Fillet Weld Group Analysis: Australian Standards AS4100

Welding is used in the fabrication of steelwork. It is particularly useful in connections and for combining several plates or sections into built-up sections with greater capacity then available rolled sections. More than one weld line forms a weld group. A weld group is subject to in-plane eccentric forces and moments.

A typical connection with a weld group is a beam to column welded connection.

As per Cl 9.6.3.10 of AS4100, the capacity of each weld line, \(\phi v_w\) (N/mm) is given by:

$$ \phi v_w = \phi \times 0.6 \times t_t \times f_{uw} $$

Where:

\( \rlap{t_t} \hspace{2.5em}\): weld thickness (mm)
\( \rlap{f_{uw}} \hspace{2.5em}\): nominal tensile strength of weld metal (MPa)

As per Cl 9.7 of AS4100, elastic analysis of weld groups for in-plane loading is permitted using the Instantaneous Centre of Rotation (ICR) concept. The ICR is the point at which the weld group rotates about when subjected to overall weld group actions. The ICR enables us to calculate the distribution of loads to each weld line in a weld group.

The method is not described further in AS4100, but is summarised below based on guidance in Steel Designers Handbook.

Analysis of the weld group uses the ICR concept together with superposition. For a weld group with in-plane design loading, a pure moment acting on a weld group has the ICR positioned at the weld group centroid. Whereas, when the same weld group is subject to shear force only, the ICR is at infinity. Therefore, for a weld group seeing in-plane shear and moments, superposition of the two individual action effects means uniformly distributing shear forces to all welds in the group while also assuming the weld group rotation from moment effects occurs about the group centroid.

👉 Based on superposition of in-plane loading, the weld group ICR is in the same position as the weld group centroid.

Design actions \( F^*_x, \space F^*_y, \space M^*_z \) applied away from the centroid of the weld group may be treated as being applied at the centroid plus moments, with forces \( F^*_x, \space F^*_y \) and a resolved moment \(M^*_o\).

In summary, the analysis of weld groups follows these steps:

1. The centroid of the weld group is evaluated based on the inputted weld group geometry.
2. All applied loads \( F^*_x, \space F^*_y, \space M^*_z \) are calculated as a concentrated resultant load \( F^*_x, \space F^*_y, \space M^*_o \) at the centroid of the weld group.
3. The resultant loads are distributed to each weld line by calculating the shear force \(v^*_w\) at the start and end of each weld line because the largest shear force for any given load on a weld line will occur at the ends. The \(v^*_w\) on each weld end is proportional to the distance from the weld end to the group centroid.
4. The 'critical' weld end is considered to be the weld end furthest from the centroid, which is used for the design check on the overall weld group.

Here are the equations you will need...

The resultant design force per unit length of each weld line \(v^*_w​\) (N/mm) is:

$$\begin{align*}
v^*_w &= \sqrt{[v^*_x]^2 + [v^*_y]^2} \vphantom{\frac{0}{0}}\\
&\text{for:} \vphantom{\frac{0}{0}}\\
v^*_x &= \frac{F^*_x}{l_w} - \frac{M^*_o y_s}{I_{wp}} \vphantom{\frac{0}{0}}\\
v^*_y &= \frac{F^*_y}{l_w} + \frac{M^*_o x_s}{I_{wp}} \vphantom{\frac{0}{0}}\\
M^*_o &= F^*_x e_y + F^*_y e_x - M^*_z \vphantom{\frac{0}{0}}
\end{align*}$$

Where:

\(\rlap{v^*_x, v^*_y}\hspace{2.5em}\): x- & y-axis design forces in the welds per unit length
\(\rlap{x_s​,y_s}​\hspace{2.5em}\): x- & y-axis distances of a weld line end from the group centroid
\(\rlap{M^*_o}\hspace{2.5em}\): resolved in-plane moment about the group centroid
\(\rlap{l_w}\hspace{2.5em}\): total length of the welds in the weld group
\(\rlap{I_{wp}}\hspace{2.5em}​\): polar second moment of area of the weld group

The weld group centroid coordinates \((\bar{x}, \bar{y})\) are given by:

$$\begin{align*}
\bar{x} &= \frac{\sum(d_s \times x_i)}{\sum d_s} \vphantom{\frac{0}{0}}\\
\bar{y} &= \frac{\sum(d_s \times y_i)}{\sum d_s} \vphantom{\frac{0}{0}}
\end{align*}$$

Where:

\(\rlap{x_i​, y_i}​\hspace{2.5em}\): coordinates of the centers of a weld line
\(\rlap{d_s}\hspace{2.5em}​\): length of a weld line, such that \(\rlap{l_w=\sum d_s}\hspace{5em}\)

The polar second moment of area of the weld group, \(I_{wp}\)​ is given by:

$$\begin{align*}
I_{wp} &= I_x + I_y \vphantom{\frac{0}{0}}\\
&\text{for:}\\
I_x &= \sum(I_{x,o} + y_c^2 d_s) \vphantom{\frac{0}{0}}\\
I_y &= \sum(I_{y,o} + x_c^2 d_s) \vphantom{\frac{0}{0}}
\end{align*}$$

Where:

\(\rlap{I_x​, I_y}\hspace{5em}\)​: second moment of areas about the weld group centroid in the x- and y-axis
\(\rlap{I_{x,o}​, I_{y,o}}​\hspace{5em}\): second moment of areas about the center of each weld line
\(\rlap{x_c^2 d_s, y_c^2 d_s}\hspace{5em}\)​: added second moment of areas due to the offset between the weld group centroid and the center of each weld line