Saturday Morning Question - Torsion 6

[inertia4u]

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?





-----
Nert

 

[civeng80]

If the tape is laid straight on a level floor i.e. no cantilever effect at all , the same thing happens. I just tried it now. So gravity is not the answer nor the potential energy explanation either.

So its the torsional stiffness (or lack of it) that keeps the tape horizontal at the tip ?

RIGHT????????????

 

[civeng80]

Oh yes another thing!

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 !!

 

[inertia4u]

Civeng80,

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.

-----
Nert

 

[inertia4u]

Oh and be careful not to throw statics out the window!

-----
Nert

 

[youngstructural]

And laying the tape on the floor does not remove gravity... It's still in the gravitational field of the earth, and still effected by the same downward resistance to 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...

 

[inertia4u]

Some things worth considering:

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.


-----
Nert

 

[civeng80]

inertia 4u

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?

 

[civeng80]

inertia4u

That was a good example got the brain cells working.

Got any other challenging examples?

 

[swearingen]

Let's look at this from a different angle. Say you start by extending your tape with the body already on its side. You'll pay some out and then it will LTB as a channel would - towards its open side. It immediately buckles locally and heads straight for the ground.

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

 

[prex]

civeng80,
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

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