Welded connections

How fillet welds are designed to EN 1993-1-8: the throat, the directional and the simplified methods with β_w, weld groups under shear and moment, and the welds of a fin plate and an end plate, by hand and on the EN routes of the STATIX fin plate and end plate calculators.

1. Learning outcomes

After this lesson you can:

find the throat and the effective length of a fillet weld;
resolve a weld force into σ_⊥, τ_⊥ and τ_∥ and check it by the directional method;
use the simplified method and say when it is too conservative;
check the weld of a fin plate and the flange and web welds of an end plate, including the full-strength web rule;
read the weld rows of the STATIX fin plate and end plate calculators.

2. Before you start

Lesson 5 (the fin plate and its eccentricity).
The free fin plate and end plate calculators.
A pocket calculator and about 55 minutes.
The same lesson on the SA code: Steel Design 1, lesson 6 (SANS 10162-1).

3. Fillet welds

Fillet and butt welds. Most structural welds are fillets: a triangle of weld in the corner between two plates. Its strength is set by the throat a, the smallest section through it (4.5.2): for an equal-leg fillet a = 0.7 s. A full-penetration butt weld is as strong as the plate it joins (4.7.1) and is not designed separately.

Effective length (4.5.1). A fillet counts over its length at full size. Very short fillets are not load-bearing, and very long ones in lap joints are reduced. The calculators take the full length of the welds they check and do not reduce them.

4. The design resistance

The stresses on the throat (4.5.3.2). Whatever the load, it is resolved on the throat plane into a normal stress σ_⊥, a shear across the weld τ_⊥ and a shear along it τ_∥. A force at right angles to a fillet gives σ_⊥ = τ_⊥; a force along it gives τ_∥ only.

The directional method (4.5.3.2). The throat stresses are combined like a von Mises stress and compared with f_u/(β_w γ_M2); the correlation factor β_w (Table 4.1) depends on the grade of the parts joined. The normal stress alone is also limited.

force per mm F at right angles to a fillet: σ_⊥ = τ_⊥ = F / (a √2) force per mm F along a fillet: τ_∥ = F / a directional (4.1): √[σ_⊥² + 3(τ_⊥² + τ_∥²)] ≤ f_u / (β_w γ_M2) and σ_⊥ ≤ 0.9 f_u / γ_M2

The simplified method (4.5.3.3). The design shear strength f_vw,d times the throat gives a resistance per millimetre that is taken the same in every direction. It is always safe, and quick for weld groups; the directional method can give more for loads across the weld.

Direction matters. Loaded along its length, a fillet gives the same resistance by both methods. Loaded across, the directional method gives √(3/2) ≈ 1.22 times as much. The calculators use the directional method.

5. Weld groups

A weld group under shear and moment. The fin plate’s two fillets along its depth carry the shear evenly along their length and the moment V e as a linear stress, largest at the ends. At the ends the two line forces combine. The calculator takes e as the bolt group’s eccentricity from lesson 5.

6. End plate welds

End plate welds. The tension flange is welded to the plate with a fillet on each side; the bolt rows pull on the plate, and the end plate page gives the whole sum of the row forces to the flange welds, which is on the safe side. The web welds carry the shear, and the page also checks them as full strength.

Full-strength welds. SCI P398 recommends that the web of a moment connection is welded to develop the web’s own strength, so that the weld never limits the joint’s ductility. The check compares the two fillets with the web plate itself, not with the applied load.

7. What the calculators do

Practical points. The calculators take the fillet leg s and work with a = 0.7 s; β_w and f_u follow the steel grade. Butt welds, minimum fillet sizes for the plate thickness, weld returns and fatigue are for the designer to check.

Which engines the pages run (checked): the fin plate page sends its inputs to the server’s fin plate engine, whose EN route checks the two fillets by 4.5.3.2 with the line forces V/2h_p along and V e/(2h_p²/6) across, f_u by thickness from EN 1993-1-1 Table 3.1 (S355: 490 MPa up to 40 mm) and β_w 0.9, γ_M2 1.25. The end plate page (EN 1993-1-8 only) checks the flange weld pair for the sum of the bolt row forces, the web welds for the shear on 2 h_w, and the full-strength web rule of SCI P398, all by the directional method. For these welds it takes f_u of the weaker part joined, by thickness from EN 1993-1-1 Table 3.1 (S355: 490 MPa up to 40 mm, and every part here is thinner); Example B follows the page.

The welds in STATIX: the fin plate calculator takes one fillet leg for its two runs; the end plate calculator takes a flange and a web leg. Both use the directional method on the EN route and list each weld as a row.