1P | The fundamental rotational frequency |
Ab | Bolt stress area |
Af | Effective cross-sectional area for the compressed flanges |
As | Surface area to be protected |
Amid | Area inscribed by the mid-thickness line |
A | Cross-sectional area |
CMxoff | Offset of rotor nacelle assembly (RNA) along x from tower-top centerline |
CMyoff | Offset of RNA along y from tower-top centerline |
CMzoff | Offset of RNA along z from tower-top centerline |
Cd | Drag coefficient |
Cm | Added mass coefficient |
C | Constant in the σ–N curve |
DTRb | Tower-base DTR |
Table Continued |
DTRt | Tower-top DTR |
DTR | Diameter-to-thickness ratio |
Db | Tower-base outer diameter (OD) |
Dt | Tower-top OD |
Dbc | Bolt circle diameter in the flange connection |
Dfat | Fatigue damage |
Dsh,m | Shell mid-wall diameter |
Dsh | Shell OD |
EUUtil | Shell buckling utilization ratio |
Eb | Bolt material Young's modulus |
Ef | Flange material Young's modulus |
E | Young's modulus |
Fd | Generic, design (factored) load within the load resistance factor design (LRFD) approach |
Fj | Forcing associated with the j-th mode of vibration |
Fk | Generic, characteristic load within the LRFD approach |
Fp | Bolt preload |
Ft | Bolt tension load |
Fz | Shell tension load |
Fsi | Horizontal load from vessel impact |
Ft,RD | Bolt strength load |
Fu,A | Shell equivalent load in the failure mode A according to the flange segment-model |
Fu,B | Shell equivalent load in the failure mode B according to the flange segment-model |
Fu,C | Shell equivalent load in the failure mode C according to the flange segment-model |
Fult | Ultimate resistance load of the flange connection |
FxRNA | Force from the RNA along the x axis |
FyRNA | Force from the RNA along the y axis |
Fz1 | Threshold value of Fz tension load in Schmidt/Neuper's method |
Fz2 | Threshold value of Fz tension load in Schmidt/Neuper's method |
FzRNA | Aerodynamic force from the RNA along the z axis |
Fzcr | Value of Fz tension load that would cause flange separation |
Table Continued |
GLUtil | Global buckling utilization ratio |
Gf | Gust factor |
Hw | Wave height |
Htwr2 | Height of tower waist |
Ixx | Mass second moment of inertia about the x axis |
Ixz | Mass cross-moment of inertia about the x and z axes |
Iyy | Mass second moment of inertia about the y axis |
Izz | Mass second moment of inertia about the z axis |
I | Protective current density (A/m2) |
Jxx | Cross-sectional area moment of inertia |
Kα | Ratio of bolt stiffness to total connection stiffness |
Kβ | Ratio of flange stiffness to total connection stiffness |
Kb | Bolt axial stiffness |
Kf | Equivalent stiffness of the compressed flange pair |
Kx | Equivalent soil–structure interaction (SSI) spring constant along x (=y) axis |
Kz | Equivalent SSI spring constant along z axis |
Kθx | Equivalent SSI rotational (about x (=y) axis) spring constant |
Kθz | Equivalent SSI torsional (about z axis) spring constant |
Lb | Bolt effective length |
Lp | Pile embedment length |
L | Tower length, or SSt length |
Md | Design (factored) bending moment load at the station of interest |
Mp | Bending moment load resistance at the tower station of interest |
Mx | Component of the bending moment along the x axis at the station of interest |
My | Component of the bending moment load along the y axis at the station of interest |
Mz | Torsion moment load along the z axis at the station of interest |
MPl,2 | Flange equivalent plastic bending (resistance) load in failure mode C according to the flange segment-model |
MPl,3,MN | Shell equivalent plastic bending (resistance) load in failure modes B and C according to the flange segment-model, accounting for bending and tension interaction |
MPl,3 | Shell equivalent plastic bending (resistance) load in failure modes B and C according to the flange segment-model |
MxRNA | RNA aerodynamic moment along the x axis |
Table Continued |
MyRNA | RNA aerodynamic moment along the y axis |
MzRNA | RNA aerodynamic moment along the z axis |
Nd | Design (factored) normal load at the tower station of interest |
Ni | Number of cycles at failure for the i-th load range level |
Np | Normal (axial) load resistance at the tower station of interest |
NDEL | Number of cycles at failure for the damage equivalent stress (DES) stress range |
NPl,3 | Shell equivalent plastic (resistance) load in failure modes B and C according to the flange segment-model |
P–Δ | P–Δ effect |
Q | Practical current capacity (Ah/kg) |
R(fd) | Probability distribution of the generic, design (factored) material resistance within the LRFD approach |
S(Fd) | Probability distribution of the generic, design (factored) load within the LRFD approach |
St | Strouhal number |
Sa,i | i-th bin load-range |
TL | Expected lifetime of the component |
Tc | Expected useful lifetime of the coating |
Td | Design (factored) shear load at the station of interest |
Tx | Component of the shear load along the x axis at the station of interest |
Ty | Component of the shear load along the y axis at the station of interest |
Ucr | Critical wind velocity for vortex shedding |
Uref | Hub height reference wind speed in simple design load case (DLC) loads' analysis |
Corrosion rate | |
Number of cycles at failure for the i-th load range level, accounting for partial safety factors (PSFs) | |
Unit vector along x axis | |
Unit vector along y axis | |
Uw | Wave and current velocity |
Uhub | Wind velocity at hub height |
U | Wind velocity |
fa | Force per unit length due to wind aerodynamic drag |
fw | Force per unit length due to wave and current kinematics |
ω0,j | First natural frequency in rad associated with the j-th mode of vibration |
asi | Added mass coefficient during collision (1.4–1.6 sideway impact, 1.1 bow or stern collision) |
a | Distance from bolt centerline to flange edge |
b | Distance from bolt centerline to shell mid-wall centerline in the flange connection |
cf | Flange circular segment net length (segment-model) |
cj | Damping coefficient for the j-th mode of vibration |
cs | Shell circular segment length (segment-model) |
cc,j | Critical damping coefficient for the j-th mode of vibration |
csi | Stiffness of the impacting part of the vessel |
db | Bolt hole diameter |
dw | Water depth |
f0 | First natural frequency in Hz |
fd | Generic, design (factored) resistance within the LRFD approach |
fk | Generic, characteristic material resistance within the LRFD approach |
fy | Characteristic yield stress |
fobj | Objective function in the optimization problem formulation |
fu,b | Bolt characteristic ultimate strength |
fy,b | Bolt characteristic yield strength |
fy,f | Flange characteristic yield strength |
fy,s | Shell characteristic yield strength |
gcnt | Constraint function in the optimization problem formulation |
g | Gravity acceleration |
j | Protective current density (A/m2) |
ki | Interaction (axial-hoop stresses) factor in the local buckling utilization calculation |
kj | Stiffness associated with the j-th mode of vibration |
kw | Dynamic pressure factor to calculate hoop stresses—a function of cylinder dimensions and external pressure buckling factor per [2] |
kz | Exponent factor for the axial stress ratio, in the local buckling utilization calculation |
klat | Lateral restraint spring constant |
krot | Rotational restraint spring constant |
Table Continued |
ma | Anode mass |
mj | Modal mass associated with the j-th mode of vibration |
mRNA | RNA mass |
msi | Displacement mass of impact vessel |
mtwr | Tower mass, or SSt mass |
m | Inverse exponent in the σ–N curve |
nP | n-blades times the fundamental rotational frequency |
nb | Number of bolts in the flange connection |
ni | Number of cycles at the i-th load range |
nDEL | Reference number of cycles for the damage equivalent load (DEL) load range |
n | Number of rotor blades |
qmax | Maximum wind dynamic pressure |
tf | Flange thickness |
ts | Shell thickness |
u(xd) | States in the optimization problem formulation |
vsi | vessel impact speed |
xd | States in the optimization problem formulation |
xj | Degree of freedom (DOF) variable associated with the j-th mode of vibration |
y | Local tower station horizontal displacement |
zRNA | z coordinate of the RNA center of mass (CM) |
zhub | Hub height above mean sea level (MSL) |
z | Altitude above MSL |