Calculating Reaction Force at A for a Beam with Pin Joint | Beam Homework

[Jonski]

Homework Statement

Calculate the reaction force at A?

Homework Equations

ΣMb = 0

The Attempt at a Solution

As there is a pin joint at B it is possible to consider the bar only from A-B.
From here I applied
ΣMb = 0
120 + 20*2 + Ay*4 = 0
This gives Ay = -40kn
Also since there are no forces in the x direction Ax = 0
and Hence A = -40kn or 40n downwards
However this is wrong. I am not sure what I am doing wrong unless it is something that the sum of the y forces don't equal 0, but I think there would be a force at By= 60kn up to combat this.
Any help would be appreciated, thanks.

 

[Simon Bridge]

120kN.m is a moment about A isn't it?
What is the reasoning that suggests that you need only consider the A-B length?
The pin connection at B does not stop rotation about B caused by the force distribution on B-E - just prevents translation of that point.

 

[Jonski]

So would the FBD look like this:

The question says consider the reactions at A and D to be rollers, so thus there is no horizontal force

 

[SteamKing]

So would the FBD look like this:
View attachment 98083
The question says consider the reactions at A and D to be rollers, so thus there is no horizontal force

The pin at point B can develop a force, but it cannot sustain a moment. That's what's missing from your FBD above.

 

[Jonski]

The pin at point B can develop a force, but it cannot sustain a moment. That's what's missing from your FBD above.

So would I add a vertical and horizontal force at point B and then use the equations of equilibrium to solve?

 

[SteamKing]

So would I add a vertical and horizontal force at point B and then use the equations of equilibrium to solve?

You can add a horizontal force at pin B, but it looks like all of the applied loads are vertical.

 

[Jonski]

You can add a horizontal force at pin B, but it looks like all of the applied loads are vertical.

So you're saying it is there, but it would just be zero. Also I'm assuming then that Ex would be 0?
If i do that won't I end up with more unknowns than equations, in which case it would be unsolvable.

 

[SteamKing]

So you're saying it is there, but it would just be zero. Also I'm assuming then that Ex would be 0?
If i do that won't I end up with more unknowns than equations, in which case it would be unsolvable.

That's unlikely, since there are only two supports for the entire beam.

BTW, the beam is only resting against the wall at E. It can't develop a moment at that location, only an axial force.

 

[Jonski]

That's unlikely, since there are only two supports for the entire beam.

BTW, the beam is only resting against the wall at E. It can't develop a moment at that location, only an axial force.

So would the FBD look more like this:

 

[SteamKing]

So would the FBD look more like this:

Yes, that's more like it.

 

[PhanthomJay]

In my estimation, I believe that the wording in this problem is not very good. When it says "resting against a wall", I think it implies "resting atop a wall", otherwise, with the hinge at B, the beam would be unstable.

The force from the pin at B is internal, so when drawing the FBD of the entire beam system, that reaction doesn't enter into the equilibrium equation. I would proceeded by isolating AB first, but you have to be careful with your plus and minus signs, and interpretation of them.