Weld strength (BS EN 1993-1-8)
Fillet weld design resistance, simplified method (BS EN 1993-1-8 4.5.3.3)
- where
- design shear strength of the weld (N/mm²)
- ultimate tensile strength of the weaker part (N/mm²)
- correlation factor
- partial factor
- design resistance per mm of weld (N/mm)
- throat thickness (mm)
- design resistance of the weld (kN)
- effective weld length (mm)
Explain this equation
Works out the design strength of a fillet weld by the simplified method in BS EN 1993-1-8. Use it to check a weld size against a design force from the engineer.
Shear strength of steel is roughly its tensile strength divided by √3. β_w adjusts for the real strength of welds in each steel grade, and γ_M2 is the safety factor for connections. The result is a design shear stress, and multiplying by the throat gives the force each millimetre of weld can carry, whatever direction the load comes from. Times the effective length, divided by 1000, gives kN.
This method treats the throat as carrying shear in any direction, which is simple and slightly conservative.
Sense check: S355 (f_u 470, β_w 0.9, γ_M2 1.25) gives about 241 N/mm², so an a5.6 fillet carries about 1.35 kN per mm, about 270 kN over 200 mm.
Watch out: the effective length excludes the craters at the ends unless they are filled. Throats under 3 mm are not allowed for load-carrying welds.
Design resistance of a fillet weld per millimetre of length, regardless of load direction, using the simplified method of BS EN 1993-1-8.
Enter your values to see the result.
Good to know
Use the fu and βw of the weaker part joined. Under the UK National Annex take fu as the minimum from the product standard (BS EN 10025-2: 410 N/mm² for S275, 470 N/mm² for S355). Effective length is the full-size length; it may be taken as the overall length less 2a for end craters, and welds shorter than 30 mm or 6a should not carry load. A transversely loaded fillet is about 1.225 times stronger (see the directional method).
Common mistake
Using leg length in place of throat. Using leg overstates resistance by about 41 %.
Limits
For fillet welds between parts at 60–120°. Long lap joints over 150a need the βLw reduction (4.11). Design by a competent structural engineer.
Sources
- BS EN 1993-1-8:2005 Eurocode 3: Design of steel structures – Part 1-8: Design of joints (4.5.3.2 directional method, 4.5.3.3 simplified method, Table 4.1 correlation factor βw) and UK National Annex (γM2 = 1.25)
- ArcelorMittal/SCI Orange Book: Bolts and welds (S355 fu = 470 N/mm², βw = 0.9, γM2 = 1.25, Fw,L,Rd = fvw,d × a, transverse Fw,T,Rd = K × Fw,L,Rd with K = 1.225)
- SCI Advisory Desk AD 399: design of partial penetration butt welds (S355 fu = 470 N/mm², βw = 0.9, γM2 = 1.25; directional method checks)
- Structville: Design of fillet weld connections (worked example: fu 430 N/mm², βw 0.85, γM2 1.25, a 4 mm → fvw,d 233.66 N/mm², Fw,Rd 934.63 N/mm)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the welding procedure specification (WPS), BS EN ISO 15614/9606, BS EN 1090, BS EN 1993 and manufacturers’ data. Structural welds need qualified welders and engineered designs.