Rope/wire: Axial and bending stiffness

The line type wizard sets up axial and bending stiffness and compression is limited for a rope/wire as follows.

Axial stiffness

We derive values for axial stiffness in different ways for fibre and wire ropes.

For fibre ropes we estimate an appropriate value based on 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 from ropes which have been subjected to:

• pre-working – 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)
• slowly-varying loads (for loads varying at wave frequency, stiffness should be about twice the value shown)
• pre-soaking in water (this is most significant for nylon ropes which suffer a loss in performance when wet)

Finally, we use figures for the average performance when the mean extension is 10% (by taking the tangent of the stress-strain curve at 10%).

On this basis, we obtain 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 \begin{equation} \text{axial stiffness} = \begin{cases} 1.18{\times}10^5 d^2 \text{ kN} & \text{for nylon ropes}\\ 1.09{\times}10^6 d^2 \text{ kN} & \text{for polyester ropes}\\ 1.06{\times}10^6 d^2 \text{ kN} & \text{for polypropylene ropes} \end{cases} \end{equation} For wire ropes (with fibre or wire core), we calculate axial stiffness directly. We assume a value for Young's modulus $E$, for the 6×19 strand group, of \begin{equation} E = \begin{cases} 1.03{\times}10^8 \text{ kN/m$^2$} & \text{for fibre core}\\ 1.13{\times}10^8 \text{ kN/m$^2$} & \text{for wire core} \end{cases} \end{equation} and work on an assumed metallic area $A$, for both core types, of \begin{equation} A = 0.455\, \frac{\pi d^2}{4} \end{equation} Both of $E$ and $A$ have been obtained from the HER Group Marine Equipment & Wire Rope Handbook. Note that the additional axial stiffness arising from a wire core is accounted for in the increased Young's modulus. These values give us, for wire ropes \begin{equation} \text{axial stiffness} = \begin{cases} 3.67{\times}10^7 d^2 \text{ kN} & \text{for fibre core}\\ 4.04{\times}10^7 d^2 \text{ kN} & \text{for wire core} \end{cases} \end{equation}

Bending stiffness

For all rope construction types, the wizard gives a bending stiffness of zero. For a system in which bend stiffness is significant, you should override this value with the true value obtained from the rope supplier.

Compression is limited

Compression is not limited for ropes.