Static Equilibrium Reaction Question about Fixed Point

[Grandpa04]

Homework Statement

Determine the reaction at fixed point A

Relevant Equations

ΣFx = 0
ΣFy = 0
ΣM = 0

For this problem I set ΣFy = -3kN - 0.75kN - 3kN + Ay + By (with By representing the right side vertical force, and Ay representing the left side force). For ΣM, I used the rectangular distributed load of 0.5 kN at 3m from point A as the pivot:
ΣM = -3m*Ay - (0.5kN*4m) - 3kN*6m - 5kN*m + By*6m.
I solved the system of the two equations and found Ay to be 1.722 kN. I am unsure if I used the correct/best method for the problem and if the answer is correct.

 

[haruspex]

I see no indication of an unknown force at B. Instead, I suggest there is a torque at A.

 

[Lnewqban]

Could you explain the 0.75kN value?
If you represent the calculated value for Ay in the diagram, would the beam remain in equilibrium of forces and moments?

 

[Steve4Physics]

I am unsure if I used the correct/best method for the problem and if the answer is correct.

Hi @Grandpa04. Your answer isn't correct. In addition to the other replies, this might help.

If you have posted the complete question, then we assume that the beam’s weight is negligible - as there is no mention of the weight.

The given externally applied forces are the distributed load and the 3kN force.

The given externally applied moment (torque) is the one shown as 5 kN.m (CW.). Note that this is 'pure' moment - e.g. produced by a couple. (You may have to read-up on this if you are not familiar with it. E.g. look-up 'moment of a couple'.)

For the beam to be in equilibrium, the reaction at A must balance the given externally applied forces and moment.

So the reaction at A consists of two parts: a force ($F_A$) and a moment ($M_A$). You are required to find both of these.

There are no forces in the x-direction (as you correctly imply in your working).

You need to set up 1 equation for the sum of the y-forces; solving this gives you $F_A$.

You need to set up 1 equation for the sum of the moments about A; solving this gives you $M_A$.

Have another go and post your working and answer.