Omission ofWeb Reinforcement in

Prestressed Double TeesGeorge Burnley, P.E.

Senior EngineerHigh Concrete Structures, Inc.

^:. Denver, PennsylvaniaYu..

Alex Aswad, Ph.D, P.E.Associate Professor of EngineeringThe Pennsylvania State UniversityHarrisburg, Pennsylvania

T he double tee is a major productionitem of many integrated precast, pre-

stressed concrete manufacturers in theUnited States. Thus, the shear rein-forcement requirement by ACI-318' andits omission by producers has attractedthe interest of design engineers and pre-stressers alike.

Since 1971, several companies haveconducted tests on full size untopped ortopped double tees. 2 One of the authorsconducted a test in 1986 related toshear mesh elimination. The test objec-tive was to show that web reinforcementin the stems could be eliminated with-out impairing the flexural or shear ca-pacities of' pretensioned tees. The testobjective was met, and several produc-ers invoked the provisions of Chapter11, ACI-318, to waive the minimum areaof shear reinforcement.

The 1983 issue of the ACI-318 Code,however, added a new requirement totests used as a basis for omitting

minimum shear reinforcement. Section11.5.5.2 states that such tests shallsimulate effects of differential settle-ments, creep, shrinkage, and tempera-ture change. It is common practiceamong prudent designers to simulatesuch volume change effects on thebearings by applying a horizontal ten-sile force N = 0.20 V, where V is thevertical reaction. This force magnitudeis also mentioned in Ref. 1, Section11.9.3.4.

In flexural members subject to normalloading, the flexure-shear design of re-inforcement should be checked in addi-tion to the minimum reinforcement. Theconcrete contribution is given by:

Vc[ = 0.f y' ,.b + V .I + V iM,,rJMma.r

To expand on the available data base,the 1987 and 1988 tests were conductedat the High Concrete Structures, Inc.plant in Denver, Pennsylvania. Details

48

are presented here, along with resultsand conclusions. The tests are, in certainrespects, an extension of earlier testsconducted by other companies. How-ever, they do have some unique fea-tures:

(a) A fully precast4 in. (102 mm) thickflange.

(b) A longer span, 62 ft (18.9 m), anddeeper sections, 26 in. (660 mm)and 34 in. (864 mm), respectively.

(c) A simultaneous horizontal forceequal to 20 percent of the appliedvertical force.

(d) A higher than usual nominal liveload, 54 to 70 psf (264 to 342kg/rn2).

(e) End sleeving of strands.(f) A relatively slender leg in at least

one specimen.Consistent with PCI's SFHAD Project

No, 2, 2 the test tees contained no webreinforcement except in the outer 5 ft(1.52 m) of the member where it pro-vides protection against accidental dam-age.

TEST PROGRAM

The static load tests were conductedon full scale, totally precast double tees.The specimens were typical productiondouble tees spanning 62 ft (18.9 m), rep-resenting similar units used in normalparking structures. The specific proper-ties and dimensions of the two speci-mens tested are presented in the fol-lowing paragraphs.

Description of Specimen 1The test specimen consisted of a 10 it

wide x 34 in. deep (3.05 m x 864 mm)double tee cast on October 30, 1987,with normal weight concrete and wasdesigned for a fully precast parkingstructure application. The memberlength was 62 ft 6 in. (19.05 m) and theflange was 4 in. (102 mm) thick andcast monolithically with the double tee.The nominal concrete strength at 28

SynopsisTwo static load tests on full scale,

10 ft (3.05 m) wide, double tees wereconducted. The specimens were typi-cal production double tees spanning62 ft (18.9 m). The purpose of thetests was to demonstrate that webreinforcement in tee stems can beeliminated without impairing the flex-ure and shear behaviors of the pre-stressed unit.

The tests were, in certain respects,an extension of earlier tests con-ducted by other companies. However,they do have some unique featuressuch as: fully precast 4 in. (102 mm)thick flanges, longer spans, simulta-neous horizontal forces, end sleeving,and in one case, thin stems.

The results show that the test spec-imens without web reinforcement candevelop flexural capacities equal tothe ACI Code requirement without apremature shear failure. It is con-cluded that shear reinforcement indouble tees having similar geometriescan be omitted except in the outer 5 ft(1.52 m), provided certain conditionsare met.

days was f,' = 5000 psi (34.5 MPa),which is commonly used in the plant'smarketing area. The design service loadwas 70 psf (342 kg/r 2). Section proper-ties are listed in Fig. 1.

Fabrication of the tee was in accord-ance with the drawings reproduced asFigs. 2 and 3. The specimen containedtwelve ½ in. (13 mm) diameter, low re-laxation, Grade 270 strands tensioned to75 percent of the Ultimate TensileStrength (UTS). The second strand levelin each stem was sleeved for a length of8 ft 6 in. (2.60 m) from the ends whilethe third level was sleeved for 4 ft 6 in.(1.37 m).

PC) JOURNAL/March-April 1989 49

Width(ft)

Depth(in.)

Weight(lbs pent)

A(sq in.)

1

(in.4 )Yr

(in.)

Y,g

(in.)

S,

(in. 3 )S8

(in•3)

10 34 809 787.5 69105 8.114 25.886 851E 2669.6Precast

L Ct0n

Fig. 1. 1 ODT34 precast section dimensions and calculated section properties.

• 4 d A °

11 ousNOMINAL

° fe=5000 PSI aTO

5500 PSI

2'-6"FFF3^^^75'

5_0" 2'- 6 •'10`-0" NOMINAL

Section Properties

_-----------------------------------------

^o

Fig. 2. Double tee dimensions.

The leg mesh vertical wire was 6 gageat 7.5 in. (190 mm) on center, and themesh extended for a length of 5 ft (1.52m) at each end. The deck reinforcementconsisted of #3 (9.5 mm) reinforcingbars spaced at 12 in. (305 mm) on centerand was placed in the middle of theflange thickness. Each bearing area wasreinforced with two #4 (12.7 mm) mildsteel reinforcing bars. Details of theconcrete mix properties, along with theprestress strand data, are displayed inAppendix A. At test time the concretestrength was f,' = 6467 psi (44.6 MPa).

Description of Specimen 2The test specimen consisted ofa 10 ft

wide x 26 in. deep (3.05 in x 660 nim)double tee cast on February 23, 1988,with normal weight concrete. Themember length was 62 ft 6 in. (19.05 in)and the flange was 4 in. (102 mm) thickand cast monolithically with the doubletee. The nominal concrete strengthswere f,' = 3000 psi (20.7 MPa) andfc = 5000 psi (34.5 MPa), respectively.The service load was 54 psf (264 kg/m2).

Fabrication of the tee was in accord-

50

2'-5 7/8" 5'-o"

N0.3 BARS AT I2"U. C,a N

W N '}

- I^ FOR 5'-6°EA. LEG 4 u~i T#

-N a

WRAP STRANDSAT EACH END; AT ENDS AT MID SPAN

2 AT 16 2 AT 4I/2"

2AT14" 2 AT4"

2 AT 8" 2 AT 3I/2"

4'-6'-2 AT 6" 2 AT 3"

8'-6"--2 AT 4" 2 AT 21/2"

2 AT 2" 2 41 2"

(6) 1/2 "Ox 270K LOW-LAX STRANDS /STEMSTRESS TO 31.0K

Fig. 3. Double tee reinforcement.

ance with the drawings reproduced asFigs. 4 to 6. The specimen containedfourteen Y2 in. (13 mm) diameter, lowrelaxation, Grade 270 strands tensionedto 75 percent UTS. The second strandlevel in each stem was sleeved for alength of 8 ft (2.44 m) from the endswhile the fourth level was sleeved for 3ft 6 in. (1.07 m).

The leg mesh vertical wire was 6 gageat 7 in. (178 mm) on center, and themesh extended for a length of 5 ft (1.52m) at each end. The deck reinforcementin the northern half of the slab consistedof #3 (9.5 mm) reinforcing bars spacedat 12 in. (305 mm) on center and wasplaced in the middle of the flange thick-ness. In the southern half of the slab, thedeck reinforcement was a 12 x 4 — W2 xW4 mesh. Each bearing area was rein-forced with two #4 (12.7 mm) mild steel'reinforcing bars. Details of the concreteproperties, along with the prestressingstrand data, are displayed in AppendixB. At test time the specimen's concretestrength was f f = 5031 psi (34.7 MPa).

TEST SETUPStructural steel supports were fabri-

cated to provide a pinned bearing con-dition as well as supply the requiredhorizontal tensile force equal to 20 per-cent of the end reactions. These testsupports held the slab approximately 2 ft6 in. (762 mm) above the ground so thetee could freely deflect. One of the sup-ports had a link tilted at 11.3 degreesfrom the vertical to generate the 20 per-cent horizontal force (Fig. 7). The teewas placed directly on these supportsand welded at the bearing plates toallow for horizontal forces involved. As asafety measure, large timbers werestacked near the pivot roller support, buta few inches of clearance were availabletinder the tee.

Changes in the slab midspan camber(or deflection) were measured from theoriginal, unloaded and cambered posi-tion labeled the "zero position" untiltotal deflection changes exceeded 15 in.(381 mm).

PCI JOURNAL/March-April 1989 51

RADIUS

NOMINAL N N%=5000 Psi

TO5500 PS I

2'-6" 4.50" 5,-0,. 2^-6..

10'-0" NOMINAL

Section PropertiesWidth Depth Weight A, ! Y, Ye S, Sa

(ft) (in.) (ibs per ft) (sq in.) (in. 4 ) (in.) (in.) (in. 3 ) (in.3)Precast

Lstb011 10 26 752 722 34766 6.134 19.866 5668 1750Fig. 4. 1ODT26 precast section dimensions and calculated section properties.

62'- 6' O.A.

1•

LB

iv

Fig. 5. Double tee dimensions.

Fig. 8 shows an end view of the dou-ble tee setup and Fig. 9 shows the teeloaded with blocks near the end of thetest,

TEST LOADSIn these tests, large concrete blocks

measuring 10 in. x 2 ft x 8 ft (254 x tilt) x2438 mm) and weighing 2 kips (8.9 kN)each were used to simulate the quasi-uniform loading condition. Twenty-oneblocks spaced 2 ft 6 in. (762 mm) apartfor the central three blocks and 3 ft (914

mm) elsewhere were used to create auniform loading condition in the firsttwo layers. One or more blocks wereadded in the third layer until the maxi-mum test load was reached.

The placement of these blocks wasstructured so that loading would pro-gress in stages. These stages were estab-lished to compare the actual flexural be-havior with that predicted by rationalanalysis using a sophisticated methodand a computer program.I

For Specimen No. 1, the loading

52

/2"TEE-NO.35 AT 12"O.C, I NORTH SIDEOTHER HALF-12x4 W2/W4LS0UTH SIDE)SU PPORTED BY II/4"STRANDS

2'-5 7/8" I5'-0" 2'-5/8"WI

a 117/8 26" 3'-P" 26.ii

L41 m— _____

LLc N

1 71^+e 7 x PULLN104KDN ^n FOR 48"EA. LEG

7-9/6W.W.F.

O

WRAP STRANDSAT EACH END: i. AT ENDS rt AT MID SPAN

2 AT 14 2 415

2 AT 12 2 AT 41/2"

2 AT 10 2414

3'-6-2 AT 8" 2 AT

2 AT 6" 2 AT 3"

8-0'-2 A7 4 " 2 AT 21/2"

2412" 2 Al2"

(7 ) 1/2 "fi x 2 70K LOW-LA X S TRAN DS /STEM

STRESS TO 31.OK

Fig, 6. Double tee reinforcement.

stages were (see Figs. 10 to 13):Stage I — Service loading, equivalent

to 68 psf (332 kg/m 2); maximum bottomtension = 231 psi (1.6 MPa).

Stage II-0.85 (1.4 DL + 1.7 LL) asper Chapter 20, ACI Code; maximumnominal bottom tension = 1225 psi (8.4MPa).

Stage III — 1.0 (1.4 DL + 1.7 LL) asrequired by the ACI Code and mostbuilding codes.

Stage IV — k1,,, nominal flexuralstrength assuming q5 = 1.0.

For Specimen 2, the loading stageswere (see Figs. 14 to 16):

Stage I — Service Ioading, equivalentto 56 psf (273 kg/m 2); maximum bottomtension = 490 psi (3.4 MPa).

Stage II — 0.85 (1.4 DL + 1.7 LL);maximum bottom tension = 1582 psi(10.9 MPa).

Stage 111-1.0 (1.4 DL + 1.7 LL); M„,

nominal flexural strength, is calculatedbased on 0 = 1.0.

Schematic diagrams of each stage arepresented showing placement ofweights. Also included in Figs. 10through 16 are tabulations at each stageof applied loads, actual midspan mo-ments, moments at 0.4 L and predicteddeflections.

The placement of loads was carriedout in a continuous (monotonic) processfrom start to finish with occasional de-lays to permit inspection and deflectionmeasurements. The total time for eachtest .vas about 2/2 to'3 hours.

Test Results for Specimen 1The test slab carried a maximum load

of 106,000 lbs (471 kN) in addition to itsself weight. At this load, the test wasstopped for safety reasons since deflec-tion change approached 27 in. (686 mm)

PCI JOURNALIMarch-April 1989 53

TYPICAL BLOCKSWEIGH 20K EACH

PIVOT ROLLER-- ^_f-= -SUPPORT(SEE FIXEDDETAIL BELOWI PIVOT

[ I UPP(

31-0 31'•0"

620"

BEARING rt BEARINGELEVATION

wQ 2

Om-

lL

PINNED0 SUPPORTS

264_ 50 J_26I 0.2 R U HORI Z k0'•0°15L_ THRUST

PIVOT ROLLER SLAB SECTIONSUPPORT

Fig. 7. Test setup.

Fig. 8. A view of the pivot roller support.

54

and the tee was only 6 in. (152 mm)above ground. The rate of creep deflec-tion was high, and further loading wasneither prudent nor beneficial.

If the secondary moments due to thehorizontal forces are neglected as usual,then the total applied moment at 0.50 Lreached 14614 in.-kips (1651 kN-m)under the maximum test loading. Thecalculated nominal strength using thePCI Design Handbook strain compati-bility approach (Ref. 4, p. 4-63) is 14742in.-kips (1666 kN-m) at the same section.In other words, by using the PCI DesignHandbook method, the applied test loadreached 99 percent of the nominalstrength near the critical section,

Deflection changes from the zero po-sition were:• s in. (16 mnin) at the end of Stage I,

under one layer of loads equivalent to68 psf (332 kg/m2).

• 3 in. (76 mm) at the end of Stage II.• 4.25 in. (108 mm) under two layers of

blocks, equivalent to 136 psf (664kg/m2).

• 14 in. (356 mm) at the end of StageIII, visibly increasing due to highcreep rate.

• 27 in. (686 mm) when test loadingstopped.First flexural cracks appeared in the

middle of the span at the hold-down de-vice location. The loads consisted of onelayer of blocks plus two additionalblocks at the east end and correspondedto a superimposed moment of 3812 in.-kips (431 kN-m) at the 0.40 L section. Asloads were added, the flexural crackingregion became more extensive and prog-ressed toward the supports. At the max-imum test load, the nearest visible flex-ural shear cracks were between 13 and18 ft (3.96 and 5.49 in) from each bear-ing. Initially, the crack widths were ^li6

to' in. (5 to 6 mm) near the central por-tion of the span and about 1lss in. (1 mm)for the cracks nearest to the supports.

The loss of stiffness due to cracking ofthe concrete was smooth and gradual, asshown in the moment versus deflectioncurve (Fig. 17). Throughout the test

Fig. 9. 1 ODT34 beyond Stage III (1.4 DL '- 1.7 Ii) and near the end of test.

PCI JOURNAL/March-April 1989 55

STAGE I: SERVICE LOADS

Precast double tee self weight:

Given service live load: 70 psf x 10 ft

Moment due to given service live load:at midspan: 1.5 (0.700)(62)2at 0.40 L: 0.96 x 4036

Applied test load moments:at midspan: 1.5 (0.677)(62)2at 0.40L: 0.96 x 3904

DLb = 0.809 k!f

LL = 0.700 klf

= 4,036 in.-kips= 3,875 in.-kips

= 3,904 in.-kips= 3,747 in.-kips

Maximum calculated bottom tension under test load = 213 psi

Calculated camber change under test load – 0.69 in.

Measured camber change: ¼ in. = 0.63 in.

• TOTAL OF 21 BLOCKSi 1N ONE LAYER

L4< BEAR NG BEARING

Fig. 10. Stage I: service loads.

loading, flexural cracks did not propa-gate to cause flange separation, nor wasthere any sign of impending prematureshear failure at the ends or near theone-quarter points.

Test Results for Specimen 2

The test slab carried a maximum loadof 86,000 lbs (383 kN) in addition to itsself weight. At this load, the test wasstopped since deflection change ex-

ceeded 30 in. (762 mm), the tee was only2 in. (51 mm) above ground and the rateof creep deflection was high. After a fewminutes the tee legs touched theground.

If the secondary moments due to thehorizontal forces are neglected, then thetotal applied moment at 0.45 L reached12363 in.-kips (1397 kN-m) under themaximum test loading. The calculatednominal strength using the PCI DesignHandbook strain compatibility ap-

56

STAGE II: 0.85 (1.4 DL + 1.7 LL)

Total w = 0.85 (1.4 x 0.809 + 1.7x0.700) = 1,974 klf

Less existing dead load = –0.809 kit

Required additional load = 1.165 klf

Required additional moment:

at midspan: 1.5(1 .165)(62)2 = 6,719 in.-kips

at 0.40 L:0.96 x 6,719

6,450 in.-kips

Applied test load moments:at midspan: = 6,904 in.-kips

at 0.40 L: 6,584 in.-kips

Maximum calculated bottom tension under test load = 1,225 psi

Calculated camber change under test load, including assumption ofcracked sections: 2.17 ± 0.37 = 2.54 in.

Measured camber change

3.00 in.

^ 3^-0. 1 I3`0

„I 1'-s..

62-0”F-

BEARING ^ BEARING

Fig. 11. Stage II: 0.85 (1.4 DL + 1.7 LL).

proach 4 is 12206 in.-kips (1379 kN-m) atthe same section - In other words, byusing the PCI Design Handbookmethod, the applied test load reached101 percent of the nominal strength nearthe critical section.

Deflection changes from the zero po-sition were:• 1 in. (25 mm) at the end of Stage 1,

equivalent to 56 psf; no visiblecracking.

• 4 in. (102 mm) at the end of Stage 1I.

• 7.25 in. (184 mm) under two layersminus blocks marked a, b, and c onFig. 16.

• 30 in. (762 mm) when last load wasplaced at centerline, visibly increas-ing due to high creep rate.First flexural cracks appeared in the

middle of the span at the hold-down de-vice location. The loads consisted of onefull layer of blocks and corresponded to asuperimposed moment of 3750 in.-kips(424 N-m) at the 0.40 L section. As loads

PCI JOURNAL'March-April 1989 57

STAGE III: 1.0 (1.4 DL + 1.7 LL)

Total w = 1.4 x 0.809 + 1.7 x 0.700 = 2,323 kit

Less existing dead load = –0.809 kIf

Required additional load = 1.514 kIf

Required additional moment:

at midspan: 1-5 (1.514)(62) 2 = 8.727 in.-kips

at 0.40 L : 0.96 x 8,727 = 8.378 in.-kips

Applied test load moment:at midspan; = 8.905 in.-kips

at 0.40 L: = 8,518 in.-kips

1-

TYP. TYP F` _

L, 62'-0"

BEfARING.

^'-6"

BEARING

Fig. 12. Stage III: 1.0 (1.4 DL + 1.7 LL).

were added, the flexural cracking regionbecame more extensive and progressedtoward the supports. At the maximumtest Ioad, the nearest visible flexuralshear cracks were between 12 and 14 ft(3.66 and 4,27 m) from each bearing.Initially, the crack widths were /i6 to 5114

in. (5 to 8 mm) near the middle of thespan and about '/2s in. (1 mm) for thecracks nearest to the supports.

Here again, the loss of stiffness clue to

cracking of the concrete was smooth andgradual, as shown in Fig. 18. Through-out the test loading, flexural cracks didnot propagate to cause flange separation,nor was there any sign of impendingpremature shear failure at the ends ornear the one-quarter points. Diagonalhairline cracks appeared near two steinsupports at the test end, but were sosmall ( l 15o in. (0.17 mm) l as to be con-sidered inconsequential.

58

STAGE IV: M„ NOMINAL FLEXURAL STRENGTH ASSUMING th = 1.0

The theoretical strengths, "Provided M," are equivalent to M, since = 1.0 andbased on the BEAM Program by Jacques & Aswad, Inc.:

at midspan: M= 15,043 in.-kips

at 0.40 L: M= 14,539 in.-kips

When the PCI Design Handbook approach for strain compatibility is used (Ref. 4,p. 4-63), the following strengths are obtained:

at midspan: M, = 14,742 in.-kips

at 0.40 L: M„ = 14,248 in.-kips

Using the loading scheme below, the total actual applied load moments at the endof the test were:

at midspan: M = 14,614 in.-kips

at 0.40 L: M = 14,040 in.-kips

Therefore, neglecting as usual the contribution of the horizontal reactions to thebending moment, the applied test load moment at 0.50 L is within 0.9 percent of theexpected nominal strength.

YP TYP TYP YP62-0°

BEARING BEARING

Fig. 13. Stage IV: nominal flexural strength (4 = 1.0) and maximum load configuration.

Analysis for Deflectionand Shear Reinforcement

Using the BEAM Program, 5 one coin-puter run was made for each loadingstage assuming actual concretestrengths. These runs were made topredict the midspan deflection changeunder the various superimposed loadconfigurations. The results are shown inFigs. 17 and 18. The correlation be-

tween the predicted and measured val-ues is remarkably good for loads signifi-cantly higher than the service loads andslightly beyond Stage 1I, 0.85 (1.4 DL +1.7 LL.).

Two other computer runs were madewith the purpose of calculating the re-quired shear reinforcement based onACI 318' Eqs. (11 -11) and (11-13). Re-stilts of these runs are summarizedon the next page:

PCI JOURNALMarch -April 1969 59

STAGE I: SERVICE LOADS

Precast double tee self weight:

Given service live load: 54 psf x 10 ft

Moment due to given service live load:at midspan: 1 .5 (0.540)(62)2at0.40L:0.96x3,114

Applied test load moments (Run No. 5A):at midspan:at 0.40 L :

Maximum calculated bottom tension under test load(No visible signs of flexural cracking)

Calculated camber change under this test load

Measured camber change

DLb - 0.752 kit

LL 0.540 kit

= 3,114 in.-kips2,989 in.-kips

= 3,220 in.-kips= 3.152 in.-kips

490 psi

1.25 in.

= 1.00 in.

TOTAL. OF $9 BLOCSr1!1 ONE I. AVER

rt BEARING

Fig. 14. Stage I: service loads.

• Specimen 1: using f^ = 64th psi (44.6VIPs)—Required web reinforcement

based on I n : A„ = 0 in. 2 ft— Required web reinforcement

based on V,u : A, = 0 in. 2 ft• Specimen 2: using f = 5031 psi (34.7

\1Pa)—Required web reinforcement

based on 1'c$ : A n = 0.03 in.' ft— Required wet) reinforcement

based on[' :A,= 0 in. 2 ft

rC BEARING

Note: Web reinforcement is the totalarea for two steins.

CONCLUSIONS

1. the omission of web reinforce-ment in tee sterns, except in the outer 5ft (1.52 m), did not impair the shear orIlexural capacities of two full size dou-ble tee specimens when subjected tostatic, quasi- uniform loading.

60

STAGE II: 0.85 (1.4 DL + 1.7 LL)

Total w – 0.85 (1.4 x 0.752 -- 1.7 x 0.540) = 1.675 klfLess existing dead load –0.752 klfRequired additional load 0.923 klf

Required additional moment:at midspan: 1.5 (0.923)(62)2 = 5,323 in.-kipsat 0.40L: 0.96 x 5,323 = 5,110 in.-kips

Applied test load moments (Run No. 6):at midspan: 5,380 in.-kipsat 0.40 L : = 5,135 in.-kips

Maximum calculated bottom tension under test load – 1,582 psi

Minor flexural hairline cracks showed up in the central 0.20 L of the slab after fourblocks close to midspan were added. Midspan moment was M = 4,590 in. -kipsand deflection change reached 2.06 in.

Calculated camber change under test load, including assumption ofcracked sections: 2.57 -- 1.97 = 4.54 in.

Measured camber change – 4.00 in.

I,laEARING

6" 6" 3'fl" 3=6''rYR yp

62'-0"

BEARING

Fig. 15. Stage II: 0.85 (1.4 DL t 1.7 LL).

2. The presence of horizontal forcesat the bearings and partial end sleevingof strands did not cause any special dis-tress or precipitate a premature shearfailure.

3. Deflections at load levels suhstan-tially beyond cracking loads can be ac-

curately predicted using rationalmethods of analysis. The transition fromuncracked to cracked sections is gradualand smooth, reflecting the steady prop-agation of cracks from the center towardthe ends. 'There is no sudden loss ofstiffness.

PCI JOURNAL March-April 1989 61

STAGE III: M, NOMINAL FLEXURAL STRENGTH ASSUMING di = 1.0

The theoretical strengths, "Provided M.," are equivalent to M, since = 1.0 andbased on the BEAM Program by Jacques & Aswad. Inc.:

at midspan: M„ = 12,687 in.-kipsat 0.45 L : M– 12,427 in.-kipsat0.40L: M„= 12,167in.-kips

When the PCI Design Handbook approach for strain compatibility is used (Ref. 4,p. 4-63), the following strengths are obtained:

at midspan: M= 12,433 in.-kipsat 0.45 L : Mn – 12,178 in.-kips

at0.40L: M„= 11,923in.-kips

Using the loading scheme below, the total actual applied load moments at the endof the test were:

at midspan: M = 12,521 in.-kipsat0.45L: M = 12,363 in.-kipsat0.40L: M = 11,961 in.-kips

Underthe maximum load, the total immediate deflection change is reached 30 in.(t). increasing very rapidly due to the high creep. After a few minutes the slabtouched the ground. Therefore, neglecting as usual the contribution of thehorizontal reactions to the bending moment, the applied test load moment at 0.45 Lis 101 percent of the expected nominal strength by the PCI Design Handbookapproach (and more than 99 percent of the nominal strength based on Jacques &Aswad's BEAM Program).

c c b b

430 26 2- 3- 3V'• ' i6

I 'rY° 7YP TYP TIP62'-0"

BEARING BE4R3NG

Fig. 16. Stage III: nominal flexural strength (¢ = 1.0) and maximum load configuration.

62

10000-

Y

Z6000-

IflO_

I-. 600k>-I-zWM

4000-0UN0a-g 2000-

UwaU)N

PREDICTSBEAM PR

BYRA

5TM

GE9949"l(

, MA) APP

STAF,E

IED

TAGS]T.0 5U. DL 1 -7L

^S AGE I SE

NE

VIC

URE

LOA

(AC UAL DEF . CM NGE

2 3 4 5 I I I . 10 . . Is

DEFLECTION CHANGE (INS )

Fig. 17. Midspan moment versus deflection change.

10000-

z4a 8000-

o_

q 6000-

zU

g 4000-awU)O4. 2000-

w0.7)rn

5 U3E1I MA AP LIED"K81633

F1 EA ORE IAC UALDEF . CH NGE

ST GE ,0.9 (1.4 L+ 1.7 LL

dREDI TED Y

&TA E 1, ER ICE 040

I Y 3 4 5 , , 10 15DEFLECTION CHANGE (INS }

Fig. 18. Midspan superimposed moment versus deflection change.

PC! JOURNAL-March -April 1989 63

RECOMMENDATIONSGiven the results of these tests, and

considering the prior tests by the firstauthor and other researchers, and thesuccessful use of double tees withoutweb reinforcement on hundreds of proj-ects since 1971, 2 the authors offer thefollowing recommendations applicableto precast tees.

Shear reinforcement may be omittedexcept in the outer 5 ft (1.52 m), pro-vided:

(a) The tees are simply supported.(b) Loads are substantially uniform.(c) Tee depth is between 24 and 36

in. (610 and 914 min) and span-to-depth ratio is less than 30.

(d) Required shear reinforcementbased on Vrw, Eq. (11-13) of ACI-318, is essentially zero.

(e) Calculated bottom tension stressis kept below the cracking stress,7.5 v f^.

ACKNOWLEDGMENTSThe work in this paper is part of a

project sponsored by High ConcreteStructures, Inc. The authors would liketo thank Ken Baur, P.E., for his support,encouragement and comments. Anyopinions, findings and recommenda-

tions are those of the authors and do notnecessarily reflect the views of PennState University or the sponsors.

Thanks are also due to Jacques andAswad, Inc., for the use of their BEAMProgram to make several computer runsfor the stress, strength, and rational de-flection analyses.

REFERENCES

1. ACI Committee 318, "Building Code Re-quirements for Reinforced Concrete (ACI318-83)," American Concrete Institute,Detroit, Michigan, 1983, 111 pp.

2. Chosh, S. K., and Fintel, M„ "ResearchProject No. 2: Exceptions of Precast, Pre-stressed Members to Minimum Rein-forcement Requirements," PrestressedConcrete Institute, Chicago, Illinois,1986.

3. Aswad, A., et al., "Elimination of ShearReinforcement, Test Report No. 2," Stan-ley Structures, Inc., Denver, Colorado,October30, 1986.

4. PCI Design Handbook: Precast and Pre-stressed Concrete, Third Edition, Pre-stressed Concrete Institute, Chicago, Illi-nois, 1985.

5. Aswad, A., Jacques, F. J., and Barngrover,B., "Program for Analysis of PrestressedConcrete Flexural Members," publishedby Jacques & Aswad, Inc., Denver, Colo-rado, December 1987.

METRIC (SI) CONVERSION FACTORSlit =0.305m 1 psi = 0.006895 MPaI in. =25.4mm 1 kip-ft – 1356 N-m1 pcf = 16.02 kg/m3

1 kip = 4448 N1 Ib per ft – 1.488 kghn

NOTE: Discussion of this paper is invited. Please submityour comments to PCI Headquarters by December 1, 1989.

64

APPENDIX AI. Precast Concrete Data:Unit weight: 149 lbslft3;Admixtures:

Air entraining agentWater reducing agentHRWRAccelerator

Cylinder strengths:

Slump: 5 in. Cement: Type III.

8 ounces20 ounces

106 ounces13 ounces

At release: Average of two breaks: 3230 psiAt 7 days: Average of two breaks: 5149 psiAt 24 days (test time): Average of two breaks: 6467 psi

Dates: Pour date: 10130187; stripping date: 10/31/87; test date. 11/23/87.

II. Prestressing Strand Properties:Specifications: ASTM A-416, Grade 270 K, Low relaxationCross section metallic area: 0.154 in. 2 per strandBreaking strength (UTS): 43,703 Ihs; elongation in 24 in.: 6.9 percentYield strength at 1 percent extension: 38,982 ]h.sModulus of elasticity: 29,100 ksi

APPENDIX BI. Precast Concrete Data:Unit weight: 151 lbslft; Slump: 4¼ in. Cement: Type III.

Admixtures:Air entraining agent 8 ouncesWater reducing agent 20 ouncesHRWR 106 ouncesAccelerator 13 ounces

Cylinder strengths:At release: Average of two breaks: 3678 psiAt 7 days: Average of two breaks: 4837 psiAt test time: Average of two breaks: 5031 psi

Dates: Pour date: 2/23/88; stripping date: 2/24/88; test date: 3/10/88

II. Prestressing Strand Properties:Specifications: ASTM A-416; Grade 270 K, Low relaxationCross section metallic area: 0.154 in.2/strandBreaking strength (UTS): 44,321 Ibs; elongation in24 in.: 6.4 percentYield strength at 1 percent extension: 40,793 lbsModulus of elasticity: 29,100 ksi

PCI JOURNAUMarch -April 1989 65