Study On Prestress Loss Of Curved Prestressing Tendon In Post-tensioned Beam

With the development of infrastructure construction and the wide application of prestressed technology,people pay more and more attention to the calculation of prestress loss of post-tensioned beams.In recent years,many experts and scholars have devoted themselves to the study on prestress loss of post-tensioned beams with some achievements made.However,there are some defects and shortcomings in these researches,especially in the calculation of anchorage loss and long-term loss of curved prestressing tendon.Therfore,in this paper,the prestress loss of five-segment-style curved prestressing tendon which is commonly used in the post-tensioned beams is studied for the main problems existing in the present studies from the following aspects:(1)In view of the deficiency of calculating anchorage loss in the current Chinese bridge design codes,based on the classical friction theory,starting from the equilibrium condition of prestressing tendon micro-section and using the deformation compatibility condition and stress continuity condition,the precise formulas for calculating the anchorage loss and the stress balance point position considering the reverse-friction effect were derived in this paper.The calculating results on the practical bridge prestressing tendon show that the anchorage loss calculated by the simplified method in current China railway bridge design code(TB 10092-2017)is close to the exact value and the relative errors are commonly within 10%,and that the relative errors of the anchorage loss calculated by the current China road bridge design code(JTG D62-2004)are relatively large which can reach at 39.41% and even at 62.59% when unexisting the stress balance point,compared with the calculated results of the precise method in this paper.(2)On the basis of the precise formula of anchorage loss which is established in this paper,combined with the formula of friction loss before anchoring,the differences between friction and reverse-friction action of prestressing tendon are analyzed.The results of the researches show that the reverse-friction action of prestressing tendon is always smaller than friction action,and that in order to improve the accuracy of the simplified calculation method of anchorage loss in TB 10092-2017 and reflect the differences between friction and reverse-friction action of prestressing tendon,the result of anchorage loss calculated by the simplified method of TB 10092-2017 can be corrected by multiplying with a coefficient smaller than 1.(3)Based on the precise formula of anchorage loss which is established in this paper,the influence of different tension method of prestressing tendon on prestress loss was analyzed by defining the optimal selection coefficient for the tension method of post-tensioned beam.When the length of reverse-friction effect of prestressing tendon is more than half of the total length of tendon,one end tension of tension method should be adopted to reduce the prestress loss of prestressing tendon.On the contrary,when the length of reverse-friction effect of prestressing tendon is less than half of the total length of tendon,it is advisable to adopt both ends tension.The calculation results show that compared with adopting both ends tension the prestress loss at the other end of the tendon can be reduced by 28.59% when adopting one end tension.(4)In view of the deficiency of calculating long-term loss in the current Chinese bridge design codes,based on the internal force equilibrium condition of the calculation section in beams,using the deformation compatibility condition and age-adjusted effective modulus method,a unified formula for calculating long-term loss is established which is considering the influences of the regular reinforcement and the intercoupling between shrinkage and creep of concrete and relaxation of prestressing tendon.The calculating results of long-term loss on the practical bridge prestressing tendon show that compared with the calculation results of the unified formula in this paper,after ignoring the interaction between shrinkage and creep of concrete and relaxation of prestressing tendon,at the mid-span section the results calculated by the method in TB 10092-2017 are obviously smaller and the relative error can reach at 35.80%,and that at the L/4 section the results calculated by the method in JTG D62-2004 are obviously bigger and the relative error can reach at 37.95%.