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BetaRock


Jun 25, 2012, 4:29 PM
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Theory about forces in a 3-legged cordelette
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The Sterling tests that John Long's book on Climbing Anchors summarized showed that a 2-legged cordelette with unequal legs knotted on a bight experiences an average difference of 3.5 kN between the two legs. This shows that cordelettes are miserable at equalizing even when properly "pre-equalized".

What I'm wondering is what the behavior is with a 3-legged cordelette knotted on a bight?

My theory is that a 3-legged cordelette can be thought of as two, 2-legged cordelettes:

Cordelette 1: (Leg A) + (Leg BC)
Cordelette 2: (Leg B) + (Leg C)

"Leg A" in this case is simply whichever leg experienced the extra 3.5 kN of force. The remaining two would split the remainder of the load the same way a normal 2-leg cordelette would. That is, if there is a 7 kN impact force on the 3-legged cordelette, then Leg A would see 3.5 kN more than B and C combined, and B would show some proportionally large difference to C.

The resulting distribution would be something like 70% on Leg A, 20% on Leg B, and 10% on Leg C.

Have there been any tests on the 3-legged cordelette that might give me some insight on this? I feel like it would have some implications on the mini-debate on whether an equalette is more effective than a cordelette on 3 placements.


patto


Jun 25, 2012, 4:48 PM
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Re: [BetaRock] Theory about forces in a 3-legged cordelette [In reply to]
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I believe John Long did do tests with the 3 legged cordalette. But there was so much wrong with John Long's 'research' that it is hard to know where to begin.

The two legged cordalette is trivially easy to equalise well as long as there a proper 'V' angle formed. A three legged cordalette is almost impossible to get perfect but in my experience I can get rough equalisation without too much difficulty.


The two biggest flaws in John's research were:
**the presumption that near perfect equalisation is necessary.
**the false conclusion that shock loading doesn't matter



(This post was edited by patto on Jun 25, 2012, 4:49 PM)


BetaRock


Jun 25, 2012, 4:59 PM
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patto wrote:
I believe John Long did do tests with the 3 legged cordalette. But there was so much wrong with John Long's 'research' that it is hard to know where to begin.

The two legged cordalette is trivially easy to equalise well as long as there a proper 'V' angle formed. A three legged cordalette is almost impossible to get perfect but in my experience I can get rough equalisation without too much difficulty.

First, I don't think John Long himself was involved in the Sterling tests to which I'm referring. Those tests were performed by Jim Ewing, R&D manager at Sterling Ropes. The statistics were completed by Dr. Lawrence Hamilton and Dr. Callie Rennison.

Second, according to the test summary, they did not perform tests for a 3-legged cordelette rig. Only the 2-legged.

Would you mind detailing the flaws in Ewing's tests? The details of the experiments are laid out in the book and determined that the load distribution across the two legs were dismal: almost 800 pounds difference between the legs in a Factor 1 fall.

This difference in force seems significant to me. Is there debate surrounding how they performed those experiments?


(This post was edited by BetaRock on Jun 25, 2012, 5:03 PM)


patto


Jun 25, 2012, 5:25 PM
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Re: [BetaRock] Theory about forces in a 3-legged cordelette [In reply to]
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BetaRock wrote:
First, I don't think John Long himself was involved in the Sterling tests to which I'm referring. Those tests were performed by Jim Ewing, R&D manager at Sterling Ropes. The statistics were completed by Dr. Lawrence Hamilton and Dr. Callie Rennison.

Second, according to the test summary, they did not perform tests for a 3-legged cordelette rig. Only the 2-legged.

Would you mind detailing the flaws in Ewing's tests? The details of the experiments are laid out in the book and determined that the load distribution across the two legs were dismal: almost 800 pounds difference between the legs in a Factor 1 fall.

This difference in force seems significant to me. Is there debate surrounding how they performed those experiments?

Only a little bit of debate Wink Laugh

http://www.rockclimbing.com/..._reply;so=ASC;mh=25;

The fourth post and many others are by John Long. As you can see John WAS involved in the tests.

I can't speak for all the details on John's tests but basic trigonometry ensures close to equal loading if you create a decent 'V' in a two leg anchor. It seems he aligned the pieces vertically so naturally equalisation is quite poor particularly with static cord.

Your 800pound difference is meaningless unless you give it as a percentage. I would consider 20%, 20%, 60% equalisation still adequate as far anchors go. The goal is more about redundancy rather than perfect equalisation.

John Long was also incorrect in his conclusion that shock loading doesn't matter. It very much matters if there is a load at the anchor such as in a direct belay or a hanging belay.


(This post was edited by patto on Jun 25, 2012, 5:32 PM)


majid_sabet


Jun 25, 2012, 6:21 PM
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Re: [BetaRock] Theory about forces in a 3-legged cordelette [In reply to]
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are you talking about three point anchor with equal distance between each leg to anchor ?


curt


Jun 25, 2012, 6:49 PM
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patto wrote:
John Long was also incorrect in his conclusion that shock loading doesn't matter...

I don't believe that was his conclusion. His conclusion was that when one point of an anchor failed, the shock loading measured on the remaining leg(s) of the anchor were not as significant as one might anticipate.

Curt


Express


Jun 25, 2012, 7:00 PM
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A large part of my work includes structural design for cable-stayed architectural cladding systems. Perhaps I can shed some light on the mechanics of the problem we're looking at:

For a two-anchor system, you should be able to resolve the forces using basic free-body principles from physics or engineering statics --- IF the segments were perfectly unstretchable cables in a known geometric configuration. Depending on this configuration (i.e., the angles between the bolts) - the resultants at each anchor bolt would be easily calculable - but already not necessarily equal.

But things are even more complicated because you need to evaluate everything based on the geometry of the system after loading. The slings, webbing, rope, etc. stretch under load (according to a stress-strain relationship for the material) and that changes this geometry. And, what's more, the longer the sling is, the more it stretches under load.

So, to determine that final geometry under your design load, you would need to know (a) the elastic modulous of the rope or webbing in each segment, (b) it's cross sectional area, (c) the EXACT unstretched length of each segment, and (d) the exact magnitude of the loading at the masterpoint. It starts to get a little hairy when you see that the geometry, tension, and amount of stretch are all inter-related.

This is all just for a system with two anchor bolts.
For a three-point system, it you're introducing additional angles, additional internal deflection, and more uncertainty (for a human approximating everything in the real world) in the final [tensioned] geometry.

We still haven't accounted for the fact that even the best "self-equalizing" knots still deal with some amount of internal friction, the error in measurement of sling length, the assumption of linear behavior in what are typically anistropic nonlinear materials, error in measurement of applied loads, et cetera et cetera.

It starts to become a fairly difficult and complicated problem, and it's not surprising to me at all that we should see such a large differential in the loads at each anchor point.


(This post was edited by Express on Jun 25, 2012, 7:03 PM)


patto


Jun 25, 2012, 7:49 PM
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curt wrote:
I don't believe that was his conclusion. His conclusion was that when one point of an anchor failed, the shock loading measured on the remaining leg(s) of the anchor were not as significant as one might anticipate.
Curt

Which were totally false conclusions. As has been discussed numerous times here and on MP.

His test setup showed minimal shock loading as would be expected where there is no mass in the anchor system. As has been stated numerous times when there is mass at the anchor this conclusion goes out the window.


JimTitt


Jun 26, 2012, 12:15 AM
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Marc Beverly has done a lot of work on this, also covering in great detail the effect of assymetrical placements and the resultant stretch differential in the legs mentioned on the thead.
His results are predictably grim with large variations in the forces on the various legs. Other work shows the same or worse results but with the imbalance in the legs shifting which indicates the human factor tying the central point can be the dominant factor.
These tests were done in laboratory conditions where orientation to the direction of load was easy to see and with very experienced guides and rescue riggers tying the knots so we tested a random selection of climbers on the cliff and got even worse results, in some cases no load at all being placed on one of the pieces.

The dynamically equalising systems fared slightly better, only one of these failing to load one piece at all but of course the effects of extension if the belayers weight is included in the system are not to be ignored, sometimes reaching alarming proportions.

I would build the anchor attempting to equalise two pieces (which we can do fairly well) and then add in the third approximately equalised as a back-up. Our experience is that one can better equalise using clove hitches than tying a central knot and so the resulting anchor tends to end up looking like a traditional anchor built using the rope. Whether one uses the climbing rope itself or a dedicated length of cord is a personal choice and also depends on the circumstances. I would not use a dynamically equalising system in a belay.

Uneven leg lengths should be adjusted using as much low-stretch material as possible, a doubled or tripled Spectra/Dyneema sling being fairly low stretch at the loads we are considering, karabiners even more so.
Vertically orientated anchor pieces are more difficult partly because the leg lengths are considerably different, either one joins them all up in series with the rope/pord and accepts this or equalises all the legs with low-stretch material to one point.

Marc Beverlyīs paper can be read here:- http://www.caves.org/section/vertical/nh/51/Multi-point%20pre-equal%20anchors.pdf


shockabuku


Jun 26, 2012, 4:08 AM
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Re: [JimTitt] Theory about forces in a 3-legged cordelette [In reply to]
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Do you think clove hitches equalize better because they have some inherent slip that causes equalization when loaded or that, for some reason, it is a better method for the human in the system to utilize?


JimTitt


Jun 26, 2012, 4:42 AM
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They are easier for us to judge the tension and more importantly the rope path through the knot is always the same. With an overhand or 8 in a load of strands itīs anyones guess which strand goes where so even if you got everything perfectly equal to start with there is differential slip in the knot which screws things up considerably.
Beverly covers this in his paper, both practically and theoretically but in the end to no real effect on getting better equalisation which isnīt suprising.


shockabuku


Jun 26, 2012, 7:34 AM
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Sounds reasonable, thanks.


Partner rgold


Jun 26, 2012, 8:19 AM
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I've been arguing for the conclusions of the Beverly paper for about ten years now, mostly without any particular effect. Of course, I only had theoretical considerations (combined, however, with lots of practical experience) to base things on, and in the absence of experimental confirmation, the amazingly unexamined SERENE dogma prevailed.

Even now, the practical superiority of clove-hitch based anchor rigging, the relatively minor role of arm angles, and the more critical issue of arm length seems little recognized (in the US), at least from what I can observe out in the field. Part of this is because it doesn't seem to matter that much; anchors aren't failing (but it is hard to know what to make of this, since anchors are so very rarely tested).

The oft-cited tests about the irrelevance of anchor extension missed a critical point by setting things up so that anchor extension made an insignificant contribution to fall factor. Practically speaking, the model tested a solo climber falling directly onto the anchor, with anchor extension insignificant relative to fall length. Not modeled was the very different situation of a belayer being pulled off the stance, in which case that fall energy has to be absorbed by what might be a very short tie-in, in some cases (unfortunately) fabricated with static material rather than the rope.

As for modeling three-point anchors, the problem is complex because, as the civil engineers will tell you, the three point anchor is statically indeterminate---you cannot determine the arm loads from the vector equilibrium equations because you end up with more unknowns than equations and so infinitely many possible solutions. In the case of a rigid truss, extra equations are obtained from the fact that there is also a torque equilibrium, but in the case of ropes, no torques are present and the additional equations come from the elongation of the anchor arms, which depends on the rope modulus as well as the specific geometry of the anchor. A consequence is that the power point will not, in general move straight down, and its final position has to be calculated in order to calculate the anchor arm tensions. (Beverly, by the way, punts on this one in his analytical model and just assumes that the power point moves straight down. This assumption boils down to constraints on the anchor arm tensions (or restrictions on the anchor arm geometry) that are not, in general part of the picture, meaning that the model will not, a priori, account for a certain amount of anchor arm load inequality in the field.

A situation to watch out for with three-point anchors arranged horizontally is that a piece on one of the two outer arms is relatively weak. This should be avoided if possible. If an outer arm blows with the standard symmetrically rigged configuration, all the load will transfer to just a single piece, the middle piece, and the third arm will not be loaded unless that middle piece also blows, setting up the cascade failure scenario that seems the most likely way for a multi-point anchor to fail. (The fact that there is no momentary relaxing of tension in this scenario means that the extraction of anchor pieces will not reduce fall energy to any significant degree.)


(This post was edited by rgold on Jun 26, 2012, 8:20 AM)


Partner cracklover


Jun 26, 2012, 8:43 AM
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Somewhere on Supertopo Jim and Chiloe posted a bunch more figures, but I can't find them right now.

Anyway, your theory is way off. To find the force on each leg, you must treat it independently for stretch, and then also see how those stretches would interact with each other. It is not a simple problem.

GO


JimTitt


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Äs you say modelling 3 point (or more) is going to be difficult at best. The issue of whether the power point is considered to move straight down or move to a new position is one that not only makes the theory difficult but in practice means one has to take two different scenarios into account when testing. Is the load constrained in its direction or can the load move across to below the powerpoint? I can get considerably different results by using a free hanging or dropping weight or by pulling from a pre-determined point, both of which it is reasonable to assume could occur in a real situation.
The outer point failure problem is why I would prefer the belay set up as a two point anchor with the third then added in. Most experts agree that you concentrate on two good pieces as a minimum and treat everything else as a bonus which might pleasantly suprise and this seems to be the general practice evolved over the years.


jktinst


Jun 26, 2012, 10:46 AM
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Re: [cracklover] Theory about forces in a 3-legged cordelette [In reply to]
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I believe that this is the thread that cracklover is referring to.
http://www.supertopo.com/...1/Equalizing-anchors

You have to scroll a fair bit to get to the figures.

Do try and read up on the various anchor building, equalization vs extension threads (like that one) before making up your own mind about this and keep in mind that more recent threads (like yours) tend to have fewer contributors and less debate due to fatigue over the topic.


patto


Jun 26, 2012, 11:36 AM
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It is odd though. That we have an entire WORLD of climbers, many of which are engineers or other such professions, yet we have so little real insight into the discussion.

The same couple of names always reappear to bring rational thought into the discussion.


Thankfully in the country that I mostly climb in, all these dynamic anchors have never been in vogue. Its cordelettes and rope anchors all the way!


Partner cracklover


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jktinst wrote:
I believe that this is the thread that cracklover is referring to.
http://www.supertopo.com/...1/Equalizing-anchors

You have to scroll a fair bit to get to the figures.

Do try and read up on the various anchor building, equalization vs extension threads (like that one) before making up your own mind about this and keep in mind that more recent threads (like yours) tend to have fewer contributors and less debate due to fatigue over the topic.

Exactly. Thanks for finding that. BTW, perusing through that thread I notice that a lot of the pics and figures I posted (as GOclimb) seem to be gone. If there's anything you want to see of mine from over there, let me know, and I'm sure I can dig up the originals.

GO


blondgecko
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Jun 28, 2012, 9:33 PM
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rgold wrote:
and the more critical issue of arm length...

This is an interesting point that I always found myself pondering while tying rope anchors. The problem, of course, is that a shorter arm has less absolute distance to stretch than a longer arm under the same load, and so under a falling situation the shortest arm will end up taking the brunt. A fairly simple workaround is to deliberately tie the powerpoint so that the shorter arms remain loose when the anchor is unloaded. It should be relatively straightforward to work out a rule-of-thumb: for every foot of extra length, tie that arm x inches short so that under a moderate load the arms stretch to (relatively reasonable) equalisation.

Like this:



It takes a bit more thought and playing around and will never be perfect, but I'd bet money that once perfected it would outperform the standard approach.
Attachments: 3-arm_stretch.gif (7.48 KB)


JimTitt


Jun 28, 2012, 10:51 PM
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Certainly itīs a concept but exactly how well we can do this is going to be the problem, trying to get the tensions equal is virtually impossible so controlling the unequality is going to be equally as hard if you see what I mean.
I tried a couple of other ideas such as using a mix of dynamic and low stretch material, different numbers of strands on a cordalette and various diameters of cord but for the typical belay setup it all seemed as bad as ever and sometime worse! For example thin cord should stretch more but the amount of slip through the knot is less so it ends up not extending as much as the thicker rope.
All of which presumes that you actually do want to get the forces equal which assumes you know all the pieces have the same strength which is another matter altogether!


blondgecko
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Jun 29, 2012, 12:07 AM
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Well, I agree you're never going to get it perfect (probably not even close to it), but you can definitely get it closer than with the "initially equalised powerpoint case". Here's my reasoning, in a slightly more formal form.

Assume for the sake of argument that each leg of the anchor is perfectly elastic (that is, assume that it follows Hooke's law, F = -kx, where F is the force, k is the spring constant (equal to the elastic modulus divided by length) and x is the change in length). Further assume the simplest case: that all three anchor points are in line both with each other and with the direction of fall. What we want to do is optimise so that at some moderately severe fall (say 6-7 kN?) F is equal for all three legs - say, 2 kN for each.

Plugging in a reasonably realistic rope modulus (20 kPa), it comes out that under these circumstances you want each leg of the rope to have stretched by 10% at the one point in space. This is what this idealised system looks like for a 3-leg anchor with legs 10, 50 and 100cm long:



At low forces, the load is entirely taken by the longest leg. Not ideal, but at least this is under the lowest forces. The nice thing is that as the force increases towards your "optimum" level everything gets closer and closer to equal. Once you get past that it all diverges again with the force in the shortest leg very quickly growing to dominance - but in the standard case that divergence starts from zero force.

Obviously non-ideality in rope behaviour and good old trigonometry complicate the situation somewhat, but there is a basic truth here: when building an anchor make your longest arm tight and leave a little slack in the shorter arms, and you'll have at least slightly better equalisation under any substantial load.
Attachments: anchor.gif (9.08 KB)


JimTitt


Jun 29, 2012, 1:18 AM
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I shall play with this in the morning on the test rig and see how it works out. In the meantime we will need an i-phone app to cope with more random anchor pieces!


blondgecko
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Jun 29, 2012, 2:07 AM
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Cool! I'll look forward to seeing what happens.


patto


Jun 29, 2012, 8:10 AM
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All this is grossly violating the K.I.S.S. principle.


Partner rgold


Jun 29, 2012, 8:40 AM
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It is going to be hard to know "what happens" unless Jim can do a very large number of trials.

I like theory as much as anyone, but I doubt, given the probabilistic nature of the arm-slack choices, that there is much likelihood of achieving a better load distribution by guessing how much slack to put in the shorter arms. I think the time spent fiddling with arm lengths would be better spent climbing and belaying, but I'll be delighted if Jim's results suggest otherwise.

Moreover, considering the "cascade failure" potential for rigs with horizontally oriented anchor points and long outside arms, it might actually be better to have lower loads on the outside arms as a bit of insurance against having one of them blow first.

Unless something definitive emerges, I think the best operating assumption is that one of your pieces is going to get at least half the load.

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