Page 164 - Introduction to Naval Architecture

150 STRENGTH

If the shear deflection over a short length, dx, is:

where C is the shear modulus.
The shear deflection can be obtained by integration.
If the ratio of the shear to bending deflections is r, r varies as the
square of the ship's depth to length ratio and would be typically
between 0.1 and 0.2.

DYNAMICS OF LONGITUDINAL STRENGTH

The concept of considering a ship balanced on the crest, or in the
trough, of a wave is clearly an artificial approach although one which
has served the naval architect well over many years. In reality the ship
in waves will be subject to constantly changing forces. Also the
accelerations of the motions will cause dynamic forces on the masses
comprising the ship and its contents. These factors must be taken into
account in a dynamic analysis of longitudinal strength.
In Chapter 6 the strip theory for calculating ship motions was outlined
briefly. The ship is divided into a number of transverse sections, or
strips, and the wave, buoyancy and inertia forces acting on each section
are assessed allowing for added mass and damping. From the equations
so derived the motions of the ship, as a rigid body, can be determined.
The same process can be extended to deduce the bending moments
and shear forces acting on the ship at any point along its length. This
provides the basis for modern treatments of longitudinal strength.
As with the motions, the bending moments and shear forces in an
irregular sea can be regarded as the sum of the bending moments and
shear forces due to each of the regular components making up that
irregular sea. The bending moments and shear forces can be
represented by response amplitude operators and energy spectra derived in
ways analogous to those used for the motion responses. From these the
root mean square, and other statistical properties, of the bending
moments and shear forces can be obtained. By assessing the various sea
conditions the ship is likely to meet on a voyage, or over its lifetime, the
history of its loading can be deduced.
The response amplitude operators (RAOs) can be obtained from
experiment as well as by theory. Usually in model tests a segmented
model is run in waves and the bending moments and shear forces are
derived from measurements taken on balances joining the sections.
Except in extreme conditions the forces acting on the model in regular