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Properties of Extension of Steel Wire Ropes

Any assembly of steel wires spun into a helical formation, either as a strand or wire rope, when subjected to a tensile load, can extend in three separate phases, depending on the magnitude of the applied load.

There are also other factors which produce rope extension which are very small and can normally be ignored.

Phase 1—Initial or Permanent
Constructional Extension

At the commencement of loading a new rope, extension is created by the bedding down of the assembled wires with a corresponding reduction in overall diameter. This reduction in diameter is accommodated by a lengthening of the helical lay. When sufficiently large bearing areas have been generated on adjacent wires to withstand the circumferential compressive loads, this mechanically created extension ceases and the extension in Phase 2 commences. The Initial Extension of any rope cannot be accurately determined by calculation and has no elastic properties.

The practical value of this characteristic depends upon many factors, the most important being the type and construction of rope, the range of loads and the number and frequency of the cycles of operation. It is not possible to quote exact values for the various constructions of rope in use, but the following approximate values may be employed to give reasonably accurate results.

 % of Rope Length
Lightly loaded
Factor of Safety about 8:1
Fiber Core
0.25
Steel Core
0.125
Normally loaded
Factor of Safety about 5:1
0.500.25
Heavily loaded
Factor of Safety about 3:1
0.750.50
Heavily loaded
with many bends and/or
deflections
Up to 2.00Up to 1.00

The above figures are for guidance purposes. More precise figures are available upon request.

Phase 2—Elastic Extension

Following Phase 1, the rope extends in a manner which
complies approximately with Hookes Law (stress is
proportional to strain) until the Limit of Proportionality or
Elastic Limit is reached.

It is important to note that wire ropes do not possess a
Young’s Modulus of Elasticity, but an ‘apparent’ Modulus of
Elasticity can be determined between two fixed loads.

The Modulus of Elasticity also varies with different rope constructions, but generally increases as the cross-sectional area of steel increases. By using the values given, it is possible to make a reasonable estimate of elastic extension, but if greater accuracy is required it is advisable to carry out a modulus test on an actual sample of the rope. As rope users will find it difficult to calculate the actual metallic steel area, the values can be found in the Wire Rope Users Manual or obtained from Bridon Engineering.

Elastic Extension = WL (inches)

EA

W = load applied (pounds)

L = rope length (inches)

E = elastic modulus (pounds/in2)

A = rope area (in2)

Phase 3—Permanent Extension

The permanent, non-elastic extension of the steel caused by tensile loads exceeding the yield point of the material.

If the load exceeds the Limit of Proportionality, the rate of extension will accelerate as the load is increased, until a loading is reached at which continuous extension will commence, causing the wire rope to fracture without any further increase of load.

Thermal Expansion and Contraction

The coefficient of linear expansion (?) of steel wire rope is (6.94 x10-6 per °F) and therefore the change in length of 1 foot of rope produced by a temperature change of t (°F) would be;

Change in length ?L = ?L t where

? = coefficient of linear expansion

L = original length of rope (in)

t = temperature change (°F)

The change will be an increase in length if the temperature rises and a decrease in length if the temperature falls.

Extension due to Rotation

The elongation caused by a free rope end being allowed to rotate.

Extension due to Wear

The elongation due to inter-wire wear which reduces the
cross-sectional area of steel and produces extra
constructional extension.
Example: What will be the total elongation of a 200 Ft length of 1-1/8” diameter Blue Strand 6x41 IWRC wire rope at a tension of 20,000 Ibs and with an increase in temperature of 20°F.

Permanent Constructional Extension =

0.25% of rope length = .5 = 6”

Elastic Extension = WL = 20,000 x 200 x 12 = 5.73”

EA 13,500,000 x .62

Thermal Expansion =

Δ L = ∞ L0 t = 6.94 x 106 x 200 x 20 = .33”

Therefore total extension = 6” + 5.73” + .33” = 12.06”

This page reprinted with permission from Bridon American