Refined Calculation Of Long-term Deformation Of Simply Supported Post-tensioned Prestressed Concrete Bridges

As the most common structural form of bridge structures,reinforced concrete and prestressed concrete bridges have made great contributions to China's transportation and economic development,but at the same time,these concrete bridges suffer from different degree of deteriorations.Cracking and excessive deflection are one of the deteriorations,especially for long-span concrete bridges.Many factors contribute to the long-term deformation of bridges beyond expectations including the impact of design,construction and the management during the service life at the engineering level,and insufficient understanding of concrete shrinkage and creep behavior and limitations in design codes(using simplified and empirical methods)at the scientific level.In order to control the long-term deformation of the bridge within the expected range,in addition to fine design,fine construction and strengthened management at the engineering level,at the scientific level,it is also necessary to strengthen the research on the fundamental theory of bridges.Based on the creep theory of concrete and considering the effects of concrete shrinkage and relaxation of the prestressed tendon,this study presents the refined calculation method of long-term deformation of simply supported post-tensioned prestressed concrete bridges.The first purpose is to provide reference for the improvement and revision of bridge design codes,and the second is to provide a basis for the study of the refined calculation method for longterm deformation of long-span prestressed concrete bridges.Main contents and conclusions of this study are as follows:(1)The refined calculation method for calculating the stress,strain and long-term deformation of the post-tensioned prestressed concrete beam is studied.The whole process of post-tensioned prestressed concrete bridge from the manufacture,construction and putting into operation is divided into five stages.Considering the characteristics of each stage of the bridge subjected to the loading,shrinkage and creep of concrete and stress relaxation of prestressed tendons,based on the superposition principle of concrete creep,the refined calculation formula for long term deformation at each stage is proposed.The calculation method of long-term deformation of prestressed concrete members proposed in this study is based on concrete creep theory,which is different from the method of multiplying short-term deformation by the empirical amplification factor in current bridge design code.(2)The refined calculation method of the concrete stress and long-term deformation of reinforced concrete girders caused by concrete shrinkage is studied.For the stage before applying prestress of the post-tensioned prestressed concrete members,based on the principle of superposition of the concrete creep,the cross-sectional concrete strain integral equation is established through the cross-sectional analysis.Based on the principle of the mean value theorem for integrals,the integral equation is transformed into the algebraic equation and the formula for calculating the coefficient of the median value for the time is proposed.Method for calculating the long-term deformation of reinforced concrete members under concrete shrinkage and external load is proposed.Results indicated that results calculated by the proposed method show good agreement with the numerical results.(3)The refined calculation method of the deformation of post-tensioned prestressed concrete members and time-dependent prestressing losses are studied.Considering the coupling effect between the concrete shrinkage,relaxation of prestressed tendon and the concrete creep.based on the principle of superposition of the concrete creep,the integral equation of concrete strain for the prestressed concrete members is established.The integral equation is transformed into the algebraic equation by using the mean value theorem for integrals.The calculation formulas for the stress,deformation of concrete and time-dependent prestressing losses is proposed.The coefficient of the median value for the time is proposed through numerical analysis.Formula for time-dependent prestressing loss of bidirectional prestressed concrete members considering the Poisson effect of concrete and the interaction between the bidirectional prestressing is proposed.Results shows that within the time scale considered in this study the calculated results of the time-dependent prestressing loss proposed in this study show good agreement with the numerical analysis and test results;the proposed time-dependent prestressing loss of bidirectional prestressing is applicable to the top,bottom and side slabs of box-section bridges.(4)The refined calculation method for the deformation of post-tensioned prestressed concrete bridge from the first stage load,project completion to the end of the design service life is investigated.On the basis of considering the influence of concrete shrinkage,creep and the relaxation of prestressed tendons on the long-term deformation of the bridge in the early stages,the refined calculation method for the deformation of the bridge from the first stage load,the completion to the end of the design service life is proposed with consideration of the creep of the bridge concrete under the first stage load,the second stage load and the quasi-permanent vehicle loads after opening the traffic is proposed.Results shows that stress and deformation of the concrete calculated by the median integral method proposed in this paper are close to the results calculated by the numerical recursion method.(5)The long-term loading test of post-tensioned prestressed concrete beams was carried out and the long-term deformation refined calculation method proposed in this paper was verified.Six prestressed concrete T-beams with different prestressing levels subjected to long?term loading was tested.Based on the creep model provided in Fib MC 2010 and ACI 209,concrete strain and deformation of prestressed concrete members is calculated with respected to proposed the refined calculation method.Referring to Appendix A of Eurocode "design of concrete structures-Part 2:concrete bridges"(EN 1992-2:2005),the method of modifying the parameters of the creep model in the design code is discussed,this method is based on the creep test data of concrete in the proposed site of the bridge and it suitable for the as-built bridge.Results indicated that based on the creep model in code FIB MC 2010 and report ACI 209,the curve calculated by the refined deformation calculation method proposed in this paper is roughly parallel to the curve obtained by the test,but there is some difference in the value;Results predicted by the creep model in code FIB MC 2010 is lower than the test results,and the results calculated by the creep model in report ACI 209 is larger than the test results.This indicated that the refined calculation method of deformation of post-tensioned prestressed concrete members proposed in this study is feasible,and the concrete creep model has a great influence on the calculated results.The mid span deflection calculated by the modified creep model show good agreement with the measured results.