Chain: Mechanical properties

Catalogue data

When modelling mooring chain, the line type wizard aims to derive data for a line type whose characteristics are equivalent to that of a chain.

Warning: The values generated by the wizard are approximate, and are intended as first estimates for preliminary use. They are offered in good faith, but due to variations in properties between products they cannot be guaranteed. We recommend that you use suppliers' data where this is available.

In deriving these data, some of the available catalogue data will prove useful and we outline here the relevant aspects. The mooring chain figure shows the geometry of a pair of chain links. The values are given in terms of the nominal bar diameter $d$ of the chain, assumed to be in metres, for both a studless chain and, where different, for a studlink chain. This geometry is based on catalogue data from the chain manufacturer Scana Ramnas (1990 & 1995), as is the following expression for chain mass per metre length, $m$ \begin{equation} m = \begin{cases} 19.9 d^2 \text{ te/m} & \text{(studless)}\\ 21.9 d^2 \text{ te/m} & \text{(studlink)} \end{cases} \end{equation} The same catalogue gives the following value for the Young's modulus of the chain, deduced from stress-strain relationships in which the cross sectional area of two bars is taken to be the load bearing area \begin{equation} E = \begin{cases} 5.44{\times}10^7 \text{ kN/m$^2$} & \text{(studless)}\\ 6.40{\times}10^7 \text{ kN/m$^2$} & \text{(studlink)} \end{cases} \end{equation}

Minimum breaking loads

The properties window displays, for your information, minimum breaking loads. These depend on the nominal diameter and chain grade, and are derived using the following relationship (obtained from the manufacturer's catalogue) \begin{equation} \text{min breaking load} = c\, d^2 (44-80d) \text{ kN} \end{equation} where $c$ is a grade-dependent constant, given in the catalogue as grade 2: 1.37e4, grade 3: 1.96e4, ORQ: 2.11e4, R4 - 2.74e4.

Studless and studlink chains with the same nominal diameters are stated to withstand the same break- and proof-loads.

Derived data

It will be useful to know the centreline length of bar needed to make a single link. We can obtain this by noting that, for a long chain, there is one chain link every $4d$ metres length of chain. Hence, the number of links per metre of chain is $n = 1/(4d)$, and thus for a single link \begin{equation} \text{mass per link} = \frac{m}{n} = \begin{cases} 79.6 d^3 \text{ te} & \text{(studless)} \\ 87.6 d^3 \text{ te} & \text{(studlink)} \end{cases} \end{equation} Assuming that the chain is made from steel, and using $\rho_\textrm{s}$ as the density of steel (= 7.8 te/m$^3$), we obtain the volume per link, $v$ \begin{equation} \label{v_mass} v = \frac{m}{n}\frac{1}{\rho_\textrm{s}} = \begin{cases} 10.2 d^3 \text{ m$^3$} & \text{(studless)} \\ 11.2 d^3 \text{ m$^3$} & \text{(studlink)} \end{cases} \end{equation} But, by considering the geometry of a link, we also have \begin{equation} \label{v_geom} v = l\, \pi d^2/4 \end{equation} where $l$ is the centreline length of bar needed to make a single link (including the stud in the case of the studlink chain).

Hence, from equations (\ref{v_mass}) and (\ref{v_geom}) \begin{equation} l = \begin{cases} 13.0 d \text{ m} & \text{(studless)} \\ 14.3 d \text{ m} & \text{(studlink)} \end{cases} \end{equation}