1. CRS5 - Partly submerged general shaped cross section

This cross section is used for floating structural members. It can only be used for elements with local z-axis approximately parallel the global z-axis pointing in the same direction. The roll and pitch angles are restricted to 30\(\mathrm {^{\circ}}\) as a practical upper limit. The stiffness properties are based on two symmetry planes, while area and hydrodynamic force coefficients are calculated based on the cross section description represented by offset points symmetric with regard to the vertical (z) axis. For hydrodynamic load computation the element is divided into subelements specified in data section Segment specification. NSEG input lines. The cross section can only be used when consistent formulation is applied (see STAMOD: External, static loads) and for nonlinear dynamic analysis with regular waves.

1.1. Data group identifier

NEW COMPonent CRS5

1.2. Component type identifier

Identical to Component type identifier for CRS2.

1.3. Mass and volume

Identical to Mass and volume.

1.4. Stiffness properties classification

Identical to Stiffness properties classification for CRS2

1.5. Axial stiffness. Case 1, IEA=1

Identical to Axial stiffness. Case 1

1.6. Axial stiffness. Case 2, IEA=N

Identical to Axial stiffness. Case 2

1.7. Bending stiffness. Case 1, IEJ=1 IPRESS=0

Identical to Bending stiffness. Case 1

1.8. Bending stiffness. Case 2, IEJ=1 IPRESS=1 (not implemented)

Identical to Bending stiffness. Case 2

1.9. Bending stiffness description. Case 3 IEJ=N IPRESS=0

Identical to Bending stiffness description. Case 3 IEJ=N IPRESS=0 for CRS2

1.10. Bending stiffness. Case 4 IEJ=N1, IPRESS=N2 (not implemented)

Identical to Bending stiffness. Case 4 IEJ=N1

1.11. Damping specification

Identical to Damping specification for CRS2

1.12. Hydrodynamic force coefficients

CDX CDY CDZ CDTMOM AMX

  • CDX: real: Drag force coefficient per length, tangential \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDY: real: Drag force coefficient per length, local y-axis \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDZ: real: Drag force coefficient per length, local z-axis \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDTMOM: real: Drag coefficient around local x-axis

    • Dummy in present version.

  • AMX: real: Added mass per length, tangential \(\mathrm {[M/L]}\)

All hydrodynamic force coefficients applies to fully submerged cross section. That is, the actual coefficients are proportional to submerged volume. The drag force coefficients are to be scaled according to consistent units used, see Unit names and gravitational constant.

The tangential drag force which is a friction force acting along the local x-direction is calculated according to:

  • \(\mathrm {F_t=CDX\times (A_{sub}/A_{tot})\times V_{x,rel}\times |V_{x,rel}|}\)

The viscous normal force per unit length is calculated using the drag force term in Morison’s equation and assuming the drag force direction is parallel the instantaneous relative velocity transverse component:

  • \(\mathrm {F_y=CDY\times (A_{sub}/A_{tot})\times \sqrt{V^2_{y,rel}\times V^2_{z,rel}}\times V_{y,rel}}\)

  • \(\mathrm {F_z=CDZ\times (A_{sub}/A_{tot})\times \sqrt{V^2_{y,rel}\times V^2_{z,rel}}\times V_{z,rel}}\)

where: * \(\mathrm {A_{sub}}\): is instantaneous cross section submergence * \(\mathrm {A_{tot}}\): is total external areal of the cross section * \(\mathrm {V_{x,rel}}\): is relative water velocity in local x-direction * \(\mathrm {V_{y,rel}}\): is relative water velocity in local y-direction * \(\mathrm {V_{z,rel}}\): is relative water velocity in local z-direction

1.13. Description of cross section shape

NOB NSUB NROLL NDFS

  • NOB: integer: Number of offset points to describe the cross section shape.

    • Only one half of the shape is described due to assumed symmetry about local z-axis.

    • 3 <= NOB <= 20

  • NSUB: integer, default: 20: Number of points of submergence in table of submerged volume as function of submergence and roll angle.

  • NROLL: integer, default: 20: Number of roll angles in table of submerged volume as function of submergence and roll angle.

  • NDFS: integer, default: 20: Number of points of submergence in table of added mass and poten- tial damping as function of submergence.

The submerged cross section area is calculated for a number of submergence positions and relative roll angles in the range (0 - \(\mathrm {\pi }\)/2). The instantaneous submerged area is found by linear interpola- tion for points lying between those given in the table.

Tables of two-dimensional added mass and potential damping as function of submergence are calculated using the Frank.closefit technique. The instantaneous added mass and damping are found by linear interpolation for points lying between those given in the tables.

1.14. Offset points

INB YB ZB

  • INB: integer: Offset point number

  • YB: real: Local y-coordinate for offset point INB

  • ZB: real: Local z-coordinate for offset point INB

Only one half of the cross section shape is modelled due to the assumed symmetry about local z-axis.

The offset points must be given in increasing order with decreasing value of the z-coordinate. YB and ZB are referred to the principal local axis. YB >= 0 and first and last value of YB has to be zero, see the figure below.

um ii fig126
Figure 1. Example of modelling cross sectional shapes of frame elements

1.15. Capacity parameter

Identical to Capacity parameter for CRS2