Radius of Curvature Equation

Here is the relationship of the radius of curvature:

M/I= σ/y = E/R

Where,

M = bending moment;

       I = second moment of inertia;

       σ =  stress;

       y = distance from neutral axis;

       E = modulus of elasticity;

       R = radius of curvature.

Design Basics (Rule of Thumb)

1) Water Depth VS its Hydrostatic Pressure:

• P=ρgh
  Rule of thumb: 100 m water depth = 10 barg = 1 MPa

2) Barg vs Bara:

• barg means bar gauge - it is gauge pressure referenced above atmospheric pressure;
• bara means bar absolute - it is absolute pressure which includes atmospheric pressure.
Hence, bara = barg + atmospheric pressure (Atm);
Where, standard atmospheric pressure is 1.01325 Bara.

3) Laybarge / Vessel Motions

It is defined by six degrees of freedom.

Translation:

• Surge - linear axial motion (front/back);
• Sway - linear lateral motion (left/right);
• Heave - linear vertical motion (up/down);

Rotation:

• Roll - rotation of vessel about its axial axis;
• Pitch - rotation of vessel about its lateral (transverse) axis;
• Yaw -rotation of vessel about its vertical axis

References:

• http://en.wikipedia.org/wiki/Ship_motions
• http://gamedev.stackexchange.com/questions/6502/water-ocean-simulation-and-physics