(II-7-27)

(d) A mooring system is composed of many lines, but only those in tension contribute to the stiffness

or effective spring constant ktot given by

(II-7-28)

where the index *n *sums over all head, stern, and spring lines in tension during surge motion (breast lines are

conservatively assumed to provide no restoring force in surge), θn is the angle the line makes in the horizontal

plane with the perpendicular to the ship, and φn is the angle the line makes in the vertical plane between the

ship and the dock.

(e) For a taut mooring line in which sag is negligible and deflections are small, the individual stiffness

(II-7-29)

where *T*n is the axial tension or load and ∆*l*n is the elongation in the mooring line. The elastic behavior of

fiber ropes is difficult to ascertain since it is a function of material, construction, size, load and load history,

time, and environmental conditions. Typically, manufacturers supply elongation curves based on

experimental data, which show percent elongation gn as a function of load as a percent of the breaking

strength of the mooring line (Figure II-7-45). A new rope undergoes construction stretch or permanent strain,

which occurs when initial loading places the fibers in paths different from their initial construction. Elastic

stretch occurs for subsequent loading and is repeatable each time the rope is loaded. Under high loads for

a long time, the rope may undergo cold flow of the fibers and eventually break. Thus, previously elongated

rope does not stretch as much as new rope and separate elongation curves may be provided. Percent

elongation is related to *∆l*n by

∆*l*n

gn ' 100

(II-7-30)

where *l*n is the length of the mooring line. This formulation assumes that cable dynamics can be neglected,

and that the natural frequency of the mooring line in longitudinal and transverse vibration is much higher than

the surge frequency of the ship.

(f) Therefore, the natural period of a moored ship in surge is a function of displacement, and number,

type, length, size, and tension of the mooring lines. As the ship is off-loaded, displacement of the ship will

decrease and this will change the ship response characteristics. Proper ballasting can be used to prevent surge

conditions from developing. If this is not possible, other remedies can be sought. The natural period of the

moored ship can be adjusted by changing the mooring line configuration or tension. Increased tension will

make the moored ship stiffer and will reduce its resonant period of oscillation. A decrease in the mooring

line tension will make the moored ship less prone to shorter-period resonant modes. If this is not practical,

the number and type of mooring lines can be changed to affect the response of the moored ship.

II-7-66

Harbor Hydrodynamics

Integrated Publishing, Inc. |