超高层建筑风重耦合效应及等效静力风荷载研究
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摘要
随着城市化进程的加快,越来越多的超高层建筑往轻柔方向发展,结构设计也出现许多急需解决的问题,风重耦合效应就是其中之一。风重耦合效应是指高柔结构在风荷载作用下产生的水平位移,重力的存在,使结构弯矩增大,从而进一步增大水平位移,这样的作用机理在静力方面表现为结构水平位移的增大,在动力上表现为结构固有频率的改变和和结构响应的变化。在实际工程中,超高层建筑的风重耦合效应已有报道,进一步细化分析风重耦合效应的影响显得十分必要。
本文主要目的是为了分析风重耦合效应的影响因素,发现高柔结构由于重力影响在风振中的特性改变,同时给出一般超高层结构分析计算方法。总体而言主要做了以下几个方面的工作。
利用悬臂梁模型,推导出计入结构大变形和重力的作用的风重耦合的动力方程,利用差分法可以求解风振时程响应,时程计算表明风重耦合效应使脉动风的幅值比传统计算的结果要大。
结构顺风向随机风振计算可以按平均风荷载和脉动风荷载将方程分解成平均风方程和脉动风方程,其中平均风方程相当于静力非线性方程,求解容易；另一个脉动风方程是非线性动力方程,通过振型分解和等效线性化处理可以得到结构响应的解。参数分析表明,重刚比是影响风重耦合效应最重要的参数,其值越大,结构振动固有频率越小,结构响应越大。当结构重刚比较小时,地面粗糙度、结构固有阻尼和平均风速对风重耦合效应影响不大,但当重刚比较大时,风重耦合效应随着结构固有阻尼和平均风速的增大而减小。
等效静力风荷载是工程设计中常用的方法。本文采用结构恢复力等价的原则,经推导可以得到沿高度分布的荷载。结果表明,计入风重耦合效应的等效风荷载表达式比常规高层建筑风荷载多了附加重力等效风荷载项。加入各分项的峰值系数可以得到设计等效静力风荷载。计入风重耦合效应后的顺风向风振系数与规范给出的风振系数存在着差异,风重耦合效应引起在建筑物中风振系数中下部分布值减小和上部分布值增大,结构的重刚比是影响风振系数的重要因素,其他因素影响不大。
横风向风重耦合效应与顺风向类似,对横风向风重耦合效应来说重刚比仍旧是一个决定性因素,但横风向作用机理与顺风向不同,其风重耦合效应与顺风向存在一定的差异,特别是平均风速的影响有所不同,当平均风速较小时,结构响应随着重刚比增长而增长,当平均风速加大时,结构响应先是随着重刚比增长而增长,达到峰值后随着重刚比增长而下降。风重耦合效应使整条响应对重刚比曲线左偏。对于矩形截面的超高层结构,风重耦合与截面深宽比有关,当在深宽比小于2时,风重耦合效应先是减小再是增大,当深宽比大于2时,没有确切的规律。横风向静力等效荷载的变化规律和顺风向类似。
对于一般超高层建筑的风重耦合的计算除了考虑顺风向和横风向的风荷载还必须考虑扭转向的风荷载。为了实现频域分析一般结构的方法,本文以每层的三个自由度为未知数建立计入风重耦合效应的有限元方程。分析表明,在质量偏心率较小情况下固有频率随着重刚比增大而减小,但当结构质量偏心率较大时,固有频率反而随着重刚比增大而增大,对于刚心偏位的情况也有类似结论。对于偏心结构,风重耦合效应使顺风向和横风向响应增大,但对于扭转向是减小的。不同角度对风重耦合的影响是发生周期性变化,偏心率较小时,偏心位置的角度对风重耦合效应影响不大,而随着偏心率的增大,角度影响就很明显。
本文以LCVA作为实例分析调谐减振器在超高层建筑中减振规律。各参数分析表明质量比是减振中一个重要参数,质量比加大能明显起到减振作用,实际上只要水体质量达到建筑物质量1%-2%时就可以起到较好的减振效果。水管截面比、长度比以及水头损失系数亦是关系减振率的重要参数。在优化设计中要使减振器达到较好的减振效果,必须使减振器的振动频率接近或等于主结构的固有基频。当主结构计入风重耦合效应后,计算结果会与传统计算方法产生较大的差异,一般规律是主结构重刚比较小时计入风重耦合效应的结构减振率大,而主结构重刚比较大时风重耦合计算结果就比传统结果要小。对高柔结构减振设计必须考虑风重耦合效应,才能正确分析减振效果。
在顺风向和横风向计算结果的对比分析中,本文提出了比规范更为严格的刚度限制要求,供设计者借鉴。
超高层结构风重耦合效应研究是一个新的方向,本文只做了部分工作,建议今后进一步深入这一领域相关问题研究。
Structures of tall-buildings are becoming light and slender with urbanization developing rapidly recent year. Wind-gravity coupling effect (WGCE) is one of problems which should be to solve in structural designing. WGCE is a phenomenon that horizontal displacement of the high flexible structure induced by wind load is enlarged by gravity. Performance of WGCE in statics is larger displacement. That in dynamics is natural frequencies reduced and response of structure changed. It was reported in engineering that WGCE of extra-tall buildings is notable, so studying on WGCE is necessary.
The ambition of thesis is to determine influential factor of WGCE, to find different dynamic characteristics under the influence of gravity and to present a method to calculate WGCE of general extra-tall buildings. In general, works listed below had been finished.
The dynamic equation including large deformation and WGCE is concluded using cantilever model. Response of structures can be calculated at any point of time by differential equations. Schedule calculation about the tall-building acted by wind shows amplitude produced by pulse wind is changed. The result including WGCE is larger than traditional result.
The along-wind dynamics equation can be written as two equations by average wind load and pulse wind load. Average wind load equation is just as nonlinear static equation which is easy to solve. Pulse wind load equation is nonlinear dynamic equation which can be solve through mode superposition and equivalent linearization. Calculated result indicates gravity-rigidity ratio is an important parameter for WGCE. Natural frequency of structure decreases and response of structure increases with gravity-rigidity ratio of structure. Ground roughness, natural damping and average wind speed little impact on WGCE as value of gravity-rigidity ratio is small. While value of gravity-rigidity ratio is large, WGCE decreases with natural damping and average wind speed.
Equivalent static wind load (ESWL) is a general method in structural design. Mean square deviation of restoring force is taken as ESWL by equivalent principle and distributed ESWL along height direction can also be concluded. It is shown that ESWL expression including WGCE contain gravity equivalent wind load that does not exist in common ESWL expression. The designing ESWL can be obtained after crest factors are added to every item of ESWL expression. Wind load factor are different between WGCE's method and traditional method. WGCE makes distribution of wind load factor reduction in middle and lower part of structures and increasing at top part of structures. Gravity-rigidity ratio is an important factor for WGCE expressed in ESWL and other factors are not evident.
Across-wind WGCE is similar to along-wind one. Gravity-rigidity ratio is also a decisive factor for across-wind WGCE. Because mechanism of across-wind is different from that of along-wind, across-wind WGCE have some differences to along-wind WGCE. Response of structures increases with Gravity-rigidity ratio as lower average wind load. While average wind load become strong, responses of structures increases with gravity-rigidity ratio at first, then decreasing after reaching peak point. WGCE makes curve of responses to gravity-rigidity ratio turn to left. WGCE of across-wind associates to section aspect ratio for tall buildings with rectangular cross-section. Influence of WGCE first decreases then increases as aspect ratio is less than2and it is no law as aspect ratio is more than2. ESWL of across-wind is similar to that of along-wind.
There is torsional wind load besides along-wind load and across-wind load in calculation of general extra-high building including WGCE. In order to obtain general analysis method in frequency domain, FEM equations with WGCE are concluded from3degrees of freedom in every storey. It is shown that natural frequency decreases with gravity-rigidity ratio increasing as mass eccentricity is small. The opposite is the case as mass eccentricity is large. The same conclusion is for rigidity eccentricity. WGCE makes response of eccentric structure increasing in along-wind direction and across-wind direction, but decreasing in torsional direction. Influence of WGCE takes place periodic changes at different angles. As eccentricity is small, eccentric angle have little impact on WGCE. While eccentricity is large, eccentric angle is an important factor to WGCE.
Liquid column vibration absorber(LCVA) is used as an example to explain what change of structure with vibration absorber including WGCE. The result is shown that mass ratio is an important parameter that can reduce vibration effectively when it increases. In fact, vibration is decreased very quickly as mass of vibration absorber up to1%～2%of main structure. Section ratio, length ratio and head loss coefficient are also key parameters relative to damping rate. If we want to reach optimal damping rate, natural frequency of LCVA should equal to or near to that of main structure. There is some different about calculating result between WGCE method and tradition method. The general law is that value of WGCE about damping rate shows large as gravity-rigidity ratio is small while it is small as gravity-rigidity ratio increases. In order to get correct result, it should be taken into account WGCE for tall slender structure damping design.
It is proposed to use restrict stiffness instead of the code from results of along-wind and across-wind in the paper. That provides experience for engineering design.
WGCE is an new research area in wind engineering. Some parts of work are done in the paper. It is suggested to go a step to new research direction about WGCE.
本文主要目的是为了分析风重耦合效应的影响因素,发现高柔结构由于重力影响在风振中的特性改变,同时给出一般超高层结构分析计算方法。总体而言主要做了以下几个方面的工作。
利用悬臂梁模型,推导出计入结构大变形和重力的作用的风重耦合的动力方程,利用差分法可以求解风振时程响应,时程计算表明风重耦合效应使脉动风的幅值比传统计算的结果要大。
结构顺风向随机风振计算可以按平均风荷载和脉动风荷载将方程分解成平均风方程和脉动风方程,其中平均风方程相当于静力非线性方程,求解容易；另一个脉动风方程是非线性动力方程,通过振型分解和等效线性化处理可以得到结构响应的解。参数分析表明,重刚比是影响风重耦合效应最重要的参数,其值越大,结构振动固有频率越小,结构响应越大。当结构重刚比较小时,地面粗糙度、结构固有阻尼和平均风速对风重耦合效应影响不大,但当重刚比较大时,风重耦合效应随着结构固有阻尼和平均风速的增大而减小。
等效静力风荷载是工程设计中常用的方法。本文采用结构恢复力等价的原则,经推导可以得到沿高度分布的荷载。结果表明,计入风重耦合效应的等效风荷载表达式比常规高层建筑风荷载多了附加重力等效风荷载项。加入各分项的峰值系数可以得到设计等效静力风荷载。计入风重耦合效应后的顺风向风振系数与规范给出的风振系数存在着差异,风重耦合效应引起在建筑物中风振系数中下部分布值减小和上部分布值增大,结构的重刚比是影响风振系数的重要因素,其他因素影响不大。
横风向风重耦合效应与顺风向类似,对横风向风重耦合效应来说重刚比仍旧是一个决定性因素,但横风向作用机理与顺风向不同,其风重耦合效应与顺风向存在一定的差异,特别是平均风速的影响有所不同,当平均风速较小时,结构响应随着重刚比增长而增长,当平均风速加大时,结构响应先是随着重刚比增长而增长,达到峰值后随着重刚比增长而下降。风重耦合效应使整条响应对重刚比曲线左偏。对于矩形截面的超高层结构,风重耦合与截面深宽比有关,当在深宽比小于2时,风重耦合效应先是减小再是增大,当深宽比大于2时,没有确切的规律。横风向静力等效荷载的变化规律和顺风向类似。
对于一般超高层建筑的风重耦合的计算除了考虑顺风向和横风向的风荷载还必须考虑扭转向的风荷载。为了实现频域分析一般结构的方法,本文以每层的三个自由度为未知数建立计入风重耦合效应的有限元方程。分析表明,在质量偏心率较小情况下固有频率随着重刚比增大而减小,但当结构质量偏心率较大时,固有频率反而随着重刚比增大而增大,对于刚心偏位的情况也有类似结论。对于偏心结构,风重耦合效应使顺风向和横风向响应增大,但对于扭转向是减小的。不同角度对风重耦合的影响是发生周期性变化,偏心率较小时,偏心位置的角度对风重耦合效应影响不大,而随着偏心率的增大,角度影响就很明显。
本文以LCVA作为实例分析调谐减振器在超高层建筑中减振规律。各参数分析表明质量比是减振中一个重要参数,质量比加大能明显起到减振作用,实际上只要水体质量达到建筑物质量1%-2%时就可以起到较好的减振效果。水管截面比、长度比以及水头损失系数亦是关系减振率的重要参数。在优化设计中要使减振器达到较好的减振效果,必须使减振器的振动频率接近或等于主结构的固有基频。当主结构计入风重耦合效应后,计算结果会与传统计算方法产生较大的差异,一般规律是主结构重刚比较小时计入风重耦合效应的结构减振率大,而主结构重刚比较大时风重耦合计算结果就比传统结果要小。对高柔结构减振设计必须考虑风重耦合效应,才能正确分析减振效果。
在顺风向和横风向计算结果的对比分析中,本文提出了比规范更为严格的刚度限制要求,供设计者借鉴。
超高层结构风重耦合效应研究是一个新的方向,本文只做了部分工作,建议今后进一步深入这一领域相关问题研究。
Structures of tall-buildings are becoming light and slender with urbanization developing rapidly recent year. Wind-gravity coupling effect (WGCE) is one of problems which should be to solve in structural designing. WGCE is a phenomenon that horizontal displacement of the high flexible structure induced by wind load is enlarged by gravity. Performance of WGCE in statics is larger displacement. That in dynamics is natural frequencies reduced and response of structure changed. It was reported in engineering that WGCE of extra-tall buildings is notable, so studying on WGCE is necessary.
The ambition of thesis is to determine influential factor of WGCE, to find different dynamic characteristics under the influence of gravity and to present a method to calculate WGCE of general extra-tall buildings. In general, works listed below had been finished.
The dynamic equation including large deformation and WGCE is concluded using cantilever model. Response of structures can be calculated at any point of time by differential equations. Schedule calculation about the tall-building acted by wind shows amplitude produced by pulse wind is changed. The result including WGCE is larger than traditional result.
The along-wind dynamics equation can be written as two equations by average wind load and pulse wind load. Average wind load equation is just as nonlinear static equation which is easy to solve. Pulse wind load equation is nonlinear dynamic equation which can be solve through mode superposition and equivalent linearization. Calculated result indicates gravity-rigidity ratio is an important parameter for WGCE. Natural frequency of structure decreases and response of structure increases with gravity-rigidity ratio of structure. Ground roughness, natural damping and average wind speed little impact on WGCE as value of gravity-rigidity ratio is small. While value of gravity-rigidity ratio is large, WGCE decreases with natural damping and average wind speed.
Equivalent static wind load (ESWL) is a general method in structural design. Mean square deviation of restoring force is taken as ESWL by equivalent principle and distributed ESWL along height direction can also be concluded. It is shown that ESWL expression including WGCE contain gravity equivalent wind load that does not exist in common ESWL expression. The designing ESWL can be obtained after crest factors are added to every item of ESWL expression. Wind load factor are different between WGCE's method and traditional method. WGCE makes distribution of wind load factor reduction in middle and lower part of structures and increasing at top part of structures. Gravity-rigidity ratio is an important factor for WGCE expressed in ESWL and other factors are not evident.
Across-wind WGCE is similar to along-wind one. Gravity-rigidity ratio is also a decisive factor for across-wind WGCE. Because mechanism of across-wind is different from that of along-wind, across-wind WGCE have some differences to along-wind WGCE. Response of structures increases with Gravity-rigidity ratio as lower average wind load. While average wind load become strong, responses of structures increases with gravity-rigidity ratio at first, then decreasing after reaching peak point. WGCE makes curve of responses to gravity-rigidity ratio turn to left. WGCE of across-wind associates to section aspect ratio for tall buildings with rectangular cross-section. Influence of WGCE first decreases then increases as aspect ratio is less than2and it is no law as aspect ratio is more than2. ESWL of across-wind is similar to that of along-wind.
There is torsional wind load besides along-wind load and across-wind load in calculation of general extra-high building including WGCE. In order to obtain general analysis method in frequency domain, FEM equations with WGCE are concluded from3degrees of freedom in every storey. It is shown that natural frequency decreases with gravity-rigidity ratio increasing as mass eccentricity is small. The opposite is the case as mass eccentricity is large. The same conclusion is for rigidity eccentricity. WGCE makes response of eccentric structure increasing in along-wind direction and across-wind direction, but decreasing in torsional direction. Influence of WGCE takes place periodic changes at different angles. As eccentricity is small, eccentric angle have little impact on WGCE. While eccentricity is large, eccentric angle is an important factor to WGCE.
Liquid column vibration absorber(LCVA) is used as an example to explain what change of structure with vibration absorber including WGCE. The result is shown that mass ratio is an important parameter that can reduce vibration effectively when it increases. In fact, vibration is decreased very quickly as mass of vibration absorber up to1%～2%of main structure. Section ratio, length ratio and head loss coefficient are also key parameters relative to damping rate. If we want to reach optimal damping rate, natural frequency of LCVA should equal to or near to that of main structure. There is some different about calculating result between WGCE method and tradition method. The general law is that value of WGCE about damping rate shows large as gravity-rigidity ratio is small while it is small as gravity-rigidity ratio increases. In order to get correct result, it should be taken into account WGCE for tall slender structure damping design.
It is proposed to use restrict stiffness instead of the code from results of along-wind and across-wind in the paper. That provides experience for engineering design.
WGCE is an new research area in wind engineering. Some parts of work are done in the paper. It is suggested to go a step to new research direction about WGCE.
引文
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