合成桥面桁梁悬索桥静动力分析理论研究
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摘要
本文针对合成桥面桁梁建立等效的连续模型，开展了一系列的理论研究和参数分析，主要包括合成桥面桁梁的约束扭转和剪力滞效应，以及合成桥面桁梁悬索桥的静力效应和自振特性。主要研究工作如下：
(1)对已修建悬索桥中的桁架加劲梁的型式和结构参数作了归纳和统计分析，分析了主桁、横联和水平联等桁片各自可选型式的特点，给出了桁梁高度等设计参数的经验取用规则。阐述了合成桥面桁梁的结构特点和构造型式，并以澧水大桥为工程背景，对照原设计的常规桁梁及混凝土桥面方案，设计了采用合成桥面桁梁作加劲梁的方案，对比分析了混凝土桥面和合成型钢桥面的技术经济特点。
(2)合成桥面桁梁是正交异性钢桥面和空间桁梁的组合结构。桁梁连续化方法的基本思想是将腹杆系转化成等效的剪切薄壁。本文将这一方法扩展到合成桥面桁梁中，提出了钢桥面的等效正向厚度和等效剪切厚度的概念，以体现其抵抗纵向变形和切向变形能力的差异，而桁架腹杆系的等效正向厚度取为零。由此桁梁、合成桥面桁梁形成参数形式上统一的比拟薄壁梁，再根据乌氏第二理论的基本原理分析它们的约束扭转问题，获得它们的扭转特征。在此基础上进一步分析了主桁、平联和桥面参数对合成桥面桁梁扭转性能的影响，并从扭转应变能的角度揭示薄壁梁扭转属性，提出了以翘曲应变能与总的扭转应变能的比率作为衡量标准，当其小于0.05时结构扭转行为趋于自由扭转，还给出了该比率与控制性的无量纲参数——截面翘曲系数ν和杆件扭转系数的关系，揭示了悬索桥中常规桁梁、合成桥面桁梁、扁平钢箱梁的截面翘曲特点和扭转属性。
(3)合成桥面桁梁中钢桥面作为整个桁梁的翼缘参与整体受力，在竖向横力弯曲时会出现剪力滞问题。同样地将合成桥面桁梁转化成等效的薄壁梁，利用能量变分方法分析它的剪滞效应。针对合成桥面桁梁的结构特点，分析时引入梁的挠度、截面转角和翼缘最大纵向位移差三个独立的广义位移，同时引入一个全截面上均匀纵向位移以满足截面正应力平衡的条件，总势能计算时考虑主桁的比拟腹板的剪切应变能，也考虑了钢桥面作为加劲翼缘与平板翼缘的差异。按照最小势能原理建立了关于三个广义位移的基本微分方程。进一步分析了剪滞翘曲函数阶次的合理选取，以及桥面跨宽比、桥面板厚度、加劲肋板厚、加劲肋型式等结构参数影响有效宽度系数的变化规律。比较分析了多个外国规范中对加劲板翼缘有效宽度系数的具体规定，给出了推荐的方法。提出了节间剪滞效应的概念来分析主桁节点处桥面的应力集中问题。
(4)基于线性挠度理论，运用直接迭代解法分析悬索桥的竖向静力行为，获得了加劲梁在设计活载下的弯矩、剪力分布，再结合剪力滞理论解析地揭示了合成桥面桁架加劲梁在典型控制内力工况下的剪力滞特点，在集中荷载的直接作用截面，桥面应力的不均匀分布仍然可观。合成桥面桁架加劲梁的各个截面在最大弯矩工况下的桥面有效宽度系数很相近，这是有别于无缆索支承的单纯梁结构的特征。对于悬索桥的横向静力行为，运用三角级数解法求解横向膜理论，分析比较了合成桥面桁梁悬索桥与常规钢桁梁、钢箱梁悬索桥的横风荷载效应差异。
(5)推演了包含主缆和加劲梁完备位移的空间耦合振动方程，揭示了悬索桥面内振动和空间振动时的位移耦联关系。建立面内竖向—纵向耦合振动的实用分析模型，其中计入了主缆纵向位移因素，获得了低阶反对称竖向振动和纵向振动的耦合振动频率的估算公式，分析了缆、梁结构参数对耦合效应的影响，在实际的缆、梁结构参数范围限定下，这种耦合振动对于加劲梁纵向无约束的悬索桥是普遍存在的。针对设置中央扣的悬索桥，建立了考虑跨中位移的分段的主缆相容方程，以及跨中断面主缆纵向位移与中央扣、加劲梁变形的协调条件。从附加缆力发生变化的角度阐明了中央扣对各类振型的影响效果，在反对称扭转振动时，主缆在中央扣前后会产生反对称的附加缆力，从而提高该振型的频率。推演出设置中央扣的悬索桥的扭转振动方程，求得振动频率方程和振型表达式，提取了决定自振特征的无量纲参数，诸如主缆弹性刚度与主缆重力刚度及加劲梁刚度之和的比率等，并作了参数分析，得到了缆、梁结构参数和中央扣结构参数对扭转振型和频率的影响效果，还用里兹法得到包含中央扣影响的扭转频率估算公式。最后利用振动性状结果对背景工程澧水大桥的合成桥面桁梁方案作了风致稳定性评估。
In terms of the steel truss with integral steel deck (ISDT), an equivalent continuummodel is established, and theoretical investigation together with parametric analyses arestudied in the dissertation, primaryly focusing on warping torsion and shear lag effectsof ISDT, static behavior and free vibration characteristics of suspension bridge stiffenedby ISDT. The main contribution in the dissertation is as follows:
(1) The structural types and parameters of stiffening trusses of those in-servicesuspension bridges are summarized and statistically analyzed. The structural features ofthe types of different components are investigated, including the main truss, transversebracing, and lateral bracing. Based on statistic data, a criterion is proposed to determinethe key design parameters, such as the stiffening truss height. In addtition, the structuralcharacteristics and details of ISTD are described. Taken the Lishui Suspension Bridge asexample, an alternative scheme design using ISDT as stiffening girders is presentedcomparing with the original design using conventional stiffening truss with detachedreinforced concrete deck, and comparisons in terms of technology&economy are madebetween the reinforced concrete deck and the integral steel deck.
(2) the ISDT bridge is a composite structure consisting of orthotropic steel deckand spatial truss. The basic idea of continuum model method in analyzing struss bridgeis to transform the web member systems into equivalently continuous distributed shearthin-walls. By extending this method to the application of ISDT, concept of theequivalent normal and shear thickness are proposed for the orthotropic steel deck,reflecting its different abilities in resisting the normal strains and the shear strains; whilethe equivalent normal thickness of web member systems is taken as zero. Consequently,both conventional truss and ISDT are converted into the analogy thin-walled girders inthe form of identical parameters. According to the basic principles of Umansky’s secondtheory, warping restrainted torsion of the analogy girder is theoretically studied, and itstorsional characteristics are explicitly derived.
In addition, the influence of the variations in the geometrical dimensions of maintruss, lateral bracing and intergal steel deck on the torsional behavior of ISDT issubjected to parametric analysis. From the perspective of the torsional strain energy, thetorsional properties of thin-walled girder are revealed. The ratio of warping strainenergy to total strain energy is set as an estimate criteria. When this ratio is less than 0.05, the restrainted torsional behavior of the structure can be regarded as pure torsion.The correlations between this energy ratio with both the warping coefficient ofcross-section and the torsion coefficient of thin-walled girder are developed. Warpingcharacteristics and torsional properties of conventional truss, ISDT and flat box girderadopted in the suspension bridge, are revealed.
(3) The integral steel deck, acting as a flange, participates in overall mechanicalbehavior of ISDT bridge. Therefore, when the ISDT is under the vertical load, shear lagphenomenon will appear on the deck, similar as a common thin-walled girder with wideflange. By transfoming the ISDT into equivalent thin-walled girder, the shear lag effectof ISDT is studied with energy variation method. Considering the structuralcharacteristics of ISDT girder, three independent generalized displacement functions areemployed in the analysis, including the deflection, rotation angle of the girder and themaximum difference of warp displacement on flange. In addtion, an uniform warpingdisplacement on the whole cross section is chosen to meet the axial self-equilibriumcondition for normal stresses on section. When calculating general potential energy,shear strain energy of the analogy web of main trusses is taken into consideration, thefeature of the steel deck as stiffened flange distinguished from flat flange is alsoconsidered. The fundamental equations concerning the three generalized displacementare derived by the principle of minimum potential energy.
Furthmore, the reasonable order of shear lag warping function on flange isdiscussed. The correlations between the effective width coefficient and differentstructural parameters are developed, including deck span-width ratio, deck platethickness, stiffener thickness and the stiffener type. Based on the comparison of theeffective width coefficients of the stiffened flange among different specifications, therecommended method is presened.The concept of shear lag in panel truss is proposed for analyzing the stressconcentration on the integral deck near the main truss nodes.
(4) Based on the linear deflection theory, vertical static analysis of suspensionbridge is studied using direct iteration solution, obtaining the distribution patters ofbending moments and shear forces of stiffening girders. Combined with the shear lagtheory, the characteristics of shear lag in the stiffening ISDT girder are presented undertypical disadvantageous load cases. Non-uniform stress distribution on the deck is stillconsiderable at the position where concentrated load acts on. The effective widthcoefficients of the stiffening ISDT girder is similar along longitudinal axis, which isdifferent from a single girder without cables supporting. In addition, the lateral membrane theory in analysising the lateral static behaveor ofsuspension bridge, is solved with the application of trigonometric series method, theanalysis and comparison of loading effect caused by lateral wind forces are madebetween the suspension bridges stiffened by ISDT, and those bridge stiffened byConventional steel truss or steel box girder.
(5) The coupled vibration equations of the suspension bridge are deduced,involving the complete spacial displacements of the two cables and the stiffening girder,which reveals the multi-degree displacements coupling relationship on the cases ofin-plane vibration and spacial vibration of suspension bridge as a result.The practical simplified model is established for the in-plane vibration coupedlongitudinal and vertical motions, in which the effect of the cable’s longitudinal motionis considered. The frequency estimation formula to the lower-order antisymmetricvertical and longitudinal coupling mode is developed. The influence of the cables’ andthe stiffening girder’s geometric parameters on coupling effect is investigated. As tosuspension bridges without longitudinal constraint to stiffening girder, this kind ofcoupling vibration is generally common considering the practically-adopted parametersof cables and stiffeding girder of these existing bridges.
For the suspension bridge with center ties, the cables are respectively employed foreach half bridge, to establish the compatibility equations considering the longitudinaldisplacement of the cable at mid-span. In addition, the compatibility condition betweenthe longitudinal displacements of cables and the deformation of both center ties andstiffening girder at mid-span is established. Based on the variation of additional cabletension caused by center ties, the effects of center tie to various mode cases are clarified.For the antisymmetric torsional vibration, the center tie’s restriction on the cable’slongitudinal movement causes an antisymmetric additional cable tensions at mid-span,which will enhance its natural frequency as a result. The torsional vibration differentialequation of the suspension bridge with center ties is derived theoretically, and thegeneral expressions of mode shapes and the implicit equations of frequencies arepresented. The dimensionless parameters controlling the vibration characteristics, suchas the ratio of cables’ elastic stiffness to the sum of cables’ gravity stiffness togetherwith girder’s stiffness, are defined and discussed, to reveal the effectes of themechanical parameters of cables, stiffening girder and center ties on the torsional modesand frequencies. The approximate estimates for torsional symmetric and antisymmetricfundamental frequencies are obtained by the Ritz approach.
Finally, as to Lishui Suspension Bridge, the wind-induced stability assessment is evaluated for the proposed design scheme of the bridge stiffened by ISDT, based on thefree vibration analyse mentioned.
(1)对已修建悬索桥中的桁架加劲梁的型式和结构参数作了归纳和统计分析，分析了主桁、横联和水平联等桁片各自可选型式的特点，给出了桁梁高度等设计参数的经验取用规则。阐述了合成桥面桁梁的结构特点和构造型式，并以澧水大桥为工程背景，对照原设计的常规桁梁及混凝土桥面方案，设计了采用合成桥面桁梁作加劲梁的方案，对比分析了混凝土桥面和合成型钢桥面的技术经济特点。
(2)合成桥面桁梁是正交异性钢桥面和空间桁梁的组合结构。桁梁连续化方法的基本思想是将腹杆系转化成等效的剪切薄壁。本文将这一方法扩展到合成桥面桁梁中，提出了钢桥面的等效正向厚度和等效剪切厚度的概念，以体现其抵抗纵向变形和切向变形能力的差异，而桁架腹杆系的等效正向厚度取为零。由此桁梁、合成桥面桁梁形成参数形式上统一的比拟薄壁梁，再根据乌氏第二理论的基本原理分析它们的约束扭转问题，获得它们的扭转特征。在此基础上进一步分析了主桁、平联和桥面参数对合成桥面桁梁扭转性能的影响，并从扭转应变能的角度揭示薄壁梁扭转属性，提出了以翘曲应变能与总的扭转应变能的比率作为衡量标准，当其小于0.05时结构扭转行为趋于自由扭转，还给出了该比率与控制性的无量纲参数——截面翘曲系数ν和杆件扭转系数的关系，揭示了悬索桥中常规桁梁、合成桥面桁梁、扁平钢箱梁的截面翘曲特点和扭转属性。
(3)合成桥面桁梁中钢桥面作为整个桁梁的翼缘参与整体受力，在竖向横力弯曲时会出现剪力滞问题。同样地将合成桥面桁梁转化成等效的薄壁梁，利用能量变分方法分析它的剪滞效应。针对合成桥面桁梁的结构特点，分析时引入梁的挠度、截面转角和翼缘最大纵向位移差三个独立的广义位移，同时引入一个全截面上均匀纵向位移以满足截面正应力平衡的条件，总势能计算时考虑主桁的比拟腹板的剪切应变能，也考虑了钢桥面作为加劲翼缘与平板翼缘的差异。按照最小势能原理建立了关于三个广义位移的基本微分方程。进一步分析了剪滞翘曲函数阶次的合理选取，以及桥面跨宽比、桥面板厚度、加劲肋板厚、加劲肋型式等结构参数影响有效宽度系数的变化规律。比较分析了多个外国规范中对加劲板翼缘有效宽度系数的具体规定，给出了推荐的方法。提出了节间剪滞效应的概念来分析主桁节点处桥面的应力集中问题。
(4)基于线性挠度理论，运用直接迭代解法分析悬索桥的竖向静力行为，获得了加劲梁在设计活载下的弯矩、剪力分布，再结合剪力滞理论解析地揭示了合成桥面桁架加劲梁在典型控制内力工况下的剪力滞特点，在集中荷载的直接作用截面，桥面应力的不均匀分布仍然可观。合成桥面桁架加劲梁的各个截面在最大弯矩工况下的桥面有效宽度系数很相近，这是有别于无缆索支承的单纯梁结构的特征。对于悬索桥的横向静力行为，运用三角级数解法求解横向膜理论，分析比较了合成桥面桁梁悬索桥与常规钢桁梁、钢箱梁悬索桥的横风荷载效应差异。
(5)推演了包含主缆和加劲梁完备位移的空间耦合振动方程，揭示了悬索桥面内振动和空间振动时的位移耦联关系。建立面内竖向—纵向耦合振动的实用分析模型，其中计入了主缆纵向位移因素，获得了低阶反对称竖向振动和纵向振动的耦合振动频率的估算公式，分析了缆、梁结构参数对耦合效应的影响，在实际的缆、梁结构参数范围限定下，这种耦合振动对于加劲梁纵向无约束的悬索桥是普遍存在的。针对设置中央扣的悬索桥，建立了考虑跨中位移的分段的主缆相容方程，以及跨中断面主缆纵向位移与中央扣、加劲梁变形的协调条件。从附加缆力发生变化的角度阐明了中央扣对各类振型的影响效果，在反对称扭转振动时，主缆在中央扣前后会产生反对称的附加缆力，从而提高该振型的频率。推演出设置中央扣的悬索桥的扭转振动方程，求得振动频率方程和振型表达式，提取了决定自振特征的无量纲参数，诸如主缆弹性刚度与主缆重力刚度及加劲梁刚度之和的比率等，并作了参数分析，得到了缆、梁结构参数和中央扣结构参数对扭转振型和频率的影响效果，还用里兹法得到包含中央扣影响的扭转频率估算公式。最后利用振动性状结果对背景工程澧水大桥的合成桥面桁梁方案作了风致稳定性评估。
In terms of the steel truss with integral steel deck (ISDT), an equivalent continuummodel is established, and theoretical investigation together with parametric analyses arestudied in the dissertation, primaryly focusing on warping torsion and shear lag effectsof ISDT, static behavior and free vibration characteristics of suspension bridge stiffenedby ISDT. The main contribution in the dissertation is as follows:
(1) The structural types and parameters of stiffening trusses of those in-servicesuspension bridges are summarized and statistically analyzed. The structural features ofthe types of different components are investigated, including the main truss, transversebracing, and lateral bracing. Based on statistic data, a criterion is proposed to determinethe key design parameters, such as the stiffening truss height. In addtition, the structuralcharacteristics and details of ISTD are described. Taken the Lishui Suspension Bridge asexample, an alternative scheme design using ISDT as stiffening girders is presentedcomparing with the original design using conventional stiffening truss with detachedreinforced concrete deck, and comparisons in terms of technology&economy are madebetween the reinforced concrete deck and the integral steel deck.
(2) the ISDT bridge is a composite structure consisting of orthotropic steel deckand spatial truss. The basic idea of continuum model method in analyzing struss bridgeis to transform the web member systems into equivalently continuous distributed shearthin-walls. By extending this method to the application of ISDT, concept of theequivalent normal and shear thickness are proposed for the orthotropic steel deck,reflecting its different abilities in resisting the normal strains and the shear strains; whilethe equivalent normal thickness of web member systems is taken as zero. Consequently,both conventional truss and ISDT are converted into the analogy thin-walled girders inthe form of identical parameters. According to the basic principles of Umansky’s secondtheory, warping restrainted torsion of the analogy girder is theoretically studied, and itstorsional characteristics are explicitly derived.
In addition, the influence of the variations in the geometrical dimensions of maintruss, lateral bracing and intergal steel deck on the torsional behavior of ISDT issubjected to parametric analysis. From the perspective of the torsional strain energy, thetorsional properties of thin-walled girder are revealed. The ratio of warping strainenergy to total strain energy is set as an estimate criteria. When this ratio is less than 0.05, the restrainted torsional behavior of the structure can be regarded as pure torsion.The correlations between this energy ratio with both the warping coefficient ofcross-section and the torsion coefficient of thin-walled girder are developed. Warpingcharacteristics and torsional properties of conventional truss, ISDT and flat box girderadopted in the suspension bridge, are revealed.
(3) The integral steel deck, acting as a flange, participates in overall mechanicalbehavior of ISDT bridge. Therefore, when the ISDT is under the vertical load, shear lagphenomenon will appear on the deck, similar as a common thin-walled girder with wideflange. By transfoming the ISDT into equivalent thin-walled girder, the shear lag effectof ISDT is studied with energy variation method. Considering the structuralcharacteristics of ISDT girder, three independent generalized displacement functions areemployed in the analysis, including the deflection, rotation angle of the girder and themaximum difference of warp displacement on flange. In addtion, an uniform warpingdisplacement on the whole cross section is chosen to meet the axial self-equilibriumcondition for normal stresses on section. When calculating general potential energy,shear strain energy of the analogy web of main trusses is taken into consideration, thefeature of the steel deck as stiffened flange distinguished from flat flange is alsoconsidered. The fundamental equations concerning the three generalized displacementare derived by the principle of minimum potential energy.
Furthmore, the reasonable order of shear lag warping function on flange isdiscussed. The correlations between the effective width coefficient and differentstructural parameters are developed, including deck span-width ratio, deck platethickness, stiffener thickness and the stiffener type. Based on the comparison of theeffective width coefficients of the stiffened flange among different specifications, therecommended method is presened.The concept of shear lag in panel truss is proposed for analyzing the stressconcentration on the integral deck near the main truss nodes.
(4) Based on the linear deflection theory, vertical static analysis of suspensionbridge is studied using direct iteration solution, obtaining the distribution patters ofbending moments and shear forces of stiffening girders. Combined with the shear lagtheory, the characteristics of shear lag in the stiffening ISDT girder are presented undertypical disadvantageous load cases. Non-uniform stress distribution on the deck is stillconsiderable at the position where concentrated load acts on. The effective widthcoefficients of the stiffening ISDT girder is similar along longitudinal axis, which isdifferent from a single girder without cables supporting. In addition, the lateral membrane theory in analysising the lateral static behaveor ofsuspension bridge, is solved with the application of trigonometric series method, theanalysis and comparison of loading effect caused by lateral wind forces are madebetween the suspension bridges stiffened by ISDT, and those bridge stiffened byConventional steel truss or steel box girder.
(5) The coupled vibration equations of the suspension bridge are deduced,involving the complete spacial displacements of the two cables and the stiffening girder,which reveals the multi-degree displacements coupling relationship on the cases ofin-plane vibration and spacial vibration of suspension bridge as a result.The practical simplified model is established for the in-plane vibration coupedlongitudinal and vertical motions, in which the effect of the cable’s longitudinal motionis considered. The frequency estimation formula to the lower-order antisymmetricvertical and longitudinal coupling mode is developed. The influence of the cables’ andthe stiffening girder’s geometric parameters on coupling effect is investigated. As tosuspension bridges without longitudinal constraint to stiffening girder, this kind ofcoupling vibration is generally common considering the practically-adopted parametersof cables and stiffeding girder of these existing bridges.
For the suspension bridge with center ties, the cables are respectively employed foreach half bridge, to establish the compatibility equations considering the longitudinaldisplacement of the cable at mid-span. In addition, the compatibility condition betweenthe longitudinal displacements of cables and the deformation of both center ties andstiffening girder at mid-span is established. Based on the variation of additional cabletension caused by center ties, the effects of center tie to various mode cases are clarified.For the antisymmetric torsional vibration, the center tie’s restriction on the cable’slongitudinal movement causes an antisymmetric additional cable tensions at mid-span,which will enhance its natural frequency as a result. The torsional vibration differentialequation of the suspension bridge with center ties is derived theoretically, and thegeneral expressions of mode shapes and the implicit equations of frequencies arepresented. The dimensionless parameters controlling the vibration characteristics, suchas the ratio of cables’ elastic stiffness to the sum of cables’ gravity stiffness togetherwith girder’s stiffness, are defined and discussed, to reveal the effectes of themechanical parameters of cables, stiffening girder and center ties on the torsional modesand frequencies. The approximate estimates for torsional symmetric and antisymmetricfundamental frequencies are obtained by the Ritz approach.
Finally, as to Lishui Suspension Bridge, the wind-induced stability assessment is evaluated for the proposed design scheme of the bridge stiffened by ISDT, based on thefree vibration analyse mentioned.
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