The primary strength, loads, and bending of a ship's hull are the loads that affect the whole hull, viewed from front to back and top to bottom. Though this could be considered to include overall transverse loads (from side to side within the ship), generally it is applied to longitudinal loads (from end to end) only. The hull, viewed as a single beam, can bend
down in the center, known as sagging
up in the center, known as hogging.
This can be due to:
hull, machinery, and cargo loads
wave loads, with the worst cases of:
sagging, due to a wave with length equal to the ship's length, and peaks at the bow and stern and a trough amidships
hogging, due to a wave with length equal to the ship's length, and a peak amidships (right at the middle of the length)
Primary hull bending loads are generally highest near the middle of the ship, and usually very minor past halfway to the bow or stern.
Primary strength calculations generally consider the midships cross section of the ship. These calculations treat the whole ships structure as a single beam, using the simplified Euler-Bernoulli beam equation to calculate the strength of the beam in longitudinal bending. The moment of inertia (technically, second moment of area) of the hull section is calculated by finding the neutral or central axis of the beam and then totaling up the quantity