Determine the horizontal and vertical components


Determine the horizontal and vertical components of reaction at the pin A and the reaction of the rocker B on the beam.

Determine the horizontal and vertical components

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

Solution:
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Let us first draw a free body diagram showing all the forces affecting the beam. Remember that since the beam is in equilibrium, all forces added must equal 0.

Determine the horizontal and vertical components

 

We can first solve for N_B by writing a moment equation at point A.

\circlearrowleft^+ \Sigma M_A=0;

N_B\text{cos}\,(30^0)(8)-4(6)=0

N_B=3.464kN

 

Now, we can write an equation along the x-axis like so:

\rightarrow^+\Sigma F_x=0;

A_x-3.464\text{sin}\,(30^0)=0

A_x=1.732 kN

 

Next, we can write another equation along the y-axis:

\uparrow^+\Sigma F_y=0;

A_y+3.464\text{cos}\,(30^0)-4=0

A_y=1 kN

 

Final Answers:

A_x=1.73 kN

A_y=1.00 kN

N_B=3.46kN

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