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:
Show me the final answer↓
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
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
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}
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}
A_y=8 kN
M_A=20.2 \,\text{kN}\cdot\text{m}
Can I find out which app is drawing these shapes
I don’t use an app, I draw them by hand using illustrator. ?
Thank you very much
You’re welcome!
do you have more questions for practice?
No, but you should try to do as many questions from your textbook as possible.
good
thanks