Saturday Morning Question - Torsion
Saturday Morning Question - Torsion
(OP)
OK, lets say I have a Stanely 25' tape measure. It doesn't have to be Stanely, but just pretend it is. The tape cross-section is a little concave, essentially creating a shallow "u" section.
Now, let's say that I extend that tape measure out, while holding it in my hand, and effectively creating a cantilever of the tape since the base is still in my hand. If I extend the tape out 3 inches, and rotate the base 90 deg in my hand, the free end of the tape rotates 90 deg. However, if I carefully extend the tape out 10 feet still maintaining a cantilever (without the tape "buckling"), I can rotate the base of the tape measure 90 deg and the end of the tape doesn't rotate at all.
Question 1: What is the mechanism behind this phenomena?
Question 2: How do you free body this?
Now, let's say that I extend that tape measure out, while holding it in my hand, and effectively creating a cantilever of the tape since the base is still in my hand. If I extend the tape out 3 inches, and rotate the base 90 deg in my hand, the free end of the tape rotates 90 deg. However, if I carefully extend the tape out 10 feet still maintaining a cantilever (without the tape "buckling"), I can rotate the base of the tape measure 90 deg and the end of the tape doesn't rotate at all.
Question 1: What is the mechanism behind this phenomena?
Question 2: How do you free body this?
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Nert






RE: Saturday Morning Question - Torsion
I suspect it has something to do with the downward curvature helping keep the CG of the cantilever as low as possible. My tape did twist a little at the end but nowhere near as much as the end I was holding. Good thought provoker.
old CA SE
RE: Saturday Morning Question - Torsion
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Nert
RE: Saturday Morning Question - Torsion
I think of the opposing torsion as one-half the width across the short face of the tape times the weight of tape per length. The more rigid the tape, the more torsion produced into the end when twisted. And therefore, a longer length of tape must be extended in order to accumulate enough to resist that torsion.
RE: Saturday Morning Question - Torsion
While the same equations don't apply just think back to your old MM equations for torsion of a circular shaft...
angle of twist = torque*length/(j*g)
note that the angle of twist is proportional to the length...same idea applies to your tape except the equations are modified due to the cross section (and probably due to the rotational large displacement)..otherwise the concepts are the same...
As for a FBD it is just the same as any other FBD...cut a section and put the internal/external forces on the diagram....
Ed.R.
RE: Saturday Morning Question - Torsion
RE: Saturday Morning Question - Torsion
But for the first sitution, where the 3 inch cantilever is rotated 90 degrees, I don't believe there is any applied torsion for this problem because the system rotates as one unit (rigid body rotation).
For the second situation, gravity is applying a torsional moment on the tape (concave cross-section is not doubly symmetric),and because of the lack of torsional stiffness, the tape can rotate 90 degrees.
RE: Saturday Morning Question - Torsion
Exactly what I was thinking as I read the thread; A star for you!
Cheers,
YS
B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...
RE: Saturday Morning Question - Torsion
RE: Saturday Morning Question - Torsion
RE: Saturday Morning Question - Torsion
RE: Saturday Morning Question - Torsion
RE: Saturday Morning Question - Torsion
Proving the above might take more than a Saturday!
Cheers
Greg Locock
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Saturday Morning Question - Torsion
As for the bending if it is elastic (and it is) it can be decoupled from the torsion and its just a cantilever with a self load (although the resulting displacements may be large).
It is true that the actual computations require modification to the basic torsion equations (and bending) but as I tried to indicate earlier the basic system is just a cantilever unless I'm missing something.....
Ed.R.
RE: Saturday Morning Question - Torsion
Cheers
Greg Locock
SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Saturday Morning Question - Torsion
RE: Saturday Morning Question - Torsion
The fact that the section is not doubly symmetric doesn't explain it, as, following this way of reasoning, it would be necessary for the CoG to go up during the rotation, to explain the resistance to the rotation at the free end. But if the rotation applied by hand is about the CoG, then the whole length could rotate about it without any change in potential energy and consequently with the same energy of deformation.
The explanation is more subtle and involves the (much) different bending stiffness of the tape along its two principal axes. I'm sure (though didn't try it) a similar phenomenon can be observed with a long strip of paper or a metallic flat bar or anything similar.
The point is that, when the strip is cantilevered the large face horizontal, it will experience a bending deformation much larger than when it is cantilevered the large face vertical.
This means that, when going from the first to the second configuration, as in the experiment proposed by inertia4u, the free end of the strip would have to go up to arrange for the lower bending deformation. Going up would raise the potential energy, and this explains the resistance to rotation.
With a short strip the phenomenon is not (or much less) observed, because the bending deformation is lower (goes down with the 4th power of length, or a bit less when dealing with large deformations) and the torsional stiffness (goes up with the inverse of length) is sufficient to overcome the change in potential energy.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads
RE: Saturday Morning Question - Torsion
The fact that the stiffness of the tape is greater in a vertical position than in a horizontal position is another way of saying that the tape has a low torsional stiffess and this decreases as the tape extends)e.g. if the tape cross section were a tube then stiffness would be the same in both hor and vert but the torsional stiffness would be very high (and could thus also rotate maybe) so really asixth and I are saying the same thing that you are in different words.
Cheers Mate
RE: Saturday Morning Question - Torsion
It just goes to prove that engineering does not have answers to everything.
RE: Saturday Morning Question - Torsion
You can't pay me enough to prove this analytically. But it is a nice subject for us.
RE: Saturday Morning Question - Torsion
So its the torsional stiffness (or lack of it) that keeps the tape horizontal at the tip ?
RIGHT????????????
RE: Saturday Morning Question - Torsion
If you put the tape on edge again on the floor and you turn the handle again the tip doesn't rotate.
It hasn't got the ridgity to twist !
Guys try it !!!
Cheers !!
RE: Saturday Morning Question - Torsion
If you lay it on the floor and twist, you now have friction keeping it from rotating. Point the tape straight up and rotate the base and you'll see the end rotate. So I submit that gravity etc has a lot to do with this.
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Nert
RE: Saturday Morning Question - Torsion
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Nert
RE: Saturday Morning Question - Torsion
No matter how complicated anyone wants to make the explanation (the energy involved, the potential/kinetic separation of energy involved, the gravitational field interacting with the newtonian laws on the tape, etc, etc, etc) the problem still requires no more complicated a solution than asixth gave back on the 13th.
Cheers,
YS
B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...
RE: Saturday Morning Question - Torsion
1. Laws of statics still apply. Sum Moments = 0.
2. Because the length of the tape is so long, it actually bends downward because of gravity.
3. Draw a line tangent (parallel) along the length of the tape from the base in your hand and continue infinitely (you'll need a lot of paper :) ). There is, however a point where the tape starts to diverge away from the axis because it is bending down under gravity. Call that Point "A"
4. When you rotate the tape at the base, you are only rotating about the tape axis. The divergent part of the tape, if you think about it, is a mass at a distance beyond the tape axis (tape curves away from the tape axis).
5. So, when you rotate the tape, you can easily do so for the tape along the axis, but at the point where the tape diverges you are actually trying to overcome the mass*distance of the divergent tape- which for reasons of poor open section torsional stiffness, can not over come.
In other words, I think of the problem like this:
Get a 10 foot pole. on the end of that pole attach another perpendicular rod, say 2 feet long, and at the end of that 2'pole attach 10 lbs. Now, try to rotate that rod in your hand- you notice that it becomes quite difficult trying to lift up that mass in torsion - about 20 ft-lbs. I submit that the same thing is happening with the tape.
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Nert
RE: Saturday Morning Question - Torsion
Fair enough !
I guess my analysis included friction and gravity after all.
But at the end of the day the tape end doesn't rotate because its too weak torsionally right?
RE: Saturday Morning Question - Torsion
That was a good example got the brain cells working.
Got any other challenging examples?
RE: Saturday Morning Question - Torsion
Now, could you get a channel to LTB the other way? Sure - if the load was past the shear center to the other side. Essentially, we have created the condition where a channel has gone through LTB failure to its strong side where it just so happens that it reaches a new state of equilibrium. Unlike the case above, local effects haven't taken over to make it crash to the ground - that won't happen until it is extended even further. If you keep paying out the tape, it will eventually buckle locally and crash to the ground.
If you "heard" it on the internet, it's guilty until proven innocent. - DCS
RE: Saturday Morning Question - Torsion
you are proposing a different configuration, but gravity is indeed involved in your experiment.
When the tape (or the flat bar, that's exactly the same in all the configurations proposed in this thread) is laid down onto the floor and you turn one end to make it vertical, you are effectively raising the CoG of the bar, by about half its width, and this change in potential energy is resisted by the bar that undergoes torsion to (partly) avoid it.
Of course this effect is comparatively smaller than in the experiment proposed by inertia4u, so we can expect that a lower torsional stiffness is required to observe it.
Concerning your second experiment, where the bar is initially vertical over all its length and you turn one end flat against the floor, I can't confirm your result (the other end stays vertical?), you should better specify the conditions of your test.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads