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Knot Strength - or Weakness

Page history last edited by DerekSmith 11 years, 12 months ago

Knot Strength - or Weakness

by DerekSmith

 

 

Seems a long time ago now since I used to think that knots made rope stronger - more rope present so naturally a knot is going to be stronger than just a single thickness of rope...  isn't it?   It wasn't until I took up climbing that I was disillusioned of that idea and it came as something of a shock that just a little old Overhand knot could reduce the strength of my climbing rope by a whopping great 50%.  But I didn't think to question why or how this occurred until relatively recently.  That is when a fascination with just what steals away the strength of a cord or rope grabbed my interest and with it came the challenge of finding ever stronger ways of connecting to a rope.

 

So, how do knots weaken a rope?  There are two basic modes - Stretching and perhaps surprisingly Compression.  One of the easiest ways of visualising the way a cord suffers from force is to have a play with some cold cooked spaghetti.

 

Stretching  --  Wrap a length of spaghetti around the index fingers of each hand, then pull gently on the connecting strand - it will snap - no surprises there.  The spaghetti is a weak starch mono filament, stretching it applies a tension all along the strand and eventually the tension exceeds the strength of the weakest point and the monofilament snaps.  Now repeat the experiment, but this time pull the strand down across the rounded edge of a cup or glass.  This time, if the radius is tight enough, the break will happen with regularity right on the bend.  One of the things that is making this break happen is that the outer curve of the spaghetti is longer than the inner curve, so it gets stretched more and is consequently subject to a localised increase in tension on that outer curve.  When that tension exceeds the strength of the weakest point on that curve, the outer surface cracks and dumps the tension it was holding into the layers of starch just beneath the outer edge.  This overstretched surface, now weakened by a developing crack, gives way again and so the force focusses onto less and less area of strand until the strand breaks.

When a loaded cord makes a tight turn around another cord in a knot, its outer curve is highly stretched, focussing the tension onto just a few of the fibres in the outer layers of the cord.  When the tension exceeds the strength of the weakest fibre, it snaps and dumps its load onto its neighbouring fibres - fewer fibres, more load, again the weakest one snaps and eventually the cascade of snapping fibres results in total failure of the whole cord at the point focussed by the tight bend.

 

 

Diagram 'A' represents a piece of un-tensioned cord with two marks drawn across it, the arrows indicating the un-stretched length of the cord.

Diagram 'B' represents the cord under load sufficient to create a 50% extension, here the arrows indicate the uniform stretch involved.

Diagram 'C' represents the loaded cord wrapped around a cord of the same diameter.  The middle of the cord is still stretched to 50% extension, but the tight curve on the inside has actually had to 'bunch up' while the outside has to take a much longer path and has had to stretch much more.

Lets look at this as a graph of the cord length as we go from the inner part of the curve to the outside.

 

You can see that for about a quarter of the thickness of the cord it is under compression.  None of this shaded area is taking any of the load.

You can also see that the cord goes right up to 1.25 times extension  - but this cord breaks at 0.9 time extension, so the RHS quarter is all at, or above, the breaking point for this cord.

 

As you might have expected, this explanation is too simplistic to describe the reality of a cord working in a knot.

As the tension builds fast in the outside strands, they start to exert an inward pressing force that manages to flatten the cord into a D shape.  Although this takes the outer radius away from tensions which would break the cord, it does mean that when the forces continue to build, a large number of fibres move quickly into an over extended position and failure will then spread rapidly when the weakest strand breaks.

The other aspect of the complexity of reality is that the compressed zone not only does not take up any of the tension, but it also requires some of the tension from the tensioned fibres immediately above it in order to compress it.  So a significant portion of the cord is removed from taking any of the load.  The combination of a weakened outside and a wasted inside leaves the one diameter tight turn seriously compromising the total cord capacity.

By contrast, take the cord around a two diameter turn  and the theoretical graph looks like this :-

 

 

Notice no compression zone and only a trace of excessive stretching which in practice would be lost to the D shape change which would happen as the load was applied.

 

BUT THIS IS ALL WORKED THROUGH USING A CORD WITH A 90% EXTENSIBILITY - HOW WOULD THIS CHANGE IF THE CORD WERE FAR LESS ELASTIC ??

 

Compression --  How on earth could compression make a polyester braid cord snap??  To explain, lets go back to the spaghetti.  Take a strand between finger and thumb and gently squeeze.  It should snap with a definite fracture across its strand.   What made this happen.  To see where the forces that made this happen came from, get hold of a large soft pencil eraser and squeeze it in the middle.  As you squeeze in the sides, you will see the ends squeeze outwards, and here is the clue, squashing in one dimension causes extension (tension) in dimensions at right angles to it.  So pinching the sides of the spaghetti caused the middle of the strand to be 'push' stretched until it gave way and this time the strand snapped from the inside - out.  Exactly the same happens in all the fibres and filaments used in making string, cord and ropes and many materials are severely weakened by squeezing or nipping.  Demonstrate this for yourself by tying a Sliding Grip hitch using a cotton string, then slowly load the knot until it eventually breaks and examine the broken ends. 

 

 

 

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You will see that the cord broke right where the straight cord entered the ferocious nip of the first holding wraps.  The ends will look frayed as if the cord has actually broken outside of the knot, but in reality, the nip triggered the failure of the first strands and then strands broke inside and outside of the knot wherever their weak points happened to be.  Oddly enough, the knot itself gave some support to the fibres inside it, once the pressure started to be relieved by strands breaking.  Weak strands inside the knot are able to share their load with closely held neighbours which shared the load as the weaker fibre tried to snap, while fibres outside of the knot had no such neighbourly support and failed in turn as each met its breaking limit. ( In one small way my preconception that knots made cord stronger was in fact correct !!)

 

So, the weak points, and therefore the failure points, of a knot are going to be tight turns and nipping points - not forgetting that a tight turn is in fact a combination of stretching on the outside radius and compression (nipping) on the inside radius.  (There is one more aspect of knot strength which will have to be the subject of another article and that is the rate at which the force is applied - gradually or as a shock wave.  For the shock wave loading another aspect of the knot comes into play and that is how much 'packing' or 'cushioning' the knot contains).

 

 

 

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