Page 102 - Marine Structural Design

78 Part I Structural Design Principles

up is the nominal permissible bending stress and it may be taken as 17.5 Mv/cm2. The
second equation calculates the minimum required section modulus. The constant C,, depends
on the length, and the block coefficient, C, .

If the top or the bottom flange, or both, consist of higher-strength material, the section
modulus calculated above may be reduced by a factor Q, according to the following equation:
SM,, = Q SM (4.8)
Q depends on the yield strength and is 0.78 for grade H32 or 0.72 for grade H36 material.
In classification rules, equations and charts are available for calculating still-water bending
moment, wave bending moment amidships and wave shear force as well as distribution factor
for wave bending moment.
Shear Stress
The distribution of the shear force on the sides and on the bulkheads is very complicated, and
hence the required thickness is not easily expressed with a simple formula. Each classification
society has its own empirically based formulae for shear force and its distribution along the
longitudinal direction.
The general equation for the net thickness is:

(4.9)

where F, is the still-water shear force and F, is the vertical wave shear force, which is zero
for in-port conditions.
The net thickness of the side shell plating is given by
(4.10)

and the thickness of the longitudinal bulkhead is given by:
(F, + R,)*Di *S
ti 2 (4.1 1)
I-0,
In these equations, I, is the moment of inertia of the net hull girder section at the position
considered. S, is the first moment of the net hull girder section about the neutral axis of the
area between the vertical level at which the shear stress is being determined and the vertical
extremity of the section, which is being considered. As mentioned above, 0, is the
permissible shear stress, which is defined for either sea or in-port conditions. It is equal to
14.96 divided by Q for sea conditions and 10.87 divided by Q for in-port conditions. Q is the
material conversion factor and depends consequently on the material. D is the shear
distribution factor, which depends on the design of the longitudinal bulkheads.