How to determine the torsional load on a beam?

[dalecyr]

Please see the attached drawing.

beam tortion load.jpg

Assuming two loads connected by a free running cable over two pulleys;
Assuming the loads are perfectly balanced;
Assuming the left pulley is V feet higher than the right pulley;
Assuming the two pulleys are H feet apart;
Assuming the pulley assemblies are securely and rigidly attaching to wide flange beams;
Ignoring friction;

How do I determine the tortional load on the righthand beam?

[jboggs]

Each pulley sees two loads, one in each direction of the rope. Use vector analysis to convert those combined vectors into a single resultant vector acting on the axle of the pulley. Then use vector analysis to convert that force on the pulley into a normal force and a lateral force. The lateral force and the the distance from the pulley axle to the center of the beam produce the torsional moment load on the beam.

[dalecyr]

<muttering> vector analysis! harumph! Have to dust off a LOT of cobwebs to access that memory... </muttering>


Ok, then.
Something like this?

Vector Analysis.jpg

[jboggs]

<muttering> vector analysis! harumph! Have to dust off a LOT of cobwebs to access that memory... </muttering>

I have similar reactions to sines and cosines, etc. I definitely work better in a graphic world. I have resolved (or at least confirmed) most of my trigonometric questions over the last several years using Autocad.
I put together this little graphic to explain my thought process. It might help.

Drawing2 Model (1).pdf

[PinkertonD]

This is not a trivial issue to resolve, especially if large loads are involved relative to the beam cross-sectional strength and unsupported length.

I would ask, why you only want to know about the lower beam and not both as they will both be under the same (or very near) loading.

Torsional deflection is a very significant issue when it comes to beam failures as only a small angular deflection can result in a rapid loss of load carrying ability.

Do some research on these three individuals Heins, Johnston and Hotchkiss as they have all contributed significantly to understanding the issues. Not a trivial pursuit.

[dalecyr]

I put together this little graphic to explain my thought process. It might help.

Thanks Joe, I think this confirms my drawing, although I went about it a slightly different way.

Do some research on these three individuals Heins, Johnston and Hotchkiss as they have all contributed significantly to understanding the issues. Not a trivial pursuit.

Thanks. I will research these guys this morning.

Other than changing the angle, does the distance between the two beams play any role in lateral force, provided the vertical distance between the beams does not change?

[jboggs]

The only change would come from the slight change in the angle of the connecting rope segment.

[jboggs]

Dale,
Just a quick response. I'll be out for the weekend.
First, if you relocate the beam suspension attachment point upward or move the pulley axle downward, so that those two points were nearer to or even on the same centerline axis, your tendency to twist the beam would go away.

Second, the outer beams are probably twisting more because the wrap angles and loading on the pulleys create a larger horizontal force vector at the pulley axle. think about it - the near the upper rope is to vertical, the less your horizontal force vector will be.

Keep digging. Talk to you later.

[PinkertonD]

Lemme jump in here with a hint, nag or comment or two.

Vector analysis has very-little-to-nothing to do with the torsional loading assesment.

Moving the pulley center-line will only have a minimal effect on torsional loading as long as the load rope/cord/cable is outside the flange and offset from the beam center-line.

At the risk of repeating myself, this is not trivial and solvable with a few lines of simple calculations. You are loading a beam in a way that is encouraging it to fail. You need to design beyond that. Since you have stated "theatrical," I assume humans can be under this structure and all that, that, pertains to with safety factors. Time for a structural Engineer to get on the payroll.

Just one old fart's opinion.

Over and out.

[zeke]

The problem as described is not only indeterminate but far too complex for the OP given the way it is being calculated.with his lack of experience in fundamental physics.

You first have to solve the indeterminate problem for static equilibrium before you worry about the easy part of torsion.

As Dave suggests, playing with vectors won't get it done ;get a pro to help.

[jboggs]

Dale,
Just a question to help clarify things for me: is the beam actually deflecting torsionally? Or is it just twisting (rotating) as a unit?
Joe

[zeke]

Dale,

You can't expect useful answers when you first present the problem showing only 2 forces ( a single vector force) acting on a beam of finite length, and then proceed to tell us ,Oh there are other points on the beam the have forces acting and finally tell us there are still other cable out-of plane forces from cables at various angles supported by a continuous "uniform ??" load.

I suppose I was remiss in not informing you at the outset that the first thing you do is take the beam and do a free body force equilibrium analysis.


If you did that, you would find that you couldn't analyze that beam classically, since you would have more unknowns than equations ; the problem is called "indeterminate" but is solvable using various energy methods.

That is why I gave you my opinion.

I suppose you thought that by giving us a "simplified " version of the problem we could help. But that is the problem. Too often, in trying to simplify the problem , it makes our job more difficult. In this case , we ended up missing the whole problem.

I wish hat posters would state the WHOLE problem at the outset.

[jboggs]

zeke,
I wholeheartedly agree with your sentiments that often posters leave out critical information. On the other hand I have learned that, at least for myself, I am often guilty of imposing my own assumptions on the information I read here, and end up trying to answer a question that wasn't there. Maybe that is the case here, but I don't think so.

Like you I have gotten to "know" some of the frequent posters on here such as yourself. I have learned that they have a great amount of both academic and experiential knowledge, and I have a great respect for that. I would put Dale in that category myself.

The last time I solved an integral or did any real thermodynamic calculations was 30 years ago. I have successfully avoided both throughout my career, and want nothing to do with either one, thank you very much. But there are other areas I use almost daily. I certainly can't fault any of the older farts around here for being a little rusty in certain areas. I KNOW I am.

Unlike you and Dave, and maybe incorrectly, I saw this thing as a free-body issue rather than a beam deflection issue from the beginning. That's why my responses aimed in that direction.

Joe

[dalecyr]

Zeke:

Ah, but I did not want an answer to the whole problem.
At least not initially.

In thinking about the various forces involved in the whole problem,
I realized that I did not know how to calculate the simple rotational force
when the force vectors were about 100 degress apart.

I know how to calculate resultant force, and I know how to calculate rotational force.
But I was having a problem making the connection from resultant to rotational.

I knew I could use vectors, and I can even build a simple mechanism to actually measure
the horizontal component. (or actually any component force of this particular problem.)

But I was hoping for a more "mathematical" answer.
(which I found by googling)

That was the genesis of the original question.
That is all I wanted.

Sorry to bother you with such a "fundamental physics" problem.

[zeke]

Joe,
Sorry I used the editorial "we" inappropriately.

Dale,

I,m glad that you got something out of all this.

But fundamental physics is required for a total understanding of the problem.

The title of your OP "How to determine the torsional load on a beam" doesn't square with your
less ambitious interest.

I finally gather that you needed a tutorial on how to solve it. I doubt that googling gave you enough.

Forums are not very good at giving tutorials

You would be better off reviewing your mechanical/structural engineering books on the subject.

Good luck .

[PinkertonD]

A beam in a working theater appears to be in the beginning stages of failing.

This statement bothers me some, though. Rather than sitting around discussing the esoterica of why it could/will/might/should fail, if there are some concerns that the structure may be unsafe, should not an inspection authority be notified?

Perhaps give the property owner a heads-up on the concerns and strongly express a suggestion that it is checked out by an Engineer.

If that fails to elicit any productive response, then OSHA, or the Actor's Guild, or Animal Control, or... or... or something -- someone?

To do nothing is to get ready for an "I told you so," moment at the expense of possible injury and/or death to innocent people.