pyflange.flangesegments
This module contains FlangeSegment
classes, which model the mechanical
behavior of a flange sector containig one bolt only.
Currently, the only two type of FlangeSegment available are an L-Flange segment and a T-Flange segment, implementing a polinomial relation between shell pull force and bolt force / bolt moment. Nonetheless, this module has been structured to be easily extensible with other types of FlangeSegment model, such as Multilinear (Petersen) L-Flanges, Multilinear T-Flanges, etc.
The models implemented in this module are based on the following references:
- [1]: Marc Seidel, SGRE TE TF PST: IEC 61400-6 AMD1 Background Document
Fatigue design for ring flange connsections in wind turbine support structures. Draft version 2024-09-27
- [2]: IEC 61400-6:2020/AMD1 - wIND ENERGY GENERATION SYSTEMS - Part 6: Tower and foundation
design requirements - AMENDMENT 1 Draft version 2024-10-01
- [3]: Petersen, C.: Nachweis der Betriebsfestigkeit exzentrisch beanspruchter Ringflansch-verbindungen
(Fatigue assessment of eccentrically loaded ring flange connections). Stahlbau 67 (1998), S. 191-203. https://onlinelibrary.wiley.com/doi/abs/10.1002/stab.199800690
- [4]: Petersen, C.: Stahlbau (Steel construction), 4. Auflage Braunschweig: Wiesbaden: Springer Vieweg 2012.
- [9]: Tobinaga, I.; Ishihara, T.: A study of action point correction factor for L‐type flanges of wind turbine towers.
Wind Energy 21 (2018), p. 801-806. https://doi.org/10.1002/we.2193
- class pyflange.flangesegments.FlangeSegment
Abstract FlangeSegment class, meant to be extended and not to be instatiated directly.
Each FlangeSegment child class must implement the two methods
.bolt_axial_force(Z)
and.bolt_bending_moment(Z)
.
- class pyflange.flangesegments.PolynomialFlangeSegment
This is a generic FlangeSegment that implements a polynomial relation between shell pull Z and bolt axial force Fs or bolt bending moment Ms.
It is not meant to be instantiated directly, but to be subclassed instead.
The polynomial functions
.bolt_axial_force(Z)
and.bolt_bending_moment(Z)
are defined based on 4 points, through which the polynomials pass. Those points are implementation specific.The 4 reference points for the Fs(Z) polynomial are:
P1 = (Z1, Fs1)
representing the flange segment state at rest (no loads applied, other than the self-weight). Each implementatio of this class should define Z1 asshell_force_at_rest
property and Fs1 asbolt_force_at_rest
property.P2 = (Z2, Fs2)
representing the flange segment ultimate tensile limit state (failure state B). Each implementatio of this class should define Z2 asshell_force_at_tensile_ULS
property and Fs2 asbolt_force_at_ultimate_ULS
property.P3 = (Z3, Fs3)
representing the flange segment in small tensile deformation condition. This point is meant to define the initial slope of the polynomial. Each implementatio of this class should define Z3 asshell_force_at_small_displacement
property and Fs3 asbolt_force_at_small_displacement
property.P4 = (Z4, Fs4)
representing the gap closure state. Each implementatio of this class should define Z4 asshell_force_at_closed_gap
property, while Fs4 is automatically defined.
The 4 reference points for the Ms(Z) polynomial are:
Q1 = (Z1, Ms1)
corresponding to P1 as defined above. Each implementation of this class should define Ms1 asbolt_moment_at_rest
property.Q2 = (Z2, Ms2)
corresponding to P2 as defined above. Each implementation of this class should define Ms2 asbolt_moment_at_tensile_ULS
property.Q3 = (Z3, Ms3)
corresponding to P3 as defined above. Each implementation of this class should define Ms3 asbolt_moment_at_small_displacement
property.Q4 = (Z4, Ms4)
corresponding to P4 as defined above. Each implementatio of this class should define Z4 asshell_force_at_closed_gap
property, while Ms4 is automatically defined.
- bolt_axial_force(shell_pull)
Bolt axial force due to a given shell pull force Z.
The relation between shell pull force Z and bolt axial force Fs, is a polynomial function, as defined in ref.[1], section 8.2 and in ref.[2], section G.4.2.
The passed shell_pull parameter must be either a real number or a numpy.array. If a numpy.array is passed, then the corresponding array of Fs values will be returned.
- bolt_bending_moment(shell_pull)
Bolt bending moment due to a given shell pull force Z.
The relation between shell pull force Z and bolt bending moment Ms, is a polynomial function, as defined in ref.[1], section 8.3 and in Ref.[2], section G.4.2.
The passed shell_pull parameter must be either a real number or a numpy.array. If a numpy.array is passed, then the corresponding array of Ms values will be returned.
- class pyflange.flangesegments.PolynomialLFlangeSegment(a: float, b: float, s: float, t: float, R: float, central_angle: float, Zg: float, bolt: Bolt, Fv: float, Do: float, washer: Washer, nut: Nut, gap_height: float, gap_angle: float, gap_shape_factor: float = 1.0, tilt_angle: float = 0.0, E: float = 210000000000.0, G: float = 80770000000.0, s_ratio: float = 1.0, r: float = 0.01, k_shell: float = None)
This class provide a
PolynomialFlangeSegment
implementation for L-Flanges, based on ref. [1] and Ref. [2].For this particular case of flange, this class defines the polynomial reference points
P1
,P2
,P3
,P4
,Q1
,Q2
,Q3
,Q4
and inherits the polynomial functions.bolt_axial_force(Z)
and.bolt_bending_moment(Z)
from the parent class.The parameters required by this class are:
a
float
Distance between inner face of the flange and center of the bolt hole.
b
float
Distance between center of the bolt hole and center-line of the shell.
s
float
Shell thickness.
t
float
Flange thickness.
R
float
Shell outer curvature radius.
central_angle
float
Angle subtended by the flange segment arc.
Zg
float
Load applied to the flange segment shell at rest (normally dead weight of tower + RNA, divided by the number of bolts). Negative if compression.
bolt
pyflange.bolts.Bolt
Bolt object representing the flange segment bolt.
Fv
float
Applied bolt preload, after preload losses.
Do
float
Bolt hole diameter.
washer
pyflange.bolts.Washer
Washer object representing the fastener wahsers. If this parameter is
None
, then no washer is considered to be present.
nut
pyflange.bolts.Nut
Nut object representing the fastenrr nut.
gap_height
float
Maximum longitudinal gap height.
gap_angle
float
Angle subtended by the gap arc from the flange center.
gap_shape_factor
float
[optional]A correction factor that applies to
Fs2-Fs1
and toFs3-Fs1
to account for gap shape different that the default sinusoidal shape. If omitted, it defaults to 1.0 (sinusoida shape).
tilt_angle
float
[optional]Flange tilt angle, in radians. If omitted, it default to 0 rad.
E
float
[optional]Young modulus of the flange. If omitted, it will be taken equal to 210e9 Pa.
G
float
[optional]Shear modulus of the flange. If omitted, it will be taken equal to 80.77e9 Pa.
s_ratio
float
[optional]Ratio of bottom shell thickness over s. If omitted, it will be take equal to 1.0, threfore, by default, s_botom = s.
r
float
[optional]Radius of the rouding between the shell and the flange. If omitted, it defaults to 0.01.
k_shell
float
[optional]Optional individual initial shell stiffness value. This value can be calculated in a separate FE analysis. The unit must be [N/m/m]. If omitted, the interpolated formula from [1] will be used.
The given parameters are also available as attributes (e.g.
fseg.a
,fseg.Fv
, etc.).This class is designed to be immutable, therefore modifying the attributes after instantiation is not a good idea. If you need a segment with different attributes, just create a new one.
- failure_mode(fy_sh, fy_fl, gamma_0=1.1)
Determine the failure mode of this flange
Parameters:
fy_sh
float
Yield stress of the shell material.
fy_fl
float
Yield stress of the flange material.
gamma_0
float
[optional]Material factor. If omitted, it defaults to 1.1.
Return value
It returns a tuple of two values: - A string describing the failure mode: eiter “A”, “B”, “D” or “E”. - The list [Zu_A, Zu_B, Zu_D, Zu_E] of the shell pull values at which each failure mode occurs.
- validate(fy_sh, fy_fl, gamma_0=1.1)
Check if this flnage segment matches the model assumptions
Check if this L-Flange Segment matches the assumptions, that is, if it fails according to failure mode B. If not, it will throw an exceptions.
The required parameters are:
fy_sh
float
Yield stress of the shell material.
fy_fl
float
Yield stress of the flange material.
gamma_0
float
[optional]Material factor. If omitted, it defaults to 1.1.
- property shell_force_at_rest
Shell force when no external loads are applied
The shell loads at rest are normally the self-weights of the structure supported by the flange.
- property bolt_force_at_rest
Bolt axial force when no external loads are applied
The bolt force at rest is just the bolt pretension.
- property bolt_moment_at_rest
Bolt bending moment when no external loads are applied
- property shell_force_at_small_displacement
Intermediate shell pull, between rest and tensile failure
This is an auxiliary point that gives the polynomial the right value of initial slope. It is evaluated according to ref. [1], sec.8.2.2.3 and to ref. [2], section G.4.2.
- property bolt_force_at_small_displacement
Intermediate bolt pull, between rest and tensile failuse
This is an auxiliary point that gives the polynomial the right value of initial slope. It is evaluated according to ref. [1], sec.8.2.2.3 and to ref. [2], section G.4.2.
- property bolt_moment_at_small_displacement
Intermediate bolt moment, between rest and tensile failuse
This is the bolt bending moment corresponding to the shell pull Z3 (
.shell_force_at_small_displacement
)`.`
- property shell_force_at_tensile_ULS
Ultimate Limit State shell pull
This is shell pull that brings the flange segment system in its tensile ultimate limit state. It is evaluated according to ref. [1], sec.8.2.2.2 and to ref. [2], section G.4.2, where it is referred to as Z2.
- property bolt_force_at_tensile_ULS
Bolt axial force at tensile failure
This is the bolt tensile force corresponding to the ultimate shell pull (
.shell_force_at_rensile_ULS
).Assuming the failure mode B, in the ULS, the bolt is subjected to its maximum tensile capacity.
In refs. [1] and [2], this value is colled Fs2.
- property bolt_moment_at_tensile_ULS
Bolt bending moment at tensile failure
This is the bolt bending moment corresponding to the ultimate shell pull (
.shell_force_at_rensile_ULS
).In refs. [1] and [2], this value is colled Ms2.
- property shell_force_at_closed_gap
Shell force necessary to completely close the imperfection gap.
- class pyflange.flangesegments.PolynomialTFlangeSegment(a: float, b: float, s: float, t: float, R: float, central_angle: float, Zg: float, bolt: Bolt, Fv: float, Do: float, washer: Washer, nut: Nut, gap_height: float, gap_angle: float, gap_shape_factor: float = 1.0, tilt_angle: float = 0.0, E: float = 210000000000.0, G: float = 80770000000.0, s_ratio: float = 1.0, r: float = 0.01, k_shell: float = None)
This class provide a
PolynomialFlangeSegment
implementation for T-Flanges, based on ref. [1].For this particular case of flange, this class defines the polynomial reference points
P1
,P2
,P3
,P4
,Q1
,Q2
,Q3
,Q4
and inherits the polynomial functions.bolt_axial_force(Z)
and.bolt_bending_moment(Z)
from the parent class.The parameters required by this class are:
a
float
Distance between inner face of the flange and center of the bolt hole.
b
float
Distance between center of the bolt hole and center-line of the shell.
s
float
Shell thickness.
t
float
Flange thickness.
R
float
Shell outer curvature radius.
central_angle
float
Angle subtended by the flange segment arc.
Zg
float
Load applied to the flange segment shell at rest (normally dead weight of tower + RNA, divided by the number of bolts). Negative if compression.
bolt
Bolt
Bolt object representing the flange segment bolt.
Fv
float
Applied bolt preload, after preload losses.
Do
float
Bolt hole diameter.
washer
pyflange.bolts.Washer
Washer object representing the fastener wahsers. If this parameter is
None
, then no washer is considered to be present.
nut
pyflange.bolts.Nut
Nut object representing the fastenrr nut.
gap_height
float
Maximum longitudinal gap height.
gap_angle
float
Angle subtended by the gap arc from the flange center.
gap_shape_factor
float
[optional]A correction factor that applies to
Fs2-Fs1
and toFs3-Fs1
to account for gap shape different that the default sinusoidal shape. If omitted, it defaults to 1.0 (sinusoida shape).
tilt_angle
float
Inclination angle of the Flange, where the inclination angle is defined per side of the connection. If omitted, it will be take equal to 0.0
E
float
[optional]Young modulus of the flange. If omitted, it will be taken equal to 210e9 Pa.
G
float
[optional]Shear modulus of the flange. If omitted, it will be taken equal to 80.77e9 Pa.
s_ratio
float
[optional]Ratio of bottom shell thickness over s. If omitted, it will be take equal to 1.0, threfore, by default, s_botom = s.
r
float
[optional]Radius of the rouding between the shell and the flange. If omitted, it defualts to 0.01.
k_shell
float
[optional]Optional individual initial shell stiffness value. This value can be calculated in a separate FE analysis. The unit must be [N/m/m]. If omitted, the interpolated formula from [1] will be used.
The given parameters are also available as attributes (e.g.
fseg.a
,fseg.Fv
, etc.). This class is designed to be immutable, therefore modifying the attributes after instantiation is not a good idea. If you need a segment with different attributes, just create a new one.- failure_mode(fy_sh, fy_fl, gamma_0=1.1)
Determine the failure mode of this flange
Parameters:
fy_sh
float
Yield stress of the shell material.
fy_fl
float
Yield stress of the flange material.
gamma_0
float
[optional]Material factor. If omitted, it defaults to 1.1.
Return value
It returns a tuple of two values: - A string describing the failure mode: eiter “A”, “B”, “D” or “E”. - The list [Zu_A, Zu_B, Zu_D, Zu_E] of the shell pull values at which each failure mode occurs.
- validate(fy_sh, fy_fl, gamma_0=1.1)
Check if this flnage segment matches the model assumptions
Check if this L-Flange Segment matches the assumptions, that is, if it fails according to failure mode B. If not, it will throw an exceptions.
The required parameters are:
fy_sh
float
Yield stress of the shell material.
fy_fl
float
Yield stress of the flange material.
gamma_0
float
[optional]Material factor. If omitted, it defaults to 1.1.
- property shell_force_at_rest
Shell force when no external loads are applied
The shell loads at rest are normally the self-weights of the structure supported by the flange.
- property bolt_force_at_rest
Bolt axial force when no external loads are applied
The bolt force at rest is just the bolt pretension.
- property bolt_moment_at_rest
Bolt bending moment when no external loads are applied
- property shell_force_at_small_displacement
Intermediate shell pull, between rest and tensile failure
This is an auxiliary point that gives the polynomial the right value of initial slope. It is evaluated according to ref. [1], sec.8.2.2.3 and to ref. [2], section G.4.2.
- property bolt_force_at_small_displacement
Intermediate bolt pull, between rest and tensile failuse
This is an auxiliary point that gives the polynomial the right value of initial slope. It is evaluated according to ref. [1], sec.8.2.2.3 and to ref. [2], section G.4.2.
- property bolt_moment_at_small_displacement
Intermediate bolt moment, between rest and tensile failuse
This is the bolt bending moment corresponding to the shell pull Z3 (
.shell_force_at_small_displacement
)`.`
- property shell_force_at_tensile_ULS
Ultimate Limit State shell pull
This is shell pull that brings the flange segment system in its tensile ultimate limit state. It is evaluated according to ref. [1], sec.8.2.2.2 and to ref. [2], section G.4.2, where it is referred to as Z2.
- property bolt_force_at_tensile_ULS
Bolt axial force at tensile failure
This is the bolt tensile force corresponding to the ultimate shell pull (
.shell_force_at_rensile_ULS
).Assuming the failure mode B, in the ULS, the bolt is subjected to its maximum tensile capacity.
In refs. [1] and [2], this value is colled Fs2.
- property bolt_moment_at_tensile_ULS
Bolt bending moment at tensile failure
This is the bolt bending moment corresponding to the ultimate shell pull (
.shell_force_at_rensile_ULS
).In refs. [1] and [2], this value is colled Ms2.
- property shell_force_at_closed_gap
Shell force necessary to completely close the imperfection gap
- pyflange.flangesegments.bolt_markov_matrix(fseg, flange_markov_matrix, bending_factor=0.0, macro_geometric_factor=1.0, mean_factor=1.0, range_factor=1.0)
Returns the bolt Markov matrix, given the shell Markov matix
Parameters:
- fsegpyflange.flangesegments.PolynomialFlangeSegment
The flange segment object that contains the force and moment transfer function that convert shell forces to bolt forces.
WARNING: Notice that currently this function works only with PolynomialFlangeSegments, while it should be extended to work with any FlangeSegment object.
- flange_markov_matrixpandas.DataFrame
The flanges bending moments markov matrix, containg the colums ‘Cycles’, ‘Range’, ‘Mean’.
- bending_factorfloat [optional]
The factor that considers the bending portion of the total stress range. If omitted, it will be taken equal to 0.0.
- macro_geometric_factorfloat [optional]
The factor that considers macro geometric influences. The factor affects the deadweigt of the tower, the mean values of the markov matrix and the range values of the markov matrix. If omitted, it will be taken equal to 1.0.
- mean_factorfloat [optional]
The factor that multiplies the mean values of the bending moments of the tower If omitted, it will be taken equal to 1.0.
- range_factorfloat [optional]
The factor that multiplies the range of the bending moments of the tower If omitted, it will be taken equal to 1.0.
- pyflange.flangesegments.shell_stiffness(shell_radius, shell_thickness, gap_angle)
Axial stiffness of a flange-segment shell
This function will return the linear interpolation of the flange stiffnesses measured in 2160 different FEA analyses with several values of shell radius, shell thickness and gap angle.