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.