Elongation of Wire Rope
Elongation of Wire Rope
(OP)
I wonder if anybody can help me determine how much elongation you get from a wire rope under an applied load. I downloaded the USS Wire Rope Engineering Hand Book from SlideRuleEra's web site (http: //www.slid eruleera.n et/USSWire RopeEngrHa ndBook.zip - Thanks for hosting it). It has some information on stretch of rope, but I'm concerned it might be dated, being from 1968. Page 29 of the Hand Book has a table for approximate metallic areas of wire rope based on your diameter and rope type. Page 30 has a table for approximate moduli of elasticity, based on your material.
This sounds easy enough, but it's not like pulling "A36" from a table where you know you have a match. There are decent variations even between the closest two options.
I have seen the following equation in another engineer's work, but I don't know the source of it:
AE = 7,140,000*D^2 (where D=wire rope diameter)
For a 1/2" rope, this gives you AE=1,785,000 #.
Perhaps not coincidentally, if you used an effective diameter of 56%*D, and an E of 29,000,000 psi, you get the following:
De = 0.56*0.5" = 0.28"
Ae = pi/4*De^2 = 0.06158 in^2
AE = Ae*E = 1,785,681 #, virtually the same answer. This makes more sense to me, but who knows if it's correct.
Does anybody here know where the 7,140,000*D^2 equation comes from? Is there any validity to the "effective diameter" method? How do others here go about calcualting the stretch of a wire rope?
This sounds easy enough, but it's not like pulling "A36" from a table where you know you have a match. There are decent variations even between the closest two options.
I have seen the following equation in another engineer's work, but I don't know the source of it:
AE = 7,140,000*D^2 (where D=wire rope diameter)
For a 1/2" rope, this gives you AE=1,785,000 #.
Perhaps not coincidentally, if you used an effective diameter of 56%*D, and an E of 29,000,000 psi, you get the following:
De = 0.56*0.5" = 0.28"
Ae = pi/4*De^2 = 0.06158 in^2
AE = Ae*E = 1,785,681 #, virtually the same answer. This makes more sense to me, but who knows if it's correct.
Does anybody here know where the 7,140,000*D^2 equation comes from? Is there any validity to the "effective diameter" method? How do others here go about calcualting the stretch of a wire rope?






RE: Elongation of Wire Rope
There is also a table for the approximate metalic area for 1" wire rope based on construction type. For other than 1" diameter rope you multiply the 1" number by your ropes diameter squared. Then they calculate stretch by PL/AE. The metallic area for 1" rope varies from 0.23 sq in to 0.505 sq in depending on type of construction.
Example
6x19 1" Seale IWRC E=12,000,000 psi A=0.470 sq in
stretch=P*L/(12,000,000*0.470)
RE: Elongation of Wire Rope
In the meantime, could I talk you out of the E and A values for 1/2" 6x19 EIPS IWRC?
RE: Elongation of Wire Rope
I gave you the more common Seale 6x19 IWRC. The E for all three in 6x19 class is the same. This is the E for less than 20% of breaking strength.
E= 12,000,000 psi
6x25 FW A=0.483 sq in
6X26 WS A=0.476 sq in
RE: Elongation of Wire Rope
RE: Elongation of Wire Rope
As stated in the first reply "For other than 1" diameter rope you multiply the 1" number by your ropes diameter squared." So for 1/2" wire rope you multiply the approximate metalic area of 1" diameter wire rope by 1/2 squared or 0.25.
RE: Elongation of Wire Rope
RE: Elongation of Wire Rope
The rough-as-guts formula you ask about (7140000*D^2) is very similar to the approach I take when confronted with a need to guesstimate the stretch characteristics of a wire rope about which I know nothing more that its notional diameter. I use:
Eeffective = 0.5*Ematerial
to allow for the twisted strands,
and Aeffective = 0.6*Agross
to allow for the "circles within circles aspect of the cross section.
This leads to
(AE)effective = 0.3*Agross*Ematerial)
where your formula corresponds to
(AE)effective = 0.303*Agross*Ematerial)
Note that this approach really is as rough as guts, and you should always make every effort to ascertain the correct extensibility.