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6 2.1 Current Applications of CFRP in Prestressing A survey of state departments of transportation (DOTs) and the District of Columbia was conducted to gather information on the state of practice of CFRP prestressing. Thirty-four DOTs responded to the survey. Only one DOT (Michigan) reported that their bridge inventory includes CFRP prestressed concrete bridge beams; the other DOTs reported no CFRP prestressed concrete bridge beams in their inventory. Michigan DOT provided information on the design details of the bridges in their inventory. According to this information, AASHTO LRFD Bridge Design Speci- fications (2017; henceforth referred to as AASHTO LRFD) was used to determine the load factors, live load distribution, allowable concrete stresses, elastic losses, and some components of long-term losses. ACI 440.4R-04: Prestressing Concrete Structures with FRP Tendons (ACI Committee 440, 2011) was used for shear provisions of bent CFRP bars and to determine strand stresses to avoid creep rupture. Michigan DOT also modified the design procedures to calculate long-term losses and shear resistance. 2.2 Field Applications A review of the literature indicated that CFRP has been used for prestressing in about 80 demonstration bridges worldwide. Several technical committees from seven countries have published 20 guidelines and specifications related to the internal and external use of CFRP; these are included in the list of references. Also, technical committees, associations, engineering societies, and manufacturers have provided information and examples of concrete bridges prestressed with CFRP systems [e.g., ACI 440.4R-04 (2011); Manual No. 5: Prestressing Concrete Structures with FRPs (SIMTReC, 2008; henceforth referred to as SIMTReC Manual No. 5); Market Development Association; and CFRP manufacturers]. In addition, Khalifa et al. (1993) compiled examples of pedestrian and road bridges constructed with CFRP tendons. Details of some bridges that have been reported in the literature are described in the following: â¢ Shinmiya Bridge is the first documented CFRP prestressed bridge built in the world (Tokyo Rope, 2000). It was constructed in Ishikawa Prefecture, Japan, in 1988 as a replacement of the old bridge that exhibited deterioration of girders caused by seawater exposure. The bridge is 20 ft long and 23 ft wide and was built with 24 pretensioned I-girders with CFRP strands. Although built over seawater in an aggressive environment, the Shinmiya Bridge is reported to currently have no deterioration. â¢ The Beddington Trail bridge in Calgary, Canada, is the first bridge constructed in North America with CFRP prestressed concrete girders; it was opened to traffic in 1993. The bridge is a two-span skewed bridge with 75 ft and 63 ft spans. The spans consist of 13 bulb-tee precast girders with a 6 in. thick concrete deck. Two types of prestressing FRP strands were used in C H A P T E R 2 Literature Review and Current Design Practices
Literature Review and Current Design Practices 7 six precast concrete girders. CFRP cables were used in four girders and CFRP bars were used in pretensioning the other two girders (Rizkalla and Tadros, 1994). â¢ The Taylor Bridge in British Columbia, Canada, was built in 1997 using prestressing CFRP. Four out of 40 girders were prestressed with straight and draped prestressing CFRP cables or bars. Two of the four girders had CFRP stirrups as shear reinforcement and the others had epoxy coated steel stirrups. The bridge was designed using information from tests performed in previous studies. Cross diaphragms were used to provide an alternate load path and avoid a progressive collapse in case of failure of any component (Shehata and Rizkalla, 1999). â¢ The Bridge Street Bridge, built in the City of Southfield, Michigan, in 2001 is the first CFRP prestressed concrete bridge built in the United States. It comprises two parallel and inde- pendent structures with three spans skewed at an angle of 15Â° over its 204 ft. length (Grace et al., 2002). One of the bridge superstructures is constructed with equally spaced AASHTO Type III precast concrete I-girders using steel reinforcement with a continuous cast-in-place concrete deck slab. The other bridge structure consists of four double-tee girders prestressed with CFRP tendons in each of the three spans. The double-tee girders were pretensioned with CFRP bars and post-tensioned (both longitudinally and transversely) with CFRP cables. The longitudinal post-tensioning strands were draped at the bottom of the double-tee beams. CFRP stirrups, CFRP grid reinforcement, and stainless-steel stirrups were also used as non- prestressed reinforcement. Pretensioning strand forces, concrete strains, deflections, and post-tensioning forces were monitored during construction. In addition, the design equations and assumptions were verified by calculations, finite element analysis, and laboratory testing of scaled double-tee prestressed beams. 2.3 Existing Analytical Models This section summarizes the analytical models reported in the literature for determining the capacity and deformability of CFRP prestressed beams, prestress losses, transfer and devel- opment lengths of the prestressing CFRP tendons and stresses in unbonded CFRP in post- tensioned beams. 2.3.1 Analytical Models for Flexural Capacity Prestressed Beams with Bonded Prestressing CFRP The concept of strain compatibility and balanced reinforcement ratio (rb) has been used in concrete beam design for several decades. The provided reinforcement ratio compared to the balanced ratio of a section with steel prestressing gives an indication of the expected perfor- mance of the section. Because of the brittle nature of FRP, failure occurs either by rupturing the FRP (r > rb) or by crushing of concrete: (r > rb); the balanced reinforcement ratio is an indica- tor of the failure mode. The stress in the FRP depends on the location of the neutral axis, depth of the structure, and the structural configuration (Dolan, 1991). In the case of multi-layer FRP tendons, the farthest tendon will rupture first and hence the approach of using the moment arm to the centroid of the group of tendons can provide an inaccurate moment capacity estimate. Dolan and Swanson (2002) developed an equation for flexural strength of beams with vertically distributed tendons (described in Section 2.5.6). Prestressed Beams with Unbonded Prestressing CFRP Although many researchers have investigated the strength of unbonded post-tensioned beams, there is no unified approach for estimating the force in unbonded tendons. The force in an unbonded tendon is governed by the deformation of the whole member and it is uniform throughout the member. Hence, the principle of strain compatibility at any cross section of
8 Design of Concrete Bridge Beams Prestressed with CFRP Systems unbonded beams does not accurately reflect the governing mechanics of these elements. Most of the models reported in the literature for estimating the force in the unbonded tendons at the ultimate load were derived for prestressing steel with the assumption that the yield strength will not be reached and the elastic modulus of the tendon can be used to estimate the increase in tendon stress. Thus, these models can be used for prestressing CFRP tendons or serve as a basis for developing new models. Table 2.1 lists some equations proposed in different studies and used in the design guidelines for estimating the stress at ultimate for an unbonded tendon. 2.3.2 Analytical Models for Deformability Beams that are prestressed with CFRP tendons do not exhibit ductility because CFRP materials exhibit elastic behavior and a brittle response. Ductility is a measure of a beamâs deformation at Sources Model Naaman and Alkhairi (1991b) = + Î© Îµ â Finding (perfect correlation): Î© = . for one-point loading = . for third-point or uniform Recommendation: Î© = . for one-point loading = . for third-point or uniform where is the effective prestressing stress, Î© is the strain reduction factor, is the total length of the prestressing tendon, and is the distance from the extreme compression fiber to the centroid of the prestressing steel. Adapted by: Naaman et al. (2002), ACI 440.4R-04 (2011), SIMTReC Manual No. 5 (2008), CAN/CSA S806-12 (2017), AASHTO LRFD (1994) ACI Committee 318 (2014) = + + 10,000 + 60,000 â¤ 35 = + 300Ï + 10,000 + 30,000 > 35 where is the effective stress in prestressing reinforcement after all prestress losses (psi), , is the specified yield strength of prestressing reinforcement (psi), is the ratio of to and is the area of prestressed longitudinal tension reinforcement (in.2). AASHTO LRFD (2017) = + 900 â â¤ = 1 + 2â where c is the distance from extreme compression fiber to the neutral axis (in.), is effective tendon length (in.), is the length of the tendon between anchorages (in.), is the number of support hinges crossed by the tendon between anchorages or discretely bonded points, is the yield strength of prestressing steel (ksi), and is the effective stress in prestressing steel at the section under consideration after all losses (ksi). Table 2.1. Models for estimating stresses in unbonded tendons at the ultimate load.
Literature Review and Current Design Practices 9 ultimate to that when the reinforcement yields. Since CFRP reinforcements do not yield, ductil- ity cannot be defined in this manner. Instead, deformability has been proposed as a measure of the performance of beams reinforced or prestressed with FRP [ACI 440.4R-04 (2011); SIMTReC Manual No. 5 (2008); and CAN/CSA S6-06: Canadian Highway Bridge Design Code (Canadian Standards Association, 2014)]. Deformability is a measure of a beamâs deformation at ultimate to its deformation under service loads. Models proposed by some researchers for estimating deform- ability index are listed in Table 2.2. For bridge beams, where energy dissipation is not a primary consideration, deformability is a suitable parameter for evaluating safety and performance. Deformability may be defined based on deformation prior to failure considering parameters such as deflection at ultimate and deflection at cracking, and a deformability index could provide a reasonable measure of the performance of the CFRP prestressed beams (Abdelrahman et al., 1995; Zou, 2003a). 2.3.3 Analytical Models for Prestress Losses Because of the differences in material characteristics between prestressing CFRP tendons and prestressing steel strands, relaxation losses for prestressing CFRP tendons differ from those for steel strands. Also, the difference in coefficients of thermal expansion for prestressing CFRP and concrete causes a change in effective prestressing force (loss or gain) when the temperature changes. Existing analytical models for prestress relaxation and thermal effects are presented in the following. However, concrete creep, and shrinkage losses are primarily related to concrete and do not depend on the prestressing strand type. Hence, these losses can be calculated in a similar manner to that used for steel prestressing strands but using the elastic modulus of the CFRP material (ACI 440.4R-04, 2011). Prestress Relaxation Loss Long-term relaxation tests on prestressing CFRP cables at the initial stress of 0.7 fpu (70% of design tensile strength) were carried out by Enomoto et al. (1990) for a duration of 33,000 hours. Sources Model Naaman and Jeong (1995) = 0.5 + 1 where is the total energy under the load-deflection curve, and is the elastic energy at ultimate. Jaeger et al. (1995) and Mufti et al. (1996) = . Ã . where . is the moment at a concrete compression strain of 0.001, . is curvature at a concrete compression strain of 0.001, is the ultimate moment, and is curvature at ultimate. Abdelrahman et al. (1995) Âµ = Î Î where Î is the deflection at ultimate and Î is the equivalent deflection of an uncracked section for the same ultimate moment. Gowripalan et al. (1997) = Ã where is the ultimate load, is the cracking load, is the total energy at ultimate, and is the elastic energy at ultimate. Zou (2003a) = â â where â is deflection at ultimate, â is the deflection at first cracking, is the ultimate moment, and is the cracking moment. Table 2.2. Models for estimating deformability index for FRP prestressed beams.
10 Design of Concrete Bridge Beams Prestressed with CFRP Systems The results showed that stress relaxation losses were linearly related to the logarithm of the time; the best fit line was obtained by regression analysis and expressed by the following formula: Relaxation % 0.056 0.396 log 24 (Eq. 2.1)( ) ( )= + t where t is time after stressing in days. Saadatmanesh and Tannous (1999) proposed the following equation to predict the relaxation losses of CFRP tendons: Relaxation % 100 log 24 (Eq. 2.2)1 1[ ] [ ]( )( )( ) = Ã - -P P a b t P Pu u where P1/Pu is the ratio of the tendon load 1 hour after the prestressing transfer to the ultimate tensile capacity of the tendon, a and b are constants determined from regression analysis, and t is the elapsed time in days. In this model, all seating losses, including slip between the tendon and the grips, were assumed to take place within the first hour after stress release. Therefore, the measurement of relaxation loss starts after the first hour. The value of P1 can be calculated based on the differences of the measured tendon strain at the time of release and 1 hour after release. Temperature Effects Because the longitudinal CTE of CFRP is lower than that of concrete, an increase of the ambient temperature will potentially generate compressive stresses in the concrete and tensile stresses in the prestressing CFRP (prestress gain). A reduction in temperature may cause tensile stresses in the concrete and compressive stresses in the prestressing CFRP, which leads to a prestress loss. By assuming full bond between the concrete and prestressing CFRP, and considering strain compatibility and equilibrium, Elbadry et al. (2000) derived the following equations for estimating the thermally induced stresses in prestressing CFRP (sf) and concrete (sc) due to a uniform temperature change (DT) in a concentrically prestressed concrete prism: 1 (Eq. 2.3)( )s = Î± - Î± D + T E A E A E f c L L f L c c (Eq. 2.4)s = - sA A c f c f where Î±c = CTE of concrete; Î±L = the longitudinal CTE of CFRP; Af and Ac = cross-sectional areas of prestressing CFRP and concrete (in.2), respectively; and EL and Ec = longitudinal modulus of elasticity of the prestressing CFRP and concrete (ksi), respectively. 2.3.4 Analytical Models for Development and Transfer Length Several models were proposed for determining the development length (Ld) of CFRP tendons. By modifying the formulation in ACI 318-14: Building Code Requirements for Structural Concrete (ACI Committee 318, 2014) and assuming a nominal bond stress of 333 psi, Lu et al. (2000) proposed the following model: L f d f f dd se b r se b( )= + -1 3 3 4 (Eq. 2.5)
Literature Review and Current Design Practices 11 where db is the diameter (in.), fr is the rupture strength (psi), and fse is the effective prestress (psi) of the tendon, respectively. Mahmoud et al. (1999) proposed the following model for estimating the transfer length, lt, based on an experimental study of 52 CFRP pretensioned concrete beams and prisms: (Eq. 2.6) 0.67 = Î± â² l f d f t pi b t ci where fpi = initial prestressing level in the CFRP tendon before transfer (psi), db = diameter of the prestressing CFRP (in.), fci = concrete strength at transfer (psi), and Î±t = coefficient that varies based on the type of prestressing CFRP tendon. (It was found to be 25.3 and 10.0 for prestressing CFRP cable and bar, respectively.) Grace (2000) proposed a different value of the constant, Î±t, in Equation 2.6 based on regres- sion analysis of experimental results of two types of prestressing CFRP tendons. The proposed values are 11.2 and 10.2 for prestressing CFRP cable and bar, respectively. Zou (2003d) proposed the following equation to predict the transfer length of prestressing CFRP bar with a fiber spiral indented surface condition: l f t ci = Ï480 (Eq. 2.7) 0.5 where Ï is the diameter of the prestressing CFRP (in.) and fci is the concrete cylinder strength at transfer (psi). 2.3.5 Analytical Models for Strength Reduction Due to Harping The induced tensile stresses due to harping of prestressing CFRP tendons, sh, can be obtained based on the following expression (Dolan et al., 2000): E r R h frp ch s = (Eq. 2.8) where Efrp is the elastic modulus of CFRP (ksi), r is the radius of the prestressing CFRP (in.), and Rch is the radius of curvature of the harped prestressing CFRP that can be taken as the radius of the harping device (in.). Quayle (2005) indicated that Equation 2.8 overestimates the harping stress and recom- mended that the value of Rch in the equation be taken as the greater of the radius of the harp- ing device or the natural radius of curvature of the harped tendon, Rn, as estimated by the following equation: R r E P n frp ( ) = Ï - q2 1 cos (Eq. 2.9) 2 where r is the radius of the prestressing CFRP (in.), P is the prestressing force in the CFRP tendon (kips), and q is the harping angle.
12 Design of Concrete Bridge Beams Prestressed with CFRP Systems 2.4 Experimental Investigations Reported in Literature 2.4.1 Flexural Behavior of CFRP Prestressed Beams Due to the relatively low modulus of elasticity of CFRP compared to that of steel, larger curvatures and deflections are induced under the same level of flexural load for beams prestressed with CFRP tendons than those prestressed with steel tendons (ACI 440.4R-04, 2011). Deformation of CFRP prestressed beams that fail due to the rupture of CFRP tendons is smaller than that of the prestressed steel beams as the CFRP tendons do not yield and elongation at rupture is consider- ably smaller than that of steel tendons (Abdelrahman and Rizkalla, 1997). Prestressed Beams with Bonded Prestressing CFRP The general design approach for prestressed beams is to meet the strength and serviceability requirements by providing prestressing tendons of sufficient number and size to ensure flexur- ally dominant behavior, while satisfying the serviceability requirements. Steel prestressed beams that are designed for flexure deform elastically until concrete cracks and exhibits increased deformations after steel yielding until either the steel tendon ruptures or the concrete crushes. However, beams with prestressing CFRP tendons do not exhibit yielding; hence, the deforma- tions after the cracking of concrete increase linearly with load and one of the two modes of failure will occur: rupture of the CFRP tendon or crushing of the concrete. Because of the linear- elastic nature of prestressing CFRP tendons and their low rupture strain compared to steel (â¼2% for prestressing CFRP tendons and â¼6% for prestressing steel), the deformation at ultimate load for beams with bonded CFRP tendons is less than that for beams with prestressing steel if both are designed to fail by rupture of the prestressing tendons. However, to fail by crushing of concrete, the deflections of both beams at the time of failure will be comparable (Abdelrahman, 1995). The level of prestressing, prestressing reinforcement ratio, and the presence of unstressed reinforcement in the tensile zone has a significant effect on the deformation of the beams pre- tensioned with CFRP bars (Abdelrahman and Rizkalla, 1997). The sudden brittle failure of the CFRP prestressed beams can be addressed by arranging the prestressing CFRP tendons in layers along the depth of the member. Although this arrangement will reduce the ultimate capacity (for the same prestressing reinforcement ratio), the beam will exhibit a significant deformation after the ultimate capacity is reached due to progressive rupture of successive layers of CFRP (Abdelrahman and Rizkalla, 1997; Grace et al., 2013). Prestressed Beams with Unbonded Prestressing CFRP The flexural behavior of post-tensioned beams with unbonded CFRP tendons has not been studied as extensively as that of prestressed beams with bonded CFRP tendons. The failure of unbonded post-tensioned beams is generally attributed to concrete crushing even if the pre- stressing reinforcement levels are significantly below the balanced ratio for the corresponding bonded post-tensioned concrete beams (Lee et al., 2017). The unbonded tendons lead to release of stresses at critical sections and lower average stress along the tendonâs length, and thus a lower load in the tendon than their bonded counterpart is achieved. Therefore, the ultimate strength of the bonded beams is higher than that of the unbonded beams. Few experimental studies are reported in the literature on the internal applications of unbonded prestressing CFRP tendons. The majority of the studies considered a beam length ranging from 6.6 ft. to 10.5 ft. with a depth ranging from 6 to 16 in. The results showed that unbonded beams have an energy absorption comparable to steel counterparts (Kato and Hayashida, 1993; Kakizawa et al., 1993; Maissen and De Smet, 1995; Maissen and De Smet, 1998; Jo et al., 2004; and Heo et al., 2013). Heo et al. (2013) found that concrete crushing was always associated with the ultimate load regardless of the type of auxiliary (unstressed) reinforcement used. Maissen and De Smet (1998) showed that continuous beams with unbonded prestressing CFRP tendons
Literature Review and Current Design Practices 13 can provide the same level of deformability as those with steel strands. However, the beams prestressed with bonded CFRP tendons do not redistribute the moment as there is no reserved capacity once the cable ruptures at the plastic hinge above the center support. Another type of prestressing is the unbonded post-tensioning of beams by tendons placed out- side the cross section of the member. Mutsuyoshi and Machida (1993), Grace and Abdel-Sayed (1998), Elrefai et al. (2007), Du and Au (2009), and Ghallab (2013) investigated the flexural behavior of beams with external prestressing CFRP. The results were similar to those prestressed with steel tendons. Grace et al. (2001) investigated the behavior of multi-span continuous CFRP prestressed concrete bridges with external longitudinal post-tensioning using draped tendons and bonded transverse post-tensioning, and reported that a progressive failure of CFRP tendons was observed at the ultimate load stage. A listing of previous experimental studies is presented in Table 2.3. The shaded cells indicate the parameter considered in the cited reference. For example, Mutsuyoshi et al. (1990) tested seven rectangular post-tensioned beams (bonded and unbonded) having depths less than 10 in., span length less than 15 ft., a straight tendon profile, and two jacking stress levels: 30% to 60% and more than 60% of the tensile strength were applied. Different modes of failure were observed. As shown in the table, the reported tests were conducted on rectangular beams with depths less than 20 in. and spans less than 30 ft. Although these members do not necessarily exhibit the behavior that can be expected from full-scale bridge beams, the data was used to supplement those obtained from the tests performed in this project on full-scale bridge beams representing current design and construction practices. 2.4.2 Durability Durability of prestressing CFRP is affected by environmental and mechanical factors. Envi- ronmental factors include moisture and saline environment, alkaline environment, high tem- perature and fire, freezeâthaw cycles, and ultraviolet exposure. Mechanical effects include creep rupture and fatigue. The influence of these factors, individually or in combination, on the properties of CFRP materials has been studied extensively by many researchers. Environmental Factors Fluid ingress has no effect on carbon fibers but it affects the resin matrix and fiber-matrix inter- face and thus such exposure affects the performance of CFRP composites. For unidirectional carbon composites, this exposure usually leads to a large reduction in compressive and transverse shear strength and a small reduction in tensile strength (Dejke, 2001). Hancox and Mayer (1994) reported minimal weight gain and tensile strength loss for carbon/epoxy specimens exposed to 65% humid- ity for more than 4 months and immersed in boiling water for more than 3 weeks. A study of specimens exposed to saltwater indicated a reduction in bond strength (Ghosh and Karbhari, 2004). Benmokrane et al. (2015) evaluated the durability performance of prestressing CFRP cables exposed to elevated temperature and an alkaline environment. The pH of the alkaline solution was kept above 12 to simulate the environment inside the concrete. Four temperatures (72Â° F, 104Â° F, 122Â° F, and 140Â° F) and four exposure durations (1,000 hours, 3,000 hours, 5,000 hours, and 7,000 hours) were used. The extreme exposure condition (140Â° F and 7,000 hours) resulted in a 7% reduction in the tensile strength of the CFRP cable. Tanks et al. (2016) evaluated the durability of prestressing CFRP cables loaded to 75% of ultimate tensile capacity in a simulated concrete environment. After 2,000 hours of immersion in a solution with a pH of 12.7 at 140Â° F, the prestressing CFRP cables retained 96% of their uniaxial tensile capacity.
Authors # o f P re st re ss ed C F R P te st s Beam Details Prestressing Details Failure Mode Section Shape Beam Span Section Depth Jacking Stress Tendon Profile Bond Type R ec ta ng ul ar I' sh ap ed T ee o r do ub le T ee B ox â¤ 15 ft . 15 - 30 ft . > 3 0 ft. â¤ 10 " 10 " -2 0" > 2 0" â¤ 0. 3 f fu 0. 3 f fu -0 .6 f fu > 0 .6 f f u S tr ai gh t D ra pe d H ar pe d B on de d U nb on de d P re te ns io ne d P os t- te ns io ne d F le xu ra l T en si on F le xu ra l C om pr es si on S he ar O th er Mutsuyoshi et al. (1990) 7 Kakizawa et al. (1993) 14 Kato and Hayashida (1993) 14 Yonekura et al. (1994) 10 Zhao (1994) 2 Abdelrahman et al. (1995) 4 Currier (1995) 1 Arockiasamy et al. (1995) 9 Bryan and Green (1996) 6 Fam et al. (1997) 5 Abdelrahman and Rizkalla (1997) 8 Maissen (1997) 2 Park and Naaman (1999) 11 Mahmoud et al. (1999) 39 Stoll et al. (2000) 2 Svecova and Razaqpur (2000) 7 Burke and Dolan (2001) 4 Dolan and Swanson (2002) 3 Salib et al. (2002) 4 Zou (2003a) 8 Jo et al. (2004) 7 Grace et al. (2004) 3 Table 2.3. Summary of experimental studies on beams prestressed with CFRP.
Authors # of v al id te st Beam Details Prestressing Details Failure Mode Section Shape Beam Span Section Depth Jacking Stress Tendon Profile Bond Type R ec ta ng ul ar I' sh ap ed T ee o r do ub le T ee B ox â¤ 15 ft 15 - 30 ft > 3 0 ft h â¤ 10 " 10 " -2 0" > 2 0" â¤ 0. 3 f fu 0. 3 f fu -0 .6 f fu > 0. 6 f fu S tr ai gh t D ra pe d H ar pe d B on de d U nb on de d P re P os t F le xu ra l T en si on F le xu ra l C om pr es si on S he ar O th er BalÃ¡zs and BorosnyÃ³i (2004) 3 Grace et al. (2005) 6 Aziz et al. (2005) 1 Braimah et al. (2006) 3 Grace et al. (2006) 3 Mertol et al. (2006) 9 Grace et al. (2008) 3 Liang et al. (2011) 4 Noel and Soudki (2011) 3 Saiedi et al. (2011) 5 Wang et al. (2011) 4 Du et al. (2011) 9 Grace et al. (2012) 2 Elrefai et al. (2012) 14 Nabipay and Svecova (2012) 6 Roberts et al. (2012) 5 Heo et al. (2013) 7 Grace et al. (2013) 1 Sevil (2016) 2 Selvachandran et al. (2017) 4 The shaded boxes indicate that the parameter under consideration applies to the corresponding reference.
16 Design of Concrete Bridge Beams Prestressed with CFRP Systems The effect of freezeâthaw cycles on prestressing CFRP tendons was studied solely and/or in combination with other environmental effects by various researchers (Mashima and Iwamoto, 1993; Tannous, 1997; Micelli and Nanni, 2004; Mertol et al., 2006). No physical damage to the prestressing CFRP tendons or measurable change in the mechanical properties was observed. The influence of the freeze and thaw cycles on the bond strength of prestressing CFRP tendons was also studied and was found to be insignificant. Prestressing CFRP exposed to ultraviolet (UV) radiation combined with environmental effects showed no significant damage and no decrease in physical and mechanical properties (Micelli and Nanni, 2004). Mechanical Effects Creep and Creep Rupture. ACI 440.1R-15: Guide for the Design and Construction of Struc- tural Concrete Reinforced with Fiber-Reinforced Polymer Bars (ACI Committee 440, 2015) defines creep rupture as a sudden failure of FRP material when subjected to a constant tension over a period of time (referred to as the endurance time). As the ratio of sustained tensile stress to the initial strength of the FRP increases, the time to rupture (i.e., endurance time) decreases. The creep rupture endurance time can also irreversibly decrease under adverse environmental conditions such as elevated temperature, ultraviolet radiation, high alkalinity and wet/dry cycles. Limited data are currently available for endurance times beyond 10,000 hours. The extraction of generalized design criteria is hindered by the lack of standard creep test methods and the variety of constituents and processes used to produce FRP products. These factors have led to the use of conservative design criteria. Yamaguchi et al. (1997) conducted creep rupture tests on 0.25 in. diameter prestressing CFRP bars in air at room temperature for 100 hours. The ratio of stress at creep rupture to the initial strength of CFRP was linearly extrapolated to 500,000 hours (57 years) and found to be 0.93. Saadatmanesh and Tannous (1999) investigated the creep deformation of two types of commercial prestressing CFRPâa bar and a cable. The specimens were tested in three envi- ronmental conditionsâair and at room temperature solutions with a pH of 3 and 12. The applied stress was fixed at 40% of the ultimate tensile strength. The results indicated higher creep strain in the larger-diameter bars and those immersed in the acidic solution; the CFRP bars tested in the air had the lowest creep strains. The recorded creep strain after 3,000 hours ranged from 0.002% to 0.037%. Dolan et al. (2000) conducted a study on creep rupture of aramid and carbon tendons encased in concrete surrounded by saltwater and subjected to a constant load of 50% to 80% of the ultimate capacity for more than 12,000 hours (1.4 years). The residual strength of the CFRP and aramid FRP (AFRP) were, respectively, 90% and 80% of their initial static capacities. The extrapolated strengths for CFRP and AFRP after 100 years of exposure were, respectively, 70% and 55% of the tendonâs initial ultimate strengths. Tokyo Rope (2000) conducted 1,000 hour creep tests on prestressing CFRP cables subjected to a constant load of 65% of the CFRP ultimate tensile strength. The tensile rupture strength of CFRP cables in an indoor environment was extrapolated to 100 years of exposure time and found to be 85% of the initial ultimate tensile strength. Fatigue. The behavior of prestressing CFRP under fatigue loading has been studied by few researchers (Uomoto et al., 1995; Saadatmanesh and Tannous, 1999); the fatigue behavior of CFRP prestressed beams has been studied by others (Abdelrahman et al. 1995; Bryan and Green, 1996; Saiedi et al., 2011). Abdelrahman et al. (1995) tested four beams with two types of bonded prestressing CFRP (cable and bar) under monotonic and fatigue loading ranging from 70%
Literature Review and Current Design Practices 17 to 100% of the cracking load. The beams survived 2 million cycles with little effect on beam stiffness. The load carrying capacity of the beams after the 2 million cycles was comparable to that of similar beams under monotonic loading. Dolan et al. (2000) also observed that a beam pretensioned with CFRP tendons experienced no reduction in capacity due to fatigue loading. Extreme environmental condition did not affect the load carrying capacity of CFRP prestressed beams nor caused any deterioration (Mertol et al., 2006). Bryan and Green (1996) and Saiedi et al. (2011) studied the behavior of bonded CFRP beams at a low temperature (-17Â°F) with and without fatigue loading. After cracking, no continuity was found between the strain at the concrete surface and the strain in the CFRP bar. It was determined that the bar had debonded from the concrete over some length of the cracked region. The low temperature resulted in slight increase of the cracking load and deflection of the beams. It was also found that concrete-CFRP bond can be weakened by cyclic loading, low temperature, sustained and monotonic loading, and high prestressing levels. The stiffness of the CFRP prestressed beam decreased by about 25% after 1 million cycles. Very few studies investigated the fatigue behavior of beams post-tensioned with internal unbonded CFRP tendons. Failures of these beams occurred at the anchorage-tendon assembly resulting in premature failure of the tendon (Braimah et al., 2006). 2.4.3 Prestress Losses Prestress losses refer to the changes in the tensile stress of a prestressing tendon from the time when the strand is initially tensioned to the end of the service life of the prestressed ele- ments due to effects other than applied loads. An accurate prestress loss prediction is required to ensure serviceability. Beams designed based on underestimated prestress losses may exhibit tensile cracking and large deformation under service loads, while overestimation of losses may lead to uneconomical design or excessive camber. The sources of prestress losses are strongly interrelated, and determination of each loss component is extremely difficult due to this inter- dependency (PCI Committee on Prestress Losses, 1975). Prestress losses in CFRP prestressed concrete beams are classified into two categories that consider the source and time of occur- rence (ACI 440.4R-04, 2011). These are short-term losses (elastic shortening, anchorage seating at the transfer of prestressing, and frictional losses) and long-term losses (creep and shrinkage of the concrete, long-term anchorage loss for beams with unbonded prestressing only, relax- ation of tendons, and temperature effects). Prestress losses from elastic shortening, concrete creep, and shrinkage in CFRP prestressed beams are calculated in manners similar to those used for steel prestressed concrete beams. Losses due to the relaxation of tendons, long-term anchorage loss, and temperature effects require special considerations. Relaxation of CFRP Tendons Stress relaxation of CFRP composites depends on the factors that affect the viscoelastic behavior of prestressing CFRP (e.g., type of prestressing tendon; volume fraction of the carbon fibers; alignment of the carbon fibers; type and modulus of elasticity of the matrix resin; environ- mental conditions such as humidity, temperature, and exposure to aqueous solutions; and the level of initial prestressing). Table 2.4 lists details of previously conducted relaxation tests on prestressing CFRP tendons. As shown, only a few relaxation tests have been conducted, all had relatively short test durations (less than 3,000 hours), and none addressed the effect of anchorages or length of the prestressing CFRP tendons.
18 Design of Concrete Bridge Beams Prestressed with CFRP Systems Stress relaxation of the prestressing CFRP tendons was found to be linearly related to the logarithm of the time and to have a direct relationship to the level of initial prestressing. There- fore, several analytical models were developed by using the curve fitting methods (presented in Section 2.3.3). By extrapolating the test results, the stress relaxation of prestressing CFRP tendons after 1 million hours (i.e., 114 years of service life) was estimated to be between 2% and 12% of the initial prestressing level. Overall, little information is available on the effect of long-term anchorage loss in grouted anchors due to the interaction of the expansive material (grout) and prestressing CFRP inside the steel anchor or creep of the expansive material. In addition, the effect of the length of the prestressing CFRP tendons on the stress relaxation of prestressing CFRP systems has not been assessed. Temperature Effects Thermally induced losses occur primarily due to a difference in the CTE of CFRP and con- crete (Bryan and Green, 1996). This difference results in a loss or gain in prestressing force when temperature changes. The longitudinal CTE depends on the properties of the fibers and the transverse coefficient is related to the properties of the resin. A higher transversal CTE of prestressing CFRP than that of the concrete results in radial pressure and circumferential ten- sile stresses at the interface between the prestressing CFRP and concrete when the temperature increases. These stresses may cause the formation of cracks in the radial direction across the boundary of prestressing CFRP and concrete, as illustrated in Figure 2.1. The occurrence of such cracks depends on the type of CFRP reinforcement, type of concrete, presence of transverse reinforcement, and geometry of the cross section (e.g., concrete clear cover thickness). Splitting tensile cracks could lead to the deterioration of bond between prestressing CFRP and concrete. The effects of thermal exposure on the performance of concrete structures prestressed with CFRP systems are incorporated in design guidelines by considering the CFRP material prop- erties. Vogel and Svecova (2007) investigated the bond strength deterioration of concrete beams with prestressing CFRP and GFRP bars exposed to thirty thermal cycles ranging between -40Â°F and 104Â°F. The concrete strength was 7.2 ksi and the minimum concrete cover was in Sources CFRP Type Temperature (Â°F) Test Duration (Hours) Initial Stress Level (% of fpu) CFRP Length (ft.) Number of Tests Enomoto et al. (1990) 0.5 in. cable 68, 140, 176, 212 1,000 70 N/A 15 Saadatmanesh and Tannous (1999) 0.3 in. cable 0.3 in. bar â22, 77 and 140 3,000 40 and 60 1.3 24 Table 2.4. Reported investigations on stress relaxation of prestressing CFRP. Radial cracks Radial stresses Figure 2.1. Formation of the cracks due to circumferential tensile stresses.
Literature Review and Current Design Practices 19 accordance with CAN/CSA S806-12: Design and Construction of Building Components with Fibre- Reinforced Polymers (Canadian Standards Association, 2017) specifications for all test beams. Jacking stresses were 30% and 60% of the ultimate tensile strength for the GFRP and CFRP bars, respectively. The bond performance was evaluated from development length testing on both weathered and control beams (un-weathered). The results indicated that prestressing CFRP and GFRP bars exhibited sufficient bond and no deterioration occurred due to the differential swelling between FRP and concrete. In another study, Saiedi et al. (2011) investigated the com- bined effect of thermal and fatigue loading on beams prestressed with CFRP tendons. Bond performance of the prestressing CFRP was also evaluated in specimens subjected to a constant load level at room temperature and at a low temperature of â27Â°C. The results showed that the low temperature exposure has no effect on the long-term deflection of the beams subjected to sustained loads but the flexural strength of the beams was 19% less than that of similar control specimens at room temperature due to premature bond failure. Overall, several research studies and design guidelines have recognized the thermal effects on the mechanical performance of FRP reinforcements and FRP-reinforced concrete structures. However, limited studies addressed the thermal effects on prestressed concrete structures with CFRP tendons. Also, the effect of thermal fluctuation cycles on bond characteristics and con- crete-CFRP interface has not been adequately investigated; further experimental and analytical examinations appear necessary. 2.4.4 Harping Characteristics of Prestressing CFRP Application of prestressing CFRP materials with harped strand profiles requires that the CFRP tendons be bent around hold-down points. The resulting curvature and bearing against the hold-down assembly causes stress concentrations and localized bending. Because of the brittle- ness of CFRP materials, these stress concentrations may lead to failure of the harped tendons before the desired jacking load levels are reached, and the friction between the prestressing CFRP and the hold-down device can degrade the tendon tensile capacity. Previous studies have iden- tified several parameters that affect the capacity of harped prestressing CFRP tendons; these are type, size, and strength of prestressing CFRP; deviator type and size; harping angle; and interface characteristics (presence or absence of lubrication or cushioning material). Table 2.5 lists the details of the previously conducted harping tests on CFRP tendons. These investigations have resulted in the following findings: â¢ Increasing the deviator size or reducing the harping angle increases the tensile strength reten- tion of the harped CFRP tendon, â¢ Use of cushioning material between the CFRP tendon and the deviator increases the tensile strength retention of the harped prestressing tendon, â¢ Harped CFRP prestressing cables retained higher tensile capacity than harped CFRP pre- stressing bars, and â¢ For CFRP prestressing bars, use of a deviator plate with a minimum diameter of 40 in. and jacking stresses of no more than 45% of the design tensile strength of the prestressing CFRP bar are expected to provide acceptable performance. 2.4.5 Long-term Deflection Behavior of Pretensioned Beams The long-term deflection behavior of beams pretensioned with FRP tendons depends on the type of FRP, level of sustained load, concrete strength, the age of loading, environmental condition, and the level of prestressing. The lower modulus of elasticity of CFRP tendons in comparison to that of prestressing steel results in lower long-term prestress losses for CFRP
20 Design of Concrete Bridge Beams Prestressed with CFRP Systems prestressed beams. For the same level of initial prestressing force, CFRP prestressed beams have similar deflection to those of prestressed steel beams (Braimah et al., 2006; Zou, 2003b, Zou, 2003c). The long-term deflection of the CFRP prestressed beams decreases as the concrete strength increases (Zou, 2003b, Zou 2003c). 2.5 Current Codes, Guidelines, and Specifications A review of the available guidelines for designing CFRP prestressed bridge beams is provided in this section. These are (1) SIMTReC Manual No. 5 (2008), (2) CAN/CSA S806-12 (2017), (3) CAN/CSA S6-06 (2014), (4) ACI 440.4R-04 (2011), (5) âRecommendation for Design and Construction of Concrete Structures using Continuous Fiber Reinforcing Materialsâ pub- lished in the Concrete Engineering Series 23 (JSCE, 1997; henceforth referred to as JSCE CES 23), and (6) Model Code 2010 published in fib Bulletin No. 65 and No. 66 (2012; henceforth referred to as fib Model Code 2010)). The review compared the following provisions: â¢ Environmental reduction factors, â¢ Stress limits for prestressing CFRP tendons, â¢ Prestress relaxation losses, â¢ Temperature effects, â¢ Transfer and flexural bond lengths, â¢ Flexural design, â¢ Minimum reinforcement, and â¢ Strength reduction factors. 2.5.1 Environmental Reduction Factors Environmental reduction factors that account for reduction in the design tensile strength of prestressing CFRP exposed to environmental effects such as moisture, saline, and alkaline environments; high temperature; freeze-thaw cycles; and ultraviolet exposure is considered in Sources CFRP Type Deviator Diameter (in.) Cushion Material Harping Angle (Â°) Number of Tests Mutsuyoshi and Machida (1993) 0.5 in. cable 16 NO 11 6 Adachi et al. (1997) 0.5 in. cable 20 YES* 10 N/A Jerrett (1997) 0.3 in. bar 1, 2, and 20 NO 5 and 7 N/A Grace and Abdel- Sayed (1998) 0.5 in. cable 0.4 in. bar 2 and 20 YES** 3, 5, and 10 18 Dolan et al. (2000) 0.3 in. bar 2.25, 4.5, 9, 18, 36, and 72 NO 5 16 Quayle (2005) 0.25 in. cable 0.37 in. bar 4, 8, 20, 40, and 80 NO 2, 3, 5, 6, 9, 10, and 15 22 Soudki and Noel (2010) 0.5 in. bar 20 and 40 NO 2 N/A *Polyethylene sheets **Material type not specified Table 2.5. Reported investigations on harped prestressing CFRP.
Literature Review and Current Design Practices 21 some design guidelines (see Table 2.6). ACI 440.2R-08: Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI Committee 440, 2008) and Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Structures (National Research Council, Rome, Italy, 2004) are design guidelines appli- cable for strengthening of concrete structures using FRP, ACI 440.1R-15 (2015) is applicable for FRP-reinforced concrete, and SIMTReC Manual No. 5 (2008) is applicable for FRP prestressed concrete. 2.5.2 Stress Limits for Prestressing CFRP Tendons Current design guidelines define the maximum permissible jacking stress for prestressing CFRPs as a percentage of the design tensile capacity. This limit is set to prevent creep rupture and anchorage failure and to provide reserve strain capacity to resist applied loads. Generally, stress limits for prestressing CFRP are lower than those for prestressing steel. For straight prestressing CFRP, the stress limits at jacking and at transfer range from 65% to 75% and from 60% to 65% of the design tensile strength, respectively (Burke and Dolan, 2001). The stress limits for prestressing CFRP at jacking and transfer reported in the literature are listed in Table 2.7. References Exposure Condition Environmental Reduction Factor ACI 440.2R-08 (2008) Interior exposure 0.95 Exterior exposure (e.g., bridges, piers and unenclosed parking garages) 0.85 Aggressive environment (e.g., chemical plants and wastewater treatment facilities) 0.85 ACI 440.1R-15 (2015) Concrete not exposed to earth 1.00 Concrete exposed to earth 0.9 Interior exposure 0.95Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Structures (National Research Council, Rome, Italy, 2004) Exterior exposure 0.85 Aggressive environment 0.85 SIMTReC Manual No. 5 (2008) Aggressive environment 0.75* *Includes material resistance factor combining both strength reduction and environment reduction factor. Table 2.6. Environmental reduction factors. References At Jacking At Transfer ACI 440.4R-04 (2011) 65 60 CAN/CSA S806-12 (2017) 70 65 CAN/CSA S6-06 (2014) 70 65 SIMTReC Manual No. 5 (2008) 70 60 JSCE CES 23 (1997) 70 65 fib Model Code 2010 (2012) - 75 Table 2.7. Stress limits for prestressing CFRP tendons (% of design stress).
22 Design of Concrete Bridge Beams Prestressed with CFRP Systems 2.5.3 Prestress Relaxation Losses For evaluating the relaxation loss (RL), CAN/CSA S6-06 (2014) states that the amount of prestress relaxation should be evaluated based on the type of CFRP tendon and comply with the manufacturerâs specifications. fib Model Code 2010 (2012) estimates a prestress relaxation loss of 2% to 10% for CFRP tendons after 50 years of loading. SIMTReC Manual No. 5 (2008) and ACI 440.4R-04 (2011) divide the relaxation loss into three components (relaxation of the polymer, RL1; straightening of the fibers, RL2; and relaxation of the fibers, RL3) after Dolan et al. (2000). Each component is determined based on the material properties of the CFRP tendons as follows: % of initial prestress level (Eq. 2.10a)1 2 3 ( )= + +RL RL RL RL (Eq. 2.10b)1 = Ã uRL nr r 1.0 2.0% (Eq. 2.10c)2 = -RL 0.0 5.0% (Eq. 2.10d)3 = -RL where nr and ur are the modular ratio of resin to the fiber and the volume fraction of the resin, respectively. SIMTReC Manual No. 5 (2008), according to CAN/CSA S806-12 (2017), provides the fol- lowing empirical expression to calculate the prestress relaxation loss in prestressing CFRP tendons as: % 0.231 0.345 log (Eq. 2.11)( ) ( )= +RL t where t is time in days. 2.5.4 Temperature Effects The temperature effects on the prestressing force (loss/gain) are considered in SIMTReC Manual No. 5 (2008), CAN/CSA S806-12 (2017), and JSCE CES 23 (1997) as a linear function of the modulus of elasticity of CFRP, Efrp, and the difference between the coefficients of thermal expansion of the concrete, Î±c, and the CFRP, Î±frp, as follows: (Eq. 2.12)P T ET frp c frp( )D = D Î± - Î± where DT is the temperature change. CAN/CSA S6-06 (2014), ACI 440.4R-04 (2011), and fib Model Code 2010 (2012) do not consider temperature induced prestressing loss. 2.5.5 Transfer and Flexural Bond Lengths The development length for pretensioned beams is defined in CAN/CSA S806-12 (2017) and SIMTReC Manual No. 5 (2008) as the summation of the transfer and the flexural bond lengths. JSCE CES 23 (1997) and CAN/CSA S6-06 (2014) provide expressions for directly calculating the development length. ACI 440.4R-04 (2011) provides procedures for estimating the development length in addition to the transfer and flexural bond length components. fib Model Code 2010 (2012) refers to fib Bulletins 65 and 66 for calculating the development and transfer lengths of
Literature Review and Current Design Practices 23 prestressing CFRP tendons. ACI 440.4R-04 (2011), CAN/CSA S806-12 (2017), and SIMTReC Manual No. 5 (2008) use the following formulation, adopted from Mahmoud et al. (1999), for estimating the transfer length: (Eq. 2.13) 0.67 = Î± â² l f d f t pi b t ci where fpi is the initial prestressing level in the CFRP tendons (psi), db is the diameter of the tendon (in.), f â²ci is the concrete strength at transfer (psi), and Î±t is a coefficient based on the type of the CFRP tendons. The flexural bond length is defined as the embedment length beyond the transfer length that is required to develop the full tensile strength of the prestressing CFRP. ACI 440.4R-04 (2011), CAN/CSA S806-12 (2017) and SIMTReC Manual No. 5 (2008) estimate the flexural bond length in a similar manner to that used for the transfer length by considering the diameter and design tensile strength of the prestressing tendons, fpu, as follows: (Eq. 2.14)0.67 ( )= - Î± â² l f f d f fb pu pe b fb ci where fpe is the effective stress in prestressing CFRP after losses (psi), db is the diameter of the tendon (in.), f â²ci is the concrete strength at transfer (psi), and Î±fb is a coefficient based on the type of CFRP tendons (e.g., 14.8 for prestressing CFRP cables and 5.3 for prestressing CFRP bars). Table 2.8 lists the equations provided by JSCE CES 23 (1997), CAN/CSA S6-06 (2014), and ACI 440.4R-04 (2011) for estimating the development length. These equations consider the effects of tendon surface properties, location and the contribution of transverse reinforcement. 2.5.6 Flexural Design Prestressed Beams with Bonded Prestressed CFRP Tendons The flexural design of CFRP prestressed beams described in all guidelines is based on the strength and serviceability design approach. The objective is to meet the strength and service- ability requirements for a selected cross section by providing a sufficient number of prestressing tendons. This design approach assumes that the tendons are perfectly bonded to the surrounding References Development Length Model CAN/CSA S6-06 (2014) A f f E E Kd kk l cr FRPu s FRP trcs d + = 4145.0 where k1 is the bar location factor, k4 is the bar surface factor, and Ktr is the transverse reinforcement index JSCE CES23 (1997) 4 Î±1 bod d d f f l = where fd is the design tensile strength of CFRP and fbod is the design bond strength of concrete ACI 440.4R-04 (2011) bpepubped dffdfl â+= 4 3 3 1 where fpe is the effective stress in prestressing CFRP after losses (psi) and db is the diameter of the tendon (in.) Table 2.8. Equations for estimating development length.
24 Design of Concrete Bridge Beams Prestressed with CFRP Systems concrete (i.e., strain compatibility is satisfied). The design is performed by considering two failure modes: rupture of CFRP tendons and crushing of concrete. The ultimate strain of the outermost fiber of concrete in compression, ecu, is defined as 0.003 in ACI 440.4R-04 (2011) and as 0.0035 in CAN/CSA S806-12 (2017), CAN/CSA S6-06 (2014), SIMTReC Manual No. 5 (2008), JSCE CES 23 (1997), and fib Model Code 2010 (2012). Because of the brittle nature of prestressing CFRP tendons, for multiple layers of prestress- ing tendons, the failure occurs when the bottom tendon reaches its tensile capacity (Dolan and Swanson, 2002). The strain in each layer of tendons due to the applied load is proportional to its distance from the neutral axis. Dolan and Swanson (2002) developed an equation for estimat- ing the depth ratio (ratio of depth of each individual tendon to the depth of bottom tendon) to calculate the flexural strength of a beam with multiple layers. The flexural resistance of a beam prestressed with CFRP is determined based on whether the critical section is compression-controlled (concrete crushing) (Figure 2.2a) or tension-controlled (CFRP rupture) (Figure 2.2b). The flexural behavior of beams prestressed with CFRP tendons is considered in a similar manner to that of beams prestressed with steel tendons. The design equa- tions are based on equilibrium and strain compatibility. For rectangular or T-sections with multiple layers of prestressing tendons, the location of neural axis and CFRP cable stress are computed using the following set of equations: For a T-section: (Eq. 2.15a) 1 1 1 1 â ( ) = -Î± â² - Î± â²Î² =c A f f b b h f b px px c w f x np c w (b) Tension-controlled (a) Compression-controlled Figure 2.2. Stress and strain of a typical I-section with three layers of prestressing CFRP.
Literature Review and Current Design Practices 25 For a rectangular section: (Eq. 2.15b)1 1 1 â = Î± â²Î² =c A f f b px px x np c The magnitude of c may be determined via an iterative solution by considering the equations of compatibility as follows: (Eq. 2.16a)e = e + e -d c c px pe cc px (Eq. 2.16b)= ef Epx f px For compression-controlled (concrete crushing) sections: (Eq. 2.16c)e = ecc cu For tension-controlled (CFRP rupture) sections: (Eq. 2.16d)1e = ep pu (Eq. 2.16e) 1 ( )e = e - e - c d c cc pu pe p where c = distance from the extreme compression fiber to the neutral axis (in.); x = prestressing CFRP layer number, with 1 being closest to the tension face; np = total number of prestressing CFRP layers; Apx = area of prestressing CFRP in layer x (in.2); fpx = stress in the CFRP in layer x (ksi); b = effective width of the compression face of the member (in.) [for a flanged section in compression, the effective width of the flange as specified in Article 188.8.131.52 of the AASHTO LRFD Bridge Design Specifications (2017)]; bw = web width (in.); hf = depth of compression flange (in.); Î±1and Î²1 = stress-block factors calculated according to AASHTO LRFD Bridge Design Speci- fications (2017); epx = total strain in the CFRP at layer x (in./in.); epe = strain in the prestressing CFRP due to effective prestress (in./in.); ecc = strain in the concrete compression zone (in./in.); ecu = failure strain of concrete in compression (in./in.); dpx = distance from the extreme compression fiber to the centroid of prestressing CFRP in layer x (in.); and Ef = modulus of elasticity of prestressing CFRP (ksi). For CFRP prestressed tension-controlled sections, the failure is governed by rupture of the CFRP. For design purposes, a design failure modeâtension-controlled (CFRP rupture) or compression-controlled (concrete crushing)âis first selected. The failure mode conditions are then applied, and the strains and stresses in the materials and the corresponding moment in the section are obtained by iterative solution of the equilibrium and strain compatibility equations for the location of the neutral axis.
26 Design of Concrete Bridge Beams Prestressed with CFRP Systems Prestressed Beams with Unbonded Prestressed CFRP Tendons The design strength of post-tensioned beams with unbonded tendons is determined by estimating the stress in the tendon at failure, fp, which is calculated as the summation of the effective prestress, fpe, and the additional stress due to loading, Dfp (fp = fpe + Dfp). Because there is no bond between the tendons and the concrete in unbonded post-tensioned beams, the strain compatibility concept does not apply and the unbonded tendon stresses depend on the deforma- tion of the whole member and are calculated using an iterative method. The bond reduction coefficient, W, that was originally proposed for prestressing steel [Naaman and Alkhairi (1991b), ACI 440.4R-04 (2011); SIMTReC Manual No. 5 (2008)] can be applied to beams prestressed with unbonded CFRP tendons by considering the properties of CFRP (Naaman et al., 2002). The bond reduction coefficient at ultimate depends on factors such as loading conditions and span-to-depth ratio. Another approach for calculating the additional stress due to loading is by estimating the total deformation of the tendon between the anchorage ends as the summation of deformations in elastic and plastic zones at the tendon level. However, because the deformations of the elastic zones are very small compared to those in the plastic zone, they can be neglected. This approach was investigated by several researchers (MacGregor, 1989; Harajli and Kanj, 1992; Lee et al., 1999; Harajli, 2006; Ozkul et al., 2008; Harajli, 2011) and adopted by AASHTO LRFD (2017). 2.5.7 Minimum Reinforcement For tension-controlled members, AASHTO LRFD (2017) states that the total amount of pre- stressed and non-prestressed steel reinforcement should develop a factored flexural resistance, Mr, at least equal to the lesser of (1.33Mu and Mcr) where Mu is the factored moment, and Mcr is the cracking moment. The calculation of the factored flexural resistance should consider the flexural cracking strength of concrete, variability of prestressing, and the ratio of the nominal yield stress of reinforcement to ultimate. A minimum amount of prestressed and non-prestressed reinforcement sufficient to develop a factored flexural resistance of ÏMn greater than the smaller of 1.5 times the cracking strength or, in case of a tension-controlled section, 1.5 times the moment due to factored loads is required by ACI 440.4R-04 (2011). This requirement was based on CAN/CSA S806-12 (2017), and considers the load factors noted in the Canadian design specifications. 2.5.8 Strength Reduction Factors In principle, resistance factors or strength reduction factors (Ï) in the LRFD formulation are adopted and calibrated (along with the load factors) such that properly designed members will exhibit a probability of failure approaching a target value. Existing design guidelines for CFRP prestressed members define this factor either based on the failure mode (i.e., CFRP rupture if r â¤ rb or crushing of concrete if r > rb) or the sectional and material properties (i.e., strain in the extreme tension reinforcement) of the member. The Ï factors for beams prestressed with CFRP tendons included in different guidelines are listed in Table 2.9. These guidelines use different approaches regarding the resistance factors and different load factors. 2.6 Factors Affecting the Design of CFRP Prestressed Beams The factors affecting the design of CFRP prestressed beams were investigated by reviewing the database of existing experimental studies and evaluating the performance of existing design models.
Literature Review and Current Design Practices 27 2.6.1 Database of Experimental Investigations A database of experiments on CFRP prestressed beams was compiled (Table 2.3). The data- base includes 264 beams that were reported in 41 publications (journals, research reports, proceedings of international symposia and conferences, and dissertations). The database was compiled to assess the current state of experimental research, identify the parameters influenc- ing the design of concrete beams prestressed with CFRP that have been investigated, validate the different analytical models, and help with the calibration of the strength reduction factor for CFRP prestressed beams. 2.6.2 Performance Evaluation of Existing Design Models The data reported for sixty beams (43 beams with bonded and 17 beams with unbonded CFRP tendons) were used to perform flexural capacity predictions according to the existing design models/guidelines. The predicted flexural capacities of these beams were compared with the reported ultimate moment at failure. For bonded CFRP prestressed beams, all the data required to predict the capacity were reported for 29 beams, and sufficient information to make reasonable assumptions for capacity calculations was available for 14 beams. The sectional analysis was performed based on the mechanics of the problem and using four published models in North America [SIMTReC Manual No. 5 (2008), CAN/CSA S806-12 (2017), CAN/CSA S6-06 (2014), ACI 440.4R-04 (2011)]. Since the three Canadian guidelines (SIMTReC Manual No. 5, CAN/CSA S806-12, CAN/CSA S6-06) are essentially the same, only predictions from SIMTReC Manual No. 5 (2008) are presented. For unbonded CFRP prestressed beams, complete data were reported for 17 beams. The models in ACI 440.4R-04 (2011), AASHTO LRFD (2017), and ACI 318-14 (2014) were used to estimate the capacities. As noted earlier, the ACI 440.4R-04 (2011) approach to estimate the stress at ultimate for unbonded tendon is similar to that of AASHTO LRFD (1994). Bonded CFRP Prestressed Beams Figures 2.3 through 2.5 compare the experimental and predicted moment capacity values. These figures indicate that the predicted values for the small-scale beams are in good agreement with the experimental moment capacity. The predictions based on ACI 440.4R-04 (2011) and SIMTReC Manual No. 5 (2008) provided comparable mean and coefficient of variation (COV) values. The mean values of prediction/experiment were 1.13, 1.13 and 1.11, and the COV val- ues were 0.13, 0.14 and 0.15 for analytical prediction using the Whitney stress-block factors Î±1 and Î²1 (see Section 4.4), ACI 440.4R-04 (2011), and SIMTReC Manual No. 5 (2008), respec- tively. All predictions were comparable because the flexural capacity is calculated based on a sectional analysis that satisfies equilibrium and compatibility. The primary differences between the guidelines are the predictions of the ultimate strain and stress-strain relationship of concrete. References cfrp Prestress Construction Method ACI 440.4R-04 (2011) 0.85* 0.65** CAN/CSA S806-12 (2017) 0.85 Pretensioned SIMTReC Manual No. 5 (2008) 0.85 0.80 Post-tensioned, bonded Post-tensioned, unbonded CAN/CSA S6-06 (2014) 0.80 Both bonded and unbonded Both bonded and unbonded JSCE CES 23 (1997) 0.77â0.87 Both bonded and unbonded *For failure by CFRP rupture. **For failure by concrete crushing. e Table 2.9. Resistance factors for concrete beams prestressed with CFRP.
28 Design of Concrete Bridge Beams Prestressed with CFRP Systems Inc rea se in the Be am Si ze Figure 2.3. Experimental moment capacities versus predicted values by analytical procedure for bonded CFRP prestressed beams. Inc rea se in the Be am Si ze Experimental Moment (kip-ft.) Experimental Moment (kip-ft.) P re di ct ed M om en t (k ip -f t. ) P re di ct ed M om en t (k ip -f t. ) Figure 2.4. Experimental moment capacities versus predicted values by ACI 440.4R-04 (2011) for bonded CFRP prestressed beams. Inc rea se in the Be am Si ze P re di ct ed M om en t (k ip -f t. ) Experimental Moment (kip-ft.) Experimental Moment (kip-ft.) P re di ct ed M om en t (k ip -f t. ) Figure 2.5. Experimental moment capacities versus predicted values by SIMTReC Manual No. 5 (2008) for bonded CFRP prestressed.
Literature Review and Current Design Practices 29 The relatively low COV values (0.13 to 0.15) indicate that the current model formulations for flexure can reasonably predict the capacity. Further examination of the database and the figures indicated the availability of a limited number of experimental studies on full-scale beams. Unbonded CFRP Prestressed Beams The models in ACI 440.4R-04 (2011), AASHTO LRFD (2017), and ACI 318-14 (2014) for steel unbonded post-tensioned design were used to estimate the capacities of the unbonded CFRP pre- stressed beams and the increase in cable stress. For these models, the ultimate concrete strain was taken as 0.003. It was found that the three models have comparable mean and COV. The mean values of experiment/prediction were 1.04, 1.17, and 1.17, and the COV values were 0.11, 0.12, and 0.10 for ACI 440.4R-04 (2011), AASHTO LRFD (2017), and ACI 318-14 (2014), respectively. Figure 2.6 indicates that the predictions for the small-scale beams were closer to the experimental moment capacity than for large-scale beams. Only Heo et al. (2013) reported the increase in the stress of internal unbonded prestressing CFRP cables at ultimate; these results are insufficient to make a conclusive assessment. (a) ACI 440-4R-04 (2011) (b) AASHTO LRFD (2017) (c) ACI 318-14 (2014) Experimental Moment (kip-ft.) Experimental Moment (kip-ft.) Experimental Moment (kip-ft.) P re di ct ed M om en t (k ip -f t. ) P re di ct ed M om en t (k ip -f t. ) P re di ct ed M om en t (k ip -f t. ) Figure 2.6. Experimental moment capacities versus predicted values for unbonded CFRP prestressed beams.