1. The 2 nd 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 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. For a prism structureFor a curved structure Roughness on the surface Oncoming wind speed Flow viscosity Geometric appearance … 1 2

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

4. 1.Experimental setting and simulated turbulent flow 2.Zoning of domed roofs 3.Approximation model for power spectra 4.Approximation model for cross spectra 5.Conclusions Presentation content

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

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

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

8. Experimental setting and simulated turbulent flow Acrylic domed models D = 300mm f/D (roof height to span) 0.00.10.20.30.40.5 h/D (cylinder height to span) 0.0NoneB0C0D0E0F0 0.1A1B1C1D1E1F1 0.2A2B2C2D2E2F2 0.3A3B3C3D3E3F3 0.4A4B4C4D4E4F4 0.5A5B5C5D5E5F5 35 domed models for wind pressure measurements However, only f/D=0.5 is discussed in this presentation! D f h x z x y

9. Experimental setting and simulated turbulent flow Reynolds number ranges For U G =11.1m/sec U H = 5.1m/sec ~ 7.5m/sec Re = 1.06×10 5 ~ 1.56×10 5 R e : Reynolds number ρ : air density; U H : mean wind speed model height D: model span (300mm) μ: viscosity constant According to Fu [12] and Hongo [50], when Re>10 5, 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 Contours of C p,mean f/D=0.5 h/D=0.0h/D=0.1 h/D=0.2h/D=0.5 Top View Side View

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

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

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

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

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

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

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

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

19. 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) Cross spectra Approximation model for cross spectra Co-coherence Root-coherence Phase Side View Wind

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

21. Approximation model for cross spectra Cross spectra F0 (f/D=0.5, h/D=0.0) 7 8 10 17 Ch.7 – Ch.10 Ch.8 – Ch.17 Ch.9 – Ch.23 Ch.18 – Ch.24 9 18 23 24 Ch.3 – Ch.21 Ch.2 – Ch.26 2 326 21 Side View Wind

22. Approximation model for cross spectra Ch3-Ch4Ch3-Ch5Ch18-Ch19 Ch7-Ch10Ch7-Ch18Ch7-Ch27 345710181927 WindwardSeparationWake Cross spectrum features 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. Top View

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

24. Approximation model for cross spectra

25. Conclusions 1)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. 2)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. 3)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. Thank you very much for your listening. The 2 nd Cross-Strait Symposium on Dynamical Systems and Vibration 13-19 December 2012