488 DOCK ENGINEERING.
1. That the vessel is a rigid structure—i.e., there is no bending or
yielding in any part of the keel.
2. That the blocks are perfectly elastic—i.e., the amount of compression
is proportional to the load.
3. That the line of keel coincides with the line of blocks—i.e., there is
no initial stress due to a cambered keel.
The converse of all these postulates is equally likely to hold good in
practice.
Let A B = 1, represent the total length of a ship (fig. 480), and O R, the
vertical line through its centre of gravity, taken for simplicity through the
centre of the ship. Let W be the total weight.
If now the vessel be supported uniformly throughout its entire length,
the pressure diagram will be the rectangle A B C D, in which if A D = a,
and A B = Z, then al — W.
I
Secondly, suppose the vessel to have an overhang equivalent to one-fourth
of her length, so that the supported portion of her keel is K B = ^ Z. If
the load were distributed over the supported portion only, so that the
centre of pressure coincided with the middle point, Y, of that length, there
would be a uniform intensity, a„ determined by the considération,
a1 x ^ 1 = W. .... (134)
But this is not the case, for the centre of pressure is still at O, while
the centre of support is at Y, giving an
eccentricity O Y =
KJ
6
i.e.,
one-sixth of the supported length. Now, we have already determined in
connection with stresses in wall joints (Chap. v.) that when the eccen-
tricity of pressure is one-sixth of the length of the base, the intensity is
zero at the inner, or further, edge, and a maximum of twice the mean
uniform stress at the outer edge. Hence, if we draw K L = 2av and join