【正文】 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。 FRP。 Longterm。 Prestress loss。 Prestressed concrete 。 Relaxation。 Shrinkage Nomenclature A area of cross section d vertical distance measured from top fiber of cross section 2 E modulus of elasticity ageadjusted elasticity modulus of concrete fpu ultimate strength of prestressing tendon h total thickness of concrete cross section I second moment of area O centroid of ageadjusted transformed section t final time (end of service life of concrete member) t0 concrete age at prestressing y coordinate of any fiber measured downward from O χ aging coefficient χr reduced relaxation coefficient α ratio of modulus of elasticity of FRP or steel to that of concrete Δεc(t,t0) change in concrete strain between time t0 and t ΔεO change in axial strain at the centroid of ageadjusted transformed section O Δσc(t,t0) stress applied gradually from time t0 to its full amount at time t Δσpr intrinsic relaxation reduced relaxation Δσp total longterm prestress loss Δψ change in curvature εcs shrinkage strain of concrete between t0 and t εc(t0) instantaneous strain at time t0 (t, t0) creep coefficient between t0 and t σc(t0) stress applied at time t0 and sustained to a later time t σp0 initial stress of prestressing tendon ρ reinforcement ratio ψ curvature Ω the ratio of the difference between the total prestress loss and intrinsic relaxation to the initial stress Subscripts 3 1 transformed section at t0 c concrete cc concrete section f FRP reinforcement or flange p prestressing FRP tendon ps prestressing steel tendon s steel reinforcement Article Outline Nomenclature 1. Introduction 2. Relaxation of FRP prestressing tendons 3. Proposed method of analysis . Initial steps . Timedependent change in concrete stress . Longterm deflection 4. Application to continuous girders 5. Development of design aids 6. Illustrative example 7. Summary Acknowledgements References 1. Introduction The use of fiber reinforced polymer (FRP) tendons as prestressing reinforcements have been proposed in the past decade and a few concrete bridges have already been constructed utilizing fiber reinforced polymer (FRP) tendons. Compared to conventional steel prestressing tendons, FRP tendons have many advantages, including their noncorrosive and nonconductive properties, lightweight, and high tensile strength. Most of the research conducted on concrete girders prestressed with 4 FRP tendons has focused on the shortterm behavior of prestressed members。 research findings on the longterm behavior of concrete members with FRP tendons are scarce in the literature. The recent ACI Committee report on prestressing concrete structures with FRP tendons (ACI [1]) has pointed out that: “Research on the longterm loss of prestress and the resultant timedependent camber/deflection is needed …” Most of the research and applications of FRP tendons in concrete structures have adopted either carbon fiber reinforced polymer (CFRP) or aramid fiber reinforced polymer (AFRP) tendons. The use of glass fiber reinforced polymers (GFRP) has mostly been limited to conventional reinforcing bars due to their relatively low tensile strength and poor resistance to creep. Therefore, this paper focuses on prestressed members with either CFRP or AFRP tendons. Creep and shrinkage of concrete, and relaxation of prestressing 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)。 and (2) inaccuracy of the method of analysis used. The objective of this pape