Strengthening of reinforced concrete beams constructed with substandard steel reinforcement termination

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Composite Structures 85 (2008) 10–19 www.elsevier.com/locate/compstruct

Strengthening of reinforced concrete beams constructed with substandard steel reinforcement termination Yung-Chih Wang *, Kai Hsu Department of Civil Engineering, National Central University, Jhongli, Taoyuan 32001, Taiwan Available online 17 October 2007

Abstract Practical applications for the use of fibre reinforced polymer (FRP) composite materials for the seismic strengthening of reinforced concrete beams that have been constructed with a substandard beam bar termination method were experimentally investigated in this study. Results suggest that the cut-off reinforced concrete beam design does not meet the standard design codes and that if no extra shear reinforcement is arranged in the curtailed region, the beam may be subject to brittle failure. Installation of FRP plates for flexural and shear strengthening can successfully correct the deficiency. The results show that the FRP composite beams could withstand rotation levels greater than those expected to be imposed during an earthquake event. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: FRP; Strengthening; Reinforced concrete beams; Steel reinforcing termination

1. Introduction In Taiwan reinforced concrete (RC) beams are often used for the in situ construction of large-scale commercial buildings, such as shopping malls, public parking garages, and high-rise buildings. However, the seismic response of such buildings may not be adequate due to the fact that the main reinforcing bars in the beams have been curtailed in a manner not specified in the standard codes [1,2]. In other words this method of steel reinforcing termination was not considered in the detailed design process. Meanwhile, site engineers all too often are tempted to waive detailed reinforcement arrangements during the construction stage. For example it is specified in ACI 318-02 of the code, that additional stirrups should be arranged in the neighbourhood of the rebar curtailment to prevent the formation of shear cracks near the cut-off point. Similar to columns or bridge piers, it is expected there may not be *

Corresponding author. Fax: +886 3 4252960. E-mail address: [email protected] (Y.-C. Wang).

0263-8223/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2007.10.019

enough transverse reinforcement to prevent unexpected shear failure in the area where longitudinal bars have been curtailed. Reports based on reconnaissance after Japan’s 1995 Hanshin Earthquake [3] and Taiwan’s 1999 Chi-Chi Earthquake [4] indicated that longitudinal bar termination might have triggered the severe damage caused by flexureshear cracks in bridge piers. Given this experience, the authors propose to investigate and evaluate how to improve the seismic performance of the cut-off beam bar building structure. A simple method for the assessment of RC beams with rebar curtailment is proposed [5]. The purpose of the method is to evaluate reinforced concrete T-beams with longitudinal bar curtailment deficiencies which may lead to flexure-shear failures. An important conclusion can be made, that this method of beam bar curtailment may trigger unexpected flexure-shear cracking, to which the frame responses with brittle behaviour. In this research, an experimental programme was carried out to verify the above conclusion. A discussion of the seismic retrofitting of deficient T-beams using glassfibre/epoxy (GFRP) laminates is also included in the study.

Y.-C. Wang, K. Hsu / Composite Structures 85 (2008) 10–19

2. Experimental programme 2.1. Description of the test units Two cantilever T-beams were selected from a half span of a moment-resisting frame designed following the seismic design recommendations of the ACI 318-02 building code [1]. The primary earthquake resisting system of the designed building consisted of a grid of moment resisting frames spaced 5.5 m and 5.0 m apart in the vertical and horizontal directions. A slab was designed to transfer gravity loading via two-way action. The lateral force coefficient for seismic induced forces was 0.09. The top longitudinal

11

reinforcement of the beam was designed to completely sustain the bending moment demand caused by the worst-case combination of gravity and lateral load that would induce negative moments. In other words the contribution of slab reinforcement was not taken into consideration in the design. The beam bars were curtailed according to code specifications [2] but no additional steel stirrups in the neighbourhood of the curtailed points were added, making this a substandard design. Fig. 1 shows the detailed rebar arrangement of the tested T-beams. The beam flange width and the slab thickness were 960 mm and 120 mm, respectively. The overall depth of the beam was 550 mm and the web was 350 mm wide.

Fig. 1. Reinforcing details of test units.

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Y.-C. Wang, K. Hsu / Composite Structures 85 (2008) 10–19

The concrete strength was 20 MPa. The yield strength of the steel reinforcement was 320 MPa. Three tests were carried out on two identical units as follows:

ted using TYFO S GFRP plates with 1.27 mm nominal ply-thickness [6,7]. These plates were primarily reinforced in one direction. 2.2. Test set-up

Test Unit T1 – Stage 1:To test and observe the seismic performance of the as-built unit. Test Unit T1 - Stage 2:To repair the damaged beam and to observe the seismic performance of the repaired unit. Test Unit T2: To retrofit the unit and then test and observe the seismic performance of the retrofitted unit. The units were cast in the desired position. The compressive strength of the concrete (100 mm diameter by 200 mm high cylinders) on the day of testing was 24 and 18 MPa for Units T1 and T2, respectively. The measured properties of the reinforcing steel and the GFRP plate used in the tests are given in Table 1. Test units were repaired and retrofit-

Fig. 2 shows the test set-up. The fixed end of the T-beam, which was connected with lateral edge beams and a column stub, was bolted down to a strong floor, as the column location. A vertical load was applied at the beam’s free end by means of a hydraulic actuator. A strong steel beam, bolted opposite to the beam span, provided a fixed end at column face and overturning moment resistance during testing. Fig. 3a shows the test sequence. Load controlled cycles were initially imposed to the units to find the secant stiffness and vertical displacement at 75% of the estimated capacity of the unit in each direction of loading; see Fig. 3b. When

Table 1 Material properties of test units Materials

Nominal area (mm2)

Yield strength (MPa)

Concrete, unit T1 Concrete, unit T2 Steel D28 D24 D10 R10 GFRP TYFO SEH-51a

–

–

–

–

615 452 78.5 78.5

316 320 316 354

–

–

a b

Ultimate strength (MPa)

Elastic modulus (GPa)

Hardening strain (%)

Ultimate strain (%)

20

–

–

–

18

–

–

–

198 200 212 201

1.8 2.1 2.7 –

12 24 22 –

–

–

454 475 464 469 387b

One-ply nominal thickness is 1.27 mm. Values were determined from standard test in accordance with ASTM D 3039 [11].

Fig. 2. Test set-up.

18.7b

Y.-C. Wang, K. Hsu / Composite Structures 85 (2008) 10–19

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the column face is also plotted. In order to compare the predicted values with the test results, the small influence of gravity loading on the predicted capacity must be removed. Prototype Unit T1 behaved as expected when loaded upwards. A positive plastic hinge formed in the beam at the column face and extensive yielding of the beam bottom longitudinal reinforcement was observed in this region. As anticipated the measured and predicted capacity agreed very well. Under downward loading, cracking in the beam extended from the column face to near the point of the application of the loading. When the beam was pushed into the inelastic range, a large diagonal crack, inclined at 42° to the horizontal, opened up 1.3 m from the column face. The final extent of cracking at the end of the test is shown in Fig. 6a. It is apparent in Fig. 5a that the negative flexural strength, calculated at the face of the column and considering the slab reinforcement, was not attained. When the drift angle was 1% the main diagonal crack was 4.8 mm wide and the capacity of the beam had begun to drop due to imminent flexure-shear failure. The residual drift angle and the associated damage were considered to be the limit after which a satisfactory repair scheme could not be carried out on a structure. Consequently, the test was halted at this point and the repair work conducted. Fig. 3. Test sequence: (a) load regime; (b) define the yield displacement of test units.

loaded beyond the elastic range, controlled displacement cycles were then applied to the units. The displacement ductility lD term is defined as the ratio of the applied vertical displacement D to the vertical displacement when first yielding Dy occurs. The first vertical displacement yielded is defined as 4/3 times the vertical displacement observed for the controlled loading cycles at 75% the flexural strength capacity of the test unit. Vertical displacement was measured at the point of application of loading. Linear potentiometers were placed quadrilaterally on the web side of the beam so as to enable the average shear and flexural deformation of each ‘‘gauged region” to be estimated. Fig. 4 depicts the average flexural and shear distortion components captured for this arrangement of linear potentiometers. Each quadrilateral setting contained six linear potentiometers 400 mm in width by 300 mm in height. Geometrical measurements at peak loads could be used to find deformation due to flexure and shear in each quadrilateral. 3. Test results 3.1. General behaviour of prototype Unit T1 Fig. 5 shows the hysteric response of all test units. The predicted capacity Pn calculated based on the section at

3.2. Application of GFRP laminate The deficiency of the flexural/shear strength found in the tested unit T1 was corrected using GFRP fibrwrap fibreglass/epoxy laminates [6–10]. Fig. 7 illustrates the repair work in detail. GFRP laminates were applied to the top of the test beams. U-shaped GFRP strips were applied to the sides of the beams to improve the shear resistance of the beam in the curtailed location. The ends of these strips were not anchored. GFRP flexure strengthening was done to provide additional passive negative flexural resistance along the length of the beam, except at the column face (see Fig. 7). Consideration was given in the retrofitting scheme to limiting the longitudinal tensile strain in the GFRP plate bonded to the slab to ep = 0.4%, as well as to limiting the average bond stress between pffiffiffiffi the GFRP plate and the concrete to less than 0.17 fc0 (MPa) [12]. This tensile strain limit was chosen so as to avoid premature deterioration of the shear strength mechanism in the beam where the longitudinal reinforcement had been cut-off. The average bond stress limit selected was sufficient to avoid premature debonding of the plate. The U-shaped GFRP plates were designed to control the width of diagonal cracks and, hence, to delay the loss of shear transfer through the aggregate interlock. The shear capacity was expected to be enhanced by the bonding of the U-shaped GFRP plates to the critical region of the beam, as illustrated in Fig. 7. This would prevent shear-

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Fig. 4. Flexure and shear deformations measured by the quadrilaterally gauged regions on the web side of the test beam: (a) a diagram; (b) a photo.

flexure failure if maximum loading was reached, due to the formation of a plastic hinge at the column face. As mentioned earlier, loading on the as-built beam, unit T1, was increased until flexure-shear failure developed. The damaged unit T1 was repaired by the injection of epoxy into the main cracks, the application of two 1.38 m wide GFRP plates to the slab and by the application of GFRP strips to the sides of the beam in the damaged region as shown in Fig. 6a. The concrete surfaces where the GFRP strips were to be applied were carefully ground to remove any laitance and then cleaned with oil-free air pressure. A thick layer of epoxy primer was applied to the concrete surface before the application of the epoxy-saturated GFRP plates. Since the interface bond between the GFRP and the concrete surface is critical, care was taken to ensure that, at the point of application, the downward loading would be transferred directly to the beam without clamping the GFRP strips. Unit T2 was retrofitted prior to damage in the same manner as unit T1. 3.3. General behaviour of repaired unit T1 and retrofitted unit T2 The hysteric responses of unit T1 (repaired) and unit T2 (retrofitted) are compared with the responses of the prototype unit T1; see Fig. 5. The significant strength increase under negative loading was due to the contribution of the slab reinforcement. An unexpected brittle fail-

ure could be occurred in the location where the beam bars were curtailed, as prototype unit T1, if the contribution of the slab reinforcement was neglected. In other words, retrofitting of the deficient beams is necessary, as repaired unit T1 and retrofitted unit T2. It is evident that the bonding of the composite plate to the slab was very effective in forcing the development of a negative plastic hinge in the beam at the column face in stead of at the beam bar curtailment. Besides, U-shaped GFRP plates provided for a moderate confinement in the beam bar cut-off, reacted as closely spaced steel stirrups specified in the standard code. Cracking due to negative loading was more evenly distributed in the latter two tests than in the first test, as can be seen in Fig. 6. Wide cracks occurred in the beams only at the column face. In the latter two cases debonding of the three-sided U-shaped GFRP plates (see Fig. 8a) commenced from the top, in the region where the top longitudinal beam reinforcement had been cut-off, then slowly propagated downwards and sideways. This suggests that the bonding of side plates to the web of reinforced concrete beams, without anchoring would not be a reliable way to enhance the shear strength of the beam. Both units reached two cycles to a 2% drift angle at a displacement ductility of lD = 2 with minimum strength degradation. The hysteretic loops showed some pinching due to the formation of diagonal cracks that developed in the beam at the top longitudinal bar cut-off points; see Fig. 5b and c. The test-

Y.-C. Wang, K. Hsu / Composite Structures 85 (2008) 10–19 Vertical load (kN)

a (+)

Pn=168kN

150 100

positive moment

-80

200

-3

-2

-60

-40

-1 50 0 -20 -50 0

1

2 20

3

4

40

60

-200 -250 -300

-2%

-3

-2

-60

-40

drift angle

Pn=-314kN

-350 -1% Vertical load (kN)

b

-80

80

-150

negative moment

-3%

μΔ

5

Displacement (mm)

-100 (-)

15

1%

2%

200

3%

Pn=168kN

150 100

-1 50 0 -20 -50 0

1

2 20

3 40

4

5 60

μΔ 80

Displacement (mm)

-100 -150 -200 -250 -300 -3%

-2%

Vertical load (kN)

c

-3 -80

-2 -60

-1 -40

Pn=-314kN

-1%-350

1%

drift 3% angle

2%

200

Pn=164kN

150 100 50

0 -20 -50

1

2 20

34

5

μΔ

40

60

80

Displacement (mm)

-100 -150 -200 -250 -300 -3%

-2%

Fig. 6. Crack pattern developed in test units when loaded downward: (a) prototype unit T1; (b) repaired unit T1; (c) retrofitted unit T2.

-350 -1%

Pn=-311kN 1%

2%

drift 3% angle

Fig. 5. Measured hysteretic response: (a) prototype unit T1; (b) repaired unit T1; (c) retrofitted unit T2.

ing of these two units ended when, at a displacement ductility of lD = 3 at a 3% drift angle, the upper GFRP plates suddenly peeled off; see Fig. 8b. The separation of the plate was most likely induced by the large amount of shear distortion that occurred in the curtailed region of the beam 1.3 m from the column face after the side strips became ineffective. 3.4. Moment and shear deformation Fig. 9 shows the deformation components due to flexure and shear in the beams. The distance is taken from the col-

umn face (see Fig. 4). The top part of the figures displays the loading cycle results in the positive direction while the bottom part shows the loading cycle components in the negative direction. It can be seen that obvious variation in flexural rotation appeared in prototype unit T1 when the loop reached the first cycle of negative displacement ductility lD = 0.8, in the area 1200–1600 mm away from the column face, where the main diagonal crack developed. At the same time the shear deformation in this zone becomes larger. It is believed that the reinforcement in this area where the main diagonal crack developed will be the first to yield after continuous loading and that shear deformation becomes larger soon after the curvature of the main diagonal crack starts to increase. This is evidenced in Fig. 9a where most of the deformation in negative loading direction is concentrated in the deficient zone. The deformation response to positive loading of the prototype unit T1 was occurred adjacent to the column face, due mostly to flexure. The behaviour of the units strengthened by GFRP in relation to flexure and shear was different from that of the prototype unit. For negative loading of the repaired/ retrofitted units, as shown in Fig. 9b and c, deformation due to flexure and shear spread throughout the beam. This was because the local flexural and shear strengths in the deficient zone were enhanced by the fibreglass/epoxy laminates bonded to the beam.

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Y.-C. Wang, K. Hsu / Composite Structures 85 (2008) 10–19

2500 2 strips of GFRP fibrwrap, width=1380 principal fibres parallel to beam axis

633

550

410

120

50

1380

1-layer U-shape GFRP, principal fibres perpendicular to beam axis &1-layer long. GFRP, principal fibres parallel to beam axis Note: The thickness of 1-layer GFRP fibrwrap is 1.27 mm. Fig. 7. Retrofit scheme of test units T1 and T2.

Fig. 8. Delamination of GFRP plates: (a) at the web sides of beam; (b) at the top of beam.

3.5. Bond stress of longitudinal GFRP laminates The longitudinal strain on the GFRP plates was measured at the centreline of the beam. Clip gauges, typically with a 250 mm gauge length, were employed for this purpose. The results of plate strain measurement in the repaired unit T1 adjacent to both plate ends after inelastic loading cycles fluctuated due to instrument malfunction. The T2 strain profile showed stable values, which could

be used for study. Fig. 10b depicts the strain profiles for the GFRP plate bonded to the slab, for retrofitted unit T2, at the peak of cycle when the beam was subjected to downward loading. 2.0  1 in Fig. 10b represents the GFRP plate strains were measured when the beam was subjected to downward loading after reaching peak loading of the first cycle to a displacement ductility of lD = 2. The local plate bond stress was also determined from the difference between two consecutive plate strains as in Eq. (1)

13 15

1.4x2 = 2nd cycle to positive displacement ductility 1.4

1 1 1 20 17 13 1 11 9 - 1 -2

-2 -2

1 2 1 2

1 2

1 2

Y.-C. Wang, K. Hsu / Composite Structures 85 (2008) 10–19

-2 - 2

1200-1600 mm

1

800 -1200 mm

1 1 1 1 1 1 30 29 21 20 15 13 12

0-400mm 400-800mm 5 -1 -7 -8 -11 -10 -6 -1 -2 -2

6

2 1 2 -1

2 1 2 1

1

2

3

0

1

1

3 -1

1

1

1

2 1 3 1

1

1

2

2

9 -7

0

1

1

1

-1 -1

-1 -1 -1 -2

2

5

4 1

1

1

5 1

-1 -2 -2 -2 -2 -2 -3 -2

1600-2000mm(distance from column face ) -8 -9 -9 -8 -4 -5 -5 -4

2

1

1600-2000mm (distance from column face ) 2 2 2 1 1 1 1 2 1 2

3 3 8 -1 -3 -18

2

0

-8 -8 -3 -4

2.2x1

1600 -2000mm(distance from column face ) 1 0 0 0 0 0

1 2 3 -2 - 2 - 4

2

-12 -12

-8 -9 -10 -10 -9 -10 -8 -10-10 -12 -15 -16 -16 -18 -12 -15 -13 -15 -14 -11 -17 -3 -4 -2 -22 -5 -6 -8 -3 -3 -4 -3 -2 -8 -3 -4 -4 -3 -34 -35 -7 -7

-1 -1 -1 -1

-1.2x2 = 2nd cycle to negative displacement ductility 1.2

5

2

2

-17

1 1 2 2 12 13 13 11

-7 -3

1200-1600mm -6 -7 -7 -7 -4 -4 -4 -4

800-1200mm -8 -7 -4 -4

1.0x2

-20

7

69 1 5 1 1

2 6

1 4

2 8

-4

2 4

2 10

-3 -4

400-800 mm

-3

-1.2x1

-30

4

52

-4

-9 -11 -13 -15 -15 -15 -17 -12 -12 -13 -3 -4 -4 -4 -3

2.0x2

1.0x1

shear

-3

shear

2.0x1

-0.9x2

flexure

-2

-16 -17

1 21 16 14 12 7 -1 -1 -1 -1

0-400mm

-23 -23 -21 -2 -2 -2 flexure

1.4x2

0.75x2

-40 -50

(c) Retrofitted Unit T2

80 70 60 50 40 30 20 10 0 -10 -20

0 -10 -20 -30 -40

-3.5x1

2.4x2

-2.2x1

17

Fig. 9. Deformation components, expressing as a percentage of total deformation, at each quadrilateral measurement: (a) Prototype Unit T1; (b) Repaired Unit T1; (c) Retrofitted Unit T2.

-50

-1.2x2

1.4x1

(a) Prototype Unit T1

80 60 40 20 0 -20

0 -10 -20

5 45 43 2

31 3 3 3 3 2 2 2 13 12 12 13 10 10 11

-1.2x2

-30

1 5

3.2x1

1200 -1600 mm

-1.2x1

shear

1 5

800 -1200 mm

2.1x2

flexure

1 7

400-800 mm

-0.8x2

-40 -50

1 8

(b) Repaired Unit T1

80 70 60 50 40 30 20 10 0 -10 -20 0-400mm

-1

2.2x1

2.1x1 -2.2x2

2.4x1

-1.2x1

-1.2x2

2.0x2

-0.8x1

-2.5x1

-3.5x2

3.2x1

2.0x1

1.1x2

-2.0x2

3.6x1

0 0 -1 -2 -3 -4 -6 -7 -7 -8 -8 -6 -6 -5 -4 -1 -1 -9 -9 -9 -10 -9 -9 -8 -10 -10 -9 -10 -7 -7 -7 -7 -15 -15 -14 -14 -1 -2 -2 -3 -1 -2 -2 -2 -3 -3 -4 -2 -4 -4 -5 -5 -3 -3 -3 -3 -2 -3 -3 -3

-10

1.0x2 -0.9x2

1.0x2

-1.2x1

2.1x2

-0.6x2 1.1x1

-2.0x1

-3.5x2

-0.5x1

1.0x1

-1.0x2

3.6x1

1.0x1 -0.9x1

0.75x2

-1.2x2

1.0x1

-0.9x1

-1.2x1

-2.5x1

-1.2x2

0.75x1

-1.0x1

-3.5x1

3.2x1

-0.75x2

2.4x2

-0.5x2

0.8x2

-2.0x2

-1.2x1 -3.5x1

-0.75x1

-3.5x2

-0.8x2

1.4x2

-0.6x1

2.1x2

2.4x2

-2.5x1

3.6x1

2.1x1

1.4x1

-0.5x2

-0.8x2 -2.2x2

-2.0x2

-0.9x2

-0.75x1

-2.2x2

2.0x1 2.1x1

-2.2x1

2.4x1 -2.0x1

-3.5x1

-2.5x1

-2.2x1

0.8x2

1.1x2

1.0x2 -1.0x2

2.4x2 -2.0x2

2.4x1

0.8x1

1.1x1

-2.2x2

-0.8x1

2.2x1

-0.5x2

2.4x1

-0.6x2

2.0x2

1.0x2

-2.2x1

1.1x2

2.0x1

1.0x2 -2.0x1

0.75x2

-1.2x1

0.8x1

-2.0x1

1.0x2 -0.9x2

1.0x1

-1.2x2

-0.5x1

-3.5x2

1.1x1

1.4x1 -1.2x2

-1.0x2

-0.9x1

-1.0x2

1.0x1 -0.9x1

0.75x2 -1.0x1

0.75x1

-1.0x1

1.4x2 -0.8x1

-0.5x1

-1.0x1

-3.5x1

-0.6x1

1.4x1 -0.6x2

1.0x1

0.75x1

-0.75x2

2.4x2

-0.5x2

0.8x2 -0.6x1

-1.2x2

2.0x1 -2.2x2

-2.0x1

1.0x2

0.8x1

-1.2x2

-0.75x2

-2.2x1

1.0x2 -1.0x2

0.75x1

-1.2x2

1.0x1 -1.0x1

-3.5x2

-0.75x2

0.8x2 -0.6x1 1.1x1

-0.5x1

0.8x1

3.2x1

2.2x1 3.2x1

-0.75x1

-1.2x1

0.75x2 -0.75x2

3.6x1 -2.5x1

-0.9x2

1.0x1

2.2x1

-1.2x1

2.0x2 -1.2x1

2.1x2

-0.8x2

2.4x1 -2.0x2

-0.9x1

0.75x1 -0.75x1

3.6x1

-0.75x1

1.1x2

2.0x2 2.1x2

1.4x2 -0.8x1 2.1x1

-0.6x2

1.1x1

-0.8x2 2.1x1

1.4x1 -0.6x1

1.0x2

1.4x2 -0.8x1

0.8x2 -0.5x2

1.0x1

-0.6x2 1.1x2

0.8x1 -0.5x1

Components of positive displacement, % Components of negative displacement, %

Components of positive displacement, % Components of negative displacement, %

Components of positive displacement, % Components of negative displacement, %

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Y.-C. Wang, K. Hsu / Composite Structures 85 (2008) 10–19

a

Tensile strain, %

b

Distance from column face, mm

Bond stress, MPa

c

Distance from column face, mm Fig. 10. Longitudinal GFRP plate strain and bond stress measured in Retrofitted Unit T2: (a) measured strain; (b) raw data reduced to GFRP bond stress.

sp ¼

Ep Ap ðep2  ep1 Þ bp Dx

ð1Þ

where sp is the GFRP plate bond stress, assuming uniform stress distribution between two measured points ep1 and ep2; ep1 and ep2 are the measured GFRP plate strains for two consecutive points; Dx is the length between two consecutive measured points; Ep is the elastic modulus of longitudinal GFRP laminates applied to the top of the beam flange; Ap is the sectional area of the longitudinal GFRP plate; and bp is the width of the GFRP plate. In Fig. 10, it is apparent that the observed behaviour of the top GFRP plate compares very well with the strain limit of 0.4% chosen for the retrofitting. The maximum strain gradient occurred in the GFRP plate between 1.7 m and 2.5 m from the column face and the local bond stress obtained was 0.6 MPa; see p Fig. ffiffiffiffi 10c. The average bond stress in this region was 0.07 fc0 (MPa) which was the value associated with the bond failure observed in the test. The main reason for such a low observed bond stress value might the large kinking induced on the top GFRP plate (see Fig. 8b). This occurred as a result of web shear

distortion in the region where the longitudinal reinforcement had been curtailed. 4. Design concept for FRP strengthening Wang [5] discussed a method for assessing the lateral load resistance of a beam. The method can be used to determine the location where such plastic hinging can occur, particularly for negative hinging that may form in a beam away from the column face. This is most common in Taiwan in older or long-span RC buildings and can occur as a result of the presence of slab reinforcement and of poor development of longitudinal reinforcement in the beam. To shift negative plastic hinging from the deficient region to the beam end it is necessary to increase both the flexural and shear strength [13,14]. Both strength enhancements can be achieved by either using GFRP or CFRP longitudinal laminates to affix slab top strips for flexure and U-shaped side strips for shear; see Fig. 7. To avoid excessive shear deformations in the strengthened region, it is proposed here that the longitudinal strain

Y.-C. Wang, K. Hsu / Composite Structures 85 (2008) 10–19

in the laminate be equal to or less than 0.004. The value of 0.004 is made based on the measured results depicted in Fig. 10b. The deficient region should also be checked for shear. The shear force demand should be evaluated in relation to the flexural strength and the likely negative and positive plastic hinging. U-shaped FRP side strips that have been anchored at the end should be used to prevent unexpected delaminating; see Fig. 8. 5. Conclusions Experimental results indicate that under some circumstances, the critical moment resisting region of beam frames designed for earthquake resistance, but constructed with the substandard steel reinforcing termination design, may be subject to the formation of negative plastic hinges in apparently unexpected regions. This occurs due to the combined effects of slab reinforcement and longitudinal beam bar curtailment on the overall seismic response of the frame. The experimental results for seismic retrofitting of RC beams with design deficiencies of the beam bar curtailment type, indicate that due to the negative moment, flexural enhancement is necessary. It is recommended that the flexural strength at the bar cut-off points be enhanced to ensure that a strain limit of 0.4% can be imposed on the GFRP plate. U-shaped GFRP strips were glued to three sides of the beam frame. These acted as shear steel stirrups in the area of the cut-off region and enhanced the shear capacity of the beams so as to prevent premature flexure-shear cracking from occurring. However, the bonding of this type of strip to the sides of a beam is ineffective in resisting shear unless they are properly anchored at their ends. Acknowledgements This research was carried out with the financial support of the Taiwan National Science Council, under the grant NSC93-2211-E-008-019. The authors would like to express

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appreciation to Taiwan NSC and also to NCU graduate students who contributed to the experimental work. References [1] ACI 318-02. Building code requirements for reinforced concrete. American Concrete Institute, Committee 318, 2002. [2] Taiwan Civil 401. Engineering design specification and commentary of concrete structures. Civil and Hydraulic Engineering, Committee of Concrete Engineering, Taiwan, 2004 [in Chinese]. [3] Park R et al. The Hyogo-ken Nanbu earthquake (the great Hanshin earthquake) of 17 January 1995. Bull New Zealand Natl Soc Earthquake Eng 1995;28(1):1–98. [4] Taiwan NCREE. Reconnaissance report on Taiwan Chi-Chi Earthquake of 21 September 1999 – buildings (NCREE 99-054) and bridges (NCREE 99-055), National Centre for Research on Earthquake Engineering, Taiwan 1999 [in Chinese]. [5] Wang YC. The influence of steel bar curtailment on seismic resistance of RC beams in buildings. J Chinese Inst Civil Hydraul Eng 2002;14(3):523–9. [6] Wang YC, Chen CH. Analytical study on reinforced concrete beams strengthened for flexure and shear with composite plates. Compos Struct 2003;59(1):137–48. [7] Wang YC, Lee MG, Chen BC. Experimental study of FRPstrengthened RC bridge girders subjected to fatigue loading. Compos Struct 2007;81(4):491–8. [8] Garden HN, Hollaway LC. An experimental study of the influence of plate end anchorage of carbon fibre composite plates used to strengthen reinforced concrete beams. Compos Struct 1998;42(2):175–88. [9] Hadi MNS. Retrofitting of shear failed reinforced concrete beams. Compos Struct 2003;62(1):1–6. [10] Lee J, Hollaway L, Thorne A. Long-term static testing of an FRP prototype highway structure. Compos Struct 1994;28(4):441–8. [11] ASTM D 3039. Standard test method for tensile properties of polymer matrix composite materials. American Society for Testing and Materials 1995. [12] Sierra-Ruiz V, Destrebecq J, Gre´diac M. The transfer length in concrete structures repaired with composite materials: a survey of some analytical models and simplified approaches. Compos Struct 2002;55(4):445–54. [13] Paulay T, Priestley MJN. Seismic design of reinforced concrete and masonry building. New York: John Wiley & Sons; 1992. [14] Pham H, Al-Mahaidi R. Experimental investigation into flexural retrofitting of reinforced concrete bridge beams using FRP composites. Compos Struct 2004;66(1):617–25.