扁平箱梁颤振计算公式中联合折减系数的量化研究
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摘要
扁平箱梁已广泛应用于大跨度桥梁的主梁设计中,其颤振性能通常会借助物理和数值风洞的方法获得,测试周期长、费用高。尽管采用颤振计算公式可以简便计算扁平箱梁的颤振临界风速,但当前公式中未考虑扁平箱梁气动外形和来流攻角的具体影响,计算误差较大,无法用于实际工程设计。为了提升颤振计算公式中联合折减系数的准确度,利用节段模型风洞试验开展气动外形和风攻角对扁平箱梁颤振性能影响的研究。在分析各种气动构件和外形参数对扁平箱梁颤振性能的影响后,确定以斜腹板倾角和宽高比为气动外形变量,设计制作3组12个节段模型,分别在5个风攻角下测试了有栏杆扁平箱梁的颤振性能。在此基础上,根据节段模型风洞试验获得的颤振临界风速,结合弯扭耦合颤振闭合解计算公式,量化了气动外形和风攻角变化对扁平箱梁颤振的影响,给出不同条件下扁平箱梁颤振计算公式中的联合折减系数。最后,基于实际桥梁的颤振临界风速算例,验证利用联合折减系数计算颤振临界风速的准确性和适用性。研究结果表明:在0°风攻角和正风攻角下,当扁平箱梁的宽高比分别为11,9时,斜腹板倾角的减小有利于颤振临界风速提高,宽高比为7时,斜腹板倾角对颤振临界风速没有影响;在负风攻角下,3组宽高比模型斜腹板倾角的减小均会引起扁平箱梁颤振临界风速的降低;联合折减系数与扁平箱梁截面的颤振性能正相关,可直接反映其颤振性能,相对于目前《公路桥梁抗风设计规范》中扁平箱梁颤振临界风速计算时的固定折减系数,该系数能够具体和准确反映气动外形和风攻角对扁平箱梁颤振的影响,可以结合颤振计算公式快速、准确地计算出大跨度桥梁颤振临界风速。
Flat box girders have been widely used in the design of the main girders of long span bridges. The flutter performance of a flat box girder is usually predicted by physical methods or numerical wind tunnel model methods, which are time-intensive and involve high costs. Although the flutter onset speeds of flat box girders can be calculated by the flutter calculation method, the errors are large enough that they cannot be used in the actual engineering designs without considering the influences of aerodynamic configurations and wind attack angles. To ensure the accuracy of the flutter reduction coefficient, a study on the influence of the aerodynamic configuration and wind attack angle on the flutter performance of a flat box girder was conducted. A total of 12 sectional models were designed, and the flutter onset speeds of different sectional models with handrails were tested under 5 different wind attack angles via wind tunnel tests. Based on these observations, according to the flutter onset speed and closed-solution formula for bending-torsion, the effects of the aerodynamic configuration and wind attack angle on flutter performance are quantified by the flutter factors as the reduction coefficients; the reduction coefficients are positively correlated with flutter performance and can reflect the flutter performance directly. Finally, a case study was conducted, in which the flutter onset speeds of an actual bridge were calculated, the accuracy was verified, and the corrected joint reduction coefficients were used to predict flutter onset speeds. The results show that for 0° and positive wind attack angle and for flat box girders with side ratios of 11 and 9, the flutter onset speeds increase when the slope of the inclined web decreases. However, for the flat box girder with a side ratio of 7, the slope of the inclined web had no influence on flutter performance. For negative wind attack angles, the flutter onset speeds of the three groups of models decrease when the slope of the inclined web decreases. Compared to the fixed reduction coefficient available in the present Wind-resistant Design Specification for Highway Bridges, the reduction coefficients calculated herein can specifically reflect the influences of the aerodynamic configurations and wind attack angles on flutter performance, and the reduction coefficients can further be used to calculate acceptable flutter onset speeds quickly and accurately in conjunction with the flutter calculation formula.
Flat box girders have been widely used in the design of the main girders of long span bridges. The flutter performance of a flat box girder is usually predicted by physical methods or numerical wind tunnel model methods, which are time-intensive and involve high costs. Although the flutter onset speeds of flat box girders can be calculated by the flutter calculation method, the errors are large enough that they cannot be used in the actual engineering designs without considering the influences of aerodynamic configurations and wind attack angles. To ensure the accuracy of the flutter reduction coefficient, a study on the influence of the aerodynamic configuration and wind attack angle on the flutter performance of a flat box girder was conducted. A total of 12 sectional models were designed, and the flutter onset speeds of different sectional models with handrails were tested under 5 different wind attack angles via wind tunnel tests. Based on these observations, according to the flutter onset speed and closed-solution formula for bending-torsion, the effects of the aerodynamic configuration and wind attack angle on flutter performance are quantified by the flutter factors as the reduction coefficients; the reduction coefficients are positively correlated with flutter performance and can reflect the flutter performance directly. Finally, a case study was conducted, in which the flutter onset speeds of an actual bridge were calculated, the accuracy was verified, and the corrected joint reduction coefficients were used to predict flutter onset speeds. The results show that for 0° and positive wind attack angle and for flat box girders with side ratios of 11 and 9, the flutter onset speeds increase when the slope of the inclined web decreases. However, for the flat box girder with a side ratio of 7, the slope of the inclined web had no influence on flutter performance. For negative wind attack angles, the flutter onset speeds of the three groups of models decrease when the slope of the inclined web decreases. Compared to the fixed reduction coefficient available in the present Wind-resistant Design Specification for Highway Bridges, the reduction coefficients calculated herein can specifically reflect the influences of the aerodynamic configurations and wind attack angles on flutter performance, and the reduction coefficients can further be used to calculate acceptable flutter onset speeds quickly and accurately in conjunction with the flutter calculation formula.
引文
[1] LARSEN A. Aerodynamic Aspects of the Final Design of the 1 624 m Suspension Bridge Across the Great Belt [J]. Journal of Wind Engineering and Industrial Aerodynamics, 1993, 48 (2/3): 261-285.
[2] MIYATA T. Historical View of Long-span Bridge Aerodynamics [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2003, 91 (12/13/14/15): 1393-1410.
[3] LUCA B, GIUSEPPE M. Importance of Deck Details in Bridge Aerodynamics [J]. Structural Engineering International, 2002, 12 (4): 289-294.
[4] YANG Yong-xin, Ge Yao-jun. Some Practices on Aerodynamic Flutter Control for Long-span Cable Supported Bridges [C]// AWAS. Proceedings of the 4th International Conference on AWAS'08. Seoul: AWAS, 2008: 1474-1485.
[5] LIN Y Y, CHENG C M, LAN C Y. Effects of Deck's Width-to-depth Ratios and Turbulent Flows on the Aerodynamic Behaviors of Long-span Bridges[J]. Wind and Structures, 2003, 6: 263-278.
[6] 鲜荣,廖海黎.封闭式扁平钢箱梁颤振稳定性气动优化措施风洞试验研究[J].世界桥梁,2008,36(3):44-47. XIAN Rong, LIAO Hai-li. Wind Tunnel Test Study of Aerodynamic Optimization Measures for Flutter Stability of Closed Flat Steel Box Girder[J]. World Bridges, 2008, 36 (3): 44-47.
[7] 王骑,廖海黎,李明水,等.流线型箱梁气动外形对桥梁颤振和涡振的影响[J].公路交通科技,2012,29(8):44-50. WANG Qi, LIAO Hai-li, LI Ming-shui, et al. Influence of Aerodynamic Shape of Streamline Box Girder on Bridge Flutter and Vortex-induced Vibration [J]. Journal of Highway and Transportation Research and Development, 2012, 29 (8): 44-50.
[8] 朱乐东,张宏杰,胡晓红.1 400 m跨径钢箱梁斜拉桥方案颤振控制气动措施试验研究[J].桥梁建设,2011(2):9-12. ZHU Le-dong, ZHANG Hong-jie, HU Xiao-hong. Test Study of Aerodynamic Measures for Flutter Control of a Proposed 1 400 m Span Steel Box Deck Cable-stayed Bridge [J]. Bridge Construction, 2011 (2): 9-12.
[9] 于舰涵.斜腹板倾角对桥梁气动稳定性影响的数值模拟研究[D].成都:西南交通大学,2014. YU Jian-han. Study on Numeric Simulation of Influence of Inclined Webs on Flutter Instability of Long-span Bridges [D]. Chengdu: Southwest Jiaotong University, 2014.
[10] 周健,樊泽民,王骑,等.基于节段模型风洞试验的莫桑比克马普托大桥主梁选型研究[J].世界桥梁,2014,42(2):6-11. ZHOU Jian, FAN Ze-min, WANG Qi, et al. Main Girder Type Selection for Maputo Bridge in Mozambique Based on Sectional Model Wind Tunnel Test[J]. World Bridges, 2014, 42 (2): 6-11.
[11] 颜宇光.基于PIV技术的闭口箱梁桥梁断面颤振和涡振性能的气动选型[D].上海:同济大学,2015. YAN Yu-guang. Aerodynamic Selection for Flutter and Vortex Induced Vibration Performance of Closed Box Girders Based on PIV Technology [D]. Shanghai: Tongji University, 2015.
[12] LARSEN A, SAVAGE M. Investigation of Vortex Response of a Twin Box Bridge Section at High and Low Reynolds Numbers [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96 (6/7): 934-944.
[13] GE Y J, YANG Y X, et al. VIV Sectional Model Testing and Field Measurement of Xihoumen Suspension Bridge with Twin Box Girder [C]// ICWE. Proceedings of 13th ICWE. Amsterdam: ICWE, 2011: 1-7.
[14] DIANA G, BELLOLLI M, ROCCHI D. On the Vortex Shedding Forcing on Suspension Bridge Deck [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2006, 94 (5): 341-363.
[15] CHEN X. Improved Understanding of Bimodal Coupled Bridge Flutter Based on Closed-form Solutions [J]. Journal of Structural Engineering, 2007, 133 (1): 22-31.
[16] MATSUMOTO M. Aerodynamic Damping of Prisms [J]. Journal of Wind Engineering and Industrial Aerodynamics, 1996, 59 (2/3): 159-175.
[17] 杨詠昕.大跨度桥梁二维颤振机理及其应用研究[D].上海:同济大学,2002. YANG Yong-xin. Two-dimensional Flutter Mechanism and Its Application for Long-span Bridges [D]. Shanghai: Tongji University, 2002.
[18] JTG/T D60-01—2004,公路桥梁抗风设计规范[S]. JTG/T D60-01—2004, Wind-resistant Design Specification for Highway Bridges [S].
[19] LARSEN A, WALL A. Shaping of Bridge Box Girders to Avoid Vortex Shedding Response [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2012, 104-106: 159-165.
[20] 马存明, 秦浩.普立特大桥抗风性能研究报告[R].成都:西南交通大学,2011. MA Cun-ming, QIN Hao. Report of Wind-resistant Design for Puli Bridge[R]. Chengdu: Southwest Jiaotong University, 2011.
[21] 周继.大跨度悬索桥成桥状态颤振分析[D].成都:西南交通大学,2011. ZHOU Ji. Flutter Analysis of a Long-span Suspension Bridge During Completed Stage [D]. Chengdu: Southwest Jiaotong University, 2011.
[22] 丁泉顺.大跨度桥梁耦合颤抖振响应的精细化分析[D].上海:同济大学,2001. DING Quan-shun. Refinement of Coupled Flutter and Buffeting Analysis for Long-span bridges [D]. Shanghai: Tongji University, 2001.
[23] 张建,郑史雄,唐煜,等.基于节段模型试验的悬索桥涡振性能优化研究[J].实验流体力学,2015,29(2):48-54. ZHANG Jian, ZHENG Shi-xiong, TANG Yu, et al. Research on Optimizing Vortex-induced Vibration Performance for Suspension Bridge Based on Section Model Test [J]. Journal of Experiments in Fluid Mechanics, 2015, 29 (2): 48-54.
[24] 王骑, 卓凌骏.万州驸马长江大桥抗风性能研究报告[R].成都:西南交通大学,2014. WANG Qi, ZHUO Ling-jun. Report of Wind-resistant Design for Fuma Bridge of Wanzhou [R]. Chengdu: Southwest Jiaotong University, 2014.
[25] 杨詠昕.官山至秀山公路秀山大桥抗风性能研究报告[R].上海:同济大学,2015. YANG Yong-xin. Report of Wind-resistant Design for Xiushan Bridge of the Road Link of Guanshan-Xiushan [R]. Shanghai: Tongji University, 2015.
[26] 白桦,高慧,李宇,等.借助三分力系数的桥梁颤振稳定性评价[J].中国公路学报,2014,27(7):68-73 BAI Hua, GAO Hui, LI Yu, et al. Estimation of Flutter Stability of Bridge by Using Three-component Coefficients [J]. China Journal of Highway and Transport, 2014, 27 (7): 68-73.
[27] 白桦,方成,王峰,等.桥梁颤振稳定性快速评价参数及其应用[J].中国公路学报,2016,29(8):92-99 BAI Hua, FANG Cheng, WANG Feng, et al. Rapid Evaluation Parameters of Flutter Stability of Bridge and Their Application [J]. China Journal of Highway and Transport, 2016, 29 (8): 92-99.
[2] MIYATA T. Historical View of Long-span Bridge Aerodynamics [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2003, 91 (12/13/14/15): 1393-1410.
[3] LUCA B, GIUSEPPE M. Importance of Deck Details in Bridge Aerodynamics [J]. Structural Engineering International, 2002, 12 (4): 289-294.
[4] YANG Yong-xin, Ge Yao-jun. Some Practices on Aerodynamic Flutter Control for Long-span Cable Supported Bridges [C]// AWAS. Proceedings of the 4th International Conference on AWAS'08. Seoul: AWAS, 2008: 1474-1485.
[5] LIN Y Y, CHENG C M, LAN C Y. Effects of Deck's Width-to-depth Ratios and Turbulent Flows on the Aerodynamic Behaviors of Long-span Bridges[J]. Wind and Structures, 2003, 6: 263-278.
[6] 鲜荣,廖海黎.封闭式扁平钢箱梁颤振稳定性气动优化措施风洞试验研究[J].世界桥梁,2008,36(3):44-47. XIAN Rong, LIAO Hai-li. Wind Tunnel Test Study of Aerodynamic Optimization Measures for Flutter Stability of Closed Flat Steel Box Girder[J]. World Bridges, 2008, 36 (3): 44-47.
[7] 王骑,廖海黎,李明水,等.流线型箱梁气动外形对桥梁颤振和涡振的影响[J].公路交通科技,2012,29(8):44-50. WANG Qi, LIAO Hai-li, LI Ming-shui, et al. Influence of Aerodynamic Shape of Streamline Box Girder on Bridge Flutter and Vortex-induced Vibration [J]. Journal of Highway and Transportation Research and Development, 2012, 29 (8): 44-50.
[8] 朱乐东,张宏杰,胡晓红.1 400 m跨径钢箱梁斜拉桥方案颤振控制气动措施试验研究[J].桥梁建设,2011(2):9-12. ZHU Le-dong, ZHANG Hong-jie, HU Xiao-hong. Test Study of Aerodynamic Measures for Flutter Control of a Proposed 1 400 m Span Steel Box Deck Cable-stayed Bridge [J]. Bridge Construction, 2011 (2): 9-12.
[9] 于舰涵.斜腹板倾角对桥梁气动稳定性影响的数值模拟研究[D].成都:西南交通大学,2014. YU Jian-han. Study on Numeric Simulation of Influence of Inclined Webs on Flutter Instability of Long-span Bridges [D]. Chengdu: Southwest Jiaotong University, 2014.
[10] 周健,樊泽民,王骑,等.基于节段模型风洞试验的莫桑比克马普托大桥主梁选型研究[J].世界桥梁,2014,42(2):6-11. ZHOU Jian, FAN Ze-min, WANG Qi, et al. Main Girder Type Selection for Maputo Bridge in Mozambique Based on Sectional Model Wind Tunnel Test[J]. World Bridges, 2014, 42 (2): 6-11.
[11] 颜宇光.基于PIV技术的闭口箱梁桥梁断面颤振和涡振性能的气动选型[D].上海:同济大学,2015. YAN Yu-guang. Aerodynamic Selection for Flutter and Vortex Induced Vibration Performance of Closed Box Girders Based on PIV Technology [D]. Shanghai: Tongji University, 2015.
[12] LARSEN A, SAVAGE M. Investigation of Vortex Response of a Twin Box Bridge Section at High and Low Reynolds Numbers [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96 (6/7): 934-944.
[13] GE Y J, YANG Y X, et al. VIV Sectional Model Testing and Field Measurement of Xihoumen Suspension Bridge with Twin Box Girder [C]// ICWE. Proceedings of 13th ICWE. Amsterdam: ICWE, 2011: 1-7.
[14] DIANA G, BELLOLLI M, ROCCHI D. On the Vortex Shedding Forcing on Suspension Bridge Deck [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2006, 94 (5): 341-363.
[15] CHEN X. Improved Understanding of Bimodal Coupled Bridge Flutter Based on Closed-form Solutions [J]. Journal of Structural Engineering, 2007, 133 (1): 22-31.
[16] MATSUMOTO M. Aerodynamic Damping of Prisms [J]. Journal of Wind Engineering and Industrial Aerodynamics, 1996, 59 (2/3): 159-175.
[17] 杨詠昕.大跨度桥梁二维颤振机理及其应用研究[D].上海:同济大学,2002. YANG Yong-xin. Two-dimensional Flutter Mechanism and Its Application for Long-span Bridges [D]. Shanghai: Tongji University, 2002.
[18] JTG/T D60-01—2004,公路桥梁抗风设计规范[S]. JTG/T D60-01—2004, Wind-resistant Design Specification for Highway Bridges [S].
[19] LARSEN A, WALL A. Shaping of Bridge Box Girders to Avoid Vortex Shedding Response [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2012, 104-106: 159-165.
[20] 马存明, 秦浩.普立特大桥抗风性能研究报告[R].成都:西南交通大学,2011. MA Cun-ming, QIN Hao. Report of Wind-resistant Design for Puli Bridge[R]. Chengdu: Southwest Jiaotong University, 2011.
[21] 周继.大跨度悬索桥成桥状态颤振分析[D].成都:西南交通大学,2011. ZHOU Ji. Flutter Analysis of a Long-span Suspension Bridge During Completed Stage [D]. Chengdu: Southwest Jiaotong University, 2011.
[22] 丁泉顺.大跨度桥梁耦合颤抖振响应的精细化分析[D].上海:同济大学,2001. DING Quan-shun. Refinement of Coupled Flutter and Buffeting Analysis for Long-span bridges [D]. Shanghai: Tongji University, 2001.
[23] 张建,郑史雄,唐煜,等.基于节段模型试验的悬索桥涡振性能优化研究[J].实验流体力学,2015,29(2):48-54. ZHANG Jian, ZHENG Shi-xiong, TANG Yu, et al. Research on Optimizing Vortex-induced Vibration Performance for Suspension Bridge Based on Section Model Test [J]. Journal of Experiments in Fluid Mechanics, 2015, 29 (2): 48-54.
[24] 王骑, 卓凌骏.万州驸马长江大桥抗风性能研究报告[R].成都:西南交通大学,2014. WANG Qi, ZHUO Ling-jun. Report of Wind-resistant Design for Fuma Bridge of Wanzhou [R]. Chengdu: Southwest Jiaotong University, 2014.
[25] 杨詠昕.官山至秀山公路秀山大桥抗风性能研究报告[R].上海:同济大学,2015. YANG Yong-xin. Report of Wind-resistant Design for Xiushan Bridge of the Road Link of Guanshan-Xiushan [R]. Shanghai: Tongji University, 2015.
[26] 白桦,高慧,李宇,等.借助三分力系数的桥梁颤振稳定性评价[J].中国公路学报,2014,27(7):68-73 BAI Hua, GAO Hui, LI Yu, et al. Estimation of Flutter Stability of Bridge by Using Three-component Coefficients [J]. China Journal of Highway and Transport, 2014, 27 (7): 68-73.
[27] 白桦,方成,王峰,等.桥梁颤振稳定性快速评价参数及其应用[J].中国公路学报,2016,29(8):92-99 BAI Hua, FANG Cheng, WANG Feng, et al. Rapid Evaluation Parameters of Flutter Stability of Bridge and Their Application [J]. China Journal of Highway and Transport, 2016, 29 (8): 92-99.