Toe weld L1 = Lw x cx/90 with cx = 27 mm. What is L1 and why?

37.7 mm; moment equilibrium about the back weld keeps the weld group centroid at the angle centroid

88.0 mm; toe takes the larger share

2071 Bhadra · 10 marks

Weld length for ISA 90x90x12, 100 kN

Short answer

Use 6 mm fillet welds. Total weld length 126 mm; for balanced c.g., toe weld 38 mm and back weld 88 mm, each increased by 12 mm for craters to 50 mm and 105 mm.

In truss ISA 90 × 90 × 12 mm is subjected to the factored tension load of 100 kN. It is to be connected to a gusset using fillet welds at the toe and back. Find the length of welds required so that the centre of gravity of the welds lies in plane of the centre of gravity of angle. Fe410

Given: ISA 90×90×12 in a truss, factored tension 100 kN, Fe410 ( $f_u=410$ N/mm²), fillet welds at the toe and back. Centroid of the angle $c_x\approx27$ mm from the back of the connected leg (SP 6 value $\approx27$ mm).

Weld size

Thickness of the thicker part 12 mm → minimum size 5 mm (Table 21). Maximum size at the angle edge $=t-1.5=10.5$ mm. Use $s=6$ mm (shop weld).

$f_{wd}=\dfrac{410}{\sqrt3\times1.25}=189.4$ N/mm²
Strength per mm $=189.4\times0.7\times6=795.4$ N/mm

Length of weld

L_w=\frac{100\times10^3}{795.4}=125.7\ \text{mm}

Distribution so that the c.g. of the welds lies in the c.g. plane of the angle

Moments about the back weld ( $L_2$ ): $L_1\times90=L_w\times c_x$ , hence

Toe weld: $L_1=\dfrac{125.7\times27}{90}=37.7$ mm (force $30.0$ kN)
Back weld: $L_2=125.7-37.7=88.0$ mm (force $70.0$ kN)

Add $2s=12$ mm to each for the end craters, and keep every weld at least $4s=24$ mm long.

Answer: 6 mm fillet weld; toe weld 50 mm, back weld 105 mm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Weld length for ISA 90x90x12, 100 kN

Weld size

Length of weld

Distribution so that the c.g. of the welds lies in the c.g. plane of the angle

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