What is meant by fatigue failure
RiLiWEA  guideline for wind turbines
Actions and proof of stability for tower and foundation
 DIBt / Lower Saxony 
Version October 2012
(Nds.MBl. No. 10a of 07.03.2014 p. 237)
Corrected version March 2015
archive ^{2005}
The corrected version of March 2015 does not contain any changes in content compared to the version of October 2012, only clarifications and editorial corrections. Therefore, the designation of the 2012 version was retained with the addition "Corrected version March 2015".
1 scope
This guideline applies to the evidence of the stability of the tower and the foundation of wind turbines. At the same time, based on the stipulations of DIN EN 614001, it contains regulations on the effects on the entire wind turbine, including the associated safety factors, which help determine the internal forces acting on the tower and the foundation from the machine (see Section 9.2.4) their assessment are to be used as a basis. The assessment of the machine itself is not part of this guideline. The ninth ordinance on the Product Safety Act (Machinery Ordinance) (9th ProdSV) for the implementation of Directive 2006/42 / EC of the European Parliament and of the Council of May 17, 2006 on machinery and for the amendment of Directive 95/16 / EC (ABl. L 157 of 06/09/2006 p. 24, L 76 of 03/16/2007 p. 35) is referred to.
Furthermore, if necessary, requirements of the plantrelated water protection according to § 62 WHG (Water Management Act) must be taken into account.
DIN EN 614001 applies to the safety requirements for the machine.
In addition, the safety system must contain two or more braking systems (mechanical, electrical or aerodynamic) that are suitable for bringing the rotor from any operating state to a standstill or idle. At least one braking system must be able to keep the system in an intrinsically safe state even in the event of a power failure.
The following editions of DIN EN 614001 are permitted to determine the effects. The standard applies in each case with all associated corrections and appendices, whereby in the text of this guideline only reference is made to the respective base document with details of the year of issue (hereinafter printed in bold).
DIN EN 614001: 201108  Alternatively: DIN EN 614001: 200408 
DIN EN 614001 Correction 1: 200512 
The output used in each case is to be used in its entirety with regard to the determination of the effects. Mixing is not permitted. This applies, for example, to details regarding the load case definitions and the evaluation methods. Any existing specifications for the construction, dimensioning and execution of the tower and the foundation do not apply in connection with this guideline.
If this guideline refers to DIN EN 614001 without specifying the date of issue, then the regulations of the particular edition selected for overall application apply accordingly.
One exception concerns the determination of the effective turbulence within a wind farm, which must be carried out in accordance with DIN EN 614001: 201108.
Wind turbines with a swept rotor area of less than 200 m^{2} and which generate a voltage that is less than 1,000 V AC or 1,500 V DC may be verified in accordance with DIN EN 614002. In particular, even for small wind turbines, the safety system must contain two or more brake systems (mechanical, electrical or aerodynamic) which are suitable for bringing the rotor from any operating state to standstill or idle. At least one braking system must be able to keep the system in an intrinsically safe state even in the event of a power failure.
The construction, dimensioning and execution of the tower and the foundation of wind turbines are based on the relevant technical building regulations for comparable structures, such as antenna structures, chimneys, masts and the like, unless other provisions are made in this guideline.
In addition, requirements regarding inspection and maintenance of the system are made so that the stability of the tower and the foundation is ensured over the intended design life.
The guideline does not take into account the special features of wind turbines that are built in the open waters of the North and Baltic Seas (offshore systems). The special features of vertical axis systems and braced systems are also not taken into account in this guideline. However, the rules given here can also be applied to such systems.
2 Terms and designations
2.1 Terms
The definitions of the following terms are to be understood in connection with the rules of this guideline. Under certain circumstances, they can deviate from the definitions used in energy yield calculations and in other regulations.
• Wind turbine (WEA):
System that converts the kinetic energy of the wind into electrical energy• Foundation and soilstructure interaction (soil torsion spring):
The foundation is a steel, reinforced concrete or prestressed concrete component in contact with the ground, including a concrete base over a natural or filled foundation base and soil. The soilstructure interaction influences the dynamic properties of the structure. An essential parameter of the soilstructure interaction is the restraint stiffness, which is described with the help of the soil torsion spring. This is to be determined taking into account the static or dynamic soil parameters.• Tower:
Part of a wind turbine above the foundation that supports the machine, including any bracing
 Steel tower: Tower consisting of one or more tubular steel segments
 Prestressed concrete tower: prestressed insitu concrete or precast tower
 Hybrid tower: reinforced concrete or prestressed concrete tower with an attached tubular steel tower
• machine:
The machinetechnical part of the wind energy installation arranged on the tower, these include, among others. the rotor blades as well as the hub, the shaft, the gearbox, the control and electrotechnical components, the generator, the bearings and the brakes• Design life:
the calculated duration on which the design of the wind turbine is based• Rated capacity:
maximum continuous power, which results from the power curve• Rated speed n_{R.}:
Speed of the rotor at nominal wind speed• Neutral:
Operational state of a wind turbine without power output, in which the rotor rotates slowly• mean wind speed v_{m}(z):
(10minute mean) the wind speed at a height z above ground• Average 50year wind speed v_{m50}(z):
mean wind speed, at height z above ground, depending on the topography of the location, which statistically is reached or exceeded once every 50 years (corresponds to an annual probability of exceeding 0.02). Corresponds to v_{m}(z) according to DIN EN 199114 taking into account DIN EN 199114 / NA• Average 1year wind speed v_{m1}(z):
Average wind speed at height z above ground, depending on the topography of the location, which statistically is reached or exceeded once a year on average• 50year gust speed v_{p50}(z):
Extreme value of the wind speed (3second average) at height z above ground, depending on the topography of the location, which is reached or exceeded once every 50 years; corresponds to v_{p}(z) according to DIN EN 199114 / NA.• 1year gust speed v_{p1}(z):
Extreme value of the wind speed (3second average) at height z above ground, depending on the topography of the location, which is reached or exceeded once a year.• Base wind speed vb:
50year wind at a height of 10 m in flat, open terrain, averaged over a period of 10 minutes (v_{b}= v_{b, 0} because c_{season} and c_{to you} = 1, see DIN EN 199114 in conjunction with DIN EN 199114 / NA)• Reference wind speed v_{b, 0}:
50year wind at a height of 10 m in flat, open terrain, which is averaged over a period of 10 minutes• Annual mean wind speed v_{ave}:
Wind speed averaged over several years at hub height• Nominal wind speed v_{r}:
the lowest mean wind speed at which the nominal power is reached• Cutin wind speed v_{in}:
the lowest mean wind speed at which the wind turbine is operated• Cutoff wind speed v_{out}:
the greatest mean wind speed at which the wind turbine is operated
2.2 Designations
A.  surface 
a  horizontal distance between the tower axes of two neighboring wind turbines 
c_{to you}  Directional coefficient according to DIN EN 199114 
c_{f}  aerodynamic force coefficient 
c_{s}c_{d}  Structure coefficient according to DIN EN 199114 
c_{season}  Season factor according to DIN EN 199114 
D.  Rotor diameter 
F.  Strength, burden 
f_{0}  Natural frequency 
f_{R.}  Excitation frequency of the running rotor 
H  Height of the rotor center point (hub height) above the terrain, tower height 
I._{T}  Turbulence intensity 
M.  moment 
m  Number of rotor blades, exponent of the Wöhler curve 
m_{E.}  Ice mass 
N  Number of load cycles 
n_{R.}  Nominal speed of the rotor 
q  Velocity pressure (dynamic pressure) 
R.  Rotor radius 
s  Dimensionless horizontal distance between the tower axes of two neighboring turbines based on the rotor diameter 
T_{ed}  Reference temperature 
T_{0}  Exposure time 
t_{s}  Depth of the rotor blade at the tip with linear extrapolation of the leading and trailing edge 
t_{w}  greatest depth of the rotor blade near the root 
v_{b}  Base wind speed 
v_{m50}  mean 50year wind speed 
v_{m1}  mean 1year wind speed 
v_{p50}  50year gust speed 
v_{p1}  1 year gust speed 
v_{hub}  Wind speed at hub height 
v_{ave}  Annual mean of the wind speed at hub height 
v_{out}  Cutoff wind speed at hub height 
v_{in}  Cutin wind speed at hub height 
v_{r}  Nominal wind speed at hub height 
x y z  Coordinates (see picture 4) 
α  Terrain roughness exponent 
β  Angle of attack 
γ_{F.}  Partial safety factor for the action 
γ_{M.}  Partial safety factor for the resistance 
δ  logarithmic decrement of damping 
ϑ  Ratio with respect to the depth of the rotor blade, ϑ = t_{s}/ t_{w} . 
ξ  dimensionless longitude on the rotor blade 
ρ  Airtightness 
ρ_{E.}  Density of ice 
σ  tension 
Δσ  Stress range 
Foot pointer  
d  Rated values 
k  characteristic values 
1  1year value 
50  50year value 
2.3 Comparison of terms and designations
Table 1
DIN EN 614001: 2004  DIN EN 614001: 2011  DIBt guideline 
Formula symbol Designation / meaning  Formula symbol Designation / meaning  Formula symbol Designation / meaning 
v_{ref} Reference wind speed Basic parameters for defining the type classes. Further relevant design parameters are derived from this. 10min mean value of the extreme wind speed in Hub height with a return period of 50 years.  v_{ref} Reference wind speed Basic parameters for defining the type classes. Further relevant design parameters are derived from this. 10minute mean value of the extreme wind speed at hub height with a return period of 50 years.  v_{m50}(H) Average 50year wind speed Average wind speed at hub height calculated in accordance with DIN EN 199114 + NA or in accordance with Chapter 7.3.2.1, taking into account the wind zone and terrain category with a return period of 50 years. 
v_{r} Rated wind speed  v_{r} Rated wind speed  v_{r} Nominal wind speed 
Rated power  Rated power  rated capacity 
A (abnormal) Type of design state  A (abnormal) Type of design state  A (exceptional) Group of 
A detailed comparison of the wind speed designations can be found in Appendix A (informative).
3 technical documents
The structural engineering documents include:
A. Technical data of the wind turbine with the following information in particular:
1 model name
2 manufacturers
3 configuration (data sheet)
4 control and braking system
5 rotor blade type
6 operating data that are required for the determination of the effects and for the dimensioning of the tower
B. Complete overview of the facility and, if necessary, site plan
C. Building description of the tower and foundation with the following information:
 Wind speed zone (design and, if applicable, location)
 Design life
 Subsoil conditions
D. Internal forces for the verification of the tower and foundation and further principles for the design (see Section 9)
E. Verification of stability for tower and foundation (verifications in the limit state of loadbearing capacity and serviceability) including vibration tests
F. Construction drawings for the tower and foundation with all necessary information and technical requirements for the execution of steel structures (see series of standards Eurocode 3: Dimensioning and construction of steel structures) and of reinforced and prestressed concrete structures (see series of standards Eurocode 2: Dimensioning and construction of reinforced concrete and prestressed concrete structures) .
G Assembly instructions (e.g. clamping instructions, manufacturing instructions for the foundation according to DIN EN 13670)
H Expert opinion from an expert on the foundation (subsoil report) In addition, the following documents must be available for wind turbines:
I. Expert opinions in which, if necessary, requirements for the construction and operation of the wind turbine are to be formulated
 Expert opinion from an expert to confirm the internal forces for the verification of the tower and foundation, rotor blades and mechanical engineering (load report)
 Expert opinion from an expert on the evidence of the safety devices (safety report)
 Expert opinion from an expert on the evidence of the rotor blades
 Expert opinion from an expert on the evidence of the mechanical engineering components and the cladding of the nacelle, hub (machine report)
 Expert opinion from an expert on the evidence for the electrotechnical components and lightning protection
Further documents that have to be examined by the machine expert:
J instruction manual
K Commissioning report (form)
L. Maintenance obligations book (see section 15)
4 Technical building regulations
Unless otherwise specified in this guideline, the technical building regulations apply, in particular with regard to the effects of DIN EN 199111, 13 and 14, for steel structures the basic standards of the DIN EN 1993 series of standards, for reinforced concrete and Prestressed concrete structures comply with the DIN EN 1992 series of standards, as well as DIN EN 1997 for the subsoil. All standards of the Eurocode series must always be used in conjunction with their national annexes.
Furthermore, the regulations of DIN EN 199332, Chapter 5.2 may be used for steel towers.
5 Materials and building materials, building products and execution
Only materials that comply with the technical building regulations may be used. The use of other materials requires special proof of usability in accordance with the building regulations, e.g. through a general building approval or approval in individual cases.
The construction of reinforced concrete and prestressed concrete components is carried out in accordance with DIN EN 13670.
Tensioning methods that are used to tension wind turbines must be suitable for the intended use in the wind turbine or for this corresponding area of application.
6 execution classes
Steel towers of wind turbines or parts of wind turbines in steel construction are to be assigned to the stress category SC2 and the damage consequence class CC2 according to DIN EN 10902 Appendix B. As a result, the minimum requirement for wind turbines is execution class EXC3. Corresponding requirements for the execution can be found in DIN EN 10902 Appendix A.3.
7 actions
7.1 General
Influences on the wind turbine are to be assumed in accordance with DIN EN 614001, see also Section 1. In addition, further effects in accordance with this section and combinations of effects in accordance with Section 8 must be taken into account.
7.2 Inertia and gravitational loads
7.2.1 Permanent gravitational loads (dead loads)
The characteristic values of the dead loads are to be determined using the calculated values according to DIN EN 199111. If materials are used that are not included in these standards, their actual weights must be used as a basis for the load determination.
7.2.2 Inertial forces from mass eccentricities
The rotor imbalances described in DIN EN 614001 must be applied. In addition, the additional inertial forces from mass eccentricities due to ice loads are to be determined in the event that 1 rotor blade is not iced up (see Section 7.4.6), if operation under ice loads cannot be safely ruled out.
7.2.3 Earthquake
Effects from earthquakes are to be taken into account in accordance with DIN EN 19981 including DIN EN 19981 / NA, whereby importance category 1 may be assumed.
The superposition with the loads of the wind turbine based on load cases D.5 and D.6 is a simplified consideration here. Alternatively, a closer look can be carried out in accordance with DIN EN 614001: 2011.
7.3 Aerodynamic loads
7.3.1 General
The aerodynamic loads are to be determined in accordance with DIN EN 199114, taking into account the special provisions of DIN EN 614001 and this guideline.
In general, the wind conditions according to DIN EN 614001 apply. Deviations from DIN EN 614001 are specified below.
In deviation from DIN EN 199114ρ = 1.225 kg / m^{3} be accepted.
The wind speed is to be assumed to be effective regardless of the direction of the compass (c_{to you} = 1).
The maximum aerodynamic imbalances specified for rotor production must be taken into account.
7.3.2 Wind conditions
7.3.2.1 Extreme wind conditions
The wind speed of the mean 50year wind to be assumed according to the wind zone of the wind turbine, v_{m50}(h) is to be determined according to DIN EN 199114 including NA.
The calculation of the height profile of the mean 50year wind speed v_{m50}(z) and the turbulence I._{v}(z) For terrain roughness up to a maximum of terrain category III, the formulas in accordance with table NAB.2 or NAB.4 in DIN EN199114 / NA are used.
Roughness greater than in terrain category III must not be used.
For locations in terrain category I and terrain category II, the equations (GL1) and (GL2) may be used in simplified form.
In simplified terms, the turbulence intensity can be assumed as follows:
lv (z) = 0.128 * (z / 10) ^{0,05}  (GL 1) 
The corresponding height profile for the mean 50year wind speed (including the mean wind profile for the turbulent wind field) can be assumed as follows:
v (z) = 1.15 * v_{b, 0} * (z / 10) ^{0,121}  (GL 2) 
The values for the mean 1year wind, v_{m1}(z) are determined from the mean 50year wind, v_{m, 50}(z), by multiplying by a factor of 0.8.
These specifications relate to the EWM wind model, i.e. the wind conditions must be adapted accordingly for the corresponding load cases from DIN EN 614001.
7.3.2.2 Operating wind conditions
The annual mean of the wind speed at hub height, v_{ave}, is to be assumed according to equation (GL 3) or equation (GL 4), provided that no lower values can be demonstrated for the specific location.
v_{ave} = 0.18 * v_{m50}(H)  (GL 3) 
v_{ave} = 0.20 * v_{m50}(H)  (GL 4) 
The equation (GL 4) applies to islands in the North Sea.
The annual mean of the wind speed v_{ave} in WZ 1 and WZ 2 the value of WZ 3 is to be used.
It is recommended to provide evidence of the system for the turbulence intensity of turbulence category A according to DIN EN 614001 in order to ensure coverage of all German locations when setting up individual systems. If this is deviated from, a sitespecific turbulence assessment is required, see Chapter 16.
It is permissible to specify operating and extreme wind conditions for wind turbines, including the turbulence category, regardless of wind zones in accordance with DIN EN 199114, and to prove this in the context of a type test.
This information must be included in the type test and in the load report. Covered wind zones and terrain categories are to be explicitly stated.
7.3.3 Influences of neighboring structures, roughness of the terrain and topography on the suitability of the location
A sitespecific investigation must be carried out to determine whether local increases in turbulence as a result of the influences of neighboring wind turbines or site wind conditions endanger the suitability of the site.
The site suitability test must be carried out in accordance with Chapter 16 "Site suitability of wind turbines".
The loads acting on the wind turbine are to be determined at least with the sitespecific values of the wind parameters.
If the system was designed for turbulence category A, the influence of the local increase in turbulence on the suitability of the location does not need to be examined if the following conditions are met:
a ≥ 8D for v_{m50} (h) ≤ 40m / s  (GL 5) 
a ≥ 5D for v_{m50} (h) ≥ 45 m / s  (GL 6) 
Fig. 1: Schematic representation of the required distances (hatched area)
Where:
a  Distance between the tower axes of neighboring wind turbines 
D.  the larger rotor diameter in each case 
v_{m50}(H)  Average 50year wind at hub height 
For intermediate values of v_{m50} (h) a is to be interpolated linearly. The combinations of wind speed and terrain category that occur in Germany have already been taken into account.
7.3.4 Wind loads for the state during installation or maintenance
For the investigation of the conditions during assembly, the wind speed v_{b} or the speed pressure, which results from the wind speed, can be reduced depending on the duration of this state and, if applicable, the selected protective measures according to DIN EN 199114, taking into account DIN EN 199114 / NA.
The manufacturer must specify the maximum permissible mean wind speed for the examination of the maintenance conditions. It must be ensured that the maintenance work is only carried out up to the maximum mean wind speed specified by the manufacturer.
In order to achieve a sufficient safety distance to the permissible mean wind speed, the wind speed must be increased appropriately for the determination of the loads. The following values are to be assumed for this:
 When using a deterministic wind field, an EOG (= extreme operating gust) according to DIN EN 614001: 2006, based on an average wind speed of 10 m / s above the permissible average wind speed, must be taken into account.
 When using a turbulent wind field, the mean wind speed must be increased by 5 m / s compared to the permissible mean wind speed.
7.3.5 Wind load in the event of ice formation
In the event of ice formation, the wind load on the reference surface of the structure, which has been enlarged by the ice formation on all sides (see Section 7.4.6), is to be determined. In the case of trusses, the aerodynamic force coefficients are to be set according to the degree of completeness changed by the icing.
7.3.6 Effects from vortex shedding
Effects from vortex shedding can lead to vibrations at right angles to the wind direction (transverse vibrations), especially in towers with circular or approximately circular crosssections, see Section 9.4.
7.4 Other influences
7.4.1 Imperfections, actions from uneven settlement
In addition to the elastic deformations of the supporting structure and the subsoil under the influence of external loads, the following undesired deviations of the tower axis from the vertical must be taken into account as permanent effects:
 Inclination of the tower axis with 5 mm / m to record manufacturing and assembly inaccuracies and influences from onesided solar radiation
 Inclination due to uneven subsidence of the subsoil or change in support conditions ^{1}
Actions from imperfections and uneven settlement must be added to the actions resulting from the overall dynamic calculation, acting in an unfavorable direction.
7.4.2 Pretensioning force
The pretensioning of concrete structures is taken into account in accordance with DIN EN 199211.
7.4.3 Earth pressure
Resulting earth pressures that have an unfavorable effect (e.g. on slopes) must be taken into account.
7.4.4 Groundwater pressure
Unfavorable groundwater pressures must be taken into account. If no other values are proven, a design water level at the height of the top of the ground is to be used. Correspondingly higher water levels must be taken into account in floodplain areas.
In the case of type calculations, the underlying design water level must be specified in the planning documents.
Note: The bed water pressure is to be set as a permanent load. If the water level is set up to the OK area, γ_{F.} = 1.1 can be calculated.
7.4.5 Heat exposure
In order to record the effects of the temperature compared to the installation temperature of 15 ° C and the effects of solar radiation, the following temperature components must be taken into account for towers made of prestressed concrete (Fig. 2):
 a component ΔT that acts constantly over the circumference and the crosssectional thickness_{N, 1} = ± 35 K
 a portion ΔT which runs cosineshaped over the circumference along a circumferential sector of 180 ° and is constant over the crosssectional thickness_{N, 2} = ± 15 K
 a temperature difference ΔT that changes linearly over the wall thickness in the longitudinal and ring direction_{m} = ± 15 K
A larger, linearly variable temperature difference can arise from the operation of the system, which instead of ΔT_{m} = ± 15 K must be taken into account.
Figure 2: Representation of the temperature range ΔT_{N, 1,} Δ T_{N, 2} and Δ T_{m}
In the limit state of the loadbearing capacity, the temperature load cases (equation (GL 7)) are to be superimposed with the characteristic value of group N (Table 2: LC D.1). The combination coefficient is ψ_{temp} = 0.6 to be applied.
In the serviceability limit state, the temperature load case, depending on the type of prestressing, is to be superimposed on the associated load case according to Table 2:
Prestressed concrete without bond: quasipermanent combination: D.3
Prestressed concrete with bond: frequent combination: D.2
In both cases, the combination coefficient is ψ_{temp} = 0.6 to be applied.
In the case of superimposition, the temperature components are to be applied individually or in combination according to equation (GL 7).
(GL 7) 
7.4.6 Ice loads
When systems are at a standstill, the ice loads for all structural parts exposed to the weather must be determined in accordance with DIN 10555.
If operation under ice loads cannot be safely ruled out, the ice buildup on the rotor blades can be assumed to be a mass m distributed over the length of the rotor blade_{E.}(ξ) according to Fig. 3 and equation (GL 8) must be taken into account. The ice mass is assumed to act on the leading edge of the profile of the rotor blade.
m_{E.}(0.5) = c_{E.}(R) * ϑ (1+ ϑ) • ρ_{E.} • t^{2}_{w}  (GL 8) 
Where:  
c_{E.}(R) = 0.3 * e^{0.32R} + 0,00675  (GL 9) 
Fig. 3: Ice accumulation on rotor blades in systems in operation
ξ dimensionless longitude on the rotor blade
8 combinations of actions
To determine the stresses, the external conditions and effects listed in DIN EN 614001 must be combined, taking into account the additional specifications from Table 2 and Table 3, see paragraph 1 of DIN EN 614001.
The respective partial safety factors to be applied according to Table 5 or Table 6 are defined with the correspondingly assigned groups of action combinations.
For the groups of action combinations designated with F (fatigue), only the fatigue safety verification is to be carried out. The effects of the individual operating states are to be accumulated here.
The action combinations of groups N (normal and extreme), A (extraordinary) and T (transport and construction) must be examined separately.
The extreme wind speed model (EWM) is a turbulent extreme wind model based on the mean wind speed (50year wind from_{m50}(z) or. 1year wind from_{m1}(z)).
Alternatively, a stationary extreme wind model based on the gust wind speed (50year gust v_{p50}(z) or 1year gust v_{p1}(z)) can be applied. The values for the 1year gust wind speed, v_{p1}(z) are determined from the 50year gust wind speed, v_{p50}(z) by multiplying by the factor 0.8.
In the limit state of the loadbearing capacity, the temperature load cases according to Chapter 7.4.5 are to be superimposed with the characteristic value of group N (Table 2: LC D.1).
The temperature loads must be taken into account in the verification of decompression or verification of the crack width limitation in accordance with Section 11.2.5.
Table 2: Additional load cases
Operating conditions (Reference to DIN EN 614001)  DLC  Wind conditions  Other requirements  Group of action combinations or load groups to be evaluated 
Different operating conditions according to the load cases to be evaluated  D.1  Note: The specified load cases are used for verifications in the serviceability limit state. V._{in} ≤ V_{hub} ≤ V_{out}  Characteristic value: Design value of all evaluated load cases (evaluation according to DIN EN 614001)  N and T (without earthquake) 
D.2  Frequent impacts: Stresses with a probability of exceeding p = 10^{4} (corresponds to 17.5 hours in 20 years)  The evaluation includes all load cases in Table 3  
D.3  Quasipermanent actions: Stresses with a probability of exceeding p = 10^{2} (corresponds to 1,750 hours in 20 years)  
1. Production plant  D.4  NWP v_{hub} = v_{r}  Ice loads (see 7.4.6)  F. 
D.5  NWP v_{hub} = v_{r}  earthquake  A.  
5. Emergency shutdown  D.6  NWP V_{hub} = v_{r}  earthquake  A. 
6. Parking (Standstill or idle)  D.7  EWM Return period 50 years v_{hub} = v_{m50}(H)  Yaw error β = 0 *  N (γ_{F.}=1.5) 
D.8  EWM Return period 50 years v_{hub} = v_{m50}(H)  Analogous to DLC 6.1 according to DIN EN 614001, but with Wind conditions according to Section 7.3.2  N  
D.9  EWM Return period 50 years v_{hub} = v_{m50}(H)  Analogous to DLC 6.2 according to DIN EN 614001, but with Wind conditions according to Section 7.3.2  A.  
D.10  EWM Return period 1 year v_{hub} = v_{m1}(H)  Analogous to DLC 6.3 according to DIN EN 614001, but with Wind conditions according to Section 7.3.2  N  
7. Parking (Standstill with error)  D.11  EWM Return period 1 year v_{hub} = v_{m1}(H)  Analogous to DLC 7.1 according to DIN EN 614001, but with Wind conditions according to Section 7.3.2  A. 
8. Transport, maintenance, repair  D.12  EWM Return period 1 year v_{hub} = v_{m1}(H)  Analogous to DLC 8.2 according to DIN EN 614001, but with Wind conditions according to Section 7.3.2  A. 
Table 3: Load cases for the verification of fatigue safety
Operating conditions (Reference to DIN EN 614001)  DLC (DIN EN 614001: 2006)  DLC (DIN EN 614001: 2004)  Wind conditions  Other requirements  Frequency to be used 
1. Production plant  D.4  D.4  NWP v_{hub} = v_{r}  Ice loads  7 days a year 
1.2  1.2  NTM V_{in} ≤ V_{hub} ≤ V_{out}  According to wind speed distribution  
2. Production operation with an error occurring  2.4  2.3  NTM V_{in} ≤ V_{hub} ≤ V_{out}  1. Overspeed @ V_{r} 1. Overspeed @ V_{out}  7 times a year 3 times a year 
NTM V_{in} ≤ V_{hub} ≤ V_{out}  Operation with extreme yaw error  24 hours a year  
NTM  Power failure  20 times a year, different wind speeds are applied according to the wind speed distribution  
3. Start  3.1  3.1  NWP  Start @ V_{in} Start @ V_{r} Start @ V_{out}  1,000 x per year 50 times a year 50 times a year 
4th stop  4.1  4.1  NWP  Stop @ V_{in} Stop @ V_{r} Stop @ V_{out}  1,000 x per year 50 times a year 50 times a year 
6. Parking (Standstill or idle)  6.4  6.2  NTM V_{hub} ≤ 0,7 v_{m50}(H),_{0}  According to wind speed distribution 
Hints:
 Depending on the system concept (control, operational management, maintenance, etc.), additional load cases or other frequencies for fatigue (fatigue evaluation) may have to be taken into account.
 Load case D.4 must be taken into account if operation under ice loads cannot be safely ruled out.
9 Determination of the design internal forces
9.1 General
The internal forces for dimensioning the tower and foundation are to be determined by an overall dynamic calculation taking into account the regulations according to Section 9.2.
Notwithstanding this, a simplified calculation of the tower structure may also be carried out for horizontal axis systems in accordance with Section 9.3 if there is sufficient spacing between the natural frequencies f during continuous operation_{0, n} of the tower from the excitation frequencies f_{R.} or f_{Rm} is guaranteed in accordance with equation (GL 10) and equation (GL 11). The simplified procedure can also be used for systems in the "out of service" state.
In continuous operation, there is a sufficient spacing between the natural frequencies f_{0, n} of the tower from the excitation frequencies f_{R.} or f_{R, m} according to equations (GL 10) and (GL 11).
(f_{R.} / f_{0,1}) ≤ 0,95  (GL 10)  
(f_{R, m} / f_{0, n}) ≤ 0,95  or  (f_{R, m} / f_{0, n}) ≤ 1,05  (GL 11) 
Where:
f_{R.}  max.rotation frequency of the rotor in the normal operating range 
f_{0,1}  first natural frequency of the tower 
f_{R, m}  Pass frequency of the m rotor blades 
f_{0, n}  nth natural frequency of the tower 
The number n of natural frequencies to be determined must be selected to be at least large enough that the highest calculated natural frequency is at least 20% higher than the blade passage frequency.
The natural frequencies of the tower are to be determined and specified for the vibration system to be examined assuming elastic material behavior. The influence of the foundation must also be taken into account.
In order to take into account uncertainties when calculating the natural frequencies, the calculated values must be varied by ± 5%.
In the case of systems in which equation (GL 10) and equation (GL 11) are not met during continuous operation, i.e. that are operated in the nearresonance range, operational vibration monitoring must be carried out.
9.2 Overall dynamic calculation
9.2.1 General
Stresses on the overall system by means of an overall dynamic calculation are to be determined according to the theory of elasticity. It should be noted that influence components can also have a beneficial effect on some verifications. The individual components of the internal forces generally do not have the same phase, so that the most unfavorable points in time have to be selected here.
The partial safety factor method cannot be used for an overall dynamic calculation in the time domain. In this case, proceed according to Section 10.2.
9.2.2 Requirements
In the case of an overall dynamic calculation of the wind turbine, the following influencing parameters with regard to the wind model, aerodynamics, structural dynamics and function must be taken into account.
• Wind model
The wind model must meet the requirements of DIN EN 614001. In addition, the following must be observed:
The influences from the tower shadow can be estimated according to the potential theory.
Annotation: Satisfactory results can generally be obtained at a wind speed sample rate of 4 per second and a load sample rate of 20 per second.
A number of at least 10 * 10 points (depending on the diameter), based on the rotor, is recommended.
For proof of fatigue safety, a simulation time of 600 seconds per wind speed class with a class width of approx. 2.0 m / s is recommended.
• aerodynamics
When calculating the aerodynamic loads, the following influences must also be taken into account:
 Hub and tip vertebrae
 Blade adjustment, pendulum, etc.
 Stall (dynamic stall)
 Dynamic wake behavior
Annotation: In general, satisfactory results can be achieved using the blade element theory with 15 elements per rotor blade.
• Structural dynamics
When examining the structural dynamics, the following influences must also be taken into account:
 Influence of centrifugal force on rotor blade stiffness
 Torsional stiffness of the drive train
 Elastic mounting of the machine
 Stiffness and damping of the generator (network can be viewed as infinitely stiff)
 Foundation with soil properties
Annotation: In general, it is sufficient to only consider natural frequencies <5 Hz.
• Function
Controller properties are to be mapped realistically. The chronological progressions, such as yawing and braking, must be taken into account.
For all action combinations with the exception of DLC 6.1, 6.2 and 6.3 according to DIN EN 614001, a yaw error according to the operational management, but at least a yaw error angle in the range between β = 0 ° and β = ± 8 °, must be expected.
For the action combinations DLC 6.1, 6.2 and 6.3, the yaw error angle according to DIN EN 614001 is to be assumed.
9.2.3 Consideration of the foundation
The rigidity of the subsoil is of particular importance for the operating behavior of wind turbines. The soilstructure interaction must always be taken into account. In the case of an overall dynamic calculation, this can be captured to a good approximation using springs for rotation and horizontal displacement, independent of frequency, with dynamic soil parameters (see Section 12.2.1).
The determination of the spring stiffness or the soil parameters for the overall dynamic calculation can be determined taking into account the stiffness of the foundation body and the shear distortions occurring in the soil. The shear distortions for the load level are to be determined, which results from load case D.3 (quasipermanent actions).
The stiffness modulus for very small strains E_{s, max} can be estimated depending on the stiffness modulus for static loads, whereby the lower value of the specified bandwidth is to be used without more precise evidence.
Notes on the size of dynamic soil properties are contained in the recommendations of the "Subsoil Dynamics" working group ^{2}.
9.2.4 Internal Forces
The result of the overall dynamic calculation is the time course of all internal forces for the investigated combinations of actions in the crosssections relevant for the design of the tower and foundation. These internal forces are to be determined for the verifications in the limit state of the loadbearing capacity and serviceability.
Table 4: Representation of the internal forces for verifications in the ultimate limit state or serviceability
(For the designation of the coordinate axes, see Figure 4)
Interface:  
Limit state: loadbearing capacity / serviceability  
DLC *)  v (h) [m / S]  ß °  F._{x} [kN]  F._{y} [kN]  F._{z} [kN]  M._{x} [kNm]  M._{y} [kNm]  M._{z} [kNm]  F._{res} [kNm]  M._{res} [kNm]  
max F_{x}  ....  
min F_{x}  
max F._{y}  
min F_{y}  
max F_{z}  
min F_{z}  
max M_{x}  
min M_{x}  
max M_{y}  
min M_{y}  
max M_{z}  
min M_{z}  
max F_{res}  
max M_{res} 
*) Combination of actions, see Section 8
For the verification of strength and stability failure as well as for the verification in the limit state of serviceability, only the extreme values of the internal forces together with the other internal forces occurring at the same time for the crosssections under consideration may be given for the sake of simplicity (see Table 4).
The internal forces for the proof of fatigue safety are generally allowed ^{3} can be given in simplified form in the form of load collectives, if necessary with the associated mean values (see Section 9.6.2).
Fig. 4: Coordinate system for the tower
9.3 Simplified calculation
9.3.1 General
The simplified calculation may only be used for verifications of the tower structure within the framework of the regulations of Section 9.1. The internal forces determined from an overall dynamic calculation and specified in Table 4 at the machine / tower interface are to be used as effects on the tower. The internal forces at all other points on the tower are then derived from these actions. The amount and direction of the wind load on the tower of the respective combination of actions must be taken into account (see Section 9.6.2).
For the sake of simplicity, all components of the influence may be assumed to act simultaneously with their maximum value or, if they have a favorable effect, with their minimum value.
The actions at the machine / tower interface may also be used for other tower variants, provided that these have at least the same flexural and torsional rigidity and also meet the condition according to equation (GL 10) in continuous operation.
When using the simplified calculation, in addition to the internal forces at the machine / tower interface according to Section 9.2.4, the machine's masses and moments of inertia as well as the tower's natural frequencies on which the calculation is based must be specified.
9.3.2 Windinduced vibrations of the tower in the direction of the wind
In the case of verifications according to Section 9.3.1 for systems in the "out of operation" state, the vibration effect of the tower in the wind direction caused by the gusty wind must be recorded by applying a static equivalent load. When using the turbulent extreme wind model EWM in a quasistatic calculation, the wind load directly acting on the tower in the wind direction as a result of the gust wind speed (3s average of the 50year gust v_{p50}(z) or 1year gust v_{p1}(z)) to be multiplied by the structural factor cscd. A corresponding method for determining cscd is given in DIN EN 199114, taking DIN EN 199114 / NA into account.
In the case of tower constructions that are not susceptible to vibration in accordance with DIN EN 199114, the stationary extreme wind model EWM, based on the gust wind speed (3 s mean value of the 50year gust v_{p50}(z) or 1year gust v_{p1}(z)), then the structure coefficient for c_{s}c_{d} = 1 can be assumed.
In the case of verifications in accordance with Section 9.6.1 for plants in the "in operation" state, the vibration effect of the tower in the wind direction caused by the gustiness of the wind may not be taken into account, i.e. the structural coefficient for c_{s}c_{d} = 1 can be assumed.
9.4 Eddyexcited transverse vibrations
The stresses caused by eddyexcited vibrations at right angles to the wind direction (transverse vibrations) in towers with circular or approximately circular crosssections must be determined using the method specified in DIN EN 199114.
The damage caused by vortexexcited transverse vibrations can be neglected up to a value of D = 0.10. Otherwise, the damage from eddyexcited transverse vibrations and the damage in the transverse direction as a result of the load cases defined in Table 3 must be added for the proof of fatigue safety.
When calculating the stresses from eddyexcited transverse vibrations, the aerodynamic damping (see 9.5) must not be applied.
9.5 Logarithmic decrement of damping
The total damping is made up of the two components of structural damping and aerodynamic damping (see 9.4, however). The logarithmic decrement δ for the total damping results in
δ = δ_{s} + δ_{a}  (GL 12) 
Where:
δ_{s} logarithmic decrement of the structural damping
δ_{a} logarithmic decrement of the aerodynamic damping
Unless more precise values are documented, a logarithmic decrement for the structural damping may be used
 for steel towers δs = 0.015
 for prestressed concrete towers δ_{a} = 0,04
be accepted.
In the case of hybrid towers, more precise considerations are required, taking into account the geometry, material and eigenmodes.
The logarithmic decrement of the aerodynamic damping δ_{a} may be used to determine the effects of earthquakes using the modal method, unless a more precise calculation is made, for all tower types with δ_{a} = 0.05 can be assumed.
9.6 Internal forces for the proof of fatigue safety
9.6.1 Requirements
To determine the internal forces for the proof of fatigue safety, the actions according to DIN EN 614001 and Section 7, the influencing parameters according to Section 9.2.2 and the following specifications must be taken into account:
 In the regulation, start and normal shutdown processes are to be assumed, taking into account the dynamic increases when passing through the tower resonance with the frequencies according to Table 3.
 If operation under ice loads cannot be safely ruled out, ice loads according to Section 7.4.6 are to be assumed on 7 days per year at nominal power, whereby 1 rotor blade is not iced up, the others are iced up with 50% of the ice mass according to Figure 3.
 Unless otherwise specified, the duration of the action of the internal forces from vortex shedding can be assumed to have the following values:
 0.5 years for the state of the assembly, without machine
 1 year for the state of standstill and maintenance, with machine
 The design service life of the system can be assumed to be at least 20 years.
9.6.2 Collective strains
If the proof of fatigue safety is carried out on the basis of load collectives, then these are to be determined mathematically for the crosssections under consideration by simulating the requirements for fatigue according to Section 9.6.1 and, if necessary, supported by measurements according to IEC TS 6140013. The amplitudes of the internal forces are to be superimposed in an unfavorable way.
The collectives can be represented in a simplified way as envelopes (e.g. in trapezoidal form) of the stress collectives obtained from the simulation. Uniform numbers of load cycles should be specified for all components of the action. The associated mean values are to be stated.
Annotation: In general (if Δ My> Δ Mx), the consideration of the action components rotor thrust F is_{x}, Pitching moment M_{y} and tower torsional moment M_{z} sufficient. The pitch and tower torsional moment may be assumed to be 90 ° out of phase with one another.
10 security concept
10.1 General
The verifications are to be carried out for different limit states by methods with the help of partial safety factors. These limit states, when exceeded, the structure no longer meets the design requirements
 Limit states of the loadbearing capacity
 Limit states of serviceability.
10.2 Limit states of the loadbearing capacity
In the case of an overall dynamic calculation (according to Section 9.2), the actions must include
γ_{F.} = 1.0 can be assumed. If it is not possible to differentiate between individual action components in the internal forces, the structural safety verifications must also be provided
γ_{F.} fold internal forces are performed, whereby the largest partial safety factor of the respective group of the action combinations according to table 5 or table 6 is to be applied.
Table 5: Tells safety factors
γ_{F.} the actions for verifications in the limit states of the loadbearing capacity with verification according to DIN EN 614001: 2004
Impact  Group of action combinations  
N normal and extreme  A. out of the ordinary  T Transport / erection  
Inertial and gravitational loads  
unfavorable  1,35 *  1,1  1,25  
Cheap  1,0  1,0  1,0  
Preload **  1,0  1,0  1,0  
Wind loads  1,35 ***  1,1  1,5  
Functional forces  1,35  1,1  1,5  
Exposure to heat  1,35      
earthquake    1,0    

Table 6: Relay safety factors γ_{F.} the actions for verifications in the limit states of the loadbearing capacity with verification according to DIN EN 614001: 2011
Unfavorable loads Type of design state (see table 3)  Cheap loads ^{1}  
Impact  Normal (N)  Abnormal (A)  Transport and erection (T)  All design states 
Inertial and gravitational loads, Wind loads, functional forces  1,35*, ***  1,1  1,5  0,9 
Preload **  1,0  1,0  1,0  0,9 
Exposure to heat  1,35      0,9 
  1,0    1,0  
1) Prestressing and gravitational loads, which significantly reduce the overall stress, are beneficial loads. *) For the design load case DLC 1.1, load calculation using statistical extrapolation for wind speeds between V_{in} and V_{out} a partial safety factor for the loads of γ_{F.} = 1.25 to be assumed. If, for normal design conditions, the characteristic value of the gravitational load F_{gravity} can be calculated for the relevant design state and gravitation is an unfavorable load, the partial safety factor for the combined loading of gravitation and other influences may be assumed as follows: **) Possible spreads of the prestressing are to be considered in the limit state of the serviceability according to DIN EN 199211, 5.10.9. In the ultimate state of fatigue, the relevant value is r_{inf}, r_{sup} according to DIN EN 199211, 5.10.9. The value γ_{F.} = γ_{P} = 0.9 relates to the determination of the effects according to DIN EN 614001: 2011. In the limit state of the loadbearing capacity, DIN EN 199211, 2.4.2.2 and 5.10.8 apply to the design of prestressed concrete structures. Thereafter, in deviation from Table 6 i. d. R. γ_{P} = 1,0. ***) The cutting forces for the tower and foundation of the action combination DLC 6.1 according to DIN EN 614001 are both with γ_{F.} = 1.35 as well as with γ_{F.} = 1.5 to be determined, where in the case of γ_{F.} = 1.5 no inclined flow (angle of incidence β = 0, see DLC D.7 according to table 2) needs to be taken into account. The most unfavorable internal size combination of the two variants is decisive. 
When verifying against strength and stability failure, the increase in the internal forces due to nonlinear influences (e.g. 2nd order theory, state II) must be taken into account. In the case of an overall dynamic calculation with dynamic soil parameters, these verifications result in additional effects from the 2nd order theory. These additional effects are to be determined using static soil parameters that result for a load level with characteristic actions (load case D.1).
For the proof against fatigue is with γ_{F.} = 1.0 to be calculated.
The following verifications must be carried out in the ultimate limit states:
proof against
Notes on the size of dynamic soil properties are contained in the recommendations of the "Subsoil Dynamics" working group ^{4}.
10.3 Limit states of serviceability
The design values of the actions are to be used for verifications in the serviceability limit states with the characteristic values (γ_{F.} = 1.0).
The following verifications are to be carried out in the serviceability limit states:
proof the
11 Evidence for the tower
11.1 Verifications in the ultimate limit states
11.1.1 Tells safety factors
The resistances are taking into account the partial safety factors
γ_{M.} to be determined in accordance with the relevant regulations (see Section 4). With regard to the partial safety factors γ_{M.} for the verification against fatigue see Section 11.1.4.
11.1.2 Strength failure
The verifications are to be carried out with the most unfavorable of all action combinations of groups N, A and T.
DIN EN 199211 is to be used for the verification for reinforced concrete and prestressed concrete. The internal forces of the tower shaft may be determined according to the tube bending theory, provided the wall thickness is at least 1/20 of the radius. This does not apply to local verifications in the area of tower openings and to the determination of the stresses from the effects of heat according to Section 7.4.5.
The DIN EN 19931 series of standards is to be used for the verification of steel towers.
In cylindrical and conical tubular steel towers, the stresses required for the proof of structural safety may be calculated according to the shell membrane theory. This means, for example, for the transfer of wind loads, that the elementary tube bending theory may be applied. Shell bending moments from wind pressure unevenly distributed over the circumference of the tower or constraining stresses from edge disturbances on flanges or stiffeners do not need to be taken into account. At transitions with different conicity, the local circumferential membrane forces and shell bending moments resulting from force deflection must be taken into account. Section 13.2 must be observed for tower areas with weak openings.
Annotation: In the terminology of DIN EN 199311, the verification described here corresponds to an elastic structural calculation with plastic crosssectional loads for the local tower wall internal forces, but elastic crosssectional loads for the global tower internal forces.
11.1.3 Failure of stability
The verifications are to be carried out with the most unfavorable of all action combinations of groups N, A and T.
The buckling safety proof for the wall of a tubular steel tower or other shellshaped steel components may also be performed as a numerically supported buckling safety proof in accordance with paragraphs 8.6 and 8.7 of DIN EN 199316.
11.1.4 Fatigue failure of steel structures
The proofs are to be carried out with the action combinations of group F according to table 3.
For tower structures made of steel, the verification is based on DIN EN 199319. Regular maintenance and the recurring inspection according to Section 14 are a prerequisite for this. The partial safety factor to be applied is shown in Table 7.
Deviating from the regulations in DIN EN 199319, no threshold value of the fatigue strength may be used for load cycles N> 10^{8} must be applied (see Fig. 5).
Figure 5: Fatigue strength for steel (Wöhler curve)
Table 7: Tells safety factor γ_{M.} for verifications against fatigue in steel towers
Inspectable  γ_{M.}  
Damage tolerant components  Nondamage tolerant components  
Yes  1,0  1,15 
No  1,15  1,25 
Annotation: In the case of wind turbines, there are usually nondamagetolerant components. In general, a partial safety factor of 1.15 is to be used for inspectable components.
All components that are accessible are regarded as "inspectable". This includes, for example, all round and longitudinal seams of tubular steel towers as well as the screws of ring flange connections. These components are to be examined as part of the recurring tests (see Chapter 15).
Deviating from this, a coefficient of 1.25 must be taken into account if monitoring measures are not possible within the scope of the inspection, e.g. in the case of concrete components.
The reference value of the fatigue strength Δσ_{c} can be found in the notch case catalogs of DIN EN 199319, Tables 8.1 to 8.10 and DIN EN 199332 Appendix C in accordance with the present notch class.
Note on DIN EN 199332 C2 (1): An increase in the notch classes is not permissible simply by changing the quality level of the weld seam. An increase in the notch class is to be justified experimentally, e.g. according to the rules of DIN EN 1990.
As an alternative to the nominal stress concept, the structural stress concept according to DIN EN 199319 Appendix B can be used. For sheet thicknesses t> 25 mm, there is a sheet thickness reduction k_{s}= (25 / t)^{0,2} to be used, whereby t is to be used in [mm].
In addition to the notch catalogs, the notch detail Tflange / jacket sheet is regulated as follows:
 The notch class according to DIN EN 199319, Table 8.5 Detail 1, is to be used for the cladding sheet (notch point 1 in Fig. 6).
 For the Tflange (notch point 2 in Fig. 6), the conservative approach is a notch class 90 with sheet thickness reduction k_{s} = (25 / t_{F.})^{0,2} for sheet thickness t_{F.} ≥ 25 mm to be used. The decisive bending stresses are to be determined by applying a uniform stress distribution from the concrete pressings, unless more favorable approaches are justified by more precise investigations.
Figure 6: Verification points for the detail "Tflange / jacket plate"
Annotation: Tests carried out showed that other regulations of the Eurocode for the parameter range of wind turbines can lead to highly conservative interpretations.
11.1.5 Fatigue failure of reinforced and prestressed concrete structures
For towers and foundations made of prestressed concrete or reinforced concrete, proof of fatigue safety must be carried out for the concrete, the reinforcing steel and the prestressing steel. The arithmetical damage of different stress ranges may be added up when verifying against fatigue according to the PalmgrenMiner rule. The damage sum D_{Ed} fulfill the following condition due to the decisive fatigue stress:
D._{Ed} = Σ [n (Δσ_{i}) / N (Δσ_{i})] < 1,0  (GL 13) 
It is
n (Δσ_{i}) the number of load changes applied for a stress range Δσ_{i}
N (Δσ_{i}) the number of load changes that can be absorbed for a stress range Δσ_{i}
For the verification of the reinforcing and prestressing steel, the Wöhler curves according to DIN EN 199211, Paragraph 6.8.4 are to be applied.
The fatigue verifications for prestressed concrete structures are to be carried out both for the prestressing force immediately after the press is set down and for the prestressing force after creep, shrinkage and relaxation, if no more precise calculation is carried out over time. The timedependent losses due to creep, shrinkage and relaxation according to DIN EN 199211, section 3.1.4 must be taken into account.
The Wöhler lines for the concrete are to be used for the verification of the concrete under pressure or shear force loading:
Fig. 7: Wöhler curves of the concrete under compressive stress
The Wöhler line according to Figure 7 is based on the following equations ^{5} based on:
For
0cd, min < 0,8
logN_{1} = (12 + 16 * S_{cd, min} + 8 * S_{cd, min}^{2}). (1  p_{cd, max})
log N_{2} = 0.2 * log N_{1} * (log N_{1}  1)
log N_{3} = log N_{2} (0.3  (3S_{cd, min} / 8)) / ΔS_{CD}
if logN_{1} ≤ 6 then logN = logN_{1}
if logN_{1} > 6 and ΔS_{CD} ≥ 0.3  (3S_{cd, min} / 8) then logN = logN_{2}
if logN_{1} > 6 and ΔS_{CD} <0.3  (3S_{cd, min} / 8) then logN = logN_{3}
With  S._{cd, min} = γ_{Sd} * σ_{c, min} * η_{c} / f_{cd, fat} S._{cd.max} = γ_{Sd} * σ_{c, max} * η_{c} / f_{cd, fat} ΔS_{CD} = S_{cd, max}  S._{cd, min} 
For wind turbines with a nominal number of load cycles_{nom} = m * n_{R.} * T_{O} ≤ 2 * 10^{9} a detailed proof for the concrete is not required if the condition according to (GL 14) is met:
S._{cd, max} ≤ 0.40 + 0.46 * S_{cd, min}  (GL 14) 
Where:
S._{cd, min} = γ _{Sd} * σ_{c, min} * η_{c} / f_{cd, fat}
S._{cd, max} = γ_{Sd} * σ_{c, max} * η_{c} / f_{cd, fat}
γ_{Sd}= 1,1  Partial safety factor for recording the inaccuracies of the model for stress calculation 
σ_{c, max}  Amount of the maximum concrete compressive stress under the action combinations of group F according to table 2 
σ_{c, min}  Amount of the minimum concrete compressive stress in the compression zone at the same point at which σ_{c, max} occurs, determined for the lower value of the action (for tensile stresses, σ_{c, min} = 0 to be set) 
η_{c}  Factor for taking into account the uneven distribution of the concrete compressive stresses according to booklet 439 ^{6}, Eq. (8th); simplifying is allowed η_{c} = 1.0 can be set. 
f_{cd, fat}  Design value of the fatigue strength of concrete under compressive stress: f_{cd, fat} = 0.85 * β_{cc}(t) * f_{ck} * (1  f_{ck}/ 250) / γ_{c} 
f_{ck}  characteristic cylinder compressive strength in N / mm^{2} 
γ_{c}  Partial safety factor for concrete 
β_{cc}(t)  Coefficient to take into account the timedependent increase in the strength of the concrete. β_{cc}When using the simplified equation (GL 14), (t) must not be set higher than 1.0, corresponding to a cyclic initial load in a concrete age k 28 days. In the case of cyclic initial loading, the concrete is of an earlier age 
In principle, the following must be examined in the simplified verification procedure:
 Maximum amplitude,
 Stress range with the greatest concrete compressive stress σ_{c, max},
 Stress range with the smallest concrete compressive stress σ_{c, min,}
 Stress range with the largest mean value of the concrete compressive stress.
11.2 Verifications in the serviceability limit states
11.2.1 Combinations of actions
For the verifications in the serviceability limit states, the actions are defined in Table 2:
 DLC D.1: Characteristic (rare) effects
 DLC D.2: Frequent Actions
 DLC D.3: Quasipermanent actions
These effects are to be used for the verifications defined in the relevant technical standards in combination with the effects of temperature.
11.2.2 Telephony safety factor
For verifications in the serviceability limit states, the partial safety factor for the resistance values is γ_{M.} = 1,0.
11.2.3 Deformation limitation
Unless special requirements arise from the operation of the system, deformations do not need to be limited.
11.2.4 Voltage limitation
For towers and foundations made of prestressed concrete or reinforced concrete, the concrete compressive stresses for the rare action combination D.1 according to Table 2 are 0.6 f_{ck} to limit. Otherwise, substitute measures must be taken in accordance with DIN EN 199211, Section 7.2 (2).
In addition, in the case of towers and foundations made of prestressed concrete, the concrete compressive stresses under the permanent effects of dead loads and prestressing are at 0.45 f_{ck} according to DIN EN 199211, paragraph 7.2 (3).
In the case of composite towers made of prestressed concrete, evidence of decompression must be provided for the quasipermanent combination of actions D.3 according to Table 2.
11.2.5 Limitation of the crack width
The proof of the crack width limitation is to be provided for a calculated crack width of 0.2 mm. The quasipermanent action combination D.3 according to Table 2 is to be used for components made of reinforced concrete and prestressed concrete without bond, the frequent action combinations D.2 according to Table 2 for components made of prestressed concrete with bond.
12 Evidence for the establishment
12.1 Foundation body
12.1.1 Security concept
The safety concept described in Sections 10, 11 and 12 must be used for verifications of components made of reinforced and prestressed concrete as well as for components made of steel.
12.1.2 Steel components
Steel components must be verified in accordance with Section 11.1.4.
12.1.3 Reinforced concrete components
Reinforced concrete components are to be verified according to Sections 11.1 and 11.2.5. The evidence against fatigue for the concrete, the reinforcing steel, the prestressing steel and the fasteners are to be carried out in accordance with Section 11.1.5 of this guideline.
Components of the foundation body that extend no more than half a meter into the ground are to be verified with a crack width of 0.2 mm, all others with a crack width of 0.3 mm.
If bases are carried out on foundations, the verifications for the stress and crack width limitation are to be carried out as for the tower (see also 11.2.4 and 11.2.5).
12.1.4 Design of piles
The internal loadbearing capacity of foundation piles is to be determined according to Sections 12.1.2 and 12.1.3. The verification of the external pile loadbearing capacity must be carried out in accordance with Section 12.2.4.
12.2 Subsoil
12.2.1 Condition of the subsoil
It must be ensured that the properties of the subsoil at the site correspond to the requirements in the static and dynamic calculation.
With regard to the minimum requirements for the scope and quality of geotechnical investigations, the foundations of wind turbines are to be assigned to geotechnical category 3 according to DIN EN 19971, paragraph 2.1 or DIN 1054, paragraph A 2.1.2.
For dynamic calculations, the stiffness or shear modulus for unloading and reloading processes are decisive, for static calculations, on the other hand, as a rule  provided the soil is not preloaded  the modules for initial loading. The soil stiffness is generally dependent on the magnitude of the shear distortion induced by the load. The stiffness is maximum for very small shear distortions and, moreover, the modules for relieving / reloading and initial loading are identical, because the soil in this area reacts almost linearly and elastically. They are also referred to as "dynamic" shear modules or stiffness modules because highfrequency loads usually result in correspondingly small shear distortions. The shear modulus G, tabulated for many soil types_{Max}
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