Page 53 - Marine Structural Design

30 Part I Structural Design Principles

V = Hull girder deflection
mS = Ship mass per unit length
r = Radius of gyration of the sectional mass m, in rotation about a horizontal
transverse axis through the section’s center of mass
The theories and equations described in this Section are used to calculate the wave induced
bending moment. This bending moment along with the stillwater bending moment, can help
determine the longitudinal strength of the ship, which is applied during the scantling design of
the ship. It would be useful to refer to Chapter 4 to obtain a description of bending moments
and scantling design.
For stress analysis of ships (e.g. container ships), reference is made to Pedersen (1983)
2.3.4 Slamming and Green Water on Deck
So far only loads occurring at wave encounter frequency have been discussed. However,
waves can also cause loads at much higher frequencies due to impacts between the ship’s hull
and the water surface, such as slamming and green water on deck. Slamming occurs when the
forward part of the ship hits the water surface after a bow emergence. If the slam takes place
with a relatively high velocity, there is a probability of damaging the ship, because a high
impulsive load is created in the ship’s bow structure. Green water on deck takes place when
the deck becomes submerged under water. The water on the deck may cause structural damage
to the deckhouse of the ship and to the deck facility and cargo. Both slamming and green
water on deck are to be avoided as much as possible during a ship’s lifetime due to the damage
they may cause. The ship’s speed is usually reduced or the heading is changed if such an
action reduces the probability of slamming or green water on deck.
Both slamming and green water on deck loads are fbnctions of the relative motion of the ship
with respect to the sea. Two conditions need to be satisfied for slamming to occur at any
section of the ship. First, the relative vertical motion, r)(x,t) should be larger than the draught
at the section being considered. Also, the relative velocity, Dr)/Dt, must be larger than the
threshold velocity v,.
(2.28)

In a stationary stochastic seaway both 17 and qT are normally distributed parameters with zero
mean values. Thus, it is possible to determine the likelihood of slamming on the ship through
the statistical probability of the occurrence of r) and qr . The resultant load can then be
calculated and used in the ship design. The sectional force, qSL(x,t) associated with a slam,
has been found to be approximately proportional to the square of the relative velocityq, .
(.,
qsL 4 = av: (2.29)
Eq. (2.29) may be included in Eq. (2.23), to account for all the wave loads experienced by a
ship in a global wave load analysis. Eq. (2.29) is useful to describe what is known as bow flare
slamming, that occurs when the bow flare of a ship hits the sea surface. Another type of
slamming is bottom slamming where the flat bottom of a ship hits the water. This type of
slamming cannot be described by Eq. (2.29), because bottom slamming is not directly related
to the relative vertical motion and velocity of the ship, which are the two starting points of the