双肢薄壁高墩刚构桥悬臂施工稳定性与风效应研究
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摘要
作为一种无支架施工方法,平衡悬臂施工法在连续梁桥、连续刚构桥、斜拉桥施工中得到了普遍的采用。双肢薄壁高墩连续刚构桥因经济上的竞争力和施工上的方便性,在国内得到了较多的采用。但这种结构在平衡悬臂施工阶段存在一些问题,本文研究主要集中于施工阶段稳定性分析和风效应研究:
1) 以稳定性分析为目标,基于弹性力学基本方程和变分原理,推导了单层、多层门式刚架的临界荷载表达式和带双横联的双肢薄壁墩平衡悬臂施工阶段稳定性系数计算的简化计算公式,该计算式简单明了、方便使用。以贵阳小关桥3号桥墩平衡悬臂施工多个阶段的稳定性计算为例,比较了本文算法和有限元分析结果,计算结果偏差小说明了本文方法的可靠性和工程适用性。
2) 以双肢薄壁高墩连续刚构桥平衡悬臂施工的简化计算模型出发,运用拉格朗日方程推导了其运动方程并获得了其自由振动频率,对特征方程的处理使得该方法可用于单横联双肢薄壁墩刚构桥、单薄壁墩刚构桥,具有较好的工程适用性。以贵阳小关桥为例,通过有限元分析、现场动力试验和本文结果对比,验证了本方法在计算双肢薄壁高墩刚构桥平衡悬臂施工阶段动力特性上的可靠性。该法只需计算器运算而无需有限元专用程序计算,简单方便,适合于工程单位使用。
3) 完成了小关桥3号墩双肢薄壁刚构平衡悬臂施工多个工况的现场动力试验,模态分析的现场试验结果与有限元分析、本文动力特性快速算法结果的一致性好。研究思路形成了以现场动力试验结果为依据,以模型修正技术为手段,通过修正简化动力模型,由稳定性快速算法及时判断施工结构稳定安全性的方法。
4) 采用CFD方法模拟了连续刚构桥双肢薄壁高墩在纵桥向和横桥向风作用下的风载特性。针对工程实际范围内的单肢截面长宽比和双薄壁间净距变化,分别研究了纵桥向风作用下这些参数变化对上下游薄壁阻力系数的影响,以及横桥向风作用下当这些参数变化时薄壁顺风向风力系数和横风向风力系数的变化。借助数值风洞结果,研究了小关桥平衡悬臂施工最大悬臂阶段的驰振稳定性。
5) 采用既考虑脉动风又考虑了结构尾流中的漩涡脱落引起的脉动风荷载的三维风荷载模型。提出了利用有限元分析法获得双肢薄壁高墩内力的影响函数,并以此计算由平均风荷载响应和背景响应所产生的墩底内力方法。提出了利用主要模态计算墩底内力的共振响应部分,利用峰值因子建立背景响应、共振响应与最大响应之间关系的方法,以此获得双肢薄壁墩墩底内力的最大响应。以小关桥平衡悬臂施工最大悬臂为例研究了三维风荷载作用下的墩底内力响应,计算结果显示了充分考虑风荷载的三维效应的必要性。
Balanced cantilever erection for continuous girder bridges, continuous rigid frame bridges(CRFB) and cable-stayed bridges has been recognized as one of the most efficient methods of building bridges without the needs for falsework. Because of its economy and convenience for construction, the CRFB with high flexible twin piers(HFTP) are commonly built in China. While several problems exist in cantilever construction stage, this paper focus the studies mainly on stability and wind effects.1) The critical loads of single-floor, multi-floor rigid frame were deduced, and simplified formula of stability coefficient relative to the HFTP with two horizontal connecters during cantilever erection were also obtained. This simple formula is of convenient, and can be used to analysis the stability of different cantilever construction stage of the XiaoGuan Bridge, the efficiency and validity were confirmed after comparing the results to that of from FEM.2) The moving equation of the structural model, which was simplified from the balanced cantilever structure of the CRFB with the HFTP, was deduced by using the Lagrange Equation. Accordingly, the free vibration frequency could be obtained. This method was employed to obtain the dynamic characteristic of the XiaoGuan Bridge. It was found that the results of the presented method were in better consistence to that of from FEM and field tests. This simple and fast algorithm could be used without help of FEM program, which is suitable for bridge construction.3) Ambient vibration tests were carried out on 3~(nd) pier of the XiaoGuan Bridge during the balanced cantilever erection, the results from the field mode tests were compared with that of FEM and that of the present algorithm, good agreements were found. So, a new fast approach connecting the construction stability, model updating technology and field mode test was presented to duly evaluate the structure stability.4) The CFD method was applied to study the Wind loads on HFTP of CRFB, both in longitudinal and lateral directions. The effects on aerodynamic drag coefficient subject to change of geometrical parameters in HFTP were studied. Based on aerodynamic coefficients from CFD, the galloping stability of the XiaoGuan Bridge during the maximum cantilever stage was also studied.5) A wind load model of CRFB with HFTP at erection stages was employed taking into account all wind effects on girder and piers. The influence function was presented which could be attained by the FEM. The wind effects on inner forces at bottom of piers were decomposed into different parts that could be acquired from different way. The peak maximum was obtained by using the gust factor to set up the relation between the buffeting effect and the peak maximum. Finally, the application was illustrated with reference to the XiaoGuan Bridge. It was shown that taking all the roles of different loading components into consideration is very important.
1) 以稳定性分析为目标,基于弹性力学基本方程和变分原理,推导了单层、多层门式刚架的临界荷载表达式和带双横联的双肢薄壁墩平衡悬臂施工阶段稳定性系数计算的简化计算公式,该计算式简单明了、方便使用。以贵阳小关桥3号桥墩平衡悬臂施工多个阶段的稳定性计算为例,比较了本文算法和有限元分析结果,计算结果偏差小说明了本文方法的可靠性和工程适用性。
2) 以双肢薄壁高墩连续刚构桥平衡悬臂施工的简化计算模型出发,运用拉格朗日方程推导了其运动方程并获得了其自由振动频率,对特征方程的处理使得该方法可用于单横联双肢薄壁墩刚构桥、单薄壁墩刚构桥,具有较好的工程适用性。以贵阳小关桥为例,通过有限元分析、现场动力试验和本文结果对比,验证了本方法在计算双肢薄壁高墩刚构桥平衡悬臂施工阶段动力特性上的可靠性。该法只需计算器运算而无需有限元专用程序计算,简单方便,适合于工程单位使用。
3) 完成了小关桥3号墩双肢薄壁刚构平衡悬臂施工多个工况的现场动力试验,模态分析的现场试验结果与有限元分析、本文动力特性快速算法结果的一致性好。研究思路形成了以现场动力试验结果为依据,以模型修正技术为手段,通过修正简化动力模型,由稳定性快速算法及时判断施工结构稳定安全性的方法。
4) 采用CFD方法模拟了连续刚构桥双肢薄壁高墩在纵桥向和横桥向风作用下的风载特性。针对工程实际范围内的单肢截面长宽比和双薄壁间净距变化,分别研究了纵桥向风作用下这些参数变化对上下游薄壁阻力系数的影响,以及横桥向风作用下当这些参数变化时薄壁顺风向风力系数和横风向风力系数的变化。借助数值风洞结果,研究了小关桥平衡悬臂施工最大悬臂阶段的驰振稳定性。
5) 采用既考虑脉动风又考虑了结构尾流中的漩涡脱落引起的脉动风荷载的三维风荷载模型。提出了利用有限元分析法获得双肢薄壁高墩内力的影响函数,并以此计算由平均风荷载响应和背景响应所产生的墩底内力方法。提出了利用主要模态计算墩底内力的共振响应部分,利用峰值因子建立背景响应、共振响应与最大响应之间关系的方法,以此获得双肢薄壁墩墩底内力的最大响应。以小关桥平衡悬臂施工最大悬臂为例研究了三维风荷载作用下的墩底内力响应,计算结果显示了充分考虑风荷载的三维效应的必要性。
Balanced cantilever erection for continuous girder bridges, continuous rigid frame bridges(CRFB) and cable-stayed bridges has been recognized as one of the most efficient methods of building bridges without the needs for falsework. Because of its economy and convenience for construction, the CRFB with high flexible twin piers(HFTP) are commonly built in China. While several problems exist in cantilever construction stage, this paper focus the studies mainly on stability and wind effects.1) The critical loads of single-floor, multi-floor rigid frame were deduced, and simplified formula of stability coefficient relative to the HFTP with two horizontal connecters during cantilever erection were also obtained. This simple formula is of convenient, and can be used to analysis the stability of different cantilever construction stage of the XiaoGuan Bridge, the efficiency and validity were confirmed after comparing the results to that of from FEM.2) The moving equation of the structural model, which was simplified from the balanced cantilever structure of the CRFB with the HFTP, was deduced by using the Lagrange Equation. Accordingly, the free vibration frequency could be obtained. This method was employed to obtain the dynamic characteristic of the XiaoGuan Bridge. It was found that the results of the presented method were in better consistence to that of from FEM and field tests. This simple and fast algorithm could be used without help of FEM program, which is suitable for bridge construction.3) Ambient vibration tests were carried out on 3~(nd) pier of the XiaoGuan Bridge during the balanced cantilever erection, the results from the field mode tests were compared with that of FEM and that of the present algorithm, good agreements were found. So, a new fast approach connecting the construction stability, model updating technology and field mode test was presented to duly evaluate the structure stability.4) The CFD method was applied to study the Wind loads on HFTP of CRFB, both in longitudinal and lateral directions. The effects on aerodynamic drag coefficient subject to change of geometrical parameters in HFTP were studied. Based on aerodynamic coefficients from CFD, the galloping stability of the XiaoGuan Bridge during the maximum cantilever stage was also studied.5) A wind load model of CRFB with HFTP at erection stages was employed taking into account all wind effects on girder and piers. The influence function was presented which could be attained by the FEM. The wind effects on inner forces at bottom of piers were decomposed into different parts that could be acquired from different way. The peak maximum was obtained by using the gust factor to set up the relation between the buffeting effect and the peak maximum. Finally, the application was illustrated with reference to the XiaoGuan Bridge. It was shown that taking all the roles of different loading components into consideration is very important.
引文
1. Aas-Jakobsen K., Strommen E.(1999), Dynamic response of a box girder bridge during construction, Proc, 10~(th) Int. Conf. on Wind Engineering, Copenhagen, 827-832.
2. A.G Smyrell(1993), Approximate formulate for determining the effective length of steel columns to BS5950. Structural Engineering, 71(5): 79-81
3. B.A.D.Piombo, A.Fasana, S.Marchesiello, etal(2000), Modelling and entification of the dynamic response of a supported bridge. Mechanical Systems and Signal Processing, 14(1): 75-89
4. Bijaya,Jaishil,Wei-Xin Ren(1995), Structural Finite Element Model Updating Using Ambient Vibration Test Results. Engineering structure, 131: 617-628
5. Casas J R(1997), Reliability-based partial safety factors in cantilever construction of concrete bridges, Journal of Structural Engineering, 123(3), 305-312.
6. Charles Brinstiel, Jeorme, S.B(1980), Factors influencing frame stability, Journal of the structural engineering, ASCE, 106(2): 491-504.
7. Davenport, A.G (1967), Gust response factors. J Struct Div, ASCE , 93,11-34.
8. Davenport, A.G (1995), How can we simplify and generalize wind loads, J. Wind Eng. Ind. Aerod., 54-55, 657-669.
9. Dyrbye, C, Hansen, S.O. (1997), Wind loads on structures. New York, Wiley. 10. Francois Cheong-Siat-moy(1986). K-factor paradox. Journal of Structural Engineering, ASCE, 111(8): 1747-1760.
11. Holmes, J.D. (1994), Along-wind response of lattice tower: part I -derivation of expressions for gust response factors, Eng. Struct., 16, 287-292.
12. J.Chen, Y.L.Xua, R.C.Zhang (2004), Modal parameter identification of TsingMa suspension bridge under Typhoon Victor: EMD-HT method. Journal of Wind Engineering and Industrial Aerodynamics, 92:805 - 827.
13. J.Dario Aristizabal-ochoa(1994), K-factor for columns in any type of construction nonparadoxical approach,. Journal of Structural Engineering, ASCE, 120(4): 1272-1290.
14. J.Dario Aristizabal-ochoa(1994), Slenderness K-factor for leaning columns, Journal of Structural Engineering, ASCE, 120(10): 2977-2991.
15. Johnston D.E(1960), Stability of frames by energy method, Journal of the Engineering Mechanics, ASCE., 95(4): 732-768.
16. Kasperski, M. (1992), Extreme wind load distributions for linear and nonlinear design, Eng. Struct., 14, 27-34.
17. Kavanagh.T.C(1962), Effective length of framed column. Journal of the Structural Engineering, ASCE, 127(11): 2663-2682.
18. Lian Duan, Wai-Fah Chen(1989), Effective length factor for columns in Unbraced frames, Journal of Structural Engineering, ASCE, 115(1): 149-165.
19. Mende, P.A. and Branco, F.A. (2001), Unbalanced wind buffeting effects on bridges during double cantilever erection stages, Wind & Structures., 4(1), 45-62.
20. N.Hu, X.Wang, H.Fukunaga, Z.H.Yao, etal(2001), Damage assessment of structures using modal test data.International Journal of Solids and Structures 38: 3111-3126.
21. O.S.Salawu, C.Williams(1995), Review of full-scale dynamic testing of bridge structures.Engineering Structures, (17): 113-121.
22. Piccardo, G and Solari, G (1998), Closed form prediction of 3-D wind-excited response of slender structures, J. Wind Eng. Ind. Aerod., 74-76: 697-708.
23. Piccardo, G and Solari, G (2000), 3-D wind-excited response of slender structures:Closed form solution, J. Struct. Engng., ASCE,126(8): 936-943.
24. Piccardo, G and Solari, G (2002), 3-D gust effect factor for slender vertical structures, Prob. Eng. Mech., 17,143-155.
25. Raul Goncalves S(1992), New stability Equation for columns in braced frames, Journal of Structural Engineering, ASCE, 118(7): 1853-1870.
26. Rosseland, S. and Thorsen, T. A. (2000), The Stolma Bridge - world record in free cantilevering, Proceedings of the Second International Symposium on Structural Lightweight .Aggregate Concrete, Kristiansand, Norway
27. Rumman W. S. (1970), Basic structural design of concrete chimneys, J. Power Div.,ASCE, 96:309-318.
28. Russell Q. Bridge, Donald J. Fraser(1987), Improved G-Factor Method for Evaluating Effective lengths of Columns, Journal of Structural Engineering, 113(6): 1341-1356.
29. S. Alampalli(2000), Effects of testing, analysis, and environment on modal parameters. Mechanical Systems and Signal Processing, 14(1): 63-74
30. Schmidt, S. and Solari, G (2003) , 3-D wind-induced effects on bridges during balanced cantilever erection stages ,Wind & Struct.,4(1): 1-22.
31. Shyi-Lin Lee, P.K.Basu(1992), Bracing requirement of plane frames. Journal of Structural Engineering, ASCE, 118(6): 1527-1546.
32. Solari, G(1982), Aongwind response estimation: closed form solution, J. Struct Div,ASCE,108: 225-244.
33. Solari, G(1983), Analytical estimation of the alongwind response of structures, J. Wind Eng. Ind. Aerod.,17:467-477.
34. Solari, G(1988), Equivalent wind spectrum technique: theory and applications, J. Struct Eng. ASCE,114:1303-1323.
35. Solari, G(1993), Gust buffeting Ⅰ : Peak wind velocity and equivalent pressure. J. Struct Eng. ASCE, 119: 365-382.
36. Solari, G(1993), Gust buffeting Ⅱ: Dynamic alongwind response. J. Struct Eng. ASCE,119: 383-398.
37. Solari, G ,Pagnini, L.C. and Piccardo, G. (1997), A numerical algorithm for the aerodynamic identification of structures , J. Wind Eng. Ind. Aerod., 69-71: 719-730.
38. S.S.Law, H.S.Ward, G.B.Shi, etal(1995), Dynamic assessment of bridge load-carrying capacities I . Journal of Structural Engineering, 478-487.
39. Stein Fergestad, Sturla Rambjoer(1999), A cantilevered bridge with a lightweight concrete main span of 298m, Structural Engineering International, 5:56-68.
40. Timoshenko S, Gele J(1961). Theory of Elastic stability, 2nd Edition, McGraw-Hill Inc.
41. Vickery, B. J. and Clark, W. (1972), Lift or across-wind response of tapered stacks, J. Struct. Div. ASCE, 98: 1-20.
42. Vickery B. J. and Basu R. I. (1983), Across-wind vibration of structures of circular cross-section, Part I, Development of a two-dimensional model for two-dimensional conditions, J. Wind Eng. Ind. Aerodyn., 12: 49-73.
43. Wal-Fah Chert, Lian Duan(2000), Bridge Engineering Handbook, Boca Raton: CRC Press.
44. Wei-Xin Ren, Wael Zatar, Issam E. Harik(2004). Ambient Vibration-basedseismic evaluation of a continuous girder bridge. Engineering Structures 26:631-640.
45. Wei-Xin Ren,Xue-Lin Peng,You-Qin Lin(2005). Experimental and analytical studies on dynamic characteristics of a large span cable-stayed bridge. Engineering Structures 27:535-548.
46. Wood, R.H(1974). Effective length of columns in multi-storey buildings, structural engineering, 52(7): 235-244.
47. Wood, R. H(1974), Effective length of columns in multi-storey buildings, structural engineering, 52(8): 295-302.
48. Wood, R.H(1974), Effective length of columns in multi-storey buildings, structural engineering, 52(9): 341-346.
49.陈艾荣,林志兴,项海帆(1998),大跨刚构桥梁气动弹性问题,第五届全国风工程及空气动力学学术会议论文集。
50.陈艾荣,项海(1998),悬臂施工的刚构桥梁的风荷载计算方法,公路,3:26-34。
51.陈长樱(1994),三门峡黄河公路大桥在风荷载及施工荷载作用下的稳定性分析,桥梁建设,3:24-29。
52.陈长缨,寿楠椿,王用中(1994),三门峡黄河公路大桥在风荷载及施工荷载作用下的稳定性分析,桥梁建设,3:30-35。
53.陈惠发,周绥平(1999),钢框架稳定设计,世界图书出版公司。
54.陈骥(2001),钢结构稳定理论与设计,科学出版社。
55.陈绍蕃(1996),钢结构稳定设计指南,中国建筑工业出版社。
56.埃米尔 希缪,罗伯特.H.斯坎伦著.刘尚培,项海帆和谢霁明译(1992),风对结构的作用,上海:同济大学出版社。
57.公路桥涵设计通用规范(J7G D60-2004)(2004),北京:人民交通出版社。
58.黄本才(1 998),深圳某高层建筑顺风向风荷载分析与研究。结构工程师(增刊)。
59.黄本才(2000), 结构抗风分析原理及应用,上海:同济大学出版社。
60.黄东州,李国豪(1988),桁梁桥的弹塑性侧倾稳定,同济大学学报,16(4).
61.李存权(2000),结构稳定和稳定内力,人民交通出版社。
62.刘光栋,罗汉泉(1988),杆系结构稳定,北京:人民交通出版社。
63.李国豪(2002),桥梁结构稳定与振动,北京:中国铁道出版社。
64.刘刚亮,王文中,黄建辉等(1995),虎门大桥270m连续刚构悬臂施工中的抗风计算及抗风安全措施,桥梁建设,2:57-60。
65.刘志刚,陈艾荣(2002),等长双悬臂梁等效风荷载实用计算方法,同济大学学报, 5:599～603。
66.刘刚亮(1995),虎门大桥270m连续刚构悬臂施工中的抗风计算及其抗风安全措施,桥梁建设,2:34-39。
67.李开禧,魏明钟(1988),钢构件稳定,四川科学技术出版社。
68.罗志斌.潘有昌(1988),结构稳定理论,高等教育出版社。
69.吕烈武(1983),钢结构构件稳定理论,中国建筑工业出版社。
70.吕烈武,沈世钊,沈祖炎等(1983),钢结构构件稳定理论,北京:中国建筑工业出版社。
71.马保林,李子青(2001),高墩大跨连续刚构桥,北京:人民交通出版社。
72.缪玉岭(1998),大跨刚构桥的风荷载内力计算,第五届全国风工程及空气动力学学术会议论文集。
73.钱莲萍,项海帆(1987),桥梁结构第一类弹塑性稳定分析及适用计算方法,第一届全国城市桥梁学术会议论文集。
74.任伟新,曾庆元(1994),钢压杆稳定极限承载力分析,中国铁道出版社。
75.唐家祥(1989),结构稳定理论,中国铁道出版社。
76.王俊奎,张志民(1980),板壳的弯曲与稳定,国防工业出版社。
77.王仕统(1997),结构稳定,华南理工大学出版社。
78.吴恒立(1979),拱式体系的稳定计算 人民交通出版社。
79.吴连元(1996),板壳稳定性理论,华中理工大学出版社。
80.吴明德(1988),弹性杆件稳定理论,高等教育出版社。
81.肖明心(1993),板的稳定理论,四川科学技术出版社。
82.项海帆,林志兴等(1996),公路桥梁抗风设计指南.北京:人民交通出版社。
83.项海帆,刘光栋(1991),拱结构的稳定与振动,人民交通出版社。
84.张建仁,徐福友(2002),连续梁桥悬臂施工整体稳定性可靠度分析,长沙交通学院学报,18(1):26-29。
85.钟善桐(1991),钢结构稳定设计,中国建筑工业出版社。
86.祝志文(2002),桥梁风效应的数值方法及其应用,中南大学博士学位论文,中南大学土木建筑学院。
87.李开言(2004),连续刚构桥双肢薄壁高墩风荷载研究,桥梁建设,6(3)。
88.李开言(2004),双肢薄壁高墩施工过程稳定性分析的快速算法,铁道学报,10(5)。
2. A.G Smyrell(1993), Approximate formulate for determining the effective length of steel columns to BS5950. Structural Engineering, 71(5): 79-81
3. B.A.D.Piombo, A.Fasana, S.Marchesiello, etal(2000), Modelling and entification of the dynamic response of a supported bridge. Mechanical Systems and Signal Processing, 14(1): 75-89
4. Bijaya,Jaishil,Wei-Xin Ren(1995), Structural Finite Element Model Updating Using Ambient Vibration Test Results. Engineering structure, 131: 617-628
5. Casas J R(1997), Reliability-based partial safety factors in cantilever construction of concrete bridges, Journal of Structural Engineering, 123(3), 305-312.
6. Charles Brinstiel, Jeorme, S.B(1980), Factors influencing frame stability, Journal of the structural engineering, ASCE, 106(2): 491-504.
7. Davenport, A.G (1967), Gust response factors. J Struct Div, ASCE , 93,11-34.
8. Davenport, A.G (1995), How can we simplify and generalize wind loads, J. Wind Eng. Ind. Aerod., 54-55, 657-669.
9. Dyrbye, C, Hansen, S.O. (1997), Wind loads on structures. New York, Wiley. 10. Francois Cheong-Siat-moy(1986). K-factor paradox. Journal of Structural Engineering, ASCE, 111(8): 1747-1760.
11. Holmes, J.D. (1994), Along-wind response of lattice tower: part I -derivation of expressions for gust response factors, Eng. Struct., 16, 287-292.
12. J.Chen, Y.L.Xua, R.C.Zhang (2004), Modal parameter identification of TsingMa suspension bridge under Typhoon Victor: EMD-HT method. Journal of Wind Engineering and Industrial Aerodynamics, 92:805 - 827.
13. J.Dario Aristizabal-ochoa(1994), K-factor for columns in any type of construction nonparadoxical approach,. Journal of Structural Engineering, ASCE, 120(4): 1272-1290.
14. J.Dario Aristizabal-ochoa(1994), Slenderness K-factor for leaning columns, Journal of Structural Engineering, ASCE, 120(10): 2977-2991.
15. Johnston D.E(1960), Stability of frames by energy method, Journal of the Engineering Mechanics, ASCE., 95(4): 732-768.
16. Kasperski, M. (1992), Extreme wind load distributions for linear and nonlinear design, Eng. Struct., 14, 27-34.
17. Kavanagh.T.C(1962), Effective length of framed column. Journal of the Structural Engineering, ASCE, 127(11): 2663-2682.
18. Lian Duan, Wai-Fah Chen(1989), Effective length factor for columns in Unbraced frames, Journal of Structural Engineering, ASCE, 115(1): 149-165.
19. Mende, P.A. and Branco, F.A. (2001), Unbalanced wind buffeting effects on bridges during double cantilever erection stages, Wind & Structures., 4(1), 45-62.
20. N.Hu, X.Wang, H.Fukunaga, Z.H.Yao, etal(2001), Damage assessment of structures using modal test data.International Journal of Solids and Structures 38: 3111-3126.
21. O.S.Salawu, C.Williams(1995), Review of full-scale dynamic testing of bridge structures.Engineering Structures, (17): 113-121.
22. Piccardo, G and Solari, G (1998), Closed form prediction of 3-D wind-excited response of slender structures, J. Wind Eng. Ind. Aerod., 74-76: 697-708.
23. Piccardo, G and Solari, G (2000), 3-D wind-excited response of slender structures:Closed form solution, J. Struct. Engng., ASCE,126(8): 936-943.
24. Piccardo, G and Solari, G (2002), 3-D gust effect factor for slender vertical structures, Prob. Eng. Mech., 17,143-155.
25. Raul Goncalves S(1992), New stability Equation for columns in braced frames, Journal of Structural Engineering, ASCE, 118(7): 1853-1870.
26. Rosseland, S. and Thorsen, T. A. (2000), The Stolma Bridge - world record in free cantilevering, Proceedings of the Second International Symposium on Structural Lightweight .Aggregate Concrete, Kristiansand, Norway
27. Rumman W. S. (1970), Basic structural design of concrete chimneys, J. Power Div.,ASCE, 96:309-318.
28. Russell Q. Bridge, Donald J. Fraser(1987), Improved G-Factor Method for Evaluating Effective lengths of Columns, Journal of Structural Engineering, 113(6): 1341-1356.
29. S. Alampalli(2000), Effects of testing, analysis, and environment on modal parameters. Mechanical Systems and Signal Processing, 14(1): 63-74
30. Schmidt, S. and Solari, G (2003) , 3-D wind-induced effects on bridges during balanced cantilever erection stages ,Wind & Struct.,4(1): 1-22.
31. Shyi-Lin Lee, P.K.Basu(1992), Bracing requirement of plane frames. Journal of Structural Engineering, ASCE, 118(6): 1527-1546.
32. Solari, G(1982), Aongwind response estimation: closed form solution, J. Struct Div,ASCE,108: 225-244.
33. Solari, G(1983), Analytical estimation of the alongwind response of structures, J. Wind Eng. Ind. Aerod.,17:467-477.
34. Solari, G(1988), Equivalent wind spectrum technique: theory and applications, J. Struct Eng. ASCE,114:1303-1323.
35. Solari, G(1993), Gust buffeting Ⅰ : Peak wind velocity and equivalent pressure. J. Struct Eng. ASCE, 119: 365-382.
36. Solari, G(1993), Gust buffeting Ⅱ: Dynamic alongwind response. J. Struct Eng. ASCE,119: 383-398.
37. Solari, G ,Pagnini, L.C. and Piccardo, G. (1997), A numerical algorithm for the aerodynamic identification of structures , J. Wind Eng. Ind. Aerod., 69-71: 719-730.
38. S.S.Law, H.S.Ward, G.B.Shi, etal(1995), Dynamic assessment of bridge load-carrying capacities I . Journal of Structural Engineering, 478-487.
39. Stein Fergestad, Sturla Rambjoer(1999), A cantilevered bridge with a lightweight concrete main span of 298m, Structural Engineering International, 5:56-68.
40. Timoshenko S, Gele J(1961). Theory of Elastic stability, 2nd Edition, McGraw-Hill Inc.
41. Vickery, B. J. and Clark, W. (1972), Lift or across-wind response of tapered stacks, J. Struct. Div. ASCE, 98: 1-20.
42. Vickery B. J. and Basu R. I. (1983), Across-wind vibration of structures of circular cross-section, Part I, Development of a two-dimensional model for two-dimensional conditions, J. Wind Eng. Ind. Aerodyn., 12: 49-73.
43. Wal-Fah Chert, Lian Duan(2000), Bridge Engineering Handbook, Boca Raton: CRC Press.
44. Wei-Xin Ren, Wael Zatar, Issam E. Harik(2004). Ambient Vibration-basedseismic evaluation of a continuous girder bridge. Engineering Structures 26:631-640.
45. Wei-Xin Ren,Xue-Lin Peng,You-Qin Lin(2005). Experimental and analytical studies on dynamic characteristics of a large span cable-stayed bridge. Engineering Structures 27:535-548.
46. Wood, R.H(1974). Effective length of columns in multi-storey buildings, structural engineering, 52(7): 235-244.
47. Wood, R. H(1974), Effective length of columns in multi-storey buildings, structural engineering, 52(8): 295-302.
48. Wood, R.H(1974), Effective length of columns in multi-storey buildings, structural engineering, 52(9): 341-346.
49.陈艾荣,林志兴,项海帆(1998),大跨刚构桥梁气动弹性问题,第五届全国风工程及空气动力学学术会议论文集。
50.陈艾荣,项海(1998),悬臂施工的刚构桥梁的风荷载计算方法,公路,3:26-34。
51.陈长樱(1994),三门峡黄河公路大桥在风荷载及施工荷载作用下的稳定性分析,桥梁建设,3:24-29。
52.陈长缨,寿楠椿,王用中(1994),三门峡黄河公路大桥在风荷载及施工荷载作用下的稳定性分析,桥梁建设,3:30-35。
53.陈惠发,周绥平(1999),钢框架稳定设计,世界图书出版公司。
54.陈骥(2001),钢结构稳定理论与设计,科学出版社。
55.陈绍蕃(1996),钢结构稳定设计指南,中国建筑工业出版社。
56.埃米尔 希缪,罗伯特.H.斯坎伦著.刘尚培,项海帆和谢霁明译(1992),风对结构的作用,上海:同济大学出版社。
57.公路桥涵设计通用规范(J7G D60-2004)(2004),北京:人民交通出版社。
58.黄本才(1 998),深圳某高层建筑顺风向风荷载分析与研究。结构工程师(增刊)。
59.黄本才(2000), 结构抗风分析原理及应用,上海:同济大学出版社。
60.黄东州,李国豪(1988),桁梁桥的弹塑性侧倾稳定,同济大学学报,16(4).
61.李存权(2000),结构稳定和稳定内力,人民交通出版社。
62.刘光栋,罗汉泉(1988),杆系结构稳定,北京:人民交通出版社。
63.李国豪(2002),桥梁结构稳定与振动,北京:中国铁道出版社。
64.刘刚亮,王文中,黄建辉等(1995),虎门大桥270m连续刚构悬臂施工中的抗风计算及抗风安全措施,桥梁建设,2:57-60。
65.刘志刚,陈艾荣(2002),等长双悬臂梁等效风荷载实用计算方法,同济大学学报, 5:599～603。
66.刘刚亮(1995),虎门大桥270m连续刚构悬臂施工中的抗风计算及其抗风安全措施,桥梁建设,2:34-39。
67.李开禧,魏明钟(1988),钢构件稳定,四川科学技术出版社。
68.罗志斌.潘有昌(1988),结构稳定理论,高等教育出版社。
69.吕烈武(1983),钢结构构件稳定理论,中国建筑工业出版社。
70.吕烈武,沈世钊,沈祖炎等(1983),钢结构构件稳定理论,北京:中国建筑工业出版社。
71.马保林,李子青(2001),高墩大跨连续刚构桥,北京:人民交通出版社。
72.缪玉岭(1998),大跨刚构桥的风荷载内力计算,第五届全国风工程及空气动力学学术会议论文集。
73.钱莲萍,项海帆(1987),桥梁结构第一类弹塑性稳定分析及适用计算方法,第一届全国城市桥梁学术会议论文集。
74.任伟新,曾庆元(1994),钢压杆稳定极限承载力分析,中国铁道出版社。
75.唐家祥(1989),结构稳定理论,中国铁道出版社。
76.王俊奎,张志民(1980),板壳的弯曲与稳定,国防工业出版社。
77.王仕统(1997),结构稳定,华南理工大学出版社。
78.吴恒立(1979),拱式体系的稳定计算 人民交通出版社。
79.吴连元(1996),板壳稳定性理论,华中理工大学出版社。
80.吴明德(1988),弹性杆件稳定理论,高等教育出版社。
81.肖明心(1993),板的稳定理论,四川科学技术出版社。
82.项海帆,林志兴等(1996),公路桥梁抗风设计指南.北京:人民交通出版社。
83.项海帆,刘光栋(1991),拱结构的稳定与振动,人民交通出版社。
84.张建仁,徐福友(2002),连续梁桥悬臂施工整体稳定性可靠度分析,长沙交通学院学报,18(1):26-29。
85.钟善桐(1991),钢结构稳定设计,中国建筑工业出版社。
86.祝志文(2002),桥梁风效应的数值方法及其应用,中南大学博士学位论文,中南大学土木建筑学院。
87.李开言(2004),连续刚构桥双肢薄壁高墩风荷载研究,桥梁建设,6(3)。
88.李开言(2004),双肢薄壁高墩施工过程稳定性分析的快速算法,铁道学报,10(5)。