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Fillet Weld Group Calculator to AS4100's banner

Fillet Weld Group Calculator to AS4100

Verified by the CalcTree engineering team on July 30, 2024

This calculator analyses and checks each fillet weld in a weld group for in-plane loading. The weld group is analysed using the Instantaneous Centre of Rotation (ICR) concept and then the shear force at each end of each weld line is checked to ensure the critical design shear is considered.
All calculations are performed in accordance with AS4100-2020.

Calculation

Assumptions



Weld Properties



tw
:6mm​


Fillet weld size



Weld category
:1​


Weld category



Weld electrode type
:43​


Weld electrode type



Φ
:0.6​



fuw
:430MPa​



Φv_w
:657N/mm​


Weld capacity



Weld Group Geometry


380​
100​
50​
0​


Check
:Weld group geometry OK. All weld lines are orthogonal to the x- & y-axis.​



x_centroid
:11.8mm​



y_centroid
:207.9mm​


Weld group centroid




I_wp
:1.01e+7mm4​


Polar second moment of area



Design Loads



F*x
:30.00 kN​



F*y
:100.00 kN​



ex
:{"mathjs":"Unit","value":0.3,"unit":"m","fixPrefix":false}​



ey
:{"mathjs":"Unit","value":0.2,"unit":"m","fixPrefix":false}​



M*z
:{"mathjs":"Unit","value":10,"unit":"kN m","fixPrefix":false}​



M*o
:26kN m​

👉Note:
  1. input the design actions
    
    using the sign convention in the image below
  2. 
    
    and
    
    are the force eccentricities from the weld group centroid. Refer to the coordinates of the weld group centroid in order to determine your
    
    and
    
    .
Weld group loaded by in-plane actions: (a) initial in-plane actions, (b) resolved actions about group centroid



Design Check



Design summary
:Weld end on weld line #3 fails. Use stronger weld.​


#1​
1​
-11.8​
172.1​
416.8​
SAFE​
#1​
2​
-11.8​
-207.9​
611.7​
SAFE​
#2​
3​
88.2​
172.1​
566.7​
SAFE​
#2​
4​
-11.8​
172.1​
416.8​
SAFE​
#3​
5​
38.2​
-207.9​
656.8​
FAIL​
#3​
6​
-11.8​
-207.9​
611.7​
SAFE​
​
​
​
​
​
​
​
​
​
​
​
​


Explanation

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 then 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.
Beam to column welded connection


Weld capacity

As per Cl 9.6.3.10 of AS4100, the capacity of each weld line,

is given by:

ϕvw=ϕ×0.6×tt×fuw\phi v_w = \phi \times 0.6 \times t_t \times f_{uw}
Where:
  1. 
    
    is the weld thickness
    
    
  2. 
    
    is the nominal tensile strength of weld metal
    
    

Analysis of weld groups

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 from 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

applied away from the centroid of the weld group may be treated as being applied at the centroid plus moments, with forces

and a resolved moment

.
Weld group loaded by in-plane actions: (a) initial in-plane actions, (b) resolved actions about group centroid

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
    
    are calculated as a concentrated resultant load
    
    at the centroid of the weld group.
  3. The resultant loads are distributed to each weld line by calculating the shear force
    
    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
    
    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

is:

vw∗=[vx∗]2+[vy∗]2for:vx∗=Fx∗lw−Mo∗ysIwpvy∗=Fy∗lw+Mo∗xsIwpMo∗=Fx∗ey+Fy∗ex−Mz∗v^*_{w} = \sqrt{[v^*_x]^2+[v^*_y]^2}\\ \text{for:}\\ v^*_x = \dfrac{F^*_x}{l_w} - \dfrac{M^*_oy_s}{I_{wp}} \\ v^*_y = \dfrac{F^*_y}{l_w} + \dfrac{M^*_ox_s}{I_{wp}} \\ M^*_o = F^*_x e_y + F^*_ye_x - M^*_z
Where:
  1. 
    
    are the x- & y-axis design forces in the welds per unit length
  2. 
    
    are the x- & y-axis distances of a weld line end from the group centroid
  3. 
    
    is the resolved in-plane moment about the group centroid
  1. 
    
    is the total length of the welds in the weld group
  2. 
    
    is the polar second moment of area of the weld group

The weld group centroid coordinates

are given by:

xˉ=∑(ds×xi)∑dsyˉ=∑(ds×yi∑ds\bar{x}=\dfrac{\sum (d_s \times x_i)}{\sum d_s}\\\bar{y}=\dfrac{\sum (d_s \times y_i}{\sum d_s}
Where:
  1. 
    
    are the coordinates of the centers of a weld line
  2. 
    
    is the length of a weld line, where
    
    

The polar second moment of area of the weld group,

is given by:

Iwp=Ix+Iyfor:Ix=∑(Ix,o+yc2ds)Iy=∑(Iy,o+xc2ds)I_{wp}=I_x+I_y\\\text{for:}\\I_x=\sum (I_{x,o}+y_c^2d_s)\\I_y=\sum ( I_{y,o}+x_c^2d_s)
Where:
  1. 
    
    are the second moment of areas about the weld group centroid in the x- and y-axis
  2. 
    
    are the second moment of areas about the center of each weld line
  3. 
    
    are the added second moment of areas due to the offset between the weld group centroid and the center of each weld line

Related Resources

  1. Bolt Group Calculator to AS 4100
  2. Steel Base Plate Designer to EC3
  1. Steel Baseplate Designer to AISC 360