The 2 nd Cross-Strait Symposium on Dynamical Systems and Vibration 13-19 December 2012

1. The 2nd Cross-Strait Symposium on Dynamical Systems and Vibration 13-19 December 2012 Spectrum Characteristics of Fluctuating Wind Pressures on Hemispherical Domes Yuan-Lung Loren Lo Chung-Lin Fu Chii-Ming Cheng Dept. Civil Eng., Tamkang University, Taiwan

2. Background For a prism structure For a curved structure 1 • Roughness on the surface • Oncoming wind speed • Flow viscosity • Geometric appearance • … 2 Since the span of dome roof sometimes stretches to more than 100 or 200 m, wind fluctuations on the roof may dominate rather than earthquake loading.

3. Objective This research intends to investigate spectrum characteristics of wind pressures on dome structures and intends to provide a general model for practical applications. Roof height simplifying Cylinder height Evaluating response Wind Tunnel Test Evaluating pressures

4. Presentation content Experimental setting and simulated turbulent flow Zoning of domed roofs Approximation model for power spectra Approximation model for cross spectra Conclusions

5. Experimental setting and simulated turbulent flow Urban terrain is attempted. UG: mean wind speed at boundary layer height UG=5.9m/sec and 11.1m/sec

6. Experimental setting and simulated turbulent flow Power spectra of oncoming winds where Г(-): gamma function; β: shape parameter; L(z): length constant. β=2: Karman-type spectrum

7. Experimental setting and simulated turbulent flow Wind pressure measurement devices Fs=1000Hz T=120sec Transition characteristics of tubing

8. Experimental setting and simulated turbulent flow Acrylic domed models y x D z f h x 35 domed models for wind pressure measurements However, only f/D=0.5 is discussed in this presentation!

9. Experimental setting and simulated turbulent flow Reynolds number ranges For UG=11.1m/sec UH = 5.1m/sec ~ 7.5m/sec Re = 1.06×105 ~ 1.56×105 Re: Reynolds number ρ: air density; UH: mean wind speed model height D: model span (300mm) μ: viscosity constant According to Fu [12] and Hongo [50], when Re>105, and turbulence intensity larger than 15~18%, the distribution of wind flow will be stable. Scaling of domed models • According to the time scale, 1/70, • 8192 samples in tunnel = 10 minute in field scale • 14 segments of 8192 samples are taken averaged.

10. Zoning of domed roofs Side View Contours of Cp,mean f/D=0.5 Top View h/D=0.0 h/D=0.1 h/D=0.2 h/D=0.5

11. Zoning of domed roofs Side View Contours of Cp,RMS f/D=0.5 Top View h/D=0.0 h/D=0.1 h/D=0.2 h/D=0.5

12. Zoning of domed roofs f/D=0.5 Side View D Cp,mean along meridian Cp,RMS along meridian z f/D=0.5 f/D=0.5 f x h

13. Zoning of domed roofs Side View Correlation coefficients f/D=0.5 h/D=0.0 h/D=0.1 h/D=0.2 h/D=0.5

14. Approximation model for power spectra f/D=0.5 h/D=0.0 Power spectra Ch.29 Separation Windward Wake fD/UH Ch.3 Ch.2 Ch.1 Wind Side View

15. Approximation model for power spectra Power spectra Ch.5 f/D=0.5 h/D=0.0 Velocity-pressure admittance Karman velocity spectrum

16. Approximation model for power spectra Power spectra f/D=0.5 h/D=0.0 Ch.15 Ch.26

17. Approximation model for power spectra Power spectra Weighting for approximation Wind Side View

18. Approximation model for power spectra Power spectra Weighting for approximation For f/D=0.5 h/D=0.0 Ch.25 Distribution of weighting factors for typical power spectrum modelshows the variation of turbulence energy

19. Approximation model for cross spectra Cross spectra Cross spectrum characteristics of two fluctuating wind pressures are concerned when integrating wind loads over certain area or the whole surface of the roof. F0 (f/D=0.5, h/D=0.0) Co-coherence Root-coherence Wind Side View Phase

20. Approximation model for cross spectra Cross spectra Ch.10 – Ch.12 Ch.22 – Ch.23 Ch.3 – Ch.4 F0 (f/D=0.5, h/D=0.0) 16 12 17 10 22 Ch.16 – Ch.17 Ch.25 – Ch.27 Ch.3 – Ch.5 5 23 4 25 Wind 3 Side View 27

21. Approximation model for cross spectra Cross spectra Ch.7 – Ch.10 Ch.9 – Ch.23 Ch.3 – Ch.21 F0 (f/D=0.5, h/D=0.0) 17 18 21 10 9 23 Ch.8 – Ch.17 Ch.18 – Ch.24 Ch.2 – Ch.26 8 7 24 Wind 3 26 Side View 2

22. Approximation model for cross spectra Cross spectrum features Top View Ch3-Ch4 Ch3-Ch5 Ch18-Ch19 3 4 5 7 10 18 19 27 Ch7-Ch10 Ch7-Ch18 Ch7-Ch27 Windward Separation Wake Generally, there are (1)five different distributions of co-coherences can be indicated among all data. In addition, (2)with the distance between two points increases, decaying tendency also changes.

23. Approximation model for cross spectra Approximation model for cross spectra To approximate root-coherences and phases, Ogawa and Uematsu have applied the following expression. Kanda’s model Sakamoto’s model 1 2 1 2 • Co-coherence value at zero frequency • Decaying tendency • Peak at lower frequency 3 This research • Phase shift at zero frequency

24. Approximation model for cross spectra Approximation model for cross spectra

25. Conclusions Based on the categories of models and the divisions of zones, same as wind pressure coefficients, power and cross spectra were also investigated to show their various characteristics. From the examination of cross spectrum characteristics, it was shown that various features occur when the two points of cross spectrum are located in different wind flow patterns. A general co-coherence model was proposed by adding three parameters to the commonly used formula. From the approximation results, a uniform model for any location was shown to be insufficient.

26. The 2nd Cross-Strait Symposium on Dynamical Systems and Vibration 13-19 December 2012 Thank you very much for your listening.