Evaluation of Shear Crack Width in I-Shaped Prestressed ReinforcedConcrete BeamsSudhira De Silva', Hiroshi Mutsuyoshi2 and Eakarat Witchukreangkrai3

AbstractRecently, Prestressed Reinforced Concrete (PRC) has been accepted as a reasonable structural member that permitscracking. A PRC member is a visible design alternative to either reinforced concrete (RC) or fully prestressed concrete(PC). In Japan, PRC has been widely used for bridge structures because it is economical. PRC members are generallydesigned to allow cracking under full service loads. Flexural cracking in PRC beams has been already studied and theflexural crack width can be accurately predicated by equations available in the present codes (ACI, CEB-FIP, JSCE,etc.). On the other hand, shear cracking behavior in PRC members is barely understood. The objective of the presentstudy is, therefore, to experimentally explore the shear cracking behavior of PRC beams. Three I-shaped RC and four 1-shaped PRC beams were tested under four-point monotonic loading. The experimental program was carried out focus-ing on the influence of prestressing force, side concrete cover, stirrup spacing, bond characteristics of stirrup and theamount of longitudinal reinforcement on shear crack width. The study revealed that the prestressing force significantlyreduced shear crack width in PRC beams as compared to RC beams. In addition, an equation was proposed to calculateshear crack width in RC and PRC members. The proposed formula for shear crack width shows better correlation be-tween calculated values and experimental data than the other formulae.

Prestressed concrete (PC) structures can generally becategorized into three classes (ACI-ACSE Committee423 1999) according to cracking criteria. The first classis defined as fully prestressed members since no tensilestresses are pennitted in concrete under full serviceloading. Fully prestressed concrete girders have beenwidely used in bridge spans exceeding about 60 m.However, one of the drawbacks of using fullyprestressed concrete beams is that the high-strength ma-terials required for prestressing are relatively expensive.In the second class of PC structures, an allowable levelof tensile stress is permitted in the concrete under fullservice loading, while cracks are not permitted. Thethird class is defined as partially prestressed concrete(PPC). PPC is made by introducing a low amount ofnon-prestressed steel into a fully prestressed member.On the other hand, if a certain amount of prestressingforce is introduced into reinforced concrete (RC), it re-sults in an alternative member called prestressed rein-forced concrete (PRC). In Japan, PRC beams have been

ISenior Lecturer, Department of Civil andEnvironmental Engineering, Faculty of Engineering,University of Ruhuna, Sri Lanka.E-mai/:sudhira@cee.ruh.ac.lk2Proffessor, Department of Civil and EnvironmentalEngineering, Graduate School of Science andEngineering, Saitama University, Japan.3Engineer, Civil Engineering, Technology Division,Shimizu Corporation, Japan.

widely used in bridge spans with lengths ranging fromaround 40 m to 60 m because they are economical.

In PRC, cracks are permitted within allowable limitsof crack width under full service loading. PRC membersincorporate non-prestressed reinforcements as well asprestressed steels, and both contribute to member resis-tance. PRC members demonstrate that there are solu-tions intermediate between fully prestressed concreteand ordinary reinforced concrete offering numerousadvantages. For example, permitting tensile stresses andcracking in the concrete allows for more latitude in de-ciding the amount of prestressing force required toachieve optimum structural performance under particu-lar loading conditions. PRC members are excellent as ameans of obtaining a suitable degree of control overcracking. The small amount of prestressing steel used toprovide this crack control is insufficient to ensure therequired strength, so additional non-prestressed rein-forcement is used. PRC members result in more eco-nomical design with smaller cross sections and a re-duced amount of prestressing steel. The non-prestressedreinforcement used in PRC members enhances strengthand also controls the formation of cracks and crackwidth.

Cracking behavior, control of crack width and the dis-tribution of crack spacing are significant factors in thedesign of PRC structural members. The cracking behav-ior of RC beams and PRC beams has been investigatedin many studies over the last five decades (Adebar andLeeuwen 1999; De Silva 2005; Frosch 1999, Hassan elal., 1991, Kakuta, Y., el al., 1970, Krishna Mohan Raoand Dilger 1992, Piyasena el al., 2004, Oh and Kang1987). Most of these studies have focused on flexural

cracking behavior, while very few have been concernedwith shear cracking. Most existing design methodolo-gies evaluate the flexural crack width in RC and PRCmembers, whereas there is a little mention of shearcrack width in RC members (Adebar and Leeuwen1999; Fukuyama et al., 2000; Shinomiya and Watanabe2002). Indeed, there is no existing design methodologyfor evaluating shear crack width in PRC members. Theequations stipulated in the ACI (2002), CEB-FIP ModelCode (1978) and Japan Society of Civil Engineers(JSCE, 2002) codes give very accurate determinationsof flexural crack width in RC and PRC members. How-ever, there are no specific prescribed design guidelinesfor evaluating shear crack width in PRC members. Fur-ther, there has yet been no clarification of the parame-ters that influence shear crack width in PRC members.

Recently, shear cracking in concrete structures hasbecome an important issue concerning the durability ofconcrete structures. In Japan, the case of a PRC bridgethat developed serious cracks including shear cracks justafter completion was reported (JSCE Mid-Term Report(2005)). This emphasizes the importance of investigat-ing methods of controlling shear crack width in both RCand PRC beams. For RC beams, control has beenachieved by limiting stirrup strain as defined in the ACIand the JSCE standard specifications. The JSCE stan-dard specification and previous studies (Hsiung andFrantz 1985; Hassan et al., 1991; Witchukreangkrai etal., 2004; De Silva 2005) show that strain in the webreinforcement is the most significant parameter affect-ing shear crack width in RC beams. The strain devel-oped in the web reinforcement is associated with thecharacteristics of the stirrups such as bar diameter, spac-i'ng, orientation with respect to the member axis andbonding properties, concrete strength, web width, theratio of shear span to effective depth and the amount oflongitudinal reinforcement. The recent studies (Hsiungand Frantz 1985; Zararis and Papadakis 2001; Zararis2003) have indicated that adjusting the quantity of stir-

Non-prestressed Effective depth StirrupBeam # reinforcement to prestressing spacing

Top Bottom bar (dp, mm) (mm)IRC-I 125IRC-2

- 125~IRC-3

4025 250* 125IPRC-I

4022 (ds=450mm)125

IPRC-2(ds'= /y=685 MPa

225IPRC-3

40mm)125T1;,'=

2 D29 and400 250MPa 2 D38

IPRC-4 (ds=450 125mm)

fv=685 MPa* no prestressing§ maximum side concrete cover (c = 69 mm)t plain stirrups

rups only may not be sufficient to control shear cracking,but that the amount of longitudinal reinforcement canhave a significant influence on the opening of criticalshear cracks. Thus there have been a few studies (Yoonet al., 1996; Hassan et al., 1991; Tompos and Frosch2002) of the parameters that affect shear crack width inRC members, but barely any investigation of such pa-rameters for PRC members.

In order to focus on only shear cracks that occur inthe web, it is necessary to design test beams that willfail with many shear cracks in the shear span. Therefore,test beams with I-shaped cross sections, consisting ofboth RC and PRC beams, were used in the present studybecause the thinner web in an I-section induces largershear stresses, which then cause many shear cracks inthe web independent of flexural cracks. It was expectedthat the beams would fail with parallel shear cracks dis-tributed uniformly throughout the web over the entireshear span. The objective of this study is to investigateexperimentally the effects of different parameters on theshear crack width of these I-shaped RC and PRC beams.The experimental variables include prestressing force,side concrete cover, stirrup spacing, stirrup bondingcharacteristics and the amount of longitudinal rein-forcement. In addition, simplified rational equationswere proposed to calculate shear crack spacing andshear crack width in RC and PRC beams. The proposedequations are compared comprehensively with experi-mental results such as crack spacing and crack width.

2. Experimental procedure

2.1 Test detailsIn order to investigate the influence of various parame-ters including prestressing force on shear crack width inPRC beams, an experimental program was carried outas follows. The prestressing force (or compressive stressin concrete due to prestress, Gc.pc), side concrete cover,stirrup spacing, type of stirrup and amount of longitudi-nal reinforcement were the main experimental parame-ters (Table 1). The test beams consisted of three RC andfour PRC beams with 1- shaped cross sections. Thesetest beams were designed in accordance with the JSCEstandard specification (JSCE 2002). The total beamlength was 3600 mm. Cross-sectional details and typicallayouts are shown in Figs. 1 and 2, respectively. Themechanical properties of the non-prestressed steel andprestressed steel used in the experiment are listed inTable 2. The material properties (i.e., yield strength,ultimate strength and young's modulus) of high-strengthsteels (USD 685) and prestressing steel were providedby the manufacturer and the material properties of nor-mal steel (SD 345) were experimentally determined. Inall the test beams, two different sizes of stirrup barswere provided: D6 (D = deformed bar, 6 = diameter inmm) and DIO. The D6 bars were used in the left span ofthe beams while the DIO bars were used in the rightspan to ensure that the main shear crack would occur in

each stirrup. This is necessary because the random oc-currence of shear crack may influence stirrup strainsdepending on the location of cracks. This arrangementallows clarification of the relationship between thestrains of the stirrups and the width of shear cracks. Inaddition, strain gages were attached to the tensile rein-forcements and the prestressing tendon at mid-span.Contact chips were pasted on the surface of each beam

-1 100mm -1 500 mm 300 mms = 06@125mm ... •. ~..••. s = 010@125mm

, . , . , , ,, Ill~• ,,"/ . ! r..• ~ Contact chips / •Stirrup strain gages

1350 mm Load cell for prestressing

the left span. Ready mixed concrete with a maximumaggregate size of 20 mm was used for all beams.

2.2 InstrumentationA total of 49 steel strain gages were placed on the stir-rups to measure stirrup strains in the shear span. Thelocations of the strain gages are shown in Figs. 2 and 3.Seven strain gages were attached at equal spacing in

111026 mm(3.0 MPa)

4025

IPRe -3

Fig. 1 Cross sectional details of beams.

100mm T

wmm~75mm

225 mm ---1---1s = 06@225mm ...~ ~..•~ 1----1- 225 mms = 010@225mm

, . , , ,,. ., ~"j. , : ~,

•••• Contact chips / ,/ •Stirrup strain gages1350 mm

1800 mm

ID6@t2smm

EE E

- ~ EN l{)

N(")

I

Type 1

rt

L! ---!L-

at three locations in the shear span to measure the prin-cipal strains and their directions. A contact gage with anaccuracy of 0.001 mm was used to measure the dis-placement in each direction of the contact chips. Linearvoltage displacement transducers (LVDT) were installedto measure the mid-span deflection of the beam. A straingage was attached to the top surface of the beam in themid-span region to monitor the compressive strain in theconcrete. A load-cell was placed on the loading beam toobtain the applied load. In the case of PRC beams, aload cell was also attached at the anchorage end of theprestressing tendon to monitor change of the appliedprestressing force and to make sure that the beam wasunder uni-axial compressive force throughout the load-ing test.

2.3 Loading and crack width measurementsThe test beams were subjected to four-point monotonicloading as shown in Fig. 4. The loading configurationconsisted of simple supports and two point loads 300mm apart at the mid-span. The ratio of shear span toeffective depth (a/d) was 3.0 for all beams. A prestress-ing force of375 kN was introduced into all PRC beams,causing 3.0 MPa of compressive stress in the concrete.The sheath containing the prestressing tendon was filledwith grout cement after prestressing. A hand-operatedhydraulic jack was used to apply loading to the beamthrough the loading beam. A digital microscope with aresolution of 0.001 mm was used to capture digital im-ages of cracks in the left span of the beam (Fig. Sea»~.These digital images were used to measure crack width.Crack widths perpendicular to the crack surface wereobtained at three arbitrary points chosen close to therequired points (that is, at strain gage locations) (Fig.S(b). The average of the three measurements was takenas the crack width at that location. Moreover, the propa-

Type of <I>Typet J... Es x 103

bar (mm) (MFa) (MPa)Plain bar 106 353 167.7

06SO 345* 438 180.4

010 376Deformed 022 397

200.0

bar 025 720029 USO 685*B 735 206.0038 726

PC bar <p26 SBPR1205 200.01080*/1230§

Japanese standard type bars* Yield strength of bar in MPa§ Ultimate strength of bar in Mpa

gation and distribution of the cracks were carefully ob-served and marked at each loading increment until thefailure of the beam.

(a) Measuring crack width byusing digital microscope

Stirrup I 1. 0.496 mm}2. 0.501 mm Avg: 0.509 mm3. 0.529 mm

(b) Digital image ofmeasured crack width

Fig. 5 Measuring shear crack width with digital micro-scope.

3.1 Load-displacement characteristicsAs described above, an extensive experimental programwas conducted to investigate the shear cracking behav-ior of I-shaped RC and PRC beams. The observedcracking loads and failure modes are summarized inTable 3. The compressive strength of the concrete attesting is summarized in Table 3. Figures 6(a) and 6(b)show the load versus mid-span deflection relationshipsfor the RC and PRC beams, respectively. The load at thetime of the first visible flexural crack in the mid-span

800

700

600

Z 500:.

400"tl IRC.1'"0 300...J

200--IRC-1

-.-. -IRC-2100

·······IRC-30

0 5 10 15 20Displacement (mm)

800

700

600

Z 500:."tl 400'"0 300...J

200

100

00

--IPRC-1 - - - - IPRC-2

....... IPRC·3 --IPRC-4

Fig. 6(b) Load versus mid-span deflection for PRebeams.

region ranged between 80 kN and 90 kN (15% of theultimate capacity of each RC beam) for RC beams,while that for PRC beams was in the range of 165 kN to175 kN (25% of the ultimate capacity of each PRCbeam). This difference is mainly attributed to theprestressing force (375 kN) applied to the PRC beams.With increasing load, the inclined shear cracks in theshear span region widened rapidly and propagated to-wards the loading points, while flexural crack widths inthe mid-span region remained almost constant. The ul-timate failure load was greater for the PRC beams thanthat for the RC beams (Table 3). In PRC beams, theultimate load of the beam IPRC-4, with a large amount

Ic Flexural Shear UltimateBeam cracking cracking failure Final failure mode

(MPa) load (\eN) load (\eN) load (\eN)IRC-l 40.3 90.0 220.4 559.7 Shear compressionlRC-2 45.4 82.5 194.8 579.8 Shear tension-IRC-3 44.0 85.0 220.1 629.0

lPRC-I 41.8 165.0 290.9 706.8 Shear compressionlPRC-2 49.3 175.0 310.2 644.0lPRC-3 45.0 165.0 290.2 622.7 Shear tensionlPRC-4 43.2 170.0 310.0 745.0 Shear compressioncrushing In concrete near the loading POint after occunence of dIagonal cracks

2 failure due to diagonal cracks

of longitudinal reinforcement, was greater than that forthe beam IPRC-I. The failure mode of all beams wasshear failure with wide shear cracks in the shear span.Previous studies by Zararis (200 I and 2003) distin-guished diagonal tension failure as "initial shear crackpropagates abruptly or gradually toward the loadingpoint crossing the compression zone with a wide shearcrack in the shear span" and shear compression failureas "crushing of concrete in the compression zone at thetop of the critical shear crack". The same definitions ofdiagonal tension failure and shear compression failurewere followed in this study (see Table 3). Beams IRC-2and IPRC-3 failed in diagonal tension failure mode withwide shear cracks in the shear span region, while allother beams failed in shear compression failure modewith crushing of the concrete at the upper flange nearthe left-hand loading point. Furthermore, at failure, allstirrups crossing the critical diagonal crack (D6 stirrupsin the left span) were at yield and without yielding ofthe longitudinal reinforcement.

3.2 Crack patterns and crack distributionFigure 7 shows the crack patterns and shear crack ori-entations for all beams. The inclination of shear crackswas determined by averaging the crack angles measured

IRC-1

0=39.3°

IRC-30=41.5°

IPRC-1

0=33.8°

in the shear span region. The average angle of shearcracks to the beam axis in PRC beams was lower thanthat in RC beams. The average angle of shear cracksmeasured in RC beams was about 40 degrees while thatin PRC beam varied between 30 and 35 degrees. Thisdifference may be attributed to the a~ial stress compo-nent in the horizontal direction in PRC beams. Thisprestressing force caused greater reduction in the prin-cipal tensile stress in PRC beams than in RC beams,leading to the lower observed inclination of shear cracksin the PRC beams. Diagonal shear cracks in PRC beamsintersect a larger number of stirrups than those in RCbeams. Therefore, stirrups are more effective in trans-mitting shear force across cracks in PRC beams than inRC beams. It is noteworthy that prestressing force playsa more significant role in influencing the shear crackangle than the stirrup spacing in PRC beams. Table 4shows the average measured shear crack spacing in thehorizontal direction and the vertical direction for eachbeam. The crack spacings were measured when the loadreached 70% of the ultimate load (that is, approximatelythe service load of the beam). The average spacing ofthese shear cracks in RC beams is larger than in PRCbeams. This difference may be attributed to the com-pressive stress in the concrete resulting from the

IRC-2

0=42.6°

IPRC-4

0=33.4°

Horizontal crack spacing Vertical crack spacing

BeamSmx, mm)' Smy, (mm:)

Max. crack Avg. crack Max. crack Avg. crackspacing spacing spacing spacing

IRC-I 248.25 167.00 138.00 108.29IRC-2 344.60 241.46 250.00 250.00lRC-3 254.20 208.93 167.50 158.75

IPRC-I 198.80 198.80 233.00 203.15IPRC-2 235.60 200.95 155.50 127.75IPRC-3 195.60 190.65 142.60 120.50IPRC-4 290.50 287.15 166.40 157.30

3.3 Effect of various parameters on shear crackwidth3.3.1 Prestressing forceThe effect of prestressing force can be discussed bycomparing the relationship between shear crack widthand shear force, as shown in Figs. 8(b) and 8(e). BeamIRC-3 was designed with a prestressing tendon insidethe concrete section without prestressing force, whilebeam IPRC-I was given an effective prestressing forceof 375 kN. The prestressing force in beam IPRC-I wasexpected to increase the shear cracking load comparedto the RC beam (see Fig. 8(e)). The load at which the

300

Z 250

"""Q) 200t.)

0 150u..

m 100-+-IRC-1

Q).r::: -D-IRC-2CfJ

50---lr-IRC-3

0

0 0.2 0.4 0.6 0.8rv1axirrum shear crack width (mm)

(a)

300

250Z""" 200Q)t.)

1500u..

ro 100Q) -+-IPRC-1.r:::

CfJ 50-D-IPRC-3

0

0 0.2 0.4 0.6 0.8rv1axirrum shear crack width (mm)

shear crack width begins to increase or the stirrup strainstarts to accumulate in the stirrup strain gages was con-sidered as the shear cracking load (see Fig. 9(e)). Theprestressing force in PRC beams also results in a reduc-tion of maximum shear crack width compared to beamIRC-3 at the same shear force level This implies thatthe prestressing force produces a significant increase inshear cracking load. After the occurrence of shearcracks, the increment in shear crack width with shearforce is found not to be affected by prestressing force inPRC beams.

3.3.2 Prestressing tendon as a tension rein-forcementThe impact of providing a prestressing tendon at thecentroid of the beam section was discussed by compar-ing the relationship between shear force and maximumcrack width of beams IRC-I, IRC-3 (Peff = 0 kN) andIPRC-l (PefT = 375 kN) as illustrated in Figs. 8(b) and9(b). It can be seen that in beam IRC-3, in which aprestressing tendon was provided without prestressingforce, the shear crack width was smaller at the sameshear force level compared to beam IRC-I. The reasonfor this may be that the prestressing tendon at the cen-troid of the beam section may help to resist the exter-nally applied load as a form of tension reinforcement bymeans of dowel action.

300

250Z"""Q) 200t.)

0 150u..

m 100Q).r:::CfJ

50

0

0

-+-IRC-1

-D-IRC-3

---lr-IPRC-1

0.2 Q4 Q6 0.8

rv1axirrum shear crack width (mm)

- 250Z"""-; 200t.)

o 150u..

m 100.r:::CfJ 50

oo 0.2 0.4 0.6 0.8

rv1axirrum shear crack width (mm)

3.3.3 Side concrete coverFigure 8(a) shows the relationship between shear forceand maximum shear crack width. The side concretecover of beams IRC-I and IRC-2 were 25 mm and 69mm, respectively. It can be seen that the occurrence ofshear cracks was delayed in beam IRC-2 compared tobeam IRC-I. At the same shear force level, beam IRC-2showed smaller shear crack width than beam IRC-I.Further, the maximum stirrup strain variation with shearforce shows almost the same rate of stirrup strain in-crease in both beams (Fig. 9(a)). The relationship be-tween average shear crack width and stirrup strain isshown in Fig. 10(a). It is very clear that a wider sideconcrete cover tended to increase the shear crack widthat the same stirrup strain level. However, the shear crackpattern in beam IRC-2 shows relatively wide spacingsof shear cracks compared to the other RC beams (Fig.7). Further investigation is necessary to verify the effectof side concrete cover on shear crack width.

3.3.4 Type of stirrupIt can be observed from Fig. 8(e) that, for a particularshear force, beam IPRC-3 with plain stirrups (roundbars) showed a larger shear crack width compared tobeam IPRC-I with deformed stirrups. More interest-ingly, the relationship between shear crack width and

stirrup strain for plain stirrups was found to be non-linear (a polynomial curve), as opposed to a linear rela-tionship in the case of deformed stirrups (Fig. tOed)).For the same stirrup strain, shear crack width tended tobe larger in the beam with plain stirrups. This may bebecause a plain stirrup undergoes more slip than a de-formed stirrup because of its inferior b~nding character-istics. Stirrup slip is considered to be a major factor inthe opening of shear cracks. The width of shear cracksat a given stirrup strain level will be greater for the plainstirrups compared with the deformed stirrups. Due tothe better bonding with deformed bar strain of deformedbar shows smaller at a distance from crack intersection.As a result, overall strain with a deformed bar is smallerand causes smaller shear crack width. Due to inferiorbonding between plain stirrups and concrete, stirrupstrain in plain stirrups shows uniform and smaller stir-rup strain distribution compared to deformed type stir-rups. The effect of bond condition of stirrups in PRCbeams on shear cracking behavior is similar to that ob-served for RC members in a previous study by Hassanetal. (1991).

3.3.5 Amount of longitudinal reinforcementTo examine the influence of longitudinal reinforcementratio on shear cracking behavior in PRC beams, the re-

300 300

Z 250 Z 250.:.!.

==-Q) 200 Q) 200() ()

0 0l.L. 150 l.L. 150ro -+-IRC-1 ro -+-IRC-1Q) 100 Q) 100.r::: .r:::

(J) -O--IRC-2 (J) -O--IRC-350 50

----6-1 RC-3 ----6-IPRC-1

0 0

0 2000 4000 6000 8000 0 2000 4000 6000 8000tvlaxirrum stirrup strain (IJ) tvlaxirrum stirrup strain (IJ)

(a) (b)

300 300

250 250Z Z.:.!. .:.!.

200200Q) Q)() ()

0 150 0 150l.L. l.L.

ro 100 ro 100Q) Q) -+-IPRC-1.r::: -+-IRC-3 -o--IPRC-1 .r:::(J)

50(J)

50----6- IPRC-3 ~IPRC-4 -O--IPRC-2

0 0

0 2000 4000 6000 8000 0 2000 4000 6000 8000tvlaxirrum stirrup strain (IJ) tvlaxirrum stirrup strain (IJ)

(e) (d)

Fig. 9 Shear force versus maximum stirrup strain.

0.5

EE 0.4

-'=~ 0.33:~u 0.2~utii 0.1Q)

-'=(J)0

0 1000 2000 3000 4000 5000Stirrup strain (~)

0.5E-S 0.4

-'=i5'3: 0.3~u~ 0.2utii

0.1Q)

-'=(J)

0

0

oo 0 0 o 0

---~, m 0---l§l~ .IPRC-1

1000 2000 3000 4000 5000Stirrup strain (~)

0.5 0.5

E +IPRC-1 0E-S 0.4 o IPRC-2 -S 0.4 +

-'= + ....i5 -'='3: 0.3 i5 0.3~ '3:u

0.2~

~ u 0.2rou Utii 0.1 tii 0.1Q)

-'= Q)(J) -'=

0 (J)0

0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000Stirrup strain (~) Stirrup strain (~)

inforcement ratio (p, = Ajbd) was increased from 1.13%(beam IPRC-I) to 1.98% (beam IPRC-4). Beam IPRC-4has 75% more longitudinal reinforcement than beamIPRC-I. The rate of increase in shear crack width withshear force was found to be unaffected by the amount oflongitudinal reinforcement (Fig. 8(e)). Further, the rateof stirrup strain increase was found to be the same inboth beams IPRC-l and IPRC-4 (Fig. 9(e)). It seemsthat the amount of longitudinal reinforcement has aninsignificant effect on the shear cracking behavior ofPRC beams.

3.3.6 Stirrup ratioTo investigate the effect of the stirrup ratio on shearcrack width in beams IPRC-I and IPRC-2, the stirrupratio was changed from 0.338% (stirrup spacing, s =125 mm) to 0.188% (s = 225 mm), respectively, asshown in Figs. 1 and 2. Figure 8(d) shows the relation-ship between shear crack width and shear force. Thisimplies that shear cracking load is not affected by thestirrup ratio in PRC beams. Further, the maximum shearcrack width seems to be independent of the stirrup ratio,particularly at lower shear forces, in PRC beams. Thisinsignificant effect on shear crack width is attributed tothe high prestressing force (e.g. Peff = 375 kN) in PRCbeams. However, in RC beams as well as PRC beamswith low prestressing force (P eff:'S 150 kN), the stirrup

ratio had a significant influence on maximum shearcrack width (Hassan et 01., 1991, De Silva, 2005). Thusthere is a need to further investigate the effect of stirrupratio on maximum shear crack width in the case of PRCbeams.

3.4 Distribution of stirrup strain over beamheightFigures 11(a) to 11(d) show the distribution of stirrupstrain (in the stirrup placed at a distance of 500 mmfrom the loading point) at different loading stages, overthe beam height for beams IRC-I, IPRC-I, IPRC-2 andIPRC-3, respectively. A shear crack intersecting a stirrupcauses a sudden increase in strain measured by the stir-rup strain gage attached close to the location of thecrack intersection. In the case of beam IPRC-I, shearcracks appeared with a lower angle to the member axiscompared with beam lRC-1 (Fig. 7). As a result, there isno large increase in stirrup strain in the upper straingages on the stirrups of this beam (Fig. 11(b)). However,a different stirrup strain distribution was seen in beamIPRC-3, which had plain (round bar) stirrups (Fig.11(d)). Small stirrup strains were observed due to infe-rior bonding characteristics between the plain stirrupand the concrete. This is because slip occurs when ashear crack intersects the stirrup.

IRC-1 Load 150

~250 100E

-+--300 E 50.r:

~375 0.0OJ

20 00 "0

-0-400 Eco -50OJ--.-450 1Il

-100____ 500

-150Stirrup strain ()J)

(a) IRC·1 (5 =125 mm)

EE 50.r:g. 0"0

~ -50OJ

1Il

-100

150IPRC-2 Load

100 ~250E -E 50 -+--300.r:0.

0 ~350OJ"0

E 20000 -0-400co -50OJ1Il --.-450

-100--+--- 500

-150Stirrup strain ()J)

(c) IPRC·2 (5 =225 mm, Pe = 375 kN)

Load

~250

~350

15000 20 I 00 -0- 400

Stirrup strain ()J)

(b) IPRC·1 (5 =125 mm, Pe = 375 kN)

IPRC-3 Load

-+--300

~350EE 50.r:g. 0"0

EgJ -50

1Il

20 00 --.-450

~500

(d) IPRC·3 (5 =125 mm (plain stirrups),Pe = 375 kN)

3.5 Distribution of shear crack width over thebeam heightFigures 12(a) to 12(d) show the variation of maximumshear crack width over the beam height. Shear crackwidths were distributed uniformly over the beam depthin both RC and PRC beams at each load increment. Theaverage load at which the stirrups yield was between300 kN and 400 kN for both RC and PRC beams. Themaximum shear crack width over the beam depth in RCbeams was observed to be greater than 0.3 mm ((Fig.12(a)). However, in PRC beams, it was 0.2 mm, a muchlower value. It is clear that the prestressing force in PRCbeams significantly controls shear crack width up to theservice load. Beam IPRC-2 was designed to have largerstirrup spacing than beam IPRC-I. Therefore, with in-creasing load, a sudden increase in shear crack widthswas observed in beam IPRC-2 (Fig. 12(c)). This is dueto the wider stirrup spacing, resulting in a smaller re-straining effect against the growth of shear cracks in theweb. In addition, beam IPRC-3, which had a plain(round bar) stirrup, exhibited a sudden increase in shearcrack width as beam IPRC-2 when the load increased(Fig. 12(d)). This results from the inferior bonding be-

tween web reinforcement and concrete, which leads togreater shear displacement along the plain stirrups.

4. Proposed design methodology for shearcrack width

4.1 Evaluation of existing equationsThe test results presented in the previous studies (Ade-bar and Leeuwen 1999; De Silva 2005), and in the pre-sent study have shown that strains of stirrups are themost important factor affecting the shear crack width ofRC and PRC beams. Although the shear crack widthscan be related to the strain of stirrup, there is a largervariation of shear crack widths at the same stirrup strainlevel. For this reason, no general conclusion can bemade on the exact relationship between shear crackwidth and stirrup strain. Some researchers (Fukuyama etal., 2000; Shinomiya and Watanabe 2002) suggested asimple linear relationship, while some other researchers(Hassan et al. 1991; Piyamahant 2002) proposed a sec-ond order polynomial relationship. Table 5 shows asummary of available formulae for predicting shearcrack width for RC beams. It should be noted that the

150Load IPRC-1'E-100 Load

---....-130 E ---....-200--l:r-160 1: 50

Ol --l:r- 250'a;_220 I

1 0.0 -+-280Q) 0.6 0.8 10-0--290 s:E -0--300

~325 CtlQ) ~350co-100

-.--350 -.--400 .-150

'E- 100E1: 50.Ql

Q)

I.0

~ECtlQ)

co-100

---....-225

--l:r- 250

-+-300-0--340

~375

-.--420

-e--435

1: 50Ol'a;I.0

~ECtl

~ -100

150IPRC-3 Load

'E' 100E ---....-2001: 50Ol --l:r- 260'a;I 0 -+-310.0Q) 0 1.2 14s: -50 -0--350ECtl ~400~ -100

Maxirrum Crack Width (mm)

(d) IPRC-3 (s =125 mm (plain stirrups),Pe = 375 kN)

formulae are empirically obtained from the fitting ofexperimental data of shear crack width and stirrup strain.Although some prediction formulae for estimating shearcrack width have been proposed by some investigators,most of them are based on semi-empirical methods.Moreover, such prediction formulations were originallydeveloped for RC members, hence parameters concern-ing the effect of prestress are not considered. Therefore,the applicability of existing shear crack width predictionformulae in PRC members needs to be carefully investi-gated.

To verify the applicability of available formulae forpredicting shear crack width in PRC members, theshear crack widths calculated by various predicationequations are compared with experimentally measuredvalues as illustrated in Figs. 13(a) and 13(b) for beamsIRC-I and IPRC-l, respectively. It was clear that theshear crack widths predicted by all equations seem to beoverestimated, despite the fact that the predicted crackwidths are average crack widths. This may be attributedto the fact that the parameters related to prestressingforce, the presence of prestressing tendon in PRC beamsand the crack control characteristics of both longitudinalreinforcement and transverse reinforcement, can affectthe shear crack widths. However, these effects are not

4.2 Derivation of shear crack width formulaThe proposed equation to calculate the shear crackwidth ofRC and PRC members was developed based onthe assumption that there is an almost linear relationshipbetween shear crack width (w) and stirrup strain (cw). Asdiscussed in the preceding sections (3.3.1 to 3.3.6), thefactors affecting the shear crack width and stirrup strainrelationship are stirrup spacings, prestressing force,presence of prestressing tendon at the centroid of thesection, etc. By neglecting the effect of tension stiffen-ing, the average shear crack width is equal to the prod-uct of the average spacing of shear cracks, SIIII}, and thestirrup strain, Cw'

4.2.1 Shear crack spacing modelThe concept of this approach is based on the smearedcrack model, in which the actual complex crack patternis idealized as a series of parallel cracks occurring at anangle of e to the longitudinal axis of the member (Fig.14). This means that shear cracks are uniformly distrib-

Researchers Proposed equations Description of parametersw

k=1.7kww

m

C is the concrete cover, s is the spac-ing of the reinforcement bars

CEB-FIP Model wm =s rmlism (s~ 15rp),kl for deformed bars 0.4 andCode (1978)

[ s] ¢ d-x 0.8 for plain bars, k!= 0.25, rp is bars~ =2 C+- +k\k,--:;'-.- diameter, pI' is AsIAc,ej, E:,m, is the10 p, sma

stirrup strainFor plain barK\ = 2.4

[ ¢ ] k\k,S = 4x 103£. + 2x I06(£w)'

wm = 1000 S kJ,kp

For deformed bar

Hassan el al., K\ =2.0

(1991) [ r [' ]XS = 8x I03£w+ 2x I06(£w)'

k-~ 'k-~ K1 : 1.2 for vertical stirrupsp - 0.004 ' J' - 19.6 :1.0 for inclined stirrups

Ic' is the compressive strength ofconcrete

Fukuyama el al., B D : overall depth of the section (mm)W =0.9D~

(2000) scr J2 .E, = stirrup strain

W =1 *B p,=A.[(2Cb+<p)/b], b is beam width,Shinomiya el al.,

01 C1I 1.0\'

C6 = (s,,-rp)/2; c is the side concrete(2002) lav=2[ Cs+cb +~ ]+O.I~ cover, s,. is the stirrup spacing, s is

2 10 Pe the distance between stirrup legs

Piyamahant 2d s Ic' is the compressive strength ofW = v • S = B.(6+3500B,,) concrete, dv = diameter of stirrup, s =(2002) ",' (.t;' / 20)X ' normalized slip, E:w = stirrup strain

uted with constant crack angle (8) and crack spacing(SIIIO), as shown in Fig. 15(a). The spacing of the shearcracks, S1II8, depends on the crack control characteristicsof both the longitudinal and transverse reinforcement, asshown in Figs. 15(b) and 15(c), respectively. The CEB-FIP Model Code (1990) provides an expression for anaverage crack spacing in two orthogonal directions, asshown in Eq. (2).

sm(J=I~~~)mx my

where SIIIX is the average horizontal crack spacing (thatwould result if the member is subjected to axial tension),and SillY is the average vertical crack spacing (that wouldresult if the member is subjected to transverse tension).The idea of these crack spacings is estimated from thecrack spacing expression written in the CEB-FIP ModelCode (1978):

The crack spacing expression in the CEB-FIP ModelCode (1978) was intended to calculate crack spacing onthe member surface. Further, this expression considerscrack spacing in the shear span region of the member

and the distribution of cracks inclined to the reinforce-ments. To account for the fact that the shear crack spac-ing increases as the distance between the member sur-face and the reinforcement increases, the maximum dis-tance away from the reinforcement (cx and cy) instead ofside concrete cover, c, was used. Therefore Eq. (3) wasmodified as the following equations to calculate thehorizontal crack spacing (SIIIX) and the vertical crackspacing (SillY)'

Smx = 2al [c +~ ] + k k a dbx (4a)x 10 I 2 I

Px

Smy = 2fJI [c + ~ ] + k k fJ dbv (4b)y 10 \ 2 \ Pv

whereCx : distance from the horizontal centre line of the sec-tion to longitudinal reinforcements (see Fig, 16)cy: distance from the centre line of the section to theinner edge of vertical reinforcement (see Fig. 16)SX: longitudinal reinforcement spacingSy: web reinforcement spacingk/: coefficient representing the bond characteristics ofthe bars (0.4 for deformed bars and 0.8 for plain bars)k;: coefficient representing the influence of the form ofthe stress diagram (0.25 for pure tension)dbx: diameter of longitudinal reinforcementdbv: diameter of web reinforcementpx: amount of longitudinal reinforcement;

1.0 .Exp IRC-1

E(a)

DCEB-FIPE 08 X

~ XHassan!C 0.6.~ ~Shinomiya-"C.l ~E 0.4 o Piyamahant 0C.l"-IIIC1l 02~en ••••

0.00 1000 2000 3000 4000 5000 6000

Stirrup strain (IJ)

10 .Exp IPRC-1

E (b)

08 DCEB-FIPE~ XHassan!C 0.6.~

~Shinomiya-"C.lE 0.4C.l"-IIIC1l 0.2~en

0.00 1000 2000 3000 4000 5000 6000

Stirrup strain (IJ)

Fig. 13 Accuracy of available prediction formulae forshear crack width.

Ae,ej effective concrete area [2.5x(h-dJx width of sec-tion(bx)] (CEB-FIP Model Code (1990»h: overall height of the sectionde: effective depth based on total longitudinal steel In-cluding prestressing tendonbx: width of the hatch sections (see Fig. 16) along theeffective height (i.e., 2.5x{h-dJ)Ax: total area of longitudinal reinforcementApx: total area of prestressing steel

o

__ A_,,_Pv: amount of web reinforcement; p" -b" s,

Av: total area of web reinforcementbw: web width in mm

In addition, the proposed crack spacing model takesinto account the presence of prestressing tendons (Apx)in PRC beams. The total area of longitudinal reinforce-ments is distributed in the effective concrete area (Ac.ef)as shown in Fig. 16. The effective concrete area (Ae,ef) iscalculated based on the steel centroid (that can be ob-tained using Apx and AJ. In the case of different shapesof cross sections (e.g. I-shaped), Ae,ef is calculated basedon the width of the flange and the width of the webalong the effective height. The correlation factors, aland PI, are determined from the regression analysis ofexperimental values. It was found that at and PI areequal to 0.36.

4.2.2 Verification of shear crack spacing modelTable 6 shows a comparison of the calculated shearcrack spacing values and the experimental results. Thecalculated shear crack spacing values show reasonablygood agreement with the experimental values. However,beam IRC-2 shows relatively wide spacings of cracks(Fig. 7) compared to the other RC beams. Therefore itseems that the proposed crack spacing model overlyunderestimates the crack spacing in beam IRC-2.

4.3 Design methodology for shear crack widthA design methodology for average shear crack width isproposed in Eq. (5). To incorporate the effect of shearcrack angle, a shear crack spacing parameter (smO) isincluded. The shear crack spacing, SmO, can be deter-mined using the horizontal crack spacing Sm." and verti-cal crack spacing, smY' from the provision suggested inthe CEB-FIP Model Code 1978, as discussed in the pre-ceding section. The average shear crack width, Wk, canbe expressed as follows;

Wk: average shear crack width perpendicular to the cracksurface

••• ••••Smx

kw: coefficient for effect of web reinforcement angle,(1.2 for vertical stirrups; 0.8 for stirrup with 45° to 60°angle to member axis)SmO: average shear crack spacingCw: strain in web reinforcement (equation stipulated inJSCE (2002) code based on truss theory)

The proposed shear crack spacing 'model and shearcrack width formula are compared with experimentaldata measured in this study. The accuracy of the pro-posed equation for calculating the shear crack width inbeam IRC-I and beam IPRC-I are illustrated in Figs.17(a) and 17(b), respectively. The average shear crackwidth is calculated using Eq. (5). In this calculation,stirrup strain is the measured stirrup strain at the samelocation of the measured crack width. The calculatedshear crack widths show good correlation with themeasured shear crack widths. In addition, it can be seenfrom Table 7 that the scatter, characterized by the stan-dard deviation (a) and the correlation of variance(COV) indicated in that table, are smaller in the pro-posed equation than in the other prediction formulae.However, it should be noted that the proposed equationis based on a rather limited number of test data andrange of variability of the parameters studied.

An experiment was conducted with three I-shaped rein-forced concrete (RC) beams and four I-shapedprestressed reinforced concrete (PRC) beams to investi-gate the effect of various parameters on maximum shearcrack width and the shear crack distribution. The majorvariables used were prestressing force, side concretecover, stirrup spacing, type of stirrup and amount oflongitudinal reinforcement. Further, equations for theprediction of shear crack spacing and shear crack widthin RC and PRC members are proposed. The followingconclusions can be drawn from this study:

Effective concretearea (Ac,ef)

I i I

I . I

~SiX

Calculated crack Ratio cal/exp Diagonal crack spacing (mrn)spacing

BeamRatio Ratio 5mB, 5mB, Ratio:Smx Smy Smx Smy Cal Exp Exp/Cal

IRC-1 158.96 104.62 1.0 1.0 89.24 92.92 1.0IRC-2 158.96 72.94 0.7 0.3 70.72 173.73* 0.4 .IRC-3 165.87 104.62 0.8 0.7 90.74 127.59 0.7IPRC-I 165.87 104.62 0.8 0.5 88.56 147.54 0.6IPRC-2 165.87 162.97 0.8 1.3 120.08 107.91 1.1IPRC-3 165.87 168.56 0.9 1.4 122.67 101.94 1.2IPRC-4 152.85 104.62 0.5 0.7 86.59 137.99 0.6

Table 7 Statistical analysis of ratio between measuredvalues and calculated values (wexp/Wca/).

IRC-I IPRC-IResearcherls

Avg Std COV% Avg Std COV%

CEB-F1PModel Code 0.754 0.28 37.8 0.856 0.23 27.0

( 1978)Hassan el al., 0.491 0.22 45.5 0.555 0.23 40.5(1991 )Fukuyama el

0.208 0.08 37.8 0.249 0.06 27.0al., (2000)

Shinomiya el0.637 0.24 37.8 0.761 0.20 27.0

al., (2002)Piyamahant

0.679 0.36 53.0 0.744 0.37 50.3(2002)

Proposed 0.619 0.23 37.8 0.750 0.20 27.0

Avg. - average valueStd. - standard deviationCOV% - Correlation of variance

(1) The prestressing force provided in PRC beams in-creases their shear cracking load compared to RCbeams. However, after the initial formation of shearcracks, the effect of this prestressing force was notpronounced. At a same level of shear force, agreater prestressing force tended to decrease shearcrack widths and stirrup strains. The compressivestress in the concrete due to prestressing force at thecentroid of the section had some effect on the rela-tionship between shear crack width and stirrupstrain in PRC beams.

(2) The presence of a prestressing tendon at the cen-troid of the beam section helps with resistance tothe externally applied load by means of dowel ac-tion. Beams with a prestressing tendon but withoutprestressing force exhibited a smaller shear crackwidth than RC beams at the same level of shearforce. The prestressing tendon at the mid-depth ofthe section acts as longitudinal reinforcement to re-strain the opening of crack width in the longitudinaldirection, thereby reducing the shear crack width.

(3) Stirrup strain was found to be the most important

1.0(a) /

E /

0.8 +50%.s /

ili /

()0.6£~ /.~ ,.'

"" 0.4 •0~/~E -35%

0 ..~:0 •~tQj 0.2 ~X~/./··~

Ul

#1 • Proposed IRC-1/

0.00.0 0.2 0.4 0.6 0.8

Shear crack width, Exp. (mm)

1.0

(b)

E 0.8.sili()

0.6£~.~"" 0.40

E0~'"'" 0.2~

Ul

0.00.0 ~2 ~4 ~6 ~8 1~

Shear crack width, Exp. (mm)

factor affecting shear crack width in both RC andPRC beams. The relationship between shear crackwidth and stirrup strain for deformed stirrups waslinear, while it was non-linear (polynomial curve)in the case of plain stirrups. Further, due to the poorbonding between stirrup and concrete in the case ofplain stirrups, the shear crack displacement in-creased in the stirrup direction and so the shearcrack width was greater.Increasing the amount of side concrete cover re-sulted in a larger shear crack width at the same stir-rup strain level. However, owing to the extraordi-nary crack pattern observed in the beam tested inthis study, further investigation is needed to fullyclarify the effect of side concrete cover on shear

crack width.(5) The amount of tension reinforcement and the stir-

rup spacing were found to have an insignificant ef-fect on maximum shear crack width in PRC beamswith a prestressing force of375 kN.

(6) By considering the above investigated parametersas variables, a simplified shear crack spacing modeland an equation for predicting shear crack width inRC and PRC members were proposed. The shearcrack widths computed from the proposed equationshowed better correlation with the test results com-pared to other prediction formulae.

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