Question

Compute the size of fillet weld for a bracket-connection with ISMB 300 column as shown in figure. Permissible shear stress in weld = 110 MPa.

• A. 5
• B. 8
• C. 6
• D. 10

Answer 1

The correct option is B 8


Assuming throat thickness of the weld = t mm

Let CG of weld be at $\overline{X}$ from left edge as shown

$\therefore \overline{X}=\frac{A_1\overline{X_1}+A_2\overline{X_2}}{A_1+A_2}$

$\therefore \overline{X}=\frac{300\times t\times 0+(250\times t\times 2)\times 125}{(250\times 2+300)t}$

$=78.125mm$

$f_d=directshearstress$

$\overline{X}=\frac{Force}{Effectiveareaofweldresistingshear}$

$\overline{X}=\frac{100\times {10}^3}{t\times \left(800\right)}=\frac{125}{t}N/m{m}^2$

$Torsionalshearstress\left(f_t\right)=\frac{Tr}{J}$

$r=\sqrt{(250-\overline{X}{)}^2+{150}^2}$
$=\sqrt{(250-78.125{)}^2+{150}^2}$
$=228.125mm$

Torsion (T) = F x e
$=100\times {10}^3\times (425-\overline{X})$

$=100\times {10}^3\times (425-78.125)$
$=34.6875\times {10}^{6}Nmm$

Polar moment of inertia (J) = $I_{xx}+I_{yy}$
For weld,

$I_{xx}=\frac{t\times {300}^3}{12}+2\times 250\times t\times (150{)}^2$
$I_{xx}=13.5t\times {10}^{6}m{m}^4$

$I_{yy}=300\times t\times \overline{X^2}+2[\frac{t\times (250{)}^3}{12}+(250\times t\left)\right(125-\overline{X}{)}^2]$

$I_{yy}=300\times t\times (78.125{)}^2+2[\frac{t\times {250}^3}{12}+250\times t(125-78.125{)}^2]$
$=5.534t\times {10}^{6}m{m}^4$

$\therefore f_t=\frac{Tr}{J}=\frac{34.6875\times {10}^6\times 228.125}{(5.534+13.5)t\times {10}^6}$

$=\frac{415.734}{t}N/m{m}^2$

$cos\theta =\frac{250-\overline{x}}{r}=\frac{250-78.125}{228.125}=0.753$

Resultant stress

$\left(f_r\right)=\sqrt{f_d^2+f_t^2+2f_{df}cos\theta }$

$f_r=\sqrt{{\left(\frac{125}{t}\right)}^2+{\left(\frac{415.734}{t}\right)}^2+2\times \left(\frac{125}{t}\right)\times \left(\frac{415.734}{t}\right)\times 0.753}$

$f_r=\frac{516.45}{t}N/m{m}^2$

Now,
$f_r\le 110MPa$

$\Rightarrow \frac{516.45}{t}\le 110MPa$

$\Rightarrow t\ge 4.695mm$

$\Rightarrow 0.7S\ge 4.695mm$

$\Rightarrow S\ge 6.707mm$

$\therefore$ Adopt size of weld (s) = 8 mm. fillet weld