Construction and Building Materials 30 (2012) 265–273

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Construction and Building Materials

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Experimental investigation to compare the modulus of rupture in high strengthself compacting concrete deep beams and high strength concrete normal beams

Mohammad Mohammadhassani ⇑, Mohd. Zamin Jumaat, Mohammed JameelDepartment of Civil Engineering, University of Malaya, Malaysia

a r t i c l e i n f o

Article history:Received 16 July 2011Received in revised form 3 November 2011Accepted 2 December 2011

Keywords:Deep beamsNormal beamsFirst crackingModulus of rupture

0950-0618/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.conbuildmat.2011.12.004

⇑ Corresponding author. Tel.: +989133420110; fax:E-mail address: mmh356@yahoo.com (M. Moham

a b s t r a c t

This paper investigates and compares the cracking moment and modulus of rupture in deep and normalbeams. Eight high-strength-self-compacting concrete (HSSCC) deep beams and nine high-strength con-crete (HSC) normal beams are casted and tested. The results from ACI 318-95 and CSA-94 codes showthe discrepancies in values of modulus of rupture for HSSCC deep and normal beams. These differencesare due to non-consideration of load transfer mechanism in deep beams and high strength of concrete.Based on the present study ACI 318-95 is recommended for calculating modulus-of-rupture in HSSCCdeep beams whereas CSA-94 is suggested for HSC normal beams.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Development of HSC dates back to the early 1930s, when con-crete compressive strengths above 97 MPa were achieved. With re-cent development in concrete sciences, HSC is defined as concretewith strength more than 41.1 MPa. With the advent of super-plast-icizers and other additives, HSC has now become an economicalsolution for the construction of bridges and tall buildings. Strengthrequirement for commercial concrete has been increasing over theyears. Concrete with strength up to 124 MPa have been success-fully used in some high-rise buildings e.g. the Water Tower Place(Chicago, USA) and the East Huntington, W.V., bridge over the(Ohio River, USA).

Manufacturing of HSC involves making optimal use of the basicmaterials that constitute normal-strength concrete (NSC). Thestrength of the aggregate, the optimum size of the aggregate, thebond between the cement paste and the aggregate, and the surfacecharacteristics of the aggregate influence the ultimate strength ofHSC. It would be difficult to produce HSC mixtures more than70 MPa without using admixture and additives. The properties ofHSC have been studied with different additives by many research-ers [1,2] using different material. Khanzadi and Behnood [1] hadstated that using copper slag aggregate instead of limestone aggre-gate showed an increase of about 10–15% of compressive strengthand 10–18% in tensile strength of HSC. Using various types ofmaterial with different proportions, many grades of HSC with vary-ing mechanical and durability properties can be produced. For in-

ll rights reserved.

+60 3 79675218.madhassani).

stance researcher such as Elahi et al. [2] stated that using silicafume improves strength development better than other supple-mentary cementitious materials.

However, most of the current design codes were developedusing experimental results based on NSC; therefore existing codeslimits the maximum concrete strength based on it. These limita-tions reflect the lack of research development rather than theinability of the material to perform its capacity. Thus adequateinvestigation of its behaviour in structural members is highlydesirable. It is well known that concrete is weak in tension andstrong in compression. Therefore, its primary purpose in a rein-forced concrete structural member is to sustain compressiveforces, while steel reinforcement is used to sustain tensile forces.The concrete protects the steel from corrosion effects of the envi-ronment. As concrete is used to sustain compressive forces, it isessential that its strength and deformational response under suchconditions are determined. In this regard, one of the main param-eter that needs to be investigated is the modulus of rupture, due toinherent drawback of concrete in tension. The other important as-pect is the cracking moment. It is the moment that is required forthe first crack to appear in extreme tension fibre. The importanceof modulus of rupture and cracking moment is, at this point thesteel reinforcement in the beam is exposed to the environmentand possible corrosion. The application of modulus of rupture ismost useful for structures such as concrete dams and nuclear reac-tor vessels, for which the safety concerns are particularly vital andextremely high.

There are many investigations on cracks in concrete structures[3–8] and many researchers studied the modulus of rupture of nor-mal beams experimentally and analytically for high and low

Table 1HSSCC mix design.

Characteristic cube strength 75 MPaAggregate type Crushed granite and natural sandCement type Ordinary Portland cementSlump of concrete More than 650 mmCoarse aggregate content 553 kg/m3

Fine aggregate content 887 kg/m3

Water/binder 0.25Silica fume/cement 0.1

Fig. 1. Workability of HSSCC.

Fig. 2. Casting arrangement of deep beam.

266 M. Mohammadhassani et al. / Construction and Building Materials 30 (2012) 265–273

strength concrete [9–18]. The general finding of these aforemen-tioned investigators is that the modulus of rupture decreases withincreasing beam size. This is due to the stress and strain distribu-tion in plane section which remains planar after bending. In specialcases where the shear deformation is dominant such as in concretedeep beams, experimental work to determine the modulus of rup-ture is not found. The behaviour of deep beams is unknown com-pared to normal beams; this creates more problems in additionto the problems already faced due to its material behaviour.

Deep beams are widely used structural elements with compar-atively small ratios of span (L) to depth. Deep beams have variousstructural applications, e.g., transfer girders in tall buildings, pilecaps, foundations, offshore structures and others. The differentia-tion of normal beam and deep beams is unclear. For example, theACI code [19], CEB-FIP model code [20] and CIRIA Guide 2 [21]use the span/depth ratio limit to define RC deep beams; and theCanadian code [22] employs the concept of shear span/depth ratio.Also, the design concept of deep beams is not same as normalbeams. In normal beams the plane sections remain planar beforeand after bending. But in deep beams, due to a different load trans-ferring mechanism and domination of shear deformation, this con-cept is not applicable. The failure of these elements is more inshear mode rather than flexural. The stress and strain distributionin deep beams is nonlinear in contrast to normal beams. Also,many of the equations for normal beams are not applicable fordeep beams as there is more than one neutral axis in deep beamscompared to the single neutral axis in normal beams [23].

Many investigations have been published over past two decadeson design and behaviour of deep beams [24–29], but very littlework has been reported on deep beam bending behaviour andthe first crack occurrence. Since crack limitation factor is used asa serviceability requirement for concrete elements, it is importantto investigate the appearance of first crack in HSC deep beams.However, many practicing engineers and designers face difficultiesin choosing an appropriate average tensile concrete strain to applyin designing deep beams and have expressed reservations aboutusing the existing provisions. Also, the information on first crackoccurrence is a key requirement for finite element softwares.

1.1. Research significance

The aim of present study is to determine the modulus of ruptureand first bending crack for both normal and deep beams which arevery useful in finite element solutions. Further to propose possiblecode provisions for deep beams, to identify the natural progressionof crack which is the limitation of concrete behaviour and its ser-viceability. This paper presents useful data on the effective param-eters of HSC deep beams to determine the possibility of thecracking moment of deep beams and comparing it with the corre-sponding data regarding normal beams. Eight HSSCC deep beamsand nine HSC normal beams with different tensile bar percentagesare casted and tested. The beams are tested gradually till failure oc-curs. The load corresponding to first flexural crack is recorded foreach beam. The corresponding flexural moment and modulus ofrupture are calculated and compared with existing design codes.

2. Materials and methods

2.1. Test program

Eight HSSCC deep beams have been designed and casted, corresponding to ten-sile bar percentage (q) of qmin, 0.1qb, 0.2qb, 0.3qb, 0.4qb, 0.5qb, 0.6qb and 0.7qb. Thebeam lengths, depths and thicknesses are kept constant while varying the tensilereinforcements. Two groups of HSC normal beams with low and high tensile barpercentages are chosen. Based on ACI code provisions, five beams with low tensilebar percentages (qmin, 0.2qb, 0.3qb, 0.4qb, 0.5qb) and four beams with high tensilebar percentages (0.75qb, 0.85qb, qb, 1.2qb) are designed and casted. All the beamsare loaded until failure occurred.

2.2. Materials

2.2.1. High strength self compacting concrete deep beamsThe material used for the present experimental study is HSSCC. Self-compacting

concrete is a highly flow able, non-segregating concrete that can spread into amould and fill the formwork and encapsulate the reinforcement without any needfor consolidation. Because of density of reinforcing bars in deep beams, the vibra-tion of concrete is not an easy task. Therefore, the use of self compacting concreteis highly desirable. Moreover, self compacting concrete requires no additional com-paction and therefore relatively less labour is required. The HSSCC mix design is gi-ven in Table 1 and the other required details are discussed in [29]. In the mix designlocal aggregate of maximum 20 mm diameter, ordinary Portland cement, naturalriver sand, microsilica and super plasticizer are used.

The desired workability of HSSCC has been achieved avoiding segregation andbleeding. Fig. 1 shows the workability of the HSSCC.

To prevent segregation workability is kept within the range of 550–740 mm. Foreach beam, nine cubes (100 mm � 100 mm � 100 mm) and three cylinders(150 mm diameter, 300 mm height) are casted as control specimens. Cubes aretested for measuring strength at 7 days, 28 days, and the age of loading. The cylin-

Table 2Specification of tested deep beams.

Beam f 0c (Mpa) q (%) As (mm2)

BD1 91.5 0.219 191BD2 91.5 0.269 236BD3 91.1 0.410 383BD4 93.72 0.604 558BD5 79.1 0.809 760BD6 87.5 0.938 854BD7 82.24 1.05 964BD8 97.2 1.26 1165

Table 3Bar specifications.

Diameter of bars (mm) fy (Mpa) fu (Mpa)

U9 353.0 446.0U10 614.4 666.0U12 621.6 678.4U16 566.3 656.0

Table 4Bar schedule specification of deep beams.

Beam no. Tensile bar d (mm) a/d

BD1 3£9 435.5 0.920BD2 3£10 438.5 0.910BD3 2£10 + 2£12 469.0 0.850BD4 2£10 + 2£16 462.0 0.860BD5 2£10 + 3£16 470.0 0.850BD6 1£8 + 4£16 455.0 0.880BD7 2£10 + 4£16 460.0 0.760BD8 2£10 + 5£16 451.0 0.778

Fig. 4. Experimental setup for HSSCC deep beams.

M. Mohammadhassani et al. / Construction and Building Materials 30 (2012) 265–273 267

ders are tested for splitting tensile strength at 28 days. All cylinders and cube sam-ples used for strength control are demoulded after 24 h and cured in humidconditions.

Fig. 2 shows the mould of deep beam with reinforcement and strain gauges. Thetest samples are covered with canvas and plastic after 3 days of casting. The canvasis watered twice a day for 11 days.

The properties of hardened cementitious materials and the tensile bar percent-age for deep beams are listed in Table 2. The concrete strength mentioned is anaverage strength of three cube samples at age of loading for each beam.

In this table q, f 0c and As are tensile bar percentage, concrete compressivestrength of cube samples at loading age, and the corresponding area of tensilebar in each deep beam respectively.

2.2.1.1. Steel. Except for 9 mm non-deformed steel bar, the other used reinforcingbars are high tensile deformed bars with the properties mentioned in Table 3.The properties are determined by carrying out tests on samples taken from eachsupplied batch. In Table 3 fy and fu are the yield and ultimate stress of the barsrespectively.

2.2.1.2. Deep beam details. All deep beams have a section of 500 mm depth, 200 mmwidth and 1500 mm length. Table 4 shows the deep beam reinforcement details.The geometrical parameters of deep beams are shown in Fig. 3.

Fig. 3. Geometrical specific

As shown in Fig. 3, the anchorage of the main tension reinforcements is en-hanced by providing 90-degree hooks at the bar ends for preventing bondingfailure.

2.2.1.3. Test setup and loading process. All simply supported beams are subjected totwo static point loads as shown in Fig. 4. The loads are applied using a hydraulicjack, until failure occurred. Fig. 4 also shows the details of experimental setupadopted for the present study.

The beams are supported on two steel cylinders with diameter 10 cm. After thebeam is centred and levelled the steel beam is placed on the test specimen and theload is applied at midpoint with 20 KN intervals until the first flexural crack oc-curred. The load at which the first flexural/vertical crack occurred is recorded. Peri-odically during the test, loading is paused to observe cracks. The loads at whichcracks occurred are determined by visual inspection. After the appearance of firstflexural crack the loading interval is changed to 50 KN until complete failure is no-ticed. Strains and deflections are recorded at each step of loading using straingauges and transducers. In loading process, the specimens are vertically alignedto reduce failure due to irregularity of supports. To avoid errors in data collection,the data acquisition system is electronically zeroed prior to testing. The observa-tions are marked on deep beam surface using markers.

2.2.2. High strength concrete normal beamsNine HSC normal beams having dimensions 2000 � 200 � 300 mm are casted to

investigate modulus rupture. Table 5 shows the HSC mix design for normal beams.Details such as tensile strength and flexural strength are discussed in [30,31]. In themix design local aggregate of maximum 20 mm diameter, ordinary Portland ce-ment, natural river sand, microsilica and super plasticizer is used.

Table 6 shows area of steel (As), effective depth (d), tensile bar percentage andstrength of concrete for HSC normal beams. The concrete strength mentioned in Ta-ble 6 is an average strength of three cube samples at age of loading for each beam.

2.2.2.1. Steel properties in HSC normal beams. The properties of steel bars used in HSCnormal beams are given in Table 7. The average yield (fy) and ultimate stresses (fu)of bars are determined by carrying out tests on five samples taken from each sup-plied batch.

ations of deep beams.

Table 5HSC mix design.

Material Coarseaggregate

Fineaggregate

Water/cement

Silica fume/cement

Superplasticizer

Weight (kg/m3) 723 647 0.32 0.08 11.7

Table 6Specification of normal beams.

Beam no. As (mm2) d (mm) q (%) f 0c (kgf/cm2)

B1 308 256 0.61 670B2 628 266 1.25 680B3 1020 258 2.03 675B4 1260 250 2.52 700B5 1520 250 3.05 700B6 2464 256 4.81 710B7 2866 266 5.39 705B8 3512 258 6.81 718B9 4004 250 8.01 725

Table 7Bar specifications.

Diameter of bars (mm) fy (Mpa) fu (Mpa)

U14 398.1 451.0U18 373.6 412.2U20 401.9 464.8U22 369.7 432.6

Table 8Reinforcement details of normal beams.

Beam no. Tensile bar Stirrup

B1 2£14 £8@7.5 cm c/cB2 2£20 £8@7.5 cm c/cB3 4£18 £8@7.5 cm c/cB4 4£20 £8@7.5 cm c/cB5 4£22 £8@7.5 cm c/cB6 4£28 £12@10 cm c/cB7 4£28 + 2£16 £12@7.5 cm c/cB8 6£22 + 2£28 £12@7.5 cm c/cB9 6£28 + 2£14 £12@7.5 cm c/c

268 M. Mohammadhassani et al. / Construction and Building Materials 30 (2012) 265–273

2.2.2.2. Normal beam details. Fig. 5 shows a typical reinforcement detail of HSC nor-mal beam. Bars having four different diameters 14 mm, 18 mm, 20 mm and 22 mmare used in design. Table 8 shows reinforcement details for all the normal beamsunder study. The beams having a cross section of 200 � 300 mm is considered.

2.2.2.3. Test setup and loading process for normal beams. The testing arrangement isshown in Fig. 6. All simply supported beams are subjected to two static point loads.The loads are applied using a hydraulic jack, until failure occurred. Two plates areused to distribute the load and prevent local failure in compression area. The beamis divided into two symmetric halves. Demec gauges in four lines along the depth ofbeam are mounted to measure the strain variation. The distance kept between eachDemec gauge line is 100 mm.

3. Results and discussions

3.1. Cracking moment and modulus of rupture in HSSCC deep beams

With the appearance of the first crack there is a sudden signif-icant change in tensile bar strain. Definition of stress correspond-ing to the appearance of first crack is important in recognisingthe change of concrete from linear elastic condition to non-linear

Fig. 5. Geometrical specifica

plastic condition. The concept of modulus of rupture is based onelastic beam theory. The modulus of rupture is defined as the max-imum normal stress in the beam calculated from ultimate bendingmoment under the assumption that the beam behaves elastically.

As the beam load exceeds the load corresponding to crackingmoment Pcr, a hairline crack will appear near the bottom mid-span.By increasing the load, the crack will propagate towards the neu-tral axis. Additional cracks are observed at the mid-span of thebeam towards the supports. The crack mechanism in deep beamsand normal beams are different. In deep beam, cracking followsthe compression struts that form at ultimate load. In normalbeams, cracks occur after the bending of the plane section. Flexuralcracks appear first followed by shear cracks at the end of the flex-ure cracks.

At mid-span the stresses in the beam are primarily flexural ten-sion and compression. These stresses are horizontal and result invertical cracks. The increasing shear stress towards the supportcauses the cracks to be more inclined towards the load point; theseinclined cracks are known as ‘diagonal tension’ cracks associatedwith shear. The stress and strain distributions are different alongthe beams length based on geometry and load variation. Thus thedefinition of B-region (Beam or Bernoulli) and D-region (Disturbedor Discontinuity) is necessary to recognise for internal force distri-butions. ACI code defines B and D regions in deep beams based onthe St. Venant strain distribution.

The St. Venant’s principle hypotheses states that a localised dis-turbance such as a concentrated load will dissipate within onebeam height from the load point. It is useful to classify portions ofthe structure as either B-regions or D-regions as shown in Fig. 7.The discussion of these regions is vital in understanding the internaldistribution of forces in a reinforced concrete structure.

The B-regions of a member have internal states of stress distri-bution that are simply obtained from the sectional forces in bend-ing, shear, etc. In these regions, the strain in reinforcement andconcrete is directly proportional to the distance from the neutralaxis and the beam behaves elastically.

tions of normal beams.

Fig. 6. Details of testing arrangement.

h

Ph

h

h

D B D D DB

h h h

Fig. 7. B-regions and D-regions.

Fig. 8. Common types of strut 9 (a) prism, (b) bottle and (c) fan.

M. Mohammadhassani et al. / Construction and Building Materials 30 (2012) 265–273 269

The D-regions are regions adjacent to the concentrated loadpoints that are affected by abrupt change in load and reactionspoints or adjacent to abrupt changes in geometry, such as internalholes or changes in cross section. In D-regions, the strain distribu-tions are not linear. For structural members where plane sectionsare non-planar after bending, the strain distribution is non-linearand therefore the linear approach does not apply. The elasticstress distribution in a D-region is difficult to determine and itchanges as cracks progress. Schlaich et al. [32] introduced a designmethod on plasticity theory using a Strut and Tie Model (STM).The model could be used for both the ultimate and serviceabilitycheck. In this model, the internal forces can be calculated usingSTMs. These models have three components, the strut, the tie,and the node(s). Schlaich and Schafer described three strut config-urations that should adequately cover all cases of compressionstress fields:

� Prismatic stress fields (Fig. 8a).� The bottle shaped stress field which develops considerable

transverse stress (Fig. 8b).� Fan shaped stress fields which does not develop transverse

stresses (Fig. 8c).

Based on the Schlaich and Schafer method, the fan and bottleshaped stress fields are normally found in the D-regions whilethe prismatic stress field is found in the B-regions. The theory oflinear elastic behaviour is applicable in B-regions and it is non-applicable in D-regions. The mid span area between the two pointloads undergo linear prismatic stress and therefore it is a B-region.Some investigators, such as Schlaich et al. [32] and Schlaich andSchäfer [33], state that the structure will crack due to the elasticstresses, and if the structure is reinforced according to these stres-ses, cracking can be minimised. Fig. 9 shows evidence of vertical

cracks due to horizontal strain distribution in pure flexure zoneof beam BD1.

Before cracking, the concrete is nearly elastic in tension and lar-gely unaffected by the presence of reinforcement. The experimen-tal cracking moments Mcr,exp is computed with the correspondingmoments based on Eq. (1):

Mcr ¼fr � Ig

ytð1Þ

Fig. 9. Crack progressions in BD1.

Fig. 10. The (a) shear diagram and (b) moment diagram of tested deep beams.

B1 (a) B2 (b) B3 (c)

0

5

10

15

20

25

30

35

40

45

50

-0.001 0 0.001 0.002

sect

in h

eigh

t (cm

)

strain

0

5

10

15

20

25

30

35

40

45

50

-0.0002 0 0.0002

Sect

ion

Hei

ght (

Cm

)

Strain

0

5

10

15

20

25

30

35

40

45

50

-0.0001 0.0089

Sect

ion

heig

ht (

Cm

)

Strain

Fig. 11. The stress and strain distribution of beams BD1, BD2 and BD3 at theoccurrence of the first crack in mid-span.

B4 (a) B5 (b) B6 (c)

0

5

10

15

20

25

30

35

40

45

50

-0.007 0.0065 0.02

Sect

ion

heig

ht (

Cm

)

Strain

0

5

10

15

20

25

30

35

40

45

50

-0.01 0.04

Sect

ion

heig

ht (

cm)

Strain

0

5

10

15

20

25

30

35

40

45

50

-0.002 0.028 0.058

Sect

ion

heig

ht (

cm)

Strain

Fig. 12. The stress and strain distribution of beams BD4, BD5 and BD6 at theoccurrence of the first crack in mid-span.

Table 9Corresponding load and distance of the extreme compression fibre from neutral axis.

Testedbeams

Load correspondingto first crack (kN)

Percentage of firstcrack load toultimate load

Distance of theextreme compressionfibre from the N.A (mm)

BD1 215.8 0.42 330BD2 187.3 0.25 180BD3 242.0 0.30 280BD4 285.0 0.42 360BD5 239.0 0.36 250BD6 307.0 0.25 270BD7 198.0 0.13 250BD8 325.0 0.17 190

Table 10Corresponding experimental moment and the modulus of rupture of deep beams.

Deep beam no. Mcr (exp) (N mm) fr (exp) (MPa) a

BD1 377,65,000 5.98 0.625366BD2 327,77,500 2.83 0.296060BD3 423,50,000 5.69 0.596339BD4 498,75,000 8.62 0.890247BD5 478,00,000 5.74 0.644942BD6 537,25,000 6.96 0.744350BD7 346,50,000 4.16 0.458504BD8 568,75,000 5.19 0.526118

Table 11Comparison of the various modulus of rupture.

Reference and authors fr (MPa) frðf 0c ¼ 70Þ (MPa)

ACI 318-95 [36] 0.62ffiffiffiffif 0c

p5.18

ACI 363 [37] 0.97ffiffiffiffif 0c

p8.12

CSA94 [38] 0.30ffiffiffiffif 0c

p2.51

Ahmad and Shah [35] 0.42ðf 0c ;150Þ0:68 7.58

Proposed equation 0.60ffiffiffiffif 0c

p5.02

270 M. Mohammadhassani et al. / Construction and Building Materials 30 (2012) 265–273

where fr is the modulus of rupture; Ig is the moment of inertia ofgross concrete section and yt is the distance of extreme tension fibrefrom neutral axis.

Fig. 10 shows a general shear force and bending moment dia-gram of all the tested deep beams. The maximum bending momentobtained is 350�P (kN mm). Based on Eq. (1), the location of firstneutral axis depth (N.A.D) is important for determining the valueof yt.

For this purpose, at the emergence of the first crack, the stress–strain distribution at mid-span of beam is analyzed and drawn inFigs. 11 and 12. The mid-span readings are taken from the strain

Fig. 13. Corresponding loads to the first crack in normal beams.

Table 12Ratios of load corresponding to the first crack to ultimate failure load in normalbeams.

Normalbeamnumber

Load correspondingto first crack (kN)

Failureload (kN)

The ratio of loadcorrespond to first crackto ultimate failure load

B1 42.60 167.30 0.250B2 56.60 324.00 0.170B3 34.60 464.00 0.070B4 32.60 554.00 0.050B5 42.60 670.00 0.060B6 44.86 972.88 0.040B7 48.88 1054.20 0.046B8 48.20 1277.50 0.030B9 51.08 1226.20 0.041

Table 13Comparison of theoretical (ACI codes) and experimental cracking moment for normalbeam.

Bam’s number McrACI (kN cm) Mcr(exp) (kN cm) McrðEXPÞMcrðACIÞ

fr(exp) (kN/cm2)

B1 1522.50 958.0 0.63 0.319B2 1533.80 1273.0 0.83 0.424B3 1528.10 778.0 0.51 0.259B4 1556.20 734.0 0.47 0.245B5 1566.20 958.0 0.61 0.319B6 1567.30 1010.0 0.64 0.337B7 1561.70 1100.0 0.70 0.367B8 1576.10 1084.6 0.69 0.362B9 1583.70 1148.0 0.72 0.383

M. Mohammadhassani et al. / Construction and Building Materials 30 (2012) 265–273 271

gauges for the upper portion and the Demec gauges for the lowerportion (refer to Fig. 4).

As observed from Figs. 11 and 12, the stress–strain distributionof deep beams is non-linear even at the occurrence of first crackand there is more than one neutral axis depth. The correspondingloads of the first bending crack and the neutral axis depth is pre-sented in Table 9. It shows that out of eight deep beams tested,

Table 14Predictions of the cracking moment for HSC normal beams.

Researches Number of beams Concrete strengthf 0c (MPa)

Tensilratio

Current study 9 67–72.5 0.61–Rashid and Mansur [9] 16 43–126 1.25–Ashour [39] 9 49–102 1.18–Lambotte [40] and Taerwe 6 34–81 0.48–Paulson, [41] Nilson, and Hover 9 37–91 1.49Shin [42] 28 27–100 0.41–

six beams had indexes more than 25% and it is supported by thefinding of Maco [34]. The beams that had indexes less than 25%are the beams with additional support widths which results in in-crease in ultimate load capacity and consequently decrease in theratio.

For a better comparison of modulus of rupture with code provi-sions, an a coefficient is added to the concrete strength as shown inEq. (2):

fr ¼ affiffiffiffif 0c

qð2Þ

Experimental cracking moment corresponding to the first crackand the modulus of rupture are shown in Table 10. Also the valueof a calculated from the respective concrete strengths (refer Ta-ble 2) using Eq. (2) are presented in Table 10.

From Table 10, amean = 0.6 is calculated. The modulus of rupturefor deep beams studied with a/d ratio of 0.8 is shown in Eq. (3).

fr ¼ 0:6ffiffiffiffif 0c

qMPa ð3Þ

Table 11 shows the comparison of modulus of rupture in HSSCCdeep beams with code provisions, Ahmad and Shah [35] and theproposed equation from this study.

Based on Table 11, the modulus of rupture from ACI 318-95 [36]is the value nearest to that obtained from the proposed modulus ofrupture in this study. Thus based on this study, the ACI 318-95code provision is an acceptable conservative prediction for themodulus of rupture in HSSCC deep beams.

3.2. Cracking moment and modulus of rupture in HSC normal beams

In normal beams, the tension reinforcement and the concrete incompression both behave elastically up to yield of the reinforce-ment. Based on experimental results, the first crack occurs at theextreme tension fibre at different loads for each of these beams.Fig. 13 presents the corresponding load to the first crack in normalbeams.

Table 12 shows the ratio of load corresponding to first crack toultimate failure load in normal beams. Table 13 shows the compar-ison between the theoretical cracking moment using ACI codes andthe experimental cracking moment from this study for normalbeams. Table 14 shows comparison between present study, otherresearchers and code provisions for normal beams. Fig. 13 and Ta-bles 13 and 14 show results of a thorough evaluation of the mod-ulus of rupture for normal beams.

As per Table 12 the ratio of load corresponding to the first crackto ultimate failure load ranges between 3–25% with a mean of 8.4%.In comparison with the deep beams, this ratio is relatively lower.Cracking moment has been evaluated with ACI code provisionusing Eq. (1). The results of this theoretical and experimental studyare then compared and presented in Table 13. Based on Table 13and Eq. (2), the modulus of rupture for these normal beams is pro-posed in Eq. (4).

e reinforcementq (%)

Compressive reinforcementratio q0 (%)

McrðexpÞMcrðACIÞ

Mean Standard deviation

8.01 0.4 0.63 0.0595.31 0.31 and 0.94 0.90 0.1262.37 N/A� 1.02 0.1311.45 N/A� 0.77 0.207

0 to 1.49 0.68 0.1143.60 0.41–3.60 1.00 0.216

Table 15Comparison of various modulus of rupture fornormal beams.

fr (MPa)

ACI 318-95 [37] 0.62ffiffiffiffif 0c

pACI 363 [38] 0.97

ffiffiffiffif 0c

pCSA94 [39] 0.30

ffiffiffiffif 0c

pAhmad and Shah [36] 0.42ðf 0c;150Þ

0:68

Current study 0.33ffiffiffiffif 0c

p

272 M. Mohammadhassani et al. / Construction and Building Materials 30 (2012) 265–273

fr ¼ 0:33ffiffiffiffif 0c

qðMPaÞ ð4Þ

The comparison between the proposed Eq. (4), the code provi-sions and other investigators results are presented in Table 15.The value of modulus of rupture for normal HSC beams in the pres-ent study agrees with CSA 94 [38]. ACI code is found to give highlyconservative results. Therefore CSA 94 is recommended to calcu-late modulus of rupture for HSC normal beams.

3.3. Comparison of first crack appearance in normal and deep beams

The differences in ratios of corresponding load to the first crackwith ultimate failure load in deep beams and normal beams aredue to the difference in load transfer mechanism in deep beams.In normal beams, flexural cracks appear first followed by shearcracks at the end of the flexure cracks leading to failure mode. Indeep beams, part of the load is transmitted directly to the supportby compression strut without any contribution to flexural stress(refer Fig. 8). This kind of load transfer mechanism in deep beamscommonly leads to shear in the form of splitting failure and raises aneed for design concept different to normal beams. Due to this fail-ure mode and the load transfer mechanism from load point to sup-port in deep beams, the first crack will appear at a load muchhigher than in normal beams.

4. Conclusions

Deep beams show non-linear strain distribution with more thanone neutral axis depth before tensile bar yields. The modulus ofrupture of HSSCC deep beams is different from HSC normal beams.The results show that the modulus of rupture in HSSCC deep beamswith shear span to depth ratio of less than 0.80 is around 0.6

ffiffiffiffif 0c

p. In

normal beams, it is around 0.33ffiffiffiffif 0c

p. The first crack to appear in

these two types of beams is a flexural crack. Due to the shearmechanism of load transfer in deep beams, the corresponding loadto the occurrence of the first crack is around two times more thanin normal beams. Based on the present study ACI 318-95 is recom-mended for calculating modulus of rupture in HSSCC deep beamswhereas CSA 94 is suggested for HSC normal beams.

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