Free Body Diagram Reactions - Wall Mounted Component

[Davy Pee]

Hey Eng-Tips,

I have a device mounted on a wall, which I'm trying to see if it can support. I have applied load P1 at the end, and component weight applied in the center, P2, at L1 and L2, respectively. The device has two supports, A and B, which I'm trying to find the horizontal reactions for, if any.

Thanks

 

[phamENG]

Have you attempted a solution? Perhaps this should be in the student forum? No offense intended, but I would expect a second semester freshman to be able to solve this in his/her sleep...

(Also, you're neglecting your vertical reactions necessary to complete the FBD.)

 

[SWComposites]

react the applied moments, P1 * L1, etc; and react the vertical shear loads.

 

[BAretired]

The vertical reactions are split between A and B, assuming they are pinned. Conservatively, I would size both supports for V = P1+P2, assuming one is a vertical roller.

In the spirit of phamENG's post, I will not divulge the horizontal reactions.

 

[Davy Pee]

I assumed the reaction moment (Rm) would be at d/2, and from there got the following:

sum of moments about d/2 = 0 = P2L2 + P1L1 - Ra(d/2) - Rb(d/2)

P2L2 + P1L1 = Ra(d/2) + Rb(d/2)

(P2L2 + P1L1)/(d/2) = Ra + Rb; Ra = -Rb

clockwise moments are positive.

But I'm not sure this is correct. I'm not concerned about the vertical reactions.

 

[phamENG]

The 'reaction moment' is the moment formed by Ra and Rb - it doesn't occur at some point. The summation of moments about any point is zero and the moment induced at a point by a force whose vector passes through that point is zero, so a good strategy is to select such a point to sum your moments. So if you select point B and sum moments about point B, Rb drops out and you only have one unknown which allows you to solve for Ra directly.

 

[Davy Pee]

Ok so it seems I was on the right track. I know you can select any point, but I never understood why that is, but that's outside the scope of this question anyway. Thanks.

 

[phamENG]

No problem.

It's because, for the system to be in static equilibrium, the sum of all moments must be zero. This is true throughout the system, from all vantage points. If there were a point anywhere in the system that this is not true, it would not be in equilibrium. So the point you selected, along the line between A and B but halfway in between, is correct. BUT...from a mathematical point of view it's unhelpful because you have one equation and two unknowns.

 

[rb1957]

I too thought "why the mid-point ?" but I can see that it's an easy way to visualise the couple. "any" point is correct, but less intuitive, and I think the OP learnt something too !

It is easy to see, take moments about A ... Rb = (P1*L1+P2*L2)/d


"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.