offshore-marine

name	offshore-marine
description	Offshore and marine engineering — Morison equation, wave loading, API RP 2A, DNVGL, cathodic protection offshore, structural steel, fatigue in offshore, jack-up, FPSO, mooring.
metadata	{"priority":7,"promptSignals":{"phrases":["offshore","marine","Morison","wave loading","API RP 2A","DNV","jacket","FPSO","mooring","subsea"],"minScore":3}}

Offshore & Marine Engineering — Complete Skill

Wave Theory

Regular Wave Parameters

Wave height: H = 2A (crest-to-trough) [m] Wave period: T [s]; Wave length: L [m] Angular frequency: ω = 2π/T [rad/s] Wave number: k = 2π/L [rad/m]

Dispersion relation (linear theory): ω² = gk × tanh(kd) d = water depth [m]; g = 9.81 m/s²

Deep water (d > L/2): ω² ≈ gk → L = gT²/(2π) ≈ 1.56T² [m] Shallow water (d < L/20): c = √(gd) (wave speed independent of period)

Particle Velocities (Airy Linear Theory)

Horizontal: u = (πH/T) × cosh(k(z+d))/sinh(kd) × cos(kx-ωt) Vertical: w = (πH/T) × sinh(k(z+d))/sinh(kd) × sin(kx-ωt) z = vertical coordinate (z=0 at still water level, z=-d at seabed)

Deep water simplification: u = (πH/T) × e^(kz) × cos(kx-ωt) Particle orbits are circular in deep water, elliptical in shallow water.

Significant Wave Height (Irregular Seas)

H_s = H_{1/3} = average of highest 1/3 waves H_max ≈ 1.8 H_s (expected max in 3-hour sea state) T_p = peak spectral period (≈ 1.1-1.2 T_s for JONSWAP)

JONSWAP spectrum (North Sea): S(f) = αg²/(2π)⁴f⁵ × exp(-5/4 × (f_p/f)⁴) × γ^exp(...) γ = peak enhancement factor (1-7, typically 3.3 for North Sea)

Morison Equation

Inline Force on Cylinder

F/unit length = C_M × ρ × (πD²/4) × u̇ + C_D × ρ/2 × D × u|u| u = horizontal particle velocity [m/s] u̇ = horizontal particle acceleration [m/s²] D = cylinder diameter [m]

Coefficients (API RP 2A, smooth cylinders): C_D = 0.65 (smooth cylinder, supercritical Re > 5×10⁵) C_M = 1.6 (smooth cylinder, Keulegan-Carpenter KC < 5) C_D = 1.0, C_M = 2.0 (subcritical Re, conservative)

Keulegan-Carpenter number: KC = u_max × T / D KC < 5: inertia dominated (C_M governs) KC > 20: drag dominated (C_D governs) 5 < KC < 20: both significant

Marine growth: adds diameter (10-200mm) → increases C_D, C_M Clean = C_D=0.65; with marine growth = C_D=1.0-1.2

Total Wave Force on Structure

F_total = Σ Morison force over all members (numerical integration from seabed to surface) Include: kinematics up to actual surface (Wheeler stretching or full nonlinear)

API RP 2A — Fixed Platform Design

Environmental Loading (API RP 2A WSD / LRFD)

100-year return period storm (design event) Wave + current + wind loads applied simultaneously

Current velocity: tidal + wind-driven + Gulf stream (varies by location) Combined velocity: u_total = u_wave + u_current (vectorially)

Pile Foundation (API RP 2A Section 6)

Axial capacity: Q_total = Q_skin + Q_tip Q_skin = Σ f_i × A_i (unit skin friction × pile surface area per layer) Q_tip = q × A_p (unit end bearing × pile area)

For sands (API): f = K × p_o × tan(δ) [limit values per soil type] For clays: f = α × c_u (α = 0.5 typical; reduction for high c_u)

Lateral capacity (pile-soil p-y curves): API p-y curves for sand and clay; computed with LPILE/GROUP Minimum penetration: 2× water depth (rule of thumb)

Jacket Tubular Member Checks

Local capacity: D/t ≤ 60 for seismic/fatigue; D/t ≤ 80 general Hydrostatic collapse: p_y = 2E(t/D)³/(1-ν²) (elastic, D/t > critical) Combined axial+bending+hydrostatic: interaction equations per API RP 2A

Fatigue Design (API RP 2A Appendix K)

S-N curves: X (punching shear), X' (improved weld), T, K in tubular joints Miner's sum D ≤ 0.3 (critical) to 1.0 (accessible/inspectable) Hotspot stress range at weld toe; stress concentration factors (SCF): Efthymiou equations Typical platform design life: 25 years × safety factor = 2-5× life

DNV GL Standards (now DNVGL)

DNVGL-ST-0119: floating wind turbines DNVGL-RP-C203: fatigue of offshore structures (S-N curves, FAT class) DNVGL-OS-C101: structural design general DNVGL-OS-C102: structural design of offshore ships (FPSO, FSO)

DNVGL Fatigue S-N Curves (RP-C203)

Curves: B1, B2, C, C1, C2, D, E, F, F1, F3, G, W1, W2, W3 D-curve: FAT 90 (equivalent to IIW): butt welds in seawater (cathodically protected) Seawater without CP: degrade by factor of 2-3 (corrosion accelerates fatigue) Seawater with CP: use air curves if CP maintained properly

FPSO (Floating Production, Storage and Offloading)

Hull Structural Loads

Global hull girder: Sagging/hogging: M_wave from DNV ship rules (M_sw + M_wv) Vertical shear force: Q_sw + Q_wv

Fatigue-critical locations:

• Longitudinal stiffener connections to transverse frames
• Web frame cutouts (stress concentrations)
• Turret bearing structure (mooring loads)

Topsides-to-hull interface: large topsides mass (10,000-50,000 t); dynamic magnification

Turret Mooring

Spread mooring: 8-16 chains/polyester/wire ropes in catenary Turret: allows vessel to weathervane (rotate freely into weather) Mooring line tension: catenary equation for position + dynamic analysis (time domain)

Polyester ropes: axial stiffness AE = 15×10⁶ N/m (higher than chain per unit weight) Chain: grade R4: F_break = 8D² kg (D in mm); grade R3: 6.4D²

Cathodic Protection — Offshore

Sacrificial Anode Design (DNV-RP-B401)

Protection potential: E_prot ≤ -800 mV vs. Ag/AgCl/seawater (-850 mV vs CSE) Design current density: 50-100 mA/m² (steel, North Sea, bare) With paint system: 10-30 mA/m² (paint reduces bare area)

Anode mass required: M = I_c × t_design / (U_f × ε_a) I_c = total protection current [A] U_f = utilization factor (0.8 for bracelet anodes, 0.9 for flush-mounted) ε_a = anode efficiency: Al-Zn-In = 2500 Ah/kg; Zn = 780 Ah/kg

ICCP for Ships

Protection zones: underwater hull, rudder, propeller Reference electrodes (Ag/AgCl or Zn): monitor and control output Current output: 10-20 mA/m² (painted ship hull); 1-5 A anodes

Jack-Up Platform

Three-legged, can be raised/lowered: Preloading: apply large vertical load to check punch-through Bearing capacity (Brinch Hansen): Q_v = c_u × N_c × A (clay: N_c = 5.14 undrained) + q × N_q × A (sand)

Dynamic amplification: jack-up natural period T_n ≈ 5-8 s; seastate peak period T_p ≈ 10-16 s If T_n close to T_p: dynamic analysis required (DAF = 1/2ζ at resonance)

Output

Provide: Morison force F [kN/m] at design wave, total base shear [kN] and overturning moment [kNm], pile capacity Q_total [kN] vs. applied load, DNVGL fatigue damage D [vs. 0.3 or 1.0], anode mass required [kg], CP current density [mA/m²].