Perormance o Pretensioning Prestressed Concrete Beams with Ruptured Strands Flexurally Strengthened by CFRP Sheets Thi Thu Dung NGUYEN 1, Koji MATSUMOTO 2, Asami IWASAKI 3, Yuji SATO 3 and Junichiro NIWA 4 1 Ph.D Candidate, Dept. o Civil Engineering, Tokyo Institute o Technology, Japan, (2121M117 Ookayama, Meguroku, Tokyo 1528552, Japan) Email: dungnguyen.aa@m.titech.ac.jp 2 Assistant Proessor, Dept. o Civil Engineering, Tokyo Institute o Technology, Japan (2121M117 Ookayama, Meguroku, Tokyo 1528552, Japan) Email: matsumoto.k.ar@m.titech.ac.jp 3 Engineering Division, Civil Engineering Design Section, Fuji P.S Corporation, Japan (2261 Kameido, Kotoku, Tokyo 13671, Japan) Email: a.iwasaki@ujips.co.jp, y.sato@ujips.co.jp 4 Proessor, Dept. o Civil Engineering, Tokyo Institute o Technology, Japan (2121M117 Ookayama, Meguroku, Tokyo 1528552, Japan) Email: jniwa@cv.titech.ac.jp ABSTRACT This paper presents the eects o lexural strengthening method or PC beams having ruptured strands using CFRP sheets. CFRP sheets with dierent lengths and number o layers were externally bonded to the damaged PC beams. The lexural capacity o the strengthened beam was recovered up to 91.5% o that o the original one. The increase in the sheet lengths improved the member stiness. The strains in the remaining prestressing strands were reduced and the openings o lexural cracks in the constant moment region were well restrained with the increase in number o layers. Moreover, amount o the bonded sheets aected the ailure modes. The ailure modes changed rom debonding induced by lexural cracks to debonding rom the sheet ends when number o layers was greater than two. The predicted lexural capacities based on ACI 44.2R28 tended to overestimate because the end debonding ailure was not able to predict. Keywords. Flexural strengthening, prestressed concrete beam, ruptured strands, externally bonded CFRP sheets INTRODUCTION Prestressed concrete (PC) has been shown to be an advantageous concrete technology with high perormance as high strength, durability, low cost and small section. Since the irst introduction in 19s, PC has been used widely in over the world, especially or long span
bridge girders. Because o the structures ages or new requirements in upgrading the service loads, many PC bridges are considered to be repaired and strengthened. Besides, there has been a concern or the deterioration o PC girders in many countries in recent years. One o the most severe cases is the rupture o strands or tendons because o chloride attacks or external impacts. The severe damages lead to the reduction o load bearing capacity and aect the beam behaviour. These damages required not only an emergency structural inspection but also a practical repair and strengthening. Many conventional methods may be adopted to address the problems including the replacement o girders, repairing and strengthening methods using internal splices, external posttensioning tendons or steel plate jackets (Harries, 29). Nevertheless, the implements o those methods consume much time, labours and on the other hand, the repairing and strengthening materials themselves may not be prevented rom uture corrosion. In recent years, carbon iber reinorced polymer (CFRP) sheets have taken the advantage o the conventional materials in retroitting reinorced concrete (RC) structures. The beneits o CFRP sheets include high strength, light dead load added to the existing structures, high resistance to corrosion, easy implement without requirements o heavy equipments, large space and short construction time. For lexural strengthening, CFRP sheets are bonded to concrete surace at the tension side in order to enhance the load capacities, reduce the crack widths, delections, and decrease the stress in internal steels. Many studies have ocused on the application o CFRP sheets in lexural strengthening o RC structures. So ar, however, there has been little discussion about the eects o lexural strengthening o pretensioning PC beams having ruptured strands using externally bonded CFRP sheets. Hence, this study aims to evaluate the eects o externally bonded CFRP sheets on lexural strengthening o pretensioned PC beams having ruptured strands. The experimental parameters were the lengths o CFRP sheet, the presence o Ushaped anchorages and the number o CFRP sheet layers. Furthermore, this study compared the experimental results with the predicted values based on ACI guidelines (ACI 44.2R28). OUTLINE OF THE EXPERIMENT Details o specimens. The pretensioning PC beams having a rectangular crosssection o mm wide by 3 mm height and 33 mm long were prepared. First, the prestressing strands were set and an initial stress o 175 N/mm 2 was provided. Then, high early strength concrete was cast. Ater the concrete hardening, the jacking pressure was released and the prestressing orce transerred rom the strands to concrete by the bond between them. The reinorcement arrangements o the specimens are shown in Fig. 1. Four o sevenwire prestressing strands o 1.8 mm diameter, whose crosssection area was 7.8 mm 2, were used as tensile reinorcement. The deormed bar stirrups o 1 mm nominal diameter were provided to prevent the shear ailure. Specimens were classiied into three types: a control beam (); beams with one cut strand (DB1) and beams with two cut strands (DB2). In order to simulate the damage status, in the damaged beams, the prestressing strands were cut at the middle o the span. The concrete sections, then, were restored to the original rectangular shape using a high strength polymer cementitious mortar. The 28day compressive strength o mortar was 58.2 N/mm 2. In Fig. 1, the solid blue rectangles denote the locations where strain gauges were attached to prestressing strands. There were six locations where strain gauges were attached in cut strands and two locations in uncut strands. At each location, three strain gauges were attached on wires. The strain at one location was taken as the average value obtained rom these three measurements. The designed material properties o the specimens are given in Table 1.
3 9x6=54 1x= A 8 D1@6 D1@ Strain gauge 2D1 6 54 T1.8 14 14 A Strain gauges bonded DB1 DB2 to uncut strand 1 3 2 A A STRAIN GAUGES Strain gauges bonded ON WIRES to cut strand Figure 1. Arrangement o reinorcing bars and internal strain gauges (Unit: mm) Table 2. List o the experimental cases No. Name t CFRP n b l w (mm) (mm) 1 2 DB1 3 DB2 4 DB1.111 1 125 1, 5 DB12.111 1 125 2, 6 DB1284.111 1 125 2,84 7 DB1U.111 1 125 1, 18 8 DB2.111 1 125 1, 9 DB2U2b.333 2 125 1, 18 1 DB2U3b.333 3 125 1, 18 11 DB2U4b.333 4 125 1, 18 12 DB2U5b.333 5 125 1, 18 t : thickness o CFRP sheet; n : number o layers o longitudinal CFRP sheet; b : width o longitudinal CFRP sheet; l : length o longitudinal CFRP sheets; w : width o transverse CFRP sheet Table 1. Material properties Concrete Prestressing strands Steel ' c pu py y (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) 55 1,72 1,46 295 c : compressive strength o concrete; pu : ultimate tensile strength o prestressing strands; py : yield strength o prestressing strands; y : tensile strength o steel bar Table 3. Properties o CFRP sheets Type t u ε u (mm) (N/mm 2 ) (mm/mm) a.111 3,4.148 b.333 3,4.148 u, u : ultimate tensile strength and rupture strain Experimental cases. A total o 12 specimens were tested, which were divided in three categories: reerence beams (cases 13), series 1 (cases 47) and 2 (cases 812). The experimental cases are listed in Table 2. Figure 2 illustrates the layout o strengthened beams with the externally bonded CFRP sheets. In series 1, one layer o CFRP sheet with dierent lengths was attached to the bottom o the PC beams in which 25% o prestressing strands
13 3 13 Ushaped anchorage gauge n = 2,3,4,5 Longitudinal CFRP sheets Figure 2. Layout o externally bonded CFRP sheets (Unit: mm) were cut. Additionally, in case 7, one layer o the U transverse CFRP sheets were provided at both ends o the longitudinal CFRP sheet. In the second series, the damaged beams having % o strands ruptured were strengthened with the dierent number layers o CFRP sheets. The number o layers was varied rom one to ive. The widths and lengths o CFRP sheets were constant values o 125 mm and mm, respectively. In addition, one layer o Ushaped anchorages were provided in all the cases o series 2. The unidirectional CFRP sheets were bonded to the bottom o the beams by wetlayup method with ibers oriented along the longitudinal axis o the beams. The properties o CFRP sheets are given in Table 3. Ater 7day curing time, the specimens were tested to ailure. EXPERIMENTAL RESULTS Loss o capacity due to rupture o strands. Figure 3 shows the loaddelection curves o the damaged beams in comparison to. As can be seen, loss strand areas o 25% in DB1 and % in DB2 led to the reduction o 25% and 53% o the ultimate loads, repectively. The cracking loads were also decreased rom 62 kn in to 52 kn in DB1 and 25 kn in DB2. It is certain that the reduction o lexural capacity is associated with the loss o strand areas. Also, the signiicant changes in the slopes o the curves indicating the member stiness in precracking and postcracking regions were decreased when the strands were ruptured. Eects o the CFRP sheet lengths and Ushaped anchorages l Capacities and stiness. Figure 4 demonstrates the loaddelection curves o the PC beams having one cut strand (DB1) strengthened by CFRP sheets with dierent lengths and providing Ushaped anchorages. As can be seen rom the igure, the specimens showed linear elastic behaviors up to the cracking points. These points illustrate the loads when the irst crack initiated in the constant moment region. Ater the cracking points, the curves became nonlinear as numerous lexural cracks ormed in shear spans. From experimental data given in Table 4, the initial stiness was improved with increasing the sheet lengths. Particularly, when the ull length o span was bonded with CFRP sheet the initial stiness went up to 11% (DB1284) o that in. The load capacities o the damaged PC beams strengthened by one layer o CFRP sheet were enhanced as ar as 13% compared to DB1. Nevertheless, increasing the sheet lengths did not show a noticeble eect on the ultimate loads.
Load (kn) 62 52 53% 25% DB1 DB2 Cracking point 25 1 2 3 4 Delection (mm) Figure 3. Loaddelection curves o reerence beams Load (kn) ~12% ~13% DB1 DB1 DB1_ DB1_2 Cracking point DB1284 DB1_U 1 2 3 4 Delection (mm) Figure 4. Loaddelection curves o beams strengthend with dierent sheet lengths Tensile strains in the remaining prestressing strands. Figure 5 provides the relationship between the applied load and the increment o tensile strains in remaining prestressing strands, which was circled in red color. The location o strain gauges was at middle o the beam span. This graph reveals the eect o the bonded CFRP sheets on reducing the tensile strains in the remaining prestressing strands. Since the bonded CFRP sheets participated in carrying the tensile stress with the internal prestressing strands in the strengthened beams, the increment o tensile strains o the remaining prestressing strands was declined at the same load level. Eects o the number o layers o bonded CFRP sheets Capacities and stiness. Table 5 summarized the load carrying capacities and the stiness o the strengthened PC beams in series 2. There was a recognizable eect o the number o layers on the cracking loads o strengthened beams. The cracking load signiicantly reduced rom 62.3 kn in to 25. kn in the damaged beam (DB2). With larger number o layers, the strengthened beams perormed higher cracking loads and initial stiness. As can be seen, in the beam strengthened with ive layers o CFRP sheets, the cracking load was restored to Table 4. Eect o sheet lengths and Ushaped anchorages Cracking point Name P cr P u P u /P u Initial stiness (kn) (kn) (kn/mm) 62.3 142.6 2.36 DB1 52. 16.5.75 16.49 DB1 59. 124.7.87 19.1 DB12 6.8 121.1.85 2.95 DB1284 59.6 12.2.84 22.31 DB1U 57.9 123.8.87 2.31 P cr, P u : cracking and ultimate load Load (kn) DB1 DB1 DB12 DB1284 DB1U 2x1 3 5x1 3 7x1 3 Strain ( ) Figure 5. Loadstrain increment in remaining strands
Table 5. Eect o number o sheet layers on capacities and stiness Name P cr P u P u /P u Initial stiness (kn) (kn) (kn/mm) 62.3 142.6 2.36 DB2 25. 66.7 46.8% 1.92 DB2 36.2 82.4 57.6% 11.42 DB2U2b 38.5 122.6 86.% 13.4 DB2U3b 46. 13.5 91.5% 13.97 DB2U4b 49. 129. 9.5% 14.59 DB2U5b 55. 119.1 83.6% 16.71 P cr, P u : cracking and ultimate load; (1,2, etc.: number o longitudinal sheet layers).5 1 1.5 2 2.5 Crack width (mm) Figure 6. Eect o number o layers on lexural crack widths 55. kn equivalent to 88% o that o beam. Also, the initial stiness o the strengthened beams was enhanced associated with the increase in number o layers. Despite o this, the strengthened beams did not provide the higher ultimate load when greater than three layers o CFRP sheets bonded. From the data in Table 5, the ultimate loads increased with increasing number o layers up to three layers. With three layers bonded, the ultimate load was recovered up to around 91.5% o. Nevertheless, this trend o increase in lexural capacity did not continue when the number o layers went into our and ive. Evenly, the ultimate load o the beam strengthened by ive layers indicated a noticeable reduction compared to that o the beam strengthened with three layers. It is likely that debonding o CFRP sheets occurred earlier in this specimen. Hence, the CFRP sheets did not eectively utilize higher strength to the lexural capacity o the beams. Crack widths and tensile strains in the remaining prestressing strands. Figure 6 illustrates the relationship between the applied load and the widths o the lexural cracks in the constant moment regions measured by πgauges. It was certain that the openings o the cracks at midspan were well restrained and became smaller with the greater number o CFRP sheet layers. The relationship o the applied load and the increment o the tensile strains at midspan o the remaining prestressing strands (red circle) is shown in Fig. 7. In the igure, there is a clear trend o decreasing in tensile strains o the prestressing strands when the number o CFRP layers was increased. The indings show that with greater amount o CFRP sheets participating in carrying the tensile stress, the proportion o tensile stress carried by prestressing strands became smaller at the same load level. Likely, the yielding loads o the internal prestressing strands are proited rom the attaching o the larger amount o CFRP sheets. Figure 8 provides an evidence o the increasing the yielding loads. This igure compares the tensile strain (with consideration o pretensioning stress) at midspan o the remaining strands in the beams strengthened by two and three layers o CFRP sheets. It can be seen clearly, while the strain in DB2U2b reached the yielding strain ( y ) o prestressing strand, the strain in DB2U3b was still ar rom this value. Load (kn) 5 4 3 2 1 DB2
Load (kn) 4 5 3 2 1 DB2 Load (kn) DB2U3b DB2U2b y (1,2, etc.: number o longitudinal sheet layers) 4 8 12 Strain ( ) Figure 7. Eect o number o layers on increment o strains in remaining strands 7 12 Strain ( Figure 8. Comparison o tensile strains in remaining strands Failures o composite actions. The critical sections in the strengthened PC beams were shited rom the constant moment region to the portion near the sheet ends when the amount o the bonded sheets was increased. When the PC beam was strengthened with two layers o CFRP sheets, debonding was initiated by the lexural cracks and propagated rom midspan towards the end o the longitudinal sheets as shown in Fig. 9. The behaviors, however, were dierent when the beams were bonded with more than two layers. Figure 1 detailed the general behaviors in the beams strengthened by more than two layers o CFRP sheets. First, the lexural cracks were generated in the constant moment region. Ater that, as the load gradually increased, the cracks were ormed in the shear span, rom the loading points to the end o the bonded CFRP sheets. Ater the cracks at the ends o the bonded sheets opened (Fig. 1(a)), the beam stiness was reduced and the increase in the load became slow. Figure 1(b) shows the debonding o the longitudinal sheets initiated rom the sheet end in DB2 U4b, in which the solid yellow lines represent the cracks observed ater the peak load. Since the debonding occurred at the end o the CFRP sheets, the sections near the end o the sheets became critical. The debonding between the bonded CFRP sheets and concrete, then, was ollowed by the crushing o concrete at the top iber o the section near the sheet end as shown in Fig. 1(c). Finally, the Ushaped anchorages were delaminated rom the top o section. Generally, the ailures due to debonding o CFRP sheets are brittle because the CFRP sheets abruptly terminated carrying the tensile stress. (a) (b) (c) Propagating o interacial crack Bonded sheets at bottom Crack opened at the end o bonded sheets Postpeak cracks End plate debonding Concrete crushing U anchorage debonding Figure 9. Debonding in DB2U2b Figure 1. General behaviour o beams strengthened with greater than two layers
The dierences in the ailures o the strengthened beams can be explained by an interacial stress model as shown in Fig. 11. Figure 11(a) introduces the stresses acting in a concrete element near the interace between concrete and bonded sheets. The element is subjected to interacial shear stress ( ), interacial normal stress ( y ), and the tensile stress ( x ). When the tensile stress at the bottom o concrete section is due to a bending moment at a considered section, the typical distribution o interacial stresses is given in Fig. 11(b). The interacial stresses shows the high concentration at the end o the bonded sheets. According to previous studies, the interacial stresses are highly related to the distance between a support and the sheet end, elastic modulus and thickness o the bonded plate, elastic modulus o the adhesive layers and concrete compressive strength (SayedAhmed et al., 29 and Smith et al., 21). Once the combination o three stress components exceeds the strength o the weakest element the debonding occurs. Turning now to the experimental evidences on the ailure modes, they were accompanied by the behaviors o the remaining prestressing strands previously given in Fig. 8. As can be seen, when small amount o CFRP sheets bonded (e.g. two layers), the strands yielded at the middle o the span leading to the widening o lexural cracks in constant moment region. The widening o the cracks accelerated a rise in shear and normal stresses at the interace between concrete and the bonded sheets, then induced the debonding rom the crack mouth towards the support. In a dierent manner, when larger amount o CFRP sheets was bonded (e.g. three layers), the tensile strain in the remaining strands did not reach yielding strain. Hence, the width o lexural cracks in the constant moment region remained small and interacial stresses did not rise at the middle o the span. However, debonding was generated rom the end o the bonded sheets because o high concentration o the interacial stresses. From this point o view, the debonding rom the end o the bonded sheets in this study can be explained by the concentration o the stresses near the sheet ends, which reerred to the total thickness o the bonded CFRP sheets and the curtailments o the bonded sheets located in high shear and moment regions. On the other hand, it is certain that the behaviors o concrete element y (interacial normal stress) x (tensile stress) (interacial shear stress) (a) Stresses acting on concrete element near the plate end End o sheets Center line P 1.2 exp u /P cal u 1.1 1.9 Interacial shear stress Interacial normal stress (b) Conceptual interacial shear and normal stress distribution (ACI 44.2R8) Figure 11. Stresses in concrete element near the sheet end.8 1X 1 6X 2 9X 3 12X 4 15X 5 6 Total thickness o CFRP sheets (X =.111 mm) Intermediate lexural crack debonding Rupture o CFRP sheet End sheet debonding Concrete crushing Figure 12. Validation on the predicted capacities based on ACI guideline
prestressing strands are highly related to the eective stress in the strands. Thereore, the eects o prestressing stress level to debonding behavior in PC beams need to be urther taken into account. VALIDATION OF THE EQUATIONS IN THE GUIDELINES OF ACI The recent guideline o ACI (ACI 44.2R8) suggests computing the lexural capacities o the beams with externally bonded FRP sheets based on stress and strain equilibrium in a lexural section. The equation given or the lexural capacity o PC beams strengthened with externally bonded FRP sheets consists o two components: capacities carried by prestressing strands and iber sheets: 1c 1c M n A p ps ( d p ) A e ( h ) (1) 2 2 Where: A p : area o prestressing steel ps : stress in prestressing steel at beam ailure d p : eective depth to centroid o prestressing steel e : stress in iber sheet at beam ailure A : area o FRP sheets 1 : ratio o depth o equivalent rectangular stress block to depth o the neutral axis : partial reduction actor, =.85 In Eq. (1), the stress in iber sheets at the beam ailure ( e ) is determined rom the maximum strain in the FRP sheets at the sections where concrete crushes, FRP sheets are debonded or FRP sheets rupture. The eective strain o the bonded sheets in case an immediate crackinduced debonding ( d ) is predicted based on the empirical equation (2). In this equation, the debonding strain o the bonded sheets depends on compressive strength o concrete and properties o bonded sheets. ' c d.418.9 n E t Where: c : compressive strength o concrete (MPa) n : number o FRP layers E : Elastic modulus o FRP sheet (MPa) t : thickness o FRP sheet (mm) u : ultimate strain o FRP sheet u (2) Figure 12 represents the validation on lexural capacities o the strengthened PC beams between experimental data and the calculations based on ACI guidelines. The reduction actor =.85 was employed in the calculations. Even so, the calculated values were overestimated when the total thickness o CFRP sheets provided was increased, or example, in the case o our (12X) and ive layers (15X) were bonded. A possible explanation or this is the dierences o ailure modes rom the predictions. The debonding rom the sheet ends occurred in the experiments; however, the recent guideline has been unable to predict the lexural capacity o the strengthened beams ailed in end sheet debonding. Besides, as discussed previously, the dependence o the ailure behaviours o composite actions and both the bonded sheet lengths and amount needs to be taken into account.
CONCLUSIONS First, the externally bonded CFRP sheets show the eective perormance in improvement o the lexural capacities and the recovery o the stiness o PC beams having ruptured strands. Moreover, since CFRP sheets participate in carrying the tensile stress with the internal prestressing strands, the crack widths are well restrained as well as the tensile strains in the prestressing strands are reduced at the same load level. When small amount o CFRP sheets are bonded, the increase in the length o CFRP sheets or providing Ushaped anchorages at the ends o the longitudinal sheets do not result in the increment o lexural capacities because the debonding induced by lexural crack is a prior ailure. In spite o this, the member stiness is enhanced associated with increasing the sheet length. Second, the increase in the cracking loads and decrease o tensile stress carried by remaining strands are accompanied by increasing number o layers o the CFRP sheets. The ultimate load is enhanced up to 91.5% o the original beam by bonding three layers o CFRP sheets. Furthermore, the ailure modes tend to change rom debonding induced by lexural cracks to debonding rom the sheet ends when the damaged PC beams are strengthened with greater amount o CFRP sheets. The debonding rom the ends o the longitudinal CFRP sheets is caused by high stress concentration near the sheet ends which is due to (i) great amount o CFRP sheets bonded; and (ii) high shear and moment at the curtailment o CFRP sheets. Thereore, to employ the strength o CFRP sheets with a large amount o CFRP sheets eectively, suicient lengths o CFRP sheets with increasing the number o layers need to be urther studied. In addition, the existing equations in the guidelines o ACI are insuicient to predict the debonding rom the ends o bonded sheets. Thus, the calculated lexural capacities o the PC beams strengthened by externally bonded CFRP sheets tend to overestimate when this ailure occurs. REFERENCES American Concrete Institute Committee 44.28 (28). ACI 44.2R8. Guide or the design and construction o externally bonded FRP systems or strengthening concrete structures, Michigan, USA. Harries, K. A. (29). Repair method or prestressed girder bridges, Technical report, Pennsylvania Department o Transportation, Jun. 29. SayedAhmed, E.Y. et al. (29). Bond strength o FRP laminates to concrete: Stateotheart Review. Electronic Journal o Structural Engineering 9, 4561. Smith, S.T. and Teng, J.G. (21). Interacial stresses in plated beams. Engineering Structures 23, 857871.