Question

The size of fillet weld required to join a bracket plate with the flange of a column as shown in figure below will be _____.

The permissible stress $P_q$ for the fillet weld is 140 MPa.

Answer 1

Let thickness of weld throat = t mm
Vertical shear stress at weld,
$P_s=\frac{W}{2\times d\times t}\left(N/m{m}^2\right)$
$=\frac{80\times {10}^3}{2\times 250\times t}=\frac{160}{t}MPa$

Horizontal shear stress due to bending at extreme fibre,
$P_b=\frac{6We}{2t{d}^2}\left(N/m{m}^2\right)$

$=\frac{6\times 80\times {10}^3\times 200}{2\times t\times (250{)}^2}=\left(\frac{768}{t}\right)MPa$

Resultant stress at extreme fibre,

$P_r=\sqrt{p_s^2+p_b^2}=\sqrt{{\left(\frac{160}{t}\right)}^2+{\left(\frac{768}{t}\right)}^2}=\frac{768.49}{t}MPa$

$\text{Since}{P}_r\le \text{permissible stress}{P}_q$

$\Rightarrow \frac{784.49}{t}\le 140$

$\Rightarrow t\ge \frac{784.49}{140}$

$\Rightarrow t\ge 5.6mm$

Therefore size of weld,
$s=\frac{t}{0.7}=\frac{5.6}{0.7}=8mm$