CRACKING BEHAVIOR AND CRACK WIDTH … with FRP/09... · CRACKING BEHAVIOR AND CRACK WIDTH...

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Page 1 of 8 CRACKING BEHAVIOR AND CRACK WIDTH PREDICTIONS OF CONCRETE BEAMS PRESTRESSED WITH BONDED FRP TENDONS Weichen XUE Professor Tongji University Siping Road 1239#, Shanghai 200092, China [email protected]* Yuan TAN PhD Candidate Tongji University Siping Road 1239#, Shanghai 200092, China [email protected] Abstract A total of six specimens were tested under four-point loading to examine the cracking behavior of prestressed concrete beams with a combination of bonded CFRP tendons and steel/GFRP reinforcements. The investigated parameters included the partial prestressing ratio (PPR), amount of prestressed CFRP tendons, types of nonprestressed reinforcements, and jacking stress levels. The characteristics of cracking propagation, cracking spacing and crack widths of specimens were presented. Test results indicated that the prestressed concrete beam reinforced with nonprestressed GFRP rebars exhibited wider crack width and larger crack spacing than those reinforced with nonprestressed steel rebars. Based on the correlative principles recommended by ACI 224R-01, a formula modified from the Frosh equation was provided for calculating the maximum crack width of concrete beams with a combination of bonded FRP tendons and steel/FRP reinforcements. Keywords: bond CFRP tendon, concrete beam, crack behavior, crack width 1. Introduction Fiber-reinforced polymer (FRP) composites have been proposed for use as prestressing tendons in concrete structures due to their high-strength, lightweight and noncorrosive properties since 1970s [1] . Currently, remarkable progress has been made in field applications of FRP tendons in North America, Europe, Japan, China and several other countries [2] . FRP tendons and concrete are both brittle materials, so the classical ductility which requires plastic deformation is difficult to obtain in FRP prestressed concrete members. One possible technique to improve the ductile behavior of FRP prestressed concrete members is by partially prestressing the concrete beams with addition of nonprestressed reinforcements [3] . Herein, the nonprestressed reinforcements could be selected as the (anticorrosive) steel rebars with obvious yield plateaus or the GFRP rebars with relatively high strain capacity. Experimental work showed that the nonprestressed reinforcements could enhance the ductility and reduce the crack spacing and crack width of FRP prestressed beams [4] .

Transcript of CRACKING BEHAVIOR AND CRACK WIDTH … with FRP/09... · CRACKING BEHAVIOR AND CRACK WIDTH...

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CRACKING BEHAVIOR AND CRACK WIDTH PREDICTIONS OFCONCRETE BEAMS PRESTRESSED WITH BONDED

FRP TENDONS

Weichen XUEProfessorTongji UniversitySiping Road 1239#, Shanghai 200092, [email protected]*

Yuan TANPhD CandidateTongji UniversitySiping Road 1239#, Shanghai 200092, [email protected]

Abstract

A total of six specimens were tested under four-point loading to examine the crackingbehavior of prestressed concrete beams with a combination of bonded CFRP tendons andsteel/GFRP reinforcements. The investigated parameters included the partial prestressing ratio(PPR), amount of prestressed CFRP tendons, types of nonprestressed reinforcements, andjacking stress levels. The characteristics of cracking propagation, cracking spacing and crackwidths of specimens were presented. Test results indicated that the prestressed concrete beamreinforced with nonprestressed GFRP rebars exhibited wider crack width and larger crackspacing than those reinforced with nonprestressed steel rebars. Based on the correlativeprinciples recommended by ACI 224R-01, a formula modified from the Frosh equation wasprovided for calculating the maximum crack width of concrete beams with a combination ofbonded FRP tendons and steel/FRP reinforcements.

Keywords: bond CFRP tendon, concrete beam, crack behavior, crack width

1. Introduction

Fiber-reinforced polymer (FRP) composites have been proposed for use as prestressingtendons in concrete structures due to their high-strength, lightweight and noncorrosiveproperties since 1970s[1]. Currently, remarkable progress has been made in field applicationsof FRP tendons in North America, Europe, Japan, China and several other countries[2].

FRP tendons and concrete are both brittle materials, so the classical ductility which requiresplastic deformation is difficult to obtain in FRP prestressed concrete members. One possibletechnique to improve the ductile behavior of FRP prestressed concrete members is by partiallyprestressing the concrete beams with addition of nonprestressed reinforcements[3]. Herein, thenonprestressed reinforcements could be selected as the (anticorrosive) steel rebars withobvious yield plateaus or the GFRP rebars with relatively high strain capacity. Experimentalwork showed that the nonprestressed reinforcements could enhance the ductility and reducethe crack spacing and crack width of FRP prestressed beams[4].

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Extensive research work on concrete beams prestressed with bonded FRP tendons have beencarried out by researchers all over the world[2], in which some experimental programs wereconducted to examine the cracking behavior of FRP prestressed concrete beams. Abdelrahmanand Rizkalla studied the serviceability of concrete beams prestressed with CarbonFiber-reinforced polymer (CFRP) tendons or conventional steel strands (withoutnonprestressed reinforcements)[5]. Test results showed that the stabilized crack pattern forbeams prestressed with CFRP tendons occurred at a much lower strain level than for beamsprestressed with steel strands. The number of cracks of beams prestressed with CFRP was lessthan that of comparable beams prestressed with steel strands due to the lower flexural bondstrength of the CFRP tendons. Consequently, the crack width and spacing were typicallylarger for a given load level. Meng et al. compared the cracking patterns and crack widths ofconcrete beams with a combination of bonded CFRP tendons and steel/FRP reinforcements[3].It was concluded that the remarkable reduce of crack width could be found in the concretebeams with combined reinforcements. The crack widths in the prestressed concrete beamsreinforced with FRP reinforcements were larger than the corresponding values in prestressedconcrete beams reinforced with steel reinforcements for a given load level.

The ACI 440 Committee developed equations for calculating the crack widths in concretebeams reinforced with FRP bars[6], while limited studies focused on the crack widthpredictions of concrete beams with a combination of bonded CFRP tendons and steel/FRPreinforcements. This paper presents the experimental program to investigate the crackingbehavior of concrete beams with combined reinforcements. In addition, a modified formulawas provided for predicting the maximum crack width of concrete beams with a combinationof bonded FRP tendons and steel/FRP reinforcements.

2. Experimental work

2.1 Test Specimens

A total of six concrete beams (denoted as PB1 to PB6, correspondingly) were cast and tested.Each beam had a cross section of 150×300 mm and a span of 3700 mm. The mainexperimental parameters included partial prestressing ratio (PPR), amount of prestressingCFRP strands, types of nonprestressed reinforcements, and jacking stress levels. Details of thespecimens are given in Table 1 and Figure 1.

Table 1. Details of specimens

Specimens PB1 PB2 PB3 PB4 PB5 PB6

Tendons 1M12.5CFRP 1M12.5CFRP 1M12.5CFRP 1M12.5CFRP 2M12.5CFRP 2M12.5CFRP

Jacking stresses 0.55fu 0.55 fu 0.55 fu 0.65 fu 0.55 fu 0.55 fu

PPR 0.74 0.52 0.34 0.52 0.54 0.73Initial prestress

level 50.0% 50.2% 50.0% 59.2% 49.7% 49.9%

Bottom longitudinalreinforcements

(Ab)

2M10(Steel bars)

2M16

(Steel bars)

2M19

(GFRP bars)

2M16

(Steel bars)

2M22

(Steel bars)

2M14

(Steel bars)

Top longitudinalreinforcements

(At)2M8 (Steel bars)

Note: fu represents the ultimate tensile strength of CFRP tendons.

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1

1

250

11003700

1300 1300

8@100 8@1008@200

Configuration of reinforcing bars

102

80635042

350300300300300300

42 40

300

Arrangement of tendons50638010

2

250

300300300350 3003700

At

Ab Ap

135

150

250

28

210(B1)

219(B3)

Section 1-1

216( B2, B4)

112.5CFRP

150

250

28

222( B5)214(B6)

212.5CFRP

Figure 1. Reinforcing details of specimens (mm)

The measured compressive strength of the concrete cubes was 57.7 MPa at the time of testing.The average elastic modulus of concrete was 33.7 GPa, and the average tensile strength was4.5 MPa. Mechanical properties for reinforcements are listed in Table 2. Note that the highstrength CFRP strands used in this experimental program are carbon fiber composite cables(CFCC) produced by Tokyo Rope Mfg. Co. Ltd, Japan with measured ultimate strength of2400 MPa and guaranteed tensile strength of 1868 MPa. The high strength CFRP strands aremade up of seven wires that are twisted to allow better stress distribution through the crosssection. The GFRP bars used in the tests were provided by Aslan company.

Table 2. Mechanical properties of reinforcements

Mechanical propertiesConventional steel reinforcements FRP bars/tendons

M8 M10 M14 M16 M22 M19GFRP M12.5CFRP

Yielding strength fy(MPa) 418.0 318.0 341.0 321.0 324.5

Ultimate strengthfu(MPa)

541.0 471.0 513.0 498.0 481.0 698.5 2400

Modulus of elasticityEs(MPa)

1.81×105 1.68×105 1.81×105 1.71×105 1.82×105 4.15×104 1.43×105

Elongation ratio 24.5% 20.0% 23.0 % 20.0% 23.0% 6.0% 1.5%

2.2 Testing and Measurements

All beams were tested under four-point loading. A schematic and a view of the testing setupare shown in Figure 2. The load was applied at mid-span by a hydraulic actuator actingagainst a reaction frame. All beams were initially loaded in increments of 1 kN and thenreduced to increments of 0.5 kN as failure approached.

A displacement transducer located on each beam at mid-span was used to monitor thedeflection. Two displacement transducers (one at each supporting end of the beam) were usedto measure the vertical displacements. Fourteen strain gauges (five on each side, two on thetop, and two on the bottom of the beams) were used to measure the bending strainsthroughout the vertical sections of mid-span. Four strain gauges on the bottomnonprestressing bars and four on the CFRP strands were used to measure the longitudinalstrains. The strains and deformation readings captured and monitored using an automatic dataacquisition system, namely, process board type IMP 35951B SOLARTRON INSTRUMENTSLtd., U.K..

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3700

P P

100 1200 1100 1200 100

Figure 2. Loading of specimens

2.3 Test results

All specimens exhibited elastic characteristics before initial cracking of concrete. Withincrease of the vertical loads, short and fine flexural cracks initiated at constant momentregions. For all the specimens, initial cracking could be observed as the applied load increasedup to about 0.22 to 0.30Pu (Pu was the ultimate loads of specimens). Increase in the crackingloads of approximately 50% occurred in beams prestressed with two CFRP tendons. As thevertical loads continued increased, the existing fine vertical cracks extended longer and widerand meanwhile a few new cracks could be observed at constant moment regions as well asbending shear regions. As the nonprestressing steel bars yielded (except PB3), whichcorresponded to a load level of 0.58 to 0.90Pu, the measured maximum crack width was in therange of 0.20 to 0.30 mm and the maximum crack spacing ranged between 90 and 120 mm.Figure 3 shows the development of maximum crack width of specimens under the loading.

0

20

40

60

80

0 0.1 0.2 0.3 0.4 0.5w /mm

P/kN

PB1

PB2

PB3

PB4

PB5

PB6

Figure 3. Load versus maximum crack width of specimens

After yielding of nonprestressing steel bars (except PB3), deflections of mid-span and strainsof CFRP tendons increased dramatically with little vertical load gain. When reaching the peakloads, a sudden drop could be seen in the load versus deflection curves of PB1 and PB4 due tothe rupture of CFRP tendons, which indicated that the specimens failed in tension. However,obvious descending stages were observed in the load versus deflection curves of PB2, PB5

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and PB6 and the specimens failed in compression. Cracks continued to propagate upwards,and the crack width increased quickly for all specimens. In contrast, due to the linear elasticstress-strain relationship of GFRP bars, PB3 exhibited marked differences in the loadingprocess. No obvious yielding stage could be observed after cracking and it behaved linearlywith reduced stiffness till crushing of top concrete, which resulted in the failure of thespecimen. Moreover, once the cracks appeared, they extended quickly in both width andheight. Eventually, the values of crack width and spacing in PB3 were found to besignificantly larger than the corresponding values in other specimens. A comparison of themeasured load versus mid-span deflection curves of the six specimens is given in Figure 4.

0

20

40

60

80

-20 0 20 40 60 80 100 120Δ/mm

P/kN

PB1PB2PB3PB4PB5PB6

Figure 4. Load versus deflection curves of specimens

The load versus strain curves of CFRP strands are given in Figure 5. Seen from the figure, thetendons in the five specimens reinforced with steel bars behaved in a similar manner that twoobvious points, which corresponded to first concrete cracking and yielding of steelreinforcements, respectively, were found during testing. In contrast, only one pointcorresponding to first concrete cracking was observed in specimen PB3 reinforced with GFRPbars. The reason was that GFRP bars behaved linearly elastic up to failure and had no yieldpoint under tension. At ultimate, the tendon strain increments of the six specimens (PB1 toPB6) were 8242, 6003, 6014, 6099, 4509 and 5381 , respectively. The ultimate tensilestrains for both beams PB1 and PB4 were much higher than the others and reached the valueof 14000 , which was close to the nominal ultimate tensile strains of CFRP strands. Theultimate tensile strains of the remaining four specimens ranged between 10509 and 12609. This was consistent with the conclusion that PB1 and PB4 failed due to rupture of CFRPtendon prior to concrete crushing.

0

20

40

60

80

0 3000 6000 9000 12000 15000

Strain developed in CFRP/με

P/kN

PB1

PB2

PB3

PB4

PB5

PB6

Figure 5. Load versus strain curves of CFRP strands

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3. Crack Width Predictions

The ACI 440 Committee recommended the Frosch equation for calculating the crack width ofconcrete beams reinforced with FRP bars[6]. The Frosch equation was derived based on aphysical model, rather than being empirically derived[7]. With considering the different bondbehavior of FRP reinforcements compared with steel reinforcements, a corrective coefficientfor the bond quality was introduced by ACI 440.1R-06. For predicting the maximum side facecracks in concrete beams reinforced with FRP bars, the equation is given as follows:

2 22 fb c s

f

fw k d d

E (1)

where w is the maximum crack width (mm); ff is the reinforcing stress (MPa); fE is thereinforcement modulus of elasticity (MPa); is the ratio of distances to neutral axis fromextreme tension fiber and from centroid of FRP reinforcements; dc is the bottom covermeasured from center of lowest bar (mm); and ds is the side cover measured from center ofoutmost bar (mm). The bk term is a coefficient that accounts for the degree of bond betweenFRP bar and surrounding concrete. For FRP bars having bond behavior similar to uncoatedsteel bars, the bond coefficient bk is assumed equal to 1.

According to ACI 224R-01[8], the expressions given for crack prediction in nonprestressedbeams can be used to estimate the cracks for prestressed beams with considering the loadincrease above the decompression moment, i.e. prestressed member could be treated as areinforced concrete member and the stress increments in reinforcements were applied in thecalculation. For the concrete beams with a combination of FRP tendons and steel/FRP rebars,the flexural cracking was mainly controlled by the outmost layer of nonprestressedreinforcements. So the maximum crack width of concrete beams with combinedreinforcements can be predicted by:

2 22 npb c s

np

fw k d d

E

(2)

where npf is the magnitude of the tensile stress in the outmost layer of nonprestressedreinforcement in which the decompression load is taken as the reference point (MPa); npE isthe modulus of elasticity of the outmost layer of nonprestressed reinforcement (MPa); bk isthe bond coefficient corresponding to the outmost layer of nonprestressed reinforcement.When a specific value of bk is not known for FRP reinforcing bar with sand coating, indents,sand-blasted surface and molded ribs to enhance bond with concrete, it is recommended touse a conservative value of 1.4[6]. The value of bk could be taken as 1.5 for the epoxy coatedsteel bars based on the bond behavior tests[4].

The flexural crack width experiments of concrete beams with a combination of FRP tendonsand steel/FRP reinforcements are summarized in Table 3. The maximum crack widths ofspecimens were predicted by Eq. (2), and comparisons of the measured and calculatedmaximum crack widths are illustrated in Figure 5.

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Table 3. Summary of flexural crack width experiments

ReferencesNo.

SpecimensFRP

tendonNonprestressedreinforcement

Beamwidth(mm)

Beamdepth(mm)

Beamspan(mm)

PPRInitial

prestresslevel

Experimental

work in this

paper

PB1 CFRP uncoated steel 150 250 3500 0.74 50.1%

PB2 CFRP uncoated steel 150 250 3500 0.52 50.2%

PB3 CFRP GFRP bars 150 250 3500 0.34 50.0%

PB4 CFRP uncoated steel 150 250 3500 0.52 59.2%

PB5 CFRP uncoated steel 150 250 3500 0.54 49.7%

PB6 CFRP uncoated steel 150 250 3500 0.73 49.9%

Ref. [4]

BAS1-210 AFRP epoxy coated steel 150 280 3800 0.40 45.4%

BAS2-210A AFRP epoxy coated steel 150 280 3800 0.57 44.8%

BAS2-210B AFRP epoxy coated steel 150 280 3800 0.57 44.9%

BAS2-214 AFRP epoxy coated steel 150 280 3800 0.46 45.1%

BAS3-210A AFRP epoxy coated steel 150 280 3800 0.66 42.6%

BAS3-210B AFRP epoxy coated steel 150 280 3800 0.66 42.9%

BAS3-314 AFRP epoxy coated steel 150 280 3800 0.46 43.2%

BAS4-206 AFRP epoxy coated steel 150 280 3800 0.92 45.1%

BAS4-210 AFRP epoxy coated steel 150 280 3800 0.72 45.3%

BAS4-214 AFRP epoxy coated steel 150 280 3800 0.63 44.9%

Ref. [3]

B1 CFRP uncoated steel 148 307 2472 0.60 33.1%

B2 CFRP CFRP bars 150 305 2472 0.33 19.9%

B9 CFRP uncoated steel 149 300 2472 0.70 12.4%

B10 CFRP CFRP bars 149 306 2472 0.44 42.0%

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6Measured maximum crack widths (mm)

Cal

cula

ted

max

imum

cra

ck w

idth

s (m

m)

Ref.[4]

Ref.[3]

This paper

Perfect Correlation

Figure5. Comparisons of the measured and calculated maximum crack widths

As can be seen from Fig. 5, Eq. (2) provides good predictions for the maximum crack widthof concrete beams with combined reinforcements, and the mean errors are within 10%. Itshould be noted that the theoretical formula should be further verified due to a lack ofavailable test data.

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4. Conclusions

(1) Test results showed that remarkable reduce of crack width could be found in the concretebeams with combined reinforcements. The crack widths in the prestressed concrete beamsreinforced with FRP reinforcements were larger than the corresponding values in prestressedconcrete beams reinforced with steel reinforcements for a given load level.

(2) Based on Frosh crack width equation, a modified formula was provided for calculating themaximum crack width of concrete beams with a combination of bonded FRP tendons andsteel/FRP reinforcements.

Acknowledgements

The authors acknowledge the supports of Fund of Western Communications ConstructionScientific and Technological Project by the Ministry of Communications of the P.R. China(No.200631882244) and the Fund of National Natural Science Foundation of China (No.50978193).

References[1] REHM, G., FRANKE, L., “Plastic Bonded Fiberglass Rods as Reinforcement for

Concrete,” Bautechnik, Ausgabe A, Vol. 51, No. 4, Apr. 1974, pp.115-120.

[2] ACI COMMITTEE 440, “Prestressing Concrete Structures with FRP Tendons (440.4R-04),” American Concrete Institute, Farmington Hills, Mich., 2004, 35 pp.

[3] MENG, Y., GU, X. L., ANSARI, F., “Calculation Method for the Bending Capacity ofConcrete Beam Reinforced by CFRP Bars,” Proceedings of the International Conferenceon FRP Composites in Civil Engineering, Vol. Ⅱ, CICE, Hong Kong, China, 2001, pp.1161-1168.

[4] MENG, L. X., TAO, X. K., GUAN, J. G., XU, F. Q., “Experimental Study on FlexuralBehavior of Partially Prestressed Concrete Beams with Bonded AFRP Tendons,” ChinaCivil Engineering Journal, Vol. 39, No. 3, Mar. 2006, pp.10-18, 36. (in Chinese)

[5] ABDELRAHMAN, A., RIZKALLA, S., “Serviceability of Concrete Beams Prestressedby Carbon Fiber-reinforced-plastic Bars,” ACI Structural Journal, Vol. 94, No. 4,Jul.-Aug. 1997, pp. 447-457.

[6] ACI COMMITTEE 440, “Guide for the Design and Construction of Structural ConcreteReinforced with FRP Bars (ACI 440.1R-06),” American Concrete Institute, FarmingtonHills, Mich., 2004, 44 pp.

[7] FROSCH, R. J., “Another Look at Cracking and Crack Control in Reinforced Concrete,”ACI Structural Journal, Vol. 96, No. 3, May-June 1999, pp. 437-42.

[8] ACI COMMITTEE 224, “Control of Cracking in Concrete Structures (ACI 224R-01),”American Concrete Institute, Farmington Hills, Mich., 2001, 46 pp.