How do naval architects calculate shear forces and bending moments along a ship’s hull?

To calculate shear forces and bending moments along a ship’s hull, naval architects traditionally treat the hull as a beam supported by a quasi-steady wave. The calculation process involves the following steps:1

• Load Distribution: The hull is divided into 20 segments along its length. Within each segment, the weights and buoyant forces are tabulated. The difference between the sum of the weights and the sum of the buoyant forces in each segment is treated as a load applied uniformly over that segment.1
• Shear Curve: These segment loads are plotted as a function of position along the hull. Integrating this curve over the entire length of the ship produces the shear curve.1
• Bending Moment Curve: Integrating the shear curve over the length of the ship yields the bending moment curve, which typically reaches its maximum value near the mid-length of the vessel.1

While this quasi-static method was long favored, modern practice often involves finding a still-water bending moment and adding a wave-bending moment derived from empirical formulas based on the ship's size and proportions. For more complex dynamic analysis, architects may use model testing or computational methods to predict probability distributions of bending moments across various sea states.12