钢筋混凝土结构的二阶效应及非线性分析
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摘要
钢筋混凝土偏心受压构件的二阶效应一直是钢筋混凝土结构研究的重要内容,虽然国内外学者已进行了大量的研究,并取得了很多成果,且一些成果已应用于结构设计规范中,但由于问题的复杂性,很多方面还不够完善,还需要进行深入的研究。本文对钢筋混凝土轴心受压构件的非线性稳定性、偏心受压构件的二阶效应进行了研究,同时研究了钢筋混凝土结构的非线性分析方法,主要内容包括：
(1)对一般支撑和约束条件的构件进行分析,得出构件计算长度系数的计算公式及一些特定情况的简化计算公式。
(2)从非线性稳定理论出发对钢筋混凝土轴心受压构件的承载力进行了研究,给出了混凝土构件临界状态时纵向弯曲系数计算公式。研究表明,徐变对轴心受压构件的非线性稳定性有很大影响。
(3)通过几何非线性和材料非线性分析并考虑钢筋混凝土的拉伸硬化效应,对无侧移钢筋混凝土细长柱的荷载-变形特性进行了研究,提出附加变形、抗弯刚度及等效弯矩系数的计算公式。与62组等弯矩受压构件和33组不等弯矩受压构件试验结果的对比表明,本文等弯矩柱附加变形公式的计算结果好于GB500102010规范公式的计算结果,等效弯矩系数公式计算结果好于美国规范ACI318-08和欧洲规范EN1992-1-1：2004公式,与我国规范GB50010—2010相当。
(4)考虑二阶效应的计算方法,按我国规范、美国规范和欧洲规范计算了钢筋混凝土偏心受压构件和构件截面的轴力-弯矩曲线。分析表明,不考虑偏心受压构件的二阶效应时,按我国规范和欧洲规范计算的截面承载力比较接近,由于美国规范考虑了强度折减系数的影响,其计算的承载力比较小；计算考虑二阶效应的构件承载力时,我国规范的规定比较简单,美国和欧洲规范的规定较详细,均考虑了端部弯矩不同。
(5)考虑材料非线性和几何非线性对钢筋混凝土框架进行了分析。几何非线性包括了框架的P-△效应和构件的P-δ效应,分析中考虑了钢筋混凝土的拉伸硬化效应。与试验结果对比表明：本文方法计算结果与试验结果吻合较好。
The analysis of second-order effect is the most important issue for reinforced concrete members in structural design. So far, lots of researches have been made progress, and even many achievements have been adopted in the standards, but because of the complexity of the issue, there remains a series of important problem needed to be studied.
In this paper, a further research about the nonlinear stability of axial compression member, the second-order effect of eccentric compression member and frame is made based on the material and geometrical nonlinear characteristic. The detailed works listed as follows:
(1) Based on numerical analysis, the formulas for effective length of member subjected to different constraint and bearing are established.
(2) The bearing capacity of uniaxial compressive reinforced concrete members is studied from nonlinear theory's viewpoint, and longitudinal bending coefficient in concrete critical state is obtained. It is indicated that the concrete creep has a significant effect on the bearing capacity of uniaxial compressed members.
(3) Based on the material and geometrical nonlinear analysis, and by considering the tension stiffening of concrete, the load-deflection characteristic of non-sway reinforced concrete columns is studied, and the expressions for the additional deflection of columns with symmetric eccentricity at ends and equivalent uniform moment diagram factor of columns with asymmetric eccentricities at ends are provided. Comparison with the test data from different source shows that it is better than that in the Code for design of concrete structures.
(4) By taking second-order effects into account, the axial force and moment interaction diagrams are calculated according to Chinese code GB50010—2010, American code ACI318-08and European code EN1992-1-1:2004. Comparison shows that, without considering the second-order effect, the result for bearing capacity of member calculated from Chinese code is close to that of European code, but greater than that of American code, because in American code, the strength reduction factor is considered. While the second-order effect is considered in the analysis, the specification of Chinese code for bearing capacity is much simpler than that of American code and European code.
(5) By considering the material and geometrical nonlinear characteristic, the reinforced concrete frames are analyzed. While in the geometrical analysis, the P-△effect and P-δ effect are taken into account. Comparison with test data shows that the calculated method derived from the paper has good precision and accuracy.
(1)对一般支撑和约束条件的构件进行分析,得出构件计算长度系数的计算公式及一些特定情况的简化计算公式。
(2)从非线性稳定理论出发对钢筋混凝土轴心受压构件的承载力进行了研究,给出了混凝土构件临界状态时纵向弯曲系数计算公式。研究表明,徐变对轴心受压构件的非线性稳定性有很大影响。
(3)通过几何非线性和材料非线性分析并考虑钢筋混凝土的拉伸硬化效应,对无侧移钢筋混凝土细长柱的荷载-变形特性进行了研究,提出附加变形、抗弯刚度及等效弯矩系数的计算公式。与62组等弯矩受压构件和33组不等弯矩受压构件试验结果的对比表明,本文等弯矩柱附加变形公式的计算结果好于GB500102010规范公式的计算结果,等效弯矩系数公式计算结果好于美国规范ACI318-08和欧洲规范EN1992-1-1：2004公式,与我国规范GB50010—2010相当。
(4)考虑二阶效应的计算方法,按我国规范、美国规范和欧洲规范计算了钢筋混凝土偏心受压构件和构件截面的轴力-弯矩曲线。分析表明,不考虑偏心受压构件的二阶效应时,按我国规范和欧洲规范计算的截面承载力比较接近,由于美国规范考虑了强度折减系数的影响,其计算的承载力比较小；计算考虑二阶效应的构件承载力时,我国规范的规定比较简单,美国和欧洲规范的规定较详细,均考虑了端部弯矩不同。
(5)考虑材料非线性和几何非线性对钢筋混凝土框架进行了分析。几何非线性包括了框架的P-△效应和构件的P-δ效应,分析中考虑了钢筋混凝土的拉伸硬化效应。与试验结果对比表明：本文方法计算结果与试验结果吻合较好。
The analysis of second-order effect is the most important issue for reinforced concrete members in structural design. So far, lots of researches have been made progress, and even many achievements have been adopted in the standards, but because of the complexity of the issue, there remains a series of important problem needed to be studied.
In this paper, a further research about the nonlinear stability of axial compression member, the second-order effect of eccentric compression member and frame is made based on the material and geometrical nonlinear characteristic. The detailed works listed as follows:
(1) Based on numerical analysis, the formulas for effective length of member subjected to different constraint and bearing are established.
(2) The bearing capacity of uniaxial compressive reinforced concrete members is studied from nonlinear theory's viewpoint, and longitudinal bending coefficient in concrete critical state is obtained. It is indicated that the concrete creep has a significant effect on the bearing capacity of uniaxial compressed members.
(3) Based on the material and geometrical nonlinear analysis, and by considering the tension stiffening of concrete, the load-deflection characteristic of non-sway reinforced concrete columns is studied, and the expressions for the additional deflection of columns with symmetric eccentricity at ends and equivalent uniform moment diagram factor of columns with asymmetric eccentricities at ends are provided. Comparison with the test data from different source shows that it is better than that in the Code for design of concrete structures.
(4) By taking second-order effects into account, the axial force and moment interaction diagrams are calculated according to Chinese code GB50010—2010, American code ACI318-08and European code EN1992-1-1:2004. Comparison shows that, without considering the second-order effect, the result for bearing capacity of member calculated from Chinese code is close to that of European code, but greater than that of American code, because in American code, the strength reduction factor is considered. While the second-order effect is considered in the analysis, the specification of Chinese code for bearing capacity is much simpler than that of American code and European code.
(5) By considering the material and geometrical nonlinear characteristic, the reinforced concrete frames are analyzed. While in the geometrical analysis, the P-△effect and P-δ effect are taken into account. Comparison with test data shows that the calculated method derived from the paper has good precision and accuracy.
引文
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