钢—混凝土组合箱梁空间分析理论与应用研究
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摘要
钢-混凝土组合箱梁结构是在钢结构和钢筋混凝土结构基础上发展起来的一种新型结构。组合箱梁结构充分利用了钢箱结构和混凝土结构的优点。近年来,钢-混凝土组合箱梁在桥梁工程中得到了广泛的应用,特别是在异型桥梁结构中大量使用曲线组合箱梁。组合箱梁空间力学行为和使用性能的研究日益受到关注。组合箱梁结构属于新型结构,而曲线组合箱梁结构力学行为,国内尚属空白,在国外鲜有研究,组合箱梁结构的计算理论研究滞后于工程实践应用。组合箱梁结构在设计计算理论体系上,与钢筋混凝土结构相比,仍存在大量尚未解决的问题。为了解组合箱梁的力学行为以及在桥梁结构中的使用性能,在前人研究的基础上,本文对钢-混凝土组合箱梁的滑移、变形、空间位移模式、空间弹性性能、剪力滞效应、畸变效应、剪切变形等几方面进行了深入的研究,提出了钢-混凝土组合箱梁的滑移和变形分析理论,建立钢-混凝土组合箱梁的梁段有限元模型,主要的研究内容如下：
应用Goodman弹性夹层假设处理钢-混凝土组合曲线箱梁的界面非线性问题,考虑界面各种连接情况；通过引入轴线变形转角位移函数,分析钢-混凝土组合箱梁的滑移和变形与荷载的关系；推导了钢-混凝土组合箱梁以挠度和扭转角表达的平衡微分方程组,得出了方程的通解以及考虑界面滑移与曲率的挠度、扭转角和轴向变形转角位移的表达式；求出简支组合箱梁在集中力和均布荷载作用下内力、界面约束内力、混凝土板与开口钢箱梁界面内力以及界面滑移量。利用大型有限元程序ANSYS和本文提出的滑移变形理论进行组合箱梁的滑移效应分析。
基于板梁模型、符拉索夫曲线薄壁梁理论、铁摩辛柯梁理论以及组合梁理论,采用广义坐标法的原理,通过增加自由度的分析方法,在普通梁理论每个节点6个自由度的基础上增加了剪切变形、剪力滞效应、扭转翘曲、畸变角、畸变翘曲、滑移以及滑移应变等7个自由度,提出了一种基于板梁模型的有限组合梁段分析方法；推导了一种新的钢-混凝土组合曲线箱梁分析的组合箱梁梁段单元刚度矩阵,这种组合梁段单元每个节点13个自由度,考虑了组合曲线箱梁的滑移、拉压、弯曲、扭转、剪切、剪力滞效应、翘曲及畸变等特性,及纵向和横向变形的相互作用。按广义坐标法原理,组合箱梁截面上任意一点处的位移为广义位移乘以对应的广义坐标。本文以组合箱梁轴线三个方向的线位移、扭转角、畸变角、剪切变形、剪力滞、滑移等8个自由度为广义位移来描述组合箱梁横截面上任一点的位移。应用最小势能原理,在曲线坐标系下推导了组合箱梁梁段单元刚度矩阵的显式及其等效节点荷载列阵。考虑了组合曲线箱梁横截面剪心和形心不重合的影响,同时编制了相应的有限元分析程序。算例表明了本文理论和程序的正确性和有效性。
根据组合箱梁的结构特点,提出了组合箱梁的薄壁扭转分析模型,同时考虑翼缘混凝土板与开口钢箱梁两种不同的材料特性。利用薄壁结构理论对组合箱梁进行扭转分析,分别给出了相应的分析方法和计算公式。推导了组合箱梁的动力微分方程,并且利用大型通用有限元程序以及本文组合箱梁段单元分析法分别对典型组合箱梁进行动力参数分析。
从既有的异型桥梁结构中抽象出一种典型的人字形组合箱梁桥为研究对象,基于ANSYS软件对组合箱梁在人字形桥梁中的应用进行了一系列的静、动力行为的模拟研究,同时进行多方位的参数分析,指出了组合箱梁在异型桥梁结构应用中注意的问题,为异型组合箱梁桥结构的设计、结构分析提供理论参考依据。结合空间梁格分析方法,提出异型组合箱梁桥梁段单元分析的计算模型及分析计算需注意的问题。最后,对钢-混凝土组合箱梁在斜拉桥、部分斜拉桥、自锚式悬索桥以及连续刚构桥中的应用进行分析讨论。
Steel-concrete composite box beam is a new type of structure based on the development foundation of the steel structure and the reinforced concrete structure. The composite box beam may make use of the advantage both the steel box beam and the reinforced concrete slab. The steel-concrete composite box beams have been used for many years and have recently been becoming more popular in China, and most curved composite box beam in China were designed especially in special-shaped overpass bridge structure. studies for both structure behavior and operational performance of composite steel-concrete beams have attracted considerable attentions. Because of the new structure for the steel-concrete composite box beam,studies in this field is still in primary development period at home and abroad, and the studies for analytical theory of the steel-concrete composite box beams are lagging behind the engineering application. Compared with traditional reinforced-concrete box beam structure, there are a lot of issues that need to be solved in field for analytical theory of the steel-concrete composite box beams. To investigate the structural behavior of the steel-concrete composite box beams and application performance better, according to elementary beam theory, by increasing the degree of freedom analytical method, slip, deformation, space displacement model, elastic behaviors, shear lag effect, restrained torsion, distortion angle and distortion warp are studied. The main research achievements are summarized as the following.
The nonlinear problem for interface of the steel-concrete composite box beams are carried out easily according to Goodman elastic interlayer assumptions, and it can be conveniently dealed with any kinds of connection mode between steel box girder and reinforced concrete slab; the relationships between loading and slip, deformation are analyzed by introducing function of axis deformation rotation displacement; differential equations of the steel-concrete composite box beams include deformation and torsion angle are presented, expression of general solutions was derived, and computational expressions considering interface slip and curvature include distortion angle, axis deformation rotation displacement, and deflection corresponding were obtained; on the basis of the computation expressions above, internal force, deformation, internal force in interface between steel box girder and reinforced concrete slab, and interface slip were conducted under concentrated loading and uniform loading respectively. In addition, based on finite element program ANSYS and this theory, analyses for the slippage effect of the steel-concrete composite box beams were carried out respectively, and the comparison results between this theory and the numerical analysis were obtain.
Based on slab-beam model, Vlasov's thin-walled beam theory, Timoshonko's beam theory, and composite beam theory, by generalized coordinate analytical principle and increasing the degree of freedom analytical method, a new composite curved beam segment element was used, and the composite curved beam segment element include seven extra degrees-of-freedom over the normal six degrees-of-freedom beam formulation, to take into account the shear deformation, shear lag effects, torsional warping, distorsion angle, distortional warping, slip and slip strain; stiffness matrix of the composite curved beam segment element was derived, and the composite curved beam segment element include thirteen degrees-of-freedom of every node, to take into account the extension, flexure, torsion, torsional warping, slip, distorsion, shear deformation, shear lag effects and interaction between the longitudinal and transverse deformations. According to the generalized coordinate analytical principle, the arbitrary point displacement of the composite beam cross section is equal to the multiplication both generalized displacement and generalized coordinate respectively. In this paper, the generalized displacement u, Vb, vs, w,θ,θ,φ, (?)are taken as fundamental variables to describe arbitrary point displacement on the composite beam cross section. By variational principle, precise expression of element stiffness matrices and equivalent nodal load vector are obtain under local coordinate system.In the present calculating formula, the effects of eccentricity between shear center and centroid of cross section are considered, and code a finite element procedure. The comparison results of the theory analysis and the numerical simulation demonstrate that the proposed spatial composite curved beam segment element is correct and efficient.
Torsional analysis model of the composite box beams was presented according to structural characteristics of the composite box beams, and two different materials of the composite box beams are taken into account in the present formulation. According to thin-walled structure theory, torsional analysis of the composite box beams was carried out, and the analytical method and calculation formula were presented corresponding. In addition, dynamic differential equation of composite box beams was derived, dynamic parameter analysis for the composite box beams is carried out according to general finite element program ANSYS and this theory respectively.
Meanwhile, a typical Y-shape composite box beam bridge was selected from existing Y-shape composite box beam bridge as the model for the study to investigate service performance in the structure application, and the static and dynamic analysis for the typical Y-shape composite box beam bridge are conducted based on the finite element program ANSYS. Multi-direction parameter analysis for the typical composite box beam bridge are carried out, and some points for the application performance of the composite box beams are presented to provide theoretical basis for design and structural analysis of the special-shaped composite box beam bridge. Calculation model for the composite box beam segment element analysis of the special-shaped composites box beam bridge and some noticeable problems of the structural anlysis are proposed based on space beam grillage analytical method. Finally, the elementary assumption of its application in cable stayed bridge, partially cable-stayed bridge, self-anchored suspension bridge and continuous rigid frame bridge is proposed.
应用Goodman弹性夹层假设处理钢-混凝土组合曲线箱梁的界面非线性问题,考虑界面各种连接情况；通过引入轴线变形转角位移函数,分析钢-混凝土组合箱梁的滑移和变形与荷载的关系；推导了钢-混凝土组合箱梁以挠度和扭转角表达的平衡微分方程组,得出了方程的通解以及考虑界面滑移与曲率的挠度、扭转角和轴向变形转角位移的表达式；求出简支组合箱梁在集中力和均布荷载作用下内力、界面约束内力、混凝土板与开口钢箱梁界面内力以及界面滑移量。利用大型有限元程序ANSYS和本文提出的滑移变形理论进行组合箱梁的滑移效应分析。
基于板梁模型、符拉索夫曲线薄壁梁理论、铁摩辛柯梁理论以及组合梁理论,采用广义坐标法的原理,通过增加自由度的分析方法,在普通梁理论每个节点6个自由度的基础上增加了剪切变形、剪力滞效应、扭转翘曲、畸变角、畸变翘曲、滑移以及滑移应变等7个自由度,提出了一种基于板梁模型的有限组合梁段分析方法；推导了一种新的钢-混凝土组合曲线箱梁分析的组合箱梁梁段单元刚度矩阵,这种组合梁段单元每个节点13个自由度,考虑了组合曲线箱梁的滑移、拉压、弯曲、扭转、剪切、剪力滞效应、翘曲及畸变等特性,及纵向和横向变形的相互作用。按广义坐标法原理,组合箱梁截面上任意一点处的位移为广义位移乘以对应的广义坐标。本文以组合箱梁轴线三个方向的线位移、扭转角、畸变角、剪切变形、剪力滞、滑移等8个自由度为广义位移来描述组合箱梁横截面上任一点的位移。应用最小势能原理,在曲线坐标系下推导了组合箱梁梁段单元刚度矩阵的显式及其等效节点荷载列阵。考虑了组合曲线箱梁横截面剪心和形心不重合的影响,同时编制了相应的有限元分析程序。算例表明了本文理论和程序的正确性和有效性。
根据组合箱梁的结构特点,提出了组合箱梁的薄壁扭转分析模型,同时考虑翼缘混凝土板与开口钢箱梁两种不同的材料特性。利用薄壁结构理论对组合箱梁进行扭转分析,分别给出了相应的分析方法和计算公式。推导了组合箱梁的动力微分方程,并且利用大型通用有限元程序以及本文组合箱梁段单元分析法分别对典型组合箱梁进行动力参数分析。
从既有的异型桥梁结构中抽象出一种典型的人字形组合箱梁桥为研究对象,基于ANSYS软件对组合箱梁在人字形桥梁中的应用进行了一系列的静、动力行为的模拟研究,同时进行多方位的参数分析,指出了组合箱梁在异型桥梁结构应用中注意的问题,为异型组合箱梁桥结构的设计、结构分析提供理论参考依据。结合空间梁格分析方法,提出异型组合箱梁桥梁段单元分析的计算模型及分析计算需注意的问题。最后,对钢-混凝土组合箱梁在斜拉桥、部分斜拉桥、自锚式悬索桥以及连续刚构桥中的应用进行分析讨论。
Steel-concrete composite box beam is a new type of structure based on the development foundation of the steel structure and the reinforced concrete structure. The composite box beam may make use of the advantage both the steel box beam and the reinforced concrete slab. The steel-concrete composite box beams have been used for many years and have recently been becoming more popular in China, and most curved composite box beam in China were designed especially in special-shaped overpass bridge structure. studies for both structure behavior and operational performance of composite steel-concrete beams have attracted considerable attentions. Because of the new structure for the steel-concrete composite box beam,studies in this field is still in primary development period at home and abroad, and the studies for analytical theory of the steel-concrete composite box beams are lagging behind the engineering application. Compared with traditional reinforced-concrete box beam structure, there are a lot of issues that need to be solved in field for analytical theory of the steel-concrete composite box beams. To investigate the structural behavior of the steel-concrete composite box beams and application performance better, according to elementary beam theory, by increasing the degree of freedom analytical method, slip, deformation, space displacement model, elastic behaviors, shear lag effect, restrained torsion, distortion angle and distortion warp are studied. The main research achievements are summarized as the following.
The nonlinear problem for interface of the steel-concrete composite box beams are carried out easily according to Goodman elastic interlayer assumptions, and it can be conveniently dealed with any kinds of connection mode between steel box girder and reinforced concrete slab; the relationships between loading and slip, deformation are analyzed by introducing function of axis deformation rotation displacement; differential equations of the steel-concrete composite box beams include deformation and torsion angle are presented, expression of general solutions was derived, and computational expressions considering interface slip and curvature include distortion angle, axis deformation rotation displacement, and deflection corresponding were obtained; on the basis of the computation expressions above, internal force, deformation, internal force in interface between steel box girder and reinforced concrete slab, and interface slip were conducted under concentrated loading and uniform loading respectively. In addition, based on finite element program ANSYS and this theory, analyses for the slippage effect of the steel-concrete composite box beams were carried out respectively, and the comparison results between this theory and the numerical analysis were obtain.
Based on slab-beam model, Vlasov's thin-walled beam theory, Timoshonko's beam theory, and composite beam theory, by generalized coordinate analytical principle and increasing the degree of freedom analytical method, a new composite curved beam segment element was used, and the composite curved beam segment element include seven extra degrees-of-freedom over the normal six degrees-of-freedom beam formulation, to take into account the shear deformation, shear lag effects, torsional warping, distorsion angle, distortional warping, slip and slip strain; stiffness matrix of the composite curved beam segment element was derived, and the composite curved beam segment element include thirteen degrees-of-freedom of every node, to take into account the extension, flexure, torsion, torsional warping, slip, distorsion, shear deformation, shear lag effects and interaction between the longitudinal and transverse deformations. According to the generalized coordinate analytical principle, the arbitrary point displacement of the composite beam cross section is equal to the multiplication both generalized displacement and generalized coordinate respectively. In this paper, the generalized displacement u, Vb, vs, w,θ,θ,φ, (?)are taken as fundamental variables to describe arbitrary point displacement on the composite beam cross section. By variational principle, precise expression of element stiffness matrices and equivalent nodal load vector are obtain under local coordinate system.In the present calculating formula, the effects of eccentricity between shear center and centroid of cross section are considered, and code a finite element procedure. The comparison results of the theory analysis and the numerical simulation demonstrate that the proposed spatial composite curved beam segment element is correct and efficient.
Torsional analysis model of the composite box beams was presented according to structural characteristics of the composite box beams, and two different materials of the composite box beams are taken into account in the present formulation. According to thin-walled structure theory, torsional analysis of the composite box beams was carried out, and the analytical method and calculation formula were presented corresponding. In addition, dynamic differential equation of composite box beams was derived, dynamic parameter analysis for the composite box beams is carried out according to general finite element program ANSYS and this theory respectively.
Meanwhile, a typical Y-shape composite box beam bridge was selected from existing Y-shape composite box beam bridge as the model for the study to investigate service performance in the structure application, and the static and dynamic analysis for the typical Y-shape composite box beam bridge are conducted based on the finite element program ANSYS. Multi-direction parameter analysis for the typical composite box beam bridge are carried out, and some points for the application performance of the composite box beams are presented to provide theoretical basis for design and structural analysis of the special-shaped composite box beam bridge. Calculation model for the composite box beam segment element analysis of the special-shaped composites box beam bridge and some noticeable problems of the structural anlysis are proposed based on space beam grillage analytical method. Finally, the elementary assumption of its application in cable stayed bridge, partially cable-stayed bridge, self-anchored suspension bridge and continuous rigid frame bridge is proposed.
引文
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