# 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 weld 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.

Image 01 - Fillet weld thickness a at normal penetration (a) and at deep penetration (b)

#### Design Resistance of Fillet Welds

According to 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 section of the weld, leading to the normal stresses and shear stresses shown in Figure 02, as follows:

- σ
_{⊥}normal stress perpendicular to weld axis - σ
_{||}normal stress parallel to weld axis - τ
_{⊥}shear stress (in plane of fillet weld surface) perpendicular to weld axis - τ
_{||}shear stress (in plane of fillet weld surface) parallel to weld axis

Image 02 - Weld Stresses on Throat Section of Fillet Weld

The normal stress σ_{||} parallel to the axis is not considered when verifying the design resistance of the fillet weld.

The design resistance of the fillet weld will be sufficient if the following conditions are met:

$\begin{array}{l}\sqrt{{\mathrm{\sigma}}_{\perp}^{2}+3\xb7({\mathrm{\tau}}_{\perp}^{2}+{\mathrm{\tau}}_{\left|\right|}^{2})}\le \frac{{\mathrm{f}}_{\mathrm{u}}}{{\mathrm{\beta}}_{\mathrm{w}}\xb7{\mathrm{\gamma}}_{\mathrm{M}2}}\\ {\mathrm{\sigma}}_{\perp}\le 0,9\xb7\frac{{\mathrm{f}}_{\mathrm{u}}}{{\mathrm{\gamma}}_{\mathrm{M}2}}\end{array}$

where

f_{u} is the nominal ultimate tensile stress of the weaker part joined

β_{w} is the appropriate correlation factor (see EN 1993-1-8, Table 4.1)

γ_{M2} 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, f_{u} = 36.0 kN/cm², β_{w} = 0.8

Internal forces: V_{z} = 350 kN

**Center of gravity**

$${\mathrm{z}}_{\mathrm{S}}=\frac{\mathrm{\Sigma}({\mathrm{A}}_{\mathrm{i}}\xb7{\mathrm{z}}_{\mathrm{Si}})}{{\mathrm{\Sigma A}}_{\mathrm{i}}}=\frac{91.48\xb743.7240.00\xb744.0048.00\xb723.0045.00\xb71.50}{224.48}=30.88\mathrm{cm}$$

**Moment of inertia**

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

$\begin{array}{l}{\mathrm{I}}_{\mathrm{y}}=\sum ({\mathrm{I}}_{\mathrm{yi}}+{\mathrm{A}}_{\mathrm{i}}\xb7{\mathrm{z}}_{\mathrm{si}}^{2})-\frac{{\left(\sum {\mathrm{A}}_{\mathrm{i}}\xb7{\mathrm{z}}_{\mathrm{Si}}\right)}^{2}}{{\mathrm{\Sigma A}}_{\mathrm{i}}}=\\ =850,88\frac{20,00\xb72,00\xb3}{12}\frac{1,20\xb740,00\xb3}{12}\frac{15,00\xb73,00\xb3}{12}91,48\xb743,72\xb240,00\xb744,00\xb248,00\xb723,00\xb245,00\xb71,50\xb2-\\ -\frac{(91,48\xb743,7240,00\xb744,0048,00\xb723,0045,00\xb71,50)\xb2}{224,48}=\\ =71.095{\mathrm{cm}}^{4}\end{array}$

**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:

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) = 1,700 cm³

S_{y,3} = A_{3} ∙ (z_{S} - z_{S,3}) = 45.00 ∙ (30.88- 1.50) = 1,322 cm³

**Design of welds**

$\begin{array}{l}{\mathrm{\tau}}_{\left|\right|,\mathrm{Vz},\mathrm{i}}=\frac{-{\mathrm{V}}_{\mathrm{z}}\xb7{\mathrm{S}}_{\mathrm{y},\mathrm{i}}}{{\mathrm{I}}_{\mathrm{y}}\xb7{\mathrm{\Sigma a}}_{\mathrm{w},\mathrm{i}}}\le \frac{{\mathrm{f}}_{\mathrm{u}}}{\sqrt{3}\xb7{\mathrm{\beta}}_{\mathrm{w}}\xb7{\mathrm{\gamma}}_{\mathrm{M}2}}=\frac{36,0}{\sqrt{3}\xb70,8\xb71,25}=20,78\mathrm{kN}/\mathrm{cm}\xb2\\ {\mathrm{\tau}}_{\left|\right|,\mathrm{Vz},1}=\frac{-350\xb71.175}{71.095\xb72\xb70,4}=-7,23\mathrm{kN}/\mathrm{cm}\xb220,78\mathrm{kN}/\mathrm{cm}\xb2\\ {\mathrm{\tau}}_{\left|\right|,\mathrm{Vz},2}=\frac{-350\xb71.700}{71.095\xb72\xb70,5}=-8,37\mathrm{kN}/\mathrm{cm}\xb220,78\mathrm{kN}/\mathrm{cm}\xb2\\ {\mathrm{\tau}}_{\left|\right|,\mathrm{Vz},3}=\frac{-350\xb71.322}{71.095\xb72\xb70,4}=-8,13\mathrm{kN}/\mathrm{cm}\xb220,78\mathrm{kN}/\mathrm{cm}\xb2\end{array}$

**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 modeling, 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.

#### Literature

#### Author

#### Sonja von Bloh, M.Sc.

Product Engineering & Customer Support

Ms. von Bloh provides technical support for our customer and is responsible for the development of the SHAPE‑THIN program.

#### Keywords

Fillet weld Weld Weld stress Weld seam design Fillet weld design

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The limit stresses in RF-/STEEL can be user-defined for each thickness range.SHAPE-THIN determines the effective cross-sections according to EN 1993-1-3 and EN 1993-1-5 for cold-formed sections. You can optionally check the geometric conditions for the applicability of the standard specified in EN 1993‑1‑3, Section 5.2.

The effects of local plate buckling are considered according to the method of reduced widths and the possible buckling of stiffeners (instability) is considered for stiffened sections according to EN 1993-1-3, Section 5.5.

As an option, you can perform an iterative calculation to optimize the effective cross-section.

You can display the effective cross-sections graphically.

Read more about designing cold-formed sections with SHAPE-THIN and RF-/STEEL Cold-Formed Sections in this technical article: Design of a Thin-Walled, Cold-Formed C-Section According to EN 1993-1-3.

- What is the purpose of a fillet weld in SHAPE‑THIN?
- Is it possible to model cold-formed sections in SHAPE‑THIN 8 and to design them in RF‑/STEEL Cold-Formed Sections?
- When calculating a cross-section, I get a message saying that the weld is not connected to two elements. What should I do?
- When calculating a stiffened panel, I get the message that the boundary c/t-zone of the panel is not supported. What should I do?
- When calculating a longitudinally stiffened panel, I get a message saying that the stiffener cannot be at the end of the panel. What should I do?

- When calculating a buckling panel, I get a message saying that some elements are connected to the panel, but they are not defined as stiffeners. What should I do?
- When selecting the elements for a stiffener of a stiffened panel, I get a message saying that at least one of the selected elements is a null element. What should I do?
- How does the calculation of the moments of inertia differ when the cross-section consists of several unconnected or connected partial cross-sections?
- Is it possible to assign the identical section or cross-section names with the SHAPE‑THIN program?
- How is the automatic creation of c/t-parts carried out?