Journal of King Saud University – Engineering Sciences (2016) 28, 147–156King Saud UniversityJournal of King Saud University – Engineering L ARTICLEA study of factors affecting the flexural tensilestrength of concreteMohd. Ahmed *, Javed Mallick, Mohd. Abul HasanCivil Engineering Department, Faculty of Engineering, King Khalid University, Abha, Saudi ArabiaReceived 6 February 2014; accepted 8 April 2014Available online 19 April 2014KEYWORDSCompressive strength;Flexural tensile strength;Modulus of rupture;Statistical procedures;Concrete confinement;Age of concreteAbstract The deflection and cracking behavior of concrete structure depend on the flexural tensilestrength of concrete. Many factors have been shown to influence the flexural tensile strength of concrete, particularly the level of stress, size, age and confinement to concrete flexure member, etc. Theconcrete members, in general, are of large continuous size and have at least minimum reinforcementintroducing a confining effect to the concrete. The confining reinforcement increases ductility andlarge deflections in structures provide a good warning of failure prior to complete failure of the flexure member and also for efficient use of constructional material, it is desirable to take full advantageof long-term strength gain. Therefore, the effect of the factors like level of stress, age and confinement of concrete member should be given prime importance while studying the flexure tensilestrength of concrete. This paper presents an experimental study done to predict the flexural tensilestrength considering the confinement conditions and age of concrete for a wide range of concretestrengths (from 30 to 85 MPa). It is concluded that the factors like confinement conditions andage of concrete should be given due consideration in deriving the flexural tensile strength and compressive strength proportionality equations.ª 2014 Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open accessarticle under the CC BY-NC-ND license ).1. IntroductionThe cracking and deflection behavior of concrete structureunder flexure and minimum flexural reinforcement of concretemembers depends upon the flexural tensile strength or modulus of rupture of concrete in addition to other factors. The* Corresponding author. Tel.: 966 17 2418439.E-mail address: moahmedkku@gmail.com (Mohd. Ahmed).Peer review under responsibility of King Saud University.Production and hosting by Elsevierequations proposed to determine the flexural tensile strengthare of the power equation type: flexural tensile strength, fr bfcn where fc is the compressive strength of the concrete and,b (varies from 0.33 to 0.94) and n (1/2 or 2/3) are coefficientswhich depend on factors such as strength levels, aggregateproperties and mineralogy, admixtures types, moisture contentof specimen, compaction and curing conditions, specimengeometry and confinement, age of concrete, etc. The valuereported for the flexural tensile strength by various investigators and standards in square root form (n 1/2) ranges from0.3 to 1.0 fc0.5 MPa (Ahmed et al., 2008). Légeron and Paultre(2000) have derived equations for flexural tensile strengthusing published database as fr,min 0.68 fc0.5, fr,avg 0.94fc0.5 fr,max 1.2 fc0.5, where fr,min, fr,avg and fr,max are the 1018-3639 ª 2014 Production and hosting by Elsevier B.V. on behalf of King Saud University.This is an open access article under the CC BY-NC-ND license ).
148Mohd. Ahmed et al.imum, average and maximum values of the modulus of rupture. They also recommended to use fr,min for deflection andcrack control and fr,max to behave as flexure member in a ductile manner. Raphael (1984) was the first to use power equation(n 2/3) for predicting the flexural tensile strength of highstrength concrete based on its compressive strength. One ofthe reasons for variation in reported flexural tensile strength,explained by Raphael (1984), is that the co-relating equationsare derived from elastic theory, which assumes elastic behaviorof concrete to the point of failure. Abdul Razak and Wong(2004) have conducted a test on high performance concreteto evaluate the strength relationship and concluded that thesquare-root function recommended by most codes of practiceis inadequate when applied to concretes of higher strength,particularly in the case for tensile strength prediction. The flexural strength co-relation studied for manufactured sand in selfcompacting concrete is mentioned by Kothai and Malathy(2012). Ahmed et al. (2014) have assessed the square root(n 1/2) and power model (n 2/3) proportionality equations relating flexural tensile strength and compressive strengthreliability and concluded that power model is more reliableand applicable to a large range of concrete strength level.The researchers have also devoted their work to study thefactors causing variability in flexural tensile strength of concrete. The effect of curing of concrete member on flexural tensile strength, cured under standard testing conditions andcured under site conditions, is studied by Légeron andPaultre (2000). They found significant differences betweenthe modulus of rupture of concrete specimens and this difference is varied from 35% to 100% for HPC. The effect ofadmixtures of the concrete on flexural tensile strength is studied by Siddiqui (2011) and Amudhavalli and Mathew (2012).They concluded that optimum amount of silica fume is 10–15% and of fly ash is about 15% for maximum compressiveand flexural strength. Gonen and Yazicioglu (2009) carriedout research work on the influence of mineral admixtureson the short and long term performance of concrete and concluded that silica fume contributed to both short and longterm properties of concrete, where as fly ash shows its beneficial effect in a relatively longer time. Koksal et al. (2008)have conducted the flexural strength testing of concrete incorporating hooked steel fibers and silica fume. They foundgreater flexural strengths of concretes containing 1% steelfiber than those of the concrete with 0.5% steel fiber with various silica fume contents. The standard test method for theflexural tensile strength of concrete with its size dependenceis proposed by Bazant and Novak (2001). They concludedthat the flexural tensile strength decreases with increase ofstructural element size. Ahmed et al. (2014) have studiedthe effect of the size of specimen on the flexural tensilestrength of concrete. They concluded that the concretemember size has a significant effect and proposed an equationincorporating the effect of size of concrete for predicting theflexural tensile strength of concrete given as, fr ¼ 0:827f2/3c ,h0;1where MOR(t) is the flexural tensile strength at any given time(t, in days), t is the age of concrete (day), and MOR28d is flexural tensile strength at 28 days.A review of past studies indicates that in spite of numerousworks reported on flexural tensile strength, little attention hasbeen paid to study the parameters affecting the flexural tensilestrength of concrete. The effect of the factors like age and confinement of concrete on flexural strength has not been investigated properly and proper inter-dependency of various factorsthat affect the flexural strength has not been co-related. Theeffect of confinement on flexural tensile strength is an interesting issue as most of the concrete members are of large continuous size and other smaller size members have at leastminimum reinforcement giving the confining effect to the concrete members. The confining reinforcement increases ductilityand large deflections in structures, providing a good warningof failure in the form of tensile cracks prior to complete failureof the flexure member. In the available literature, the relationship for predicting flexural tensile strength of low strength andhigh strength concrete has been reported separately. The combined effect of low and high strength including the transitionfrom normal strength to high strength of concrete on flexuraltensile strength may also be investigated. For efficient use ofconstructional material, it is desirable to take full advantageof long-term strength gain. Therefore, the flexural tensilestrength of concrete should be further investigated for a widerrange of concrete strengths considering the long term and confinement conditions of members. The present study is devotedto investigate the flexural tensile behavior under concrete confinement using four concrete mixes having 28-days compressive strength ranges from 30 MPa to 85 MPa. The flexuraltensile behavior of concrete at 7 days and 56 days concretestrength has also been studied at different confinement conditions of concrete.where fc is compressive strength and h is depth of beamin mm. NCHRP (2004) has proposed an equation to determine the flexural tensile strength (MOR) at different age, if28-day flexural tensile strength of concrete is given, as t t 2 0:01566log10MORðtÞ 1þlog10 MOR28d0:07670:07672.2. Admixture2. Materials and methodologyAn experimental program was carried out in the present workto investigate the flexural tensile strength of concrete takinginto consideration the level of compressive strength of concrete, age of concrete and confinement of concrete specimen.2.1. Cement and aggregatesType- I Ordinary Portland cement with specific gravity 3.15was used. The initial and final setting times were found as60 min and 300 min respectively. Fine aggregate used is ordinary siliceous sand with a fineness modulus and the specificgravity of 2.61 and 2.45 respectively. Crushed Basalt of nominal maximum size of 10 mm was used as coarse aggregate. Thespecific gravity of coarse aggregate is found to be 2.75. Thecoarse aggregates have water absorption of 1.01% in SSDcondition.Super plasticizer is used to obtain a constant slump of 10 cmfor all concrete mix. Silica fume is used as a partial replacement for cement on equal weight basis.
Factors affecting the flexural tensile strength of concrete149cured in water for 7-days, 28-days and 56-days. The minimumreinforcement is provided for confined beam specimen tests.The reinforcement details for confined beam specimen aregiven in Fig. 2. The beam specimen is simply supported ontwo rollers of 4.5 cm diameter. The flexural tensile strength iscalculated as the ratio of the calculated bending moment andsection modulus of the beam specimen and is presented inTables 2 and 3. Table 4 show the flexural tensile strength afterdeducting the flexural tensile strength (approximate) ofprovided reinforcement. The flexure test set-up is shown inFig. 3.2.3. Mix proportionIn this study, four different concrete mixes were used. Mix proportion for each mix is given in Table 1. These mixes weredesigned to achieve different concrete compressive strength.2.4. Concrete propertiesSlump test according to ASTM C143 (1978) was done on thefresh concrete while tests for compressive strength and flexuraltensile strength, were carried out on hardened concrete.3. Result and discussion2.4.1. Compressive strength testCompression test on the 150 mm diameter · 300 mm heightcylinder specimens was conducted on the 1000 kN universaltesting machine. The specimens were cured in water for 7-days,28-days and 56-days. The cube compressive strength is calculated as crushing load per unit area and is presented in Table 2.For each mix three specimens were tested and average valuesare reported. The compression test set-up is shown in Fig. 1.The results of flexural tensile strength experimental study aregiven in Tables 2–4 for different concrete mixes at 7-days,28-days and 56-days and specimens under different confinement. Table 5 depicts the level of concrete strength effect onthe flexural tensile strength without confining conditions ofconcrete. It is clear that the flexural tensile strength increaseswhen the compressive strength and age of the concreteincrease. Moreover, the increase in the flexural strength islower than the corresponding increase in the compressivestrength at same age of concrete. The percentage increase inflexural tensile strength decreases with the increase of level ofconcrete strength. For compressive strength of 24.1 MPa,2.4.2. Flexural tensile strength testThe Three-Point bending test is conducted on a loading frameto determine the flexural tensile strength on standard beamspecimens of size 750 · 150 · 150 mm. The specimens wereTable 1Mix ingredients for different mixes.MixCement content (kg/m3)Sand (kg/m3)Basalt (kg/m3)Silica fume (%)w/(c 0100100.520.330.260.26Table 2MixIIIIIIIVCompressive and flexural tensile Strength (without confining reinforcement).Compressive strength (MPa)Flexural strength 555.445.64.856.126.846.965.357.088.158.29Figure 1Compression test set-up.
150Mohd. Ahmed et al.Figure 2Table 3MixIIIIIIIVConfined beam specimen detail.Compressive and flexural tensile strength (with confining reinforcement).Compressive strength (MPa)Flexural strength Table 4 Compressive and flexural tensile strength (withconfining condition after deducting reinforcement strength).MixCompressiveStrength (MPa),28-daysFlexuralStrength 219.12Figure 3Flexure test set-up.31.8 MPa and 37.7 MPa, the flexural strength are 3.17 MPa,4.85 MPa and 5.35 MPa at 7-days, 28-days and 56-daysrespectively whereas for compressive strength of 58.7 MPa,81.2 MPa and 98.6 MPa, the flexural tensile strength are5.6 MPa, 6.96 MPa and 8.29 MPa respectively on same corresponding ages. It is due to the different concrete compressionand flexure failure mechanism of low and high strength concrete. The crack began in the interface region due to tensilestrain produced by the compressive load and then micro crackextended into the mortar matrix. Under the flexure loading,the cracks are initiated in the interfacial zone at low stressesand extend into the mortar matrix at high stresses and theresistant to cracks results from the cement paste only.Table 6 and Fig. 4 show the effect of confinement conditions on flexural tensile strength of concrete with different levelof concrete strength. The flexural tensile strength increasesunder confinement at different level of strength and theincrease in flexural tensile strength decreases with the increaseof level of concrete strength under the confining condition ofconcrete.Table 7 shows the effect of confinement conditions on flexural tensile strength of unconfined concrete. The percentageincrease remains more or less the same with the increase ofage of concrete at same level of strength of concrete but withthe increase of level of stress, the flexural tensile strengthincreases many fold. This is attributed to the behavior of compression and tension zone of flexure concrete member underconfining condition at different age of concrete. The initiatedcracks in tension zone are arrested and whole compressionzone is also divided into smaller component zones due thepresence of confinement reinforcement. For compressivestrength of 24.1 MPa, 31.8 MPa and 37.7 MPa at 7-days, 28days and 56-days, corresponding percentage increase of theconfined flexural tensile strength over unconfined flexural tensile strength are respectively 66.9%, 46.8% and 61.7%. Forcompressive strength of 58.7 MPa, 81.2 MPa and 98.6 MPa,the confined flexural tensile strength percentage increase to202.9%, 228.6% and 231.3% at 7-days, 28-days and 56-daysrespectively. Table 7 also shows the confined flexural tensilestrength after deducting the flexural tensile strength of provided reinforcement simulating the large continuous concretemember. The maximum increase in the flexural tensile strengthis still 175% over the unconfined flexural tensile strength evenafter deducting the flexural tensile strength of reinforcement.Table 8 presents the effect of age of concrete on flexure tensile strength under different confining conditions of concrete.It is inferred from the table that the flexural tensile strengthincreases with the age of concrete. There is no clear relation-
Factors affecting the flexural tensile strength of concreteTable 5Mix151Effect of level of concrete strength on flexural tensile strength (unconfined).Compressive Strength, fc (MPa)Flexural strength, fr (MPa)7-days (% increasein level of stress)28-days (% increasein level of stress)56-days (% increase inlevel of stress)7-days28-days56-daysIIIIIIIV24.130.9 (28.2%)58.5 (89.3%)58.7 (0.34%)31.844.95 (41.4%)78.2 (74.0%)81.2 (3.8%)37.758.5 (55.2%)89.0 (52.1%)98.6 (10.8%)3.174.55 (43.5%)5.44 (19.6%)5.6 (2.9%)4.856.12 (26.2%)6.84 (11.8%)6. 96 (1.7%)5.357.08 (32.3%)8.15 (15.1%)8.29 (1.7%)Table 6Effect of level of concrete strength on confined flexural tensile strength.MixFlexural StrengthConfined flexural strength, fr (MPa)IIIIIIIV7-days28-days56-days5.298.74 (65.2%)13.38 (53.1%)16.96 (26.8%)7.9213.38 (68.9%)20.07 (50%)22.87 (13.95%)8.6515.91 (83.9%)24.02 (50.1%)27.53 (14.6%)Figure 4Table 7Mix4.179.63 (130.9%)16.32 (69.5%)19.12 (17.2%)Effect of confinement on Flexural Tensile Strength of unconfined concrete.Effect of confinement over Flexural Tensile Strength of UNCONFINED concrete.Flexural StrengthPercentage increase in confined frover without confinement frIIIIIIIVConfined flexural strength after deductingthe reinforcement strength (at 28-days age)7-days28-days56-daysPercentage increase in confined fr overwithout confinement after deducting thereinforcement flexural strength (at 28-days 194.7231.30.057.4138.6174.7ship between the increase in level of compressive strength andincrease in flexural tensile strength of concrete with increase ofage of concrete under different confining conditions. The per-centage increase in flexural tensile strength at lower age is morethan the percentage increase at higher age of concrete underwith and without confined conditions. The percentage increase
152Table 8MixMohd. Ahmed et al.Effect of age on unconfined flexural tensile strength.Compressive Strength, fc e 5Table 9Flexural Strength, fr (MPa)Percentage increasein fc (28-days to 56-days)Percentage increasein fc (7-days to 28-days)Percentage increasein fr (7-days to 28-days)Percentage increasein fr (28-days to 18.919.720.4Effect of age on flexural tensile strength of concrete.Value of b1 and b2 under different age and confinement conditions.Eqn. modelValue of b1 and b2UnconfinedSquare Root (1/2) 420–0.4300.3130.4840.410.412(2/3) modelFlexural strength (MPa)Compressive strength (MPa)ConfinedAge (days)Age (days)1.6772.0691.58 (deducting reinf.)2.281.4442.4892.1971.9900.8921.0400.791 (deducting reinf.)1.1130.7261.2521.0871.010728285675628 567 28 56728285675628 567 28 567282856282828 567 28 567282856282828 567 28 56in flexure tensile strength at different level of concrete strengthis 53%, 29.6%, 25.7% and 24.3% when age of concreteincreases from 7-days to 28-days while at similar level of concrete strength, percentage increase in flexure tensile strength is10.3%, 15.7%, 19.2% and 19.4% when age of concreteincrease from 28-days to 56-days. The percentage increase inflexural tensile strength of confined concrete at higher age isconstant on various levels of concrete strength while it is
Factors affecting the flexural tensile strength of concrete153Figure 6Comparative analysis of predicted flexure strength of different age and confining conditions using square root model equations.Figure 7Comp
flexural tensile strength of concrete given as, f r ¼ 0:827 h0;1 f c 2/3, where f c is compressive strength and h is depth of beam in mm. NCHRP (2004) has proposed an equation to deter-mine the flexural tensile strength (MOR) at different age, if 28-day flexural tensile strength of concrete is given, as MORðtÞ 1þlog 10 t 0:0767 0 .
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