薄壁箱梁剪力滞效应的理论分析与试验研究
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摘要
随着箱形梁桥向长悬臂板、大肋间距的简洁型单箱单室截面方向发展，其剪力滞效应日益受到人们关注。近年来，许多专家、学者致力于箱梁剪力滞效应的研究，取得了一些研究成果，但仍有一些问题没有得到解决，特别是在变截面箱梁和曲线箱梁的剪力滞效应方面，有必要进一步深入开展研究工作。
本文以薄壁杆理论为基础，应用薄壁箱梁结构分析的能量泛函变分原理，建立了一套适合于薄壁箱梁的弯曲、弯扭、压弯和剪力滞效应的理论分析和计算方法，主要侧重于薄壁箱梁剪力滞效应的理论分析、试验研究及其对桥梁结构行为的影响。本文共有6章，第1章综述了薄壁箱梁剪力滞的研究理论和研究方法；第2章基于最小势能原理，分别建立了是否考虑剪切变形影响的剪力滞弹性力学求解的控制微分方程，结合边界条件，给出了剪力滞计算公式；第3章介绍了负剪力滞效应及其产生的机理,分析了悬臂箱梁和连续梁的负剪力滞及其影响因素；第4、5章利用能量变分法建立了薄壁曲线箱梁剪力滞效应的控制微分方程并给出了特定边界条件下的解析表达式，通过模型试验对曲线箱梁的力学特性、剪力滞效应进行了分析，研究了预应力对曲线箱梁剪力滞效应的影响；第6章对几种典型的单箱截面桥梁的剪力滞系数进行了三种计算方法的求解与分析，研究了几个典型桥梁考虑施工阶段的剪力滞分布规律。本文主要完成了以下工作:
1.以具有代表性的梯形箱梁为分析对象，结合薄壁杆理论和能量泛函变分原理，建立了薄壁箱梁弯曲和弯扭剪力滞效应的弹性力学求解体系，完善了薄壁箱梁剪力滞计算方法。
2.根据是否考虑剪切变形，构造了薄壁箱梁的剪力滞翘曲位移函数，依据能量泛函变分原理，分别建立了两种情况的剪力滞弹性力学求解的控制微分方程；结合边界条件，利用数学方法给出了控制微分方程的闭合解；给出了考虑剪力滞效应时简支梁和连续梁在集中荷载和均布荷载作用下应力和挠度的计算表达式；依据计算结果探讨了剪切变形效应对剪力滞效应的影响；结合计算实例对推导的理论公式进行了验证。
3.以悬臂箱梁和连续梁为例，阐述了负剪力滞现象及其产生机理，确定了正、负剪力滞效应的临界点，分析了剪切变形、泊松比、跨宽比、宽高比、宽厚比及刚度比等因素对悬臂梁和连续梁负剪力滞效应的影响。
4.针对薄壁曲线箱梁，依据薄壁曲杆理论，在曲线箱梁翼缘板的基本变形中补充了剪力滞翘曲位移函数，考虑曲线箱梁约束扭转时二次剪切变形对翘曲位移的影响，用能量变分原理建立了曲线箱梁剪力滞效应分析的控制微分方程及相应边界条件，将薄壁直线箱梁剪力滞的能量泛函变分原理推广到了曲线箱梁中，建立了弯、扭、剪力滞耦合的弹性控制微分方程，给出了计算简支曲梁的剪力滞计算解析表达式，并通过算例进行了验证；制作了有机玻璃模型，对两跨独柱支撑连续曲线刚构的剪力滞效应进行了试验研究，对该类型桥梁的设计和施工提供了科学依据。探讨了预应力曲线箱梁的剪力滞效应特点，采用理论分析与模型试验对比分析方法探讨了预应力对曲线箱梁剪力滞的影响。
5.应用变分法和Ansys有限元法对几种典型单箱截面桥梁进行剪力滞效应的分析与对比研究，得到了剪力滞效应对桥梁结构行为的影响规律，基于这些成果对箱形梁的设计给出了一些建议,对于同类型桥梁的剪力滞效应的研究和初步设计具有参考意义。
Along with the long cantilever plate, the big rib spacing,concise and the single-boxsingle-chamber box bridge, the shear lag effect has been payed attention gradually by people.In recent years, many experts and scholars have devoted themselves to the research of theshear lag effect, and have obtained some achievements. But some problems are still notsolved, especially the shear lag effect of the variable cross-section and curved box girders andit is necessary to research further.
Based on the theory of the thin walled bar and the application of the energy functionalvariation principle of the thin-wall box girder, a set of the theoretical calculation methodsuitable for the bending, bending and twisting, bending and the shear lag effect of thethin-walled box girders is established, and it mainly focuses on the theoretical analysis andtest research of the thin-wall box girder shear lag effect and the influence on the bridgebehavior. This paper has six chapters in common. the research theory and method of thethin-walled box girders shear lag are reviewed in the chapter one; Based on the principle ofthe minimum potential energy in chapter two,the shear lag governing differential equation isrespectively established whether the influence of shear deformation is considered or not. Theshear lag formula is given combined with the boundary conditions. The negative shear lageffect and the mechanism of generation are introduced, and the negative shear lag and itsinfluence factors of the cantilever box girder and continuous beam are analyzed in the chapterthree. The control differential equation of the thin wall curved bridge shear lag effect and theanalytical expression under the specific boundary conditions are established by using theenergy variation method in chapter4,5. The mechanical properties and the shear lag effect ofthe curved bridge are analyzed through the model test, and the influence of prestress on theshear lag effect of the curved bridge is studied. The shear lag coefficient of several typicalsingle-box bridge is solved and analyzed by adopting the three kinds of calculation methodsin chapter six, and the distribution regularity of shear lag is studied when the constructionstages of several typical bridge are considered.The following work is mainly completed in thispaper:
1. Based on the typical trapezoidal box girders, combined with thin walled bar theory andenergy functional variation principle,the elastic mechanics analysis system of the thin-wallbox girder bending and bending torsional shear lag effect is established and the calculationmethod of thin-wall box girder shear lag is improved.
2. According to whether shear deformation is considered, The warping displacement functionswith the shear lag for the thin-walled box girder have been constructed. Furthermore, basedon energy functional variation principle, the governing differential equations for theory ofelasticity in box girders are established on both cases; combining boundary conditions, usingmathematical method gives a closed solution of the governing differential equations; shear lag calculation formula of free beam and continuous beam under concentrated loads and uniformloads has been given; Based on calculation results, discuss on how shear deformationinfluences shear lag effect; and then combining analyzing examples to verifying whetherdeduced theoretical formula is correct.
3. Take cantilever girders and continuous girder as examples, to introduce the negative shearlag effect and how the mechanism resulting. confirming the critical point of positive andnegative shear lag effect, analyzing shear deformation, Poisson's ratio, cross-width ratio,aspect ratio, width-thickness ratio and stiffness ratio other factors on the cantilever beam andcontinuous beam of negative shear lag effect.
4. Take the thin-walled curved box girder as an example, according to the theory ofthin-walled curved bar, the shear lag warp displacement functions in fundamental deformationof flange in curved box girders are completed. Considering the effect of the secondary sheardeformation on warp displacement in restraint torsion, the governing differential equations ofthe shear lag effect and boundary conditions are established by the energy variation methodfor thin-walled curved box girders. The energy functional variation principle in shear lag ofstraight box girders is popularized to curved box girders, and the governing differentialequations with consideration of bending, torsion and shear lag coupling are derived, The shearlag effect of two-span single-pillar continuous curve rigid frame bridge are studied by test andlucite model, which has provided helpful experience for design and construction of the similarbridges. The characteristics of shear lag in curved box girder under pre-stress are discussed,compared with the model test, the impact of pre-stress on shear lag of curved box girder areobtained.
5. Applied variation method and ANSYS finite element method on several typical single boxsection bridge of shear lag effect for analysis and comparative studies, gaining regular patternof the shear lag effect on behavior of the bridge structure, Based on the above results, somesuggestions on design and construction of box girders are provided, these also have referencevalue on shear lag effect and preliminary design for the same type of bridges.
本文以薄壁杆理论为基础，应用薄壁箱梁结构分析的能量泛函变分原理，建立了一套适合于薄壁箱梁的弯曲、弯扭、压弯和剪力滞效应的理论分析和计算方法，主要侧重于薄壁箱梁剪力滞效应的理论分析、试验研究及其对桥梁结构行为的影响。本文共有6章，第1章综述了薄壁箱梁剪力滞的研究理论和研究方法；第2章基于最小势能原理，分别建立了是否考虑剪切变形影响的剪力滞弹性力学求解的控制微分方程，结合边界条件，给出了剪力滞计算公式；第3章介绍了负剪力滞效应及其产生的机理,分析了悬臂箱梁和连续梁的负剪力滞及其影响因素；第4、5章利用能量变分法建立了薄壁曲线箱梁剪力滞效应的控制微分方程并给出了特定边界条件下的解析表达式，通过模型试验对曲线箱梁的力学特性、剪力滞效应进行了分析，研究了预应力对曲线箱梁剪力滞效应的影响；第6章对几种典型的单箱截面桥梁的剪力滞系数进行了三种计算方法的求解与分析，研究了几个典型桥梁考虑施工阶段的剪力滞分布规律。本文主要完成了以下工作:
1.以具有代表性的梯形箱梁为分析对象，结合薄壁杆理论和能量泛函变分原理，建立了薄壁箱梁弯曲和弯扭剪力滞效应的弹性力学求解体系，完善了薄壁箱梁剪力滞计算方法。
2.根据是否考虑剪切变形，构造了薄壁箱梁的剪力滞翘曲位移函数，依据能量泛函变分原理，分别建立了两种情况的剪力滞弹性力学求解的控制微分方程；结合边界条件，利用数学方法给出了控制微分方程的闭合解；给出了考虑剪力滞效应时简支梁和连续梁在集中荷载和均布荷载作用下应力和挠度的计算表达式；依据计算结果探讨了剪切变形效应对剪力滞效应的影响；结合计算实例对推导的理论公式进行了验证。
3.以悬臂箱梁和连续梁为例，阐述了负剪力滞现象及其产生机理，确定了正、负剪力滞效应的临界点，分析了剪切变形、泊松比、跨宽比、宽高比、宽厚比及刚度比等因素对悬臂梁和连续梁负剪力滞效应的影响。
4.针对薄壁曲线箱梁，依据薄壁曲杆理论，在曲线箱梁翼缘板的基本变形中补充了剪力滞翘曲位移函数，考虑曲线箱梁约束扭转时二次剪切变形对翘曲位移的影响，用能量变分原理建立了曲线箱梁剪力滞效应分析的控制微分方程及相应边界条件，将薄壁直线箱梁剪力滞的能量泛函变分原理推广到了曲线箱梁中，建立了弯、扭、剪力滞耦合的弹性控制微分方程，给出了计算简支曲梁的剪力滞计算解析表达式，并通过算例进行了验证；制作了有机玻璃模型，对两跨独柱支撑连续曲线刚构的剪力滞效应进行了试验研究，对该类型桥梁的设计和施工提供了科学依据。探讨了预应力曲线箱梁的剪力滞效应特点，采用理论分析与模型试验对比分析方法探讨了预应力对曲线箱梁剪力滞的影响。
5.应用变分法和Ansys有限元法对几种典型单箱截面桥梁进行剪力滞效应的分析与对比研究，得到了剪力滞效应对桥梁结构行为的影响规律，基于这些成果对箱形梁的设计给出了一些建议,对于同类型桥梁的剪力滞效应的研究和初步设计具有参考意义。
Along with the long cantilever plate, the big rib spacing,concise and the single-boxsingle-chamber box bridge, the shear lag effect has been payed attention gradually by people.In recent years, many experts and scholars have devoted themselves to the research of theshear lag effect, and have obtained some achievements. But some problems are still notsolved, especially the shear lag effect of the variable cross-section and curved box girders andit is necessary to research further.
Based on the theory of the thin walled bar and the application of the energy functionalvariation principle of the thin-wall box girder, a set of the theoretical calculation methodsuitable for the bending, bending and twisting, bending and the shear lag effect of thethin-walled box girders is established, and it mainly focuses on the theoretical analysis andtest research of the thin-wall box girder shear lag effect and the influence on the bridgebehavior. This paper has six chapters in common. the research theory and method of thethin-walled box girders shear lag are reviewed in the chapter one; Based on the principle ofthe minimum potential energy in chapter two,the shear lag governing differential equation isrespectively established whether the influence of shear deformation is considered or not. Theshear lag formula is given combined with the boundary conditions. The negative shear lageffect and the mechanism of generation are introduced, and the negative shear lag and itsinfluence factors of the cantilever box girder and continuous beam are analyzed in the chapterthree. The control differential equation of the thin wall curved bridge shear lag effect and theanalytical expression under the specific boundary conditions are established by using theenergy variation method in chapter4,5. The mechanical properties and the shear lag effect ofthe curved bridge are analyzed through the model test, and the influence of prestress on theshear lag effect of the curved bridge is studied. The shear lag coefficient of several typicalsingle-box bridge is solved and analyzed by adopting the three kinds of calculation methodsin chapter six, and the distribution regularity of shear lag is studied when the constructionstages of several typical bridge are considered.The following work is mainly completed in thispaper:
1. Based on the typical trapezoidal box girders, combined with thin walled bar theory andenergy functional variation principle,the elastic mechanics analysis system of the thin-wallbox girder bending and bending torsional shear lag effect is established and the calculationmethod of thin-wall box girder shear lag is improved.
2. According to whether shear deformation is considered, The warping displacement functionswith the shear lag for the thin-walled box girder have been constructed. Furthermore, basedon energy functional variation principle, the governing differential equations for theory ofelasticity in box girders are established on both cases; combining boundary conditions, usingmathematical method gives a closed solution of the governing differential equations; shear lag calculation formula of free beam and continuous beam under concentrated loads and uniformloads has been given; Based on calculation results, discuss on how shear deformationinfluences shear lag effect; and then combining analyzing examples to verifying whetherdeduced theoretical formula is correct.
3. Take cantilever girders and continuous girder as examples, to introduce the negative shearlag effect and how the mechanism resulting. confirming the critical point of positive andnegative shear lag effect, analyzing shear deformation, Poisson's ratio, cross-width ratio,aspect ratio, width-thickness ratio and stiffness ratio other factors on the cantilever beam andcontinuous beam of negative shear lag effect.
4. Take the thin-walled curved box girder as an example, according to the theory ofthin-walled curved bar, the shear lag warp displacement functions in fundamental deformationof flange in curved box girders are completed. Considering the effect of the secondary sheardeformation on warp displacement in restraint torsion, the governing differential equations ofthe shear lag effect and boundary conditions are established by the energy variation methodfor thin-walled curved box girders. The energy functional variation principle in shear lag ofstraight box girders is popularized to curved box girders, and the governing differentialequations with consideration of bending, torsion and shear lag coupling are derived, The shearlag effect of two-span single-pillar continuous curve rigid frame bridge are studied by test andlucite model, which has provided helpful experience for design and construction of the similarbridges. The characteristics of shear lag in curved box girder under pre-stress are discussed,compared with the model test, the impact of pre-stress on shear lag of curved box girder areobtained.
5. Applied variation method and ANSYS finite element method on several typical single boxsection bridge of shear lag effect for analysis and comparative studies, gaining regular patternof the shear lag effect on behavior of the bridge structure, Based on the above results, somesuggestions on design and construction of box girders are provided, these also have referencevalue on shear lag effect and preliminary design for the same type of bridges.
引文
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