From billfoote@aol.com Fri Apr 21 18:14:13 EST 1995
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From: billfoote@aol.com (BillFoote)
Newsgroups: rec.climbing
Subject: Re: Fall Factor Math - Was Need Help Phys/Engr
Date: 19 Apr 1995 15:17:24 -0400
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Anthony Bubb replied directly to author and wrote (paraphrased)

|> No... the rope will exceed the elastic limit and go into plastic
deformation...


I would suggest that if a rope is designed to withstand a factor-2 fall,
then it will not reach it's elastic limit (yield point) when loaded below
that factor-2 force, so the analysis should be fairly correct in that load
range.

If the rope DOES go into plastic deformation, it is in the process of
failing.  OK, it might in a really bad fall (factor 2 perhaps), but as
illustrated below
the max forces calculated should still be conservative numbers.

As shown below, (QUALITATIVELY),  when a material reaches it's elastic
limit, or yield point, Y, the stress-strain curve levels off.  The slope
of the curve shown below is the material's Modulus of Elasticity, or the
reciprocal
of the "spring constant" k used in my analysis.  So, as the material
is loaded beyond Y, the change in the slope (modulus) will result in the
actual forces being less than those calculated using the original
equation.
(The equation assumes a straight line stress-strain relationship).

As originally stated, this is a CONSERVATIVE analysis, and ACTUAL forces
should not exceed the values produced by this equation.  This is not to
say
that the effect on the rope is less severe.  Exceeding the elastic limit
means severe damage to the rope, and it should be retired!



            |               *<-results from the provided equation
            |              *
            |             *
            |            *                +      U = ultimate strenght
(breaks here)
            |           *           +
            |          *      +     ^
            |         *   +         |__ more realistic stress-strain curve
            |        * Y
            |       *+
Force    |     +
(stress) |    +
            |   +
            |  +
            | +
            |+
           +----------------------------------------------------
									  
            Stretch
		(strain)


BillFoote@aol.com

P.S. A interesting thing to note:  According to this analysis, there is no
difference (impact force - wise) between a 2-foot factor-2 fall and a
160-foot factor-2 fall, or a 2-inch factor-2 fall!

Should a rope be retired if one, for example, falls 4 inches with only 4
inches of rope paid out?  THIS IS A FACTOR-2 FALL!!!