Rope/Wire: Axial and Bending Stiffness

The Line Type Wizard sets up Axial and Bending Stiffness and Limit Compression for a Rope/Wire as follows

Axial Stiffness

The expressions for axial stiffness are calculated in different ways for the two groups of fibre ropes and wire ropes.

For Fibre Ropes we use the catalogue data. Load/extension characteristics depend on previous load history, whether the rope is wet or dry, and the rate of application of the load. To reflect the likely working environment of the rope we use data associated with ropes that have been tested under the following conditions:

• the rope has been pre-worked – loaded to 50% of breaking load and then rested for 24 hours (this causes the rope to bed down so that its elastic behaviour is more consistent and repeatable)
• subjected to slowly varying loads (for loads varying at wave frequency, stiffness should be about twice the value shown)
• a wet rope – pre-soaked in water (this is most significant for Nylon ropes which suffer a loss in performance when wet)
• we use figures for the average performance when the mean extension is 10% (by taking the tangent of the stress-strain curve at 10%).

Incorporating all of the factors indicated above we can produce values of axial stiffness for a range of rope diameters. Once again using simple statistical techniques we obtain the following expression for axial stiffness of fibre ropes:

Axial Stiffness = 1.18 x 10⁵ D² kN (for Nylon ropes).

Axial Stiffness = 1.09 x 10⁶ D² kN (for Polyester ropes).

Axial Stiffness = 1.06 x 10⁶ D² kN (for Polypropylene ropes).

Axial stiffness for Wire Ropes is calculated directly, rather than estimated from empirical relationships. We assume a value for Young's Modulus, for the 6x19 strand group, of:

E = 1.03 x 10⁸ kN/m² (for Wire ropes with fibre core).

E = 1.13 x 10⁸ kN/m² (for Wire ropes with wire core).

and work on an assumed metallic area of:

A = 0.455 (πD²/4) m² (for both wire ropes).

Both of these quantities have been obtained from the HER Group Marine Equipment & Wire Rope Handbook. Note that for wire ropes with a wire core the additional axial stiffness is accounted for in the enhanced Young's modulus. This leads to:

Axial Stiffness = 3.67 x 10⁷ D² kN (for Wire ropes with fibre core).

Axial Stiffness = 4.04 x 10⁷ D² kN (for Wire ropes with wire core).

Bending Stiffness

For all rope construction types the bending stiffness offered by the Wizard is zero. For systems where bend stiffness is a significant factor you should override this value with the true value obtained from the rope supplier.

Limit Compression

In conjunction with a zero value for bend stiffness Limit Compression is set to yes.