1

STRENGTHENING OF SHORT SHEAR SPAN RC-T JOISTS WITH FRP COMPOSITES

Francesco Micelli§ Ph.D Candidate, Innovation Engineering Dept.

University of Lecce Via per Monteroni, 73100 Lecce – ITALY

Office: 0039 832 320 241 FAX: 0039 832 320 241

francesco.micelli@unile.it

Raghu H. Annaiah

MS, The University of Missouri-Rolla Structural Engineer

Crawford, Murphy & Tilly, Consulting Engineers Inc. Springfield, Illinois

rannaiah@cmtengr.com

Antonio Nanni Vernon and Maralee Jones Endowed Professor

The University of Missouri-Rolla Center for Infrastructure Engineering Studies

218 Engineering Research Lab Rolla, Missouri 65409-0710

nanni@umr.edu Keywords: Composite Materials, Fiber Reinforced Polymers, FRP Shear Strengthening, Shear

Capacity.

§ Corresponding author

2

ABSTRACT

Several studies have investigated the shear strengthening of reinforced concrete (RC) beams

with fiber reinforced polymers (FRP) composites for long shear span members. Analytical

models and ACI 440 design guidelines were developed to predict the contribution of FRP in

increasing shear capacity of RC beams. All these models are based on experimental results of

long shear span RC beams.

In this work, the results of an experimental study conducted in a 1964-vintage building are

presented. Twelve RC-T joists strengthened with FRP composites were loaded until failure in a

short shear span configuration. Different strengthening schemes, including different FRP

materials and a new FRP anchorage system, were adopted in order to compare the performance

of the different installations. Carbon FRP (CFRP) and Aramid FRP (AFRP) sheets in an epoxy

matrix were bonded to the RC joists using the wet lay-up technique.

All the joists were loaded close to one end support and showed similar cracking patterns at

failure. The design calculations were based on experimental results. All the unanchored FRP

strengthened beams showed failure due to peeling, while the anchored FRP strengthened

members showed failure due to anchor-pull out at higher load values. It was found that an

increase in the amount of FRP did not result in a proportional increase in the shear capacity, as

expected by design equations, but all the beams showed considerable increase in stiffness.

The experimental results are compared with the results expected by analytical models in order to

discuss the structural behavior of FRP strengthened beams tested in a real building with a short

shear span.

3

INTRODUCTION

Several studies demonstrated that strengthening of RC structures, using externally bonded carbon

FRP sheets is an effective method to enhance the structural performance under both service and

ultimate load conditions. The mechanical properties and lightweight of FRP composites allowed

to use these materials in construction, for repairing and retrofitting of damaged buildings, or to

enhance the load capacities. In recent years, several studies have been conducted to investigate

the flexural strengthening of RC members (Triantafillou 1992, Nanni, 1997) however, few have

concentrated on shear strengthening (Raghu 2000, Khalifa et al. 1999, Triantafillou 1998).

The FRP shear reinforcement of RC beams could be placed using different amounts and

configuration in order to exploit the high strength of the fibers. Experimental studies have shown

that different schemes of reinforcement translate into different performances of the FRP

strengthened elements.

Theoretical studies (Gendron et al. 1999) demonstrated the higher capacity of FRP strengthened

beams assuming perfect bonding between FRP and concrete and fiber fracture at failure.

Experimental results showed premature failure modes due to debonding of the FRP sheets, and

rarely rupture of the fibers. Analytical models and design codes based on the experimental

results were developed taking into account the real behavior of the shear strengthened beams

(Khalifa et al.1998, Triantafillou 2000). These models appear to be accurate for the calculation

of the contribution of FRP to the shear capacity of a RC beams, in a long shear span beam

loading scheme, for different amounts of reinforcement and different strengthening schemes.

Recommendations and limit values for the design guidelines were provided in order to prevent

premature failures and to allow the highest exploitation of the FRP sheets.

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RESEARCH SIGNIFICANCE

The overall goal of this study was to investigate the shear performance and modes of failure of

RC T-shaped joists strengthened with externally bonded FRP sheets and loaded close to one of

the supports in a short shear span configuration. In order to achieve this goal, an experiment

consisting of testing of twelve full-scale RC joists was carried out at the Malcolm Bliss Hospital

(St. Louis, Missouri, USA). The selected building was completed in 1964 and provided an ideal

test bed for carrying out experiments on an existing structure. To date research in shear

strengthening has been restricted to laboratory experimentation. As part of the research program,

the study examined the effectiveness of FRP reinforcement in enhancing the shear capacity of

RC joists. Furthermore, an innovative end anchor system, which allowed a better exploitation of

the strengthening system, was also tested.

EXPERIMENTAL PROGRAM

This research work was conducted in a decommissioned building, where twelve RC T-joists

were tested. The joists were isolated by saw cutting from the rest of the floor to avoid load

redistribution effects. The compressive strength of the concrete was determined by testing

sample cores acquired from different locations of the building. These cores were 80 mm in

diameter and 150 mm in length (3.1x6.0 in). Core test confirmed the validity of fc’ equal to

20.68 MPa (3000 psi) as for the assumption from the original design. The average yield strength

of steel was assumed to be 345 MPa (50000 psi) with elastic modulus of 200,000 MPa (29000

ksi).

5

The strengthening FRP systems consisted of carbon and aramid FRP sheets. The material

properties are presented in Table 1 with reference to fiber content only.

The cross-section of the joists is shown in Figure 1. The test specimens were 2743 mm (108 in)

long. Longitudinal steel reinforcement was provided by 2-13-mm (0.5 in) and 2-19-mm (0.75

in) diameter steel rebars. No transverse reinforcement for shear was provided. Five different

shear strengthening schemes were considered for evaluation. The different schemes are presented

in Table 2. The end anchoring of FRP sheets adopted for JS3 and JS5 specimens was carried out

by inserting 13-mm (0.5 in) glass FRP rods into grooves made at the intersection of the joist web

and the flange. The grooves were 1.5 times the diameter of the glass FRP rods, and were filled

with a high viscosity epoxy paste.

The specimens were instrumented with linear variable displacement transducers (LVDT) all

along the span length to measure deflection. In addition, inclinometers were used to read the

rotation of the end-sections; this helped in ascertaining the fixity of the end supports of the

member. For each strengthened member, four strain gauges were attached directly to the FRP on

the sides of the strengthened joists, these strain gauges were oriented in the vertical direction

(parallel to the fibers). The strain gauges were located at the most likely position of occurrence

of a shear crack. A strain gauge was placed on the concrete, at the location of the load, to

measure the compressive strain. Extensometers were also used for measuring strain in the

sheets. The loading was applied using one or more hydraulic jacks reacting against the floor

above, and recorded with a load cell (Mettemeyer, 1999). The experimental set-up is illustrated

in Figure 2. An automatic data acquisition system was used to collect data.

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ANALYTICAL APPROACH

The analytical approach used for estimating the shear capacity of the FRP strengthened members

was derived from published analytical models and design recommendations (Khalifa et al. 1998,

Triantafillou 2000, ACI 440 DRAFT, 2000). For RC beams strengthened with externally bonded

FRP reinforcement, the shear strength may be expressed as follows:

fscn VVVV ++= (1)

where:

Vc = shear contribution of concrete

Vs = shear contribution due to stirrups

Vf = shear contribution of externally bonded FRP

Since the concentrated load acted closer than 2.4d to the end support, the joists were considered

as deep flexural members. The contribution of Vc to the shear capacity of the joists was

computed according to ACI Code 11.8, and was found to be 101 kN (23 kips). A simplified

computation according to ACI code 11.3.1 used for a shallow beam, would give a value of Vc

equal to 45 kN (10 kips). Although no reserve of strength after diagonal cracking is considered

in design, a higher capacity can be computed considering the beam as a tied arch (arching effect).

7

According to previous models (Kim et al. 1999), the arch contribution to the shear capacity was

calculated as follows:

( ) bdad r 6.0

9.0arch 1204V

+

×−= ρρ

(2)

where:

Varch = shear transferred by arch action (kN)

ρ = longitudinal steel reinforcement ratio

a = shear span between load point and support (mm)

b = beam width (mm)

d = effective beam depth (mm)

r = (d/a)0.6 (ρ)-0.1 = internal moment arm length index

According to Eq.2 the contribution of the arching effect was found to be 31 kN (7 kips).

The theoretical value of Vc, computed taking in account the two mentioned contributions, was

considered to be 132 kN (30 kips).

The prediction of the contribution of Vf has been made according two analytical models that

were developed in accordance with experimental results (Khalifa et al., 1998, Triantafillou,

2000).

8

According to Khalifa’s model, the contribution of Vf for beams strengthened with continuous

900 FRP sheets is given by Eq.3.

Vf = 2 n tf ffe df (3)

Where:

n = number of FRP plies

tf = thickness of FRP ply (mm)

df = effective FRP depth (mm)

ffe = effective average strength in the FRP sheet (MPa)

The value ffe is expressed in Eq.4. as a function of the ultimate nominal strength ffu (MPa):

fufe fRf = (4)

The reduction coefficient is determined based on the possible failure modes. The failure can be

expressed in terms of fracture of the CFRP sheet (failure mode 1), or debonding of CFRP sheet

from concrete substrate (failure mode 2). In either case, an upper limit of the reduction

coefficient is established to control the shear crack width and the loss of aggregate interlock.

The controlling failure mode is determined by taking the lowest reduction coefficient, based on

the equations (5), (6) and (7):

9

Where:

ρf = FRP reinforcement ratio = 2tf / bw for continuous U wrap

bw = web width (mm)

Ef = fiber stiffness for failure mode controlled by FRP rupture (GPa)

εfu = ultimate strain of FRP sheet

f’c = compressive strength of concrete (MPa)

wfe = effective width of the FRP sheet (mm)

In the case of a U-jacket, the value of wfe is equal to (df -Le), where Le is the effective bond

length. The value of effective bond length is based on experimental results (Maeda et al., 1997,

Miller 1999) and is a function of the thickness of the FRP sheet and the elastic modulus of the

( ) ( ) 0.78Eρ1.22Eρ0.56R ff2

ff1 +−=

(5)

( ) ( )[ ] 6ff

ffu

fe32

c2 10Et4.06738.93

dεwf'R −×−=

(6)

fu3 ε

0.006R = (7)

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FRP. An increase in the amount of FRP stiffness should reduce the effective anchorage length as

reported in Eq. 8:

( )ff Ete eL ln58.0134.6 −= (8)

Where:

Le = effective length of FRP ply (mm)

For this study, the values of ρf Ef for the members JS2 and JS3, strengthened with a single CFRP

ply is 0.49 GPa, while for the members JS4 and JS5, strengthened with two CFRP plies it is 0.98

GPa.

According to previous recommendations the presence mechanical U anchors should avoid the

debonding (Khalifa et al. 1999). It means that for the specimen series JS3, JS5, and JS6 the

failure mode 1 should be used in the design approach.

The contribution of FRP for shear in a strengthened member is given by Eq (3), but cannot

exceed the Vf,Lim, given by Eq. 9, which is the controlling factor to prevent failure due to concrete

crushing.

swc

Limf Vdbf

V −=3

2 '

, (9)

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In summary, according to the computation of Vc and Khalifa’s model for the FRP contribution to

shear capacity, the analytical expected results for this project are reported in table 3.

Another analytical approach has been used to compute Vf for the FRP strengthened RC-T joists

investigated in this study. The value of Vf computed in the model calibrated by Triantafillou is

expressed in Eq. 10 for 90° oriented continuous FRP sheets:

dbEV wfffef ρε9.0= (10)

Where Vf is expressed in kN and all the symbols are as already defined.

According to Triantafillou’s recommendations, a limit value for debonding can be determined

based on the amount of FRP reinforcement ρfEf:

3/2'56.0/1

max

3

lim1065.0)( cff fE

×=

−

εαρ

(11)

where:

α = 0.8

εmax = 0.005 (assumed as limit for design)

Efρf = amount of FRP (GPa)

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When the value of Efρf exceeds the limit value calculated by Eq.11 CFRP, debonding should be

expected. For the twelve RC T-joists investigated in this study, debonding should dominate

according to Triantafillou’s analytical calibration. The value of εfe in Eq. 10, when debonding is

the failure mode, is computed as follows:

3

56.0'

1065.0 ×

=

ff

cfe E

fρ

ε (12)

Where:

εfe = effective FRP strain

Efρf = amount of FRP (GPa)

fc’ = compressive strength of concrete (MPa)

The presence of the anchors is not considered in the model, however it could be assumed that

anchored sheets behave similarly to fully-wrapped ones. This means to assume that shear failure

is combined with or followed by FRP rupture.

According to Triantafillou’s model the value of εfe for fully wrapped beams was computed by

Eq. 13:

fuff

cfe E

f ερ

ε ×

=

30.0'

17.0 (13)

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Where:

εfu = ultimate strain for FRP (for CFRP εfu= 0.015)

For the members JS6A and JS6B, that were strengthened with anchored AFRP sheets, the same

assumptions for anchored CFRP sheets were made, so the value of εfe is computed as follows:

fuff

cfe E

fε

ρε ×

=

47.0'

048.0 (14)

Where:

εfu = ultimate strain for FRP (for AFRP εfu= 0.035)

All the Vf values computed using Triantafillou’s analytical calibration of experimental results are

reported in Table 3.

When the ACI 440 DRAFT (2000) recommendations are followed to design the FRP

strengthening schemes, the values reported in Table 3 are found. In this computation the only

difference is the limitation of εfe=0.004.

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It must be noted that the computed values of Vf are related to analytical models calibrated on

experimental data obtained from simply supported shallow beams tested in laboratories. All the

safety coefficients and design recommendations are not taken in account in order to compare the

experimental results.

EXPERIMENTAL RESULTS

The experimental values measured in-situ are reported in Table 4. JS(i) A and JS(i) B, represent

two repetitions of the same specimen type. The first column shows the maximum applied load,

the second column shows the ultimate shear force. Since the end supports showed differential

settlements recorded by LVDTs and inclinometers the values of Vuexp were computed taking into

account moment redistribution.

Specimen JS1A, one of the two control specimens showed a diagonal shear failure. The initial

shear cracks appeared close to the near-end support at a loading of 133 kN (29.9 kips). The

diagonal cracks, once formed, spread towards and partially into the compression zone becoming

flat in the region close to the flange-web intersection. The widening of one of the shear cracks in

the web region, and its propagation at its ends led to eventual failure of the specimen in the left

shear span at a load of 315kN (71 kips), as shown in Figure 3. The arch action was evidenced by

the typical cracking (figure 3): after the formation of the shear and flexural cracks, the capacity

of the beams to support additional loads is developed thanks to a new structural arch form that

has greater capacity for load than the original system. The joist JS1B showed a similar failure

mode, with an ultimate load of 320 kN (72 kips).

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The specimens JS2 A and B were strengthened with a single U-wrap of CFRP (90O), placed

perpendicular to the longitudinal axis of the member. The positive flexure strengthening was

carried out with a single CFRP ply applied to the soffit of the joist. The negative flexure

strengthening was carried out by applying a single CFRP sheet on the flange of the joist. The

specimens JS4 A and B were U-wrapped with two CFRP sheets. The positive flexure

strengthening was carried out by applying three plies of CFRP sheets and the negative

strengthening was carried out by applying two plies of CFRP sheets. The failure as observed in

both the cases was due to premature peeling of CFRP sheets.

Specimens JS2 A and B failed at an ultimate load of 355 kN (80 kips) and 351 kN (79 kips)

respectively, whereas the specimens JS4 A and B failed at an ultimate load of 364 and 311 kN

(82 and 70 kips), respectively. In all cases, shear failure of the member lead to severe

delamination of the CFRP sheets in the near end corner. The failure of the member JS2 A due to

peeling is shown in Figure 4.

Specimens JS4 A and B failed at a higher load then the single wrapped JS2 members. The failure

mode JS4 was similar to that of JS2. The high shear developed at the near end lead to severe

delamination, which in turn resulted in fiber rupture at the bottom of the member.

The specimens JS3 A and B were strengthened with a single U-wrap of CFRP sheet, with end

anchors, while the specimens JS5 A and B were strengthened with two anchored plies. The

function of the end-anchors is to prevent the premature peeling of the CFRP sheets.

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Specimens JS3 A and B failed at an ultimate load of 440 kN (99 kips) and 414 kN (93 kips),

whereas the specimens JS5 A and B failed at an ultimate load of 418 kN (94 kips) and 400 kN

(90 kips). The joists JS6 A and B were strengthened with two plies of aramid fibers. Specimens

of JS6 A and B failed at an ultimate load of 404 kN (91 kips). The failure of the members JS3,

JS5 and JS6 was due to end-anchor pulling out (Figure 5).

DISCUSSION

The experimental Vu values show a higher than expected shear capacity measured for the control

specimens. The high shear value can be attributed to a deep beam and arching effect. These two

contributions that are usually neglected in the design computation can be explained with the

short shear span used. The cracking load, corresponding to Pmax/2.4, confirmed a behavior

typically observed in deep beams (MacGregor1997).

In the Figures 6 and 7, the load vs. deflection curves are plotted for all specimen types. The

values of deflection were measured at the point of loading.

All the strengthened members showed improved mechanical properties, in terms of higher

ultimate strength and stiffness. The minimum observed gain in terms of capacity was 12% for a

single U-wrap member (JS2), and a maximum gain of 39% for a single U-wrap member with end

anchors (JS3).

A comparison based on number of plies used for strengthening suggests that the best

performance in terms of load capacity was observed for a member strengthened with a single ply.

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The presence of end anchors prevented the peeling of FRP sheets. This resulted in an increase in

the load carrying capacity of the member.

The application of additional layers of FRP sheets resulted in a 2% increase in the shear capacity

in unanchored members (Figure 6), while a significant increase of 36%, in the stiffness of the

member was observed. For the anchored members (Figure 7) when the number of plies was

increased no gain in shear strength and stiffness was observed. A comparison between the

members strengthened with different FRP materials but with the same scheme, highlights that

CFRP strengthened joists had higher values of strength and stiffness as compared to members

strengthened with AFRP sheets, in accordance with the expected behavior.

Figure 8 illustrates the strains measured by a strain gauge located at a distance of 355 mm (14 in)

from the near end support in the FRP sheets. From Figure 8 it can be seen that, after point Q the

members registered a sudden increase in the strain readings in the FRP sheets. This indicates the

appearance of diagonal shear cracks on the near end support of the beam. It was observed that all

the beams had similar cracking behavior. At low loads initial diagonal shear cracks were

observed. As the load increased these cracks propagated through the web-flange intersection,

resulting in the eventual failure of the members.

COMPARISON WITH ANALYTICAL MODELS

The comparison of experimental data with the expected values calculated with the analytical

models (Khalifa 1998, Triantafillou 2000) and ACI recommendations is presented herein in

order to investigate the structural behavior of RC-T joists tested in a short span configuration.

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The diagram in Figure 9 shows the comparison between the expected shear contribution of FRP

to the shear capacity of the tested RC-T beams according to the analytical models, and the

experimental values. The experimental values are average values obtained considering Vc=211

kN that is the average value of Vu for the unstrengthened specimens. The theoretical values were

calculated without the safety factors recommended for the design.

It can be seen that the experimental values are lower than the expected Vf, especially for the

unanchored strengthened members. It means that applying the models based on long shear span

experimental data could do overestimations of the FRP contribution to shear capacity, when the

contribution of Vc is high such as in the case of RC deep beams loaded near to the end supports.

The first explanation could arise from the fact that the specimens showed cracks that are

different from the typical 45 degrees inclined web lesions due to the shear stresses, and this is the

result of the arch configuration that the beams are able to assume. A flat crack (figure 5) near the

web-flange interface was observed for all the beams. This represented the region in which the

FRP sheet peeled off. The FRP strengthening action is interrupted as soon as the cracks develop

in the upper side of the web, and become flat. Although mechanical anchors are provided, the

crack propagation at the web flange corner caused the anchors pull out. In this cases the

presence of the anchorages allowed to reach a higher capacity, but could not avoid the debonding

failure.

It is proposed that the anchorage length Le calculated in Khalifa’s model to determine the

effective width of the FRP sheet can not be used to estimate the effectiveness of the FRP in a

region of a beam that presents such a cracking patterns. (Figure 10)

This analysis allows to assert that the strengthening action of the FRP in the precracking phase is

evidenced by the increased cracking load; the presence of the FRP influences the cracking

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development, and the arch configuration of the RC cracked beam, but the shear contribution is

lower than expected by the present theoretical models based on shallow beams with higher shear

span.

CONCLUSIONS

An extensive experimental program consisting of twelve, full size, RC joists was performed at

the Malcolm Bliss Hospital, St. Louis, MO, (USA). The variables considered in this series were:

number of plies used for shear strengthening and different FRP materials. In addition to this a

novel end-anchor system, which allowed a better exploitation of the strengthening system was

also validated.

The tests results described in this study indicated that the strengthening technique based on

externally bonded CFRP composites can be used to increase shear capacity of RC beams, with

efficiency that varies depending on the test variables.

Based on the experimental results, the following conclusions are drawn:

• The members strengthened with one or two plies, with and without end anchors showed

failure due to premature peeling if compared to expected values of Vf.

• Increasing the amount of CFRP may not result in a proportional increase in the shear strength

especially if debonding of CFRP controls the failure. A proportional increase in shear

capacity with increasing CFRP amount may be achieved when debonding is delayed such in

the case of beams with end anchor.

• The experimental verification of the end anchor system shows its effectiveness in increasing

the shear capacity of RC beams. The values of Vf for the anchored FRP sheets demonstrate a

higher effectiveness of the strengthening technique. Existing evidence clearly indicates that

20

the end anchor system can make FRP strengthening even more attractive and economical for

concrete repair and strengthening.

• The observed deep beam behavior conditioned the structural response of the FRP

strengthening: the short span configuration led to a high shear capacity for the

unstrengthened specimens, while the shear crack development caused the peeling or the

anchor pullout of the FRP sheets.

• The cracking geometry, that showed the presence of the arch effect, can be used to explain

the different behavior of the strengthened beams, if compared to the results expected by the

analytical models and design codes.

• Effectiveness of shear strengthening schemes must be investigated for beams having short

shear span, as it was observed that the beam could split from the slab along the corners.

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ACKNOWLEDGMENTS

This research was supported by The “Repair of Buildings and Bridges with Composites

(RB2C)”of the CIES at the University of Missouri Rolla (USA), and the Innovation Engineering

Dept. of the University of Lecce (Italy).

22

REFERENCES

ACI 440 DRAFT (2000), “Guide for the Design and Construction of Externally Bonded FRP

Systems for Strengthening Concrete Structures”, ACI 440 Committee, Externally Bonded FRP

Systems for Strengthening Concrete Structures, pp.54-58.

Challal, O., Nollet, M.J., and Perraton, D. (1998),”Shear Strengthening of RC Beams by

Externally Bonded Side CFRP Strips”, Journal of Advanced Composites, (Vol. II) 1998, pp. 111-

113.

Duthinh, D., (1998) “Draft Guidelines For Concrete Beams Externally Strenthened With FRP”,

Proceedings of the NIST Workshop on Standards Developments for the use of FRP for the

Rehabilitation of Concrete and Masonry structures, NISTIR 6288 NIST Document, Tucson,

Arizona, 1998, pp.3-113, 3-120.

Gendron, G., Picard, A., and Guerin, M.C.,(1999) “A Theoretical Study on Shear of Reinforced

Concrete Beams Using Composite Plates”, Composite Structures, Vol.45, No.4, pp.303-309.

Khalifa, A., Gold, W., Nanni, A., and Abdel -Aziz M. I., (1998), “Contribution of Externally

Bonded FRP to the Shear Capacity of RC Flexural Members”, Journal of Composites for

Construction, ASCE, Vol. 2, No. 4, pp.195-202.

23

Khalifa, A., Tumialan, G., Nanni, A., and Belarbi, A., (1999), “Shear Strengthening of

Continuous RC Beams Using Externally Bonded CFRP Sheets”, Proceedings of the Fourth

International Symposium, Fiber Reinforced Polymer Reinforcement for Reinforced Concrete

Structures, ACI International, Maryland, USA, pp. 995-1008.

Kim, D., Kim, W., and White, R.N., (1999), “Arch Action in Reinforced Concrete Beams – A

rational Prediction of Shear Strength ”, ACI Struct. J., Vol. 96, No. 4, pp.586-593.

Maeda, T., Asano, Y., Sato, Y., Ueda, T., and Kakuta, Y., “A Study on Bond Mechanism of

Carbon Fiber Sheet”, Proceedings of the Third Symposium Non Metallic (FRP) Reinforcement

for Concrete Structures, Vol. 1, Japan, pp.279-286.

MBraceTM (1998), “Composite Strengthening System”, Engineering Design Guidelines, Second

Edition, Master Builders Inc., Cleveland, Ohio, pp. 3-3, 3-6.

Mettemeyer, M. (1999),”In Situ Rapid Load Testing of Concrete Structures”, MSc Thesis,

Department of Civil Engineering, The University of Missouri, Rolla, USA, pp. 10-11

Miller, B.D., (1999), “Bond Between CFRP Sheets and Concrete”, MSc Thesis, Dept. of Civil

Engineering, The University of Missouri, Rolla, MO.

Raghu H.A. (2000), ”Shear Performance of RC Beams Strengthened In-Situ with Composites”,

MSc Thesis, Department of Civil Engineering, The University of Missouri, Rolla, MO, 2000.

24

Nanni, A., (1997) “A Behavior of Simply Supported and Continuous RC-beams Strengthened

with Carbon FRP sheets”, Second Symposium on Practical Solutions for Bridge Rehabilitation,

BASAR II, Kansas City, Iowa State University, pp.261-270.

Triantafillou, T.C. Plevris, N., (1992), "Strengthening of R/C Beams with Epoxy-Bonded Fiber-

Composite Materials", Mater. And Struct. No.25, 1992, pp. 201-211.

Triantafillou, T.C., (1998), “Shear Strengthening of Reinforced Concrete Beams Using Epoxy-

Bonded FRP Composites” ACI Struct. J., Vol. 95. No.2, 1998, pp. 107-115.

Triantafillou, T.C. (2000), “Design of Concrete Flexural Members Strengthened in Shear with

FRP”, J. of Comp. for Constr., ASCE, 4(4), 2000, pp.198-205.

25

TABLES AND FIGURES

Table 1 Engineering Properties of FRP Sheets (MBraceTM 2000)

Materials Dimensions

tf (mm)

Tensile Strength

ffu (MPa)

Elastic Modulus

Ef (MPa)

CFRP-CF 130 0.165 3790 228,000

AFRP-AK40 0.300 1517 117,000

1ksi = 6.894 MPa

1 in = 25.4 mm

26

External strengthening

Schemes

Shear Member

FRP type

Plies Anchor

Positive flexure

(102-mm wide ply)

Negative flexure

(508-mm wide ply)

JS1 A and B -- 0 No -- --

JS2 A and B Carbon 1 No 1 1

JS3 A and B Carbon 1 Yes 1 1

JS4 A and B Carbon 2 No 3 2

JS5 A and B Carbon 2 Yes 3 2

JS6 A and B Aramid 2 Yes 3 2

Length of positive flexure plies = joist length Length of negative flexure plies = 1219 mm

1 in = 25.4 mm

Table 2 Different strengthening systems for series JS

27

Table 3 FRP Shear Contribution

1 kip = 4.448 kN

Khalifa Triantafillou ACI 440F Specimen

R1 R2 R3 Vf

(kN)Vf,lim (kN)

Vf (kN)

Vf (kN)

Expected

failure

JS2A JS2B 0.314 0.248 0.360 86 173 60 64 debonding

JS3A JS3B 0.314 0.600 0.360 109 173 112 84 FRP

rupture JS4A JS4B 0.200 0.199 0.360 279 173 81 94 debonding

JS5A JS5B 0.200 0.600 0.360 279 173 182 126 FRP

rupture JS6A JS6B 0.200 0.194 0.325 242 173 173 86 FRP

rupture

28

Table 4 Experimental values

Specimen Pmax

(kN)

Vuexp

(kN)

Vcexp

(kN)

Vfexp

(kN)

JS1A 315 209 209 -

JS1B 320 212 212 - JS2A 355 236 - 25 JS2B 351 233 - 22 JS3A 440 298 - 87 JS3B 414 277 - 66 JS4A 364 256 - 45 JS4B 311 208 - 0 JS5A 418 298 - 87 JS5B 400 285 - 74 JS6A 404 245 - 34 JS6B 360 218 - 9

1 kip = 4.448 kN

29

All dimensions in mm2- 13

2-19

254 152 254

305381

76

CROSS SECTION @ X-X

LONGITUDINAL CROSS SECTION

X-X914

2743

762

Far end supportNear end support

29

25

Figure 1: Cross section of control specimen (JS1)

30

1 in = 25.4 mm

Linear Variable Displacement Transducers

Shoring

ExtensionsLoad Cell

Hydraulic JackMember being tested

Figure 2: Experimental Set-Up

31

Figure 3: Diagonal Shear Failure of JS1

32

Figure 4: Peeling Failure of JS2

Peeling

Fiber rupture.

JS2A

Near End Support beam

C L

Load

Shear cracks Sheet peeled off to reveal the shear cracks

33

Anchor pullout

Cracks on the bottom face of flange

Diagonal shear cracks

Saw cut

JS3A JS3B

Figure 5: Peeling failure of members JS3-A and JS3-B

34

0

50

100

150

200

250

300

350

400

450

500

0 2 4 6 8 10 12 Deflection (mm)

Loa

d (k

N)

JS1A-(Control)JS2A-(CFRP- 1 ply U-Wrap) JS4-(CFRP-2 plies U-wrap)

1727

914 P

JS4A

JS1A

JS2A

Figure 6: Load-vs-Deflection Curve for Members without End Anchors

1 kip = 4.448 kN 1 in = 25.4 mm

35

0

50

100

150

200

250

300

350

400

450

500

0 2 4 6 8 10 12

Deflection (mm)

Loa

d (k

N)

JS1A-(Control)JS3A-(CFRP-1 ply with anchor)JS5A-(CFRP-2 plies with end anchors)JS6A-(AFRP 2 plies with end anchors)

JS1A

JS3AJS5A

JS6A1727

914 P

Figure 7: Load-vs-Deflection Curves for Members with End Anchors

1 kip = 4.448 kN 1 in = 25.4 mm

36

0

50

100

150

200

250

300

350

0 2000 4000 6000 8000Strain

Tot

al L

oad

(kN

)

JS5A-(2 plies with end anchors)JS3A-(1 ply with end anchors)JS6A-(AFRP-2 plies with end anchors)

JS3A

JS5AJS6A

Q

Figure 8: Load-vs-Strain Diagrams

The point Q in the diagrams represents the shear-cracking load. 1 kip = 4.448 kN

37

0

20

40

60

80

100

120

140

160

180

200

220

0.49 0.49 0.98 0.98 0.92Ef x ρf (GPa)

Shea

r Cap

acity

Vf (

kN)

ExperimentalKhalifaTriantafillouACI

Single plywithout anchors

Single ply with anchors*

Double ply with anchors*

Double ply without anchors

Double ply with anchors*(AFRP)

Figure 9: Comparison between Experimental Shear Contribution of FRP sheets and the theoretical values. 1 Msi = 6.894 GPa; 1 kip = 4.448 kN

*The anchored FRP plies were considered as the case of a fully wrapped beam in Triantafillou’s model, assuming FRP rupture as expected failure mode, and the values of effective strains in the FRP plies was limited to 0.004 for ACI.

38

Figure 10: Cracking Patterns for a FRP Strengthened Short-Shear Span Beam

Shear crack observed for short span beams

Le

Continuous connection

Anchorage length in Khalifa’s model