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Time-dependent deformations of concrete beams reinforced with CFRP bars
Composites: Part B 31 (2000) 577±592
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Time-dependent deformations of concrete beams reinforced with CFRP bars M. Arockiasamy a,*, S. Chidambaram a,b, A. Amer a, M. Shahawy c a
Center for Infrastructure and Constructed Facilities, Department of Ocean Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA b Petro-Marine Engineering of Texas, Inc., Houston, TX 77077, USA c Structural Research Center, Florida Department of Transportation, Tallahassee, FL 32310, USA
Abstract Carbon FRP is recently used as a reinforcing element in concrete structures in view of its excellent resistance to corrosion. The paper presents studies of the long-term behavior of the beams reinforced with carbon±epoxy FRP under uniform sustained loading. Four rectangular concrete beams reinforced with CFRP bars were cast in two sizes; 152 mm £ 203 mm £ 2438 mm; and 152 mm £ 152 mm £ 2438 mm: The beams were simply supported and subjected to a uniform sustained loading. The beams were instrumented and monitored to observe the changes in the behavior due to creep and shrinkage of concrete. Observations were recorded regularly for nearly two years. An analytical method is developed to predict the long-term behavior of CFRP internally reinforced concrete beams. The calculated de¯ections, strains and curvatures compare reasonably with the experimental values. A simpli®ed equation for calculating the long-term de¯ection is proposed for CFRP reinforced concrete beams. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: B. Creep; Age-adjusted section
1. Introduction Reinforcing steel in concrete structures is susceptible to corrosion that severely affects the serviceability and the safety of the structure. The extent of the steel corrosion and the resulting concrete degradation depend on the environment and the type of the structure. The corrosion effect is more pronounced in harsh marine environments and for structures exposed to deicing agent. Millions of dollars are spent every year for the repair and rehabilitation of the structures. The need is, therefore, very great for a new material such as ®ber reinforced polymer (FRP) composites, which would offer excellent resistance to corrosion. The commercially available FRPs include aramid (AFRP), carbon (CFRP) and glass (GFRP) matrix. Of all the FRPs, carbon composites exhibits a higher tensile strength, higher Young's modulus and lower ductility. The other merits of carbon FRP are derived from its (i) lightweight, (ii) nonmagnetic characteristics, and (iii) relatively low relaxation. Durability tests [1,2] have been conducted on CFRP tendons exposed to seawater, alkali and atmospheric conditions for different time duration. The test results showed that there is no signi®cant strength reduction of CFRP tendons. It is * Corresponding author. Tel.: 11-561-297-3434; fax: 11-561-297-3885. E-mail address: [email protected] (M. Arockiasamy).
noted that the failure time of the CFRP due to creep rupture is high for a given specimen when compared to the GFRP and AFRP at any given stress level [4]. Only very limited information on long-term studies have been published on CFRP reinforced concrete members under sustained loading. Bazant, [3,5] reported that the concrete creep and shrinkage cause excessive de¯ection and cracking, which severely affects the serviceability and strength of the structure. Deformations due to creep and shrinkage are usually several times larger than instantaneous deformation in concrete structures. In the case of prestressed concrete members, the loss of the prestress occurs due to creep and shrinkage. This paper presents the study on the long-term behavior of beams reinforced with CFRP under sustained uniform loads. 2. Research signi®cance The application of carbon FRP as reinforcing element is ideally suited for use in bridge decks and girders exposed to deicing salts in colder regions, and columns and piles in harsh marine environment. The objective of the current research is to study the long-term behavior of the beams reinforced with carbon FRP under sustained loading. The prediction of the CFRP reinforced beam deformations will aid in the design of structural elements in ¯exure.
1359-8368/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S 1359-836 8(99)00045-1
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Nomenclature A0 Ac Ec E 0c t; t0 I I0 Ic L M Mapplied Mcracked m n 0 t; t0 rc2 t0 x y yc Di DL D 10 Dc D c1 D c2 10 1 t0 1cs t; t0 1cs t; t 0 1cs u fu f t; t0 h k l r0 c c t c t0 c1 c2 z1
area of the age-adjusted transformed section area of concrete in compression modulus of elasticity of concrete at the time of application of the load age-adjusted modulus of elasticity of concrete moment of inertia of the transformed section moment of inertia of age-adjusted transformed section moment of inertia of concrete about the centroid after age adjustment the length of the beam bending moment applied bending moment cracking moment modular ratio of the reinforcement ECFRP =ESteel age adjusted modular ratio Ic/Ac time of loading time-dependent factor distance to the depth from the centroid of the transformed section distance between centroids of the effective concrete area and the age adjusted transformed area instantaneous de¯ection at the midspan total de¯ection at time t at the midspan time-dependent change in strain at the centroid of the section time-dependent change in curvature due to creep and shrinkage the change in curvature of the uncracked section the change in curvature of the cracked section instantaneous strain at the centroid of the transformed section strain at any depth shrinkage strain from time t0 to t free shrinkage which occurs between t 0 at the end of curing period and any time t ultimate shrinkage strain at in®nite time ultimate creep coef®cient creep coef®cient from time t0 to t axial strain reduction factor curvature reduction factor a modi®ed factor compression reinforcement ratio of CFRP bars instantaneous curvature of bending mean curvature at time t mean curvature at time of loading the instantaneous curvature for an uncracked section the instantaneous curvature for a cracked section the coef®cient for instantaneous curvature
3. Experimental program 3.1. Specimen fabrication Four rectangular concrete beams reinforced with CFRP bars were cast in two sets. The ®rst set of beams (B1 and B2) and the second set of beams (B3 and B4) were of size 152 mm £ 203 mm £ 2438 mm 6 in: £ 8 in: £ 8 ft and 152 mm £ 152 mm £ 2438 mm 6 in: £ 8 in: £ 8 ft:, respec-
tively. Each beam is reinforced with two 7.5 mm diameter longitudinal CFRP bars and two 7.5 mm diameter hanger CFRP bars (Figs. 1 and 2). The spacing of the #3 steel stirrups is 76.2 mm (3 in.) at both ends and the spacing gradually increases to 152 mm (6 in.) at the mid span. Concrete blocks of sizes 305 mm £ 305 mm £ 610 mm 1 ft £ 1 ft £ 2 ft and 305 mm £ 152 mm £ 610 mm 1 ft £ 6 in: £ 2 ft were cast at the same time, which were used to simulate the sustained distributed loads.
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579
Fig. 1. Reinforcement details of the beams.
3.2. Material properties Concrete: The concrete properties for the two set of beams are shown in Table 1. Carbon FRP: Materials used for manufacturing carbon FRP are carbon ®ber of the PAN base system and matrix resins. The properties of carbon ®ber, matrix resin and carbon FRP are presented Table 2.
4. Test setup and instrumentation The ¯exural strains at midspan are measured using ®ve and three electrical surface strain gages for beams in set I and set II, respectively. The surface strain gages are protected from moisture intrusion by epoxy coating. For all the beams, embedded strain gages are also attached along the CFRP bars. Both surface and embedded strain gages are monitored by the strain indicator (beams B1 and B2)/data acquisition system 4000 (beams B3 and B4). The de¯ections at the midspan of the beams are recorded using de¯ectometer. After the beams were cured, the beams were set up over the simple supports and subjected to sustained distributed loads (Fig. 3). The distributed loads were simulated by using concrete blocks. The details of the loading are shown in Fig. 4. Beam B1 is subjected to 77% of the ®rst cracking moment. Beams B2, B3 and B4 are subjected to 123, 110 and 123% of their respec-
tive cracking moments. The effect of cracks is evaluated in the study of the long-term behavior of CFRP reinforced concrete beams. For the ®rst three weeks, the strains and the de¯ections at the midspan of the beams were recorded twice a day and thereafter, once a day for a three month period. As the recorded data indicated a steady trend, the time interval between successive observations was increased to one week. Beams B1 and B2 were subjected to the sustained load for about 20 months, whereas beams B3 and B4 for 15 months. It was noticed that new cracks developed during the ®rst couple of weeks in the precracked beams B2, B3, and B4.
Table 1 Properties of concrete Items
Beam set I
Beam set II
Cement: sand: aggregate (by weight) Cylinder compressive strength after 28 days f 0c Modulus of elasticity of concrete (Ec)
1:1.88:2.68
1:1.31:2.14
32.11 MPa (4657 psi)
42.75 MPa (6200 psi)
26.80 GPa (3887 ksi)
30.92 GPa (4484 ksi)
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Table 2 Properties of the carbon FRP bars Item
Property
Carbon ®ber
Tensile strength Tensile modulus Elongation at break Type of resin Tensile strength Elongation at break Diameter of the rod Effective cross sectional area Modulus of elasticity
Matrix resin Carbon FRP reinforcement
211 MPa 137 GPa 1.5% Denaturated epoxy resin 51.5 MPa 4.2% 7.5 mm 30.4 mm 2 137.34 GPa
5. Experimental results 5.1. Loading The concrete blocks were added one at a time to the beams B1, B2, B3 and B4 over the course of approximately three hours. The de¯ection measurements were made at the completion of this loading t 0. 5.2. De¯ections Fig. 5 shows the long-term de¯ections at the midspan for the beams B1, B2, B3 and B4. The long-term de¯ections are obtained by subtracting the instantaneous de¯ection from the total de¯ection. It shows that the de¯ection at the midspan increases with the time. The beams B1, B2, B3 and B4 are loaded to 77, 120, 110 and 123% of their cracking moment, respectively. The load intensity in beam B3 is smaller than that in beam B4 and hence beam B3 exhibits smaller long-term de¯ections than those of beam B4. Beam B1 remained uncracked and exhibited a very small increase in long term de¯ection. The increase in de¯ections over the instantaneous values for a period of 470 days is 15, 115, 65 and 71% for beams B1, B2, B3 and B4, respectively. Beams B1 and B2 showed an increase in de¯ection of 28 and 125% after a period of 610 days. 5.3. Concrete strains Fig. 6 shows the total time-dependent compressive strains observed at the top concrete surface for beams B1, B2, B3 and B4. Beam B1 was uncracked and subjected to a load intensity less than beam B2 and hence it exhibits a small compressive strain. The compressive strain at the top surface of the beam B4 is only marginally higher than that in beam B3, since the load intensity in beam B4 is more than that in beam B3. The increase in the strains over the instantaneous values for a period of 470 days is 101, 151, 209 and 245% for beams B1, B2, B3 and B4, respectively. 5.4. Curvature Fig. 2. Reinforcement in position before concrete pour.
Fig. 7 shows the variation of the curvature observed at the midspan of the beams B1, B2, B3 and B4. The beam B2
M. Arockiasamy et al. / Composites: Part B 31 (2000) 577±592
Fig. 3. Test setup for beams B1 and B2.
Fig. 4. Details of distributed sustained loading of the beams.
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Fig. 5. Variation of long-term de¯ection with time.
with a larger depth than B3 and B4 shows a smaller curvature. The load intensity on beam B3 is smaller than that in beam B4 and hence it exhibits curvatures smaller than those of B4.
the time-dependent curvature, strains and de¯ections induced by creep and shrinkage are calculated based on the age-adjusted elastic modulus method [6]. 6.1. Instantaneous deformation
6. Theoretical prediction of the long-term deformation of the CFRP reinforced concrete beams The total deformation at any time is the sum of the instantaneous and time-dependent deformations. The instantaneous curvature, strains and de¯ections due to lateral loads can be determined from the elastic analysis whereas,
The instantaneous curvature of bending is given by c
M Ec I
1
where I is the moment of inertia of the transformed section, M the bending moment and Ec the modulus of elasticity of concrete at the time of application of the load.
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Fig. 6. Strain observed at the top surface of the beams.
The strain at any depth is given by
Mean curvature at time of loading, t0 is given by c t0 1 2 z1 c1 1 z1 c2
2
where c1 is the instantaneous curvature for an uncracked section; c2, instantaneous curvature for a cracked section; z 1 coef®cient for instantaneous curvature 8 !2 > > < 1 2 Mcracked for a cracked section Mapplied : z1 > > : 0 for an uncracked section Instantaneous de¯ection is calculated by assuming parabolic variation of curvature, with zero de¯ection at the ends and maximum at the center and the midspan de¯ection is given by,
Di
c t0 ´L 9:6
2
where L is the length of the beam
3
1 t0 10 1 yc t0
4
where 1 0 is the instantaneous strain at the centroid of the transformed section and y, the distance to the depth from the centroid of the transformed section (point O in Fig. 8(a)). Fig. 8(b) shows the instantaneous strain distribution due to loading at age t0, whereas the change in strain distribution for the period t 2 t0 and the total strain variation at time t are shown in Fig. 8(c) and (d), respectively. 6.2. Total deformations including time-dependent effects Mean curvature at time t is given by c t 1 2 z2 c1 1 Dc1 1 z2 c2 1 Dc2
5
where Dc1 is the change in curvature of the uncracked
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Fig. 7. Variation of curvature with time.
section; Dc2, change in curvature of the cracked section; z 2, coef®cient for long-term curvature
The total de¯ection at the midspan at time t is given by
8 !2 > > < 1 2 0:5 Mcracked Mapplied z2 > > : 0
DL for a cracked section for an uncracked section
:
c tL2 9:6
6
The time-dependent change in strain at the centroid of the section and the time-dependent change in curvature due to
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585
Fig. 8. Strain distribution at a cross-section.
creep and shrinkage are given by, D10 hf t; t0 10 1 cyc 1 1cs t; t0
7
y Y Dc k f t; t0 c 1 10 2c 1 1cs t; t0 2c rc rc
8
where rc2
Ic Ac
h
Ac A0
k
Ic I0
where f t; t0 is the creep coef®cient from time t0 to t; 1cs t; t0 ; the shrinkage strain from time t0 to t; yc, the distance between centroids of the effective concrete area and the age-adjusted transformed area; Ac, the area of concrete in compression; A 0 , the area of the age adjusted transformed section; Ic, the moment of inertia of concrete about the centroid after age adjustment; I 0 , the moment of inertia of age adjusted transformed section using modular ratio n 0 t; t0 in which, n 0 t; t0
Fig. 9. Flowchart for calculation of deformations of CFRP reinforced concrete beams.
ECFRP E 0c t; t0
where E 0c t; t0 is the age-adjusted modulus of elasticity of concrete. The strain at any depth in the transformed section at time t is computed as the algebraic sum of the instantaneous strain and change in strain from time t0 to t due to creep and shrinkage at the ®ber under consideration (Fig. 8(d)). In the present study, the creep and shrinkage coef®cients are ®rst calculated based on ACI
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Fig. 10. (a) Comparison of experimental and predicted de¯ections for beam B3; (b) Comparison of experimental and predicted de¯ections for beam B4.
committee 209 and CEB 1990 approaches. Based on the experimental results, an equation is proposed for the creep coef®cient. 6.3. Creep and shrinkage coef®cients 6.3.1. ACI committee 209 approach Based on the extensive research work of Branson et al.,
the ACI committee 209 [7] recommended the following expressions for creep and shrinkage of concrete:
f t; t0 1cs t; t 0
t 2 t0 0:6 fu 10 1 t 2 t0 0:6 t 2 t0 1 35 1 t 2 t 0 cs u
M. Arockiasamy et al. / Composites: Part B 31 (2000) 577±592
587
Fig. 10. (continued)
where f t; t0 is the creep coef®cient at time t for age at loading t0; 1cs t; t 0 ; the free shrinkage which occurs between t 0 at the end of curing period and any time t; f u, ultimate creep coef®cient; and (1 cs)u, ultimate shrinkage strain at in®nite time. Coef®cients f u and (1 cs)u depend on atmospheric humidity, the member size, slump of concrete, cement content, ®ne aggregate percent, air content in percent and type of curing.
6.3.2. CEB-FIP approach The creep coef®cient according to CEB-FIP [8] is given by
f t; t0 fRH b fcm b tc bc t 2 t0 where the factors f RH, b fcm ; b t0 ; bc t 2 t0 take into account the corrections for the atmospheric humidity, mean compressive strength of the concrete, time of loading and duration of loading, respectively.
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Fig. 11. (a) Comparison of experimental and predicted top surface strains for beam B3. (b) Comparison of experimental and predicted top surface strains for beam B4.
The strain due to shrinkage or swelling according to CEB-FIP is given by,
model takes into consideration both reversible and irreversible creep.
1cs 1cs0 bs t 2 t where 1 cs0 is a function of mean compressive strength of concrete, type of cement and relative humidity, bs t 2 t 0 is a function of duration of loading. This
7. Evaluation of results and discussions A user-friendly C program was written to calculate the beam curvature, de¯ections and strains based on the
M. Arockiasamy et al. / Composites: Part B 31 (2000) 577±592
589
Fig. 11. (continued)
theoretical approach. A ¯owchart of the program is shown in Fig. 9. The test setup is arranged in an openair facility in tropical weather conditions to simulate the actual ®eld conditions. The predicted deformations take into account the change in the relative humidity of the atmosphere, CFRP material characteristics, member size, concrete strength, sustained load intensity and
duration of loading. Comprehensive comparisons of the measured curvatures, strains and de¯ections against the theoretical predictions are presented in Ref. [9]. The main parameters in the comparison are the maximum and minimum daily relative humidities. The minimum and maximum relative humidities were used in the theoretical prediction. Typical comparisons of the
590
M. Arockiasamy et al. / Composites: Part B 31 (2000) 577±592
Fig. 12. Comparison of beams reinforced with aramid, glass and steel with CFRP.
measured and theoretical deformations are presented in this paper. The experimental de¯ections at the midspan are compared with the analytical predictions based on the ACI and CEB coef®cients. Deformations based on ACI creep coef®cient and shrinkage strain compared closely with those computed using CEB coef®cient. Therefore, only the results based on the ACI creep coef®cient are presented in this paper. Typical comparison of experimental de¯ections for beams B3 and B4 with the theoretical predictions are presented in Fig. 10. It can be seen that the experimental results are in reasonable agreement with the predicted values. The experimental strains across the cross-section at the
midspan of the beam are compared with the analytical predictions. Typical compressive strains at the top surface of the beams B3 and B4 are compared with the predicted values based on ACI approach (Fig. 11). De¯ections of the beams reinforced with carbon FRP are compared with similar beams reinforced with aramid, glass and steel. The de¯ections are based on the ACI and CEB models for calculation of creep and shrinkage coef®cients. The de¯ections are higher for the FRP reinforced beams with lower Young's modulus. The experimental de¯ection for the beams reinforced with carbon FRP compares well with the theoretical computations. The de¯ections for beam B2 are computed for different FRPs using ACI approach with daily maximum humidity values and presented in Fig. 12.
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591
Fig. 13. Variation of time-dependent factor x.
8. The proposed equation for long-term de¯ection The calculation of long-term defelection at any time t, is a tedious and complex process. The ACI 318-97 code can be used to calculate the additional long-term de¯ection resulting from creep and shrinkage of steel reinforced concrete beams by multiplying the instantaneous de¯ection by a
factor. The additional long term de¯ection for beams reinforced with CFRP bars can similarly be determined by multiplying the instantaneous de¯ection, by a modi®ed factor given by
l
x 1 1 50mr 0
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Acknowledgements
Table 3 Recommended time-dependent factor x Loading period
ACI 318/318-97 for steel Proposed values based on reinforced concrete beams experiments for CFRP reinforced concrete beams
3 months 6 months 12 months 5 years or more
1.0 1.2 1.4 2.0
a
0.7 0.85 1.15 1.4 a
This value is based on test for two years.
where m is the modular ratio of the reinforcement ECFRP =ESteel ; r 0 ,compression reinforcement ratio of CFRP bars; and x, time-dependent factor for sustained load. Fig. 13 shows the variation of time-dependent factor x with time for beams reinforced with CFRP from the experimental results and ACI speci®ed values for the steel reinforced concrete beams. Recommended values of time-dependent factor x for the beams reinforced with carbon FRP are shown in Fig. 13 and in Table 3. 9. Conclusions Based on the limited experimental and analytical studies, the following observations can be made on the long-term behavior of concrete beams reinforced with CFRP 1. The time-dependent de¯ection, strain and curvature increase with the increase in the applied moment in the beams. 2. The rate of increase in strains and de¯ections are higher in the initial period of loading and tends to reduce with time under sustained loading. 3. The age-adjusted elastic modulus method used in the study appears to be realistic in predicting the long-term behavior of concrete beams reinforced with CFRP. 4. The time-dependent de¯ections of beams reinforced with CFRP are computed using a simpli®ed procedure based on the age of loading and compression CFRP reinforcement ratio.
The authors wish to express sincere thanks to Florida Department of Transportation (FDOT) for the ®nancial support of the study presented in this paper (research project: studies on carbon FRP (CFRP) prestressed concrete Bridge Columns and Piles in Marine Environment, Principal investigator: Dr M. Arockiasamy, Project Manager: Dr M. Shahawy). They wish to express their appreciation to Dr S.E. Dunn, Professor and Chairman, Department of Ocean Engineering, and Dr J. Jurewicz, Dean, College of Engineering, Florida Atlantic University for their continued interest and encouragement.
References [1] Arockiasamy M, Zhuang M. Experimental studies on the behavior of concrete bridges prestressed with carbon ®ber composite cables. Final report, new technology division, Itochu Corporation, Japan, 1996. [2] Arockiasamy M, Zhuang M, Sandepudi K. Durability studies on prestressed concrete beams with CFRP tendons, non-metallic (FRP) reinforcement for concrete structures. Proceedings of the International RILEM Symposium, (FRPRCS-2). 1995. p. 456±62. [3] Bazant ZP. Creep and shrinkage in concrete structures, Mathematical models for creep and shrinkage of concrete. New York: Wiley, 1982. p. 163±258. [4] Uomoto T, Nishimura T, Ohga H. Static and fatigue strength of FRP rods for concrete reinforcement, non-metallic (FRP) reinforcement for concrete structures. Proceedings of the International RILEM Symposium, (FRPRCS-2). 1995. p. 100±7. [5] Bazant ZP. Creep analysis of structures. Mathematical modelling of creep and shrinkage of concrete. New York: Wiley, 1988. p. 217±73. [6] Bazant ZP. Prediction of concrete creep effects using age-adjusted effective modulus method. J Am Conc Inst 1972;69(4):212±17. [7] ACI. Prediction of creep, shrinkage, and temperature effects in concrete structures, Committee 209, American Concrete Institute, Detroit, MI, 1992. [8] CEB-FIP. Evaluation of the time dependent behavior of concrete. Laussane, Switzerland, 1990. [9] Chidambaram S. Time dependent behavior of beams and columns reinforced with carbon FRP (CFRP), Masters Thesis, Florida Atlantic University, Boca Raton, FL. August, 1997.
www.elsevier.com/locate/compositesb
Time-dependent deformations of concrete beams reinforced with CFRP bars M. Arockiasamy a,*, S. Chidambaram a,b, A. Amer a, M. Shahawy c a
Center for Infrastructure and Constructed Facilities, Department of Ocean Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA b Petro-Marine Engineering of Texas, Inc., Houston, TX 77077, USA c Structural Research Center, Florida Department of Transportation, Tallahassee, FL 32310, USA
Abstract Carbon FRP is recently used as a reinforcing element in concrete structures in view of its excellent resistance to corrosion. The paper presents studies of the long-term behavior of the beams reinforced with carbon±epoxy FRP under uniform sustained loading. Four rectangular concrete beams reinforced with CFRP bars were cast in two sizes; 152 mm £ 203 mm £ 2438 mm; and 152 mm £ 152 mm £ 2438 mm: The beams were simply supported and subjected to a uniform sustained loading. The beams were instrumented and monitored to observe the changes in the behavior due to creep and shrinkage of concrete. Observations were recorded regularly for nearly two years. An analytical method is developed to predict the long-term behavior of CFRP internally reinforced concrete beams. The calculated de¯ections, strains and curvatures compare reasonably with the experimental values. A simpli®ed equation for calculating the long-term de¯ection is proposed for CFRP reinforced concrete beams. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: B. Creep; Age-adjusted section
1. Introduction Reinforcing steel in concrete structures is susceptible to corrosion that severely affects the serviceability and the safety of the structure. The extent of the steel corrosion and the resulting concrete degradation depend on the environment and the type of the structure. The corrosion effect is more pronounced in harsh marine environments and for structures exposed to deicing agent. Millions of dollars are spent every year for the repair and rehabilitation of the structures. The need is, therefore, very great for a new material such as ®ber reinforced polymer (FRP) composites, which would offer excellent resistance to corrosion. The commercially available FRPs include aramid (AFRP), carbon (CFRP) and glass (GFRP) matrix. Of all the FRPs, carbon composites exhibits a higher tensile strength, higher Young's modulus and lower ductility. The other merits of carbon FRP are derived from its (i) lightweight, (ii) nonmagnetic characteristics, and (iii) relatively low relaxation. Durability tests [1,2] have been conducted on CFRP tendons exposed to seawater, alkali and atmospheric conditions for different time duration. The test results showed that there is no signi®cant strength reduction of CFRP tendons. It is * Corresponding author. Tel.: 11-561-297-3434; fax: 11-561-297-3885. E-mail address: [email protected] (M. Arockiasamy).
noted that the failure time of the CFRP due to creep rupture is high for a given specimen when compared to the GFRP and AFRP at any given stress level [4]. Only very limited information on long-term studies have been published on CFRP reinforced concrete members under sustained loading. Bazant, [3,5] reported that the concrete creep and shrinkage cause excessive de¯ection and cracking, which severely affects the serviceability and strength of the structure. Deformations due to creep and shrinkage are usually several times larger than instantaneous deformation in concrete structures. In the case of prestressed concrete members, the loss of the prestress occurs due to creep and shrinkage. This paper presents the study on the long-term behavior of beams reinforced with CFRP under sustained uniform loads. 2. Research signi®cance The application of carbon FRP as reinforcing element is ideally suited for use in bridge decks and girders exposed to deicing salts in colder regions, and columns and piles in harsh marine environment. The objective of the current research is to study the long-term behavior of the beams reinforced with carbon FRP under sustained loading. The prediction of the CFRP reinforced beam deformations will aid in the design of structural elements in ¯exure.
1359-8368/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S 1359-836 8(99)00045-1
578
M. Arockiasamy et al. / Composites: Part B 31 (2000) 577±592
Nomenclature A0 Ac Ec E 0c t; t0 I I0 Ic L M Mapplied Mcracked m n 0 t; t0 rc2 t0 x y yc Di DL D 10 Dc D c1 D c2 10 1 t0 1cs t; t0 1cs t; t 0 1cs u fu f t; t0 h k l r0 c c t c t0 c1 c2 z1
area of the age-adjusted transformed section area of concrete in compression modulus of elasticity of concrete at the time of application of the load age-adjusted modulus of elasticity of concrete moment of inertia of the transformed section moment of inertia of age-adjusted transformed section moment of inertia of concrete about the centroid after age adjustment the length of the beam bending moment applied bending moment cracking moment modular ratio of the reinforcement ECFRP =ESteel age adjusted modular ratio Ic/Ac time of loading time-dependent factor distance to the depth from the centroid of the transformed section distance between centroids of the effective concrete area and the age adjusted transformed area instantaneous de¯ection at the midspan total de¯ection at time t at the midspan time-dependent change in strain at the centroid of the section time-dependent change in curvature due to creep and shrinkage the change in curvature of the uncracked section the change in curvature of the cracked section instantaneous strain at the centroid of the transformed section strain at any depth shrinkage strain from time t0 to t free shrinkage which occurs between t 0 at the end of curing period and any time t ultimate shrinkage strain at in®nite time ultimate creep coef®cient creep coef®cient from time t0 to t axial strain reduction factor curvature reduction factor a modi®ed factor compression reinforcement ratio of CFRP bars instantaneous curvature of bending mean curvature at time t mean curvature at time of loading the instantaneous curvature for an uncracked section the instantaneous curvature for a cracked section the coef®cient for instantaneous curvature
3. Experimental program 3.1. Specimen fabrication Four rectangular concrete beams reinforced with CFRP bars were cast in two sets. The ®rst set of beams (B1 and B2) and the second set of beams (B3 and B4) were of size 152 mm £ 203 mm £ 2438 mm 6 in: £ 8 in: £ 8 ft and 152 mm £ 152 mm £ 2438 mm 6 in: £ 8 in: £ 8 ft:, respec-
tively. Each beam is reinforced with two 7.5 mm diameter longitudinal CFRP bars and two 7.5 mm diameter hanger CFRP bars (Figs. 1 and 2). The spacing of the #3 steel stirrups is 76.2 mm (3 in.) at both ends and the spacing gradually increases to 152 mm (6 in.) at the mid span. Concrete blocks of sizes 305 mm £ 305 mm £ 610 mm 1 ft £ 1 ft £ 2 ft and 305 mm £ 152 mm £ 610 mm 1 ft £ 6 in: £ 2 ft were cast at the same time, which were used to simulate the sustained distributed loads.
M. Arockiasamy et al. / Composites: Part B 31 (2000) 577±592
579
Fig. 1. Reinforcement details of the beams.
3.2. Material properties Concrete: The concrete properties for the two set of beams are shown in Table 1. Carbon FRP: Materials used for manufacturing carbon FRP are carbon ®ber of the PAN base system and matrix resins. The properties of carbon ®ber, matrix resin and carbon FRP are presented Table 2.
4. Test setup and instrumentation The ¯exural strains at midspan are measured using ®ve and three electrical surface strain gages for beams in set I and set II, respectively. The surface strain gages are protected from moisture intrusion by epoxy coating. For all the beams, embedded strain gages are also attached along the CFRP bars. Both surface and embedded strain gages are monitored by the strain indicator (beams B1 and B2)/data acquisition system 4000 (beams B3 and B4). The de¯ections at the midspan of the beams are recorded using de¯ectometer. After the beams were cured, the beams were set up over the simple supports and subjected to sustained distributed loads (Fig. 3). The distributed loads were simulated by using concrete blocks. The details of the loading are shown in Fig. 4. Beam B1 is subjected to 77% of the ®rst cracking moment. Beams B2, B3 and B4 are subjected to 123, 110 and 123% of their respec-
tive cracking moments. The effect of cracks is evaluated in the study of the long-term behavior of CFRP reinforced concrete beams. For the ®rst three weeks, the strains and the de¯ections at the midspan of the beams were recorded twice a day and thereafter, once a day for a three month period. As the recorded data indicated a steady trend, the time interval between successive observations was increased to one week. Beams B1 and B2 were subjected to the sustained load for about 20 months, whereas beams B3 and B4 for 15 months. It was noticed that new cracks developed during the ®rst couple of weeks in the precracked beams B2, B3, and B4.
Table 1 Properties of concrete Items
Beam set I
Beam set II
Cement: sand: aggregate (by weight) Cylinder compressive strength after 28 days f 0c Modulus of elasticity of concrete (Ec)
1:1.88:2.68
1:1.31:2.14
32.11 MPa (4657 psi)
42.75 MPa (6200 psi)
26.80 GPa (3887 ksi)
30.92 GPa (4484 ksi)
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Table 2 Properties of the carbon FRP bars Item
Property
Carbon ®ber
Tensile strength Tensile modulus Elongation at break Type of resin Tensile strength Elongation at break Diameter of the rod Effective cross sectional area Modulus of elasticity
Matrix resin Carbon FRP reinforcement
211 MPa 137 GPa 1.5% Denaturated epoxy resin 51.5 MPa 4.2% 7.5 mm 30.4 mm 2 137.34 GPa
5. Experimental results 5.1. Loading The concrete blocks were added one at a time to the beams B1, B2, B3 and B4 over the course of approximately three hours. The de¯ection measurements were made at the completion of this loading t 0. 5.2. De¯ections Fig. 5 shows the long-term de¯ections at the midspan for the beams B1, B2, B3 and B4. The long-term de¯ections are obtained by subtracting the instantaneous de¯ection from the total de¯ection. It shows that the de¯ection at the midspan increases with the time. The beams B1, B2, B3 and B4 are loaded to 77, 120, 110 and 123% of their cracking moment, respectively. The load intensity in beam B3 is smaller than that in beam B4 and hence beam B3 exhibits smaller long-term de¯ections than those of beam B4. Beam B1 remained uncracked and exhibited a very small increase in long term de¯ection. The increase in de¯ections over the instantaneous values for a period of 470 days is 15, 115, 65 and 71% for beams B1, B2, B3 and B4, respectively. Beams B1 and B2 showed an increase in de¯ection of 28 and 125% after a period of 610 days. 5.3. Concrete strains Fig. 6 shows the total time-dependent compressive strains observed at the top concrete surface for beams B1, B2, B3 and B4. Beam B1 was uncracked and subjected to a load intensity less than beam B2 and hence it exhibits a small compressive strain. The compressive strain at the top surface of the beam B4 is only marginally higher than that in beam B3, since the load intensity in beam B4 is more than that in beam B3. The increase in the strains over the instantaneous values for a period of 470 days is 101, 151, 209 and 245% for beams B1, B2, B3 and B4, respectively. 5.4. Curvature Fig. 2. Reinforcement in position before concrete pour.
Fig. 7 shows the variation of the curvature observed at the midspan of the beams B1, B2, B3 and B4. The beam B2
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Fig. 3. Test setup for beams B1 and B2.
Fig. 4. Details of distributed sustained loading of the beams.
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Fig. 5. Variation of long-term de¯ection with time.
with a larger depth than B3 and B4 shows a smaller curvature. The load intensity on beam B3 is smaller than that in beam B4 and hence it exhibits curvatures smaller than those of B4.
the time-dependent curvature, strains and de¯ections induced by creep and shrinkage are calculated based on the age-adjusted elastic modulus method [6]. 6.1. Instantaneous deformation
6. Theoretical prediction of the long-term deformation of the CFRP reinforced concrete beams The total deformation at any time is the sum of the instantaneous and time-dependent deformations. The instantaneous curvature, strains and de¯ections due to lateral loads can be determined from the elastic analysis whereas,
The instantaneous curvature of bending is given by c
M Ec I
1
where I is the moment of inertia of the transformed section, M the bending moment and Ec the modulus of elasticity of concrete at the time of application of the load.
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Fig. 6. Strain observed at the top surface of the beams.
The strain at any depth is given by
Mean curvature at time of loading, t0 is given by c t0 1 2 z1 c1 1 z1 c2
2
where c1 is the instantaneous curvature for an uncracked section; c2, instantaneous curvature for a cracked section; z 1 coef®cient for instantaneous curvature 8 !2 > > < 1 2 Mcracked for a cracked section Mapplied : z1 > > : 0 for an uncracked section Instantaneous de¯ection is calculated by assuming parabolic variation of curvature, with zero de¯ection at the ends and maximum at the center and the midspan de¯ection is given by,
Di
c t0 ´L 9:6
2
where L is the length of the beam
3
1 t0 10 1 yc t0
4
where 1 0 is the instantaneous strain at the centroid of the transformed section and y, the distance to the depth from the centroid of the transformed section (point O in Fig. 8(a)). Fig. 8(b) shows the instantaneous strain distribution due to loading at age t0, whereas the change in strain distribution for the period t 2 t0 and the total strain variation at time t are shown in Fig. 8(c) and (d), respectively. 6.2. Total deformations including time-dependent effects Mean curvature at time t is given by c t 1 2 z2 c1 1 Dc1 1 z2 c2 1 Dc2
5
where Dc1 is the change in curvature of the uncracked
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Fig. 7. Variation of curvature with time.
section; Dc2, change in curvature of the cracked section; z 2, coef®cient for long-term curvature
The total de¯ection at the midspan at time t is given by
8 !2 > > < 1 2 0:5 Mcracked Mapplied z2 > > : 0
DL for a cracked section for an uncracked section
:
c tL2 9:6
6
The time-dependent change in strain at the centroid of the section and the time-dependent change in curvature due to
M. Arockiasamy et al. / Composites: Part B 31 (2000) 577±592
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Fig. 8. Strain distribution at a cross-section.
creep and shrinkage are given by, D10 hf t; t0 10 1 cyc 1 1cs t; t0
7
y Y Dc k f t; t0 c 1 10 2c 1 1cs t; t0 2c rc rc
8
where rc2
Ic Ac
h
Ac A0
k
Ic I0
where f t; t0 is the creep coef®cient from time t0 to t; 1cs t; t0 ; the shrinkage strain from time t0 to t; yc, the distance between centroids of the effective concrete area and the age-adjusted transformed area; Ac, the area of concrete in compression; A 0 , the area of the age adjusted transformed section; Ic, the moment of inertia of concrete about the centroid after age adjustment; I 0 , the moment of inertia of age adjusted transformed section using modular ratio n 0 t; t0 in which, n 0 t; t0
Fig. 9. Flowchart for calculation of deformations of CFRP reinforced concrete beams.
ECFRP E 0c t; t0
where E 0c t; t0 is the age-adjusted modulus of elasticity of concrete. The strain at any depth in the transformed section at time t is computed as the algebraic sum of the instantaneous strain and change in strain from time t0 to t due to creep and shrinkage at the ®ber under consideration (Fig. 8(d)). In the present study, the creep and shrinkage coef®cients are ®rst calculated based on ACI
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Fig. 10. (a) Comparison of experimental and predicted de¯ections for beam B3; (b) Comparison of experimental and predicted de¯ections for beam B4.
committee 209 and CEB 1990 approaches. Based on the experimental results, an equation is proposed for the creep coef®cient. 6.3. Creep and shrinkage coef®cients 6.3.1. ACI committee 209 approach Based on the extensive research work of Branson et al.,
the ACI committee 209 [7] recommended the following expressions for creep and shrinkage of concrete:
f t; t0 1cs t; t 0
t 2 t0 0:6 fu 10 1 t 2 t0 0:6 t 2 t0 1 35 1 t 2 t 0 cs u
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587
Fig. 10. (continued)
where f t; t0 is the creep coef®cient at time t for age at loading t0; 1cs t; t 0 ; the free shrinkage which occurs between t 0 at the end of curing period and any time t; f u, ultimate creep coef®cient; and (1 cs)u, ultimate shrinkage strain at in®nite time. Coef®cients f u and (1 cs)u depend on atmospheric humidity, the member size, slump of concrete, cement content, ®ne aggregate percent, air content in percent and type of curing.
6.3.2. CEB-FIP approach The creep coef®cient according to CEB-FIP [8] is given by
f t; t0 fRH b fcm b tc bc t 2 t0 where the factors f RH, b fcm ; b t0 ; bc t 2 t0 take into account the corrections for the atmospheric humidity, mean compressive strength of the concrete, time of loading and duration of loading, respectively.
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Fig. 11. (a) Comparison of experimental and predicted top surface strains for beam B3. (b) Comparison of experimental and predicted top surface strains for beam B4.
The strain due to shrinkage or swelling according to CEB-FIP is given by,
model takes into consideration both reversible and irreversible creep.
1cs 1cs0 bs t 2 t where 1 cs0 is a function of mean compressive strength of concrete, type of cement and relative humidity, bs t 2 t 0 is a function of duration of loading. This
7. Evaluation of results and discussions A user-friendly C program was written to calculate the beam curvature, de¯ections and strains based on the
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589
Fig. 11. (continued)
theoretical approach. A ¯owchart of the program is shown in Fig. 9. The test setup is arranged in an openair facility in tropical weather conditions to simulate the actual ®eld conditions. The predicted deformations take into account the change in the relative humidity of the atmosphere, CFRP material characteristics, member size, concrete strength, sustained load intensity and
duration of loading. Comprehensive comparisons of the measured curvatures, strains and de¯ections against the theoretical predictions are presented in Ref. [9]. The main parameters in the comparison are the maximum and minimum daily relative humidities. The minimum and maximum relative humidities were used in the theoretical prediction. Typical comparisons of the
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Fig. 12. Comparison of beams reinforced with aramid, glass and steel with CFRP.
measured and theoretical deformations are presented in this paper. The experimental de¯ections at the midspan are compared with the analytical predictions based on the ACI and CEB coef®cients. Deformations based on ACI creep coef®cient and shrinkage strain compared closely with those computed using CEB coef®cient. Therefore, only the results based on the ACI creep coef®cient are presented in this paper. Typical comparison of experimental de¯ections for beams B3 and B4 with the theoretical predictions are presented in Fig. 10. It can be seen that the experimental results are in reasonable agreement with the predicted values. The experimental strains across the cross-section at the
midspan of the beam are compared with the analytical predictions. Typical compressive strains at the top surface of the beams B3 and B4 are compared with the predicted values based on ACI approach (Fig. 11). De¯ections of the beams reinforced with carbon FRP are compared with similar beams reinforced with aramid, glass and steel. The de¯ections are based on the ACI and CEB models for calculation of creep and shrinkage coef®cients. The de¯ections are higher for the FRP reinforced beams with lower Young's modulus. The experimental de¯ection for the beams reinforced with carbon FRP compares well with the theoretical computations. The de¯ections for beam B2 are computed for different FRPs using ACI approach with daily maximum humidity values and presented in Fig. 12.
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Fig. 13. Variation of time-dependent factor x.
8. The proposed equation for long-term de¯ection The calculation of long-term defelection at any time t, is a tedious and complex process. The ACI 318-97 code can be used to calculate the additional long-term de¯ection resulting from creep and shrinkage of steel reinforced concrete beams by multiplying the instantaneous de¯ection by a
factor. The additional long term de¯ection for beams reinforced with CFRP bars can similarly be determined by multiplying the instantaneous de¯ection, by a modi®ed factor given by
l
x 1 1 50mr 0
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Acknowledgements
Table 3 Recommended time-dependent factor x Loading period
ACI 318/318-97 for steel Proposed values based on reinforced concrete beams experiments for CFRP reinforced concrete beams
3 months 6 months 12 months 5 years or more
1.0 1.2 1.4 2.0
a
0.7 0.85 1.15 1.4 a
This value is based on test for two years.
where m is the modular ratio of the reinforcement ECFRP =ESteel ; r 0 ,compression reinforcement ratio of CFRP bars; and x, time-dependent factor for sustained load. Fig. 13 shows the variation of time-dependent factor x with time for beams reinforced with CFRP from the experimental results and ACI speci®ed values for the steel reinforced concrete beams. Recommended values of time-dependent factor x for the beams reinforced with carbon FRP are shown in Fig. 13 and in Table 3. 9. Conclusions Based on the limited experimental and analytical studies, the following observations can be made on the long-term behavior of concrete beams reinforced with CFRP 1. The time-dependent de¯ection, strain and curvature increase with the increase in the applied moment in the beams. 2. The rate of increase in strains and de¯ections are higher in the initial period of loading and tends to reduce with time under sustained loading. 3. The age-adjusted elastic modulus method used in the study appears to be realistic in predicting the long-term behavior of concrete beams reinforced with CFRP. 4. The time-dependent de¯ections of beams reinforced with CFRP are computed using a simpli®ed procedure based on the age of loading and compression CFRP reinforcement ratio.
The authors wish to express sincere thanks to Florida Department of Transportation (FDOT) for the ®nancial support of the study presented in this paper (research project: studies on carbon FRP (CFRP) prestressed concrete Bridge Columns and Piles in Marine Environment, Principal investigator: Dr M. Arockiasamy, Project Manager: Dr M. Shahawy). They wish to express their appreciation to Dr S.E. Dunn, Professor and Chairman, Department of Ocean Engineering, and Dr J. Jurewicz, Dean, College of Engineering, Florida Atlantic University for their continued interest and encouragement.
References [1] Arockiasamy M, Zhuang M. Experimental studies on the behavior of concrete bridges prestressed with carbon ®ber composite cables. Final report, new technology division, Itochu Corporation, Japan, 1996. [2] Arockiasamy M, Zhuang M, Sandepudi K. Durability studies on prestressed concrete beams with CFRP tendons, non-metallic (FRP) reinforcement for concrete structures. Proceedings of the International RILEM Symposium, (FRPRCS-2). 1995. p. 456±62. [3] Bazant ZP. Creep and shrinkage in concrete structures, Mathematical models for creep and shrinkage of concrete. New York: Wiley, 1982. p. 163±258. [4] Uomoto T, Nishimura T, Ohga H. Static and fatigue strength of FRP rods for concrete reinforcement, non-metallic (FRP) reinforcement for concrete structures. Proceedings of the International RILEM Symposium, (FRPRCS-2). 1995. p. 100±7. [5] Bazant ZP. Creep analysis of structures. Mathematical modelling of creep and shrinkage of concrete. New York: Wiley, 1988. p. 217±73. [6] Bazant ZP. Prediction of concrete creep effects using age-adjusted effective modulus method. J Am Conc Inst 1972;69(4):212±17. [7] ACI. Prediction of creep, shrinkage, and temperature effects in concrete structures, Committee 209, American Concrete Institute, Detroit, MI, 1992. [8] CEB-FIP. Evaluation of the time dependent behavior of concrete. Laussane, Switzerland, 1990. [9] Chidambaram S. Time dependent behavior of beams and columns reinforced with carbon FRP (CFRP), Masters Thesis, Florida Atlantic University, Boca Raton, FL. August, 1997.