Page 151 - Introduction to Naval Architecture

STRENGTH 137

NA as possible. However, the change in the lower of the two original
stresses must be watched. The general problem of adding material to a
cross section is discussed later.

Sections with two materials

Some ships' strength cross section is composed of two different
materials. Typically the hull may be steel and the superstructure
aluminium. Other materials used may be wood or reinforced plastic. In
such a case it is convenient to think in terms of an effective modulus in
one of the materials. Usually this would be in terms of steel.
The stress, o, in a beam at a point z from the NA is Ez/R, where R is
the radius of curvature. Provided transverse sections of the beam or
ship remain plane, this relationship will hold as the extension or strain
at, any given z will be the same. For equilibrium of the section, the net
force across it must be zero. Hence using subscripts s and a for steel and
aluminium:

The corresponding bending moment is:

where J E is the effective second moment of area.
The composite cross-section can therefore be considered made up of
material s, usually steel, if an effective area of material a is used in place
of the actual area. The effective area is the actual multiplied by the ratio
EZ/ES. For different steels the ratio is effectively unity, for aluminium
alloy/steel it is about | and for grp/steel it is about ^.