StructuralAnalysesOfJack-upsInElevatedCondition

Structural Analyses of Jack-ups in Elevated Condition 2013-01-21, presented by Thomas Jahnke & Jochen Künzel

Necessessity of global structural analyses of Jack-ups Determination of • Leg strength • Jacking system loads • Overturning stability • Local force flow between leg and hull

Properties of Jack-ups in elevated condition Stiffness • Hull is stiff • Legs relative soft Masses • hull mass is high • leg mass relative small Percent critical damping e • Soil 0% – 2% • Hydrodynamic 2% - 3% • Material/Friction 0% – 2% • Total: often 7% assumed Natural Periods: • between 4s und 10s

In more Detail: Overall Leg Stiffness depends on:  Leg Bending Stiffness (Iyy)  Total Leg Length (Penetration+Waterdepth+Airgap+Height of Lower Support)  Fixity at Spud Can

Class Requirements (conservative):  Maximization of the total free leg length (Penetration, Waterdepth, Airgap)  Fixity at Spud Can = 0 (conservative for leg strength, overturning moment and jacking loads, but may not be conservative for dynamic effects)

Operational Requirements:  Site Specific Assessment (minimum soil bearing capacity, penetration, sliding)  Results of SSA should confirm that the jack-up can work on the specific location within the limits of the Operating Manual

Overview of Required Steps for a Structural Analysis of Jack-ups 1. Modal analysis Result: Natural periods of the jack-up 2. Dynamic analysis Single Degree of Freedom Method (SDOF) Time-domain non-linear analysis Result: Inertia loadset 3. Static analysis (including inertia loadset) Results: a) Spud can (footing) reactions b) Overturning stability check c) Sectional forces and stresses  code checks d) Jacking system forces

Modal analysis – Transeverse and Longitudinal Modes Transverse

Thormodal_w d-50_he9_r0-quer.av i

Longitudinal

Thormodal_w d-50_he9_r0-laengs.av i

Loads in a global analysis constant, quasi-constant Loads • Weights • Crane • Wind • Current Time varying loads • Waves (irregular sea with varying wave periods and wave heights) • Wave periods between 4s-18s • RESONANCE possible

Method for dynamic analyses of jack-ups (1/2) • Determination of DAF (Dynamic Amplification Factor) due to wave excitation • Comparison with a single degree of freedom system (SDOF) or • Statistial assessment of the reponses of the jack-up due to time history wave loads (1-3 hours simulation time of qualified seastate)

Defintion: DAF=Fdynamic/Fstatic =(Fstatic+Finertia)/Fstatic,, i.e. Finertia =(DAF-1)* Fstatic

1

DAF 1

Tn T

2

2

Tn 2 e T

2

Method for dynamic analyses of jack-ups (2/2) Base Shear BS is the total horizontal load at reaction point • BSmax=1500 kN • BSmin=-800 kN • BSamp=(BSmax-BSmin)/2 = 1150 KN • BSmean =(BSmax+BSmin)/2 = 350 KN Inertia Load: Finertia=BSamp*(DAF-1) acting at CoG or distributed over the legs

Wave according WAVEL Force [kN]

Elevation [m ] 2.000

2000

1.500 1500 1.000 1000 0.500

500

0.000

-0.500 0 0

45

90

135

180

225

270

315

360

405

450

495

540 -1.000

-500 -1.500

-1000

Wave Load Contour [kN]

-2.000 Phase [Deg]

Wave Elevation [m]

Wave loads on transparent Structures Morison equation (empirical formula for hydrodynamic loads on cylindrical member) F

Fd

Fm

1 D Cd v v A Cm u 2 Fd = Drag force Fm = Inertia force r = Density of water D = Reference diameter of cylindrical member A = Total cylindrical area of member Cd = Drag coefficient Cm = Mass coefficient v = relative particle velocity normal to member axis ( v~H/2*w*sin[wt-a] + vcur) u = relative particle acceleration normal to member axis ( u~H/2*w**2*cos[wt-a] )

F

Total Loads and non-linear Effects Total Load on a Wind Turbine Installation Vessel F = FGravity + FCrane + FWind + FWave/Current + FInertia All Loads are depend on load directions except gravity Non-linear effects • at spud can reaction point due to non-linear soil condition • wave loads according to drag term of Morison equation • P-D effect on legs (equilibrium at deformed shape)

References:

Society of Naval Architects & Ocean Engineers (SNAME): Technical & Research Bulletin 5-5A “Guidelines for Site Specific Assessment of Mobile Jack-up Units”, Rev.3 2008 and ISO 19905-1 and ISO 19905-2 “Site Specific Assessment of Mobile offshore units”

Thank you

Thomas Jahnke, Tel: +49 40 36149 – 106 Jochen Künzel, Tel: +49 40 36149 – 7424