2. Automatic Wave Loads Calculation of Wave Load Values
7. Determine the amount of marine growth, if any, on the considered
object based on the defined marine growth parameters or the wave
overwrites.
8. Determine the drag and inertia coefficients for the considered object
based on the defined drag and inertia coefficient parameters or the
wave overwrites.
9. Apply the Morison Equation to calculate the force exerted by the wave
at a particular location on the object.
10. Calculate the buoyant forces acting on the object.
Wave Wind Load
The program calculates the force exerted by a wave wind load at a particular
location on a structural object using the following steps. Note that wave wind
loads are applied only to the portions of the structure that are above the
wave surface.
1. Calculate the design wind speed.
2. Determine the section dimensions (not including marine growth or ice)
based on the defined section properties or the wave overwrites.
3. Determine the amount of marine growth, if any, on the considered
object based on the defined marine growth parameters or the wave
overwrites.
4. Determine the amount of ice, if any, on the considered object based
on the wave overwrites. Note that if both marine growth and ice is
specified at a location, only the marine growth value is used.
5. Determine the shape coefficient used for wind loads for the considered
object based on the defined shape coefficient that applies to all
elements or the wave overwrites.
6. Determine the wind load shielding factor, if any, on the considered
object based on the wave overwrites. The wind load on the object is
multiplied by this shielding factor.
7. Calculate the wind drag at a particular location on the object.
Overview Page 2 of 9
3. Automatic Wave Loads Calculation of Wave Load Values
Apparent Wave Period
The wave period input in the wave definition data does not include the effect
of the current. The wave period used when calculating the wave water particle
velocities and accelerations must include the effect of the current component
in the direction of the wave. The wave period that includes the effect of the
current is called the apparent wave period, Tapp. The apparent wave period is
calculated by solving a system of three simultaneous nonlinear equations.
Those equations, which are documented in Section C2.3.1b1 of the
commentary of the API Recommended Practice (American Petroleum Institute
2000), are:
I
app
V
TT
+=
λλ
)/2(tan
22
λπ
πλ
dg
Tapp = C2.3.1b1
dz
dz
zU
d
V
d
cI
+
= ∫− λ
π
λπ
λπ )(4
cosh)(
)/4sinh(
/4 0
where
λ = Wave length.
T = Wave period as input by user (not considering the current).
appT = Apparent wave period (considers the current).
IV = Effective current speed in the direction of the wave.
g = Acceleration due to gravity.
z = Elevation referenced to the storm water level (positive above
storm water level).
Apparent Wave Period Page 3 of 9
4. Automatic Wave Loads Calculation of Wave Load Values
)(zUc = Component of steady current profile at elevation z in the
wave direction and not multiplied by the current blockage
factor.
d = Storm water depth.
Wave Kinematics
Wave kinematics yield the wave water particle velocities and accelerations.
The velocities and accelerations are calculated from a specified wave theory
or they are user-defined. Regardless of which method is used to obtain the
wave water particle velocities and accelerations, they are then modified by
the wave kinematics factor, which is intended to account for wave directional
spreading and irregularity in the wave profile shape.
The modification consists of multiplying the horizontal velocities and
accelerations by the wave kinematics factor. The vertical velocities and
accelerations are not modified.
Current Profile
The user specifies the current profile (velocity and direction of current as a
function of height) from the mud line to the storm water level. The user
specifies that either a Linear or a Nonlinear current stretching method is used
to stretch or compress the current to the wave surface at a particular
location. The current velocity at a particular location determined from
applying the current stretching technique is multiplied by the current blockage
factor to obtain the current velocity that is combined with the wave velocity.
Linear Current Stretching
Linear current stretching is based on the following equation, which is found in
Section 2.3.1b-5 of the API Recommended Practice (American Petroleum
Institute 2000). The equation is solved directly for z'.
η+
+=+
d
d
dzdz )()'( 2.3.1b-5
where
Wave Kinematics Page 4 of 9
5. Automatic Wave Loads Calculation of Wave Load Values
z = Elevation of the location where the water particle current
velocity is desired referenced to the storm water level (positive
above storm water level).
z' = Elevation of the location in the user-specified current profile
where the current velocity should be obtained referenced to the
storm water level (positive above storm water level).
η = Elevation of the wave surface directly above the water particle
referenced to the storm water level (positive above storm water
level).
d = Storm water depth.
Nonlinear Current Stretching
Nonlinear current stretching is based on the following equation, which is
found in Section C2.3.1b-5 of the commentary of the API Recommended
Practice (American Petroleum Institute 2000). The equation is solved
iteratively for z'.
( )( )
( )n
n
d
dz
zz
λπ
λπ
η
/2sinh
/'2sinh
'
+
+= C2.3.1b-5
where
z = Elevation of the location where the current velocity is desired
referenced to the storm water level (positive above storm water
level).
z' = Elevation of the location in the user-specified current profile
where the current velocity should be obtained referenced to the
storm water level (positive above storm water level).
η = Elevation of the wave surface referenced to the storm water
level (positive above storm water level).
d = Storm water depth.
η = Wave length.
Current Profile Page 5 of 9
6. Automatic Wave Loads Calculation of Wave Load Values
Morison Equation
The Morison equation is used to calculate the force exerted by the wave at a
particular location on an object. The equation is given in Section 2.3.1b-10 of
the API Recommended Practice (American Petroleum Institute 2000).
dt
dU
V
g
w
CUUA
g
w
CFFF mDID +=+=
2
2.3.1-1
where
F = Hydrodynamic force per unit length acting normal to the object
longitudinal axis.
DF = Drag force per unit length.
IF = Inertia force per unit length.
DC = Drag coefficient.
w = Weight density of water.
g = Gravitational acceleration.
A = Projected area normal to object axis per unit length. For pipes
and circles this is the effective diameter of the object, including
marine growth. For other section types, it is the dimension of
the side of the rectangle that encloses the section (including
marine growth, if any) that is normal to the direction of the
load.
V = Displaced volume per unit length. For pipes and circles this is
π D2
/4 where D is the effective diameter of the object, including
marine growth. For other section types it is the product of the
dimensions of two adjacent sides of the rectangle that encloses
the section (including marine growth, if any).
U = Component of the water particle velocity acting normal to the
axis of the object.
Morison Equation Page 6 of 9
7. Automatic Wave Loads Calculation of Wave Load Values
U = The absolute value of U.
MC = Inertia coefficient.
= Component of the water particle acceleration acting normal to
the axis of the object.
Buoyant Forces
Buoyant forces are included only when so indicated in the wave load
definition. Buoyant forces are applied only to objects (or portions of objects)
that lie above the mud line and below the wave surface. Buoyant forces
consist of a uniform projected Z direction load applied to objects that are not
vertical and concentrated compressive axial forces applied to the ends of all
objects.
Uniform Load
The magnitude of the uniform load is calculated as:
wVfz =
where
fz = A uniform load in the projected Z direction.
w = Weight density of the water.
V = Displaced volume per unit length of the object.
For pipes and circles the displaced volume V is calculated as V = π d2
/4, where
d is the diameter including marine growth, if any. For other sections V is
calculated as V = bd, where b and d are the width and height of a rectangle
that would enclose the section.
Concentrated Compressive Loads at Object Ends
The magnitude of the concentrated compressive axial load at each end of
each object is calculated as:
hwAP c=
where
dt
dU
Buoyant Forces Page 7 of 9
8. Automatic Wave Loads Calculation of Wave Load Values
P = A concentrated compressive axial load.
w = Weight density of the water.
Ac = Cross sectional area to which the load is applied.
h = Height of the water.
The magnitude cross-sectional area to which the load is applied depends on
whether the object is flooded. All objects are assumed to not be flooded
unless the are specifically indicated to be flooded in the wave overwrites.
If the object is not flooded, for pipes and circles the cross sectional area Ac is
calculated as Ac = π d2
/4 where d is the diameter, including marine growth, if
any. For other sections, Ac is calculated as Ac = bd, where b and d are the
width and height of a rectangle that would enclose the section.
If the object is flooded, the cross-sectional area Ac is taken equal to the area
specified for the section property that is assigned to the object.
Wind Loads
The wave wind loads are calculated based on Sections 2.3.2b-1 and 2.3.2c of
the API Recommended Practice (American Petroleum Institute 2000).
Design Wind Speed
The design wind speed is calculated using the following equations that are
taken directly from the API Recommended Practice.
−=
0
ln)(41.01)(),(
t
t
zIzUtzu u 2.3.2-1
where the one hour mean wind speed U(z) (ft/sec) at level z (ft) is given by:
+=
8.32
ln1)( 0
z
CUzU 2.3.2-2
00457.010573.0 UC +=
and where the turbulence intensity Iu(z) at level z is given by:
Wind Loads Page 8 of 9
9. Automatic Wave Loads Calculation of Wave Load Values
[ ]
22.0
0
8.32
0131.0106.0)(
−
+=
z
UzIu 2.3.2-3
Wind Drag Force
The wind drag force is calculated using the following equation that is taken
directly from the API Recommended Practice.
ACuF s
2
2
=
ρ
2.3.2-8
where
F = Wind force
ρ = Mass density of air (slugs/ft3
)
u = Wind speed (ft/sec)
Cs = Shape coefficient
A = Are of element (ft2
)
Wind Loads Page 9 of 9
