钢—混凝土结合梁桥动力性能及损伤识别的理论分析与模型试验研究
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摘要
钢—混凝土结合梁桥是继钢结构桥梁与混凝土桥梁之后兴起的一种新型结构,它通过抗剪连接件将钢梁和混凝土板连接在一起,使二者形成组合作用,共同受力,充分发挥钢(抗拉)和混凝土(抗压)两种不同材料的特点。正是由于这种优点,钢—混凝土结合梁在公路、市政、轨道交通和铁路桥梁领域应用日益广泛。虽然钢—混凝土结合梁具有上述明显的优势,但由于材料和结构本身的限制,也不可避免地存在着一些问题,如负弯矩区混凝土容易开裂,收缩和徐变问题会导致结合梁挠度加大以及混凝土板裂缝,连接性能在长期荷载作用下容易劣化,动力作用下结合梁的受力和滑移机理不明确等问题。本文结合国家重点基础研究发展计划973项目、国家自然科学基金项目以及铁道部科技研究开发计划资助项目,以钢—混凝土结合梁桥为研究对象(文中简称为结合梁桥),通过理论推导、数值分析和模型试验,重点研究结合梁桥的动力行为,对其自振特性、外力荷载激励下的响应、车桥动力相互作用分析和损伤识别进行了深入的研究。主要工作和结论如下：
(1)建立了考虑钢梁与混凝土板之间相对滑移、阻尼的简支直线钢—混凝土结合梁的基本振动方程。运用直接平衡法,考虑了阻尼对结构响应的影响,把钢梁和混凝土板均视作Euler-Bernoulli梁,建立了简支直线钢—混凝土结合梁的基本振动方程,针对一定的边界条件进行求解,重点研究钢梁与混凝土板之间的相对滑移对结合梁桥自振特性的影响,分析其与单一材料梁的区别。在此基础上,得到了结合梁的质量、刚度和阻尼矩阵的正交条件,为下文的车桥动力相互作用分析提供了理论基础。
(2)给出了考虑滑移、简谐荷载共同作用的结合梁挠度通用表达式。通过本文建立的结合梁基本动力理论,得到了集中荷载(或其它形式的荷载)作用下结合梁静挠度的通用级数表达式,通过一定的变换,使其符合级数求和条件；将其相应的Bernoulli函数和Bernoulli数代入,即可得到与静力方法一致的结合梁挠度通用表达式,且能体现滑移引起的附加挠度以及简谐力的影响,为求解结合梁的挠度通用表达式提供了一种思路。
(3)根据结合梁的动力特性,提出了钢—混凝土简支结合梁的“动力刚度折减系数”和“频率折减系数”的概念。通过理论推导,得到了结合梁的动力刚度折减系数的表达式,并与《钢结构设计规范》(GB50017-2003)中的公式进行了比较。对静力刚度折减系数的取值进行了分析,研究了其与动力刚度折减系数的联系和区别及应用的范围。结果表明,在结合梁的动力计算中,不能直接套用静力计算的公式来计算结合梁的等效刚度,否则会引起较大的误差。
(4)建立了钢—混凝土结合梁桥车桥动力相互作用分析模型。考虑铁路桥梁的行车特点、车—桥耦合特征以及结合梁桥的构造特点,对移动荷载作用下结合梁桥的动力响应进行了分析,推导了移动质量、简谐荷载、簧上质量、车辆作用下结合梁的振动方程,并进行了求解,重点分析移动荷载作用下钢梁与混凝土板之间的相对滑移对结合梁桥动力响应的影响。本文的理论分析结果表明,通过本文的结合梁动力理论所得到的结果与试验结果吻合良好,在某些条件下可以从结合梁的动力理论得到集中荷载作用下结合梁的挠度通用表达式。
(5)根据铁路结合梁桥实桥的构造特点,对6片钢—混凝土结合梁进行了动力特性的模型试验研究,其中包括两种连接刚度(完全连接、部分连接),对结合梁的自振特性、模型车辆移动荷载作用下梁的响应、简谐荷载持续作用下钢梁与混凝土板之间的相对滑移规律等进行了重点研究；并预设了6种栓钉损伤工况,针对栓钉连接件发生不同程度损伤时的动力特性进行测试。根据试验现象和结果,与理论分析、数值分析相互验证,进一步深入揭示铁路结合梁桥在静、动力荷载下的受力机理。结果表明结合梁的连接刚度对其动力特性产生重大影响,小范围损伤对其自振特性的影响甚微。
(6)进行了钢—混凝土结合梁桥状态评估与损伤识别研究。针对钢—混凝土结合梁桥的构造特点,基于现有的结构损伤识别方法,对常见的损伤识别方法应用在结合梁损伤识别中的适用性进行了评估,尤其是针对栓钉局部损伤的有效识别方法进行了研究和探讨。分析结合梁的刚度特点,找到了适合于结合梁桥的损伤识别方法,并以某钢—混凝土简支结合试验梁为例,应用曲率模态分析方法,对抗剪连接件进行了损伤识别方法研究。结果表明：由于结合梁栓钉抗剪连接件的存在,结合梁的整体刚度是不连续的,呈阶段性分布；以自振频率和自振模态等整体动力参数为识别指标的损伤识别方法效果并不理想,无法对损伤位置和程度进行量化；对结合梁的前3阶曲率模态进行综合分析,可以很好地识别混凝土板和钢梁之间的栓钉布置情况、栓钉的损伤位置。
本文共有图109幅,表40个,公式259个,参考文献146篇。
The steel-concrete composite beam (short for "composite bridge") bridge, which is composed of steel girder and concrete slab integrated by shear connectors, is a new-type bridge arose after steel and concrete bridges. By combining the advantages of steel (tensile) and concrete (compressive) members, composite bridges are widely applied in highway, urban road, rail transit and railway bridges. However, there are inevitably some obvious problems owing to the material and structure limitation, such as cracking in negative moment regions, bigger deflection and cracks due to concrete shrinkage and creep, connection performance degradation under long duration loads, uncertainty of slip and mechanical behaviors under dynamic loads, etc. In this paper, the dynamic behaviors of composite bridges, including natural vibration characteristics, dynamic responses of external force load excitation, vehicle-bridge interaction dynamic analysis and damage identification are investigated, by theoretical derivation, numerical analysis and model test. The research is sponsored by the State Fundamental Research Funds "973" Program, the National Nature Science Foundation of China and the Scientific Research and Development Projects of Ministry of Railways of China. The main work and conclusions are as follows:
(1) By employing the direct equilibrium method and treating the steel girder and concrete slab as Euler-Bernoulli beams, the fundamental motion equations of simply-supported straight composite bridge are established, considering relative slip at the interface of steel girder and concrete slab, as well the damping, and the equations are solved for certain boundary conditions. The effect of relative slip on the natural vibration characteristics of the composite bridge is analyzed. On this basis, the orthogonality conditions for the mass, stiffness and damping matrices are obtained, which provides a theoretical basis for further vehicle-bridge interaction analysis.
(2) By the established fundamental theory, and considering the relative slip and harmonic load, the general series expressions of composite beam displacement under concentrated forces (or other types) are derived. Then a certain transformation is conducted to meet the summation conditions of the series. By substituting the corresponding Bernoulli functions and Bernoulli numbers to the above expressions, the general displacement expression of simply-supported composite beam is obtained, which is consistent with that derived by static methods, and can reflect the influences of slip and harmonic load, providing an analytical method for solving the displacement of composite beams.
(3) The concepts "dynamic stiffness reduction factor (DSRF)" and "frequency reduction factor (FRF)" are proposed based on the mechanical behaviors of composite beams. The DSRF expression is obtained by theoretical derivation, and compared with the expression in the Code for steel structures (GB50017-2003). The valuing range of static stiffness reduction factor, the connection and difference, and the application area are analyzed. It shows when conducting dynamic calculations, the static expression cannot be directly applied to the equivalent stiffness of composite beam, for it will lead to obvious error.
(4) The dynamic analysis model of the composite bridge concerning vehicle-bridge interaction is established. In views of the characteristics of train running, dynamic interaction between vehicle and composite beam structure, the equations of motion of composite beams under moving loads, harmonic load, sprung mass and vehicles are derived and solved. Especially, the relative slip effect on the dynamic responses of composite beams under moving loads is analyzed. The theoretical results agree well with the test results. Under certain conditions, the general deflection expression of composite beams under concentrated force can be obtained using the proposed dynamic theory.
(5) The dynamic test was conducted on six composite beam models with full and partial connection stiffnesses, in which the natural characteristics, dynamic responses under model vehicle, slip law under impact load, etc., are studied. In the test, the dynamic responses of the composite beams are measured for six pre-set damage conditions with different damage degrees of shear connectors. The results from the test, theoretical analysis and numerical calculation verify well each other, which further reveals the mechanical behaviors of railway composite beams under static and dynamic loads. It shows the connection stiffness has a significant impact on the dynamic behaviors of composite beams, while localized damage has little impact.
(6) The dynamic assessment and damage identification of composite beams are studied. Aimed at the structural features, the applicability of existing damage identification methods in composite beams is assessed and studied, especially for the identification method for local damage of studs. Through analysis on the stiffness characteristics of composite beams, a suitable identification method is proposed. Taking a model composite beam as an illustrative case study, the curvature model method is employed to analyze the identification method for connector damage. The results show that due to shear connectors, the integral stiffness of composite beam is discontinuous and distributed in a staged form; the identification methods based on global indices such as natural frequencies and modes are unsatisfactory and difficult to position and qualify the damage; by comprehensive analysis on the first3curvature modes, the stud distribution and damage position can be well identified.
Altogether there are109figures,40tables,259equations and146references in this paper.
(1)建立了考虑钢梁与混凝土板之间相对滑移、阻尼的简支直线钢—混凝土结合梁的基本振动方程。运用直接平衡法,考虑了阻尼对结构响应的影响,把钢梁和混凝土板均视作Euler-Bernoulli梁,建立了简支直线钢—混凝土结合梁的基本振动方程,针对一定的边界条件进行求解,重点研究钢梁与混凝土板之间的相对滑移对结合梁桥自振特性的影响,分析其与单一材料梁的区别。在此基础上,得到了结合梁的质量、刚度和阻尼矩阵的正交条件,为下文的车桥动力相互作用分析提供了理论基础。
(2)给出了考虑滑移、简谐荷载共同作用的结合梁挠度通用表达式。通过本文建立的结合梁基本动力理论,得到了集中荷载(或其它形式的荷载)作用下结合梁静挠度的通用级数表达式,通过一定的变换,使其符合级数求和条件；将其相应的Bernoulli函数和Bernoulli数代入,即可得到与静力方法一致的结合梁挠度通用表达式,且能体现滑移引起的附加挠度以及简谐力的影响,为求解结合梁的挠度通用表达式提供了一种思路。
(3)根据结合梁的动力特性,提出了钢—混凝土简支结合梁的“动力刚度折减系数”和“频率折减系数”的概念。通过理论推导,得到了结合梁的动力刚度折减系数的表达式,并与《钢结构设计规范》(GB50017-2003)中的公式进行了比较。对静力刚度折减系数的取值进行了分析,研究了其与动力刚度折减系数的联系和区别及应用的范围。结果表明,在结合梁的动力计算中,不能直接套用静力计算的公式来计算结合梁的等效刚度,否则会引起较大的误差。
(4)建立了钢—混凝土结合梁桥车桥动力相互作用分析模型。考虑铁路桥梁的行车特点、车—桥耦合特征以及结合梁桥的构造特点,对移动荷载作用下结合梁桥的动力响应进行了分析,推导了移动质量、简谐荷载、簧上质量、车辆作用下结合梁的振动方程,并进行了求解,重点分析移动荷载作用下钢梁与混凝土板之间的相对滑移对结合梁桥动力响应的影响。本文的理论分析结果表明,通过本文的结合梁动力理论所得到的结果与试验结果吻合良好,在某些条件下可以从结合梁的动力理论得到集中荷载作用下结合梁的挠度通用表达式。
(5)根据铁路结合梁桥实桥的构造特点,对6片钢—混凝土结合梁进行了动力特性的模型试验研究,其中包括两种连接刚度(完全连接、部分连接),对结合梁的自振特性、模型车辆移动荷载作用下梁的响应、简谐荷载持续作用下钢梁与混凝土板之间的相对滑移规律等进行了重点研究；并预设了6种栓钉损伤工况,针对栓钉连接件发生不同程度损伤时的动力特性进行测试。根据试验现象和结果,与理论分析、数值分析相互验证,进一步深入揭示铁路结合梁桥在静、动力荷载下的受力机理。结果表明结合梁的连接刚度对其动力特性产生重大影响,小范围损伤对其自振特性的影响甚微。
(6)进行了钢—混凝土结合梁桥状态评估与损伤识别研究。针对钢—混凝土结合梁桥的构造特点,基于现有的结构损伤识别方法,对常见的损伤识别方法应用在结合梁损伤识别中的适用性进行了评估,尤其是针对栓钉局部损伤的有效识别方法进行了研究和探讨。分析结合梁的刚度特点,找到了适合于结合梁桥的损伤识别方法,并以某钢—混凝土简支结合试验梁为例,应用曲率模态分析方法,对抗剪连接件进行了损伤识别方法研究。结果表明：由于结合梁栓钉抗剪连接件的存在,结合梁的整体刚度是不连续的,呈阶段性分布；以自振频率和自振模态等整体动力参数为识别指标的损伤识别方法效果并不理想,无法对损伤位置和程度进行量化；对结合梁的前3阶曲率模态进行综合分析,可以很好地识别混凝土板和钢梁之间的栓钉布置情况、栓钉的损伤位置。
本文共有图109幅,表40个,公式259个,参考文献146篇。
The steel-concrete composite beam (short for "composite bridge") bridge, which is composed of steel girder and concrete slab integrated by shear connectors, is a new-type bridge arose after steel and concrete bridges. By combining the advantages of steel (tensile) and concrete (compressive) members, composite bridges are widely applied in highway, urban road, rail transit and railway bridges. However, there are inevitably some obvious problems owing to the material and structure limitation, such as cracking in negative moment regions, bigger deflection and cracks due to concrete shrinkage and creep, connection performance degradation under long duration loads, uncertainty of slip and mechanical behaviors under dynamic loads, etc. In this paper, the dynamic behaviors of composite bridges, including natural vibration characteristics, dynamic responses of external force load excitation, vehicle-bridge interaction dynamic analysis and damage identification are investigated, by theoretical derivation, numerical analysis and model test. The research is sponsored by the State Fundamental Research Funds "973" Program, the National Nature Science Foundation of China and the Scientific Research and Development Projects of Ministry of Railways of China. The main work and conclusions are as follows:
(1) By employing the direct equilibrium method and treating the steel girder and concrete slab as Euler-Bernoulli beams, the fundamental motion equations of simply-supported straight composite bridge are established, considering relative slip at the interface of steel girder and concrete slab, as well the damping, and the equations are solved for certain boundary conditions. The effect of relative slip on the natural vibration characteristics of the composite bridge is analyzed. On this basis, the orthogonality conditions for the mass, stiffness and damping matrices are obtained, which provides a theoretical basis for further vehicle-bridge interaction analysis.
(2) By the established fundamental theory, and considering the relative slip and harmonic load, the general series expressions of composite beam displacement under concentrated forces (or other types) are derived. Then a certain transformation is conducted to meet the summation conditions of the series. By substituting the corresponding Bernoulli functions and Bernoulli numbers to the above expressions, the general displacement expression of simply-supported composite beam is obtained, which is consistent with that derived by static methods, and can reflect the influences of slip and harmonic load, providing an analytical method for solving the displacement of composite beams.
(3) The concepts "dynamic stiffness reduction factor (DSRF)" and "frequency reduction factor (FRF)" are proposed based on the mechanical behaviors of composite beams. The DSRF expression is obtained by theoretical derivation, and compared with the expression in the Code for steel structures (GB50017-2003). The valuing range of static stiffness reduction factor, the connection and difference, and the application area are analyzed. It shows when conducting dynamic calculations, the static expression cannot be directly applied to the equivalent stiffness of composite beam, for it will lead to obvious error.
(4) The dynamic analysis model of the composite bridge concerning vehicle-bridge interaction is established. In views of the characteristics of train running, dynamic interaction between vehicle and composite beam structure, the equations of motion of composite beams under moving loads, harmonic load, sprung mass and vehicles are derived and solved. Especially, the relative slip effect on the dynamic responses of composite beams under moving loads is analyzed. The theoretical results agree well with the test results. Under certain conditions, the general deflection expression of composite beams under concentrated force can be obtained using the proposed dynamic theory.
(5) The dynamic test was conducted on six composite beam models with full and partial connection stiffnesses, in which the natural characteristics, dynamic responses under model vehicle, slip law under impact load, etc., are studied. In the test, the dynamic responses of the composite beams are measured for six pre-set damage conditions with different damage degrees of shear connectors. The results from the test, theoretical analysis and numerical calculation verify well each other, which further reveals the mechanical behaviors of railway composite beams under static and dynamic loads. It shows the connection stiffness has a significant impact on the dynamic behaviors of composite beams, while localized damage has little impact.
(6) The dynamic assessment and damage identification of composite beams are studied. Aimed at the structural features, the applicability of existing damage identification methods in composite beams is assessed and studied, especially for the identification method for local damage of studs. Through analysis on the stiffness characteristics of composite beams, a suitable identification method is proposed. Taking a model composite beam as an illustrative case study, the curvature model method is employed to analyze the identification method for connector damage. The results show that due to shear connectors, the integral stiffness of composite beam is discontinuous and distributed in a staged form; the identification methods based on global indices such as natural frequencies and modes are unsatisfactory and difficult to position and qualify the damage; by comprehensive analysis on the first3curvature modes, the stud distribution and damage position can be well identified.
Altogether there are109figures,40tables,259equations and146references in this paper.
引文
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