Abstract:
A mechanical device was invented for prestressing of carbon fiber reinforced polymer (CFRP) sheets. Significant features of this device are that the CFRP sheets are directly anchored to the mechanical device itself, the prestressing forces are applied with a manual torque wrench without the need for power operated hydraulic jacks and the prestressing transfer is accomplished under slow strain rates. Experimental investigation clearly indicates that the device was efficient in applying prestressing to the CFRP sheets and prestress losses during stressing were maintained at a minimum.

Description:
BACKGROUND OF THE INVENTION  
       [0001]    Much research has been conducted to date to study the behavior of reinforced concrete (RC) beams strengthened with prestressed fiber reinforced polymer (FRP) sheets and plates. By inducing prestressing the FRP system can be used more efficiently, leading to an increase in the flexural capacity and serviceability of the strengthened beams (Triantafillou et al., 1992; Char et al., 1994; Quantrill and Hollaway, 1998; El-Hacha et al., 2001a; 2001b; El-Hacha et al., 2003). Literature review shows that strengthening of RC beams with prestressed FRP sheets and plates can be grouped under three installation methods. 
         [0002]    The first installation method consists of an indirect method for achieving prestress in the FRP system. Saadatmannesh and Ehsani (1991) have investigated an indirect method for prestressing glass FRP (GFRP) plates. Stressing in the GFRP system was achieved by initially cambering the beam upwards with the use of hydraulic jacks followed by bonding the plates to the underside of beams. After the epoxy adhesive was properly cured the cambering system was released; thereby, inducing prestressing in the GFRP plates. Some of the disadvantages associated with this method are that it is labor intensive, only low levels of prestressing can be induced in the plates, not easy to achieve the desired level of prestressing in the plates or sheets, and the reacting floor or foundation must be capable of sustaining the applied vertical loads. 
         [0003]    Researchers have also investigated two other methods consisting of directly or indirectly applying the prestress to the FRP system. These next two methods include three phases to achieve the desired level of prestressing. First, the stress is applied with a power operated hydraulic jack or similar device and the prestressing in the FRP system must be controlled with either strain gages or load cells. Second, the sheets or plates are bonded to the concrete surface with an epoxy adhesive or simply anchored to the beam itself. Finally, after the epoxy adhesive has properly cured, the sheets are cut near the ends and the prestressing device is removed. 
         [0004]    In the second method or designated as the direct method, the FRP sheets or plates are first anchored at one end (dead end) and then tensioned from the other end (live end) using a power operated hydraulic jack (Wight et al., 2001; Saeki et al., 1997; El-Hacha et al., 2001b). According to this method the FRP sheets or plates must be anchored to the beam itself at either end. The dead end is first anchored before stressing and the live end is subsequently anchored after the stress is applied to the FRP system. In many instances these anchors serve as a permanent anchorage to the FRP system leading to a costly solution due to the high costs associated with fabricating the specialized prestressing anchors and plates. To achieve a cost effective solution these anchorages can be optionally removed for usage in further applications. If left in place, permanent steel anchors are likely to be exposed to significant weathering or galvanic corrosion due to contact with the carbon fibers. Also, the anchors may need to be removed for aesthetics reasons, leading to potential debonding of the prestressing sheets or plates. In order to avoid premature debonding it may be necessary to install U-wraps before removal of the anchors and plates. However, because of the presence of these anchors and plates, the U-wraps must be placed away from the ends of the prestressed FRP system. Other disadvantages that can be associated with this method are that it tends to be laborious, and the beam surface must be properly treated (ACI 546, 1996) prior to drilling for installation of the anchors. 
         [0005]    A third method consists of first bonding the end of FRP sheets or plates to steel plates or other devices, which are then tensioned against an external reacting frame (Triantafillou et al., 1992; Char et al., 1994; Garden et al., 1998; Quantrill and Hollaway, 1998). In many of the systems proposed in the literature the prestressing release was carried out by cutting the sheets in specified unbonded regions. In many of these systems the release method was carried out under high strain rates leading to premature debonding and further accentuating the need for end anchorages. In addition, many of the systems proposed in the literature require the use of specialized equipment. 
         [0006]    The new innovative external mechanical device was invented for prestressing FRP sheets, which follows within this third method. The invention can overcome some of the disadvantages outlined for each of the three methods. An attractive feature of the device is that the prestressing was achieved with a manual torque wrench without the need for using power operated hydraulic jacks or any other type of sophisticated equipment. In typical prestressing applications, transfer of the prestressing is achieved under high strain rates, which increases the propensity for end debonding at low prestressing levels (Pornpongsaroj and Pimanmas, 2003). This issue can be mitigated by the proposed device because the prestressing release is achieved under low strain rates. For higher prestressing levels in which debonding of the CFRP sheets cannot be prevented solely by controlling the strain rate at transfer, U-wraps can be easily installed at the ends of the prestressing FRP system. 
       BRIEF SUMMARY OF THE INVENTION  
       [0007]    A simple mechanical device was invented for prestressing of carbon fiber reinforced polymer (CFRP) sheets that can overcome on some of the disadvantages of currently used prestressing systems. Significant features of this device are that the CFRP sheets are directly anchored to the mechanical device itself, the prestressing forces are applied with a manual torque wrench without the need for power operated hydraulic jacks, and the prestressing transfer is accomplished under slow strain rates. Experimental investigation clearly corroborates that the device was efficient in applying prestressing to the CFRP sheets and prestress losses during stressing were maintained at a minimum. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
         [0008]    As shown in  FIGS. 1 and 2 , the mechanical device consists of one WT steel section and four regions, including two anchorage and two loading regions. A summary of main components and dimensions of the mechanical device is also presented in Table 1. Located at each end of the WT section, each anchorage region consists of: (1) a removable steel plate, designated as part A, (2) a steel plate welded to the WT-section, designated as part B, and (3) the corresponding bolts and nuts. Located away from the anchorage regions, each loading region consists of: (1) one steel strip welded to two steel threaded rods, designated as parts C and D, respectively, and (2) two steel nuts and two thrust bearings, designated as parts E and F, respectively. 
           [0009]    The system with one CFRP sheet under prestressing is shown in  FIG. 4 . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
     Main Components 
       [0010]    Referring to  FIGS. 1 and 2 , the mechanical device consists of one WT steel section and four regions, including two anchorage and two loading regions. A summary of main components and dimensions of the mechanical device is also presented in Table 1. Located at each end of the WT section, each anchorage region consists of: (1) a removable steel plate, designated as part A, (2) a steel plate welded to the WT-section, designated as part B, and (3) the corresponding bolts and nuts. Located away from the anchorage regions, each loading region consists of: (1) one steel strip welded to two steel threaded rods, designated as parts C and D, respectively, and (2) two steel nuts and two thrust bearings, designated as parts E and F, respectively. The thrust bearings are a vital component because they must be used to decrease the friction between the steel nuts and the WT section. 
       Assemblage 
       [0011]    The first step in the assembly operation consisted of impregnating the CFRP sheets to their full length with an epoxy resin, similar to the process used to prepare FRP sheets for tension tests (ACI, 2004). The epoxy resin was a mixture of two components, which works as a matrix to protect the fibers and transfer the stresses between the adjoining fibers (Karbhari, 2001). After the epoxy resin has cured, the CFRP sheets were bonded to the removable steel plates (part A) using the same epoxy resin (see  FIG. 1   b ). 
         [0012]    The next step consisted of fixing the removable steel plates and bonded CFRP sheets to the welded steel plates (part B) by tightening four steel nuts in the anchorage regions ( FIG. 2   a ). High pressure was applied to the CFRP sheets through these steel plates to avoid bond slip and to prevent prestress losses during prestressing. 
         [0013]    Design of the Anchorage Region Steel Plates: A total of 3 bond tests were performed according to the test setup shown in  FIG. 3   a.  These tests were performed to estimate the average bond strength between the CFRP sheets and the anchorage plate A (see  FIG. 1 ), and to subsequently size anchorage plates A and B. Unlike in the mechanical device, these tests were performed without applying the clamping force between plates A and B. This will clearly lead to conservative values and a safe design for the anchorage square plates. 
         [0014]    As shown in  FIG. 3   a,  these specimens consisted of two steel plates separated by a 50 mm (2 in.) gap and bridged across with CFRP sheets on either side of the steel plates. The CFRP sheets were 51 mm (2 in.) wide by 0.165 mm (0.0065 in.) thick and were bonded to the steel plates with an anchorage length of 254 mm (10 in.). 
         [0015]    The computed average strain gage data obtained from the three tests and from the strain gages installed along the length of the CFRP sheets is shown in  FIG. 3   b  and summarized in Table 2. These results were further investigated to obtain the average bond stress distribution. Average bond stresses, μ ave , are shown in  FIG. 3   b  and were determined using the following expression 
         [0000]    
       
         
           
             
               
                 
                   
                     μ 
                     ave 
                   
                   = 
                   
                     
                       
                         t 
                         f 
                       
                        
                       
                         E 
                         f 
                       
                        
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           ɛ 
                         
                         
                           Δ 
                            
                           
                               
                           
                            
                           x 
                         
                       
                     
                     = 
                     
                       
                         0.165 
                         × 
                         228 
                         , 
                         000 
                         × 
                         
                           
                             ( 
                             
                               
                                 9 
                                 , 
                                 300 
                               
                               - 
                               
                                 6 
                                 , 
                                 375 
                               
                             
                             ) 
                           
                           50.8 
                         
                          
                         
                           ( 
                           
                             S 
                              
                             
                                 
                             
                              
                             I 
                           
                           ) 
                         
                       
                       = 
                       
                         2.20 
                          
                         
                             
                         
                          
                         MPa 
                          
                         
                             
                         
                          
                         
                           ( 
                           
                             314 
                              
                             
                                 
                             
                              
                             psi 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where t f  and E f  are the thickness and the elastic modulus of the CFRP sheets, respectively, and Δε and Δx are the variations in strain and distances between the strain gages, respectively. Based on material properties the results presented in Table 4 and Eq. (1) the computed average bond strength was 2.20 MPa (314 psi). This bond strength was then used to size the plates necessary to develop the required bonding surface area. Finally, the length of the plates in the longitudinal direction was based the relation 
         [0000]    
       
         
           
             
               
                 
                   
                     b 
                     p 
                   
                   = 
                   
                     
                       
                         
                           λ 
                           cr 
                         
                          
                         
                           f 
                           fu 
                         
                          
                         
                           A 
                           f 
                         
                       
                       
                         
                           μ 
                           ave 
                         
                          
                         
                           b 
                           f 
                         
                       
                     
                     = 
                     
                       
                         
                           0.55 
                           × 
                           3 
                           , 
                           709 
                           × 
                           
                             ( 
                             
                               203 
                               × 
                               0.165 
                             
                             ) 
                           
                         
                         
                           2.2 
                           × 
                           203 
                         
                       
                       = 
                       
                         153 
                          
                         
                             
                         
                          
                         
                           mm 
                            
                           
                             ( 
                             
                               6.0 
                                
                               
                                   
                               
                                
                               
                                 in 
                                 . 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where b f  is the width of the CFRP sheet, λ cr  is the creep rupture stress limit in FRP composites where for carbon fibers this is limited by ACI 440 (2002) at 0.55, f fu  and A f  are the tensile strength and area of the CFRP sheets, and μ ave  is the average bond strength determined from the tests shown in  FIG. 3  and results presented in Eq. (1). Since the anchorage plates in the mechanical device were 279 wide×203 long mm (11×10 in.), results presented in Eq. (2) clearly show that the design of the plates was well within safe limits and will certainly prevent pull-out of the CFRP sheets from the anchorage plates during stressing. 
         [0016]    Stressing the CFRP Sheets: After the anchorage regions were created, the desired prestress level was achieved by alternately tightening the steel nuts (part E) in the loading region (see  FIG. 2   b ). This action displaces the threaded rods (part D) and forces the steel strips upwards (part C), thereby creating an uplift displacement in the CFRP sheets ( FIGS. 2 and 4 ). It is this uplift, ΔH, that imposes the desired prestressing in the CFRP sheets. 
         [0017]    Leveling of the CFRP sheets was easily controlled in the transverse and longitudinal direction, namely across the length of the steel strips (part C) and CFRP sheets, respectively, by using a carpenter leveler. Leveling is necessary to ensure a uniform and planar surface that is free of significant twisting and warped edges before bonding of the prestressed CFRP sheets to the RC beam. 
         [0018]    The removable steel plates and steel strips were fabricated with a slight rounding at the corners to decrease any stress concentrations in the CFRP sheets due to the change in the sheets direction and to prevent damage to the CFRP sheets during prestressing.  FIGS. 2 and 4  show the mechanical device with the CFRP sheets depicting well the uplift displacement of the CFRP sheets. At this stage, the weight of the device was nearly 100 kg (220 lb), and the length was 3.35 m (11 ft). The mechanical device after prestressing was easily handled in the laboratory without also the need for heavy lifting equipment. 
       Theoretical Prestress 
       [0019]    In order to simplify usage of the device it is advantageous to relate the vertical displacement, ΔH (see  FIG. 2 ), to the stress in the CFRP sheets, σ 2 . Establishing a relationship between ΔH and σ 2  avoids the need for electronic measuring devices, such as strain gages, or linear variable differential transformers (LVDT&#39;s) in field applications. 
         [0020]    The theoretical prestress was derived based on the geometric relations of the prestressing system and the deformed CFRP sheets. As shown in  FIG. 4   b  and before prestressing, the FRP sheet has a straight ABCD profile. After the sheets are deformed upwards by the vertical displacement, ΔH, this straight profile changes to the three segment AB 1 C 1 D profile. At this stage, the prestress in the horizontal B 1 C 1 segment, σ 2 , and the total elongation of the sheet, ΔL, are, respectively 
         [0000]    
       
         
           
             
               
                 
                   
                     σ 
                     2 
                   
                   = 
                   
                     
                       
                         σ 
                         1 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       θ 
                     
                     = 
                     
                       
                         
                           σ 
                           1 
                         
                          
                         
                           L 
                           1 
                         
                       
                       
                         
                           
                             L 
                             1 
                             2 
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               H 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     L 
                   
                   = 
                   
                     
                       
                         
                           
                             σ 
                             2 
                           
                           
                             E 
                             f 
                           
                         
                          
                         
                           L 
                           2 
                         
                       
                       + 
                       
                         
                           
                             2 
                              
                             
                               σ 
                               1 
                             
                           
                           
                             E 
                             f 
                           
                         
                          
                         
                           
                             
                               L 
                               1 
                               2 
                             
                             + 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 H 
                                 2 
                               
                             
                           
                         
                       
                     
                     = 
                     
                       2 
                        
                       
                         ( 
                         
                           
                             
                               
                                 L 
                                 1 
                                 2 
                               
                               + 
                               
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   H 
                                   2 
                                 
                               
                             
                           
                           - 
                           
                             L 
                             1 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where σ 1  is the prestress in the diagonal AB 1  and C 1 D segments, E f  is the elastic modulus of the CFRP sheets, and θ is the angle between the original segment AB and the deformed segment AB 1 . Finally, based on Eqs. (3) and (4), the normalized prestress, σ 2 /f fu  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         σ 
                         2 
                       
                       
                         f 
                         fu 
                       
                     
                      
                     
                       ( 
                       % 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         2 
                          
                         
                           
                             L 
                             1 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     L 
                                     1 
                                     2 
                                   
                                   + 
                                   
                                     Δ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       H 
                                       2 
                                     
                                   
                                 
                               
                               - 
                               
                                 L 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             L 
                             1 
                           
                            
                           
                             L 
                             2 
                           
                         
                         + 
                         
                           2 
                            
                           
                             ( 
                             
                               
                                 L 
                                 1 
                                 2 
                               
                               + 
                               
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   H 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                      
                     
                       
                         E 
                         f 
                       
                       
                         f 
                         fu 
                       
                     
                     × 
                     100 
                      
                     % 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where dimensions L 1  and L 2  are measured directly from the device, and f fu  is the ultimate tensile strength of the CFRP sheets (see  FIG. 4   b ). When ΔH is known by straight measurement, the prestress in the CFRP sheet, σ 2 , can be derived from Eq. (5). 
         [0021]    In this research program the vertical displacement was measured by using LVDT&#39;s for added precision and continuous reading and subsequently correlated to the prestress in the CFRP sheet, σ 2 , by Eq. (5). In field conditions a Vernier caliper can be used to measure ΔH and by using design charts one can easily estimate σ 2 . A Vernier caliber is a standard measuring devise used to get high precision readings. For example,  FIG. 5  shows a chart that can be used to calculate σ 2  when the vertical uplift displacement ΔH is known. 
         [0022]    In this figure different geometric relations were considered as a function of length L 2 , and L 1  was kept constant at 457 mm (18 in.). It is clear that as length L 2  increases so does the required vertical uplift and for very long sheets, say L 2  greater than 11 m (36 ft) the vertical uplift is within 230 mm (9 in.). Although not investigated in this program, future research should concentrate on developing design charts that can be used to design the diameter of the threaded rods as a function of the desired prestress level and length of the CFRP sheet, L 2 . These charts will be very much like  FIG. 5  and will be based on preventing buckling or significant bending of the vertical threaded rods, shown as part D in  FIG. 2   b.    
       Application of the Invention in Strengthening of RC Beams 
       [0023]    After the CFRP sheets were prestressed, the next step consisted of bonding the prestressed CFRP sheet to the RC beam, as shown in  FIG. 6 . Another advantage of this device is that end anchors can be easily installed before the sheets are released because there is adequate clearance between the sheets and the WT steel section. According to the design guidelines set by ACI 440 committee (2002), the surface of the beam was roughened until the aggregates were exposed, followed by vacuum cleaning to remove dust and loose particles. After bonding, the prestressing device stayed in place for at least 80 hours, which was more than sufficient time to properly cure the epoxy resin. 
         [0024]    Prestressing Transfer: Transfer of the prestressing was carried out by slowly releasing the threaded rods (part D) in the loading region. This process was accomplished by alternately completing 2 full turns in all four steel nuts (part E). The total time taken to release the prestress in all beams was nearly 5 minutes. For the beam prestressed with 40% (see Table 3) this corresponds to a rate of nearly 180 N/sec (40 lbs/sec). For the other beams the release was performed at a slower rate and the rates are reported in Table 2. After release of the CFRP sheets was achieved, the sheets were cut close to the steel strips and the mechanical device was removed and cleaned for further applications. Properties for the materials used in this research are shown in Table 4. The CFRP sheets used were 0.165 mm (0.0065 in.) thick and 203 mm (8 in.) wide leading to a total reinforcement area of 33.55 mm 2  (0.052 in. 2 ). 
         [0025]    Test Matrix: Of a total of eight RC beams investigated in this research program, six RC beams were retrofitted with prestressed CFRP sheets that were stressed using the device developed in this research. The other two beams were used as the control specimens and consisted of one unstrengthened beam and one strengthened beam with CFRP sheets, but without prestressed. The remaining beams were strengthened with CFRP sheets that were prestressed to 15%, 30% and 40% of the tensile strength of the CFRP sheets. The RC beams were then tested under a four-point bending system. Test results show that the device was efficient in prestressing the CFRP sheets to the specified stress levels, initial prestress losses were negligible, and prestress losses after transfer were within 10% of the initial prestress. Furthermore, test results clearly showed that the beams strengthened with the prestressed CFRP sheets achieved a higher yielding and ultimate loading. 
         [0026]    Creep-Rupture Limits: According to ACI-440 (2002) after consideration of a long-term environmental factor, the sustain stress limit for CFRP composites is f fs =0.55 f fu , where f fu  is the design strength. Therefore, in the retrofit of RC beams using prestressed CFRP sheets consideration was given to the creep-rupture limit because in these applications the sheets are continuously subjected to high sustained stresses after prestressing. As such, the levels of prestressing investigated in this research are below the permissible limit of 55%. 
         [0027]    Field Application Setup: It is recognized that these laboratory conditions do not match exact field conditions for strengthening in positive moment regions, in which the prestressing apparatus needs to be “hanging” from the RC beams. This is to some extent, more complex than the simpler “from the top” procedure shown in  FIG. 6 . This should not constitute, however, a limitation of the proposed mechanical device for the following: i) the fully assembled device with the prestressed CFRP sheets was easily moved and rotated in the laboratory, ii) the device weight was close to 1 kN (200 lbs) and iii) it was easily maneuvered by two people. 
         [0028]    A potential field application on the underside of a beam is shown in detail in  FIG. 7 . As in laboratory conditions, prestressing can be easily accomplished in a location near the beam to be strengthened and with the device conveniently positioned, as shown in  FIG. 4 . Next the device can be easily lifted to the underside of the beam and because of its light weight it can be supported by U-straps and fastened to the sides of the RC beam with anchor bolts. In field applications other lighter materials such as aluminum may be considered for construction of the mechanical device. 
         [0000]    
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Summary of Mechanical Device Main Components Dimensions 
               
             
          
           
               
                 Component ID 
                   
                   
                 Dimensions US 
               
               
                 (see FIGS. 1 and 2) 
                 ID 
                 Dimensions SI 
                 Customary 
               
               
                   
               
               
                 Removable Plate 
                 A 
                 279 × 254 × 9.5 mm 
                 11 × 10 × ⅜ in. 
               
               
                 Welded Plate 
                 B 
                 279 × 254 × 9.5 mm 
                 11 × 10 × ⅜ in. 
               
               
                 Steel Strip 
                 C 
                 203 × 63.5 × 25 mm 
                 8 × 2.5 × 1.0 in. 
               
               
                 Threaded Rods 
                 D 
                 400 × 19 mm 
                 16 × ¾ in. 
               
               
                 Nuts 
                 E 
                 25 mm Ø × 19 mm 
                 1 in Ø × ⅜ in. 
               
               
                 Thrust Bearings 
                 F 
                 38 (o.d.) × 19 (i.d.) mm 
                 1.5 (o.d.) × 0.75 (i.d.) in. 
               
               
                 WT 8 × 18 Section 
                 — 
                 178 (b) × 201 (d) mm 
                 7 (b) × 7.93 (d) in. 
               
               
                 Plate A &amp; B Clamping Bolts 
                 — 
                 4-19 Ø mm 
                 4-⅜ Ø in. 
               
               
                   
               
               
                 o.d. outside diameter 
               
               
                 i.d. inside diameter 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Bonding Test Results (Average results from three tests) 
               
             
          
           
               
                 Load 
                 Measured Strain 
                 Measured Strain 
                 Calculated Stress 
                 Applied Force 
               
               
                 Level 
                 at x = 0 mm (0 in.) 
                 at x = 50.8 mm (2 in.) 
                 MPa (ksi) 
                 kN (kips) 
               
               
                   
               
             
          
           
               
                 1 
                 9300 
                 6375 
                 2116 (306.9) 
                 17.8 (4.0)  
               
               
                 2 
                 7500 
                 5125 
                 1707 (247.5) 
                 13.3 (3.0)  
               
               
                 3 
                 6000 
                 4000 
                 1366 (198.0) 
                 11.1 (2.5)  
               
               
                 4 
                 4875 
                 2750 
                 1110 (160.9) 
                 8.9 (2.0) 
               
               
                 5 
                 3700 
                 2000 
                  842 (122.1) 
                 6.7 (1.5) 
               
               
                 6 
                 2750 
                 1125 
                  626 (90.75) 
                 4.4 (1.0) 
               
               
                 7 
                 1250 
                 500 
                  285 (41.25) 
                 2.2 (0.5) 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Strengthening Schemes 
               
             
          
           
               
                   
                 Prestress/tensile 
                 End 
                 Prestress Release Rate 
               
               
                 Beam 
                 strength (%) 
                 Anchors 
                 N/sec (lbs/sec) 
               
               
                   
               
               
                 A 
                 — 
                 — 
                 — 
               
               
                 B 
                  0 
                 — 
                 — 
               
               
                 C 
                 15 
                 — 
                  68 (15) 
               
               
                 D 
                 15 
                 — 
                  68 (15) 
               
               
                 E 
                 15 
                 U-Wraps 
                  68 (15) 
               
               
                 F 
                 30 
                 — 
                 135 (30) 
               
               
                 G 
                 30 
                 U-Wraps 
                 135 (30) 
               
               
                 H 
                 40 
                 — 
                 180 (40) 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Material Properties 
               
             
          
           
               
                   
                 Tensile strength 
                 Ultimate 
                 Elastic modulus 
                 Compressive strength 
               
               
                   
                 MPa (ksi) 
                 strain (%) 
                 GPa (ksi) 
                 MPa (ksi) 
               
               
                   
                   
               
             
          
           
               
                 Concrete 
                 — 
                 — 
                 — 
                 43.4 (6.3) 
               
             
          
           
               
                 Steel bars 
                 432 
                 (62.7) 
                 — 
                 195 
                 (28,300) 
                 — 
               
               
                 CFRP sheet* 
                 3790 
                 (550) 
                 1.7 
                 228 
                 (33,000) 
                 — 
               
               
                 Saturant 
                 55 
                 (8.0) 
                 7.0 
                 1.8 
                 (260) 
                 — 
               
               
                   
               
               
                 *Af = 0.165 mm (0.0065 in.) thick × 203 mm (8 in.) wide = 33.55 mm 2  (0.052 in. 2 ). 
               
             
          
         
       
     
       REFERENCES 
       [0000]    
       
         ACI Committee 440 (2002) “Guide for Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (440.2R-02),” American Concrete Institute, Farmington Hills, Mich., 2002, 45 pp. 
         ACI Committee 440, (2004), “Guide Test Method for Fiber Reinforced Polymers (FRP) for Reinforcing or Strengthening Concrete Structures (440.3R-04),” American Concrete Institute, Farmington Hills, Mich., 2004, 40 pp. 
         ACI Committee 546, (1996), “Concrete Repair Guide (ACI 546R-96),” American Concrete Institute, Farmington Hills, Mich., 1996, 26 pp. 
         Char, M. S., Saadatmanesh, H., and Ehsani, M. R., (1994), “Concrete Girders Externally Prestressed with Composite Plates”,  PCI Journal,  May-June 1994, Vol. 39, no. 3, pp 40-51. 
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         Karbhari, V. M., (2001), “Materials Consideration in FRP Rehabilitation of Concrete Structures,”  ASCE Journal of Materials in Civil Engineering,  2001, Vol. 13, No. 2, pp. 90-97. 
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         Yang, C., Nanni, A. and Dharani, L. (2001), “Effect of Fiber Misalignment on FRP Laminates and Strengthened Concrete Beams,” Proceedings of the 9th International Conference on Structural Faults and Repair, London, UK, Jul. 4-6, 2001, M. C. Forde, Ed., Engineering Techniques Press, CD_ROM, version, 10 pp.