Page 97 - Marine Structural Design

Chapter 4 Scantling ofship’s Hulls by Rules 73

the weight and buoyancy forces led to a moment that would have displaced the floating body
further from its original position, it would have been a case of negative stability, as shown in
Figure 4.2(b). Thus, when designing a ship, it is very important to ensure that the centers of
gravity and buoyancy are placed in a position that results in positive stability for the ship.

4.2.2 Strength
Another essential aspect of ship design is the strength of the ship. This refers to the ability of
the ship structure to withstand the loads imposed on it. One of the most important strength
parameters is the longitudinal strength of the ship, which is estimated by using the maximum
longitudinal stress that the hull may withstand. The shear stress is another relevant parameter.
The longitudinal strength of the ship’s hull is evaluated based on the bending moments and
shear forces acting on the ship. Considering a ship as a beam under distributed load, the shear
force at location X, V(X), may be expressed as

where b(x) and w(x) denote buoyancy force and weight at location x respectively. The bending
moment at location X, M(X) is the integral of the shear curve,

M(X) = fV(X)dX (4.2)
This is further illustrated in Figure 4.3 for a ship in still-water (e.g. in harbors). As may be
seen in Figure 4.3(a), an unloaded barge of constant cross-section and density, floating in
water would have an equally distributed weight and buoyancy force over the length of the
barge. This is represented by the weight and buoyancy curves, seen in Figure 4.3(b). If the
barge were loaded in the middle (Figure 4.3(c)), the weight distribution would change and the
resulting curve is shown in Figure 4.3(d). This difference between the weight and buoyancy
curves results in a bending moment distribution over the length of the ship. This bending
moment is known as the still water bending moment, M, , as seen for a loaded barge in Figure
4.3(e).
For a ship in waves, the bending moment is further separated into two terms:
M=M,+M, (4.3)
where M, and M, denotes still water and wave bending moment respectively. Figure 4.4
illustrates a ship in a wave equal to its own length. Figure 4.4(a) shows the stillwater condition
where the only bending moment acting on the ship is the still water bending moment. Figure
4.4(b) shows the condition when the wave hollow is amidships (i.e. in the middle of the ship).
This results in a larger buoyancy distribution near the ends of the ship and thus the ship
experiences a sagging condition. In a ‘sagging’ condition, the deck of the ship is in
compression while the bottom is in tension.
Figure 4.4(c) shows a wave crest amidships. In this case, the buoyancy force is more
pronounced in the amidships section than at the ends of the ship thus resulting in a hogging
condition. ‘Hogging’ means that the ship is arching up in the middle. Thus, the deck of the
ship will be in tension while the bottom will be in compression.