Ship Structures & Seakeeping

Keeping the hull in one piece and the ship comfortable at sea. Learn longitudinal strength (still-water and wave bending, hogging and sagging), hull girder section modulus and stresses, IACS rules, framing systems and structural members, local strength and buckling, fatigue and corrosion, materials and welding, ship motions in waves (six degrees of freedom), natural roll period, response amplitude operators, slamming and green water, roll stabilisation — with Python for hull girder stress and roll period.

A ship is a long hollow beam supported unevenly by waves: when a wave crest is amidships the ends droop (hogging); with crests at the ends the middle sags. The hull girder must resist these bending moments plus local loads from cargo, water pressure and slamming.

Seakeeping studies how the ship moves in waves — roll, pitch, heave — affecting safety, cargo, crew comfort and operability. Structural failures (e.g. breaking in two) and excessive motions have caused many losses.

An analogy

A ship in waves is like a plank bridging two moving supports: when the supports are at the ends it sags in the middle; when there's one support in the middle, the ends droop — the hull must be strong for both.

Longitudinal strength

Weight and buoyancy are distributed differently along the ship; the difference produces shear forces and bending moments. The hull girder (deck, bottom, side shell, longitudinal bulkheads) resists them like an I-beam: deck and bottom are the flanges. Loading computers check still-water values against class limits for every condition.

Structural arrangement

Hull components:

Seakeeping basics

Six degrees of freedom: surge, sway, heave (translations), roll, pitch, yaw (rotations). Motions depend on wave spectrum and ship response (RAOs). Roll is lightly damped and can resonate; pitch and heave cause slamming, green water and propeller racing. Operability criteria (vertical acceleration, roll angle) guide design and routing.

Fatigue, corrosion and stabilisation

Wave-induced stress cycles (~10⁸ over a lifetime) make fatigue critical at welded details; corrosion reduces thickness (coatings, anodes, thickness gauging at surveys). Direct strength analysis with FEM and spectral fatigue assessment support class approval. Roll reduction: bilge keels, anti-roll tanks, active fin stabilisers, gyro stabilisers. Weather routing avoids extreme seas.

Formulas

Worked example: Section modulus needed

Given: Total moment 2894 MN·m, allowable 175 MPa

Find: Z_min.

Answer: 16.5 m³ (ship has 28 m³ — OK)

Worked example: Wave length

Given: Wave period 10 s

Find: λ.

Answer: 156 m — similar to ship length: large bending

Worked example: Roll period

Given: B 30 m, GM 1.5 m, k = 0.4B

Find: T_φ.

Answer: 19.7 s

Hull girder stress and roll period

# Hull girder bending: still-water + wave bending moment vs section modulus
L, B, Cb = 180.0, 30.0, 0.80
C = 10.75 - ((300 - L) / 100) ** 1.5           # IACS wave coefficient (90 <= L <= 300)
Mw_hog = 0.19 * C * L**2 * B * Cb / 1000      # kN*m -> MN*m  (IACS UR S11)
Msw = 1500.0                                   # MN*m still-water hogging (loading manual)
Z = 28.0                                       # m3 deck section modulus
sigma = (Msw + Mw_hog) / Z                     # MPa (MN*m / m3)
print(f"wave coefficient C = {C:.2f}, wave hogging moment {Mw_hog:.0f} MN*m")
print(f"total {Msw + Mw_hog:.0f} MN*m -> deck stress {sigma:.0f} MPa (allowable ~175 MPa for mild steel)")
# Roll natural period: T = 2*k*B/sqrt(GM), k ~ 0.4
GM = 1.5
import math
T_roll = 2 * math.pi * 0.4 * B / math.sqrt(9.81 * GM)     # kxx ~ 0.4 B
print(f"natural roll period {T_roll:.1f} s")
# wave coefficient C = 9.44, wave hogging moment 1394 MN*m
# total 2894 MN*m -> deck stress 103 MPa (allowable ~175 MPa for mild steel)
# natural roll period 19.7 s

The wave bending moment is similar in size to the still-water moment, so loading sequences matter: a badly loaded bulk carrier can exceed its allowable moment even in port. A 20 s roll period is comfortable but beware parametric resonance when wave encounter period is half the roll period.

Common mistakes

Applications

Key takeaways

Going further