Page 163 - Introduction to Naval Architecture
P. 163
STRENGTH 149
Hull deflection
Consider first the deflection caused by the bending of the hull. From
beam, theory:
where R is the radius of curvature.
If y is the deflection of the ship at any point x along the length,
measured from a line joining the two ends of the hull, it can be shown
that:
For the ship only relatively small deflections are involved and (dy/dx) 2
will be small and can be ignored in this expression. Thus:
The deflection can be written as:
In practice the designer calculates the value of / at various positions
along the length and evaluates the double integral by approximate
integration methods.
Since the deflection is, by definition, zero at both ends B must be
zero. Then:
The shear deflection is more difficult to calculate. An approximation
can be obtained by assuming the shear stress uniformly distributed over
the 'web' of the section. If, then, the area of the web is A^ then:
