X型超高层建筑三维风荷载与风致响应研究
摘要
随着经济的发展,近年来高层建筑尤其是体型复杂的超高层建筑得到了蓬勃的发展。风荷载是超高层建筑的主要控制荷载,气流经过高耸结构物会产生明显的三维风荷载效应,即顺风向、横风向和扭转风荷载,从而引起结构在三个方向上的振动。高层建筑三维风荷载形成机理复杂,影响因素众多,一直以来都是风工程研究的热点问题。但目前大多数的研究都集中于矩形等少数规则平面的高层建筑,而对复杂体型高层建筑的风荷载则较少涉及。
本文以某X型超高层建筑为研究背景,分别从高层建筑风荷载的时空分布特征、风压与风荷载的频谱特性、偏心与非偏心状态下的结构响应以及高层建筑等效风荷载等四个方面对复杂体型超高层建筑风荷载与风致响应问题进行研究和探讨;
(1)高层建筑风荷载的空间分布特征研究。采用刚性模型对X型超高层建筑进行了多点同步测压风洞试验;研究和探讨了平均风压和脉动极值风压、局部和整体体型系数以及风载合力的空间分布特征。
(2)风压与风荷载合力的频谱特性研究。由准定常假定出发,推导了由风速谱得到结构迎风面风压谱的转化公式,结构侧风面的风压功率谱曲线则根据试验数据拟合得到;研究了高层建筑各点脉动风压的水平和竖向相关特性,并通过公式拟合得到迎风面测点水平和竖向相干函数;分析了结构顺风向、横风向以及扭转方向风荷载系数平均值和均方根值沿高度的变化规律;研究了结构顺风向、横风向和扭转方向风载合力功率谱的数学模型,给出了功率谱模型的拟合公式;文中还探讨了顺风向、横风向和扭转方向各自风载合力以及三个方向之间楼层风载合力的相干特性,并给出了相应的数学计算模型。
(3)偏心与非偏心状态下高层建筑风致响应研究。首先通过自振特性分析确定弯剪型层模型作为超高层建筑的简化计算模型;计算发现,对于各阶频率稀疏分布的高层建筑,完全二次组合(CQC)法和平方和开平方(SRSS)法几乎是等效的;在振型分解法的基础上,直接对模态力矩阵[S_(FF)(ω)]进行Choleskey分解,改进了传统的虚拟激励方法中对荷载功率谱[S_(PP)]进行Choleskey分解的做法,并证明其等效性,使得计算量大大减小。探讨了高阶振型、一阶频率、一阶阻尼比等因素对结构风致响应的影响;计算得到各风向角下的基于一阶惯性力方法的风振系数,并与我国规范中的风振系数进行对比。
在偏心高层建筑特征值问题的求解中首次引入矩阵扰动理论,从而利用未偏心结构的自振频率和模态直接得到偏心结构的自振频率和模态;分析了偏心位置和偏心程度对结构自振频率以及模态耦合的影响;计算了不同偏心位置和偏心程度下结构的三维耦合风致响应,计算过程中考虑了平-扭响应耦合对结构风振的影响,并对影响机理作了简单的探讨;首次研究了不同偏心程度下单向与双向偏心结构的风致平-扭位移比和加速度比随结构一阶平-扭周期比的变化规律。
(4)高层建筑等效风荷载的研究。首先对高层建筑顺风向等效风荷载的计算方法进行探讨,包括背景等效风荷载计算的阵风荷载因子(GLF)法、荷载响应相关(LRC)法和阵风荷载包络(GLE)法,共振等效风荷载计算的GLF法和惯性力法,并阐述了传统GLF方法计算共振等效风荷载的缺陷;讨论和分析了平均、背景、共振等效风荷载的线性组合方式以及不同结构响应类型下的背景等效风荷载;最后文中将GLF方法扩展到横风向和扭转等效风荷载的计算中,针对背景等效风荷载计算的LRC方法也被引入到横风向和扭转方向的背景等效风荷载的计算中,并将两种方法得到的等效风荷载进行了对比和讨论。
High-rise buildings are brought into a period of prosperity recent years with the economy booming. Wind load is one of the control loads of tall buildings. The 3-D wind load in alongwind, acrosswind and torsional direction which induced the building's vibration in three direction, will be produced when airflow go through the building. Wind load on high-rise building is always a focal problem in wind engineering because of its' complex mechanism and numerous influencing factors. Presently majority of research has been focus on the buildings with regular shape such as rectangular shape, but few of attention has been attached to buildings with irregular plan figures.
Based on the background of the high-rise building with X-shape, investigation and discuss on the wind load and wind-induced vibration of the tall building is carried out in this thesis. The research mainly includes four sections, such as spatio-temporal distribution character of wind load on the tall building, feature of wind pressure and wind load in frequency domain, wind-induced vibration of the building under the state of eccentricity and non-eccentricity and equivalent static wind load of the building.
(1) Research on spatio-temporal distribution character of the tall building. Wind tunnel test of mutli-point synchronous pressure measurement on rigid model of the tall building is conducted. Spacial distribution characters of average and peak values of pulsant wind pressure, local and global body coefficient as well as resultant wind force are investigated and discussed.
(2) Study of power spectrum and frequency-domain features of wind pressure and resultant wind force. Based on the quasi-static assumption, relationship of power spectrum between wind pressure and wind velocity on windward surface is formed. The power spectrum density(psd) functions of wind pressure on side-ward surface is fitted according to the test data. Horizontal and vertical correlation features between different test points are studied and horizontal and vertical coherence curves between points on windward surface are fitted by using least square fitting algorithm. Law of average and root mean square(rms) value of drag, lift and torque coefficients are discussed. Then the mathematical model of power spectrum density functions of the resultant wind force in alongwind, acrosswind and torsional directions are studied and the fitted formulas are proposed. Coherence functions of wind load in different height in three directions are discussed and their analytical models are also proposed in this thesis.
(3) Investigation on wind-induced vibration of high-rise building under status of eccentricity and non-eccentricity. Bending-shear layer model is decided to be used as simplified calculated model of tall building through modal analysis. Result shows that method of complete quadratic combination (CQC) is equal to method of square root of the sum of squares(SRSS) for buildings with frequency sparse distributed. On the basis of mode decomposition method, traditional pseudo-excitation method(PEM) that makes Choleskey decomposition to wind force matrix [S_(pp)] is modified by making Choleskey decomposition to modal force matrix [S_(FF)] which enhances the computation efficiency enormously. Equality of this new method to the traditional ones is confirmed by formula deducing. The parametric study over the following variables is processed for wind-induced vibration, such as high mode, first-order frequency, first-order damping ratio and so on. The wind vibration factor based on the first-order inertia force method is generated under different wind angles and is compared with the wind vibration factor given by the Chinese wind load code.
Matrix perturbation theory is adopted in solving of the eigenvalue problem of the eccentric high-rise building and the frequency and mode shapes can be expressed in term of those of corresponding torsionally uncoupled system. Influence of eccentric displacement and level to the structural vibration feature is analyzed. Calculation of torsionally coupled wind-induced vibration of the structure under status of different eccentric displacement and level is conducted. Influence of the lateral-torsional coupling items to structural response is also taken in consideration. Variety law of lateral-torsional response ratio for structure under single and double axis eccentricity cases in different eccentric levels with the changing of the ratio of first-order lateral-torsional period is firstly investigated. Concept of equivalent eccentric ratio directly towards the torsional wind load for high-rise building is drawn.
(4) Study on equivalent static wind load(ESWL) of high-rise buildings. The computational method for ESWL in alongwind direction of tall buildings is firstly discussed, including the gust loading factors(GLF), load-response correlation(LRC) and gust loading envelope(GLE) method for background ESWL calculation and GLF method, inertia force method for resonant ESWL calculation. The fault of traditional GLF method in calculation of resonant ESWL is elaborated. The linear combination of average, background and resonant items and calculation of background ESWL under different structural response type are analyzed. GLF method is tended to calculation of ESWL in acrosswind and torsional direction. LRC method towards background ESWL is adopted in computation of background ESWL in acrosswind and torsional direction. The ESWL from two different methods is compared and discussed.
本文以某X型超高层建筑为研究背景,分别从高层建筑风荷载的时空分布特征、风压与风荷载的频谱特性、偏心与非偏心状态下的结构响应以及高层建筑等效风荷载等四个方面对复杂体型超高层建筑风荷载与风致响应问题进行研究和探讨;
(1)高层建筑风荷载的空间分布特征研究。采用刚性模型对X型超高层建筑进行了多点同步测压风洞试验;研究和探讨了平均风压和脉动极值风压、局部和整体体型系数以及风载合力的空间分布特征。
(2)风压与风荷载合力的频谱特性研究。由准定常假定出发,推导了由风速谱得到结构迎风面风压谱的转化公式,结构侧风面的风压功率谱曲线则根据试验数据拟合得到;研究了高层建筑各点脉动风压的水平和竖向相关特性,并通过公式拟合得到迎风面测点水平和竖向相干函数;分析了结构顺风向、横风向以及扭转方向风荷载系数平均值和均方根值沿高度的变化规律;研究了结构顺风向、横风向和扭转方向风载合力功率谱的数学模型,给出了功率谱模型的拟合公式;文中还探讨了顺风向、横风向和扭转方向各自风载合力以及三个方向之间楼层风载合力的相干特性,并给出了相应的数学计算模型。
(3)偏心与非偏心状态下高层建筑风致响应研究。首先通过自振特性分析确定弯剪型层模型作为超高层建筑的简化计算模型;计算发现,对于各阶频率稀疏分布的高层建筑,完全二次组合(CQC)法和平方和开平方(SRSS)法几乎是等效的;在振型分解法的基础上,直接对模态力矩阵[S_(FF)(ω)]进行Choleskey分解,改进了传统的虚拟激励方法中对荷载功率谱[S_(PP)]进行Choleskey分解的做法,并证明其等效性,使得计算量大大减小。探讨了高阶振型、一阶频率、一阶阻尼比等因素对结构风致响应的影响;计算得到各风向角下的基于一阶惯性力方法的风振系数,并与我国规范中的风振系数进行对比。
在偏心高层建筑特征值问题的求解中首次引入矩阵扰动理论,从而利用未偏心结构的自振频率和模态直接得到偏心结构的自振频率和模态;分析了偏心位置和偏心程度对结构自振频率以及模态耦合的影响;计算了不同偏心位置和偏心程度下结构的三维耦合风致响应,计算过程中考虑了平-扭响应耦合对结构风振的影响,并对影响机理作了简单的探讨;首次研究了不同偏心程度下单向与双向偏心结构的风致平-扭位移比和加速度比随结构一阶平-扭周期比的变化规律。
(4)高层建筑等效风荷载的研究。首先对高层建筑顺风向等效风荷载的计算方法进行探讨,包括背景等效风荷载计算的阵风荷载因子(GLF)法、荷载响应相关(LRC)法和阵风荷载包络(GLE)法,共振等效风荷载计算的GLF法和惯性力法,并阐述了传统GLF方法计算共振等效风荷载的缺陷;讨论和分析了平均、背景、共振等效风荷载的线性组合方式以及不同结构响应类型下的背景等效风荷载;最后文中将GLF方法扩展到横风向和扭转等效风荷载的计算中,针对背景等效风荷载计算的LRC方法也被引入到横风向和扭转方向的背景等效风荷载的计算中,并将两种方法得到的等效风荷载进行了对比和讨论。
High-rise buildings are brought into a period of prosperity recent years with the economy booming. Wind load is one of the control loads of tall buildings. The 3-D wind load in alongwind, acrosswind and torsional direction which induced the building's vibration in three direction, will be produced when airflow go through the building. Wind load on high-rise building is always a focal problem in wind engineering because of its' complex mechanism and numerous influencing factors. Presently majority of research has been focus on the buildings with regular shape such as rectangular shape, but few of attention has been attached to buildings with irregular plan figures.
Based on the background of the high-rise building with X-shape, investigation and discuss on the wind load and wind-induced vibration of the tall building is carried out in this thesis. The research mainly includes four sections, such as spatio-temporal distribution character of wind load on the tall building, feature of wind pressure and wind load in frequency domain, wind-induced vibration of the building under the state of eccentricity and non-eccentricity and equivalent static wind load of the building.
(1) Research on spatio-temporal distribution character of the tall building. Wind tunnel test of mutli-point synchronous pressure measurement on rigid model of the tall building is conducted. Spacial distribution characters of average and peak values of pulsant wind pressure, local and global body coefficient as well as resultant wind force are investigated and discussed.
(2) Study of power spectrum and frequency-domain features of wind pressure and resultant wind force. Based on the quasi-static assumption, relationship of power spectrum between wind pressure and wind velocity on windward surface is formed. The power spectrum density(psd) functions of wind pressure on side-ward surface is fitted according to the test data. Horizontal and vertical correlation features between different test points are studied and horizontal and vertical coherence curves between points on windward surface are fitted by using least square fitting algorithm. Law of average and root mean square(rms) value of drag, lift and torque coefficients are discussed. Then the mathematical model of power spectrum density functions of the resultant wind force in alongwind, acrosswind and torsional directions are studied and the fitted formulas are proposed. Coherence functions of wind load in different height in three directions are discussed and their analytical models are also proposed in this thesis.
(3) Investigation on wind-induced vibration of high-rise building under status of eccentricity and non-eccentricity. Bending-shear layer model is decided to be used as simplified calculated model of tall building through modal analysis. Result shows that method of complete quadratic combination (CQC) is equal to method of square root of the sum of squares(SRSS) for buildings with frequency sparse distributed. On the basis of mode decomposition method, traditional pseudo-excitation method(PEM) that makes Choleskey decomposition to wind force matrix [S_(pp)] is modified by making Choleskey decomposition to modal force matrix [S_(FF)] which enhances the computation efficiency enormously. Equality of this new method to the traditional ones is confirmed by formula deducing. The parametric study over the following variables is processed for wind-induced vibration, such as high mode, first-order frequency, first-order damping ratio and so on. The wind vibration factor based on the first-order inertia force method is generated under different wind angles and is compared with the wind vibration factor given by the Chinese wind load code.
Matrix perturbation theory is adopted in solving of the eigenvalue problem of the eccentric high-rise building and the frequency and mode shapes can be expressed in term of those of corresponding torsionally uncoupled system. Influence of eccentric displacement and level to the structural vibration feature is analyzed. Calculation of torsionally coupled wind-induced vibration of the structure under status of different eccentric displacement and level is conducted. Influence of the lateral-torsional coupling items to structural response is also taken in consideration. Variety law of lateral-torsional response ratio for structure under single and double axis eccentricity cases in different eccentric levels with the changing of the ratio of first-order lateral-torsional period is firstly investigated. Concept of equivalent eccentric ratio directly towards the torsional wind load for high-rise building is drawn.
(4) Study on equivalent static wind load(ESWL) of high-rise buildings. The computational method for ESWL in alongwind direction of tall buildings is firstly discussed, including the gust loading factors(GLF), load-response correlation(LRC) and gust loading envelope(GLE) method for background ESWL calculation and GLF method, inertia force method for resonant ESWL calculation. The fault of traditional GLF method in calculation of resonant ESWL is elaborated. The linear combination of average, background and resonant items and calculation of background ESWL under different structural response type are analyzed. GLF method is tended to calculation of ESWL in acrosswind and torsional direction. LRC method towards background ESWL is adopted in computation of background ESWL in acrosswind and torsional direction. The ESWL from two different methods is compared and discussed.
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