Question

A component is attached to a horizontal column by means of three identical rivets as shown in the figure. The maximum permissible shear stress for the rivets is $50N/m{m}^2$. The magnitude of maximum force is____kN.

• A. 16.7

Answer 1

The correct option is A 16.7
$r_1=80mm{r}_2=0r_3=80mme=80mm$



Primary direct force,

$P_1^{\prime }=P_2^{\prime }=P_3^{\prime }=\frac{P}{3}=\frac{20\times {10}^3}{3}$

= 6666.67 N

Secondary shear force,

$C=\frac{P.e}{r_1^2+r_2^2+r_3^1}=\frac{20\times {10}^5\times 80}{(80{)}^2+(0{)}^2+{80}^2}=\frac{20\times {10}^5\times 80}{2\times (80{)}^2}=125N/mm$

For maximum load,

$P_1^{\prime \prime }=P_s^{\prime \prime }=C.r.$

= 125 x 80 = 1000 N

Resultant shear force

$P=P_1^{\prime }+P_1^{\prime \prime }=6666.67+10000$

=1666.67 N

=16.7 kN