土木工程外文文献翻译--决定用frp筋制作的预应力混凝土构件的长期行为的方法-建筑结构(编辑修改稿)

土木工程外文文献翻译--决定用frp筋制作的预应力混凝土构件的长期行为的方法-建筑结构(编辑修改稿)内容摘要：

can be obtained by dividing the stress values by the modulus of elasticity of concrete at t0, Ec(t0). Step 2: Free creep and shrinkage of concrete. The distribution of hypothetical free change in concrete strain due to creep and shrinkage in the period t0 to t is defined by its value (Δεcc)free at the centroid of the area of the concrete section, Ac (defined as the gross area minus the area of the FRP reinforcement, Af, minus the area of the prestressing duct in the case of posttensioning, or minus the area of the FRP tendons, Ap, in case of pretensioning) at y = ycc as shown in Fig. 3, such that (Δεcc)free= εcc(t0)+εcs (7) where ycc is the y coordinate of the centroid of the concrete section, is the creep coefficient for the period t0 to t, and εcs is the shrinkage in the same period and εcc(t0) is the strain at the centroid of the concrete section given by 9 εcc(t0)=ε1(t0)+(yccy1)ψ(t0) (8) where y1 is the centroid of the transformed area at t0, and ψ(t0) is the curvature (slope of the strain diagram) at t0. Also free curvature is Δψfree= ψ(t0) (9) (15K) Fig. 3. Typical prestressed concrete section and the strain diagram immediately after transfer. Step 3: Artificial restraining forces. The free strain calculated in Step 2 can be artificially prevented by a gradual application of restraining stress, whose value at any fiber y is given by (10) where is the ageadjusted modulus of concrete [5] and [6], used to account for creep effects of stresses applied gradually to concrete and is defined as (11) The artificial restraining forces, ΔN at the reference point O (which is the centroid of the ageadjusted transformed section), and ΔM, that can prevent strain changes due to creep, shrinkage and relaxation can be defined as (12) and 10 (13) where Ic, yp, and are the second moment of Ac about its centroid, y coordinate of the centroid of the FRP tendons, and the reduced relaxation stress between times t0 and t. It should be noted that if the section contains more than one layer of prestresssing tendons, the terms containing Ap or ypAp should be substituted by the sum of the appropriate parameters for all layers. Step 4: Elimination of artificial restraint. The artificial forces ΔN and ΔM can be applied in reversed direction on the ageadjusted transformed section to give the true change in strain at O, ΔεO, and in curvature, Δψ, such that (14a) (14b) where is the second moment of about its centroid and is the area of ageadjusted transformed section defined as (15) where Ef and Ep are the moduli of elasticity for the FRP reinforcement and tendons, respectively, and the is as defined in Eq. (11). Substituting Eqs. (12) and (13) into Eqs. (14a), (14b) and (15) gives (16) and (17) 11 where (18) The timedependent change in strain in prestressing tendons Δεp can then be evaluated using Eq. (19) and the timedependent change in stress in prestressing tendons (described by Eq. (20)) is the sum of EpΔεp and the reduced relaxation. Δεp=ΔεO+ypΔψ (19) (20) Substitution of Eqs. (16) and (17) into Eq. (20) gives an expression for the longterm prestress loss, Δσp, due to creep, shrinkage, and relaxation as (21) It should be noted that the last term in Eq. (21), , is zero in the case of prestressed members using CFRP tendons. (23) (24) 4. Application to continuous girders Prestressing of continuous beams or frames produces statically indeterminate bending moments (referred to as secondary moments). As mentioned previously, ε1(t0) and ψ(t0) (Eqs. (7), (8) and (9)) represent the strain parameters at a section due to dead load plus the primary and secondary moments due to prestressing. The 12 timedependent change in prestress force in the tendon produces changes in these secondary moments, which are not included in Eq. (21). This section considers the effect of the timedependent change in secondary moments on the prestress loss. Step 1: Considering a twospan continuous beam, as shown in Fig. 4(a) where the variation of the tendon profile is parabolic in each span, the statically indeterminate beam can be solved by any method of structural analysis (such as the force method) to determine the moment diagram at time t0 due to dead load and prestressing. (14K) Fig. 4. Twospan continuous prestressed girder. (a) Dimensions and cable profile。 (b) Locations of integration points (sections). Step 2: The timedependant sectional analysis can be performed as shown previously for each of the three sections shown in Fig. 4(b) and determine (Δψ)i for each section, where i = A, B and C. Step 3: Use the force method to determine the change in internal forces and displacements in the continuous beam. The released structure with the shown coordinate system in Fig. 5(a) can be used. It can be assumed that the change in angular discontinuity at middle support between t0 and t is ΔD1 and that the unknown change in the connecting moment is ΔF1. The change in angular discontinuity ΔD1 is then evaluated as the sum of the two end rotations of each of the simple spans l1 and l2. Using the method of elastic weights and assuming a parabolic variation of curvature in each span, ΔD1 can be expressed as 13 (25) (10K) Fig. 5. Analysis by the force method. (a) Released structure and coordinate system。 (b) Moment diagram due to unit value of connecting moment. Step 4: Due to unit load of the connecting。