Evaluation of Evaluation of shell thicknessesshell thicknesses

Prof. Ch. BaniotopoulosProf. Ch. Baniotopoulos

I. Lavassas, G. Nikolaidis, P.ZervasI. Lavassas, G. Nikolaidis, P.Zervas

Institute of Steel StructuresInstitute of Steel StructuresAristotle Univ. of Thessaloniki, GreeceAristotle Univ. of Thessaloniki, Greece

Hand calculationHand calculation

h

p

H

M

F

G

t

t

H-h

Hand calculationHand calculation

h

p

H

M

F

G

t

t

H-h

Linear modelLinear model

Computational model (Linear):Computational model (Linear):

All sections of the tower are simulated via linear beam All sections of the tower are simulated via linear beam elements.elements.Rotor & blade system is simulated as a mass at the top Rotor & blade system is simulated as a mass at the top of the tower placed with eccentricityof the tower placed with eccentricity in x and z axes in x and z axes

Soil-structure interaction Soil-structure interaction isis simulated by the use of simulated by the use of translational spring in z direction &translational spring in z direction & rotational spring rotational springss along X and Y directionsalong X and Y directions

Kz=15400 kN/m3Kz=15400 kN/m3

Linear modelLinear model Wind loadingWind loading

Bending momentBending moment& shear force diagrams& shear force diagrams

M=88212.83 kNmM=88212.83 kNmV=1273.63 kNV=1273.63 kN

Bending momentBending moment& shear force diagrams& shear force diagrams

M=26928.47 kNmM=26928.47 kNmV=476.74 kNV=476.74 kN

(almost 30% of the (almost 30% of the corresponding for wind corresponding for wind loading)loading)

Need to be combined with Need to be combined with 18 m/s wind loading when 18 m/s wind loading when load data on the tower top load data on the tower top are availableare available

Linear modelLinear model Response spectrumResponse spectrumanalysisanalysis

FE modelFE model

Rotor & blade system is simulated as a mass at the top of the Rotor & blade system is simulated as a mass at the top of the tower placed with eccentricitytower placed with eccentricity in x & z axes in x & z axes

Soil-structure interaction is simulated by unilateral contact Soil-structure interaction is simulated by unilateral contact springs below the foundation.springs below the foundation.

Model details to the flange positionsModel details to the flange positions

FE model details

Connection type for the flanges

FE model detrails (foundation)FE model detrails (foundation)Foundation shape is octagonal. Foundation shape is octagonal. Equivalent circular diameter (Beq=17.46 m) Equivalent circular diameter (Beq=17.46 m) has been used for the modelhas been used for the model Rotor & blade system is simulated as a mass Rotor & blade system is simulated as a mass at the top of the tower placed with at the top of the tower placed with eccentricityeccentricity

Soil-structure interaction is simulated by Soil-structure interaction is simulated by unilateral contact springs below the unilateral contact springs below the foundation.foundation.Ground load above foundation has been taken Ground load above foundation has been taken into accountinto account

Tower loads

Tower Loads:Tower Loads:

a) Vertical loadsa) Vertical loads Self mass & weight is estimated directly by the FE softwareSelf mass & weight is estimated directly by the FE software the total mass on the tower top, is the total mass on the tower top, is 106700106700 kg kg

(eccentricity of (eccentricity of +0.725+0.725 m horizontal, m horizontal, +0.50m+0.50m vertical). vertical).

b) Wind loads Top of the tower (estimated): F=550 kN , M=4000 kNm

Tower stem (calculated acc. EC1-1-4)

z ≤ 2,00m : FW = 0,51•D

z > 2,00m : FW = 0,013•ln(20•z)•

• [ln(20•z) + 7]•D

Pressure distribution along the circumference

Types of analysis

LA (Linear analysis)LA (Linear analysis)MNA & MNA & LBALBA ( (Material non-linear analysis & Material non-linear analysis & Linear buckling analysis)Linear buckling analysis)GMNA (Geometric & material non-linear analysis)GMNA (Geometric & material non-linear analysis)Eigenvalue analysis & Response spectrum analysisEigenvalue analysis & Response spectrum analysis

Eigenvalue analysis results

Dynamic characteristicsFE Model k=15400

FE Model k=14950

Linear k=15400

Linear k=14950

1st eigen frequency (sec-1) 0.357 0.357 0.324 0.322

3rd eigen frequency (sec-1) 2.820 2.822 2.626 2.61

9 th eigen frequency (sec-1) 7.520 7.490 7.85 7.833

11StSt & & 22ndnd ,, 3 3rdrd & & 44thth ,, 55thth & 6 & 6thth mode mode sshapes hapes

Eigenvalue analysis results (linear model)

Eigenvalue analysis results (FE model)

11StSt & & 22ndnd ,, 3 3rdrd & & 44thth ,, 55thth to 8 to 8thth (not participating)(not participating) , , 9 9thth & & 1010thth mode mode sshapes hapes

GMNA analysis results (wind loading)

Tower displacements & foundation uplift for Tower displacements & foundation uplift for the wind loadingthe wind loading

GMNA analysis results (wind loading)

Von mises stress distributionVon mises stress distribution

Max Vm (334 Mpa) stress to the Max Vm (334 Mpa) stress to the door positiondoor position

Vm variation around the door Vm variation around the door occurs due to the coexistence occurs due to the coexistence of circumferencial stressof circumferencial stress

Meridional stress (max 297 Mpa) Meridional stress (max 297 Mpa) distributiondistribution

Skirts 1 & 2 are stiffer than the Skirts 1 & 2 are stiffer than the needed for pure bending due needed for pure bending due to the presence of the doorto the presence of the door

GMNA analysis results (wind loading)

GMNA analysis results (wind loading)

Negative circumferencial stress distributionNegative circumferencial stress distribution

Mainly to the flange position (min -90 Mpa)Mainly to the flange position (min -90 Mpa)

Almost disappears in a distance <10 cm Almost disappears in a distance <10 cm

Affects the areas above & below the door Affects the areas above & below the door

(min -64 Mpa)(min -64 Mpa)

Response spectrum analysis

SSeismic loading:eismic loading:

Response spectrum analysis for the seismic loading

Three eigenmodes are mainly participating.

Response spectrum analysis results

Displacements, Von mises stresses & circumferencial (~zero) stressesDisplacements, Von mises stresses & circumferencial (~zero) stresses

(almost 30% of the (almost 30% of the corresponding for corresponding for wind loading)wind loading)

Need to be combined Need to be combined with with 18 m/s wind loading 18 m/s wind loading when load data on the when load data on the tower top are tower top are availableavailable

In this type of analysis In this type of analysis negative negative circumferencial circumferencial stresses are very stresses are very small small due to the absence of due to the absence of loading variation loading variation along the along the circumference as in circumference as in wind loadingwind loading