The basic steps required, as per BS 5950, for fillet weld design calculations where the welded jointed structure is subjected to bending moment load are:

**Calculation of unit throat weld area (Au):**If you have a fillet weld line of, say, 50 mm long (**L)**, then the unit throat area of the welding joint can be calculated as:**Au =L*1=50 * 1=50 sq. mm…………………….eq.1**

Similarly, if your joint is in between a plate and a rectangular cross sectional tube with two sides of the rectangle are 10mm and 20mm. Then the periphery of the rectangle is **2x(10+20)=60 mm. **So, the unit throat area for this case will be **60 sq.mm.**

**Design strength of the welded joint (Pw):**It is the maximum permitted weld stress value for a particular welding joint . Design your fillet joint in such a manner that the stress developed on the joint does not cross the design strength (Pw).The values of the design strength are fixed and depends upon the kind of electrode used and the kind of parent material.

You should get the

**Pw**value as a input while performing the fillet weld size calculation. However, if yo don’t get the**Pw**value as an design input then use the following rule of thumb:

**Pw=0.5*fu………………………………………………..eq.2**

* *Where,

**fu**is the ultimate tensile strength of the parent material.

**Calculate unit area moment of inertia (Iu) for the welded joint:**This is the area moment of inertia value of the weld section considering throat length as one. For details refer How to calculate unit area moment of inertia for circular welded joint.**Calculate direct shear stress (τs):**Two types of shear stress will be developed in the joint subjected to only bending:**direct shear stress (τs)**and**shear stress due to bending (τb).**

**τs=F/Au………………………………………………..eq.3**

Where,

**F** is the applied load

**Au** is the unit throat weld area, calculated according to **eq.1**

**Calculate shear stress due to bending (τb):**The following equation is used here:

**τb=M*Y/Iu…………………………………………eq.4**

Where,

**M** is the applied bending moment to the welded joint

**Y **is the distance between the centre axis and the extreme fibre of the section of the welded joint. For, the rectangular cross section, the value of the **Y **is equal to the half of the depth of the cross section.

**Calculate the resultant stress (τ):**The resultant stress of the bending and shear stress is calculated by:

**τ= √(τs* τs + τb* τb)…………………………….eq.5**

**Calculate the weld throat size (t):**The resultant stress calculated above (**τ)**above are for the unit throat size of the weld. The throat size required for keeping the resultant stress below (or equal) to the design stress (**Pw**) is:

** t= τ/Pw………………………………………………….eq.6**

*Where,*

**τ **is the resulted stress experienced by the joint

**Pw** is the design stress for the fillet welding

**Calculate leg length of the weld (L):**The leg length of the weld can be found from the below equation:

** L=1.4141*t…………………………………………….eq.7**

*Where,*

t is the weld throat size

For the sake of practicality, the next higher value to the value of the weld leg length obtained from the weld strength design calculation is to be take into account for the weld connection design.

I have to solve one typical simplel fillet weld calculation. One centre plate of thickness 30mm and 2 side plates of 10 mm thick are welded to the center plate. The distance between center plate top face and side plate top face is 10 mm. In this gap, 7mm fillet weld is filled. If my vertical load of 100 KN is at center of the center plate, what will be shear load on weld? Is there any bending moment load acting on this weld?

What is the reference of these equation? which book/s do they come from, please?

BS 5950