Cement Science and Concrete Technology, No.63, 2009

592

ABSTRACT：In this paper, the carbon fiber reinforced plastic（CFRP）bars were used as the reinforcement at the tensile side of RC beams. There were three different types of the main tensile reinforcement arrangement in the RC beams with shear steel stirrups. For the three different types of the main reinforcement arrangement, there were one, two and three rebars placed at the tensile side of reinforcement with the sizes of D16 steel rebars and the CFRP bars. Moreover, the sizes of D10 CFRP bars were used in the experiment. All the RC beam specimens with steel rebars and CFRP bars were bending failure. The results of RC beams with steel rebars and CFRP bars were compared in deflection and in rebar strain of FEM results at maximum flexural strength. Comparing the maximum experimental flexural strengths with the FEM results, the RC beam specimens with steel rebars were greater than the FEM results in average. Similarly, the RC beam specimens with CFRP bars were greater than the FEM results in average also. From the FEM results, the yielding strain of steel rebar was reached before the failure of RC beams for all three types of RC beams with steel rebars. Moreover, from the FEM results of the RC beam with CFRP bars, the CFRP tensile strength was reached before the failure of RC beams for the one and two CFRP bars placed at the tensile side. However, for the three CFRP bars placed at the tensile side, the failure of RC beams was before the CFRP tensile strength was reached. As seen from the experimental and FEM results, the load-deflection relationships of both results were coincident to each other.

THE FINITE ELEMENT ANALYSIS ON STEEL REBARS AND CFRP BARS USED AS THE MAIN REINFORCEMENT IN RC BEAMS

Ming-Chien HSU*1, Tetsukazu KIDA*1, Tadashi ABE*1 and Yeou-Fong LI*2

*1　 NIHON UNIVERSITY, College of Industrial Technology, Dept. of Civil Engineering（1-2-1 Izumi-cho, Narashino-shi, Chiba 275-8575, Japan）

*2　 NATIONAL TAIPEI UNIVERSITY OF TECHNOLOGY, Dept. of Civil Engineering（1, Sec. 3, Chung Hsiao East Road, Taipei 10608, Taiwan, R.O.C.）

KEY WORDS：RC beam, CFRP bar, Steel rebar, Maximum flexural strength, Failure criteria

1.　Introduction

　Over the years, reinforced concrete（RC）structures were damaged by the natural weather, earthquakes, and overloadings. The most critical effects to the RC structures are chloride contamination and corrosion of rebars, which mostly affect the steel rebars in the RC structures. Therefore, finding a substitute material for the steel rebars is one of the focuses of researchers. The fiber reinforced plastic（FRP）1, 2, 3）

composite material has been considered as one of the best substitute materials to steel rebar since it has anti-corrosion, lightweight, as well as high strength and high elastic modulus properties. In this paper, the authors used carbon fiber reinforced plastic（CFRP）bars as the reinforcement at the tensile side of the RC beams 4, 5, 6） instead of steel rebars. The maximum flexural strength of the RC beam with CFRP bars was

compared with steel rebar. RC beams were calculated by using finite element method（FEM）in this paper. Moreover, the strain of steel rebars and CFRP bars will be considered in this paper as well.

2.　Preparation of Experimental Specimens

2. 1　Materials used for experimental specimens

　Normal concrete with the compression strength of 22.45N/mm2 was used for the RC beams in the experiments. This uniaxial concrete compression strength was done in the laboratory, and the young’s modulus was found form it. D16 was used as the main steel rebars and D10 was used as the steel stirrup. The CFRP bars, similar in size to D10 steel rebars, were used in the tensile side of the RC beams. The properties of concrete, steel rebars and CFRP bars are shown in Table 1 and Table 2 4, 5, 6）.

Cement Science and Concrete Technology, No.63, 2009

593

2. 2　Specimen size and steel rebar arrangement

　All the RC beam’s specimens were 180×220×1350mm in size. However, the arrangements of tensile reinforcements were different. There were three different arrangements of the rebars in the tensile side of the RC beams for experiments. In the first type, the steel rebars were placed at the center of the RC beam with one D16 located at the tensile side and two D16 located at the compression side. The D10 steel stirrup were included in the RC beams with a distance of 80mm between each other. However, the steel stirrups were not placed within a 300mm range at the center of the RC beams. For the second type, there are two steel rebars placed at the tensile side with the center-to-center distance of 104mm away from each others. Other steel rebar setups were same as Type One for the compression side and the steel stirrups. For the third type, there are three steel rebars placed at the tensile side with the center-to-center distance of 52mm away from each others. Other steel rebars setups were the same as Type One for the compression side and the steel stirrups.　Fig. 1（a） shows the different arrangements of tensile rebars in RC beams with steel rebars and CFRP bars. Fig. 1（b） shows one example of the RC beam with one steel rebar in the tensile side, the dimensions, and other layouts for the experiment.　For RC beams with CFRP bars, the dimensions and rebar arrangements of RC beams were the same as the RC beam with steel rebars. However, the tensile side was replaced by CFRP bars. Fig. 1（c） just shows an example of RC beams with one CFRP bars, the dimensions and stirrup steel rebar arrangements.　Hereafter, the RC beams with one, two and three longitudinal steel rebars are named N-S1S2, N-S2S2, and N-S3S2, respectively. The RC beams with one, two, and three CFRP bars are named N-C1S2, N-C2S2, and N-C3S2, respectively. The N indicates the normal strength concrete. The S and C indicate the steel rebars and CFRP bars. The numbers indicate the number of rebars located at the tensile side and the compression side.2. 3　Experimental method

　The monotonic loading was carried out, and the loading area was 180×300mm at the center of the span. The load was increased until the experimental specimens failed. The deflections of the RC beams were being recorded during the experiments. Fig. 1（b） and （c） show the location of the loading area.

3.　FEM Analysis of RC Beams

　The three-dimensional RC beam’s finite element model was created by DIANA7） to simulate the specimens under monotonic loading. Moreover, an eight-node iso-parametric solid brick element was used for the concrete elements. The longitudinal steel rebars, CFRP bars and steel stirrups were included in the model, as well. However, the authors assume the interface between steel rebars and concrete was fully bonding. Also, it was the same as the interface

Table 1　Concrete and steel rebar material properties

Testspecimen

Concrete Steel rebar（SD295A/D16）

Compressivestrength（N/mm2）

Young’smodulus（N/mm2）

Yieldstrength（N/mm2）

Tensilestrength（N/mm2）

Young’s modulus

（kN/mm2）

N-SS22.45 5600 395.71 520 200

N-CS

Table 2　CFRP bar’s material properties

Name of CFRPCross Section（mm2）

Tensile strength（N/mm2）

Young’s modulus（kN/mm2）

CFRP bars 72.48 854.72 92.12

（a）Rebars arrangements at the tensile side

（b）Steel rebars（For example：N-S1S2）

（c）CFRP bars（For example：N-C1S2）

Fig. 1　 The dimension and rebars arrangement of RC beams 4, 5, 6）

Cement Science and Concrete Technology, No.63, 2009

594

between the CFRP bars and the concrete.3. 1　Constitutive parameter

　The material properties for the concrete, the steel rebars and CFRP bars were done in the laboratory. However, some material properties of the concrete and steel were adopted from the specification for concrete structures in Japan8）, such as concrete tensile strength, concrete tensile ultimate strain, concrete compression yield strength, steel rebar after yielding, and etc.（1）Concrete tensile strength　The tensile strength was calculated from the compressive strength and shown in Fig. 2（a） that was from the Standard Specifications for Concrete Structures 8）. For the concrete tensile softening curve, the linear tensile softening was chosen from DIANA’s manual 7）. The ultimate tensile strain in the softening curve is shown in Fig. 2（a）. The shear retention should also consider into the cracking modeling, and the full shear retention was used in the modeling of concrete cracking. On the other hand, the shear modulus did not reduce in the calculation. For the concrete cracking, the Smeared-cracking modeling 7, 9, 10） would be used.（2）Concrete compressive strength　The uniaxial compressive test had been done in the laboratory. The compressive strengths are listed in Table 1 and the relevant strain of maximum compressive strength was 0.006 4, 5, 6）. However, the characteristic of the compressive curve needs to be adopted from the Standard Specifications for Concrete Structures 8）. The equations and compressive curve are listed in Fig. 2（a）. The Young’s modulus of concrete had been found from the uniaxial concrete compression strength at laboratory. The yield strength, was 1/3 of compressive strength, were found in the Standard Specifications for Concrete Structures, too. The plasticity for the concrete according to Drucker-Prager 7, 11） was used.（3）Steel rebars’ parameter　The main steel rebars in the RC beams had been done in the experiment 4, 5, 6）. The bi-linear strain-stress curve for steel rebars was used. After the yielding strength of the steel, the slope（tangent modulus）of 0.01Es would be used. Fig. 2（b） shows the properties of steel. The Von Mises 7, 11, 12） yield surface for the steel rebars was used in this paper.（4）CFRP bars’ parameter　The main CFRP bars in the RC beams had been done in the experiment 4, 5, 6）. The strength of CFRP bars drops to zero when it reached to the tensile strength. Fig. 2（c） shows the properties of steel rebars.

3. 2　Analysis Procedure

　The load steps were used for the non-linear analysis calculation. For the iteration processing, Quasi-Newton method 7）, using the information of previous solution vectors and out-of-balance force vectors during the increment to achieve a better approximation, was used with displacement and force norms for convergence criteria. Forty iterations would be used for each load steps, and convergence tolerance would be 0.001. The stop criterion for the FEM calculation was 0.006 that the concrete compressive strength reached.

4.　Maximum Flexural Strength

　The maximum flexural strength, deflection and failure condition are listed in Table 3. Fig. 3 shows the experimental and FEM results. Fig. 4 shows the cracking patterns of RC beams at failure.

（a）Concrete

（b）Steel rebars

（c）CFRP bars

Fig. 2　 The material constitutive models for FEM analysis 8）

Cement Science and Concrete Technology, No.63, 2009

595

4. 1　Experimental results

（1）N-S1S2　The RC beam N-S1S2 had the maximum flexural strength of 93.79kN, and the deflection was 17.68mm. The failure conditions were bending failure. The cracks developed from the bottom of the RC beam with approximately 45 degrees angle up towards the loading area are shown in Fig. 4（a）.（2）N-S2S2　The RC beam N-S2S2 had the maximum flexural strength of 137.86kN, and the deflection was 18.59mm. The failure conditions were bending failure. The cracks developed from the bottom of the RC beam with approximately 45 degrees angle up towards the loading area are shown in Fig. 4（b）.（3）N-S3S2　The RC beam N-S3S2 had the maximum flexural strength of 187.61kN, and the deflection was 18.69mm. The failure conditions were bending failure. The cracks developed from the bottom of the RC beam with approximately 45 degrees angle up towards the loading area are shown in Fig. 4（c）.（4）N-C1S2　The RC beam N-C1S2 had the maximum flexural strength of 56.51kN, and the deflection was 10.62mm. The failure conditions were bending failure. The cracks developed from the bottom of the RC beam and went up directly towards the loading area as shown in Fig. 4（d）. The maximum flexural strength of the RC beam N-C1S2 was approximately 40 ％ less than that of the RC beam N-S1S2.（5）N-C2S2　The RC beam N-C2S2 had the maximum flexural strength of 108.00kN, and the deflection was 15.22mm. The failure conditions were bending failure. The cracks developed from the bottom of the RC beam and went up directly towards the loading area as shown in Fig. 4（e）. The maximum flexural strength of the RC beam N-C2S2 was approximately 22 ％ less than that of the RC beam N-S2S2.

（6）N-C3S2　The RC beam N-C3S2 had the maximum flexural strength of 154.63kN, and the deflection was 18.99mm. The failure conditions were bending failure. The cracks developed from the bottom of the RC beam and went up directly towards the loading area as shown in Fig. 4（f）. The maximum flexural strength of the RC beam N-C3S2 was approximately 18 ％ less than that of the RC beam N-S3S2.4. 2　FEM results

　The assumption for the FEM RC beams failure was based on the uniaxial compression experimental results of maximum flexural strain. The location to be checked in the RC beams model is on the top center edge of the RC beams model under the loading area.（1）N-S1S2　The RC beam N-S1S2 had the maximum flexural strength of 69.75kN, and the deflection was 11.50mm. Comparing the maximum flexural strength, the FEM result was approximately 34 ％ less than the experimental results.（2）N-S2S2　The RC beam N-S2S2 had the maximum flexural strength of 117.00kN, and the deflection was 8.98mm. Comparing the maximum flexural strength, the FEM result was approximately 18 ％ less than the experimental results.（3）N-S3S2　The RC beam N-S3S2 had the maximum flexural strength of 160.50kN, and the deflection was 8.37mm. Comparing the maximum flexural strength, the FEM result was approximately 17 ％ less than the experimental results.（4）N-C1S2　The RC beam N-C1S2 had the maximum flexural strength of 55.25kN, and the deflection was 13.20mm. Comparing the maximum flexural strength, the FEM result was approximately 2 ％ less than the experimental results.（5）N-C2S2　The RC beam N-C2S2 had the maximum flexural strength of 98.00kN, and the deflection was 13.26mm. Comparing the maximum flexural strength, the FEM result was approximately 10 ％ less than the experimental results.（6）N-C3S2　The RC beam N-C3S2 had the maximum flexural strength of 118.00kN, and the deflection was 12.20mm. Comparing the maximum flexural strength, the FEM result was approximately 31 ％ less than the experimental results.

Table 3　 Maximum flexural strength, deflection and failure modes

SpecimenMaximum flexuralstrength（kN） Exp. Deflection（mm） Failure

ConditionExperiment FEM FEM Experiment FEM

N-S1S2 93.79 69.75 1.34 17.68 11.50 Bending

N-S2S2 137.86 117.00 1.18 18.59 8.98 Bending

N-S3S2 187.61 160.50 1.17 18.69 8.37 Bending

N-C1S2 56.51 55.25 1.02 10.62 13.20 Bending

N-C2S2 108.00 98.00 1.10 15.22 13.26 Bending

N-C3S2 154.63 118.00 1.31 18.99 12.20 Bending

Cement Science and Concrete Technology, No.63, 2009

596

（c）N-S3S2 （f）N-C3S2

（b）N-S2S2 （e）N-C2S2

（a）N-S1S2 （d）N-C1S2

Fig. 3　Loading-Deflection relationships of RC beams with steel rebars and CFRP bars

（d）N-C1S2

（e）N-C2S2

（f）N-C3S2

（a）N-S3S2

（b）N-S1S2

（c）N-S2S2

Fig. 4　Crack patterns 1）

Cement Science and Concrete Technology, No.63, 2009

597

5.　Strain of Rebars for the FEM Results

　Fig. 5 shows the strain results of FEM for the steel rebars and CFRP bars. By using the experimental results, the yielding strain of the steel rebars had been checked and recorded from the FEM modeling results. Also, the tensile strain of the CFRP bars had been checked and recorded. The results can be found and calculated from Tables 2 and Table 3. The yielding stain of steel rebar is 1.978550×10－3（＝395.71N/mm2/200000N/mm2）. The tensile stain of CFRP bar is 9.278332×10－3（＝854.72N/mm2/92120N/mm2）.5. 1　Loading-strain relationships of steel rebars

　As seen from Fig. 5（a）, for N-S1S2, the result of FEM calculation for the steel yield strain was between 50.00kN to 51.00kN. For N-S2S2, the result of FEM calculation for the steel yield strain was between 96.50kN to 97.00kN. For N-S3S2, the result of FEM calculation for the steel yield strain was between 145.25kN to 145.50kN. Moreover, as seen from Fig. 3（a） to （c） for the FEM results, the steel yield strain was reached before the failure of the RC beams that were 69.75kN, 117.00kN, and 160.50kN for N-S1S2,

N-S2S2, and N-S3S2, respectively. From the behavior of rebars’ strain, we can notice that the first cracks would happen around 12.00kN, 14.00kN, 15.00kN for N-S1S2, N-S2S2, and N-S3S2, respectively. Finally, the FEM results of RC beams with steel rebars were similar to the experimental results.5. 2　Loading-strain relationship of CFRP bars

　As seen from Fig. 5（b）, for N-C1S2, the result of FEM calculation for the CFRP tensile force was between 46.00kN to 47.00kN. For N-C2S2, the result of FEM calculation for the CFRP tensile force was between 84.00kN to 85.00kN. For N-C3S2, the result of FEM calculation for the CFRP tensile force was between 126.00kN to 127.00kN. Moreover, as seen from Fig. 3（d） to （f） for the FEM results, the CFRP tensile force was reached before the failure of the RC beams that were 55.25kN and 98.00kN for N-C1S2 and N-C2S2, respectively. However, the CFRP tensile force was reached before the failure of the RC beams that was 118.00kN for N-C3S2. From the behavior of rebars’ strain, we can notice that the first cracks would happen around 10.00kN, 11.00kN, 11.00kN for N-C1S2, N-C2S2, and N-C3S2, respectively. Finally, the FEM results of CFRP bars were similar to the experimental results also.

6.　Conclusion

（1） Comparing the load-displacement results of RC beams with steel rebars and CFRP bars, the maximum flexural strength of specimens N-S1S2, N-S2S2, and N-S3S2 were approximately 66 ％, 28 ％ and 21 ％ greater than the specimens N-C1S2, N-C2S2, and N-C3S2, respectively.

（2） Comparing the experimental results with the FEM results, the maximum experimental flexural strengths of specimens N-S1S2, N-S2S2, and N-S3S2 were 34 ％, 18 ％ and 17 ％ greater than the FEM results, respectively. Similarly, the maximum experimental flexural strengths of Specimens N-C1S2, N-C2S2 and N-C3S2 were 2 ％, 10 ％, and 31 ％ greater than the FEM results, respectively.

（3） For the RC beams with steel rebars, the cracks developed from the bottom of the RC beam with approximately 45 degrees angle up towards the loading area. For the RC beams with CFRP bars, the cracks developed from the bottom of the RC beam and went up directly towards the loading area. Moreover, all the RC beam specimens with the steel rebars or with the CFRP bars were bending failure.

（a）Steel rebars

（b）CFRP bars

Fig. 5　 Loading-Strain relationships of steel rebars and CFRP bars

Cement Science and Concrete Technology, No.63, 2009

598

（4） For the FEM results of all the RC beams with steel rebars, the yielding strain of steel rebars was reached before the strain of the uniaxial compression strength that was done in the laboratory. For the RC beams with one and two CFRP bars in the tensile side of the RC beams, the tensile strengths of CFRP bars were reached before the strain of the uniaxial compression strength. However, for the three CFRP bars in the tensile side of the RC beam, the tensile strain was reached after the strain of the uniaxil compression strength. This means that the RC beam with three CFRP bars had not over the CFRP bars’ elastic region when the RC beams were assumed to fail in the FEM results.

（5） As seen from Fig. 3, the FEM results show that the FEM calculations have similar patterns to the experimental results. In other words, the FEM input parameters should be reconsidered again and the interface between concrete and the steel rebars or FRP bars need to be included.

References：1） Abdalla, H. A.：“Evaluation of Deflection in Concrete Members Reinforced with Fibre Reinforced Polymer（FRP）Bars,” Composite Structures, Vol. 56, No. 1, pp. 63-71（2002）

2） Toutanji, H. and Deng, Y.：“Deflection and Crack-Width Prediction of Concrete Beams Reinforced with Glass FRP Rods,” Construction and Building Materials, Vol. 17, No. 1, pp. 69-74（2003）

3） Wegian, F. M. and Abdalla, H. A.：“Shear Capacity of Concrete Beams Reinforced with Fiber

Reinforced Polymers,” Composite Structures, Vol. 71, No. 1, pp. 130-138（2005）

4） Li , Y.-F. , Lin, C.-T. , Jau, W.-C. , et al .：“A Feasibility Study on the Flexural RC Beams Using GFRP Rebars as the Main Reinforcement,” Structural Engineering（Taiwan）, Vol. 22, No. 4, pp. 113-128（2007）

5） Li, Y.-F., Lin, C.-T., Hung, M.-J., et al.：“A Feasibility Study on Mechanics Behavior of the High Strength Concrete Beams with CFRP Bars,” Structural Engineering（Taiwan）, Vol. 24, No. 2, pp. 33-54（2009）

6） Hsu, M.-C., Kida, T., Abe, T., et al.：“A Study on the Maximum Flexural Strength of RC Beams with Steel Rebars and CFRP Bars by Using FEM Analysis,” JSCE 2009 Annual Meeting, V-564, pp. 1125-1126（2009）

7） DIANA Finite Element Analysis User’s Manual：TNO Building and Construction Research（2000）

8） Japan Society of Civil Engineers：Standard Speci-fications for Concrete Structures - 2002, Structural Performance Verification（2002）

9） Okamura, H., Maekawa, K.：Nonlinear Analysis and Constitutive Models of Reinforced Concrete, GIHODO printing, pp. 7-4（1991）

10） Jan Gerrit Rots：Computational modeling of concrete fracture, PhD thesis, Delft University of Technology（1988）

11） Chen, W. F.：Plasticity in Reinforced Concrete, McGraw-Hill Book Company, pp. 83-85（1982）

12） Jan G. M. van Mier：Fracture Processes of Con-crete, CRC Press, Inc., Ch. 5（1997）