# Determine the components of the support reactions

Determine the components of the support reactions at the fixed support A on the cantilevered beam.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

### Solution:

Our first step is to draw a free body diagram like so:

Remember that since the beam is attached at a fixed support, a moment is also created at A.

Let us now write an equilibrium equation for the x-axis forces.

$\rightarrow^+ \Sigma F_x=0;$

$4\text{cos}\,(30^0)-A_x=0$

$A_x=3.464$ kN

Next, we can write one for the y-axis forces.

$\uparrow^+ \Sigma F_y=0;$

$A_y-6-4\text{sin}\,(30^0)=0$

$A_y=8$ kN

Lastly, we can write a moment equation at point A.

$\circlearrowleft^+\Sigma M_A=0;$

$M_A-6(1.5)-(4\text{sin}\,(30^0))(1.5+1.5+1.5\text{cos}\,(30^0))-(4\text{cos}\,(30^0))(1.5\text{sin}\,(30^0))=0$

$M_A=20.196 \,\text{kN}\cdot\text{m}$

$A_x=3.46$ kN
$A_y=8$ kN
$M_A=20.2 \,\text{kN}\cdot\text{m}$