Infinitely rigid beam creating torque?

[pryphnoq]

I need to settle an argument between two mech eng colleagues... Here goes.

There is an infinitely rigid beam running between two walls. The attachment points are fixed. There is a force acting downwards on the center of the beam. The disagreement is on whether there is a reactive torque in the fixing points.
One side argues that, due to the infinite rigidity, there will only be straight, downwards forces - effectively exerting shearing on the fixing point.
The other side argues that, since there is a lever arm (1/2 of the beam) and a perpendicular force, there is torque. There always is. The infinite rigidity is moot.

So, who's right?

Also: the example is of course highly theoretical. What happens in a practical scenario, where the beam is not infinitely rigid, but just comparatively very, very rigid...?

 

[Dr.D]

In the unreal case proposed, there would only be a shear force and no moment at either wall. Transmission of a moment requires rotation, and the infinitely rigid beam will not have any rotation.

For the real case, the more rigid the beam is the, the smaller the end moments are.

 

[russ_watters]

In the unreal case proposed, there would only be a shear force and no moment at either wall. Transmission of a moment requires rotation, and the infinitely rigid beam will not have any rotation.

For the real case, the more rigid the beam is the, the smaller the end moments are.

Agreed. I think the other engineer is having trouble accepting and incorporating the impossible assumption...or perhaps is improperly cutting the problem (the beam) in half.

 

[pryphnoq]

Excellent - thank you both!

 

[russ_watters]

I've engaged via PM with a new member (possibly the referenced colleague?) who I invite to join the thread to discuss @Dr.D's second scenario further (as well as anyone else interested).

The issue is what does the "real" case entail; in particular, can a real connection be completely rigid per the definition of the word "fixed".

In my opinion, as there is nothing in the universe perfectly rigid, any "real" beam/column(wall) connection will flex by a non-zero amount. It appears to me that in structural engineering, it is often but not always assumed that a connection point can be "fixed" to be perfectly rigid. While this assumption is factually wrong, it is nevertheless close enough to true to be useful in most situations.

I'm an HVAC/mechanical engineer and a little thin on the practical aspects of the structural engineering, so I've done some research and what I've said above appears to me to be true. One case where the "fixed" assumption appears to fail and is discarded is in earthquake resistance. See image below:

Imagine this structure first without the bracing. You see that a lot on the US east coast. The connection between the beam and column is generally called a "shear" (pinned) connection, with only vertical strength and assumed no resistance to rotation/moments. Now, this isn't quite true -- if it were really pinned you could push over the structure with a little nudge. The arrangement of the bolts provides a little bit of resistance to rotation. But not much. So the "pinned" assumption is close to true.

A more robust connection (such as connecting the flanges and not just the web of the beam to the columns) would provide resistance to rotation and is called a "moment" connection. (descriptions and examples of "shear" and "moment" connections here: https://engineering.purdue.edu/~jliu/courses/CE470/PPT_PDF/AISC_ConnectionsJL.pdf )

So why isn't a typical moment connection used to resist earthquakes? Why is bracing needed/used? Because a normal moment connection still isn't strong enough. It's resistance to rotation is in fact not infinite, but is limited by the particular properties of the joint. The bracing makes for a longer lever arm than anything you do at the joint can provide, making the structure/joint much more (but still not infinitely) rigid.

Indeed, moment frames appear to come in three flavours: "ordinary", "intermediate" and "special", based on how much they actually resist rotation:
https://www.penhall.com/blog/differences-between-ordinary-and-special-moment-frames/
https://www.atcouncil.org/pdfs/nistgcr9-917-3.pdf

Thoughts?

 

[Name2000]

Yes, there is a lot of different connections in Engineering?? But a fixed attachment has a very clear definition. When using a fixed attachment there is clear rules and formulas defined in every Engineering book on the shelf.

We are now into a discussion on how you define an attachment point. That was not really the issue.

Can we agree on this simple thing: In a basic structural engineering perspective, there is a beam running between to walls with FIXED attachment point in both ends – changing the stiffness of the beam will NOT influence the moment in the attachment points?

Agree or disagree?

 

[Nidum]

For a uniform beam as described and a central point load the bending moment at the walls is just PL/8 . Does not depend on the beam stiffness .

The stiffness of the beam just determines how much it will deflect .

 

[Name2000]

For a uniform beam as described and a central point load the bending moment at the walls is just PL/8 . Does not depend on the beam stiffness .

The stiffness of the beam just determines how much it will deflect .

Thank you.

 

[russ_watters]

We are now into a discussion on how you define an attachment point. That was not really the issue.

Can we agree on this simple thing: In a basic structural engineering perspective, there is a beam running between to walls with FIXED attachment point in both ends – changing the stiffness of the beam will NOT influence the moment in the attachment points?

Agree or disagree?

Agree.

Can we also agree that such an attachment point does not exist in real life, but rather is only assumed to exist in order to make the math easier?

Yes, they are different issues. They are clearly stated to be different issues. And I find both to be interesting.

 

[russ_watters]

For a uniform beam as described and a central point load the bending moment at the walls is just PL/8 . Does not depend on the beam stiffness .

The stiffness of the beam just determines how much it will deflect .

Please note: there are two scenarios being described, and that is the answer agreed on for one of them. Please clarify which scenario you are referring to and provide your answer to the other one as well.

 

[Name2000]

Agree.

Can we also agree that such an attachment point does not exist in real life, but rather is only assumed to exist in order to make the math easier?

Yes, they are different issues. They are clearly stated to be different issues. And I find both to be interesting.

I´m not sure where you are going with this and I don’t quite follow you. If you want me to say that all matter in the universe are in constant movement and nothing is fixed – Yes - I can agree to that.

But this was a simple structural engineering question about the possibility to decrease the end moment in the attachment point by increasing the stiffness of the beam. The answer for that is NO. This is based on simple beam theory that is used by all structural engineers around the world to design varies of different structures for use in REAL life.

I understand that it may be difficult to visualise the moment in a beam with both ends fixed. But it is there, and it is the same no matter how stiff the beam is. This was what it was all about.

 

[russ_watters]

I´m not sure where you are going with this and I don’t quite follow you...

But this was a simple structural engineering question about the possibility to decrease the end moment in the attachment point by increasing the stiffness of the beam.

For my part, I can't understand why you aren't seeming to want to answer a second scenario. Are you really not understanding that there is a second scenario being discussed? Do I need to number them? Do you think it is a trick? It's not a trick.

I gave a simple one word answer to the first scenario and would appreciate your reciprocating with the second.

I understand that it may be difficult to visualise the moment in a beam with both ends fixed.

Actually, no, that's the simpler scenario, which is why [it appears to me] to be assumed to represent real life even though it does not.

 

[Name2000]

For my part, I can't understand why you aren't seeming to want to answer a second scenario. Are you really not understanding that there is a second scenario being discussed? Do I need to number them? Do you think it is a trick? It's not a trick.

I gave a simple one word answer to the first scenario and would appreciate your reciprocating with the second.

Actually, no, that's the simpler scenario, which is why [it appears to me] to be assumed to represent real life even though it does not.

This has turned into a funny discussion:)

My only goal was just to prove that in the scenario you agreed to and with the engineering definition: “Fixed attachment” - The stiffness of the beam did not have any effect on the moment. That was the discussion we had at work.

If we take another sceanario where we say that the attachement is not fixed because the attachment point will move or rotate due to the forces applied. Then I fully agree that we have 2 different scenarios and different situations.

In you earthquake scenario you actually have a fixed joint. The joint between the column and the ground seems to be defined as a fixed attachment? But it is true - that the other joint can not be stated as fixed.

 

[Nidum]

Can we also agree that such an attachment point does not exist in real life, but rather is only assumed to exist in order to make the math easier?

A simple end on bolted connection of the basic beam can never have a very high bending stiffness .

Increasing the stiffness almost always needs some additional structural components .

With welded connections surprisingly few added bits of plate are actually needed to make connections very much stiffer .

It is possible to design attachment points with bending stiffness so high that for practical purposes they can be considered rigid .

 

[Nidum]

In the design of earthquake resistant structures the dynamic response of the structure is a major consideration .

The simplest form of analysis would be for a skeletal frame with floor slabs at different heights and basal excitation .

Often the stiffest structure is not the best solution for earthquake resistance .

 

[russ_watters]

This has turned into a funny discussion:)

Agreed. The apparent lack of agreement on what the scanerios even say (or that there is more than one!) is driving me nuts.

My only goal was just to prove that in the scenario you agreed to and with the engineering definition: “Fixed attachment” - The stiffness of the beam did not have any effect on the moment. That was the discussion we had at work.

And we're still agreed on the sceneario you described. But there's an important caveat: your scenario does not match the OP...or rather, I think you think it does, but he would disagree.

His scenario has the beam completely rigid whereas your statement about stiffness doesn't matter doesn't clearly indicate if that includes complete rigidity. In other words, we're agreed unless you are claiming that a completely rigid bean will apply a torque at the connection point (per the statement in the OP). It can't.

These small wording differences are part of our problem here. Wording needs to be exact a consistent order to be clear

If we take another sceanario where we say that the attachement is not fixed because the attachment point will move or rotate due to the forces applied. Then I fully agree that we have 2 different scenarios and different situations.

Great! And I'd really like to hear your interpretation of all the scenarios, not just your own. I'll try to be more specific and concise in an effort to get us in full agreement:

1. For a theoretical completely rigid beam attached to a column with a theoretical fixed moment joint, there is no moment applied to the joint. [the scenario in the OP]

2. For a real beam attached to a column with a theoretical fixed moment joint, the bending moment applied to the joint does not depend on the stiffness of the beam. [your scenario]

3. For a real beam attached to a column with a real moment joint, the bending moment applied to the joint does depend on the stiffness of the beam. [Dr. D's second scenario]

[assumption differences bolded, conclusion differences italicized]

Are we now in agreement that all three of these statements are true?

 

[russ_watters]

A simple end on bolted connection of the basic beam can never have a very high bending stiffness .

Increasing the stiffness almost always needs some additional structural components .

With welded connections surprisingly few added bits of plate are actually needed to make connections very much stiffer .

It is possible to design attachment points with bending stiffness so high that for practical purposes they can be considered rigid .

Yes, "for practical purposes". This is the sort of caveat I was interested in exploring. A similar example for mechanical/HVAC is that I almost always assume air is incompressible and constant density regardless of changes in temperature, pressure or altitude. This is assumed "for practical purposes" and like the rigid-or-not attachment of a beam to a column, it is important to know when this assumption can be applied and when it would cause a problem.

 

[256bits]

Are we now in agreement that all three of these statements are true?

disagree.
One will run into problems with completely rigid members.

Try a completely rigid cantilever attached to a wall, or a column, and subjected to a vertical downward force at its end.
If there is only shear stress in the rigid cantilever, then the column should not bend.
Shear would produce only an axial force on the column.

For a beam, cutting the beam at two locations, and noticing only the shear, results in a section that will rotate, with upward shear on one cut and and downwards on the other.