大跨度桥梁多目标等效静力风荷载基向量法
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摘要
由于结构抖振响应计算复杂,目前主流风荷载设计规范均采用等效静力风荷载做等代替换。文中以桥梁结构为研究对象,对抖振响应的多目标等效静力风荷载计算方法进行研究。首先,采用经典的荷载-响应相关(LRC)法获得大跨度桥梁主梁各节点处的等效静力风荷载向量,并组成荷载矩阵F_(LRC);其次,采用本征正交分解(POD)技术获得F_(LRC)的本征模态矩阵Φ_(LRC);然后,以主梁的抖振响应极值为等效目标,选取Φ_(LRC)的前i阶本征模态作为构建等效静力风荷载的基向量,获得最小二乘意义的多目标等效静力风荷载;最后,以东海大桥为例对该方法的有效性进行验证。结果表明,由于Φ_(LRC)同时包含了脉动风荷载和抖振响应的主要信息,同时是依据重要程度排序,按照文中方法获得的多目标等效静力风荷载在抖振响应计算精度和荷载分布的合理性方面均表现良好。
The buffeting response of a structure is very complex, and in main wind resistant design codes/specifications of structures, the equivalent static wind loads(ESWL) is adopted to instead the real dynamic buffeting analysis. The multi-target ESWL calculation method of long-span bridges is studied from a new perspective. Firstly, load response correlation(LRC) method was used to estimate ESWL vectors at the nodes of girders of the long-span bridge and then to form the ESWL matrix F_(LRC). Secondly, the proper orthogonal decomposition(POD) technique was applied to attaining the proper orthogonal matrix Φ_(LRC) of F_(LRC). Thirdly,with the buffeting response extreme values of the girder regarded as the equivalent targets, the first i-order proper modes of Φ_(LRC) were used as the base vectors to reconstruct ESWL, so that the multi-target ESWL can be obtained in least square meaning. Finally, East Sea cable-stayed bridge was used as an example to validate the effectiveness of the method. The results indicate that the accuracy of buffeting responses calculated by multi-target ESWL and the rationality of ESWL distribution are acceptable by using the proposed method,because after POD, the matrix Φ_(LRC) contains both the fluctuating wind pressure information and the buffeting response information, which are ordered according to the significance.
The buffeting response of a structure is very complex, and in main wind resistant design codes/specifications of structures, the equivalent static wind loads(ESWL) is adopted to instead the real dynamic buffeting analysis. The multi-target ESWL calculation method of long-span bridges is studied from a new perspective. Firstly, load response correlation(LRC) method was used to estimate ESWL vectors at the nodes of girders of the long-span bridge and then to form the ESWL matrix F_(LRC). Secondly, the proper orthogonal decomposition(POD) technique was applied to attaining the proper orthogonal matrix Φ_(LRC) of F_(LRC). Thirdly,with the buffeting response extreme values of the girder regarded as the equivalent targets, the first i-order proper modes of Φ_(LRC) were used as the base vectors to reconstruct ESWL, so that the multi-target ESWL can be obtained in least square meaning. Finally, East Sea cable-stayed bridge was used as an example to validate the effectiveness of the method. The results indicate that the accuracy of buffeting responses calculated by multi-target ESWL and the rationality of ESWL distribution are acceptable by using the proposed method,because after POD, the matrix Φ_(LRC) contains both the fluctuating wind pressure information and the buffeting response information, which are ordered according to the significance.
引文
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[8]Katsumura A,Tamura Y,Nakamura O.Universal wind load distribution simultaneously reproducing largest load effects in all subject members on large-span cantilevered roof[J].Journal of Wind Engineering and Industrial Aerodynamics,2007,95(9/10/11):1145-1165
[9]Blaise N,Denoel V.Principal static wind loads[J].Journal of Wind Engineering and Industrial Aerodynamics,2013,113:29-39
[10]Blaise N,Canor T,Denoel V.Reconstruction of the envelope of non-Gaussian structural responses with principal static wind loads[J].Journal of Wind Engineering and Industrial Aerodynamics,2016,149:59-76
[11]Chatterjee A.An introduction to the proper orthogonal decomposition[J].Current Science,2000,78(7):808-817
[12]董锐,葛耀君,杨詠昕.基于虚拟激励法的大跨度桥梁位移多目标等效静力风荷载[J].土木工程学报,2014,47(11):84-91(Dong Rui,Ge Yaojun,Yang Yongxin.Multi-target equivalent static wind loading of long-span bridges based on pseudo-excitation method and displacement responses[J].China Civil Engineering Journal,2014,47(11):84-91(in Chinese))
[13]黄融,葛耀君.东海大桥主航道桥抗风性能及颤振控制研究[J].世界桥梁,2004(增1):45-49(Huang Rong,Ge Yaojun.Study of wind performance and flutter control of main navigable spans of Donghai bridge[J].World Bridges,2004(S1):45-49(in Chinese))
[14]Jain A,Jones N P,Scanlan R H.Coupled aeroelastic and aerodynamic response analysis of long-span bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,1996,60:69-80
[15]Scanlan R H.Problematics in formulation of wind-force models for bridge decks[J].Journal of Engineering Mechanics,1993,119(7):1353-1375
[16]Davenport A G.Buffeting of a suspension bridge by storm winds[J].Journal of the Structural Division,1962,88(3):233-270
[17]Liepmann H W.On the application of statistical concepts to the buffeting problem[J].Journal of Aeronautical Science,1952,19(12):793-800
[18]Kaimal J C,Wyngaard J C,Izumi Y,et al.Spectral characteristics of surface-layer turbulence[J].Quarterly Journal of the Royal Meteorological Society,1972,98:563-589
[19]Lumley J L,Panofsky H A.The structure of atmospheric turbulence[M].New York:Wiley,1964
[20]Simiu E,Scanlan R H.Wind effects on structures:fundamentals and applications to design[M].3rd edition.New York:John Wiley&Sons Inc.,1996
[21]JTG/T D60-01-2004公路桥梁抗风设计规范[S].北京:中国标准出版社,2004(JTG/T D60-01-2004Wind-resistent design specification for highway bridges[S].Beijing:Standards Press of China,2004(in Chinese))
[2]Kasperski M,Niemann H J.The L.R.C.(loadresponse-correlation)-method:a general method of estimating unfavorable wind load distribution for linear and non-linear structural behavior[J].Journal of Wind Engineering and Industrial Aerodynamics,1992,41/42/43/44:1753-1763
[3]Davenport A G.The representation of the dynamic effects of turbulent wind by equivalent static wind loads[C]//Proceedings of the 1985 International Engineering Symposium on Structural Steel.Chicago:American Institute of Steel Construction,1985:1-13
[4]Irwin P A.The role of wind tunnel modeling in the prediction of wind effects on bridges[C]//Bridge Aerodynamics.Rotterdam,the Netherlands:A.A.Balkema Pubilishers,1998:99-118
[5]Holmes J D.Along-wing response of lattice towers-III.Effective load distributions[J].Engineering Structures,1996,18(7):489-494
[6]Zhou Y,Gu M,Xang H F.Along wind static equivalent wind loads and responses of tall buildings,Part I:Unfavorable distributions of static equivalent wind loads[J].Journal of Wind Engineering and Industrial Aerodynamics,1999,79(1/2):135-150
[7]Chen X Z,Kareem A.Equivalent static wind loads for buffeting response of bridges[J].Journal of Structural Engineering,2001,127(12):1467-1475
[8]Katsumura A,Tamura Y,Nakamura O.Universal wind load distribution simultaneously reproducing largest load effects in all subject members on large-span cantilevered roof[J].Journal of Wind Engineering and Industrial Aerodynamics,2007,95(9/10/11):1145-1165
[9]Blaise N,Denoel V.Principal static wind loads[J].Journal of Wind Engineering and Industrial Aerodynamics,2013,113:29-39
[10]Blaise N,Canor T,Denoel V.Reconstruction of the envelope of non-Gaussian structural responses with principal static wind loads[J].Journal of Wind Engineering and Industrial Aerodynamics,2016,149:59-76
[11]Chatterjee A.An introduction to the proper orthogonal decomposition[J].Current Science,2000,78(7):808-817
[12]董锐,葛耀君,杨詠昕.基于虚拟激励法的大跨度桥梁位移多目标等效静力风荷载[J].土木工程学报,2014,47(11):84-91(Dong Rui,Ge Yaojun,Yang Yongxin.Multi-target equivalent static wind loading of long-span bridges based on pseudo-excitation method and displacement responses[J].China Civil Engineering Journal,2014,47(11):84-91(in Chinese))
[13]黄融,葛耀君.东海大桥主航道桥抗风性能及颤振控制研究[J].世界桥梁,2004(增1):45-49(Huang Rong,Ge Yaojun.Study of wind performance and flutter control of main navigable spans of Donghai bridge[J].World Bridges,2004(S1):45-49(in Chinese))
[14]Jain A,Jones N P,Scanlan R H.Coupled aeroelastic and aerodynamic response analysis of long-span bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,1996,60:69-80
[15]Scanlan R H.Problematics in formulation of wind-force models for bridge decks[J].Journal of Engineering Mechanics,1993,119(7):1353-1375
[16]Davenport A G.Buffeting of a suspension bridge by storm winds[J].Journal of the Structural Division,1962,88(3):233-270
[17]Liepmann H W.On the application of statistical concepts to the buffeting problem[J].Journal of Aeronautical Science,1952,19(12):793-800
[18]Kaimal J C,Wyngaard J C,Izumi Y,et al.Spectral characteristics of surface-layer turbulence[J].Quarterly Journal of the Royal Meteorological Society,1972,98:563-589
[19]Lumley J L,Panofsky H A.The structure of atmospheric turbulence[M].New York:Wiley,1964
[20]Simiu E,Scanlan R H.Wind effects on structures:fundamentals and applications to design[M].3rd edition.New York:John Wiley&Sons Inc.,1996
[21]JTG/T D60-01-2004公路桥梁抗风设计规范[S].北京:中国标准出版社,2004(JTG/T D60-01-2004Wind-resistent design specification for highway bridges[S].Beijing:Standards Press of China,2004(in Chinese))