ACI STRUCTURAL JOURNAL TECHNICAL

ACI STRUCTURAL JOURNAL

TECHNICAL PAPER

Title no. 102-S65

Repair of Bridge Girders with Composites: Experimental and Analytical Validation by Marco Di Ludovico, Antonio Nanni, Andrea Prota, and Edoardo Cosenza This paper deals with a laboratory study to investigate the flexural behavior of full-scale damaged prestressed concrete (PC) bridge girders upgraded with externally bonded carbon fiber-reinforced polymer (CFRP) laminates. The experiments described in the paper concern tests on three beams: one was used as the control beam and the other two, damaged by removing the concrete cover and by cutting two and four strands, respectively, were repaired with CFRP laminates. Analytical predictions compared to tests results in terms of flexural capacity, deflections, strains, and failure modes are discussed. The results indicate that the used upgrade technique is structurally efficient in providing the damaged beams with stiffness and strength very close to that of the original undamaged beam. Keywords: bridge; composites; fibers; flexure; polymers; prestressed concrete; repair; shear; strength.

INTRODUCTION Every year, many prestressed concrete (PC) bridge girders are accidentally damaged by overheight vehicles or construction equipment during site clean-up. When this happens, questions arise about the repair strategy. Considering that a girder may be significantly damaged, the only alternative to repair is its replacement, which, although effective, is typically the most expensive solution. In addition, the replacement option requires the closure of traffic lanes and a lengthy disruption of traffic. There has been relatively limited research on the damage assessment and repair of PC bridge girders subjected to vehicular impact. With reference to traditional repair techniques, laboratory investigations by Zobel, Carrasquillo, and Fowler (1997) were conducted to evaluate application methods and performance characteristics of several prepackaged repair materials combined with pressure epoxy injection as well as strand splice assemblies. Under the repetitive nature of highway loading, repair methods such as internal strand splices and external post-tensioning were found to be only partially satisfactory because they could not restore the ultimate strength of the damaged member (Olson, French, and Leon 1992; Zobel and Jirsa 1998). Other studies were conducted on prestressed and nonprestressed concrete deep beams predamaged in shear and strengthened with steel clamping units that acted as external stirrups (Teng et al. 1996). Fiber-reinforced polymer (FRP) systems have emerged as alternatives to traditional materials and techniques (externally bonded steel plates, steel or concrete jackets, and external post-tensioning). The strengthening of reinforced concrete (RC) and PC structures using externally bonded steel plates and composite laminates has proven to be an effective method for increasing or restoring their structural capacity (Dolan, Rizkalla, and Nanni 1999; Shahawy et al. 1996; Aboutaha, Leon, and Zureick 1997). Klaiber et al. (1999) and Russo et al. ACI Structural Journal/September-October 2005

(2000) presented the outcomes of experiments conducted both in the field and in the laboratory on undamaged and damaged PC beams strengthened with carbon FRP (CFRP). Strengthening of impact-damaged girders with FRP laminates (Nanni 1997) and, in particular, with CFRP laminates installed by manual layup (Shahaway and Beitelman 1996; Nanni, Huang, and Tumialan 2001) has already been explored. To provide an experimental validation for the FRP strengthening techniques of damaged PC girders, laboratory tests were conducted at the University of Missouri-Rolla. The experimental campaign was aimed at proving that the CFRP upgrade technique could restore the original ultimate flexural capacity of the damaged girder. Tests on three specimens—one undamaged (Specimen 1, named S-1) and two on differently predamaged and CFRP upgraded beams (Specimens 2 and 3, referenced in the following as S-2 and S-3, respectively)—indicate that the CFRP upgrade technique is structurally efficient in providing the damaged beams with stiffness and strength very close to that of the original undamaged beam. The motivation for the development of the present research came from two real cases of accidentally damaged PC girders: Bridge A10062, St. Louis County, Mo. (Nanni, Huang, and Tumialan 2001), and Bridge A5657 over the Gasconade River, south of Dixon, Mo. (Parretti et al. 2003). In both cases, two strands were fractured due to an accidental impact. To upgrade the damaged girders, CFRP unidirectional laminates, applied to the bottom of the girder, were used (Fig. 1). RESEARCH SIGNIFICANCE The present paper deals with the full-scale laboratory validation of an FRP strengthening technique that has

Fig. 1—Impacted and CFRP upgraded PC girders on: (a) Bridge A5657, south of Dixon, Mo. (U.S.); and (b) Bridge A10062, St. Louis County, Mo. (U.S.) ACI Structural Journal, V. 102, No. 5, September-October 2005. MS No. 03-319 received August 6, 2003, and reviewed under Institute publication policies. Copyright © 2005, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the July-August 2006 ACI Structural Journal if the discussion is received by March 1, 2006.

639

Marco Di Ludovico is a PhD candidate at the University of Naples Federico II, Italy. His research interests include performance of fiber-reinforced polymer-reinforced members and strengthening of prestressed concrete structures with advanced materials. Antonio Nanni, FACI, is the V&M Jones Professor of Civil Engineering at the University of Missouri-Rolla, Rolla, Mo., and Professor of Structural Engineering at the University of Naples Federico II. He was the founding Chair of ACI Committee 440, Fiber Reinforced Polymer Reinforcement, and is current Chair of ACI Committee 437, Strength Evaluation of Existing Concrete Structures. He is also a member of ACI Committees 544, Fiber Reinforced Concrete, and 549, Thin Reinforced Cementitious Products and Ferrocement; and Joint ACI-ASCE-TMS Committee 530, Masonry Standards Joint Committee. His research interests include the performance of concrete-based structures. Andrea Prota is an assistant professor of structural engineering at University of Naples Federico II. He received his MSc in civil engineering at the University of Missouri-Rolla and his PhD in structural engineering at the University of Naples Federico II. His research interests include the seismic behavior of reinforced concrete and masonry structures, the use of advanced materials for new construction, and the retrofit of existing structures using innovative techniques. Edoardo Cosenza is a professor of structural engineering at the University of Naples Federico II. His research interests include seismic engineering, steel-concrete composite structures, and composite materials for construction.

already been used in the field. The experimental and analytical work allows quantifying the benefits of the use of CFRP composites applied by manual layup to damaged PC girders and provides experimental evidence for the development of practical design criteria.

EXPERIMENTAL PROGRAM Specimen geometry and preparation To study real PC girder cross sections, the design of test specimens was based on a Type 2 (Missouri Department of Transportation [MoDOT], Bridge Manual, Section 3.55) girder cross section, traditionally used by the MoDOT in bridge construction. Three 11 m-long girders were fabricated in a precast yard; the cross section is shown in Fig. 2. Once the girders were delivered to the laboratory, a concrete slab with dimensions of 0.81 x 0.15 m was cast to attain the final specimen cross section (Fig. 2). The shear reinforcement was designed to avoid shear failure during the test, while the number and diameter of strands were chosen to provide a flexural capacity consistent with standard practice. Specimens S-2 and S-3 were predamaged at midspan by: 1) removing the concrete cover for a total length of 0.25 m, and then 2) by cutting two (Strands No. 1 and 2 for Specimen S-2) and four (Strands No. 1 trough 4 for Specimen S-3) out of the 12 strands (Fig. 3). In both cases, the damage was limited to one side of the girder to simulate a vehicular impact. Once the damaged zone was patched using a cementitious mortar, the FRP flexural strengthening was applied. Specimens S-2 and S-3 were upgraded with unidirectional CFRP laminates applied to the bottom of the girder with fibers parallel to the beam’s longitudinal axis (Fig. 4). Furthermore, to prevent the FRP delamination, CFRP strips were U-wrapped around the bulb of the girder over the longitudinal laminates (Fig. 5). The number and geometrical dimensions of the plies together with U-wrap width and spacing for each specimen are reported in Table 1. For Specimen S-2, the outermost ply was extended 150 mm (the minimum FRP laminate development length suggested by ACI Committee 440 [2002]) after the location where the damaged strands became fully effective (1.375 m from midspan). For Specimen S-3, the FRP laminate development for outermost ply was increased to 455 mm, taking into account the interfacial shear stresses

Fig. 2—Specimen cross section (dimensions in mm).

Fig. 4—Repair scheme for S-2 and S-3.

Fig. 3—Intentional damage on S-2 and S-3. 640

Fig. 5—U-wrap disposition for S-2 and S-3. ACI Structural Journal/September-October 2005

increment due to the fact that one more CFRP ply was installed. Approximately the same amount of U-wraps (0.57 m/mL for Specimen S-2 and 0.51 m/mL for Specimen S-3) was used in the two specimens; however, the width and spacing were varied. Material properties Each girder was prestressed with 12 low-relaxation, seven-wire, 9.5 mm-diameter steel strands. The initial prestress applied by the fabricator was 76.5 kN per strand for a total initial prestress force Pi = 919 kN. On Specimens S-2 and S-3, the initial prestress force became equal to Pi = 766 and 613 kN, respectively, once the damage was performed. Four 12.7 mm-diameter mild steel bars were used to reinforce the deck and stirrups 9.5 mm diameter at 150 mm were used in the girder as shear reinforcement (Table 2). Table 2 also shows the two different concrete compressive strengths used for the deck and the girder, and also reports the strength of the cementitious mortar used to patch the damaged areas in S-2 and S-3. The properties of the carbon fibers used to upgrade the specimens are summarized in Table 2. The CFRP system was installed by manual layup. Once the damaged area of the girder was restored with cementitious mortar, the installation procedure involved: a) surface preparation by rounding the edges of the girder to 15 mm radius and sandblasting the concrete surface; b) primer and putty application to fortify and level the concrete surface; and c) application of the first layer of saturant and gently pressing on the first fiber ply. The same sequence was repeated for additional plies. Finally, a layer of saturant was applied to protect the laminate.

Table 1—CFRP flexural strengthening for Specimens S-2 and S-3

Test setup and instrumentation Each specimen was tested in a four-point bending configuration. The distance between supports was 10.36 m, and the constant moment region was 2.74 m (Fig. 6). Two hydraulic jacks were used to apply the load, which was recorded by load cells placed on each jack. Real-time measurement of the structural response was achieved using an electronic data acquisition system. The load was applied in cycles of loading and unloading. Two stringer-type linear variable displacement transducers (LVDTs) were placed at girder midspan, and four more LVDTs were located along the specimen (two at 1.37 m from midspan, and two at the support position). For each specimen, strain gauges were also installed on the strands (prior to casting of the girder), the concrete slab, and the longitudinal FRP laminates. EXPERIMENTAL RESULTS The experimental results for each specimen are discussed with reference to: a) the specimen global behavior (cracks pattern, failure modes, and load-deflection relationship); and b) the local behavior of the midspan cross section (momentstrain and moment-curvature relationships). The experimental moment values discussed in the following sections are the sum of the moments due to the applied load and the dead load of the specimens (MDL = 107.5 kN⋅m). Global behavior For Specimen S-1, the first crack was detected within the constant moment region at a load value equal to 392 kN corresponding to Mcr = 854 kN⋅m. Post-cracking behavior is clearly shown in the load-deflection curve at the load value of 392 kN where a change of the curve slope is recorded (Fig. 7). By increasing the load, other flexural cracks (vertical) opened along the girder within the constant moment region, approximately spaced at 150 mm (Fig. 8). These reached the

CFRP plies, 1st ply 2nd ply 3rd ply, Number U-wrap U-wrap Speci- Number wide, length, length, length, of width, spacing, men of plies m m m m U-wraps m m S-2 S-3

2 3

0.36 0.36

3.36 4.27

3.05 3.96

— 3.66

8 22

0.25 0.10

0.46 0.20

Table 2—Material properties

Prestressing steel

Mild steel

Concrete

Carbon fiber

Strand type

Low relaxation

Strand tensile strength, MPa Nominal diameter, mm

1862 9.5

Strand area, mm2

54.8

Modulus of elasticity, GPa

200

Bars, nominal diameter, mm

12.7

Bar area, mm2

129

Stirrup nominal diameter, mm

9.5

Stirrup area, mm2 Tensile strength, MPa

413

Modulus of elasticity, GPa Concrete deck, MPa

200 27.6

PC girder, MPa Cementitious mortar, MPa

55.2 47

Nominal thickness per ply, mm Ultimate tensile strength, MPa

0.165 3800

Modulus of elasticity, GPa

227

Fig. 6—Test setup (dimensions in m).

71

ACI Structural Journal/September-October 2005

Fig. 7—Load-deflection curves (at girder midspan). 641

top of the girder at a load value of approximately 534 kN; in the last load cycle, until the failure of the specimen, they progressed into the deck. Shear diagonal cracks were observed outside the constant moment region after a load of 445 kN. During the ultimate load cycle, as a load of approximately 580 kN was approached, the girder started attaining deflections much larger than L/100 (where L is the distance between supports). The test was continued up to a deflection of approximately L/60 (172 mm); at this stage, the load remained almost constant and arching started to occur. At this point, the test was stopped and the girder was considered to be failed. The failure load was equal to 582 kN, which corresponds to a failure moment of 1216 kN⋅m. During the tests on Specimens S-2 and S-3, the first crack was detected at load values of 346 and 230 kN, respectively,

Fig. 8—Flexural cracks on Specimen S-1 (constant moment region, load = 534 kN).

Fig. 9—Cracks on Specimen S-2.

corresponding to Mcr = 767 kN⋅m for S-2 and Mcr = 546 kN⋅m for S-3. As the load increased, both specimens showed a horizontal crack at the top of the girder web, on the side opposite to the damage (Fig. 9 and 10). The flexural cracks that opened in the constant moment region were not vertical as in S-1 (on the damage side, the cracks fanned out from the location of the cut strands). In S-2 and S-3, they showed a different progression on the two sides of the specimen (Fig. 9 and 10). This was due to the prestress force eccentricity resulting from cutting two and four strands, respectively. The failure of Specimens S-2 and S-3 was due to the rupture of an U-wrap close to midspan on the undamaged girder side. Such rupture was immediately followed by delamination of the longitudinal CFRP laminates (Fig. 11). Failure loads were equal to 616 and 533 kN, respectively, corresponding to a failure moment of 1281 kN⋅m for S-2 and 1123 kN⋅m for S-3. Load versus midspan deflection curves are depicted for Specimens S-2 and S-3 in Fig. 7. The deflections recorded at ultimate load were 67.2 and 58.9 mm, respectively. Such curves show that there is a considerable loss of ductility with respect to S-1 as the deflection at maximum load of the strengthened specimens averages 35% that of the control specimen. Local behavior Experimental moment-concrete strain curves at the midspan cross section are depicted in Fig. 12. Such curves show that the maximum strain achieved in Specimen S-1 (0.0028) was much higher than those recorded in Specimens S-2 and S-3 (equal to 0.0016 and 0.0018, respectively). Figure 12 shows that, for the same moment level, concrete strains become higher as the percentage of prestress loss increases. For instance, considering a moment equal to 60% of the ultimate flexural capacity of the undamaged beam (service moment equal to approximately 730 kN⋅m), the compressive strain recorded in the deck goes from 0.02% for S-1 up to 0.03% and 0.05% for S-2 and S-3, respectively. Figure 13 shows the moment-FRP strains relationship at a cross section located at 100 mm from midspan. Both curves show a clear change of slope corresponding to the cracking moment; the maximum values attained by FRP laminates in that cross section are 0.0094 and 0.0077 for S-2 and S-3, respectively. The maximum strains of 56 and 46%, respectively, of the ultimate nominal FRP strain, confirm that failure occurred by debonding.

Fig. 10—Cracks on Specimen S-3.

Fig. 11—CFRP failure on Specimens S-2 and S-3. 642

Fig. 12—Moment-strain on concrete deck at midspan on Specimens S-1, S-2, and S-3. ACI Structural Journal/September-October 2005

At the midspan cross section of Specimen S-1, the strain gauge placed on Strand No. 3 measured a maximum strain equal to 0.0037 (after this the gauge stopped functioning), that, when added to 0.0064 strain due to the prestress, gives a total maximum value of 0.0101. This value is almost 20% more than the guaranteed yielding strain (0.0086). At the midspan cross section of Specimen S-2, the maximum strain was attained on the same strand and its value was 0.0110, including the prestressing stage. Finally, at the midspan cross section of Specimen S-3, the maximum strain recorded on Strand No. 5 (Strand No. 3 was cut) was equal to 0.0132, including the prestressing stage. Using data provided by stain gauges applied on both the concrete deck and strands (for Specimen S-1) or on concrete deck and CFRP laminates (for Specimens S-2 and S-3), it was possible to derive the moment-curvature diagrams as depicted in Figure 14. The slopes of the three curves shows that the CFRP strengthening provided the damaged beams with a stiffness very close to that of the original undamaged beam. For Specimen S-1, the moment-curvature relationship stops slightly past the yielding moment because of the strain gauge failure. ANALYSIS AND DISCUSSION Theoretical analysis Theoretical predictions for cracking and ultimate moment were performed for each specimen. The cracking moment was computed by limiting the concrete tensile stress at the bottom fiber level at value of fr (tensile strength of the concrete girder). The computed cracking moments and calculations that support these results are reported in the Appendix. For the computation of the nominal moment capacity of the control specimen, S-1, the conventional approach as given in ACI 318 and the PCI Design Handbook (5th Edition) was used. This included the conventional assumptions for prestress loss to derive the effective prestress. For the two damaged and CFRP upgraded specimens, S-2 and S-3, the analytical computation of the nominal moment capacity was initially attained following guidelines of ACI 440.2R-02 (ACI Committee 440 2002) for RC members. The calculation procedure is reported in the Appendix and the results are summarized in Table 3. This allowed verifying the opportunity of extending the ACI 440.2R (ACI Committee 440 2002) provisions to PC members. Toward this objective, particular attention was paid to the term κm (that is, κm = 1/60εfu(1 – [n Ef t f /360,000]) for the adopted laminates) that determines the effective strain attainable in the external reinforcement as controlled by debonding. In a second step, a more accurate analysis was performed to compute the ultimate moment capacity of the damaged and CFRP upgraded specimens without neglecting the effect of the eccentricity of the prestress force due to the cutting of two and four strands. If such effect is taken into account, it is necessary to assess a bending moment vector with components in both vertical and horizontal directions (the neutral axis is not perpendicular to the axis of the girder web). Calculations were carried out also considering the eccentricity effect so that a comparison, and an understanding at the extent of the influence of eccentricity on strength predictions, between the two approaches could be possible. A comparison in terms of ultimate moment capacity between the simplified calculation (neglecting the eccentricity caused by the strands cut) and that taking into account such ACI Structural Journal/September-October 2005

effect is reported in Table 4. The latter was performed by using a model that divides the cross section into rectangular elements having dimensions 10 x 2.5 mm. The solution is found by iterations; both neutral axis depth and inclination (assuming plane sections remain plane) are obtained from the translational equilibrium and the vertical alignment between the compressive and tensile centroid of the reactive regions. Then, the different material contributions (compressive concrete and mild longitudinal steel, tensile prestressing tendons, Table 3—Comparison between experimental and theoretical ultimate results Ultimate moment, kN⋅m Modes of failure (E.-T.)/ Specimen no. Experimental Theoretical E., %* Experimental Theoretical

*

S-1

1216

1044

14.1

S-2

1281

1198

6.5

S-3

1123

1127

–0.4

Strand Concrete yielding crushing CFRP CFRP delamination delamination CFRP CFRP delamination delamination

E. = experimental; and T. = theoretical.

Table 4—Ultimate moment capacity and neutral axis slope with and without eccentricity effect for Specimens S-2 and S-3 Neutral axis slope α, degree Specimen Without With Difference, Without With no. eccentricity eccentricity % eccentricity eccentricity S-2 1198 1179 1.58 0.0 1.4 Ultimate moment Mn, kN⋅m

S-3

1127

1104

2.04

0.0

2.1

Fig. 13—Load-strain on CFRP bottom surface (100 mm from midspan.)

Fig. 14—Experimental moment-curvature between S-1, S-2, and S-3.

comparison

643

and FRP laminates) are computed in terms of forces and the corresponding ultimate moment calculated by equilibrium around the found neutral axis. To compute the contributions in terms of forces, the following constitutive relationships were adopted for the materials 1. Deck and girder concrete: σ(ε) =

1000f c′ ε ( – 250ε + 1 ) for ε < 0.002 f c′ for 0.002 < ε < 0.003

;

the ultimate strain of concrete εcu is assumed equal to 0.003. 2. Mild steel: σ(ε) =

ε s′ E s for ε s′ < ε y f y for ε s′ > ε y

3. Prestressing tendons:

σ(ε) =

ε p E ps for ε p < 0.0086 0.04 270 – ------------------------ for ε p > 0.0086 ε p – 0.007

4. Composite materials: σ(ε) =

ε f E f for ε f < κ m ε fu ε fu = 0.0167

;

the Young’s modulus is E f = 227,000 MPa. Table 4 reports: a) the ultimate moments computed by following ACI 440.2R (ACI Committee 440 2002) recommendations (first column); b) the components of the ultimate moment in the vertical direction computed considering the eccentricity effect (second column); c) the difference between the results obtained by the two approaches (third column); and d) the slope of the neutral axis with respect to a horizontal axis for each case (last two columns). The nominal moments obtained by the two analyses are very close due to the small inclination of the neutral axis that in the analyzed cases is equal to 1.4 and 2.1 degrees for Specimens S-2 and S-3, respectively. This confirms that the

Fig. 15—Comparison of experimental-theoretical momentcurvature (Specimens S-1 and S-2). 644

simplified theoretical predictions are reliable and sufficiently accurate for the analyzed cross sections. Experimental-theoretical comparison The theoretical computation of the cracking moment (refer to the Appendix) shows that a greater percentage of tendon loss causes a considerable decrease of the cracking moment (the theoretical cracking moment goes from 789 kN⋅m for Specimen S-1 to 693 and 596 kN⋅m for Specimens S-2 and S-3, respectively); such outcome is also confirmed by the experimental results. This effect can be justified considering that, as more strands are cut, the initial prestress force decreases and, consequently, the tensile strength at the bottom fiber is attained sooner. With reference to the ultimate moment, Table 3 indicates that the experimental ultimate moment attained by S-2 (1281 kN⋅m) was slightly greater than the ultimate moment achieved by S-1 (1216 kN⋅m); such a result, confirmed also by analytical computations (1198 kN⋅m for S-2 against 1044 kN⋅m for the S-1 control specimen), shows that the upgrade technique used was valid and that it allowed restoring the targeted ultimate moment capacity. Considering the results provided by Specimen S-3, it is possible to underline that the upgrade technique used was still valid to increase the moment capacity of the damaged member, but not sufficient to achieve the experimental moment capacity of the undamaged specimen. Table 3 shows that theoretical prediction using ACI 440.2R (ACI Committee 440 2002) guidelines is less conservative when the prestress loss is high and, consequently, the amount of external reinforcement is also high. The percentage difference between theoretical and experimental prediction values goes from 14.1% for Specimen S-1 to 6.5% for Specimen S-2 and –0.4% for Specimen S-3. This outcome suggests investigating how the κm expression could be modified to preserve a constant safety factor between theoretical prediction and experimental results. If the coefficient 1/60 would change to 1/90 in the κm expression, an approximately constant difference between analytical and experimental results could be obtained. By using such coefficient, in fact, the theoretical ultimate moment of Specimens S-2 and S-3 would be equal to 1091 and 987 kN⋅m, respectively, with a percentage difference of 14.9 and 12.2%, which are very close to that obtained with Specimen S-1 (14.1%). This recalibration of κm could give the opportunity to safely extend existing ACI Committee 440 (2002) recommendations to the case of impacted PC girders. Further experimental evidence is needed to confirm the suggested change to the κm expression that would decrease the effective strain by a factor of 0.67 for PC members. In Fig. 15 and 16, an experimental-theoretical comparison in terms of moment-curvature diagrams was performed for Specimens S-1 and S-2 and for Specimens S-1 and S-3, respectively. The experimental moment-curvature relationship for Specimen S-1 was obtained using strain readings from gauges applied to the concrete deck and the tendons. For Specimens S-2 and S-3, the curvature was computed using strain readings from gauges applied to the concrete deck and the laminates. For Specimen S-1, the moment-curvature relationship stops past the yielding moment because of the strain gauge failure. The theoretical curves, depicted with a dashed line, are trilinear (connecting cracking, yielding, and ultimate moment-curvature points computed according to ACI 318-02 and ACI 440.2R-02). Both diagrams show that ACI Structural Journal/September-October 2005

maximum amount of the external reinforcement that can be installed, is considered the upper limit. The graph of Fig. 17 could easily be repeated with reference to any bridge girder type to provide practical design normographs that would allow the design engineer to immediately assess of the possibility of repair using composite materials.

Fig. 16—Comparison of experimental-theoretical momentcurvature (Specimens S-1 and S-3).

Fig. 17—Nominal moment as a function of number of strands lost and number of CFRP plies. CFRP reinforcement allowed restoring the stiffness of the specimen cross section as the slope of the curves referred to Specimens S-2 and S-3 before cracking is very close to that of the undamaged specimen, S-1. Curves for Specimens S-2, in particular, and S-3 show that after first cracking, the theoretical curves are below the experimental ones. This is explained by considering that the theoretical curve is drawn with reference to an effective moment of inertia of the cracked cross section Ie, whereas the experimental data refer to a cross section that may not be necessarily cracked. As the distance between a cracked cross section and that where the gauges are applied increases, the difference between theoretical and experimental values becomes larger. The experimental and theoretical results trend seems to indicate that there is an upper limit of damage amount beyond which the externally bonded FRP laminates are no longer adoptable as a repair solution. To define such a limit, a parametric study using the approach with no eccentricity effect and the original ACI formulation for κm was performed on the cross section of Fig. 2 to evaluate the amount of external CFRP strengthening necessary to repair a girder with different damage levels. The outcomes are depicted in Fig. 17 where it is shown that two 0.36 m-wide CFRP plies allow restoring the flexural capacity of the virgin beam up to a percentage of 25% of tendon loss. Up to 33% of tendon loss, the CFRP upgrade technique could be still effective, if three 0.36 m-wide plies were applied. Such percentage of damage, considering three plies as the ACI Structural Journal/September-October 2005

CONCLUSIONS The paper presented laboratory tests on three full-scale PC girders—one undamaged and two intentionally damaged and upgraded using externally bonded CFRP laminates. The laboratory work originated from the need to provide an experimental validation of the effectiveness of the proposed repair technique already adopted in several impacted PC bridges. As field cases showed that the use of composites could represent a sound alternative to traditional methods from a constructibility standpoint (financially competitive, easy and fast installation, no disruption of traffic lanes), this investigation now demonstrates that it is also structurally effective and could allow damaged PC girders to recover their original flexural capacity and stiffness. It was observed that even though U-wraps were used, the CFRP-strengthened members failed by delamination of the flexural reinforcement rather than by fiber rupture. Future investigations are needed to assess the possibility of modifying the laminate’s anchoring system to prevent or further delay the delamination and then exploit the full capacity of the FRP system. The laboratory work also confirmed the loss of member ductility, as failure is controlled by a brittle mechanism such as FRP delamination. Laboratory results allowed checking the possibility of extending the ACI Committee 440 (2002) recommendations to the case of FRP-strengthened PC members; experimentaltheoretical comparisons showed that a recalibration of the coefficient κm could be advisable. A modified equation of κm for PC members has been proposed, but further tests are needed for its confirmation. The theoretical analysis also allowed for understanding of the insignificant influence of the eccentricity due to tendons loss for the computation of the flexural capacity at the ultimate limit state. ACKNOWLEDGMENTS The support of both the University Transportation Center and the NSF Industry/University Cooperative Research Center on Repair of Building and Bridges with Composites (RB2C) based at UMR is kindly acknowledged.

NOTATION Acg Acs Af Ap As′ b c cb d′ dp Ecg Ef Eps Es ES e

= = = = = = = = = = = = = = = =

eg

=

f c′

=

area of concrete girder area of complete cross section area of FRP external reinforcement total area of prestressed steel total area of mild steel deck width neutral axis depth distance from bottom fiber to cross section centroid concrete cover distance from prestressed tendons to compressive fiber modulus of elasticity of girder concrete tensile modulus of elasticity of FRP modulus of elasticity of prestressed reinforcement modulus of elasticity of steel elastic shortening eccentricity (distance from tendons centroid to cross section centroid) girder eccentricity (distance from tendons centroid to girder cross section centroid) compressive strength of concrete deck

645

fcir

=

ffe fps fpu fr fs′ h Icg Ics Ie Kcir Kes Mcr MDL Mg Mn n P Pi Sb tf wf β1

= = = = = = = = = = = = = = = = = = = = = =

εbi εcu εf εfe

= = = =

εfu εp εs′ εy

= = = =

κm

=

concrete stress at center of gravity of prestressing force immediately after transfer effective stress in FRP; stress level attained at section failure stress in prestressed reinforcement at nominal strength of member ultimate strength of prestressing steel tensile strength of concrete girder stress level in mild steel total height of cross section moment of inertia of girder moment of inertia complete cross section effective moment of inertia for computation of deflection 0.9 for pretensioned members 1.0 for pretensioned members cracking moment moment due to self-weight of specimen moment due to girder self-weight nominal moment strength number of plies of FRP reinforcement effective prestress force considering total losses initial prestress force section modulus with respect to bottom fiber of cross section nominal thickness of one ply of FRP reinforcement width of FRP reinforcing plies ratio of depth of equivalent rectangular stress block to depth of neutral axis strain level in concrete substrate at time of FRP installation ultimate concrete strain strain level in FRP reinforcement effective strain level in FRP reinforcement; strain attained at section failure design rupture strain of FRP reinforcement strain in prestressed steel reinforcement strain in mild steel strain corresponding to yield strength of nonprestresssed steel reinforcement bond-dependent coefficient for flexure

REFERENCES Aboutaha, R.; Leon, R. T.; and Zureick, A. H., 1997, “Rehabilitation of Damaged AASHTO Type II Prestressed Girder Using CFRP,” Proceedings of the 2nd Symposium on Practical Solutions for Bridge Strengthening and Rehabilitation, Kansas City, Mo., Apr., pp. 293-301. ACI Committee 318, 2002, “Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (318R-02),” American Concrete Institute, Farmington Hills, Mich., 443 pp. ACI Committee 440, 2002, “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI 440.2R-02),” American Concrete Institute, Farmington Hills, Mich., 45 pp. Dolan, C. W.; Rizkalla, S. H.; and Nanni, A., eds., 1999, Fiber ReinforcedPolymer Reinforcement for Concrete Structures, Proceedings of the Fourth International Symposium, SP-188, American Concrete Institute, Farmington Hills, Mich., 1182 pp. Klaiber, F. W.; Wipf, T. J.; Russo, F. M.; Paradis, R. R.; and Mateega, R. E., 1999, “Field/ Laboratory Testing of Damaged Prestressed Concrete Girder Bridges,” Iowa DOT Report HR-397, Iowa State University, Ames, Iowa, Dec., 261 pp. Master Builders Technologies, 1998, MBrace Composite Strengthening System-Engineering Design Guidelines, Second Edition, Cleveland, Ohio, 140 pp. Nanni, A., 1997, “Carbon FRP Strengthening: New Technology Becomes Mainstream,” Concrete International, V. 19, No. 6, June, pp. 19-23. Nanni, A.; Huang, P. C.; and Tumialan, J. G., 2001, “Strengthening of Impact Damaged Bridge Girder Using FRP Laminates,” Ninth International Conference on Structural Faults and Repair, London, July 4-6, 7 pp. Olson, S.A.; French, C. W.; and Leon, R. T., 1992, “Reusability and Impact Damage Repair of Twenty-Year-Old AASHTO Type III Girders,” Research Report No. 93-04, University of Minnesota, Minneapolis, Minn. Parretti, R.; Nanni, A.; Cox, J.; Jones, C.; and Mayo, R., 2003, “Flexural Strengthening of Impacted PC Girder with FRP Composites,” Field Applications of FRP Reinforcement: Case Studies, SP-215, S. Rizkalla and A. Nanni, eds., American Concrete Institute, Farmington Hills, Mich., pp. 249-262. Precast/Prestressed Concrete Institute, 1999, PCI Design Handbook, 5th Edition, Chicago, pp. 4.1 to 4.96 and 11.1 to 11.36. Russo, F. M.; Wipf, T. J.; Klaiber, F. W.; and Paradis, R., 2000, “Evaluation and Repair of Damaged Prestressed Concrete Girder Bridges,” Mid-Continent Transportation Symposium Proceedings, pp. 109-114.

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Shahawy, M. A., and Beitelman, T., 1996, “Structural Repair and Strengthening of Damaged Prestressed Concrete Bridges Utilizing Externally Bonded Carbon Materials,” 41st International SAMPE Symposium, Florida Department of Transportation, Mar. 24-28, pp. 1131-1138. Shahawy, M. A.; Beitelman, T.; Arockiasamy, M.; and Sowrirajan, R., 1996, “Experimental Investigation on Structural Repair and Strengthening of Damaged Prestressed Concrete Slabs Utilizing Externally Bonded Carbon Laminates,” Composites, Part B 27B, pp. 217-224. Teng, S.; Kong, F.-K.; Poh, S.-P.; Guan, L. W.; and Tan, K.-H., 1996, “Performance of Strengthened Concrete Deep Beams Predamaged in Shear,” ACI Structural Journal, V. 93, No. 2, Mar.-Apr., pp. 159-171. Zobel, R. S.; Carrasquillo, R. L.; and Fowler, D. W., 1997, “Repair of Impact Damaged Prestressed Bridge Girder Using a Variety of Materials and Placement Method,” Construction and Buildings Materials, V. 11, No. 5-6, pp. 319-326. Zobel, R. S., and Jirsa, J. O., 1998, “Performance of Strand Splice Repair in Prestressed Concrete Bridges,” PCI Journal, V. 43, No. 6, pp. 72-84.

APPENDIX This Appendix shows results in terms of prestressing force and cracking and ultimate moments with reference to Specimens S-1, S-2, and S-3, according to ACI 318 and ACI 440.2R. To minimize the length of the Appendix, detailed calculations are provided only for Specimen S-2. Based on the same rationale, calculations were carried out for S-1 and S-3, and the results are summarized in Table 5 (SI units). Detailed calculations for Specimen S-2 Prestress force—The effective prestress computed by the following expression

force

is

P = Pi – ApES = 748 kN where Pi = 0.75fpuAp = 766 kN; fpu = 1862 MPa; Ap = 0.548 × 10 = 548 mm2; ES = kesEps fcir/Ecg = 33.03 MPa; Kes = 1.0; Eps = 200,000 MPa; Ecg = 42,332 MPa; 2 P Pi eg   M g e g f cir = k cir  -------i- + ----------- – ------------ = 6.99 MPa; I cg   I cg   A cg

kcir = 0.9; Acg = 202,400 mm2; eg = 272.6 mm; Icg = 0.0142 m4; and Mg = 66.79 kN⋅m. Cracking moment—The cracking moment of the cross section is computed by the following expression P Pe M cr = S b  f r + ------- + ------ = 693 kN⋅m  A cs S b  where Sb = Ics/cb = 0.062625 m3; Ics = 0.0320 m4; cb = 512 mm; fr = 3.29 MPa; P = 748 kN; Acs = 290,760 mm2; and e = 436 mm. ACI Structural Journal/September-October 2005

Ultimate moment—In this case, it is necessary to compute

d p – c ε p = ε 1 + ε 2 ( ε fe + ε bi )  ------------- = 0.019  h – c

M DL P Pe ε bi = ------------– ---------------- – ------------- = – 0.00014 S b E cg E cg A cs S b E cg

P ε 1 = -------------- = 0.0068 E ps A p

where MDL = 107.5 kN⋅m; Sb = 0.0626 m3; Ecg = 42,332 MPa; P = 748 kN; Acs = 290,640 mm2; and e = 435 mm.

2 Mg e P Pe ε 2 = ---------------- + --------------- – -------------- = 0.0002 A cg E cg E cg I cg E cg I cg

ε fe = min { k m ε fu ;ε f } = k m ε fu = 0.01320

nt f E f  1 - = 0.79 κ m = ------------  1 – ------------------- 60ε fu 360, 000 

if κ m ε fu < ε f then FRP failure ε fu = 0.0167

εfu = 0.0167; n = 2; tf = 0.1651 mm; and Ef = 227,000 MPa.

– c ε f =  ε cu h---------- – ε bi = 0.02831  c 

κm εfu = 0.79 × 0.0167 = 0.0132 Using the trial-and-error procedure, it is possible to determine the depth to the neutral axis by checking equilibrium

where h = 960 mm and εcu = 0.003

f ps A p + ffe Af = 0.85f c′ β 1 cb + A′s ε′s E s

dp = 883 mm ffe = εfeEf = 2995.6 MPa

where 0.004 - = 1861.7 MPa f ps = f pu –  ---------------------- ε p – 0.007

where Ef = 227,000 MPa

Table 5—Summary of theoretical calculations Specimen Prestress force P = P i – A p ES

Cracking moment

Pi, kN

S-1

S-2

S-3

919

766

613

Ap, mm2

658

548

438

ES, MPa P, kN

39.63 893

33.03 748

26.65 601

Sb , m3

0.0627

0.0626

0.0623

fr , MPa

3.29

3.29

3.29

Acs, mm2

290,640

290,760

290,560

e, mm Mcr, kN⋅m

436 789

436 693

436 596

Ultimate moment

fps, MPa

1860.9

1861.7

1861.6

For Specimen 1:

dp, mm

883

883

883

β1

0.87 67.9

0.75 92.4

0.73 88.9

Pe- P- + ----M cr = S b  f r + ----- A cs S b 

β 1 c β1 c M n = A p f ps  d p – ------- + As ′ fs ′  ------- – d′   2  2  For Specimens S-2 and S-3: β 1 c β 1 c M n = A p f ps  d p – ------- +A f f fe  h – ------  2  2  β1 c + As′ fs′  ------- – d′  2 

c, mm As′ , mm2

516

516

516

fs′ , MPa d′, mm εbi

200.0 50.8 —

128.0 50.8 0.0001

102.0 50.8 0.0001

κm

—

0.79

0.69

κm εfu

—

0.0132

0.0114

Af , mm2

—

119

178

ffe, MPa

— 960 1044

2995.6 960 1198

2601.7 960 1127

h, mm Mn, kN⋅m

ACI Structural Journal/September-October 2005

647

Af = nwf tf = 119 mm2 where n = 2; wf = 360 mm; and tf = 0.01651 mm.

d ′ = 50.8 mm Es = 200,000 MPa fs = ε s′ Es = 128 MPa

f c′ = 27.6 MPa

Therefore, from equilibrium equation c = 92.4 mm

–1

( ε c ⁄ ε c′ ) – tan ( ε c ⁄ ε c′ ) - = 0.75 β 1 = 2 – 4 ⋅ -----------------------------------------------------------2 2 ( ε c ⁄ ε c′ )ln ( 1 + ε c ⁄ ε ′c )

Finally, the nominal flexural capacity of the section with FRP external reinforcement can be computed from the following equation

b = 810 mm

648

A s′ = 1.29 × 4 = 516 mm2

β 1 c β 1 c - + A f f fe h – ------M n = A p f ps  d p – ------  2  2 

c – d′ ε′s = ( ε fe + ε bi )  ------------- = 0.00064  h – c

β1 c - – d′ = 1198 kN⋅m + A′s f s′  ------ 2 

ACI Structural Journal/September-October 2005