倾斜与P-Δ效应对高层建筑结构响应耦合影响

COUPLED EFFECTS OF INCLINATION AND P-Δ EFFECT ON STRUCTURAL RESPONSE OF HIGH-RISE BUILDINGS

  • 摘要: 高层建筑结构倾斜会增大结构P-Δ效应,从而增大结构的变形和内力,对结构安全、使用功能和经济价值带来诸多不利影响。我国规范均对建筑倾斜率有严格的限值要求,其中《建筑地基基础设计规范》(GB 50007−2011)规定,对于高度大于100 m的多层及高层建筑,其整体倾斜率不大于0.2%。该文针对倾斜和P-Δ效应耦合作用特点,并采用悬臂欧拉梁理论对高层结构变形和内力展开研究,基于竖向集中荷载模型并结合均布荷载模型结果进行修正,得出考虑倾斜与P-Δ效应耦合时变形及内力增幅的修正计算公式。计算结果表明,倾斜率、刚重比以及剪重比是影响结构变形和内力的三项参数,内力增幅计算结果要小于变形增幅。从控制变形增幅的角度出发,基于修正计算公式给出了变形增幅在5%以内以及10%以内时的倾斜率限值,限值计算结果表明对于剪重比在3%以下的常见高层结构,变形增幅控制在5%以内时倾斜率最大不得超过0.10%,变形增幅控制在10%以内时倾斜率最大不得超过0.23%。

     

    Abstract: The inclination of high-rise building structures can increase the structural P-Δ effect, thereby increasing the deformation and internal forces of the structure, which has many adverse impacts on structural safety, serviceability, and economic value. Chinese building codes impose strict limits on building inclination rates. Specifically, the Code for Design of Building Foundation (GB 50007−2011) stipulates that for multi-story and high-rise buildings exceeding 100 meters in height, the overall inclination rate shall not exceed 0.2%. Focusing on the coupling characteristics between inclination and the P-Δ effect, this study employs the cantilever Euler beam theory to investigate the deformation and internal forces of high-rise structures. Based on a vertical concentrated load model and incorporating the corrections derived from a uniformly distributed load model, a modified calculation formula is proposed to quantify the amplification of deformation and internal forces when considering the coupling between inclination and P-Δ effect. The calculation results indicate that the inclination rate, stiffness-to-weight ratio, and shear-to-weight ratio are three key parameters influencing structural deformation and internal forces. The amplification of internal forces is found to be smaller than that of deformation. From the perspective of controlling deformation amplification, this study provides inclination rate limits for deformation amplifications within 5% and 10%, based on the proposed modified calculation formula. The results indicate that for common high-rise structures with a shear-to-weight ratio below 3%, the maximum inclination rate should not exceed 0.10% when the deformation amplification is controlled within 5%, and should not exceed 0.23% when the deformation amplification is controlled within 10%.

     

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