Page 152 - Introduction to Naval Architecture

138 STRENGTH

Changes to section modulus
It is often desirable to change the section modulus in the early design
stages. The effect of changes is not always immediately obvious.
Consider the addition of an element of structure above the neutral axis,
but below the upper deck, as in Figure 7.9, Assume the element is of
area a and that the original section had area A, and radius of gyration
k. With the addition of a the NA is raised by az/(A + a) = dz.

Figure 7.9 Changing section modulus

The new second moment of inertia is:

For a given bending moment, the stesses will not increase if the section
modulus is not reduced. This condition is that:

As depicted <5/is positive and dz/z% is negative so dl/Iis always greater
than dz/z at the deck provided the material is added within the section.
At the keel the condition becomes:

Thus to achieve a reduction in keel stress the material must be added
at a height greater than t?/z\ from the neutral axis.