ashour et al_1999_effect of the concrete compressive stength and tensile reinforcement ratio

8/10/2019 Ashour Et Al_1999_Effect of the Concrete Compressive Stength and Tensile Reinforcement Ratio

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Engineering Structures 22 (2000) 11451158

www.elsevier.com/locate/engstruct

Effect of the concrete compressive strength and tensilereinforcement ratio on the flexural behavior of fibrous concrete

beams

Samir A. Ashour *, Faisal F. Wafa, Mohmd I. Kamal

Civil Engineering Department King Abdulaziz University, Jeddah, Saudi Arabia

Received 18 January 1999; received in revised form 22 April 1999; accepted 4 June 1999

Abstract

Twenty seven reinforced concrete beams were tested to study the effects of steel fibers, longitudinal tensile reinforcement ratioand concrete compressive strength on the flexural behavior of reinforced concrete beams.

Concrete compressive strengths of 49, 79 and 102 MPa and tensile reinforcement ratios of 1.18, 1.77 and 2.37% were used. The

fiber contents were 0.0, 0.5 and 1.0% by volume. The results show that the additional moment strength provided by fibers was notaffected by the amount of tensile reinforcement ratio. However, the concrete compressive strength influenced the fiber contributionsignificantly. The flexural rigidity increases as the concrete compressive strength and steel fiber content increases. The transitionof effective moment of inertia from uncracked to fully cracked sections depends strongly on the considered variables. A previouslyproposed formula in the literature for the estimation of the effective moment of inertia is modified to consider the effect of reinforce-ment ratio and concrete compressive strength as well as fiber content. 2000 Published by Elsevier Science Ltd. All rights reserved.

Keywords: Beams (supports); Compressive strength; Cracking; Deflection; Flexural strength; Flexural rigidity; High-strength concrete; Moment of

inertia; Reinforced concrete; Steel fibers; Tensile reinforcement ratio

1. Introduction

The maximum potentiality of high-strength concrete(HSC) cannot be realized fully in structures due to thebrittleness of the material and the serviceability prob-lems associated with the resulting reduced cross-sec-tional dimension. Addition of fibers to high-strength con-crete converts its brittleness into a more ductile behavior.When concrete cracks, the randomly oriented fibersarrest both microcracking and its propagation, thusimproving strength and ductility. Addition of fibers onlyslightly influences the ascending portion of the stress-strain curve but leads to a noticeable increase in the peakstrain (strain at peak stress) and a significant increase inductility [1,2].

Researches conducted on the flexural behavior of fiberreinforced concrete (FRC) beams have been concen-

* Corresponding author. Tel.: +966-2-695-2488; fax: +966-2-695-

2179.

E-mail address:[email protected] (S.A. Ashour).

0141-0296/00/$ - see front matter 2000 Published by Elsevier Science Ltd. All rights reserved.

PII: S0 1 4 1 - 0 2 9 6 ( 9 9 ) 0 0 0 5 2 - 8

trated on the prediction of the ultimate flexural strengthand the load deformation behavior in terms of variousmaterial parameters [315]. Less attention was given tothe flexural rigidity of FRC beams in the service loadrange. Several methods have been proposed for calculat-ing the deflections of reinforced concrete flexural mem-bers subjected to short and long-term loadings [1620],however, those methods deal mainly with nonfibrousconcrete, and differences may exist for FRC beams.

The determination of short-term deflection requiresthe estimation of the moment of inertia, I, of the beamwhich depends on the degree of cracking that has takenplace in the member. For loads below the cracking load,computation of deflection may be based on the grossconcrete section, Ig. However, as the load increasesabove the cracking load, the member will crack at dis-crete intervals because the tensile strength of the con-crete has been exceeded, and all tensile stress is carriedby the steel reinforcement. The neutral axis will fluctuatebetween cracks causing variation of the curvatures alongthe member length and reducing the flexural rigidity ofthe section. The value ofIchanges along the beam span


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1135S.A. Ashour et al. / Engineering Structures 22 (2000) 11451158

Fig. 1. Details of test beams and testing arrangement.


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1136 S.A. Ashour et al. / Engineering Structures 22 (2000) 11451158

Table 1

Concrete mix proportioning

Mix Mix W/C Super- Silica fcDesignation Proportion Ratio plasticizer Fume (MPa)

C:FA:CA (%) (%)

(1) (2) (3) (4) (5) (6)

N 1:1:2 0.37 2 0 49

M 1:1.2:1.8 0.24 6 0 79

H 1:1:2 0.23 6 20 102

Table 2

Experimental modulus of elasticity, Ec (MPa)

Vf(%)

0.0 0.5 1.0

Mix Designation (1) (2) (3) (4)

N 24612 26823 30131

M 35443 37169 38247

H 38423 40241 41889

effect of concrete compressive strength, tensilereinforcement ratio and steel fiber content on the deflec-tion and strength of reinforced concrete beams. Modifi-cations to a previously proposed formula for the effec-tive moment of inertia are presented.

Fig. 2. Compressive stress-strain diagram of concrete cylinders.

Fig. 3. Experimental secant modulus of concrete.

2. Experimental program

2.1. Test specimen

Twenty seven fiber reinforced concrete beams weretested in this investigation. All beams were singlyreinforced and provided with shear reinforcement exceptat the constant moment zone. The variables were theconcrete compressive strength,fc, the steel fiber content,Vf, and the longitudinal tensile reinforcement ratio, r.The compressive strengths used were 49, 79 and 102MPa, the fiber contents were 0.0, 0.5 and 1.0% by vol-


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Table 3

Mechanical properties of test beams

Beam (1) As (2) r (%) (3) Vf(%) (4) fc (MPa) (5) fr (MPa) (6) fsp (MPa) (7)

B-0.0-N2 218 1.18 0.0 48.61 5.64 3.69

B-0.5-N2 218 1.18 0.5 55.82 5.88 4.67

B-1.0-N2 218 1.18 1.0 65.16 7.95 6.72B-0.0-N3 318 1.77 0.0 48.61 5.64 3.69

B-0.5-N3 318 1.77 0.5 55.82 5.88 4.67

B-1.0-N3 318 1.77 1.0 65.16 7.95 6.72

B-0.0-N4 418 2.37 0.0 48.61 5.64 3.69

B-0.5-N4 418 2.37 0.5 55.82 5.88 4.67

B-1.0-N4 418 2.37 1.0 65.16 7.95 6.72

B-0.0-M2 218 1.18 0.0 78.50 7.04 5.05

B-0.5-M2 218 1.18 0.5 81.99 7.24 6.01

B-1.0-M2 218 1.18 1.0 87.37 9.75 7.69

B-0.0-M3 318 1.77 0.0 78.50 7.04 5.05

B-0.5-M3 318 1.77 0.5 81.99 7.24 6.01

B-1.0-M3 318 1.77 1.0 87.37 9.75 7.69

B-0.0-M4 418 2.37 0.0 78.50 7.04 5.05

B-0.5-M4 418 2.37 0.5 81.99 7.24 6.01

B-1.0-M4 418 2.37 1.0 87.37 9.75 7.69B-0.0-H2 218 1.18 0.0 102.40 9.36 5.59

B-0.5-H2 218 1.18 0.5 106.93 10.13 6.53

B-1.0-H2 218 1.18 1.0 111.44 11.23 8.13

B-0.0-H3 318 1.77 0.0 102.40 9.36 5.59

B-0.5-H3 318 1.77 0.5 106.91 10.13 6.53

B-1.0-H3 318 1.77 1.0 111.44 11.23 8.13

B-0.0-H4 418 2.37 0.0 102.40 9.36 5.59

B-0.5-H4 418 2.37 0.5 106.93 10.13 6.53

B-1.0-H4 418 2.37 1.0 111.44 11.23 8.13

ume, and the longitudinal tensile reinforcement ratiosused were 1.18, 1.77 and 2.37%.

Fig. 1 presents the detailed testing program. Eachbeam is designated to indicate the fiber content, com-pressive strength level and amount of longitudinalreinforcement. Thus, Beam B-1, 0-M3 represents a beamwith 1.0% fiber content, medium compressive strengthof approximately 79 MPa, and three 18 mm diametersteel bars that provide a reinforcement ratio of 1.77%.

2.2. Materials

Deformed steel bars having yield strength of 530 MPa(76 800 psi) were used as flexural reinforcements. Threeconcrete mix proportions were used to provide therequired compressive strengths as presented in Table 1

Ordinary Portland cement (Type-I), desert sand witha fineness modules of 3.1, and coarse aggregate (crushedbasalt) of 10 mm (3/8 in.) maximum size were used.Light gray densified microsilica (20% by weight ofcement) with a specific gravity of 2.2, a bulk density of6.0 kN/m3 (37.4 lb/ft3) and a specific surface of 2.3 m2/gwas used for the high-strength concrete mix (H).Hooked-ends mild carbon steel fibers with averagelength of 60 mm (2.36 in.), nominal diameter of 0.8 mm(0.03 in.), aspect ratio of 75 and yield strength of 1100MPa (159 500 psi) were used. A superplasticizer was

used, and enough mixing time was allowed to produceuniform mixing of concrete without any segregation.

Six 150300 mm (612 in.) cylinders were cast todetermine the concrete compressive and splitting tensilestrengths. Additionally, three 150150530 mm(6621 in.) prisms were cast to determine the modulusof rupture of the concrete used. The concrete was placedin three layers and was vibrated internally and externallyimmediately afterward. All beams and control specimenswere cast and cured under similar conditions. The beamsand specimens were kept covered with polyethylenesheets for 28 days until 24 hours before testing.

2.3. Test procedure

The test beams were simply supported and were sub-jected to two-point loads as shown in Fig. 1. The dis-tance between the two loading points was kept constantat 500 mm (20 in.). The beam midspan deflection and theend rotation were measured with the help of transducers.Strains in the tensile steel were measured by electricalfoil-type strain gages. Compressive strains at the centerof the top surface of the concrete at three locations weremeasured with electrical resistance wire-type straingages. These gages were located in the constant momentzone at midspan. The load was applied in 25 to 35increments up to failure by means of a 400 kN (90 kips)


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hydraulic testing machine. At the end of each loadincrement, observations and measurements wererecorded for the midspan deflection, end rotation, straingage readings, and crack development and propagationon the beam surfaces.

Fig. 4. Mechanical properties of test beams (a) Concrete compressive

strength, fc; (b) Modulus of rupture, fr; (c) Splitting tensile strength,

fsp.

3. Experimental results

3.1. Compressive stress-strain diagram

Fig. 2 shows the stress-strain diagram of 150300concrete cylinder tested in compression. The effect of

steel fibers is obvious on the stress-strain diagramespecially for the lower strength concrete (fc=49 MPa).As the fiber content increases the maximum compressivestrength increases slightly, and the slope of the ascend-ing portion increases accordingly. The ascending part ofthe high-strength concrete (fc=102 MPa) is almost astraight line up to the maximum compressive strength.The concrete secant modulus, Ec, was evaluated at astress level of 0.5 fc and is given in Table 2 and Fig.3. The secant modulus of concrete, Ec, is increased asVf and fc increase. The increase of the fiber contentsfrom 0.0 to 1.0% increasesEcby 22.4, 7.9 and 9.0% forconcrete with f

c

of 49, 79 and 102 MPa, respectively.Table 3 and Fig. 4 present the mechanical properties

of the FRC used in the test beams. The increase of thefiber contents from 0.0 to 1.0% increases the compress-ive strength by 34.0, 11.3 and 8.8%, increases the modu-lus of rupture by 41.0, 38.5 and 20.0%, and increasesthe splitting tensile strength by 82.1, 52.3 and 45.4% forconcrete with 49, 79 and 102 MPa compressivestrengths, respectively.

3.2. Flexural behavior

The test beams were designed to fail in flexure. All

beams exhibited vertical flexural cracks in the constant-moment region before final failure of the beams due tocrushing of concrete. The presence of fibers reduced thecrack width, increased the number of cracks, increasedthe ductility, and delayed the final crushing of concrete.The effectiveness of steel fibers in arresting cracks isrelated to the average spacing of fibers inside the matrix.The spatial distribution and orientation of fibers in FRCbeams are random, however, boundary conditions suchas edges constrain the fiber orientation in a uni-direc-tional alignment.

Fig. 5 shows the load versus deflection relationshipsfor all test beams. The test results clearly show the fiberscontribution on the stiffnesses and strengths of allbeams. The fibers have a clear enhancement of the postcracking stiffness and ductility (area under P- curve)for all beams.

Table 4 presents the experimental cracking moment,Mcr(exp), the moment at first yielding of the flexuralreinforcement,My(exp), and the ultimate moment, Mu(exp),of the test beams. Test results show that the increase ofVfincreaseMcr(exp),My(exp), andMu(exp), for all test beamsirrespective to the fc and r values. However, theincrease due to the presence of fibers is reduced as rincreases.


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Fig. 5. Load deflection curves for beams.

The additional moment enhancement at ultimate stagedue to the presence of steel fiber, Mf, can be estimatedas the difference between the ultimate moments ofbeams with Vfof 0.0 and 1.0%, and are shown in Table5 and Fig. 6. The figure shows that the increase of fcincreasesMf, however, a lower rate of increase is noticedwhen fc increases from 79 to 102 MPa. Fig. 6 alsoshows that the value of r has no effect on Mf. Theenhancement of the flexural capacities varies between7.52 and 26.43%.

3.3. Cracking moment

The analytical evaluation of deflection depends gre-atly on the cracking moment of the beam. The theoreticalcracking moment Mcr(th) is estimated as:

Mcr(th)frIg

yt(2)

The use of the untracked transformed moment of iner-tia, Iut, instead ofIg in Eq. (2) will give a better predic-tion ofMcr(th), Fig. 7 shows the variation ofMcr(exp)/Mcr(th)ratio as a function of fiber content and concrete com-

pressive strength for the different reinforcement ratios.The figure shows that the experimental crackingmoments are about 55 to 85% of the theoretical crackingmoments calculated using the modulus of rupture values.Thus, the use offr, to calculate the cracking moment Eq.(2) overestimated the experimental cracking moments,and this overestimation increases as the concrete com-pressive strength increases. This is attributed to the sizeeffect phenomena. For normal and medium concretestrengths, the value of Mcr(exp)/Mcr(th) ratio increases asVf increases from 0.0 to 0.5%, and thereafter decreasesas Vfincreases to 1.0%.

3.4. Neutral axis depth

The experimental neutral axis depth, c, of the testbeams is obtained from the experimentally measuredstrain values in the concrete and the tensile reinforce-ment. The variation of the ratio ofc to the effective depthof the section, d, in the constant moment zone is shownin Fig. 8. For loading levels below the cracking load,Ma/Mcr=1, the c/d ratio is about 0.6. When cracksoccurred, the neutral axis shifted upward and the c/dvalue drops to a value of about 0.4 and remains constant


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Table 4

Experimental and theoretical results of test beams

Beam (1) Mcr(exp) (kN- My(exp) (kN- Mu(exp) (kN- Icr(exp) Icr(th) (Ec.Icr)exp m (8) c/d(th) (9) c/d(exp) (10)

m) (2) m) (3) m) (4) (mm4103) (mm4103) (109N-

(5) (6) mm2) (7)

B-0.0-N2 8.02 50.29 58.17 103.14 110.81 2.54 1.96 0.355 0.290B-0.5-N2 9.39 54.47 60.17 94.84 104.14 2.54 1.97 0.343 0.331

B-1.0-N2 9.61 60.27 64.50 98.22 95.34 2.96 1.49 0.328 0.326

B-0.0-N3 8.64 74.40 77.08 126.78 147.51 3.12 1.55 0.415 0.359

B-0.5-N3 9.92 74.85 83.8 117.67 139.07 3.16 1.56 0.402 0.392

B-1.0-N3 11.51 86.35 87.72 119.38 128.25 3.60 1.10 0.385 0.390

B-0.0-N4 9.82 94.06 98.37 153.08 178.28 3.77 1.19 0.460 0.384

B-0.5-N4 11.29 101.22 103.98 135.30 168.67 3.63 1.34 0.447 0.423

B-1.0-N4 11.51 105.04 105.77 96.48 135.16 2.91 0.88 0.428 0.441

B-0.0-M2 8.97 49.51 55.27 77.09 84.23 2.73 2.36 0.307 0.246

B-0.5-M2 9.82 56.58 63.34 76.38 81.09 2.84 2.37 0.301 0.247

B-1.0-M2 11.51 65.13 69.88 78.90 79.40 3.02 1.61 0.298 0.355

B-0.0-M3 9.81 75.16 80.86 86.91 114.15 3.08 2.14 0.361 0.312

B-0.5-M3 10.97 80.97 89.62 98.85 110.30 3.67 2.03 0.355 0.348

B-1.0-M3 11.82 86.77 92.05 105.22 108.73 4.02 1.34 0.351 0.380

B-0.0-M4 10.56 97.44 103.77 108.81 138.94 3.86 1.72 0.403 0.362B-0.5-M4 12.56 109.36 113.59 114.80 135.54 4.27 1.52 0.396 0.385

B-1.0-M4 13.67 113.48 115.70 104.79 132.74 4.01 1.19 0.392 0.402

B-0.0-H2 9.18 48.56 55.89 75.21 82.48 2.89 3.23 0.297 0.226

B-0.5-H2 10.77 58.27 62.60 70.75 77.08 2.85 2.5 0.292 0.259

B-1.0-H2 11.82 68.93 69.25 73.49 73.96 3.08 1.96 0.287 0.292

B-0.0-H3 10.35 77.48 82.76 82.71 109.12 3.18 2.13 0.350 0.308

B-0.5-H3 11.54 84.35 89.84 91.00 104.01 3.66 2.43 0.344 0.348

B-1.0-H3 13.20 91.31 95.64 85.67 100.96 3.59 1.84 0.338 0.333

B-0.0-H4 11.82 100.91 108.10 100.31 132.31 3.85 1.85 0.391 0.344

B-0.5-H4 12.77 107.78 114.96 108.84 128.07 4.38 1.52 0.385 0.356

B-1.0-H4 14.78 113.38 120.61 107.81 124.48 4.52 1.91 0.379 0.338

Table 5Moment enhancement due to fibers addition (%)

Concrete compression strength

r (%) N M H

1.18 10.88 26.43 23.90

1.77 13.8 13.84 15.56

2.37 7.52 11.50 11.57

upto the yielding of the reinforcement. Some fluctuationsof the c/dvalues took place at low level of loading dueto the sensitivity of the strain gage readings speciallybefore cracking. It is noticed that the value of c doesnot vary between the cracking and yielding levels. Fora specific level of loading, Ma/Mcr, the neutral axis depthis larger for the lower compressive strength, irrespectiveof the amount of flexural reinforcement. The c valueincreases as Vf increases, and this is attributed to thedecrease in curvature of the beam, and also due to thatthe fibers bridge the cracks and reduce crack widthwhich in turn reduce the strain in the tension zone. Thetheoretical depth of the neutral axis can be obtained fromthe statistical moment given by:

Fig. 6. Fiber contribution in moment enhancement.

bc2

2nAs(dc)

20 (3)

Table 4 gives the theoretical and experimentalc/dvaluesfor the tested beams. The theoretical values generallyunderestimated the experimental values, however, forbeams with 1.0% fiber content the theoretical c/dvaluesoverestimate slightly the experimental values.


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Fig. 7. Ratio of experimental to theoretical cracking moment.

3.5. Experimental moment of inertia

Based on the elastic deformation theory, the experi-mental moment of inertia of a simply supported beamsubjected to a two-points load is obtained as:

IexpPa(3l24a2)

48Ecexp(4)

where;P=applied load; a=shear arm;l=clear span of thebeam; exp=experimental midspan deflection;Ec=experi-mental secant modulus of elasticity of concrete.

However, as shown in Fig. 2 the value of Ec varies

as a function of load level, therefore it is more appropri-ate to consider the effect of the fc, rand Vfon the flex-ural rigidity, (Ec.I)exp, of the beam rather than consider-ing the experimental moment of inertia, Iexp, alone. Fig.9 shows the variation of (Ec.I)exp obtained using Eq. (4)as a function of level of loading, Ma/Mcr. In general, the

flexural rigidity increases with the increase of the fibercontent.

The effect of concrete strength on the experimentalflexural rigidity is shown in Fig. 10. For beams with nofibers, fc has very little effect on (Ec.I)exp, however, forbeams with fibers, fc has a significant influenceespecially for beams with high r, The test results showthat the higher the flexural reinforcement ratio, thehigher the flexural rigidity and the lesser the rate of tran-sition of the flexural rigidity from the uncracked to fullycracked section values. This suggests that the exponentin Bransons equation Eq. (1) is inversely proportionalto r, which supports the conclusion by Al-Sheikh et al.[26] that the exponent of 3 in Bransons equation shouldbe reduced as r increases.

3.6. Cracked moment of inertia

The value ofIexp is assumed to approach Icr(exp) whenthe applied moment approaches My, which is a realisticassumption [25]. At that level of loading, the Mcr/Maratio is quite small and the contribution of Ig in Eq. (1)is negligible. The calculation of deflection during theservice stage of a structure depends mainly on thecracked moment of inertia,Icr. The experimental cracked

moment of inertia is obtained by considering:

Icr(exp)Pya(3l

24a2)

48Ecexp(5)

where Py=the load that causes yielding in the steelreinforcement.

The values ofIcr(exp)and (EcIcr)exp, are calculated usingEq. (5) and are presented in Table 4. The value ofIcr(exp)decreases asVfincreases, however, the value of (EcIcr)expincreases as Vf increases.

3.7. Modification of Bransons equation

In the evaluation of the deflection of the test beams,the determination of Mcr, Ec, and Icr, are the requiredparameters in calculating Eq. (1). These parameters con-trol the serviceability and deflection calculation.

Al-Sheikh et al. [26] proposed the following formulato include the effect of reinforcement ratio in Bransonsequation [18]:

IeMcrMa

mIg1McrMa

mIcr (6)where m=30.8r.


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Fig. 8. Behavior of neutral axis depth.

Eq. (6) was based on beams with 33 MPa concretecompressive strength. Ashour [23] showed that the tran-sition rate of Ie from Ig to Icr drops quicker as fcincreases, and proposed a modification on Bransonsequation to consider the effect of fc as:

m30.8r33fc (7)where fc33 MPa.

The experimental variation of the exponent m in Eq.(6) as a function of the level of loading, Ma/Mcr, can be

evaluated by replacing Ieand Igby the values ofIexpandIut respectively:

m

logIexpIcr(exp)IutIcr(exp)

logMcr(exp)

Ma

(8)

The variation ofm obtained from Eq. (8) as a functionof Ma/Mcr, is shown in Fig. 11 for all test beams. Ingeneral, the value ofm increases as fc increases and Vfand r decrease.

Fig. 11 shows that the value ofm for each test beamhas an almost constant value for level of loadings Ma/Mcrbetween 1.5 to 6.0. The experimental average value ofm obtained for each beam within this range of level ofloading is given in Table 4.

Based on the test results, a regression analysis is per-formed and an empirical formula that incorporates theconsidered variables (r, fc and Vf) in the expression ofm is proposed as:

m

30.8r33fc1+0.4Vf (9)

For beams with no fibers and with 33 MPa compress-ive strength, Eq. (9) is reduced to Eq. (6).

The deflection calculation requires the determinationof other factrors such as Mcr, Ec and Icr. The variationsof the secant modulus of concrete in terms of fc and Vfare given in Fig. 12. Based on regression analysis, thesecant modulus of FRC,Ecf, in terms of the that of plainconcrete, Eco is given as:

EcfEco(1600(Vf

fc)2) (10)


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Fig. 9. Experimental flexural rigidity as a function ofVf.

where Eco for high-strength concrete is given as [27]:

Eco3200fc6900 (11)

Eqs. (10) and (11) are presented in Fig. 12. The equa-tions give good estimation of the experimental values,however, the equations overestimate the value for nor-mal strenth concrete. As discussed earlier and shown inFig. 7, the ratio of Mcr(exp)/Mcr(th) are about 55 to 85%.Thus the use of fr to calculate the cracking moment Eq.(2) overestimated the experimental values. Thus areduced value offrshould be used to predict with reason-

able accuracy the beam deflection:

Mcr(th)0.6frIg

Yt(12)

Ashour [23] proposed an equation to predict the theoreti-cal cracked moment of inertia and is given as:

Icr(th)Icr[1.1290.0011fc0.0133r] (13)

where Icr is the cracked moment of inertia and isgiven by:

Icr

bc3

3nA

s(dc)2 (14)

where n=Es/Ecfand c is the neutral axis depth.The predicted deflections of the test beams are evalu-ated in terms ofm (Eq. (9)), Mcr (Eq. (12)) and Icr (Eq.(13)), and the values are presented in Fig. 13. The figureshows that the predicted deflections give good estimationof the experimental values.

4. Conclusions

Based on the test results of twenty seven reinforcedconcrete beams tested in flexure, the following con-clusions are drawn:

1. The presence of steel fibers reduces the crack propa-gation in the tested beams.

2. The flexural rigidity increases as fc and Vfincreases.3. The increase of the fiber content increase the crack-

ing, the yielding and the ultimate moments.4. The predicted cracking moments estimated in terms

of the modulus of rupture overestimated the experi-mental values.

5. Additional moment strength due to the presence offibers is almost independent of the amount ofreinforcement,r. However, this additional moment isproportional to concrete compressive strength, fc.


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Fig. 10. Experimental flexural rigidity as a function of fc.

Fig. 12. Theoretical secant modulus of concrete.

6. The rate of decay of the beam effective moment ofinertia from the untracked transformed to a fullycracked section is lower for beams with fibers thanthat of beams with no fibers.

7. The exponent, m, in Bransons equation decreases asVfincreases, however, it increases as fc increases.


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Fig. 11. Variation of exponent, m, in Eq. (7).

Fig. 13. Prediction of deflection for some test beams.


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ashour et al_1999_effect of the concrete compressive stength and tensile reinforcement ratio

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