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Re: [JimTitt] Theory about forces in a 3-legged cordelette:
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rgold
Jun 26, 2012, 3:19 PM
Views: 21776
Registered: Dec 3, 2002
Posts: 1804
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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, 3:20 PM)
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Post edited by rgold
() on Jun 26, 2012, 3:20 PM
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