Moment and reaction couple moment 1

[leer77]

Why is the reaction moment at a fixed support a couple moment and not a moment specific to a point? Is this reaction couple moment created in order to counteract the couple moment created by the applied force and reaction force at the fixed support?
Thank you in advance.

 

[rb1957]

I don't understand the question. A moment can be a distributed set of loads (like a varying distributed load, as opposed to a uniform load) or a discrete pair of forces (a couple).

In a cantilever the base reaction is a force and a moment (which reacts the couple created by the load and its reaction). I don't understand what you mean by the difference between "a couple moment" and "a moment specific to the point" ? They are the same thing.

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

 

[BridgeSmith]

I may get pushback on this overly simplified explanation, but a moment is essentially the same as a torque. It's force x distance. If the moment has some value more than zero, and distance is zero, the force is infinitely large. Correspondingly, there has to be a distance between the centroids of the 2 opposing forces for there to be a moment.

 

[Luceid]

I think Bridge’s infinite force idea is a good explanation. If you are looking at a big FBD of a beam, you treat the fixed end to provide a “point moment” reaction since it makes the statics calculations simpler, less forces to keep track of. But as soon as you zoom into the actual connection, there has to be some sort of force couple creating that moment.

 

[rb1957]

sorry, never seen an infinite force before, and besides an infinite force*zero distance = zero moment (yes, the finite force get larger as the finite distance gets smaller).

Analytically we model the end condition as a point, a force and a moment at a point. This is of course not the real world, so that's when we say "ok I have (analytically) a force (and a moment acting at this point, but I have a (or several) shear splice physically somewhere nearby and the loads on these elements are equivalent to my analytical loads".

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

 

[driftLimiter]

Point moment, Couple Moment, Torque. These are all terms for the rotation effect on a body of a force times a distance. This comes down to semantics.

The 'Moment' is the F x D. A couple moment is shorthand way to say that the 'Moment' Is being resolved by forces acting at a distance from each other.

 

[leer77]

Thank you every one for replying. Sorry for posting an unclear question. I am a noob in mechanic. What I meant to ask was, R.C. Hibbeler’s statics textbook 14th edition (page 209) explains Fixed support will prevent both translation and rotation of a beam and to do this a force and couple moment must be developed on the beam at its point of connection.
In earlier chapters in this textbook it also explains that couple moment is a free vector unlike ‘a moment about a fixed point’ which is a fixed vector. My question was why is there a couple moment (reaction) developed on the beam instead of ‘a moment about a fixed point’(reaction) when there is a fixed support.
My guess now is, the couple moment (reaction) is developed on the beam instead of ‘a moment about a fixed point’(reaction) because the applied load and the reaction force to the applied load results in a couple moment being created on the beam. Now the beam will exert this couple moment onto the wall or a fixed support, and as the system is in equilibrium the wall or the fixed support will in turn exert an equal but opposite couple moment (reaction) on the the beam.
Am I thinking this correctly?
Thank you again.

 

[BridgeSmith]

Analysis of the structure typically begins with quantifying the external load effects and reactions on the members. Modeling moment as if it's about a point, is a simplification for that analysis. Once the moment applied to the beam has been determined, the internal forces and the stresses in the beam and at the connection are analyzed.

I don't know if that answers your question, since I haven't seen the particular text you're referring to.

 

[rb1957]

"this textbook it also explains that couple moment is a free vector unlike ‘a moment about a fixed point’ which is a fixed vector." what an odd thing for a text to say. Maybe they mean that a couple has a specific vector direction unlike a generalised moment ? but then that is the opposite of the description !!??

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

 

[BAretired]

A moment about a fixed point is a moment about any point. There is no distinction.

If the moment has some value more than zero, and distance is zero, the force is infinitely large.

That is a very confusing statement. A moment greater than zero can be applied anywhere on a structure. For equilibrium, it must be balanced by an equal and opposite moment anywhere on the structure.

In the case of a simple beam of span L, if a moment M is applied to an arbitrary point on the span, reactions will be M/L at each support such that the moment is balanced. The location of the applied moment makes absolutely no difference.

 

[BridgeSmith]

That is a very confusing statement. A moment greater than zero can be applied anywhere on a structure. For equilibrium, it must be balanced by an equal and opposite moment anywhere on the structure.

Sorry for the confusion. I should have clarified that the distance I was referring to is the distance between the opposing forces of the couple.

 

[rb1957]

yeah, but that is still wrong. the moment is the force couple times the distance between. So for some finite moment, as the distance gets smaller the force gets bigger ... but if the distance is zero, then there is no moment (and the two forces self react, cancel each other).

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

 

[BridgeSmith]

yeah, but that is still wrong. the moment is the force couple times the distance between. So for some finite moment, as the distance gets smaller the force gets bigger ... but if the distance is zero, then there is no moment (and the two forces self react, cancel each other).

Semantics.

When you model a beam as a line, there's no separation of, or distance between, the opposing forces in the couple (AKA moment) for the analysis model. Obviously, the beam itself has to have a depth so that there is separation between the centers tension and compression forces within the beam, or it would have no bending strength.

How about this - in order for there to be equilibrium, there has to be a force couple - 2 equal opposing forces separated by some distance, to counteract a moment. Otherwise, there is movement, rotational movement to be more precise.

 

[rb1957]

mathematics, not semantics.

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

 

[BAretired]

I had never heard of a "free vector" before reading this thread, but I think Hibbeler is differentiating between free and fixed vectors as illustrated below. Moment F*L is fixed because F is fixed in position. F*r is a free vector because it causes the same fixed end moment wherever it's placed; but its location does affect internal stresses in the beam.

The notion of "free versus fixed vectors" does not help in understanding statics, in my opinion.

 

[GregLocock]

Perhaps the author is trying to differentiate between a a torque applied to a rigid body, where its location is unimportant, and one applied at a particular point along a flexible body. No, I'm not convinced either.

Cheers

Greg Locock


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[leer77]

Moment F*L is fixed because F is fixed in position. F*r is a free vector because it causes the same fixed end moment wherever it's placed; but its location does affect internal stresses in the beam.

As explained by BAretired, I think Hibbeler is referring to the couple moment as free vector because when a couple moment is applied on a body, it is same through the body at any point. Whereas, with a moment of a single force (and not a couple) is different at different location as moment is f*d and as d change, moment changes therefore moment at a point being a fixed vector.

In a cantilever the base reaction is a force and a moment (which reacts the couple created by the load and its reaction). I don't understand what you mean by the difference between "a couple moment" and "a moment specific to the point" ? They are the same thing

And I think rb1957 clarified my doubt on the matter of reaction couple moment beimg created at the fixed connection. The reaction couple moment is created on the cantilever beam to counteract the couple moment developed because of the applied load and equal and opposite reaction force.