strengthened deep beam

7/29/2019 Strengthened Deep Beam

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ABSTRACTSHEAR BEHAVIOR OF REINFORCED CONCRETE DEEP BEAMSSTRENGTHENED W ITH CFRP LAMINATES

ByJon Erik Moren

Considerable research has been performed using CFRP plates bonded to norm alreinforced concrete beam s, the objective being to improve shear and f lexuralstrength. However, very few tests have been pe rformed on reinforced concretedeep beam s with CFRP as shear reinforcemen t. The purpose of this experime ntis to investigate the behavior of the deep beam in shear with variousarrangem ents of Sika CarboD ur laminates bonded to the sides. The beam s weredesigned to b e shear d eficient with stirrups om itted, except at the supp orts anddirectly unde r the load. In total eight beam s were tested , four with one-po intloading and four w ith two-point loading. Each loading cond ition contained o necontrol beam without CFRP, and three beams w ith the CFRP laminates attachedat zero, forty-five, and ninety degree s w ith respect to the neu tral axis. Theult im ate loading capacity and behavior for each beam bonde d with the CFRPlaminate was observed and recorded.

The m ode o f failure was shear in al l the b eam s tested, which typicallyresulted from the delaminating between the concrete and the epoxy. The presenttest results show that the orientation of the CFRP about the ne utral axis had adirect effect on the shear strength of the be am and its ductil ity. The forty-fivedegree al ignment of C FRP plates gave the greatest increase in shear capacityand du ctility, whereas the ninety-degree alignment gave the least amoun t.


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SHEAR BEHAVIOR OF REINFORCED CONCRETE DEEP BEAMSSTRENGTHENED WITH CFRP LAMINATES

ByJon Erik Moren

A ThesisSubm itted to the Faculty ofNew Jersey Institute of TechnologyIn Partial Fulfillment of the Req uirements for the Degree ofMaster of Science in Civil Engineering

January 2002


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APPROVAL PAGESHEAR BEHAVIOR OF REINFORCED CONCRETE DEEP BEAM SSTRENGTHENED W ITH CFRP LAMINATES

Jon Erik Moren

Dr. Cheng-Tzu Thom as Hsu, Thesis AdvisorateProfessor of Civil Engineering, NJITProfessor Edward G. Dauenheimer, Committee MemberateProfessor of Civil Engineering, NJIT

Professor W alter Konon, Com mittee Memb erateProfessor of Civil Eng ineering, NJIT


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BIOGRAPHICAL SKETCH

Author:on Erik MorenDegree:aster of ScienceDate:anuary 2002Undergraduate and G raduate Education:

Master of Science in Civil Eng ineeringNew Jersey Institute of Technology, Newark, NJ, 200 2

Bach elor of Science in Civil EngineeringNew Jersey Institute of Technology, Newa rk, NJ, 2001

Major:ivil Engineering


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To my beloved family


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TABLE OF CONTENTS

Chapterage1 INTRODUCTION11.1 History/ Literature Review1.2 Objectives32 DESIGN, FABRICATION AND MATERIALS52.1 Design of Reinforced Concrete Deep Beam5

2.1.1 Flexural Design and Reinforcement52.1.2 Bond Length62.1.3 Shear Design and Reinforcement72.2 Fabrication of Re-bar Cage and Forms92.2.1 Fabrication and Assembly of the Re-bar Cage92.2.2 Form Design and Construction10

2.3 Casting of Concrete Beams112.3.1 Concrete Mix Design and Ultimate Strength112.3.2 Casting Procedure132.3.3 Curing Procedure32.4 Sika CarboDur Strengthening System and Installation142.4.1 Sika CFRP Laminate142.4.2 Sikadur-30 Adhesive152.4.3 CFRP Laminate Bonding Procedure162.4.4 CFRP Laminate Spacing and Orientation17

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LIST OF TABLES

Table Page2.1 Batch requirements22.2 Maximum compressive strength of concrete cylinders ...........22.3 CFRP laminate properties52.4 Sikadur-30 adhesive properties63.1 Experimental results for one-point loading83 .2 Experimental results for two-point loading .... ..... . ............2


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LIST OF FIGURES

Figureage2.1 Shear and flexural reinforcement2.2 Re-bar cage assembly02.3 Forms for deep beams12.4 Beams and test cylinders curing42.5 CFRP laminate alignment for deep beams83.1 Reinforced concrete beam testing frame93 .2 Typical example of one- and two-point loading13 .3 Mechanical strain gauge and demec gauge location23 .4 Variation in shear with aid for rectangular beam ..............33 .5 Modes of failure in deep beam53 .6 Modes of failure in short beam63.7 Failure of control beam 1-183 .8 Failure of beam 1-2 with mid-strip CFRP location03 .9 Failure of beam 1-3 with 90 degree aligned CFRP13.10 Beam 1-3 failure reverse side photo13.11 Failure of beam 1-4 with 45 degree aligned CFRP23.12 Beam 1-4 failure reverse and top view photo33.13 Failure of control beam 2-143.14 Failure of beam 2-2 with mid-strip CFRP location . ............ ........53.15 Failure of beam 2-3 with 90 degree aligned CFRP at left support63.16 Failure of beam 2-3 with 90 degree aligned CFRP at right support6

x i


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LIST OF FIGURES(Continued)

Figureage3.17 Failure of beam 2-4 with 45 degree aligned CFRP at left support373.18 Failure of beam 2-4 with 45 degree aligned CFRP at right support383.19 Combined load deflection curve for one-point loading393.20 Moment-curvature curve for one-point loading condition413.21 Combined load deflection curve for two-point loading423.22 Moment-curvature curve for two-point loading condition44A.1eep beam calculations one-point loading48A .2eep beam calculations one-point loading continued49A.3 Deep beam calculations two-point loading50B .1oncrete mix design51B.2 Concrete mix design continued52B.3 Compressive strength of cylinders one-point loading53B.4 Compressive strength of cylinders two-point loading53C.1oad deflection curve beam 1-154C.2 Load deflection curve beam 1-254C.3 Load deflection curve beam 1-355C.4 Load deflection curve beam 1-455C.5 Load deflection curve beam 2-156C.6 Load deflection curve beam 2-256C.7 Load deflection curve beam 2-356

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LIST OF FIGURES(Continued)

FigureageC.8 Load deflection curve beam 2-457D .1oment-curvature curve beam 1-158D.2 Moment-curvature curve beam 1-258D.3 Moment-curvature curve beam 1-359D.4 Moment-curvature curve beam 1-459D.5 Moment-curvature curve beam 2-160D.6 Moment-curvature curve beam 2-260D.7 Moment-curvature curve beam 2-361D.8 Moment-curvature curve beam 2-461


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CHAPTER 1INTRODUCTION

1.1 History/Literature ReviewThere is both a great interest and need in the Un ited States and abroad to repairand strengthen structural elem ents such as colum ns, beam s, and slabs within aparticular building system. The primary reasons to upgrade and repair an existingstructure include building code changes, accidents, design errors or building usechanges. Cu rrently, there are several options available to repair and strengthenexisting structures in both flexure and shear.

For the past twenty-five years, the m ost popular method for strengtheningand rep airing structures is to epoxy-bond stee l plates to the critical areas of thestructure. The benefits are that the life cycle of the structure can be extended andthat the cost of replacement of the structure can be avoided. The maindrawbacks to this method are the amount of weight the steel adds to thestructure, and the fact that steel rusts when exposed to harsh environments;therefore, is not suitable for al l appl ications. In addit ion, the plates' weightrequires the use of special tools and equipment to ensure proper installation.

The use of composite material such as GFRP and CFRP offer manyadvantag es over steel. FRP has a high corrosive resistance and strength toweight ratio. Its light weight m akes it easy to handle and install. The ma terial hasthe ad ditional ben efit of being available in any length a nd the flexibi l ity to bem olded to ma tch any surface irregularities. The m ajor drawback to the use ofFRP composites is their higher cost over steel, and the fact that they are

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anisotropic, m eaning they don 't possess the sam e properties in each direction,as does steel. The first carbon FRP repair and strengthening system wasintroduced in Switzerland in 198 4 by Meier, who rem ains an innovator in the field

of FRP research. (1)Over the last decade, FRP plates and fabrics have been use d extensively

in Europe and aroun d the world to increase the m om ent capacity of f lexuralmembers. The first full-scale use of CFR P strengthening for flexure in theUnited States was in 19 94 to rehabilitate a bridge in W ilmington, Delaware. (2)Since then the use of FRP com posi tes has ga ined a w ider acceptance in theUnited States, particularly in California were it has been used to updatestructures to m eet new se ismic code requirements. How ever, the use of FRP forshear reinforcemen t has not been as widely researched or applied. The reason isdue to the nature of the shear failure itself. Unlike bending failure, which is ductileand gives a w arning before failure, shear failure is brittle and o ccurs with little orno w arning. For this reason, the ACI (Am erican Concrete Institute) forbids thedesign of over-reinforced con crete structures in its design proced ures. Therationale being that if the structure is under-reinforced, the occupants will be ableto see that the structure is com promised by observing d eflections or cracks, andtherefore have an opportunity to evacuate the structure.

In the last two years, various pape rs have been published on the subjectof shear reinforcement u sing C FRP comp osite m aterials. In 1 999 , Khal ifa andNann i, from the research lab at the U niversity of M issouri at Rol la, published apaper t it led "Imp roving sh ear capacity of existing RC T-sect ion b eam s using


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CFRP comp osites." Six full-s ized s imply supported b eam s w ere strengthenedwith various arrangem ents of CFR P sheets. The expe rimental results indicatedthat "externally bonded CFRP can increase the shear capacity of the beamsignificantly." (3) In that same year, Taljsten and Elfgren, from Lulea University ofTechnology in Sw eden, pub l ished a p aper on the research of the shear forcecapacity of beams b efore and after strengthening using CFRP fabrics and tapes.Their test results dem onstrated that bon ding CFR P fabrics to the face of theconcrete beam s increased the shear strength. (4) In 200 0, Dr. Hsu and Ph.D.student Zhan g at N ew Jersey Institute of Technology in N ew Jersey investigatedthe shear beha vior and m odes of failure for norma lly reinforced concrete beam sstrengthened with CFRP laminates. They concluded that CFRP couldsignificantly increase the serviceability, ductility and ultimate strength ofreinforced concrete beams. (5) However, after extensive research no informationcould be found on CFRP reinforcement on deep beam s, thus the objective of mypaper.

1.2 Objectives

The objectives of this experiment are to :1. Invest igate the du ct il ity, shear be havior, and fai lure m odes of reinforced

concrete deep be am s with shear deficiencies after strengthening w ith SikaCarboDur strengthening system.


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2. To increase the da tabase on shear strengthening u sing external ly bond edCFRP laminates.

3. To determ ine the optimum configuration of CFRP lam inates that will im partthe greatest shear strength and increase in ductility.


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CHAPTER 2DESIGN, FABRICATION AND MATERIALS

2.1 Design of Reinforced Concrete Deep Beam

W hen designing a bea m , there are three possible mode s of fai lure that canoccur: shear, bending and bon d length. In order to investigate how the CFR Plaminates benefit the shear strength of the beam , the beam must fail in shear. Ifthe beam were to fail in bending or bond length, there would be no way ofdetermining exactly how much strength the CFRP laminates contributed.

The deep beam was designed as an under-reinforced section inaccordance with the Am erican Con crete Insti tute (ACI) B ui lding Code. (6) T oguarantee that the m ode of failure wou ld be shear, horizontal and vertical shearreinforceme nt was o m itted from the design, except in special c ircum stancesdiscussed later. In practice, this is avoided b ecause of the lack of w arning andsudden na ture of brittle failure. Howeve r, for this case, it was necessa ry in orderto investigate how the C FRP plates improved the shear strength of the deepbeam . The design for the beam is broken down into the fol lowing three areas :flexural, bond length and shear.

2.1.1 Flexural Design and ReinforcementThe beam s designed for this experiment are considered to be norm al beams inf lexure, in accordance w ith AC I 10.7.1. AC1 d oes no t have a spe cific designprocedure for beams w ith a height to clear span ratio greater than .8 and requiresnon-linear analysis to determine the flexural design. The height to clear span

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ratio for the deep beam in the experiment is .3, which allowed the assum ption ofWh itney's Rectangular Stress Distribution to d etermine the flexural strength.

The flexural design cal ls for the use o f four individual num ber four re-bar

as reinforcem ent w hich represents a steel reinforcem ent rat io of .02 50. Th isvalue is within the ACI maximum of seventy-five percent of the steelreinforceme nt at the balanced cond ition, which is equal to .0283 . Figure 2 .1show s the location of the flexural and tem perature con trol re-bar used in theexperiment. The complete flexural design for the deep beam is located inAppen dix A, ACI Reinforced Concrete Deep B eam .

2.1.2 Bond LengthA deep beam is a special case wh ere the loading condition creates a m ulti-axialstate of stress in the beam . The shear stresses and strains generated w ithin adeep beam are non-linear and have compo nents in both the X and Y direct ion.This state of multi-axial stress within the deep beam places a large am ount ofstress on the anchorage zone an d the ma in tension reinforcement. (7) Thedevelopm ent length for the tension bar terminating in a standard hook w asdetermined by using ACI 7.1 and 7.2. A value of eleven inches was determ inedfor the de velopment length for both loading co nditions. The calculations for thedevelopme nt length are furnished in Append ix A, ACI Reinforced Concrete DeepBeam Design.


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2.1.3 Shear Design and ReinforcementShear is very important consideration when dealing with deep beam design. TheACI code 11.8 classifies a deep beam as having a clear span to depth ratio of

less than five for a distributed loading condition. This translates into a shear spanto depth ratio of 2.5 or less for concentrated loads. The beam designed for theexperiment has a shear span to depth ratio of 1.88, which classifies it as a deepbeam for shear by the A C I.

Special design procedures are required by the AC I when designing a deepbeam for shear. They include the following recommendations : For aconcentrated load, the critical distance for shear design is located at a distance.5 times the shear span length from the support. The use of a special multiplier isrequired when determining the shear carrying capacity of the concrete. This isdue to the fact, that as the beam is loaded, a tied-arch effect occurs, which givesthe concrete increased shear capacity even after shear cracks have formed. TheACI detailed method is used with the multiplier to calculate the shear capacity ofthe plain concrete in the experiment. The shear capacity of the beam for one-and two-point loading was calculated to be 15.8 kip and 24.0 kip, respectively.The calculations for the shear capacity of the concrete are furnished in AppendixA , AC I Reinforced Concrete D eep B eam D esign.

The shear reinforcement provided in the beam consists of two individualnumber two stirrups at each support and one individual number two stirruplocated directly under the load. This was done so that the beam would notexperience local failure. In total, the one-point loading condition contained five


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stirrups while the two-point loading condition used six stirrups. Figure 2.1 sho wsthe arrangement of the shear and flexural reinforcement for each loadingcondition used in the experiment. Shea r reinforceme nt was excluded from the

beam in the areas where the CFRP w as to be attached.

Figure 2.1 Shea r and flexural reinforcement


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2.2 Fabrication of Re-bar Cage and Forms2.2.1 Fabrication and Assembly of the Re-bar CageThe size of the beam designed gave som e interesting fabrication problems. This

was particularly evident in the area of bending the steel for the flexuralreinforcem ent. The beam designed (three feet long, nine inches high and fourinches wide) required that the steel be bent to very exacting tolerances. Ma nyattempts were made to bend the steel by cold working, however, the end productwas too d istorted to use. An oxygen acetylene torch w as then used to heat thesteel so that it could be bent into the exact shape required. After someexperim entation and fabricating special ly designed form s, numb er two stirrupsand n um ber four f lexural reinforcement re-bar were ben t and cut to length. Thiswas no t in accordance w ith ACI recom m endations, which require that al l thesteelwork be done cold. How ever, due to the small dim ensions of the beam , itwas unavoidable.

After the individual com ponents of the bea m had be en fabricated, theywere com bined together to form the re-bar cage. (See Figure 2.2) Num ber twore-bar was used for temperature control at the top of the beam and also servedas location points to attach the stirrups under the load. Standard tie wire wasused to secure the stirrups and flexural reinforcement together.

In order to maintain the half-inch of clear cover around the steelreinforceme nt, a spot weld was used at the top of the stirrup to keep the re-barcage from expanding. Under normal conditions, this is not recommendedbecause it mak es the stirrup continuous. How ever, it was nece ssary in order to


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maintain proper spacing. To insure consistency from beam to beam , each stirrupwithin the beam w as secured with a spot weld.

Figure 2.2 Re-bar cage assembly

2.2.2 Form Design and ConstructionThe forms w ere constructed from G rade A/A three-quarter inch pressure treatedplywood to insure that the beams had a sm ooth surface on w hich to bond theCFRP laminates. The surfaces of the forms w ere painted with num erous coats ofpaint to protect the wood from the concrete. (See Figure 2.3) The form s weredesigned so that four beam s could be cast simultaneously, which increased theconsistency from beam to beam . This a l lowed a l l the beam s f rom the sameloading condition to be made with the same identical concrete mix, whicheliminated a po tential difference in strengths from beam to beam .


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Figure 2.3 Forms for deep beams

2.3 Casting of Concrete Beams2.3.1 Concrete Mix Design and Ultimate StrengthThe concrete m ix was designed in accordance with ACI 211 "Standard Pract icefor Selecting Proportions for N ormal, Heavyw eight, and M ass Con crete" which isbased on the absolute volume m ethod. A computer program called Mathcad wasused to calculate the e xact quantit ies and proportions neede d for the d esign.Included in the m ix proportions are enough c oncrete to fill five eight inch tall byfour inch diameter cylinders, and four three foot by nine inch by four inch beam s.Table 2.1 lists the batch requirem ents for one batch consisting of four beams an dfour test cylinders. The target strength for the m ix design was f ive thousandpound s per square inch, with a water cement ratio of .41, and a predicted slum pand air content of 3 inches and two percent, respectively. The entire mix designis located in the Appe ndix B, Concrete M ix Design and Te st Cyl inder StressStrain Curves.


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Table 2.1 Batch requirementsIngredients Quantities

Water 29.6 lbs.Cement Type I 65.6 lbs.

Coarse Aggregate 159.7 lbs.Fine Aggregate (3/8) 105.9 lbs.

Total Volum e Required 2.5 cu.ft.

The cylinders were tested for compressive strength at the same time the beam swere tested. The first batch contained five of test cylinder specimens and thesecond ba tch contained four. The results of the individual com pressive tests arerecorded in Table 2.2, and the average com pressive strength for each ba tch iscalculated. The average compressive strength was used to calculate thetheoretical shear capacity of the concrete and the flexural strength of the beam .The stress-strain curves for the compressive cylinder tests are included inAppendix B, C oncrete Mix Design and Test Cylinder Stress Strain Curves.

Table 2.2 Maximum compressive strength of concrete cylindersNum ber ofCylinder

Ultimate strength fc ' (psi)Concrete Batch 1 Concrete Batch 21 6526 6446

2 6367 60483 5570 56604 5809 66855 6446 X

Average 6143.6 6207.3

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Figure 2.4 Beam s and test cylinders curing

2.4 Sika CarboDur Strengthening System and InstallationThe Sika CarboD ur heavy duty strengthening system w as used as the shearreinforcement for the deep beams in the experiment. It was selected based on itsprevious use in CFRP e xperiments at NJIT (5) an d because of its famil iarity andavailability. The Sika CarboDur strengthening system is comprised of twocomponents: Sikadur-30 adhesive bonding reinforcement and Sika CFRPlaminates. (8)

2.4.1 Sika CFRP LaminateThe Sika C FRP lam inates are com prised of a base of "Carbon f ibre reinforcedpolymer with C fibres (Toray T 700) and an epoxy resin matrix." (1) Theunidirectional carbon fiber strips come in two varieties : Type 50 with a 50 -mmwidth and Type 80 with an 80-m m width. Each is available in one- and two-m ill im eter thickness and are ava ilable in any length desired. The Typ e 50 withone-m ill im eter thickness was selected as the lam inate to be used as the she ar


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15reinforcement for this experiment. The ma terial arrived in on e continuous lengthand w as very easy to w ork with, requiring a pair of t in snips to cut the C FRP intothe desired lengths. Table 2.3 lists properties of the Type 50 CFRP lam inate.

Table 2.3 CFRP laminate propertiesProperties Sika CarboDur laminate

Description Pultruded carbon Fiber LaminateTensile Strength 406,000psi ( 2,800 N/ mm 2 )Tensi le Modulus 23.9msi ( 165,000 N/mm 2 )Elongation at Break 1.9%Nom inal Thickness .047in. ( 1.2mm )Tensile Strength per inch W idth 19,0821bs./layer ( 84.5KN )

2.4.2 Sikadur-30 AdhesiveThe other com ponent of the Sika CarboDur strengthening system is Sikadur-30adhesive for bonding reinforcement. "The purpose o f the adhesive is to producea continuous bond betw een f ibre reinforced polym er (FRP) and concrete toensure tha t full compo site action is developed by the tran sfer of shear stressacross the thickness of the adhe sive layer."(1) Sikadur-30 is described a s a"solvent free, thixotropic, epoxy-based 2-com ponen t adhesive."(9) A "pre-dosed"pack of Sikadur-30 was used for the experiment that consisted of twocomp onents, which were m ixed together with a low spe ed electric mixer. Greatcare was taken to ensure that addit ional air was not introduced in the epoxy,which w ould reduce its effectiveness and strength. The f inal product wa s easy toma nage for close to an hou r and took o n a l ight gray appearance similar to thatof concrete. The properties of Sikadur-30 are given in Table 2.4.


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18laminates for the two-point load due to the fact that there is no shea r between thetwo loads.

Figure 2.5 C FRP laminate alignment for deep beams


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CHAPTER 3CFRP REINFORCED DEEP BEAM TESTING

Figure 3.1 Reinforced concrete beam testing frame

3.1 Testing Equipment and Procedures3.1.1 Testing Equipment

Located in the b asem ent of the A rchitectural Building at N JIT is the reinforcedconcrete beam testing facil ity where the e xperiments w ere carried out. At theheart of the facility is a cu stom installed two-story fram e, pictured above. (Figure3.1) This frame has a high degree of stiffness and can be modified toaccommodate different configurations of beams as well as other structuralelemen ts. All of the beam s were tested using the MTS (M aterial Testing System),which is a closed loop servo hydraulic testing system controlled by the M TS teststar digital system located within the frame . The m aximum capacity of the loadcell used in this experime nt was f ifty kips. The experiment w as executed in loadcontrol with the autom atic data acquisition system m onitoring and recording both

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the load and the deflection m id span. Al l of the beam s were statical ly tested tofail in one loading cycle.

3.1.2 One- and Two-Point Loading ConditionsEach of the three-foot long beam s to be tested was simply supported by tw o,two-inch diameter steel rollers located three inches from each end of the beam . Asteel plate w as inserted between the concrete and the steel roller to ensure thatlocal failure did not occur at the support. It was necessary to place two four-inchthick concrete blocks under each support to elevate the beams so that the strokeof the testing m achine could reach the spe cimen . For the one -point loadingcondition, a one-inch diameter steel bal l bearing suspen ded betw een two steelplates was used to transfer the load evenly from the load cell to the surface of thetest specimen. This same procedure was used with the two-point loadingcondition with one add itional step. A special device was used to se parate theload into two equal components exactly ten inches apart. The device is placed sothat each load com ponent is located f ive inches from the centerline of the beam .Figure 3.2 show s the typical set-up used for the one- and two-point loadingconditions. The device located m id span under the b eam is the external LVDT,which was used to measure the deflection of the beam a s it was loaded.


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Figure 3 .2 Typical example of one- and two-point loading

3.1.3 Moment-Curvature CurveThe ductil ity of the deep beam s reinforced with the C FRP lam inate wasmeasu red during the experiment by using a mecha nical strain gauge. Four pairsof mechanical strain gauges , also known as dem ec gauges, we re installed on theface of each of the beams tested. A typical arrangement of the demec gauges isshown in Figure 3.3. O ne set of gau ges is located five inches to the right of thecenterline of the beam, while the othe r set is located five inches to the left of thecenterline. Each row pictured is ap proximately two inches a part and distributedevenly across the web of each beam.Initial readings w ere taken w ith a mechan ical strain gauge after a slight load w asapplied to the beam. S ubsequent readings w ere taken in three kip intervals untilthe beam failed. The strain length change was determined and plotted versus itslocation on the face of the beam . The ang le formed between the strain lengthchange a nd its location on the face of the beam is the angle of curvature for thebeam a nd was m easured using excel. The angle of curvature was then use d to


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determine the radius of curvature for each of the beams tested. The radius ofcurvature is inversely related to the horizontal curvature of the beam and is agood indicator of ductility in beams. The shorter the radius of curvature the morecurvature the beam experiences and this translates into increased ductility. Byplotting the bending moment versus the longitudinal curvature of the beam , theductility of the beam can be observed. By plotting all four of the mom ent-curvature curves on the same graph, the ductility between beams with differentalignm ents of CFRP lam inate can be compared.

Figure 3.3 Mecha nical strain gauge an d dem ec gauge location

3.2 Behavior of Beams without Shear Reinforcement3.2.1 General

The factors that influence shear be havior and strength in simply suppo rtedreinforced concrete beams are numerous and complex and not completelyunderstood. These factors include the size and shape of the beam's cross


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4. Long beam s which, possess a shear span to effective depth ratio greater thansix. (7)

For this experimen t, the beam designed wo uld be considered a short beam b ytraditional definit ion ho wever, ACI classif ies any beam with an shea r span toeffective depth ratio of less than tw o point f ive be designed as a de ep beam . Forthe purpose of th is experim ent, on ly the deep bea m and short beam shearbehavior will be discussed.

3.2.2 Deep Beam FailuresFor beam s that have a shear span to depth ratio of less than one shear stresshas the m ost effect. Once the inclined crack has formed, the beam behaves as acompressive tied arch, wh ich has large reserve capa city; this allows the concreteof the beam to carry a larger shear capacity than a no rmal concrete beam . Thereare several modes of failure once the t ied arch system has taken effect. Theyinclude anch orage , bearing, f lexure, and a rch-rib failure. Figure 3.5 p art (a)shows the forma tion of the com pression arch for a simply supported deep bea munder two -point loading. Figure 3.5 pa rt (b) labels and dem onstrates the locationof the failure zones that result after the compressive arch has formed.


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Figure 3 .5 Modes of failure in deep beam (7)

3.2.3 Short Beam FailuresFor beam s that have a shear span to depth ratio between one and two point five,the shear strength exceeds the inclined cracking strength, just like a deep beam .Wh en the beam is loaded, flexural-shear cracks develop which extend from thetension zone and continue to develop into the com pression zone as the load isincreased. Secondary cracks form along the tension reinforcement and progresstoward the suppo rt. The failure may be either anchorag e fai lure, at the tensionreinforcement also kn ow n as "shea r tension" fai lure, or the concrete in thecompression zone directly under the load crushes known as "shear compression"failure. (7)(10) See Figure 3. 6.


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Figure 3.6 Modes of failure in short beam (7)

3.3 Behavior of Beams with CFRP Shear ReinforcementThere are four main failure mechanisms, which can limit the shear strength thatthe externally bonded CFRP laminate can contribute to the overall shear strengthof the beam.

3.3.1 Concrete Bond FailureThe most common type of failure experienced occurs between the surface of theconcrete and the epoxy. "In this failure mechanism, the Sika CarboDur platedebonds from the beam by shearing the surface of the concrete." (1) With thisparticular failure mode the total shear strength of the CFRP laminate and epoxyis not completely utilized. The shear strength of the system is limited to the"ultimate bond strength of the concrete surface that anchors the FRP". (1) A loudbang is accompanied by this failure mode which results from the CFRP laminate


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3 .3 .4 Strain Cap acity of Con crete is ReachedACI limits the amount of strain in concrete to .00 3 in their design procedure. If thestrain levels in the concrete reach a value greater than 0 .004, the con crete wil lexperience a loss of aggrega te interlock causing it to crack and m ove resulting inthe com plete col lapse o f the elem ent. (1) This crushing a ction rep resents brittlefai lure, which a d esign engineer need s to avoid. The fai lure mod e is similar tothat of an over-reinforced sect ion wh ere the crushing of the concrete occursbefore the stee l yields representing a ca tastrophic failure that occurs sudd enlywithout warning.

3 .4 Discussion of Beam Behavior and Fai lure Mode3.4.1 One-Point LoadingFigure 3.7 Failure of control beam 1-1

3 .4 .1 .1 C ont ro l Beam 1 -1 . The nom enclature used for the beam testing issimple w ith the f irst num ber (either a one or tw o) standing for the loadingcondit ion and the second num ber representing the orientation of the CFRPlaminate on the beam . The f irst beam tested wa s control beam 1-1, which failedin shear-compression. (Figure 3.7). As the beam was loaded be yond 1 6 kips, a


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sm all crack develope d directly unde r the load followed b y flexural-shear cracksdeveloping at each o f the supports. These flexural-shear cracks developed a t aforty-five degree angle between the load and the supports. Once the loadreached its maximu m of 21.2 kips, the flexural-shear cracks from the supp ortconnected with the crack under the load, resulting in sh ear-compression fai lurewith the load dropping to 20 k ips. At this point, the experiment w as halted so thatthe beam could be used in future experiments where it could be repaired and re-tested.

3.4.1.2 Beam 1-2 Mid-Strip CFRP Location. The next beam tested was beam1-2 w ith the CFRP lam inate attached at the neutral axis, as pictured in Figure3.8. The m ode of fai lure for the beam was she ar-comp ression failure sim ilar tothe control beam. As the load on b eam increased past 17 kips, the f irst flexural-shear crack forme d below the C FRP lam inate near the right supp ort. This crackformed a t a forty-five degree angle with respect to the load and extended towardthe load location as the load increased. At the ultim ate load of 22.0 k ips, thecrack reached the load locat ion and the be am fai led sud denly w ith the loaddropping 17.0 kips.


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Figure 3 .8 Failure of beam 1-2 w ith mid-strip CFRP location

3.4.1.3 Beam 1-3 90 Degree Aligned CFRP. Beam 1-3 with the ninety-degreeal igned CFRP laminates with respect to the n eutral axis of the b eam failed inshear after the CFRP lam inate debonded from the beam by shearing the surfaceof the concrete. During the testing procedure the first small flexural-shear crackappeared in the beam at 25 kips near the m iddle of the span on the tension sideof the beam . As the load increased, more flexural cracks developed and sm allshear cracks develop at the supports betwee n the CFRP laminates. As the loadreaches a m aximum of 37.8 kips, the flexural cracks continued to grow larger andthe deflection increased without any further load increase. At this point, there wasa loud popping sound as the bond between the CFRP and the concrete surfaceruptured. The load dropped dramatically from 37.0 kips to 6.0 kips resulting in anexplosive failure causing large pieces of concrete from the beam to scatter. TwoCFRP lam inates located third and fourth from the left support becam e comp letelydislodged. (Pictured in Figure 3.9) Figure 3 .10 is a p icture of the reverse side of


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the beam showing that only the second CFRP laminate from the left supportbecame dislodged.

Figure 3.9 Failure of beam 1 -3 with 90 degree aligned C FRP

Figure 3.10 B eam 1 -3 failure reverse side photo

3.4.1.4 Beam 1-4 45 Degree Aligned CFRP. Beam 1-4, with the forty-fivedegree aligned CFRP laminates (with respect to the neutral axis of the beam),failed in shear after the CFRP laminate debonded from the beam by shearing thesurface of the concrete. As the beam was loaded, local failure was observeddirectly under the load at about 20 kips with no other crack development until


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approximately 28 kips. At this point, flexural cracks began to form directly underthe load on the tension side of the beam, and as the load increased these crackscontinued up into the compression zone of the beam. During this period, shear

cracks began to form perpendicularly to the CFRP laminates as pictured inFigure 3.11. As the load increased to a maximum of 45.9 kips the flexural crackswere approaching the neutral axis of the beam when the bonding between theCFRP laminate and the concrete surface yielded. This action was accompaniedby a loud popping sound with the CFRP delaminating from the concrete withexplosive force. The entire section located under the load fractured with largeportions of concrete being dislodged and falling off. Figure 3.12 shows that theregion from the load to the right support has become completely dislodged fromthe beam.

Figure 3.11 Failure of beam 1 -4 with 45 degree aligned C FRP


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Figure 3.12 Beam 1-4 failure reverse and top view photo3.4.2 Two-Point Loading

3.4.2.1 Control Beam 2-1. The first two-point loading test was con ducted oncontrol beam 2 -1, which failed in shear-comp ression. (Figure 3.13 ). As the beamwa s loaded past 9 .0 kips, a small crack formed d irectly unde r the left loadingpoint. At 18 kips a sm all flexural shear crack developed at the right support andcontinued to lengthen as the load w as increased. At 24 kips a f lexural shearcrack developed at the left support, while the crack at the right support reachedthe neutral axis of the beam. These cracks developed at a forty-five degree anglebetween the load and the supports. Once the load reached its ma ximum of 32.5kips, the crack from the right suppo rt connected w ith the crack und er the loadresulting in the load dropping to 3 0.0 kips. The experimen t was term inated afterthe load dropped to 20 k ips.


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Figure 3.13 Failure of control beam 2-1

3.4.2.2 Beam 2-2 Mid-Strip CFRP Location. The next beam tested was beam2-2 with the CFRP laminate attached at the neutral axis as pictured in Figure3.14. The mode of failure for the beam was shear-compression. As the load onthe beam increased past 24 kips, the first flexural shear crack formed below theCFRP laminate near the right support. This crack formed at a forty-five degree

angle with respect to the load and extended toward the load location as the loadincreased. At an ultimate load of 45.9 kips, the crack reached the location of theload and the beam suddenly failed with the load dropping to 37.0 kips. As theload was maintained and the deflection increased, the CFRP laminate began tosplit apart and the experiment was terminated after the deflection point reachedfour inches.


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3 5

Figure 3.14 Failure of beam 2 -2 with m id-strip CFRP location

3.4.2.3 Beam 2-3 90 Degree Aligned CFRP. Beam 2-3 with the ninety-degreealigned CFRP laminates (with respect to the neu tral axis of the bea m ) failed inshear after the CFRP lam inate debonded from the beam by shearing the surfaceof the concrete. During the testing procedure the first small flexural crackappeared in the beam at 28 kips near the m iddle of the span on the tension sideof the beam . As the load increased, more flexural cracks developed and sm allshear cracks developed at the supports betwee n the CFR P laminates. As theload reached a m aximum of 46.7 kips, there w as a loud popping sound a s thebond betw een the CFR P and the concrete surface ruptured. The load droppeddram atically from 4 6.7 kips to 31 .0 kips resulting in the three CFR P lam inates atthe left support to debond from the concrete surface causing the beam to fail inshear. Pictured in Figure 3.15 are the three CFRP laminates that debonded atfailure. The entire portion of the laminate in the p icture is hang ing by a threa d


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3.4.2.4 Beam 2-4 45 Degree Aligned CFRP. Beam 2-4 w ith the forty-fivedegree al igned CFRP laminates (with respect to the neutral axis of the beam )failed in shear after the CFRP laminate debonded from the beam by shearing the

surface of the concrete. At 12 kips, local failure was observed directly under bothof the loading points. As the load reached 3 0 k ips, flexure-shear cracks began todevelop direct ly und er the loads on the tension side of the beam . The crackspropagated in the direction of the load location as the load increased inm agnitude. Whe n the load increased to approximately 40 kips, shear cracksbegan to form pe rpendicularly to the CFRP lam inates, as pictured in Figure 3.17.As the load increased to a maxim um of 54.1 kips, the f lexural cracks passed theneutral axis of the beam and connected w ith the shear cracks that had formedperpendicular ly to the CFRP laminate. At this point, there w as a loud poppingsound as the CFRP d elaminated from the surface of the concrete. The entireconcrete surface located from the support to the load location point fractured andseparated from the be am . Figure 3.17 and Figure 3.18 show that the fai lurecondition occurred at bo th supports.

Figure 3.17 Failure of beam 2-4 w ith 45 degree aligned CFRP at left support


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Figure 3 .18 Failure of beam 2-4 w ith 45 degree aligned C FRP a t right support3.5 Test Results

3.5.1 One-Point LoadingA summary of the one-point loading results is provided in Table 3.1. Included inthis table are the values for the ultimate load and deflection, the CFRP shearcapacity increase and the final failure mode of the beam. Figure 3.19 combinesall four of the beam load deflection curves onto the same graph for easycomparison. The individual load deflection curves are located in the Appendix C,Individual Load D eflection C urves.

Table 3.1 Experimental results for one-point loading

BeamNumber UltimateLoad (Ibs) D eflection atUltimate (in.) C FRP ShearCapacity(lbs) Mode ofFailure1-1 21199 .090872 ShearCompression1-2 21999 .081659 800 ShearCompression1-3 37801 .129618 16602 StripDelamination1-4 43499 .205680 22300 StripDelamination


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LOAD-DEFLECTION CURVE (beam 1-1 thru 1-4)

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Figure 3.19 C ombined load deflection curve for one-point loading

3.5.1.1 Strength. It can be observed from Table 3.1 and Figure 3.19 that theexternally bonded CFRP laminate increased the load carrying capacity of thereinforced concrete deep beams tested. Since the mode of failure was shear inall four beams tested, a direct connection can be made between the arrangem entof the CFRP laminate and the increase in shear capacity of the deep beams. Thebeam with the forty-five degree aligned CFRP laminate experienced a 22.5 kipincrease in ultimate shear capacity over the control beam. This was the largestincrease in shear capacity followed by the ninety-degree aligned CFRP laminate,which contributed a 16.6 kip increase in shear capacity. The zero degree alignedCFRP laminate increased the shear strength the least, with only an 800 poundincrease over the control beam.


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3.5.1.2 Ductility. Referring to Table 3.1, the ult ima te deflection at the time offailure for the bonded CFRP laminate wa s significantly increased over the con trolbeam for the forty-f ive and ninety degree C FRP orientations. The forty-f ivedegree aligned CFRP lam inate beam increased in deflection by a hundred andtwenty percent, while the ninety-degree al igned CFRP laminate beam increasedin deflection by forty percent over the control beam. The b eam with the m id-stripCFR P lam inate location did not experience a ny increase in deflection over thecontrol beam; in fact, it experienced a ten- percent loss. The increase indeflection for the bonded forty-five and ninety-degree aligned CFRP laminateover the control beam indicates that not only is the shear cap acity of the beamincreased, but also its serviceability.

By m easuring and recording the strain and load on the b eam during theexperiment, the longitudinal curvature was determ ined and com pared to thecontrol beam. If the radius of curvature (the inverse of the longitudinal curvature)for the control beam is longer than the radius of curvature for the bonded CFRPlaminate beam , it can be surmised that the CFRP bond ed laminate increases theductility of the beam . By plotting the m om ent-curvature cu rve for all four of thebeam s tested on the sam e graph, it can be observed which CFRP a l ignm entarrangem ent has the m ost increase in ductility. The forty-five and ninety-degreealigned CFRP laminate beam s experienced a significant increase in du ctil ity overthe control beam. The areas un der the moment-curvature curve for the forty-fiveand ninety-degree aligned CFRP lam inate is more than doub le that of the control


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beam area. (Figure 3.20) Also see Appendix D, Individual Moment-Curvaturecurves

Moment Curvature Curve One-Point Loading (Beam 1-1 thru1-4)

Figure 3 .20 Mom ent-curvature for on e-point loading condition

3.5.2 Two-Point LoadingA summary of the two-point loading results is provided in Table 3. 2. Included inthis table are the values for the ultimate load and deflection, the CFRP shearcapacity increase and the final failure mode of the beam. Figure 3.21 combinesall four of the beam load-deflection curves onto the same graph. The individualload deflection curves are located in the Appendix C, Individual Load DeflectionCurves.


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Table 3.2 Experimental results for two-point loading

BeamNumber

UltimateLoad (lbs)

Deflection atUltimate (in.)

CFRP ShearCapacity(lbs)

Mode ofFailure2-1 32502 .076493 ShearCompression2-2 45900 .108075 1339 8 ShearCompression2-3 46702 .122223 14200 StripDelamination2-4 54103 .109607 21601 StripDelamination

Figure 3.21 Combined load deflection curve for two-point loading

3.5.2.1 Strength. It can observed from Table 3.2 and Figure 3.21 that theexternally bonded CFRP laminate increased the load carrying capacity of thereinforced concrete deep beams tested. Since the mode of failure was shear in


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all four beams tested, a direct connection can be made between the arrangementof the CFRP laminate and the increase in shear capacity of the deep beams. Thebeam with the forty-five degree aligned CFRP laminate experienced the largest

increase in shear capacity with a 21.6 kip increase in ultimate shear capacityover the control beam. The ninety and the zero degree aligned CFRP laminatecontributed 1 4.2 kip and 1 3.3 kip, respectively to the shear capacity of the beam .

3.5.2.2 Ductility. Referring to Table 3.2 the ultimate deflection at the time offailure for the bonded CFRP laminate was significantly increased over the controlbeam for all the CFRP orientations. The beam with the ninety-degree alignedCFRP laminate increased in deflection by sixty percent. While the forty-five andzero degree aligned CFRP laminates increased in deflection by forty percentover the control beam. The increase in deflection for the bonded zero, forty-five,and ninety-degree aligned CFRP laminate over the control beam indicates thatnot only is the shear capacity of the beam increased, but also its serviceability.

By monitoring the strain in the beams during the experiment, thelongitudinal curvature can be calculated and compared to the control beam.When the radius of curvature (the inverse of the longitudinal curvature) of thecontrol beam is longer than the radius of curvature for the CFRP bonded beams,it can be surmised that the bonded CFRP laminate increases the ductility of thebeam. By plotting the moment-curvature of all four beams on the same graph itcan be observed that the zero, forty-five, and ninety-degree aligned CFRPlaminate beam s exp erienced a significant increase in ductility. (Figure 3 .22)


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Moment Curvature Curve Two-Point Loading (Beam 2-1 thru 2-4)

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Figure 3 .22 Mom ent curvature curve for two-point loading condition


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Chapter 4SUMMARY AND CONCLUSION

This experim ent investigated the behavior of reinforced concrete deep b eam swith shear deficiencies strengthened with different configurations of CFRPlaminates. The test results indicate that the external ly bon ded C FRP lam inatesenhance the shear capacity of the deep bea m s tested. For the on e-point loadingcondition the shear increase ranged from o ne hun dred and five percent for thebeam 1-4 to three and a half percent for beam 1-2. The two-point loadingcondition had shear increases that ranged from sixty-six percent for beam 2-4 toforty percent for beam 2-2.

The orientation of zero, forty-five, and ninety-degree aligned CFRPlaminates w ere evaluated in two se parate loading cond itions. The forty-fivedegree aligned CFRP laminates for the one- and two-loading conditionsincreased the shear strength of the deep beam the largest amount. The ninety-degree configuration had the next largest increase in shear capacity withseventy-eight percent increase for the o ne-point loading an d forty-four percentincrease for the two -point loading cond ition. The zero degree al igned CFR Plaminate for the on e-point loading cond ition did not con tribute a not iceableam ount of shear strength with only a three percent increase. The zero-degreealigned CFRP laminate for the two-point loading condition, however, experienceda forty percent increase in shear strength, which was unexpected. In experimentsby Khalifa and N anni, "the zero degree aligned ply did not contribute to the shearstrength of the test specim en" (3). A possible explan ation for this result is that a

45


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46com pressive arch formed du ring loading, which gave the beam an increasedshear-carrying capacity. If this were the case, then the mode of failure could bechanged from shear compression failure to arch-rib failure.

The external ly bonded CFR P laminate improved the serviceabil ity of mostof the beam s tested. The forty-f ive and ninety degree al igned C FRP laminateincreased the serviceabil ity of the beam the m ost. The deflection at the ult im ateload increased by as m uch as one hundred an d twenty percent in the case ofbeam 1-4. Al l the beam s tested with the exception of beam 1-2 experienced aforty percent increase in deflection over their respective control beams.

The ductility of the beams tested also increased with the externallybonded CFRP laminates. The forty-five and ninety degree aligned CFRPlaminate increased the area under the m om ent-curvature curve by as m uch astwo time s that of the control beam . In all the exp erimen ts conducted, w ith theexception of beam 1 -2 the ductility of the deep beam was increased by externallybonded CFRP laminate.

The type of shear failure experienced by both con trol beams w as a bit of adisappointment. It was hoped that wh en the beam s were loaded a com pressivearch would form giving the beam a large am ount of reserve shear capacity.Instead the fai lure observed w as typical shear com pression fai lure, with onlybeam 2-2 demonstrating any unusual shear caring capacity. This could beexplained b y the fact that deep be am behavior is inf luenced by the h eight towidth ratio of the beam. The height of the beam for this experiment may not havebeen large enou gh for the compression arch to develop. The scale of the beam


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47tested in this exper iment m ay also have had an influence on the shear beha viorobserved. The beam tested represents a q uarter s ize of an actual ACI classif ieddeep b eam . The shea r behavior m ay be different for a half-size or ful l-size beam

based on the dimensions used for the beam tested.The expe r im ents performed on the deep be am s introduced in this thesis

should only be considered a starting point for a better understanding of thestrengthening effect of CFRP laminates in shear. Many more tests must beconducted on full-sized deep beams in order to understand exactly how thefailure mechanisms are influenced. The condition of the structure must becompletely understood before CFRP strengthening system is applied. If theCFRP laminate is installed incorrectly, the mode of failure could change fromducti le bend ing fai lure to brittle com pressive fai lure. This m ust be avo ided at al lcost, for the safety of the public is the enginee r's num ber one p riority. Howe ver,with this in mind the experiments conducted demonstrate that reinforcedconcrete deep beam s can be strengthened in shear.


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APPENDIX AACI REINFORCED CONCRETE DEEP BEAM DESIGN

In this Appendix, the ACI flexural strength and shear capacity of the deep beam

is calculated by hand.

Figure A.1 D eep beam calculations one-point loading

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Figure A.2 D eep beam calculations one-point loading continued

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Figure A.3 Deep beam calculations two-point loading

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APPENDIX BCONCRETE MIX DESIGN AND TEST CYLINDER STRESS STRAIN CURVES

This Appendix contains the computer printout of the mix specifications and

proportions as well as the stress s tain curves for the test cylinders.This program calculates a CONCRETE MIX DESIGN based on the ABSOLUTE VOLUME METHOD aspresented in ACI 211.1. The user needs to know the requ ired SLUMP and STRENGTH, MAXAGGREGATE SIZE and FINENESS MODULUS. Additionally, the SATURATED SURFACE DRYEDSPECIFIC GRAVITIES of the COARSE and FINE AGGREGATES are needed as well as the %MOISTUREand %ABSORBANCE for both aggregates. Intermediate calculations are provided to aid in understandingthe ABSOLUTE VOLUME METHOD.

Required Slump (consult Table 6.3.1) 3-4 inches 0 Required Strength000 psi FinenessModulus of Fine Aggregate 2.79Maximum Coarse Aggregate Size/4 inchEstimated Water (per cubic y d.) from Tab. 6.3.3Estimated Entrapped Air %rom Tab. 6.3.3Water/Cement Ratiorom Tab. 6.3.4aDry Rodded Unit We ight of Coarse Aggreg ateVolume of Coarse Aggregate per unit volumeSpecific Gravity of Coarse AggregateSpecific Gravity of Fine Aggregate

1--imeeA 1.......11.4ea1//m.+1,rtelFigure B.1 C oncrete mix design

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Figure B.2 C oncrete mix design continued


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Figure B.3 Compressive strength of cylinders one-point loading

Figure BA Compressive strength of cylinders two-point loading


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APPENDIX CINDIVIDUAL LOAD DEFLECTION CURVES

The individual load deflection curves for the one- and two-point loading

conditions are located in this Appendix.

Figure C.1 Load deflection curve beam 1-1


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LOAD-DEFLECTION CURVE (control beam 2-1)

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LOAD-DEFLECTION CURVE (90 deg. align beam 2-3 )

5 7




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APPENDIX DINDIVIDUAL MOMENT-CUVATURE CURVES

In this Appendix the individual moment-curvature curves are displayed for both

the one- an d two-point loading conditions

Figure D.1 Mome nt-curvature curve beam 1-1

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Figure D.2 Mom ent-curvature curve beam 1 -25 9

Figure D.3 Mom ent-curvature curve beam 1 -3


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Figure D.4 Mom ent-curvature curve beam 1-460

Figure D.5 Mom ent-curvature curve beam 2-1


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Figure D.6 Mom ent-curvature curve beam 2 -26 1




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REFERENCES

1 . Sika C orporation Marketing D epartment "Sika C arboD ur C ompositeStrengthening Systems, Engineering Guidelines for Design andApplication" 201 Polito Avenue Lyndhurst, NJ. Date 8/10/99

2. C hajes, M., and Finch Jr., W., "Rehabilitation of Foulk Road bridge #26(Wilmington, Delaware) using advanced composite materials," Researchproject University of Delaware.

3 . Khalifa, A . and N anni, A., "Improving shear capacity of existing RC T-sectionsusing CFRP composites," Cement & Concrete Composites, 22, 2000, pp.165-174

4. Taljsten, B . and E lfgren, L., "Strengthening concrete beams for shear usingCFRP materials: evaluation of different application methods," Composites:part B 31 , 2000, pp. 87-965 . Zhang, Z., and H su, T., "Shear be havior of reinforced concrete beamsstrengthened by Sika CFRP laminates" Technical Report Structural seriesNo. 2000-16 . A C I C ommittee 3 18, "B uilding code requirements for structural concrete," AC IB uilding C ode. AC I 318-997. Wang, C ., and Salmon C . G., "Reinforced C oncrete D esign," 5 th Edition, New

York, Harper and Row, 19 928. Sika. 199 5. "Sika C arboD ur High-duty C FRP S trengthening System." ProductD ata Sheet N.p.: n.p.9 . Sika. 199 5. "Sikadur-30 A dhesive for B onding R einforcement." Product D ataSheet N .p.: n.p.10. B resler, B ., and MacG regor, J. G., "Review of Co ncrete B eams Fa iling in

Shear," Journal of the Structural Division, ASCE, Vol. 93, No. St-1, Feb.196 7, pp. 343-372

strengthened deep beam

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