PROCEEDINGS PAPER

Flexural Behavior of Prestressed Split-BeamComposite Concrete Sections

by J. O. Bryson, L. F. Skoda and D. Watstein*

SYNOPSISAn investigation of the general flexural characteristics of prestressed com-

posite concrete beams is described. The composite beams were made byseparately forming the tensile and compressive sections of the beams. Thetensile section was cast first and prestressed, and the compressive sectionwas formed with plain concrete bonded to the prestressed element. Thesecomposit beams are referred to as "Prestressed Split Beams".

Three sets of split beams with interfaces at different levels were testedin duplicate and the results compared with those from two sets of duplicateconventionally prestressed beams. The results of the tests indicate that thestructural characteristics of the split beams failing in flexure are essentiallythe same as those of conventionally prestressed beams.

Since the prestressing is confined to the tensile portion in the split beamswhile the compressive portion is stress free, this design concept affords sig-nificant savings in the amount of prestressing steel as compared with aconventionally prestressed beam.

INTRODUCTION

An experimental investigation ofthe flexural properties of compositeconcrete beams was carried out atthe Structural Engineering Sectionof the National Bureau of Standardsat the request of the Bureau ofYards and Docks. The compositebeams known as split beams con-sisted of a prestressed tensile por-tion bonded to a stress free com-pressive portion. The portions ofthe beam termed tensile and com-pressive are those which would re-

*Structural Research Engineer, StructuralResearch Engineer and Chief, respective-ly, Structural Engineering Section, Build-ing Research Division, National Bureauof Standards, Washington, D.C.

sist tensile and compressive stressesrespectively in a simply supportedbeam. The concept of split-beamprestressing was proposed by A.Amirikian of the Bureau of Yardsand Docks.'.

Since in the split beams the pre-stressing is confined to the tensileportion of the beam, the total pre-stressing force required to producethe necessary compressive stress inthe outermost fiber of the pre-stressed portion is materially lessthan the force required to prestressthe entire cross section of a conven-tionally prestressed beam. Conse-quently, a significant reduction inthe amount of prestressing steel canbe achieved by using the split-beammethod of construction.

June 1965 77

It must be emphasized that inconstructing composite beams bythe split-beam method, the pre-stressed portion of the beam mustbe supported along its entire lengthwhen the fresh concrete of the com-pressive portion is deposited. Thisprocedure was adopted so that theweight of the bonded non-pre-stressed portion does not disturb theinitial stress block in the prestressedportion. Only after the non-pre-stressed portion reaches its designstrength, can the supports be re-moved and the split beam attain itsproperties as a composite beam.

SCOPE

The objective of the investigationwas to compare the structural prop-erties of split beams of differentdesigns with conventionally pre-stressed beams referred to here asreference beams. Three sets of splitbeams were tested in duplicate andcompared with two sets of refer-ence beams.

The depths of the prestressedportions of the split beams varied,so that the location of the interfacebetween the prestressed and non-prestressed portions varied with re-spect to the midplane of the com-posite beam; the magnitude ofprestress at the interface also varied.These variables were introduced toinvestigate the effect of abruptchanges of stress at the interfaceon the cracking pattern and resist-ance to bending moment of thesplit beams.

The location of the prestressingtendons in the two sets of referencebeams was also a variable. In oneset the tendons were located so asto produce zero stress in the topoutermost fiber, and in the other setthey were placed at such a levelas to produce a tension of 500 psi inthe top outermost fiber.

TEST SPECIMENS

Concrete

The concrete used throughout theinvestigation was a mixture of TypeIII cement, siliceous sand and peagravel proportioned 1:3.3:2.7 byweight. The cement factor was 5.5bags per cu. yd., and the watercontent varied from 7.2 to 8.6 gal.per sack.

The concrete was mixed in a tur-bine-type mixer of Yz cu. yd. ca-pacity. The concrete strengths inthe two elements of the split beamsand in the reference beams at thetime of testing are given in Table1. These strengths represent the av-erage value determined from com-pressive tests of three 6- by 12-in.control cylinders.

Prestressing Steel

Two grades of high strength steelbars were used as prestressing ten-dons in this investigation. The stress-strain curves from tensile tests ofthe two steels are shown in Fig. 1.

M

70 ^- A

lOr/ / .0002

Fig. 1—Stress-strain relationships for prestress-ing steel. Curve A is for 3/a-in. diameter barused in split beams. Curve B is for 1-in. di-ameter bar used in reference beams.

78 PCI Journal

CD

05C7[

Table 1 Observed and Computed Characteristics of Beams

-BEAMDesignation

Compressive Strengthof concrete at time

of Test, f' cEffectivedepth atmidspan,

Ratio of Preatresaipreinforcement force —

Computed 2/prestress —at interface

Ultimateload

Steel stressat ultimate

load 3/

Shear Stress 4/at maximum load Type of Failure

CompressiveElement

TensileElement

d p atinterface, average,

vc_33 VIb

vbd

A-1psi

4770psi5440

in.10.25

%1.07

lb27,000

psi0

lb 23,500

psi92,500

psi328

psi271 Flexural Comçreaaion

A-2 4970 6360 10.25 1.07 27,000 0 22,200 90,400 308 254 Flexural Coaçreasion

B-1 5340 6230 10.25 1.07 27,980 547 23,000 90,700 311 265 Flexural Cnepreaaion

B-2 • 5000 5240 10.25 1.07 27,980 547 23,200 89,600 315 268 Flexural Compression

C-1 5290 5420 10.25 1.07 28,080 -381 22,580 91,800 306 259 Flexural Co ression

C-2 4530 5810 10.25 1.07 28,080 -381 23.150 91,700 304 266 Flexural Compression

R1-1 5270 8.13 2.43 ' 54,110 24,700 85.300 339 Flexural Coepresaion

R1-2 5040 8.13 2.43 54,000 23,600 84,800 — 321 Flexural Compression

R2-1 4720 9.30 2.12 41,980 25,800 79,800 313 Flexural Compression

R2-2 4350 9.30 2.12. 41.980 23,500 77.200 282 Flexural Compression

The prestressing force for each beam was adjusted immediately before testing.Minus sign. indicate tension.Tension in tendon was measured with dynamometer located at one end of the beam.The values of Shear stress were computed at the center of the shear span. The effective depth at thissection for the split beems, the RI beams, and the R2 beams were 9.70 in., 7.58 in., and 8.75 in., respectively.

CD

' IBEAM A BEAM B BEAM C BEAM RI BEAM R2

Cold finished steel bars 3/a in. indiameter were used as prestressingtendons in the split beams. Tensiletests of these bars indicated a stress-strain relationship that was essen-tially linear up to a stress of 68,000psi, and an initial tangent modulusof approximately 27 x 106 psi. Theyield strength of the steel was 102,-000 psi as determined by the 0.2percent offset method and the ten-sile strength was 124,500 psi.

The prestressing tendons in thereference beams were 1-in, diame-ter heat-treated, stress-relieved steelbars. Tensile tests of these barsshowed a linear stress-strain rela-tionship up to a stress of 72,000 psi.The initial tangent modulus of thesteel was approximately 30x 106psi. The yield strength of the steelwas 124,500 psi as determined bythe 0.2 percent offset method andthe tensile strength was 137,800 psi.

Sections

The test specimens includedthree types of prestressed splitbeams designated A, B, and C andtwo sets of conventional prestressedreference beams designated R-1 andR2. The cross-section at the mid-span of the three split beams andthe two reference beams are illus-trated in Fig. 2. In the A beamsthe interface of the prestressed ele-ment and the compressive elementcoincided with the midplane of the

composite unit, while in the B andC beams the interfaces were, re-spectively I in. below and 1'/z in.above the midplane of the beams.The location of the prestressing ten-don in the RI beams was selectedto give zero stress at the compres-sive face at midspan. The prestress-ing tendon in the R2 beams wasI'/s in. closer to the tensile surfacethan in the RI beams.

All beams were 4 in. by 12 in. incross section and 10 ft. in Iength.In each case the calculated pre-stress at the midspan in the bottomfiber of the beam was 2250 psi. Thisvalue of prestress was based on 0.45f', where f', was assumed to be5000 psi. The prestress included theeffect of the weight of the beamon a 9-ft simply supported span.

The beams were post-tensionedand the tendons were unbonded. Asingle steel bar fixed in a parabolicprofile served as the prestressingtendon.

The splitting stresses at the endsof the beams caused by the bearingthrust were resisted by spiral rein-forcement. The spiral reinforcementconsisted of a '/4-in, diameter steelbar fabricated into a 3-in, diametercoil with a 1-in. pitch. This rein-forcement encircled the prestress-ing tendon and extended over alength of approximately 11 in. start-ing I in. in from each end of thebeam.

fig. 2—Nominal cross section of test beams at midspan. Cross -hatched portion indicates the non -prestressed element of beam. The dotted circle indicates the position of prestressing tendon at endof beam.

80 pCI Journal

Thin-wall steel tubing (electricalconduit) of 1-in. O.D. and As-in.wall thickness was located in theprestressed element of the splitbeams in the position specified forthe prestressing tendon. The tubingprovided a channel for the unbondedtendons. The tubing was fixed in po-sition at the ends of the form andat the midspan.

For the reference beams, insteadof using tubing as in the split beams,the tendons were coated with a thicklayer of high density lubricatinggrease and then wrapped in a dou-ble layer of 6 mil polyethylene sheet-ing.

In the split beams, a thin sheetmetal spacer served to position thetendons at midspan. The spacer waswedge shaped, tapering from a 4-in. width at the level of the tendonsto 1 in. at the bottom of the form.The tendons in the reference beamswere held in place by one loop oftie wire fixed to the bottom of theform.

Shear connectors were not pro-vided in the split beams, thus theresistance to horizontal shear at theinterface of the two beam elementswas dependent solely on the bonddeveloped between the two layersof concrete.

Casting and Curing

One 4-cu. ft. batch of concretewas mixed to cast each element ofthe split beams and two 4-cu. ft.batches were mixed to cast each ref-erence beam.

All beams were cast in a metalform of adjustable depth. The pre-stressing tendon and the spiral rein-forcement were fixed in position andthe concrete was placed in twoequal layers. All freshly cast con-crete was vibrated with a high fre-quency internal vibrator.

In order to aid in the develop-

ment of a good bond between thetwo elements of the split beams,the top surface of the prestressedelement was treated in the followingmanner. Approximately 1 1/2 hr. afterplacing the concrete in the form,the excess material was screedec!off with a wood screed. The screed.ing was carried out only to the extent of providing a plane surfaceFollowing the screeding operation,the concrete was undisturbed foiapproximately 2 hr. which was suf-ficient time for the initial set to takeplace. At this time a stiff wire handbrush was used to roughen the fur.face to such an extent that the hargest size aggregate was exposed.

After curing overnight under wetburlap, the element to be pre.stressed along with the adjustablebottom was lifted up and supportedon the top of the form. The elementremained in this position wrappedin wet burlap and a single sheet oftwaterproof building paper until theconcrete developed the desiredstrength for prestressing as deter-mined by test of 6- by 12-in. conixocylinders. Following the prestress:inboperation described below, the ele-ment was placed back into the formand the concrete for the compres-sive element of the split beam wascast. After remaining covered over-night, the beam was removed fromthe form and placed on supportsspaced 9 ft. apart. Wet burlap andwaterproof building paper were ap-plied to the split beam in the samemanner as described above for cur-ing.

Prestressing ProcedureThe split beams were prestressed

by post-tensioning a '3/4 in. diam-eter tendon that was threaded oneach end. The tensioning force inthe tendon was measured with asteel dynamometer attached to the

June 1965 81

tendon at the end of the beam op-posite to the jacking end. This forcewas distributed over the ends ofthe prestressed element, with 1 in.thick bearing plates. Heavy dutycold pressed stainless steel nuts boreagainst the dynamometer on oneend and the bearing plate on theother end to maintain the prestress-ing force in the beam. The 1-in.diameter tendons in the referencebeams were post-tensioned in a sim-ilar manner, except that the bearingplates covered the entire cross sec-tion at each end and were 11/Z in.thick.

INSTRUMENTATION

Gage lines for a 10-in. Whitte-more strain gage were establishedon each side of the beams, parallelto the longitudinal axis, at the timeof casting with gage plug insertsfastened to the inside of the form.There were four gage lines on eachside of the split beams and twogage lines on each side of the ref-erence beams. The gage lines werelocated at midspan approximately1 in. from the top and bottom sur-faces on all the beams and 1 in.

above and below the interface onthe split beams.

Initial readings on all gage lineswere made one day after castingeach element of the split beams andthe reference beams. The use ofWhittemore strain gage instrumen-tation allowed observation of thestrains in the concrete during theearly stages of curing and served toreveal the nature of the stress blockdeveloped over the cross-section ofthe beams.

Type A3 and A9 bonded wireelectric resistance strain gages wereused to measure longitudinal con-crete strains in the beams duringload tests. These gages weremounted on the specimens with aquick setting adhesive immediatelybefore testing. Three A9 gages, witha gage length of 6 in., were placedend to end on the top (compressive)surface of the beam centered atthe midspan giving a coverage of18 in. The gages were connectedin series to show the average strain.The A3 gages with a gage lengthof 1%s in., were mounted on bothsides of the beams at midspan. Thesegages were located at various points

Fig. 3—View of Beam in Testing Machine

82 PCI Journal

I2

I---4^

A_f4̂ -

6"

It

6" F• Y7 000 le

It x3Te zzso

2250

2250

2" 335 597 -3T572

5I " F•Y7.Y6ole

+ 2463 2251

41^Y042

12"

BEAM C t 1^1 _ F• Y^ e,oso le

^ 3^^4 J 2314

MIDSPAN CROSS-SECTION STAGE STAGE 2 STAGE 3

Stage 1—Prestress plus weight of prestressed elementStage 2—Prestress plus weight of prestressed and compressive elements combined.Stage 3—Prestress plus weight of split beam plus effect of applied load producing

zero stress at bottom surface of beam.

Fig. 4—Midspan stress condition in the split beams computed for three stages of loading. Themagnitude of the stress is shown on the stress blocks; minus signs indicate tension. F equals pre-stressing force.

BEAM A

BEAM B

along the depth of the beam toshow the distribution of strains overthe cross-section.

The deflections of the beams atmidspan were measured with re-spect to tjie platen of the testingmachine with 0.001-in. dial indica-tors.

TEST PROCEDURE

The beams were tested simplysupported in a 600,000 lb. capacityhydraulic testing machine. A viewof the beam set up for test in thetesting machine is shown in Fig. 3.One end of the beam rested on a1 in. thick steel bearing plate thatextended across the width of thebeam. This bearing plate was sup-ported by a ball-socket assemblywhich provided longitudinal and

transverse rotational freedom. Theother end of the beam was sup-ported by a roller assembly. A '/4

in. thick strip of leather was placedbetween the beam and the up-ports.

The prestress was adjusted andthe load was applied at the thirdpoints through a steel loading beamsupported on plate-roller assemblies.Load in increments of 2000 lb. -wasapplied until failure except betweenthe loads of 10,000 to 14,000 lb.which was the critical cracking rangewhere increments of 500 lb. wereused in most cases. After the appli-cation of each load increment, thedeflection of the beam, the forcein the tendon, the strain in the con-crete, and the extent of crackingwere recorded.

June 1965 83

RESULTS AND DISCUSSION

The values of observed and com-puted characteristics of the splitbeams and reference beams are giv-en in Table 1. The magnitude ofprestress in the bottom fiber of theconcrete section at midspan of 2250psi was based on an assumed con-crete compressive strength of 5000psi at the time of test. The pre-stressing forces applied to the beamswere 27,000 lb. for the type Abeams; 27,980 lb. for the type Bbeams; 28,000 lb. for the type Cbeams; 54,000 lb. for the type RIbeams; and 41,980 lb. for the typeR2 beams. One of the variables forthe three types of split beams wasthe magnitude of the prestress atthe interface. The computed stressin the prestressed element at the in-terface of the beam at midspan cor-responding to the effect of prestressand the weight of the beam (Fig.4, Stage 2) was zero for type Abeams, 547 psi in compression inthe type B beams, and 381 psi intension in the type C beams.

The stress conditions at the mid-

span for three stages of loading areshown in Fig. 4. The stress blocksillustrated are idealized omitting theeffect of shrinkage and creep inthe materials (shrinkage and creepwere minimized by the curing tech-nique previously described). Stage1 in Fig. 4 represents the stress de-veloped in the concrete due to theprestressing force and the weightof the prestressed element. Only theprestressed element of the splitbeam is involved at this stage. Atstage 2 the weight of the compres-sive element is added to stage 1.As was pointed out earlier, the pro-cedure for forming the split beamrequires that the prestressed ele-ment be supported along its lengthin its cambered position while thecompressive element is beingformed. However, because of theshort span length and the relativelylight weight of the compressive ele-ment for the test beams in thisstudy, initial stress allowances weremade for the prestressed elementto support the added weight of thecompressive element. Stage 3 rep-resents the stress condition in the

DEFLECTION AT MIDSPAN

Fig. 5—Observed load-midspan deflection relationships. Arrows indicate cracking loads estimatedat points where curves departed from straight lines.

84 PCI Journal

beam corresponding to the appliedload that reduced the initial pre-stress at the tensile surface to zero.

The load-deflection curves for allbeams are presented in Fig. 5. Thedeflections were measured withrespect to the platen of the testingmachine. Corrections for movementat the supports were unnecessarysince the platen of the testing ma-chine is extremely rigid under theloads applied in these tests. A com-parison of the observed deflectionswith theoretical deflections showedvery good agreement. The theoret-ical deflections were computed witha modified version of Maney's2formula for the deflection of a rein-forced concrete beam. The observedstrain on the compressive surfaceof the beam was divided by thedistance from this surface to theneutral axis giving a measure of

EI. This value multiplied by the ap-

propriate constant and the square ofthe span is equal to the deflection.For 1/3 point loading:

0=0.1065L2kd

where: L = span lengthe0 = strain on the compres-

sive surfacekd = distance from compres-

sive surface to neutralaxis of beam

The load-deflection curves reflectthe nature of the response of thebeams to loading. As seen from thecurves, the response to loading canbe divided into two phases. In thefirst phase the beam exhibits a lin-ear load-deflection relationship. Inthe second phase the beam hascracked and the propagation of thecracks through the cross section isindicated by a constantly increasingrate of deflection with load.

It is noted that the slopes of theload-deflection curves for both splitbeams and reference beams prior tocracking were very nearly equal.This would indicate that the addi-tion of the electrical conduit to thesplit beams had no measurable ef-fect on the rigidity of the beamsup to the cracking load, even thoughthe conduit increased the ratio ofreinforcement by 42% in the splitbeams.

The exact point in loading atwhich the first phase of the load-deflection relationship ends andthe second phase begins was notprecisely determined in these tests.However, two different methodswere used to determine approxi-mately the cracking load. In onemethod the cracking load was de-termined as the point at which heload-deflection curve departed froma straight line. This point of depar-ture was determined graphically.In the second method, the relation-ship between the applied load andthe distance to the neutral axis, kd,was examined; the cracking loadwas defined as the load at whichthe value of kd departed from aconstant value. Typical load-kd re-lationships are illustrated in Figs. 6and 7 for split beams and referencebeams respectively. These relation-ships were developed from the dis-tributions of strains over the cress-section of the beams as illustratedin Figs. 8 through 11.

Table 2 gives the approximatecracking loads determined fromboth the load-deflection relation-ship and the load -kd relationship.In general, the approximate crack-ing loads determined by the twomethods were in good agreement.The computed value of the appliedload for producing zero stress atthe bottom fiber was 12,000 lb. for

June 1965 85'

22.1( E40

2

i I 2 3 4 5 6 7 8 9 10

kE, .

Fig. 6—Relation between applied load and dis-tance to neutral axis, kd, typical of split beams.

0 I 2 3 4 5 6 7 8 9 10

64, in.

Fig. 7—Relation between applied load and dis-tance to neutral axis, kd, typical of referencebeams.

all beams. Lower cracking loads cross section in these beams prac-were expected in the split beams tically undisturbed.than in the reference beams because Beam R2-1 developed severalapproximately 9 sq. in. of the bot- cracks in the top surface after pre-tom portion of the midspan cross stressing. These cracks were plainlysection of the split beam was occu- visible and extended approximatelypied by a thin sheet metal template 2 in. from the top of the beam.used to position the longitudinal Consequently, the prestress distri-reinforcement. The longitudinal re- bution in this beam was somewhatinforcement in the reference beams different from that which waswas held in place at midspan by planned, and higher initial stressone loop of tie wire fixed to the was obtained at the bottom surfacebottom of the form which left the than in any of the other beams. A

Table 2 Approximate Cracking Loads

BeamCracking

Method 1Deflection Data

Loads Estimated ByMethod 2

Initial Shift of Neutral axis

lbs lbsA-1 12,000 ----°A-2 12,200 12,500B-1 12,100 11,500B-2 13,000 13,000C-1 13,200 13,000C-2 12,500 12,500

R1-1 14,500 13,500R1-2 12,500 13,000R2-1 14,500 ----° eR2-2 14,500 15,000

° Erratic readings from electrical resistance strain gages on the concrete.°° This beam developed cracks on the top surface after prestressing. During the load test,

the initial shift of the neutral axis was attributed to the closing of these cracks ratherthan the development of new cracks on the bottom surface.

86 PCI Journal

CCCS

^{` NTERFACE

CIRCLED NUMBERS INDICATEAPPLIED LOAD IN LANDS

O SR-4 GAGE MEASUREMENTSD WHITTEMORE GAGE MEASUREMENTS

600 400 200 d 200 400 600 800 1000 1200 1400810-G

TENSION STRAIN COMPRESSION

Fig. 8—Strain Distribution in Split Beams of Type A

CIRLLIE N AD IN INDICATEAPPLIED LOAD IN INDICT

3•

D SR-4 GAGE MEASUREMENTSM 0 WHITTEMORE GAGE MEASUREMENTS

600 400 200 200 400 600 800 1000 1200 1400010-6

TENSION STRAIN COMPRESSION

Fig. 9—Strain Distribution in Split Beams of Type B

iNTM.EAaE-------- U A----------------------------

oAo

D SR-A GAGE MEASUREMENTSD WHTTEMORE GAGE MEASUREMENTS

600 400 200 1 200 400 600 800 1000 1200 140OX10-6

TENSION STRAIN COMPRESSION

Fig. 10—Strain Distribution in Split Beams of Type Ccc

TENSION STRAIN COMPRESSION

Fig. 11—Strain Distribution in Reference Beams R1 and R2

slight difference in the performanceof this beam as compared with theother reference beams can be seenfrom the difference in slope of thelinear portion of the load-deflectioncurve (Fig. 5) and in the appliedload-compressive strairr relationship(Fig. 12).

The linear distribution of strainsover the cross-section of a beamunder load is a positive indicationof monolithic beam action. The lin-ear distribution of strains observedin all split beams is illustrated inFigs. 8 through 10; the distributionof strain for the reference beams isshown in Fig. 11. One graph foreach of the three types of splitbeams and the reference beams ispresented as typical of the speci-mens. These graphs clearly showthat the split beams responded toloading in accordance with the elas-tic theories of strain distribution,indicating that the abrupt changesof the strain gradients at the inter-face in the B and C beams prior toloading (see Fig. 4, Stage 2) hadno apparent effect on the linear

strain distribution of the beams un-der the applied load.

Fig. 12 shows the relation be-tween the compressive strain in theoutermost fiber in the constant-mo-ment span and the applied load.The strains are the average valuesover the 18-in, length covered bythe three type A-9 gages. The com-pressive strains developed in essen-tially the same manner in all beams,except for the reference beam R2-1.It will be recalled that this beamdeveloped several tensile cracks atthe compressive face during pre-stressing resulting in greater appar-ent compressive strain during load-ing than in the other referencebeams.

All beams tested in this investi-gation failed by flexural-compres-sion which is defined here as: crush-ing of the concrete in the region ofconstant moment above a flexuralcrack which has reduced the areaavailable for resisting compressivestresses. The ultimate loads carriedby the beams are given in Table 1.The average values of ultimate load

Fig. 12—Relationship between compressive strain and applied load in the region of constant moment.

88 PCI Journal

for duplicate specimens of the A,B, C, RI, and R2 beams were 22,-850 lb., 23,100 lb., 22,860 lb., 24,150lb., and 24,650 1b. respectively. Al-though the differences between thereference beams and split beamswere not considered to be of prac-tical importance, it should bepointed out that the strength of thereference beams were all largerthan those for split beams exceptfor the tied results for beams A-Iand R2-2.

The magnitude of stress in thetendon at ultimate load was ap-proximately 91,000 psi (0.80 f .,) forsplit beams; 85,400 psi (0.69 f,)for the R1 beams and 78,500 psi(0.63 ff) for the R2 beams. Atthese stress levels the tangent mod-uli for the steels in the split beams,the RI, and the R2 beams wereapproximately 10.8 X 106 psi, 22.9X 106 psi and 26.3 X 106 psi, re-spectively. These values were esti-mated from the stress-strain curvesshown in Fig. 1. Thus, at loadsnear the ultimate, the stress in thetendons of the split beams was inthe curvilinear range of the stress-strain curve while the stress in thetendons of the reference beams wasessentially in the elastic range.

The greater stiffness of the ref-erence beams as compared with thesplit beams may be attributed tothe larger ratio of reinforcement inthe reference beams and the morenearly linear stress-strain curve forits tendon at loads approaching themaximum values. No attempt wasmade to gauge the effect of theelectrical conduit in the split beamsafter cracking.

Crack patterns typical of those inall beams are shown in Fig. 13. Aswas stated earlier, the first crack inall beams developed at or very nearmidspan and was shortly followed

by additional cracks symmetricallylocated about the midspan. Duringthe loading operation close attentionwas given to the progress of cracksas they approached the interfacein the split - beams to see if thecracks would propagate along theinterface. However, the cracks in allcases proceeded to develop in thesplit beams with no particular re-gard to the plane of the interface.

CONCLUSIONS

The flexural behavior of the splitbeams and the reference beams asindicated by the load-deflection re-lationships and the strains devel-oped over the cross section underload was similar up to the crackingload. Beyond the cracking load thereference beams exhibited a greaterdegree of stiffness than the splitbeams although the difference inthe ultimate loads was very small.

The abrupt changes of the straingradient at the interface in the splitbeams due to prestressing had nomeasurable effect on the develop-ment of strains over the cross sec-tion of the beams under the appliedload. The abrupt changes in stresswere introduced by varying the lo-cation of the interface in the splitbeams with respect to the midplarteof the cross section while the loca-tion of the tendon in the split beamremained fixed.

The procedure that was used forcombining the two elements of fluesplit beams proved to be adequatefor the development of sufficientbond for monolithic beam actionthroughout the tests. In all cases,cracks developed in the split beamswith no particular regard to theplane of the interface.

For the same working load capac-ity (load producing zero stress inbottom fiber of beam), the prestres;;-

June 1965 89 -

4 >

INTERFACE

w E

--- -------------- — -------- ----------INTERFACE --------

6

® O

!BEAM

O

5

A

-----INTERFACE

w N E

__INTERFACE _____

G

o,®

2

BEAM

O

B

----- - --- ----- --- - ' - ----INTERFACE ---------

w Nt E

------'-----------------' -----'------ --- -'-'------INTERFAC --------

4

Q

OmBEAM

(

7

C

OO

w E

© 7 6

BEAM9

R

Fig. 1S Typical crack patterns in split beams of types A, B, and C, and reference beams. Encirclednumbers indicate order of occurence of cracks.

90 PCI Journal

ing force required for split beamsis considerably less than that re-quired for a conventionally pre-stressed beam, and consequentlya significant reduction in the amountof reinforcing steel can be achievedby this method of construction.

REFERENCES1. Amirikian, A., "Split-Beam Prestress-

ing", The Navy Civil Engineer, Vol. 4,No. 11, 1963, p. 35.

2. Maney, G. A., "Relation Between De-formation and Deflection in Reinforced-Concrete Beams", ASTM Proceedings,Vol. 14, Part 2, 1914, p. 310.

Presented at the Tenth Annual Convention of the Pre-stressed Concrete Institute, Washington, D.C., September 1964.

June 1965 JI