Evaluation of shell thicknesses Prof. Ch. Baniotopoulos I. Lavassas, G. Nikolaidis, P.Zervas Institute of Steel Structures Aristotle Univ. of Thessaloniki, Greece

Hand calculation

Linear model Computational model (Linear): All sections of the tower are simulated via linear beam elements. Rotor & blade system is simulated as a mass at the top of the tower placed with eccentricity in x and z axes Soil-structure interaction is simulated by the use of translational spring in z direction & rotational springs along X and Y directions Kz=15400 kN/m3

Linear model Wind loading Bending moment & shear force diagrams M= kNm V= kN

Bending moment & shear force diagrams M= kNm V= kN (almost 30% of the corresponding for wind loading) Need to be combined with 18 m/s wind loading when load data on the tower top are available Linear model Response spectrum analysis

FE model Rotor & blade system is simulated as a mass at the top of the tower placed with eccentricity in x & z axes Soil-structure interaction is simulated by unilateral contact springs below the foundation.

Model details to the flange positions FE model details Connection type for the flanges

FE model detrails (foundation)‏ Foundation shape is octagonal. Equivalent circular diameter (Beq=17.46 m) has been used for the model Rotor & blade system is simulated as a mass at the top of the tower placed with eccentricity Soil-structure interaction is simulated by unilateral contact springs below the foundation. Ground load above foundation has been taken into account

Tower loads Tower Loads: a) Vertical loads Self mass & weight is estimated directly by the FE software Self mass & weight is estimated directly by the FE software the total mass on the tower top, is kg the total mass on the tower top, is kg (eccentricity of m horizontal, +0.50m 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 = 0,51D z > 2,00m : FW = 0,013ln(20z) [ln(20z) + 7]D Pressure distribution along the circumference

Types of analysis  LA (Linear analysis) ‏  MNA & LBA (Material non-linear analysis & Linear buckling analysis) ‏  GMNA (Geometric & material non-linear analysis) ‏  Eigenvalue analysis & Response spectrum analysis Eigenvalue analysis results

1 St & 2 nd, 3 rd & 4 th, 5 th & 6 th mode shapes 1 St & 2 nd, 3 rd & 4 th, 5 th & 6 th mode shapes Eigenvalue analysis results (linear model)

Eigenvalue analysis results (FE model) 1 St & 2 nd, 3 rd & 4 th, 5 th to 8 th (not participating), 9 th & 10 th mode shapes 1 St & 2 nd, 3 rd & 4 th, 5 th to 8 th (not participating), 9 th & 10 th mode shapes

GMNA analysis results (wind loading) Tower displacements & foundation uplift for the wind loading

GMNA analysis results (wind loading) Von mises stress distribution Max Vm (334 Mpa) stress to the door position Vm variation around the door occurs due to the coexistence of circumferencial stress

Meridional stress (max 297 Mpa) distribution Skirts 1 & 2 are stiffer than the needed for pure bending due to the presence of the door GMNA analysis results (wind loading)

Negative circumferencial stress distribution Mainly to the flange position (min -90 Mpa) Almost disappears in a distance <10 cm Affects the areas above & below the door (min -64 Mpa) (min -64 Mpa)

Response spectrum analysis Seismic loading: Response spectrum analysis for the seismic loading Three eigenmodes are mainly participating.

Response spectrum analysis results Displacements, Von mises stresses & circumferencial (~zero) stresses (almost 30% of the corresponding for wind loading) Need to be combined with 18 m/s wind loading when load data on the tower top are available In this type of analysis negative circumferencial stresses are very small due to the absence of loading variation along the circumference as in wind loading