# Design of Fillet Welds According to EN 1993-1-8

### Technical Article

A fillet weld is the most common weld type in steel building construction. According to EN 1993‑1‑8, 4.3.2.1 (1) [1], fillet welds may be used for connecting structural parts where the fusion faces form an angle between 60° and 120°.

The effective throat thickness a of a fillet weld is generally assumed to be the height of the triangular axis (isosceles or not isosceles) that is measured up to the theoretical root point, see Figure 01.

#### Ultimate limit state of fillet welds

According to 1993-1-8 [1] , the ultimate limit state of fillet welds is usually determined by the directional method or the simplified method. The direction-related method is shown below.

The applied stress is assumed to be distributed uniformly over the seam cross-section and results in the following normal and shear stresses as shown in Figure 02:

• σ normal stress perpendicular to the weld axis
• σ || Normal stress parallel to the weld axis
• τ Shear stress (in the plane of the fillet weld surface) perpendicular to the weld axis
• τ || Shear stress (in the plane of the fillet weld surface) parallel to the weld axis

When determining the resistance of the fillet weld, the normal stresses σ || Neglected parallel to the weld axis.

The ultimate limit state of a fillet weld is sufficient if the following conditions are fulfilled:

$$\begin{array}{l}\sqrt{\mathrm\sigma_\perp^2\;+\;3\;\cdot\;(\mathrm\tau_\perp^2\;+\;\mathrm\tau_{\vert\vert}^2)}\;\leq\;\frac{{\mathrm f}_{\mathrm u}}{{\mathrm\beta}_{\mathrm w}\;\cdot\;{\mathrm\gamma}_{\mathrm M2}}\\{\mathrm\sigma}_\perp\;\leq\;0,9\;\cdot\;\frac{{\mathrm f}_{\mathrm u}}{{\mathrm\gamma}_{\mathrm M2}}\end{array}$$

Where is
f u the tensile strength of the weaker of the connected structural components,
β w is the correlation factor (see EN 1993-1-8, Table 4.1),
γ M2 is the partial safety factor for the resistance of welds.

#### Example

Design of the fillet welds of the beam shown in Figure 03 from [2] .

Material: S235, f u = 36.0 kN / cm², β w = 0.8
Internal forces: V z = 350 kN

Center of gravity

$${\mathrm z}_\mathrm S\;=\;\frac{\mathrm\Sigma({\mathrm A}_\mathrm i\;\cdot\;{\mathrm z}_\mathrm{Si})}{{\mathrm{ΣA}}_\mathrm i}\;=\;\frac{91,48\;\cdot\;43,72\;+\;40,00\;\cdot\;44,00\;+\;48,00\;\cdot\;23,00\;+\;45,00\;\cdot\;1,50}{224,48}\;=\;30,88\;\mathrm{cm}$$

Moment of inertia
The moment of inertia is related to the centroidal axis:

$$\begin{array}{l}{\mathrm I}_{\mathrm y}\;=\;\sum({\mathrm I}_{\mathrm{yi}}\;+\;{\mathrm A}_{\mathrm i}\;\cdot\;\mathrm z_{\mathrm{si}}^2)\;-\;\frac{\left(\sum{\mathrm A}_{\mathrm i}\;\cdot\;{\mathrm z}_{\mathrm{Si}}\right)^2}{{\mathrm{ΣA}}_{\mathrm i}}\;=\\=\;850,88\;+\;\frac{20,00\;\cdot\;2,00³}{12}\;+\;\frac{1,20\;\cdot\;40,00³}{12}\;+\;\frac{15,00\;\cdot\;3,00³}{12}\;+\;91,48\;\cdot\;43,72²\;+\;40,00\;\cdot\;44,00²\;+\;48,00\;\cdot\;23,00²\;+\;45,00\;\cdot\;1,50²\;-\\-\;\frac{(91,48\;\cdot\;43,72\;+\;40,00\;\cdot\;44,00\;+\;48,00\;\cdot\;23,00\;+\;45,00\;\cdot\;1,50)²}{224,48}\;=\\=\;71.095\;\mathrm{cm}^4\end{array}$$

Static moments
Based on the centroidal axis, the structural moments for the cross-section parts connected by means of the seams ➀, ➁, and ➂ are calculated:
S y, 1 = A 1 ∙ (z S, 1 - z S ) = 91.48 ∙ (43.72 - 30.88) = 1,175 cm³
S y, 2 = S y, 1 + A 2 ∙ (z S, 2 - z S ) = 1175 + 40.00 ∙ (44.00 - 30.88) = 1700 cm³
S y, 3 = A 3 ∙ (z S - z S, 3 ) = 45.00 ∙ (30.88- 1.50) = 1322 cm³

Design of welds

$$\begin{array}{l}{\mathrm\tau}_{\vert\vert,\mathrm{Vz},\mathrm i}\;=\;\frac{-{\mathrm V}_\mathrm z\;\cdot\;{\mathrm S}_{\mathrm y,\mathrm i}}{{\mathrm I}_\mathrm y\;\cdot\;{\mathrm{Σa}}_{\mathrm w,\mathrm i}}\;\leq\;\frac{{\mathrm f}_\mathrm u}{\sqrt3\;\cdot\;{\mathrm\beta}_\mathrm w\;\cdot\;{\mathrm\gamma}_{\mathrm M2}}\;=\;\;\frac{36,0}{\sqrt3\;\cdot\;0,8\;\cdot\;1,25}\;=\;20,78\;\mathrm{kN}/\mathrm{cm}²\\{\mathrm\tau}_{\vert\vert,\mathrm{Vz},1}\;=\;\frac{-350\;\cdot\;1.175}{71.095\;\cdot\;2\;\cdot\;0,4}\;=\;-7,23\;\mathrm{kN}/\mathrm{cm}²\;<\;20,78\;\mathrm{kN}/\mathrm{cm}²\\{\mathrm\tau}_{\vert\vert,\mathrm{Vz},2}\;=\;\frac{-350\;\cdot\;1.700}{71.095\;\cdot\;2\;\cdot\;0,5}\;=\;-8,37\;\mathrm{kN}/\mathrm{cm}²\;<\;20,78\;\mathrm{kN}/\mathrm{cm}²\\{\mathrm\tau}_{\vert\vert,\mathrm{Vz},3}\;=\;\frac{-350\;\cdot\;1.322}{71.095\;\cdot\;2\;\cdot\;0,4}\;=\;-8,13\;\mathrm{kN}/\mathrm{cm}²\;<\;20,78\;\mathrm{kN}/\mathrm{cm}²\end{array}$$

SHAPE-THIN
In SHAPE-THIN, you can specify the shear stress (in the plane of the fillet weld surface) parallel to the weld axis τ || at fillet welds and the ultimate limit state are determined. When modeling, please note that the weld must be connected to the edges of two elements. One of these elements can also represent a Null element.

In column H "Continuous Element" of Table 1.6 Welds, you can define the continuous elements. No weld stresses are calculated on these elements. If no element is specified in column H, the weld stresses are determined on all elements to which the weld is connected. These elements can be assigned to column B "Elements No." are taken from.

Figure 04 shows the definition of the weld for the example described in this article.

Table 5.1 Weld Threads shows the stresses τ || for the welds defined in Table 1.6 Welds. Figure 05 shows the weld stresses for the example described in the table.

#### References

 [1] Eurocode 3: Design of Steel Structures - Part 1-8: Design of connections; EN 1993-1-8: 2005 + AC: 2009 [2] Petersen, C .: Steel Structures, 4. Edition. Wiesbaden: Springer Vieweg, 2013