用简化的瞬态测压方法研究高层建筑的风振响应及等效荷载
摘要
随着经济的发展、科技的进步以及城市人口的增加，超高层建筑得以迅速发展。利用新型的建筑材料，通过先进的施工技术建造起来的现代超高层建筑，通常轻质、高柔度、阻尼小。这类高层建筑对风特别敏感，风荷载是它的一项非常重要的、控制设计的荷载。
对于超高层建筑风振效应的研究，一般都通过风洞试验来完成。在现行的风洞试验技术中，气动弹性模型试验模型制作复杂、试验周期长、费用高，而高频底座天平试验则只能考虑结构的基阶振型并假定其为线性，且由于只能测得基底倾覆弯矩，无法测量各层的平均风荷载，故而无法确定结构各层的等效设计荷载。
本文以CAARC高层建筑标模作为研究对象，尝试在瞬态测压试验的基础上，利用脉动风荷载的竖向相干性分析其风振响应以及等效设计荷载。首先分析了各测点层合力的相干特性，结果显示各测点层所受顺风向风荷载之间的相干函数基本成单调衰减规律，而横风向脉动风荷载在漩涡脱落频率处存在和顺风向不同的显著相关性。据此本文采用拟合的方法提出了各测点层顺风向和横风向脉动风荷载的相干函数经验公式，并结合随机振动理论给出了采用脉动测压技术分析高层建筑风振响应与等效荷载的简化方法。按照简化方法计算的基底倾覆弯矩功率谱、基底弯矩响应、顶部加速度和位移响应等参数均能与高频底座天平试验的结果较好的符合，等效设计荷载的计算结果也与按照《建筑结构荷载规范》的计算结果具有一定的可比性。采用本文方法可以克服天平方法要求结构的基阶模态必须线性且不能给出结构沿高度的荷载分布等缺点。本文结合一具体的工程实例，分析了深圳新万基大厦的风振响应和等效设计荷载。
在上述分析的基础上，本文进一步研究了CAARC标模各测点层合力风力谱特性。结果表明，由于漩涡脱落导致横风向层风力谱以及相干函数均出现明显尖峰，而流场湍流度的增加则对漩涡脱落有抑制作用。进一步拟合了顺风向和横风向各测点层层风力谱的经验公式，并给出了以此为基础的计算CAARC标模风振响应的流程，从而建立起完整的标模风振响应以及等效荷载计算的数学模型。
Since the development of economy and progress of science and technology and the increase of population in cities, more and more super-high-rise buildings have been built. The modern super-high-rise buildings, Which are constructed with new materials and advanced erection technology, are usually light and flexible and their damping is usually very low. Such super-high-rise buildings are prone to wind and the wind load is one of the most important loads to control the structure design.
Wind tunnel test is usually used to analyze the wind-induced response of super-high-rise buildings. Aero-elastic model tests have a long test period and cost much, high frequency force balance technique can only consider the foundational vibration type of the structure and it must be assumed as linear. Because this technique can not get the average wind loads on each floor of the building, it can not give the equivalent design loads of structures.
In this paper, a simplified method of calculating wind-induced response and design loads of super-high-rise buildings was proposed. Coherence properties of wind load on typical tall building were analyzed and the results show that cross-wind loads at different height have strong coherence at vertex shedding frequency, and the coherence function's value here is near to 1. On basis of this property a new type of coherence function was proposed and a simplified method of analyzing structure's wind-induced response and equivalent load was proposed. Wind tunnel experiments with the CAARC standard tall building model was executed to verify the proposed method with the dynamic balance technique. The comparisons show the good agreement on the basis of linear mode shape assumption that is used in balance technique. Finally, the proposed method was used to analyze the wind induced response and equivalent static loads of Shenzhen Xiwanji Tower.
Further more, power spectrum density (PSD) of each test section was analyzed, and its experiential formula was given. Combined with experiential the formula of coherence function, the mathematic model for calculating the CAARC standard tall building's wind-induced response was set up.
对于超高层建筑风振效应的研究，一般都通过风洞试验来完成。在现行的风洞试验技术中，气动弹性模型试验模型制作复杂、试验周期长、费用高，而高频底座天平试验则只能考虑结构的基阶振型并假定其为线性，且由于只能测得基底倾覆弯矩，无法测量各层的平均风荷载，故而无法确定结构各层的等效设计荷载。
本文以CAARC高层建筑标模作为研究对象，尝试在瞬态测压试验的基础上，利用脉动风荷载的竖向相干性分析其风振响应以及等效设计荷载。首先分析了各测点层合力的相干特性，结果显示各测点层所受顺风向风荷载之间的相干函数基本成单调衰减规律，而横风向脉动风荷载在漩涡脱落频率处存在和顺风向不同的显著相关性。据此本文采用拟合的方法提出了各测点层顺风向和横风向脉动风荷载的相干函数经验公式，并结合随机振动理论给出了采用脉动测压技术分析高层建筑风振响应与等效荷载的简化方法。按照简化方法计算的基底倾覆弯矩功率谱、基底弯矩响应、顶部加速度和位移响应等参数均能与高频底座天平试验的结果较好的符合，等效设计荷载的计算结果也与按照《建筑结构荷载规范》的计算结果具有一定的可比性。采用本文方法可以克服天平方法要求结构的基阶模态必须线性且不能给出结构沿高度的荷载分布等缺点。本文结合一具体的工程实例，分析了深圳新万基大厦的风振响应和等效设计荷载。
在上述分析的基础上，本文进一步研究了CAARC标模各测点层合力风力谱特性。结果表明，由于漩涡脱落导致横风向层风力谱以及相干函数均出现明显尖峰，而流场湍流度的增加则对漩涡脱落有抑制作用。进一步拟合了顺风向和横风向各测点层层风力谱的经验公式，并给出了以此为基础的计算CAARC标模风振响应的流程，从而建立起完整的标模风振响应以及等效荷载计算的数学模型。
Since the development of economy and progress of science and technology and the increase of population in cities, more and more super-high-rise buildings have been built. The modern super-high-rise buildings, Which are constructed with new materials and advanced erection technology, are usually light and flexible and their damping is usually very low. Such super-high-rise buildings are prone to wind and the wind load is one of the most important loads to control the structure design.
Wind tunnel test is usually used to analyze the wind-induced response of super-high-rise buildings. Aero-elastic model tests have a long test period and cost much, high frequency force balance technique can only consider the foundational vibration type of the structure and it must be assumed as linear. Because this technique can not get the average wind loads on each floor of the building, it can not give the equivalent design loads of structures.
In this paper, a simplified method of calculating wind-induced response and design loads of super-high-rise buildings was proposed. Coherence properties of wind load on typical tall building were analyzed and the results show that cross-wind loads at different height have strong coherence at vertex shedding frequency, and the coherence function's value here is near to 1. On basis of this property a new type of coherence function was proposed and a simplified method of analyzing structure's wind-induced response and equivalent load was proposed. Wind tunnel experiments with the CAARC standard tall building model was executed to verify the proposed method with the dynamic balance technique. The comparisons show the good agreement on the basis of linear mode shape assumption that is used in balance technique. Finally, the proposed method was used to analyze the wind induced response and equivalent static loads of Shenzhen Xiwanji Tower.
Further more, power spectrum density (PSD) of each test section was analyzed, and its experiential formula was given. Combined with experiential the formula of coherence function, the mathematic model for calculating the CAARC standard tall building's wind-induced response was set up.
引文
[1] Melbourne W H. Comparison of Measurements on the CAARC Standard Tall Building Model in Simulated Model Wind Flows. Journal of Wind and Industrial Aerodynamics ,1980,6,73-88
[2] Boggs D W, Peterka J A. Aerodynamic Model Tests of Tall Buildings. Journal of Engineering Mechanics,1989, Vol 115, 618-635
[3] Boggs D. W, Wind loading and response of tall structures using aerodynamic models. Journal of Engineering Mechanics, ph. D. Dissertation, Colorado State University, 1991
[4] Zhou Y, Gu M, Xiang H F. Alongwind static equivalent wind loads and response of tall buildings, Part Ⅰ: Unfavorable distributions of static equivalent wind loads. Journal of Wind Engineering and Industrial Aerodynamics, 79 (1999) 135-150
[5] Kawai H. Local peak pressure and conical vortex on tall building. Journal of Wind Engineering and Industrial Aerodynamics, 90(2002) 251-263
[6] Solari G. Turbulence Modeling for Gust Loading. Journal of Structure Engineering,1987,Vol 113,1550-1569
[7] Okuda Y. Pressure on buildings with a square section, Doctoral Dissertation, Osaka City University, 1994
[8] Shuguo Liang, Shengchun Liu, Liangliang Zhang, Ming Gu. Mathematic Model of crosswind dynamic loads on regular tall buildings. J of Wind Engineering No.89 2001.10
[9] A. Kareem. Model for predicting the crosswind response of buildings. Department of Civil Engineering, University of Houston, Houston, Texas, USA, 1982
[10] J. D. Holmes, R. E. Lewis. Optimization of dynamic-pressure-measurement systems.Ⅱ. Parallel tube-manifold systems. Journal of Wiod Engineering and Industrial Areodynamics,25 (1987) 275-290
[11] KwokKCS. Cross-wind response of tall buildings. Eng Srtuct,1982,4:256-262
[12] Ahsan Kareem. Across wind response of buildings. J Structural Division, 1982a, 108(ST4):869-887
[13] Ahsan Kareem. Fluctuating wind loads in buildings. J Eng MechDiv,1982b, 108(EMr):1086-1102.
[14] Ahsan Kareem. Dynamic response of hight-rise buildings to stochastic wind loads. J Wind Engineering and Industrial Aerodynamics, 1992,41-44:1101-1112.
[15] Islam M Saiful, Ellingwood Bruce, Corotis Ross B. Transfer function models for determining dynamie wind loads on buildings. J of Wind Engineering and Industrial Aerodynamics, 1990,36:449-458.
[16] Cheng C.M, Lu P.C, Chen R.H. Wind loads on square cylinder in homogeneous turbulent flows. J of Wind Engineering and Industrial Aerodynamics, 1992,41-44:739-749.
[17] Kanda J Choi H. Correlating dynamic wind force components on 3-d cylinders. J of Wind Engineering and Industrial Aerodynamics, 1992,41-44:785-796
[18] Marukawa H, Ohkuma T, Momomura Y, Across-wind and torsional acceleration of prismatic high-rise building. J of Wind Engineering and Industrial Aerodynamics, 1992,41-44:1139-1150.
[19] Kwok K.C.S ,Melbourn WH. Cross-wind response of structures due to displacement dependent lock-in excitation. J of Wind Engineering and Industrial Aerodynamics, 1979,2:458-472.
[20] Cermark J.E Progress in physical modeling for wind engineering. J of Wind Engineering and Industrial Aerodynamics,Vol 54,1995,439-455
[21] Nakayama M. et al. A comparison of wind response of high-rise buildings. J of Wind Engineering and Industrial Aerodynamics, 1995
[22] Dutton R and Isyumov N. Reduction of tall building motion by aerodynamic treatments. J of Wind Engineering and Industrial Aerodynamics, Vol36,1990,739-747
[23] Hayashida H. & lwasa Y. Aerodynamic shape effects of tall building for vortex induced vibration. J of Wind Engineering and Industrial Aerodynamics, Vol41-44, 1992, 1976-1983
[24] Holmes J.D. Mode shape correction for dynamic response to wind. Eng.Struct. Vol 9,1987, 210-212
[25] Yin Zhou, Ming Gu, Haifan Xiang. Along wind Static Equivalent wind Loads and response of tall buildings. J of Wind Engineering and Industrial Aerodynamics,1999,79:135-150
[26] 倪振华，《振动力学》，西安交通大学出版社，1989
[27] 张景绘，王超．《工程随机振动》西安交通大学出版社，1988
[28] 刘尚培，项海帆，谢霁明译 风对结构的作用——风工程导论，同济大学出版社，1992
[29] 倪振华，姚伟军，谢壮宁．高层建筑风致振动研究的瞬态风压积分法．振动工程学报，2000，13(4)，544-551
[30] 建筑结构荷载规范．北京，中国建筑工业出版社，2002，24-47
[31] 顾明等．用高频动态天平方法研究金茂大厦的动力风荷载和风振响应．建筑结构学报，2000，21(4)，55-61
[32] 梁枢果，李辉民，瞿伟廉．高层建筑风荷载计算中的基本振型表达式分析，同济大学学报，2002，30(5)，578-582
[33] 谢壮宁等．脉动风压测压管路系统的动态特性分析．应用力学学报．2002．19(1)，5-9
[34] 梁枢果等．矩形高层建筑横风向动力风荷载解析模型．空气动力学学报．2002．20(1)，32-39
[35] 全涌，顾明．超高层建筑横风向气动力谱．同济大学学报．2002．30(5)，627-632
[36] 张相庭．工程结构风荷载理论和抗风计算手册，同济大学出版社，1990
[37] 张相庭．高层建筑抗风抗震设计计算，同济大学出版社，1990
[38] 王凤元．用高频测力天平技术研究高层建筑的气动荷载与风效应．同济大学硕士学位论文．1998
[39] 黄本才．结构抗风分析原理及应用．同济大学出版社，2001
[40] 叶丰，顾明．高层建筑顺风向背景响应及其等效风荷载的计算方法．建筑结构学报．Vol 23，No．1 2002，58-61
[41] 黄本才．高层建筑风振系数简化方法和实用计算表格．建筑结构学报．2001，21(3)
[42] 朱川海，黄本才．高耸结构风振系数简化分析方法，特种结构，2000，17(3)
[2] Boggs D W, Peterka J A. Aerodynamic Model Tests of Tall Buildings. Journal of Engineering Mechanics,1989, Vol 115, 618-635
[3] Boggs D. W, Wind loading and response of tall structures using aerodynamic models. Journal of Engineering Mechanics, ph. D. Dissertation, Colorado State University, 1991
[4] Zhou Y, Gu M, Xiang H F. Alongwind static equivalent wind loads and response of tall buildings, Part Ⅰ: Unfavorable distributions of static equivalent wind loads. Journal of Wind Engineering and Industrial Aerodynamics, 79 (1999) 135-150
[5] Kawai H. Local peak pressure and conical vortex on tall building. Journal of Wind Engineering and Industrial Aerodynamics, 90(2002) 251-263
[6] Solari G. Turbulence Modeling for Gust Loading. Journal of Structure Engineering,1987,Vol 113,1550-1569
[7] Okuda Y. Pressure on buildings with a square section, Doctoral Dissertation, Osaka City University, 1994
[8] Shuguo Liang, Shengchun Liu, Liangliang Zhang, Ming Gu. Mathematic Model of crosswind dynamic loads on regular tall buildings. J of Wind Engineering No.89 2001.10
[9] A. Kareem. Model for predicting the crosswind response of buildings. Department of Civil Engineering, University of Houston, Houston, Texas, USA, 1982
[10] J. D. Holmes, R. E. Lewis. Optimization of dynamic-pressure-measurement systems.Ⅱ. Parallel tube-manifold systems. Journal of Wiod Engineering and Industrial Areodynamics,25 (1987) 275-290
[11] KwokKCS. Cross-wind response of tall buildings. Eng Srtuct,1982,4:256-262
[12] Ahsan Kareem. Across wind response of buildings. J Structural Division, 1982a, 108(ST4):869-887
[13] Ahsan Kareem. Fluctuating wind loads in buildings. J Eng MechDiv,1982b, 108(EMr):1086-1102.
[14] Ahsan Kareem. Dynamic response of hight-rise buildings to stochastic wind loads. J Wind Engineering and Industrial Aerodynamics, 1992,41-44:1101-1112.
[15] Islam M Saiful, Ellingwood Bruce, Corotis Ross B. Transfer function models for determining dynamie wind loads on buildings. J of Wind Engineering and Industrial Aerodynamics, 1990,36:449-458.
[16] Cheng C.M, Lu P.C, Chen R.H. Wind loads on square cylinder in homogeneous turbulent flows. J of Wind Engineering and Industrial Aerodynamics, 1992,41-44:739-749.
[17] Kanda J Choi H. Correlating dynamic wind force components on 3-d cylinders. J of Wind Engineering and Industrial Aerodynamics, 1992,41-44:785-796
[18] Marukawa H, Ohkuma T, Momomura Y, Across-wind and torsional acceleration of prismatic high-rise building. J of Wind Engineering and Industrial Aerodynamics, 1992,41-44:1139-1150.
[19] Kwok K.C.S ,Melbourn WH. Cross-wind response of structures due to displacement dependent lock-in excitation. J of Wind Engineering and Industrial Aerodynamics, 1979,2:458-472.
[20] Cermark J.E Progress in physical modeling for wind engineering. J of Wind Engineering and Industrial Aerodynamics,Vol 54,1995,439-455
[21] Nakayama M. et al. A comparison of wind response of high-rise buildings. J of Wind Engineering and Industrial Aerodynamics, 1995
[22] Dutton R and Isyumov N. Reduction of tall building motion by aerodynamic treatments. J of Wind Engineering and Industrial Aerodynamics, Vol36,1990,739-747
[23] Hayashida H. & lwasa Y. Aerodynamic shape effects of tall building for vortex induced vibration. J of Wind Engineering and Industrial Aerodynamics, Vol41-44, 1992, 1976-1983
[24] Holmes J.D. Mode shape correction for dynamic response to wind. Eng.Struct. Vol 9,1987, 210-212
[25] Yin Zhou, Ming Gu, Haifan Xiang. Along wind Static Equivalent wind Loads and response of tall buildings. J of Wind Engineering and Industrial Aerodynamics,1999,79:135-150
[26] 倪振华，《振动力学》，西安交通大学出版社，1989
[27] 张景绘，王超．《工程随机振动》西安交通大学出版社，1988
[28] 刘尚培，项海帆，谢霁明译 风对结构的作用——风工程导论，同济大学出版社，1992
[29] 倪振华，姚伟军，谢壮宁．高层建筑风致振动研究的瞬态风压积分法．振动工程学报，2000，13(4)，544-551
[30] 建筑结构荷载规范．北京，中国建筑工业出版社，2002，24-47
[31] 顾明等．用高频动态天平方法研究金茂大厦的动力风荷载和风振响应．建筑结构学报，2000，21(4)，55-61
[32] 梁枢果，李辉民，瞿伟廉．高层建筑风荷载计算中的基本振型表达式分析，同济大学学报，2002，30(5)，578-582
[33] 谢壮宁等．脉动风压测压管路系统的动态特性分析．应用力学学报．2002．19(1)，5-9
[34] 梁枢果等．矩形高层建筑横风向动力风荷载解析模型．空气动力学学报．2002．20(1)，32-39
[35] 全涌，顾明．超高层建筑横风向气动力谱．同济大学学报．2002．30(5)，627-632
[36] 张相庭．工程结构风荷载理论和抗风计算手册，同济大学出版社，1990
[37] 张相庭．高层建筑抗风抗震设计计算，同济大学出版社，1990
[38] 王凤元．用高频测力天平技术研究高层建筑的气动荷载与风效应．同济大学硕士学位论文．1998
[39] 黄本才．结构抗风分析原理及应用．同济大学出版社，2001
[40] 叶丰，顾明．高层建筑顺风向背景响应及其等效风荷载的计算方法．建筑结构学报．Vol 23，No．1 2002，58-61
[41] 黄本才．高层建筑风振系数简化方法和实用计算表格．建筑结构学报．2001，21(3)
[42] 朱川海，黄本才．高耸结构风振系数简化分析方法，特种结构，2000，17(3)