混凝土箱梁剪力滞效应的分析理论与应用研究
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摘要
混凝土箱梁是目前简支梁、连续梁、连续刚构、刚性系杆拱桥和混凝土斜拉桥等桥梁常用的主梁结构形式。本文针对翼板厚度沿横向变化的混凝土箱梁,通过理论研究并结合数值模拟和试验结果,系统研究了混凝土箱梁剪力滞效应理论分析中的关键问题。
主要研究成果如下：
(1)针对翼板沿截面宽度方向变厚度的混凝土箱梁,利用势能变分原理,在引入广义截面特性参数的基础上,建立了可以考虑翼板厚度变化的混凝土箱梁的剪力滞效应分析通用分析方法。针对简支梁和悬臂梁等基本结构体系,建立了集中力、均布荷载和集中弯矩等典型荷载作用下剪力滞效应分析的通用公式。
(2)从薄壁箱梁的剪力滞效应是由于翼板剪切变形所致这一本质出发,通过分析箱梁在竖向弯曲时翼板的剪力流分布规律,创造性地提出了利用翼板剪切变形规律来定义其剪力滞翘曲函数的新方法。针对常见的单室箱梁,定义出截面仅有一个未知翼板剪切变形最大差,各翼板符合剪切变形规律的新翘曲位移函数。通过对典型结构的剪力滞效应分析得出,本文分析结果与模型试验值、基于板壳元的数值解以及截面具有3个未知剪切变形最大差的变分解吻合良好。证明了本文提出的基于翼板剪切变形规律的剪力滞翘曲位移函数不仅原理明确,而且具有未知变量少、适用性广和分析精度高等特点。
(3)针对能量变分法研究箱梁剪力滞效应时引入截面中性轴与形心轴重合而产生的附加轴力问题,利用截面的静力平衡条件,建立了抛物线型翘曲位移函数下截面附加轴力的表达式,讨论了附加轴力的基本特点,并通过引入附加轴向应力比直观反映附加轴力的相对大小。通过简支梁、悬臂梁和连续梁等典型结构算例,并结合常规混凝土箱梁的统计研究,表明附加轴向应力对常规混凝土箱梁的影响在初等梁应力的5%以内,可以在定义抛物线型剪力滞翘曲位移函数时不进行轴向位移的修正以简化分析。
(4)结合考虑翼板厚度变化的混凝土箱梁剪力滞效应通用解答和基于翼板剪切变形规律的剪力滞翘曲位移函数,建立了翼板厚度变化混凝土箱梁的理论分析方法。通过对算例混凝土箱梁的剪力滞效应采用板壳数值解和本文理论解的对比分析,验证了本文分析方法的精度。通过改变翼板厚度,系统研究了翼板厚度变化对混凝土箱梁：正、负剪力滞和剪力滞附加挠度的影响规律。
(5)针对预应力混凝土箱梁,结合能量变分原理建立了直线布束、折线布束和曲线布束情况下,预应力等效荷载引起的剪力滞效应计算公式,完善了既有研究仅针对预应力锚固于形心轴的剪力滞效应计算方法。通过对静定简支梁、悬臂梁和超静定连续梁在常规配束下的剪力滞效应基本规律的系统研究表明,以提供截面抵抗弯矩为主的预应力筋,剪力滞效应将增大梁体弯矩和弯曲应力。预应力的剪力滞效应在锚固端、折角处及中间支座部位较为突出,而在曲线配束段较不明显。同时,根据预应力剪力滞效应的分布规律,提出了预应力设计的相关建议。
(6)在研究剪力滞效应对混凝土箱梁变形影响机理的基础上,首次提出采用剪力滞系数和有效翼缘分布宽度两种修正方法考虑剪力滞效应对挠度的影响,完善了既有规范中以实心梁为基础的挠度计算公式。通过典型算例表明,剪力滞系数的修正方法精度较高,但考虑到设计的方便性,建议在剪力滞系数未知的情况下可采用有效翼缘分布宽度修正方法考虑剪力滞效应对刚度的影响。
Concrete box beams are commonly used as mail girders for simply supported girder bridges, continuum girder bridges, continuous rigid frame bridges, rigid tied arch bridges and concrete cable-stayed bridges. In this paper, key problems of shear lag calculation for concrete box beam are systematically studied through theoretical analysis, numerical simulation and experimental results. The mail work and achievements are as follows.
(1) Based on variational principle of potential energy, new analysis method for shear lag effect is presented for commonly single cell concrete box beam which flanges' depth varying along cross section. General solution formulae of longitudinal stresses and bending deflections for simply supported girders and cantilever girders are developed under concentrated force, uniform load and concentrated bending moment.
(2) For vertical bending box beams, shear lag occurs because of shear deformations of wide flanges in planes of themselves. According to this mechanism of shear lag, new method for defining functions of shear-lag warping displacement is presented. For commonly single cell box beam, new shear-lag warping displacements are defined which only includes one unknown maximum angular rotation but satisfies shear deformation principle. The governing differential equations for shear lag of box girders are established based on variational principles. After shear lag analysis according to typical structures, it's shown that the results obtained using new warping displacement are in good agreement with model test results, finite element results and variational results with 3 maximum angular rotations. It's proved that the new method to define warping displacement of shear lag concerned on the shear deformations of flanges has the features of clear mechanism, fewer variables and higher precise.
(3) When analysis shear lag of box girder by variation principle method and beam finite element method, the shear lag warping displacement of spanwise sheet is always supposed to be parabola. It will cause additional axial force when supposing the neutral axis through the sectional centroid. Based on the balance condition of whole section, the formula of additional axial force is presented for parabolical shear lag warping displacement, and the basic character of additional axial force is discussed. For measure the value of additional axial force, the parameter of ratio of additional axial stress (RAAS) is posed. The RAAS of simple supported, cantilever and continuous beam are analyzed under concentrated load and uniform load. It's shown for common concrete bridges RAAS are usual less than 5%, so additional axial force has little influence for precision of stresses, and the parabolical shear lag warping displacement has high analysis precision and needless to be revised with axial displacement.
(4) Based on new shear lag method and new warping displacement functions, shear lag analysis method is developed for concrete box with varying flanges depth along cross section. For example concrete box girders, shear lag effect which calculated using this paper's theoretical formulae are good agreement with shell finite element method. By changing the depth of flanges, influence of varying depth on positive, negative shear lag and additional deformation caused by shear lag is investigated.
(5) For prestressed concrete (PC) box girders, calculation method for shear lag effect caused by prestressed tendons is developed based on equivalent load method. Shear lag effect of PC continuum box girders with straight and arbitrary lineshape tendons is analyzed. It's drown for prestressed tendons which are mainly used to resist bending moment, shear lag effect will commonly increase the bending moment and stress. Prestressed tendons can always cause more significant shear lag effect in regions of near anchor end, angle changing and intermediate supports than smoothing curve regions. Finally, suggestions of prestressing design are presented according to distribution rules of shear lag for PC box girders.
(6) Based on study of shear lag influence on deflection for box girders, two methods which are shear lag coefficient (SLC) and effective flange width (EFW) are presented to modify box girder's deflection. Researches for typical box girders show despite SLC method has more accuracy than EFW, EFW method can be used to calculation box girders'deflection when SLC is unknown.
主要研究成果如下：
(1)针对翼板沿截面宽度方向变厚度的混凝土箱梁,利用势能变分原理,在引入广义截面特性参数的基础上,建立了可以考虑翼板厚度变化的混凝土箱梁的剪力滞效应分析通用分析方法。针对简支梁和悬臂梁等基本结构体系,建立了集中力、均布荷载和集中弯矩等典型荷载作用下剪力滞效应分析的通用公式。
(2)从薄壁箱梁的剪力滞效应是由于翼板剪切变形所致这一本质出发,通过分析箱梁在竖向弯曲时翼板的剪力流分布规律,创造性地提出了利用翼板剪切变形规律来定义其剪力滞翘曲函数的新方法。针对常见的单室箱梁,定义出截面仅有一个未知翼板剪切变形最大差,各翼板符合剪切变形规律的新翘曲位移函数。通过对典型结构的剪力滞效应分析得出,本文分析结果与模型试验值、基于板壳元的数值解以及截面具有3个未知剪切变形最大差的变分解吻合良好。证明了本文提出的基于翼板剪切变形规律的剪力滞翘曲位移函数不仅原理明确,而且具有未知变量少、适用性广和分析精度高等特点。
(3)针对能量变分法研究箱梁剪力滞效应时引入截面中性轴与形心轴重合而产生的附加轴力问题,利用截面的静力平衡条件,建立了抛物线型翘曲位移函数下截面附加轴力的表达式,讨论了附加轴力的基本特点,并通过引入附加轴向应力比直观反映附加轴力的相对大小。通过简支梁、悬臂梁和连续梁等典型结构算例,并结合常规混凝土箱梁的统计研究,表明附加轴向应力对常规混凝土箱梁的影响在初等梁应力的5%以内,可以在定义抛物线型剪力滞翘曲位移函数时不进行轴向位移的修正以简化分析。
(4)结合考虑翼板厚度变化的混凝土箱梁剪力滞效应通用解答和基于翼板剪切变形规律的剪力滞翘曲位移函数,建立了翼板厚度变化混凝土箱梁的理论分析方法。通过对算例混凝土箱梁的剪力滞效应采用板壳数值解和本文理论解的对比分析,验证了本文分析方法的精度。通过改变翼板厚度,系统研究了翼板厚度变化对混凝土箱梁：正、负剪力滞和剪力滞附加挠度的影响规律。
(5)针对预应力混凝土箱梁,结合能量变分原理建立了直线布束、折线布束和曲线布束情况下,预应力等效荷载引起的剪力滞效应计算公式,完善了既有研究仅针对预应力锚固于形心轴的剪力滞效应计算方法。通过对静定简支梁、悬臂梁和超静定连续梁在常规配束下的剪力滞效应基本规律的系统研究表明,以提供截面抵抗弯矩为主的预应力筋,剪力滞效应将增大梁体弯矩和弯曲应力。预应力的剪力滞效应在锚固端、折角处及中间支座部位较为突出,而在曲线配束段较不明显。同时,根据预应力剪力滞效应的分布规律,提出了预应力设计的相关建议。
(6)在研究剪力滞效应对混凝土箱梁变形影响机理的基础上,首次提出采用剪力滞系数和有效翼缘分布宽度两种修正方法考虑剪力滞效应对挠度的影响,完善了既有规范中以实心梁为基础的挠度计算公式。通过典型算例表明,剪力滞系数的修正方法精度较高,但考虑到设计的方便性,建议在剪力滞系数未知的情况下可采用有效翼缘分布宽度修正方法考虑剪力滞效应对刚度的影响。
Concrete box beams are commonly used as mail girders for simply supported girder bridges, continuum girder bridges, continuous rigid frame bridges, rigid tied arch bridges and concrete cable-stayed bridges. In this paper, key problems of shear lag calculation for concrete box beam are systematically studied through theoretical analysis, numerical simulation and experimental results. The mail work and achievements are as follows.
(1) Based on variational principle of potential energy, new analysis method for shear lag effect is presented for commonly single cell concrete box beam which flanges' depth varying along cross section. General solution formulae of longitudinal stresses and bending deflections for simply supported girders and cantilever girders are developed under concentrated force, uniform load and concentrated bending moment.
(2) For vertical bending box beams, shear lag occurs because of shear deformations of wide flanges in planes of themselves. According to this mechanism of shear lag, new method for defining functions of shear-lag warping displacement is presented. For commonly single cell box beam, new shear-lag warping displacements are defined which only includes one unknown maximum angular rotation but satisfies shear deformation principle. The governing differential equations for shear lag of box girders are established based on variational principles. After shear lag analysis according to typical structures, it's shown that the results obtained using new warping displacement are in good agreement with model test results, finite element results and variational results with 3 maximum angular rotations. It's proved that the new method to define warping displacement of shear lag concerned on the shear deformations of flanges has the features of clear mechanism, fewer variables and higher precise.
(3) When analysis shear lag of box girder by variation principle method and beam finite element method, the shear lag warping displacement of spanwise sheet is always supposed to be parabola. It will cause additional axial force when supposing the neutral axis through the sectional centroid. Based on the balance condition of whole section, the formula of additional axial force is presented for parabolical shear lag warping displacement, and the basic character of additional axial force is discussed. For measure the value of additional axial force, the parameter of ratio of additional axial stress (RAAS) is posed. The RAAS of simple supported, cantilever and continuous beam are analyzed under concentrated load and uniform load. It's shown for common concrete bridges RAAS are usual less than 5%, so additional axial force has little influence for precision of stresses, and the parabolical shear lag warping displacement has high analysis precision and needless to be revised with axial displacement.
(4) Based on new shear lag method and new warping displacement functions, shear lag analysis method is developed for concrete box with varying flanges depth along cross section. For example concrete box girders, shear lag effect which calculated using this paper's theoretical formulae are good agreement with shell finite element method. By changing the depth of flanges, influence of varying depth on positive, negative shear lag and additional deformation caused by shear lag is investigated.
(5) For prestressed concrete (PC) box girders, calculation method for shear lag effect caused by prestressed tendons is developed based on equivalent load method. Shear lag effect of PC continuum box girders with straight and arbitrary lineshape tendons is analyzed. It's drown for prestressed tendons which are mainly used to resist bending moment, shear lag effect will commonly increase the bending moment and stress. Prestressed tendons can always cause more significant shear lag effect in regions of near anchor end, angle changing and intermediate supports than smoothing curve regions. Finally, suggestions of prestressing design are presented according to distribution rules of shear lag for PC box girders.
(6) Based on study of shear lag influence on deflection for box girders, two methods which are shear lag coefficient (SLC) and effective flange width (EFW) are presented to modify box girder's deflection. Researches for typical box girders show despite SLC method has more accuracy than EFW, EFW method can be used to calculation box girders'deflection when SLC is unknown.
引文
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