Strengthening of reinforced concrete continuous beams in sagging and hogging moment regions using CFRP

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Tanta University

Strengthening of reinforced concrete continuous beams in sagging and hogging moment regions using CFRP by

Abdel-Hakim Abdel-Khalik Khalil

Associate Professor, Structural Engineering Department, Faculty of Engineering,

Tanta, Egypt.

Abstract

This study presents an extensive experimental program for the strengthening of ten full-scale, reinforced concrete two spans continuous beams in sagging and hogging moment regions using CFRP laminates and sheets. The practical problem of installation restrains at the intermediate column (inhibiting the continuity of the CFRP laminates at the maximum negative moment region) was investigated. The experimental results indicated that the contribution of externally bonded CFRP plates and sheets for flexural capacity in sagging and hogging moment regions is significant and dependent on the variables considered such as strengthening configuration, position and end wrapping of CFRP plates. External strengthening resulted in a higher load capacity, less ductility, higher stiffness and less deflection compared to control beams. At failure, most of the strengthened beams showed peeling for CFRP plates. However, wrapping CFRP plate ends lead to enhancement in strengthening efficiency, more ductility, less deflection and fewer bond stress. The configuration used for strengthening of continuous beams with stumps over the intermediate support showed nearly same efficiency as those without stumps. Based on the equation stated in the ACI guidelines for the design and construction of externally bonded FRP systems for strengthening concrete structures, ACI 440.2R-02, an equation was proposed for the estimation of nominal flexural strength of strengthened beams taking into account the effect of compression steel, CFRP plates at sagging and hogging moment regions.

Keywords: flexural capacity; continuous beams; strengthening; ductility; strain; bond; CFRP; reinforced concrete.

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Introduction

The negative moment region or the support region of reinforced concrete (RC) beams is a critical one due to the simultaneous occurrence of maximum moment and shear. In addition, the presence of columns makes it difficult to strengthen this region using conventional techniques like steel plate bonding, section enlargement, external stirrups etc. Little experimental work on the behavior of repaired or strengthened RC continuous beams has been reported ( Sharma, 1992, [8]; Adruini et al., 1997, [2]; Khalifa et al., 1999, [6]; Grace et al., 1999, [5]; El-Refaie et al., 2001, [3];Sinaph et al., 2002, [9]; and El-Refaie et al., 2003, [4]).

Khalifa et al., 1999, presented the results of an experimental investigation of nine RC continuous beams with shear deficiencies strengthened with externally bonded CFRP sheets. It was concluded that, the externally bonded reinforcement can be used to enhance the shear capacity of the beams in positive and negative moment regions and the use of U shape CFRP sheets wrapping the entire beam span was more effective in increasing the beam capacity. EI-Refaie et al., 2001, presented the results of testing of five RC continuous beams strengthened in flexure with different arrangement of CFRP plates and sheets. The main conclusions were that the load beam capacity was increase by up to 55%, however, the ductility of the strengthened beams was reduced. Sinaph et al., 2002 studied the shear and flexural behavior of three RC T-beams strengthened in the negative moment regions with CFRP plates. For all specimens, column stumps were also cast and used as point of application of load. They concluded that the externally bonded CFRP plates were very effective in enhancing the strength, both flexural and shear, stiffness of the negative moment region of T-beam. Also, it found that the restraint offered to the application of strengthening system due to the presence of column did not affect the strength of the beam. El-Refaie et al., 2003 reported the sagging and hogging strengthening of eleven continuous RC beams strengthened by CFRP sheets in two groups according to the arrangement of internal steel reinforcement. The main parameters studied were the position, length, and number of CFRP layers. The main conclusions of the study were that an external strengthening using CFRP sheet was found to increase the beam load capacity, less ductility compared with control beam and showed undesirable sudden failure modes. Also, there was an optimum number of CFRP layers beyond which there was no further enhancement in the beam capacity. The study found that extending the CFRP sheet to cover the entire hogging and sagging zones did not prevent peeling failure. beam sag laminate column

In this study, an extensive experimental program consisted of ten reinforced concrete continuous beams cast, strengthened with different configurations of CFRP plates and sheets, and tested up to failure was conducted. The existence of a column at the intermediate support was taken into consideration. The main behavior of strengthened beams like crack propagation and width, deflection, enhancement in failure load, strain of steel and CFRP at hogging and sagging zones, bond stress of CFRP plates and sheets, ductility of strengthened beams, strain distribution, and the modes of failure were studied. The program was accomplished by a proposed equation following the format of ACI 440.2R-02 [1] for estimating the nominal flexural strength of the reinforced concrete continuous beams strengthened at negative and positive moment regions.

Research significance

This paper concentrates on studying the effect of discontinuity of strengthening material over the central support due to the existence of columns on the behavior of the continuous RC beams strengthened over this support. The effects of different configuration of strengthening material on the bond stress distribution, strain distribution over cross section, crack propagation, crack widths, ductility, and load capacity were also investigated.

Test Program

The test program included the testing of ten - two spans - continuous beams. The concrete cross section of all beams was 120 mm width and 250 mm in depth. The overall length of each beam was 4200 mm divided into two equal loaded spans of 2000 mm. Reinforcements of all beams were similar; two bars of 10 mm diameter were extended to cover the whole span in the positive moment region. To cover the negative moment, over the intermediate support, each beam was provided with two 12 mm diameter bars. Positive and negative reinforcement were made of high tensile steel (360/520). For shear reinforcement; 8mm diameter stirrups spaced at 200mm, made of normal mild steel 240/350, were used to resist shear. Details of the tested beams are shown in Figure 1.



Figure 1: Details of reinforcement for different specimens.

The tested beams were divided into two groups. First group, G1, consisted of six continuous beams with no installation restrains. The second group, G2, consisted of four beams; each of these beams was cast with column stump to resemble the installation restrain condition at field.

Strengthening schemes and test setup

To accomplish the objectives of this research; the behavior of continuous reinforced concrete beams, strengthened in flexure using CFRP composites with different configurations, was investigated. Two beams, G11 and G21, were tested without any strengthening and considered as reference beams. The effect of strengthening RC continuous beams in positive moment region was investigated in beams G13; however, strengthening the negative moment zone was conducted in beam G14. Combining the effect of strengthening in Sagging and hogging moment regions was studied in beams G12, G15, G16, G22, G23, and G24. In beams G16 and G23; the curtailments of the CFRP plates were wrapped with carbon fiber sheets to study the effect of end wrapping on the flexural behavior of beams. Effect of discontinuity of the CFRP plate over supports was investigated in beams G15, G22, G23 and G24. Full details and different strengthening configuration of the beams are shown in figures 2 and 3 and listed in Table 1.

Figure 2: Strengthening scheme for group G1

Figure 3: Strengthening scheme for group G2

Table 1: Details of tested beams and strengthening configuration

Beam notation	Strengthening scheme	End anchorage	Beam key
	Sagging	Hogging
G11	N/A	N/A	N/A
G12	CFRP plate 50 * 1800 * 1.3 mm For each span	CFRP plate 50 * 1200 * 1.3 mm over intermediate support	N/A
G13	CFRP plate 50 * 1800 * 1.3 mm For each span	N/A	N/A
G14	N/A	CFRP plate 50 * 1200 * 1.3 mm over intermediate support	N/A
G15	CFRP plate 50 * 1800 * 1.3 mm for each span	2 * 50 * 1200 * 1.3 mm on beam sides	N/A
G16	CFRP plate 50 * 1800 * 1.3 mm for each span	CFRP plate 50 * 1200 * 1.3 mm over intermediate support	One layer of CFRP sheet was wrapped around the beam section's perimeter at the end of sagging and hogging plates
G21	N/A	N/A	N/A
G22	CFRP plate 50 * 1800 * 1.3 mm for each span	2 L shape CFRP unidirectional sheets with virtual thickness 0.13 mm	N/A
G23	CFRP plate 50 * 1800 * 1.3 mm for each span	2 L shape CFRP unidirectional sheets with virtual thickness 0.13 mm	One layer of CFRP sheet was wrapped around the beam section's perimeter at the end of sagging and hogging plates
G24	CFRP plate 50 * 1800 * 1.3 mm for each span	2 CFRP plates 50 * 1200 * 1.3 mm on beam sides + 2 L shaped sheets	N/A

Instrumentations and measurements

Many types of instrumentation were used in this investigation. The use of strain gauges (S.G.) was dominant for the measurements of strains on reinforcement and on CFRP plates. Demec points were fixed down the depth of the beam at positive and negative moment zones to help in the prediction of strain distribution along the depth. Dial gauges were mounted to measure deflection at mid spans. Figure 4 shows details of instrumentations fitted along beams' length; however not necessarily all of them were used at the same time for a specific beam.

The cracks' widths were measured at a level of the centerline of the lower reinforcement, at different locations within the constant moment region using an illuminated microscope of 0.02 mm precision.

Figure 4: Details of Instrumentations

properties of concrete and strengthening materials.

The beams were cast from concrete with characteristic compressive strength of about 30 MPa. The mechanical properties of the CFRP plates and sheets used for external applications and for the steel reinforcement are shown in Table 2.

Table 2: Mechanical properties of CFRP material and steel

Material	Dimension, mm	Tensile strength, MPa	Modulus of elasticity E, MPa	Elongation at break %
CFRP Plate	b.t = 50X1.3	2800	El= 1.65*105	1.70
CFRP Sheets	tf= 0.13	3500	Ef= 2.3*105	1.50
Steel	s = 8, 10, 12	240 & 360	2.2*105	1.5

Test results, presentation and discussion

Load deflection

Figure 5 shows load deflection relations for all tested beams, as follows figure (5.a) for group G1 and Figure (5.b) for group G2, respectively.

Figure 5: Load deflection relationships

At a specific load level of 100 kN, for group G1; beams G12, G13, G14, G15 and G16 exhibited 0.74, 0.73, 0.82, 0.52 and 0.54, respectively, of the deflection of the reference beam G11. However, for group G2; beams G22, G23 and G24 showed 0.88, 0.59 and 0.57 of the deflection of the reference beam for that group G21, respectively. The difference in deflection for the beams of both groups may be a result of the various strengthening schemes that gave diverse stiffness effects. Generally, all strengthened beams showed higher stiffness and less deflection at the same level of load compared to non-strengthened reference beams.

To show the effect of strengthening discontinuity due to the existence of stumps resembling column existence in the field, comparisons were made and shown in figure 6. Figure 6.a Shows comparison of load deflection relations for beams G11 and G21 which represents control specimens for the two groups G1 and G2. The deflection of G21 was 0.75 of the deflection of beam G11. This lower value may be attributed to the existence of stumps, resembling columns that resulted in a lower redistributed value of sagging moment of the beams of group G2. The same behavior was dominant for the strengthened beams as shown in figures 6.b and 6.c.

Load strain for steel and CFRP

The relationships between the applied loads and the strains on steel for groups G1 and G2 are shown in Figure 7. The strains were measured at mid-span for positive reinforcement while they were measured over intermediate support for negative reinforcement. All beams in both groups showed less strain values, (higher stiffness), if compared with the control beams. However the differences in strain value were varied with the variation in strengthening scheme.



Figure 6: Load deflection relations of beams with and without stumps.



Figure 7: Load strain relationships for main steel

The existence of stumps resulted in less strain values on positive reinforcement; this is shown for reference beams in Figure 8. All strengthened specimens showed nearly the same trend in behavior.

The strain values on the CFRP plates for both groups G1 and G2 within sagging and hogging moment regions are shown in Figures 9.a and 9.b. From these figures it could be said that the CFRP plate in the sagging moment zone carried less strains with the existence of the CFRP plate in the hogging moment zone. It could be noticed that for group G1, the tensile strain values measured at mid span of the CFRP plates glued to the beams' soffits were different from beam to another. For beam G13, the highest tensile strain was recorded however, the lowest strain values were noticed for beams G12 and G16. This may be a manifistation of the effect of different strengtheneing schemes on the efficiency of strengthening. In other words, wrapping the CFRP plate end in the sagging moment zone enhanced the efficiecy of strengthening.



Figure 8: Load strain relationships for control beams

Figure 9: Load strain relationships for CFRP plates

The same trend dominated the behavior of group G2 in which beam G23 showed the highest perfomance among the beams of this group followed by beam G24 reassuring the effect of strengthening schemes on the beams' behavior. Unexpectedily beam G22 showed the lowest strains recorded along the second half of the curve , which might be a result of faulty strain gauge reading.

Bond stress distribution

This section of the study presents the bond stress distributions along the plate length. The bond stress is a result of the difference between the tensile forces at different sections of the plate. Figure 10 shows the bond stress distribution for Beams G12, G15 andG16. This sample was chosen to show the trend of the behavior of the beams. The bond stress curves were plotted at different load increments to cover the loading up to a level very close to failure.

Figure 10: Bond stress distribution for beams G12, G15 and G16

All beams showed low bond stresses along the bonded length of the plate at low loads. The rate of change in the bond stresses along the CFRP plate was small until about 60% of the failure load. After this, the rate of change in the bond stresses was higher To assist in assimilating the data, comparisons of bond stresses of different beams and strengthening schemes are presented. Figure 11 shows the bond stress distribution for beams G12, G15 and G16 at load levels 60 kN and 120kN. The strengthening schemes seems to be affecting to a large extent the bond stresses along the plate as it appears from the bond stress value recorded on the lower CFRP plate for beam G16 as a result of the end wrapping.



Figure 11: Bond stress distribution at different load levels

Strain distribution over beam depth

The strain distribution at mid span over beams' depth at load level of 50 kN and 100 kN for groups G1 and G2 is presented in Figures 12 and 13 respectively. From these figures it could be easily said that, all strengthened beams successfully achieved a nearly linear strain distribution from the extreme compression fiber of the beam to the extreme tension fiber of the concrete section. However, a small kink in the slope of the strain distribution line was observed for that part of the curve between the reinforcement level and the CFRP plate level; this might be an indication of the beginning of debonding between the concrete and the plate. It may be also noted that wrapping the plate ends led to a proper utilization of the strengthening plate properties. From the figures; it is obvious that the neutral axis depth, measured from extreme compression fiber of the section, for beam G16 was deeper than the other beams. This might lead to a belief that the strengthening technique will affect the position of the neutral axis. At low load levels, the effect of different strengthening scheme could be easily identified; however this effect was insignificant at load level near failure.



Figure 12: Strain distribution at mid span at 50 kN

Figure 13: Strain distribution at mid span at 100 kN

Failure loads

Figure 14 Shows the percentage of the increase in failure load of the beams in groups G1 and G2 relative to the individual control specimen of each group. Generally, all strengthened beams in either groups showed higher failure loads than the reference beams, however, G24 showed an increase of 125% compared to 122% for G15. Also, G23 showed an increase of nearly 135% compared to 128% for G16. Despite of the minimal difference in the percentage of the increase in load capacity of the beams, it might be concluded that the strengthening schemes used for group G2 ended with nearly the same results as those achieved in group G1.



Figure 14: Percentage of increase in failure load

Crack width

Cracks widths were measured for all specimens at the level of lower reinforcement for cracks at mid spans and at the level of upper reinforcement for cracks over intermediate support. The cracking loads for different specimens are shown in Table 3. In the following paragraph, the relationships between crack widths at different load levels for groups G1 and G2 are presented.

At mid spans of specimens of group G1, the least crack width was recorded for beam G16 followed by G15. Quite the contrary, Beams G11 showed, as expected, the largest crack width followed by G14.as shown in figure 15. Over the intermediate support of the beams of this group, the smallest crack width was noticed again in beam G16 followed by G14. While the largest crack width was achieved in beam G11 followed by G13, as shown figure 16. At mid spans of group G2, the same trend of group G1 dominated the cracking pattern. This was reflected in the less crack width of beam G23 and G24 and in the large crack width of specimens G21 followed by G22; this may be seen in figure 17.



Figure 15: crack width for group G1 at mid span

Figure 16: crack width for group G1 over intermediate support

Figure 17: crack width for group G2 at mid span

Failure modes

In this study, three modes of failure were depicted; ductile failure of the beam, debonding of CFRP plate and peeling of CFRP plate.



Figure 18: Crack pattern for ductile failure

Ductile failure; in this failure mode the failure initiated by yielding of main reinforcement which gave ductility for the tested beam and finally; crushing of concrete in compression side of the beam was noticed. This mode of failure was clear for control beams G11 and G21, an example of crack pattern is shown in figure 18. Debonding of CFRP; Separation of the CFRP plate with a thin concrete layer attached to it is named debonding. This appeared to be due to crack initiation at different locations along the plate. This mode of failure was noticed for beams G16 and G23 in which the ends of the plates were wrapped by CFRP sheets. Debonding of the CFRP plate was noticed at a load, nearly, equal to 85% of the ultimate failure load and the beam continued to carry load up to failure. A sample for crack pattern in the area of mid span and plate debonding is shown in figure 19.

Figure 19: Crack pattern and debonding of the CFRP plate

Peeling failure; In the rest of the specimens, the failure of the beams initiated by separation of the CFRP plate with a relatively thick layer of concrete cover attached to it. This type of failure occurred in the concrete cover along the steel reinforcement level adjacent to the external CFRP composite. A sample of this type of failure is shown in Figure 20

Figure 20: Crack pattern and peeling of CFRP plate

Ductility and moment enhancement

The deflection ductility index "µÄ" derived for simply supported beams by Mukhopadhyaya, Swamy and Lynsdale, 1998 [7] and adopted by El-Refaie et al,2003 [4] for the continuous beam, (defined as the ratio between the mid span deflection at ultimate load of the beam and that of yield load of the tensile steel reinforcement), was used in this research. According to the deflection ductility indices, all strengthened beams exhibited less ductility than their reference beams. Except specimen G14, specimens G16 and G23 showed the higher ductility compared to all other strengthened beams in their groups. This may be a result of wrapping the ends of the CFRP plates leading to a better utilization of the plate due to the delaying in plate debonding. This was manifested as a higher mid span deflection values for that beam. Ductility indices for beams G12, G15 and G22 were nearly the same. G14 as expected, showed the highest value of ductility index as there was no CFRP plate in the tension side of that specimen. The lowest ductility index of Beam G13 may be as a result of a premature failure. Extra strengthening of specimen G24 over intermediate support was shown in a higher ductility index than G22. A summary of the test results in that area is shown in Table 3.

Table 3: A summary of the test results:

Group	Beam	Crack Load kN	Crack Load enhancement %	Ultimate Load kN	Moment enhancement ratio M.E.	Ductility Index µÄ
G1	G11	22.5	1.00	120	1.00	3.01
	G12	30	1.33	130	1.08	1.26
	G13	35	1.56	148	1.23	1.12
	G14	30	1.33	131	1.09	1.94
	G15	40	1.78	145	1.21	1.21
	G16	45	2.00	155	1.29	1.36
G2	G21	25	1.00	120	1.00	2.91
	G22	25	1.00	136	1.13	1.24
	G23	45	1.8	162	1.35	1.62
	G24	25	1.00	148	1.23	1.35

8. Proposed nominal strength for flexure based on ACI format.

General equation for the calculation of nominal flexural strength of beam sections with FRP external reinforcement in simple beams with tension steel only was proposed by ACI 440.2R-02 as the following:

Equation 1

For continuous beams strengthened in sagging and hogging moment regions, equation 1 may be modified to take into considerations the effect of secondary steel and CFRP external strengthening in sagging and hogging moment regions. General scheme for the internal strain and stress for a rectangular section according to the proposed format may be drawn considering the equilibrium of the section under the forces shown in Figure 21.



Figure 21: Internal strain and stress distribution for a strengthened rectangular section at sagging and hogging moment regions under flexure at ultimate stage

The final proposed equation may be written in the form:

Equation 2

Where:

FRP lever arm in compression side of the beam.

the effective stress level in the FRP reinforcement, (MPa)

the area of main steel reinforcement, (mm2)

stress in tension steel reinforcement, (MPa)

additional FRP strength-reduction factor

area of FRP external reinforcement (mm2)

ratio of the depth of the equivalent rectangular stress block to the depth of the neutral axis

distance from extreme compression fiber to the neutral axis (mm)

overall thickness of a member (mm)

area of compression steel reinforcement (mm)

stress in compression steel reinforcement, (MPa)

distance from extreme compression fiber to the axis of compression reinforcement(mm)

tensile modulus of elasticity of FRP (MPa)

effective strain level in the FRP reinforcement, (MPa)

design rupture strain of FRP reinforcement

design ultimate tensile strength of FRP (MPa)

maximum usable compressive strain of concrete

bond dependent coefficient

nominal thickness of FRP reinforcement laminate (mm)

number of plies of FRP reinforcement

 modulus of elasticity of steel (MPa)

strain level in tensile steel reinforcement

strain level in compressive steel reinforcement

Verification of the proposed equation

The proposed equation was adopted for different continuous beams strengthened and tested experimentally up to failure. Table 4 shows the values of nominal moment calculated by proposed equation (Mproposed) and the nominal strength based on the experimental results (Mexperimental).

Table 4: Verification of proposed equation

Specimen	Mexp. kN.m	Mproposed kN.m
G12	29.51	38.19
G13	33.6	33.17
G14	38.2	38.98
G15	32.92	42.74
G16	35.19	38.2

Figure 22 shows the ratio between (Mproposed) and (Mexperimental). From the figure it could be said that, the nominal flexural strength calculated using the proposed equation for beams strengthened externally by CFRP plates at sagging or hogging moment region gave close results to the values obtained from the experimental tests. While, application of the proposed equation for beams strengthened with external CFRP reinforcement at the sagging and hogging moment regions exceeded the experimental values by about 29%.

Figure 22: (Mproposed) / (Mexperimental) for group G1

Conclusions

Based on the results obtained in this work, the following main conclusions can be drawn as:

All strengthened beams showed higher stiffness and less deflection ranged between 0.52 and 0.82 at the same level of load compared to non-strengthened beams.

Existence of stumps resembling column in the field decreased deflection of the beam compared to those without stumps.

All strengthened beams showed less strain on steel compared to control beams. The difference in strain values varied with the variation of strengthening schemes.

Existence of CFRP plate in hogging moment region lead to less strain in CFRP plate in sagging moment region.

Wrapping the CFRP plate ends lead to enhancing the efficiency of strengthening and, to a large extent, the bond stress along the plate.

Strengthening configuration affected the position of neutral axis within the beam section.

The provision of CFRP external reinforcement was found to increase load capacity of up to 122% to 138% according to strengthening schemes compared to the un-strengthened control beams; however this was accompanied by reduction in ductility.

Cracks widths for strengthened beams were found to be narrower than that of the control beams. Cracking load of strengthened beams was higher than the control beams.

Sudden peeling failure of thick concrete cover attached to CFRP plate was the dominant failure mode of most of tested beams; however, wrapping the CFRP ends lead to debonding mode of failure and enhancement of ductility of beam.

Strengthening schemes for hogging moment region followed in this research for continuous beams with stumps showed similar behavior that was as good as continuous beams without stumps.

An equation for the nominal strength of the strengthened beams based on ACI format was proposed considering secondary reinforcement and CFRP plates at sagging and hogging moment regions. Proposed equation showed close results to the values obtained from the experimental tests for beams strengthened in either sagging or hogging moment region. However, the application of the proposed equation for beams strengthened with external CFRP reinforcement at the sagging and hogging moment regions overestimated the experimental behavior of such beams by about 29%.

Refrences

[1] American Concrete Institute (ACI), Committee 440.2R-02. “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures,” July, 2002.

[2] Arduini, M.; Nanni, A.; Tommaso, A. D.; and Focacci, F.,”Shear Response of Continuous RC Beams Strengthened with Carbon FRP Sheets” Non Metallic (FRP) Reinforcement for Concrete Structures, Proceeding of the Third International Symposium (FRPRCS-3), Vol. 1, Japan, Oct., 1997, pp. 459-466.

[3] El-Refaie, S. A.; Ashour, A. F.; and Grrity, S. W.,”Strengthening of Reinforced Concrete Continuous Beams with CFRP Composites,”The International Conference on Structural Engineering, Mechanics and Computation, South Africa, Apr., 2001, pp. 1591-1598.

[4] El-Refaie, S. A.; Ashour, A. F.; and Grrity, S. W.,”Sagging and Hogging Strengthening of Continuous Reinforced Concrete Beams Using Carbon Fiber-Reinforced polymer Sheets,”ACI Structural Journal, July-Aug., 2003, pp. 446-453.

[5] Grace, N. F.; Soliman, A. K.; Abdel-Sayed, G.; and Saleh K. R.,”Strengthening of Continuous Beams Using Fiber Reinforced Polymer Laminates," Fiber Reinforced Polymer Reinforcement for Reinforced Concrete Structures, Proceedings of the Fourth International Symposium, SP-188,C. W. Dolan, S. H. Rizkalla, and A. Nanni, eds., America Concrete Institute, Farmington Hills, Mich.,1999, pp. 647-657.

[6] Khalifa, A.; Tumialan, G.; Nanni, A.; and Belarbi, A.,"Shear Strengthening of Continuous Reinforced Concrete Beams Using Externally Bonded CFRP Sheets,” Fiber Reinforced Polymer Reinforcement for Reinforced Concrete Structures, Proceedings of the Fourth International Symposium, SP-188,C. W. Dolan, S. H. Rizkalla, and A. Nanni, eds., America Concrete Institute, Farmington Hills, Mich.,1999, pp.995-1008.

[7] Mukhopadhyaya, P.; Swamy, R. N.; and Lynsdale, C.,”Optimizing Structural Response of Beams Strengthened with GFRP Plates,” Journal of Composite for Construction,May, 1988, pp 87-95.

[8] Sharma, A. K.,”Testes of Reinforced Concrete Continuous BeamsRepaired with and without Fibro Ferrocrete,” Concrete International, V. 14, No. 3, Mar., 1992, pp. 36-40.

[9] Namboorimadathil, S. M.; Tumialan, J. G.; and Nanni, A.,”Behavior of RC T-Beams Strengthened in the Negative Moment Region with CFRP Laminates,” ICCI, San Francisco, CA, June, 2002.

Appendix

Notations

= area of FRP external reinforcement (mm2)

= the area of main steel reinforcement, (mm2)

= area of compression steel reinforcement (mm)

= distance from extreme compression fiber to the neutral axis (mm)

D = diameter

= distance from extreme compression fiber to axis of compression reinforcement (mm)

= tensile modulus of elasticity of FRP (MPa)

= modulus of elasticity of steel (MPa)

= the effective stress level in the FRP reinforcement, (MPa)

= stress in tension steel reinforcement, (MPa)

= stress in compression steel reinforcement, (MPa)

= design ultimate tensile strength of FRP (MPa)

= overall thickness of a member (mm)

= FRP lever arm in compression side of the beam.

= bond dependent coefficient

= number of plies of FRP reinforcement

= nominal thickness of FRP reinforcement laminate (mm)

= ratio between depth of equivalent rectangular stress block to depth of neutral axis

= additional FRP strength-reduction factor

µÄ = deflection ductility index

= maximum usable compressive strain of concrete

= effective strain level in the FRP reinforcement

= design rupture strain of FRP reinforcement

= strain level in tensile steel reinforcement

= strain level in compressive steel reinforcement

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