Effect of Initial StrandSlip on the Strength

of Hollow-Core Slabs

Mark D. Brooks*Project EngineerTru-Span Structures Inc.San Diego, California

Kurt H. GerstleProfessor of Civil EngineeringUniversity of ColoradoBoulder, Colorado

Donald R. LoganPresidentStresscon CorporationColorado Springs, Colorado

U nder certain conditions, some of thetypical machine processes for

making hollow-core slabs may some-times produce concrete with insufficientcompaction or paste formation in the re-gion surrounding the pretensionedstrand. This can result in a deficiency inthe bond capacity which is evidencedby excess initial strand slip upon trans-fer of the prestressing force throughtransverse saw-cutting of the product.The producer is then faced with theproblem of evaluating the effect of such

• Pbnnrrly, Graduate Assistant, Civil, En irmi-mental, and Architectural Engineering, Universityof Colorado, Boulder, Colorado.

tMast, Robert F., ABAM Engineers, 'Tacoma,Washington, 1980, Unpublished Report.

slip on the structural capacity of theproduct.

Several tests and studies carried out inpast years on hollow-core slabs 1.2 haveestablished that excess initial strand slipdoes have adverse effects on the capac-ity of such slabs. Anderson and Ander-son o suggested that the magnitude of"free end slip" is directly related totransfer bond quality and to flexuralboncj..quality, and can be used as a directmeasure of transfer length if the transferof prestress is assumed to take placelinearly. An allowable free end slip wasthus computed directly from the transferlength equation derived from the ACICommentary (see Fig. 12.9,1, = fR,.dbl3).

In 1980, Mastt suggested that theflexural bond length could also be ex-

90

pressed linearly (in proportion to freeend slip), that bilinear strand develop-ment diagrams could he created for in-dividual strands, and that a similar pro-cedure, utilizing the weighted averageof the computed bilinear developmentdiagrams for all strands, would enablethe computation of a bilinear momentcapacity diagram for each end of anyspecific member. These concepts arecollectively referred to as the "sliptheory" in this paper.

In order for prestress transfer lengthto be limited to the ACT Code value(f4 613), the Anderson-Anderson equa-tion' limits the allowable initial strandslip to the range of approximately i/aa to%2 in. (1 to 3 mm), depending on stranddiameter and the initial and final levelsof prestress in the strand,

Preliminary tests on slabs with initialstrand slips exceeding the allowablevalues were conducted in ColoradoSpringst and the results appeared toverify the applicability of the sliptheory. Additional tests were conductedat the University of Wisconsin, Milwau-kee,t§ to evaluate the relationship of ex-cess initial strand slip to observed ca-pacity and to compare the results ofthese tests with the slip theory.§ A closecorrelation resulted, but there were in-sufficient data to evaluate that compari-son in the flexural bond region of thestrand development curve.

The availability of several rejectedslabs from the Colorado Springs pro-duction facility provided an opportunityto obtain additional data for verification

t Logan, Donald R., Colorado Springs, Colorado,informal Load Test Series, 1980, Unpublished Re-port.

# Computerized Structural Design Inc., "Effectof the Amount of Initial Strand Slip on Strength andRcharior of Spancrete Plank," First Drat Report tothe Spancrete Manufacturers' Association Techni-cal Committee, Unpublished Report, December 5.1983.

§ Logan, Dona[d R., "Analysis of Strand Slip LoadTests at University of Wisconsin/Milwaukee in De-cember 1983." Unpublished Report, January 1984.

SynopsisThe object of this experimental

study was to examine the effects of ex-cess intial strand slip on strand devel-opment in hollow-core slabs. Resultswere obtained from eleven concen-trated load tests conducted on sevenhollow-core slab test specimens-

The observed capacities in the testswere compared to predicted capac-ities computed according to twomethods:

1. ACI 318-83 Section 12.9.1, De-velopment of Prestressing Strand -This section of the ACI Code is in-tended for conditions where consoli-dation of the freshly placed concretearound pretensioned strands is suffi-cient to create normal bond quality. Itis not applicable to cases where sub-standard bond quality, as evidenced byexcess initial strand slip, may result inincreased prestress transfer lengthand flexural bond length of thestrands.

2. A strand slip theory, suggestedby Mast in 1980 and based on por-tions of the work of Anderson and An-derson, which extends the ACI for-mulas to account for the effects of ex-cess initial strand slip.

Results of the test program appearto confirm the applicability of the ACICode equations where initial strandslip is limited to allowable values, butindicate that these equations do notsafely predict the capacity of slabshaving excess initial strand slip. Thestrand slip theory, on the other hand,appears to adequately predict the re-duced capacity and failure mode ofslabs having such excess slip.

The test program was conducted inthe laboratories of the Civil, Environ-mental, and Architectural EngineeringDepartment of the University of Col-orado at Boulder,

PCI JOURNAtJJanuary-February 1988 91

of the slip theory over a broader range ofconditions. In the following, this theoryis first outlined and then applied. Thecurrent tests are described and their re-sults are compared to predictions by theexisting ACI Code equations and by theslip theory.

THE STRANDSLIP THEORY

Section 12.9 of the ACI Code 3 pro-vides that development length 1, t shallnot be less than:

ld = Ifvd - 2 f3 )

de (la)

in which the symbols are defined in theNotation section (see Appendix).

Eq. (la) can be rewritten as:

ld =l ( + 1 6 = f" db +(f,–f,.)dn (lb)

in which the first term represents theprestress transfer length Z r, and the sec-ond term represents the flexural bondlength Ib• When excess initial end slip isevident upon transfer of the prestress, agreater development length may result.In fact, Section 12.9 of the ACI Com-mentary to the Code' states that thisprovision "... may not represent thebehavior of strand in low water-cementratio, no-slump concrete."

The slip theory assumes that the ini-tial slip of the strand from the saw-cutface of the concrete is a direct indication

of the bond quality of the concrete. Thisslip is therefore directly related to thetransfer length d i and the flexural bondlength 1b.

The measured initial strand slip 8 isrelated to the strand force by assuming alinear increase of this force, as shown inFig. 1. The average strand force in thetransfer zone F fi y = F t/2, is then re-lated to the end slip through the steelstrains:

8 = F t^ave^li = Fit}(2)

An,E 2 Ap,E

Rearranging this relation and intro-

ducing the steel stress fi = thetransfer length can be written as:

j _ 2 8A P,E 2 SLR' (3)r — r

F , f,

When l,', as obtained from Eq. (3), islarger than l r derived from Eq. (lb), itcan be deduced that the strand slip isgreater than the allowable value, 8.11.This value, S all , can be found by equat-ingl,from Eq. (Ib)to1; from Eq. (3):

2 8E _ fdn3

or

San

/1

_ ( I )

(4)

6 E

The allowable slip, 8Rtj , is defined asthe initial strand slip at the saw-cut endof a slab which results in a transfer

Table 1. Allowable initial strand slip for various prestress levels and strand diameters.

Prestress levels in strand

Allowable initial strand slip

Strand diameter

% in. '3z in.fn = 150 ksi if,, — 120 ksif, = 165 ksi i ff = 135 ksif = 180 ksi I f;,p = 150 ksi

0,040 in. (1/32 in.)

0.050 in. (2/32 in.)0.060 in. (2/32 in.)

0.054 in. (2/32 in,)0.066 in, (2132 in.)0.080 in. (3132 in.)

Note: 1 in. = 25.4 mm; I ksi = 6.895 MNa.

92

INITIAL UNSTRESSED DIA OF STRANDSTRAND SLIP FS

(AFTER SAW CUTTING PRESTRESSED D1A.AT END OF SLAB) OF STRAND

HOLLOW CORESLAB

'e o

Fj FROM BULKHEADBEFORE TRANSFEROF PRESTRESS

Fi=f5iAps

TRANSFERREDFORCE

Fi (AVE1 = F'^12

DISTANCE FROM END OF STRAND

Fig. 1. Transfer of prestress in pretensioned concrete.

length equal to that computed by theACI equation, 1, = f dh13, for specificvalues of f,,, f ,e , db , and E.

Table 1 shows allowable initial strandslip for various prestress levels andstrand diameters of % and ½ in. (9.5 and13 mm). The tabulation is based on E _28,000 ksi (193,000 MPa).

As the transfer length 1, increases to avalue of 1 according to Eq. (3), theflexural bond length lb is also assumed toincrease to a value of lb in the ratio de-rived from Eq. (lb):

lb =3 d b (5)

J Re

Fig. 2a shows the developable strandstress f,„ over the transfer length andthe flexural bond length, both accordingto ACI Section 12.9 (disregarding excessinitial strand slip) and also as affected byexcess initial slip according to the sliptheory, i.e., Eqs. (3) and (5).

For this latter case, assuming a linearvariation of steel stress, the developable

steel stress will be:

xj=-_f wherex --lil;

f ti =f,+ (x l (f,-.f.,.) (6)lb where I, -_x =l,

fdev,=fp„ where lx

in which x is the distance from the slabend.

The average developable strandstress,},,, for all strands, at each slabend, can be computed using theweighted average of the bilinear devel-opment diagrams for all strands (see Ap-pendix A).

The nominal moment strength M. forany section can be calculated as a func-tion of the average developable strandstress, f,a„, according to the strengthdesign method in Chapter 10 of the ACICode, as follows:

PCI JOURNALJanuary-February 1988 93

SLIP THEORY

pr Qn pb Qr A C I

f ps —

rf dev(SLIP

fdev(ACI)

tSe THEORY)

HCLLOW CORE SLAB

HHL=DE$IGN SPAN

END OF BRG. BRG.SPECIMEN NORTH SOUTH^^^---III

a. DEVELOPABLE STRESS IN STRAND fdev ACCORDING TOACI EQUATIONS AND STRAND SLIP THEORY

M n (Ad)

E

^ _MFAIL

r

\

M n(SLIP THEORY)

END OFSPECIMEN

H I[ BRG. RG.NORTH SOUTH

b. COMPARISON OF OBSERVED ULTIMATE MOMENT CAPACITYWITH ACI AND STRAND SLIP THEORY PREDICTIONS

rlg. . Lompanson of developable stress and flexural capacity.

MR = A,^f4,,..I d (1 – O.59p f ,.) I.f, )(7)

A plot of M. is shown in Fig. 2b. Itprovides a moment strength envelope,upon which a moment diagram due tothe factored applied loads can be su-perimposed to check the flexural

strength. In Fig. 2h, the dash-dottedmoment diagram, representing any loaddistribution (here a point load), permitsprediction of the flexural failure bymatching the peak moment with themoment strength envelope. Where loadsare applied sufficiently close to the endof the specimen, the strength of the slab

94

48.0 ^ SYM.

2 5/16 CORE LOC.I–3.875" -1.375 3.875 1.5 1.375"

ca 3 SIMILAR

SI S2 S3 n^ift 3SP5.25°=15.75"

5.125" 3A" oz

1.375° STRAND LOC. 3 u wf8°DIA.STR. I /is

I/2" D1A. STR, 13/a

a CROSS SECTION,TYPICAL TEST SLAB*

* MATERIAL PROPERTIES: f 5ksi, fgu=270kSi, E5=28000ksi

TEST NOS. I, 2,4,5,6,9,10,11,STRAND PATTERN JACKING FORCE STRESS LEVEL

fj = .7'PuS2 ,S 3 ,S4 ,5 5 I/2"(270ksi) 4Cd 28.9k

S I ,S 6 3/8"(270ksi) 2(0 13.8k fj= - 6 fpu

Fj= 143.2k

TEST NOS.3,7,8STRAND PATTERN JACKING FORCE STRESS LEVEL

S2,Ss I/2"(270ks1) 2(a 28.9k fj= .7 fpu

S I ,S 6 3/8"(27Oksi) 2(M 13.8k fj= .6 fpu

S 3 ,S 5 3/8°(27Oksi) 2na 16.1k fj= .7 fpu

F j = 117.6k

b.PRESTRESSING STRAND, FORCES AND STRESS LEVELS

Fig. 3. Cross section and strand information (test slabs).

is reduced because of decreasing capac-ity of the strand where it is not yet fullydeveloped. The strength of the speci-men in this region is reduced furtherwhere excess initial strand slip occurs.

The shear strength of pretensionedslabs can also be affected by an increasein the prestress transfer length due to

excess initial strand slip. to ACT Eq.(11.13):

V p =(3.5 \+' +0.3f )bi d+Va(8)

where f, is the effective concrete stressdue to prestress at the centroid of thecritical concrete shear section. If, due toexcess initial strand slip, the transfer

PCI JOURNAUJanuary-February 1988 95

Table 2. Summary of load test data.

1 2 3 4 5 6 7 8 9 1 10 J 11 12 13 14

Avg. Slip Predicted failure loadP (kips)- initial Slip theory

Per ACT Code, Per slip theory,slip S theory flexuralDesign Shear at transfer bond Applied governed by governed by

span span near length length load atStrand StrandTest L A end 1; 1 failure Mode of

No. (in.) (in.) (in.) (in.) (in.) P.(kips) failure Vr,r Vrj development Vr,r V« development

1 331-5 9.75 0.208 68 124 22.78 Bond 24.37x 44.23 33.57 21.65 28.22 9.97y2 311.5 20.50 0.135 47 83 17.88a Bond 25.53x 34.48 31.79 23.37 22.73 15.08y3 246.0 20.25 0.135 50 94 20.23 Bond 26.28x 33.49 29.63 24.14 21.12 11.89y4 228.0 44.75 0.141 47 86 16.78 Bond 30.73 21.99x 23.72 28.22 21.80 17.66v5 331.5 45.75 0.182 63 115 11.83 Bond 27.44 18.91x 20.49 24.47 15.73 10.64v6 276.0 69.75 0.177 61 112 12.63 Bond 32.40 16.39x 18.96 29.11 16.39 11.91y7 331.5 69.75 0.063h 23 43 15.00 Bond-Flexure(c) 13.25x 14.15f 13.25y 14.15f8 331.5 69.75 0.156 57 107 11.60 Bond 13.25x 14.15f 13.25 8.49y9 331.5 92.75 0.177 60 110 10.39 Bond 13.55x 13-62f 13.55 9.49y

10 331.5 117.75 0.177 61 112 10.92 Flexure-Shear (d) 13.51 11.57xf 13.51 9-02y11 331.5 139.50 0.203 70 128 10.75 Bond 14.24 10.68x1 14.24 8.49y

Note:1 in. = 25.4 mm; 1 kip = 4.448 kN.

a - Test No.2 reached a maximum load of 17.88 kips aitereracking at 19.53 kips.h - Test No. 7 was the only test specimen that had initial strand slip (<3/32 in.) conforming to AC1 allowable limits.c - Three strands exhibited slippage during the test, then the remaining three strands broke.d - Flexure-shear crack caused a catastrophic failure with no loss of bond.x - Controlling prediction according to the AC! Code.y - Controlling prediction according to the slip theory.I - Flexural failure was predicted as opposed to ash-and development (bond) failure.AC I I, - 22 in.1 6 =41 in. for Test Nos. 3, 7, and h.ACl 1,=25 in.1 = 44 in. for Test Nos. 1,2,4, 5, 6, 9,10, and 11.

HYDRAULIC ACTUATOR

L.V.D.T's ON 40F6STRAND ENDS TO LOAD CELLMEASURE SLIPPAGEDURSNG TESTS. LOADING BEAM `W6K V5

HOLLOW CORE SLAB

3"BRG. 3° BRG.

A B

L = DESIGN SPAN

. BRG. BRG. Q.

NEAR END FAR END

Fig. 4. Arrangement for testing specimens.

length is increased in accordance withEq. (3), then the effective prestress ff iscorrespondingly reduced, as is the shearstrength which is given by Eq. (8).

Flexure-shear failure is predicted byAC! E. (11.11):

Vei =0.6 j bU' d +Vq+ V f rr (9)Mm,,,r

in whichMcr = (If ye) (6 y.fc +f,. -f)

Any reduction of the effective pre-stress f,,, in accordance with the strandslip theory will therefore reduce thecracking moment bM cr and with it theshear strength V.

TEST PROGRAMSeven hollow-core slabs, of cross sec-

tions, strand patterns, and materialproperties shown in Fig. 3, were pro-vided by Stresscon Corporation, Col-orado Springs, Colorado. Six of theseseven slabs had excess initial strandslip of average value greater than 0.08

in. (2 mm) at each end, as shown in Col-umn 4 of Table 2. In no case was theaverage slip greater than' in. (6 mm).

Concentrated loads were applied atvarious points for which the slip theoryand the AC! Code predicted widelydiffering strengths. Figs. 4, 5 and 6show the test setup, and Table 2 showsspan lengths and load points for theeleven tests.

The slabs were supported with abearing length of 3 in. (76 mm), similarto prevailing constriction practice. Aneoprene strip [11/16 in. (17 mm) thick]was provided at the bearing over the fullwidth of the slab to alleviate stress con-centrations at the support. A full widthroller at one end and a pin support atthe other end were used to permit endrotation and prevent axial constraints.The point load was applied by hydraulicjack and distributed through a W6 x 15transverse beam over the full width ofthe slab.

Instrumentation consisted of a loadcell and deflection gage at the load point.Additional slip of the strands during thetest was measured by LVDT gages

PCI JOURNAUJanuary- February 1988 97

Fig. 5. Testing arrangement,

bearing on four of the strand ends andattached to the end of the slab. Concretestrains were measured in some of thespecimens at the level of the steel andon the compression side of the slab overthe transfer zone, but these strains arenot reported.

TEST RESULTS

The results of the test program aresummarized in Table 2. The actual ap-plied failure load for each test is shownin Column 7 and the mode of failure isdescribed in Column 8.

Note that the initial strand slip did notexceed Sw, in Test No. 7 and that the testload was applied (Fig. 12) at a distancefrom the end of the slab approximatelyequal to the strand development lengthcalculated in accordance with the ACIequation. This permitted a check on theapplicability of the ACI equation to acase where the initial strand slip waswithin acceptable limits, and the results

confirm its applicability in a situationwhere even a small increase in devel-opment length would have resulted in apremature failure by loss of bond capac-ity in the strands.

It should be noted that both the ACIequations and the slip theory predicteda shear/moment failure (Vd) at a valueslightly less than its flexural capacity butthat the actual mode of failure was inflexure accompanied by tensile failureof half of the strands in the slab. Thefailure was ductile, with significantwarning deflection prior to failure, andthe actual failure load exceeded thepredicted flexure failure load by 6 per-cent.

In Test No. 10, the slip theory pre-dicted a premature failure by loss ofbond at a test load of 9.02 kips (40.12kN). In fact, the test load at failure oc-curred at 10.92 kips (48.57 kN), but themode of failure was in shear/flexure (V4 ,)and there was no loss of bond prior tothe sudden failure of this specimen.

In all of the remaining nine cases in

98

Fig. 6. End support with LVDT's and strain gages.

which excess initial strand slip oc-curred, the mode of failure was loss ofbond capacity in the strands (strand de-velopment). In none of these cases wasbond failure predicted by the ACIequations, while the slip theory pre-dicted bond failure in all of these cases.

In most of the tests, some of thestrands experienced additional slipduring application of increasing testload. Despite this partial bond loss,these slabs were able to carry additionalload, suggesting that the strands whichexhibited additional slip were able tosustain tensile capacity while the re-maining strands were able to continue tocarry increasing tensile load until they,too, lost bond and general bond lossfailure resulted.

This phenomenon, typical for mosttests, is shown for Test No. 8 in Figs.7 and 8, showing the deflection andadditional strand slip during loading, re-spectively. The apparent drops in loadindicated in Fig. 7 are the result of atemporary reduction in the hy-

draulically applied load upon the sud-den increase in slab deflection whichaccompanies flexural cracking.

COMPARISON BETWEENPREDICTED AND

OBSERVED STRENGTHSColumns 9, 10 and 11 of Table 2 indi-

cate, for each test, the predicted failureload computed by applicable ACI Codeequations for V,, k, V and developmentcapacity or tensile capacity (designated"f") of the strand, respectively. Note thatthe ACI equations, which are not in-tended to account for excess initialstrand slip, predict shear failure in TestsNo. 1 through No. 9 and tensile failure ofthe strand in Tests No. 10 and No. 11,whereas bond failure was the actualmode of failure in all cases except TestsNo. 7 and No. 10 as described above. Inall cases where initial strand slip ex-ceeded , the ACI equations predicted

PCI JOURNALJJanuary-February 1988 99

TEST NO.B

a I5^ FIRST INDICATION OF ADDITIONAL STRANDY - / SLIP DURING APPLICATION OF TEST LOAD

C] f

p IoJ 4 5 6

i 3

SEQUENCE OF CRACK FORMATION

5DEFLECTION OF ACTUATOR (INCHES)

Fig. 7. Slab deflection versus applied load (Test No. 8).

higher capacities than the failure loadsobserved in the tests.

Columns 12, 13 and 14 indicate, foreach test, the predicted failure loadcomputed by the slip theory, which cor-rectly predicted the failure mode in allcases except Test No. 10, described

above. It also predicted conservativefailure loads in all cases except Test No.4, where it overpredicted failure by 5percent.

In Fig. 9, the ratios of observed failuremoment to predicted failure moment areplotted against the location of the criti-

0.2

U)Li

Uz

aJU)

00,1

I-U)

J

20I-D

DEFLECTION OF ACTUATOR (INCHES)

Fig. 8. Additional strand slip during test versus slab deflection (Test No. 6).

X - M fail / M, (SLIP THEORY)

X O M foil /Mn iACI] wLL

X NX x

x Xq xx C

0 0o o 0 wlL

o

D

DISTANCE FROM BRG. TO APPLIED LOAD(INCHES)

Fig. 9. Comparison of observed and predicted strengths (University of Colorado Test

Series, 1985).

i

cal moment section along the span of thetest specimen. A value of unity of theseratios indicates exact agreement be-tween prediction and observation. Avalue larger than unity indicates a safeprediction, while a value less than unityindicates an unsafe prediction.

Fig. 9 shows that, in general, the AC1formulas cannot be used to safely pre-dict failure for products having excessinitial strand slip, while predictions bythe strand slip theory are generally con-servative. The slip theory appears tounderestimate the actual capacity by awide margin for very short shear spans,possibly because of the simplified as-sumption that strand developmentwithin the prestress transfer length islinear rather than convexly curved.

Figs. 10, 11 and 12 examine failuremoments in detail for three cases: TestNo, 5, in which the critical section fallswithin the transfer length; Test No. 9, inwhich the critical section is within theflexural bond length; and Test No. 7,in which the initial strand slip does notexceed fi i,, and the load is applied at adistance slightly greater than the devel-opment length computed by the ACI

equation (which is nearly identical tothat computed by the slip theory).

These diagrams illustrate the dif-ferences in failure mode wherein TestNo. 7 is a flexural failure with significantductility; Test No. 9, while eventuallyfailing in loss of bond, also showed sig-nificant ductility; and Test No. 5, whichfailed in loss of bond and which wouldhave resulted in a sudden failure undera gravity load test with little or nowarning deflection.

Fig. 13 shows the unpublished resultsof the series of tests performed at theUniversity of Wisconsin at Mil-waukee." , ' These tests were conductedon 8 in. (203 mm) machine cast slabs inwhich the manufacturing process wasdeliberately altered in order to produce

• Computerized Structural Design inc., "Ellectof the Amount o1 initial Strand Slip on Strength andBehavior of Spancrete Plank," First Draft Report tothe Spancrete Manufacturers' Association Techni-cal Committee, Unpublished Report, December 5,1983.

t Logan, Donald R., "Analysis of Strand Slip LoadTest at University of WisconsinlMilwaukee in De-cember 1 983,"J anuary 1984. Unpublished Report.

PCI JOURNAL1January-February 1985 101

rt NORTH (k. SOUTHG.

BONDFAILURE

P

NORTH 5 SOUTH

U-Mn {ACI) =78.41

2 60.62 Mfail =49.96w-

&AVG.;O.177' ^Mn(SLIPTHEORY)=46.048AVG.=O.I82'

13-9 3/4 l0'-O" 3'9 4 1ve

I BRG. ORG.

O.MOMENT DIAGRAMS

•71

151- ,CRACK NO. I

FIRST INDICATION OF ADDITIONALSTRAND SLIP DURING APPLICATION OFTEST LOAD

5 ICDEFLECTIONS OF ACTUATOR(INCHES)

b. LOAD / DEFLECTION DIAGRAM

a_

0

0J

C. OBSERVED CONDITIONS AT FAILURE

rlg. 10. Load Test No. 5 (load applied within transfer length).

102

P_ NORTH I SOUTH

+ 9t,- Mn {ACI 11=94.550. 94.55--Y M fail = 6.58 ^^ `^^

60.62—W Mn (SLIP \ 'p THEORY)

^^ =71.58

ô=0.177" b= 0.i35"

i 783/4" 6I 13' 9314. 11/2

BRG.BRG.

a. MOMENT DIAGRAMS

25

20 ADDITIONAL STRAND SLIPDURING APPLICATION OF

15 TEST

T INDICATION OFF

I— 6 734

5 2^S SEQUENCE OF CRACKFORMATION

5 k0

DEFLECTIONS OF ACTUATOR (INCHES)

b. LOAD! DEFLECTION DIAGRAM

n

BONDFAILURE-1

OUIHIRS.

C. OBSERVED CONDITIONS AT FAILURE

Fig. 11. Load Test No. 9 (load applied within flexural bond length).

a_

n0J

PCI JOURNALJanuary-February 1988 103

P

NORTHI.

7a- Mfai1 = 84.30

80.40 —i

w 50.37

2 I6AVG.=0.078" MCI (ACI )= Mn (SLIP THEORY)-80.40

II/̂ 13'-9^"

TH

SLIP THEORYA C

6 AVG =0.053

5'-93/4' r l

C. MOMENT DIAGRAMS

25^FlT INDICATION OF

20 DDITIONAL STRAND DURING APPLICATION

TEST LOADa Y I I 1O STRANDS

° IO G7 Q I 9 BREAKINGa 450 23

5 ^SEGUENCEOFCRACKFORMATION

5 10DEFLECTIONS OF ACTUATOR(INCHES)

b. LOAD / DEFLECTION DIAGRAM

NORTH rL SOUTHI BRG I BRG.

P

3 STRANDS BROKEREMAINING 3 STRANDSSLIPPED AT FAILURE

C. OBSERVED CONDITIONS AT FAILURE

Fig. 12. Load Test No. 7 (load applied at the computed ACI development length). Note thatinitial strand slip did not exceed ACI allowable.

104

3.18

X—Mfail/Mn (SLIP THEORY)

ox5 % 0–Mf0il/Mn (ACI) W

IL

x x N

0 x x x

ox Ox OX

0 OX0

x w0

0 ° cnz

fL I I I I I I t I i

^. 5 7)

24 48 72 96 120 144

DISTANCE FROM BRG. TO (L APPLIED LOAD )INCHES)

Fig. 13. Comparison of observed and predicted strengths (University ofWisconsin-Milwaukee Test Series 1983).

slabs having excess initial strand slip.The test specimens were 10 ft (3.05 m)and 13 ft 4 in. (4.06 m) long and preten-sioned with ifs in. (9.5 min) and '/2 in.(12.7 nom) diameter strand, respectively.

The ratios of observed to predictedfailure moments are plotted against lo-cation of critical moment within thespan. In general, the ACI Code predic-tions are not conservative, whereas theslip theory safely predicts failure in 16out of 17 cases, and is generally moreconservative when the critical sectionoccurs within the transfer length.

CONCLUSIONS1. For prestress transfer length to be

limited to the ACI Code value (f,. t13),the maximum allowable initial strandslip, S,,ti , varies from approximately 1l32to `az in. (1 to 3 mm), depending uponthe strand diameter and levels of initialand final prestress.

2. In Test No. 7, in which initialstrand slip did not exceed the allowable

limit, the equations of Section 12.9.1 ofthe ACI Code appeared to correctlypredict strand development length.

3. On test specimens where the ini-tial strand slip exceeded the allowablelimits, the ACI Code equations did notappear to safely predict the capacity orfailure mode of such specimens and theequations appeared to be unconserva-tive by a significant margin.

4. The strand slip theory, which ex-tends the ACI Code equations to ac-count for excess initial strand slip, ap-peared to give reasonable, conservativepredictions for the capacity of testspecimens having such excess slip, andcorrectly predicted the mode of failure.

5. The specimens having excess ini-tial strand slip generally failed throughloss of bond on the strand, with littlewarning deflection and diminishedductility.

These conclusions are based on re-sults of the testing of 8 in. (200 mm)thick hollow-core slabs, machine cast inan extrusion processing using relativelydry, tamped concrete, and in some cases

PCI JOURNALiJanuary-February 1988 105

deliberate alteration to the machineprocess was required in order to gener-ate excess initial strand slip. Thestrength of slabs of other proportions,and those cast by other processes, needfurther study.

It should also be noted that applica-tion of test loads through hydraulic pres-sure tends to obscure and perhaps mod-ify the potential for the sudden brittlefailure, which was experienced undermore realistic gravity load applicationsin the plant test series in cases wherepremature bond loss was the mode offailure.

It is recommended that future testinginclude gravity load applications tobetter evaluate this behavior.

ACKNOWLEDGMENTSOriginal concepts, and subsequent

review and comments were provided byRobert F. Mast. Initial experimentaltesting, technical guidance, and finan-cial support were provided byDonald R. Logan (coauthor) throughStresscon Corporation, ColoradoSprings, Colorado.

Additional testing, review and com-ments were also provided by RogerBecker, Computerized Structural De-sign, Inc., Milwaukee, Wisconsin.

The test series, reported herein, werecarried out in the laboratories of theCivil, Environmental, and ArchitecturalEngineering Department of the Univer-sity of Colorado, Boulder, under the di-rection of Professor Kurt H. Gerstle (co-author).

This paper is based upon a Master ofScience thesis submitted to the De-partmentby Mark D. Brooks (coauthor).

REFERENCES1. Anderson, A. R., and Anderson, R. G., "An

Assurance Criterion for Flexural Bond inPretensioned Hollow-Core Units," ACIJournal, V. 73, No. 8, August 1976, pp.457-464.

2. WaIraven, J. C., and Mercx, W. P. M.,"The Bearing Capacity for PrestressedHollow-Core Slabs," Heron, V. 28, No. 3,1983, Delft University of Technology,Delft, The Netherlands.

3. ACI Committee 318, "Building Code Re-quirements for Reinforced Concrete (ACI318-83)," and "Commentary on BuildingCode Requirements (ACI 318-83),"American Concrete Institute, Detroit,Michigan, 1983.

4. Hanson, Norman W., and Kaar, Paul H.,"Flexural Bond Tests of PretensionedBeams," ACI Journal, V. 55, No. 7,January 1959. pp. 783-802.

5. Janney, Jack R., "Report on Stress Trans-fer Length Studies on 270 K PrestressingStrand," PCI JOURNAL, V. 8, No. 1, Feb-ruary 1963, pp.41-45.

6. Kaar, Paul H., LaFraugh, Robert W., andMass, Mark A„ "Influence of ConcreteStrength on Strand Transfer Length," PCIJOURNAL, V. 8, No. 5, October 1963, pp,41-45.

7. Martin, L. D., and Scott, N. L., "De-velopment of Prestressing Strand in Pre-tensioned Members," ACI Journal, V. 73,No.8, August 1976, pp.453-456.

8. Zia, Paul, and Mostafa, Talat, "Develop-ment Length of Prestressing Strand," PCIJOURNAL, V. 22, No. 5, September-Oc-tober 1977, pp. 54-65.

106

APPENDIX A - SAMPLE CALCULATIONS

The following sample calculations arebased on data obtained from Test No. 2.

1. Parameters given (refer to Fig.3).a. Section propertiesA = 246.5 in.'Y,pp = 3.828 in.Yb,t = 4.172 in.b,n = 14.75 in.I = 1730.2 in.4

= 451.9 in.'S,, = 414.8 in.'tc = 61.6 psf (144 pef)

b. Material strengths and modulus ofelasticity (assumed)

= 5000 psifps = 270 ksiE = 28000 ksi

c. Prestress losses as a percentage ofjacking stress (assumed)5 percent at time of initial strand slipmeasurements immediately after trans-fer of prestress.15 percent at time of load test.

d. Cross section area of strands andstrand location measured from bottom ofmember to centerline of strandDiameterof strand Area Location

% in. 0.085 in.' 1.6875 in.to in. 0.153 in.'- 1.75 in.

e. Measured initial strand slips (seeTable AI) north end of test specimen (ascast in production facility). Mea-

surements made to center wire of 7-wirestrand using tire tread gage calibrated in32nds of an inch.

2. The testing arrangement for Test No.2 is indicated in Fig. Al. The testspecimen was supported by 3 in. neo-prene bearing pads resting on pin androller supports. Test No. 2 was the sec-ond test on the specimen and the dam-aged end from the first test was removedprior to the start of the second test.

3. Strand stresses and developmentlength per AC1318.A, = 2x0.085 + 4x0.153

= 0.782 in.?d = [2x0.085(8 - 1.6875)

+ 4x0.153(8 - 1.75) 1/0.782= 6.26 in.

h = 48 i n.p = 0,7821(48x6.26)

= 0.00260= ff(1 - 0.5 Pfm,lf,)= 270(1 - 0.5x0.0026x270/5)= 251 ksi

f = 0.85 F,/A,,= 0.85[(2x13.8 + 4x28.00.782= 156 ksi (avg)

Refer to Eq. (ib):l,t = fd,13+( .f9a- f,.)dsIt = f..d813; It =(f,.-ffldbIndividual strands% in. diameter:f. = 0.85 f^= 0.85x162.4= 138ksi1, = 138x0.37513 = 17.3 in.I6 = (251 - 138)x0.375 = 42.4 in.V2 in. diameter:

Table Al. Measured initial strand slips.

Strand designation S, Sm S3 S„ S3 SB

Strand diameter, db, in. % ½ 5'2 ½ 1/z %

Jacking force, Fj , kips 13.8 28.9 28.9 28.9 28.9 13.8

Jacking stress, f,, ksi 162.4 188.9 188.9 188.9 188.9 162.4

Measured initial slip, 2 6 5 6 5 2

32ndsofan inch

PCI JOURNALrJanuary-February 1988 107

aRG. r. BRG.

DAMAGEDEND REMOVEDPRIOR TO TEST

Fig. Al. Test arrangement (Load Test No. 2).

24-3" I'

P=TEST LOAD

3"BRG. LENGTH

L = 25'- 1 1 I/2 i1/2

MODIFIED SPECIMEN LENGTH' 27-I0/2'

f — 0.85x188.9 = 161 ksiI l = 161x0.50/3=26.8 in.d +, _ (251 — 161)x0.5 = 45.0 in.Weighted average of all strandslr = (2x0,085x17.3 + 4x0.153x26.8)/0.782

=25 in.d8 = (2x0.085x42.4 + 4x0.153x45,0)l0.782

= 44 in.= 25 + 44 = 69 in.

4. Development length based on sliptheory, using measured initial strandslips.a. Each strand individually[Refer to Eq. (3)1(1) Transfer length, = 2 SE /fwhere E = 28,000 ksi

f x; = 95 percent fiS = measured initial strand slip

Examples:Strand S1:6 = 2/32 in. = 0.0625 in.

l+ _ 2x0.0625x28,000 = 23 in.

0.95x162.4

Strand S2:S = 6/32 in. = 0.1875 in.

l _ 2x0J875x28,000 = 59 in.

0.95x188.9

Se , based on individual 1' lb, andA,„ foreach strand (see Table A2).(2) Flexural bond length[Refer to Eq. (5) ]:

fxe

Examples:Strand S,:di = 23 in.

j — 3(251 — 0.85 x162.4) x23

° 0.85x162.4

=56 in.

Strand S2:l 59 in.

= 3(251 - 0.85x188.9)

x590.85x188.9

= 99 in,

(3)Development length, ld = l; + 1Examples:Strand S sda=23+56=79 in.Strand S2:I^=59+99-158 in.

h. Weighted average, Strands S 1 through

108

P

f ps -251 KSI fdev {AC1)

= 156KS1 fdev(SL1Ptsg THEORY)

143 KSI

/ 73KSi

•I/2 I' $/2" I I 31/4 ,

MIDPOINTBRO. OF SPAN

Fig. A2. Developable stress in strand (Load Test No. 2).

5. Fig. A2 shows the developable stress-es in the prestressing strand as they arelimited by development length. Thecomputation of the values of filer at thepoint of application of the test load areas follows:a. PerACI formulas:f f„ = 156 x 22/24 = 143 ksib. Per slip theory:fi., = 156 x22/47 = 73 ksi

6. The stresses from Fig. A2 are used asfollows:a. Ultimate moment capacity. The de-

velopable stresses are utilized to com-pute ultimate moment capacity at thepoint of application of load and pre-dicted test loads are computed after de-ducting the moment due to specimenweight at the same location.b. Shear capacity. Since shear capacitydepends on the level of prestress at anysection considered, Fig. A2 is also usedto calculate the value of the prestressingforce at each section investigated, up toa maximum average stress level in thestrands of 156 ksi for the example shownin Fig. A2.

Table A2. Weighted averages of strands.

Strand Ana 1;

5, 0.085 x 22.7 = 1.93 x55.7 = 4.73S y 0.153 x 58.5 = 8.95 x98.8= 15.12Sg 0.153 x 48.8 = 7.47 x82.3 = 12.59S 4 0.153 x 58.5 = 8.95 x 98.8 = 15.12S, 0.153 x 48.8 = 7.47 x 82.3 = 12.595 K 0.085 x 22.7 = 1.93 x55.7 = 4.73

0.782 36.70 64.88

36.70/0.782 = 47 in.2 hta:o^ = 64.8810.782 = 83 in.7e 1a^^= 47+83 = 130 in.

PCI JOURNALJanuary•February 1988 109

APPENDIX B - NOTATION

A, = area of prestressed reinforce- F f = maximum force in prestressedment in tension zone, sq in. reinforcement following trans-web width, in. fer, psi

d = distance from extreme corn- I = moment of inertia of section re-pression fiber to centroid of sisting externally applied loads,longitudinal prestressed ten- in.'sion reinforcement, in. lb = flexural bond length according

db = nominal diameter of prestress- to the ACI Code, in.ing strand, in. I8 = flexural bond length according

E = modulus of elasticity of pre- to the slip theory, in.stressing strand, psi Id = development length according

j^ = compressive strength of con- to the ACI Code, in.crete, psi I d = development length according

fd = stress due to unfactored dead to the slip theory, in.load, at extreme fiber of section 1, = transfer length according to thewhere tensile stress is caused ACI Code, in.by externally applied loads, psi 1 = transfer length according to the

fden = developable stress in pre- slip theory, in.stressing strand at section, psi L = design span, in.

fj = jacking stress level in pre- M,, = moment causing flexural crack-stressing strand, psi ing at section due to externally

f = compressive stress in concrete applied loads = S 5 (6 ,' + ftt),(after allowance for all prestress lb-in.losses) at centroid of cross sec- M,i, = observed ultimate moment, attion resisting externally applied failure, lb-in.loads, psi Mmax = maximum factored moment at

= compressive stress in concrete section due to externally ap-due to effective prestress forces plied loads, lb-in.only (after allowance for all M„ = nominal moment strength atprestress losses) at extreme section, lb-in.fiber of section where tensile M„ = predicted ultimate moment,stress is caused by externally lb-in.applied loads, psi P = predicted failure load (applied),

= stress in prestressed reinforce- kipsment at nominal strength of test P„ = applied failure Ioad, kipsspecimen, psi Vi., = nominal shear strength pro-

f^„ = specified tensile strength of vided by concrete when diago-prestressing strand, psi nal cracking results from corn-

-f effective stress in prestressed bined shear and moment, lbsreinforcement (after allowance V = nominal shear strength pro-for all prestress losses), psi vided by concrete when diago-

fd = stress in prestressed reinforce- nal cracking results from exces-ment following transfer, psi sive principal tensile stress in

F, t,,,,= average initial prestressing web, lbsForce in the transfer zone fol- V4 = shear force at section due tolowing transfer, lbs unfactored dead load, lbs

Fj = jacking force in prestressed re- V, = factored shear force at sectioninforcement, lbs due to externally applied loads

110

occurring simultaneously withMma ,, lbs

Vp = vertical component of effective 8prestress force at section,lbs p

We = distance from centroidal axis ofgross section, neglecting rein-

*

0

forcement, to extreme fiber intension, in.

= measured initial strand slip atend of specimen, in.

= ratio of prestressed tension re-inforcement, A,,,Ibd

= strength reduction factor

METRIC (St) EQUIVALENTS

1 ft = 0.3048 m 1 psi = 0.006895 MPa1 in. = 25.4 mm 1 ksi = 6.895 MPa1 in. 2 = 0.000654 m21 kip — 4.448 kN

NOTE: Discussion of this article is invited. Please submityour comments to PCI Headquarters by October 1, 1988.

PCI JOURNALJJanuary-February 1988 111