Shear Strength of GFRP RC Beams and Slabs

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1 Shear Strength o GFRP RC Beams and Slabs T. Alkhrdaji, M. Wideman, A. Belarbi, & A. Nanni Department o Civil Engineering, University o Missouri-Rolla, Missouri, USA ABSTRACT: ACI Committee 440 has proposed a new shear design approach or concrete members reinorced with iber reinorced polymer (FRP) reinorcement that accounts or the amount and stiness o FRP reinorcement. The applicability and limitations or the proposed design approach are not yet ully explored. In addition, the design approach imposes a very conservative strain limit or the FRP stirrups that may results in uneconomical use o the reinorcement. To investigate the proposed equations and their design limitations or shear, our beams reinorced with GFRP stirrups, three beams without stirrups, and six slabs that were designed to ail in shear were tested to ailure as simply supported members. Test results indicated that the contribution o concrete to the internal shear resistance is inluenced by the amount o the longitudinal reinorcement. The proposed ormulae or predicting the shear resistance provided by concrete and GFRP stirrups were ound to be overly conservative. 1 INTRODUCTION Previous research indicated that FRP reinorced concrete (RC) lexural members designed or ailure controlled by rupture o the FRP reinorcement (tension-controlled ailure) have lower shear strength than steel RC members with equivalent lexural strength. To this eect, researches have proposed that design criteria or shear should account or the lower stiness o the FRP reinorcement (Nagasaka et al. 1993, Sonobe et al. 1997, Michaluk et al. 1998). In many cases, the design o FRP RC lexural member is governed by serviceability requirements, which results in lexural reinorcement amount beyond that needed to achieve the desired strength. For these members, the improved lexural behavior (e.g., strength and crack width) results in an improved internal shear resistance mechanism. This is also true or steel reinorced lexural sections where recent studied indicated that c is inluenced by the ratio o lexural steel reinorcement and that or longitudinal steel reinorcement ratio ρ s less than ' the ACI equation o c bd or c could be unconservative (ACI-ASCE Committee 426, 1978). Thereore, a shear design approach that does not considers the inluence o both the stiness and amount o longitudinal FRP reinorcement ails to account or the dierent contribution o internal shear resistance and can be, thereore, overly conservative. ACI Committee 440 proposed a new shear design approach in its inal drat that accounts or the amount and stiness o longitudinal FRP reinorcement (ACI 440, 2000). However, the applicability and limitations or the proposed approach are not yet ully explored and it may not be equally applicable to beams and slabs. In addition, the design approach imposes a very conservative strain limit o or the design o FRP stirrups that usually results in an uneconomical use o the reinorcement. This paper presents the results o an experimental program aimed at producing additional data to examine the shear perormance o RC members reinorced or shear and/or lexure using GFRP bars. GFRP bars are the most common type o FRP reinorcement due to their lower price, and have been used in a large number o projects worldwide and been thereore considered or this investigation. 1.1 Shear Strength o FRP Reinorced Members For FRP RC lexural members without shear reinorcement, it was proposed that the internal shear resistance c, is a unction o the stiness o longitudinal steel and FRP bars (E s and E ) and can be evaluated as ollows (Michaluk et al., 1998): E c, = c (1) E s 1

2 The lower shear strength o FRP reinorced members could be related to a lower dowel resistance o FRP bars, smaller depth o compression block, and less eective aggregate interlock due to wider cracks. However, Eq. (1) is more appropriate or members lightly reinorced with FRP bars (tensioncontrolled ailure). GFRP bars are commercially available with modulus E that is approximately 20% o the steel modulus. Thereore, when using GFRP bars, the shear strength o the member calculated with Eq. (1) is signiicantly lower than that or steel RC member with similar geometry. The design o GFRP RC lexural member is usually governed by serviceability requirements and results in a GFRP lexural reinorcement beyond that needed to achieve the desired strength. In this case, the ailure is governed by concrete crushing (compression-controlled ailure). This results in a larger concrete compression block at ailure and smaller, more evenly distributed, cracks compared with a tension-controlled member. Due to this behavior, the internal shear resistance mechanism o the member is improved. Thereore, using Eq. (1) may yield a very conservative estimate o the shear strength o the member. A more rational approach could be achieved by accounting or the inluence o the axial stiness o the reinorcement, AE, on the behavior o the member. Following this approach, c, can be expressed in terms o the ratio o the longitudinal FRP reinorcement ρ and steel reinorcement ρ s as ollows (ACI 440, 2000): ρ E c, = c (2) ρses For practical design purposes the value o ρ s is taken as hal the maximum reinorcement ratio allowed by ACI 318 or 0.375ρ b. Using this approach, the ACI Committee 440 drat document gives the shear strength equation as ollows: ρ E c, = c (3) 90β1 ' c Eq. (3) is more appropriate or beams, where the steel reinorcement is typically in the neighborhood o 0.375ρ b. Based on the ACI 318 approach, the thickness o a RC slab is chosen so that delections will not be a problem. The desired lexural capacity is achieved by back-calculating the required amount o steel reinorcement, which may be governed by the code- speciied minimum amount o reinorcement to control cracking. Occasionally, the thickness will be governed by shear or lexure. Following this approach, the ratio o steel reinorcement o slabs could be signiicantly lower than that or beams. Accordingly, using Eq. (3) that considers a steel reinorcement ratio o 0.375ρ b or beams to predict the shear strength o FRP RC slabs could be overly conservative and may unnecessarily result in a need or increased depth o the slab to meet the shear requirement. The proposed ACI 440 s design equation to determine the shear contribution o FRP stirrups is identical to that used or steel stirrups, as ollows: Av vd = (4) s The design strength o FRP stirrups v is based on a strain o (stress o 0.002E ). This stress level must be equal to or lower than the tensile stress in the bend portion o the stirrup, b, which rarely controls the design. The strain limit was imposed to control the crack width and thereore ensure a better aggregate interlock. Accounting or the axial stiness o longitudinal reinorcement and imposing a strain limit on the transverse reinorcement penalizes the shear strength o a member twice or the same reason and ultimately results in an uneconomical use o the reinorcement. In addition, FRP bars do not corrode; thereore a strain limit o could be relaxed. Summing the shear contribution o the concrete and the stirrups gives the nominal shear, as ollows: = + (5) n c 1.2 Objectives o the research program The objective o this research program is to veriy the shear design approach and limits proposed by ACI committee 440H. In this paper, the ollowing will be addressed: 1) the contribution o c and to the shear strength o the member, 2) the inluence o the axial stiness AE o longitudinal reinorcement on c, 3) the strain limit or design o GFRP stirrups and 4) applicability o the proposed design approach to GFRP RC beams and slabs. 2 EXPERIMENTAL PROGRAM In total, seven beams and six slabs were tested to 2

3 investigate the shear perormance. Table 1 gives the dimensions and reinorcement or all specimens. Table 2 gives the properties o the constituent material. All specimens were designed to ail in shear. All beams had a cross-section o 178 mm (width) by 330 mm (height) and were 2.4 m. Although the test span envisioned or this test was 1.5 m, the beams were cast with 2.4 m length to ensure that suicient development length is provided or the longitudinal reinorcement. The depth to the centroid o the longitudinal reinorcement varied depending on their layout. All the beams were reinorced with longitudinal GFRP bars. Four beams (BM1, BM2, BM5 and BM6) were reinorced with GFRP stirrups (see Table 1). The stirrups were closed stirrups with 90 deg bents, were made o φ9.5 deormed GFRP, and had a bent radius o 19 mm, as shown in Figure 1. All the stirrups or these beams were pre-bend to speciication by the FRP manuacturer. Slabs SB 2, SB4 and SB5 had a cross-section o 460 mm (width) by 100 mm (height) while slabs SG1, SG2, and SG3 had a cross-section o 460 mm (width) by 150 mm (height). All the slabs were 2.7 m and were tested with a span o 2.1 m. The eective depth or test specimens depends on the size and layout o the reinorcement Test Setup and Instrumentation All beam specimens were tested as simply supported members subjected to a three-point load as illustrated in Figure 2. The irst beam was tested with a span o six eet. The rest o the beams were tested with a span o 1.5 m. All slab specimens were tested as simply supported beams with a span o 2.1 m and subjected to a our-point load, as shown in Figure 3. The distance between the two point loads was 0.6 m, as illustrated in Figure 3. Linear variable dierential transormers (LDTs) were used to measure the vertical displacement at mid-span and quarter-span o each specimen. Strain gages were attached to GFRP and steel longitudinal bars at mid-span and quarter-points. In the beams, at least two stirrups were instrumented with strain gages. The strain gages were attached on vertical legs, close to the bent, and at mid-height o the vertical legs. A 440-kN (beams) or a 270-kN (slabs) load cell was used to measure the applied load. measurements o applied load, longitudinal and shear reinorcement strains, delection, and crack widths. Table 1. Reinorcement type and amount. Longitudinal Beam Type A d (mm 2 ) (mm) Transverse ρ /ρ b Type A v (mm 2 ) BM1 GFRP GFRP Spacing (mm) BM2 GFRP GFRP BM5 GFRP GFRP BM6 GFRP GFRP BM7 GFRP BM8 GFRP BM9 GFRP SB2 GFRP SB4 GFRP SB5 GFRP SG1 GFRP SG2 GFRP SG3 GFRP Table 2. Material properties. Longitudinal. Transverse. Beam ' c Type (MPa) u (MPa) E (GPa) Type u E (MPa) (GPa) BM GFRP GFRP BM GFRP GFRP BM GFRP GFRP BM GFRP GFRP BM GFRP BM GFRP BM GFRP SB GFRP SB GFRP SB GFRP SG GFRP SG GFRP SG GFRP Test Procedure The data acquired or each test included 3

cycle, the load was slowly increased until the target load was achieved. At this stage, the crack widths were measured. This process was continued until ailure was achieved. 3 EXPERIMENTAL RESULTS 3.

At approximately 53 to 71 kn, lexural cracks were observed. As the load was increased, some o the cracks started to extend at 45 degree to orm shear cracks.

This was immediately ollowed by a sudden shear ailure due to rupture o at least one o the GFRP stirrups crossing a diagonal crack.

4 cycle, the load was slowly increased until the target load was achieved. At this stage, the crack widths were measured. This process was continued until ailure was achieved. 3 EXPERIMENTAL RESULTS 3.1 Beams Figure 1: GFRP stirrups. Figure 2: Beam test setup. Figure 3: Slab test setup. Each test specimen was tested under quasi-static load that was applied in several cycles. In each Beams with shear reinorcement For beams BM1, BM3, BM4, and BM5, ailure was a combination o lexure and shear. At approximately 53 to 71 kn, lexural cracks were observed. As the load was increased, some o the cracks started to extend at 45 degree to orm shear cracks. At maximum load, concrete crushing at the top was observed, indicating lexural ailure. This was immediately ollowed by a sudden shear ailure due to rupture o at least one o the GFRP stirrups crossing a diagonal crack. For all the cases, when the concrete cover was removed, rupture o the GFRP stirrup was observed at the bent o the stirrup, as shown in Figure 4. However, although in a lexural mode, the ailure load or these beams was higher than that predicted based on the theoretical shear capacity (see Table 3). For beam BM2, the irst lexural crack was observed at approximately 62 kn. The crack on the let side o the beam started to extend diagonally to orm a shear crack. This was ollowed by a number o smaller lexural and shear cracks. Failure o beam BM2 occurred at approximately 258 kn and was initiated by rupture o one o GFRP stirrup crossing the irst diagonal crack, as shown in Figure 5. Beam BM6 ailed in lexural mode at approximately 289 kn. No rupture o GFRP stirrups was observed when the concrete cover was removed. Table 3 presents comparison o the theoretical and experimental results or the beams. Three theoretical values or shear ailure were calculated, P 0.002, P and P bent based on a GFRP strain limit o 0.002, 0.004, and the strength o the bent portion o the stirrups,,b, respectively. The concrete contribution c, was calculated using ACI 440 s proposed equation, Eq. (3). The theoretical load capacities based on these three limits were calculated as ollows: = 2( ) (6) P0.002 c, P (c, Pbent 2(c, + bent) = ) (7) = (8) 4

Failure loads based on the lexural capacity o each beam P lex were also calculated. In Table 3, it can be seen that the experimental loads P exp exceeded those based on a 0.002 strain limit P 0.

97, indicating that the design approach based on this strain limit is overly conservative and that it may underestimate the shear strength by approximately 50 percent.

5 Failure loads based on the lexural capacity o each beam P lex were also calculated. In Table 3, it can be seen that the experimental loads P exp exceeded those based on a strain limit P or all the specimens. The average o P exp /P was 1.97, indicating that the design approach based on this strain limit is overly conservative and that it may underestimate the shear strength by approximately 50 percent. For all the beam specimens, the experimental results P exp were also larger than those based on strain limit P 0.004, and the average P exp /P was These results indicate that the strain limit is more appropriate and can better utilize the contribution o GFRP stirrups while maintaining a conservative design approach. The experimental ailure loads or beam BM2, the only beam to ail in shear, was smaller than that based on the strength o the bent o the GFRP stirrups P bent. A ratio o P exp /P bent o 0.85 was calculated or beam BM2. This indicates that the stirrups did not achieve the theoretical bent strength at ailure. It should be noted that, due to the ailure mode o these specimens, the actual shear strength o the beams was not determined. The experimental loads at ailure P exp o beams BM1, BM5 and BM6 compared well with their lexural capacity P lex calculated using the approach o ACI 440. The average o P exp /P lex or these beams was Figure 4: Rupture o GFRP stirrups Figure 5: Shear ailure (BM2). Table 3: Comparison o theoretical and experimental results. Analytical Experimental Beam P P P bent P lexure Exp. Failure (kn) (kn) (kn) (kn) (kn) BM Flex/S BM Shear BM Flex/S BM Flex/S Figure 6 shows a breakdown o the measured internal shear resistance or beam BM2 that ailed in shear mode. In this igure, experimental values o were calculated using the measured strain o GFRP stirrups. The strain measurements were obtained rom the strain gage located at the bent o the ruptured stirrups. As shown in this igure, prior to cracking, the internal shear resistance was provided by the solid beam section. Once the beam cracked, the shear stirrups started to pick up strain, indicating a shear resistance contribution by the stirrups. The shear resistance provided by the concrete c, ater cracking was slightly lower that that o the solid section prior to cracking. However, as the load was increased, the c, also increased and the value o the internal shear resistance provided by concrete at ailure was slightly larger than that o the solid section Beams without shear reinorcement Beams BM7 through BM9 (no shear reinorcement) ailed in shear, as given in Table 5. The test results o these beams show that the current design approach is very conservative. The average ratio o 5

6 experimental to theoretical ailure load P exp /P theo. was Figure 7 show that increasing the amount o longitudinal reinorcement signiicantly increased the shear strength o the beams. Figure 8 shows the relation between c, exp / 440 ratio and the ratio o the GFRP reinorcement to the balanced ratio o reinorcement, ρ /ρ,b., calculated per ACI 440. In this igure, it can be seen that the relationship between the two ratios is non-linear and that as the ratio o ρ /ρ,b increased, the ratio o c, exp / 440 reduced. P exp /2 (kn) Shear (kn) Figure 6: Components o internal shear resistance or (BM2). Table 5: Comparison o Beam Results (w/o stirrups). Theoretical Experimental Beam P 440 P lex. P exp. Failure P exp / P theo. (kn) (kn) (kn) BM Shear 2.66 c, BM Shear 5.18 BM Shear 3.31 Experimental Shear Strength (kn) Reinocement Ratio ρ Figure 7: Comparison o results or beams w/o stirrups. c, exp / c, ρ / ρ,b Figure 8: Comparison o results or beams w/o stirrups. 3.2 Slabs Table 6 shows a comparison o the predicted and the experimental loads at ailure o the slabs. All the slabs ailed in lexure at a load higher that predicted based on shear ailure per ACI 440. In Table 6, the theoretical ailure load values P 440 were based on the design approach o ACI 440, Eq. (3). The values o P 440 /P theo or these test varied rom 1.58 to 3.21 with an average o 2.24, indicating that the proposed design approach or GFRP RC slabs is very conservative. Table 6: Comparison o Slab Results (kips). Theoretical Beam P theo P lex. P exp Failure P exp /P theo (kn) (kn) (kn) SB Flexure 2.34 SB Flexure 1.54 SB Flexure 1.58 SG Flexure 3.21 SG Flexure 2.68 SG Flexure SUMMARY AND CONCLUSIONS The shear perormance o seven beams and six slabs reinorced with dierent amounts o longitudinal and transverse GFRP reinorcement was investigated. The objective was to examine shear design approach o ACI 440 and to produce additional data to examine the shear perormance o RC members reinorced or shear and/or lexure using GFRP bars. 6

7 GFRP bars are the most common type o FRP reinorcement and have been thereore considered or this investigation. All specimens were designed to ail in shear. Based on the test results presented in this paper or the beams and slabs with the given geometry and material properties, the ollowing conclusions can be drawn: Except or beam BM2, all the beams with shear reinorcement ailed in a lexure-shear mode. Their actual shear strength was not determined. The lexure-shear ailure mode started as lexural ailure that was ollowed by shear ailure due to GFRP stirrup rupture that was caused by the loss o the internal shear resistance provided by the compression concrete, which led to ailure o the stirrup due to overloading. Beam B2 ailed in shear mode by rupture o a GFRP stirrup at the bent. The measured stress at ailure was below the strength o the bent, b. Independent o the ailure mode, all test specimens ailed at a load signiicantly higher than that predicted using the approach by ACI 440. The strain limit o or the design o GFRP stirrups is very conservative and could be relaxed to while maintaining a reasonably conservative design. The design approach proposed by ACI 440 or the shear strength c, o GFRP RC lexural members in which the ailure mode is governed by concrete crushing (compression-controlled) is overly conservative. The experimental shear strength o the beams with no stirrups c, was proportional to the amount o longitudinal GFRP reinorcement. As the amount o GFRP reinorcement increased, the experimental shear strength increased. Due to the lexural ailure mode, actual shear strength o the slabs could not be determined. However, it can conservatively be said that or over-reinorced slabs with ρ /ρ b larger than 2, the actual shear strength o the slab can be at least 1.5 times higher than that predicted using the ACI 440 design approach. The lexural capacity o all test specimens compared well with the predicted values using the approach o ACI ACKNOWLEDGMENTS This research program is being unded by the Industry/University National Science Foundation (NSF) research center at the University o Missouri- Rolla. REFERENCES ACI Committee Building Code Requirements or Structural Concrete (ACI ) and Commentary (ACI 318R-95). American Concrete Institute, Farmington Hills, Michigan, USA. 369 pp. ACI Committee Guide or the Design and Construction o Concrete Reinorced with FRP Bars. Final Drat (in print). ACI-ASCE Committee Suggested Revisions to Shear Provisions or Building Codes. American Concrete Institute, Farmington Hills, Michigan, USA. 88 PP. Nagasaka, T., Fukuyama, H., & Tanigaki, M Shear Perormance o Concrete Beams Reinorced with FRP Stirrups. Fiber-Reinorced-Plastic Reinorcement or Concrete Structures. SP-138. American Concrete Institute. Farmington Hills, Michigan, USA Michaluk, C.R., Rizkalla, S., Tadros, G., & Benmokrane, B Flexural Behavior o One-Way Concrete Slabs Reinorced by Fiber Reinorced Plastic Reinorcement. Structural Journal 95(3): Sonobe, Y., Fukuyama, H., Okamoto, T., Kani, N., Kimura, K., Kobayashi, K., Masuda, Y., Matsuzaki, Y., Mochizuki, S., Nagasaka, T., Shimizu, A., Tanano, H., Tanigaki, M., and Teshigawara, M Design Guidelines o FRP Reinorced Concrete Building Structures. Journal o Composites or Construction 1(3):

Chidananda S. H, Khadiranaikar R. B., International Journal of Advance Research, Ideas and Innovations in Technology. 1.

Chidananda S. H, Khadiranaikar R. B., International Journal o Advance Research, Ideas and Innovations in ISSN: 2454-132X Impact actor: 4.295 (Volume3, Issue5) Available online at www.ijariit.com Flexural