Determine the components of the support reactions


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

Determine the components of the support reactions

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

Determine the components of the support reactions

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}

 

Final Answer:

A_x=3.46 kN

A_y=8 kN

M_A=20.2 \,\text{kN}\cdot\text{m}

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