Research on Equivalent Static Load of High-Rise Buildings Based on Wind-Induced Responses
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摘要: 为研究风荷载作用下高层建筑动力响应对其顺风向等效静力风荷载的影响，基于结构风致响应动力学理论、脉动风速功率谱密度函数与相干函数的维纳辛钦关系及脉动风速准定常关系，采用随机振动振型分解方法对高层建筑的风致响应进行了研究. 首先，对高层建筑的平均风响应、背景风响应和共振风响应进行了理论分析，并推导出了沿结构高度分布的高层建筑顺风向等效静力风荷载理论计算公式；其次，通过对理论公式中各参数对计算结果的影响进行分析，提出了便于实际应用的高层建筑顺风向等效静力风荷载简化计算方法；最后，设计了4个典型高层建筑算例模型，并与阵风荷载因子法（gust load factor method，GLF）和惯性风荷载法（inertial wind load method，IWL ）进行对比，研究了本文方法的可靠性和有效性. 研究结果表明：当结构高度小于250 m时，3种方法所计算出的分布风力、剪力响应和弯矩响应偏差要大一些，GLF法计算结果最大，IWL法的计算结果最小，本文方法介于二者之间；当结构高度大于350 m时，分布风力的偏差在15%以内，对于剪力响应和弯矩响应的偏差在10%以内；本文方法与IWL法在剪力响应方面的差异率在–1%～18%之间，与GLF法的差异率在–12%～5%之间；本文方法与IWL法在弯矩响应方面的差异率在–6%～10%之间，与GLF法的差异率在–16%～5%之间.Abstract: To study the influence of dynamic response of a high-rise building under wind loads on the along-wind equivalent static wind load, the wind-induced response of high-rise buildings was studied using the random vibration mode decomposition method. This method is based on the wind-induced response dynamics theory, the relationship between the pulsating wind power spectral density function and the coherent function, and the quasi-stationary relationship of the pulsating wind speed. First, theoretical analyses of the average wind response, background wind response, and resonance wind response of high-rise buildings were performed, and the theoretical calculation formula of the along-wind equivalent static wind load of high-rise buildings along its height was deduced. Second, the influence of each parameter on the calculation result in the theoretical formula is analysed, and a simplified calculation method for the along-wind equivalent static wind load of the high-rise building is presented, which is convenient for practical applications. Finally, four typical example models of high-rise buildings are designed and compared with the gust load factor（GLF）and inertial wind load（IWL）methods, and the feasibility and effectiveness of our method are investigated. The results demonstrate that when the height of the structure is less than 250 m, the deviations of the distributed wind force, shear force response, and bending moment response calculated by the three methods are large, the calculation result by the GLF method is the largest, and the calculation result by the IWL method is the smallest; the method proposed in this paper is between the two; when the structural height is greater than 350 m, the deviation of the distributed wind force is within 15%, and the deviation between the shear response and the bending moment response is within 10%; the difference between our proposed method and the IWL method in that the shear response is between –1% and 18% and that the difference between our method and the GLF method is between –12% and 5%; when our proposed method and the IWL method are applied to the moment response, the difference rate is between –6% and 10%, and the difference with the GLF method is between –16% and 5%.
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图 1 分布风力、剪力响应和弯矩响应计算结果
Figure 1. Calculation results of distribution wind force，shear response and moment response
图 2 分布风力、剪力响应和弯矩响应偏差比
Figure 2. Deviation ratios of distribution wind force，shear response and moment response
图 4 本文方法计算弯矩响应的差异率
Figure 4. Difference rate of bending moment response to use this method
表 1 算例模型参数
Table 1. Example model parameters
算例
模型高度/m 迎风面
宽度/m基频
/Hz阻尼比 基本风
压/kPa地貌 EM1 100 35 1.31 0.05 0.8 D EM2 250 45 1.12 0.04 0.65 C EM3 350 55 1.01 0.03 0.45 B EM4 500 70 0.96 0.02 0.30 A 
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