钢筋混凝土箱梁非线性分析及剪滞、剪切效应的有限段法研究
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摘要
混凝土薄壁箱梁由于具有良好的空间整体受力性能而广泛用于现代铁路桥、公路桥和城市立交桥中。箱梁的分析计算与一般梁相比具有显著差别,其中剪滞及剪切变形效应不可忽略。带裂缝工作的钢筋混凝土箱梁已表现出明显的非线性力学性能,且与剪滞及剪切变形效应互相影响。
本文针对影响钢筋混凝土箱梁力学性能和工作性能的主要因素,如剪滞、横向剪切变形、混凝土和钢筋的非线性本构关系、混凝土开裂导致的截面刚度变化等,围绕钢筋混凝土箱梁结构分析的非线性有限段法进行了研究。
设计了钢筋混凝土箱梁剪滞效应的试验方案并完成试验,测得了钢筋混凝土箱梁的荷载-位移关系,获得了箱梁截面纵向应力分布情况,以及钢筋混凝土箱梁的裂缝分布及发展情况,证实了钢筋混凝土箱梁仍存在明显的剪滞效应,为钢筋混凝土箱梁的理论研究奠定了试验基础。
在有限段单元中引入换算截面,建立了钢筋混凝土箱梁有限段单元刚度矩阵,使有限段法可方便地分析钢筋混凝土箱梁整截面工作阶段的剪滞、剪切变形双重效应,并编制了相应的FORTRAN语言程序EBOX。
基于混凝土及钢筋非线性本构关系,建立了钢筋混凝土箱梁分层有限段模型,将应力不均匀系数引入该有限段模型以考虑单元内沿长度方向钢筋应力的不均匀分布及受拉刚化效应,编制了钢筋混凝土箱梁的材料非线性有限元程序RCBB,该程序可分析混凝土开裂前及开裂后的剪滞、剪切变形效应,且具有计算量小,精度较高的特点。程序RCBB计算结果与试验结果吻合较好,验证了程序的正确性,对钢筋混凝土箱梁而言,仅计算弯曲变形引起的挠度都是偏小的,故需要同时再考虑剪滞及剪切变形所引起的挠度,对于此类箱梁截面而言,在计算挠度时,横向剪切变形效应的影响大于剪滞效应的影响。
利用所编有限段法计算程序,分析了荷载形式、结构体系、配筋量及材料非线性对剪滞、剪切效应的影响。首先计算了不同荷载形式及不同荷载等级作用下,在整截面工作阶段及带裂缝工作阶段,钢筋混凝土简支箱梁及连续箱梁的截面应力、剪力滞系数及荷载-挠度曲线；然后分析了顶板及底板配筋量变化时,对挠度及剪力滞系数的影响；最后对钢筋混凝土箱梁剪滞、剪切效应及材料非线性的相互影响进行了分析,得出了一些有助于工程应用的结论。
对钢筋混凝土箱梁进行了剪滞、剪切及材料非线性的实用计算方法研究。提出了采用换算截面进行钢筋混凝土箱梁整截面工作阶段应力计算的方法,并基于能量原理分析了纵筋剪切应变能对截面纵向应力的影响；基于等效刚度原则,提出了钢筋混凝土变截面悬臂箱梁整截面工作阶段剪力滞系数及挠度近似计算方法,并采用该方法分析了一有机玻璃悬臂箱梁及一钢筋混凝土悬臂箱梁,计算结果与按有限段法及ANSYS板壳元法计算结果接近,说明了该方法的有效性；提出了采用分段换算截面进行钢筋混凝土箱梁带裂缝工作阶段挠度的近似计算方法,计算中可考虑剪滞、剪切变形效应,算例表明分段换算截面法能满足工程精度要求；最后基于莫氏假定,推导了钢筋混凝土箱梁纵向受拉钢筋最小配筋量计算公式,该公式可考虑箱形截面顶底板几何尺寸对开裂弯矩的影响,对工程设计有一定的参考价值。
Concrete thin-walled box girders have good mechanical properties of the space and have been widely used in modern railway bridges, highway bridges and urban interchange bridges. Analysis and calculation of box beams have significant difference from others. Shear lag and shear deformation phenomenon in box beam can not be ignored. The non-linear mechanical performance is clearly in reinforced concrete box beam after crack, and interacts with the effect of shear lag and shear deformation.
Some works have been done as following:shear lag in reinforced concrete box girder, transverse shear deformation, nonlinear models of concrete and steel, concrete cracking, section stiffness, and non-linear finite element analysis considering the above issues, et..
Experiment program on shear lag effect of reinforced concrete box beam is designed, the load-displacement relationship of reinforced concrete box beam is measured, longitudinal stress distribution of box section, crack distribution and development of reinforced concrete box beam is obtained, the fact that there are still significant shear lag effect in reinforced concrete box beam is confirmed.
Based on the initial parameters equation of thin-walled box beam, the finite element stiffness matrix is established, and the corresponding FORTRAN language program EBOX is developed. The finite segment method can be easily used to analyses the double effects of shear lag and shear deformation of reinforced concrete box beam before cracking when transformed section is used in the finite segment method.
Based on the nonlinear constitutive relation models of concrete and reinforced, Hierarchical finite segment model of reinforced concrete box beam is established. Stress asymmetry coefficient is used to consider the uneven distribution of steel stress along.the length of the element and tension stiffening effect. Reinforced concrete box beam material nonlinear finite element program RCBB is developed, which can be used to analyses the double effects of shear lag and shear deformation of reinforced concrete box beam before and after cracking, and with the characteristics of small amount calculation as well as high precision. Results calculated by program RCBB are in good agreement with the experimental results, which verify the correctness of the program. In terms of reinforced concrete box beam, when calculating vertical displacement, the effect of shear-lag, shear deformation, should be considered enough. If only consider the effect of bending, the vertical displacement is less than the actual value. To the vertical displacement of reinforced concrete box beam, the effect of shear deformation is greater than the effect of shear-lag.
The influence factors of the shear-lag and shear deformation, such as load type, structural system, reinforcement, and material nonlinear are analyzed by the program. The section stress, shear-lag coefficient and load-displacement of simple supported beam and continuous beam are calculated under different load type and different load grade. Then the effect of reinforcement is analyzed. At last, the interaction effect of shear-lag, shear deformation and material nonlinear is analyzed. The conclusion is helpful for applying in actual engineering.
The practical calculation method for shear-lag, shear deformation, and material nonlinear of reinforced concrete box beam are proposed. The first simplified method is transformed section method. It can be applied to calculate the section stress in the working stage of whole cross-section. During the calculation and based on the energy principle, the effect of energy of shear strain on section stress is analyzed. The second simplified method is principle of equivalent stiffness. It can be applied to calculate the shear-lag coefficient and displacement of varying depth cantilever beam in the working stage of whole cross-section. As examples the method is used for shear lag analysis of an organic glass cantilever box beam with varying depth and a reinforced concrete box beam with varying depth. The results are agreed with the results by ANSYS well shows that the method is effective. The third simplified method is the uneven transformed section method. It can be applied to calculate the displacement of reinforced concrete box beam in the working stage after crack, and the effect of shear-lag and shear deformation can be considered in it. The fourth simplified method is minimum reinforcement calculation and helpful to design. The effects of geometries of top plate and bottom plate on cracking bending moment are considered init. All the simplified methods are explained with examples.
本文针对影响钢筋混凝土箱梁力学性能和工作性能的主要因素,如剪滞、横向剪切变形、混凝土和钢筋的非线性本构关系、混凝土开裂导致的截面刚度变化等,围绕钢筋混凝土箱梁结构分析的非线性有限段法进行了研究。
设计了钢筋混凝土箱梁剪滞效应的试验方案并完成试验,测得了钢筋混凝土箱梁的荷载-位移关系,获得了箱梁截面纵向应力分布情况,以及钢筋混凝土箱梁的裂缝分布及发展情况,证实了钢筋混凝土箱梁仍存在明显的剪滞效应,为钢筋混凝土箱梁的理论研究奠定了试验基础。
在有限段单元中引入换算截面,建立了钢筋混凝土箱梁有限段单元刚度矩阵,使有限段法可方便地分析钢筋混凝土箱梁整截面工作阶段的剪滞、剪切变形双重效应,并编制了相应的FORTRAN语言程序EBOX。
基于混凝土及钢筋非线性本构关系,建立了钢筋混凝土箱梁分层有限段模型,将应力不均匀系数引入该有限段模型以考虑单元内沿长度方向钢筋应力的不均匀分布及受拉刚化效应,编制了钢筋混凝土箱梁的材料非线性有限元程序RCBB,该程序可分析混凝土开裂前及开裂后的剪滞、剪切变形效应,且具有计算量小,精度较高的特点。程序RCBB计算结果与试验结果吻合较好,验证了程序的正确性,对钢筋混凝土箱梁而言,仅计算弯曲变形引起的挠度都是偏小的,故需要同时再考虑剪滞及剪切变形所引起的挠度,对于此类箱梁截面而言,在计算挠度时,横向剪切变形效应的影响大于剪滞效应的影响。
利用所编有限段法计算程序,分析了荷载形式、结构体系、配筋量及材料非线性对剪滞、剪切效应的影响。首先计算了不同荷载形式及不同荷载等级作用下,在整截面工作阶段及带裂缝工作阶段,钢筋混凝土简支箱梁及连续箱梁的截面应力、剪力滞系数及荷载-挠度曲线；然后分析了顶板及底板配筋量变化时,对挠度及剪力滞系数的影响；最后对钢筋混凝土箱梁剪滞、剪切效应及材料非线性的相互影响进行了分析,得出了一些有助于工程应用的结论。
对钢筋混凝土箱梁进行了剪滞、剪切及材料非线性的实用计算方法研究。提出了采用换算截面进行钢筋混凝土箱梁整截面工作阶段应力计算的方法,并基于能量原理分析了纵筋剪切应变能对截面纵向应力的影响；基于等效刚度原则,提出了钢筋混凝土变截面悬臂箱梁整截面工作阶段剪力滞系数及挠度近似计算方法,并采用该方法分析了一有机玻璃悬臂箱梁及一钢筋混凝土悬臂箱梁,计算结果与按有限段法及ANSYS板壳元法计算结果接近,说明了该方法的有效性；提出了采用分段换算截面进行钢筋混凝土箱梁带裂缝工作阶段挠度的近似计算方法,计算中可考虑剪滞、剪切变形效应,算例表明分段换算截面法能满足工程精度要求；最后基于莫氏假定,推导了钢筋混凝土箱梁纵向受拉钢筋最小配筋量计算公式,该公式可考虑箱形截面顶底板几何尺寸对开裂弯矩的影响,对工程设计有一定的参考价值。
Concrete thin-walled box girders have good mechanical properties of the space and have been widely used in modern railway bridges, highway bridges and urban interchange bridges. Analysis and calculation of box beams have significant difference from others. Shear lag and shear deformation phenomenon in box beam can not be ignored. The non-linear mechanical performance is clearly in reinforced concrete box beam after crack, and interacts with the effect of shear lag and shear deformation.
Some works have been done as following:shear lag in reinforced concrete box girder, transverse shear deformation, nonlinear models of concrete and steel, concrete cracking, section stiffness, and non-linear finite element analysis considering the above issues, et..
Experiment program on shear lag effect of reinforced concrete box beam is designed, the load-displacement relationship of reinforced concrete box beam is measured, longitudinal stress distribution of box section, crack distribution and development of reinforced concrete box beam is obtained, the fact that there are still significant shear lag effect in reinforced concrete box beam is confirmed.
Based on the initial parameters equation of thin-walled box beam, the finite element stiffness matrix is established, and the corresponding FORTRAN language program EBOX is developed. The finite segment method can be easily used to analyses the double effects of shear lag and shear deformation of reinforced concrete box beam before cracking when transformed section is used in the finite segment method.
Based on the nonlinear constitutive relation models of concrete and reinforced, Hierarchical finite segment model of reinforced concrete box beam is established. Stress asymmetry coefficient is used to consider the uneven distribution of steel stress along.the length of the element and tension stiffening effect. Reinforced concrete box beam material nonlinear finite element program RCBB is developed, which can be used to analyses the double effects of shear lag and shear deformation of reinforced concrete box beam before and after cracking, and with the characteristics of small amount calculation as well as high precision. Results calculated by program RCBB are in good agreement with the experimental results, which verify the correctness of the program. In terms of reinforced concrete box beam, when calculating vertical displacement, the effect of shear-lag, shear deformation, should be considered enough. If only consider the effect of bending, the vertical displacement is less than the actual value. To the vertical displacement of reinforced concrete box beam, the effect of shear deformation is greater than the effect of shear-lag.
The influence factors of the shear-lag and shear deformation, such as load type, structural system, reinforcement, and material nonlinear are analyzed by the program. The section stress, shear-lag coefficient and load-displacement of simple supported beam and continuous beam are calculated under different load type and different load grade. Then the effect of reinforcement is analyzed. At last, the interaction effect of shear-lag, shear deformation and material nonlinear is analyzed. The conclusion is helpful for applying in actual engineering.
The practical calculation method for shear-lag, shear deformation, and material nonlinear of reinforced concrete box beam are proposed. The first simplified method is transformed section method. It can be applied to calculate the section stress in the working stage of whole cross-section. During the calculation and based on the energy principle, the effect of energy of shear strain on section stress is analyzed. The second simplified method is principle of equivalent stiffness. It can be applied to calculate the shear-lag coefficient and displacement of varying depth cantilever beam in the working stage of whole cross-section. As examples the method is used for shear lag analysis of an organic glass cantilever box beam with varying depth and a reinforced concrete box beam with varying depth. The results are agreed with the results by ANSYS well shows that the method is effective. The third simplified method is the uneven transformed section method. It can be applied to calculate the displacement of reinforced concrete box beam in the working stage after crack, and the effect of shear-lag and shear deformation can be considered in it. The fourth simplified method is minimum reinforcement calculation and helpful to design. The effects of geometries of top plate and bottom plate on cracking bending moment are considered init. All the simplified methods are explained with examples.
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