Research On Design Methods Of Concrete Beams And Slabs Partially Prestressed With Unbonded CFRP Tendons

Carbon fiber reinforced polymer (CFRP) tendons have apparent advantages such as lightweight, high strength, corrosive protection, and so on. The load bearing capacity and durability of structures decline caused by the corrosion of prestressing tendons could be effectively avoided by CFRP tendons as prestressing tendons instead of high strength steel bars, and by epoxy coated or galvanized steel bars as non-prestressing reinforcements. However, since stress-strain relationship of CFRP tendon is linear elastic, and its modulus of elasticity is different from that of prestressing steel, so, the flexural performance of concrete beams and slabs partially prestressed with unbonded CFRP tendons is different from that of ordinary unbonded partially prestressed concrete beams and slabs. Although this kind of beam and slab has outstanding advantages, the law of stress increment of unbonded CFRP tendons at service stage and flexural load bearing capacity limit state is unclear, so it is difficult to accurately calculate crack width, deflection and load bearing capacity. Thus, this kind of continuous beam and slab with non-prestressing reinforcements still have the plastic redistribution process of internal force, it has some practical significance to research on the law of moment modification. The following works are carried out:Using deformation compatibility condition to solve the problem of plane-section assumption being not applicable, moment-curvature analysis method are used to compile nonlinear full-range analysis programs of this kind of simply supported and continuous beam and slab. The strain of compressive extreme fiber of concrete in critical section of mid-span reaching the ultimate compressive strain is the symbol of the flexural load bearing capacity limit state of simply supported beams and slabs, and the strain of compressive extreme fiber of concrete in critical section of intermediate support reaching the ultimate compressive strain is the symbol of the flexural load bearing capacity limit state of continuous beams and slabs. Full-range analysis of beams and slabs can be achieved by gradually increasing the strain of compressive extreme fiber of concrete in corresponding critical sections of beams and slabs. The computing results of equivalent reduced coefficient of unbonded CFRP tendons (ERCUCT), ultimate stress increment of unbonded CFRP tendons (USIUCT) and moment modification coefficient are in good agreement with the test results as a whole, so it indicates that the programs are reliable. The ratio of stress increment of unbonded CFRP tendons to that of bonded non-prestessing reinforcements of critical section at service stage is defined as ERCUCT. Parametric analysis shows that ERCUCT in simply supported and continuous beams and slabs increases with increasing of modulus of elasticity of CFRP tendons, non-prestressing reinforcement index or relative position of unbonded CFRP tendons. The influence of prestressing reinforcement index on ERCUCT in simply supported beams and slabs is greater than that in continuous structures. The laws of influence of load types and the ratio of span to depth on ERCUCT in simply supported flexural members and that in continuous members are different. ERCUCT in simply supported members with tendons being straight line are bigger than being parabola. ERCUCT in continuous members increases with increasing of the ratio of combined reinforcement index of intermediate support section to that of mid-span. For simply supported and continuous members, ERCUCT in T-section is less than in rectangle section. Making key parameters as independent variable, the calculation formulas of ERCUCT in simply supported and continuous beams and slabs are proposed. They provide the basis for reasonably calculating crack width and stiffness of beams and slabs in service stage.Unbonded CFRP tendons can be reduced to be a certain number of bonded tendons based on ERCUCT. The reduced unbonded CFRP tendons and the original bonded longitudinal tensile reinforcements compose the equivalent longitudinal tensile reinforcements. The ratio of the equivalent longitudinal tensile reinforcements is introduced in the stiffness formula of this kind of beam and slab, and the equivalent area of total longitudinal tensile reinforcements is introduced in equivalent stress formula in crack width formula of this kind of beam and slab. Based on corresponding experiment results, the stiffness formula and crack width formula of this kind of beam and slab unified in expressions are derived. The results following these two formulas are in good agreement with test results, so they can be used in the design of civil engineering.Parametric analysis shows that USIUCT in simply supported and continuous beams and slabs reduces with increasing of non-prestressing reinforcement index and prestressing reinforcement index, and increases with increasing of modulus of elasticity of CFRP tendons. The laws of influence of load types on USIUCT in simply supported flexural members and that in continuous members are different. USIUCT in simply supported members under single concentrated load and in continuous members reduces with increasing of the ratio of span to depth. USIUCT in continuous members reduces with increasing of combined reinforcement index of mid-span section. For simply supported and continuous beams and slabs, USIUCT in T-section is bigger than in rectangle section. Making key parameters as independent variable, the calculation formulas of USIUCT in simply supported beams and slabs and continuous beams and slabs are proposed. They provide the basis for correctly calculating flexural load bearing capacity of beams and slabs.Redistribution of internal force is caused by relative stiffness change of critical section of intermediate support and mid-span in continuous beams and slabs, so moment modification exists. Make modification target as the sum of external load moment and secondary moment. Parametric analysis shows that moment modification coefficient increases with increasing of combined reinforcement index of mid-span section, and reduces with increasing of combined reinforcement index of intermediate support section. There are some influence of load types and the ratio of span to depth on moment modification coefficient. Making key parameters as independent variable, the calculation formulas of moment modification coefficient in continuous beams and continuous slabs are proposed. They provide references for plastic design of continuous beams and slabs.