大跨度连续刚构桥设计若干关键技术问题研究
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摘要
随着交通工程建设的快速发展,能适应较宽桥面要求的单箱单室箱梁在连续梁桥、连续刚构桥建设中被广泛应用。无支架平衡悬臂施工工艺、新型高强材料的使用使其向大跨、薄壁、轻柔方向发展,这样结构的稳定问题、剪力滞问题及温度问题日益突出。因此,对此类桥梁结构的稳定性、剪力滞效应、温度场分布及其温度效应等方面的研究具有实际意义。本文以武汉天兴洲公铁两用长江大桥公路引线部分和平大道段连续刚构桥为背景,对以上相关领域进行了研究,主要工作包括如下内容。
以稳定性分析为目标,论述了稳定问题的两类数值解法及稳定评价指标与判别准则;在线弹性基础上,推导了高墩大跨连续刚构桥的自体稳定安全系数及悬臂施工阶段稳定安全系数的计算公式,对常截面与变截面墩自体稳定性的有限元解法与能量法进行了对比,并对不同施工阶段的各工况下的第一类稳定性进行了分析;引入初始缺陷,考虑几何非线性与几何、材料双重非线性的影响,采用弧长法对最大悬臂施工阶段的稳定性进行了分析,并对该桥的施工安全性能做出了评价。
基于最小势能原理的能量变分法,分别假定翼板纵向位移函数为三次抛物线和四次抛物线,得到箱梁剪力滞效应基本微分方程的变分解,在此基础上推导了集中荷载和均布荷载作用下等截面悬臂箱梁剪力滞效应系数的变分解式,并通过对影响截面剪力滞系数诸要素的分析,采用改进当量截面法,得到变截面悬臂箱梁的剪力滞系数理论解;分别分析了变截面箱梁和全桥在多种荷载工况下的剪力滞效应,有限元法与能量变分当量截面法的比较结果证实本文所采用的方法可有效准确地应用于计算变截面箱梁的剪力滞效应;分析了考虑了几何参数跨宽比、翼缘板刚度与截面总刚度对变截面悬臂箱形梁剪力滞效应的影响,翼板纵向位移函数变化规律形式对剪力滞系数计算精度的影响以及纵、横向预应力作用对箱梁剪力滞效应的影响。
在日照温度场方面,本文将预应力混凝土箱梁温度场归结为无内热源平面瞬态温度场问题,采用平面有限元方法,建立了热传导的有限元方程,推导了无内热源平面温度场有限元公式,以及混合边界单元的计算公式,将第二类边界条件与第三类边界条件统一起来,均以第三类边界条件形式进行边界处理。同时,详细阐述了影响预应力混凝土箱梁温度场分析的边界条件,研究了影响温度分布的各种因素,如桥梁方位、走向、材料特性、截面构造及环境条件等的影响,得到结构最不利温度场。根据得到结构最不利温度场,本文提出了两种适用于本工程的温度梯度分布模式。通过热-瞬态和热-结构耦合求解空间实体连续刚构桥的温度应力分布,求得求截面各点应力分布规律,并与本文提出两种温度梯度分布模式进行了对比。从而为求得适用于本工程的温度梯度模式提供了一种简化的计算公式。
With the rapid development of transportation engineering, the single-chest and single-room box girders which meet the requirements of wide bridge decks have been widely used in continuous girder bridges and continuous rigid-frame bridges. Technologies of balanceable cantilever construction without falsework, with the use of high-strength materials have made large span, thin-wall and light weight a tendency for bridges. Problems of structural stability, distribution of temperature field, thermal effect as well as shear lag effect have thereby become more and more critical. Study on these areas owns large significance for practical engineering. The relevant research has been carried out here on a real case of the large-span continuous rigid frame bridges which is a south approach of Tianxingzhou bridge in Wuhan, includeing the following works.
On the object of stability analysis, two kinds of numerical methodologies for structural stability as well as the corresponding analyzing criterions are discussed. The linear-elastic formulations for safety coefficients of both self stability and cantilever construction of continuous high-pier rigid-frame bridges are derived. Comparison is made between results of self stability analysis on both constant and varying sections by finite element method and energy method. Meanwhile, the first type stability of bridge in different constructing period under various working cases is also analyzed. In the stability analysis during the critical cantilever constructing period by arc-length method, initial deficiency, geometrical nonlinearity, as well as the dual nonlinearity are considered. On this basis, the constructing safety for the whole bridge is evaluated.
Based on the theory of minimum potential energy, the variational solution of the basic differential equations for the shear lag effect on the box beam is obtained. The displacement function is assumed as cubical and biquadratic parabolas respectively. Furthermore, the formulation of variational solution for the shear lag effect coefficient of constant-section cantilever box beam under evenly distributed load is derived. Hence, through analyzing the corresponding influencing factors, the theoretical solution of the shear lag coefficient of the box beam with reduced section is obtained with improved equivalent section method. Meanwhile, the shear lag effects of reduced-section box beam as well as the whole bridge under different working cases are also discussed. Comparison between the results from finite element method and energy method identifies that the method presented here can calculate the shear lag effect of the box beam with reduced section accurately. The influence of the width-span ratio, stiffness of flange as well as the stiffness of the section on the shear lag effect of reduced-section cantilever box beam is analyzed. The influence of the form of displacement function on the calculating accuracy of shear lag coefficient, together with the influence of lateral prestress on the shear lag effect of box beam is also discussed.
On the respect of temperature field of sunlight, the temperature filed in the prestressed concrete box beam is set on the assumption that there is no internal thermal source in planar transient state. Based on the planar finite element equations for thermal conduction being set up, the finite element formulation for the planar temperature field without internal thermal source and that for the mixed-edge element are derived. On this basis, the 2nd edge condition is integrated into the 3rd edge condition. Edge conditions that influence the analysis of temperature field of concrete box beam are represented. The least favorable temperature field of structures is obtained based on analyzing the influence factors on temperature distribution, such as orientation, trend, material properties, cross section, as well as the environment condition of the bridge. Thus, two kinds of gradient temperature distribution forms are proposed for this real case. The principles of stress distribution on sections are got by solving the temperature stress distribution of the spatial continuous rigid-frame bridge through coupling heat-transient state and heat-structure. Its comparison with the two kinds of gradient temperature distribution forms proposed here shows it has offered a simplified formulation for the calculation of gradient temperature distribution form.
以稳定性分析为目标,论述了稳定问题的两类数值解法及稳定评价指标与判别准则;在线弹性基础上,推导了高墩大跨连续刚构桥的自体稳定安全系数及悬臂施工阶段稳定安全系数的计算公式,对常截面与变截面墩自体稳定性的有限元解法与能量法进行了对比,并对不同施工阶段的各工况下的第一类稳定性进行了分析;引入初始缺陷,考虑几何非线性与几何、材料双重非线性的影响,采用弧长法对最大悬臂施工阶段的稳定性进行了分析,并对该桥的施工安全性能做出了评价。
基于最小势能原理的能量变分法,分别假定翼板纵向位移函数为三次抛物线和四次抛物线,得到箱梁剪力滞效应基本微分方程的变分解,在此基础上推导了集中荷载和均布荷载作用下等截面悬臂箱梁剪力滞效应系数的变分解式,并通过对影响截面剪力滞系数诸要素的分析,采用改进当量截面法,得到变截面悬臂箱梁的剪力滞系数理论解;分别分析了变截面箱梁和全桥在多种荷载工况下的剪力滞效应,有限元法与能量变分当量截面法的比较结果证实本文所采用的方法可有效准确地应用于计算变截面箱梁的剪力滞效应;分析了考虑了几何参数跨宽比、翼缘板刚度与截面总刚度对变截面悬臂箱形梁剪力滞效应的影响,翼板纵向位移函数变化规律形式对剪力滞系数计算精度的影响以及纵、横向预应力作用对箱梁剪力滞效应的影响。
在日照温度场方面,本文将预应力混凝土箱梁温度场归结为无内热源平面瞬态温度场问题,采用平面有限元方法,建立了热传导的有限元方程,推导了无内热源平面温度场有限元公式,以及混合边界单元的计算公式,将第二类边界条件与第三类边界条件统一起来,均以第三类边界条件形式进行边界处理。同时,详细阐述了影响预应力混凝土箱梁温度场分析的边界条件,研究了影响温度分布的各种因素,如桥梁方位、走向、材料特性、截面构造及环境条件等的影响,得到结构最不利温度场。根据得到结构最不利温度场,本文提出了两种适用于本工程的温度梯度分布模式。通过热-瞬态和热-结构耦合求解空间实体连续刚构桥的温度应力分布,求得求截面各点应力分布规律,并与本文提出两种温度梯度分布模式进行了对比。从而为求得适用于本工程的温度梯度模式提供了一种简化的计算公式。
With the rapid development of transportation engineering, the single-chest and single-room box girders which meet the requirements of wide bridge decks have been widely used in continuous girder bridges and continuous rigid-frame bridges. Technologies of balanceable cantilever construction without falsework, with the use of high-strength materials have made large span, thin-wall and light weight a tendency for bridges. Problems of structural stability, distribution of temperature field, thermal effect as well as shear lag effect have thereby become more and more critical. Study on these areas owns large significance for practical engineering. The relevant research has been carried out here on a real case of the large-span continuous rigid frame bridges which is a south approach of Tianxingzhou bridge in Wuhan, includeing the following works.
On the object of stability analysis, two kinds of numerical methodologies for structural stability as well as the corresponding analyzing criterions are discussed. The linear-elastic formulations for safety coefficients of both self stability and cantilever construction of continuous high-pier rigid-frame bridges are derived. Comparison is made between results of self stability analysis on both constant and varying sections by finite element method and energy method. Meanwhile, the first type stability of bridge in different constructing period under various working cases is also analyzed. In the stability analysis during the critical cantilever constructing period by arc-length method, initial deficiency, geometrical nonlinearity, as well as the dual nonlinearity are considered. On this basis, the constructing safety for the whole bridge is evaluated.
Based on the theory of minimum potential energy, the variational solution of the basic differential equations for the shear lag effect on the box beam is obtained. The displacement function is assumed as cubical and biquadratic parabolas respectively. Furthermore, the formulation of variational solution for the shear lag effect coefficient of constant-section cantilever box beam under evenly distributed load is derived. Hence, through analyzing the corresponding influencing factors, the theoretical solution of the shear lag coefficient of the box beam with reduced section is obtained with improved equivalent section method. Meanwhile, the shear lag effects of reduced-section box beam as well as the whole bridge under different working cases are also discussed. Comparison between the results from finite element method and energy method identifies that the method presented here can calculate the shear lag effect of the box beam with reduced section accurately. The influence of the width-span ratio, stiffness of flange as well as the stiffness of the section on the shear lag effect of reduced-section cantilever box beam is analyzed. The influence of the form of displacement function on the calculating accuracy of shear lag coefficient, together with the influence of lateral prestress on the shear lag effect of box beam is also discussed.
On the respect of temperature field of sunlight, the temperature filed in the prestressed concrete box beam is set on the assumption that there is no internal thermal source in planar transient state. Based on the planar finite element equations for thermal conduction being set up, the finite element formulation for the planar temperature field without internal thermal source and that for the mixed-edge element are derived. On this basis, the 2nd edge condition is integrated into the 3rd edge condition. Edge conditions that influence the analysis of temperature field of concrete box beam are represented. The least favorable temperature field of structures is obtained based on analyzing the influence factors on temperature distribution, such as orientation, trend, material properties, cross section, as well as the environment condition of the bridge. Thus, two kinds of gradient temperature distribution forms are proposed for this real case. The principles of stress distribution on sections are got by solving the temperature stress distribution of the spatial continuous rigid-frame bridge through coupling heat-transient state and heat-structure. Its comparison with the two kinds of gradient temperature distribution forms proposed here shows it has offered a simplified formulation for the calculation of gradient temperature distribution form.
引文
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