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66 Af , Acfrp Cross-sectional area of the FRP reinforcement, in. 2 Ac Cross-sectional area of the concrete, in. 2 a, b Constants determined from the regression analysis (Saadatmanesh and Tannous, 1999) c Distance from the extreme compression fiber to the neutral axis, in. db Nominal prestressing CFRP diameter, in. dps Distance from the extreme compression fiber to the centroid of the prestressing steel, in. Ec Modulus of elasticity of concrete, ksi EL Longitudinal modulus of elasticity of the prestressing CFRP, ksi (Elbadry et al., 2000) Ef , Efrp Modulus of elasticity of the prestressing FRP, ksi Eps Elastic modulus of the prestressing steel tendon, ksi Etot Total energy under the load-deflection curve (Naaman and Jeong, 1995) Eela Elastic energy at the ultimate (Naaman and Jeong, 1995) Fcfrp Induced forces in prestressing CFRP inside the concrete due to temperature change, kip Fc Induced forces in the CFRP prestressed concrete due to temperature change, kip f â²c Concrete compressive strength, ksi f â²ci Concrete compressive strength at time of prestress transfer, ksi fps Stress in the prestressing steel tendon at ultimate, ksi fpy Yielding strength of prestressing steel tendon, ksi (AASHTO LRFD, 2017) fpi Initial prestressing level in the prestressing CFRP prior to transfer, ksi fpj Jacking stress, ksi (AASHTO LRFD, 2017) fpt Stress in prestressing CFRP prior to transfer, ksi fpu Design tensile strength of prestressing CFRP system, ksi fpr Rupture tensile strength of prestressing CFRP, ksi fse Effective stress in prestressing steel strand after losses, psi k wobble friction coefficient per unit length of tendon, 1/ft. (AASHTO LRFD, 2017) L Length of the tendon between anchorages, in. le Effective tendon length, in. li Length of tendon between anchorages, in. ld Development length, in. lt Transfer length, in. Mu Factored moment at the section, kip-ft. Mcr Cracking moment, kip-ft. (Zou, 2003a) M0.001 Moment at concrete compression strain of 0.001, kip-ft. nr Modular ratio of the resin to the fiber (Dolan et al., 2000) Ns Number of support hinges crossed by the tendon between anchorages or discretely bonded points P Prestressing force in the prestressing CFRP, kip (Saadatmanesh and Tannous, 1999) Notations
Notations 67 P1 Load in prestressing CFRP after 1 hour from transfer, kip (Saadatmanesh and Tannous, 1999) Pu Ultimate tensile capacity of the prestressing CFRP, kip (Saadatmanesh and Tannous, 1999) r Radius of prestressing CFRP, in. (Dolan et al., 2000) Rch Radius of curvature of the harping device, in. (Dolan et al., 2000) RL Total prestress relaxation loss, % (Dolan et al., 2000) RL1 Relaxation of the polymer, % (Dolan et al., 2000) RL2 Relaxation due to straightening of fibers, % (Dolan et al., 2000) RL3 Relaxation of fibers, % (Dolan et al., 2000) t Time after prestress transfer, days Î± The total angular change between the jacking point and dead end, rad (AASHTO LRFD, 2017) Î±1 Stress-block factor Î±c Thermal expansion coefficient of plain concrete, 1/Â°F Î±cm Thermal expansion coefficient of CFRP prestressed concrete, 1/Â°F Î±cfrp Longitudinal coefficient of thermal expansions of the prestressing CFRP, 1/Â°F Î±t Coefficient for transfer length measurements based on the type of prestressing CFRP Î²1 Stress-block factor Î²T Target reliability index Dcr Deflection at first cracking, in. (Zou, 2003a) Du Deflection of prestressed beam at ultimate, in. (Abdelrahman et al., 1995) Dl Equivalent deflection of an uncracked section for the same ultimate moment level, in. (Abdelrahman et al., 1995) DfpR Prestress relaxation loss, ksi DPT Loss due to temperature change, ksi DfpF Loss due to friction, ksi (AASHTO LRFD, 2017) DT Temperature change, Â°F Âµ Coefficient of friction Âµ Ductility index by taking into account deformation parameters (Abdelrahman et al., 1995) Âµen Ductility index by taking into account energy parameters (Naaman and Jeong, 1995) ur Volume fraction of the resin (Dolan et al., 2000) Ï Diameter of the prestressing CFRP Ãu Curvature at ultimate Ã0.001 Curvature at concrete strain of 0.001 rp Prestressing steel ratio (ACI Committee 318, 2014) sh Stress increase due to harping, ksi (Dolan et al., 2000) sf Thermally induced stresses in prestressing FRP, ksi (Elbadry et al., 2000) sc Thermally induced stresses in prestressed concrete, ksi (Elbadry et al., 2000) Wu Strain or bond reduction coefficient at ultimate ecu Ultimate strain of the outermost fiber of concrete in compression ecc Concrete strain eâ²c Strain in the concrete when the compressive stress reaches f â²c esr Reserved strain after jacking