Engineering Structures 24 (2002) 1015–1025www.elsevier.com/locate/engstruct

Static, seismic and stability analyses of a prototype wind turbinesteel tower

N. Bazeos, G.D. Hatzigeorgiou, I.D. Hondros, H. Karamaneas, D.L. Karabalis∗,D.E. Beskos

Department of Civil Engineering, University of Patras, 26500 Patras, Greece

Received 11 December 2000; received in revised form 7 February 2002; accepted 8 February 2002

Abstract

Selected results of a study concerning the load bearing capacity and the seismic behavior of a prototype steel tower for a 450 kWwind turbine with a horizontal power transmission axle are presented. The main load bearing structure of the steel tower rises toalmost 38 m high and consists of thin-wall cylindrical and conical parts, of varying diameters and wall thicknesses, which are linkedtogether by bolted circular rings. The behavior and the load capacity of the structure have been studied with the aid of a refinedfinite element and other simplified models recommended by appropriate building codes. The structure is analyzed for static andseismic loads representing the effects of gravity, the operational and survival aerodynamic conditions, and possible site-dependentseismic motions. Comparative studies have been performed on the results of the above analyses and some useful conclusions aredrawn pertaining to the effectiveness and accuracy of the various models used in this work. 2002 Published by Elsevier Science Ltd.

Keywords: Wind turbine; Steel tower; Static analysis; Seismic analysis; Stability analysis

1. Introduction

This work depicts some critical aspects of the analysesperformed during the design of an almost 38 m highsteel tower supporting a prototype 450 kW wind turbinewith a horizontal power transmission axle. The entirewind turbine system, now under construction, is the firstdesigned and manufactured exclusively in Greece.

The main supporting structure of the wind turbine, asshown in Fig. 1(a), is assembled by thin-wall cylindricaland conical parts of varying diameters and wall thick-nesses. Circular stiffeners are placed at regular intervalsalong the height of the structure for further stiffeningagainst local buckling. The optimal vertical spacingbetween circular stiffeners with regard to the thicknessand the diameter of the shell structure has been the sub-ject of an extensive stability analysis study.

Furthermore, at the base of the structure a substantialdoor opening is considered. The adverse influence of this

∗ Corresponding author. Tel.:+30-610-996218; fax: +30-61-997812.

E-mail address: karabali@upatras.gr (D.L. Karabalis).

0141-0296/02/$ - see front matter 2002 Published by Elsevier Science Ltd.PII: S0141-0296 (02)00021-4

opening on the overall structural behavior of the toweris partly counterbalanced by heavy reinforcement alongits perimeter as shown in Fig. 2. However, to the bestof our knowledge there are no formal analytical pro-cedures for estimating the effectiveness of such designconfigurations.

It is also considered common practice to analyze suchtower-like structures as ‘fixed’ at their base with no con-sideration of the foundation–soil interaction. In mostcases, over-designed foundations and stiff soil conditionscould, for all practical purposes, produce such a ‘fixed’base. However, this is not always the case since in manyinstances wind turbines are installed in regions with rela-tively soft soil deposits. Under these circumstances theinteraction of the structure with the supporting soil,particularly under external dynamic or seismic loads,could become a major concern in designing the foun-dation and subsequently the entire structure of the windturbine tower.

On the basis of the previous discussion, three majoraspects of the particular design/analysis of the towerstructure and its foundation are primarily discussed inthe following work:

1016 N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

Fig. 1. (a) Steel tower, (b) flange connections, (c) circular stiffener and intermediate landing, and (d) intermediate landing.

1017N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

610

490

400

16*5

00/1

40*5

00

16*5

00/1

40*5

0

16*3

50/1

40*5

0

16*220/120*50*

16*300/1

20*50

6

45˚

15˚

300˚

170

280

350

350

450

180

220

7000

342

810

348

250

1500

350

130 200

Cover plate 16 2100*1300 St52 3N

14 welding openings100*30(a=8mm)

22.5˚

r=45

0 25˚r=250

16

Fig. 2. Details of door opening geometry, discretization and representative results of static analysis (stresses in Mpa).

Fig. 2. Continued

1018 N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

1. The accurate and efficient determination of the mini-mum load combination that would produce localbuckling phenomena on the shell structure. The com-putation of this load combination is directly relatedto a number of geometric variables associated withthe arrangement of the various load bearing elementsof the structure.

2. The influence of the door opening, and of the arrayof stiffeners used around it, on the overall structuralbehavior of the tower structure.

3. The accurate and efficient determination of thedynamic characteristics and the possible seismicbehavior of the tower structure: (a) on a fixed base,and (b) including dynamic soil–structure interaction(SSI) effects.

The main assumption underlying most of the analysesconsidered in this work is that under any load combi-nation (including any appropriate load safety factors) thematerial of the load bearing structural elements of thetower should remain in the linear elastic region of itsstress–strain diagram. Material linearity is an ‘essential’prerequisite of all the pertinent building regulations, e.g.Germanischer Lloyd [1], in view of the expectation thatwind turbines should survive and remain operational,during their entire life cycle (usually 20 years), againstfatigue damage which remains the governing cause offailure for the tower structure [2]. Low operationalstresses provide some cushion against fatigue damage[3].

The static, stability and dynamic analyses performedin this work are based on a number of refined finiteelement and other simplified models. The results of theseanalyses are used to check the load bearing capacity ofthe structure against the recommendations of widelyaccepted design codes, mainly the Eurocode 3 [4] andthe German Standards [5]. Due to lack of space, only afew characteristic examples of these analyses are shownin the next sections. For a complete list of analyses andresults the reader is referred to Beskos et al. [6] andKarabalis et al. [7].

2. Description of structure and FE model

The 36,984 m vertical steel tower, as shown in Fig.1(a), is assembled by thin-wall cylindrical and conicalpieces, of varying diameters (2800 mm at the base to1820 mm at the top) and wall thicknesses (16 mm at thebase to 10 mm at the top), which are welded togetheralong their perimeters. However, for transportation anderection purposes the entire tower is pre-assembled intothree sections which are bolted together by means ofheavy circular end-flanges (each 70 mm thickness), asshown in Fig. 1(b), and arrays of post-tensioned boltsalong their perimeter (the number of bolts varies from

56 at the base flange connecting to the foundation to 64at elevation +13.64 m and 40 at elevation +26.35 m).Circular ring stiffeners are placed at regular intervalsalong the height of the structure, as shown in Fig. 1(c).These stiffeners and a number of intermediate landings,as shown in Fig. 1(d), provide additional resistanceagainst local buckling by reducing the free heightbetween end-flanges. Steel St52, with yield stressfy,k � 360N/mm2, is used for all the load bearing struc-tural elements.

Two sets of static loads are considered:

(a) The pseudostatic aerodynamic loads under sur-vival and operational conditions suggested byRiziotis and Voutsinas [8]. The concentrated aero-dynamic loads at the elevation of the power trans-mission axis (el. +38 m), listed in Table 1, aredue to the wind resistance and/or operation of therunner. In addition, aerodynamic loads distributedalong the body of the tower itself have been com-puted by Riziotis and Voutsinas [8] and areaccounted for in the analysis under survival con-ditions. Aerodynamic loads under survival, shutdown, conditions have a recurrence period of 50years, and assume that the entire system is shutdown with the runner securely immobile. Thesafety margin of the load carrying capacity of thestructure under survival conditions should not beless than one, after, of course, the application ofthe appropriate safety factors to the loads and thestructure. The anticipated loads under operationalconditions, is used for the computation of stressesnecessary in fatigue analysis. Wind turbine struc-tures are usually designed to develop low stresslevels at operational aerodynamic loads, in aneffort to expand their productive life span.

(b) The second set of static loads due to gravity, con-sists of a concentrated load at the top of the towerrepresenting the weight of the nacelle, runner, gen-erator, gear box, etc. (236 kN with �0.75 m

Table 1Pseudo-aerodynamic loads at elevation +38 m (Riziotis and Vouts-inas [8])

Operational Survivalconditions (wind conditions (windvelocity 25 m/s) velocity 70 m/s)

Fx (kN) 75.87 216.23Fy (kN) �0.23 0.28Fz (kN) �226.25 0Mx (kN m) 161.29 96.03My (kN m) �95.40 82.92Mz (kN m) 4.88 5.38

Note: The x-axis is horizontal in the direction of the wind, while thez-axis is vertical with an upward direction.

1019N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

Fig. 3. Samples of the results obtained from the static analysis of the entire tower (stresses in Mpa, displacements in mm).

1020 N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

eccentricity along the x-axis) and the weight ofthe tower itself distributed along its height (78,500N/m3

, specific weight of steel).

The safety factors for the static loads are specifiedas [1]:

Favorable gravity loads: 1.00Unfavorable gravity loads: 1.35Aerodynamic loads: 1.50

The seismic loads are in accordance with the specifi-cations of the Greek Seismic Code [9] where the designseismic motion has a 10% likelihood of being exceededduring a period of 50 years. The corresponding elasticdesign spectrum of horizontal acceleration Re(T) isdefined as:

Re(T) � Ag1�1 � (hb0�1)TT1�, 0�T�T1

Re(T) � Ag1hb0, T1�T�T2 (1)

Re(T) � Ag1hb0

T2

T, T2 � T

where T=period in seconds; T1, T2=characteristic cut-offperiods for different soil conditions (for rock and semi-rock conditions, as in this case, T1=0.1 s, T2=0.40 s);A=site specific maximum acceleration (in this case 0.12g, for the city of Lavrio or the South Evia region);g1=significance factor (in this case g1=1.0, usual occu-pational significance); h=correction factor for dampingratios x other than 5% (h � �7/ (2 � x)); b0 � 2.5(design spectra multiplier).

According to the Greek Seismic Code [9] a total ofsix statistically independent artificial seismic motionsenveloping the above design spectrum should be used ifthe analysis is performed in time domain. For the pur-poses of this study, artificial accelerograms compatiblewith the Greek Seismic Code [9] are developed with theaid of the computer code SRP [10]. Subsequently, theseismic analysis of the tower is carried out in direct timedomain. In addition, the influence of the compliance ofthe supporting soil medium upon the dynamic character-istics of the tower, as compared to the fixed base analy-ses, is calculated as discussed in Section 3.

The static, stability and seismic analyses presented inthis work have been carried out using a refined finiteelement model in conjunction with the general-purposeprogram NISA II [11]. Fixed boundary conditions areassumed at the lower end of the tower for all static analy-ses. Quadrilateral shell elements (eight nodes perelement) are used for the tower wall, the trapezoidal ver-tical stiffeners adjacent to the flange connections and theL-shaped ring stiffeners, see Fig. 1(b). Hexahedral solidelements (20 nodes per element) are adopted for the 70

mm thick ring end-flanges, see Fig. 1(b). The intermedi-ate landings, see Fig. 1(c) and (d), are simulated bythree-dimensional (3-D) beam elements. The wholestructure is divided into 3763 elements with 12,539nodes and a total 69,186 degrees-of-freedom.

3. Numerical results and discussion

3.1. Static analysis

Pseudo-aerodynamic (survival conditions) and gravityloads are considered in static analysis. The maximumshear stresses, according to the Tresca failure criterion,appear in two small regions, in close proximity to eitherside of the door opening and their values do not exceed100 N/mm2. The maximum von Mises stresses also

Fig. 4. Distribution of normal stresses and expected buckling shape(stresses in Mpa).

1021N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

appear in two small regions on either side of the dooropening and their values do not exceed 211 MPa. Themaximum shear and von Mises stresses appear in theabove regions regardless of the directionality of the aero-dynamic loads. The geometry of the door-openingregion, the arrangement of the surrounding stiffeningelements and representative results of static analyses areshown in Fig. 2. The effectiveness of the arrangementof the stiffening elements around the door opening inkeeping the stresses at acceptable levels is evident.

The largest von Mises stress in the cylindrical or coni-cal thin-wall parts appear at 13,237 mm above the basewhen the directionality of the aerodynamic loads is suchthat compressive stresses appear over the region dia-metrically opposite to the door opening. As expected,the maximum horizontal displacement umax � 362mm,less than approximately one-hundredth of the totalheight, appears at the top of the tower. Characteristicsamples of the results obtained from the static analysesof the entire tower appear in Fig. 3.

3.2. Buckling analysis

An elastic buckling analysis is performed in order toinvestigate the critical coupled stress state due to axial,flexural and torsional loads. The purpose of this eigen-value buckling analysis is limited to the identification ofthe bifurcation points on the primary load–deflectionpath of the structure. This requires an eigenvalue extrac-tion using the governing equation:

(K � liKg)ui � 0 (2)

where K is the linear stiffness matrix, Kg the geometricor initial stress stiffness matrix, li the ith eigenvalue andui is the corresponding modal shape. In an effort toachieve an as high as possible level of convergence,more than 15 finite element models have been createdfor the generation of the stiffness and geometric stiffnessmatrices. In the beginning, a rough finite element meshis created and the critical regions are identified. Success-ive mesh refinements of the critical regions make poss-ible the precise computation of the local buckling effects.The minimum static load multiplier, i.e. the safety mar-gin based on gravity and survival aerodynamic loads,that would cause local buckling is computed to be 1.33.A few characteristic samples of the results obtained fromthe final discretization scheme are displayed in Fig. 4. Itis worth noting the bending nature of local deformationpatterns due to the essential lack of a significant tor-sional moment.

In order to illustrate the accuracy and practical useful-ness of the above finite element buckling analyses, acomparison is made with the simplified analytical pro-cedures specified in DIN 18800 (Part 4) [5] for cylindersand cones. The theoretical buckling stresses, accordingto DIN 18800 [5], can be computed only for simple cyl-

indrical and conical portions and appropriate edge con-ditions. Thus, in this work, the critical buckling load ofall the cylindrical and conical parts between stiffeners iscomputed according to DIN 18800 [5]. The intermediatestiffening elements are substituted by appropriate bound-ary conditions, i.e. depending on the type of the stiffen-ing element the radial expansion and/or the relativerotation among adjacent portions are restrained. Therelative difference between the results obtained by thefinite element based analyses and the procedures rec-ommended by DIN 18800 [5] does not exceed 1.2% [7].This agreement proves the accuracy of the finite elementmodel used in this work and the relative effectivenessof the simplified procedures recommended by DIN18800 [5].

The above, finite element based, geometrically non-linear analyses with incremental loading, can produce

1 0.000

2 2.070

3 3.070

4 7.0705 7.870

6 10.570

7 12.550

8 13.637

9 17.350

10 18.204

11 21.430

12 23.204

13 25.650

14 26.251

15 31.051

16 34.891

17 35.637

18 36.984 Altitude (m)

t= 10mm

t= 12mm

t= 14mm

t= 16mm

Fig. 5. Simplified finite element model for seismic analysis.

1022 N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

Table 2Eigenvalues of wind turbine tower

Refined model (Hz) Simplified model (Hz)

First mode 0.937 0.964Second mode 7.400 7.213Third mode 14.631 –Fourth mode 18.984 19.614

the load–deflection curve necessary for the assessmentof the influence of the P–� effect on the overall defor-mation characteristics of the tower [12]. The results ofsuch analyses [6] shows that the load–displacement dia-gram for the top of the tower has essentially linearbehavior even at levels well above the static loaddesign values.

3.3. Seismic analysis

Tall steel towers are usually designed considering theeffect of wind loads as the only source of environmentaldynamic disturbances. The effect of earthquakes as apossible source of damage or loss of serviceability isoften neglected, even in high-risk seismic areas. How-ever, neglecting earthquake effects should at least be jus-tified by means of appropriate methods of analysis inconjunction with the recommendations of applicablebuilding codes.

For the computation of the dynamic characteristics of

Fig. 6. The first four eigenmodes of the steel tower.

the wind turbine tower two different models are employ-ed:

(i) The first one is the same finite element model usedfor static and stability analysis. Although thisrefined model requires significant computationaleffort it is used for comparison purposes since itis expected to yield the most accurate results.

(ii) The second one is a simplified multi-degree offreedom oscillator with 18 concentrated masseslocated at characteristic elevations, as shown inFig. 5, and 108 degrees-of-freedom. It is a 3-Dbeam model that approximately maps the mechan-ical properties, e.g. cross area, moment of inertia,tapering, etc., of the real tower. The general-pur-pose computer program NASTRAN [13] has beenused in conjunction with this model.

3.4. Fixed-base analysis

The dynamic characteristics of the tower structure areconsidered first on the assumption of fixed boundaryconditions at its base. The first four eigenvalues of thetower, as computed by the above models, are listed inTable 2, and the corresponding eigenmodes are shownin Fig. 6. The results obtained by the two models arecoincident for all practical purposes. The third torsionalmode of free vibration cannot be detected by the simpli-fied model, since only bending and axial deformationmodes are considered. However, the contribution of the

1023N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

Fig. 7. Discrete model for seismic analysis including soil–structureinteraction.

torsional mode on the overall seismic behavior of thisstructure is negligible.

3.5. Elastic subgrade analysis

The effect of the SSI on the dynamic characteristicsof the structure under investigation can be assessed byintroducing a set of discrete springs and dashpots at thesoil–foundation interface, see, for example, Mullikenand Karabalis [14]. In this case the previously discussedfinite element models are modified by adding stiffeningand damping elements at the foundation–soil interfaceand taking into consideration the mass of the foundation,as shown in Fig. 7. In addition, a portion of the soilmass, considered to move ‘ in phase’ with the foundationshould be taken into account [14].

For the purposes of this study semi-rock soil con-ditions are assumed at the particular installation site with

Table 3Spring constants and added soil mass for the three most prominent modes of vibration

Footing 10×10 m2 Footing 12.5×12.5 m2

Spring constant Added mass Spring constant Added mass

Horizontal 14,070×103 kN/m 177×103 kg 17,588×103 kN/m 347×103 kgVertical 17,457×103 kN/m 593×103 kg 21,821×103 kN/m 1158×103 kgRocking 371,429×103 11,852×103 kg m2 725,446×103 36,170×103 kg m2

kN/m/rad kN/m/rad

Poisson ratio 0.3, specific weight 21 kN/m3 and shearmodulus 520 MPa. Two foundation designs are proposedfor the particular tower structure, one is a 10×10×1.80m3 concrete block and the other is a 12.5×12.5×1.80 m3

concrete block. Either one of these footings is assumedto be rigid. Based on the previous soil properties, foun-dation geometries and the related formulae proposed byMulliken and Karabalis [14], the spring constants andadded soil mass are computed as listed in Table 3.

The influence of SSI upon the first three eigenfrequ-encies of the tower structure are presented in Table 4. Itis worth noting the significant influence of SSI on thefirst, and by far most important, mode of free vibration,in spite of the relatively stiff soil conditions consideredin this example. However, there is an even more signifi-cant influence of SSI on the higher modes of freevibration.

The seismic response of the tower structure to thedesign seismic motions described in the previous sectionof this work have been computed using: (a) the refinedfinite element model along with standard modal superpo-sition procedures and (b) the simplified finite elementmodel of Fig. 5 in a direct time domain analysis. Thesetwo computations produce essentially identical results,representative samples of which are shown in Fig. 8. Thedomination of the seismic response of the structure bythe first mode of vibration becomes obvious. Themaximum values of several design variables are listedin Table 5.

In spite the low damping ratio (x � 0.5%) and theelastic design spectra used for the development of theseismic motions, the wind turbine tower under investi-

Table 4Influence of soil–structure interaction on the dynamic characteristicsof the tower structure

Eigenvalue Fixed base SSI with SSI withconditions (Hz) foundation foundation

10×10 m2 (Hz) 12.5×12.5 m2

(Hz)

1 0.964 0.873 0.7122 7.213 1.935 1.9353 19.614 3.736 2.751

1024 N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

Fig. 8. Seismic response along the three principal coordinate axes,versus time, at the top of the tower: (a) accelerations (mm/s2), and (b)displacements (mm).

Table 5Maximum values of design variables at several elevations as producedby seismic analysis

Node Max V (kN) Max M (kN m) Max sz

number- (MPa)elevation(m)

1 (0.000) 132.884 3939.472 40.6822 (2.070) 129.634 3671.001 43.2504 (7.070) 126.971 3544.032 48.6096 (10.570) 120.325 2787.272 38.2298 (13.637) 113.178 2323.501 43.47010 (18.204) 106.473 1841.506 48.11212 (23.204) 102.736 1323.035 34.56614 (26.251) 98.983 1011.394 39.54418 (36.896) 85.892 0 (free end) 0 (free

end)

gation presents low levels of stresses, smax � 50MPa,which is by far lower than the maximum stress producedin static analysis for pseudo-aerodynamic loads undersurvival conditions.

Furthermore, based on the above dynamic analyses,a third approximate model can be developed for handcalculations. This simplified model is a one degree-of-freedom oscillator in the form of a cantilever with a con-centrated mass at its free end. The concentrated mass isequal to the mass of the tower and the mass of thenacelle, generator, gearbox, etc. at the top of the struc-ture. The stiffness of this oscillator is computed fromthe total concentrated mass and the period of the firsteigenmode as it is computed by the refined model. Theseismic response of the tower can be computed easilyusing this model in conjunction with either the responsespectrum analysis, for the computation of the maximumresponse of the system, or any of the standard time step-ping algorithms and the accelerograms described pre-viously. The results produced by this model present aless than 15% deviation from the results obtained by theother two models used in this work.

4. Conclusions

The design of the prototype wind turbine tower underinvestigation is proven to be successful as far as strengthand operational requirements are concerned. The refinedand simplified models developed for the static and seis-mic analyses are in remarkable agreement. For this typeof structures the refined finite element models are neces-sary for the static and buckling analysis since a highlevel of accuracy is required at specific critical locations.Simplified analytical models, as those usually rec-ommended by building codes, can predict with relativeaccuracy critical loads related to local buckling phenom-ena for this type of structures. However, if such modelsare used, great care should be exercised in incorporatingappropriately the boundary conditions at the ends of eachsection of the structure. Approximate numerical modelscan also produce quite accurate results for seismic analy-sis as well. In most of these types of tower structures aseismic analysis produces no critical response.

References

[1] Germanischer Lloyd. IV-Non-marine technology, Part 1—Windenergy. Hamburg; 1993.

[2] Spera DA. Fatigue design of wind turbines. In: Spera DA, editor.Wind turbine technology. New York: ASME Press; 1994. p. 547–88 [chapter 12].

[3] Eggleston DM, Stoddard FS. Wind turbine engineering design.New York: Van Nostrand Reinhold, 1987.

[4] Eurocode 3: design of steel structures-Part 1.4: general rules-sup-

1025N. Bazeos et al. / Engineering Structures 24 (2002) 1015–1025

plementary rules for stainless steels, ENV 1993-1-4. Brussels; 1996.[5] German Standards (DIN 18800, Part 4). Berlin: Beuth Verlag

GmbH; 1978.[6] Beskos DE, Karabalis DL, Hatzigeorgiou GD, Karamaneas H.

Design of a wind turbine tower—450 kW. Technical Report tothe Center for Renewable Energy Sources, Department of CivilEngineering, University of Patras; 1996.

[7] Karabalis DL, Beskos DE, Hondros ID. Design of a wind turbinetower and foundation—450 kW. Technical Report to the Centerfor Renewable Energy Sources, Department of Civil Engineering,University of Patras; 1997.

[8] Riziotis B, Voutsinas S. EPET II, Project #573: design of a windturbine—450 kW. Technical Report to the Center for RenewableEnergy Sources, Department of Mechanical Engineering,National Technical University of Athens; 1996.

[9] Greek Seismic Code. Organization for Seismic Design and Pro-tection. Athens; 1999.

[10] Karabalis DL, Cokkinides GJ, Rizos DC, Mulliken JS. Simulationof earthquake ground motions by a deterministic approach. AdvEng Softw 2000;31:329–38.

[11] NISA II. Numerically integrated elements for system analysis,Version 7.0. Troy, MI: Engineering Mechanics Research Corpor-ation; 1997.

[12] Chen WF, Lui EM. Structural stability—theory and implemen-tation. New York: Elsevier, 1987.

[13] Nastran, Version 67. Los Angeles: The MacNeal-SchwendlerCorporation; 1992.

[14] Mulliken JS, Karabalis DL. Discrete models for through-soilcoupling of foundations and structures. Earthquake Eng StructDyn 1998;27:687–710.