Question

A moment M of magnitude 50 kN-m is transmitted to a column flange through a bracket by using four 20 mm diameter rivets as shown in the figure. The shear force induced in the rivet A is ______.

• A. 125 kN
• B. 250 kN
• C. 175.8 kN
• D. 88.4 kN

Answer 1

The correct option is C 175.8 kN

Distance of each rivet from of rivet group,
$r=\sqrt{{50}^2+{50}^2}$
$=50\sqrt{2}mm$

All rivets have equal area = A
Shear force in rivet A
= Shear stress x Area
$=\frac{Mr}{J}.A$
$=\frac{Mr}{\sum A{r}^2}.A$

$=\frac{Mr}{\sum r^2}=\frac{50\times {10}^6\times 50\sqrt{2}}{4\times {\left(50\sqrt{2}\right)}^2}$
= 176776.7 N
= 176.77 kN