考虑风速风向联合分布的超高层建筑风致振动研究1
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摘要
对于矩形超高层建筑,若不考虑风速风向联合分布,一般认为建筑正面迎风时风致响应最大,且以此进行结构设计偏于安全。正是基于上述考虑,建筑正面迎风工况下的顺风向、横风向和扭转方向的风荷载和风振响应研究较多,而其他非正面迎风工况下的建筑风荷载和风致响应研究很少。但是对于其他复杂截面的超高层建筑,是否仍然符合这一情况,还需要进行详细的验证。事实上,偏于安全的设计等同于偏保守的设计,是以大量人力、财力和物力为代价的。对于造价昂贵的超高层建筑,这种代价是非常可观的。显然考虑风速风向联合分布下的全风向风振响应分析是更为合理,更为精细的分析设计方法,是解决上述矛盾的有效手段之一。而且日益完善的风速风向观测技术和逐步积累的观测资料,则为全风向风振分析提供了可靠的基础。
本文以重庆农村商业银行大厦实际工程为例,通过风洞试验系统的研究了超高层建筑在典型风向角下的风荷载;然后基于概率论的乘法定理,推导了风速风向联合分布模型;再结合风速风向数据,建立了重庆地区风速风向的连续型联合概率密度模型,同时给出了基于重现期的考虑风速风向联合分布的各风向基本风速;最后结合风振响应和各风向基本风速,提出了可供设计参考的各响应基本风速风向因子。基于此,本文主要开展了以下几个方面的工作:
①通过超高层建筑的刚性模型风洞试验,研究了在典型风向角下角部凹角方形截面超高层建筑的表面风压幅值特性、频域特性以及相关性。与一般规则方形截面超高层建筑相比,在正面迎风时,此类截面超高层建筑的力系数平均值要小。
②在刚性模型风洞试验基础上,详细研究了此截面超高层建筑在典型风向角下的层风荷载幅值特征、频域特征以及空间相关性。分析了风力系数平均值、根方差、层风力系数谱和竖向相关性随风向角的变化情况,建立了超高层建筑在各典型风向角下的层风荷载幅值模型、风荷载谱模型和竖向相干函数模型。
③基于概率论的乘法定理,推导了风速风向联合分布模型。结合重庆地区30年日极值风速风向样本,建立了重庆地区风速风向的连续型联合概率密度模型。其中,对风速条件概率密度模型采用多种典型概率分布模型进行了对比分析,发现采用对数正态分布概率模型效果较好。对风向变量的处理采用了修正的风向概率直方图,采用3参数Weibull分布和均匀分布叠加的混合概率密度模型进行了拟合,经检验混合概率密度模型能满足概率相容原理。
④根据典型风向角的风荷载模型,用随机振动分析方法,在频域上求解了超高层建筑在典型风向角下的位移响应,并与时域计算结果进行对比,验证了荷载模型的准确性。超高层建筑在某些非0风向角的响应大于正面迎风工况下的响应,验证了此类截面超高层建筑按传统设计方法仅考虑正面迎风工况是不够的。最后讨论了建筑动力特性和风场参数变化对响应比的影响,其中建筑基阶周期的影响较大。
⑤根据风速风向联合分布模型计算了各风向100年一遇基本风速,结合超高层建筑典型风向角的响应比,分析了超高层建筑在不同朝向下各风向的响应风向系数,并取最大的响应风向系数反向推导了此朝向下建筑按正面迎风计算的等效基本风速,由此得出了各响应的基本风速风向因子。最后在风向因子中考虑了周围建筑的干扰效应,计算了超高层建筑在确定朝向下的基本风速综合风向因子。
For the super tall building, it is general realized that the wind-induced response of the building is the largest response when the maximum wind which is not considered with wind angle load on. The response is smaller when the building suffers the other wind direction wind, so it is generally analyzed only when the high-rise building faces the wind condition and the wind speed is the maximum wind which does not consider the role of wind direction. The design under this condition is considered safe. Because the weak axis direct of the building and the maximum wind speed direct may not coincide, and the frequency probability of the wind in this direct is not the greatest, to test the previous idea this article on the one hand, on the other hand in order to optimized design with more information of the wind speed and wind angle, this article research the response of a high-rise building in a different wind direction carefully by means of wind tunnel tests. Combined with the data of the extreme wind speed sample at Chongqing of 30 years, the wind direct factors of the basic wind speed for the different response are derived into account the wind direction and a comprehensive model of the wind factor is proposed considering the Interference factor of the surrounding buildings.
In this paper, some works has been studied as follows:
①By means of the rigid model wind tunnel test of Super Tall buildings, the amplitude characteristics, frequency domain characteristics and correlation of the wind pressure of the Super Tall Building under the typical wind direction is analyzed in order to have a comprehensive understanding of wind pressure characteristics.
②based on the rigid model wind tunnel test of Super Tall buildings, the layer wind force coefficient amplitude characteristics, frequency characteristics and spatial correlation of Super Tall Building with typical wind direction is detailed studied. The change of the mean value, the root variance, the spectrum and the vertical correlation of the wind force coefficient with the height of the layer and the wind direction is discussed in detail and the mathematical model of the layer wind load of the super tall building is established.
③Based on the multiplication theorem of probability theory, the joint distribution of wind speed and direction model has been acquired. Basis on the sample data of extreme wind speed and direction of Chongqing for 30 years, the joint distribution of wind speed and direction model of the Chongqing region is studied and a joint probability density function model of the wind speed and direction is established. Varieties of typical probability distribution models for Conditional probability density model of the wind speed are compared and it can be found that the lognormal probability model is better. For the wind direction, a modified probability histogram is used and the mixed probability density model composed by 3 parameter Weibull distribution and uniform were used to fit. It can be found that the mixed probability model can meet the probability of compatibility principles.
④According to the established wind loads mathematical model, using random vibration analysis, the pulsating response of the Super Tall Building in typical wind direction is calculated in the frequency domain. Associate with the mean response, the total response is obtained. The Response Ratio in typical wind direction can be calculated through comparing the response of the super tall building in typical wind direction with the response when the weak axis direct of the building and the maximum wind speed direct coincide. The frequency-domain results are the same as the time-domain results, which in turn verified the validity of the above load model. The Response Ratio at some non-0 attack angle is greater than zero which demonstrates that considering this condition is necessary. Finally, the effect of the dynamic characteristics of the building and wind field parameters on the Response Ratio is discussed in detail, and the conclusion can be made that the effect of the building height is large and the other parameters effect can be ignored.
⑤According to the joint probability density function mode of wind speed and direction, the basic wind speed of each wind angle in 100 years is calculated. It is found that the maximum wind speed of each wind angle in 100 years and the basic wind speed without considering the wind angle is basically the same, which verify the effective of the sampling and the reasonable of the method. Then the basic wind speed ratio can be obtained. Associate with the Response Ratio, the Response Wind Angle Coefficient of the super tall building and the equivalent basic wind speed under the conservative directions can be calculated, and then the Direction Factors of the basic wind speed for the different response can be obtained. Finally, consider the impact of surrounding buildings, the Composite Direction Factors combine with the Interference Factor can be obtained, which can be used for the sophisticated analysis and design of the super tall building.
本文以重庆农村商业银行大厦实际工程为例,通过风洞试验系统的研究了超高层建筑在典型风向角下的风荷载;然后基于概率论的乘法定理,推导了风速风向联合分布模型;再结合风速风向数据,建立了重庆地区风速风向的连续型联合概率密度模型,同时给出了基于重现期的考虑风速风向联合分布的各风向基本风速;最后结合风振响应和各风向基本风速,提出了可供设计参考的各响应基本风速风向因子。基于此,本文主要开展了以下几个方面的工作:
①通过超高层建筑的刚性模型风洞试验,研究了在典型风向角下角部凹角方形截面超高层建筑的表面风压幅值特性、频域特性以及相关性。与一般规则方形截面超高层建筑相比,在正面迎风时,此类截面超高层建筑的力系数平均值要小。
②在刚性模型风洞试验基础上,详细研究了此截面超高层建筑在典型风向角下的层风荷载幅值特征、频域特征以及空间相关性。分析了风力系数平均值、根方差、层风力系数谱和竖向相关性随风向角的变化情况,建立了超高层建筑在各典型风向角下的层风荷载幅值模型、风荷载谱模型和竖向相干函数模型。
③基于概率论的乘法定理,推导了风速风向联合分布模型。结合重庆地区30年日极值风速风向样本,建立了重庆地区风速风向的连续型联合概率密度模型。其中,对风速条件概率密度模型采用多种典型概率分布模型进行了对比分析,发现采用对数正态分布概率模型效果较好。对风向变量的处理采用了修正的风向概率直方图,采用3参数Weibull分布和均匀分布叠加的混合概率密度模型进行了拟合,经检验混合概率密度模型能满足概率相容原理。
④根据典型风向角的风荷载模型,用随机振动分析方法,在频域上求解了超高层建筑在典型风向角下的位移响应,并与时域计算结果进行对比,验证了荷载模型的准确性。超高层建筑在某些非0风向角的响应大于正面迎风工况下的响应,验证了此类截面超高层建筑按传统设计方法仅考虑正面迎风工况是不够的。最后讨论了建筑动力特性和风场参数变化对响应比的影响,其中建筑基阶周期的影响较大。
⑤根据风速风向联合分布模型计算了各风向100年一遇基本风速,结合超高层建筑典型风向角的响应比,分析了超高层建筑在不同朝向下各风向的响应风向系数,并取最大的响应风向系数反向推导了此朝向下建筑按正面迎风计算的等效基本风速,由此得出了各响应的基本风速风向因子。最后在风向因子中考虑了周围建筑的干扰效应,计算了超高层建筑在确定朝向下的基本风速综合风向因子。
For the super tall building, it is general realized that the wind-induced response of the building is the largest response when the maximum wind which is not considered with wind angle load on. The response is smaller when the building suffers the other wind direction wind, so it is generally analyzed only when the high-rise building faces the wind condition and the wind speed is the maximum wind which does not consider the role of wind direction. The design under this condition is considered safe. Because the weak axis direct of the building and the maximum wind speed direct may not coincide, and the frequency probability of the wind in this direct is not the greatest, to test the previous idea this article on the one hand, on the other hand in order to optimized design with more information of the wind speed and wind angle, this article research the response of a high-rise building in a different wind direction carefully by means of wind tunnel tests. Combined with the data of the extreme wind speed sample at Chongqing of 30 years, the wind direct factors of the basic wind speed for the different response are derived into account the wind direction and a comprehensive model of the wind factor is proposed considering the Interference factor of the surrounding buildings.
In this paper, some works has been studied as follows:
①By means of the rigid model wind tunnel test of Super Tall buildings, the amplitude characteristics, frequency domain characteristics and correlation of the wind pressure of the Super Tall Building under the typical wind direction is analyzed in order to have a comprehensive understanding of wind pressure characteristics.
②based on the rigid model wind tunnel test of Super Tall buildings, the layer wind force coefficient amplitude characteristics, frequency characteristics and spatial correlation of Super Tall Building with typical wind direction is detailed studied. The change of the mean value, the root variance, the spectrum and the vertical correlation of the wind force coefficient with the height of the layer and the wind direction is discussed in detail and the mathematical model of the layer wind load of the super tall building is established.
③Based on the multiplication theorem of probability theory, the joint distribution of wind speed and direction model has been acquired. Basis on the sample data of extreme wind speed and direction of Chongqing for 30 years, the joint distribution of wind speed and direction model of the Chongqing region is studied and a joint probability density function model of the wind speed and direction is established. Varieties of typical probability distribution models for Conditional probability density model of the wind speed are compared and it can be found that the lognormal probability model is better. For the wind direction, a modified probability histogram is used and the mixed probability density model composed by 3 parameter Weibull distribution and uniform were used to fit. It can be found that the mixed probability model can meet the probability of compatibility principles.
④According to the established wind loads mathematical model, using random vibration analysis, the pulsating response of the Super Tall Building in typical wind direction is calculated in the frequency domain. Associate with the mean response, the total response is obtained. The Response Ratio in typical wind direction can be calculated through comparing the response of the super tall building in typical wind direction with the response when the weak axis direct of the building and the maximum wind speed direct coincide. The frequency-domain results are the same as the time-domain results, which in turn verified the validity of the above load model. The Response Ratio at some non-0 attack angle is greater than zero which demonstrates that considering this condition is necessary. Finally, the effect of the dynamic characteristics of the building and wind field parameters on the Response Ratio is discussed in detail, and the conclusion can be made that the effect of the building height is large and the other parameters effect can be ignored.
⑤According to the joint probability density function mode of wind speed and direction, the basic wind speed of each wind angle in 100 years is calculated. It is found that the maximum wind speed of each wind angle in 100 years and the basic wind speed without considering the wind angle is basically the same, which verify the effective of the sampling and the reasonable of the method. Then the basic wind speed ratio can be obtained. Associate with the Response Ratio, the Response Wind Angle Coefficient of the super tall building and the equivalent basic wind speed under the conservative directions can be calculated, and then the Direction Factors of the basic wind speed for the different response can be obtained. Finally, consider the impact of surrounding buildings, the Composite Direction Factors combine with the Interference Factor can be obtained, which can be used for the sophisticated analysis and design of the super tall building.
引文
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