長跨徑人行拱橋近年來深受工程師青睞，此型橋梁除滿足交通需求外，更能扮演當地景觀地標角色。因人行橋面版窄大多採用單拱設計，由於單拱缺乏側向支撐，拱順風向之氣動力反應也越趨明顯。而傳統斜張橋或懸索橋氣動力分析只考慮橋面版風力，因此無法適用於拱橋上。所以本研究建立一數值分析模式，以主梁斷面及橋拱斷面之顫振導數及風力係數為基礎，推導整體橋梁顫振與抖振理論。並採用兩例題，分別為單面吊索及雙面吊索拱橋，利用所推導之數值分析模式，配合橋拱斷面實驗求得之實驗數據進行顫振與抖振分析，來探討加入橋拱氣動力參數對整體顫振臨界風速與抖振位移反應影響。
　　例題結果顯示，橋梁顫振臨界風速主要受主梁氣動力控制，所以將橋拱順風向顫振導數（P1*、P4*）納入分析時，其對顫振影響並不顯著，兩例題之臨界風速提高不到1%。至於抖振分析，兩例題結果都顯示拱風力對拱及主梁順風向及扭轉向反應有顯著影響。當橋面高度之平均風速60m/s時，加入橋拱風力對例題一主梁順風向與扭轉向之抖振位移反應分別提高1.9%及44.11%；至於對橋拱本身順風向及扭轉向分別提高了764%及792%。由於此例題橋拱與主梁結構耦合不明顯，拱反應主要是作用於拱的風力貢獻，因此才有上述巨幅提升。例題二方面，風速60m/s時加入橋拱風力對橋面版順風向與扭轉向則分別提升了11.99%及133%；橋拱順風向及扭轉分別向則分別提高了57.87%及64.6%。此例題橋拱與主梁結構耦合較例題一明顯，作用於拱的風力對主梁及拱本身抖振反應都有明顯貢獻。由上述分析結果顯示，無論是單面吊索或雙面吊索橋，拱風力對主梁及拱本身抖振反應影響極為顯著，因此分析時須詳加考慮。

The long-span arch bridges have been a favorable choice for the design of pedestrian bridges during the past decades in Taiwan. This is because the type of bridges not only can satisfy the transportation needs but also may become the landmark in the local area. In these pedestrian bridges, a single arch is the only choice due to the narrow bridge deck. Since the single arch lacks lateral support and its height increases with the bridge span length, the drag responses in the arch become significant and cannot be negligible. To predict the aerodynamic responses of the arch, the traditional analysis used for cable-stayed and suspension bridges, considering wind forces acting on bridge decks only, cannot be used. In this thesis, an analytical approach based on flutter and buffeting theory associated with the information measured from section model tests is presented. Two examples are used to demonstrate the validity and applicability of this approach and to investigate the effects of the forces acting on the arch on the flutter wind speed and buffeting responses of bridge decks.

The results show that the critical flutter wind speeds in these two examples are dominated by the flutter derivatives of bridge decks. The increases of the critical flutter wind speeds considering flutter derivatives of arches are less than 1%. For the buffeting responses, the effects of the forces acting on arches are significant on both drag and torsional responses of arches and bridge decks. In Example 1 incorporating forces acting on the arch into the analysis, the drag and torsional responses of the bridge deck increase 1.9% and 44.1%, respectively. The increases of the drag and torsional responses of the arch are 764% and 792%, respectively. Since the structural coupling between the bridge deck and the arch is minor in this example, the main contribution to the responses of the arch is the forces acting on the arch itself. Therefore, the results with huge increases are expected. In Example 2 incorporating forces acting on the arch into the analysis, the drag and torsional responses of the bridge deck increase 11.99% and 133%, respectively. The increases of the drag and torsional responses of the arch are 57.87% and 64.6%, respectively. In this example, the structural coupling between the bridge deck and the arch is more obvious than in example 1. The effects of the forces acting on the arch on the responses of the arch and the bridge deck are significant. From the results stated above, the forces acting on the arch should be considered in the analysis.

目錄	I
表目錄	IV
圖目錄	V
第一章 緒論	1
1-1 研究動機	1
1-2 研究目的與方法	2
1-3 論文架構	3
第二章 文獻回顧	4
2-1人行拱橋發展歷史	4
2-2 橋梁氣動力效應	5
2-2-1 多振態顫振與抖振分析之研究	6
2-3顫振導數之研究	7
2-3-1 順風向顫振導數之研究	7
第三章 拱橋顫振及抖振理論推導	10
3-1 前言	10
3-2 運動方程式建立	10
3-3 拱橋顫振理論推導	13
3-3-1橋面版與橋拱自身擾動力	13
3-3-2顫振臨界風速	16
3-4 拱橋抖振理論推導	21
3-4-1主梁與橋拱抖振擾動力	21
3-4-2風力頻譜	25
3-4-3橋面版與橋拱風力頻譜	28
3-4-4抖振位移反應	36
第四章 實驗配置	39
4-1 前言	39
4-2 風洞實驗室與儀器介紹	39
4-2-1風洞實驗室特性	39
4-2-2皮托管	40
4-2-3 壓力轉換器	41
4-2-4 雷射位移計	41
4-3 實驗模型製作	42
4-4 實驗架構	42
4-4-1 實驗架設	42
4-4-2 實驗數據採樣分析	43
4-4-3 實驗分析方法	44
4-5 實驗結果	47
第五章 例題分析與結果	50
5-1前言	50
5-2人行吊索拱橋	51
5-2-1 結構形式與斷面性質	51
5-2-2 結構振態分析	51
5-3顫振臨界風速分析	53
5-4抖振位移反應分析	55
第六章 結論與建議	59
6-1結論	59
6-2建議	62
參考文獻	63
附表	66
附圖	73

 
表目錄
表5-1：人行拱橋之橋面版斷面性質	66
表5-2（a）：單面吊索斷面性質	66
表5-2（b）：雙面吊索斷面性質	67
表5-3：人行拱橋之橋拱斷面性質	67
表5-4（a）：單面吊索之自然結構振態頻率	68
表5-4（b）：雙面吊索之自然結構振態	68
表5-5（a）：單面吊索之參與質量分布表	69
表5-5（b）：雙面吊索之參與質量分布表	70
表5-6（a）：單面吊索例題之顫振臨界風速分析	71
表5-6（b）：雙面吊索例題之顫振臨界風速分析	71
表5-7：風速60m/s下橋面版三方向最大抖振位移反應	72
表5-8：風速60m/s下橋拱三方向最大抖振位移反應	72

 
圖目錄
圖2-1 Tsurumi bridge橋面版斷面【17】	73
圖2-2 Deer Isle bridge橋面版斷面【17】	73
圖4-1風力係數與顫振導數之實驗儀器配置流程圖	74
圖4-2斷面模型照片	75
圖4-3斷面模型照片	75
圖4-4力感應器作用於模型上之幾何示意圖	76
圖4-5風力係數實驗架構圖	77
圖4-6順風向顫振導數實驗架構圖	78
圖4-7橋拱斷面實驗之風力係數	79
圖4-9 B/D=1.6各風速下時間歷時	80
圖4-8 B/D=1.2各風速下時間歷時	81
圖4-10 B/D=1.6無風狀況下自由振動時間歷時放大圖	82
圖4-11 B/D=1.2顫振導數實驗結果	82
圖4-12 B/D=1.6顫振導數實驗結果	83
圖4-13（a）B/D=1.2顫振導數實驗結果與近似式	83
圖4-13（b）B/D=1.6顫振導數實驗結果與近似式	84
圖5-1（a）本研究單面吊索連接示意圖	85
圖5-1（b）本研究雙面吊索連接示意圖	85
圖5-2 邊界條件模擬示意圖	86
圖5-3（a）主梁斷面尺寸示意圖	86
圖5-3（b）B/D=1.2橋拱斷面尺寸示意圖	87
圖5-3（b）B/D=1.6橋拱斷面尺寸示意圖	87
圖5-4（a）單面吊索例題橋面版形狀函數圖（mode shape）	88
圖5-4（b）單面吊索例題橋拱形狀函數圖（mode shape）	89
圖5-5（a）雙面吊索例題橋面版形狀函數圖（mode shape）	90
圖5-5（b）雙面吊索例題橋拱形狀函數圖（mode shape）	91
圖5-6 參考文獻之主梁斷面模型實驗風力係數及顫振導數【28】	92
圖5-7（a）例題一各風速下橋面版三方向位移反應	93
圖5-7（b）例題一各風速下橋拱三方向位移反應	94
圖5-8（a）例題二各風速下橋面版三方向位移反應	95
圖5-8（b）例題二各風速下橋拱三方向位移反應	96
圖5-9（a）例題一在不同風速下橋面版垂直向最大位移比較	97
圖5-9（b）例題二在不同風速下橋面版垂直向最大位移比較	97
圖5-10（a）例題一在不同風速下橋面版順風向最大位移比較	98
圖5-10（b）例題二在不同風速下橋面版順風向最大位移比較	98
圖5-11（a）例題一在不同風速下橋面版扭轉向最大位移比較	99
圖5-11（b）例題二在不同風速下橋面版扭轉向最大位移比較	99
圖5-12（a）例題一在不同風速下橋拱垂直向最大位移比較	100
圖5-12（b）例題二在不同風速下橋拱垂直向最大位移比較	100
圖5-13（a）例題一在不同風速下橋拱順風向最大位移比較	101
圖5-13（b）例題二在不同風速下橋拱順風向最大位移比較	101
圖5-14（a）例題一在不同風速下橋拱扭轉向最大位移比較	102
圖5-14（b）例題二在不同風速下橋拱扭轉向最大位移比較	102

1.A.S.Nazmy. Stability and load-carrying capacity of three-dimensional long-span steel arch bridges. Computers & Structures Vol.65(6).857~868,1997
2.Kuranishi, S. Yabuki, T. Lateral load effect on steel arch bridge design. Journal of Structural Engineering,ASCE,1984,110,2263~2274
3.周達華,廖海黎,李永樂 等. 大跨度拱橋氣動彈性模型風洞試驗研究//第五屆全國風工程及工業氣動力學學術會議論文集.成都 2002
4.廖海黎.杭州市錢江四橋風洞模型試驗與分析研究.成都:西南交通大學風工程試驗研究中心,2003
5.葛耀君,宋錦忠,曹豐產 等.上海盧浦大橋風荷載及抗風穩定性研究//第十五屆全國橋梁學術會議論文集.上海:同濟大學出版社,2002
6.胡曉紅.大跨度拱橋等效風荷載試驗研究.上海:同濟大學土木工程學院,2002
7.Scanlan, R. H., Tomko, J. J., “Airfoil and Bridge Deck Flutter Derivatives,” Journal of Engineering Mechanical Division, ASCE, Vol. 97, pp.1717-1737 1971.
8.Simiu, E., Scanlan, R. H., “Wind Effects on Structures ,” John Wiley & Sons. 1986.
9.Kazama, K., Yamada, H. and Miyata, T., “Wind Resistant Design for Long Span Suspension Bridges,” Journal of Wind Engineering and Industrial Aerodynamics, No. 54/55, pp.65-74 (1995)
10.Agar, T.J.A,”Aerodynamic Flutter Analysis of Suspension Bridges by a Modal Technique”,Eng.Struct,Vol. 11,pp.75-82(1989)
11.Agar, T.J.A,”The Analysis of Aerodynamic Flutter of Suspension Bridges”, Computer & Structures, Vol. 30,NO. 3,pp. 593-600(1988).
12.Agar, T.J.A,”Dynamic Instability of Suspension bridges”, Computer & Structures, Vol. 41,NO. 6,pp. 1329-1460(1991).
13.Qu, W.L. and H.F.Xiang,”An analysis Method for Buffeting response of Flexible Bridge with Aerodynamic Coupling Between Modes,”Proceedings of the Third Asia-Pacific Symposium on Wind Engineering,pp.181-185.
14.A.Jain, N.P.Jones and R.H.Scanlan, ”Coupled Flutter and Buffeting Analysis of Long-Span Bridges,” Journal of Structural Engineering,ASCE,Vol.122,Issue7,pp.716-725,1996
15.S.S.Mishra,K.Kumar and P.Krishna,”Multimode Flutter of Long-Span Cable-Stayed Bridge Base on 18 Experimental Aeroelastic Derivatives,”Journal of Wind Engineering and Industrial Aerodynamics,Vol.96,Issue 1,pp.83-102,2008
16.R.H.Scanlan,”Interpreting Aeroelastic Models of Cable-Stayed Bri-dges,”Journal of Engineering Mechanics,ASCE,Vol.113,No.4,pp.555-575,1987.
17.L.Singh,N.P.Jones,R.H.Scanlan and O.Lorendeaux,”Identification of Lateral Flutter Derivatives of Bridge Deck”Journal of Wind Engineering and Industrial Aerodynamics,Vol.60,pp.81-89,1996.
18.X.Zhang and J.M.W. Brownjohn,”Some Considerations on the Effect of the P-Derivatives on Bridge Deck Flutter,” Journal of Sound and Vibration,Vol.283,Issue 3-5,No.25,pp.957-969,2005
19.H.Yamada, H.Katsuchi and P.H.Kien ,”A study on Understanding of Coupled Flutter of Long-Span Bridges,” 4th International Symposium on Computational Wind Engineering(CWE),Yokohama,Japan,July 16-19,2006.
20.Tanaka, H. ,Yamamura, N. and Tatsumi, M. ,”Coupled Mode Flutter Analysis Using Flutter Derivatives,”Journal of Wind Engineering and Industrial Aerodumamics,Vol.41-44,pp1279-1290(1992)
21.李鳳娟,”振態耦合對大跨度橋梁自勵振動現象之影響,”私立淡江大學土木工程研究所碩士論文,1995.
22.Kaimal, J.C.,”Spectrum Characterics of Surface-Layer Turbulence,”J.Royal Meteorol.Soc.,98,pp.563-589,1972.
23.Simiu, E., Scanlan, R.H.,”Wind Effects on Structures,”John Wiley& Sons. 1986.
24.Vickery, B. J., “On the Reliability of Gust Loading Factors,” Proceedings of the Technical Meeting Concerning Wind Loads on Buildings and Structures, National Bureau of Standards, Building Science Series 30, Washington, D.C.,pp. 93-104(1970)
25.Liepmann, R. W., “On the application of statistical concept to the buffeting problem, ” J. Aero. Sci ., Vol.19, No.12 , 1952.
26.Sarkar, P. P., Jones, N. P. and Scanlan, R. H. (1992), "System identification for estimation of flutter derivatives", Journal of Wind Eng. and Industrial Aerodynamics, 41-44, pp.1243-1254.
27.Scanlan, R. H. and Tomko, J. J.(1971),“Airfoil and Bridge Deck Flutter Derivatives”,Journal of Eng.Mech.Div., Vol.97, pp.1717-1737
28.鄭啟明,林堉溢,蔡明樹,黃明慧,鄭詩穎,”橋梁風洞實驗結果報告書”,淡江大學風工程研究中心,2010.