Weld length for ISA 100x100x8, 200 kN

Given: ISA 100×100×8 (centroid $c_x=27.5$ mm from the back), factored tension 200 kN, Fe410 ($f_u=410$ N/mm²), fillet welds at the toe and back, shop welding.

Weld size and strength (IS 800:2007 cl. 10.5)

• Minimum size (Table 21): 3 mm if the thicker part (gusset) is up to 10 mm thick, 5 mm if it is 10-20 mm. Maximum size at the rounded toe of the 8 mm angle $\approx\tfrac34t=6$ mm ($t-1.5=6.5$ mm at a square edge). Use $s=6$ mm.
• $f_{wd}=\dfrac{f_u}{\sqrt3\gamma_{mw}}=\dfrac{410}{\sqrt3\times1.25}=189.4$ N/mm²
• Strength per mm $=f_{wd}\times0.7s=189.4\times4.2=795.4$ N/mm

Total length

$$L_{w}=\frac{200\times10^3}{795.4}=251.5\ \text{mm}$$

Distribution (so that the resultant coincides with the centroid)

Take moments about the back weld (length $L_2$ at the heel):

• Weld at toe: $L_1=L_w\dfrac{c_x}{100}=69.2$ mm (carries $200\times0.275=55$ kN)
• Weld at back (heel): $L_2=L_w-L_1=182.3$ mm (carries 145 kN)

Add $2s=12$ mm to each for the end craters (overall length = effective length + $2s$).

Answer: 6 mm fillet weld, toe weld 85 mm and back weld 195 mm long (total effective length about 251 mm).