REPLACEMENT OF CONVENTIONAL STEEL STIRRUPS BY INTERNAL REINFORCING CFRP GRIDS IN SHEAR OF CONCRETE BEAMS

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1 Journal o JSCE, Vol. 5, , 217 REPLACEMENT OF CONVENTIONAL STEEL STIRRUPS BY INTERNAL REINFORCING CFRP GRIDS IN SHEAR OF CONCRETE BEAMS Sirapong SUWANPANJASIL 1, Takuro NAKAMURA 2, Koji MATSUMOTO 3 and Junichiro NIWA 4 1 Member o JSCE, Ph.D. Candidate, Dept. o Civil and Environmental Eng., Tokyo Institute o Technology ( M1-17 O-okayama, Meguro-ku, Tokyo , Japan) suwanpanjasil.sirapong@gmail.com 2 Member o JSCE, Assistant Proessor, Dept. o Civil and Environmental Eng., Tokyo Institute o Technology ( M1-17 O-okayama, Meguro-ku, Tokyo , Japan) nakamura-takuro@cv.titech.ac.jp 3 Member o JSCE, Project Assistant Proessor, Institute o Industrial Science, The University o Tokyo (4-6-1 Komaba, Meguro-ku, Tokyo , Japan) km312@iis.u-tokyo.ac.jp 4 Fellow o JSCE, Proessor, Dept. o Civil and Environmental Eng., Tokyo Institute o Technology ( M1-17 O-okayama, Meguro-ku, Tokyo , Japan) jniwa@cv.titech.ac.jp This study proposes an innovative idea o shear reinorcement in concrete beam by replacing the conventional steel stirrups with CFRP grids at the shear span inside concrete cover. The compatibility between the internal grids and the surrounded concrete was investigated irst in the elementary test. Flexural perormances o two concrete elements reinorced by dierent spacing o internal grids were compared and discussed. Ater that, a concrete beam test was conducted with a total o eight RC beams varied in the number o grid strips in the shear span and the spacing o reinorcing grids. The experimental results showed that the shear capacity and the shear carried by internal CFRP grids signiicantly improved with a higher amount o grid strips; however, the increasing ratio o shear capacity was not proportional to the shear reinorcement ratio. Moreover, the location o internal grid in the shear span was an important part o the shear-resisting eectiveness in this study since the more number o grid strips located near the center o the shear span was much more eective to resist the propagation o diagonal shear crack than the grids at the edge. Finally, a model or evaluating shear carried by internal CFRP grids was introduced. Validity o the proposed model was explained by comparing with the experimental results and also other sets o experimental results. Key Words : CFRP grid, internal shear reinorcement, shear capacity, shear carried by FRPs 1. INTRODUCTION Carbon Fiber Reinorced Polymer (CFRP) is one o the most well-known materials in concrete engineering nowadays due to its many beneits, such as high strength, high durability, ease o application, and aesthetic appearance. Various types o CFRP, such as sheets, strands, rods and plates, have been produced based on purposes o use (types and shapes o structure, required strength, application method) and cost eectiveness. At the moment, one o the popular techniques o concrete beams with CFRP is to use CFRPs as a strengthening material in the shape o CFRP sheets. In this technique, CFRP sheets are attached to the surace o existing concrete members, and the third component like epoxy resin is then applied to make a good bond between CFRP sheets and the concrete. A great property o carbon ibers in term o high tensile strength is really eective to enhance structural perormance o concrete beams both in lexure and shear 1), 2). However, this technique still has some drawbacks due to the weaknesses o epoxy resin, including low ire resistance, degradation under UV light, and low compatibility with the substrate material 3). Such problems can reduce the ability o epoxy resin to transer stress to the 377

2 concrete, leading to an unexpected damage to the members. Additionally, the epoxy can be a potential hazard to workers during the application and the toxic umes can be released in a ire event 4). To avoid using epoxy resin, a new method called Textile Reinorced Concrete (TRC) has been developed. This system comprises a cementitious matrix and high-perormance structural ibers such as alkali-resistance (AR) glass ibers or carbon ibers in the orm o textile abric 5). Remarkable improvement in structural perormance o RC beams due to the TRC system has been veriied by many researchers 5)-8). In addition, this system shows some interesting proits due to the textile shape. According to Brückner et al. 9), the single ibers in the textile can be positioned in almost any direction and nearly perectly adopted to the orientation o the applied load. Moreover, since the diameter o the textile reinorcement is normally one or two times lower than the necessary diameter o steel bars, it is possible to develop very thin concrete elements. In order to develop a new challenge o CFRP or concrete beams while retaining the advantages o textile reinorcements, this study presents a new alternative shear improvement by using another type o textile reinorcement such as CFRP grid as a replacement or conventional steel stirrups at the shear span inside concrete beams. With this new method, the deects o the application o CFRP due to the ire and UV light degradation can be eliminated since the grids are covered by concrete rom the beginning without additional cementitious matrix or epoxy resin. Moreover, the grid type o CFRP can provide a better anchorage owing to its lattice points, compared with the abric type o TRC system, which requires an overlap area o the abric to ensure a good anchorage during an installation. The main objective o this study is to investigate the shear characteristic o concrete beams reinorced with internal CFRP grids. The contents o this paper can be classiied into two parts. The compatibility between the reinorcing grids and concrete was studied irst in the elementary test. Ater that, eight concrete beams with and without CFRP grids in the shear span were tested. The parameters included the number o CFRP grid strips in the shear span and the spacing o grids which varied between mm and mm. The experimental results in terms o shear capacities, load-displacement relationships, crack patterns, and shear-resisting mechanism were presented and discussed. Lastly, a model or evaluating the shear carried by internal CFRP grids in concrete beams was introduced. The validity o the proposed model was considered by comparing the calculatated results with experimental results and also with a set o experimental data rom Kim et al. 1). 2. ELEMENTARY TEST (1) Outline o elementary test Beore heading to the shear test o CFRP grid-reinorced concrete beams, it is important to guarantee at the beginning that the bond between the selected reinorcing CFRP grids and the designed concrete is good enough to resist the orce eectively, without a slip o internal grid rom the surrounded concrete. In order to do that, a bending test o concrete elements with the same type o CFRP grids as used in the shear test has been conducted, instead o testing by a direct pull-out test. The actual tensile strength o the reinorcing grids obtained rom the bending test in this elementary test will be compared with their ultimate strength taken rom the uni-axial test. This comparison is to estimate the perormance o CFRP grids when they are used as reinorcing materials inside concrete members. (2) Specimen details in elementary test Two concrete elements reinorced with internal CFRP grids in lexure were prepared in this test. The two specimens have a total length (l) o 1 mm, width (b) o 2 mm, and height (h) o mm. The shear span-to-eective-depth ratio (a/d) is 4.8 and both o them are designed to ail in lexure as shown in Fig. 1. The dierence between these two concrete specimens is the amount o internal reinorcing grids. One specimen, named C, was reinorced by two strips o mm-spacing CFRP grid and another specimen, named C, was reinorced by our strips o Unit: mm 2 Displacement transducer a=3 CFRP 1 2 grid Fig. 1 Details o specimens in elementary test. C Fig. 2 Schematic o specimens in elementary. t t C 378

3 Maximum size o coarse aggregate (mm) Water cement ratio (%) Sand aggregate ratio (%) Table 1 Mix proportions o sel-compacting concrete. Water Cement Limestone powder Unit weight (kg/m 3 ) Fine aggregate Coarse aggregate Superplasticizer Viscosity improver mm One strip o CFRP grid mm One strip o CFRP grid mm mm C C Fig. 3 CFRP grids with spacing o mm and mm. Fig. 4 Uni-axial test o CFRP grids. mm-spacing CFRP grid as shown in Fig. 2. Hence, the lexural capacity o C was expected to be about double o that o C. (3) Materials used in elementary test a) Concrete The sel-compacting concrete (SCC) was selected in this study because a high workability and consistency o matrix are guaranteed so that the resh concrete can be ully penetrated into the grid without segregation, ensuring the good bond between iber and matrix 11). As shown in Table 1, the mix proportions consists o high-early strength cement, limestone powder, ine aggregates, coarse aggregates, viscosity improver and superplasticizer (high-perormance air entrained water-reducing agent). The concrete is designed with an average seven-day age strength o 35 N/mm 2. b) CFRP grids The two orthogonal CFRP grids have the same nominal thickness or one strip o 2.64 mm and width or one strip o 5 mm. Thus, the cross-sectional area or one strip o the grids is about 13.2 mm 2 both in mm-spacing grid and mm-spacing grid as can be seen in Fig. 3. According to JSCE-E ), the uni-axial test or tensile properties o the CFRP grid used in the elementary test was conducted as shown in Fig. 4. The results rom the uni-axial tensile test o ive samples or each case showed that the average ultimate tensile strength and Young s modulus o the reinorcing CFRP grids were 1934 N/mm 2 and 11 kn/mm 2 in the case o the mm-spacing grid, and 1914 N/mm 2 and 118 kn/mm 2 in the case o the mm-spacing grid. In addition, the rupture strain o both two-sized grids varied between 1.43% to 1.72%. (4) Loading method and measurements The ailure location o specimens was designed to happen in a uniorm bending region; thus, the our-point bending test with spacing between the two loading point o 2 mm was perormed. Measurement items included displacement transducers, electrical strain gauges, and π-gauges. Four displacement transducers were set up at the mid-span and supports o specimens. The 2 mm gauge length strain gauges were attached on the internal CFRP grids and the 3 mm gauge length types were attached at the top surace o concrete. All the gauges were attached at the mid-span. The mm π-gauges were attached at the bottom o the specimens to check the starting o lexural crack. Moreover, the cracks on the side surace were recorded by digital cameras during the test. (5) Test results o elementary test a) Load displacement relationships, lexural capacities and ailure modes The relationships o the applied load and displacement or C and C are presented in Fig. 5. The irst crack o C and C was observed when the load reached 6.2 kn and 9.1 kn, respectively. Then, the load dropped a bit and increased again due to the internal reinorcing grids. As a smaller number o grid strips in C, a wider irst crack was obtained when compared with the irst crack o C and that led to a larger reduction o load ater the irst drop as shown in the green line in Figs. 5 and

4 Load C C 33. kn Load kn kn kn Displacement (mm) Fig. 5 Load displacement relationships in elementary test kn kn C C Strain (%) Fig. 6 Load Strain o CFRP grids in elementary test. ε c : strain o concrete (data rom strain gauges) x C' C d =72.5 z = d-x/3 ε : strain o CFRP grids (data rom strain gauges) T orce Fig. 8 Equilibrium o strain and orce in elementary test. C Fig. 7 Failure pattern o specimens at peak load. Some new cracks were generated ater the irst crack, causing a swing o the curves in both C and C. Note that an extension o the internal grids also started ater the irst crack at the same load level as can be seen in Fig. 6. Ater that, the load gradually increased with a propagation o lexural cracks at the mid-span o the specimens until the peak load. The lexure ailure due to the total rupture o the grid was evidenced in C when the load reached 15.7 kn, leading to a collapse o the specimen as shown in Fig. 7. A good reinorcing eiciency o the internal grid was obtained in C where even the total rupture o the grid was not ound. This was conirmed rom the load-strain curve o C in Fig. 6 which exhibited that the strain o the grid had already reached its limit (1.43% to 1.72%). The peak load o C was 33. kn, which was about double that o C as expected, and the ailure mode was considered as shear ailure since a severe shear crack was observed at the peak as seen in Fig. 7. b) Actual tensile strength o internal CFRP grids The mechanical properties o concrete in both C and C were identical in which the compressive strength ( c ) was 43. N/mm 2, the tensile strength ( t ) was 2.63 N/mm 2, and Young s modulus (E c ) was 32.4 kn/mm 2. To calculate the actual tensile strength ( p ) o the internal CFRP grids rom the elementary test, Eq. (1) was considered. p M (1) A z where M is the bending moment at the peak load; A is the total cross-sectional area o CFRP grids in the specimens (26.4 mm 2 in C and 52.8 mm 2 in C); and z is the moment arm length which can be deined as explained in Fig. 8. The results o the actual tensile strength rom Eq. (1) was 1457 N/mm 2 in C and 156 N/mm 2 in C. The comparison o the tensile strength o CFRP grids rom the bending test and its maximum values rom the uni-axial test (1934 N/mm 2 in C and 1914 N/mm 2 in C) revealed that the dierence was 24.7% in C and 18.5% in C. Even though the calculation rom Eq. (1) was based on the assumption 38

5 C C Fig. 9 Dispersed ailure o CFRP grids rom the uni-axial test. that the internal grids had reached their maximum tensile strength, it was remarkable to note that the internal grid in C was still considered by this equation even i the ailure mode was shear ailure. Although a rupture o the grids did not occur in C, the tensile strength o CFRP grid was very close to its maximum at the time the specimen had ailed. This was evidenced by the strain o CFRP grid which was very close to its ultimate, and by the peak load o C which was about two times that o C as mentioned beore. This corresponded to the amount o CFRP grid in C which was two times that o C. In addition, the 18.5% dierence in the case o C was also lower than that o 24.7% in the case o C. The deviation o the tensile strength was considered to have happened mainly because o the localized ailure. In the bending test, the ailure o CFRP grids occurred in only one racture section; however, a dispersed ailure was ound in all tested grids in the uni-axial test as seen in Fig. 9. In summary, the results rom this elementary test demonstrates that the proposed internal grid system is practically productive to enhance the ability o concrete elements and there is no bond problem between the selected CFRP grids and the surrounding concrete. Thereore, this internal reinorcing system by the same type o CFRP grids can reasonably apply to the shear test o CFRP grid-reinorced concrete beams in urther studies. 3. TEST PROGRAMS OF SPECIMENS IN CONCRETE BEAM TEST (1) Specimen details and cases A total o eight RC beams were prepared and tested in this study. One beam was the control beam (CON) in which no reinorcement was provided in the shear span o this specimen. The other seven RC beams were reinorced in shear in dierent numbers and spacing o internal grids as shown in Fig. 1. The reinorced specimens were divided into two groups according to the spacing o CFRP grids in the shear span. Specimens were named according to spacing o CFRP grid and number o CFRP grid strips. In Group I, the beams were reinorced with the CFRP grid with spacing o mm and the number o grid strips was increased proportionally rom three strips in C-3 to ive and seven strips in C-5 and C-7, respectively. Similarly, the number o CFRP grid strips o specimens in Group II were varied rom two strips in C-2 to six, ten, and ourteen strips in C-6, C-1, and C-14, respectively. However, the spacing o CFRP grid in Group II was changed to mm. Deormed high-strength steel bars with the reinorcement ratio o 3.4% were provided as tensile reinorcements in all tested beams to prevent lexure ailure and a number o steel strirrups were ully arranged in the untested shear span to control the ailure side o the specimens as seen in Fig. 1. All specimens have a total length (l) o 18 mm, width (b) o 2 mm, height (h) o 3 mm, length o shear span (a) o 7 mm and shear span eective depth ratio (a/d) o 2.8. In addition, specimens in this study were designed to ail in shear in all cases. (2) Materials used in concrete beam test The mix proportion o concrete and the reinorcing CFRP grids used in this RC beam test had the same properties as used in the elementary test. The designed compressive strength o seven-day curing age o concrete was also 35 N/mm 2. The reinorcing grids were attached to the steel reinorcements in advance by using the binding wires as commonly used in steel stirrups. Since the spacing o reinorcing grids had already been set, it became very comortable or the grid attachment. Three deormed high-strength reinorcing bars with 25.4-mm nominal diameter (A s =7.7 mm 2 ) and 1187 N/mm 2 yield strength were arranged as tensile reinorcing bars. Two deormed bars with 9.53-mm nominal diameter (A s =71.3 mm 2 ) and 345 N/mm 2 yield strength were provided as compression bars. In the untested shear span, 12.7-mm nominal diameter (A s =126.7 mm 2 ) with yield strength o 45 N/mm 2 deormed bars were arranged with spacing o mm. In addition, round bars with 6-mm diameter (A s =28.3 mm 2 ) and yield strength o 39 N/mm 2 were provided to prevent ailure at the point load in all cases as displayed in Fig

6 C-3 D13 SD345 CL 2 D1 SD295A Unit: mm Ф6 SR235 D25 SBPD18 Strain gauge CL CL C-5 C-6 CL CL Test span a=7 2 Internal reinorcing grid 125 C-7 C-1 CL CL C-2 C-14 Fig. 1 Details o specimens in concrete beam test. Displacement transducer Plates and nuts internal CFRP grids, tensile bars, and also compression bars at the location as shown in Fig. 1. Strain gauges with 3 mm gauge length were attached on a top iber at the mid-span to measure the strain o concrete at the peak load. In addition, digital cameras were set to record the propagation o cracks on the side surace throughout the loading test. Loading point Camera 4. TEST RESULTS AND DISCUSSION IN CONCRETE BEAM TEST Fig. 11 Environment during the our-point loading test. (1) Shear capacity a) Evaluation method o shear carried by internal CFRP grid rom the experiments In the conventional way to determine the shear capacity o normal RC beams, a total shear capacity can be separated into two components, namely the shear carried by concrete (Vc) and the shear carried by steel stirrups (Vs). The term Vc has actually included the eects o the shear in the compression zone, the vertical component o the aggregate interlock, and the dowel action in its calculation already13). Similarly, the total shear capacity o the reinorced beams observed rom the experiment (Vexp) in this study is also a summation o the shear carried by concrete (Vc) and the shear carried by internal CFRP grids (Vg) as expressed in Eq. (2). The Vc o each reinorced specimens can be reerred rom Vc o the control beam (Vc_con). However, it is readjusted as (3) Loading method Figure 11 shows the environment during the loading test o C-6. A our-point load was set up with the load generated rom a 2-kN loading machine. To ensure a suicient anchorage o tensile bars, the anchorage plates and nuts were equipped at the end o the bars as seen in Fig. 11. Telon sheets with grease were placed on the roller supports to prevent the riction in horizontal direction and a load distribution beam was placed below the applied loading point to reduce the stress concentration. (4) Measurements The displacement o specimens was measured by attaching our displacement transducers at the mid-span and supports. Three mm π-gauges were attached to the bottom o specimens to investigate the starting point o lexure crack. Electrical strain gauges with 2 mm gauge length were attached to all 382

7 Table 2 Summary o concrete beam test results. Specimen designation shown in Eq. (3) because o the inequality o compressive strength o concrete between the control specimen (ʹc_con ) and the others. That inequality is proportional to the third root o the compressive strength o concrete according to the equation o RC beams without shear reinorcement proposed by Niwa et al. 14). V Mechanical properties o concrete c (N/mm 2 ) c V E c (kn/mm 2 ) exp c _ con V V (2) c g ' ' 1/ 3 V (3) c V exp c _ con V c V gexp CON C C C C C C C ' c = compressive strength, E c = Young s modulus, V exp = total shear capacity rom experiment, V c = shear carried by concrete, V gexp = shear carried by internal CFRP grids rom experiment Group I Group II C-14 C-1 C-6 C-2 C-7 C-5 C-3 CON Vgexp Vc 1 2 Shear capacity Fig. 12 Clariication o shear capacity in concrete beam test. As a consequence, the evaluation method o shear carried by internal CFRP grids rom the experiments (V gexp ) is presented as ollows: V gexp V V (4) b) Shear capacity and shear carried by internal CFRP grid rom the experiments Table 2 lists the summary o experimental results and Fig. 12 clariies the augmentation o shear capacity due to the internal CFRP grids. The values o V c in each specimens was slightly dierent since the variation o compressive strength o concrete in each specimen was not ar rom that o the CON beam. It can be said that the total shear capacity and shear carried by internal CFRP grids in each group signiicantly increased with an addition o the number o CFRP grid strips in the shear span; however, such increment o capacities was not proportional to the amount o the reinorcing grid strips. In Group I, the total shear capacities o C-3, C-5, and C-7 were higher than that o the CON beam by 49.5%, 76.7%, and 79.7%, respectively. Besides, the shear carried by internal CFRP grid increased by 59.5% in C-5 and 66.2% in C-7 when compared with V gexp o C-3. Similarly, the total shear capacities o C-2, C-6, C-1, and C-14 in Group II were higher than that o the CON beam by 71.7%, 97.6%, 19.5%, and 114.7%, respectively. Comparing the increase in shear carried by internal CFRP grid in this group showed that the V gexp o C-6, C-1, and C-14 was higher than that o C-2 by 4.8%, 56.7%, and 61.1%, respectively. The results o shear capacities implied that the eectiveness o concrete beam reinorced with internal CFRP grids tended to be small when a greater amount o reinorcing grids was provided. This act was obviously ound when comparing the V gexp o C-5 and C-7 because the dierence in V gexp was only 4.2% even when the number o grid strips in C-5 was lower than that o C-7 by about 4%. Again, the dierence in V gexp o C-1 and C-14 was only 2.8%, while the dierence o number o grid strips was also 4%. Furthermore, the comparison o shear carried by CFRP grid between the -mm spacing grid and the -mm spacing grid revealed that a higher shear-reinorcing eiciency o internal grids was obtained rom specimens with a higher number o grid strips near the center o shear span. From Fig. 12, it was evident that the capacities o C-2 was signiicantly larger than those o C-3 even when the number o grid strips in shear span was smaller and this was conirmed again when comparing the capacities between C-6 and C-7. The reason or this phenomenon will be explained again in the next section o this paper. exp c 383

8 (2) Load-displacement relationships and crack patterns The relationships between the applied load and displacement o specimens in Groups I and II are presented in Figs. 13 and 14. The main diagonal crack (red line) and crack patterns o all specimens are illustrated in Fig. 15. Besides, the location o the internal reinorcing grids is also indicated by the blue dashed line in the shear span o all reinorced specimens in this igure. The diagrams in Figs. 13 and 14 show that the shapes o curves or all specimens except that o the CON are basically similar. The irst lexural crack o all specimens initiates when the load level is about 25-4 kn. Then, the loads increase steadily until they reach 1-17 kn. At this level, the initiation o diagonal shear crack is observed around the middle height o the shear span and this leads to the peak load o the control beam at the load level o kn. The ailure mode o the CON beam is the diagonal tension ailure, which is a typical ailure type o concrete beams w ithout shear reinorcement as shown in Fig. 15(a). In the case o the beams reinorced with CFRP grids, the loads still increase ater the appearance o the diagonal shear crack due to the internal CFRP grids. However, a reduction in stiness can be seen in Figs. 13 and 14. Ater that, the loads gradually Load P max P max P max P max CON C-3 C-5 C-7 Load P max CON C-2 C-6 C-1 C-14 P max P P max max P max Flexural crack Displacement (mm) Fig. 13 Load displacement relationships in Group I. Flexural crack Displacement (mm) Fig. 14 Load displacement relationships in Group II. (a) CON (b) C-3 (c) C-5 (d) C-7 (e) C-2 () C-6 (g) C-1 (h) C-14 Fig. 15 Crack patterns at peak load. 384

9 C L C-5 Load C-1 1 Initiation o shear crack grid 5 grid 4 grid 3 grid 2 grid 1 Load Fig. 16 Location o the strain gauges according to the number Strain o internal CFRP grid (x1-6 ) Fig. 17 Actual strain o grids in C-5. Load Initiation o shear crack grid 5 grid 4 grid 3 grid 2 grid 1 1 Initiation o shear crack grid 1 grid 9 grid 8 grid 7 grid Strain o internal CFRP grid (x1-6 ) Strain o internal CFRP grid (x1-6 ) Fig. 18 Actual strain o grids in C-1 (grid 1-5 in the let graph and grid 6-1 in the right graph). develop with a small extension in displacement and the crack width o the main shear crack becomes clearer and bigger in this stage. Finally, the loads o all specimens reach their peaks when the main diagonal shear crack extends to connect between the loading point and supports. The compressive strains o concrete rom the gauges at the top iber get to their limiting strain and crushing o concrete is clearly observed in some specimens at the location near the loading point as the examples in Figs. 15(b), 15(e), and 15(g). Thereore, the ailure mode o all reinorced specimens is considered the shear compression ailure. In addition, the longitudinal reinorcing bars and the steel stirrups in untested shear span do not yield in all cases since the actual tensile strain o the bars obtained rom the strain gauges do not reach their yielding strain. (3) Shear resisting mechanism in concrete beam test The location o strain gauges according to the number is illustrated in Fig. 16. The relationships between the applied load and actual tensile strain o each strip o internal CFRP grid rom C-5 and C-1 are presented in Figs. 17 and 18. Since the shear-resisting mechanisms o all reinorced specimens are quite similar, the graph o C-5 is considered as a representative or the beams with -mm spacing grid and the graph o C-1 is considered as a representative or the case o the -mm spacing grid. At the begining state o the loading, all beams behave in the linear manner prior to the occurrence o lexural crack and ollowed by a diagonal shear crack. Ater that, the internal CFRP grids start to resist the shear load. The evidence o this action can be described by the irst inclination o the graphs in Figs. 17 and 18 at the load level around 1-17 kn, which correspond to the peak load o the control beam. This assumption is similar to the utilization o steel stirrups in the conventional RC beams. 385

10 Load C-3 C-2 C-5 C-6 C-7 C-1 C Strain o internal CFRP grid (x1-6 ) Fig. 19 Actual strain o grids near the center o shear span. The a propagation o the main diagonal shear crack in the next stage is clearly observed in Figs. 17 and 18 where the reinorcing grids in the shear span do not equally resist the shear orce. While the grids located at about the center o shear span are hugely elongated, the grids located near the supports are not elongated signiicantly. Because o this, the shear carried by the internal CFRP grid does not increase signiicantly even i the number o grid strips is increased as ound in the comparison o V gexp between C-5 and C-7, or C-1 and C-14. Since the initiation o shear crack o RC beams having shear span eective depth ratio (a/d) more than 2.5 usually occurs at about the center o a shear span, the more number o grid strips at the center o a shear span, the more eective it is in resisting a widening and growing o the shear crack. This is the reason why the shear-resisting perormance o specimens with the -mm spacing grid is better than with the -mm spacing grid. V gexp o C-2 becomes close to V gexp o C-5 because the two grid strips o C-2 are extremely elongated and the actual tensile strain obtained rom the gauges located near the center o the shear span (position 3 in C and position 5 or 6 in C according to Fig. 16) rom C-2 shows the maximum value among all specimens in this study with the tensile strain o 9684x1-6 (about 6% o the ultimate strain o the grids) as shown in Fig. 19. From this point o view, the location o internal CFRP grid in the shear span is very important in concrete beams reinorced with internal CFRP grids. The inluence o the location o reinorcement on the shear capacity o concrete beams corresponds to the results rom the previous study done by the authors in which the strengthening mesh that is not used at the center o the shear span exhibits a much lower perormance than the mesh located at the center despite the same amount o mesh provided 15). Fig. 2 Inside CFRP grids ater loading test in C-2. Although the internal CFRP grids are able to enhance the shear capacity o concrete beams by resisting the propagation o the diagonal shear crack, they cannot yield like conventional stirrups. At the critical point, the grids no longer restrained an expansion o the crack since it became very big (more than 1 mm) and very easy to be seen by the naked eye. The loads o reinorced specimens reached its peak when the main diagonal shear crack extended to the loading point, or the concrete in compression zone above the diagonal crack was crushed. Even i CFRP grids are commonly known as brittle materials, it is important to note that a total rupture o the reinorcing grids and a sudden collapse o the beams are not observed in all specimens during and ater the test including C-2 in which a very small number o grids is provided. This is conirmed again by opening concrete cover and investigating the inside grids ater the loading test as the example in Fig. 2. One o the possibilities to describe this incident is the deiciency o the grid s nodes in the vertical direction. According to Dutta et al. 16), the orce transer in a composite grid is concentrated at the intersecting grid lines (nodes) while the surace on the grid ribs is essentially no load transer. Thereore, the number o nodes between the upper and lower longitudinal bars in C-2 might not be adequate to provide a deserving anchorage, which could lead to a rupture o the reinorcing grid. However, since the explanation here is only a supposition, urther studies about the bond between concrete and FRP grids are needed since the inormation is now still limited. 5. MODELING OF SHEAR CARRIED BY INTERNAL CFRP GRIDS (1) Calculation method o shear carried by internal CFRP grid In order to model the equation or evaluating shear carried by internal CFRP grid based on the experi- 386

11 Strain o each grid at peak / Total strain at peak (%) mental results o specimens in this study, the reinorcing ability o each grid strip in the shear span is considered one by one. The distributions o shear load on each internal grid strips at the peak load are shown in Fig. 21. It can be seen rom the igure that the grid strips located near the center o the shear span are elongated the most as mentioned beore in Section 4(3). In order to model the equation, the distributions rom Fig. 21 are rearranged as shown in Fig. 22. Based on the rearrangement, the shear carried by internal grid can be expressed as shown in Eq. (5). V Distance rom the center o shear span, x i (mm) Fig. 21 Shear distribution on each grid strip rom experiments. -.6 y = N g Strain proportion o grid strip at the center or each N g (%) gcal Exp. Approx. R 2 = N g N g Fig. 23 Relationship between strain proportion o grid strip at the center o shear span and N g. i 1 1 N g xi 1 z cot /.6 2 A C-3 C-5 C-7 C-2 C-6 C-1 C-14 u (5) α = 43N g -.5 Angle o distribution or each N g (α) Exp. Approx. R 2 = N g Fig. 24 Relationship between the angle o distribution and N g. Strain o each grid at peak / Total strain at peak (%) C-3 C-5 C-7 C-2 C-6 C-1 C Distance rom the center o shear span, x i (mm) Fig. 22 Rearrangement o shear distribution on each grid strip. where V gcal is the calculated value o shear carried by internal CFRP grids ; N g is the number o internal grid strips; x i is the distance rom the center o shear span to the concerned grid strip (mm); z is the distance between the horizontal compression and tension members (mm) [z = (7/8)d]; α is the angle o shear load distribution on internal grid or each N g [α = 43N g -.5 ]; A is the total cross-sectional area o CFRP grid or one strip (mm 2 ) [A = 2 t l where t and l are thickness and width or one strip o the grid]; and u is the ultimate tensile strength o CFRP grid (N/mm 2 ) From Eq. (5), it is explained that the reinorcing eiciency o the internal grid strip located at the center o shear span (x i = ) is the highest one and the eiciency becomes lower as x i with linear relationship increases as shown in Fig. 22. Finally, the eiciency is equal to zero when x i is extended to be as large as z cot α /2. To speciy the magnitude o the triangles or each specimen in Fig. 22, the relationships between the total number o grid strip (N g ) and the strain proportion at the center o shear span in each case are plotted as shown in Fig. 23. Besides, the relationships between the total number o grid strip (N g ) and the angle o shear load distribution (α) are also plotted as shown in Fig. 24. By using the least-squares procedure, power regression models are obtained as shown in the irst term o Eq. (5) and also shown in the calculation o α. The new proposed model or shear carried by internal CFRP grid is based on the assumption that the anchorage between the internal grid and the surrounded concrete is absolutely suicient. Thereore, the strain proportion at the center o shear span in Fig. 23 can be equal to one when there is only one grid strip in the shear span (N g = 1). The power regressions obtained rom Figs. 23 and 24 demonstrate 387

12 Table 3 Comparison o experimental values (V gexp ) and calculated values (V gcal ) and JSCE values or externally bonded CFRP sheets. Specimen A (mm 2 ) u (N/ mm 2 ) N g (strips) α V gcal Eq.(5) V gexp V gexp /V gcal s (mm) ρ (1-4 ) E (kn/ mm 2 ) ʹc (N/ mm 2 ) ԑ (1-4 ) V Eq.(7) V gexp /V R K JSCE V d Eq.(1) Eq.(9) C C C C C C C V gexp /V d V gexp /V gcal Avg. =.95 C.V. = 13.3% C-3 C-5 C-7 C-2 C-6 C-1 C-14 Specimen designation Fig. 25 Accuracy o proposed model. the reasonable tendencies that the strain proportion at the center o shear span and the angle o distribution should be close to zero when the number o grid strip is signiicantly increased. However, the proposed model at this stage limited the number o grid strips rom 2 to 14 strips since it is developed only rom the experimental results in this study. (2) Comparison o experimental values and calculated values The summary o the shear carried by internal CFRP grids rom the experiments as derived by Eq. (4) and rom the proposed model as calculated by Eq. (5) is presented in Table 3. As a comparison between the experimental values and the calculated values, a moderate accuracy is obtained with the average (avg.) o.95 and the coeicient o variation (C.V.) o 13.3% as shown in Fig. 25. However, the experimental value o C-3 seems to be comparatively low when compared with the calculation rom Eq. (5). This deviation is considered to have happened due to an insuicient node points in the C-3 specimen. As mentioned beore, the orce transer in a grid is concentrated mainly at the nodes. From that point, the horizontal components o internal grid does not directly resist the shear load; however, they provide the node points that are necessary or the anchorage between the FRP grids and concrete. For this reason, the only three nodes in the vertical direction o C-3 may not be suicient to generate shear capacity to be at the level as it should be resulting in the 3% reduction o shear capacity compared with the calculation rom the proposed model. Moreover, the insuicient node point in C-3 also causes a dierent load-displacement curve when compared with other reinorced specimens as can be seen in Fig. 13. For C-3, the diagonal crack propagated to the loading point very ast since the anchorage between the grid and concrete was quite low. However, ater reaching the peak load, the concrete below the loading point was still able to carry a bit shear load. This resulted in the post peak behavior in this specimen. (3) Validity o the proposed equation with other experimental results Due to the many advantages oered by FRPs, the researches on FRP bars used as lexural reinorcement have been perormed extensively, as well as the FRP sheets attached externally to the surace o concrete beams in terms o strengthening. However, the number o papers ocusing on FRP reinorcement 17), 18) as a substitute or steel stirrups is still limited and the model to estimate the shear carried by internal reinorcing FRP in shear still need improvement. One o the papers ocusing on the same aspect as in this study has been done by Kim et al. 1). In that paper, nine concrete beam specimens reinorced with the FRP plate material with opening were investigated. The parameters included the type o FRP, shape o FRP shear reinorcement, and the amount o the FRP reinorcement. 388

13 Specimen t (mm) Table 4 Comparison o experimental results rom Kim et al. with the proposed equation. l (mm) A (mm 2 ) u (N/mm 2 ) ʹc (N/mm 2 ) ρ v V c N g (strips) z (mm) GB GB GB GB AB CB α V gcal V cal V exp V exp /V cal The average compressive strength measured at 28 days in that paper was 44.6 MPa. Two layers o 1 deormed steel bars with a diameter o 25 mm were used as longitudinal reinorcement with their tensile strength and modulus o elasticity o MPa and 2 GPa, respectively. Aramid iber-reinorced polymer (AFRP), CFRP, and GFRP were used in the manuacturing o the FRP shear-reinorced plates. All concrete specimens had the same size with the section o 3x42 mm, the shear span o 813 mm, the eective depth o 342 mm, and the a/d ratio o 2.4. Table 4 shows the results o estimating the shear strength o concrete with FRP shear reinorcement (V cal ) using the shear carried by concrete rom JSCE as shown in Eq. (6) and calculating the shear carried by FRP shear reinorcement by the proposed equation in Eq. (5). However, the parallelogram shape in that paper was not included in this comparison since Eq. (5) did not concern the eect o the inclined grid strip. Also, the number o grid strip (N g ) shown in Table 4 counted only the strips inside the shear span. V c.2( ' c ) ( v) 3.75 bwd (6) d a / d The comparison in Table 4 indicates that the empirical model gives airly conservative values to the experimental data rom Kim et al. with an accuracy o 1.11 on the average and the coeicient o variation (C.V.) o 6.7%. However, it is noted that the estimation o shear strength by Eq. (6) gives a higher accuracy than the equations rom ACI which have been used or calculating shear strength o specimens in that paper. By using the ACI equations, the ratio o V exp /V cal is more than 1.3 on the average. (4) Comparison o the eectiveness between the proposed internal grid system and other systems or concrete beams with FRPs in shear In this section, the shear reinorcing eectiveness o the internal grid system rom this study is compared with two existing systems or concrete beams with FRPs in shear. One is the beams reinorced internally with FRP rods and another is the beams strengthened externally by FRP sheets. Both o them are now recommended in the guideline books o the Japan Society o Civil Engineers (JSCE) 19), 2). As shown in Eq. (7), the shear carried by FRP rods is estimated by the 45º truss analogy method similar to the calculation or conventional steel stirrups. However, the strain in FRP rods in Eq. (7) is not the ultimate strain o the material and the value has been limited as evaluated rom Eq. (8). V A E z / s (7).1 h ' s Es 4 c 1 (8) 3 E where V is the FRP transverse reinorcement shear resistance ; A is the total cross-sectional area o FRP shear reinorcement (mm 2 ); ԑ is the strain in the FRP shear reinorcement; z is the distance between the horizontal compression and tension members (mm) [z = (7/8)d]; s is the spacing o shear reinorcement (mm); h is the height o the member (mm); ʹc is the compressive strength o concrete (N/mm 2 ); ρ s is the longitudinal steel reinorcement ratio [ρ s = A s /(b w d)]; E s is the modulus o elasticity o longitudinal steel reinorcement (kn/mm 2 ); ρ is the FRP shear reinorcement ratio [ρ = A /(b w s )]; and E is the modulus o elasticity o FRP shear reinorcement (kn/mm 2 ). By using Eq. (7) to evaluate the shear capacity o internal CFRP grid in this study, the results can be seen as shown in Table 3 with the average with the experimental results o The comparison obviously indicates that the evaluation method or FRP rods is too conservative or evaluating the shear capacity o internal CFRP grids. Moreover, rom this point o view, the reinorcing eectiveness o the internal FRP grid might be better than that o the internal FRP rods. Nevertheless, the eiciency o the 389

14 internal grid system might be inerior to the internal FRP rod system when considering the conining eect. Unlike the lat shape o FRP grids in this study, conventional steel stirrups and internal FRP rods have always been bent to enclose concrete core resulting in a better conining eect in a seismic event. To solve this, 3-D cages o FRP grid that are analogous to the steel reinorcement cages may be a good choice or the development o concrete beams reinorcened with FRP grids in shear. This type o material is produced by the FRP grid called as NEFMAC in the market 21). Apart rom the internal FRP reinorcement, the eectiveness o the internal grid system is also compared with the externally bonded FRP sheet system which is well-known or retroitting deteriorated concrete structures. JSCE has proposed the equation or estimating the shear capacity o the strengthening FRP sheets as ollows: V d K A sin cos / s z (9) JSCE u K JSCE R (1) u R ;.5 2. ' E R (11) E c where K JSCE is the shear reinorcing eiciency o continuous iber sheets; A is the total cross-sectional area o continuous iber sheets in space s (mm 2 ); s is the spacing o continuous iber sheet (mm); u is the tensile strength o continuous iber sheet (N/mm 2 ); E is the modulus o elasticity o continuous iber sheet (kn/mm 2 ); ʹc is the compressive strength o concrete (N/mm 2 ); α is the angle ormed by continuous iber sheet about the member axis; and z is the distance between the horizontal compression and tension members (mm) [z = (7/8)d]. It can be seen rom Eq. (9) that the composition o equation rom JSCE is also not ar rom the 45º truss analogy method. However, instead o limiting the strain value o FRP, the ultimate tensile strength o FRP sheet has been multiplied by the reinorcing eiciency (K JSCE ) which can be assessed by Eq. (1). It is assumed that the same size o RC beams is externally bonded by CFRP sheets with the same reinorcement ratio, the same tensile property o FRP and the same compressive strength o concrete as the experiments in this study. Thus, the K JSCE rom Eq. (1) and the shear carried by FRP rom Eq. (9) can be obtained as presented in Table 3. The comparison implies that the reinorcing eiciency o the internal grid seems to be much smaller than that o the external FRP sheet when a number o 1 FRPs is provided in the shear span as ound in C-7 or C-14. However, the eiciency rom the two systems has a little dierence when RC beams are reinorced with a limited amount o FRPs near the center o the shear span as observed in C-5 and C-6. Moreover, the internal system becomes much more eective than the external system in C-2 where the specimen is reinorced by a very small amount o FRPs at the center o the shear span. However, it should be noted that both o the equations recommended by JSCE are based on the assumption that the reinorcing/strengthening FRPs have been provided or the whole shear span o concrete beams and the shear capacity obtained rom each FRP strip is assumed to be equaled. The inluence o the location o FRP in the shear span as studied in this paper has not been concerned in their equations yet. Hence, it is quite unair to compare the eectiveness o each FRP rom each system except those FRPs in specimens C-7 and C-14 in which the reinorcing grids have been provided or the whole shear span. 6. CONCLUSIONS The new reinorcing system o concrete beams by internal CFRP grid in lexure and shear was studied. Based on the experimental and calculated investigations, the ollowing conclusions can be drawn: 1) The new alternative reinorcement by internal CFRP grid system was conirmed to enhance the perormance o concrete elements both in lexure and shear. The reinorcing grids started their tensile-resisting ability ater the occurrence o lexure crack in the lexure test and ater the diagonal shear crack in the shear test. 2) From the elementary test, since a good reinorcing eiciency o the internal grids was obtained and the actual tensile strength o the grids was not ar rom its ultimate strength, it is reasonable to apply this system or reinorcing concrete beams. 3) In the shear reinorcing system, the location o internal grid in the shear span o concrete beams is very important. The more number o grid strips at the center o the shear span, the more eective it is in resisting the propagation o the diagonal shear crack, resulting in a higher shear capacity o the beams. In act, the shear resisting eectiveness o the grids became smaller when the grid strips were ully provided or the whole shear span. 4) With the same spacing o CFRP grids, a greater amount o the internal reinorcing grids in the 39

15 shear span o concrete beams can lead to a higher shear carried by internal grid (V g ) and also a higher total shear capacity (V exp ). However, the increment o V g is not proportional to the number o grid strips because each strip o the grids does not equally resist the shear orce. 5) A model considering the inluence o the location o CFRP grid in the shear span is reasonable to evaluate the shear capacity o the internal CFRP grid. The average o the values between experimental results and calculated results was.95 and the coeicient o variation was 13.3%. ACKNOWLEDGMENT: The authors would like to acknowledge Nippon Steel & Sumikin Materials Co., Ltd. or providing the CFRP grids used in this study. REFERENCES 1) Nguyen, T. T. D., Matsumoto, K., Sato, Y., Iwasaki, A., Tsutsumi, T. and Niwa, J. : Eects o externally bonded CFRP sheets on lexural strengthening o pretensioned prestressed concrete beams having ruptured strands, Journal o Japan Society o Civil Engineers (Materials, Concrete Structures & Pavements), Vol. 2, No. 1, pp , ) Zhang, Z. and Hsu, C. : Shear strengthening o reinorced concrete beams using carbon iber reinorced polymer laminates, Journal o Composites or Construction, Vol. 9, No. 2, pp , 25. 3) Triantaillou, T. C. and Papanicolaou, C. G. : Shear strengthening o reinorced concrete members with textile reinorced mortar (TRM) jackets, RILEM, Materials and Structures, Vol. 39, Issue 1, pp , 26. 4) De Caso y Basalo, F., Matta, F. and Nanni, A. : Fiber reinorced cementitious matrix composites or inrastructure rehabilitation, Composites & Polycon, American Composites Manuacturers Association, Tampa, 29. 5) Brückner, A., Ortlepp, R. and Curbach, M. : Anchoring o shear strengthening or T-beams made o textile reinorced concrete (TRC), RILEM, Materials and Structures, Vol. 41, Issue 2, pp , 28. 6) Weiland, S., Ortlepp, R. and Curbach, M. : Strengthening o pre-deormed slabs with textile reinorced concrete, Proceedings o the 2 nd ib-congress, Università di Napoli Federico II, Naples, 26. 7) Larbi, A. S., Contamine, R., Ferrier, E. and Hamelin, P. : Shear strengthening o RC beams with textile reinorced concrete (TRC) plate, Elsevier, Construction and Building Materials, Vol. 24, Issue 1, pp , 21. 8) Papanicolaou, C. G. and Papantoniou, I. C. : Mechanical behavior o textile reinorced concrete (TRC) / concrete composite elements, Journal o Advanced Concrete Technology, Japan Concrete Institute, Vol. 8, No. 1, 21. 9) Brückner, A., Ortlepp, R. and Curbach, M. : Textile reinorced concrete or strengthening in bending and shear, RILEM, Materials and Structures, Vol. 39, 26. 1) Kim, D. J., Kim, M. S., Choi, J., Kim, H., Scanlon, A. and Lee, Y. H. : Concrete beams with iber-reinorced polymer shear reinorcement, ACI Structural Journal, Vol. 111, No. 4, pp , ) Li, H. and Xu, S. : Sel-compacting concrete or textile-reinorced elements, First International Symposium on Design, Perormance and Use o Sel-Consolidating Concrete (SCC 25), Changsha, Hunan, China, ) Japan Society o Civil Engineers (JSCE) : Test method or tensile properties o continuous iber reinorcing materials, JSCE-E 531, 21. (in Japanese) 13) Wight, J. K. and Macgregor, J. G. : Reinorced Concrete : Mechanics and Design (6 th Edition), New Jersey, Pearson Education, ) Niwa, J., Yamada, K., Yokozawa, K. and Okamura, H. : Revaluation o the equation or shear strength o reinorced concrete beams without web reinorcement, Concrete Library o JSCE, No. 9, ) Suwanpanjasil, S., Matsumoto, K. and Niwa, J. : A new alternative shear improvement o concrete beams by internally reinorcing PBO iber mesh, Journal o Japan Society o Civil Engineers (Materials, Concrete Structures & Pavements), Vol. 3, No. 1, pp. 67-8, ) Dutta, P. K., Bailey, D. M., Tsai, S. W., Jensen, D. W. and Hayes Jr, J. R. : Composite grids or reinorcement o concrete structures, No. CERL-TR-98/81, Construction Engineering Research Lab (Army), ) El-Sayed, K., El-Salakawy, E. F. and Benmokrane, B. : Shear capacity o high-strength concrete beams reinorced with FRP bars, ACI Structural Journal, Vol. 13, No. 3, pp , ) Sundarraja, M. C. and Rajamohan, S. : Strengthening o RC beams in shear using GFRP inclined strips an experimental study, Construction and Building Materials, Vol. 23, No. 2, pp , ) Japan Society o Civil Engineers (JSCE) : Recommendations or design and construction o concrete structures using continuous iber reinorcing materials, Concrete Engineering Series, No. 23, JSCE, Tokyo, ) Japan Society o Civil Engineers (JSCE) : Recommendations or upgrading o concrete structures with use o continuous iber sheets, Concrete Engineering Series, No. 41, JSCE, Tokyo, ) Wilkins, D. J., Ashizawa, M., DeVault, J. B., Gill, D. R. and Karbhari, V. M. : Advanced manuacturing technology or polymer composite structures in Japan, Japanese Technology Evaluation Center Baltimore MD, (Received March 1, 216) 391