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loaded on tall buildings with rectangular cross-section, Doctor Liangbo took a series of local wind pressure measurement

wind tunnel tests and high frequency balance wind tunnel tests for 6 building models in 1995. In his wind tunnel test report,

he showed wind force coefficients of all models, and power spectra, correlations and corresponding mathematical models of

generalized wind forces, local wind forces and base forces.

In order to build a wind loads database of buildings and structures, I attempt to pick up some useful test data from his report

today.

1.Wind Tunnel Test Introduction

1.1. Wind Tunnel

The wind tunnel test is carried out in the Boundary-Layer Wind Tunnel with 3.1 meters wide and 2.0 meters high and 16

meters long, Wind Engineering Institute

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- 1. Test Data of High-rise Building Wind Tunnel Tests from Dr. Liangbo QUAN YongIn order to study the power spectra and time-spatial correlations of along-wind, across-wind and torsional wind forcesloaded on tall buildings with rectangular cross-section, Doctor Liangbo took a series of local wind pressure measurementwind tunnel tests and high frequency balance wind tunnel tests for 6 building models in 1995. In his wind tunnel test report,he showed wind force coefficients of all models, and power spectra, correlations and corresponding mathematical models ofgeneralized wind forces, local wind forces and base forces.In order to build a wind loads database of buildings and structures, I attempt to pick up some useful test data from his reporttoday.1.Wind Tunnel Test Introduction1.1. Wind TunnelThe wind tunnel test is carried out in the Boundary-Layer Wind Tunnel with 3.1 meters wide and 2.0 meters high and 16meters long, Wind Engineering Institute.1.2. Test Wind FieldThe blocks and spires are used to generate a boundary layer. The wind tunnel flow features, for example: mean wind speedprofile, turbulence intensity and turbulence scale, are shown in Fig.1, According to “AIJ Recommendations for Loads onBuildings”, the experimental flow features belong in terrain roughness category 2. Fig.1 Features of Testing Wind Field1.3. Testing ModelsThe length scale of the experimental model was set at 1/500. The dimensions the six testing models, whose cross-sectionareas are same, were given in the Tab. 1 below. Tab.1 Model Dimensions1.4. Measuring Method1.4.1. Local wind forces
- 2. The investigation of local wind forces included the measurement of along-wind force, across-wind force and torsionalmoment. The levels in the vertical direction are shown in Fig.2. Fig.2 Measure Levels of Local Forces in the Vertical DirecionThe measured points of each horizontal level were shown from Fig. 3~4. Fig.3 Measure Points of Local Forces of Each Horizontal Level Fig.4 Measure Points of Local Wind Forces (D:B=1:1)Fig. 5 showed the multi-hold method for obtaining wind pressure.
- 3. Fig.5 Multi-hold Method for Obtaining Wind PressureThe time interval of sampling point was 1.6ms, and the total number of sampled points is 16992. So the sampled length isabout 27 seconds.The mean and fluctuating wind force coefficients of local wind forces were defined as: C FD ( z ) = FD ( z ) /( Bq H ); C FL ( z ) = FL ( z ) /( Bq H ); C M Z ( z ) = M Z ( z ) /( BDqH ) (1) ′ C FD ( z ) = σ FD ( z ) /( BqH ); C FL ( z ) = σ FL ( z ) /( BqH ); C M Z ( z ) = σ M Z ( z ) /( BDqH )in which,FD (z ) and FL (z ) : mean wind forces at height z;σ F (z ) and σ F (z ) : standard deviations of wind forces at height z; D LM Z (z ) and σ M Z (z ) : mean value and standard deviation of torsional moment at height z;B, D and qH: projected breadth of model, depth of model and velocity pressure at the top of model.1.4.2. Base forcesThe definition of five components of base force was shown in Fig.9. Fig.9 Definition of five components of base forceThe time interval of sampled points is 6.2ms, and the total number of sampled point is 10000. So the sampling length is 62seconds.The mean and fluctuation wind force coefficients of base forces were defined as: C FD = FD /( BHq H );C FL = FL /( BHq H ); C M D = M D /( BH 2 Dq H ); C M L = M L /( BH 2 Dq H ); C M Z = M Z /( BH 2 Dq H ) (2) ′ ′ ′ ′ ′ C FD = σ FD /( BHq H ); C FL = σ FL /( BHq H ); C M D = σ M D /( BH 2 Dq H ); C M L = σ M L /( BH 2 Dq H ); C M Z = σ M Z /( BH 2 Dq H )in which, FD and σ FD : mean value and standard deviation of base shear force in along-wind direction;FL and σ FL : mean value and standard deviation of base shear force in across-wind direction;M D and σ M D : mean value and standard deviation of across-wind base overturning moment;M L and σ M L : mean value and standard deviation of along-wind base overturning moment;M Z and σ M Z : mean value and standard deviation of torsional moment;H, B, D and qH: height, breadth, depth of model and velocity pressure at the top of model.
- 4. 2. Test Results2.1 Base Force (For Model 1-4)2.1.1 Wind force coefficients obtained from base forces (For Model 1-4) Tab.2 Wind force coefficients obtained from base forces2.1.2 Normalized power spectra of base forces (For Model 1-4)2.1.3 Cross-correlation between different base forces (For Model 1-4)2.2 Local Wind Force2.2.1 Wind force coefficients obtained from local wind force Tab.3 Wind force coefficients obtained from local wind force2.2.2 Local wind force coefficients
- 5. 2.2.3 Normalized power spectra of local wind forces (For Model 1-4)2.2.4 Auto-correlation coefficient (For Model 1-4)
- 6. 2.2.5 Root-correlation and phase (For Model 1-4)2.2.5.1 Same type local wind forces between different levels (For Model 1-4)
- 7. 2.2.5.2 Different type local wind forces between same level (For Model 1-4)
- 8. 3. Mathematical Model of Wind Forces3.1 Root-coherence and Phase3.1.1 Base forcesThe root-coherence and phase between across-wind base shear and torsional base moment of modelswith square cross-section are given by following equations: COH = 0.9 exp(− Kf ) (3) K = 1, f = fB / VH ⎧ ⎪− 16000( f − f 0 / 2) + 220, if 2 f < f 0 = 0.1 (4) Φ=⎨ ⎪180 exp[−50( f − f 0 )], ⎩ if f ≥ f0in which, Φ is in degree, f is the frequency (Hz).3.1.2 Different type local wind forces at the same levelThe root-coherence and phase between local across-wind force and local torsional moments at level3H/4 are given by following equations: COH = 0.8 exp(− Kf ) (5) K = 0.5, f = fB / VH ⎧− 180 − 480 f if D / B < 1 and f < 0.25 ⎪ ⎪60 if D / B < 1 and f ≥ 0.25 ⎪− 160 if D / B = 1 and f < f 0 = 0.14 − 0.01( H / D) (6) ⎪ Φ=⎨ ( ⎪20 f − f 0 ) if D / B = 1 and f ≥ f 0 ⎪− 160 + 800 f if D / B > 1 and f < 0.2 ⎪ ⎪0 ⎩ if D / B > 1 and f < 0.23.1.3 Same type local wind forces between different levels3.1.3.1 Local along-wind forceThe root-coherence and phase between local along-wind forces between level i and level j are given byfollowing equations:
- 9. COH = R0 exp(− Kf ) (7) ⎧1.0 − 0.11∆z / H , if H / BD ≤ 3 ⎪ K = 6, f = ∆zf / VH , ∆z = zi − z j , R0 = ⎨ ⎪1.0 − 0.20∆z / H , if H / BD > 3 ⎩ Φ=0 (8)in which, f is the frequency (Hz), and zi , z j are heights of level i and j VH is mean wind speed at the top of model3.1.3.2 Local across-wind forceThe root-coherence and phase between local along-wind forces between level I and level j are given byfollowing equations: ⎧⎪ f + [1 − 0.6(∆z / H )] if f < f 0 and D / B < 3 ⎧ ⎪ ⎪⎨ COH = ⎨⎪ R0 ⎩ if f < f 0 and D / B ≥ 3 (9) ⎪ ⎪ R0 exp[− K ( f − f 0 )] if f ≥ f 0 ⎩ K = 4, R0 = 1.0 − 0.27(∆z / H ), f 0 = 0.33(∆z / H ), f = f∆z / VH , ∆z = zi − z j ⎧ ⎪0.4(∆z / H ) × 90 if f < f 0 Φ=⎨ (10) ⎪Φ 0 exp[− K ( f − f 0 )] if f ≥ f 0 ⎩ K = 4, Φ 0 = (∆z / H ) × 180, f 0 = 0.5(∆z / H ), f = f∆z / VH , ∆z = zi − z j3.1.3.3 Local torsional momentThe root-coherence and phase between local torsional moments between level I and level j are given byfollowing equations: ⎧ R0 ⎪ if f < f 0 COH = ⎨ ⎪ R0 exp[− K ( f − f 0 )] ⎩ if f ≥ f 0 (11) K = 4, f 0 = 0.33(∆z / H ), f = f∆z / VH , ∆z = zi − z j ⎧0.94 − 0.6(∆z / H ) if H / BD ≥ 4 and D / B = 1 R0 = ⎨ ⎩1.0 − 0.65(∆z / H ) otherwise ⎧ [ ] ⎪ 20 f + 1.5(∆z / H ) × 90 / 4 Φ=⎨ if f < f0 ⎪Φ 0 exp[− K ( f − f 0 )] (12) ⎩ if f ≥ f0 K = 20, Φ 0 = 6.1(∆z / H ) × 90 / 4, f 0 = 0.23(∆z / H ), f = f∆z / VH , ∆z = zi − z j3.2 Normalized Power Spectra3.2.1 Local along-wind forceThe normalized power spectra of local along-wind forces at any level of building are given byfollowing equations: −1 fS FD ( z , f ) fξβ ⎡ ⎛ z fB ⎞2 ⎤ = ⎢1 + ⎜ ⎟ ⎥ σ FD 2 [ 1 + η ( fβ ) 2 ] 1.08 ⎜ ⎢ ⎝ H V ( z) ⎠ ⎥ ⎣ ⎟ ⎦ (13) LH = 100( H / 30)0.5 , V ( z ) = V10 ( z / 10)α if D / B ≥ 1 : β = (LH / VH )(D / B ) (z / H )0.15 , ξ = 9.3 − 0.5 , η = 142 if D / B < 1 : β = (LH / VH )(D / B ) − 0.5 , ξ = 9.3( D / B) − 0.3 , η = 142( D / B) − 0.5in which, V (z ) = mean wind speed at height z V10 = mean wind speed at height 10m α = power law index of vertical profile of mean wind speed LH = turbulence scale at height H3.2.2 Local across-wind forceThe normalized power spectra of local across-wind forces at any level of building are given byfollowing equations:
- 10. fS FL ( f ) fS ST ( f ) fSVS ( f ) = + σ FL 2 σ ST 2 σ VS 2 fS ST ( f ) = B1 fS / k + T1 (f /k ) 3 [1 + ξ ( f )] [1 + 0.48( f )] S σ ST 2 /k c 2 .5 /k 2 7 S S fSVS ( f ) B2 ⎡ ⎛ ln f s + 0.5δ 2 ⎞ ⎤ 2 = exp ⎢− 0.5⎜ ⎜ ⎟ ⎥ ⎟ σ VS 2 δ 2π ⎢ ⎝ δ ⎠ ⎥ ⎣ ⎦ 0.12VH / B fs = f / fs , fs = , ξ = 0.62e− 0.3 z [ 1 + 0.38( D / B) 2 0.89 ] ⎧1.3 / D / B ⎪ if D / B ≥ 1 k =⎨ ⎪1.3 / 1.5D / B ⎩ if D / B < 1 ⎧1.0 if D / B ≤ 1 η=⎨ 3 ⎩1.0 / D / B if D / B > 1 ⎧1.5 if D / B ≤ 1 c=⎨ − 0.04 ⎩1.5(1 − z ) ( D / B) if D / B > 1 0.07 ⎧0.4 I ( H / 3) / D / B if D / B < 1 ⎪ δ = ⎨ I ( H / 3) if D / B = 1 ⎪2( D / B) I ( H / 3) if D / B > 1 ⎩ (14) I ( z ) = 0.1( zG / z ) α + 0.05 , z = z/H T1 = 9.4 I ( H / 3) ⎧1.6 / (1.0 + z ) if D / B ≤ 1/ 3 ⎪0.46 1/ 3 < D / B < 1 ⎪ if B1 = ⎨ ⎪0.63(4 B / H ) if D / B =1 ⎪0.63 ⎩ if D / B >1 ⎧1.6 if D / B ≥ 1 B2 = ⎨ ⎩1.6(1 − z ) if D / B < 1 0.3in which, S ST ( f ) = effects of the signature turbulence layers SVS ( f ) = effects of the vortex shedding fS = Strouhal frequency I ( z) = turbulence intensity at height z zG = gradient height α = power law index of vertical profile of mean wind speed3.2.3 Local torsional momentThe normalized power spectra of local across-wind forces at any level of building are given byfollowing equations:
- 11. fS FT ( f ) fS ST ( f ) fSVS ( f ) fS FP ( f ) = B0 F ( f ) + B1 ` + B2 ` σ FT 2 σ ST 2 σ VS 2 σ FP 2 fS ST ( f ) fS / k = σ 2 ST [1 + ξ ( f S /k ) ] c1 c 2 fSVS ( f ) 1 ⎡ ⎛ ln f s + 0.5δ12 ⎞ ⎤ 2 = exp ⎢− 0.5⎜ ⎜ ⎟ ⎥ ⎟ ⎥ σ VS 2 δ1 2π ⎢ ⎝ δ1 ⎠ ⎦ ⎣ fS FP ( f ) 1 ⎡ ⎛ ln f s + 0.5δ 2 2 ⎞ ⎤ 2 = exp⎢− 0.5⎜ ⎜ ⎟ ⎥ ⎟ ⎥ σ FP 2 δ 2 2π ⎢ ⎝ δ2 ⎠ ⎦ ⎣ 0.12VH / B fs = f / fs , fs = , ξ = 0.62e− 0.3 z [1 + 0.38( D / B) ] 2 0.89 ⎧0.25 if D / B < 1 f m = f / f m , f m = kmVH / BD , km = ⎨ ⎩0.30 /( D / B) 0.35 if D / B ≥ 1 { [ F ( f ) = 1 + 1.5 sin π /(1 + ( f s / γ )3 ) ]} −1 ⎧ I ( H / 3) if D / B ≤ 1 δ 2 = 2.5 I ( H / 3) , δ1 = ⎨ ⎩5 I ( H / 3) if D / B > 1 k = 1.5 , I ( z ) = 0.1( zG / z )α + 0.05 , z = z / H ⎧1.5 if D / B ≤ 1 γ =⎨ ⎩1.5( D / B) if D / B > 1 ⎧1.5 if D / B = 1 C2 = 3.75C1 , C1 = ⎨ ⎩1.0 if D / B ≠ 1 ⎧1.2 if D / B ≤ 1 B0 = ⎨ ⎩0.63 if D / B > 1 ⎧0.21(1 − z ) + 0.5( D / B) if D / B < 1 ⎪ B1 = ⎨0.21(1 − z ) /(4 B / H ) if D / B = 1 ⎪0.21(1 − z )( D / B) − 2 if D / B > 1 ⎩ ⎧0.05(1 + z ) /(4 B / H ) if D / B = 1 B2 = ⎨ ⎩0.05(1 + z )( D / B) (15) if D / B ≠ 1in which, S ST ( f ) = effects of the signature turbulence layers SVS ( f ) = effects of the vortex shedding S FP ( f ) = effects of the flipping phenomenon fS = Strouhal frequency I (z ) = turbulence intensity at height z zG = gradient height α = power law index of vertical profile of mean wind speed

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