JCSS PROBABILISTIC MODEL CODE PART 2 : LOADS

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1 Febrari JCSS-LUNGU & RACKWITZ JCSS PROBABILISTIC MODEL CODE PART : LOADS.3 WIND Table of contents:.3. Introdction.3. Wind forces.3.3 Mean wind velocity.3.4 Terrain roghness (category).3.5 Variation of the mean wind with height.3.6 Intensity of trblence.3.7 Power spectral density and atocorrelation fnction of gstiness.3.8 Coherence fnction.3.9 Peak velocities.3. Mean velocity pressre and the roghness factor.3. Gst factor for velocity pressre.3. Exposre factor for peak velocity pressre.3.3 Aerodynamic shape factors.3.4 Uncertainties consideration Related Literatre and References List of symbols: f c = Coriolis parameter (= Ω sin φ) f =meanfreqencyoferopcrossing,inh g = peak factor (no dimension) G (n), G v (n), G w (n) = half-sided power spectral density for longitdinal, transversal and vertical components of velocity flctations I () = trblence intensity of longitdinal velocity flctations (dimensionless) k = von Karman`s constant (=.4) L () = integral length scale for longitdinal velocity flctations, in m L v () = integral length scale for transversal velocity flctations, in m L w () = integral length scale for vertical velocity flctations, in m N = nmber of erence time, in years n = freqency, in Hert n, n v, n w = dimensionless freqency of flctations in longitdinal, transversal and vertical direction = erence wind velocity pressre Q

2 Febrari List of symbols: Q ( ) = mean velocity pressre at height (=(/) ρ U ( )) S ij (n) = cross spectral power density T = erence time T ( p ) = mean recrrence interval of maximm annal mean velocity, in years U = erence wind velocity, in m/s U ( ) = mean longitdinal velocity of the wind at height = mode of the maximm annal mean wind speed in Gmbel distribtion (x,,t)= = longitdinal component of the wind velocity flctations, in m/s v(y,,t)=v = transversal component of wind velocity flctations, in m/s w(,t)=w = vertical component of wind velocity flctations, in m/s = height above grond, in m = roghness length, in m r = a erence height above grond, in m = the erence height above grond ( - 3 m) α = dispersion parameter for the maximm annal mean wind speed in Gmbel distribtion δ = height of the atmospheric bondary layer κ = srface drag coefficient (dimensionless) (=[k/ln( / )] ) λ k = k-th moment of spectral density ν(x) = mean pcrossing rate for level x φ = geographical latitde ρ = air density (=.5 kg/m 3 ), v, w = standard deviation of velocity flctations in x-, y- and -direction, in m/s

3 Febrari 3.3. Introdction Wind effects on bildings and strctres depend on the general wind climate, the exposre of bildings, strctres and their elements to the natral wind, the dynamic properties, the shape and dimensions of the bilding (strctre). The section presents basic data and procedres for the estimation of wind loads on bildings and strctres. Tropical cyclones, tornados, thnderstorms and orographic wind phenomena reqire separate treatment. The field of wind velocities over horiontal terrain is decomposed into a mean wind (average over mintes) in the direction of general air flow (x-direction) averaged over a specified time interval and a flctating, trblent part with ero mean and components in the longitdinal (x) direction, the transversal (y-) direction and the vertical (-) direction.3. Wind forces The wind force acting per nit area of strctre is determined with the relations: (i) For rigid strctres of smaller dimensions: w=c c c Q = c c Q a g r a e () (ii) For strctres sensitive to dynamic effects (natral freqency < H) and for large rigid strctres: w=c c c d a eq () where: Q c r c g c a c d = the erence (mean) velocity pressre = roghness factor = gst factor = aerodynamic shape factor = dynamic factor..3.3 Mean wind velocity The erence wind velocity, U is the mean velocity of the wind averaged over a time interval of min = 6 s, determined at an elevation of m above grond, in horiontal open terrain exposre ( =.3 m). The distribtion of the mean wind velocities (for any terrain category, height above grond and averaging time interval) is the Weibll distribtion: k x F ( x) = exp U (3) with k close to. The same distribtion is valid for direction dependent mean wind flows. Generally, it can not be assmed that the mean wind direction is niformly distribted over the circle. For other than min averaging intervals, in open terrain exposre, the following relationships h min min(fastest mile) 3sec may be sed: 5. U =. U =.84U = 67. U.

4 Febrari 4 Mean wind velocities vary over the year. If no data are available it can be assmed in the northern hemisphere that (t) [+ a cos(π(t-t )/365] with the constant a between /3 and / and t 5 to 45, with t in days. The mean wind velocities are highly atocorrelated. Mean wind velocities with separation of abot 4 to (8 on average) hors can be considered as independent in most practical applications. If seasonal variations are neglected, the mean period the mean wind velocities are between levels x and x ( x x ) is asymptotically [ ] ET, = T[ F ( x ) F ( x )] (4) x x U U with T the erence time. For higher levels of x the distribtion of individal times above x is approximately [ F ( x)]/ ν( x) with ν( x) the mean pcrossing rate for level x. U The maximm mean wind speeds for longer periods follows a Gmbel distribtion for maxima. Generally, it is not possible to infer the maxima over more years from observations covering only a few years. If the annal maxima are sed, provided that the maximm annal data are homogenos as exposre and averaging time, the distribtion fnction is: F ( x) = exp{ exp[ α ( x )]} max U (5) The mode and the parameter α of the distribtion are determined from the mean m and the standard deviation of the set of maximm annal velocities: =m 577. /α, α = 8. /.The coefficient of variation of maximm annal wind speed, V = /m depends on the climate and is normally between. and.35. For reliable reslts, the nmber of the years of available records mst be of the same order of magnitde like the reqired mean recrrence interval. The lifetime (N years) maxima of wind velocity is also Gmbel distribted and the mean and the standard deviation of lifetime maxima are fnctions of the mean and of the standard deviation of annal maxima: m N +.78 ln N, N =. Under special climatic conditions, the distribtion of mean wind speeds is a mixed distribtion lecting different meteorological phenomena. For load combination prposes it is proposed to model storms, for example those wind regimes where a mean velocity > m/s lasts for some time, as an intermittent rectanglar wave renewal process. The nmber of storms per year is approximately 5 corresponding to the freqency with which weather systems pass by, at least in middle Erope. The mean dration of the storm is approximately 8 hors. Consective storms are independent. The representative mean wind velocity in a storm can also be modeled by a Weibll distribtion. The exponent of the Weibll distribtion shold be arond. The location parameter shold be based on local data..3.4 Terrain roghness (category) The roghness of the grond srface is aerodynamically described by the roghness length,which is a measre of the sie and spacing of obstacles on the grond srface. Alternatively, the terrain roghness can be described by the srface drag coefficient, κ corresponding to the roghness length :

5 κ k = ln 99-CON-DYN/M4 Febrari 5 (6) where k.4 is von Karman s constant and is the erence height (Table, Table 3). Varios terrain categories are classified in Table according to their approximate roghness lengths. The distribtion of the srface roghness with wind direction mst be considered. Table. Roghness length, in meters, for varios terrain categories Terrain category A. Open sea. Smooth flat contry ) ) Terrain description Range of Recommended vale Areas exposed to the wind coming from large bodies of water; snow srface; Smooth flat terrain with ct grass and rare obstacles. B. Open contry High grass (6 cm) hedges, and farmland with isolated trees; Terrain with occasional obstrctions having heights less than m (some trees and some bildings) C. Sparsely bilt-p rban areas. Wooded areas D. Densely bilt-p rban areas. Forests E. Centers of very large cities Sparsely bilt-p areas, sbrbs, fairly wooded areas (many trees) Dense forests in which the mean height of trees is abot 5m; Densely bilt-p rban areas; towns in which at least 5% of the srface is covered with bildings having heights over 5m Nmeros large high closely spaced obstrctions: more than 5% of the bildings have a height over m ) Smallervalesof provoke higher mean velocities of the wind ) For the fll development of the roghness category, the terrains of types A to D mst prevail in the p wind direction for a distance of at least of m, respectively. For category E this distance is more than 5 km..3.5 Variation of the mean wind with height The variation of the mean wind velocity with height over horiontal terrain of homogenos roghness can be described by the logarithmic law. The logarithmic profile is valid for moderate and strong winds (mean horly velocity > m/s) in netral atmosphere (where the vertical thermal convection of the air may be neglected). U() k ln = *( ) δ δ δ δ 3 4 ( > d >> ) (7) where:

6 Febrari 6 () = δ = U ( ). 5ln * ( ) 6 fc = friction velocity in m/s = depth of bondary layer in m U ( ) = mean velocity of the wind at height above grond in m/s = height above grond in m = roghness length in m k = von Karman s constant (k.4 d = the lowest height of validity of Eq.(7) in m f c =Ωsin(φ) = Coriolis parameter in /s Ω =.76-4 = anglar rotation velocity in rad/s φ = latitde of location in degree For lowest. δ or m of the bondary layer only the first term needs to be taken into accont (Harris and Deaves, 98). The lowest height of validity for Eq.(7), d, is close to the average height of dominant roghness elements : i.e. from less than m, for smooth flat contry to more than 5 m, for centers of cities. For d a linear interpolation is recommended. In engineering practice, Eq.(7) is conservatively sed with d =. With respect to the erence (open terrain) exposre, the relation between wind velocities in two different roghness categories at two different heights can be written approximately as (Bietry, 976, Simi, 986): U ( ) U = ln ln,,.7. (8) At the erence height, the ratio of the mean wind velocity in varios terrain categories to the mean wind velocity in open terrain is given by the factor p in Table. The corresponding ratio for the mean velocity pressre is p. Table. Scale factors for the mean velocity (and the mean velocity pressre) at erence height in varios terrain exposre Terrain category A. Open sea. Smooth flat contry B. Open contry C. Sparsely bilt-p rban areas. Wooded areas D. Densely bilt-p rban areas. Forests E. Centers of large cities, m 5 3 p Intensity of trblence The trblent flctations of the wind velocity can be assmed to be normally distribted with mean ero. The root mean sqared vale of the velocity flctations in the airflow, deviating from the longitdinal mean velocity, may be normalised to the friction velocity as follows:

7 * v * 99-CON-DYN/M4 Febrari 7 = β Longitdinal (9a) δ = β v Transversal (9b) δ w = β w * δ Vertical. (9c) The approximate linear variation with height (Hanna, 98) can be sed only in moderate and strong winds. For netral atmosphere, the ratios v / and w / near the grond are constant irrespective the roghness of the terrain (ESDU 993): v w 4 π = 5. cos (a) δ 4 π = 55. cos (b) δ For <<δ the variance of the velocity flctations can be assmed independent of height above grond : v w = β* (a) = βv* (b) = βw* (c) and, for <. δ: v 75. (a) w 5. (b) The variance of the longitdinal velocity flctations can also be expressed from non-linear regression of measrement data, as fnction of terrain roghness (Solari, 987): 45. β = ln 75. (3) The longitdinal intensity of trblence is the ratio of the root mean sqared vale of the longitdinal velocity flctations to the mean wind velocity at height (i.e. the coefficient of variation of the velocity flctations at height : I ( ),t / ( ) = = ( ) U ( ) U ( ) (4) The trblence intensity at height can be approximated by:

8 Febrari 8 β I ( ) = 5.ln ln (5) The transversal and vertical intensities of trblence can be determined by mltiplication of the longitdinal intensity I () by the ratios v / and w /. Representative vales for intensity of trblence at the erence height are given in Table 3. Table 3: Wind parameters depending on terrain category Terrain category A. Open sea. Smooth flat contry B.Open contry C. Sparsely bilt-p rban areas. Wooded areas D. Densely bilt-p rban areas. Forests E. Centers of large cities [m] d [m] κ β β v β w [m] 5 3 I( ) Power spectral density and atocorrelation fnctions of gstiness The normalised half-sided von Karman power spectral densities and atocorrelation fnctions of gst velocity are given in Table 4. Table 4. The von Karman model of isotropic trblence Component of gst velocity Longitdinal I= Transversal I=v Vertical i=w Normalised spectral density ng ( n) i i 4n ( +. n ) ni( +. ni ) / 6 ( n ) 88 6 i / Normalised atocorrelation fnction ρ i (τ i ) 3 / Γ / 3 ( ) τ /3 K /3 ( τ ) 3 / 3 / τi K3 / ( τi) τik3 / ( τi) Γ( / 3) The notations in Table 4 are as follows: i = variance of velocity flctations in direction i, in m /s ;i=,vorw n i =n i () = nl ( ) i = is a non-dimensional height dependent freqency U ( ) n = freqency, in Hert U () = longitdinal mean velocity at height, in m/s

9 Febrari 9 L i () = length of integral scale of trblence in direction i, in m/s. τu () τ i = al i () = non-dimensional time (a =.339) K µ ( ) = modified Bessel fnction of second kind of order µ τ =timelag,ins The integral length scale of trblence in direction i at the height is: L i () = U() ρ ( τ )dτ i i i (6) where the atocorrelation ρ i (τ i ) is the Forier transform of spectral density. An estimation of the length of the integral scale of longitdinal trblence, for heights p to 3 m is given by ESDU (993), as: L () = 3 / 3 A ( / ) 3 / 5. K ( / h) ( / h) * (7) where A = δ K =.88[-(-/ c ) ] / c /δ =.39 * f c 8 / 6 3 / For the lateral and vertical direction (ESDU, 993): L v () =.5 ( v / ) 3 L () L w () =.5 ( w / ) 3 L () L v ().4 L () L w ().8 L () (8a) (8b) (8c) (8d).3.8 Coherence fnctions The cross-spectral density for two separated points P and P with distance r perpendiclar to direction i are given in terms of the point spectra and the coherence fnction by: with: / / / (,, ) (,, ) (,, ) (,, ) S n P P S n P P S n P P Coh n P P (9) ij ii jj ij / Longitdinal Coh ( r,k ) ( 5 / 6) 5 / 6 ψ. 5 / 6 / 6. 5 [ K ( ψ ) ψ K ( ψ )] exp( 5ψ = (a) Γ

10 Febrari / Transversal Coh ( r,k ) vv / Vertical Coh ( r,k ) ww = = ψ Γ ψ 5 / 6 v Γ ( 5 / 6) 5 / 6 w ( 5 / 6) K5 / 6 K5 / 6 6 ( ) ( rk ) ψ v + 3ψ + 5( rk ) ( ψ ) w v ( rl) 6 3ψ w + 5 ( rk ) ψ v K / 6 ψ wk / 6. 3 ( ψ ) exp(. 65ψ ) v v (b). 3 ( ψ ) exp(. 65ψ ) w w (c) where k n = π / and ψ i = ( r k + r / L i ). All coherence fnction Cohij ( n P P) U m assmedtovanish.,, with i j canbe The longitdinal coherence can also be approximated by (Kareem, 987): Coh / r nr r, exp + L U m + m ( n r) / () implying a coherence coefficient of C= + r / m and where m = Um = U( ) U( ). For strctres of small dimension, i.e. r mch smaller than L, r can be taken as ero..3.9 Peak velocities Spectral moments, λ i of higher than the i = order formally do not exist for trblence spectra (inclding von Karman and other spectra) flfilling the Kolmogorov asymptote (asymptotic f 53 / behavior). However, for high freqencies the spectra fall off more rapidly so that trncation of these spectra at freqencies of 5 H makes them finite. Also, filtering by finite areas on which the wind blows removes this mathematical inconvenience. Then, the distribtion of extreme gst velocities, max is asymptotically a Gmbel distribtion with mean: and variance: [ max,, ] ( ln / ln ) E λ λ t = ν t+ γ ν t λ () [ ] Var max λ, λ, t = [( π / 6) / ln νt] λ (3) γ=.577 is Eler s constant, t = 6 s and ν is the mean freqency of ero pcrossing, in H:

11 Febrari ν = λ / λ. (4) The mean and standard deviation of the random peak factor for gst velocities, g are defined as: g = ln ν t / ln ν t (5) g = π 6 ln ν t (6) The calclation of g from trblence spectra is sensitive to the choice of ct-off freqency (5- H). Empirically and theoretically one can assme that the mean of g is abot 3. for hor (3.8 for 8 hors) and its standard deviation abot.4. Since the flctating velocity pressre is a linear fnction of flctating velocity of gsts, the above vales of g and g also apply to the peak pressre..3. Mean velocity pressre and exposre factor The mean wind velocity pressre )atheightisdefinedby: Q() = ρu ( ) (7) where ρ is the air density (ρ=.5 kg/m 3 for standard air). The coefficient of variation of the maximm annal velocity pressre is approximately the doble of the coefficient of variation of the maximm annal velocity, V :V Q V. The roghness factor describes the variation of the mean velocity pressre with height above grond and terrain roghness as fnction of the erence velocity pressre. From Eq.(3) one gets: c r Q ( ) U ( ), ( ) = = = Q U ln, 7. ln (8) and Q() = c r () Q (9).3. Gst factors for velocity pressre The gst factor for velocity pressre is the ratio of the peak velocity pressre to the mean velocity pressre of the wind: Conversion of the open contry velocity pressre for different averaging time intervals can be gided by the following vales obtained from Section.3.: h min min(fastest mile) 3s. Q = Q = 7. Q =. 44Q

12 q ( ) peak c ( ) g = = Q ( ) Q ( ) + g Q ( ) q = + g V g[ I ( ) q = + ] 99-CON-DYN/M4 Febrari (9) where: Q() = the mean velocity pressre of the wind / q = q (,t ) = the root mean sqared vale of the longitdinal velocity pressre flctations from the mean V Q = coefficient of variation of the velocity pressre flctations (approximately eqal to the doble of the coefficient of variation of the velocity flctations): V Q I() g = the peak factor for velocity pressre. Approximately, the longitdinal velocity pressre flctation, q(,t) is a linear fnction of the velocity flctation. Since: it is: ρ[ U( ) + t (, )] = ρu( ) + ρu( t ) (, ) + ρt (, ) ρu( ) + ρu( t ) (, ) Q( ) = ρu( ) qt (, ) ρu( t ) (, ) and conseqently, the mean vale and the standard deviation of the peak factor for min. velocity pressre are the same like that for the gst velocity g 3. and g.4. The vales of the peak factor depend on the averaging time interval of the erence velocity Exposre factor for peak velocity pressre The peak velocity pressre at the height above grond is the prodct of the gst factor: the roghness factor and the erence velocity pressre; Q g () = c g () c r () Q (3) The exposre factor is defined as the prodct of the gst and roghness factors: c e () = c g () c r (). (3) 3 min min min min h h Since: = c ( c Q ) = c ( c Q ) c ( c Q ) q = from Section.3.8, the following peak g r approximate relations hold: c g min g r min = 7. c = h g c g g r

13 Febrari Aerodynamic shape factors The aerodynamic shape factor, c a is the ratio of the aerodynamic pressre exerted by the wind on the srface of a strctre and its components to the velocity pressre. The aerodynamic pressre is acting normal to the srface. By convention c a is assmed positive for pressres and negative for sctions. As the pressre exerted on a srface is not niformly distribted over the whole area of the srface or on the different faces of a bilding, the aerodynamic coefficients shold be assessed separately for the different parts and faces of a bilding. The aerodynamic shape factors er either to the mean pressre or to the peak pressre of the wind. The shape factors are dependent on the geometry and the dimensions of bilding, the angle of attack of the wind i.e. the relative position of the body in the airflow, terrain category, Reynolds nmber, etc. In certain cases the aerodynamic factors for external pressre mst be combined with those for internal pressre. There are two different approaches to the practical assessment of wind effects on rigid strctres: sing pressre coefficients and sing force coefficients. In the former case the wind force is the reslt of the smmation of the aerodynamic forces normal to a certain srface. It is intended for parts of the strctre. In the later case, the wind force is the prodct of the velocity pressre mltiplied by the overall force coefficient times the frontal area of the bilding. This approach is sed within the procedres for calclating the strctral response. Typical vales of the aerodynamic shape factors can be selected from appropriate national and international docments or from wind tnnel tests. The aerodynamic shape factors shold be determined in wind tnnels capable of modelling the atmospheric bondary layer..3.4 Uncertainties consideration The factors involved in the assessment of the wind forces on strctres contain ncertainties. The mean and the coefficient of variation of the wind forces expressed throgh the prodct of ncorrelated variables in Eq.() or Eq.() may be written as follows: and E(w) = E(c g )E(c a )E(c r )E(Q ) (3) V = V + V + V + V (33) w cg ca cr Q E(w) = E(c d )E(c a )E(c r )E(Q ) (34) V = V + V + V + V. (35) w cd ca cr Q Statistics of the above factors are sggested in Table 5.

14 Febrari 4 Table 5 Statistics of random variables involved in the assessment of the wind loading Q Variable c r c a - pressre coefficients - force coefficients c g c d Strctre period - small amplitdes - large amplitdes Strctre damping - small amplitdes - large amplitdes Ratio Expected Compted Coefficient of variation, V Reference Davenport, 987 Vanmarcke, 99 Generally, bt not necessarily, the lognormal distribtion is the recommended probability distribtion fnction for each of the partial factors involved in Eq. (3) and Eq. (34). Relevant Literatre and References Arya S.P., 993. Atmospheric bondary layer and its parametriation. Proceedings of the NATO Advanced Stdy Institte on Wind Climate in Cities, Waldbronn, Germany, Jly 5-6, Klwer Academic Pblishers, Dordrecht/Boston/London, p.4-66 ASCE 7-93, 993 and Draft of ASCE7-95, 995. Minimm design loads for bildings and other strctres. American Society of Civil Engineers, New York CIB W8 Commission, 994. Actions on strctres. Wind loads, 6th draft, May Davenport N.G., 995. The response of slender strctres to wind. In the wind climate and cities. Klwer Academic Pblishers, p.9-39 Davenport A.G., 987. Proposed new international (ISO) wind load standard. High winds and bilding codes. Proceedings of the WERC/NSF Wind engineering symposim. Kansas City, Missori, Nov., p Davenport A.G., 967. Gst loading factors. Jornal of the Strctral Division, ASCE, Vol.93, No.3, p Davenport A.G., 964. Note on the distribtion of the largest vale of a random fnction with application to gst loading. Proceedings. Instittion of Civil Engineering, London, England, Vol. 8 Jne, p Davenport A.G., 96. The application of statistical concepts to the wind loading of strctres. Proceedings, Instittion of Civil Engineering, London, England, Vol.9, Ag., p ESDU 85, Characteristics of atmospheric trblence near the grond. Part II: single point data for strong winds (netral atmosphere), April 993, 36 p. London, U.K. ESDU 86, Characteristics of atmospheric trblence near the grond. Part III: variation in space and time for strong winds (netral atmosphere), Sept. 99, 33 p., London, U.K. Eropean Prestandard ENV 99--4, 994. EUROCODE : Basis of design and actions on strctres, Part.4 : Wind actions, CEN Gerstoft P., 986. An assessment of wind loading on tower shaped strctres. Technical University of Denmark, Lingby, Serie R, No.3 Ghiocel D., Lng D., 975. Wind, snow and temperatre effects on strctres, based on probability. Abacs Press, Tnbridge Wells, Kent, U.K. Harris R.I., Deaves D.M., 98. The strctre of strong winds. The wind engineering in the eighties. Proceedings of CIRIA Conference /3 Nov., Constrction Indstry, Research and Information Association, London, p ISO / TC 98 / SC3 Draft International Standard 4354, 99. Wind actions on strctres. International Organisation for Standardisation Joint Committee on Strctral Safety CEB-CECM-CIB-FIP-IABSE, 974. Basic data on loads. Second draft. Lisbon Kareem, A., Wind Effects on Strctres, Prob. Eng. Mech.,, 4, 987, pp. 66- Karman v., T., 948. Progress in statistical theory of trblence. Proceedings, National Academy of Science, Washington D.C., p Lmley J.L., Panofsky H.A., 964. The strctre of atmospheric trblence. J.Wiley & Sons

15 Febrari 5 Lng D., Gelder P., Trandafir R., 995. Comparative stdy of Erocode, ISO and ASCE procedres for calclating wind loads. IABSE Colloqim, Basis of design and actions on strctres, Backgrond and application of Erocode, Delft, The Netherlands, 996 NBC of Canada, 99. Code National d Bâtiment d Canada, 99 and Spplement d Code, Comité Associé d Code National d Bâtiment, Conseil National de Recherche, Canada Plate E.J., 993. Urban climates and rban climate modelling: An introdction. Proceedings of the NATO Advanced Stdy Institte on Wind Climate in Cities, Waldbronn, Germany, Jly 5-6, Klwer Academic Pblishers, Dordrecht/Boston/London, p.3-4 Plate E.J., Davenport A.G., 993. The risk of wind effects in cities. Proceedings of the NATO Advanced Stdy Institte on Wind Climate in Cities, Waldbronn, Germany, Jly 5-6, Klwer Academic Pblishers, Dordrecht/Boston/London, p.- Rscheweyh H., 995. Wind loads on strctres from Erocode, ENV In Wind climate in cities. Klwer Academic Pblishers, p.4-58 Schroers H., Lösslein H., Zilch K., 99. Unterschng der Windstrctr bei Starkwind nd Strm. Meteorol. Rdsch., 4, Oct., p.- Simi E., Scanlan R.H., 986. Wind effects on strctres. Second edition. J. Wiley & Sons Simi E., 98. Revised procedre for estimating along-wind response. Jornal of the Strctral Division, ASCE, Vol.6, No., p.- Simi E., 974. Wind spectra and dynamic along-wind response. Jornal of the Strctral Division, ASCE, Vol., No.9, p Solari G., 993. Gst bffeting. I Peak wind velocity and eqivalent pressre. Jornal of Strctral Engineering, ASCE, Vol.9, No., p Solari G., 993. Gst bffeting. II Dynamic along-wind response. Jornal of Strctral Engineering, Vol.9, No., p Solari G., 988. Eqivalent wind spectrm techniqe: theory and applications. Jornal of Strctral Engineering ASCE, Vol.4, No.6, p Solari G., 987. Trblence modelling for gst loading. Jornal of Strctral Engineering, ASCE, Vol.3, No.7, p Therer W., Bachlin W., Plate E.J., 99. Model stdy of the development of bondary layer above rban areas. Jornal of Wind Engineering and Indstrial Aerodynamics, Vol. 4-44, p , Elsevier Uniform Bilding Code, 99 Edition. International Conference of Bilding Officials, Whittier, California Velloi J., Cohen E., 968. Gst response factors. Jornal of the Strctral Division, ASCE, Vol.97, No.6, p Vickery B.J., 994. Across - wind loading on reinforced concrete chimneys of circlar cross-section. ACI Strctral Jornal, May-Jne, p Vickery B.J., Bas R., 983. Simplified approaches to the evalation of the across-wind response of chimneys. Jornal of Wind Engineering and Indstrial Aerodynamics, Vol.4, p Vickery B.J., 97. On the reliability of gst loading factors. Proceedings, Technical meeting concerning wind loads on bildings and strctres, Bilding Science Series 3, National Brea of Standards, Washington D.C., p.93-4 Vickery B.J., 969. Gst response factors. Discssion. Jornal of the Strctral Division, ASCE, ST3, March, p Wieringa J., 993. Representative roghness parameters for homogenos terrain. Bondary Layer Meteorology, Vol.63, No.4, p Wind loading and wind-indced strctral response, 987. State of the art report prepared by the Committee on Wind effects of the Strctral Division of ASCE. ASCE, N.Y.