Forums: Climbing Information: The Lab: Re: [BetaRock] Theory about forces in a 3-legged cordelette: Edit Log


Jun 25, 2012, 7:00 PM

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Re: [BetaRock] Theory about forces in a 3-legged cordelette
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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)

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Post edited by Express () on Jun 25, 2012, 7:03 PM

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