大跨度混凝土箱梁结构空间效应研究
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摘要
钢筋混凝土和预应力混凝土箱梁结构以其诸多优点,在国内外桥梁建设中获得广泛应用。箱梁结构的空间力学效应一直以来是各国学术界和工程界广泛关注的问题。本文在总结和完善经典薄壁杆件理论的基础上,针对目前混凝土箱梁结构的约束扭转和畸变效应研究中所存在的主要问题,以国内典型的混凝土箱梁桥为工程背景,对以下几方面进行了深入研究。
1.箱梁约束扭转理论的对比分析和完善：在对已有的箱梁约束扭转理论进行对比分析和完善的基础上,基于混合变分原理,建立了一种新的约束扭转理论,该理论充分考虑了全部次生剪切变形的影响。基于新理论,在研究约束扭转剪应力成分对剪切变形的影响及其影响程度的基础上,分析了该理论与已有开口、闭口约束扭转理论的统一。研究表明,各种理论差异的根源在于对次生剪切变形考虑的不同；乌曼斯基闭口理论和符拉索夫开口理论所得结果偏于保守。
2.箱梁畸变理论的对比分析和完善：在对已有的箱梁畸变理论进行对比分析和完善的基础上,首次证明了以畸变角为位移参数和以畸变挠度为位移参数所建立的两类理论是一致的,并建立了两者的互换方程。对畸变广义坐标的确定提出了改进方法,同时基于混合变分原理,建立了一种新的畸变理论,该理论充分考虑了全部次生剪切变形的影响。基于新理论,在研究畸变剪应力成分对剪切变形的影响及其影响程度的基础上,分析了该理论与已有理论的统一。明确解释了为什么在闭口薄壁杆畸变分析中可以采用畸变角的一阶导数作为翘曲函数、而在闭口薄壁杆约束扭转分析中不能采用扭转角的一阶导数作为翘曲函数这一长期未能辨清的问题。
3.带悬臂翼缘板箱梁的约束扭转和畸变：在经典薄壁箱梁理论的基础上,分析了带悬臂翼缘板的薄壁箱梁在约束扭转和畸变时的内力状态,基于混和变分原理,建立了开、闭口混合截面杆件的约束扭转和畸变效应分析的实用理论。研究指出悬臂翼缘板对整个截面约束扭转和畸变效应的贡献主要体现在悬臂翼缘板的扇形惯矩所占整个截面的扇形惯矩的比例,悬臂翼缘板使得闭口箱的约束扭转正应力和畸变正应力发生了明显的重分布,对于常规的铁路和公路箱梁,悬臂板的贡献不可忽略。
4.厚壁箱梁的约束扭转和畸变：采用广义坐标法,基于混合变分原理,建立了考虑壁厚效应的厚壁箱梁约束扭转和畸变解析理论；同时建立了考虑壁厚效应的厚壁箱梁约束扭转和畸变分析的分层方法。其中,指出了已有研究中考虑壁厚效应方法所存在的问题；首次提出了新力素-圣维南约束扭转力矩,该力素与圣维南自由扭转力矩的区别主要在于参与了扭转翘曲正应力的平衡,同时提出了新力素-圣维南纯畸变力矩和圣维南约束畸变力矩,该力素在传统畸变理论中均被忽略了,并指出了在单箱室箱梁畸变中不存在布莱特纯畸变。
5.变截面箱梁空间分析的有限梁段模型：基于本文所建立的理论基础,取直线箱梁控制微分方程的齐次解作为位移模式,利用二次形函数对变截面梁段的截面特性参数进行插值,根据变分原理导出了变截面箱梁的单元刚度矩阵和荷载列阵,从而建立了一种考虑约束扭转和畸变效应的半解析有限段模型。该有限梁段模型能以极少的离散自由度得到较高的计算精度,也能方便地纳入普通梁杆单元程序系统,提高了求解效率,为箱梁空间效应研究提供了一条有效的途径。
6.箱梁的空间力学效应及其对桥梁行为影响的研究：对公路典型的扁平箱梁、铁路客运专线箱梁、公路整体式箱梁及数座大跨度连续刚构桥的约束扭转和畸变效应进行了研究,得出其空间应力状态及应力放大系数,获得了一些有益结论。结合箱梁结构形式和尺寸,研究了箱梁桥的跨度、截面宽高比、梯形箱梁腹板斜度和横隔板的设置等因素对约束扭转和畸变效应的影响,揭示了一些基本规律。
RC and PC box-girder structure, with its various advantages, have been widely applied in bridge engineering at home and abroad. Considerable Research of spatial mechanical effects of box girder is under way throughout the world. On the basis of generalizing and improving the classical thin-walled beam theory, the aim of this dissertation is to deal with the existing problems in the calculation and analysis of restrained torsion and distortion of concrete box girder structure. Based on the typical concrete box girder bridges in china, in-depth research has been carried out on the following aspects.
1. Comparative Analysis and improving of restrained torsion theory of box girder:Based on comparative analysis and improving of restrained torsion theory of box girder, a new theory of restrained torsion is presented based on the mixed variational principle, which fully take into account the secondary shear deformation effects. Based on the new theory, the uniformity between the new theory and the existed open and closed thin-walled theories is analyzed. Research shows that differences among these theories rooted in differences of taking into account the secondary shear deformation. The calculation results based on Umanskii's closed thin-walled theory and Vlasov's open thin-walled theory are conservative.
2. Comparative Analysis and improving of distortion theory of box girder:Based on comparative analysis and improving of distortion theory of box girder, it is first proved that calculation results of the two kind of theory which respectively takes distortion deflection and distortion angle as displacement variable are consistent, and their reciprocal equations are established. A new approach determining generalized coordinates of box-girder distortion was put forward, and based on the mixed variational principle, a new theory of distortion is presented, which fully take into account the secondary shear deformation effects. Based on the new theory, the uniformity between the new theory and the existed theories is analyzed. The research clearly explained why, the first-order derivative of distortion angle can be used as warping function in the distortion analysis of closed thin-walled beam, while the first-order derivative of torsion angle can not be used as warping function in the restrained torsion analysis of closed thin-walled beam.
3. Restrained torsion and distortion of thin-walled box girder with cantilever flanges:Based on the classical thin-walled box girder theory and analyzing the internal stress state of thin-walled box girder with cantilever flanges under restrained torsion and distortion, a practical theory analyzing restrained torsion and distortion of thin-walled beam with open and closed cross-section is established. The research shows that contribution of cantilever flanges of thin-walled box girder to its behavior in restrained torsion and distortion lies in the proportion of its warping moment of the whole, and cantilever flanges cause significant redistribution of restrained torsion normal stress and distortion normal stress, and the contribution can not be ignored for common concrete box girder of railway ang highway.
4. Restrained torsion and distortion of thick-walled box girder:Based on the generalized coordinates principle, a analytical theory of the restrained torsion and distortion of thick-walled box girder is established, and then it's existing problems are found. At the same time, a layered approach for analyzing that is established. In the research, one new internal force(St.Venant's restrained torsional moment)is first put forward, the differences between it and St.Venant's pure torsional moment is that the new internal force participates in the balance of warping normal stress. At the same time, tow new internal forces (St.Venant's pure distortional moment and St.Venant's restrained distortional moment) are first put forward. It is proved that so-called Bredt's pure distortion does not exist in the distortion of box girder with single cell and single box section.
5. The variable cross-section segment element model considering restrained torsion and distortion effects of box girder:Based on the above theories, taking the homogeneous solutions derived from the governing differential equations as the displacement patterns of finite segment, using second-degree shape function to interpolate cross-section characteristic parameter of the variable cross-section segment element, its stiffness matrix and load column matrixes are derived by means of variation principle. Thus a semi-solution beam-segment element model is established considering restrained torsion and distortion effects. The proposed approach can achieve higher calculation accuracy with extremely few discretization nodal unknowns, and conveniently bring into the program system for the conventional beam-bar elements as well as improve resolution efficiency, thus laying a foundation for the study of the restrained torsion and distortion of box girder.
6. Research on the spatial mechanics effects in box girder and the influence on behavior of bridges:The dissertation has analyzed that restrained torsion and distortion effects of typical highway flat box girders, high-speed railway box girders, integral type box girders, and concrete continuous rigid frame bridges in china, and then has obtained their restrained torsion and distortion stresses and the amplification coefficients of stress. Based on the analysis of the results, some important conclusions have been made for the spatial mechanics effect of box girder bridges. Combining the structure type and size for box girder, the author has found that the factors such as the span, height to width ratio of cross-section, slope ratio of web plate, diaphragm have a great effect on restrained torsion and distortion, and brought to light the objective law governing restrained torsion and distortion of box girder.
1.箱梁约束扭转理论的对比分析和完善：在对已有的箱梁约束扭转理论进行对比分析和完善的基础上,基于混合变分原理,建立了一种新的约束扭转理论,该理论充分考虑了全部次生剪切变形的影响。基于新理论,在研究约束扭转剪应力成分对剪切变形的影响及其影响程度的基础上,分析了该理论与已有开口、闭口约束扭转理论的统一。研究表明,各种理论差异的根源在于对次生剪切变形考虑的不同；乌曼斯基闭口理论和符拉索夫开口理论所得结果偏于保守。
2.箱梁畸变理论的对比分析和完善：在对已有的箱梁畸变理论进行对比分析和完善的基础上,首次证明了以畸变角为位移参数和以畸变挠度为位移参数所建立的两类理论是一致的,并建立了两者的互换方程。对畸变广义坐标的确定提出了改进方法,同时基于混合变分原理,建立了一种新的畸变理论,该理论充分考虑了全部次生剪切变形的影响。基于新理论,在研究畸变剪应力成分对剪切变形的影响及其影响程度的基础上,分析了该理论与已有理论的统一。明确解释了为什么在闭口薄壁杆畸变分析中可以采用畸变角的一阶导数作为翘曲函数、而在闭口薄壁杆约束扭转分析中不能采用扭转角的一阶导数作为翘曲函数这一长期未能辨清的问题。
3.带悬臂翼缘板箱梁的约束扭转和畸变：在经典薄壁箱梁理论的基础上,分析了带悬臂翼缘板的薄壁箱梁在约束扭转和畸变时的内力状态,基于混和变分原理,建立了开、闭口混合截面杆件的约束扭转和畸变效应分析的实用理论。研究指出悬臂翼缘板对整个截面约束扭转和畸变效应的贡献主要体现在悬臂翼缘板的扇形惯矩所占整个截面的扇形惯矩的比例,悬臂翼缘板使得闭口箱的约束扭转正应力和畸变正应力发生了明显的重分布,对于常规的铁路和公路箱梁,悬臂板的贡献不可忽略。
4.厚壁箱梁的约束扭转和畸变：采用广义坐标法,基于混合变分原理,建立了考虑壁厚效应的厚壁箱梁约束扭转和畸变解析理论；同时建立了考虑壁厚效应的厚壁箱梁约束扭转和畸变分析的分层方法。其中,指出了已有研究中考虑壁厚效应方法所存在的问题；首次提出了新力素-圣维南约束扭转力矩,该力素与圣维南自由扭转力矩的区别主要在于参与了扭转翘曲正应力的平衡,同时提出了新力素-圣维南纯畸变力矩和圣维南约束畸变力矩,该力素在传统畸变理论中均被忽略了,并指出了在单箱室箱梁畸变中不存在布莱特纯畸变。
5.变截面箱梁空间分析的有限梁段模型：基于本文所建立的理论基础,取直线箱梁控制微分方程的齐次解作为位移模式,利用二次形函数对变截面梁段的截面特性参数进行插值,根据变分原理导出了变截面箱梁的单元刚度矩阵和荷载列阵,从而建立了一种考虑约束扭转和畸变效应的半解析有限段模型。该有限梁段模型能以极少的离散自由度得到较高的计算精度,也能方便地纳入普通梁杆单元程序系统,提高了求解效率,为箱梁空间效应研究提供了一条有效的途径。
6.箱梁的空间力学效应及其对桥梁行为影响的研究：对公路典型的扁平箱梁、铁路客运专线箱梁、公路整体式箱梁及数座大跨度连续刚构桥的约束扭转和畸变效应进行了研究,得出其空间应力状态及应力放大系数,获得了一些有益结论。结合箱梁结构形式和尺寸,研究了箱梁桥的跨度、截面宽高比、梯形箱梁腹板斜度和横隔板的设置等因素对约束扭转和畸变效应的影响,揭示了一些基本规律。
RC and PC box-girder structure, with its various advantages, have been widely applied in bridge engineering at home and abroad. Considerable Research of spatial mechanical effects of box girder is under way throughout the world. On the basis of generalizing and improving the classical thin-walled beam theory, the aim of this dissertation is to deal with the existing problems in the calculation and analysis of restrained torsion and distortion of concrete box girder structure. Based on the typical concrete box girder bridges in china, in-depth research has been carried out on the following aspects.
1. Comparative Analysis and improving of restrained torsion theory of box girder:Based on comparative analysis and improving of restrained torsion theory of box girder, a new theory of restrained torsion is presented based on the mixed variational principle, which fully take into account the secondary shear deformation effects. Based on the new theory, the uniformity between the new theory and the existed open and closed thin-walled theories is analyzed. Research shows that differences among these theories rooted in differences of taking into account the secondary shear deformation. The calculation results based on Umanskii's closed thin-walled theory and Vlasov's open thin-walled theory are conservative.
2. Comparative Analysis and improving of distortion theory of box girder:Based on comparative analysis and improving of distortion theory of box girder, it is first proved that calculation results of the two kind of theory which respectively takes distortion deflection and distortion angle as displacement variable are consistent, and their reciprocal equations are established. A new approach determining generalized coordinates of box-girder distortion was put forward, and based on the mixed variational principle, a new theory of distortion is presented, which fully take into account the secondary shear deformation effects. Based on the new theory, the uniformity between the new theory and the existed theories is analyzed. The research clearly explained why, the first-order derivative of distortion angle can be used as warping function in the distortion analysis of closed thin-walled beam, while the first-order derivative of torsion angle can not be used as warping function in the restrained torsion analysis of closed thin-walled beam.
3. Restrained torsion and distortion of thin-walled box girder with cantilever flanges:Based on the classical thin-walled box girder theory and analyzing the internal stress state of thin-walled box girder with cantilever flanges under restrained torsion and distortion, a practical theory analyzing restrained torsion and distortion of thin-walled beam with open and closed cross-section is established. The research shows that contribution of cantilever flanges of thin-walled box girder to its behavior in restrained torsion and distortion lies in the proportion of its warping moment of the whole, and cantilever flanges cause significant redistribution of restrained torsion normal stress and distortion normal stress, and the contribution can not be ignored for common concrete box girder of railway ang highway.
4. Restrained torsion and distortion of thick-walled box girder:Based on the generalized coordinates principle, a analytical theory of the restrained torsion and distortion of thick-walled box girder is established, and then it's existing problems are found. At the same time, a layered approach for analyzing that is established. In the research, one new internal force(St.Venant's restrained torsional moment)is first put forward, the differences between it and St.Venant's pure torsional moment is that the new internal force participates in the balance of warping normal stress. At the same time, tow new internal forces (St.Venant's pure distortional moment and St.Venant's restrained distortional moment) are first put forward. It is proved that so-called Bredt's pure distortion does not exist in the distortion of box girder with single cell and single box section.
5. The variable cross-section segment element model considering restrained torsion and distortion effects of box girder:Based on the above theories, taking the homogeneous solutions derived from the governing differential equations as the displacement patterns of finite segment, using second-degree shape function to interpolate cross-section characteristic parameter of the variable cross-section segment element, its stiffness matrix and load column matrixes are derived by means of variation principle. Thus a semi-solution beam-segment element model is established considering restrained torsion and distortion effects. The proposed approach can achieve higher calculation accuracy with extremely few discretization nodal unknowns, and conveniently bring into the program system for the conventional beam-bar elements as well as improve resolution efficiency, thus laying a foundation for the study of the restrained torsion and distortion of box girder.
6. Research on the spatial mechanics effects in box girder and the influence on behavior of bridges:The dissertation has analyzed that restrained torsion and distortion effects of typical highway flat box girders, high-speed railway box girders, integral type box girders, and concrete continuous rigid frame bridges in china, and then has obtained their restrained torsion and distortion stresses and the amplification coefficients of stress. Based on the analysis of the results, some important conclusions have been made for the spatial mechanics effect of box girder bridges. Combining the structure type and size for box girder, the author has found that the factors such as the span, height to width ratio of cross-section, slope ratio of web plate, diaphragm have a great effect on restrained torsion and distortion, and brought to light the objective law governing restrained torsion and distortion of box girder.
引文
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