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Προσδιορισμός των βασικών ταχυτήτων αναφοράς που εφαρμόζονται στον Ευρωκώδικα 1-4.Definition of basic wind velocities, for use according to structural Eurocode 1-4.

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  • . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 63

    , - ( 1, 2-4). 31 .. - 40 . . .

    1.

    - - . : - [1], [2], [3] [4], 39 - [5] ... , , (National Application Document, NAD), ( - 3 ). - ( 1 8) ( 2 7 9). : (ENV) ().

    , . DIN 1055 [6]. - , , - [7]. [8], - -. , [8], : ( m/s ) (- Beaufort1). -

    : ( ) 24 - 13 . 82 - 23 . , - [8], , , , . [8] (. 1). [8] - 50 :1. ( 10km ): 36m/s2. : 30m/s

    1: 50 ( [8]).

    Figure 1: Map of equal wind velocities with return period of 50 years (from [8]).

    : 15.12.2000 : 14.5.2001

    . .

    ..

  • 64 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 65

    , ( ) ( , , - ..). .

    , , 1, 2-4 [9]. : ) - 1, 2-4 (ENV) (EN) ) , -. , [12], - .

    [10] ( ), (- 4) , , 50 100 , ( 5).

    2.

    v (z,t): vm(z) :

    10 minvm,II,10 :

    10min, 10m .

    vb: vm,II,10vk:

    k v50,v100:

    50 100

    v(z,t):

    z: (m), :

    ( 1)

    kt, z, zmin ( 1)

    qb: qp: : (1,25 Kg/m3 -

    15 C 1 atm)ce(z): cr(z): ct(z): kP:

    3.5 Iv(z):

    cp:

    w: P[.] : [.]: u,c: Gumbel

    3. H 1, 2-42

    - v .

    - . (.. 10min 1h) - z . v v

    m v,

    ( 3.1):v(z,t)=v

    m(z)+v(z,t) (3.1)

    - . : Davenport - . Davenport [11] , :

  • 64 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 65

    10zvzv 10,II,mm

    (3.2):vm,II,10

    10min, 10m .

    , ( 1).

    z ( m).

    , , :

    min0

    min10,II,mtm

    min0

    10,II,mtm

    zzzzlnvk)z(v

    200mzzzzlnvk)z(v

    (3.3):k

    t, z

    , z

    min

    ( 1). , - , . - ( 5.1)

    Vm(z)=const

    10min

    1h

    ?V(z,t)

    2: .

    Figure 2: Wind velocity variation with time.

    1: . Table 1: Definition of roughness categories.

    , 5km.

    I , .

    II , , ..

    IV , .

    V .

    1: ( (3.2) (3.3)), - .

    Table 1: Terrain parameters (eq. (3.2) and (3.3)).

    ,

    (3.2)

    , (3.3)

    -- z0 (m) kt zmin (m)

    0.10 1.30 0.005 0.161 0.2I 0.15 1.00 0.05 0.189 0.9II 0.20 0.85 0.20 0.208 2.2IV 0.25 0.67 0.5 0.222 4.6V 0.35 0.47 1 0.233 7.7

    . q

    b

    :

    2bv2

    1qb (3.4)

    :

    : (1.25kg/m3 15C 1atm),

    vb: , 10min, 10m, . , 3.2 3.3 :vb=vm,II,10. vb.

    qp

    :

    )z(cq)z(q ebp (3.5)

  • 66 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 67

    :

    ce(z): z , . :

    )z(Ik21)z(c)z(cc vp2t2re (3.6)

    :Iv(z): :

    0t

    v

    zzln)z(c

    1)z(I

    zzmin

    (3.7)I

    v(z)=I

    v(z

    min) z

  • 66 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 67

    . -. .. [14] . [15], , Bachmann et al. [16] Gumbel, Gumbel - . [17] (Gumbel) . CEN [12] (Gumbel) ( , - Weibull). , 12 , , . Gumbel ( ) [18].

    , , Gumbel , , Weibull3, , - x. , - , Gumbel Weibull, , -, , .

    , , 4:1. .2. 3. . -.

    , - . (v

    max), -

    (.. ), v

    k .

    [12]: - (v

    max)

    , , v

    k*. v

    max/

    vk* 1.5,

    v

    k,

    . ( v

    max/ v

    k* >1.5) -

    , v

    k*,

    () . .

    5.

    5.1. (profile)

    2 - : ( (3.2)), - ( (3.3)). , -. 2 : : - 1.8m/s. .

    - Weibull ( : 1.5 m/s) ( : 1.8 m/s)

    2: - .

    Table 2: Comparison of the characteristic values calculated according to the exponential and the logarithmic law.

    / m/s

    , . (3.2)

    , . (3.3)1 22.6 23.22 26.4 26.63 / 30.4 30.44 23.1 22.75 23.4 22.96 27.7 28.37 25.4 25.08 24.6 25.29 26.7 27.0

    10 28.3 29.011 31.4 31.412 24.1 23.613 28.6 30.414 28.0 28.715 35.2 35.2

  • 68 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 69

    16 20.9 20.717 21.7 21.618 29.8 29.519 29.0 28.720 33.2 34.021 33.7 33.922 20.1 19.823 28.8 29.224 31.8 32.125 31.2 31.526 29.7 29.327 34.4 35.728 21.9 21.429 28.5 28.430 22.1 22.131 / 26.7 27.3

    27.4 27.6

    ( - : 1.9 m/s, 1.7 m/s & 2.1 m/s Gumbel, Weibull ) ( : 2.2 m/s, 1.6 m/s & 1.9 m/s Gumbel, Weibull ). . , - [9].

    5.2.

    3 - : Gumbel, - - Weibull, - . (profile) - . 3 Weibull - ( 10% Gumbel), Gumbel . Gumbel : 1.2m/s. - ( - ).

    Gumbel, .

    3: .Table 3: Comparison of the three probability distributions.

    / m/sGumbel Weibull/

    1 23.2 20.9 22.52 26.6 24.1 25.73 / 30.4 27.5 29.54 22.7 20.6 21.95 22.9 20.6 22.26 28.3 25.4 27.57 25.0 22.8 24.28 25.2 23.0 24.49 27.0 24.8 26.1

    10 29.0 26.8 28.111 31.4 28.3 30.512 23.6 21.3 22.913 30.4 27.5 29.414 28.7 25.9 27.815 35.2 32.7 34.116 20.7 19.0 20.117 21.6 19.6 20.918 29.5 26.8 28.519 28.7 26.1 27.820 34.0 30.5 32.921 33.9 31.8 32.922 19.8 17.9 19.723 29.2 26.3 28.324 32.1 28.8 31.325 31.5 28.5 30.526 29.3 26.3 28.527 35.7 32.3 34.528 21.4 19.4 20.829 28.4 25.6 27.530 22.1 20.0 21.431 / 27.3 24.6 26.6

    27.6 25.0 26.7

    5.3.

    4 , Gumbel, : , . .

  • 68 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 69

    4 , , . - 30.8m/s 25.1m/s - : 29.2m/s : 33.9m/s. - . - Weibull ( - ).

    4: .able 4: Comparison of the three estimation methods.

    / m/s

    -

    1 23.2 24.4 24.12 26.6 27.8 26.53 / 30.4 32.2 33.44 22.7 23.6 23.65 22.9 24.1 22.46 28.3 30.0 29.17 25.0 26.3 25.08 25.2 26.3 26.89 27.0 27.9 26.9

    10 29.0 30.3 29.511 31.4 32.9 30.312 23.6 24.6 24.713 30.4 31.8 32.614 28.7 30.0 28.215 35.2 36.6 38.216 20.7 21.7 21.717 21.6 22.5 22.218 29.5 31.1 29.019 28.7 30.1 30.520 34.0 36.0 32.721 33.9 34.8 33.822 19.8 21.9 18.923 29.2 32.6 33.924 32.1 33.8 33.925 31.5 34.0 32.426 29.3 30.9 29.227 35.7 37.2 37.928 21.4 22.4 21.5

    29 28.4 29.6 29.530 22.1 23.1 21.831 / 27.3 30.8 25.1

    27.6 29.1 28.2

    5.4.

    , - - - : , Gumbel :

    cukvek evvP

    (5.1) u c . (5.1), 2% 1% - , 5, 50 100 . 5 1.1m/s 2.7m/s .

    5: =50 =100 .

    Table 5: Characteristic velocities with return period T=50 and T=100 years.

    / m/sV50 (=50) V100 (=100)

    1 23.2 24.82 26.6 28.43 / 30.4 32.54 22.7 24.15 22.9 24.66 28.3 30.47 25.0 26.58 25.2 26.69 27.0 28.3

    10 29.0 30.411 31.4 33.712 23.6 25.213 30.4 32.314 28.7 30.715 35.2 36.816 20.7 21.817 21.6 23.018 29.5 31.219 28.7 30.520 34.0 36.421 33.9 35.422 19.8 21.823 29.2 31.3

  • 70 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 71

    24 32.1 34.825 31.5 33.626 29.3 31.627 35.7 38.028 21.4 22.929 28.4 30.330 22.1 23.731 / 27.3 29.5

    5.5.

    3 -

    50 . , 5m/s. , , .

    6.

    , . 31 40 . :

    3: 50 .Figure 3: Map of equal wind velocities with return period 50 years.

  • 70 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 . . . . , , . 2 2001, Tech. Chron. Sci. J. TCG, I, No 2 71

    , , - . -, .

    1 [8] 3 - . - - . [8].

    , , .. . , . , , - : ( 10km ) . - . - , 36m/s () 31m/s () . .

    : ) , - 30m/s . 33m/s. )