How Do You Calculate Reaction Forces in Static Equilibrium?

[Kasthuri]

Homework Statement

Question: The plate shown, picture is attached, is subjected to force F and 3 reaction forces R1 R2 R3. Find R1

Homework Equations

equations of equilibrium:
sum of Fx = 0
sum of Fy = 0
sum of moment about point O = 0

The Attempt at a Solution

sum of Fx = 0: (going right is positive)

-R1 - R2 + 3/5 R3 = 0

sum of Fy = 0: (going up is positive)

-56kN + 4/5 R3 = 0
so, R3 = 70kN

sum of moment about point O = 0 (going anticlockwise is positive)

R1 x (0.11m) - R2 x (0.11m) = 0
so, R1 = R2

therefore, R1 = R2 = 21kN

I am unsure of whether I have done this question correctly, in particular the moment about O.
Also, how do you figure out which direction the moment is in (anticlockwise/clockwise). As in, I took R1 x 0.11m as positive due to anticlockwise and
R2 x 0.11m as negative due to clockwise moment.
is this correct?

Thanks for any help you can offer!

 

[CWatters]

R3=70Kn appears correct.

As for the moment...

R1*110 + (-R2*110) = 0

So

R1 = R2

Both same sign

Horizontally, if left is positive...

-R3*3/5 + R1 + R2 = 0

-R3*3/5 + R1 + R1 = 0

-R3*3/5 + 2R1 = 0

R1 = R3*3/(5*2)

= 21kN

which is a +ve number so to the left.

R1 = R2

so R2 also to the left.

 

[Kasthuri]

Thank you!

 

[pongo38]

To check whether you are correct, just take moments about any other point. The sum should be zero.

 

[rezeew]

I would like to commend you on your attempt at solving the problem. Your approach using the equations of equilibrium is correct. As for the direction of the moment, it is important to establish a consistent direction convention and stick to it throughout the problem. In this case, you have taken anticlockwise as positive and clockwise as negative, which is a valid convention. However, it is important to clearly state this convention in your solution so that it is clear to the reader. Other than that, your solution seems correct and you have found the value of R1 to be 21kN. Keep up the good work!