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SpringerWien NewYork CISM COURSES AND LECTURES Series Editors: The Rectors Giulio Maier - Milan Jean Salençon - Palaiseau Wilhelm Schneider - Wien The Secretary General %HUQKDUG 6FKUHÁHU 3DGXD Executive Editor 3DROR 6HUDÀQL 8GLQH The series presents lecture notes, monographs, edited works and SURFHHGLQJV LQ WKH ÀHOG RI 0HFKDQLFV (QJLQHHULQJ &RPSXWHU 6FLHQFH and Applied Mathematics. 3XUSRVH RI WKH VHULHV LV WR PDNH NQRZQ LQ WKH LQWHUQDWLRQDO VFLHQWLÀF DQG WHFKQLFDO FRPPXQLW\ UHVXOWV REWDLQHG LQ VRPH RI WKH DFWLYLWLHV RUJDQL]HG E\ &,60 WKH ,QWHUQDWLRQDO &HQWUH IRU 0HFKDQLFDO 6FLHQFHV ,17(51$7,21$/ &(175( )25 0(&+$1,&$/ 6&,(1&(6 &2856(6 $1' /(&785(6 1R :,1' ())(&76 21 %8,/',1*6 $1' '(6,*1 2) :,1' 6(16,7,9( 6758&785(6 (',7(' %< 7(' 67$7+2328/26="" &21&25',$ 81,9(56,7="" vo.="" negative="" values="" of="" cp="" are="" observed="" on="" roofs="" and="" sides="" of="" building.="" 7kh ="" zdnh ="" uhjlrq ="" lq ="" )ljxuh ="" ="" lv ="" fkdudfwhul]hg ="" e\ ="" olwwoh ="" suhvvxuh ="" judglhqw ="" %huqrxool¶v ="" equation="" is="" not="" applicable="" but="" pressure="" coefficients="" can="" also="" be="" expressed="" in="" dimensionless=""> CP w Pw Po (13) 1 / 2 UVo 2 Pressure coefficients in wake are invariably negative. Typical time series of pressure coefficients along with variation of wind speed and their statistics are shown in Figure 13. Definitions of Cpmean and Cppeak are: Mean pressure coefficient: Cpmean = CP Peak pressure coefficient: Cppeak = GC P 'Pmean 1 / 2 UVmean 2 'Ppeak 1 / 2 UVmean 2 (14) (15) The location of separation points and the geometry of the wake have a substantial influence on the pressure distribution and the total forces on the bluff obstacle. In the case of rectangular cylinder the separation points were dictated by the geometry of the prism. The boundary layer, which builds up on the front surface, fails to flow around the sharp corners boundary layer, which builds up on the front surface, fails to flow around the sharp corners and separates. For other bluff shapes particularly for those with curved surfaces such as wires, chimneys, and circular tanks the separation points are not easy to predict. For a circular cylinder, for example, separation takes place at different positions depending on the magnitude of the viscous forces, which dominate the flow within the boundary layer. The relative magnitude of these viscous forces can be expressed in the form of a dimensionless parameter known as the Reynolds number Re: Re UVo 2 D 2 in ertia forces v V viscous forces P o D2 D (16) T. Stathopoulos Thus R e Vo D (17) Q in which ȡ is the density, µ is the dynamic viscosity, and Ȟ is the kinematic viscosity of the air. Figure 14 shows the variation of pressure coefficients on the surface of a circular cylinder for different values of Re. Clearly the influence on the side face and the leeward side is significant. Figure 13. Wind pressure and wind speed traces indicating mean and peak values The time-averaged aerodynamic forces on structures can be expressed as along wind or drag forces (FD) and across wind or lift forces (FL). The latter should not be confused with the upward lift forces acting on horizontal building elements such as roofs. The drag force is normally larger, as far as static loads on buildings is concerned. Both drag and lift forces can be expressed also in terms of coefficient form, as follows: Drag coefficient C D FD 1 / 2 UVo 2 h (18) ,QWURGXFWLRQ WR :LQG (QJLQHHULQJ :LQG 6WUXFWXUH :LQG %XLOGLQJ ,QWHUDFWLRQ where h = projected frontal width or height of building Lift coefficie