Question

A column is subjected to a load through a bracket as shown in the figure.

The resultant force (in kN, up to one decimal place) in the bolt 1 is____ .

Answer 1

P = 10 kN, e = 15 cm
$r_1=r_2=r_3=r_4=5cm$

$Directloadtobolt\left(1\right)=\frac{P}{4}$

$F_1=\frac{10}{4}=2.5kN$

Force in bolt (1) due to moment

$=\frac{Pe{r}_1}{\sum r_i^2}$
$F_2=\frac{10\times 15\times 5}{4\times 5^2}=7.5kN$


Angle between force
$F_{1}and{F}_2={135}^o$

$R=\sqrt{F_1^2+F_2^2+2F_1{F}_{2}cos\left({135}^o\right)}$

$=\sqrt{{2.5}^2+{7.5}^2+2\times 2.5\times 7.5cos\left({135}^o\right)}$

= 5.99 kN