具有自加劲板的多塔斜拉桥双曲线索塔研究
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摘要
本文以赤石大桥为工程背景，为解决多塔斜拉桥的刚度偏弱问题，提出了一种具有自加劲板的多塔斜拉桥双曲线索塔结构，并解决了两个技术难题：①多塔斜拉桥与常规斜拉桥(双塔或独塔斜拉桥)相比，具有较弱的整体刚度；②由于桥面以下的塔柱较高，如何减少结构在季节温差下的附加内力以及主梁热胀冷缩引起的桥面位置处塔柱水平位移。
本文完成了双曲线索塔的设计，对采用双曲线索塔后的赤石大桥进行静力分析、极限承载能力分析以及索塔塔柱的模型试验，并对组成索塔结构的自加劲板进行相关研究，主要完成了以下工作：
(1)分析多塔斜拉桥整体刚度偏弱的原因，并探讨了一些常用提高多塔斜拉桥整体刚度的方式以及实际工程应用。比较多塔斜拉桥的稳定性问题与一般的斜拉桥的稳定问题的不同之处。参考世界著名多塔斜拉桥索塔设计思想，结合本桥的实际情况，首次提出了可用于高墩多塔斜拉桥的双曲线索塔设计方案并应用于赤石大桥。对赤石大桥分别进行索塔优化前和优化后的有限元分析，比较结构静力、稳定性和动力特性等方面的结构响应以及对优化后的双曲线索塔的哑铃型双肢薄壁墩高度、上塔柱斜腿柱间距及结构体系进行了敏感性分析。
(2)通过对试验模型①和②进行理论计算和试验研究，分析双曲线索塔结构的传力途径，即恒载和活载引起的竖向荷载通过上塔柱的四肢将传递至中塔柱的双肢，再由中塔柱的双肢哑铃型结构传递至下塔柱的独柱箱形结构。通过试验模型应力分布规律及裂缝分布揭示双曲线索塔结构的受力状态，通过试验结果完善赤石大桥的索塔结构设计，弥补了设计时的盲区，从技术上保证了赤石大桥的这种索塔结构的技术可靠性。
(3)提出了自加劲板的概念和设计，并将这种设计应用于实际工程。自加劲板仅仅是通过自身几何形状的改变就获得了比普通平板更好的稳定性。提出了自加劲板的等效算法，分别按轴向刚度等效和抗弯刚度等效的原则进行等效弹性常数的推导并进行验证。根据实际边界条件进行弹性常数的修正，分析得出不需要进行弹性常数修正的一些边界条件，针对需要修正的边界条件，经过大量计算分析，整理出用于修正弹性常数的弹性系数表，计算时可查表得到弹性系数。对影响自加劲板弹性屈曲荷载的一些影响参数进行分析，探讨了自加劲板的可能屈曲模式。
(4)推导了正交异性板的弹性屈曲临界荷载计算公式并进行了验证，利用正交异性板弹性屈曲临界荷载的理论计算公式计算自加劲板的弹性屈曲临界荷载值。推导了中央布置一道加劲肋的正交异性板弹性屈曲临界荷载计算公式以及屈曲时的板件的半波个数的计算式，利用计算中央布置一道加劲肋的正交异性板弹性屈曲临界荷载的理论计算公式计算中央布置一道加劲肋的自加劲板的弹性屈曲临界荷载值及屈曲时的半波数。研究了混凝土板的几何、材料非线性分析理论，提出了同时考虑几何和材料双重非线性、并计入初始变形的自加劲板的稳定承载力分析方法。本章还分别针对无加劲肋的自加劲板和在其中央布置一道加劲肋的自加劲板进行承载能力分析，分析时比较了只考虑几何非线性、只考虑材料非线性以及同时考虑了几何和材料双重非线性三种情况对板件承载能力的影响。分别采用各国规范对钢板结构初始变形的规定以及公路工程质量检验评定标准(JTGF80-1-2004)规定斜拉桥或悬索桥索塔施工误差分析初始变形对自加劲板承载能力的影响。
(5)总结并比较结构极限承载力的三种判别准则，依据判别准则一(刚度矩阵奇异)和准则二(材料破坏)计入几何非线性和材料非线性对赤石大桥进行了施工阶段和成桥运营阶段极限承载能力分析。对下塔柱四种截面形式、混凝土的两种本构关系以及结构初始缺陷对斜拉桥极限承载力的影响进行了分析。
通过完成上述工作，静力分析结果、极限承载力分析结果以及塔柱试验结果均说明作者提出原创性的双曲线索塔可用于多塔斜拉桥结构，均能满足力学性能和桥梁美学的要求。算例结果表明对自加劲板按轴向刚度等效和抗弯刚度等效的原则进行等效―构造性正交异性板‖弹性常数的推导以及对有、无加劲肋的正交异性板的弹性屈曲临界荷载及屈曲半波数的计算公式的推导得到验证。塔柱模型试验结果表明双曲线索塔在裸塔以及成桥运营状态下均能满足规范要求。
To solve the problem of relatively lower bending stiffness of the multi-spancable-stayed bridges, a hyperbolic tower with self-stiffened plates was proposed,which solve two key problems in the design of Chishi Bridge as follows:(1)Multi-span cable-stayed bridges are of relatively lower bending stiffness and resultin higher stress amplitude of main girder under service vehicle load overconventional cable-stayed bridges with three spans (one middle span plus two sidespans);(2) How to decrease additional internal forces and horizontal displacementof high pier due to seasonal temperature variation.
The design of hyperbolic tower, static analysis, analysis of ultimate capacity,experimental research of tower and research of self-stiffened plate have done in thethesis. The main contents of this dissertation are described as following:
(1) Researching on the reason of multi-span cable-stayed bridge with relativelylower bending stiffness and discussing some methods which could improve thebending stiffness of multi-span cable-stayed bridge. The stability of multi-spancable-stayed bridge and normal cable-stayed bridge were compared in the thesis.The hyperbolic tower was designed and applied in Chishi Bridge through learningthe design of tower in some famous cable-stayed bridges. The Chishi Bridge withsingle tower and hyperbolic tower were analyzed with finite element analysis,which included the static analysis, stability analysis and dynamic analysis,respectively. Parameter of hyperbolic tower which including space between tw oinclined leg columns of the A-type pylon, height of twin pier and connection amongthe A-type pylon, pier and main girder were analysed in the thesis.
(2) The force transmission route that the vertical force caused by dead load andalive load flow from four legs of A-type pylon to twin pier and single pier, wereobtained through theoretical calculation and experimental research of test model①and test model②. The result of model test indicated the stress and cracksdistribution of hyperbolic tower. The design of tower was improved according to theexperimental result.
(3) The concept of self-stiffened plate was proposed and applied in the towerof Chishi Bridge. Compared to the flat plate, the self-stiffened plate is of betterstability by changing its own geometry. The equivalent algorithm that self-stiffened plate was equivalent with orthotropic plate was proposed, and the equivalentconstants were deduced with principle of axial rigidity and bending rigidity,respectively. Some equivalent constants need to be modified in some boundarycondition and the elasticity coefficient which was used to modify the equivalentconstant was proposed. Some influence parameters were researched to analysebucking load and buckling modal of self-stiffened plate.
(4) The formula about critical buckling load of orthotropic plate was deducedand vertified. The formula about critical buckling load of orthotropic p late was usedto calculate the critical buckling load of self-stiffened plate. The formula aboutcritical buckling load of orthotropic plate with one stiffener in the center of plate,and the formula about the amount of half-wave when the orthotropic plate was inthe buckling state were deduced, respectively. The critical buckling load and theamount of half-wave of self-stiffened plate with one stiffener in the center of platecould be calculated with the deduced formula. The analytical method aboutstabilization capability of self stiffened plate basing on geometric nonlinear,material nonlinear and initial deformation of plate was proposed. The bearingcapacity of self-stiffened plate with no stiffener and with one ribbed stiffener in thecenter of plate were analysed basing on three case: geometric nonlinear, materialnonlinear and double nonlinear.
(5) Three criterions about ultimate bearing capacity of structure werecompared. Basing on the double nonlinear including geometric nonlinear andmaterial nonlinear, the ultimate bearing capacity of Chishi Bridge in state ofconstruction and service were calculated with criterion number one(stiffness matrix)and criterion number two(material damage), respectively. The ultimate bearingcapacity of Chishi Bridge with four different cross section of single pier, twoconstitutive relation of concrete and initial deformation were researched,respectively.
The result of static analysis, ultimate bearing capacity and experimentalresearch of tower indicated the novelty hyperbolic tower with better aesthetics andmechanical property could be applied in the multi-span cable-stayed bridge throughthe research above. The calculation result of self stiffened plate indicated that thededuced formula about equivalent constants and critical buckling load were correctand valid. The result of model test indicated the hyperbolic tower satisfy thespecification in state of construction and service.
本文完成了双曲线索塔的设计，对采用双曲线索塔后的赤石大桥进行静力分析、极限承载能力分析以及索塔塔柱的模型试验，并对组成索塔结构的自加劲板进行相关研究，主要完成了以下工作：
(1)分析多塔斜拉桥整体刚度偏弱的原因，并探讨了一些常用提高多塔斜拉桥整体刚度的方式以及实际工程应用。比较多塔斜拉桥的稳定性问题与一般的斜拉桥的稳定问题的不同之处。参考世界著名多塔斜拉桥索塔设计思想，结合本桥的实际情况，首次提出了可用于高墩多塔斜拉桥的双曲线索塔设计方案并应用于赤石大桥。对赤石大桥分别进行索塔优化前和优化后的有限元分析，比较结构静力、稳定性和动力特性等方面的结构响应以及对优化后的双曲线索塔的哑铃型双肢薄壁墩高度、上塔柱斜腿柱间距及结构体系进行了敏感性分析。
(2)通过对试验模型①和②进行理论计算和试验研究，分析双曲线索塔结构的传力途径，即恒载和活载引起的竖向荷载通过上塔柱的四肢将传递至中塔柱的双肢，再由中塔柱的双肢哑铃型结构传递至下塔柱的独柱箱形结构。通过试验模型应力分布规律及裂缝分布揭示双曲线索塔结构的受力状态，通过试验结果完善赤石大桥的索塔结构设计，弥补了设计时的盲区，从技术上保证了赤石大桥的这种索塔结构的技术可靠性。
(3)提出了自加劲板的概念和设计，并将这种设计应用于实际工程。自加劲板仅仅是通过自身几何形状的改变就获得了比普通平板更好的稳定性。提出了自加劲板的等效算法，分别按轴向刚度等效和抗弯刚度等效的原则进行等效弹性常数的推导并进行验证。根据实际边界条件进行弹性常数的修正，分析得出不需要进行弹性常数修正的一些边界条件，针对需要修正的边界条件，经过大量计算分析，整理出用于修正弹性常数的弹性系数表，计算时可查表得到弹性系数。对影响自加劲板弹性屈曲荷载的一些影响参数进行分析，探讨了自加劲板的可能屈曲模式。
(4)推导了正交异性板的弹性屈曲临界荷载计算公式并进行了验证，利用正交异性板弹性屈曲临界荷载的理论计算公式计算自加劲板的弹性屈曲临界荷载值。推导了中央布置一道加劲肋的正交异性板弹性屈曲临界荷载计算公式以及屈曲时的板件的半波个数的计算式，利用计算中央布置一道加劲肋的正交异性板弹性屈曲临界荷载的理论计算公式计算中央布置一道加劲肋的自加劲板的弹性屈曲临界荷载值及屈曲时的半波数。研究了混凝土板的几何、材料非线性分析理论，提出了同时考虑几何和材料双重非线性、并计入初始变形的自加劲板的稳定承载力分析方法。本章还分别针对无加劲肋的自加劲板和在其中央布置一道加劲肋的自加劲板进行承载能力分析，分析时比较了只考虑几何非线性、只考虑材料非线性以及同时考虑了几何和材料双重非线性三种情况对板件承载能力的影响。分别采用各国规范对钢板结构初始变形的规定以及公路工程质量检验评定标准(JTGF80-1-2004)规定斜拉桥或悬索桥索塔施工误差分析初始变形对自加劲板承载能力的影响。
(5)总结并比较结构极限承载力的三种判别准则，依据判别准则一(刚度矩阵奇异)和准则二(材料破坏)计入几何非线性和材料非线性对赤石大桥进行了施工阶段和成桥运营阶段极限承载能力分析。对下塔柱四种截面形式、混凝土的两种本构关系以及结构初始缺陷对斜拉桥极限承载力的影响进行了分析。
通过完成上述工作，静力分析结果、极限承载力分析结果以及塔柱试验结果均说明作者提出原创性的双曲线索塔可用于多塔斜拉桥结构，均能满足力学性能和桥梁美学的要求。算例结果表明对自加劲板按轴向刚度等效和抗弯刚度等效的原则进行等效―构造性正交异性板‖弹性常数的推导以及对有、无加劲肋的正交异性板的弹性屈曲临界荷载及屈曲半波数的计算公式的推导得到验证。塔柱模型试验结果表明双曲线索塔在裸塔以及成桥运营状态下均能满足规范要求。
To solve the problem of relatively lower bending stiffness of the multi-spancable-stayed bridges, a hyperbolic tower with self-stiffened plates was proposed,which solve two key problems in the design of Chishi Bridge as follows:(1)Multi-span cable-stayed bridges are of relatively lower bending stiffness and resultin higher stress amplitude of main girder under service vehicle load overconventional cable-stayed bridges with three spans (one middle span plus two sidespans);(2) How to decrease additional internal forces and horizontal displacementof high pier due to seasonal temperature variation.
The design of hyperbolic tower, static analysis, analysis of ultimate capacity,experimental research of tower and research of self-stiffened plate have done in thethesis. The main contents of this dissertation are described as following:
(1) Researching on the reason of multi-span cable-stayed bridge with relativelylower bending stiffness and discussing some methods which could improve thebending stiffness of multi-span cable-stayed bridge. The stability of multi-spancable-stayed bridge and normal cable-stayed bridge were compared in the thesis.The hyperbolic tower was designed and applied in Chishi Bridge through learningthe design of tower in some famous cable-stayed bridges. The Chishi Bridge withsingle tower and hyperbolic tower were analyzed with finite element analysis,which included the static analysis, stability analysis and dynamic analysis,respectively. Parameter of hyperbolic tower which including space between tw oinclined leg columns of the A-type pylon, height of twin pier and connection amongthe A-type pylon, pier and main girder were analysed in the thesis.
(2) The force transmission route that the vertical force caused by dead load andalive load flow from four legs of A-type pylon to twin pier and single pier, wereobtained through theoretical calculation and experimental research of test model①and test model②. The result of model test indicated the stress and cracksdistribution of hyperbolic tower. The design of tower was improved according to theexperimental result.
(3) The concept of self-stiffened plate was proposed and applied in the towerof Chishi Bridge. Compared to the flat plate, the self-stiffened plate is of betterstability by changing its own geometry. The equivalent algorithm that self-stiffened plate was equivalent with orthotropic plate was proposed, and the equivalentconstants were deduced with principle of axial rigidity and bending rigidity,respectively. Some equivalent constants need to be modified in some boundarycondition and the elasticity coefficient which was used to modify the equivalentconstant was proposed. Some influence parameters were researched to analysebucking load and buckling modal of self-stiffened plate.
(4) The formula about critical buckling load of orthotropic plate was deducedand vertified. The formula about critical buckling load of orthotropic p late was usedto calculate the critical buckling load of self-stiffened plate. The formula aboutcritical buckling load of orthotropic plate with one stiffener in the center of plate,and the formula about the amount of half-wave when the orthotropic plate was inthe buckling state were deduced, respectively. The critical buckling load and theamount of half-wave of self-stiffened plate with one stiffener in the center of platecould be calculated with the deduced formula. The analytical method aboutstabilization capability of self stiffened plate basing on geometric nonlinear,material nonlinear and initial deformation of plate was proposed. The bearingcapacity of self-stiffened plate with no stiffener and with one ribbed stiffener in thecenter of plate were analysed basing on three case: geometric nonlinear, materialnonlinear and double nonlinear.
(5) Three criterions about ultimate bearing capacity of structure werecompared. Basing on the double nonlinear including geometric nonlinear andmaterial nonlinear, the ultimate bearing capacity of Chishi Bridge in state ofconstruction and service were calculated with criterion number one(stiffness matrix)and criterion number two(material damage), respectively. The ultimate bearingcapacity of Chishi Bridge with four different cross section of single pier, twoconstitutive relation of concrete and initial deformation were researched,respectively.
The result of static analysis, ultimate bearing capacity and experimentalresearch of tower indicated the novelty hyperbolic tower with better aesthetics andmechanical property could be applied in the multi-span cable-stayed bridge throughthe research above. The calculation result of self stiffened plate indicated that thededuced formula about equivalent constants and critical buckling load were correctand valid. The result of model test indicated the hyperbolic tower satisfy thespecification in state of construction and service.
引文
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