考虑滑移效应的钢—混凝土组合梁桥力学行为研究
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摘要
钢一混凝土组合梁是通过抗剪连接件将钢梁与混凝土翼板组合而共同工作的一种组合构件，它兼有钢结构和混凝土结构的优点。尽管钢—混凝土组合梁在国内外都有比较广泛的研究，然而在设计理论及实际应用中仍然存在着许多技术难题。本文以组合梁的界面滑移效应为研究对象，提出了考虑界面滑移效应的新方法，并深入研究了滑移效应对结构力学行为的影响。完成的主要工作和取得的成果如下：
（1）借鉴桩基计算的m法，把栓钉在混凝土中的力学行为，类比为桩基在土体中的力学行为，并以此建立了栓钉在混凝土中的变形微分方程，利用幂级数法求解了该微分方程的解析解，理论推导了一种计算栓钉抗滑移刚度的计算公式。在此基础上，提出了一种新的栓钉荷载—滑移本构关系。
（2）根据Goodman弹性夹层假设及弹性体变形理论，建立了考虑栓钉滑移效应的经典变分方程，遵循最小势能原理，导出简支和悬臂组合梁的挠度和滑移控制微分方程，利用边界条件得到了在均布荷载和集中荷载作用下，简支和悬臂组合梁考虑界面滑移效应的挠度计算的解析表达式。
（3）根据组合梁的构造和受力特点，提出了一种适合于组合梁计算分析的新型板梁单元。该方法通过化整为零，将组合梁离散成混凝土、钢梁和连接件三种子单元，分别推导了三种子单元的刚度矩阵；然后通过单元自由度与组合单元自由度的转化矩阵，集零为整，将子单元组拼成组合单元。并利用ANSYS软件的UPFs平台二次开发技术，实现了用户单元，为组合梁的有限元分析开辟了一条高效、便捷之路，可用于工程实践。
（4）以一座三跨预应力钢—混凝土组合梁桥为背景设计了一组1:2的节段模型静力试验和1:8的节段模型徐变试验。试验结果表明：①、普通剪力钉模型和槽钢剪力件模型的破坏形式一致，但槽钢剪力件模型的竖向破坏荷载略大。②、单纯水平加载工况下本文理论计算滑移曲线与实测滑移曲线在数值上存在一定误差，但总体趋势和规律吻合较好。③、收缩徐变模型试验结果表明，按本文方法计算得到的长期挠度随时间的变化曲线与实测长期挠度曲线趋势一致，误差较小；且采用本文方法对收缩徐变效应进行计算，应力和挠度的计算结果与实测结果均吻合较好。验证了本文方法的正确性。
（5）结合广州鹤洞大桥和九江大桥修复工程，采用本文提出的板梁有限元法和剪力连接件粘结滑移本构关系，对钢—混凝土组合梁在常规荷载作用下的力学行为和极限承载能力进行深入研究，得到了界面滑移刚度对结构受力性能的影响。
Composite beam, which comprises a steel girder and a reinforced concrete slabinterconnected by shear connectors, has both advantages of steel structure and concretestructure. Although it has been widely investigated at home and abroad, many problems stillneed to be worked over in design and in practice. In this thesis, studies have been carried onabout the relative tangential displacement (slip) between the steel girder and the concrete slab.New methods have been proposed and been used to analysis the effects of the slip onmechanical behavior of the composite bridge. The main research works are as follows:
According to the mechanical behavior, shear connector has been considered as a Winklerfoundation with an assumption of the linear relationship between the stiffness and the depth.A displacement differential equation has been set up and solved by the power seriesexpansion. An analytic method for calculating the slip stiffness of shear connector has beenproposed, and a constitutive relation between load and slip has also been established.
The differential governing equations of composite beam considering the slip effect hasbeen present based on minimum potential energy and Goodman's hypothesis. Freelysupported composite beam under uniform load concentrated load has been studiedrespectively, and the deflection expressions are obtained.
A structural modeling methodology was presented. A segment of the composite beamwas divided into several parts, which include concrete slabs, steel girders and shearconnectors. Each part is regarded as a sub-element. The stiffness matrixes of everysub-element were obtained via the variation method respectively and then assembled into asuper-element with the compatibility of deformation. Through the secondary development ofUPFs, the user element is realized on the finite element software ANSYS.
Two scale model tests have been designed to verify the methods proposed in this thesis.A three spans composite beam bridge was taken as the archetype. The first test included twocomposite beam segment models with the same scale of1:2and aimed at the stressdistribution and the relative tangential displacement of the composite beam with the differentkind of connectors. Common shear connectors were used in one model while U-steelconnectors were used in the other. Two observations as follows were found:(1) two modelsshare the same collapse mode but are different in the value of the vertical collapse load, themodel with U-steel connectors has bigger the vertical collapse load than the other;(2) whenthe model borne the horizontal force, the test slip curves and calculating curves whichobtained by using the method proposed in this thesis have the same tendency although they have some different values. After proposing a method for calculating the shrinkage and creepeffect of composite beam, The second test has been carried on to validate it based on a scalemodel which is1:8of the archetype. It was found from the test that the method is suitable forthe composite beam.
Based on the achievements in this thesis, the constitutive relation between load and slipand the super-element of composite beam, Hedong bridge and Jiujiang new bridge werestudied in detail to uncover the effect of slip stiffness on mechanical behavior and ultimatebearing capacity under the common load.
（1）借鉴桩基计算的m法，把栓钉在混凝土中的力学行为，类比为桩基在土体中的力学行为，并以此建立了栓钉在混凝土中的变形微分方程，利用幂级数法求解了该微分方程的解析解，理论推导了一种计算栓钉抗滑移刚度的计算公式。在此基础上，提出了一种新的栓钉荷载—滑移本构关系。
（2）根据Goodman弹性夹层假设及弹性体变形理论，建立了考虑栓钉滑移效应的经典变分方程，遵循最小势能原理，导出简支和悬臂组合梁的挠度和滑移控制微分方程，利用边界条件得到了在均布荷载和集中荷载作用下，简支和悬臂组合梁考虑界面滑移效应的挠度计算的解析表达式。
（3）根据组合梁的构造和受力特点，提出了一种适合于组合梁计算分析的新型板梁单元。该方法通过化整为零，将组合梁离散成混凝土、钢梁和连接件三种子单元，分别推导了三种子单元的刚度矩阵；然后通过单元自由度与组合单元自由度的转化矩阵，集零为整，将子单元组拼成组合单元。并利用ANSYS软件的UPFs平台二次开发技术，实现了用户单元，为组合梁的有限元分析开辟了一条高效、便捷之路，可用于工程实践。
（4）以一座三跨预应力钢—混凝土组合梁桥为背景设计了一组1:2的节段模型静力试验和1:8的节段模型徐变试验。试验结果表明：①、普通剪力钉模型和槽钢剪力件模型的破坏形式一致，但槽钢剪力件模型的竖向破坏荷载略大。②、单纯水平加载工况下本文理论计算滑移曲线与实测滑移曲线在数值上存在一定误差，但总体趋势和规律吻合较好。③、收缩徐变模型试验结果表明，按本文方法计算得到的长期挠度随时间的变化曲线与实测长期挠度曲线趋势一致，误差较小；且采用本文方法对收缩徐变效应进行计算，应力和挠度的计算结果与实测结果均吻合较好。验证了本文方法的正确性。
（5）结合广州鹤洞大桥和九江大桥修复工程，采用本文提出的板梁有限元法和剪力连接件粘结滑移本构关系，对钢—混凝土组合梁在常规荷载作用下的力学行为和极限承载能力进行深入研究，得到了界面滑移刚度对结构受力性能的影响。
Composite beam, which comprises a steel girder and a reinforced concrete slabinterconnected by shear connectors, has both advantages of steel structure and concretestructure. Although it has been widely investigated at home and abroad, many problems stillneed to be worked over in design and in practice. In this thesis, studies have been carried onabout the relative tangential displacement (slip) between the steel girder and the concrete slab.New methods have been proposed and been used to analysis the effects of the slip onmechanical behavior of the composite bridge. The main research works are as follows:
According to the mechanical behavior, shear connector has been considered as a Winklerfoundation with an assumption of the linear relationship between the stiffness and the depth.A displacement differential equation has been set up and solved by the power seriesexpansion. An analytic method for calculating the slip stiffness of shear connector has beenproposed, and a constitutive relation between load and slip has also been established.
The differential governing equations of composite beam considering the slip effect hasbeen present based on minimum potential energy and Goodman's hypothesis. Freelysupported composite beam under uniform load concentrated load has been studiedrespectively, and the deflection expressions are obtained.
A structural modeling methodology was presented. A segment of the composite beamwas divided into several parts, which include concrete slabs, steel girders and shearconnectors. Each part is regarded as a sub-element. The stiffness matrixes of everysub-element were obtained via the variation method respectively and then assembled into asuper-element with the compatibility of deformation. Through the secondary development ofUPFs, the user element is realized on the finite element software ANSYS.
Two scale model tests have been designed to verify the methods proposed in this thesis.A three spans composite beam bridge was taken as the archetype. The first test included twocomposite beam segment models with the same scale of1:2and aimed at the stressdistribution and the relative tangential displacement of the composite beam with the differentkind of connectors. Common shear connectors were used in one model while U-steelconnectors were used in the other. Two observations as follows were found:(1) two modelsshare the same collapse mode but are different in the value of the vertical collapse load, themodel with U-steel connectors has bigger the vertical collapse load than the other;(2) whenthe model borne the horizontal force, the test slip curves and calculating curves whichobtained by using the method proposed in this thesis have the same tendency although they have some different values. After proposing a method for calculating the shrinkage and creepeffect of composite beam, The second test has been carried on to validate it based on a scalemodel which is1:8of the archetype. It was found from the test that the method is suitable forthe composite beam.
Based on the achievements in this thesis, the constitutive relation between load and slipand the super-element of composite beam, Hedong bridge and Jiujiang new bridge werestudied in detail to uncover the effect of slip stiffness on mechanical behavior and ultimatebearing capacity under the common load.
引文
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