混凝土连续曲线梁桥在车辆荷载作用下的动力响应研究
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摘要
近年来随着我国公路建设和城市道路交通的快速发展,曲线梁桥被广泛应用于高速公路的跨线互通、大跨桥梁的桥头引道和大型立体交叉中,其中多数为混凝土曲线梁桥。曲线梁桥的静力计算理论在过去的几十年中取得了长足的发展,但对混凝土曲线梁桥的动力行为研究甚少,认识也不够深入,对混凝土曲线梁桥的动力设计尚无明确的依据可循。我国的曲线梁桥汽车荷载冲击系数的取值目前仍普遍采用直线梁桥的研究成果,对其合理性缺少足够的研究。因此,开展曲线梁桥的动力行为研究对完善曲线梁桥的结构设计理论、规范冲击系数的取值方法、养护管理和寿命评估具有重要的意义。曲线梁桥受力弯扭耦合作用效应明显,实际工程中多采用抗弯扭刚度大的箱形截面。为此,本文以曲线箱形桥梁为对象,对其动力特性及车辆荷载作用下的动力行为开展理论和试验研究,主要研究成果如下:
1、基于剪力柔性梁格理论,充分考虑翘曲刚度和转动惯量的影响,对已有的计算模型进行改进,提出了适于曲线梁桥动力分析的三梁式模型,通过环境振动测试和实体模型的动力分析结果验证了模型的可靠性。在此基础上,基于通用软件ANSYS,采用12自由度的空间3轴车辆模型,联合采用空间梁单元和质量单元、弹簧阻尼单元对车辆和桥梁模型进行离散,分别建立车辆和桥梁的有限元模型,综合考虑离心力、桥面不平度及其速度项的影响,提出了一种简便的求解曲线梁桥车桥耦合振动响应的数值分析方法,并通过桥梁的动载试验结果验证了该方法的有效性和实用性。
2、应用前面提出的模型和方法研究了单车荷载作用下,桥面不平度、曲率半径、车辆行驶偏心、轮胎的刚度和阻尼、桥梁结构阻尼比、桥梁跨数、主梁的支承类型和桥梁纵坡等多个针对曲线梁桥主要特征的参数对的桥梁的内力、位移和墩柱动力响应的影响,计算了相应工况的动力放大系数并进行了比较分析。随后研究了横向加载车道数、纵向加载车辆数、车头间距和车速对车队荷载作用下桥梁动力响应的影响。分析结果为桥梁分析实例的选择、分析和曲线梁桥冲击系数公式的确定提供了重要的参考依据。
3、在考虑随机桥面不平度及其速度项影响的基础上,根据d’Alembert原理推导了车辆由于加、减速阻力的影响而产生的荷载转移和制动力分配的具体表达式,并在变速行驶车辆-桥梁耦合振动分析中给予了考虑。基于前文提出的方法,采用变化的时间步长和车速,研究了制动力上升时间和车辆制动位置对制动过程中桥梁动力响应的影响,以及加速行驶车辆以不同初速度和加速度通过桥梁时对桥梁的动力响应和冲击效应的影响。结果表明了车辆变速行驶对车桥耦合振动响应有较大影响。
4、根据大量混凝土连续曲线梁桥实例的车桥耦合振动分析结果,采用取上界包络线的方法给出了不同桥面等级下桥梁不同位置的冲击系数与圆心角和结构竖向弯曲振动基频的函数关系。统计分析结果表明,桥梁不同位置的内力、位移和支座反力的冲击系数差别很大,为此分别给出了不同关键截面的内力和位移的冲击系数计算公式。曲线梁桥冲击系数随着圆心角和竖向弯曲振动基频的增大而减小,与我国现行桥梁设计规范中所给的直线梁桥冲击系数-基频的关系恰好相反,因此采用现行规范进行跨度较大的曲线梁桥动力设计是偏于不安全的。文中给出的冲击系数公式可为曲线梁桥的动力设计和运营维护提供参考。
With the rapid development of highway construction and urban road transportation in recent years, curved beam bridges are widely used in highway viaducts, approach of long span bridges and large interchanges, most of which are concrete curved bridges. Though great progress has been made in static analysis theory of concrete curved bridges in the last years, less theoretical and experimental research was conducted on the dynamic performances. These lead to an insufficient understanding and no specific criteria are available on dynamic design on concrete curved bridges. The impact factor assessment method of curved bridge under moving vehicles mostly adopts the usages of straight beam bridges, but not enough argumentations can demonstrate the reasonability. Thus, the dynamic performance studies of concrete curved bridges have important significance on the perfection of design theories, regulation of impact factor assessment method, maintenance management and service life evaluation for concrete curved bridges. Box girder beams are commonly used in curved bridges to resist the extant coupled bending-torsional effect. This thesis focuses on the dynamic characteristics and dynamic responses due to vehicles for curved box girder bridges. The main contents are as follows:
First, based on the shear force flexible grillage method, the triple beam model suitable for the dynamic analysis of curved bridges, in which the effects of warping stiffness and moment of inertia are both considered, is presented by improving the existing model. The model is validated by both ambient excitation test and solid model analysis. Then, based on the commercial program ANSYS, 3D beam element, mass element and spring-damper element are adopt together in building the 12 DOFs spatial vehicle model and the bridge model. A simplified numerical method is put forward for solving the coupled vehicle-bridge vibration problems, of which the effect of centrifugal force, random road roughness and its velocity term are considered comprehensively. The method is validated by comparison between the numerical simulation and dynamic loading test of a preselected bridge under vehicle at uniform velocity.
Second, by using the former presented model and numerical method, parametric studies are conducted on dynamic responses of curved bridges under a single vehicle, in which road roughness, curvature of radius, vehicle travelling eccentricities, rigidity and damping of the tyres, damping ratio of the bridge, number of bridge spans, bearing types and the longitudinal gradient of the bridge are included. Both the dynamic responses and dynamic amplification factors are calculated and compared. Then, the influence of lateral multi-lane loading, longitudinal multi-vehicle loading, space headway and velocity are also investigated for bridges under platoon. The parametric analysis results can provide good references for the selection, analysis of engineering examples and the stipulation of impact factor formulae in the later studies.
Third, the formulae of load transferring caused by accelerating and decelerating resistance are deduced by d’Alembert theorem and also the formulae of braking force distribution. These forces are all considered in the dynamic response analysis of bridges due to vehicle at various velocities. Based on the former presented method and taken varying time steps and velocities into account, the effects of braking rise time and braking position in braking process, as well as the effects of initial velocity and acceleration in the acceleration process are investigated on the bridge dynamic responses and impact effects. The results indicate that vehicle travelling at various speeds has great influence on bridge dynamic responses.
Last, an extensive investigation is conducted to determine the effects of key parameters on the impact factors of continuous concrete curved bridges. Studies on correlation among impact factors and various important parameters are conducted to determine the most important ones. Based on the results, it is found that the impact factors of internal forces at various position, deflection and support reaction have great significance. The upper-bound envelop expressions of the impact factors for maximum bending moment, torsional moment, shear force, de?ection and support reaction were deduced and given in different road roughness classes as the function of central angle and the fundamental bending vibration frequency, respectively. It is found that the impact factors of curved bridges descend as the value of central angle and the fundamental bending vibration frequency ascend, which is contrary to the relationship between impact factor and the fundamental bending vibration frequency of straight beam bridges presented in the current bridge design standard (JTG D60-2004). Therefore, it may be relative unsafe for the medium to large span concrete curved bridges whose fundamental bending vibration frequencies are low while impact factors are calculated according to the current bridge design standard (JTG D60-2004). The formulae presented in the thesis can offer references for dynamic design and maintenance of concrete curved bridges.
1、基于剪力柔性梁格理论,充分考虑翘曲刚度和转动惯量的影响,对已有的计算模型进行改进,提出了适于曲线梁桥动力分析的三梁式模型,通过环境振动测试和实体模型的动力分析结果验证了模型的可靠性。在此基础上,基于通用软件ANSYS,采用12自由度的空间3轴车辆模型,联合采用空间梁单元和质量单元、弹簧阻尼单元对车辆和桥梁模型进行离散,分别建立车辆和桥梁的有限元模型,综合考虑离心力、桥面不平度及其速度项的影响,提出了一种简便的求解曲线梁桥车桥耦合振动响应的数值分析方法,并通过桥梁的动载试验结果验证了该方法的有效性和实用性。
2、应用前面提出的模型和方法研究了单车荷载作用下,桥面不平度、曲率半径、车辆行驶偏心、轮胎的刚度和阻尼、桥梁结构阻尼比、桥梁跨数、主梁的支承类型和桥梁纵坡等多个针对曲线梁桥主要特征的参数对的桥梁的内力、位移和墩柱动力响应的影响,计算了相应工况的动力放大系数并进行了比较分析。随后研究了横向加载车道数、纵向加载车辆数、车头间距和车速对车队荷载作用下桥梁动力响应的影响。分析结果为桥梁分析实例的选择、分析和曲线梁桥冲击系数公式的确定提供了重要的参考依据。
3、在考虑随机桥面不平度及其速度项影响的基础上,根据d’Alembert原理推导了车辆由于加、减速阻力的影响而产生的荷载转移和制动力分配的具体表达式,并在变速行驶车辆-桥梁耦合振动分析中给予了考虑。基于前文提出的方法,采用变化的时间步长和车速,研究了制动力上升时间和车辆制动位置对制动过程中桥梁动力响应的影响,以及加速行驶车辆以不同初速度和加速度通过桥梁时对桥梁的动力响应和冲击效应的影响。结果表明了车辆变速行驶对车桥耦合振动响应有较大影响。
4、根据大量混凝土连续曲线梁桥实例的车桥耦合振动分析结果,采用取上界包络线的方法给出了不同桥面等级下桥梁不同位置的冲击系数与圆心角和结构竖向弯曲振动基频的函数关系。统计分析结果表明,桥梁不同位置的内力、位移和支座反力的冲击系数差别很大,为此分别给出了不同关键截面的内力和位移的冲击系数计算公式。曲线梁桥冲击系数随着圆心角和竖向弯曲振动基频的增大而减小,与我国现行桥梁设计规范中所给的直线梁桥冲击系数-基频的关系恰好相反,因此采用现行规范进行跨度较大的曲线梁桥动力设计是偏于不安全的。文中给出的冲击系数公式可为曲线梁桥的动力设计和运营维护提供参考。
With the rapid development of highway construction and urban road transportation in recent years, curved beam bridges are widely used in highway viaducts, approach of long span bridges and large interchanges, most of which are concrete curved bridges. Though great progress has been made in static analysis theory of concrete curved bridges in the last years, less theoretical and experimental research was conducted on the dynamic performances. These lead to an insufficient understanding and no specific criteria are available on dynamic design on concrete curved bridges. The impact factor assessment method of curved bridge under moving vehicles mostly adopts the usages of straight beam bridges, but not enough argumentations can demonstrate the reasonability. Thus, the dynamic performance studies of concrete curved bridges have important significance on the perfection of design theories, regulation of impact factor assessment method, maintenance management and service life evaluation for concrete curved bridges. Box girder beams are commonly used in curved bridges to resist the extant coupled bending-torsional effect. This thesis focuses on the dynamic characteristics and dynamic responses due to vehicles for curved box girder bridges. The main contents are as follows:
First, based on the shear force flexible grillage method, the triple beam model suitable for the dynamic analysis of curved bridges, in which the effects of warping stiffness and moment of inertia are both considered, is presented by improving the existing model. The model is validated by both ambient excitation test and solid model analysis. Then, based on the commercial program ANSYS, 3D beam element, mass element and spring-damper element are adopt together in building the 12 DOFs spatial vehicle model and the bridge model. A simplified numerical method is put forward for solving the coupled vehicle-bridge vibration problems, of which the effect of centrifugal force, random road roughness and its velocity term are considered comprehensively. The method is validated by comparison between the numerical simulation and dynamic loading test of a preselected bridge under vehicle at uniform velocity.
Second, by using the former presented model and numerical method, parametric studies are conducted on dynamic responses of curved bridges under a single vehicle, in which road roughness, curvature of radius, vehicle travelling eccentricities, rigidity and damping of the tyres, damping ratio of the bridge, number of bridge spans, bearing types and the longitudinal gradient of the bridge are included. Both the dynamic responses and dynamic amplification factors are calculated and compared. Then, the influence of lateral multi-lane loading, longitudinal multi-vehicle loading, space headway and velocity are also investigated for bridges under platoon. The parametric analysis results can provide good references for the selection, analysis of engineering examples and the stipulation of impact factor formulae in the later studies.
Third, the formulae of load transferring caused by accelerating and decelerating resistance are deduced by d’Alembert theorem and also the formulae of braking force distribution. These forces are all considered in the dynamic response analysis of bridges due to vehicle at various velocities. Based on the former presented method and taken varying time steps and velocities into account, the effects of braking rise time and braking position in braking process, as well as the effects of initial velocity and acceleration in the acceleration process are investigated on the bridge dynamic responses and impact effects. The results indicate that vehicle travelling at various speeds has great influence on bridge dynamic responses.
Last, an extensive investigation is conducted to determine the effects of key parameters on the impact factors of continuous concrete curved bridges. Studies on correlation among impact factors and various important parameters are conducted to determine the most important ones. Based on the results, it is found that the impact factors of internal forces at various position, deflection and support reaction have great significance. The upper-bound envelop expressions of the impact factors for maximum bending moment, torsional moment, shear force, de?ection and support reaction were deduced and given in different road roughness classes as the function of central angle and the fundamental bending vibration frequency, respectively. It is found that the impact factors of curved bridges descend as the value of central angle and the fundamental bending vibration frequency ascend, which is contrary to the relationship between impact factor and the fundamental bending vibration frequency of straight beam bridges presented in the current bridge design standard (JTG D60-2004). Therefore, it may be relative unsafe for the medium to large span concrete curved bridges whose fundamental bending vibration frequencies are low while impact factors are calculated according to the current bridge design standard (JTG D60-2004). The formulae presented in the thesis can offer references for dynamic design and maintenance of concrete curved bridges.
引文
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