# Equivalent Axial Stiffness of Horizontal Stays
## 7 Generalization of the Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cable Material** & **Density** & **Elastic** & **Ultimate** & **Specific** & **Specific** \\  & [\(kg/m^{3}\)] & **Modulus** \(E\) & **Strength**\(f_{t}\) & **Stiffness**\(E\)/**\(\rho\)** & **Strength**\(f_{t}\)/\(\rho\)** \\  & & & **[MPa]** & **[MNm/kg]** & **[kkm/kg]** \\ \hline \hline \multicolumn{1}{c}{Aramid fiber (high modulus)} & 1440 & 112 & 3000 & 77.8 & 208 \\ \multicolumn{1}{c}{Aramid fiber (normal modulus)} & 1440 & 70.5 & 2900 & 49.0 & 201 \\ \multicolumn{1}{c}{Liquid crystal aromatic} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \multicolumn{1}{c}{polyester (LCP) fiber} & 1410 & 66 & 2830 & 46.8 & 201 \\ \multicolumn{1}{c}{Polybenzoxazole (PBO) fiber} & 1560 & 270 & 3950 & 173 & 253 \\ \multicolumn{1}{c}{Carbon fiber} & 1560 & 170 & 2500 & 109 & 160 \\ \multicolumn{1}{c}{Steel strand} & 7850 & 180 & 1770 & 22.9 & 22.5 \\ \multicolumn{1}{c}{Steel wire} & 7850 & 206 & 1900 & 26.2 & 24.2 \\ \multicolumn{1}{c}{Copper} & 8940 & 110 & 240 & 12.3 & 2.68 \\ \multicolumn{1}{c}{Aluminum} & 2700 & 69 & 105 & 25.5 & 3.89 \\ \multicolumn{1}{c}{Nylon fiber} & 1140 & 4.56 & 610 & 4.0 & 53.5 \\ \multicolumn{1}{c}{Polyester fiber} & 1380 & 13.8 & 790 & 10.0 & 57.2 \\ \multicolumn{1}{c}{Cotton rope} & 1540 & 7.9 & 225 & 5.1 & 14.6 \\ \multicolumn{1}{c}{Hemp rope} & 1490 & 32 & 300 & 21.5 & 20.1 \\ \multicolumn{1}{c}{Flex rope} & 1540 & 27 & 340 & 17.5 & 22.1 \\ \multicolumn{1}{c}{Jute rope} & 1500 & 25.8 & 230 & 17.2 & 15.3 \\ \multicolumn{1}{c}{Abaca (Manila hemp) rope} & 1320 & 30 & 300 & 22.7 & 22.7 \\ \multicolumn{1}{c}{Sisal} & 1320 & 30 & 250 & 22.7 & 18.9 \\ \multicolumn{1}{c}{Silk (silkworm)} & 1320 & 10 & 650 & 7.6 & 49.2 \\ \multicolumn{1}{c}{Silk (spider)} & 1100 & 12 & 900 & 10.9 & 81.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reference values of relevant mechanical properties of various cable materials. Truly, looking at the curves in Figure 11, much more articulated and interesting conclusions can be derived about the dependence of the ratio \(E_{ft,eq}/E\) on the specific stiffness. In fact, considering two cables made with different materials, nonlinear effects are more pronounced in that characterized by bigger specific stiffness only if the densities of the materials are comparable, or the elastic moduli of the materials are considerably different, as it is evident comparing the curves pertaining to of PBO, carbon fiber and nylon cables, or those pertaining to steel and nylon cables in Figure 11.  
That behavior can be explained considering that nonlinear effects are mainly determined by the work made by the self-weight of the cable (see Equation (24)). Once the cable configuration is fixed, the work of the self-weight turns out almost independent on the elastic modulus of the material, so that its influence on \(E_{ft,eq}/E\) is more relevant for materials characterized by smaller modulus, \(E\). On the other hand, some additional conclusions can be also derived regarding the dependence of the ratio \(E_{ft,eq}/E\) on the ratio \(\sigma_{0}/(\gamma\;a)\), as a function of the cable material. Recalling Equation (30), it is clear that cables made of different materials, and having the same sag and the same chord length, are associated to the same ratios \(\sigma_{0}/(\gamma\;a)\), or \(\sigma_{0}/\gamma\). In Figure 12, the \(E_{ft,eq}/E-\sigma_{0}/\gamma\) curves for steel, carbon fiber, PBO and nylon cables are diagrammatically shown considering again two different chord lengths, \(a=100\) m and \(a=1000\) m.  
From the diagram in Figure 12, it is evident that, among the considered materials, PBO cables are characterized by the lowest \(E_{ft,eq}/E\) ratio, while nylon cables are characterized by the highest \(E_{ft,eq}/E\) ratio, and that \(E_{ft,eq}/E\) ratio is bigger for steel cables than for carbon fiber cables.