mm at 45°.

Resolve onto the throat plane:

σ⊥ = (Fw,Ed × sin θ) / a = (566 × sin 45°) / 5.66 = (566 × 0.707) / 5.66 = 400 / 5.66 = 70.7 MPa

τ⊥ = (Fw,Ed × cos θ) / a = (566 × cos 45°) / 5.66 = (566 × 0.707) / 5.66 = 70.7 MPa

τ∥ = 0 (load is in the plane perpendicular to weld axis)

Combined check:

√[σ⊥² + 3(τ⊥² + τ∥²)] = √[70.7² + 3 × 70.7²] = √[5000 + 3 × 5000] = √[20,000] = 141.4 MPa

Allowable: fu/(βw × γM2) = 430/(0.85 × 1.25) = 430/1.0625 = 404.7 MPa

141.4 < 404.7 → OK ✓

Normal stress check:

σ⊥ = 70.7 < 0.9 × fu/γM2 = 0.9 × 430/1.25 = 309.6 MPa → OK ✓

The directional method confirms ample capacity. Note that for this load case, the utilization is only 141.4/404.7 = 0.349 under the directional method vs 0.448 under the simplified method — the directional method gives a 22% lower utilization, consistent with the theoretical advantage for combined loading.

Minimum and Maximum Weld Sizes

Per EN 1993-1-8 §4.3.2 and EN 1090-2, controlled by the thicker connected part:

Maximum leg size at a plate edge: s ≤ 0.7 × t (to avoid melting the plate corner). Maximum leg size at a plate surface: s ≤ t (practical limit; exceeding the plate thickness means the electrode diameter should match).

Longitudinal vs Transverse Fillet Weld Strength

The directional method highlights an important design principle:

• Longitudinal fillet welds (parallel to load): τ∥ = F/(a×l), check against fu/(√3×βw×γM2)
• Transverse fillet welds (perpendicular to load): σ⊥ = F/(a×l), check against fu/(βw×γM2)

The ratio of transverse to longitudinal strength = √3 = 1.732. This means a 6 mm transverse fillet weld has the same capacity as an 8.8 mm longitudinal fillet weld for the same length. This is codified in the simplified method for the specific case where transverse and longitudinal welds are used together — the total resistance is the sum of longitudinal and transverse contributions, with the transverse welds multiplied by √3/0.9 ≈ 1.92 for stress redistribution.

Key Takeaways

1. The βw factor is often misunderstood. It does not directly reduce the weld capacity — it adjusts the design stress to account for the relative strength of the filler metal to the base metal. A higher βw reduces the design stress fvw,d, which is why S355 (βw=0.90) has slightly lower relative weld strength than S275 (βw=0.85) despite much higher fu.
2. The directional method can reduce weld size by 15-20% compared to the simplified method for transversely loaded welds. This economy is most impactful for large fillet welds on heavy connections.
3. Combined normal and shear stress on the throat plane is evaluated using the von Mises criterion, not a linear interaction. This is physically more accurate than older code approaches (like the British BS 5950 method which used linear vector addition).
4. Throat thickness a governs capacity, not leg size s. A deep-penetration fillet weld with a = s has the same unit strength as a butt weld.

Related Pages

• EN 1993-1-8 Bolt Design Guide — Fv,Rd, Fb,Rd, Combined
• EN 1993-1-8 Base Plate Design — T-Stub, Concrete Bearing
• EN 1993-1-1 Beam Design — IPE 300 Worked Example
• Fillet Weld Size Chart — AISC 360-22 & EN 1993
• Welding Procedure — AWS D1.1 vs EN 1090-2 Comparison