## 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 | 0.50 | 0.25 |

Heavily loaded Factor of Safety about 3:1 | 0.75 | 0.50 |

Heavily loaded with many bends and/or deflections | Up to 2.00 | Up 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/in^{2})

A = rope area (in^{2})

## 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