A Finite Segment Method For Analyzing Shear Lag And Shear Deformation Effect And Non-linear Behavior Of R.C. Box Beam

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.