The Reconstruction of Modelling Reinforcement

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International Conference on Rehabilitationand Maintenance in Civil Engineering (ICRMCE)

Solo, 21-22 March 2009

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THE RECONSTRUCTION OF MODELLING REINFORCEMENT

FOR PREVENT THE EARLY FAILURE OF DEEP BEAM

REINFORCED CONCRETE

Erwin Rommel1*

Civil Engineering Departement, Engineering Faculty, Muhammadiyah Malang University 1*

Raya Tlogomas 246 Malang 65114 Phone (0341) 4 64318 Fax (0341)468502 email : [email protected]

Abstract

The used of inclined stirrup and transverse reinforcement still can t increase the strength of deep beamsignificantly, crack propagation still concentrated of mid-span and the deep beam is have a morepossibility of flexure failure. Longitudinal shear reinforcement can be used as reinforcement to optimizethe strength increasing, so that can prevent the failure of deep beam reinforced concrete. The trial are givenof sixteen concrete beam (13x40x100) cm that have many variation of longitudinal shear reinforcement

from 2 6 mm ( = 0,136%), 4 6 mm ( = 0,272%) and 6 6 mm ( = 0,408%) with each have 4 (four)

beam and being tested in shear span ratio, respectively 0,6 ; 0,8 ; 1,0 ; and 1,2. The result of thisresearches explain that using longitudinal shear reinforcement can increase the first crack -load until 87,5%and ultimate-load until 83,2% and also shear stiffness can increase up to 175%. The crack of beam ishappen more distribute and the increasing of crack propagation can be reduce. Failure pattern of beam isthe shear failure that have a ductility in beam that given some load with ratio a/d less than 1.0.

Keyword :deep beam, longitudinal shear reinforcement

1. INTRODUCTION

The behavior of deep beam is verydifferent to conventional beam, where thecollapse occurred due to more dominantshear strength so that shear reinforcement

design into the internal reinforcing asimportant. Shear reinforcement not only canincrease the shear capacity of beam, but alsochange the beam of ductility where shearreinforcement to reduce the risk of occurredbrittle failure. In addition to stirrup shearreceive,so this research study varied useshear reinforcement longitudinal that isexpected to be contributed to received ofshear capacity deep beam.

Research of shear compressionfailure has been done on the deep beamwith ratio a/d between 1.0 to 2.5 with one

point-loading and two point-loading.Explained that strength of concrete, the ratioflexurel reinforcement, shear reinforcementin the ratio a/d 1.0 to 2.5 will affect the shear

compressive failure of deep beam (Zararis,

2003).

Design of deep beams with CIRIA usenormal and hight strength concrete has been

revision made to estimate occurred shearultimit. Given the parameters vary in theinvestigation, among other things, the ratioa/d between 0.27 to 2.7; the number offlexurel reinforcement (1.23 to 5.80%), the

number of shear reinforcement and qualityof concrete used between 25 to 100 MPa

(Leong and Tan, 2003).

Approximate of the region anddimensions of shear compressive failure canbe carried out on the deep beam with AEmethod, which measures the amount ofenergy from local sensors provided onconcrete surface. Evaluation of regionalfailure can be known from the compressiveuniaxial testing in the beam based on themaximum amplitudo measured from thestresses maximum. The length of the region

beam failure the test results appeared morethan 30% of the results of sensormeasurements made from various shapesand size of the test specimen (Watanabe,

2002).

The effect of the concentration loadwith a different shear reinforcement on deepbeams with high strength concrete (f'c> 55



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International Conference on Rehabilitationand Maintenance in Civil Engineering (ICRMCE)Solo, 21-22 March 2009

ISBN No

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MPa) have also been examined, where thetest is done entirely with top edge of thebeam, bottom edge of the beam and thecombination of top edge and bottom edge,with a ratio Ptop /Pbottom 1:1 and 2:1,

respectively. While variations shearreinforcement that tested, among other deepbeam with the inclined flexurelreinforcement, vertical shear reinforcement,combination of horizontal and vertical shearreinforcement. This research also explainsfield of beam deflection, wide crack, formpatterns, failure model, the diagonal crackload, strength and service ultimit (Tan and

Wei, 1999).

The use of variations of inclinedstirrup have been observed, where the stirrupwith slope of the 450 with a layer transverse

reinforcement will provide for increasedstiffness of beam 26%, but the crack beamhas not spread on the shear region, theconcentration of crack occur only the mid-span toward the top side of beam(Hermawan and Erwin, 2006). Failurebeams also often occur in the supported ofbeam areas, where the distribution of theshear is large enough before beam collapsedsuddenly (Fardho and Erwin, 2006). This

research aims to find out the influence ofshear longitudinal reinforcement against thecapacity of deep beam reinforced concrete

and other behavior reinforcement.

2. RESEARCH METHOD

Beam test of 12 (twelve) sized(130x400x1000) mm with a full scale test.The variables are taken 4 (four) beamswithout using shear longitudinalreinforcement, and then every 4 (four)beams using, respectively ; 1 layer Ø 6mm,2 layers of Ø 6mm Ø and 3 layers of Ø6mm, shear longitudinal reinforcement. Allbeams tested with of setting two-pointsloading, with the ratio a/d respectively; 0.6;

0.8 ; 1.0 and 1.2. The concrete used 25MPa. Testing equipment used, among otherthings, loading capacity of 30 tons of theframe, hydraulic jack capacity of 50 tons,Load ceel capacity of 30 tons, with a loadindicator with a reading accuracy up to 1 kg,the dial gauge accuracy 0,001 mm. Testsbeam is done with use a loading frame, asshown in the picture 3.4. The reading test is

done at the expense of data provided everyincrease of 250 kg, while load of the initialcracked beams, load of diagonal crackoccurred, load of the condition ultimitreached, and displacemen on the point load

(top edge and bottom edge beams). Inaddition strain also observed that occurthrough the strain gauge was installed in theflexure reinforcement, stirrup and shearlongitudinal reinforcement, as shown in thefigure-2

Figure 1: Setting of test beam with two-point

loading

Figure-.2: Reinforcement of the test beam

2 10 mm

Dial gauge

Load CellHidraulic Jack

SpecimenBeam-support

Actuator Frame

L

a

Loading Frame

Load Indicator

Hidraulic Pump

100 cm13 cm

40

2 10 mm

4 10 mm

6-100 mm

100 cm13 cm

40

2 10 mm

4 6 mm

6-100 mm

100 cm

40

6-100 mm

13 cm

4 10 mm

2 6 mm

100 cm13 cm

40

2 10 mm

6 6 mm

6-100 mm

BT-TGL0

BT-TGL2

BT-TGL1

BT-TGL3

Strain gauges



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15000

20000

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BT TGL-0 BT T GL-1 BT T GL-2 BT T GL-3

Type Balok

B e b a n r e t a k a w a l ( k g )

a/d=0,6

a/d=0,8

a/d=1

a/d=1,2

0

5000

10000

15000

20000

25000

30000

BT T GL-0 BT T GL-1 BT T GL-2 BT T GL-3

Type balok

B e b a n u l t i m i t ( k g )

a/d=0,6

a/d=0,8

a/d=1

a/d=1,2

3. DISCUSSION 3.1 Shear Capacity

Figure 3 explains that with theaddition of shear longitudinal reinforcement,increase the value of the load capacity that

can beam received deep beam for both first-crack and ultimit load. The largest increaseoccurred in the deep beams are given 3(three) layer shear longitudinalreinforcement (beam BT-TGL3) comparedwith the deep beams without shearlongitudinal. Increase load of the initialcracked beams, for the ratio a/d, respectivelyof 65.4% (ratio a/d = 0.6); 23.8% (ratio a/d =

0.8); 87.5% (ratio a/d =1.0) and 86.9% (ratioa/d=1.2). Similarly to load shear ultimit have

the same trend with increasing load ultimitby 45%; 83.2%; 72.4% and 66.7%

respectively for the ratio a/d 0.6; 0.8; 1, 0and 1.2.

Figure 3: Relations shear force of beam to shearlongitudinal reinforcement

From the results of the analysis, itcan be inferred that with the addition ofshear longitudinal reinforcement, willincrease the load capacity that can beaccepted by the deep beam. This increaseoccurred due to the additional reinforcing oflongitudinal direction or horizontal that is

able to receive shear force occurred as aresult of the loading. Longitudinalreinforcement would be able to provideaction together stirrup after diagonal crackoccurred in the region shear span. However,

the addition shear longitudinalreinforcement this must be calculated tolimit fixed rate reinforcing maximum ratio

max to avoid the over-reinforced condition.

Figure 4: Capacity of deep beam to use inclined

stirrup and transverse reinforcement( Erwin, 2006 )

If the influence of views on the useof inclined stirrup as shear reinforcement(Erwin , 2006), that shear longitudinalreinforcement clearly provide improvementsto capacity shear beam as seen from Figure4, where the combination of stirrup and

Two-point loading (a/d = 1.0)

0

5000

10000

15000

20000

B T-SV0 B T-SV1 B T-SV2 B T-SM 0 B T-SM 1

Type Balok

B e b a n

( k g )

First crack

Ultimit

diagonal crack

Two-point Loading (a/d = 1.2)

0

5000

10000

15000

20000

B T-SV0 B T-SV1 B T-SV2 B T-SM 0 B T-SM 1

Type Balok

B e b a n

( k g )

First crack

ultimit

diagonal crack

Two-point Loading (a/d = 0.8)

0

5000

10000

15000

20000

B T-SV0 B T-SV1 B T-SV2 B T-SM 0 B T -SM 1

Type Balok

B e b a n

( k g )

first crack

ultimit

diagonal crack



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0

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0,6 0,8 1 1,2

Rasio a/d

B e b a n U l t i m i t ( k g

BT TGL-0

BT TGL-1

BT TGL-2

BT TGL-3

0

5000

10000

15000

20000

25000

30000

0,6 0,8 1 1,2

Rasio a/d

B e b a n R e t a k ( k g )

BT TGL-0

BT TGL-1

BT TGL-2

BT TGL-3

transverse reinforcement that just reduce thecapacity ultimit deep beams. Even in theratio a/d = 0.8 load ultimit deep beams trendto be constant (no-effect) with the stirrupand transverse reinforcement. Increase the

load cracking diagonal and initial crack ofbeams, although the initial fluctuate but have

not seen significant.

3.2 Ratio Shear Span a/d

With see Figure-5, that changeslocation based on the ratio a/d give a verysignificant to the amount of first-crack loadthat can be accepted by the beams. In alltype beams that the more visible a smallratio a/d, so first-crack load that can beaccepted will be increasingly small. In thebeam without shear longitudinal

reinforcement (beam BTTGL-0) decreasethe shear beam of 49.8% for crack-load and51.3% for ultimit load beams. Similarly forthe deep beam with shear longitudinalreinforcement, respectively 1 layer; 2 layerand 3 layer of decrease 55.3% 59.7% 43.2%of the crack-load beams and 56.4%; 47.9%;44% of the ultimit load beams whencompared with a ratio placement location ofthe load a/d = 0.6 and 1.2.

Figure-5: Relations with the capacity of beam

ratio a/d on the deep beams

This shows that the loading of thesmall distance received beam the ability ofthe support beams to receive first-crack loadwill increase. Results of this study supportsthe results of that research has been done by

Zarraris in 2003 stating that the variationsof a/d between 1 to 2.5 with a single-point

and two-point loading determine the loadcapacity that is able to receive deep beams.

From the results of the analysis ofthe above can be concluded that changes inthe ratio a/d is very influential on theloading can be accepted by the beams. Thiscan be explained that the more a smalldistance (the distance between the supportbeam with the load), the bending momentthat there will be flexible increasingly smallso shear stress will be greater.

Figure 6: Relations ratio a/d and inclined stirrup

with shear capacity of deep beam (Erwin, 2006)

In research deep-beam in useinclined stirrup and transverse reinforcement(Er win, 2006) also illustrate that the use ofthe ratio a/d increasingly smaller yet providea significant increase in the ability tocapacity shear deep beams. The increase

Balok BT-SM0

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

one-load a/d=1.2 a/d=1 a/d=0.8

Rasio a/d

B e b a n

( k g )

First crack u ltim it

Balok BT-SM1

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

one-load a/d=1.2 a/d=1 a/d=0.8

Rasio a/d

B e b a n

( k g )

First crack u ltim it



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0

50

100

150

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250

300

350

400

450

500

BT TGL-0 BT TGL-1 BT TGL-2 BT TGL-3

Type balok

T e g a n g a n b a j a ( M P a )

tulangan pokok

tul. Geser long.

sengkang

0

10.000

20.000

30.000

40.000

50.000

60.000

70.000

80.000

90.000

BT TGL-0 BT TGL-1 BT TGL-2 BT TGL-3

Type balok (jumlah tul.geser long)

K e k a k u a n g e s e r ( k g / c m )

a/d = 1,0

a/d = 0,8

a/d = 0,6

ranged up to 10% compared to deep beamwith a stirrup of conventional (see Figure 6).Shear longitudinal reinforcement so thatsiginifikan give more ability shear beam theincrease compared with inclined stirrup, or

combination of inclined stirrup andtransverse reinforcement.

3.3 Reinforcement of Beam

In the deep beams which arelongitudinal reinforcement obtained on thebehavior stress of reinforcement differentbecause of the stirrup and shear longitudinalreinforcement as reinforcing a receivedshear force of beam and flexurereinforcement function as a reinforcingbending of beam. Figure-7 explains that theinfluence of the addition shear longitudinal

reinforcement of deep beams are visiblehigh real behave the stirrup of deep beams.The more the number of shear longitudinalwill reduce the stirrup in receive shear beam,so stress that occurs in the steel stirrup alsoshowed a decrease, but increase the value ofstress on the steel shear longitudinal.

Some of the load will hold bylongitudinal reinforcement and the other bythe stirrup. This will cause the decreasingstrain value in stirrup. The more shearlongitudinal given the increasingly smallstrain also occurred on the stirrup. However,

should note that the addition of shearlongitudinal reinforcement this must alsoremain to be the maximum limit to avoid theover-reinforced. This is seen in the behavior of differentstress in the flexure reinforcement, look atthat strain of flexure reinforcementmeasured in the middle of beam (mid-span)

continues to increase with the addition ofbending moment beams in region mid-spandue to shear of beam which is alsoincreasing.

3.4 Shear Stiffness.The tendency of changes shear

stiffness in the deep beams due to theaddition shear longitudinal reinforcementmore clearly seen in Figure 5.6 below. Fromthe relationship graph load received at the

cracked shear of beam with deflectionshown in Figure 9, that the use of deepbeams longitudinal reinforcement that will

generate more, which is also larger shearstiffness beams. Deep beam with use ofshear longitudinal reinforcement produce the

largest shear stiffness, respectively ; 49,508kg/cm for the beam with 2 layers

reinforcement (BT TGL-2) and 79,714kg/cm for the beam with 3 layersreinforcement(BT TGL-3), where increasedstiffness of deep beam reached 71% and175%, respectively in the ratio a/d = 0.8.

Figure-7: Stress on steel reinforcement of the

deep beam

Figure 8: The curve between the shear stiffnesswith type of beam

This clarify that the use of shearlongitudinal reinforcement also influencedby how the location of shear load given deep

beams. Giving the load on the beam withshear ratio a/d = 1.2 is also seen in-effectivebecause of arch action zone will beconcentrated in areas where the combinationof shear and bending moment tends to belarge. While, on the beam with 1 layer shearlongitudinal reinforcement (BT TGL-1), andthe beam without shear longitudinalreinforcement (BT TGL-0), shear stiffnessonly reached 37,900 kg/cm and 31,704



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BT TGL-0

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0 200 400 600 800 1000

Defleksi ( x 0,01 mm )

B e b a n ( k g )

a/d = 1,2

a/d = 1,0

a/d = 0,8

a/d = 0,6

BT TGL-1

0

5000

10000

15000

20000

25000

30000

0 200 400 600 800 1000

Defleksi ( x 0,01 mm)

B e b a n ( k g )

a/d = 1,0

a/d = 1,2

a/d = 0,6

a/d = 0,8

BT TGL-2

0

5000

10000

15000

20000

25000

30000

0 200 400 600 800 1000


B e b a n ( k g )

a/d = 1,2

a/d = 1,0

a/d = 0,6

a/d = 0,8

BT TGL-3

0

5000

10000

15000

20000

25000

30000

0 200 400 600 800 1000


B e b a n

( k g )

a/d = 0,8

a/d = 0,6a/d = 1,0

a/d = 1,2

kg/cm, almost the same beam with usereinforcement inclined stirrup (Erwin,

2005).

In the research that has been donebefore, about the influence of the inclined

stirrup of deep beam (Erwin, 2005) theresults that the stiffness beam only useinclined stirrup will be increased 125%compared with conventional stirrup,wherease if use a combination of inclinedstirrup and transverse reinforcement,stiffness of beam is not increasedsignificantly.

Figure 9: The curve between load and deflection

on each type of beam

This clarify that the use of shearlongitudinal reinforcement withconventional stirrup so far better than if thebeams using a combination of transversereinforcement and inclined stirrup. Give

shear longitudinal reinforcement (thehorizontal direction beams) will be able toprevent and reduce the crack, whichoccurred as a result of shear, becausetrajektori of tension on the deep beams tendto have a horizontal direction, especially inareas shear span, the ratio a/d. Meanwhile,inclined stirrup is done in-effective becausereceive compressive stress of arch actionconcrete trend to the direction perpendicularto the inclined stirrup.

3.5 Crack Propagation

Addition shear longitudinalreinforcement will improve the ability oflongitudinal beams hold the load in the first-crack, the slowly propagation crack andincrease in the ability to receive ultimit loadof beam. Relations load history and longcrack on each shear span ratio a/d given canbe seen in Figure 10. From the graph thatlooks at the ratio a/d=1, adding shearlongitudinal reinforcement provides asignificant influence on the patternpropagation crack of deep beam. In thebeam BT TGL-0, when the load reached

9,500 kg of the approaching peak load of9,635 kg, the length of the crack occurredreach 35.25 cm. But on the beam with asingle layer longitudinal reinforcement(BTTGL-1), with the same load (of 9,500 kg)long crack can be hampered, so crackoccurred only during the 24 cm. This will belong crack on the wane for the beam to getthe additional reinforcing of shearlongitudinal more than one layer. In the BTTGL-2 long crack that happens reached 15.5cm, while the BT TGL-3 long crack on thewane until 0 cm (not yet occurred in the

cracked of beam load 9,500 kg). The sametrend is also visible in the ratio a/d = 0.8 and0.6

Based on the analysis of the abovecan be concluded that the shear longitudinalreinforcement provide a very real influenceon the propagation crack of deep beam. Thepropagation crack can be hampered by theexistence of shear longitudinal



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Rasio a/d = 0,8

0

5000

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0 5 10 15 20 25 30 35 40

Panjang Retak (cm)

B e b a n

( k g )

BTTB-0

BTTB-1

BTTB-2

BTTB-3

Rasio a/d = 1

0

5000

10000

15000

20000

25000

30000

0 5 10 15 20 25 30 35 40

Panjang Retak (cm)

B e b a n ( k g )

BTTB-0

BTTB-1

BTTB-2

BTTB-3

Rasio a/d = 0,6

0

5000

10000

15000

20000

25000

30000

0 5 10 15 20 25 30 35 40

Panjang Retak (cm)

B e b a n ( k g )

BTTB-0BTTB-1

BTTB-2

BTTB-3

reinforcement, so that it can increase theload capacity that can be accepted by thedeep beams.

Figure 10: The curve between load and length

crack on the deep beams

3.6 Crack of Pattern and Failure of Beam

In the ratio a/d = 1.0 and 1.2, crack

of beams begins from the mid-span andcracked it will be long in line with additionload to the top of the beam with propagation

direction that tends to vertical. Thepropagation crack this kind shows that thepatterns of behavior occurs is flexure crack.Meanwhile, the ratio a/d = 0.6 and 0.8 crackstarted in support of beam the region towardto the concentrated of load with the patternof diagonal crack. This pattern ofpropagation shows the behavior sheardominant of beam.

Based on the pattern of crack

occurred can be concluded that the deepbeams, the failure occurred is a combinationof shear and flexure failure. Meanwhile, theratio a/d = 0.6 and 0.8 crack of beam

occurred below the point load and thenspread to the diagonal direction toward thepoint load itself, which means that thebehavior cracked more toward the behaviorof shear, but with the addition of the numberof reinforcement will change the behaviorshear of beams into the behavior of shearductility.

Based on the above discussion canbe taken conclusion that changes in the ratioa/d of beams cause differences in the typesof failure beams where with the ratio a/d =1.2 and 1.0 tend to collapse the flexure

failure, while beam with a ratio of a/d = 0.6and 0.8 tend to collapse the failure shear, buthave better ductile with the decreasing ratioof a/d.So the shear force of location determine thefailure of pattern occurred on the deepbeams. When the load is near the support ofbeam (a/d increasingly small), the failurethat occurred more patterns tend to collapsedue to shear stress. Conversely, if given theshear force that keep the support (a/d larger),then the failure that occurred more patternstend to collapse due to flexure stress.

Meanwhile, due to the addition shearlongitudinal reinforcement will change thebehavior of failure beams from the shearfailure britlle into failure ductile. This is dueto the contribution shear longitudinalreinforcement in receive the shear stress sothat failure beam more dominant caused bythe stress flexure.

CONCLUSION

Addition rshear longitudinalreinforcement as the reinforcing of deepbeams can increase the crack-load capacity

up to 87.5% (Pcraks max = 18,930 kg in theratio a/d = 1,0) and the ultimit load to 83.2%(Pult max = 24,562 kg in the ratio a/d=0.8)compared to deep beams withoutlongitudinal reinforcement, trend wheremore and more small ratio a/d, the ability todeep beam larger. Shear stiffness of deepbeam also increased to 175% in the ratio



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a/d= 1.0 due to the addition shearlongitudinal reinforcement.

Improving the ability shear of beamthe followed transfer of shear reinforcing ofdeep beams, namely the reduction of tension

on steel of stirrup so that increased tensionin steel of the shear longitudinalreinforcement.

With the shear longitudinalreinforcement propagation crackincreasingly hampered where the crackspread more evenly on the entire beam, bothin the region mid-span and the support areasof beam, with the failure occurred is theshear failure of ductile in the ratio a/d moresmall or a/d<1.0

ACKNOWLEDGMENTS

The author would like to thank all of thefinancing of this research from theDirectorate of Research and Public Servicesto the Directorate General of HigherEducation Ministry of National Education,Indonesian, Jakarta, for Fiscal Year 2008with the number of contract229/SP2H/PP/DP2M/III/2008.

REFFERENCES

1. Anonim (2005) Design of Beams for

Shear , Dept. of Civil EngineeringUniversity of Pretoria

2. Anonim (1996) ACI Code 318-95, Building Code Requirements for

St ructural Concrete, Portland Cement

Association, Illinois, Chichago

3. Erwin R (2006) Pengaruh Pemakaian

Tulangan Bagi Terhadap Rambatan dan

Lebar Retak pada Balok Tinggi,

Proceeding Seminar Nasional, 9Desember 2006, UniversitasMuhammadiyah Malang, ISBN 979-796-09-0

4. Erwin R (2006) Pengaruh Jumlah

Tulangan Bagi dan Arah Sengkang padaKemampuan Geser Balok Tinggi, JurnalTeknik GELAGAR, Volume 17, Nomor01, edisi April 2006, ISSN 0853-2850,Terakreditasi, Fakultas Teknik UMS,Surakarta.

5. Erwin R (2005) Pengaruh Jumlah dan

Arah Penulangan Geser pada Perilaku

Balok Tinggi Beton Bertulang, Laporan

Hibah Penelitian PHK-A2 Tahun 2005,Jurusan Teknik Sipil UniversitasMuhammadiyah Malang

6. Leong, C.L., and Tan. K.H (2003)Proposed Revision on CIRIA Design

Equation for Normal and High StrengthConcrete Deep Beams, Magazine ofConcrete Research, Vol.55 Issue.3, pp267-278.

7. Tan, K.H., C.Y Tang, and K.Tong,(2004) Shear Strength Prediction of

Pierced Deep Beams with Inclined Web

Reinforcement , Magazine of ConcreteResearch, Vol.56, Issue.8, pp.443-452.

8. Tan, K.H and Weng, L.W (1999) High-

strength Concrete Deep Beams with

Different Web Reinforcement under

Combined Loading, AustralianConference on the Mechanics ofStructures and Materials, 8-10December 1999, Sydney.

9. Teng, Susanto., Fung-Kew.K., Soon-Ping. P., Lingwei W.G, and Tan K.H,(1996) Performance of Strengthened

Concrete Deep Beams Predamaged in

Shear , ACI Structural Journal, Vol.93,No.2, March-April 1996, pp159-171.

10. Watanabe, Ken., Mitsuyasu Iwanami,Hiroshi Yokota, and Junichiro Niwa,(2002) Estimation of The Localized

Compressive Failure Zone of Concreteby AE Method , Proceeding of the 1st fib

Congress, Osaka, Session 13, October2002, pp.117-124.

11. Zararis, Prodromos.D., (2003) Shear

Compression Failure in Reinfor ced

Concreted Deep Beams, Journal ofStructural Engineering, Vol.129, No.4,April 2003, pp 544-553.

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The Reconstruction of Modelling Reinforcement