Shear enhancement of reinforced concrete beams strengthened with FRP composite laminates

Composites: Part B 38 (2007) 781–793 www.elsevier.com/locate/compositesb

Shear enhancement of reinforced concrete beams strengthened with FRP composite laminates Ayman S. Mosallam *, Swagata Banerjee Civil and Environmental Engineering Department, University of California at Irvine, California 92697, United States Received 1 April 2006; accepted 1 October 2006 Available online 18 January 2007

Abstract This paper presents the results of an experimental investigation on shear strength enhancement of reinforced concrete beams externally reinforced with fiber-reinforced polymer (FRP) composites. A total of nine full-scale beam specimens of three different classes, as-built (unstrengthened), repaired and retrofitted were tested in the experimental evaluation program. Three composite systems namely carbon/epoxy wet layup, E-glass/epoxy wet layup and carbon/epoxy precured strips were used for retrofit and repair evaluation. Experimental results indicated that the composite systems provided substantial increase in ultimate strength of repaired and strengthened beams as compared to the pre-cracked and as-built beam specimens. A comparative study of the experimental results with published analytical models, including the ACI 440 model, was also conducted in order to evaluate the different analytical models and identify the influencing factors on the shear behavior of FRP strengthened reinforced concrete beams. Comparison indicated that the shear span-to-depth ratio (a/d) is an important factor that actively controls the shear failure mode of beam and consequently influences on the shear strength enhancement.  2007 Elsevier Ltd. All rights reserved. Keywords: A. Polymer-matrix composites (PMCs); B. Debonding; C. Analytical modelling; D. Mechanical testing; Infrastructure

1. Introduction Behavior of a reinforced concrete beam in shear is very complex in nature and difficult to predict accurately. For this reason, the shear capacity of beams in most codes of practice is empirical or semi-empirical. The shear behavior of RC beams depends on the size of the specimen, reinforcement type and detailing as well as the type and position of applied loading. Besides the concrete shear resistance capacity, additional contributions come from external and/or internal reinforcements of a RC beam specimen. Provided reinforcements help in improving the failure nature, brittle to ductile, to some extent. External shear strengthening using FRP composites gained popularity over steel because of several reasons

*

Corresponding author. E-mail address: [email protected] (A.S. Mosallam).

1359-8368/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2006.10.002

including material cost, lightweight feature and ease of application. Moreover FRP has more reliable bondline strength as compared to steel where corrosion at the interface is unavoidable in the presence of moisture [1]. 2. Related research work Over past few years, a number of theoretical investigations to predict the shear capacity of reinforced concrete beams strengthened externally with FRP wet layup laminates or precured strips were done and analytical models were developed based on different theoretical assumptions and experimental observations. Triantafillou [2] proposed a theoretical model to compute the shear strength capacity of a beam strengthened with externally applied FRP. Later on, this proposed model was calibrated using seventy-five published experimental test results [3] which resulted in an expression to predict the effective strain in FRP laminates. In year 2001, Matthys and Triantafillou [4] made

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A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

Nomenclature Af Asl Ast a b d df dv Ef fc0 ffe ffu fly fy k1 k2 Le n

area of FRP external reinforcement, mm2 (in.2) total area of longitudinal steel reinforcement, mm2 (in.2) total area of transverse steel reinforcement, mm2 (in.2) shear span of beam, mm (in.) width of beam, mm (in.) depth of beam, mm (in.) depth of FRP shear reinforcement, mm (in.) 0.9d = effective shear depth, mm (in.) tensile modulus of elasticity of FRP, MPa (ksi) compressive stress in concrete, MPa (ksi) effective stress in the FRP; stress level attained at section failure, MPa (ksi) design ultimate tensile strength of FRP, MPa (ksi) specified yield strength of longitudinal reinforcement, MPa (ksi) specified yield strength of transverse reinforcement, MPa (ksi) modification factor applied to jv to account for the concrete strength modification factor applied to jv to account for the wrapping scheme active bond length of FRP laminate, mm (in.) number of plies of FRP reinforcement

slight modification of Triantafillou and Antonopoulos [3] expression of effective strain and indicated that in addition to all other influential factors, effective strain in FRP is also a function of the beam shear span-to-effective depth ratio. However, Matthys and Triantafillou [4] made this comment on the basis of the least square fitting of experimental results collected from past literatures. Deniaud and Roger Cheng [5] presented a review summary of several shear design methods for reinforced concrete beams strengthened with composites. Colotti et al. [6] developed a theoretical model based on the truss analogy method in conjunction with the theory of plasticity. They reported that the theoretical model provided good correlation with past experimental results. Adhikary [7] conducted an experimental study on shear strengthening characteristics of continuous unidirectional flexible carbon/epoxy laminates bonded to RC beams. Several external reinforcement schemes were evaluated and it was concluded that the U-laminate configuration is the most effective strengthening protocol for shear strength enhancement. Lately, Zhang and Hsu [8] reported the result of an experimental study conducted on eleven beam specimens strengthened with both precured and wet layup composites systems. The recent edition of the ACI 440 [9] proposed a theoretical model to compute the enhancement of shear

s sf tf Vc Vn Vs Vf wf a efe efu jv mc, mco qf ql s su w we wi wf

spacing of internal steel stirrups, mm (in.) spacing FRP shear reinforcing, mm (in.) nominal thickness of one ply of the FRP reinforcement, mm (in.) nominal shear strength provided by concrete, N (lb) nominal shear strength, N (lb) nominal shear strength provided by steel stirrups, N (lb) nominal shear strength provided by FRP stirrups, N (lb) strip width of the FRP reinforcing plies, mm (in.) a/dv = ratio of shear span to effective shear depth effective strain level in FRP reinforcement design rupture strain of FRP reinforcement bond-dependent coefficient for shear effectiveness factors of concrete FRP reinforcement ratio longitudinal reinforcement ratio V/bd = nominal shear stress, MPa (ksi) bond strength, MPa (ksi) degree of shear reinforcement degree of external shear reinforcement degree of internal shear reinforcement additional FRP strength-reduction factor

strength of RC beams using external FRP laminates. They focused on the developed effective strain in composites at failure which varies depending upon the variability of composite material properties, dimensions and the application techniques. Therefore, it is extremely difficult to make any generalize solution for the shear strength enhancement of structural members using external FRP composite reinforcements. 3. Research significance This paper provides the results of the structural evaluation of different composite systems applied to full-scale reinforced concrete beams. A total of nine (9) reinforced concrete beam specimens (with and without applying FRP external reinforcement) were fabricated and tested up to the ultimate capacity of each specimen [10]. The composite system evaluated in this study included (i) carbon/ epoxy wet layup, (ii) E-glass/epoxy wet layup system, and (iii) precured carbon/epoxy strips. All testes were conducted in accordance to AC125 [11] and all materials used in fabricating the beam specimens conformed to AC85 [12]. In conjunction with the experimental program, analysis is also performed to compare the experimental result with the available theoretical models.

A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

4.1. Unstrengthened control (as-built) specimen Three reinforced concrete control specimens (B20, B21 and B22) with identical geometrical dimensions were tested till failure to determine the average ultimate shear capacity of unstrengthened beams and to identify the associated failure mode. Extremely large spacing between the stirrups is used (#3 steel stirrups spaced at 610 mm (24 in.)) such that the beam specimens were deficient in shear. In addition, the applied point loads are positioned closer to the support to induce the shear mode failure of the beam specimens. The typical test setup for all control specimens is shown in Fig. 1. Table 1 shows all test specimens evaluated in this study. The nominal 28-day compressive strength of the concrete used in fabricating the beam specimens was 27.54 MPa (4000 psi) with 6.35 mm pea gravel, and a slump in the range of 101.6 mm (4 in.)–152.4 mm (6 in.). Standard cylinders were poured from each batch of concrete. Tests were performed on these cylinders at the same day of each test to determine the average concrete strength fc0 . 4.2. Shear strengthening application The objective of this experimental phase is to evaluate capabilities of the different composite strengthening systems in rehabilitation of shear deficient reinforced concrete beams. In designing the beam specimens, the beam spans were configured to induce shear limit states and failure modes. Extremes of dimensional, reinforcing, and compressive strength are considered following Section 5.4.2.1

of AC125 [11]. As the control (as-built) specimens, minimum shear reinforcements are used (#3@ 610 mm). The positions of the applied loads are selected such that shear failure is predominant for cross-sectional dimensions of all beams evaluated in the program which is lower than the minimum ACI-318 [13] required shear reinforcements. In all beam specimens, the spacing was taken as an extreme value of 610 mm (24 in.) which is lower than that required by ACI-318 [13] which is 559 mm (22 in.). The shear spanto-depth ratio (a/d) has been designed to induce shear failure (a/d = 1.8) which satisfies the definition of shear beam as illustrated in Fig. 2. The test set up without FRP laminates and loading scheme are shown in Fig. 3. The

Shear-compression Strength

Flexural Moment Strength

Failure Moment, Va

4. Experimental program

783

Inclined Cracking Strength, Vc

Shear-tension and Shear-compression Failures

Deep Beams

0

1

2

Diagonal Tension Failures

3

4

5

Flexural Failures

6

7

Ratio of Shear Span to Beam Depth, a/d Fig. 2. Variation of shear strength with a/d ratio for rectangular RC beams.

Fig. 1. Dimensions and internal steel reinforcement of as-built beam specimens.

Table 1 Beam strengthening test matrix Specimen type

Specimen #

Description of specimen

As-built

B20 B21 B22

As-built beam As-built beam As-built beam

Repaired

B21R B20R B22R

Two layers of unidirectional transverse E-glass/epoxy laminates One layer of unidirectional transverse carbon/epoxy laminates Precured carbon/epoxy strips @ 6 in. on each side

Retrofitted

B3 B5 B19

Two layers of unidirectional transverse E-glass/epoxy laminates One layer of unidirectional transverse carbon/epoxy laminates Precured carbon/epoxy strips @ 6 in. on each side

784

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Fig. 3. Loading regime used for shear beams evaluation.

following sections describe the details of tests performed on the three FRP repairing and three FRP strengthening systems for beam shear upgrade.

4.3. Lamination schedule for repair and retrofit applications As mentioned earlier, three FRP composite systems evaluated in this program including wet layup laminates and precured strips in different strengthen configurations.

The physical and mechanical properties of these FRPs are shown in Table 2. 4.3.1. Wet layup systems For the wet layup strengthening systems, the U-lamination schedule for both repaired (B21R and B20R) and rehabilitated beam specimens (B3 and B5) are performed as presented in Fig. 4. For the E-glass/epoxy wet layup system, two U-plies were used (specimens B3 and B21R) while only one U-ply of carbon/epoxy was applied on specimens

Table 2 Properties of FRP composites materials Beam specimens

FRP layout systems

Layer of laminate n

Applied thickness tp, mm (in.)

B3, B21R

E-glass/epoxy wet layup Carbon/epoxy wet layup Precured carbon/ epoxy strips

2

2.1 (0.083)

510 (74)

0.022

24.2 (3.5 · 103)

1

1.6 (0.063)

1061 (154)

0.012

96.5 (14 · 103)

1

1.19 (0.047)

2896 (420)

0.018

151.7 (22 · 103)

B5, B20R B19, B22R

Ultimate strength r11, MPa (ksi)

Ultimate strain e11

Modulus of elasticity E11, GPa (ksi)

Fig. 4. Typical shear strengthening details for E-glass/epoxy and carbon/epoxy wet layup systems for shear strengthening applications.

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785

Fig. 5. Dimensions and typical laminates details for precured carbon/epoxy strips systems for shear strengthening applications.

B5 and B20R with the dimensions shown in Fig. 4. In this lamination configuration, the sides of the U-shaped laminates are extended vertically from the bottom of the beam to cover the sides for a depth of 152.4 mm (6 in.) i.e. 0.6 d.

ative humidity during the test were 72 F (22 C), and 60%, respectively. The ultimate and near-ultimate tests were performed in a 488.68 kN (110 kips) universal-testing steel frame.

4.3.2. Precured carbon/epoxy strips system The FRP composite strengthening details that were adopted for all repaired (B22R) and rehabilitated (B19) beam specimens with procured carbon/epoxy strips were shown in Fig. 5. As shown in this figure, 50.8 mm · 152.4 mm (2 in. · 6 in.) precured carbon/epoxy vertical strips were bonded to both sides of the beam specimens with 101.6 mm (4 in.) center-to-center equal spacing covering the shear spans of each specimen. Prior to the application of the composite laminates to the pre-cracked beam specimens for repair and as-built beam specimens for retrofit, the concrete surface is mechanically grinded and cleaned, and the cracks and voids are filled with low-viscosity epoxy resin.

5. Test result

4.4. Loading scheme For all tests, the load was applied using a four-point loading configuration with a constant rate of ramp loading of 8.9 kN (2 kips) per minute. Loads were applied monotonically in a vertical downward direction until failure occurred and beam specimens would no longer sustain additional load. The average temperature and average rel-

5.1. As-built shear beam specimens In all tests, no cracks were observed until near the ultimate load. The development of shear cracks at the maximum shear span were developed suddenly in about 45 inclination, followed by a sudden shear failure in one side of the beam specimens as illustrated in Fig. 6. The load– deflection (P/d) curves of the as-built shear beam specimens are shown in Fig. 7. The average ultimate failure load of these as-built specimens is 69.48 kN (15.62 kips). 5.2. Repaired beam specimens 5.2.1. Carbon/epoxy wet layup repair evaluation (specimen B20R) The repair protocol composed of one ply of carbon/ epoxy wet layup system which were applied to the treated shear spans concrete surfaces of the pre-damaged beam specimen (B20) and was designated as B20R after being repaired. Fig. 8 shows the load/deflection (P/d) curves at mid span of the pre-cracked specimen (B20) and the

Fig. 6. Typical shear failure of as-built shear specimen.

A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

0.1

0.2

0.3

0.4 22.5

100

P (kN)

13.5 50 9.0 25

P (kips)

18.0

75

4.5

0

0.0 0

2

4

6

8

10

Mid Span Deflection (mm) Fig. 7. Load–deflection curves for as-built shear beam specimens.

Mid Span Deflection (in) 0

1

2

3

4

150

35

Repaired (B20R)

30

As-Built (B20)

120

90

20 15

60

P (kips)

P (kN)

25

10 30 5 0 0

20

40

60

80

0 100

Mid Span Deflection (mm) Fig. 8. Load–deflection curves before and after repair of beam specimen B20.

repaired specimen (B20R) with epoxy injection and carbon/epoxy wet layup laminates. As shown in Fig. 8, the stiffness of precracked specimen, as expected, was higher than and repaired specimen, especially at low load levels and up to 26.7 kN (6 kips) after which slight degradation in the precracked specimen is observed. It is clear that the behavior of the precracked specimen was bi-linear which indicates the brittleness of the specimen followed by a sudden localized shear failure in one of the shear spans. Unlike the precracked specimen, the ductility of the same specimen after being repaired (B20R) has been improved by switching the original brittle shear failure to a more ductile flexural failure. The ultimate capacity of the repaired specimen was 125.75 kN (28.27 kips) which indicates that the carbon/epoxy wet layup system succeeded in restoring the original capacity of the damaged beam and added a strength of 47.24% to the ultimate capacity of the as-built beam specimen (B20). The ultimate failure mode of the repaired specimen was a typical concrete crushing. The mid-span deflection at the ultimate load was 91.44 mm (3.6 in.).

5.2.2. E-glass/epoxy wet layup repair evaluation (specimen B21R) The repair protocol composed of two plies of E-glass/ epoxy wet layup system which were applied to the treated shear spans concrete surfaces of the pre-damaged beam specimen (B21) and was designated as B21R after being repaired. The behavior of this specimen was identical to that for the carbon/epoxy wet layup repaired specimen (B20R) reported earlier. Fig. 9 shows the load/deflection (P/d) curves at mid span for the pre-cracked specimen B21, and the same specimen repaired with epoxy injection and E-glass/epoxy wet layup laminates (B21R). As shown in this figure, the stiffness of the precracked specimen, as expected, was higher than the repaired specimen, especially at low load levels up to 27.36 kN (6.15 kips). The behavior of the repaired specimen was linear up to a load level of 84 kN (18.9 kips) after which, a non-linear behavior was observed and continued until the ultimate failure. The ultimate capacity of this repaired specimen was 107.06 kN (24.07 kips) which is 1.45 times higher than the capacity of pre-damaged specimen. The corresponding mid-span deflection at the ultimate load was 93.5 mm (3.681 in.). 5.2.3. Carbon/epoxy precured strips repair evaluation (specimen B22R) The repair protocol composed of five strips of carbon/ epoxy precured strips which were applied to the treated shear spans concrete surfaces of the pre-damaged beam specimen (B22) shown in Fig. 6 for a typical case and was designated as B22R. The repair scheduled was done as shown in Fig. 5 with minor modification in the spacing under the loading points due to the severity of the damage. Fig. 10 shows the load/deflection (P/d) curves at midspan for the pre-damaged specimen B22 and the same specimen after repair with the carbon/epoxy strips (B22R). As shown in this figure, the behavior of the repaired specimen

Mid Span Deflection (in) 0

1

2

3

4 35

150

Repaired (B21R)

30

As-Built (B21)

120

25 90

20

60

15

P (kips)

Mid Span Deflection (in) 0

P (kN)

786

10 30 5 0 0

20

40

60

80

0 100

Mid Span Deflection (mm) Fig. 9. Load–deflection curves before and after repair of beam specimen B21.

A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

Mid Span Deflection (in)

Mid Span Deflection (in) 0.59

1.18

1.77

0

2.36

3

4 35

Retrofitted (B5)

Repaired (B22R) 30

As-Built (B22)

120

2

150

35

150

1

30

As-Built (B20)

120

25

20

60

15 10

30

P (kN)

90

P (kips)

P (kN)

25 90

20

60

15 10

30 5

5 0

0 0

10

20

30

40

50

60

P (kips)

0

787

0 0

20

40

60

80

0 100

Mid Span Deflection (mm)

Mid Span Deflection (mm) Fig. 10. Load–deflection curves before and after repair of beam specimen B22.

was linear up to a load level of 97.41 kN (21.9 kips) after which non-linear behavior was observed up to the ultimate failure. As the load increased, a diagonal crack was initiated at the boundaries of the vertical carbon/epoxy strips. This size and length of the crack increased as the load increased until the ultimate shear failure. The predominant failure mode was a shear failure rather than flexural failure as was witnessed in the wet layup repair described in earlier two cases. This can be attributed to the fact that the FRP external reinforcement was not continuous and shear cracks initiated at the unstrengthened areas of the shear spans. The ultimate capacity of the repaired specimen (B22R) was 113.9 kN (25.6 kips) which is 1.8 times of the original capacity of the as-built specimen. The deflection at the ultimate load was 51.8 mm (2.04 in.) as compared to 5.76 mm (0.227 in.) for the as-built specimen (B22). 5.3. Retrofitted beam specimens 5.3.1. Carbon/epoxy wet layup retrofit evaluation (specimen B5) Fig. 11 shows the load/deflection (P/d) curves at mid span of the control (as-built) specimen, and the shear

Fig. 11. Load–deflection curves for composite retrofitted specimen B5 and as-built specimen B20.

strengthened specimen (B5) using carbon/epoxy wet layup system. For the shear-strengthened specimen, the behavior was linear up to a load level of 91 kN (20.48 kips) after which non-linear behavior was observed up to the ultimate load. As compared to the ultimate capacity of the unstrengthened beam (B20), the capacity of the retrofitted specimen was 1.6 times of the original capacity (133.2 kN (29.94 kips) vs. 85.4 kN (19.2 kips)). The deflection at the ultimate load was 9.8 times higher than the corresponding deflection of the as-built specimen (87.6 mm (3.45 in.) vs. 9 mm (0.35 in.)). The mode of failure was ductile flexural failure (Fig. 12) due to a localized compression under the left line load. 5.3.2. E-glass/epoxy wet layup retrofit evaluation (specimen B3) As shown in Fig. 13, the behavior of this specimen was identical to that of specimen B5 retrofitted with carbon/ epoxy laminates. However, the ultimate strength of this specimen (121.4 kN (27.29 kips)) was slightly lower than the shear strength of B5. As compared to the strength of the as-built specimen (B20), the strength of this specimen was 1.42 times of the original capacity (121.4 kN (27.29 kips) vs. 85.4 kN (19.2 kips)). The deflection at the

Fig. 12. Failure of retrofitted specimen B5.

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A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

failure of specimen B3 changed from a brittle shear mode to a more ductile flexural mode. The ultimate failure was in the form of compression crushing of the concrete near the line loads as shown in Fig. 14.

Mid Span Deflection (in) 0

1

2

3

4 35

150

Retrofitted (B3)

30

As-Built (B20)

120

90

20

60

15

P (kips)

P (kN)

25

10 30 5 0 0

20

40

60

80

0 100

Mid Span Deflection (mm) Fig. 13. Load–deflection curves for composite retrofitted specimen B3 and as-built specimen B20.

ultimate load of the retrofitted specimen (B3) was 84 mm (3.32 in.), whereas that in the as-built specimen was 9 mm (0.35 in.). Again, like specimen B5 the ultimate mode of

5.3.3. Carbon/epoxy precured strips retrofit evaluation (specimen B19) This retrofitted beam specimen (B19) is shown in Fig. 15. Fig. 16 shows the load/deflection (P/d) curves at mid-span of the as-built specimen (B20) and the strengthened specimen (B19). As shown in this figure, the behavior of the retrofitted specimen was linear up to a load level of 96.79 kN (21.76 kips) after which non-linear behavior was observed up to the ultimate failure. As the load increased, a diagonal crack was initiated at the boundaries of the third vertical carbon/epoxy procured strip as shown in Fig. 17. At the ultimate load, the shear span slide along the inclined cracked plane. This relative rigid-body movement of the two parts of the beam resulted in a cohesive failure of the second strip from the line load. As expected,

Fig. 14. Failure of retrofitted specimen B3.

Fig. 15. External shear strengthening details of specimen B19 retrofitted with precured carbon/epoxy strips.

A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

capacity of an externally FRP reinforced beam specimen. In this paper, four models are used to study the predicted shear strength capacity of the retrofitted beam specimens (B3, B5 and B19) and compare those with experimental result. The analytical models are described in the following part of this paper.

Mid Span Deflection (in) 0.0

0.5

1.0

1.5

2.0

150

35

Retrofitted (B19)

30

As-Built (B20)

120

20 15

60

P (kips)

P (kN)

25 90

10 30 5 0

0 0

10

20

30

40

789

50

Mid Span Deflection (mm) Fig. 16. Load–deflection curves for composite retrofitted specimen B19 and as-built specimen B20.

the predominant failure mode was a shear failure rather than flexural failure. This can be attributed to the fact that the FRP external reinforcement was not continuous and shear cracks initiated at the unstrengthened areas of the shear spans. The ultimate capacity of this specimen was 110.93 kN (24.94 kips) which is 1.3 times of the original capacity of the as-built specimen. The deflection at the ultimate load was 31.4 mm (1.235 in.) as compared to 9 mm (0.353 in.) for the as-built specimen (B20). 6. Analytical study In the recent past, few analytical models are developed by researchers to theoretically predict the shear strength

6.1. ACI 440 [9] model The model proposed by ACI 440 [9] is applicable to reinforced concrete beams with externally applied FRP reinforcement. According to this model, the nominal shear strength of concrete is V n ¼ V c þ V s þ wf V f

ð1Þ

where wf is the additional reduction factor given in Table 10.1 of the ACI 440 [9] document. For comparison purpose, as there is no reduction factor considered during experiment, Eq. (1) is modified as Vn ¼VcþVsþVf

ð2Þ

where the shear strength contribution form FRP is Vf ¼

Af Ef efe d f sf

ð3Þ

The effective strain, efe in FRP is assumed to be smaller than the ultimate strain, efu. This can be computed as 8 0:004 6 0:75efu > > > < for completely wrapped beams ð4Þ efe ¼ > k v efu 6 0:004 > > : for beams with two or three sides laminated

Fig. 17. Ultimate failure of specimen B19 retrofitted with procured carbon/epoxy strips.

790

kv ¼ Le ¼

A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

k 1 k 2 Le 6 0:75 11; 900efu 23; 300

ð6Þ

0:58

ðntf Ef Þ  0 2=3 fc k1 ¼ 27 ( d f Le k2 ¼

ð5Þ

df

ð7Þ ð8Þ

for two sides laminated

where, fc0 and Ef are in MPa. 6.2. Colotti et al. [6] model Colotti et al. [6] proposed that the total contribution of shear reinforcement can be expressed as w ¼ wi þ we

ð9Þ

The internal shear strength contribution coming from the internal steel reinforcement is wi ¼

Ast fy bsf 0c

According to this model, V n ¼ V c þ V s þ V f 6 V R2 ¼ 0:45mco fc0 bd Af Ef efe d f sf

ð17Þ

Tensile strength of concrete, fct ¼ 0:3ðfc0 Þ2=3 , concrete shear resistance, sR = 0.25fct, k = 1.6  d P 1 (d is in m), ql ¼ Abdsl , qf ¼ bsAff , and mco ¼ 0:7  fc0 =200 > 0:5 ðfc0 is in MPaÞ. The effective strain in this model expected was 8  2=3 0:30 > > efu 0:17 Efcf qf > > > > > > for beams fully wrapped with CFRP > >  <  2=3 0:56  2=3 0:30 efe ¼ min 0:00065 Efc q ; 0:17 Efcf qf efu f f > > > > > > for two or three sides laminated with CFRP > >  0:47 > > : 0:048 fc2=3 efu for beams fully wrapped with AFRP E f qf

ð10Þ

whereas, the external contribution form FRP is 8 2wf tf f > bsf fc0 fe > > > < for completely wrapped beams   we ¼ wf d f 2wf tf > min bs > 0 su ; bs f 0 f > f c f c > : for beams with two or three sides laminated ð11Þ where the effective stress, ffe = mfffu. The shear strength of a beam specimen   V ¼ s=fc0 bd v fc0

ð13Þ

For w > w0 "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # 2g 0 2 þa a s=fc ¼ w w A f

where g ¼ bdslv fly0 and a ¼ dav . c

6.4. Matthys and Triantafillou [4] model Matthys and Triantafillou [4] made a modification in Triantafillou and Antonopoulos [3] model and incorporated the effect of shear span to beam depth ratio in the calculation of effective strain. According to their modification, the effective strain can be expressed as

0:72efu e0:0431Cf 0:56efu e0:0455Cf

ð14Þ

ð15Þ

for beams fully wrapped with CFRP for two or three sides laminated with CFRP

ð19Þ

ð12Þ

Failure case (1) 8 pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi

1þa2 a > 1 2  a þ wa > p ffiffiffiffiffiffiffi 1 þ a for 0 6 w 6 w ¼ > 0 <2 2 1þa2 0 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi s=fc ¼ wð1 þ wÞ for w0 6 w 6 0:5 > > > :1 for w > 0:5 2 Failure case (2) For w 6 w0 ( pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 4gð1  gÞ þ a2  a for g 6 0:5 2 0 s=fc ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi

1 1 þ a2  a for g > 0:5 2

ð18Þ

efe ¼

where s=fc0 is the minimum of that obtained from the following failure cases:

ð16Þ

where Vf ¼

for U-wraps

d f 2Le df

6.3. Triantafillou and Antonopoulos [3] model

where Cf ¼

Ef qf 2=3 fc ða=dÞ

ð20Þ

7. Comparison Result from both the analytical and the experimental study are shown in Figs. 18–20 and Table 3. Fig. 18 shows the comparison of total shear capacity of beam specimen strengthened with carbon/epoxy wet lay up laminate. As this figure indicates, both the ACI 440 [9] model and Triantafillou and Antonopoulos [3] model over predict the shear capacity of the retrofitted beams, whereas Colotti et al. [6] model results nearly the same shear capacity as obtained from the current experimental program. However, in this case, Matthys and Triantafillou [4] model gives conservative result. The predicted shear strength from analytical models using E-glass/epoxy wet lay-up system and experimental results are shown in Fig. 19. This figure shows similar trend as Fig. 18, except of Matthys and Triantafillou [4] model

A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

Table 3 Experimental and analytical results of shear capacity of retrofitted beam specimens

125

Shear Capacity (kN)

100

50

0

Experimental

ACI 440 Model

Colotti et al. Model

Triantafillou and Antonopoulos Model

Matthys and Triantafillou Model

Fig. 18. Computed shear capacity for various models using carbon/epoxy laminate (1 kN = 0.225 kips).

125

Shear Capacity (kN)

FRP layout systems for shear strengthening

E-glass/ epoxy wet layup

Carbon/ epoxy wet layup

Precured carbon/epoxy strips

Retrofitted beam specimens Experimental result (kN) ACI 440 model (kN) Colotti et al. model (kN) Triantafillou and Antonopoulos model (kN) Matthys and Triantafillou model (kN)

B3

B5

B19

60.7

66.60

55.46

94.17 56.39

109.47 56.39

68.16 55.18

103.76

117.99

100.17

65.73

41.18

63.98

75

25

100 75 50 25 0

Experimental

ACI 440 Model

Colotti et al. Model

Triantafillou and Antonopoulos Model

Matthys and Triantafillou Model

Fig. 19. Computed shear capacity for various models using E-glass/epoxy laminate (1 kN = 0.225 kips).

125

100

Shear Capacity (kN)

791

75

50 25

0

Experiment

ACI 440 Model

Colotti et al. Model

Triantafillou and Antonopoulos Model

Matthys and Triantafillou Model

Fig. 20. Computed shear capacity for various models using precured carbon strips (1 kN = 0.225 kips).

that predicts similar shear capacity as the current experimental result. Results using precured carbon/epoxy strips are presented in Fig. 20. Comparison of analytical study and experimental result indicates that Triantafillou and Antonopoulos [3] model overestimates the shear capacity of the strengthened beam. Among other three analytical models, the ACI 440 [9] model results higher capacity than experimental result whereas Colotti et al. [6] model and Matthys and Triantafillou [4] model predict nearly same result (Fig. 20). From the three figures, Figs. 18–20, it is evident that the ACI 440 [9] model and Triantafillou and Antonopoulos [3] model are always provide shear strength of a FRP strengthened beam higher than these obtained from the experimental program. This can be attributed to the fact that these two models have not considered the shear span-to-depth ratio (a/d) of the beam in calculation of the shear strength. However, Matthys and Triantafillou [4] model considers that factor, and according to Figs. 19 and 20, this model results in a shear capacity nearly the same as the experimental result. Colotti et al. [6] model also have considered a/d ratio, and therefore, predicted shear force is very close to the experimental result. Hence, from these results it is evident that shear span-to-depth ratio has an important effect on the shear strength capacity of a RC FRP strengthened beams. Bousselham and Chaallal [14] showed the influence of shear span-to-depth ratio (a/d) on shear force gain for RC beams with four-point loading. According to Bousselham and Chaallal [14] conclusion, when a/d ratio is less than 2.5, the failure is predominantly by fracture and when it is greater than 3.2, failure occurs due to the debonding of the FRP reinforcement. As discussed earlier, the experimental models are constructed such that the beams have a/d = 1.8. Hence, obtained failure modes in experiment (due to fracture) are consistent with the literature [14]. In order to account for the wrapping schemes influence of the different laminates, the ACI 440 [9] model introduced the k2 factor (Eq. (9)). Fig. 21 graphically demonstrates that

792

A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793

Fig. 21. Effective width of FRP external reinforcements: (a) FRP sheets bonded two sides of beam; (b) FRP strips bonded two sides of beam.

when the beam is laminated with FRP composites in two sides, the shear cracks propagate at an angle 45 to the longitudinal axis of the beam. This figure indicates, for beams bonded with ‘continuous’ FRP laminates (FRP sheets) the consideration of k2 factor is logical, although is not true when beam is laminated with ‘isolated’ FRP strips with a gap in between two strips. For beams strengthened with equally spaced carbon/epoxy strips, deduction of twice the active bond length (Le) from the depth of FRP reinforcement (df) may result in underestimating the effective width of FRP. This is because in the case of equally spaced strips, the concrete between two adjacent FRP strips are not covered with the FRP reinforcement (Fig. 21) and shear cracks would likely to be initiated from the free concrete surface of the beam in between two adjacent FRP strips. This phenomenon is clear from the ultimate failure mode of beam specimen B19 (Fig. 17). 8. Conclusions and recommendations The objective of the experimental program was to evaluate the ultimate shear strengths, and to identify modes of failure of as-built, repaired and retrofitted beam specimens. Testing was performed per the requirements of Section 5.4 of the ICBO ES acceptance criteria for concrete and reinforced and unreinforced masonry strengthening using fiber-reinforced, composite systems (AC125), and all materials used in this programmed were sampled randomly and selected according to the requirements of ICBO ES AC85. Based on the experimental results conducted on reinforced concrete beam specimens repaired and retrofitted with the three FRP composite systems (TufLamTM-E, TufLamTM-C and TufLamTM-CS), it is evident that the FRP composite systems provided appreciable increase and enhancement in both ultimate strength and toughness of strengthened beams as compared to the original as-built beam specimens. The following points are concluded based on the comparison of the experimental result with different theoretical models discussed in this paper: (i) The ACI 440 [9] model does not consider the shear span-to-depth ratio (a/d) in prediction of the shear strength enhancement of a reinforced concrete beam strengthened with externally applied FRP laminate(s). For lesser a/d ratio (e.g. a/d = 1.8, as it is taken in the

present experimental program), the experimental shear strength capacity is always less than those predicted by the ACI 440 [9] model. (ii) As suggested by the ACI 440 [9] model, the deduction of effective FRP area due to the lamination scheme is not valid for beams strengthened with FRP strips. For this reason, the ACI 440 [9] model underestimates the shear strength capacity of such beams. (iii) Similar to the ACI 440 [9] model, Triantafillou and Antonopoulos [3] model always results in higher shear strength. This can be attributed to the fact that this model does not consider the shear span-to-depth ratio (a/d). Matthys and Triantafillou [4] model provides well prediction of the retrofitted shear strength capacity as it considers the effect of shear span-to-depth ratio (a/d). (iv) Colotti et al. [6] model provides nearly the same estimation of the shear capacity of FRP strengthened beams as compared to experimental result in all three lamination schemes reported in this paper. Based on these above observations, it is recommended that the ACI 440 [9] model should be revised in order to (i) take into account the influence of shear span-to-depth ratio (a/d) of a FRP strengthened beam in its ultimate shear capacity calculation, and (ii) to properly predict the influence of wrapping scheme on shear capacity of a strengthened beam with FRP composites strips. Acknowledgements The research study reported in this paper is a part of a comprehensive ICC-ES evaluation program for SCCI (Structural Composite Construction Inc) TufLamTM Composites Strengthening Systems. The financial support of SCCI is acknowledged and the support of Mr. J. Negele is highly appreciated. The assistance of Salter Waterproofing Company staff, headed by Mr. Slater and Mr. McCauley, in laminating the specimens is highly appreciated. The contribution of Mr. James Kiech in the experimental program is acknowledged. References [1] Mosallam A. Composites in construction. In: Kutz M, editor. Handbook of materials selection. New York: John Wiley & Sons, Inc.; 2002 [chapter 45]. [2] Triantafillou TC. Shear strengthening of reinforced concrete beams using epoxy-bonded FRP composites. ACI Struct J 1998;95(20):107–15. [3] Triantafillou TC, Antonopoulos CP. Design of concrete flexural members strengthened in shear with FRP. J Compos Construct, ASCE 2000;4(4):198–205. [4] Matthys S, Triantafillou TC. Shear and torsion strengthening with externally bonded FRP reinforcement. In: Reality A, Cosenza E, Manfredi G, Nanni N, editors. Proceedings of the international workshop on composite in construction, Capri, Italy, July 20–21, 2001. p. 203–10. [5] Deniaud C, Roger Cheng JJ. Review of shear design methods for reinforced concrete beams strengthened with fibre reinforced polymer sheets. Can J Civ Eng 2001;28:271–81.

A.S. Mosallam, S. Banerjee / Composites: Part B 38 (2007) 781–793 [6] Colotti V, Spadea G, Swamy RN. Analytical model to evaluate failure behavior of plated reinforced concrete beams strengthened for shear. ACI Struct J 2004;101(6):755–64. [7] Adhikary B. Behavior of concrete beams strengthened in shear with carbon-fiber sheets. ASCE J Compos Construct 2004;8(3): 258–64. [8] Zhang Z, Hsu C-TT. Shear strengthening of reinforced concrete beams using carbon-fiber-reinforced polymer laminates. J. Compos Construct 2005;9(2):158–69. [9] ACI Committee 440. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures (ACI 440.2R-02). American Concrete Institute, Farmington Hills, Michigan, USA; 2003. [10] Mosallam A. Structural evaluation of SCCI FRP composite system for flexure and shear repair and upgrade of reinforced concrete

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beams. CSUF Test Report # SRRS-SCCI, California State University, Fullerton; 2002. AC125. Interim criteria for concrete and reinforced and unreinforced masonry strengthening using fiber-reinforced polymer (FRP) composite systems. International Code Council’s Evaluation Service (ICC-ES), Whittier, California, USA; 2003. AC85. Acceptance criteria for test reports and product sampling. International Code Council’s Evaluation Service (ICC-ES), Whittier, California, USA; 2003. American Concrete Institute (ACI). Building code requirements for structural concrete. ACI 318-05, Farmington Hills, Michigan, USA; 2005. Bousselham A, Chaallal O. Shear strengthening reinforced concrete beams with fiber-reinforced polymer: assessment of influencing parameters and required research. ACI Struct J 2004;101(2):219–27.