ship-structures

name	ship-structures
description	Ship structures — longitudinal strength (hull girder bending), section modulus, wave bending moment, local strength, classification society rules (DNV, ABS, LR), fatigue, corrosion allowance.
metadata	{"priority":7,"promptSignals":{"phrases":["ship structure","hull girder","wave bending moment","section modulus ship","longitudinal strength","DNV ship","ABS classification"],"minScore":3}}

Ship Structures — Complete Skill

Hull Girder Concept

Ship hull acts as a beam subjected to wave-induced bending moments Hogging: wave crest amidships → hull hogged → deck in tension, keel in compression Sagging: wave trough amidships → hull sagged → deck in compression, keel in tension

Wave Bending Moment

IACS/ClassNK simplified formula: M_sw = ±C₁ L² B (C_b + 0.7) × 10⁻³ [kN·m]

L = ship length [m]; B = beam [m]; C_b = block coefficient C₁ = wave bending factor from IACS

Rule design moment: M_total = M_still_water + M_wave M_still_water: from loading manual (varies with cargo distribution) M_wave: from class rules

Required Section Modulus

Minimum section modulus (IACS UR S7): Z_min = M_design / σ_allow [cm³]

σ_allow: typically 175–235 MPa (depending on class and yield strength)

Actual section modulus: Z = I_NA / y_max I_NA = second moment of area about neutral axis y_max = distance from NA to extreme fiber (deck or keel)

Section modulus calculation (Simpson's rule or direct): Z = (Σ A_i y_i²) / y_max for longitudinal elements (deck, bottom, side shell, longitudinals)

Structural Scantlings (Classification Rules)

Plate thickness (local strength — lateral pressure): t = c × s × √(P / σ_all) + t_corr

s = plate spacing [m]; P = design lateral pressure [kPa]; c = coefficient (boundary conditions) t_corr = corrosion allowance: 1.5–3.5 mm (one side); 3.0–5.0 mm (both sides, tanks)

Frame and longitudinal section modulus: Z_frame = M_frame × s_f / σ_all (from lateral pressure bending)

Structural Systems

Transverse framing: frames cross the beam; longitudinals run fore-aft Simpler construction; less longitudinal strength; used in bulkers/tankers historically

Longitudinal framing: longitudinals run fore-aft; transverse web frames at intervals Better longitudinal strength for large ships; preferred for VLCCs, large bulkers

Double hull: inner and outer bottom/side → contains spills (MARPOL); structural redundancy

Structural Members

Tank top / main deck: thick (typically 13–20 mm for VLCCs) Shell plating: 12–22 mm for hull; varies with local pressure Longitudinals: T-bar or bulb flat; spaced 600–900 mm Web frames: intercostal plates + face plate; every 3–5 frame spacings Floors: solid plate floors at double bottom intersections

Buckling Check

Longitudinal plates (column buckling): Critical compressive stress: σ_cr = k × π² E / (12(1-ν²)) × (t/s)² Must satisfy: σ_applied < σ_cr / safety factor

IACS and class rules define minimum plate requirements to avoid buckling

Fatigue in Ships (IACS/DNV)

Critical locations: Hatch corners, longitudinal connections to web frames, hold frames (ore/bulk) Hot spots at bracket toes, weld terminations

IACS UR S11 / DNV-RP-C203: S-N curve based on structural detail (FAT class) Long-term stress spectrum from North Atlantic scatter diagram Miner's D ≤ 1.0 (cumulative damage criterion)

Hatch corner fatigue: Stress concentration K_t = 3–5 at sharp corners → elliptical or circular cutout reduces K_t

Corrosion and Protection

Corrosion allowance: added to structural thickness (above rule minimum) Typically: 0.5 mm/side (coated tanks); 1.5–2.5 mm/side (uncoated bilge)

Cathodic protection: Sacrificial anodes (zinc or aluminum) in ballast tanks and sea chests SACP (sacrificial anode cathodic protection) design: I_required = i_d × A_submerged (i_d ≈ 5–20 mA/m² depending on coating efficiency)

Coatings: IMO PSPC (Performance Standard for Protective Coatings): epoxy coating in ballast tanks Minimum DFT: 320 μm total; 2-coat system; inspection during application

Output

Provide: M_design [kN·m], Z_required [cm³], Z_actual [cm³], plate thickness [mm] (deck/keel/shell), section modulus adequacy (%), corrosion allowance [mm], fatigue damage D at critical detail, CP anode mass [kg].