Page 170 - Introduction to Naval Architecture

156 STRENGTH

Effective wave height
This probabilistic approach to strength is more realistic than the
standard calculation in which the ship is assumed balanced on a wave.
It would be interesting though, to see how the two might roughly
compare. This could be done by balancing the ship, represented by the
data in Figure 7.14, on waves of varying height to length ratio, the
length being equal to the ship length. The stresses so obtained can be
compared with those on the curve and an ordinate scale produced of
the effective wave height. That is, the wave height that would have to be
used in the standard calculation to produce that stress. Whilst it is
dangerous to generalize, the stress level corresponding to the standard
L/20 wave is usually high enough to give a very low probability that it
would be exceeded. This suggests that the standard calculation is
conservative.

Horizontal flexure and torsion
So far, attention has been focused on longitudinal bending of the ship's
girder in the vertical plane. Generally the forces which cause this
bending will also produce forces and moments causing the ship to bend
in the horizontal plane and to twist about a fore and aft axis. The
motions of rolling, yawing and swaying will introduce horizontal
accelerations but the last two are modes in which the ship is neutrally
stable. It is necessary therefore to carry out a detailed analysis of the
motions and derive the bending moments and torques acting on the
hull. Since these flexures will be occurring at the same time as the ship
experiences vertical bending, the stresses produced can be additive.
For instance the maximum vertical and horizontal stresses will be felt at
the upper deck edges. However, the two loadings are not necessarily in
phase and this must be taken into account in deriving the composite
stresses,
Fortunately the horizontal bending moment maxima are typically
only some 40 per cent of the vertical ones. Due to the different section
moduli for the two types of bending the horizontal stresses are only
about 35 per cent of the vertical values for typical ship forms. The
differing phase relationships means that superimposing the two only
increases the deck edge stresses by about 20 per cent over the vertical
bending stresses. These figures are quoted to give some idea of the
magnitude of the problem but should be regarded as very
approximate.
Horizontal flexure and torsion are assuming greater significance for
ships with large hatch openings such as in container ships. They are
also more significant in modern aircraft carriers. It is not possible to