Behaviors Of Concrete Beam Prestressed With External CFRP Tendons

The thin-walled concrete beams prestressed with external CFRP tendons would become more popular both in new construction and in strengthening of existing structures. But there is no the design code for it so far at home and abroad. The prestress increment in external prestressed tendons is always analyzed with emprical formulas or analytical model for the analysis of the unbonded prestressed tendons, which is not inapplicable or inaccuracy sometimes. So the fomula for the external prestresse increment and the behaviors of concrete beam prestressed with external CFRP tendons need to be studied better. The flexural behaviors of the concrete T/box beam prestressed with external tendons were studied experimentally and theoretically, and the following works have been done:(1) Tests were carried out on 5 beams under four-point load, of which four beams were reinforced with hybrid both external CFRP tendons and internal reinforcement and another one only reinforced with internal ordinary steel bar. The beams'bearing capacity, deformation, ductility index, cracking pattern and failure mode were studied. It was showed that the the bearing capacity of the concrete beam can ben improved effectively by external prestressed tendons. The expected failure mode is the concrete crushing rather than the externally prestressed CFRP tendons rupturing. Non-prestressing internal reinforcement can improve the flexural behaviors of beams prestressed with external CFRP tendons effectively since it can lead to a more rational crack distribution and better ductility, and the ductility index of beams prestressed with external CFRP tendons in this paper can reach about 2.5. The initial loading state on the beam before tendon jacking has no significant influence on the ultimate capacity and deflection.(2) A program was developed to predict the behaviors of those beams prestressed with externally prestressed tendons. The flexural capacity, deformation and failure modes of beams with different parameters can be analyzed using the program, such as types of plan and prestressed tendons(extrenal prestessed tendons, internal unbonded prestressed tendons, internal bonded prestressed tendons), jacking and effective stress in external prestressed tendons, configuration of the deviators, properties of tendon, ratio of span to effective depth of the beam and load pattern, initial loading state at tendon jacking, etc. (3) Nonlinear behaviors of the concrete beam prestressed with external or internal unbonded tendons were studied by the program developed. Such parameters as the percentage of ordinary reinforcment, amounts and configuration of unbonded prestressed tendons, the ratio of span to depth and the loading patterns were considered. Based on the results, the fomula for the eqivalent length of deformation zone on the beams at ultimate were developed. A simple formula was developed for the ultimate mid-span deflection of concrete beams with concept of equivalent length of deformation zone, and the deformation of beam before internal reinforcement yielding was predicted by the traditional formula for the deformation of partically prestressed concrete beam. Then an analytical model was deduced for analyzing the ultimate stress increment in those concrete beams prestressed with external or internal unbonded tendons based on the mid-span deflection.(4) Testes were carried out on a thin-walled concrete box beam presressed with external CFRP tendons to study its short-term performances under uniform load, long-term behaviors under uniform load, and full-time performance under four-point load in turn. Prestressing loss of CFRP, stress/strain distribution in flange, deformation and crack distribution were studied. The results indicated that: effective width coefficient of compression top flange increased by less than 8% due to concrete cracking, long-term loading, and ordinary tension reinforcement yielding; the test value of deflection at mid-span at 1001 day was 2.32~2.42 times of the initial deflection, plastic deformation at 20 days after unloading was 41% of 1001 day's; the strain of tensile reinforcement had a 65% increase than that of its initial value, and residual strain after unloading was about zero; the strain of compressed reinforcing steel bar had a 225%~268% increase than that of its initial value, and residual strain at 20 days after unloading was 53% of 1001 day's; compression strain on top plate of the box girder under long-term load increased quickly in the early stage and became stable after 2 years, and it had a 164%~224% increase than that of its initial value at 1001 day; the crack width increased as time increased under long-term load, then it became stable after more or less 2 years, and it was 1.59~2.69 times than that of its initial value at 1001 day; most of the cracks in the bottom plate of box girder developed from middle of bottom plate, and they were wider in the middle of the bottom plate than at the bottom ends of the webs; the strain distributed over the section depth of web agreed well with plane assumption. Based on the behaviors of concrete beams prestressed with external CFRP tendons, the comformable formulars for predicting crack width of concrete box/T girder prestressed with external CFRP tendons were proposed by modifying traditional formulas in design codes for predicting the crack with of ordinary prestressed concrete beams.(5) Based on Mindlin-Reissener theories of thick plate, the fundamental geometric nonlinearity equations for flat-shell element were set up with U.L formulas. A flat-shell element was composed with the lock-free element for thick/thin plates(Yuqiu Long) and the four-nodded arbitrary quadrilateral finite element with in-plane rotational degree of freedom. Then the fundamental equations for plate/shell bi-nonlinear finite element model were set up with layered finite method. the fundamental geometric nonlinearity equations for the unbonded prestressed tendon and double spring element were proposed, and the double spring element was used to simulate the interaction of unbonded prestressed tendon and deviator. Based on these theories mentioned above, a finite element program for bi-nonlinear analysis of plate/shell concrete structure prestressed with external tendons was developed. Using this program, either linear elastic or bi-nonlinear anslysis can be conducted for both plate/shell concrete structures prestressed with external or internal unbonded tendons or ordinary reinforced concrete plate/shell structures. Further more, analysis for prestressed structure, where from the beginning of stretching prestressed tendons to failure at last, can be simulated with the method of incremental step loading.(6) Parametric studies on the flexural behaviors of the concrete box beam prestressed with external CFRP tendons were conducted using the finite element program. It's concluded that the bearing capacity and the stiffness of the beam enhanced with the development of the concrete strength, the initial defect of the beam with crack increased and the bearing capacity and the stiffness reduced as time increased under the long-term load. The cracking load of the beam prestressed with external CFRP tendons was about same as that of beam prestressed with external stranded steel wire. The stiffness of the beam after the concrete cracking, yielding load and the ultimate bearing capacity of beam prestressed with external CFRP tendons were smaller than that prestressed with external stranded steel wire.(7) Shear-lag effect in flange of concrete box beam prestressed with external CFRP tendons was analyzed using the finite element program. The results indicated that the superposition principle can be used in the concrete box beam prestressed with external tendons in the linear elastic stage. Effective width coefficient of the flangeρf of box beam under the action of external prestressed force is the same as theρf of normal reinforced concrete box beam under the equivalent loads of external prestressed tendons. Theρf of the box girder under the action of the external prestressed tendon is basically the same as that of the reinforced concrete box girder under the action of the equivalent load of the external prestressed tendons. Basically there were no shear-lag effect existed in the elements beside the mid-span of the beam under the action of external prestressed tendons which lay out straightly with no deviator.(8) Based on the results of experimental and theoretical studies, the effective width coefficient of flange of box beam prestressed with external CFRP tendons was simplified appropriately, and design proposals of concrete beams prestressed with external CFRP tendons were put forward systematized, such as the stretching control stress of CFRP tendons, amount of the normal reinforcement, relative height of equivalent compression zone,method for ultimate bearing capacity and checking computations of the normal serviceability stage and so on.