27. Chain properties

The identification tag for this tutorial is PDS-AAR. Pregenerated input files for this tutorial are found in the folder named PDS-AAR in the provided tutorial input files.

27.1. Tutorial overview

This tutorial covers:

  • Determining DCableSegment feature properties for chain

27.2. Chain

Note

  • Chain is often used in subsea moorings and a variety of marine applications. Several chain manufacturers provide properties for their chain specifications online (found here) that can be used to set cable properties in the DCable segment in ProteusDS.
  • The following tutorial reviews how to set DCableSegment feature properties for a 30 mm diameter R3 studless chain. The properties of for the chain are given in Fig. 27.1.
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Fig. 27.1 Chain properties.

27.3. Diameter and density

Note

  • The characteristic diameter used in ProteusDS is different from the nominal diameter reported by the manufacturer. Nominal diameter referred to by the manufacturer is the diameter of the bar used to make the chain. This can be seen in Fig. 27.2.
  • The characteristic diameter $Diameter used in ProteusDS can be calculated using an equation from the ProteusDS User Manual:

\(d = \sqrt {\frac{4 M_l}{\rho_{cm} \pi}}\)

where \(M_l\) is the mass per unit length in air and \(\rho_{cm}\) is the material density.

  • The mass per unit length in air is given as 18.18 kg/m and the material is steel, therefore a material density of 7800 kg/m3 will be used.
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Fig. 27.2 Nominal diameter of studless chain.

  • The characteristic diameter $Diameter is calculated to be 5.448E-2 m.

Note

  • The $Density property is the material density when used for chain. For this steel chain, the $Density property is set to 7800 kg/m3.

27.4. Mechanical properties

Note

  • The axial stiffness of chain is the product of the elastic modulus and the cross sectional area of the chain.
  • Elastic modulus, \(E\), is required to calculate the axial stiffness. For R3 studless chain, the following equation from the ProteusDS User Manual can be used, where \(d_c\) is the nominal chain diameter in mm as specified by the manufacturer:
\(E = (5.40-0.0040 * d_c) * 10^{10} N/m^2\)
  • Using the table, \(E\) for the R3 studless chain can be determined to be 5.28e10 N/m2.

Note

\(A = 2 \pi d_c^2 / 4\)
  • The area of the chain is calculated to be 1.414e-3 m2.
  • The axial stiffness $EA property is the product of the elastic modulus and the area, therefore the $EA value is set to 7.464e7 N.

Note

  • The flexural stiffness $EI and torsional stiffness $GJ are negligible in chain and can be assumed to be zero.
  • Chain has low effective compressive elasticity, therefore the compressive elasticity property $CE may be assumed to be 0 or very low.

27.5. Drag and added mass properties

Note

  • The added mass coefficient $CAc for most chains can be 1.0, represented as long cylinders.
  • The drag coefficient for studless chain is specified in the ProteusDS User Manual as between 2.0 - 2.4 (based on DNV recommendations). In this situation 2.2 will be chosen.
  • The diameter of chain to be used in drag calculations is specified by the $FluidDiameter, which should be set to the nominal diameter of the chain, \(d_c\), as recommended drag properties for chains are based on nominal chain diameter.
  • If either of the optional parameters $FluidDiameter or $BuoyancyDiameter are not specified, the ProteusDS solver uses the value specified by $Diameter for drag and buoyancy calculations respectively.
  • For chain, set the $FluidDiameter property to the chain bar size, in this case: 30 mm (3.0e-2 m).
  • Set the $CAc property to 1.0.
  • Set the $CDc property to 2.2 (based on DNV recommendations).
  • The tangential drag coefficient $CDt is set at 1.15 (based on DNV recommendations).

27.6. All properties

Note

  • The Cable Properties Wizard can also be used to calculate the chain properties. The Cable Properties Wizard can be found here.
  • Download the Cable Properties Wizard from the DSA website and run the executable.
  • Set the nominal diameter to 30 mm, mass per unit length in air to 18.18 kg/m and material density to 7800 kg/m3. Use R3 grade studless chain. The wizard will output the required cable properties for ProteusDS.
  • The DCableSegment feature properties for a 30 mm R3 studless chain may be set as:
// Axial Rigidity
$AxialRigidityMode 0
$EA 7.464E7

// Fluid loading
$CDc 2.2
$CDt 0.01
$CAc 1

// Mechanical
$EI1 0
$EI2 0
$GJ 0
$Diameter 0.545
$FluidDiameter 0.30
$Density 7800
$AxialDampingMode 1
$AxialReferenceDampingRatio 0.5
$BCID 0
$TCID 0
$CE 0

// Strain Limit
$ElongationLimitMode 0