1 Loads

1

11 Dec 2007 Dr. S. NallayarasuDepartment of Ocean Engineering

Indian Institute of Technology Madras-36

1

Offshore Structures – Loads

Classification of water waves, Formulation of potential flow equation, Small amplitude wave theory, Finite amplitude waves (Stokian, Solitary and Cnoidal wave theories), Regular and random waves, Wave current interactions;

Ocean wave statistics, short term and long term wave height distribution, power-spectral definition of ocean waves, PM Spectra, Jonswap Spectra, and ISSC Spectra, extreme wave prediction, determination of design wave heights and periods, fatigue wave heights, Joint probability distribution of waves heights and periods;

Wave and Current Loads, Morison equation, Wind Loads; Gravity Loads, and combinations; Drilling Rig Loads; Design wave method, Spectral energy method, Wave Directions; Loads based on maximum base shear, Loads based on maximum over turning moment, Selection of drag and inertia coefficients marine growth, API RP 2A recommendations, Diffraction, Load on large diameter cylinders, Wave-Structure interaction;



2


ContentsGravity LoadsWind LoadsWave and Current Loads – Small bodiesWave and Current Loads – Large Bodies

2



3


Types of LoadsGravity Loads

Structural Dead LoadsFacility Dead LoadsFluid LoadsLive Loads

Environmental LoadsWind LoadsWave LoadsCurrent LoadsBuoyancy LoadsIce LoadsMud Loads

Seismic Loads



4


Gravity LoadsDead Loads

Dead loads includes the all the fixed items in the platform deck, jacket, bridge and flare structures. It includes all primary steel structural members, secondary structural items such as boat landing, padeyes, stiffeners, handrails, deck plating, small access platforms etc.

The primary structural steel members will be calculated based on the structural information in the model automatically when a computer program is used to analyze the structure. But the weight of secondary structural steel items shall be calculated applied to the structural model at appropriate locations.

3



5


Facility LoadsThe structure built either for drilling or wellhead type platform or for process type platform supports various equipment and facilities.

Mechanical equipmentElectrical equipmentPiping connecting each equipmentElectrical Cable traysInstrumentation items



6


Dead loadsMovable Drill floor loadsDrill string weight

Depending on the type of drilling rig used, this loads will vary. For water depth less than 70m, Jackup type rig may be used. For deeper water depths, operation of Jackup type rigs become uneconomical and deck mounted drilling rigs will be a suitable option. Weight of such rig will be around 1500 Tonnes with an additional support module of 1000 Tonnes.

Drilling Loads include reaction from Jackupcantilever type rig or Deck mounted rigs.

Drilling Loads

4



7


Live loadsLive loads are defined as movable loads and will be temporary in nature. This load vary in nature from owner to owner but a general guideline on the magnitude of the loads is given below.

10Galley4

5Access Platform3

5Walkway2

10Storage / laydown1

Load (kN/m2)LocationS.No.



8


Environmental LoadsWind Loads

The extrapolation of wind speed shall be calculated as below

81

0 10 ⎟⎠⎞

⎜⎝⎛=

yVV

The wind pressure can be calculated as

2

2Vgfw

ρ=

22 6.0 N/mVfw =

5



9


The total force on the platform can be calculated as

sywy

sxwx

CAfFCAfF

==



10


Wind load on oblique directions can be calculated using following relationship.

)sin()cos( θθθ yx FFF +=

The projected areas can be calculated as A1 = Ax cos(θ) and A2 = Ay sin (θ)

)sin())sin()cos((

)cos())sin()cos((

))sin()cos(()( 21

θθθ

θθθ

θθ

θ

θ

θ

θ

yxwy

yxwx

yxw

w

AAfF

AAfF

AAfFAAfF

+=

+=

+=+=

6



11


Where Fθx and Fθy are the components of Fein x and y directions respectively. Ratio between Fθx and Fx can be expressed as

)cos()sin()/()(cos

)cos()sin()cos((

2 θθθ

θθθ

θ

θ

xyx

x

xw

yxw

x

x

AAFF

AfAAf

FF

+=

+=



12


Similarly, ratio between Fθy and Fy can be expressed as

)cos()sin()/()(sin

)sin()sin()cos((

2 θθθ

θθθ

θ

θ

yxy

y

yw

yxw

y

y

AAFF

AfAAf

FF

+=

+=

7



13


WAVE FORCES ON SMALL BODIES



14


Wave and Current LoadsMethodology

In applying design waves load on to the offshore structures, there are two ways of applying itDesign Wave methodSpectral Method

In design wave method, a discrete set of design waves (maximum) and associated periods will be selected to generate loads on the structure. These loads will be used to compute the response of the structure.

In the spectral method, a energy spectrum of the sea-state for the location will be taken and a transfer function for the response will be generated. These transfer function will be used to compute the stresses in the structural members

8



15


Design Wave MethodThe forces exerted by waves are most dominant in

governing the jacket structures design especially the foundation piles. The wave loads exerted on the jacket is applied laterally on all members and it generates overturning moment on the structure.

Period of wind generated waves in the open sea can be in the order of 2 to 20 seconds. These waves are called gravity waves and contain most part of wave energy.

Maximum wave shall be used for the design of offshore structures. The relationship between the significant wave height (Hs) and the maximum wave height (Hmax) is

Hmax= 1.86 HsThe above equation correspond to a computation based

on 1000 waves in a record.



16

Offshore Structures – LoadsThe design wave height for various regions is tabulated below

2214North sea

125Persian Gulf

126Gulf of Thailand

188Arabian Sea

2411South China Sea

12

8

1 year

24Gulf of Mexico

18Bay of Bengal

100 yearRegion

API RP2A requires both 1 year and 100 year recurrence wave shall be used for the design of jacket and piles. Appropriate combination of loads with these waves shall be used in the design. A one-third increase in permissible stress is allowed for 100 year storm conditions.

Maximum design waves in various regions

9



17


Current Profile



18


Tidal Current ProfileThe wind driven current variation with depth canbe expressed as:

Where VT is the tidal current at any height from sea bed, VoT is the tidal current at the surface, y is the distance measure in m from seabed and his the water depth

71

⎟⎠⎞

⎜⎝⎛=

hyVV oTT

10



19


Wind Driven Current ProfileThe current variation with depth can be expressed as:

Where VW is the wind driven current at any height from sea bed, VoW is the wind driven current at the surface, y is the distance measure in m from seabed and h is the water depth

hyVV oWW =



20


Morison Equation

Flow is assumed to be not disturbed by the presence of the structureForce calculation is empirical calibrated by experimental resultsSuitable Coefficients need to be used depending on the shape of the bodyValidity range shall be checked before use and generally suitable for most jacket type structures where D/L << 0.2 where D is the diameter of the structural member and L is the wave length

11



21


Morison EquationWave and current loading can be calculated by Morison

equationMorison equation can be written as:

aCDVVDCF WMwDT ρπρ4

21 2

+=

Where FT is the total force, ρw is the density of water, CD and CM are the drag and inertia coefficients respectively, D is the diameter of the member including marine growth, V is the velocity and a is the acceleration.

The first term in the equation is drag component (FD) and the second term is the inertia component (FI). This can be expressed as:

FT = FD + FI



22


Wave Load on a MemberMorison equation is a general form and can not be applied to all members in the offshore structure. It was developed specifically for a surface piercing cylinder like pile of a structure. But in reality, the members of the offshore structure may be horizontal or inclined in space and can not used without modification

12



23


STEPSEstablish Wave Height, Period and Current Distribution along the depthEstablish Wave Theory applicable for H,T,dEstimation of Water particle kinematics including wave current interactionEstablish Cd and CmEstablish Marine GrowthEstablish Wave Kinematics factorConductor Shielding (if applicable)Current Blockage factorMorison Equation used to estimate the forces



24


WAVE CURRENT INTERACTIONPresence of current either stretches the wave or shortens it depending on the direction of current. This is called Doppler shift. The apparent wave period need to be calculated to use in the load calculationDrag term is nonlinear and hence the water particle velocities due to wave and current needs to be added vectorialy before using it in Morison equation.

13



25


Dispersion Relationship

)2tanh(2

2

dL

gTL ππ

=

)2tanh(

22

dL

g

LTπ

π=



26


Apparent Wave Period

I

app

VTL

TL

+=

∫−

+=0

)/)(4cosh()()/4sinh(

)/4(d

cIdzLdzzU

LdLV π

ππ

)2tanh(

22

dL

g

LTapp π

π=

Uc(z) – is the current profile elevation z

Following three equations needs to be solved to obtain the Tapp

14



27


Nonlinear Drag Term in Morison equation

VwVcV

aCDVVDCFWMwDT

+=

+= ρπρ4

21 2

Vc = Current Velocity

Vw = Wave Water Particle Velocity

Example

Lets assume Vc=2m/sec, Vw=3m/sec

If we calculate the drag forces separately, add, we will get 2*2+ 3*3 = 13

If we add the velocities first and compute the loads, we get (2+3)*(2+3) = 25

It under predicts the forces as much as by 50%



28


Source : API RP 2A

15



29


Water Wave KinematicsAiry wave theory is considered in the calculation of wave kinematics. Consider a progressive wave with water surface elevation depicted by cosine curve,

)cos(2

tkxH ωξ −=

and the corresponding velocity potential is given by:

)sin(sinh

)(cosh2

tkxkh

zhkk

H ωωφ −+

−=



30


Selection of wave theory for load calculation

Source : API RP 2A

16



31


Source : API RP 2A



32


Marine GrowthMarine growth around submerged structural members increases the wave/current loads as the diameter is increasedIt varies from 50mm to 150mm thickness along the depth from seabedAt also adds to additional weightThis is to be modelled such that the above is taken in to accountDensity of marine growth is around 1300 kg/m3

17



33


Current Blockage Factor

Source : API RP 2A



34


Conductor Shielding Factor

Source : API RP 2A

18



35


SELECTION OF SUITABLE DRAG AND INERTIA COEFFICIENTS



36


Cd and Cm

These are empirical Coefficients to be used in Morison equation and they have been corelated with experimental dataThese coefficients vary due to shape of the structure, surface roughness, flow velocity and direction of flowExtensive research on various shapes availableAPI RP 2A has enough information for circular cylindersDNV recommendation can be used for non-circular shapes

19



37


Cd and Cm

For Smooth cylinders Cd = 0.65, Cm=1.6For rough cylinders Cd = 1.05, cm=1.2

The values shall be used only if UT/D > 30For other region of flow, charts available literature shall be used



38


Keulegan-Carpenter Number

DTUK m 22

=

Where K is Keulegan-Carpenter Number, Um is the maximum velocity including current and T2 is the duration of half wave cycle and D is the diameter of the member

20



39


Reynold’s Number

νDUR m=

Where R is Reynold’s Number, Um is the maximum velocity including current and D is the diameter of the memberν is the kinematic viscosity



40

Offshore Structures – LoadsInertia Coefficient

Source : API RP 2A

21



41

Offshore Structures – LoadsDrag Coefficient

Source : API RP 2A



42


Non-circular shapes

22



43


The horizontal and vertical velocity and acceleration of water particle can be calculated using the following equations.

)cos(sinh

)(sinh2

)sin(sinh

)(cosh2

)sin(sinh

)(sinh2

)cos(sinh

)(cosh2

2

2

tkxkh

zhkHt

Va

tkxkh

zhkHt

Va

tkxkh

zhkHz

V

tkxkh

zhkHx

V

vv

hh

v

h

ωω

ωω

ωωφ

ωωφ

−+

=∂∂

=

−+

=∂∂

=

−+

=∂∂

=

−+

=∂∂

=

Where k is the wave number defined by 2π/T, ω is the wave circular frequency defined by 2π/T, L is the wave length, and

x is the distance of the point in consideration from origin.



44


Maximum Load on a vertical memberConsider a case of a surface piercing cylinder such as pile of a structure or a leg of a jacket, the combined drag and inertia force (total force) varies with time and will be maximum only at one occasion. In order find the maximum force, phase angle at which the maximum force occurs shall be found first.Let us express the total force on the pile by substituting the velocity and acceleration components and integrating between the limits (from surface to seabed, i.e. 0 to –h)

kTHD

hk

khkhT

HDCF DT

θππρ

θθπρ

sin24

C-

24)2sinh(

sinhcoscos

21

2

22

M

22

22

⎥⎦⎤

⎢⎣⎡ +=

23



45


Wave Loads on Jacket Structure

Storm Wave



46


The total force will be maximum when,

0=∂∂θ

TF

Substituting the values of velocity and acceleration components in to the drag and inertia force equation and differentiating with respect to θ and rearranging the terms, we get

⎥⎦

⎤⎢⎣

⎡+

−= −

khkhkh

CC

HD

D

M

22(sinhsinh2cos

21

maxπθ

24



47


Maximum Load on a horizontal memberConsider a case of horizontal cylinder such as brace of a jacket, the combined drag and inertia force (total force) varieswith time and will be maximum only at one occasion. In order find the maximum force, phase angle at which the maximum force occurs shall be found first.

Let us express the total force on the pile by substituting the velocity and acceleration,

⎥⎦

⎤⎢⎣

⎡ +

⎥⎦

⎤⎢⎣

⎡ +=

khhzkHD-C

khhzkHDCF

M

DT

sinh)(coshsin

24

sinh)(coshcoscos

4

21

222

222

θωπρ

θθωρ



48


The total force will be maximum when,

0=∂∂θ

TF

Substituting the values of velocity and acceleration components in to the drag and inertia force equation and differentiating with respect to θ and rearranging the terms, we get

⎥⎦

⎤⎢⎣

⎡+

−= −

)((coshsinh

2sin 1

max zhkkh

CC

HD

D

Mπθ

25



49


Maximum Load on a inclined memberThe resultant force on a arbitrarily oriented circular

cylinder in water waves can be calculated using vector analysis combined with Morison equation

tn

FFF→→→

+=The force in normal direction an be expressed as:

ly.respective forces inertia and drag theare and where 1

1

nnD

nn

D

n

FFFFF→→→

+=

The total force per unit length of the cylinder can be written as



50


These forces expressed as:

axiscylinder the tonormal particle fluid ofon Accelerati a

axiscylinder the tonormal particle fluid ofVelocity V

seawater ofDensity cylinder ofDiameter D

cylinder the tonormal flowfor t coefficien Inertia C

cylinder the tonormal flowfor t coefficien Drag Cwhere

41

21

n

n

nM

nD

2

=

=

===

=

=

=

→

→

→→

→→→

ρ

ρπ

ρ

nnM

n

D

nnnD

nD

aIDCF

VVDCF

26



51


The equation for tangential force can be written as

axiscylinder the tol tangentiaparticle fluid ofVelocity

cylinder the tol tangentiaflowfor t coefficien Drag 21

=

=

=

=

→

→→→

→→

t

nD

tttD

tD

tD

t

V

C

VVDCF

FF

ρ



52


These forces can be summed and expressed in terms of cylinder local axis as below:

→→→→

→→→→

→→→

+=

+=

=

znMzn

nDz

ynMyn

nDy

tttDx

aIDCVVDCF

aIDCVVDCF

VVDCF

ρπρ

ρπρ

ρ

2

41

21

41

2121

27



53


Maximum Global Loads

Maximum global loads on a platform can be calculated using two principles

Maximum Base Shear MethodMaximum Overturning Moment Method



54


Maximum Base ShearMaximum base shear or maximum total force on a structure has to be determined for the global analysis of structures. As the wave propagates across structure wave force on each member is different and all the locations will not be attaining the maximum forces. To find the maximum total force a structure, following steps need to be considered.

Position the wave crest at the origin of the structure as shown in figure. Divide one wave cycle into number of segments either in terms of θ or in terms of lengthCompute the wave forces on all members at that instant of time using water wave velocities and accelerations computedSum up the forces in horizontal direction for all the membersRepeat the calculation in step 4 for all the points for one wavecycleThe maximum of all the total forces computed in step 5 is the maximum base shear or total force.

28



55


Maximum Overturning Moment

Maximum overturning moment on a structure can be determined following the procedure for the maximum bas shear case. In this case, the loads on the members shall be multiplied by the lever arm from mud-line. This shall be summed up and the procedure shall be repeated for all the steps in the wave.



56


Hydrodynamic Factors

Wave Kinematics factor This varies between 0.8 to 0.95. This is to be applied since the calculated wave loading is based two dimensional wave theory while the actual loading is from three dimensional wave climate.

Conductor Shielding factorThe presence of rows of conductors will provide a shielding effect to the conductors behind and this depends on the spacing and number of conductors

Current Blockage FactorThis current blockage factor is used to account for the reduction in the current due to the presence of the structure in a free stream.

29



57


SELECTION OF SUITABLE WAVE THEORY

ExampleWater Depth d= 60mWave height H= 12mWave Period Tapp= 10 SecCalculate H/gTapp

2 =0.012Calculate d/gTapp

2 =0.06

Refer to API RP 2A and the Stokes Wave Theory is applicable



58


30



59


Wave / Current Direction

Wave / Current assumed to be acting in same direction

Wave Directions shall be set to maximize the total loads and pile loads

Minimum 8 directions for 4 or 8 legged jackets and 12 for tripods

Directional or Omni-directional depending on the design requirement



60


31



61


Maximum shear and moment of a single pile along phase angle

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

0 90 180 270 360

Phase angle (deg)

Shea

r (or

) Mom

ent (

kN (o

r) kN

-m)

ShearMoment



62


-400

-300

-200

-100

0

100

200

300

400

500

600

700

0 90 180 270 360

Phase angle (deg)

Shea

r (or

) Mom

ent (

kN (o

r) kN

-m)

ShearMoment

Maximum shear and moment of two pile group along phase angle

32



63


Maximum shear and moment of two pile group structure along phase angle

-500

-300

-100

100

300

500

700

900

0 90 180 270 360

Phase angle (deg)

Shea

r (or

) Mom

ent (

kN (o

r) kN

-m)

ShearMoment



64


-100

-50

0

50

100

150

200

0 90 180 270 360

Phase angle (deg)

Shea

r (or

) Mom

ent (

kN (o

r) kN

-m)

ShearMoment

Maximum shear and moment of a member in two pile group structure along phase angle

33



65


Wave slamming LoadWave slamming predominant in horizontal membersNeeds to be taken in to account together with global loadsWave Slamming is computed similar to drag forceSlamming Force Co-efficient is to assumed and the recommended value is 5.5

sswSSVVDCF

21 ρ=



66


Wave Breaking LoadWave slamming predominant in Vertical members and vertical faces of coastal structuresThe wave breaking force coefficient Csis to assumed as 5.98 for breaking wave and 2.74 for broken waveThe coefficient β for calculating the impact velocity is to taken as 0.48 for breaking wave and 0.70 for broken waveC is the speed of breaking wave

π

ρ

β

2092.1

A gTC

VVCFCV

bbwbb

b

=

=

=

34



67


FLOW INDUCED VIBRATION



68

Offshore Structures – LoadsPIV Illumination System

35



69




70


36



71

Offshore Structures – LoadsTypical PIV Image



72

Offshore Structures – LoadsImage Showing Vortex at the tail end

37



73

Offshore Structures – LoadsImage Showing Vortex developing further



74

Offshore Structures – LoadsImage Showing Vortex decay

38



75


FLOW PAST HORIZONTAL CYCLINDER



76



39



77


Assymetric Vortices



78



40



79


BOUNDARY LAYER



80


LIFT FORCES

dL

sswLL

CC

UUDCF

7.0

21

=

= ρ

41



81


FLOW PAST HORIZONTAL PLATES



82


WAVE FORCES ON LARGE BODIES

42



83


Assumption of “No disturbance” is not valid if D/L > 0.2 Part of Wave reflected once the wave touches the structure and part of it pass aroundThis phenomenon is called diffractionThese forces also can be measured experimentallyMany research papers exist for different types and shapes of structures

Diffraction Forces



84


Distribution of boundary conditions for the linear diffraction problem

43



85


Governing Equation

The governing equation for the diffracted spatial potential can be expressed as follows.

Ω=∂∂

+∂∂ in 02

2

2

2

yx

ss φφ

The velocity potential due to an incident monochromatic wave traveling in the positive direction can be expressed as follows:

)(, expcosh

)(cosh kx

kddykga ι

ωιφ +

−=



86

Offshore Structures – LoadsBoundary conditions

Free surface boundary condition The kinematic boundary condition on y=η can be written as

0=∂Φ∂

+∂∂

∂Φ∂

+∂∂

yxxtηη

which after linearisation by neglecting the nonlinear terms in equation

The dynamic boundary condition on the free surface where the atmospheric pressure and surface tension are taken as zero can be written as

0 y at 0 ==∂∂

tη

ηηφ at 0 .21

==+Φ∇Φ∇+∂∂

− y gt

44



87


The second term in the above equation is nonlinear and is neglected in the present formulation leading to

0 y at 0 ==+∂∂ ηφ g

t

s

0 y at or 02

22

2

=+∂Φ∂

=∂Φ∂

+∂Φ∂

gyyg

t

sss ω

The kinematic and dynamic boundary conditions can also be specified by combining



88


Body boundary conditionThe boundary condition on the body boundary should satisfy the no flow condition or the velocity normal to the body boundary should be equal and opposite to the incident wave velocity as follows:

o

is

qnn =∂∂

−=∂∂ φφ

Bed boundary conditionThe kinematic boundary condition on the fixed horizontal sea bed can be specified as a no flow condition as follows:

0=∂∂

−

n

sφ

45



89


Radiation boundary conditionThe boundary condition on the left and right boundaries of the computational domain should be specified in order avoid multiple reflection of scattered waves. This can be specified using the Sommerfeld radiation condition

±∞→=+∂∂ x 0s

s

ikx

φφ



90


Diffraction forces can be calculated manually for simple shapesFor Complex shapes Numerical Methods shall be used such as

Finite Difference MethodFinite element methodSource and Sink MethodBoundary Element Method

Many commercial codes including SACS, SESAM and others can be used

Diffraction Forces

46



91


Solution of Boundary Value Problem for Velocity PotentialCalculation of PressuresIntegration of Pressures to obtain Forces

Diffraction Forces



92


Boundary Value Problem

47



93


Diffraction Forces



94


Based on Empirical and Measured values

Ice Loads

48



95


ICE LOADS

Documents

1 Loads