A tie bar of 100 mm width and 16 mm thickness is to be welded to another plate using "8 mm fillet weld" (as shown in figure below). If the tensile capacity of plate is 240 kN and the shear stress in weld is 110.0 N/mm$^2$, the minimum overlap required will be:
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For fillet welds: Effective throat thickness = \(0.7 \times\) weld size. Always consider welds on both sides when applicable.
Step 1: Tensile capacity of plate.
Given tensile capacity = \(240 \, \text{kN} = 240 \times 10^3 \, \text{N}\). This load must be resisted by the weld.
Step 2: Strength of weld.
Weld strength is given by:
\[
P = \tau \times A
\]
where,
\(\tau = 110 \, \text{N/mm}^2\),
\(A = \text{throat thickness} \times \text{weld length}\).
Throat thickness of an 8 mm fillet weld:
\[
t = 0.7 \times 8 = 5.6 \, \text{mm}.
\]
So, capacity of weld per unit length (for both sides of plate):
\[
\text{Strength per mm length} = 2 \times 110 \times 5.6 = 1232 \, \text{N/mm}.
\]
Step 3: Required overlap length.
\[
\text{Length} = \frac{240 \times 10^3}{1232} \approx 194.8 \, \text{mm}.
\]
But weld is provided on both sides of the plate width = 100 mm, so overlap length required:
\[
\frac{194.8}{2} \approx 97.4 \, \text{mm}.
\]
