结构设计中如何全面考虑P-Δ效应
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（1 北京筑信达工程咨询有限公司， 北京 100043； 2 CSI公司， 伯克利 94704）［摘要］从P-Δ效应的定义入手，分析了几何刚度和线性屈曲分析的力学概念，指出这几个概念之间存在本质的联系，同时分析了建筑结构中P-Δ贡献与P-δ贡献。在介绍一阶方法、二阶方法和直接法三种方法之后，指出国内外通常考虑P-Δ效应的二阶方法是：1）在结构分析中考虑P-Δ贡献；2）在构件设计中考虑P-δ贡献。结合ETABS2013软件，提出了具体的实现方法，特别是提出建议采用线性屈曲因子作为刚重比控制条件的度量指标，可以统一和简化对刚重比的计算，还介绍了AISC针对P-Δ效应计算的基准测试问题。［关键词］P-Δ效应; 几何刚度; 线性屈曲分析; ETABS; 刚重比; 屈曲因子中图分类号：TU318，TU973 文献标识码：A 文章编号：1002-848X(2014)05-0078-05Methods to consider full P-Δ effects in structural designLi Chushu1, Li Li1, Liu Chunming2, Wei Xuhao1(1 Beijing Construction Information Solution Engineering Consulting, Beijing 100043, China; 2 Computers and Structures Inc., Berkeley 94704, USA)Abstract: Geometric stiffness and linear buckling analysis were analyzed based on the concepts for P-Δ effects, which came to the conclusion that these concepts have relationships in nature. Contributions of P-Δ and P-δ were analyzed as well. First-order method, second-order method and direct method were introduced and the common methods considering P-Δ effects in the second-order method at home and abroad were introduced as two steps, including: 1) considering P-Δ contribution in analysis phrase; 2) considering P-δ contribution in member design phrase. With ETABS2013 software, the concrete realization method was put forward. It was especially suggested that linear buckling factor can be used as the control conditions of stiffness to gravity ratio, so the computation of stiffness to gravity ratio can be unified and simplified. The benchmark problems proposed by AISC on P-Δ effects calculation were introduced as well.Keywords: P-Δ effect; geometric stiffness; linear buckling analysis; ETABS; stiffness to gravity ratio; buckling factor作者简介：李楚舒，博士，教授级高级工程师，Email：lics@cisec.cn。参考文献［1］CSI分析参考手册[M]. Computers and Structures Inc., 北京筑信达工程咨询有限公司, 2013.[2]EDWARD L WILSON. Static and dynamic analysis of structures[M]. 4th ed. Berkeley: Computers and Structures Inc., 2010.[3]POWELL G H. Modeling for structural analysis: behavior and basics [M]. Berkeley: Computers and Structures Inc., 2010.[4]扶长生, 周立浪, 张小勇. 长周期高层钢筋混凝土建筑的P-Δ效应与稳定设计[J]. 建筑结构, 2014,44（2）：1-7.[5]JGJ 3—2010 高层建筑混凝土结构技术规程[S]. 北京：中国建筑工业出版社，2011.[6]GB 50010—2010 混凝土结构设计规范[S]. 北京：中国建筑工业出版社，2011.[7]AISC 360-10 Specification for structural steel buildings [S].American Institute of Steel Construction, 2010: 276-277.
