ANNEX L SPECIAL DESIGN PROVISIONS FOR SHIP SHAPED UNITS
L.5.3 Calculation of wave induced actions
According to Recognised Classification Society Rules, normal trading ships are designed according to the following environmental criteria:
• North Atlantic wave condition, 20 year return period
• Short crested sea
• Same probability for all wave directions relative to the ship
Specific requirements for weather vaning units covered by this Annex are given below.
L.5.3.1 General
Global linear wave induced actions such as bending moments and shear forces should be calculated by using either strip theory or three dimensional sink source (diffraction) formulation. Strip theory is a slender body theory and is not recommend when the length over beam ratio is less than 3.
Generally, the most importance global responses are midship vertical bending moments and vertical shear forces in the fore and aft body of the unit and the associated vertical bending moments. These responses should be calculated for head sea conditions. Horizontal and torsional moments may be of interest depending on the structural design, alone and in combination with other action
components.
The calculation of wave induced actions may follow the following steps:
• Calculation of the relevant transfer functions (RAOs)
• Calculation of the 100 year linear response
• Evaluation of non-linear effects
When a 3-D diffraction program is used, the hydrodynamic model shall consist of sufficient number of facets. In general, the facets should be sufficiently modelled to describe the unit in a propitiate way. The size of the facets shall be determined with due consideration to the shortest wave length included in the hydrodynamic analysis. Smaller facets should be used in way of the water surface.
The mass model shall be made sufficiently detailed to give centre of gravity, roll radius of inertia and mass distribution as correct as practically possible.
L.5.3.2 Transfer functions
The following wave induced linear responses should be calculated:
• Motions in six degrees of freedom.
• Vertical bending moment at a sufficient number of positions along the hull. The positions have to include the areas where the maximum vertical bending moment and shear force occur and at the turret position. The vertical wave induced bending moment shall be calculated with respect to the section’s neutral axis.
• Horizontal and torsional moment if applicable.
The linear transfer functions shall be calculated by either strip or 3D sink –source (diffraction) theory. The responses shall be calculated for a sufficient number of wave periods in the range from 4 – 35 seconds. For short crested sea at least seven directions in a sector ± 90º relative to head sea, with maximum 30º interval, should be considered.
L.5.3.3 Viscous damping
If roll resonance occurs within the range of wave periods likely to be encountered, the effect of non-linear viscous roll damping should be taken into account. The damping coefficients that are derived within linear potential theory reflect the energy loss in the system due to generation of surface waves from the ship motions. However, in the case of roll motion some special treatment is necessary.
Viscous effects, such as the production of eddies around the hull, will mainly act as a damping mechanism, especially at large roll angles, and these effects should be included. Furthermore, the effects from roll damping devices, like bilge keels, should be evaluated. The roll damping shall be
Annex L Rev. 1, December 1998 evaluated for the return period in question. The sea state in question may be considered when the damping is calculated.
L.5.3.4 Extreme wave induced responses
Extreme wave induced responses shall be long term responses. The standard method for calculation of the 100-year wave induced long term responses (e.g. vertical moment and shear force) shall use a scatter diagram in combination with a wave spectrum (e.g. Jonswap) and RAOs.Short term
predictions of the responses are to be calculated for all significant wave heights (Hs) and peak (Tp) or zero up-crossing (Tz) periods combinations within the scatter diagram. A Weibull distribution is fitted to the resulting range of the responses against probability of occurrence. This Weibull
distribution is used to determine the response with a probability of occurrence corresponding to once every 100 years (100 year return period).
The short crested nature of the sea may be taken into account as a wave spreading function as given in NORSOK N-003.
The method described above is considered most accurate for estimating the 100-year value for the response in question. A short-term analysis based on the predicted 100-year wave height with corresponding Tz, will give comparable values if the following criteria are satisfied:
• The scatter diagram should be well developed with wave steepness approaching a constant value for the most extreme sea states
• The maximum wave induced response shall occur in a short term sea sate which is retraceable from the scatter diagram with a 100 year wave height steepness
• The Weibull fit to predict the response shall be good fit with low residual sum (deviations from the regressed line)
It should be noted that the method of calculating the 100-year wave induced response for a short- term sea state based upon the predicted 100 year wave height with corresponding single value Tz or Tp does not recognise that there are a range of possible Tz.(Tp). Therefore the range of possible Tz
(Tp) within the 100-year return period should be investigated. The range of sea states with a 100 year return period should be found by developing a 100 year contour line from the scatter diagram.
The wave bending moment should be calculated for several sea states on this contour line in order to find the maximum value.
L.5.3.5 Non-linear effects
Linear calculations as described above do not differentiate between sagging and hogging responses.
The non-linearities shall be taken into account for the vertical bending moments and shear forces.
The non-linear effects come from integration of the wave pressure over the instantaneous position of the hull relative to the waves, with the inclusion of bottom slamming, bow flare forces and deck wetness. These effects generally result in a reduction in hogging response and an increase in the sagging response (midship moment and shear fore in the fore body) compared with the linear response.