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56 4.1 Prestressing CFRP Characteristics 4.1.1 Tensile Strength and Strain The tensile strength used in design ( fpu) is a characteristic value computed according to ASTM D7290 (2017) which represents 80% lower confidence bound on the 5th-percentile value of a spec- ified population. This combination of confidence bound and the percentile level will result in the resistance factor for LRFD that is similar to other civil engineering materials (ASTM D7290, 2017). 4.1.2 Durability There is a reduction in strength when CFRP is exposed to various environmental conditions. Durability tests were performed on one type of prestressing CFRP product. However, other types are available and others may become available in the future. Since the proposed specifica- tions were intended to include a wide range of CFRP, it was necessary to use an environmental coefficient that is relevant to the materials reported in the literature and those commercially available. For prestressing CFRP enclosed in a concrete element, long-term exposure to environ- mental effects is not of a concern, but when prestressing CFRP is used externally to strengthen concrete elements and it is exposed to environmental effects, a reduction of the design tensile strength of prestressing CFRP of 10% is suggested. 4.2 Jacking Stress Limitations The limitation on jacking stress is controlled by the strain reserved for flexure after stressing. 4.2.1 Strain Reserved for Flexure Figures 4.1 and 4.2 show the design strength (fpu), rupture strength (fpr), strength not accounted for in the design (fpr â fpu), stress immediately prior to transfer of 70% (fpbt), effective prestress (fpe), prestress loss (fpbt â fpe), and extreme service stress for the prestressing CFRP cables and bars used in this research. As shown, the reserved strain after jacking (esr) is 0.0046 and 0.0036 for prestress- ing CFRP cables and bars, respectively. Also, a larger percentage of the design strength of the prestressing CFRP cable is not accounted for in the design than that for the prestressing CFRP bar. 4.2.2 Creep Rupture The literature review revealed limited investigations on the creep of FRP composites for limited test durations (12,000 hours), large variations of creep rupture stress, and linear extrapolation of C H A P T E R 4 Research Findings and Products
Research Findings and Products 57 *Extreme case refers to the occurrence of service load on a cracked girder. Figure 4.1. Stress-strain relationship of prestressing CFRP cables. *Extreme case refers to the occurrence of service load on a cracked girder. Figure 4.2. Stress-strain relationship of prestressing CFRP bars.
58 Design of Concrete Bridge Beams Prestressed with CFRP Systems test data that may not represent the long-term behavior of the materials. The creep rupture limit of the CFRP reported in the literature ranges from 70% to 93% of the ultimate tensile strength. 4.2.3 Recommendation for Stress Limits Based on consideration for the reserved strain and creep rupture, the maximum stress prior to transfer should be calculated to provide a reserved strain esr â¥ 0.004 for flexure irre- spective of the strength and modulus of elasticity of the CFRP. The recommended maximum stress immediately prior to transfer is the modulus of elasticity of prestressing CFRP times the lesser of the difference between the design strain and 0.004, and 70% of the design strain, as follows: f E minpbt f 0.004, 0.7 (Eq. 4.1)pu pu( )= Ã e â e The maximum jacking stress and stress at service for available CFRP prestressing cables and bars are provided in Table 4.1 as a percentage of the design strength. 4.3 Prestress Losses 4.3.1 Prestress Relaxation Loss Based on relaxation test results presented in Chapter 3, the stress relaxation of prestressing CFRP cable and bar systems (DfpR) can be estimated using Equations 4.2 through 4.5. Equa- tions 4.2 and 4.3 are for applications in which the anchorage is a permanent part of the CFRP prestressing system, such as for post-tensioning applications. Equations 4.4 and 4.5 are for appli- cations in which the anchorage is not a permanent part of the CFRP prestressing system, such as for precast, pretensioning applications. For post-tensioning with 0.6 in. diameter CFRP cables: 0.020 0.0066 log 24 (Eq. 4.2)( )D = ï£« ï£ ï£¬ ï£¶ ï£¸ ï£· â ï£« ï£ ï£¬ ï£¶ ï£¸ ï£·f f f t fpR pt pu pu For post-tensioning with 0.5 in. diameter CFRP bars: 0.016 0.0057 log 24 (Eq. 4.3)( )D = ï£« ï£ ï£¬ ï£¶ ï£¸ ï£· â ï£« ï£ ï£¬ ï£¶ ï£¸ ï£·f f f t fpR pt pu pu where fpt is the stress in prestressing CFRP immediately after tensioning (ksi), fpu is the tensile strength of prestressing CFRP (ksi), and t is the time immediately after prestress transfer (days). Prestressing Tendon Type Immediately prior to transfer At service after all losses CFRP cable 70% 65% CFRP bar 65% 60% Table 4.1. Stress limits for prestressing CFRP, % of design strength.
Research Findings and Products 59 For pretensioning with 0.6 in. diameter CFRP cables: 0.019 0.0066 log 24 (Eq. 4.4)( )D = ï£« ï£ ï£¬ ï£¶ ï£¸ ï£· â ï£« ï£ ï£¬ ï£¶ ï£¸ ï£·f f f t fpR pt pu pu For pretensioning with 0.5 in. diameter CFRP bars: 0.013 0.0057 log 24 (Eq. 4.5)( )D = ï£« ï£ ï£¬ ï£¶ ï£¸ ï£· â ï£« ï£ ï£¬ ï£¶ ï£¸ ï£·f f f t fpR pt pu pu 4.3.2 Temperature Effects In this study several CFRP prestressed prisms were exposed to 30 thermal loading cycles each varying from 0Â°F to 140Â°F, which is a relatively severe temperature condition for pre- stressed concrete structures. The CFRP cables did not exhibit any thermally induced prestress loss but the CFRP bars showed a prestress loss of 30% to 40% depending on the level of jacking forces. Also, the transfer length for the CFRP prestressing cables and bars increased by 70% and 100% of the initial values, respectively, after the thermal cycles. This increase is attributed to the deterioration of bond between prestressing CFRP and concrete at the transfer zone. Because the CFRP prestressed prisms may have not provided the behavior that can be expected from full-scale bridge beams with larger cross section and span length, a further investigation of long-term performance of large-scale CFRP prestressed beams due to thermal cyclic loading was necessary. It was found that the instantaneous change of temperature, DT, affects the pre- stressing level in the CFRP tendons because of the different coefficients of thermal expansion for the CFRP and concrete. An increase in temperature results in prestress gain and a reduction in temperature results in prestress loss. The gain in the prestressing force due to temperature change has no detrimental effect and may be disregarded; the thermally induced loss (DfpTH) can be calculated as follows: f T EpTH cfrp cm cfrp 0 (Eq. 4.6)( )D = D Î± â Î± â¥ where E A E A E A E A E A E A cm cfrp cfrp cfrp c c cfrp cfrp c c c c c cfrp cfrp (Eq. 4.7)Î± = Î± + + Î± + where Ecfrp and Ec = modulus of elasticity of the prestressing CFRP and concrete, respectively; Acfrp and Ac = cross-sectional areas of the prestressing CFRP and concrete, respectively; and Î±cfrp and Î±c = longitudinal coefficient of thermal expansions of the CFRP and concrete, respectively. DT is the expected temperature change at the time of prestress transfer and can be deter- mined in accordance with Articles 3.12.2 and 3.12.3 of the AASHTO LRFD (2017). Maximum and minimum temperature conditions should be considered for estimating the thermally induced losses.
60 Design of Concrete Bridge Beams Prestressed with CFRP Systems 4.4 Flexural Design 4.4.1 Prestressed Beams with Bonded Prestressing CFRP Failure of bonded CFRP prestressed beams may result from the rupture of prestressing CFRP if r > rb or crushing of concrete if r > rb. When failure is initiated by concrete crushing, the concrete strain will reach the ultimate strain ecu of 0.003; and therefore the stress-block factors from AASHTO LRFD (2017) can be used. However, when failure is initiated by rup- ture of the prestressing CFRP, the concrete strain will be lower than the ultimate strain; and therefore the stress-block factors need to be modified. The following simplified approach is proposed for calculating the rectangular stress-block factors, Î±1 and Î²1, for concrete with strengths between 5 and 15 ksi. The value of Î²1 (factor relating depth of equivalent rectangular compressive stress block to neutral axis) is calculated as follows: 4 6 2 1.1 50 0.65 (Eq. 4.8)1 ( )Î² = â e â²e â e â²e â â² â¥f cc c cc c c The value of Î±1 (factor taken as the ratio of equivalent concrete compressive stress to the compressive strength of concrete) is calculated as follows: 1 1 3 1 60 (Eq. 4.9)1 1 2 ( )Î± = Î²ï£«ï£ï£¬ ï£¶ï£¸ï£· eâ²e â eâ²eï£«ï£ï£¬ ï£¶ï£¸ï£· ï£« ï£ ï£¬ ï£¶ ï£¸ ï£· â â²fcc c cc c c In Equations 4.8 and 4.9, f â²c is the specified concrete strength (ksi), ecc is the compressive con- crete strain at the flexural compressive face, and eâ²c is the strain corresponding to f â²c, calculated as follows: 1.6 11 10 (Eq. 4.10)3( )â²e = + â² Ã âfc c NCHRP Report 595 (Rizkalla, 2007) provides more detailed information on the stress-block factors for high-strength concrete. Also, the analytical study conducted in this project indicates that the provisions for Î±1 and Î²1 provided in AASHTO LRFD (2017) for ecc < 0.003 give a good approximation of the values obtained from Equations 4.9 and 4.10 (3% difference). Additional information is presented in Appendix E. 4.4.2 Prestressed Beams with Unbonded Prestressing CFRP The design equation developed by Namaan and Alkhairi (1991b) to calculate the force in the unbonded prestressing tendons was adopted for the proposed specifications. The equation uses a strain reduction factor (Wu) to account for the lack of bond between the tendon and the concrete: (Eq. 4.11)= + W e âï£« ï£ï£¬ ï£¶ ï£¸ï£· f f E d c c ps pe u ps cu ps
Research Findings and Products 61 where 1.5W = ï£« ï£ ï£¬ ï£¶ ï£¸ ï£· L d u ps for one-point loading 3.0= ï£« ï£ ï£¬ ï£¶ ï£¸ ï£· L dps for third-point or uniformly distributed loading This equation was also adopted by ACI 440.4R-04 (2011), SIMTReC Manual No. 5 (2008), and CAN/CSA S806-12 (2017). The equation was used to calculate the force in the prestressing CFRP at ultimate for the beams reported in the test database, the full-scale beams tested in this research, and the beams considered in the numerical parametric study. The mean force obtained from the tests and FEA was 1.2 times the value predicted by this equation with a COV of 0.26. 4.5 Minimum Reinforcement Figure 4.3 shows the cracking load obtained from tests versus the cracking load calculated according to the AASHTO LRFD (2017) provisions to satisfy the minimum reinforcement. The average calculated cracking load for the minimum reinforcement requirement is 1.35 times that obtained from the tests. 4.6 Resistance Factors A study conducted as the part of this research found that for a reliability index of 4, a resis- tance factor of 0.8 is appropriate for bonded girders failing due to CFRP rupture. However, because of the tendency of brittle failure of the CFRP prestressed beams, a resistance factor of 0.75 is recommended. The resistance factor of 0.75 stipulated in AASHTO LRFD (2017) for compression-controlled (concrete crushing) beams prestressed with steel tendons is proposed for beams prestressed with CFRP because of the similarity in behavior. A resistance factor of 0.75 is also stipulated for tension-controlled beams (although more conservative than that obtained from the reliability analysis) to eliminate the need for a transition region between the two modes Figure 4.3. Experimentally measured versus calculated cracking load (according to AASHTO LRFD, 2017) for minimum reinforcement.
62 Design of Concrete Bridge Beams Prestressed with CFRP Systems of failure. The resistance factor provision for concrete crushing of 0.75 also applies to fully unbonded CFRP because failure of the beams results from concrete crushing. 4.7 Design Guidelines, Materials Specifications, and Design Examples The research produced two primary products: (1) design guidelines and (2) material specifi- cations. In addition, design examples were prepared to illustrate use of the guidelines. 4.7.1 Design Guidelines Recommended design guidelines for concrete bridge beams prestressed with CFRP systems were developed based on the research findings. These guidelines were provided to the AASHTO Committee on Bridges and Structures for consideration and publication as the AASHTO Guide Specifications for the Design of Concrete Bridge Beams Prestressed with Carbon Fiber Reinforced Polymer (CFRP) Systems. 4.7.2 Material Specifications Recommended material specifications were also developed based on the research find- ings. These material specifications were also provided to the AASHTO Committee on Bridges and Structures for consideration and incorporation in the AASHTO Guide Specifications for the Design of Concrete Bridge Beams Prestressed with Carbon Fiber Reinforced Polymer (CFRP) Systems. 4.7.3 Design Examples Five examples were prepared to illustrate the use of the proposed design approach. Three design examples considered pretensioned beams: one beam prestressed with CFRP cables in a single layer, one beam prestressed with straight CFRP cables in multiple layers, and one beam prestressed with harped CFRP cables. The examples provide the calculation for uncracked and cracked sections. The other two design examples are for unbonded post-tensioned beams: one beam prestressed with CFRP in a single layer and one beam prestressed with draped CFRP bars in multiple layers. One of the examples for unbonded post-tensioned beams also illustrated the design of the anchorage zone based on the provisions in AASHTO LRFD (2017). These examples are available online at www.trb.org and can be found by searching for âNCHRP Research Report 907.â