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Multi vs Single Strand Strength
Name: Brad
Status: Other
Grade: Other
Location: KY
Country: United States
Date: May 2006
Question:
Is a cord of 3 strands really much stronger than
3 times a single strand? How about a cord of 2 stands?
Replies:
The "short" answer is yes, but the mechanisms that are operating
are much more subtle than appears at first. A strand will begin to
break if it develops some stress cracks which then propagate
axially down the strand and radially. The result is the strand
fails. For three strands to fail by this mechanism the failure
would have to happen in all three more or less at the same time.
How a crack propagates in a particular strand depends upon its
chemical composition, which can be altered to increase its tensile strength.
But things are even more complicated because multiple strands
can be braided and/or twisted. These configurations allow the
strands to "stretch" and "slip" by one another, which to the
outside observer seems to make the composite stronger than just
single fibers which can only stretch axially. Other factors play a
role also. For example, if the strands are "normal" they get weaker
as the temperature increases, but if the strands are "rubbery" they
actually get stronger as the temperature increases moderately.
So your "simple" question actually is very complicated.
Vince Calder
There is a whole branch of engineering physics in the literature
that can compactly be described as: "the physics of ropes". A Google
search on "physics of ropes" turned up these interesting site -- but
there are many more. The topic is quite interesting and applies some
physics concepts not usually addressed in elementary courses. As you
can see from these 'hits' designing a rope is a complicated business.
http://www.bstorage.com/speleo/Pubs/rlenergy/Default.htm
http://www.physicsclassroom.com/Class/momentum/U4L1c.html
Vince Calder
First some assumptions, the cords are equal diameter ,
equal composition, material etc.
Wound cords, as 3 are stronger than 3 individual cords.
That is the principal behind cables for suspension bridges. The 3 wound have
a larger final diameter.
The outer fibers are not stressed as much as a smaller diameter, compare to a
single diameter, hence stronger final product.
Consider a beam, under a vertical load the bottom fibers
are in tension. The top in compression. So, it is rather obvious a deeper
beam is stronger than a shallower one.
Say, a failure in tension, the deeper beam has less stress on the bottom
fibers. Basically , it is the same for a wound cable.
Similarly, a 3 cable stronger than 2, if all are equal.
James Przewoznik
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Update: June 2012
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