【正文】 estressing tendons, cause longterm deformations in concrete structures. While it is generally accepted that longterm losses do not affect the ultimate capacity of a prestressed concrete member, a reasonably accurate prediction of these losses is important to ensure satisfactory performance of concrete structures in service. If prestress losses are underestimated, the tensile strength of concrete can be exceeded under full service loads, causing cracking and unexpected excessive deflection. On the other hand, overestimating prestress losses can lead to excessive camber and uneconomic design. The error in predicting the longterm prestress losses can be due to: (1) inaccuracy in estimation of the longterm material characteristics (creep and shrinkage of concrete and relaxation of prestressing tendons)。 Prestress loss。附錄 A 科技文獻(xiàn)翻譯 原文 Construction and Building Materials Volume 21, Issue 5 , May 2020, Pages 10521060 An approach to determine longterm behavior of concrete members prestressed with FRP tendons Abstract The bined effects of creep and shrinkage of concrete and relaxation of prestressing tendons cause gradual changes in the stresses in both concrete and prestressing tendons. A simple method is presented to calculate the longterm prestress loss and the longterm change in concrete stresses in continuous prestressed concrete members with either carbon fiber reinforced polymer (CFRP) or aramid fiber reinforced polymer (AFRP) tendons. The method satisfies the requirements of equilibrium and patibility and avoids the use of any empirical multipliers. A simple graph is proposed to evaluate the reduced relaxation in AFRP tendons. It is shown that the prestress loss in FRP tendons is significantly less than that when using prestressing steel, mainly because of the lower moduli of elasticity of FRP tendons. The longterm changes in concrete stresses and deflection can be either smaller or greater than those of parable girders prestressed with steel tendons, depending on the type of FRP tendons and the initial stress profile of the crosssection under consideration. Keywords: Creep。 Prestressed concrete 。 and (2) inaccuracy of the method of analysis used. The objective of this paper is to address the second source of inaccuracy by presenting a simple analytical method to estimate the timedependent strains and stresses in concrete members prestressed with FRP tendons. The method satisfies the requirements of equilibrium and patibility and avoids the use of empirical equations, which in general show loss in accuracy to enable generality. The 5 inaccuracy in the material characteristics used can be mitigated by varying the input material parameters and establishing upper and lower bounds on the analysis results. For the purpose of this paper, and to avoid confusion, a consistent sign convention is used. Axial force N is positive when it is tensile. Bending moment, M, that produces tension at the bottom fiber of a cross section and the associated curvature ψ are positive. Stress, σ, and strain, ε, are positive for tension and elongation, respectively. Downward deflection is positive. It follows that shrinkage, εcs, is negative quantity. The loss in tension in prestressing reinforcement due to relaxation Δσpr or due to the bined effects of creep, shrinkage, and relaxation, Δσp, is negative quantity. The analysis considered herein focuses on a prestressed concrete section with its centroidal principal yaxis in vertical direction with the coordinate y of any concrete fiber or steel layer being measured downward from a given reference point. 2. Relaxation of FRP prestressing tendons Similar to concrete and steel, AFRP prestressing tendons exhibit some creep if subjected to sustained strains. CFRP tendons typically display insignificant amount of creep, which can be neglected for most practical applications. When a prestressing tendon is stretched between two points, it will be subjected to a constant strain. Because of creep, the stress in the tendon decreases (or relaxes) with time to maintain the state of constant strain. This reduction in stress is known as intrinsic relaxation Δσpr. While steel tendons subjected to stresses less than 50% of the yield stress do not exhibit appreciable amount of relaxation, tests on AFRP tendons have shown that they display relaxation under very low stresses. The level of relaxation of AFRP tendons depends upon many factors, including ambient temperature, environment (., air, alkaline, acidic, or salt solutions), ratio of initial stress, σp0, to its ultimate strength, fpu, and time t lapsed after initial stressing. Based on extensive experimentation on relaxation properties of AFRP tendons, Saadatmanesh and Tannous [2] suggested a relationship of the form: 6 (1) where λ = σp1/fpu. σp1 is the stress in the tendon 1 h after stress release. Ratios of σp1/σp0 in their tests varied between and , with an average of . Tabulated values of the variables a and b were provided for λ = and λ = , and for different temperature levels and solution types. For AFRP tendons in air at a temperature of 25 176。 New York (2020). [5] H. Trost, Auswirkungen des Superpositionsprinzips auf Kriechund Relaxationsproblems bei Beton und Spannbeton, Beton Stahlbetonbaun 62 (1967) (10), pp. 230–238 (62)11: 261–269 (in German). [6] . Bazant, Prediction of concrete creep effects using ageadjusted effective modulus, ACI J 69 (1972) (4), pp. 212–217. 16 [7] Youakim SA, Karbhari VM. A Simplified method for prediction of longterm prestress loss in posttensioned concrete bridges. Caltrans Draft Report. University of