Efficient near surface mounted CFRP shear strengthening of high strength prestressed concrete beams – An experimental study

Composite Structures 180 (2017) 16–28

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Efficient near surface mounted CFRP shear strengthening of high strength prestressed concrete beams – An experimental study Vikas Singh Kuntal ⇑, Maheswaran Chellapandian, Shanmugam Suriya Prakash Department of Civil Engineering, Indian Institute of Technology Hyderabad, India

a r t i c l e

i n f o

Article history: Received 29 May 2017 Accepted 30 July 2017 Available online 1 August 2017 Keywords: CFRP laminates Prestressed concrete beams Near surface mounting Shear strengthening

a b s t r a c t Shear behavior of prestressed concrete members and its strengthening is complex due to its brittle nature of failure and a number of variables affecting its behavior. The main goal of this investigation is to assess the efficiency of different near surface mounted (NSM) strengthening configurations using CFRP (Carbon Fiber Reinforced Polymer) laminates on the shear behavior of prestressed concrete beams. The parameters considered in this study are (i) the presence of vertical stirrups and (ii) different NSM FRP shear strengthening configurations. Twelve prestressed concrete beams with and without vertical stirrups were cast and strengthened using different NSM CFRP configurations and tested under shear. All the beams were tested under three point bending at a shear span to depth (a/d) ratio of 2.5 to simulate the shear dominant behavior. Test results revealed that NSM strengthening of prestressed concrete beams using CFRP laminates at 45° was more efficient in improving the shear capacity of beams with and without vertical stirrups. It was also observed that the shear mode of failure could be converted to the flexural mode with improved ductility by designing a suitable NSM shear-strengthening scheme. Shear strength calculations of NSM strengthened beams were made using ACI codes and other analytical models. ACI calculations were found to be conservative in estimating the shear contribution of NSM laminates. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Prestressed concrete (PSC) members have gained prominence in the modern construction of buildings and bridges due to their various advantages including superior performance under serviceable conditions. Understanding the shear behavior of prestressed concrete members is still a challenge as numerous variables affect its behavior and due to its brittle mode of failure. Shear strengthening of prestressed concrete members may be required due to various reasons such as (i) change in loading, (ii) change in the usage of structural system (iii) additional load carrying capacity required due to the existing damage and (iv) corrosion of strands leading to a loss in prestressing force. Fiber reinforced polymer (FRP) composite strengthening has gained importance in the recent decades due to its various advantages. It can effectively overcome the limitations of conventional strengthening techniques such as steel jacketing and concrete enlargement [1]. Various strengthening techniques like External Bonding (EB) of FRP fabric/laminates, Near Surface Mounting (NSM) of FRP laminates/bars, and external

⇑ Corresponding author. E-mail addresses: [email protected] (V.S. Kuntal), ce15resch11005@ iith.ac.in (M. Chellapandian), [email protected] (S.S. Prakash). http://dx.doi.org/10.1016/j.compstruct.2017.07.095 0263-8223/Ó 2017 Elsevier Ltd. All rights reserved.

confinement (EC) using FRP sheets have been used in the past to successfully strengthen the deficient beams [1–6]. These studies have shown that the improvement in the behavior of prestressed concrete members due to FRP strengthening mainly depends on (i) strengthening configurations and (ii) material properties including elastic modulus of FRP material, area of FRP laminates/bars, and (iii) properties of adhesive. Many investigations have been carried out on the shear behavior of RC beams strengthened using FRP composites [7–11]. Most of these studies have focused primarily on externally bonded shear strengthening using FRP fabrics. The failure mode of RC beams strengthened using CFRP bars is governed by the formation of diagonal shear crack with the final failure occurring due to spalling of concrete cover [8]. Researchers have concluded that the external bonding of CFRP fabric in the shear zone of RC beams resulted in an increase of shear capacity with the crack pattern modified from shear to combined flexure-shear [9]. The spacing of externally bonded CFRP strips played a key role in the shear strengthening of beams [12]. Rizzo and De Lorenzis [13] studied the efficiency of FRP shear strengthening and concluded that decreasing the spacing of CFRP strips resulted in a decrease in shear capacity of reinforced concrete beams due to interaction failure with the adjacent FRP laminates. In another study, it has been observed that

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Nomenclature

ACI equation cross sectional area of FRP laminate Afv width of the beam bw, b D overall depth of the beam D effective depth of the beam dfv effective depth of FRP shear reinforcement distance of extreme compression fiber from centroid of dp prestressing strand Ef modulus of elasticity for FRP laminates compressive stress in concrete due to prestress fpe fd stress due to unfactored dead load ffe effective stress in FRP reinforcement corresponding to effective strain Mcre cracking moment of section Mmax maximum moment at selected section n number of plies of FRP reinforcement sf spacing of FRP reinforcement thickness of FRP laminates tf Vd shear force due to dead load Vf contribution to shear strength by FRP reinforcement Vi shear force at selected section width of FRP laminates wf yt distance of centroidal axis of gross-section efe effective strain in FRP reinforcement k modification factor

presence of vertical steel stirrups greatly helps in enhancing the shear capacity and reducing the width of larger diagonal cracks [14]. NSM shear strengthening can reduce the possibility of debonding failure and can lead to improved shear performance. However, review of literature clearly indicates that only handful of studies have focused on NSM shear strengthening of high strength PSC beams [15–19] and is the focus of this investigation. Recently, NSM shear strengthening of RC beams using prestressed CFRP laminates has been carried out [15]. The authors have found that prestressing could improve the peak strength by more than 15% when compared to non-prestressed laminates. Embedding through section (ETS) is a recent technique of using FRP rods to retrofit the beams under shear. Chaallaal et al. [16] concluded that ETS technique can improve the shear capacity by more than 50% and can convert the failure into flexure mode. Shear strengthening of PSC beams using segmental FRP wrapping technique has also been conducted [17]. The authors found that the U-shaped CFRP sheets were effective when the spacing between them is less than half of their effective depth [17]. Previous studies have also shown that the externally bonded systems are prone to debonding failure mode [16–19]. 2. Motivation and objectives The behavior of PSC beams shear strengthened using NSM CFRP laminates can greatly enhance the shear capacity of beams without compromising much of its ductility. However, the review of studies carried out in the past clearly indicates a lack of thorough investigation on the NSM shear strengthening of PSC beams with stirrup reinforcement. In order to fill this existing knowledge gap and to provide a better understanding of the behavior of PSC beams with and without vertical stirrups, an experimental study on shear strengthening using NSM CFRP laminates is carried out. The results

Nanni et af, bf c Ltotmin leff lmax lnet

sb

hf

al.’s equation for Vf dimensions of FRP laminate cross section clear cover of concrete total length of all FRP laminates transferring strength to shear crack of 45 degrees vertical projection of lnet maximum length from single FRP laminate that can transfer strength to crack of 45 degrees net length of FRP laminate, to account for crack in concrete cover and installation tolerances effective bond stress between FRP and concrete Inclination of CFRP laminates with respect to horizontal axis

Dias and Barros equation for Vf Es modulus of elasticity for steel fcm mean compressive strength of cylinders height of web of beam or height of beam in case of recthw angular section qf ratio of cross-sectional area of FRP laminates to that of beam qsw ratio of cross-sectional area of vertical stirrups to that of concrete

from this study can help in understanding the efficiency of NSM FRP strengthening schemes in improving the strength, stiffness, and failure mode of PSC beams. 3. Experimental program 3.1. Specimen preparation Twelve Pre-tensioned Prestressed Concrete Beams (PPSC) were cast with and without stirrups to investigate the efficiency of various NSM FRP strengthening configurations. Six of the twelve beams had no vertical stirrups while the remaining had stirrups. All the beams had a rectangular cross section of 150 mm
300 mm. The length of the beams was 1800 mm where the distance between the support beams was kept as 1650 mm. The details of the test specimen and the strengthening configuration are given in Table.1. 3.2. Material properties 3.2.1. Concrete All the high-strength prestressed concrete beams were cast at a precast plant using pre-tensioning process. Concrete mix was designed as per IS 10262 [20] with a target mean strength of 55 MPa. The strands were cut and the prestressing force was transferred to the concrete after seven days of casting. The maximum compressive stress applied on concrete due to prestress was 13.3 MPa. The beams were transferred to the curing yard and water cured for a period of 28 days to facilitate hydration process. During the casting process, cubes and cylinders were also cast to study the stress-strain behavior of concrete under compression. The average cube and cylinder compressive strength of concrete at 28 days was found to be 65 MPa and 52 MPa respectively (see Table 1).

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Table 1 Details of Test Specimens and NSM Strengthening Configuration. Specimen Designation

C C + N90° C + N45° C+S C + S + N90° C + S + N45°

Details of Cross Section b (mm)

D (mm)

150

30o0

Number of Specimens

Presence of Stirrups

Shear Strengthening Details

Orientation of CFRP Laminates

2 2 2 2 2 2

No

No Strengthening 20 mm x 1.4 mm CFRP 20 mm x 1.4 mm CFRP No Strengthening 20 mm x 1.4 mm CFRP 20 mm x 1.4 mm CFRP

– 90° 45° – 90° 45°

Yes

laminates laminates laminates laminates

**Note: C-Control Beam, S-Stirrups, N90°- NSM laminates at 90 degrees; N45°- NSM laminates at 45 degrees.

3.2.2. Reinforcing steel and prestressed tendons Two numbers of seven-wire strands, each of 12.7 mm diameter and 98.7 mm2 area, are used for prestressing the beams. The force transferred through the tendons of beams during jacking process was 100 kN corresponding to a stress of 1013 MPa. This amounts to 54.5% of ultimate strength (fpu) of strands. Coupon specimens of tendons were tested to determine the average ultimate tensile strength and modulus of elasticity. The values obtained for ultimate strength and modulus of elasticity were 1860 MPa and 196 GPa, respectively. Steel rebar of 8 mm diameter was used as the vertical stirrup. In order to hold the stirrups in position, two longitudinal bars of 8 mm diameter were provided on the compression side of the specimen. Coupon tests of normal reinforcing steel indicated yield strength of 512 MPa and a rupture strain of 7.8%. 3.2.3. CFRP laminates Carbon FRP laminates of size 20 mm
1.4 mm were used for NSM shear strengthening. Coupons of CFRP laminates were tested in tension using a servo controlled MTS tensile testing machine of 100 kN capacity. The coupons were prepared and tested as per ASTM D3039 [21]. The ultimate tensile strength of FRP laminates was found to be 2300 MPa with the modulus of elasticity and rupture strain of about 150 GPa and 1.3%, respectively. The schematic representation of various NSM strengthening schemes used in this study is shown in Fig. 1(a)–(c). 3.3. NSM CFRP shear strengthening procedure near surface mounted (NSM) CFRP strengthening of PSC beams was carried out as per ACI 440.2R provisions [22]. The detailed systematic procedure followed for NSM strengthening is illustrated in Fig. 2. Grooving was done for dimensions not less than 1.5 times the width and depth of CFRP laminates. The dimensions of the groove were kept at 30 mm
3 mm. All the grooves were cleaned to remove dust particles. Thereafter, a primer coating was applied (Base: Hardener = 2.6: 1) to improve the bonding. After 24 h, epoxy resin (Base: Hardener = 2.7: 1) was applied and the laminates were pressed against the epoxy. After 48 h of air curing, the NSM strengthened PSC beams were tested under shear. 4. Test setup and instrumentation The experimental setup and instrumentation details are shown in Figs. 3 and 4. All the beams were tested in a displacement controlled mode using servo-controlled 250 kN MTS actuator in a closed loop system. The load from the MTS actuator was transferred to the PSC beam with the help of a spreader beam. The loading beam of is placed at a distance of 625 mm (a/d = 2.5) to have a shear dominant failure mode. The loading and support beams had an I-section with the following dimensions: 60 mm flange width, 100 mm overall depth and 5 mm flange and web thickness.

Capping is provided at the bottom of loading beam using high strength cement mortar to avoid surface undulations and for uniform transfer of applied load. All the PSC beams were loaded at a rate of 0.05 mm/s. The loading is paused intermittently at intervals of 10 kN to mark the crack propagation and to observe the failure mechanism while testing. Instrumentations for measuring the data during the loading protocol is carried out with the help of Data Acquisition System (DAQ) connected with Linear Variable Displacement Transducer (LVDT) and strain gauges. A 100 mm LVDT was used to measure the displacement at the point of application of load. In addition, LVDT rosette arrangement was used to measure strains in the principal directions. Moreover, 20 mm LVDTs were placed at the compression and tension side near the loading point to measure the curvature of the beam. Strain gauges of TML make with 120 X resistance were instrumented on the surface of prestressing tendons, stirrups and FRP to measure the strains while testing. 5. Results and discussion 5.1. Load – Displacement behavior of PSC beams without stirrups 5.1.1. Control beams Load –displacement behavior of control beams tested without any vertical stirrups in the shear dominant zone is shown in Fig. 5. The specimens had an average load capacity of 149 kN corresponding to a displacement of 3.31 mm. The beam cracked initially under flexure which later converted into flexure-shear crack. The strain in the prestressing strand increased due to applied shear load. However, the strand strain did not reach its yielding strain at failure. The specimen failed in a brittle mode by the formation of large diagonaltension crack in the shear dominant zone at a displacement of 27.3 mm. All the significant test results of the tested beams are summarized in Table 2. 5.1.2. NSM strengthened beams The load-displacement behavior of PSC beams with NSM shear strengthening using CFRP laminates at 90° orientation is shown in Fig. 6. The elastic behavior of both the specimens was similar. The specimens had an average peak load of 171 kN with a displacement of 3.89 mm. Soon-after reaching the peak load, the shear cracks developed propagated rapidly and the specimens failed in diagonal shear tension mode. The failure displacement of the specimen was 20.6 mm. The improvement in load carrying capacity failure displacement was 15% when compared to the control PSC beams. The specimen had no improvement in ductility and was reduced by 32.5%. The behavior of PSC beams strengthened using CFRP laminates at 45° orientation is depicted in Fig. 7. The specimens developed multiple cracks and attained an average peak load of 224 kN corresponding to a displacement of 25.5 mm. This signifies larger energy dissipation capacity and effectiveness of 45° NSM laminates in

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Fig. 1. Schematic representation of NSM strengthening of PSC beams under shear.

restricting the shear crack propagation. The failure was more flexure dominant and ductile. NSM laminates were effective in capturing the crack propagation and changed the failure mode from shear

to flexure. The improvement in peak load capacity and failure displacement of the specimens with 45° NSM laminates was 52% and 34.4% when compared to the control PSC beams (C).

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Fig. 2. Detailed step by step procedure of NSM CFRP shear strengthening.

Fig. 3. Schematic representation of test setup and instrumentation.

5.2. Load–displacement behavior of PSC beam with shear reinforcement 5.2.1. Control beam with stirrups The load-displacement behavior of PSC beams with shear reinforcement (C + S) is illustrated in Fig. 8. These beams had an average peak load of 213 kN with a corresponding displacement of 13.9 mm. After the peak load, the specimens developed rapid shear cracking and failed under the combined flexure-shear mode. The presence of vertical stirrups helped in converting the brittle shear failure to combined flexure-shear mode. The combined flexureshear mode is denoted here as the failure of the beam by shear tension mode just after the yielding of prestressing strand. The improvement in peak load capacity and failure displacement of the specimen was 45% and 10.3% when compared to control beam without stirrups (C). Though both of the beams had a similar behavior up to peak load, their post-peak behavior was somewhat different. This could be attributed to the difference in cracking pattern and crack propagation. The role of stirrups in improved postpeak behavior was clearly evident. The specimens with stirrups had lesser post-peak strength and stiffness degradation when compared to beams with no stirrups.

5.2.2. NSM strengthened PSC beams The behavior of PSC beam with shear reinforcement and strengthened using NSM laminates at 90° orientation is represented in Fig. 9. The specimen had a peak load of 220 kN with a corresponding displacement of 27.6 mm. The displacement measurement of specimen 2 was not consistent due to instrumentation error and therefore not included in Fig. 9. However, both the beams had similar strength and failure mode. The beams initially cracked in flexure below the loading point. This crack could not propagate and convert to flexure-shear due to the presence of shear reinforcement and NSM laminates. The specimen exhibited a larger displacement with lesser post-peak strength and stiffness degradation. The specimen finally failed under combined flexureshear mode. The improvement in peak load was about 50% when compared to control beams with no improvement in failure displacement. The behavior of PSC beams with shear reinforcement and strengthened with NSM laminates at 45° orientation is represented in Fig. 10. Both the beams had a similar behavior. The specimens had an average peak load of 227 kN corresponding to a displacement of 13.2 mm. The failure occurred at a load of 218 kN after considerable deformation. The shear cracks that originated in the

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Fig. 4. Test setup and instrumentation details for PSC beam under shear.

failure. The percentage improvement in peak load carrying capacity and failure displacement of PSC beams with shear reinforcement strengthened using 45° NSM CFRP laminates was about 54% and 12.5%, respectively when compared to control beams without stirrups (C). 5.3. Overall Comparison of NSM strengthened PSC beams with and without stirrups

Fig. 5. Load - displacement behavior of control PSC beams.

shear zone of the beam were effectively arrested by CFRP laminates oriented at 45°. Due to this, the flexure crack started propagating towards the compression side below the load point. At peak load, the flexure crack started widening and the specimen failed in the flexure dominant behavior. NSM 45° strengthening configuration effectively converted the brittle shear to ductile flexure mode of

The overall comparison of NSM strengthened PSC beams with and without vertical stirrups is shown in Figs. 11 and 12. It could be observed from the figures the variability in behavior is less for beams with stirrups. For the beams without stirrups, NSM strengthening was effective in delaying the sudden shear failure and significantly improved its shear capacity. The NSM strengthening with 45° orientation resulted in the better performance with highest strength increase and ultimate displacement (Fig. 11). It also converted the brittle shear failure mode to ductile flexure mode. In the case of beams with stirrups, the strength increase was not very high due to NSM strengthening (Fig. 12). The strength increase due to 90° and 45° orientations of NSM laminates was respectively, 3.3% and 6.6% when compared to control beams with stirrups (C + S). More importantly, the failure mode of control beams with stirrups did convert from shear dominant to flexureshear mode. The failure mode of strengthened beams was more ductile due to better arresting of shear cracks by stirrups as well as NSM laminates.

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Table 2 Summary of Test Results. Specimen Series

Pre-cracking Stiffness(kN/mm)

Peak

Avg

Peak

Failure

Avg

Peak Load

Failure Mode

Set-I

65.1 73.9 66.7 113.4 66.4 69.9

138 160 161 180 211 238

149

3.56 3.05 4.15 3.63 21.5 29.4

30.1 24.5 17.4 23.8 39.2 34.2

27.3

–

–

Shear

20.6

15

-32.5

Shear

36.7

52

34.4

Flexure

64.7 93.8 111.4 87.9 90.4

212 215 220 226 227

213

11.3 15.8 27.6 13.8 12.6

30.4 29.8 28.0 32.5 28.9

30.1

45

10.3

Flexure + Shear

28.0 30.7

50 54

-2.56 12.5

Flexure + Shear Flexure

C C + N90° C + N45°

Set-II

C+S C + S + N90° C + S + N45°

Load (kN)

Displacement (mm)

171 224

220 227

% Improvement

Failure Disp.

***Note: The percentage improvement in load is calculated with respect to the control beam (C) to show the importance of NSM FRP strengthening with and without stirrups. ***The results of one beam of C + S + N90° series is neglected due to instrumentation error in the measurement of displacement.

Fig. 6. Load - displacement behavior of beams with NSM at 90°.

Fig. 8. Load - displacement behavior of controls PSC beam with stirrups.

Fig. 7. Load - displacement behavior of controls beam with NSM at 45°.

Fig. 9. Load - displacement behavior of PSC beam with stirrups and NSM 90°.

5.4. Crack Patterns and failure mode 5.4.1. PSC beams without shear reinforcement The failure pattern of PSC beams without shear reinforcement strengthened using different NSM configurations is shown in Fig. 13. The control beams without shear reinforcement cracked initially under flexure below the loading point. With the increase

in load levels, shear crack originated in the shear dominant zone. Soon after reaching the peak load, the propagation of shear crack widened and the final failure occurred due to diagonal shear tension. The beams strengthened with NSM 90° laminates initially cracked under flexure. The final failure of these specimens occurred under diagonal shear tension mode. The shear cracks were developed between the NSM CFRP laminates (Fig. 13). The

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Fig. 10. Load - displacement behavior of PSC beam with stirrups and NSM 45°.

23

5.4.2. PSC beams with vertical shear reinforcement The failure pattern of PSC beams with shear reinforcement strengthened using different NSM configurations is shown in Fig. 14. The detailed crack propagation and failure progression at different load levels are shown in Table 4. The beams with shear reinforcement initially cracked under flexure failed in flexureshear mode due to the provision of shear reinforcement. The PSC beams strengthened using 90° NSM configuration cracked initially under flexure which later converted to flexure-shear. The propagation of shear cracks was effectively restrained by the presence of NSM laminates and stirrups. Once the beam reached its peak capacity, the shear crack developed adjacent to the NSM laminates and propagated towards the compression side. Due to the provision of stirrups and NSM laminates, the failure mode changed from brittle to less brittle. The crack width was also found to reduce leading to better aggregate shear interlock and improvement in the overall shear behavior of the beam. The PSC beams strengthened with 45° NSM configuration had first-cracking in flexure. With the increase in applied load, these flexure cracks were converted to flexure-shear cracks, and the increase in their width was better arrested by the laminates leading to flexure dominant failure mode. The beams had predominantly flexure crack and exhibited a better ductility. 5.5. Load – Strain behavior of PSC beams under shear

Fig. 11. Overall load - displacement behavior of PSC beams without stirrups.

The load-strain behavior of prestressed concrete beams with and without strengthening is illustrated in Fig. 15. Since the prestressing strands do not have a well-defined yield point, the yield strain of prestressing strand is assumed 9000 mm/m [5,18]. The initial strain of 4200 mm/m due to prestressing was added to the measurements while obtained during the testing. The control beam without any shear reinforcement had a strain in the strand of about 7500 mm/m. For the beams strengthened with NSM laminates at 90° orientation, the strains in the strands reduced due to additional load resistance offered by the NSM laminates. In the case of NSM strengthening at 45°, FRP laminates were more effectively utilized due to effective arresting of shear crack propagation. In the case of PSC beams with vertical stirrups, the strain in the strand was effectively reduced due to the provision of stirrups in the shear dominant zone. Here again, the NSM strengthening at 45° was found to be more effective in restricting the crack propagation and led to the larger reduction of strain in the strands. 6. Analytical predictions of peak capacity 6.1. ACI 318 and ACI 440 provisions The shear strength of FRP strengthened prestressed concrete beams were calculated as per the provisions of ACI 440.2R [22] and ACI 318.14 [23]. The equations used for calculating the shear capacity of NSM CFRP strengthened prestressed concrete beam is mentioned below and complete details can be found elsewhere [24–25]. The shear capacity (Vci) of the beam will be a minimum value obtained from the Eqs. (1) and (2). The shear contribution of FRP laminates (Vf) can be calculated from Eq. (3). The variables used in the equations are defined in the nomenclature.

Fig. 12. Overall load - displacement behavior of PSC beams with stirrups.

45 °CFRP NSM laminates effectively restrained the shear crack propagation and converted the failure from brittle shear to ductile flexure dominant mode (Fig. 13). The detailed crack propagation and failure progression at different load levels are shown in Table 3.

qffiffiffiffi V i Mcre 0 V ci ¼ 0:05k f c bw dp þ V d þ Mmax where Mcre ¼

ð1Þ

qffiffiffiffi   0 I ð0:5k f c þ f pe  f d Þ. yt

qffiffiffiffi 0 V ci ¼ 0:14k f c bw d

ð2Þ

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Fig. 13. Failure pattern of PSC Beams without Shear Reinforcement.

Table 3 Failure Progression of NSM Strengthened PSC Beams without Shear Reinforcement at Different Load Levels.

Vf ¼

Af v f fe ðsina þ cosaÞdf v sf

0

ð3Þ

Where Af v ¼ 2ntf wf and f fe ¼ efe Ef . In the above equations, k is the modification factor which corresponds to the type of concrete. It is taken as one for the normal

weight concrete used in this study. fc corresponds to the cylinder compressive strength of high strength concrete. The prestress after all losses in the member is denoted as fpc. The strain corresponding to the maximum compressive strain is assumed to be 0.30%. The yield strain of prestressing strand is assumed to be 9000 mm/m. The shear resistance of CFRP laminates (Vf) is calculated based on

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Fig. 14. Failure pattern of PSC beams with shear reinforcement.

Table 4 Failure Progression of NSM Strengthened PSC Beams with Shear Reinforcement at Different Load Levels.

the orientation of NSM FRP laminates. This additional capacity (Vf) is added to the shear resistance of control section to obtain the total shear capacity of FRP strengthened member. The peak load of test results and ACI calculations is reported in Table 5. It is clear from the comparisons that the load predictions from ACI codes [22,23] were conservative and had a reasonable correlation with test results. Various existing analytical equations for the contribu-

tion of FRP shear resistance are available in the literature [24,25]. The efficiency of different models was reviewed by Dias and Barros [24]. They indicated that among all the available models, the equations by Dias and Barros [24], Nanni et al. [25] was found to be more accurate with less than 20% discrepancy. Hence, only these models were used for strength estimations in the following sections.

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Fig. 15. Load–strain behavior of PSC beams with and without Stirrups.

Table 5 Comparison of Peak Shear Strength with Test Results. Specimen ID

Peak Load – Exp. (PEXP) (kN)

Peak Load ACI (PACI) (kN)

Peak Load - Nanni (PN) (kN)

Peak Load – Dias and Barros (PDB) (kN)

(PEXP)/(PACI)

(PEXP)/(PN)

(PEXP)/(PDB)

Controls C + N90° C + N45° C+S C + S + N90° C + S + N45°

150 165 225 213 220 227

125 182 206 198 255 279

125 151 208 213 239 296

125 237 323 198 247 263

1.20 0.91 1.09 1.08 0.86 0.81

1.20 1.10 1.08 1.00 0.92 0.77

1.20 0.70 0.70 1.08 0.89 0.86

***Note: The Peak shear strength of test results are compared with the ACI calculations and the improved Vf equations of Nanni et al. [25] and Dias and Barros [24].

6.2. Vf equation proposed by Nanni et al. Nanni et al. [25] proposed an equation for predicting the shear resistance of FRP strengthened beams. The resistance of FRP in resisting the shear is given by Eq. (4). Where sb represents the average bond stress of FRP elements intercepted by shear cracks. Li represents the length of each NSM laminates intersected by

45° shear crack as given in Eq. (5). The corresponding equations represented below are calculated and used for obtaining the value of Vf. The calculated values are compared with the test results in Table 5. From the results, it could be observed that the predictions by Nanni et al. [25] had a close correlation with the test results.

V f ¼ ½4ðaf þ bf Þsb Ltotmin sinhf

ð4Þ

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The total length of laminate and other notations for calculating Vf are given below. The definitions for all the variables are given in the nomenclature section above.

Ltotmin ¼

X Li i

Li ¼

n

min



sf coshf þsinhf

where i ¼ 1 . . . . . . N2

lnet ¼ lb 

2c ; sinhf

ð5Þ

f

i ¼ N2 þ 1 . . . . . . N;

N¼

leff ð1 þ cothf Þ sf

6.3. Vf equation proposed by Dias and Barros The shear resistance of FRP laminates (Vf) of Dias and Barros [24] model is given by Eq. (6). The value of effective strain (efe) offered by CFRP laminates can be calculated using Eq. (7). In these equations, fcm refers to the average cylinder compressive strength and cf refers to the uncertainty factor equal to 1.3. The definitions of other variable are given in nomenclature. The predictions obtained from the equations are summarized in Table 5.

V f ¼ hw 

Af v  efe  Ef  ðcotga þ cotghf Þ  sinhf sf

ð6Þ

where 2   ( )0:460679e 6 6 E f qf þ E s qs w 0:1160261hf þ0:0010437h2f  ef e ¼ 6 63:76888  e 2=3 f cm 4

(a)/effective depth (d)) on the efficiency of proposed NSM strengthening would be worth investigating. Development of a more refined model for improved predictions is also scope for further work. 7. Summary and conclusions

 sf i; lmax minðlnet  cosh þsinh i; lmax Þ f

27

 0:0351199hf 0:0003431h2 f

3 7 7 7=c 7 f 5

ð7Þ 6.4. Comparison of test results and analytical predictions The peak load carrying capacity obtained from the experimental results were compared with the predictions obtained using the equations proposed by ACI codes [22–23], Dias and Barros [24] and Nanni et al. [25]. The capacity of PSC beams with and without vertical shear reinforcements are calculated using the equations recommended by ACI 318 [23]. It is clear that the codal equations were underestimating the peak load carrying capacity of the PSC beam (Table 5). The contribution of FRP in shear resistance is calculated using the provided equations in ACI 440.2R [22] and the obtained values are added to the control specimens to obtain the total load capacity of the beams with FRP strengthening. Moreover, the equations proposed by Dias and Barros [24] and Nanni et al. [25] were used to obtain the contribution of FRP at different orientations. For control beams strengthened using NSM laminates at 90 orientation, only the equation proposed by Nanni et al. [25] under-predicted the peak strength. For control beams strengthened using NSM laminates at 45° orientation, the peak strength predictions of ACI and Nanni et al. [25] were conservative. In the case of beams with stirrups and strengthened at 90° oriented laminates, all the equations over-estimated the peak strength by nearly 10–15%. For beams with stirrups and strengthened with 45° NSM laminates, the peak strength was over-estimate by 20%. Only limited tests were carried out as part of this investigation. Shear behavior of prestressed beams is expected to have some variability. Improving the consistency of the test results and developing an improved model for predicting the shear behavior of NSM strengthened PSC beams is scope for further work. Moreover, the size effect is very important in the shear behavior of reinforced and prestressed concrete members. The effect of differentshear span-to-depth ratios (shear span

Twelve PSC beams with and without shear reinforcements were tested with different NSM CFRP shear strengthening configurations. The peak strength from experiments was compared with ACI code equations and other popular models for estimating the shear capacity of NSM strengthened specimens. Based on the test results presented in this study, the following major conclusions can be drawn:  NSM shear strengthening of prestressed concrete beams with and without stirrups using CFRP laminates is very effective in improving the overall shear behavior of the specimen in terms of strength, stiffness and energy dissipation capacity. The 45° orientation of CFRP NSM laminate was the most efficient configuration due to better arresting of shear cracks.  Control beam with no stirrups and strengthened using CFRP laminates (90° orientation) had a marginal improvement in strength of about 15%. The failure mode of these beams was brittle with shear crack propagating between the NSM CFRP laminates.  Control beam without stirrups and strengthened using CFRP laminates (45° orientations) resulted in overall improvement of strength and failure displacement by 52.0% and 34.4%, respectively. More importantly, it changed the mode of failure from brittle shear to ductile flexure mode.  The prestressed beams with shear reinforcement had a better performance than the beams with no stirrups in terms of strength and deformation capacity. In addition, the failure mode changed to flexure-shear from shear due to effective crack arresting and better internal stress re-distribution by shear reinforcement.  Although NSM strengthening on beams with stirrups had only marginal improvement in strength, it was more effective in reducing the crack width and crack propagation. The strength improved by about 50% and 54%, respectively for 90° and 45° orientation of NSM laminates when compared to beams with no stirrups.  The ultimate shear strength of NSM strengthened beams were calculated using ACI provisions and other models. ACI 440 equation was found to be conservative. The models proposed by Nanni et al. and Dias and Barros were reasonably accurate in predicting the shear capacity of NSM laminates.

Acknowledgements The authors gratefully acknowledge R&M International Pvt. Ltd. for providing FRP materials to this research work. The prestressed concrete beams were fabricated at PRECA India Ltd., and their help is duly acknowledged. References [1] Sharaky IA, Torres L, Comas J, Barris C. Flexural response of reinforced concrete beams strengthened with near surface mounting fiber reinforced polymer bars. Compos Struct 2014;109:8–22. [2] Kim HS, Shin V. Flexural behavior of reinforced concrete beams retrofitted with hybrid fiber reinforced polymer under sustained loads. Compos Struct 2011;93:802–11. [3] Norris T, Saadamanesh H, Ehsani MR. Shear and flexuralstrengthening of reinforced concrete beams with carbon fiber sheets. ASCE J Struct Eng 1997;123(7):903–11.

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