Buckling of a drum wrapped in tensioned rope

[Denial]

I have a circular drum, around which several turns of tensioned rope have been wound. (This is the sort of situation that would apply to the winch drum in a crane, but my actual situation is not a winch drum.)

I am happy to ignore friction, to ignore complications caused by the locations where the rope begins and ends its contact with the drum, and to assume that the size of the rope is negligible relative to the size of the drum. Under these assumptions the rope tension is constant, and each complete turn of rope applies a uniform, radially-directed, distributed force of T/R to the surface of the drum, where T is the rope tension and R is the (outer) radius of the drum.

If this radial force of T/R had been applied by external hydrostatic pressure rather than a tensioned rope, the load at which the drum would buckle by ovalisation is a well known, standard result (p'=3EI/R^3). However after thinking about the problem for a while I have begun to think that this formula does not apply to the case where the loading is generated by a wound rope. More specifically, I am beginning to think that under this rope loading the drum CANNOT buckle by ovalisation.

Two questions for you mechanical engineeers out there:
(1) Is it true that the rope-loaded drum cannot buckle by ovalisation?
(2) If so, what is the drum's first buckling mode, and at what radial loading does it occur?

Thanks in advance.

 

[GregLocock]

To be honest I think you've simplified the problem to the extent that it IS directly equivalent to hydrostatic pressure, at least up until the point that elastic buckling occurs. Bear in mind that elastic buckling merely indicates an alternative system configuration that can carry the same load, it relies on Sod's law to actually make the transition between the two.

So, what is your argument that ovalling won't occur?

(I'll have to hastily read Roarke on this I've analysed winch drums, but without your simplifications)



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Denial]

With hydrostatic pressure the load intensity stays at "p" as ovalisation commences. The shape change from circular to oval can be viewed as tending to increase the amount of loading on the "flatter" sides of the oval, and tending to decrease it on the "sharper" sides. This effect tends to exacerbate the ovalisation, allowing buckling to occur once a certain load level is reached.

With the (friction free) rope loading, the curvature of the rope changes as the drum ovalises. Increased curvature equals increased load intensity (p=T/R), so the load intensity changes as the drum ovalises. We tend to get an increase in load intensity at the sharp extremes of the ovalised drum, and a decrease in load intensity at the flatter extremes. This effect tends to deflect the drum back towards its circular shape. Thus the circular shape is stable under the rope loading, and buckling cannot occur.

Visualise an extreme case. Let the "drum" have an initial shape that is highly ovalised, say an ellipse whose minor semi-axis is nearly zero. Now wrap a well-greased rope around it a couple of times and pull on both ends of the rope. Will the "drum" become more ovalised, or will it tend to deflect into a more circular shape?

Cheers.

 

[GregLocock]

OK. I agree with that argument but in reality once you have enough displacement to affect the normal pressure then you are already looking for a drycleaner.

Other reasons why the simple buckling due to external pressure calc is wrong are that the friction tends to lock in the tension of the rope, so when the reel squishes the rope detensions, and the buildup of normal load with wraps is not linear, and falls with succeeding layers.

All of this seems to me to indicate that your model is conservative. Are you trying to build something light, or safe? How is your tension controlled?

By the way Roark Table 15.2 19b seems to me to be a better equation to use.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MintJulep]

I don't have any experience in this type of analysis, but I can tell you that the forces involved are non-trivial.

Probably best to stick with an established method of calculation rather than risk an inappropriate simplification.

 

[GregLocock]

Very true. In my case I wasn't interested in the winch reel, but I was interested in the loads on some stuff that was part of the rope.

If you are designing the reel then you need to find what the crane people use. I /think/ I read on another thread that Blodgett has a chapter on it.


Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Denial]

Thanks for your contributions.

As I said at the start, my problem is NOT a winch drum. FWIW it is a lightly built fibreglass tubular tower being lifted into position, a situation it will (hopefully) experience only once in its life. The rope tension comes from the lifting ropes.

I am happy with my gross simplification to a frictionless constant rope tension around a circular shape. Yes, there are thousands of other aspects to be taken into account, and taken into account they will evenutally be. For the purposes of this exercise, all I am trying to establish is whether overall ovalisation is a potential problem or not. Up to now my thinking about the gross simplification suggests to me that it is not.

I am about to commit to this conclusion, but because it is somewhat counter-intuitive I am interested in others' views.

Cheers.

 

[zekeman]

The problem with potential ovalisation is if it tended to buckle that way, the curvature would decrease in the direction of buckling and thus decrease the radial forces there and increase the force at right angles at increased curvature (reciprocal of the radius of the curve) effectively reducing the buckling force that caused it and reshaping it back to its equilibrium circle.
I agree with the conclusion of the OP.

 

[Denial]

Greg,

My Roark was the male that survived 40 days of rain before grounding on Mount Ararat. What is the title of the Table and Case you cited above?

For orientation purposes, in my version (fifth edition) the formula I give above for the hydrostatic loading (p'=3EI/R^3) comes from Table 34, case 8, in chapter 14 "Elastic Stability".

Cheers.

 

[GregLocock]

Like I said, I think you are making conservative assumptions all the way through so you don't need the extra detail but

TABLE 15.2 Formulas for elastic stability of plates and shells (Continued)

19. Thin tube under uniform lateral
external pressure (radius of tube r)

19b. Short tube, of length l, ends
held circular, but not otherwise
constrained, or long
tube held circular at intervals
l



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MintJulep]

I'm not convinced that uniform pressure or frictionless are good assumptions. That of course depends on how the ropes are going to be attached.

Certainly there will be an axial discontinuity in stress on either side of the rope. I think friction will cause a circumferential non-uniformity as well.

 

[rb1957]

i'm thinking that lifting the drum into it's final resting place is going to be loading the drum quite differently to the case of winding a tensioned cable onto the drum ... isn't this more like a sling ?