Strengthening of reinforced concrete slabs with mechanically-anchored unbonded FRP system

Construction and Building

MATERIALS

Construction and Building Materials 22 (2008) 444–455

www.elsevier.com/locate/conbuildmat

Strengthening of reinforced concrete slabs with mechanically-anchored unbonded FRP system Tamer El Maaddawy a

a,*

, Khaled Soudki

b

Department of Civil and Environmental Engineering, UAE-University, Al Ain, P.O. Box 17555, Abu Dhabi, United Arab Emirates b Department of Civil Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 Received 12 June 2006; accepted 12 July 2007 Available online 4 September 2007

Abstract The potential use of mechanically-anchored unbonded fibre reinforced polymer (MA-UFRP) system to upgrade reinforced concrete (RC) slabs deficient in flexural strength is examined in this paper. A total of six RC slabs, each having 500 mm width, 100 mm thickness, and 1800 mm length, were constructed and tested to failure under four-point bending. Each slab was reinforced with three No. 10 deformed steel bars at tension side that corresponded to 0.8% steel reinforcement ratio. One slab was used as a control while the other five slabs were strengthened with various fibre reinforced polymer (FRP) strengthening systems, each having 0.12% external FRP reinforcement ratio. Two slabs were strengthened with externally-bonded FRP (EB-FRP) system, one slab with end-anchorage and one slab without end-anchorage. The remaining three slabs were strengthened with MA-UFRP system having various anchors’ locations. Test results showed that MA-UFRP system resulted in up to 43% enhancement in the slab flexural strength. The strength of the slabs strengthened with MA-UFRP system was on average 18% lower than that of the slab strengthened with EB-FRP system with endanchorage but only 10% lower than that of the slab strengthened with EB-FRP system without end-anchorage. The mid-span deflection at ultimate load of the slabs strengthened with MA-UFRP system was on average 56% higher than that of the slab strengthened with EBFRP without end-anchorage, 5% higher than that of the slab strengthened with EB-FRP with end-anchorage, and only 15% lower than that of the control.  2007 Elsevier Ltd. All rights reserved. Keywords: Flexural; Slabs; Strengthening; FRP; Unbonded; Anchors

1. Introduction Strengthening of reinforced concrete (RC) structures is frequently required due to inadequate maintenance, excessive loading, change in use or in code of practice, and/or exposure to adverse environmental conditions. Several strengthening techniques have been developed in the past and used with some popularity including steel plate bonding, external prestressing, and reinforced concrete jacketing. Although these techniques can effectively increase the element’s load carrying capacity, they are often susceptible *

Corresponding author. Tel.: +971 50 8310915; fax: +971 3 7623154. E-mail addresses: [email protected] (T. El Maaddawy), [email protected] (K. Soudki). 0950-0618/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2007.07.022

to corrosion damage which results in failure of the strengthening system. Consequently, non-corrosive innovative strengthening systems, such as fibre reinforced polymers (FRPs), that have the potential for extending service lives of RC structures and reducing maintenance costs are required to replace old strengthening systems. Various FRP strengthening systems are currently being used in retrofitting and upgrading of RC structures. The most popular one is the externally-bonded fibre reinforced polymer (EB-FRP) in which an FRP strip is bonded to the tension face of the flexural element using a structural adhesive. Numerous studies showed that EB-FRP strengthening system is effective in increasing the flexural capacity of RC elements [1–4]. However, EB-FRP system is often vulnerable to fail prematurely in a brittle manner due to

T. El Maaddawy, K. Soudki / Construction and Building Materials 22 (2008) 444–455

445

Nomenclature

delamination of the bonded FRP strip. Accordingly, several researchers recommended the use of various endanchorage systems to avoid such a sudden premature debonding failure and to ensure that strengthened members will develop their full flexural capacity [5–7]. EB-FRP system requires careful surface preparation and adhesive application. The concrete surface must be cleaned and sandblasted prior to the application of the FRP strip. The structural adhesive is usually two parts that must be precisely mixed and then applied to the concrete surface in a controlled manner to ensure good bonding between FRP and concrete. Surface preparation and adhesive application are time and labour consuming [8–10]. This paper aims at examining the potential use of mechanically-anchored unbonded FRP (MA-UFRP) system to upgrade RC slabs deficient in flexural strength. MA-UFRP system does not require surface preparation, adhesive application, or skilled labour. The structural performance of RC slabs strengthened with MA-UFRP system was studied and compared to that of slabs strengthened with EB-FRP system. The effect of varying the number and location of anchors along the slab span on concrete compressive strain, FRP strain, and overall flexural behaviour is investigated. A non-linear sectional analysis that accounts for the strain incompatibility between the unbonded FRP strip and the concrete is then developed and utilized to verify test results. Finally, a parametric study was undertaken to study the effect of varying the bond condition between FRP and concrete on the slab flexural behaviour. 2. Test specimen Test specimen was 1800 mm long, 500 mm wide, and 100 mm deep. Each slab was singly reinforced at tension side by three No. 10 deformed steel bars with a concrete

h height of slab external bending moment Mext Mint internal bending moment P load a1 & b1 stress block factors ec concrete strain eco concrete strain corresponding to the concrete compressive strength ecu concrete crushing strain ef CFRP strain efr CFRP rupture strain es steel strain esu steel ultimate strain esy steel yield strain v bond factor

500 100

area of steel reinforcement area of CFRP reinforcement width of slab depth of neutral axis depth of tension steel reinforcement Young’s modulus of CFRP composite steel Young’s modulus steel strain hardening modulus concrete compressive stress concrete compressive strength concrete tensile strength CFRP stress CFRP rupture strength steel stress steel ultimate strength steel yield stress

3-No.10 deformed steel bars

50 x 1.2 mm CFRP strip

Cross section

100

As Af b c d Ef Es Esp fc fc0 fcr ff ffr fs fsu fy

500

500

500

1800 Elevation (All dimensions are in mm)

Fig. 1. A typical test specimen with end-anchorage.

clear cover of 20 mm. This corresponded to a steel reinforcement ratio of about 0.8%. For the strengthened slabs, one carbon fibre reinforced polymer (CFRP) strip having a width of 50 mm and a thickness of 1.2 mm was bonded to the tension face of the slab. This corresponded to a CFRP reinforcement ratio of about 0.12%. Fig. 1 shows a schematic of a typical test specimen with end-anchorage. 3. Test matrix The test matrix is given in Table 1. A total of six slabs were used in the present study. One slab was used as a control while the other five slabs were strengthened with either EB-FRP or MA-UFRP systems. Two slabs, B-NA and BMA-2, were strengthened with EB-FRP system. Slab BMA-2 had two anchors, one anchor at each end, while slab B-NA had no anchors. The remaining three slabs, U-MA2, U-MA-3, and U-MA-4, were strengthened with MAUFRP system. Slab U-MA-2 had two anchors, one anchor at each end while slab U-MA-3 had three anchors, one

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Table 1 Test matrix Specimena

Strengthening system

Condition of CFRP

Number of anchors

Control B-NA B-MA-2 U-MA-2 U-MA-3 U-MA-4

– EB-FRP EB-FRP MA-UFRP MA-UFRP MA-UFRP

– Bonded Bonded Unbonded Unbonded Unbonded

– – 2 2 3 4

a

B and U refer to Bonded and Unbonded FRP strips, respectively. NA and MA refer to No Anchor and Mechanical Anchor, respectively.

15 mm diameter. The steel plate was placed below the CFRP strip and held in place using four M12 bolts which were inserted into holes pre-drilled through the slab thickness at desired locations. One aluminium sheet was placed between the steel plate and the CFRP strip and another one was placed between the CFRP strip and the bottom soffit of the slab in an effort to avoid premature rupture of the CFRP strip in transverse direction. The bolts were tightened at the top face of the slab using nuts and washers. A photo of the anchorage system is shown in Fig. 2. 6. Test set-up and instrumentation

anchor at the mid-span and one anchor at each end. Slab U-MA-4 had four anchors, one anchor at each end and two anchors at the ends of the middle third of the slab span. 4. Material properties The 28-day compressive strength of concrete was on average 28 MPa. The steel reinforcement was Grade 400 with nominal yield and ultimate strengths of 440 and 600 MPa, respectively. The CFRP strip was Sika CarboDur S1012. For a CFRP composite strip, the data sheet of the manufacturer specifies an elasticity modulus of 155 GPa, a rupture tensile strength of 3100 MPa, and an ultimate elongation of 1.9%. For the slabs strengthened with bonded strips, Sikadur 30 adhesive was used to attach the CFRP strip to the bottom soffit of the slab. Sikadur 30 has a nominal tensile strength of 25 MPa, a modulus of elasticity of 4.5 GPa, and an ultimate elongation of 1%. 5. Anchor details The anchor system used in the present study consisted of a steel plate, 100 · 130 · 10 mm, having four holes, each of

All slabs were tested under four-point bending with an effective span of 1500 mm and a shear span of 500 mm. Load was applied monotonically at the mid-span of the slab using a servo-hydraulic actuator having a capacity of 156 kN. A spreader beam was used to transfer the load to the slab through two loading points placed at the ends of the middle third of the slab span. The slab was supported on two steel pedestals, 1500 mm apart on centre. The pedestal rested on the rigid floor of the concrete laboratory. One linear variable differential transducer (LVDT) was placed under the mid-point of the slab to measure the deflection while a calibrated load cell was used to record the load. LVDTs were also used to measure the slip between the concrete and the CFRP strip at the end anchors (Fig. 2). Two strain gauges, each of 30 mm length, were bonded to the surface of the CFRP strip, one strain gauge at the mid-span and one strain gauge at a point mid-way between the support and one of the loading points. Similarly, two 30 mm strain gauges were bonded to the concrete at the top face of the slab. One strain gauge at the mid-span and the other one was bonded at a point mid-way between the support and one of the loading points. A photo of a test in progress is shown in Fig. 3.

Fig. 2. Anchor details.

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447

Fig. 3. A photo of a test in progress.

7. Test results and discussion

a

80 B-MA-2-N

70

7.1. Mode of failure

B-MA-2-S

The control slab exhibited a conventional ductile flexural mode of failure in which the slab failed by yielding of steel reinforcement followed by crushing of concrete. Specimen B-NA that was strengthened with EB-FRP without end-anchorage failed prematurely without warning by delamination of the CFRP strip after yielding of steel reinforcement. Specimen B-MA-2 which was strengthened with EB-FRP with end-anchorage failed in a ductile manner by crushing of concrete that was preceded by yielding of steel reinforcement. The presence of end-anchorage prevented debonding of the CFRP strip and hence the slab developed its full flexural capacity. All of the slabs strengthened with MA-UFRP system failed by crushing of concrete which was preceded by yielding of steel reinforcement and excessive CFRP end slip.

Load (kN)

60

U-MA-2-S

50 40 U-MA-2-N

30 20 10 0 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

CFRP slip (mm)

b

70 60

U-MA-4-S U-MA-4-N

U-MA-3-N

50

Fig. 4a shows the load versus CFRP end slip relationships for specimens B-MA-2 and U-MA-2 that were strengthened with EB-FRP and MA-UFRP systems with end anchorage, respectively. In this figure ‘‘S’’ and ‘‘N’’ denote the southern and northern ends of the CFRP strip, respectively. For both specimens, the CFRP end slip increased linearly up to the yield load but specimen UMA-2 exhibited higher CFRP slip than specimen B-MA2. For instance, at 40 kN specimen U-MA-2 exhibited a maximum CFRP slip of 0.2 mm while specimen B-MA-2 exhibited a maximum CFRP slip of only 0.033 mm. This indicates that bonding the CFRP strip to the concrete surface would result in reducing the CFRP end slip. Beyond the yield load, the load–CFRP slip curve of specimen BMA-2 showed a gradual increase in the CFRP slip as the load increased until the slab reached its ultimate strength. For specimen U-MA-2, the CFRP slip increased rapidly at the southern end after yielding of the steel reinforcement

U-MA-3-S

Load (kN)

7.2. Load–CFRP end slip relationship

40 30 20 10 0 0

0.25

0.5

0.75

1

CFRP slip (mm)

Fig. 4. Load versus CFRP end slip relationship: (a) specimens B-MA-2 and U-MA-2; (b) specimens U-MA-3 and U-MA-4.

with the load remaining fairly constant until the slab reached its ultimate strength. The load versus CFRP end slip relationships for specimens U-MA-3 and U-MA-4 that were strengthened with MA-UFRP system with three and four anchorages, respectively are shown in Fig. 4b. For

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both specimens, the CFRP end slip increased linearly up to the yield load but the CFRP slip of specimen U-MA-3 increased at a higher rate relative to that of specimen UMA-4. For example, at 40 kN specimen U-MA-3 exhibited a maximum CFRP end slip of 0.3 mm while specimen UMA-4 exhibited a maximum CFRP end slip of only 0.125 mm This indicates that increasing the number of anchors within half of the slab span would result in decreasing the CFRP end slip. Beyond the yield load, the CFRP slip increased at a higher rate relative to the rate in the pre-yield stage until crushing of concrete occurred at top face of the slab. 7.3. Load–CFRP strain relationship The load versus CFRP strain at mid-span section relationships are shown in Fig. 5 while the CFRP strain distribution along the slab span at a load level of 40 kN is depicted in Fig. 6. From Fig. 5, it can be seen that the magnitude of the CFRP strain at mid-span section is dependent on bond condition between CFRP and concrete and on number of anchors within half of the slab span. Specimen

70 B-MA-2 U-MA-3

60

Load (kN)

50 40

B-MA-2 with bonded CFRP strip exhibited the highest CFRP strain while specimens U-MA-2 and U-MA-3 exhibited the lowest. Higher CFRP strain at mid-span section would result in reducing the stress in the steel reinforcement at mid-span, and hence increasing the yield and ultimate loads of the slab. The load versus mid-span CFRP strain relationships for specimens U-MA-2 and U-MA-3 were identical. This is because of the fact that both slabs had no anchors along half of the slab span. At a given value of load the CFRP strain at mid-span section of specimen U-MA-4 was higher than that of specimens U-MA-2 and U-MA-3. From Fig. 6, it can be seen that the CFRP strain measured in specimen B-MA-2, with bonded CFRP strip, varied in proportion to the applied moment along the slab span to satisfy equilibrium conditions. Consequently, the CFRP strain distribution along the slab span followed same shape as that of the bending moment. For specimen U-MA-2 with unbonded CFRP strip anchored only at the ends, the strain in the CFRP strip was uniform thought the span. For specimen U-MA-4 with unbonded CFRP strip anchored at the ends and at each loading point, the strain was constant along each anchored length of the strip. The strain in the CFRP strip within the constant moment region was about 1.5 times the strain within the shear span. The CFRP strain at mid-span section of specimen B-MA-2 was 40% higher than that of specimen U-MA-2 but only 8% higher than that of specimen U-MA-4. This indicates that adding more anchors along half of the slab span would result in reducing the difference between the mid-span CFRP strain in a bonded and an unbonded CFRP strips.

U-MA-4

30

7.4. Load–concrete compressive strain relationship

U-MA-2

20 10 0 0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

CFRP strain

Fig. 5. Load versus CFRP strain at mid-span relationship.

Fig. 7 compares the load versus concrete compressive strain at mid-span section for the strengthened slabs. In this figure, the negative sign of the concrete strain is to indicate that it is a compressive strain. Specimen B-MA-2 with bonded CFRP strip exhibited the lowest concrete compressive strain while specimens U-MA-2 and U-MA-3

70

U-MA-2 B-MA-2

60

U-MA-4

U-MA-3 U-MA-4

B-MA-2 50

Load (kN)

U-MA-2

500

500

40 30

500 20 10

0.0017

0.0017 0.002 0.0026 0.0028

Fig. 6. CFRP strain distribution along the slab span at 40 kN.

0 0

-0.0005 -0.001 -0.0015 -0.002 -0.0025 -0.003 -0.0035 -0.004

Concrete strain

Fig. 7. Load versus concrete compressive strain at mid-span relationship.

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exhibited the highest. This is consistent with the results of the load versus mid-span CFRP strain relationships in which specimens U-MA-2 and U-MA-3 had the lowest mid-span CFRP strain while specimen B-MA-2 had the highest. Reducing the mid-span CFRP strain increased the strain in the tensile steel reinforcement at mid-span section which resulted in increasing the sectional curvature and the concrete compressive strain at top face of the slab. Moreover, specimens U-MA-2 and U-MA-3 had greater CFRP end slip relative to that of specimens B-MA-2 and U-MA-4 (recall Fig. 4) which resulted in increasing the mid-span sectional curvature and the mid-span concrete compressive strain. From Fig. 7, it is evident that the slabs exhibited a great variation in the concrete crushing strain. The measured concrete crushing strain was in the range of 0.0022–0.0037 exhibited by specimens U-MA-4 and UMA-3, respectively. 7.5. Load–deflection relationship The load versus mid-span deflection relationships for all specimens are shown in Fig. 8 while Table 2 summarizes the structural test results. The yield load of specimen BNA, which was strengthened with EB-FRP without endanchorage, was about 38% higher than that of the control. Its ultimate load was about 46% higher. Specimen B-NA failed prematurely by debonding of the CFRP strip. The

80 B-MA-2

70

Load (kN)

60

U-MA-4

U-MA-3 U-MA-2

50

Control

40 B-NA

30 20 10 0 0

10

20

30

40

50

Mid-span deflection (mm)

Fig. 8. Load versus mid-span deflection relationship.

Table 2 Test results Specimen

Py (kN)

Dy (mm)

Pu (kN)

Du (mm)

Mode of failure

Control B-NA B-MA-2 U-MA-2 U-MA-3 U-MA-4

38.0 52.5 52.5 44.5 45.0 47.0

14.2 15.4 13.6 15.18 15.6 15.6

41.0 60.0 66.5 49.0 58.5 55.5

38.4 21.0 31.1 34.8 35.2 28.37

Concrete crushing CFRP delamination Concrete crushing Concrete crushing Concrete crushing Concrete crushing

Py and Pu refer to yield and ultimate loads, respectively. Dy and Du refer to mid-span deflections at yield and ultimate loads, respectively.

449

mid-span deflection at ultimate load of specimen B-NA was 45% lower than that of the control. The stiffness of specimen B-NA was about 26% higher than that of the control. The presence of end-anchorage had no effect on the yield load, slightly enhanced the slab stiffness and strength but greatly increased the slab deflection at ultimate load. The ultimate load of specimen B-MA-2, which was strengthened with EB-FRP along with end-anchorage, was about 11% higher than that of specimen B-NA and 62% higher than that of the control. The mid-span deflection at ultimate load of specimen B-MA-2 was 48% higher than that of specimen B-NA and only 19% lower than that of the control. The slabs strengthened with MA-UFRP had higher yield and ultimate loads relative to those of the control but the strength gain was less than that obtained by the use of EB-FRP system. The yield load of the slabs strengthened with MA-UFRP was on average about 13% lower than that of the slabs strengthened with EB-FRP but was still 20% higher than that of the control. MA-UFRP strengthening system resulted in about 33% average strength gain relative to that of the control with a minimum and a maximum of 20% and 43%, respectively. The strength of the slabs strengthened with MA-UFRP was on average 18% lower than that of specimen B-MA-2 and only 10% lower than that of specimen B-NA. The mid-span deflection at ultimate load of the slabs strengthened with MA-UFRP system was on average 56% higher than that of specimen B-NA, 5% higher than that of specimen B-MA-2, and only 15% lower than that of the control. In the pre-yield stage, the external CFRP strip, whether bonded or unbonded, reduced the stress in the tensile steel reinforcement and hence increased the yield load of the strengthened slabs relative to that of the control. At the mid-span section, for any given value of load, the stress in an unbonded CFRP strip was lower than that in a bonded strip (recall Figs. 5 and 6). This indicates that the contribution of the CFRP strip to the beam strength is reduced when the strip is unbonded. This explains why the strength of the slabs strengthened with MA-UFRP system was lower than that of the slabs strengthened with EBFRP system. Specimens U-MA-2 and U-MA-3 had almost same yield load. This is because both slabs had no anchors along half of the slab span so that they exhibited same CFRP strain (recall Fig. 5), and hence had same yield load. The yield load of specimen U-MA-4 was about 5% higher than that of specimens U-MA-2 and U-MA-3. This is attributable to that specimen U-MA-4 exhibited higher CFRP strain at mid-span section relative to that of specimens U-MA-2 and U-MA-3, which reduced the stress in the bonded steel reinforcement at the mid-span section and hence increased the slab yield load. The ultimate load of specimen U-MA-4 was, however, lower than that of specimen U-MA-3. This can be ascribed to the variation in concrete strain at crushing (recall Fig. 7). The concrete strain measured in specimen U-MA-3 at crushing was

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0.0037 while it was only 0.0022 for specimen U-MA-4. Specimen U-MA-4 would have had higher strength than specimen U-MA-3 if both of them had failed at same crushing strain. The CFRP end slip for the slabs strengthened with MA-UFRP system was higher than that for the slabs strengthened with EB-FRP system. Higher CFRP end slip resulted in increasing the slab deflection and thus reducing the slab stiffness. Among the slabs strengthened with MA-UFRP, specimen U-MA-4 exhibited the lowest CFRP end slip, and hence it had slightly higher stiffness relative to those of specimens U-MA-2 and U-MA-3.

where fs is the steel stress, es is the steel strain, Es is the steel Young’s modulus, fy is the steel yield stress, Esp is the steel strain hardening modulus, and esy is the steel yield strain. The stress-strain relationship of the CFRP composite strip is idealized to be linear-elastic up to failure.

8. Analytical modeling

For the specimens strengthened with EB-FRP system, the strains vary linearly over the slab depth and hence the steel strain, es, and the CFRP strain, ef, can be calculated as follows:

An analytical model is developed to predict the concrete compressive strain, CFRP strain, and the yield and ultimate loads of the slabs. The model is based on realistic material laws and takes into consideration the effect of the strain incompatibility between an unbonded CFRP strip and concrete. 8.1. Material constitutive models The stress-strain relationships of concrete, steel, and CFRP used in the model are shown in Fig. 9. The stressstrain relationship of concrete in compression is described by a parabolic relationship [11], whereas in tension it is assumed to be linear-elastic [12]. The tensile stresses in the concrete after cracking are neglected. "  2 # ec 0 2ec fc ¼ fc  ð1Þ eco eco pffiffiffiffi ð2Þ fcr ¼ 0:6 fc0 MPa where fc is the concrete compressive stress, ec is the concrete strain, fc0 is the concrete compressive strength, eco is the concrete strain corresponding to the concrete compressive strength, and fcr is the concrete tensile strength. The stress-strain relationship of the steel reinforcement is idealized to be linear elastic-plastic with a post-yield strain hardening of 1% [13,14].  Pre-yield stage es E s fs ¼ ð3Þ fy þ Esp ðes  esy Þ Post-yield stage fs

fc

ff ffr

fsu fc

fy

Esp= 0.01 Es Ef Es

εct

εcr

εco

ε cu

εc

ε sy

εsu

εs

ε fr

εf

fcr fct

Concrete

Steel reinforcement

Fig. 9. Material constitutive models.

FRP composite

ff ¼ ef Ef

ð4Þ

where ff is the CFRP stress, ef is the CFRP strain, and Ef is the Young’s modulus of the CFRP composite. 8.2. Model development

ec ðd  cÞ c ec ðh  cÞ ef ¼ c

es ¼

ð5Þ ð6Þ

where ec is the concrete compressive strain at top face of the slab, d is depth of the steel reinforcement, h is the height of the slab, and c is depth of the neutral axis. For the specimens strengthened MA-UFRP system the strain in the bonded steel reinforcement, es, varies linearly with concrete compressive strain but the CFRP strain, ef, does not. Experimental test results presented earlier showed that at a given value of load the strain in an unbonded CFRP strip at mid-span section was lower than that in a similar specimen but with bonded CFRP strip. Moreover, specimen UMA-4 with four anchors exhibited higher CFRP strain than specimens U-MA-2 and U-MA-3 with two and three anchors, respectively. Consequently, a bond factor, v, is introduced to account for the strain incompatibility between an unbonded CFRP strip and concrete surface, and hence Eq. (6) can be rewritten as follows: ef ¼ ðvÞ

ec ðh  cÞ c

ð7Þ

The bond factor, v, is dependent on bond condition between the CFRP strip and the concrete. It is evident that for a bonded CFRP strip the bond factor is 1 but for an unbonded-anchored CFRP strip, the bond factor is less than one. The value of the bond factor for the slabs strengthened with MA-UFRP system is dependent on the number of anchors within half of the slab span. The bond factor is expected to decrease as number of anchors within half of the slab span decreases. Based on CFRP strain values measured experimentally at the mid-span section, bond factors of 1 and 0.9 are proposed for specimens B-MA-2 and U-MA-4, respectively while a bond factor of 0.7 is proposed for both specimens U-MA-2 and U-MA-3. At any section, equilibrium conditions are imposed in terms of axial force and bending moment. For the concrete in compression an equivalent stress block is used introducing the factors a1 and b1 [11].

T. El Maaddawy, K. Soudki / Construction and Building Materials 22 (2008) 444–455

 2 ec 1 ec a1 b1 ¼  eco 3 eco 4  ðec =eco Þ b1 ¼ 6  ð2ec =eco Þ

451

Start

ð8Þ

Impose P

ð9Þ

Compute M ext

Hence equilibrium equations after cracking in the pre-yield stage are:

Impose ε c

ec ðd a1 b1 fc0 cb  As Es

 cÞ vec ðh  cÞ  Af E f ¼0 ð10Þ c c   2 2 bc ec ðd  cÞ vec ðh  cÞ a1 b1 fc0 cb c  1 þ As Es þ Af E f ¼ M ext 2 c c

Compute α1, β1

Compute c

ð11Þ and in the post-yield stage are:

Compute M int

   ec ðd  cÞ vec ðh  cÞ a1 b1 fc0 cb  As fy þ Esp  esy  Af Ef ¼0 c c      b1 c ec ðd  cÞ 0 a1 b1 fc cb c  þ As ðd  cÞ fy þ Esp  esy 2 c þ Af E f

vec ðh  cÞ2 ¼ M ext c

No

M int ≈ M ext

ð12Þ

Yes Record P, M ext, εc, εs, εf

ð13Þ

εc ≥ εcu

No

Or

εf ≥ εfr

8.3. Analytical results Yes

A compute program was developed to solve the equilibrium equations in both pre-yield and post-yield stages. A flow chart of the program is shown in Fig. 10. Test specimens were analyzed using the developed computer program. Section geometry and material mechanical properties reported earlier were used as input data in the analysis. The bond factors proposed earlier and the concrete crushing strains measured experimentally used in the analysis are given in Table 3. The predicted and experimental load versus concrete compressive strain relationships at mid-span section are shown in Fig. 11. In this figure, the negative strain sign is to indicate that the concrete strain is compressive. From this figure, it can be seen that the concrete compressive strains predicted by the model are in good agreement with the experimentally measured strains. For specimens U-MA-2 and U-MA-3 the model tended to underestimate the concrete compressive strain in the post yield stage. This is because specimens U-MA-2 and U-MA-3 exhibited high CFRP slip after yielding of the steel reinforcement which increased the mid-span sectional curvature, and hence increased the concrete strain to a level higher than that predicted by the model. Table 4 gives the predicted and experimental yield and ultimate loads with the percent error between them. From this table it is evident that all predicted yield loads are within 10% error band which confirms the ability of the model to reasonably predict the slabs’ yield loads. All ultimate loads predicted by the model, with the exception of specimens U-MA-2 and U-MA-3, are within 8% error band. The predicted ultimate loads for specimens U-MA-2 and U-MA-3 were 15% and 24% higher than the

Stop

Fig. 10. Flow chart of the computer program.

Table 3 Bond factors and measured concrete crushing strains used in the analysis Specimen

Bond factor (v)

Concrete crushing strain (ecu)

Control B-MA-2 U-MA-2 U-MA-3 U-MA-4

N.A 1 0.7 0.7 0.9

0.00265 0.0024 0.0028 0.0037 0.0022

experimental loads, respectively. This can be ascribed to the greater CFRP end slip exhibited by these specimens that reduced the effectiveness of the CFRP strip to resist tension force from applied loads and hence reduced the slab strength to a level lower than that predicted by the model. In general it can be stated that the developed model gives reasonable prediction for the ultimate strength of the slabs. 9. Parametric study The variation in the concrete compressive strain at crushing which resulted in lowering the strength of specimen U-MA-4 with four anchors to a level lower than that of specimen U-MA-3 with three anchors motivated the

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45

Analytical Experimental

40

Analytical Experimental

60

35 50 Load (kN)

Load (kN)

30 25 20

40 30

15 20

10 10

5 0

0

0

-0.0005

-0.001

-0.0015

-0.002

-0.0025

-0.003

0

-0.0005

-0.001

Concrete strain

Control Specimen

-0.0025

-0.003

Specimen B-MA-2 80

70

Analytical Experimental

60

Analytical Experimental

70 60

Load (kN)

50

Load (kN)

-0.0015 -0.002 Concrete strain

40 30

50 40 30

20

20

10

10 0

0 0

-0.0005

-0.001

-0.0015

-0.002

-0.0025

-0.003

0

-0.0005 -0.001 -0.0015 -0.002 -0.0025 -0.003 -0.0035 -0.004

Concrete strain

Concrete strain

Specimen U-MA-2

Specimen U-MA-3

70

Analytical Experimental

60

Load (kN)

50 40 30 20 10 0 0

-0.0005

-0.001

-0.0015 -0.002 Concrete strain

-0.0025

-0.003

Specimen U-MA-4 Fig. 11. Predicted and experimental load–concrete compressive strain relationships.

need to conduct a parametric study to investigate the effect of varying the bond condition between CFRP and concrete on the flexural behaviour of CFRP-strengthened RC slabs. The slab section modelled in this study had same dimensions and reinforcement as that used in the experimental phase with four different bond factors in the range of

0.25–1. Material properties presented earlier were used as input data for the program and concrete crushing strain was assumed constant (0.003) to compare the behaviour of specimens having various bond factors. Fig. 12 shows the effect of the bond factor on flexural behaviour. In this figure, ‘‘BF’’ denotes ‘‘Bond Factor’’.

T. El Maaddawy, K. Soudki / Construction and Building Materials 22 (2008) 444–455

453

Table 4 Comparison between experimental and analytical results Errora

Specimen

Experimental Yield load (kN)

Ultimate load (kN)

Yield load (kN)

Ultimate load (kN)

Yield load (%)

Ultimate load (%)

Control B-MA-2 U-MA-2 U-MA-3 U-MA-4

38.0 52.5 44.5 45.0 47.0

41.0 66.5 49.0 58.5 55.5

35.0 47.0 43.0 43.0 45.0

38.0 64.0 61.0 67.0 60.0

8 10 3 5 4

7 4 +24 +15 +8

a

Analytical

Error (%) = 100 (Analytical–Experimental)/Experimental.

a

18 BF = 1.00 BF = 0.75 BF = 0.50 BF = 0.25

16 14

b

BF = 1.00 BF = 0.75

14

BF = 0.50

Moment (kN.m)

Moment (kN.m)

BF = 1.00 BF = 0.75 BF = 0.50

12 BF = 0.25

10 8 6

BF = 0.25

10 8 6

4

4

2

2 0

0 0

0.002

0.004

0.006 CFRP-strain

0.008

0.01

0

0.012

d

18

14

BF = BF = BF = BF =

16 BF = 0.75

14

BF = 0.50

12

0.002

0.004

0.006 0.008 Steel strain

0.01

0.012

18

BF = 1.00

BF = 1.00 BF = 0.75 BF = 0.50 BF = 0.25

16

1.00 0.75 0.50 0.25

BF = 1.00 BF = 0.75 BF = 0.50

12

BF = 0.25

Moment (kN.m)

Moment (kN.m)

BF = 1.00 BF = 0.75 BF = 0.50 BF = 0.25

16

12

c

18

10 8

BF = 0.25

10 8

6

6

4

4

2

2 0

0 0

-0.001

-0.002 Concrete strain

-0.003

-0.004

0

0.00005

0.0001

0.00015

0.0002

Curvature (ϕ)

Fig. 12. Effect of bond factor on flexural behaviour.

9.1. Effect of Bond Factor on CFRP Strain Fig. 12a shows the effect of varying the bond factor on the moment versus CFRP strain relationship. It is evident that at a given value of moment the CFRP strain decreases as the bond factor decreases. Reducing the bond factor has more pronounced effect on decreasing the CFRP strain in the pre-yield stage rather than in the post-yield stage. Reducing the CFRP strain results in decreasing the CFRP contribution to the slab strength and hence both yield and

ultimate moment capacities of the slab are reduced as the bond factor decreases. 9.2. Effect of bond factor on steel strain The effect of varying the bond factor on the moment versus steel strain relationship is shown in Fig. 12b. It can be seen that for the same value of moment, the steel strain increases as the bond factor decreases. This is because, at a given value of moment, decreasing the bond

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T. El Maaddawy, K. Soudki / Construction and Building Materials 22 (2008) 444–455

factor results in reducing the CFRP strain thereby increasing the steel strain. As the bond factor decreases the rate of increase in steel strain is increased which reduces the yield and ultimate moments of the slab. 9.3. Effect of bond factor on concrete compressive strain Fig. 12c shows the effect of varying the bond factor on concrete compressive strain relationship. In this figure the negative strain sign is to indicate that the concrete strain is compressive. The concrete compressive strain increases as the bond factor decreases. This is because lower bond factor results in increasing the steel strain which increases the sectional curvature and the concrete compressive strain. These results are consistent with the experimental results presented in Fig. 7 which shows that RC slabs strengthened with unbonded CFRP strips exhibited higher concrete compressive strains at mid-span section relative to that exhibited by the slab strengthened with bonded mechanically-anchored CFRP strip. 9.4. Effect of bond factor on sectional ductility Fig. 12d shows the moment versus curvature relationships for strengthened slabs having various bond factors. The sectional curvature, u, was calculated as follows: ec u¼ ð14Þ c Where ec is the concrete strain at extreme compression fibre of the slab and c is the depth of the neutral axis. From Fig. 12d, it can be seen that the sectional curvature increases as the bond factor decreases. The sectional ductility (uu /uy) is improved as the bond factor decreases. This suggests that although reducing the bond factor reduces the slab strength it results in improving the slab ductility. 10. Conclusions The potential use of mechanically-anchored unbonded FRP (MA-UFRP) system to strengthen reinforced concrete (RC) slabs deficient in flexural strength was evaluated in this paper. The structural performance of slabs strengthened with MA-UFRP system was studied and compared to that of slabs strengthened with externally-bonded FRP (EB-FRP) system. All slabs had 0.8% steel reinforcement ratio while strengthened slabs had an additional 0.12% external CFRP reinforcement ratio. Based on research results the following conclusions can be drawn.  EB-FRP strengthening system without end-anchorage increased the yield and the ultimate loads by about 38% and 46%, respectively relative to those of the control. The slab failed prematurely by delamination of the CFRP strip. The slab mid-span deflection at ultimate load was reduced by 45% compared with that of the control.

 The presence of end-anchorage in the EB-FRP system prevented delamination of the CFRP strip which slightly increased the slab strength but greatly improved the slab deflection at ultimate load. The ultimate load of the slab strengthened with EB-FRP with end-anchorage was about 62% higher than that of the control slab whereas the mid-span deflection at ultimate load was only 19% lower than that of the control.  MA-UFRP strengthening system was effective in increasing the slab strength but the strength gain was less than that obtained by the use of EB-FRP strengthening system. MA-UFRP strengthening system resulted in only 33% average strength gain relative to that of the control with a minimum and a maximum of 20% and 43%, respectively.  The mid-span deflection at ultimate load of the slabs strengthened with MA-UFRP system was on average 56% higher than that of the slab strengthened with EB-FRP without end-anchorage, 5% higher than that of the slab strengthened with EB-FRP with end-anchorage, and only 15% lower than that of the control.  The stiffness and yield load of the slabs strengthened with MA-UFRP system increased as number of anchors along half of the slab span was increased. For the same concrete crushing strain, the slab strength is expected to increase as number of anchors within half of the slab span is increased. Acknowledgements This work was supported by research funding from the Network of Centres of Excellence ISIS Canada on Intelligent Sensing for Innovative Structures, the Natural Sciences and Engineering Research Council (NSERC), and Sika Canada for donation of CFRP. Their contributions are greatly appreciated. The authors would like to thank the Undergraduate Research Assistants and the Civil Engineering Technicians at the University of Waterloo for their help throughout testing. References [1] Nanni A. Concrete repair with externally bonded FRP reinforcement. Concrete Int 1995;7(6):22–6. [2] Arduini M, Nanni A. Behavior of pre-cracked RC beams strengthened with carbon FRP sheets. ASCE J Compos Construct 1997;1(2):63–70. [3] Shahawy M, Chaallal O, Beitelman T, El-Saad A. Flexural strengthening with carbon fiber-reinforced polymer composites of preloaded full-scale girders. ACI Struct J 2001;98(5):735–42. [4] El Maaddawy TA, Soudki KA. Carbon-fiber-reinforced polymer repair to extend service life of corroded reinforced concrete beams. ASCE J Compos Construct 2005;9(2):187–94. [5] Sharif A, Al-Sulaimani G, Basunbul IA, Baluch M, Ghaleb B. Strengthening of initially loaded reinforced concrete beams using FRP plates. ACI Struct J 1994;91(2):160–8. [6] Spadea G, Bencardino F, Swamy RN. Structural behavior of composite RC beams with externally bonded CFRP. ASCE J Compos Construct 1998;2(3):32–139.

T. El Maaddawy, K. Soudki / Construction and Building Materials 22 (2008) 444–455 [7] Bencardino F, Spadea G, Swamy R. Strength and ductility of reinforced concrete beams externally reinforced with carbon fiber fabric. ACI Struct J 2002;99(3):163–71. [8] Lamanna A, Bank L, Scott D. Flexural strengthening of reinforced concrete beams using fasteners and fiber-reinforced polymer strips. ACI Struct J 2001;98(3):368–76. [9] Quattlebaum JB, Harries KA, Petrou MF. Comparison of three CFRP flexural retrofit systems under monotonic and fatigue loads. Advanced composite materials in bridges and structures (ACMBSIV), Calgary, Alberta, July 20–23; 2004. p. 8. [10] Aidoo, J, Harries, KA, Petrou, MF. Behaviour of reinforced concrete bridge girders retrofit with CFRP and subjected to monotonic and

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