Nonlinear Study Of Concrete Box Girder Based On Thirteen Degrees Of Freedom Fiber Beam Model

Reinforced concrete structures play an irreplaceable role in the construction and transportation infrastructure.Because the main materials of concrete and steel bar are all nonlinear materials,and most concrete structures work with cracks.In addition,the non-linearity of existing concrete structures is more prominent due to the accumulation of internal damage,creep and shrinkage,aging,environmental temperature and so on.In this paper,referred to the finite element analysis theory of bar structure,and based on the fiber beam model,a nonlinear analysis theory of concrete structure based on thirteen degrees of freedom fiber beam model was presented.For an example of concrete box girder,the nonlinear behavior considering the time-dependent under the coupling action of environment and load was studied theoretically.The main research contents are as follows:(1)Based on the Euler-Bernoulli beam element theory and classical 12-DOF beam-column elements model,a thirteenth additional degree of freedom of axial displacement was introduced by added an internal node placed at the element midlength.Firstly,according to the principle of virtual displacement,the element stiffness matrix of 13-DOF fiber beam model based on component was deduced.Then,according to the static condensation,the stiffness matrix of 13-DOF element was modified by introduced non-mechanical strain.Finally,based on NewtonRaphson iteration,the element equilibrium equations considering the time-dependent were solved by MATLAB programming,and a nonlinear research theory of concrete structure based on 13-DOF fiber beam model was presented.(2)In order to verify the correctness of 13-DOF fiber beam model theory proposed in this paper,taking an example of several box girder models that some scholars have done,the whole process nonlinearity was studied by using the method proposed in this paper,and compared with the experimental results.The results show that the load-deflection curve of midspan,loadstress curve and load-strain curve of rebar at the tension side obtained by the method are in accordance with the trend of experimental results,and the curves are in good agreement for small error.The above proves that the 13-DOF fiber beam model proposed in this paper is correct,and the method has high precision for nonlinear research of concrete structures.(3)Taking the 32 m prestressed concrete simple supported box girder of 250km/h ballastless track in China as an example,the nonlinear mechanical behavior and evolution law of box girder under the coupling of long-term environment and load were studied.It is found that the midspan load-deflection curve obtained by this method,completely conforms to the whole process mechanical characteristics and failure modes of flexural members,and the box girder haves sufficient safety reserves.By comparing the load-deflection curve with standard solution,it is found that the error of cracking load,cracking deflection and ultimate load obtained by this method are less than 9%,but the error of ultimate deflection reaches 77%,which should be taken seriously when designing.(4)The effects of prestressed tendon ratio,tension coefficient,non-prestressed tendons,loading mode and service life on the nonlinear mechanical behavior of box girder were studied.The results show that with the increase of reinforcement ratio,the bearing capacity of box girder is improved,but ductility is deteriorated.Under the same load level,the bearing capacity is increased with the increase of tension coefficient of prestressed tendons,while the ductility is deteriorated.The trend of whole process mechanical characteristics under different loading modes is consistent,but the bearing capacity is different,especially the deformation performance.With the increase of service life,the bearing capacity is decreased,midspan deflection is increased,and the ductility is deteriorated.(5)In order to analyze the rationality of the simplified calculation model of midspan fourfold moment-deflection line proposed in this paper,the nonlinear analysis for model tests was carried out.The result shows that the trend of midspan moment-deflection relationship obtained by simplified calculation method is consistent with the experimental solution in literature,the moment and deflection are in good agreement with experimental results.Therefore,the simplified calculation model of moment-deflection proposed in this paper is reasonable.