Transcript
Page 1: Tests of One-Way Post-Tensioned Slabs With Unbonded Tendons Journal... · 2018-11-01 · Tests of One-Way Post-Tensioned Slabs With Unbonded ... (18-5) requires that A, for a solid

Tests of One-WayPost-Tensioned SlabsWith Unbonded Tendons

Ned H. BurnsProfessor of Civil EngineeringThe University of Texas at AustinAustin, Texas

Finley A. Charney*AssociateWalter P. Moore & Associates, Inc.Houston, Texas

Wendell R. Vines*Project Engineer

TERA, Inc.Houston, Texas

The provisions in the ACI BuildingCode (ACI 318-77)1 for pre-

stressed concrete recognize a differ-ence in the amount of mild steel re-quired for ultimate strength and crackcontrol between bonded and un-bonded members. However, the ACICode equations are based mainly onexperience with and tests on beamswith relatively low span/depth ratioscompared to those common withpost-tensioned slabs.

Previous research efforts concern-ing members with unbonded tendonsand various span/depth ratios haveshown that the ACI• Code expressionsfor steel stress at ultimate may be un-conservative for members such asslabs with span/depth ratios as highas 40 or more, 2' 3 while reinforcementrequired for crack control may be onthe conservative side.

`Formerly Research Assistants, The University ofTexas at Austin.

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In order to obtain a better under-standing of partially prestressed con-crete slabs with unbonded tendons, atest program was carried out at TheUniversity of Texas at Austin duringwhich the strength and behavior oftwo half-scale models of prototypestructures were experimentallyevaluated 4 '5 Of major concern wasthe comparison of observed behaviorwith that predicted following theprovisions of ACI 318-77.

The specific objectives of the testprogram were to:

1. Examine the load-deflection re-sponse of the slabs before andafter initial cracking with par-ticular attention to the effects ofcracking on the observed stiff-ness of the two slabs.

2. Observe the control and dis-tribution of cracking provided bydifferent amounts of bondednon-prestressed reinforcement.

3. Determine experimentally theultimate strength of the speci-mens as well as measure the in-crease in tendon stresses as fail-ure loads were approached.

4. Compare the test results with theprovisions contained in ACI318-77.

Selection ofTest Specimens

Prestressed concrete elements arenormally proportioned on the basis ofsome limiting stress in the concrete atservice load, and then checked for ul-timate strength. Depending on themagnitude of the tensile stress in theconcrete, the service load deflectionsmay or may not be elastic.

Under normal circumstances, thelimiting tensile stress is 6 fI(0.50 f,') and the concrete remainsuncracked throughout the service loadrange. Section 18.4.2 of the ACI Code,however, allows tensile stresses as

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Table 1. Design parameters of prototype structures forSlabs A and B.

Parameter Prototype forSlab A

Prototype forSlab B

Span 20 ft. 20 ft.Slab thickness 5.5 in. 5.5 in.Design live load 50 psf 50 psfAllowable tension inconcrete at serviceload 6/ 91/f^

f/ 4000 psi 4000 psi240 ksi 240 ksi213 ksi 213 ksi

P/A stress 185 psi 140 psiInitial tendon stress 140 ksi 140 ksiPercent unbondedreinforcement 0.120 0.098Percent bonded 0.12 < 0.20 0.23 > 0.20reinforcement required by required by

ACI Code ACI Code

*Two adjacent spans loaded with live load and dead load on all spans.Note: 1 psi = 6.9 kN/mz ; 1 ksi = 6.89 MPa; 1 ft = 0.305m; 1 in. = 25.4 mm; 1 lb = 4.45 N.

high as 12[ (1.00 f, ), so long ascareful deflection computations aremade to insure satisfactory perfor-mance. With service load stresses of12 J7,' (1.00 f,) the concrete wouldcertainly be cracked (fr = 7.5 fJ or0.62 f,') and inelastic action wouldbe evident in the working load range.

In addition to the requirements formaximum tensile stresses in the con-crete, ACI 318-77 states a minimumrequirement for bonded reinforce-ment when unbonded tendons areused:

A, = 0.004A [ACI Eq. (18-5)]

whereA, = minimum bonded steel, sq in.A = area of that part of the cross

section between the flexuraltension face and the center ofgravity of cross section, sq in.

Eq. (18-5) requires that A, for a solidslab equal to 0.2 percent of the cross-sectional area be supplied as bondedreinforcement, and a primary questionto be addressed by these tests iswhether this amount of A, is realisticas a minimum requirement.

Two slabs were experimentallyevaluated incorporating characteristicsto test the adequacy of the ACI Codedesign requirements. The main vari-ables in the two specimens were theallowable tensile stress in the con-crete at service load and the amount ofbonded reinforcement. In Slab A, thetensile stresses were limited to 6 JJ(0.50 f) and in Slab B, the designtensile stresses under service loadwere 9J7 (0.75/7). ). In both casesthe bonded reinforcement providedwas that required for strength, even ifthat amount were less than that

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A B2.75°

4 5'1

30'A 2 B 3 C 4

2.25=l •° • Section A-A•

55" I 6fc at Sec. 2-2 with service load

0 1/4° 0 unbonded tendon

2.25" Section 2-2 • No.2 deformed bar

2 .2 511111 ° ° I Section B-B

Note: 1 ft = 0.305 m; 1 in. = 25.4 mm.

Fig. 1 a. Plan and section of Slab A (ideal model).

A B2.75"

41030A1

2 B 3 C

2.25" C ..° • .° ..° • Section A-A

L 55 I 9/i at Sec. 2-2 with service load

0 1/4" 0 unbonded tendon

2.25° EllIll * *° * .° . 0° 0 I Section 2-2 • No. 2 deformed bar

2.25" IlII ° • ° • ° Section B-B

Note: 1 ft = 0.305 m; 1 in. = 25.4 mm.

Fig. 1b. Plan and section of Slab B (ideal model).

specified under Section 18.9 of theACI Code. For Slab A (prototype andmodel) the bonded reinforcement was0.12 percent of cross-sectional areawhich is less than the 0.20 percent re-quired by the ACI Code.

The physical dimensions of theprototype slabs were the same forboth specimens; three equal spans of

20 ft (6 m) each, and a thickness of 5.5in. (140 mm).

Table 1 lists the design parametersfor the prototype structures. Test slabsA and B were half-scale models fromthese designs.

Figs. la and lb show a plan andsection views for the two slab speci-mens.

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Materials andFabrication

With the design conditions known,the two one-half scale model struc-tures (Slab A and Slab B) were pro-portioned accordingly. By matching thePIA stresses in the prototype, thewidth of the specimens was set as 55in. (1400 mm). Using this width, scal-ing all other dimensions down toone-half, and replacing the weight ofconcrete lost due to scaling, the mod-els would be stressed exactly as wouldthe prototype under similar loadingconditions.

The prototype slabs and half-scalemodels were designed for a 28-daycompressive concrete strength of 4000psi (27.58 MPa). The observedstrength for the models was higherwith a measured average cylinderstrength of 4700 psi (32.41 MPa) forSlab A and 5150 psi (35.51 MPa) forSlab B. The unbonded tendons wereY4 in. (6.3 mm) diameter single wirewith a measured ultimate strength of240 ksi (1655 MPa). The tendons werecoated with mastic and wrapped in

reinforced waterproof paper to pre-vent bond to the concrete. Thebonded reinforcement was deformedbar of 6 mm diameter (#2 bar) with ayield stress of 65 ksi (448 MPa).

The specimens were cast in placeover pedestals which provided linesupport across the width of the slab.Refer to Fig. 2 for the nomenclatureused in this paper for identifying sup-ports and spans.

1 A 2 B 3 C 4Fig. 2. Identifying nomenclature.

Instrumentation

Both slabs were extensively in-strumented. Stresses in tendons andbonded reinforcement were moni-tored using strain gages. Midspan andquarter span deflections were mea-sured electronically and checkedmanually with dial gages. Load cellsmonitored interior support reactions,applied, loads, and force in the un-bonded tendons.

T1 .io'

E

x in" I Load Pates Q

io' 10'

M

Fig. 3. Plan and elevation of loading system used in tests.Note: 1 ft = 0.305 m; 1 in. = 25.4 mm.

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Dead Load=69psf (TypAll Tests)

Applied Load=50psf

1 A 2 8 3 CTest 101

50

ILIJ

50

Test 102

50

Test 103

105 10550

Test 104102.5

50

Test 105

I•:

Fig. 4a. Load patterns for Slab A. Note: 1 psf = 47.9 Pa.

Note: Loads Shown in units psf (Applied Loads) 11535

69 psf DeadLoad (Typ. I A 2 8 3 C 4All Tests)

Test 20150

Test 202

•--------

••• ••

••

Test 205

Test 206115 27.5=0

Test 207

120 27.5

Test 20827.5 145

=0.4 D.L.

Test 20927.5 159 27.5

=0.4 D.L.I = 0.4 D.L.

Test 210

Fig. 4b. Load patterns for Slab B. Note: 1 psf = 47.9 Pa.,

Test Procedure

Pattern loadings designed to pro-duce maximum stress at each criticalsection were imposed on the slabs.Fig. 3 illustrates the whiffle tree

mechanism used to simulate a uniformload on the slabs. The specimenswere tested through three load ranges:elastic, inelastic (cracked), and ulti-mate.

Figs. 4a and 4b show the patterns ofloadings used in the tests. Load levels

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shown in these figures as well as inother figures in this discussion refer toapplied loads only, and as such do notinclude slab dead weight or deadweight replacement. The elastic phaseof testing (first four tests) served tocalibrate the slab and to producecracking for later tests.

The inelastic behavior was investi-gated during the next three tests todetermine the effects of cracking onreduced stiffness, and to measure theresponse of the initially crackedspecimen under various patterns ofload. After each slab was thoroughlycracked, it was then loaded in threefinal test patterns until a failure hadoccurred in each span. In these par-ticular tests, the ultimate flexuralcapacity and the increases in un-bonded tendon stress were measured.

Test Results

The test results are given first forSlab A and then for Slab B.

Slab ATests 101 to 104 tested the elastic

behavior of Slab A, with Test 104 pro-ducing first cracking. This slab wasdesigned for tensile stresses of 6 7(0.50/7) at working loads. Fig. 5shows the load-deflection curves forthese tests, indicating linear elasticbehavior associated with uncrackedsection properties.

In all cases the load-deflection re-sponse of the slab coincided with thepredicted behavior as calculated onthe basis of gross cross section. Test104 [in which the exterior spans wereloaded in 5-psf (240 Pa) increments to105 psf (5030 Pa), and the interiorspan was loaded to 50 psf (2395 Pa)],produced first cracking at a load levelof 102.5 psf (4910 Pa), when a hairlinecrack was detected on the top surfaceof the slab over Support 3.

Tests 105 to 107 loaded an initially

cracked specimen, with damage dueto cracking increasing as loading pro-ceeded. The slopes of the load-de-flection curves indicated a reducedstiffness as compared to the uncrackedpredictions of deflection as shown bythe dashed lines in Fig. 6. The extentof flexural cracking through Test 107consisted of hairline cracks at supportsections 2 and 3 (top of slab) withsingle hairline cracks approximately0.4L from the end supports (bottom ofslab). This indicates minor damageeven for levels of load reaching fac-tored design loads.

Fig. 7 shows the load-deflection be-havior during Tests 108, 109, and 110which produced failures in Spans C,A, and B, respectively. For tests 108and 109 failure was preceeded by theformation of numerous flexural cracksin the positive moment regions of theloaded spans as shown in Fig. 8. Thelocation of the positive moment fail-ure cracks was at 4 ft (1.2 m) from theinterior supports, which coincidedwith the cutoff point of the positivemoment bonded reinforcement.

As shown in Fig. 7, the load-de-flection response of the slab indicatesfailure at about the time these largecracks formed. Note that failure wasdefined as increased deflection withno increase in load, since a compres-sion failure of the concrete did notoccur. For Test 110, where the middlespan was loaded until a failure oc-curred, the maximum applied loadreached 150 psf (7185 Pa). Althoughno bonded reinforcement was pro-vided, this failure was also forewarnedby the formation of a large flexuralcrack. Collapse was confirmed by thecrushing of concrete in Span B. Theextent of flexural cracking in Slab Athrough Test 110 is shown in Fig. 8.

Besides determining the ultimatestrength of Slab A, the increases inunbonded tendon stresses were mea-sured by strain gages bonded to thetendons. As shown in Fig. 9, the in-

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220

200

180

160Na 140Vv0 120

m 100Ui

n 80

60

40

Cf

110

100

90

•_ 800,a

70C0 60

• 50aQ 40

30

20

10

0

Fig. 5. Load vs. deflection curves for Tests 101-104.Note: 1 psf = 47.9 Pa; 1 in. = 25.4 mm

CracksIO^OPSF Uncrocked /i

Predictioncracked Test 105 Test 106 Test 106 Test 107Miction i Span A i' Span A gpan C/ Spon C

tIii,_o.l in. Deflection

Fig. 6. Load vs. deflection for Tests 105-107.Note: 1 psf = 47.9 Pa; 1 in. = 25.4 mm.

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Large CrockForms 135 psf__ _ e°

Test 109Span Ai

Test 108 /Span C /

Test 110Span B

Deflection

180

160

140

U)120

V0 100JV 80

Q 60

40

20

00.25 in.

Fig. 7 Load vs. deflection for Tests 108-110. Note: 1 psf = 47.9 Pa; 1 in. = 25.4 mm.

creases in unbonded tendon stressesfor Tests 108 to 110 were relativelylow until the failure cracks hadformed and large deflections occurred,at which point the tendon stressesrapidly increased. The maximummeasured tendon stress increase was19.5 ksi (134.45 MPa) which occurredduring Test 109.

Slab BSlab B was also subjected to ten

separate load tests, as shown in Fig.

4b. With the design tensile stress of9 f,' (0.75 f,) load, the specimenwould be cracked at that stress levelfor any load pattern.

Test 201 to 204 measured the elasticresponse of the specimen to appliedload. As shown in Fig. 10, the load-deflection curve indicated linear elas-tic behavior up to the load level of 50psf (2395 Pa), but in Test 204, wherethe maximum load reached 100 psf(4790 Pa), visible cracking occurred inSpan C only after the final load in-

I A 12 B 3 C 4

Fig. 8. Crack pattern through Test 110 for Slab A

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200

180

160

y— 140n0 12000J 100vQ 80aQ 6C

4C

2C

C

1C

Test 108

I

0 2 4 6 8 10 12 14 16 18 2Tendon Stress Increase, ksi

Fig. 9. Tendon stress increase vs. applied load for Tests 108-110.Note: 1 psf = 47.9 Pa; 1 ksi = 6.89 MPa.

110

IOU

90

80t0NQ 70v0 60J.5Q

., 40Q

30

0

Test 202 Span A

fTe4

Test 201Span A

0Loo In. Deflection

Fig. 10. Load vs. deflection for Tests 201-204.Note: 1 psf = 47.9 Pa; 1 in. = 25.4 mm.

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220

200

180

160U,n. 1400J 1200m 100

80

60

40

20

0

Fig. 11. Load vs. deflection for Tests 205-207. Note 1 psf = 47.9 Pa; 1 in. = 25.4 mm.

220

200

1.80

160

a.140v0 120Jv 100

a 80

60

40

20

0

Fig. 12. Load vs. deflection for Tests 208-210. Note: 1 psf = 47.9 Pa; 1 in. = 25.4 mm.

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( I A 2 B 3 C (4

çt

Fig. 13. Crack patterns after Test 210.

crement was added. The predictedelastic response for Slab B, as shownby the dashed lines in the curves ofFig. 10, possesses a lower stiffnessthan observed during testing.

Tests 205 to 207 loaded an initiallycracked specimen, with damage dueto cracking increasing as load pro-ceeded. In each case, the specimenpossessed an inelastic stiffness lowerthan elastic yet not as low as predictedby a transformed cracked section mo-ment of inertia as shown in Fig. 11.The extent of flexural crackingthrough Test 207 was minor, with thehairline cracks at Supports 2 and 3(top cracks) and at approximately 0.4Lfrom support (single bottom cracks) inthe end spans.

Failure mechanisms of Tests 208and 209 were initiated by the forma-tion of large flexural cracks in thepositive moment regions where thebonded reinforcement had been cutoff. In Test 208, the failure crackformed at 4 ft (1.22 m) from Support 2at the rebar cutoff point. In Test 209the large crack formed 2 ft (0.61 m)from the exterior support 4, also nearthe reinforcing bar cutoff point.

Due to the nonexistence of bondedreinforcement within these failure lo-cations, deflections grew rapidly pro-ducing rotations with the deflectedshape being rather angular. Note thatfailure was defined as increasing de-flection with no increase in load.

For Test 210, the failure was ac-companied by a compression failure atmidspan of Slab B. Fig. 12 illustratesthe load-deflection curves for Tests208 through 210, and Fig. 13 showsthe crack patterns present on the sur-face of the slab upon completion oftesting Slab B.

The increases in unbonded tendonstresses in Slab B as measured duringTests 208-210 are shown in Fig. 14.The greatest tendon stress increasewas measured in Span A during Test208, with a magnitude of 21 ksi (145MPa).

Discussion of Results

In the working load range, bothSlab A and Slab B behaved well, withdeflection and cracking serviceabilityremaining under good control. It wasobserved that the immediate serviceload deflections measured were wellwithin the limits as set up by Chapter9 of the ACI Code. Table 2 lists theobserved deflections measured interms of the span length. All of theservice load deflections fall wellbelow 1/360.

In the case of Tests 105 to 108, and205 to 208, the specimens were ini-tially cracked and possessed a flexuralstiffness less than that of the elasticgross section. For Slab A, where thelimiting tensile stress was 6 ]

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200

180

160

140a

120v0J 100vd 80nQ 60

40

20

0

Test 210

20

0 2 4 6 8 1.0 12 14 16 I8 20 22Tendon Stress Increase, ksi

Fig. 14. Applied load vs. tendon stress increase for Tests 208-210.Note: 1 psf = 47.9 Pa; 1 ksi = 6.89 MPa.

220

200

180

w 1600a0 140C0J 120

• 100aa 80

60

40

20

0

Actual Curve

Calculated Usingle

ice co Carve

2 3 C 4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Deflection, Inches Span A

Fig. 15. Load vs. deflection for Test 204. Note: 1 psf = 47.9 Pa; 1 in. = 25.4 mm.

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Table 2. Deflections at service load."

SlabID

TestNo.

Spansloaded in.

SpanConstant

104 A,Ct 0.059 1/2033105 A,B 0.053 //2264

Slab A 106 A,C 0.087 //1379107 A,B,C 0.065 /11846108 A,Ct 0.105 //1142

204 A,C 0.100 //1200205 A,B,C 0.112 //1071

Slab B 206 A,B,C 0.118 //1017207 A,B 0.177 1/678208 A,C 0.211. 1/569

*Deflections are shown for a service live load of 50 psf for Slab A, 62.7 psf for Slab B.tSpan B was slightly loaded.Note: 1 in. = 25.4 mm; 1 psf = 47.9 Pa).

(0.50 ) no cracking was recorded atdesign service load, and deflectionsfollowed elastic behavior since thefull cross section was effective incontributing to elastic stiffness. ForSlab B, where the specimen wascracked at service load due to the rel-atively high tensile stress of 9 fI(0.75 f^) in the precompressed ten-sion zone, the actual cracks were fewwith only a very narrow width. Asshown in Test 204, the deflection re-sponse to applied load remained rela-tively elastic through the service loadrange, although cracks were present.

While initially uncracked or onlyslightly cracked, both specimens be-haved in a nearly elastic manner, butthe behavior was inelastic for testswhere cracking was substantial at theonset of loading. It is quite possiblethat an actual structure designed for9 f,' (0.75 f,') similar to prototypeSlab B may be initially cracked, thusaltering the predicted elastic or nearelastic behavior.

As shown in the test results, the be-havior of the initially cracked speci-men lies between purely elastic, andcompletely inelastic limits as based onthe transformed cracked section mo-ment of inertia. It is likely, therefore,

that deflection computations based onelastic section properties may be un-conservative, especially when there isa high probability that the section maybe initially cracked.

When the design allowable tensilestress in the precompressed tensionzone of a member is between 6(0.50 f,') and 12 f,' (1.00 f,' ), ACI318-77 requires that deflections bebased on a bilinear moment-curvaturerelationship, and the transformedcracked section moment of inertia.Fig. 15 shows such a bilinear load-de-flection curve as computed for Test204, Slab B, as compared to the actualmeasured curve.

Also shown in Fig. 15 is the pre-dicted load-deflection behavior aftercracking based on a modified form ofACI Eq. (9-7) for calculating an effec-tive moment of inertia. ACI Eq. (9-7)is given in Section 9.5.2.3 of the ACICode as a method for computing aneffective moment of inertia, Ie , for usein deflection calculations of non-pre-stressed one-way slabs and beams:

33IQ =1 __!!:_l 1,, + 1 – Ma Icr

Ma)

where

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Table 3. Measured vs. ACI Code ultimate tendon stress.

Observed Calculated

Afps fps Mps fpsSlab Test f5e f (obs)ID No. (ksi) (ksi) (ksi) (ksi) (ksi) fps (ACI)

108 141.5 15.6 157.1 30.3 171.8 0.91Slab A 109 141.5 19.5 161.0 30.3 171.8 0.94

110 141.5 10.6 152.1 30.3 171.8 0.89

208 146 21 167 53.4 199.4 0.84Slab B 209 146 14 160 53.4 199.4 0.80

210 146 13 159 53.4 199.4 0.79

Note: 7 ksi = 6.89 MPa.

Me,. = cracking moment (tensilestress = 7.5 f or 0.62 f71 )

Ma = maximum moment in whichdeflection is being computed

Ig = cross section moment of iner-tia

IC,. = transformed cracked sectionmoment of inertia

Although the intended use of Eq.(9-7) is for non-prestressed members,it can be adapted to prestressed con-crete by using the following expres-sion for Mer:

Mer = If (7.5 fc + .fpe -fd)C

wherec = depth from centroid to ex-

treme fiberfpe = stresses due to prestressId = dead load stressIg = gross cross section moment of

inertia

Using this procedure the load de-flection curve labeled I e of Fig. 15 wascalculated. As shown on the figure,the curve computed on the basis of lepredicts post-cracking deflection bet-ter than does the curve based on atransformed cracked section momentof inertia.

In both Slabs A and B, cracking waswell distributed by the bonded rein-

forcement. In Slab A, the bonded steelconsisted of four #2 bars in eachmaximum moment section (Spans Aand C and over Supports 2 and 3).This A8 amounts to only 0.12 percentof the cross section as compared to0.20 percent required by ACI Eq.(18-5).

The provision of 0.12 percentbonded steel in Slab A provided ade-quate crack control, thus the require-ments of Eq. (18-5) would providevery good behavior with more bondedreinforcement (0.2 percent of area).For Slab B, where seven #2 bars (0.23percent of the cross section) providedbonded reinforcement, the control ofcracking was very similar to that ofSlab A.

The increase in unbonded tendonstress at ultimate load did not reachthe value predicted by Eq. (18-4) ofACI 318-77. This equation is a con-servative version of the lower boundempirical formula developed by Mat-tock et aIs in a research program test-ing beams with a ratio of span to over-all depth of 28.

Table 3 shows the measured versuscomputed steel stresses for Slabs Aand B. The measured values wereconsistently less than the calculatedincrease, but this has substantially a

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Slab A

Slab B

U)

U)NU)

C,C

0)UsU)I-4-U)C0C0

I

22

20

18

16

14

12

10

Test 109

208

Test 108

Test 210

Test 209

0V0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Deflection, Inches1.6 1.8 2.0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Deflection, Inches

Fig. 16. Tendon stress increase vs. deflection. Note: 1 ksi = 6.89 MPa; 1 in. = 25.4 mm.

smaller effect in ultimate strength cal-culations since it is the total stresswhich is considered there. Also, thebonded reinforcement for both speci-mens supplied a significant portion ofthe tensile force which is effective inresisting external moments.

Figs. 9 and 14 illustrate how thetendon stresses increased withapplied load. These curves have ashape which is very similar to theload-deflection curves for their re-spective tests (as shown in Figs. 7 and12). Tendon stress increases plottedagainst deflections form what is virtu-ally a straight line. Inspection of Fig.16 indicates that deflections in theorder of 4 to 5 m. (102 to 127 mm)would be required for tendon stressesto reach those predicted by the ACICode equation for these slabs.

Such deflections probably wouldnot have occurred in Slabs A and Bwithout failure even if the reinforcingbars were extended in length accord-ing to the requirements of the ACICode on development length. Itwould seem then that the ACI equa-

tion for stress at ultimate in unbondedtendons, although adequate for lowerspan to depth ratios, is unconservativefor the case where the ratio is as highas 45, as in Slabs A and B. Similar re-sults were discussed in flat plate andslab research by Hemakom ,3

For all tests in which a failure oc-curred, the ultimate load carried wasgreater than the factored design loadequal to 1.4(69) + 1.7(50) = 182 psf(8718 Pa), and in all cases except Test208, the loads carried exceeded 182/0.9 = 202 psf (9676 Pa). Due to thetype of failures in Tests 108, 109, and205 and 209, where the positive mo-ment hinge (yield line) formed at ornear the reinforcing bar cutoff pointthe collapse was somewhat premature.

In Test 208 the failure was defi-nitely premature, partly because ofthe effect of patterned loads on redis-tribution of moments. Previous hing-ing over Supports 2 and 3 had an ef-fect on the strength exhibited by SpanB of both slabs, resulting in the testload falling below that predicted forTests 110 and 210.

PCI JOURNAUSeptember-October 1978 'A 81

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4.3' 5.83' 6'-0" j4-0"Test 108 Test 208

5.83' 1 4.41'Test 109

1 7 - 6 - 1/2" 2'-3",Test 209

4.63' Wv 5.3'Test 110

Fig. 17. Failure mechanisms for Tests108-110. Note: 1 ft = 0.305 m.

Table 4 shows the actual load (in-cluding dead load) carried for all testsin which a failure occurred. Alsoshown in the table is the calculatedload based on the full ACI Code un-bonded tendon stress, the yield inbonded reinforcement, and the posi-

4'-11" 5-0"Test 210

Fig. 18. Failure mechanisms for Tests208-210. Note: 1 ft = 0.305 m; 1in. = 25.4 mm.

tive moment hinge being located at theposition in the span which producesthe minimum ratio of internal work toexternal work. Figs. 17 and 18 showthe position of the bonded reinforce-ment within the failure mechanism foreach test.

Table 4. Ultimate loads carried by slabs (psf).

Slab Test Spans Failure Ultimate Yield line Ultimate loadYield line loadID No. loaded span load load

108 A,C C 206 216 0.954Slab A 109 A,B A 226 222 1.002

110 B B 221 278 0.795

208 A,C A 184 170 1.08Slab B 209 B,C C 214 205 1.04

210 B B 228 239 0.954

Note: 1 psf = 47.9 Pa.

82

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Conclusions

From the results of this test programthe following conclusions can bedrawn:

1. Load-deflection responses mea-sured during testing show that bothSlab A and Slab B, designed for 6 f^(0.50 f,') or 9 f,' (0.75 f ), respec-tively, remained serviceable underworking load.

2. The bonded reinforcementwhich consisted of #2 deformed barswith A s equal to 0.12 percent of thegross area for Slab A, and 0.23 percentfor Slab B, did an excellent job of dis-tributing cracks and keeping crackwidths under control. In the case ofSlab A, the amount of crack controlsteel was less than the 0.20 percentrequired by the ACI Code.

3. For load cases where cracksexisted prior to loading, deflectioncomputations based on gross cross-sectional properties may be too low,while computations based on thecracked section moment of inertia aretoo high. Deflection calculationsbased on an effective moment of iner-tia, similar to the method of Section9.5.2 of ACI 318-77, give realisticthough slightly conservative results ascompared to those deflections mea-sured in these tests.

4. There is a near-linear relation-ship between tendon stress increaseand deflection, for a given initial ten-don geometry.

5. Load capacity in all tests inwhich a failure occurred exceeded thefactored load (1.4D + 1.7L) eventhough the tendons did not reach theirACI Code predicted stress.

6. For Slabs A and B, failure loadductility would have been increasedand slightly higher ultimate loadwould have been observed withlonger bottom bars in the exteriorspans following ACI Code design re-quirements.

Acknowledgment

The experimental work reported in thisstudy was performed at the Civil En-gineering Structures Laboratory of TheUniversity of Texas at Austin, Austin,Texas. This work was sponsored by thePost-Tensioning Division of the Pre-stressed Concrete Institute (now thePost-Tensioning Institute) and their sup-port is gratefully acknowledged.

References

1. ACI Committee 318, "Building CodeRequirements for Reinforced Concrete(ACI 318-77)," American Concrete In-stitute, Detroit, Michigan, 1977.

2. Hemakom, R., "Behavior of Post-Ten-sioned Prestressed Concrete Slabs withUnbonded Reinforcement," Master'sThesis, The University of Texas at Au-stin, 1970.

3. Hemakom, R., "Behavior of Post-Ten-sioned Flat Plates with Unbonded Ten-dons," Doctor's Dissertation, The Uni-versity of Texas at Austin, December,1975.

4. Vines, W. R., "Strength and Behavior ofa Post-Tensioned Slab with UnbondedTendons," Master's Thesis, The Uni-versity of Texas at Austin, May, 1976.

5. Charney, F. A., "Strength and Behaviorof a Partially Prestressed Concrete Slabwith Unbonded Tendons," Master'sThesis, The University ofTexas at Austin,May, 1976.

6. Mattock, A. H., Yamazaki, J., and Kat-tula, B. T., "Comparative Study of Pre-stressed Concrete Beams With andWithout Bond," ACI Journal, V. 68, No.2, February, 1971, pp. 116-125.

Discussion of this report is invited.Please forward your comments toPCI Headquarters by March 1, 1979.

PCI JOURNALJSeptember-October 1978 83


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