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

### Technical Article

001469 18 August 2017

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 should be taken as the height of the largest triangle (with equal or unequal legs) that can be inscribed within the fusion faces and the weld surface, measured perpendicular to the outer side of this triangle, see Figure 01.

#### Design Resistance of Fillet Welds

According to EN 1993‑1‑8 [1], the design resistance of a fillet weld is usually determined using Directional Method or Simplified Method. The Directional Method is described below.

A uniform distribution of stress is assumed on the throat section of the weld, leading to the normal stresses and shear stresses shown in Figure 02, as follows:

• σ is the normal stress perpendicular to the throat
• σ|| is the normal stress parallel to the axis of the weld
• τ is the shear stress (in the plane of the throat) perpendicular to the axis of the weld
• τ|| is the shear stress (in the plane of the throat) parallel to the axis of the weld

The normal stress σ|| parallel to the axis is not considered when verifying the design resistance of the weld.

The design resistance of the fillet weld will be sufficient if the following are both satisfied:

$$\begin{array}{l}\sqrt{\mathrm\sigma_\perp^2\;+\;3\;\cdot\;(\mathrm\tau_\perp^2\;+\;\mathrm\tau_{\vert\vert}^2)}\;\leq\;\frac{{\mathrm f}_\mathrm u}{{\mathrm\beta}_\mathrm w\;\cdot\;{\mathrm\gamma}_{\mathrm M2}}\\{\mathrm\sigma}_\perp\;\leq\;0.9\;\cdot\;\frac{{\mathrm f}_\mathrm u}{{\mathrm\gamma}_{\mathrm M2}}\end{array}$$

where

 fu is the nominal ultimate tensile stress of the weaker part joined βw is the appropriate correlation factor (see EN 1993‑1‑8, Table 4.1) γM2 is the partial safety factor for resistance of welds

#### Example

Design of a fillet weld of the beam displayed in Figure 03 from [2].

• Material: S235, fu = 36.0 kN/cm², βw = 0.8
• Internal forces: Vz = 350 kN
##### Centroid

$${\mathrm z}_\mathrm S\;=\;\frac{\mathrm\Sigma({\mathrm A}_\mathrm i\;\cdot\;{\mathrm z}_\mathrm{Si})}{{\mathrm{ΣA}}_\mathrm i}\;=\;\frac{91.48\;\cdot\;43.72\;+\;40.00\;\cdot\;44.00\;+\;48.00\;\cdot\;23.00\;+\;45.00\;\cdot\;1.50}{224.48}\;=\;30.88\;\mathrm{cm}$$

##### Moment of Inertia

With regard to the centroid, the moment of inertia is:

$$\begin{array}{l}{\mathrm I}_\mathrm y\;=\;\sum({\mathrm I}_\mathrm{yi}\;+\;{\mathrm A}_\mathrm i\;\cdot\;\mathrm z_\mathrm{si}^2)\;-\;\frac{\left(\sum{\mathrm A}_\mathrm i\;\cdot\;{\mathrm z}_\mathrm{Si}\right)^2}{{\mathrm{ΣA}}_\mathrm i}\;=\\=\;850.88\;+\;\frac{20.00\;\cdot\;2.00³}{12}\;+\;\frac{1.20\;\cdot\;40.00³}{12}\;+\;\frac{15.00\;\cdot\;3.00³}{12}\;+\;91.48\;\cdot\;43.72²\;+\;40.00\;\cdot\;44.00²\;+\;48.00\;\cdot\;23.00²\;+\;45.00\;\cdot\;1.50²\;-\\-\;\frac{(91.48\;\cdot\;43.72\;+\;40.00\;\cdot\;44.00\;+\;48.00\;\cdot\;23.00\;+\;45.00\;\cdot\;1.50)²}{224.48}\;=\\=\;71,095\;\mathrm{cm}^4\end{array}$$

##### Static Moments

With regard to the centroid, the static moments of the cross‑sections connected are calculated by using the welds ➀, ➁, and ➂:

$$\begin{array}{l}{\mathrm S}_{\mathrm y,1}\;=\;{\mathrm A}_1\;\cdot\;({\mathrm z}_{\mathrm S,1}\;-\;{\mathrm z}_\mathrm S)\;=\;91.48\;\cdot\;(43.72\;-\;30.88)\;=\;1,175\;\mathrm{cm}^3\\{\mathrm S}_{\mathrm y,2}\;=\;{\mathrm S}_{\mathrm y,1}\;+\;{\mathrm A}_2\;\cdot\;({\mathrm z}_{\mathrm S,2}\;-\;{\mathrm z}_\mathrm S)\;=\;1,175\;+\;40.00\;\cdot\;(44.00\;-\;30.88)\;=\;1,700\;\mathrm{cm}^3\\{\mathrm S}_{\mathrm y,3}\;=\;{\mathrm A}_3\;\cdot\;({\mathrm z}_\mathrm S\;-\;{\mathrm z}_{\mathrm S,3})\;=\;45.00\;\cdot\;(30.88\;-\;1.50)\;=\;1,322\;\mathrm{cm}^3\end{array}$$

##### Weld Design

$$\begin{array}{l}{\mathrm\tau}_{\vert\vert,\mathrm{Vz},\mathrm i}\;=\;\frac{-{\mathrm V}_\mathrm z\;\cdot\;{\mathrm S}_{\mathrm y,\mathrm i}}{{\mathrm I}_\mathrm y\;\cdot\;{\mathrm{Σa}}_{\mathrm w,\mathrm i}}\;\leq\;\frac{{\mathrm f}_\mathrm u}{\sqrt3\;\cdot\;{\mathrm\beta}_\mathrm w\;\cdot\;{\mathrm\gamma}_{\mathrm M2}}\;=\;\;\frac{36.0}{\sqrt3\;\cdot\;0.8\;\cdot\;1.25}\;=\;20.78\;\mathrm{kN}/\mathrm{cm}²\\{\mathrm\tau}_{\vert\vert,\mathrm{Vz},1}\;=\;\frac{-350\;\cdot\;1,175}{71,095\;\cdot\;2\;\cdot\;0.4}\;=\;-7.23\;\mathrm{kN}/\mathrm{cm}²\;<\;20.78\;\mathrm{kN}/\mathrm{cm}²\\{\mathrm\tau}_{\vert\vert,\mathrm{Vz},2}\;=\;\frac{-350\;\cdot\;1,700}{71,095\;\cdot\;2\;\cdot\;0.5}\;=\;-8.37\;\mathrm{kN}/\mathrm{cm}²\;<\;20.78\;\mathrm{kN}/\mathrm{cm}²\\{\mathrm\tau}_{\vert\vert,\mathrm{Vz},3}\;=\;\frac{-350\;\cdot\;1,322}{71,095\;\cdot\;2\;\cdot\;0.4}\;=\;-8.13\;\mathrm{kN}/\mathrm{cm}²\;<\;20.78\;\mathrm{kN}/\mathrm{cm}²\end{array}$$

##### SHAPE-THIN

In SHAPE‑THIN, the shear stress (in the plane of the fillet weld surface) parallel to the weld axis τ|| can be calculated on fillet welds, and the resistance can be designed. When modelling, the weld must be connected to the edges of two elements. One of these elements can also be a dummy 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 there is no element specified in Column H, the weld stresses are determined on all elements to which the weld is connected. These elements can be taken from Column B ‘Elements No.’

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

Table 5.1 Welds displays the resulting stresses τ|| for the welds defined in Table 1.6 Welds. Figure 05 shows the weld stresses for the example described in this article.

#### Reference

 [1] Eurocode 3: Design of steel structures - Part 1‑8: Design of joints; EN 1993‑1‑8:2005 + AC:2009 [2] Petersen, C. (2013). Stahlbau, (4th ed.). Wiesbaden: Springer Vieweg.