Chain cross-section

The input for this model element will generate an Axisymmetric cross-section representing the properties for a chain.

Inputs are

  • Nominal diameter

  • Steel grade

  • Construction type:

    • Studless

    • Stud link

1. Cross-section properties

  • Mass coefficient: \(m_{coeff}=m_{air}\)

  • Chain diameter in mm: d

  • Weight in air (dry mass): \(m_{air}=a d^2\) [kg/m] (DNV-OS-E302)

Coefficient in calculating chain mass in air a

Stud link chain

0.0219

Studless chain

0.02

External cross sectional area:

\[A_{ext}=\frac{1}{\rho_{sw}} m_{air} (1-r_{air}^{sub})\\ \rho_{sw}= 1025 kg/m^3\\ r^{sub}_{air}=\frac{m_{sub}}{m_{air}}=0.87\\\]

where \(r^{sub}_{air}\) is the ratio between submerged weight to weight in air (dry mass).

Reference: Vicinay Offshore Mooring Chain website

2. Stiffness properties

The axial stiffness is given as \(EA=c_{EA} \pi d^2\) [kN] (DNV-OS-E302)

where

cEA

Grade R3

Grade R4

Grade R5

Stud link chain

30.7

Studless chain

27 - 0.02d

27.25 - 0.0125d

30 - 0.0165d

3. Capacity properties

Tension capacity: \(MBL=c_{MBL} d^2(44 - 0.08d)\) [kN] (DNV-OS-E302)

where

Grade

R3

R3S

R4

R4S

R5

cMBL

0.0223

0.0249

0.0274

0.0304

0.0320

4. Hydrodynamic force coefficients

Load formulation is Morison

Input code: Non-dimensional coefficients

Quadratic drag coefficient with respect to d

\(C_{Qx}\)

\(C_{Qy}\)

Stud link chain

1.4

2.6

Studless chain

1.15

2.4

Added mass in tangential direction \(C_{Ax}=0.5\) (Bureau Veritas NR 493)

Added mass in normal direction \(C_{Ay}=1.0\) (Bureau Veritas NR 493)

Linear drag coefficient in tangential direction \(C_{Lx}=0.0\)

Linear drag coefficient in normal direction \(C_{Ly}=0.0\)

Note that drag coefficients are according to DNV-OS-E301 and \(C_{dt}^{chain}\) quadratic drag coefficient in tangential direction is divided by \(\pi\) when filling CQx field in RIFLEX Axisymmetric cross section (CQx = 1.15/pi = 0.3661) due to RIFLEX’s convention. See also Input Reference

The added mass coefficients given in NR493 are based on effective diameter (\(1.8*D_{nominal}\)) and they are updated in RIFLEX Axisymmetric cross section to be used together with the nominal diameter in the calculations.