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Page 66
Suggested Citation:"Notations." National Academies of Sciences, Engineering, and Medicine. 2019. Design of Concrete Bridge Beams Prestressed with CFRP Systems. Washington, DC: The National Academies Press. doi: 10.17226/25582.
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Page 66
Page 67
Suggested Citation:"Notations." National Academies of Sciences, Engineering, and Medicine. 2019. Design of Concrete Bridge Beams Prestressed with CFRP Systems. Washington, DC: The National Academies Press. doi: 10.17226/25582.
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Page 67

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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 ′c Concrete compressive strength, ksi f ′ci 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 α The total angular change between the jacking point and dead end, rad (AASHTO LRFD, 2017) α1 Stress-block factor αc Thermal expansion coefficient of plain concrete, 1/°F αcm Thermal expansion coefficient of CFRP prestressed concrete, 1/°F αcfrp Longitudinal coefficient of thermal expansions of the prestressing CFRP, 1/°F αt Coefficient for transfer length measurements based on the type of prestressing CFRP β1 Stress-block factor βT 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, °F µ Coefficient of friction µ Ductility index by taking into account deformation parameters (Abdelrahman et al., 1995) µen Ductility index by taking into account energy parameters (Naaman and Jeong, 1995) ur Volume fraction of the resin (Dolan et al., 2000) φ Diameter of the prestressing CFRP Øu Curvature at ultimate Ø0.001 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 e′c Strain in the concrete when the compressive stress reaches f ′c esr Reserved strain after jacking

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Carbon fiber reinforced polymer (CFRP) is becoming a recognized alternative to traditional construction materials in a wide range of civil engineering applications. An example of such applications is the use of CFRP cables or bars as prestressing tendons for concrete bridge girders, especially in aggressive environments where steel prestressing strands are susceptible to corrosion.

Despite their promise, CFRP prestressing tendons have not frequently been used for bridge construction in the United States; their use has been hampered by the lack of recognized design specifications.

NCHRP (National Cooperative Highway Research Program) Research Report 907: Design of Concrete Bridge Beams Prestressed with CFRP Systems proposes guidelines and presents research findings that are expected to advance and facilitate the use of CFRP systems in bridge applications. In addition, five design examples that illustrate the step-by-step use of the proposed guide specifications are provided.

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