glass fibre reinforced polymer strips

Engineering Structures 210 (2020) 110412

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Shear strengthening of reinforced concrete deep beams using near-surface mounted hybrid carbon/glass fibre reinforced polymer strips Mohamed Ibrahima, Tadesse Wakjiraa, Usama Ebeada,b, a b

T

⁎

Department of Civil and Architectural Engineering, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar Structural Engineering, Department of Civil and Architectural Engineering, College of Engineering, Qatar University, P. O. Box 2713, Doha, Qatar

ARTICLE INFO

ABSTRACT

Keywords: Fibre Strength Analytical modelling Shear strengthening FRP/stirrups interaction Hybrid carbon/glass NSM-FRP Deep beams

This study investigated the efficacy of near surface mounted (NSM) hybrid carbon/glass fibre reinforced polymer (FRP) strips for strengthening of shear-deficient reinforced-concrete (RC) rectangular deep beams. A specific focus was the interaction of FRP with steel stirrups, which were arranged in both aligned and unaligned configurations for different FRP and stirrup volume fractions. Five unstrengthened reference beams and seven strengthened beams were tested. The NSM-FRP increased the beam shear strength up to 55.8%, alleviated debonding between concrete and strengthening material, and enhanced the deformational characteristics of the strengthened beams. The FRP/stirrups interaction also affected the contribution of NSM-FRP to the shear strength of the beams. Moreover, this study proposes a model based on the modified compression field theory (MCFT) to determine the shear capacity of the beams. The proposed formulation accounts for the FRP/stirrups interaction, which is not considered in the currently available models for the NSM-FRP strengthened RC beams. The average theoretical to experimental shear capacities ratio was 0.96 with a standard deviation of 3.19%.

1. Introduction The strengthening of reinforced concrete (RC) structures is a critical practice in the construction industry and constitutes an economical and environmentally viable alternative to demolition/reconstruction. Numerous factors cause RC structures to deteriorate, including corrosion of steel reinforcement, improper maintenance, unaccounted for service load augmentation, increase in live loads, alteration in usage of the structure, or errors in the design/construction process. Prior studies have examined different strengthening techniques and materials for deficient RC structures. Examples of efficient materials typically used for structural strengthening include steel plates [1,2], steel reinforced grout [3,4], fibre reinforced polymer (FRP), and fabric reinforced cementitious matrix (FRCM) [5–12]. Special concerns exist when reinforcing RC structures with deep beams, which are characterized by their relatively small critical shear span (CSS)-to-depth (a/d) ratio of less than 2.5 [13] and by their behavior, which differs from slender beams in the arch action of load transferring while bending for slender beams. Various studies have reported the effective use of FRP as a strengthening material in a variety of structural applications, such as column confinement [14–17], flexure strengthening of RC slabs [18], and flexure and shear strengthening of RC beams [19–26]. In fact, the ⁎

interaction of straining actions, such as normal and shear forces and moments, affects the behaviour of the strengthened beam [22]. Hybrid carbon/glass-FRP composites, in the form of strips, combine the advantages of both CFRP and GFRP, particularly, the strength of CFRP and ductility of GFRP [24]. Despite its high tensile strength, CFRP is characterized by its relatively smaller thickness and therefore, susceptible to local failure while being inserted in the NSM grooves due to lack of the out-of-plane resistance. On the other hand, the hybrid carbon/glass FRP strips are characterized by their relatively high thickness of 3.18 mm and therefore a high tensile strength as well as higher out-of-the plane resistance [24,27]. The FRP composites, primarily in the form of bars, are embedded in the concrete cover in the near-surface mounted (NSM) technique [25,28–31]. This technique is favoured over the externally bonded (EB) technique because it achieves significant enhancements in load capacity [32]. More importantly, the NSM technique mitigates the FRP/concrete debonding that is commonly associated with its EB counterpart [32,33]. The industry benefits from numerous studies on the FRP-strengthening of shear-deficient RC slender beams. Rizzo and Lorenzis [34] reported that using carbon FRP (CFRP) strips and rods enhanced the shear capacity of slender beams by 41% and 44%, respectively. Other researchers have reported that NSM-CFRP bars improved the shear capacity of RC slender beams by 17%–25% [35]. Dias and Barros [36]

Corresponding author at: Department of Civil and Architectural Engineering, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar. E-mail addresses: [email protected] (M. Ibrahim), [email protected] (T. Wakjira), [email protected] (U. Ebead).

https://doi.org/10.1016/j.engstruct.2020.110412 Received 30 October 2019; Received in revised form 17 February 2020; Accepted 20 February 2020 0141-0296/ © 2020 Elsevier Ltd. All rights reserved.

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Notations x

Asy Asx DFRP Esx

Pu Rs Ssy Sx Sxe VFRP Vc Vex Vsy Vth

ag bw fFRP, u fFRP kb

strain developed in the longitudinal reinforcement bars area of stirrups area of longitudinal tensile reinforcement stress distribution factor modulus of elasticity of the longitudinal tensile reinforcement bars ultimate load NSM-FRP/stirrups interaction reduction factor spacing of the stirrups vertical distance between compressive and tensile bars crack spacing shear capacity provided by NSM-FRP shear capacity provided by concrete experimentally obtained shear capacities shear capacity provided by stirrups theoretically predicted shear capacities

u c, u sl, u sv, u

FRP sx sy

CW h c fyx

reported an enhancement in the shear capacity of RC slender T-beams from 21% to 83% using NSM-CFRP laminates. Al-Mahmoud et al. [37] reported the efficacy of NSM-CFRP rods to enhance the shear capacity of slender beams, with an observed average gain of 37% [37]. Lorenzis and Nanni [38] reported the interaction between NSM rods and stirrups of slender RC T-beams. The authors concluded that the strengthened specimens without stirrups within the CSS showed an increase in the shear capacity of 100%, which is reduced to 35% for specimens with stirrups within the CSS. Chaallal et al. [39] also studied the FRP/stirrups interaction based on the experimental results of RC beams strengthened with EB-FRP, NSM-FRP rods, and embedded through section (ETS) FRP rods. The authors reported that the provision of steel stirrups reduced the gain in the load-carrying capacity of the strengthened beams, however, the effect of steel stirrups on the percentage gain in the load-carrying capacity was less pronounced in the ETS method compared with the EB and NSM methods [39]. This interaction between the strengthening system and stirrups has also been reported in other studies of FRP strengthened slender beams [40–46] and, recently, of FRCM strengthened RC deep beams [7]. The behaviour of FRP/FRCM strengthened beams has also been studied analytically [47–52]. However, only few models accounted for the interaction between the internal and external shear reinforcement [47,50,51]. In contrast to the studies on RC slender beams, studies on the shear strengthening of RC deep beams are rather limited. Islam et al. [53] reported the feasibility of using EB-FRP to enhance the shear capacity of RC deep beams, with an increase of up to 40%. Almassri et al. [54] reported the efficacy of using NSM-CFRP rods to repair corroded 28year-old RC deep beams with different a/d ratios, and results indicated a 17%–25% gain in shear capacity. Lee et al. [55] reported that EBCFRP sheets increased the load-carrying capacity of strengthened deep beams by 15%–66%. Bousselham and Chaallal [44] reported the efficacy of using EB-CFRP to improve the shear capacity of RC slender and deep T-beams, with strength increases of 10% and 43% for deep and slender beams, respectively. As presented above, the literature to date has been predominantly focused on the use of EB composites for enhancing the shear strength of the beam. Yet this EB technique is frequently associated with debonding [53,55,56]. Only limited studies have been conducted on the use of the NSM technique with FRP bars for shear strengthening deep beams [29,54]. To date, and to the best of the authors’ knowledge, no studies have been conducted using NSM hybrid glass/carbon FRP strips for the strengthening of rectangular RC deep beams critical in shear. This study is unique in the following respects:

maximum aggregate size width of the beam web ultimate stress in FRP effective stress in NSM-FRP boundary for the slender and deep beams ultimate deflection concrete compressive strains at Pu strain in the longitudinal bars at Pu strain in the steel stirrups at ultimate load reinforcement ratio of the NSM-FRP reinforcement ratio of the longitudinal tensile bars reinforcement ratio of CSS stirrups Crack width at the ultimate load Overall beam height neutral axis depth energy absorption yield strength of longitudinal bars

2. investigating the FRP/stirrups interaction effect on the shear strength enhancement of the beams. 3. investigating the effect of aligning/unaligning the FRP strips and steel stirrups along the CSS on shear strength enhancement. Therefore, this study presents a novel application of NSM-hybrid carbon/glass FRP strips for the strengthening of shear-deficient RC rectangular deep beams. The output of this study will be of interest to both researchers and practitioners involved in the strengthening of RC structures. 2. Test programme 2.1. Materials A single batch of ready-mixed concrete was used to cast the test beams. Ten standard concrete cylinders of dimensions 150 mm diameter and 300 mm height were cast for measuring the tensile and compressive strengths of the concrete. Seven cylinders were tested for compressive strength according to ASTM standard C39/C39M [57], while three cylinders were tested for tensile strength using the splitting test according to the ASTM C496/C496M [58]. The average 28 days’ compressive strength was 40 MPa, while its tensile strength was 2.93 MPa. Three sizes of standard steel rebars (16, 8, and 6 mm diameter) were used to reinforce the beams. A total of four 16-mm-diameter ribbed steel bars (double layers) were used as longitudinal tensile reinforcement, while two 8-mm-diameter ribbed steel bars were used as compressive steel reinforcement. For shear reinforcement (stirrups), 8-mmdiameter ribbed steel bars spaced at 100 mm intervals were used along the beam, with the exception of the CSS. At the CSS, a variety of shear reinforcement configurations were used. The average yield stresses were 595 MPa, 298 MPa, and 234 MPa for the 16-mm-, 8-mm-, and 6mm-diameter steel bars, respectively, as listed in Table 1. Hybrid carbon/glass FRP strips have been used for strengthening reinforcement in this study, as shown in Fig. 1. The characteristics of Table 1 Steel reinforcement properties (average).

1. using hybrid glass/carbon FRP strips in the NSM technique. 2

Bar Diameter (mm)

Yield stress (MPa)

Yield strain

6 8 16

234 298 595

0.115 0.144 0.266

(%)

y

Modulus of Elasticity (GPa) 204 207 224

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by the manufacturer to be 852 MPa and 62.91 GPa, respectively [59]. Epoxy adhesive resin, which is suitable for both tropical and hot climates [60], was used as a bonding agent. The tensile strength range of the epoxy was 17.5–28 MPa, and the average modulus of elasticity was 10 GPa [60]. 2.2. Specimens and test matrix The experimental test matrix is presented in Table 2 and shows the configuration of the twelve medium-scale RC rectangular beams. All beams were three-point monotonically loaded, keeping a clear span of 1900 mm between the supports. The loading point was applied 550 mm from one support and 1350 mm from the other support, as shown in Fig. 2. This provided a CSS of 550 mm. A concrete cover of 30 mm was used in all the test beams yielding an effective depth of 333.5 mm. Consequently, all the beams were considered deep beams with a constant CSS-to-effective depth ratio (a/d) = 1.65, as per ACI-ASCE Committee [13]. Five beam specimens were left unstrengthened to act as references, enabling different configurations of stirrups along the CSS (referred to as CSS stirrups in this paper). The remaining seven beams were NSM-FRP strengthened. The investigated test parameters were the number of steel stirrups at the CSS (three, two, and zero); the number of NSM-FRP strips used (four, three, and two); and FRP/stirrups configuration (aligned and unaligned). As shown in Fig. 3a–l, in the case of aligned configuration, the NSM-FRP strips were installed along the CSS stirrups while in the unaligned configuration the NSM-FRP strips were placed at the location between two stirrups. Each specimen is designated according to the configurations of the NSM-FRP and the CSS stirrups, as presented in Table 2. For the beam configuration, the nomenclature ‘R’ denotes the reference beams; ‘N2’, ‘N3’, and ‘N4’ denote the number of NSM-FRP strips in the strengthened beams per side as two, three, and four, respectively; ‘S0’, ‘S2’, and ‘S3’ denote beams with zero, two, and three stirrups, respectively, within the CSS; and ‘C1’ and ‘C2’ denote strengthened beams in which the FRP and the stirrups are aligned and unaligned, respectively, as shown in Fig. 3a–l.

Fig. 1. Hybrid carbon/glass FRP cross-section.

Table 2 Test matrix of beam specimens. Designation

No. of FRP strips

No. of stirrups in CSS

FRP/stirrups configuration

R-S0 N2-S0 N3-S0 N4-S0 R-S2-C1 N2-S2-C1 R-S2-C2 N2-S2-C2 R-S3-C1 N3-S3-C1 R-S3-C2 N3-S3-C2

– 2 3 4 – 2 – 2 – 3 – 3

– – – – 2 2 2 2 3 3 3 3

– No stirrups No stirrups No stirrups – Aligned – Unaligned – Aligned – Unaligned

the hybrid carbon/glass FRP are available in the manufacturer's data sheet and confirmed through lab testing elsewhere by the authors [24,27]. These FRP strips comprised carbon tows sandwiched between two layers of glass fibre mats bonded using high vinyl-ester resin [59], as shown in Fig. 1. The FRP strip roll was cut in strips 25 mm wide and 400 mm long to be used in the near-surface grooves at the CSS. The tensile strength and the modulus of elasticity of the FRP were specified

Fig. 2. Longitudinal detail (a) and cross-section of the beam specimens outside the critical shear span (b) and within the shear span (c) (dimensions in mm).

3

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Fig. 3. NSM-FRP/stirrups configurations (dimensions in mm).

flow around the FRP, creating a 2–3 mm thick layer from both sides of the FRP, as shown in Fig. 5d. This step was essential to ensure a full bond between the FRP and the concrete substrate; and (4) The surface of each groove was leveled, and the excess epoxy was removed using a shovel. Fig. 5e shows the final shape of the NSM-FRP strengthened beams.

2.3. Strengthening procedures Following the curing period (4 weeks), seven beams underwent the NSM strengthening technique as shown in Fig. 4. The FRP roll was first saw-cut into strips with a width of 25 mm and length of 400 mm, which were inserted in concrete grooves. Each groove was 15 mm wide, 26 mm deep, and ran along the height of the beam (400 mm). The grooves were cleaned from dust, debris, and any fine particles using a compressed-air-brushing machine. Once the grooves were prepared, the FRP strips were installed in the grooves, as shown in Fig. 5a–5e. In each concrete groove double layers of hybrid carbon/glass FRP laminates were installed. In this study, the double layers of the FRP laminates in a groove will be referred to as the NSM-FRP strip. The following steps were performed for each side of the beam: (1) Approximately half of the groove was filled by epoxy, as shown in Fig. 5b; (2) Two FRP laminates were completely covered by epoxy and attached together, allowing a 2–3 mm layer of epoxy in between them; (3) The double FRP strips were placed inside the groove and lightly pressed to force the epoxy to

2.4. Instrumentation Fig. 6 shows the beam test setup and the instruments used for data collection. The beams were tested under displacement controlled threepoint bending. Displacement at the point of the application of the load was measured using linear variable displacement transducers (LVDTs) placed on each side of the beam, as shown in Fig. 6. Two 60 mm-long strain gauges with a 2% maximum strain limit and 120 Ω resistance were used to measure concrete strain in the compression zone. For steel reinforcement strain monitoring, two 5 mm long strain gauges with a 2% maximum strain limit and 120 Ω resistance were 4

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Fig. 4. NSM-FRP strengthening (dimensions in mm).

glued to the bottom steel bars underneath the loading point and at the midpoints of the CSS stirrups. The crack width within the CSS was monitored using a clip-type displacement transducer. The crack gauge was fixed perpendicular to the 45° line extending from the point of the application of the load to the bottom of the beam in order to contain the main failure crack.

enhanced the ultimate load-carrying capacity of the beams, as shown in Fig. 7 and Table 3. The percentage gain in Pu ranged from 28.8% to 55.8% compared to the corresponding reference beams. The effectiveness of the strengthening system varied based on the tested variables. One important variable was the number of NSM-FRP strips. An increase in the number of strips increased Pu , as can be seen in Fig. 7 for beams without CSS stirrups. As Fig. 7 also shows, the specimens strengthened with four NSM-FRP strips exhibited the highest load-carrying capacity of 349 kN, while for the strengthened specimens without CSS stirrups and with three and two NSM-FRP strips, it was 337 kN and 311 kN, respectively. The stirrups were another variable. Fig. 8a and b shows the FRP/ CSS stirrups interaction effect on the percentage increase in the ultimate load-carrying capacity of the strengthened beams. It was observed that for specimens with a greater number of CSS stirrups, the FRP made less of a contribution to load-carrying capacity than it did for those with fewer or no CSS stirrups. For the beams with two NSM-FRP strips, the percentage increase of Pu reached 38.8% for the specimen without CSS stirrups (N2-S0) as opposed to 30.9% (average) for the specimens with two CSS stirrups (N2-S2-C1/C2), as shown in Fig. 8a. Similarly, the specimen with three NSM-FRP strips and no CSS stirrups (N3-S0) exhibited an increase in Pu of 50.4%, while the Pu of the beams with the

3. Results and discussion The results are discussed in terms of the strengthened beams’ loadcarrying capacity, load–deflection response, strain analysis, failure modes, energy absorption, and crack propagation, with special attention to the NSM-FRP/CSS stirrups interaction effect. Table 3 presents the test results for the strengthened beams with their associated references in terms of the ultimate load-carrying capacity (Pu ), the gain in Pu , deflection ( u ) under the load at Pu , energy absorption (ψ), crack width (CW), and strains in concrete ( c,u ), longitudinal tensile bars ( sl,u ), and stirrups ( sv,u ) at Pu . 3.1. Load carrying capacity The hybrid carbon/glass NSM-FRP used in this study substantially 5

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Fig. 5. NSM strengthening technique procedure.

same number of FRP strips but with three CSS stirrups (N3-S3-C1/C2) increased by 41.6% (on average), as shown in Fig. 8a. These results indicated a clear interaction between the FRP and CSS stirrups in which the presence of CSS stirrups influences the contribution of the FRP strengthening. This interaction has also been reported in previous studies using FRP to strengthen slender RC beams [40–45]. In addition, the FRP/stirrups configuration significantly affected the contribution of the NSM-FRP strips to the load-carrying capacity of the beams, as shown in Fig. 8b. Specimens with an unaligned FRP/stirrups configuration were observed to have a greater increase in Pu than those with an aligned configuration. Specifically, the specimen with three NSM-FRP strips and three steel stirrups unaligned with each other (N3S3-C2) exhibited an increase in Pu of 44.9%, while specimens with the same number of NSM-FRP strips and steel stirrups but aligned with each other (N3-S3-C1) only exhibited a 38.2% gain in Pu , as shown in Fig. 8b. Similarly, specimens with two NSM-FRP strips and two steel stirrups, aligned and unaligned with each other (N2-S2-C1 and N2-S2-C2, respectively), exhibited increases in shear capacity of 28.8% and 32.9%, respectively, as shown in Fig. 8b. This difference in the percentage gain in Pu in favor of the unaligned FRP/stirrups configuration can be attributed to the distribution of the FRP strips and steel stirrups. The strips and stirrups cover more of the CSS in the unaligned configuration; therefore, there is a smaller unreinforced area in shear in which shear cracks can initiate. The combined effect of the stirrups and NSM-FRP can also be studied in terms of the homogenized axial rigidity (Kv ) given by:

(a) The front view of the test beam setup

(b) The backside of the test beam setup Fig. 6. Beam test setup.

Kv = 6

FRP EFRP

+ Rs

sy Esy

(1)

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Table 3 Experimental result summary. Specimen ID

Pu (kN)

Gain in Pu (%)

R-S0 N2-S0 N3-S0 N4-S0 R-S2-C1 N2-S2-C1 R-S2-C2 N2-S2-C2 R-S3-C1 N3-S3-C1 R-S3-C2 N3-S3-C2

224 311 337 349 257 331 252 335 267 369 263 381

– 38.8 50.4 55.8 – 28.8 – 32.9 – 38.2 – 44.9

u

(mm)

6.3 9.5 8.9 9.5 7 8.7 7.5 8.8 6.7 17.9 6.1 11

Increase in

u

– 50.8 41.3 50.8 – 24.3 – 17.3 – 167.2 – 80.3

(%)

(kN·mm)

Increase in

741 1720 1688 1839 949 1614 1072 1621 920 4595 817 3129

– 132.2 127.9 148.3 – 70.0 – 51.2 – 399.4 – 283.2

(%)

sl,u

(µ )

2309 3602 4216 – 2421 3465 2365 4413 2573 9998 2415 7642

sv,u

(µ )

– – – – 2881 2031 3363 1343 2063 1711 2408 1411

c,u

(µ )

1060 1115 1602 1832 1179 1548 1037 1962 1491 2435 1459 2662

CW (mm)

Reduction in CW (%)

1.537 0.986 1.036 0.506 1.462 0.986 1.513 0.906 1.561 0.963 1.344 0.896

– 35.8 32.6 67.1 – 32.6 – 40.1 – 38.3 – 33.3

Fig. 7. Load-carrying capacity for all specimens.

where FRP = 2aFRP bFRP /(b w SFRP ) is the NSM-FRP reinforcement ratio; aFRP and bFRP are the dimensions of the laminate cross-section; SFRP is the spacing between the NSM-FRP; bw is the beam width; sy = asy /(bw Ssy ) is the CSS stirrups reinforcement ratio; asy is the area of the CSS stirrups; Ssy is the spacing of the CSS stirrups; EFRP is the elastic modulus of the NSM-FRP; Esy is the elastic modulus of the CSS stirrups; and Rs is the reduction factor.

Since the NSM-FRP/CSS stirrups interaction proved to be highly influential, it should be considered in determining the shear capacity of the strengthened beams. The presence of FRP strengthening decreases the stress developed in the CSS stirrups, thus reducing the CSS stirrups’ contribution to the shear strength. According to Pellegrino and Modena [61], the CSS stirrups yield only if the effective stress in the FRP is higher than the yield strength of CSS stirrups. Thus, the stress reduction factor Rs is used to account for the stress reduction in stirrups [47,50]. The value of Rs is approximated as follows [61] in terms of the neutral axis depth, c :

Rs = 0.75(1

c /d )

1

Fig. 8. Effect of FRP/stirrups interaction on the percentage gain in Pu in terms of (a) existence of steel stirrups and (b) FRP/stirrups configuration in the CSS.

(2)

In this study, the CSS stirrups yielded in all tested beams as listed in Table 3 and discussed in Section 3.4.2. As shown in Fig. 9, the load-carrying capacity of the strengthened beams showed an almost linear relationship with Kv .

deflections at the ultimate loads compared to the associated reference specimens. Overall, the average ultimate deflection for the reference beams was 6.7 mm, while it was 10.6 mm for the strengthened beams, a difference of 58.2%. The presence of the CSS stirrups exhibited a clear effect on the ultimate deflection. For specimens without CSS stirrups, an increase in the ultimate deflection was reported in the range of 41% (N3-S0, u = 8.9 mm) to 50.8% (N4-S0, u = 9.5 mm), with an average of 44.5%, relative to R-S0 ( u = 6.3 mm). Increasing the number of CSS stirrups resulted in an increase in the ultimate deflection because of the improved shear strength and the tendency to increase the deformability

3.2. Load–deflection response The ultimate deflection, which is the deflection at Pu , was recorded for each specimen and is listed in Table 3. The hybrid carbon/glass NSM-FRP strengthening resulted in a significant improvement in the deformability of the beams, which was substantiated by increased 7

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Fig. 9. Load-carrying capacity versus homogenized axial rigidity for the strengthened beams.

of the beam. Specimens with three stirrups and three NSM-FRP strips exhibited a significant increase in the ultimate deflection; this was up to 167.2% for specimen N3-S3-C1 ( u = 17.9 mm) compared to the corresponding reference specimen R-S3-C1 ( u = 6.7 mm). Specimens with the FRP/ stirrups aligned configuration were observed to have relatively higher ultimate deflections than specimens with unaligned configuration. In particular, the average increase in the ultimate deflection was 95% in the specimens with aligned configurations and 49.2% in the specimens with unaligned configurations. This can be attributed to the concentration of the stirrups and FRP at the same point in the aligned configuration, which resulted in more cracks and greater deflections. Fig. 10a shows the load–deflection plots for specimens with no CSS stirrups, and Fig. 10b and c presents the load–deflection plots for specimens with two and three CSS stirrups, respectively. Specimens with the same number of NSM-FRP strips behaved similarly, with a minor difference at the peak point. In addition, most of the specimens experienced a typical compression shear failure characterized by a sudden drop in the load at the peak. 3.3. Energy absorption Energy absorption ( ), which is the area under the load–deflection curve up to the failure point [62], is listed in Table 3 for each tested beam. As shown in the table, the NSM strengthening technique typically resulted in a significant increase in energy absorption. The energy absorption of the reference beams ranged from 741 kN·mm (R-S0) to 1072 kN·mm (R-S2-C2), with an average of 900 kN·mm. For the strengthened specimens, energy absorption ranged from 1614 kN·mm (N2-S2-C1) to 4595 kN·mm (N3-S3-C1), with an average of 2315 kN·mm. The specimens with three NSM-FRP and three stirrups (N3-S3-C1 and N3-S3-C2) exhibited the greatest increase in energy absorption, with an average of 341%. The energy absorption ratio ( / R ), which is the ratio of the energy absorption of the strengthened specimen to that of the corresponding reference specimen ( R ) has been used to assess the effect of the tested parameters on . Fig. 11 shows the energy absorption ratio for specimens with two and three steel stirrups at the CSS. The aligned configuration exhibited a marginally greater value of / R than the unaligned configuration, as shown in Fig. 11.

Fig. 10. Load–deflection plots for NSM-FRP strengthened specimens.

typically, the strengthened specimens with two NSM-FRP strips exhibited lower tensile strains than specimens with three NSM-FRP strips. The average increase in the flexural strain for specimens with two NSMFRP strips was observed to be 65%, as opposed to 196% for specimens with three NSM-FRP strips. Fig. 12a shows the load–strain curves of the flexural reinforcement for the specimens without CSS stirrup. Fig. 12b and c shows the load–strain curves of the flexural reinforcement for specimens with two and three steel stirrups at the CSS, respectively. As shown in Fig. 12a, the more FRP strips used, the higher the ultimate flexural strain. Fig. 12b shows that although both strengthened specimens N2-S2-C1 and N2-S2-C2 exhibited approximately the same ultimate load, specimen N2-S2-C1 exhibited more elastic behaviour than specimen N2-S2-S2. This could be attributed to the FRP/stirrups interaction. Lastly, as represented in Fig. 12c, the specimens with three

3.4. Strain analysis 3.4.1. Tensile reinforcement and concrete strains The ultimate strain in the tensile reinforcement was reported at the ultimate load of each specimen, as presented in Table 3. The ultimate steel strain for the strengthened specimens was observed in the range of 3465 με (N2-S2-C1) to 9998 με (N3-S3-C1), with an average of 5523 με. The number of NSM-FRP strips contributed to the maximum strain: 8

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Fig. 11. Energy absorption ratio for the strengthened beams.

NSM-FRP strips (N3-S3-C1 and N3-S3-C2) experienced a yielding in the flexural reinforcement bars before the compression shear failure. The concrete strain ( c,u ) that corresponded to the ultimate load for all the strengthened specimens did not exceed the concrete crushing strain of 3000 µ , as presented in Table 3. The average of the concrete strain for the reference specimens was 1245 με, as opposed to 1879 με for the strengthened specimens, an average increase of 56.5%. The higher the number of NSM-FRP strips, the greater the concrete strain recorded. The average percentage increase in concrete strain at Pu for beams with two and three NSM-FRP strips was 41.9% and 65.6%, respectively. This intuitive result showed that the increase in the NSMFRP strengthening amount increases the gain in the concrete strain at Pu and delays the brittle shear compression failure. 3.4.2. Stirrup strain Table 3 also presents the maximum strain in the stirrups measured at the ultimate load for each specimen. The NSM-FRP significantly reduced the transverse strains in the CSS stirrups for the strengthened specimens. This can be attributed to the interaction between the NSMFRP strips and CSS stirrups, in which the strengthening system limits the strain in the CSS stirrups while it also reduces the crack width in the CSS and then delays yielding in the steel stirrups. The strengthening system works together with the stirrups to resist the applied shear stresses, thereby reducing the maximum strain in the steel stirrups. Such interactions were also reported in the literature [3,41]. The average strain in the CSS stirrups for the reference specimens was 2679 με, as opposed to 1695 με for the strengthened specimens. Therefore, the FRP/stirrups interaction significantly affected the steel stirrup strains for all strengthened specimens. Specimens with two NSM-FRP strips (N2-S2-C1 and N2-S2-C2) exhibited an average decrease of 45% in the stirrup strain, as opposed to 29% for specimens with three NSM-FRP strips (N3-S3-C1 and N3-S3-C2), relative to the corresponding references. In addition, the aligned FRP strips and stirrups resulted in a smaller average reduction of 29% in the average strain in the steel stirrups, while the unaligned configuration decreased the strain by 51% relative to the associated references.

Fig. 12. Load–flexural steel strain plots for NSM-FRP strengthened specimens.

extensive concrete crushing was observed under the loading point for specimens N3-S3-C1 and N3-S3-C2. In all strengthened specimens, there was no significant debonding between the FRP and concrete. This can be attributed to the effectiveness of the NSM technique, which enhanced the FRP/concrete bond. Ultimate crack width, which was recorded at the ultimate load, is presented for all specimens in Table 3. Due to the strengthening system, the ultimate crack widths for the strengthened specimens were less than those of the corresponding references. The percentage decrease is presented in the last column of Table 3. The average crack width for the reference specimens was approximately 1.5 mm, as opposed to 0.9 mm for the strengthened specimens. There was no considerable difference

3.5. Failure modes and crack width analysis All specimens experienced diagonal shear failure because of a major shear crack, as shown in Fig. 13a–g. A number of specimens also had partial separation of the concrete cover at the bottom around the NSMFRP strip, as shown in Fig. 14a–g. Specimens with three NSM-FRP strips and three steel stirrups at the CCS (N3-S3-C1 and N3-S3-C2) exhibited flexural yielding before the compression shear failure. A relatively 9

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Fig. 13. Crack patterns at ultimate for NSM-FRP strengthened specimens.

in the crack width between the specimens with two and three steel stirrups at the CSS. However, the unaligned configuration exhibited slightly lower crack widths (average difference = 14%) than the aligned configuration for specimens with three and two NSM-FRP strips. Fig. 15a shows the load–crack width plots for specimens without steel stirrups, while Fig. 15b and c shows the load–crack width plots for specimens with two and three steel stirrups at the CSS, respectively. As shown in Fig. 15a, increasing the number of NSM-FRP strips in specimens with no steel stirrups significantly decreased the ultimate crack width. The greatest decrease in the crack width was 67.1% in specimen N4-S0. As shown in Fig. 15a–c, the unaligned configuration showed

lower crack width compared to the aligned configuration. For instance, Specimen N2-S2-C1 with aligned configuration showed a crack width of 0.51 mm at a load level of 200 kN, which is higher than that for Specimen N2-S2-C2 (0.26 mm) with unaligned NSM-FRP/stirrups configuration at the same load level, as shown in Fig. 15b. 4. Theoretical formulation The modified compression field theory (MCFT) [63] is considered as an exact solution for the shear strength of RC beams as it satisfies the equilibrium condition, strain compatibility condition, and stress-strain 10

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Fig. 14. Bottom cracks and concrete debonding for NSM-FRP specimens.

relationships. Thus, it is adopted in this paper as a basis for determining the shear capacity of the NSM-FRP strengthened deep beams with or without steel stirrups. Building on the MCFT, the model proposed in this paper predicts the shear capacity of RC beams with shear reinforcement, which can be internal shear reinforcement (steel stirrups), NSM-FRP, or both. For beams with CSS stirrups, the proposed model accounts for the interaction between the stirrups and NSM-FRP. Consider an RC beam internally reinforced with stirrups and strengthened with NSM-FRP as shown in Fig. 16a. From the equilibrium of stresses in Fig. 16a, the clamping stress ( fy ) is obtained by:

fy =

sy fsy

+

FRP fFRP

+ f1 + (f1 cos2

f2 sin2 )

(3)

where

fsy is the yield strength of the CSS stirrups; fFRP is the effective stress in the NSM-FRP; f1 is the principal tensile stress in concrete; f2 is the principal compressive stress in concrete; and is the angle between the horizontal axis and diagonal compressive stresses.

11

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The tensile stress factor and the inclination can be determined as given in Eqs. (7) and (8), respectively, as per the simplified MCFT (SMCFT) [64]:

=

0.4 1 + 1500

1300 1000 + Sxe

x

(7)

= (29 + 7000 x ) × 0.88 +

Sxe 2500

75°

(8)

where

Sxe is the crack spacing, and x is the strain developed in the longitudinal reinforcement bars. The value of Sxe for beams with CSS stirrups is determined in terms of the crack spacing in the x-direction (smx ) and crack spacing in the ydirection (smy ) [63] as given in Eq. (9).

Sxe =

1 sin smx

+

cos smy

(9)

The value of smx can be assumed as the stirrups’ spacing, while smy is taken as the effective depth (d ) [47]. The value of crack spacing for RC beams without stirrups is estimated as follows based on the SMCFT [64]:

Sxe =

35Sx ag + 16

0.85Sx

(10)

where ag and Sx are the maximum aggregate size and the vertical distance between the compression and tensile bars. For determining the strain developed in the longitudinal reinforcement bars, consider the equilibrium of stresses in the x-direction of Fig. 16a. The externally applied stress in the x-direction can be given by Eq. (11):

fx =

sx fsx

+ f1 sin2

f2 cos2

(11)

where sx is the reinforcement ratio of the longitudinal tensile bars. However, there is no external applied stress in the x-direction, fx = 0 . Thus, the stress in the longitudinal reinforcement can be determined as given in Eq. (12):

fsx = (f2 cos2

f1 sin2 )/

sx

(12)

Hence, the strain developed in the longitudinal bars is given by the following equation: x

= (f2 cos2

f1 sin2 )/(

sx Esx )

(13)

where Esx is the elastic modulus of tensile bars. From Eqs. (5), (6), and (13), the value of x can be determined as given in Eq. (14). Fig. 15. Load–crack width plots for NSM-FRP strengthened specimens.

x

(4)

wherev is the shear strength. However, the clamping stress is assumed to be negligible [64]. Thus, v can be determined by Eq. (5), combining Eqs. (3) and (4) for fy = 0 .

= f1 cot +

sy fsy cot

+

FRP fFRP cot

v=

where

f c' +

sy fsy cot

+

FRP fFRP cot

Es

(14)

sx

f c' + Rs

sy fsy cot

+

FRP fFRP cot

(15)

The effective stress in FRP that is intersected by the shear crack for FRP rupture failure can be determined in terms of the ultimate stress in FRP ( fFRP, u ) as proposed by Chen and Teng [65], and can be obtained by Eq. (16):

(5)

In addition, v can also be expressed as in Eq. (6),

=

f c' tan

cot

As discussed earlier, the effect of NSM-FRP/stirrups interaction should be considered in determining the shear capacity of the strengthened beams. Hence, the shear capacity of NSM-FRP strengthened beams with CSS stirrups is determined as given in Eq. (15):

From the equilibrium conditions of the MCFT [63] for stresses, the following equation is valid, as shown in Fig. 16b:

f1 + f2 = v (tan + cot )

=

fFRP = DFRP fFRP, u

(6)

(16)

where DFRP is the stress distribution factor determined as given in Eq. (17).

is the tensile stress factor. 12

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Fig. 16. NSM-FRP strengthened beam shear model based on the MCFT [63].

Fig. 17. Flowchart for the shear capacity of NSM-FRP strengthened beam.

13

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M. Ibrahim, et al.

The table also presents the experimental (Vex ) and theoretical (Vth ) shear capacities, and the Vth/Vex ratio. The average of Vth/Vex ratio was 0.96 with a standard deviation (STD) of 3.19%. Fig. 18 shows the prediction capability of the model based on the modified version of the demerit points classification (DPC) method [66] originally proposed by Collins [67]. This method is used to evaluate the model’s predictive performance in terms of safety, accuracy, and economic aspects. According to this method, a penalty is assigned to each range of the Vth/Vex ratio according to the criteria presented in Table 5. As shown in Fig. 18, The predictions for all specimens fell within the appropriate safety range, resulting in a total penalty of zero. Thus, the model accurately and safely predicted the shear capacity of the tested beams.

Table 4 Theoretical results summary. Beam designation

Vc (kN)

Vsy (kN)

VFRP (kN)

Vth (kN)

Vex (kN)

Vth/Vex

R-S2-C1 R-S2-C2 R-S3-C1 R-S3-C2 N2-S0 N3-S0 N4-S0 N2-S2-C1 N2-S2-C2 N3-S3-C1 N3-S3-C2

208 208 196 196 138 121 108 135 135 119 119

34.5 34.5 50.4 50.4 – – – 28.6 28.6 39.6 39.6

– – – – 135 187 237 136 136 189 189

243 243 247 247 273 308 345 299 299 347 347

247 242 257 253 299 324 335 318 322 355 366

0.98 1.00 0.96 0.97 0.91 0.95 1.03 0.94 0.93 0.98 0.95

5. Conclusions This study expands the existing literature on the strengthening of RC structures through its unique focus on the efficacy of using NSM-FRP strips for the shear strengthening of RC rectangular deep beams. Twelve shear-deficient RC rectangular deep beams, some with different FRP and steel stirrups configurations, were constructed and tested under three-point bending. The study further highlighted the interaction of NSM-FRP/CSS stirrups and its effect on the behaviour of the beams. Test parameters included the number of FRP strips (two, three, or four), number of steel stirrups at the CSS (zero, two, or three), and the FRP/ stirrups interaction at the CSS (aligned or unaligned). In addition, a model based on the modified compression field theory (MCFT) was used to predict the shear capacity of the tested beams. The primary conclusions drawn from this study are:

• Hybrid carbon/glass NSM-FRP can be used to significantly enhance Fig. 18. Prediction capability of the model [59].

•

Table 5 Criteria for the DPC [66]. Vth/Vex

Classification

Penalty

>2 [1.176–2] [0.869–1.176] [0.5–0.869] ≤0.5

Extra dangerous Dangerous Appropriate safety Conservative Extra conservative

10 5 0 1 2

• (17)

DFRP = 0.5(1 + )

where is the ratio of the coordinate of the upper edge of effective FRP to the coordinate of the lower edge of the effective FRP. RC deep beams exhibit higher shear capacity than slender beams [13]. In deep beams, the main contributor to the beam strength is the strength of the concrete. Thus, to include the effect of a/d ratio for RC deep beams in the proposed model, the contribution of concrete to the shear capacity is multiplied by the following factor, Ra / d :

• •

(18)

Ra / d = 1 + 2.7 (x / kb)

where x = a/ d is the CSS-to-depth ratio and kb = 2.5. Finally, the shear capacity of an RC beam strengthened with NSMFRP can be determined using Eq. (19):

V = Ra /d

fc' bw d + Rs

sy fsy b w d cot +

FRP fFRP b w d cot

•

(19)

where bw is the width of the web and d is the effective depth of the beam. This proposed model is an iterative process, as summarized in Fig. 17. Table 4 presents the results of the theoretical analysis of the shear capacity provided by concrete (Vc ), stirrups (Vsy ), and NSM-FRP (VFRP ).

•

14

the load-carrying capacity of RC deep beams critical in shear as long as the beam does not experience flexural failure prior to shear failure. Overall, the increase in the load-carrying capacity of the NSM-FRP strengthened beams ranged between 28.8% and 55.8%. For the specimens without CSS stirrups, the NSM technique increased load carrying capacity by up to 55.8%. The provision of stirrups in the critical shear span increased the load-carrying capacity of the beams but reduced the gain in Pu relative to the specimens without stirrup in the CSS. The average gain in Pu was 31% for specimens without CSS stirrups and 22% for specimens with CSS stirrups. The unaligned FRP/stirrups configuration exhibited relatively better performance. The average increase in Pu was 33.5% for the aligned configuration and 38.9% for the unaligned configuration. This can be attributed to the distribution of the NSM-FRP strips and steel stirrups. The strips and stirrups cover more of the CSS in the unaligned configuration; therefore, there is a smaller unreinforced area in which shear cracks can initiate. The NSM strengthening techniques improved the deformational characteristics of the beams. Overall, the ultimate deflection of the strengthened specimens increased by an average of 62.1%. In addition, the average increase in energy absorption relative to the reference specimens was 173.2%. The NSM strengthening technique significantly decreased crack width at the ultimate load for the strengthened beams. Overall, the average decrease in the ultimate crack width was 45% and 36% for specimens without and with steel stirrups at the CSS, respectively. Utilization of FRP to enhance shear capacity decreased the maximum strain in the steel stirrups at the CSS by an average of 39% confirming the existence of the interaction between the NSM-FRP and stirrups. The NSM strengthening technique significantly increased tensile strain in the flexural steel reinforcement and compression strain in the concrete surface. Overall, the average increase in the tensile strain of the flexural reinforcement was 128.9%, and the compression strain in the concrete surface increased by 54.2%.

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• All •

specimens failed in concrete compression shear failure. Typically, the FRP debonding failure was significantly mitigated in the strengthened specimens. Finally, this study proposes a theoretical formulation based on the MCFT to determine the shear capacity of NSM-FRP strengthened beams. The model accurately predicted the shear capacity of the beams with an average of the Vth/Vex ratio of 0.96 and a standard deviation of 3.19%.

[9] [10] [11] [12]

Further studies of different strengthening configurations and other test parameters, such as anchorage systems, fibre types, and the orientation of FRP application, will be required in order to comprehensively study the efficacy of NSM-FRP for shear strengthening RC deep beams. In addition, it will be necessary to investigate the impact of temperature on the efficiency of strengthening systems for RC deep beams.

[13] [14] [15]

CRediT authorship contribution statement

[16]

Mohamed Ibrahim: Data curation, Formal analysis, Investigation, Methodology, Visualization, Writing - original draft, Writing - review & editing. Tadesse Wakjira: Formal analysis, Methodology, Visualization, Writing - original draft, Writing - review & editing. Usama Ebead: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing.

[17] [18] [19]

Acknowledgement

[20]

This paper was made possible by NPRP grant # NPRP 7-1720-2-641 from the Qatar National Research Fund (a member of Qatar Foundation) and by Qatar University grants QUST-CENG-SPR-14/15-15 and QUST-CENG-SPR-14/15-16. The authors would also like to acknowledge Qatar University for the Graduate Assistantship, students code GTRA-CENG-2019-16 and GTRA-CENG-2019-09. The findings achieved herein are solely the responsibility of the authors.

[21] [22] [23] [24]

Declaration of Competing Interest

[25]

The authors declare that they have no conflict of interest.

[26]

Appendix A. Supplementary material

[27]

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.engstruct.2020.110412.

[28]

References

[29]

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