Development Length of Prestressing Strands [PCI]

Specially tended R&D Program

PCISFRAD Project No. 2

Development Length ofPrestressing Strands, Including

Debonded Strands, andAllowable Concrete Stresses

in Pretensioned Membersby

S. K. GhoshAssociate ProfessorDepartment of Civil EngineeringUniversity of IllinoisChicago, Alinois

Mark FintelConsulting Structural Engineer

Chicago, Illinois

38

CONTENTS

1. Summary and Conclusions ........................... 40

2. Transfer Length and Development Length .............. 41

3. Current Code Provisions ............................. 42

4. Partial Results From Industry Survey ................... 43

5. Evaluation of the ACI Code Equationfor Development Length of Strand ..................... 43

6. Evaluation of the ACI Code DevelopmentLength Provision for Debonded Strand ................. 48

7 - Permissible Concrete Stresses inPrestressed Concrete Flexural Members ............... 50

— ACI Code Provisions— Significance of the Code Provisions— Some Results From Industry Survey— Background and Evaluation of Code Provisions

References........................................... 56

Appen d ix— Notation ................................... 57

Note: This paper is an edited version of Chapter4 which is part of PCISFRAD Project No. 2, "Ex-ceptions of Precast, Prestressed Members toMinimum Reinforcement Requirements." Thefull report is available from PCI Headquarters at$10.00 to firms supporting the sponsored re-search, $15.00 to PCI Members (nonsupporting firms) and $30.00 to non-PCI Mem-bers.The edited paper, and the full report, are basedon a research project supported by the PCISpecially Funded Research and Development

(PCISFRAD) Program. The conduct of the re-search and the preparation of the final reportsfor each of the PCISFRAD projects were per-formed under the general guidance and direc-tion of selected industry Steering Committees.However, it should be recognized that the re-search conclusions and recommendations arethose of the researchers. The results of the re-search are made available to producers, en-gineers and others to use with appropriate en-gineering judgment similar to that applied to anynew technical information.

PCI JOURNAL/September-October 1986 39

1. SUMMARY AND CONCLUSIONSThis paper represents a part of the

Prestressed Concrete Institute SpeciallyFunded Research and Development(PCISFRAD) Program, Project ReportNo. 2, "Exceptions of Precast, Pre-stressed Members to Minimum Rein-forcement Requirements (of AmericanConcrete Institute Standard ACI 318-83)." 1 The results of the other parts ofthe investigation will be published inthe PCT JOURNAL and elsewhere.

In this paper the adequacy, realismand/or conservatism of Section 12.9 ofACI 318-83,2 entitled "Development ofPrestrt'ssing Strand," are examined. Par-ticular attention is paid to the doubledevelopment length requirement fordebonded strands (Section 12.9.3 of ACI318-83). The code provisions areevaluated through close scrutiny of testresults available in the literature.

Also examined are the allowable con-crete stresses of Section 18.4 of ACI318-83. The history of this section istraced back to a 1958 report by ACI-ASCE Committee 423 (323), on whichthe very first chapter on prestressedconcrete in an ACI Code (1963 edition)was based.

The following conclusions can bedrawn on the basis of discussion in thispaper:

1. The ACI 318-83 equation givingdevelopment length requirement forprestressing strand is based on good ex-perimental authority, Certain inves-tigators have proposed making the pro-visions more conservative, while othershave found the requirements adequate.There does not appear to be any com-pelling basis for any significant changeto the current provisions. In the case ofshort span members where the full de-velopment length required by the Codecannot be provided, the approachsuggested in Ref. 3 [Eqs.(3) and (4)] mayprove useful.

2. The double development lengthrequirement for debonded strand (See-

tion 12.9.3) is also based on reliable ex-perimental evidence. Beams with de-bonded strands using single develop-ment lengths have shown a lack of per-formance, while those using double de-velopment lengths have performedsatisfactorily. However, tests on beamswith debonded strands using develop-ment lengths between one and twotimes those required by the Code havenot been carried out. Such tests areneeded to justify any possible relaxationof the provisions of Section 12.9.3.

Most of the allowable concretestresses in Section 18.4 of the Code havebeen in use for a long time, and arelinked with an extended record of satis-tactory performance. The most recentmodification (1977 Code) allowing atensile stress of up to 6 \, f, immediatelyupon transfer of prestress at the ends ofsimply supported members has not gen-erated any adverse reports of lack ofperformance. Further modifications donot appear to be warranted at the pres-ent time, However, relaxation in twopossible areas may be worthwhile pur-suing in the future:

(a) Increasing the allowable compres-sive stress immediately after prestresstransfer from 0.60 f,.' to 0.70 f i at theends of simply supported members maynot have an adverse effect on perfor-mance. However, this change needsto be verified in carefully conductedtests.

(b) The allowable tensile stresses,immediately after prestress transfer, of3,f fr; and 6^ T7 are indirectly linked tothe modulus of rupture. It may be possi-ble to increase these stresses somewhat,at least for concrete produced underplant controlled conditions, if modulusof rupture tests on such concrete showsconsistently high values (significantly inexcess of 7.5^ „E ). A great many suchmodulus of rupture tests need to be car-ried out. Satisfactory performance ofmembers designed on the basis of

40

higher allowable initial tension stresseswill also have to be established throughcareful testing, before a relaxation of thecurrent stress limits can he sought.

It may be of interest to note that Her-man Himes of Thomas Concrete Prod-ucts, Oklahoma City, in reviewing thismanuscript, took issue with Conclusion2 above in the following words:

"We do agree that inadequate infor-mation is available to justify anychanges to the development length ifone is considering dynamic loading .. .However, there appears to be adequateevidence that one development lengthfor debonded strand is sufficient forstatic loading conditions. We wouldsuggest that, until additional testing isdone, the Code be left as is for dynamicconditions such as bridges and parkinggarages and a modifier added which al-lows one development length for staticload conditions such as found in mostcommercial buildings."

The authors, on re-reviewing the

Kaar-Magura test results, 4 find them-selves unable to agree with this recom-mendation.

The following observation quotedfrom Ref. 4 is relevant:

"Load-deflection observations weremade in the static tests to detect, if pos-sible, any bond slip in the strands in theworking load range during the 5 millionload cycles. The results of these obser-vations showed no evidence of bondfailure at these load levels. The load-deflection relation was linear and innone of the girders tested was there asignificant difference between the rela-tion at the first loading and that after 5million load cycles."

Yet in subsequent static tests to fail-ure, the performance of the beam withdebonded strands using single de-veloliment length was poorer than thatof similar beams using double develop-ment lengths, and also poorer than theperformance of beams with nonblan-keted strands.

2. TRANSFER LENGTH ANDDEVELOPMENT LENGTH

The following two paragraphs,adopted from Ref. 5, clarify some . of thebasic concepts that are relevant to thediscussion in this paper:

In pretensioned members, the totalforce of prestressing is transferred to theconcrete entirely by the bonding of theprestressing strand to the concrete sur-rounding it. This differs from post-tensioned construction, where the fullcompressive force is transferred to theconcrete cross section by means of spe-cial end anchorages and bearing plates.

The bond mechanism in pretensionedmembers is accomplished in two ways,that is by transfer bond and flexuralbond. Transfer bond is mobilized by theinitial tensioning and release of thestrand, and the length over which theinitial prestress force is delivered to the

concrete is termed the "transfer" bondlength. Flexural bond becomesmobilized as the member is subjected tobending as a result of externally appliedloads. As external loads increase, the re-sulting stress in the strand also in-creases. The additional length overwhich this increase in force is trans-ferred is known as the "flexural" bondlength. As the ultimate capacity of themember is approached, the length ofstrand required to transfer the full forcein the strand, transfer length plusflexural bond length, is termed the "de-velopment" length.

If inadequate development length isprovided, ultimate strength is governedby bond rather than by flexure.'' Bondslippage of the strands occurs in threestages: (1) progressive bond slip begins

PC1 JOURNAL/September-October 1986 41

at flexural cracks, (2) general bond slip isinitiated along the entire developmentlength, and (3) the mechanical interlockbetween the helical strand surface andthe concrete is destroyed.

Kaar and Magura' pointed out that themechanical interlock is adequate tomaintain considerable strand stresseven after extensive bond slip. In many

cases the strand stress after generalbond slip drops only toward the pre-stress level and not to zero as one mightsear. Thus, the final effect of inadequatedevelopment length may be a prematureflexural failure at a reduced strandstress, corresponding to a final bendingmoment less than the computed ulti-mate strength in flexure.

3. CURRENT CODE PROVISIONSThe present provisions for develop-

ment length of prestressing strand arecontained in Section 12.9 of ACI 318-83. 1 The provisions read as follows:

Section 12.9.1 - Three- or seven-wirepretensioning strand shall be bondedbeyond the critical section for a de-velopment length, in inches, not lessthan:

(f,- 3 f.)d (1)

wherefps

stress in prestressed reinforce-ment at nominal strength, ksi

f, = effective stress in prestressedreinforcement (after allowancefor all losses), ksi

d8 = nominal strand diameter, in.and the expression in parentheses isused as a constant without units.

Section 12.9.2 — Investigation may belimited to cross sections nearest eachend of the member that are required todevelop full design strength underspecified factored loads.

Section 12.9.3 -- Where bonding of astrand does not extend to end ofmember, and design includes tension atservice load in precompressed tensilezone as permitted by Section 18.4.2, de-velopment length specified in Section12.9.1 shall be doubled.

In the Commentary to the ACI Cade,'the equation in Section 12.9.1 is rewrit-ten as:

Id = f db + (}Pf —f.) do (2)

where the first and second terms repre-sent transfer length and flexural bondlength, respectively.

The effective steel stress fx obviouslydepends on the initial prestress, f m , andthe amount of prestress loss. Zia andMostafae have pointed out that the de-nominator "3" in the exprcssion fortransfer length represents a conservativeaverage concrete strength in k.,i_

Similarly, in the expression for flex-ural bond length, a denominator of 1 ksi(6.9 MPa) is implied, which representsan average bond stress of 250 psi (1.7MPa) within the development Iength[see Eq. (8)1.

According to the ACI Code require-ment, the transfer length would be 47nominal strand diameters and theflexural bond length would be 110strand diameters for 250 ksi (1725 MPa)grade strand, assuming an initial pre-stress of 0.7fpu (where f,,,, is the spec-ified tensile strength of prestressingstrand, ksi) and a 20 percent loss of pre-stres5.K

Similarly, for 270 ksi grade strand, thetransfer length would be 51 strand di-ameters and the flexural bond lengthwould he 119 strand diameters. Notethat the value of 50 strand diametersis mentioned as the assumed transferlength in Section 11.4.3 of ACT 318-83.

42

4. PARTIAL RESULTS FROM INDUSTRY SURVEY

As a part of the broader investigation'of which this study formed a part,American and Canadian prestressedconcrete producers were surveyed°about their concerns with the ACI Coderequirements governing the design andmanufacture of precast prestressed ele-ments. One of the questions included inthe survey was: "Do the provisions gov-erning the development of prestressingstrand (Section 12.9) pose anyhardship?" The answers were 10 yesand 29 no. Of the 10 yes answers, 8 re-lated to doubling the developmentlength for sheathed strands:

1. Section 12.9.3 is too severe (fromtwo respondents).

2. Section 12.9.3 does not make anysense. Why should ld be doubled? Doesit make any difference if the strand isdebonded in 6 in. (150 mm) length orsay 10 ft (3 m) length? Per this sectiondebonding will cause problems in mostprestressed members of moderate 20 to30 ft (6 to 9 m) length.

3. Doubling the development lengthfor wrapped strands.

4. Seems excessive; otherwise not aproblem for our members.

5. For sheathed strand the extendedbond development is too great based onour observations. Otherwise, I do notconsider the strand development provi-sions a "hardship."

6. Masking is a real problem if com-plying with Section 12.9.3.

Other comments claiming hardshipwere:

1. On very short span members thedevelopment length creates a theoreti-cal problem in flexural strength.

2. Difficulties are experienced onheavily loaded short spans.

3. Development length is long andposes some difficulties when holes arecut in hollow-core floor slabs. Researchto prove that the ultimate tensilestrength of strand can be developed in ashorter length would be welcome. Not aproblem insofar as double tees are con-cerned.

4. Section 12.9.1 of ACI 318-83 needs170 d5, development length.

5. The term (f, – ff) d, in the Codeequation for development Iength is ex-cessive. However, this requirement isgenerally a problem in short simplespan members in which case the stranddiameter must be reduced. Experiencewith railroad ties seems to indicate theconservative nature of this requirement.

6. Our experience shows that the pre-vention of splitting during detensioningmerits the use of short length (5 ft) (1.5m) shear reinforcing in the ends ofdouble tees. There is reinforcing then,in the ends in the development lengthregion regardless of Code provisions.

7. Generally, double tees have longspans and development is not a prob-lem.

8. Dapped end reinforcing is tooheavy. Development length of 2.0 td

causes congestion in dapped regions.The factor 1.01d worked before provi-sions were changed.

5. EVALUATION OF THE ACI CODE EQUATION FORDEVELOPMENT LENGTH OF STRAND

More than 30 separate investigationshave been reported in the literatureconcerning bond development lengthfor prestressing steel$ However, many

of these tests were performed with smallwires and not the multi-wire strandscurrently used in the United States andCanada. Discussion here is limited to

PCI JOURNAL/September-October 1986 43

250

200N

C t50

100

50

Eq. (4)

•

Eq. ( 3 ) 1 /4 diameter strand

250

200

. I50

I00

50

0

Eq. (4) •

///•Eq .(3) 3/8 diameter strand

Eq.(4)

•

•

•

Eq.(3) 1/2" diameter strand

I!1 9n --

250

200

R 15OC.-

00

50

0.0 of rV Ei(J 90 100 110 120 130 140 150

In)

Fig. 1. Comparison of Martin-Scott equations' with test results by Hanson and Kaar.6

44

250

200

, L50a

100

50

Eq. (4)

a0 •e cut endodead end

1/4" din. strand-Eq.(3)

250 Eq. (4 )

200 ao:^

WO • cut endodeod end

1003/B" dia strand

50 Eq. (3)

0 10 20 30 40 50 601 x (in) £x(ln)

250

zoo

I50

100

50

0

250

Eq. (4) 200

150

•cut end 100o dead end

/2dlo. strand 50

0

0 • Eq, (40o eCP I

• cut end0 dead end

Eq.(3) 0.6dla. strand

0 10 20 30 40 50 60 0 10 20 30 40 50 60

1 (in) 4x (in)

Fig. 2. Comparison of Martin-Scott equations' with test results by Kaar, LaFraugh, andM ass."

tests that are relevant to prestressedconcrete in popular use today.

Early investigations on the nature ofbond were conducted in the 1950's. "•`u•"

These tests concluded that strand diam-eter, method of releasing the strand, andthe physical condition of the strandwere all factors influencing the transferbond length and flexural bond length.As a result of these tests, primarily theones reported in Ref. 6, ACI 318-63adopted what is still the current expres-sion for development strength. TheHanson-Kaar tests' were run on mem-

bers prestressed with clean' , %, and'in. (6, 10 and 13 mm) diameter strand.The test specimens had a wide range ofsteel percentages and the strands werereleased slowly, rather than cut by flameor saw.

In most of the specimens there was asignificant increase in load carryingcapacity between the point at which firstbond slip was detected by strain gaugesand final bond failure. The difference inload carrying capacity was due to me-chanical interlock of the strand. TheACI Code equation approximates the

PCI JOURNALJSeptember-October 1986 45

/.

A

5CEq. (5

40

'A 30

//OM 00 O 20

/Qf5/8"

0 0.7" I 0/ a 3/4"

5

30C

EW

Eq. (51/

/*/

/ °

5/8" STRAND

5

3

2

9

h0 50hpr j.Eq.(5}

Do/o / L° 40o /

h /O/

nn ° 30

LhAP/

h h • 1 /420

had • • 5/16a 5/16 3-WIRE

P. ° 103/8I 3/8 END REINF 101-

/ o° ° 1/2% 1/2 END REINF

010 20 3o 40 50 60

kt =

`/ I.3-4'db-2.3.f

0 o / o Less conservativeo i than Eq.(5)

hh

/ LO/

h °^

^/ !h^

L0

h 0/ o • i/4 in

h• L

^5/i6in

• ° 3/8 in0lo / 21n

10 20 30 40 50

0 10 20 30 40 50

f"—db (in)fciSudden Release

0 20 30 40

fsifci db (in)

Gradual Release

Fig. 3. Comparison of Zia-Mostafa equations' with experimental results from varioussources (L indicates low strength concrete with ff < 2000 psi; h indicates high strengthconcrete withfd' > 8000 psi).

46

average value of all the points repre-senting first bond slip and final bondfailure

Results of tests performed by Kaar,LaFraugh, and Mass 12 greatly added tothe knowledge concerning transferlength, Tests were performed on mem-bers with varying strand diameters andconcrete strengths. The results indi-cated that, although higher strengthconcrete could develop 75 to 80 percentof the transfer bond in a shorter distancethan lower strength concrete, the totaldistance required to develop 100 per-cent of the transfer bond was approxi-mately the salve irrespective of concretestrength.

In recent years, several researchershave proposed new equations for trans-fer and development lengths. Martinand Scott, in a statistical evaluation ofthe early tests performed by Hanson andKaar, fl proposed the following expres-sions (see Figs. land 2):For lx less than 80 db:

it 135+ 3i (3)f:.g^ 80d4 daa

where I, is the distance from the end ofthe member to the section under con-sideration, in inches.For 1,. greater than 80 db:

fug 135 + 0.391,^(4)dbib db

In no case shall f,,8 be greater than thatgiven by Eq. (18-3) of ACI 318-83 or thatobtained from a determination based onstrain compatibility.

The above expressions provide an ap-proach to designing precast, preten-sioned units for spans too short to pro-vide an embedment length that will de-velop the full strength of the strand, andthus allay some of the concerns raised inresponse to the survey mentioned ear-lier. However, here is Zia's and Mos-tafa'sa evaluation of these expressions:

"Martin and Scott proposed a transferlength of 80 diameters for strands of all

sizes, and a flexural bond length of 160,187, and 200 diameters for the ¼, ^, andyz in. (6, 10 and 13 mm) diameterstrands, respectively. These values areconsiderably higher than thosespecified by the current ACI Code."

On the other hand, based on the re-sults of a test program of 36 preten-sioned hollow-core units, Anderson andAnderson'' concluded that the currentACI Code requirement on the develop-ment length is adequate provided thatthe free end slip of the strand, upontransfer of prestress, does not exceed anempirical value which is roughly 0.2times the strand diameter.

Zia and Mostafa," in a comprehensivestudy of all past research, proposed thefollowing expressions (see Fig. 3):

1.5 f,; db _I t = 4.6 (5)fCf

i= 1.25 (f a –f )dd (6)

Id = I, f Ib(7)

wheref = stress in prestressing steel at

transfer, ksiR = compressive strength of con-

crete at time of initial prestress,ksi

Ii = transfer length of prestressingstrand, in.

d o = flexural bond length of pre-stressing strand, in.

Eq. (6) is based on the theoreticallyderived expression:

Ib = }'1x –.f^ do (8)4 uace

where u,,, is average bond stress withinIb . Note that in the current ACI Code, itis implied that u = 250 psi (1.7 MPa).Eq. (6) assumes an ua„, – 200 psi (1.4MPa).

The Zia-Mostafa equation for transferlength is applicable for concretestrength ranging from 2000 to 8000 psi(14 to 55 MPa). It accounts for effects of

PCI JOURNAUSeptember-October 1986 47

Table 1. Comparison of Eq. (5) with ACI Code requirement for transfer length! (in.).

250-K Gradef i = 175 ksi, f„' = 140 ksi

270-K Gradefa, = 189 ksi, f e = 151 ksi

Strand size, in. f f, = 3500 psi f,', = 4000 psi ACI f,, = 3500 psi f f, = 4000 psi ACT

'6 14 12 12 16 13 13%6 19 16 15 21 18 16% 24 20 18 26 22 19716 28 24 21 31 26 22'l2 33 28 24 36 31 25

Nato: 1 in. = 25.4 min; I ksi = 6.91MPa; 1 psi = 0.0069 MPa.

strand size, the initial prestress and theconcrete strength at transfer. The equa-tion for transfer length gives comparableresults as the current ACI Code re-quirement for small sized strands, but ismore conservative than the ACI Code,

particularly for cases where the concretestrength at transfer is low (see Table 1).The flexural bond length specified bythe current ACT Code (ACT 318-83) isincreased by 25 percent by the Zia-Mostafa proposal.

6. EVALUATION OF THE ACI CODE DEVELOPMENTLENGTH PROVISION FOR DEBONDED STRAND

Kaar and Magura4 have pointed outthat the development length requiredby Eq. (1) was based on tests of beamswith all strands bonded from the sectionof maximum moment to the beam ends.The end of the development length canthen overlap the stress transfer lengthnear the beam supports, where a state offlexural precompression exists even athigh loads, and where a lateral compres-sion is provided by the vertical beamsupport reaction. When strands areblanketed for a considerable distanceinto a member, however, both stresstransfer and flexural bond developmentmay take place in a concrete regionsubjected to tension, and even cracking,before the ultimate load is reached.Under these conditions, the embedmentlength given by Eq. (1) may be inade-quate.

Tests reported in Ref. 14 were con-ducted to accurately determine pre-stress losses and creep camber in pre-stressed girders. The tests included a

study of beams containing debondedstrands, one with normal weight con-crete and one with lightweight concrete.The study, which compared the beamscontaining debonded strands withbeams containing draped bondedstrands, concluded that the midspanprestress losses for a given concretewere about the same for both designsstudied and that beams with debondedstrands can be designed to have lessinitial and time-dependent camber thanbeams containing draped strands.

Later tests reported in Ref. 15 wereperformed on both half sized and fullsized girders containing draped bondedstrands, debonded "wrapped" strands,and debonded strands with end anchors.The beams were designed using onedevelopment length and the debondedstrands were "wrapped" with a cage ofmild steel reinforcement in the transferregion to confine the concrete im-mediately surrounding the strands,thereby eliminating the possible need

48

for longer development lengths. All thetest beams performed satisfactorily.However, fatigue was not a considera-tion in these tests. Also, later tests con-ducted at the Portland Cement Associa-tion showed that wrapping has little, ifany, benefit.

Tests by Kaar and Magura4 exploredthe possible effects of blanketing or de-bonding on the flexural behavior at ser-vice load and on the ultimate flexural,bond, and shear strength of preten-sioned prestressed girders.

Three girders were designed andtested for the study of flexural behavior.Girder 1 had no strands debonded.Girder 2, designated as "partially blan-keted," had strands so debonded thatthe development lengths were twicethose computed by Eq. (1). The "fullyblanketed" Girder 3 was designed withdevelopment lengths of the blanketedstrands equal to the lengths required byEq. (1). All three girders were over-reinforced with stirrups to prevent in-terference of shear distress with flexuraland bond behavior.

The girders were subjected to 5 mil-lion cycles of the design live Ioad priorto static testing to failure. Each girderwas first loaded statically through fiveIive load cycles. Thereafter, the girderwas loaded dynamically, with static testscarried out after approximately 1, 2½,and 5 million cycles. At the completionof the 5 million cycles, the girder wasremoved and tested statically to de-struction.

The shear investigation involvedstatic testing to destruction of anonblanketed girder, Girder 4, and agirder with partially blanketed strands,Girder 5. The girders were similar tothose in the flexural study except thatthe number of stirrups was reduced inorder that any effects on shear capacityof blanketing strands would be demon-strated.

The three tests utilizing dynamicloads showed no detrimental effects ofstrand blanketing on pretensioned

members subjected to 5 million repeti-tions in the working load range.

Beyond the cracking load and understatic loading, some bond slip occurredfor all blanketed strand.

The results from the two tests inwhich the girders had less than the re-quired shear reinforcement indicated nodetrimental effects of blanketing uponshear strength.

There was evidence that the ACICode requirement for bond develop-ment length of the strand cannot be di-rectly applied to blanketed strand.However, the performance of blanketedstrand girders with developmentlengths twice those required by Eq. (1)closely matched the flexural perfor-mance of a similar pretensioned girderentirely without blankets.

The provisions of Section 12.9.3 ofACI 318-83 are based on the Kaar-Magura tests,' modified as indicatedbelow.

An experimental investigation, sub-sequent to the Kaar-Magura tests, hasbeen carried out at the Portland CementAssociation to determine the effect ofrepetitive loading on the behavior andstrength of girders with blanketedstrands. '° Controlled variables in thetest program were load level, develop-ment length, and use of ties to confinethe concrete in the stress transfer regionof the blanketed strands.

The test program called for 5 millioncycles of loading between dead load anddead plus live load. Static tests to fulldead load plus live load were performedbefore cyclic loading and after 1, 2'1x,and 5 million load cycles. At the com-pletion of 5 million cycles, the girderswere tested to destruction under staticload.

The results of the fatigue tests indi-cated the following:

1. For similar loading conditions, thebehavior and strength were the same forgirders having either blanketed ordraped strands.

2. The fatigue life of specimens de-

PCI JOURNAL/September-October 1986 49

signed for a maximum tensile stress of6 ,f fT psi (0.5 yi' MPa) under full ser-vice load was significantly less thanthat of specimens designed for zerotension.

3. In specimens designed for zerotension in the concrete under serviceload condition, and having blanketedstrands designed for one developmentlength [as given by Eq. (1)], the be-havior and strength of the specimenswith blanketed strands were similarto those of girders with drapedstrands.

4. In the specimen designed for amaximum tensile stress of 6 psi inthe uncracked concrete under full ser-vice load and having blanketed strandsdesigned for twice the developmentlength given by Eq. (1), only small slipof the strands occurred. This indicatedadequate bond of the blanketed strandsfor about 3 million cycles of repetitiveloading.

5. In the specimen designed for amaximum tensile stress of 6 Y f,' psi* inthe uncracked concrete under full ser-vice load and having blanketed strandsdesigned for one development length,blanketed strands slipped, indicatingoccurrence of bond fatigue.

6. In the three specimens where cy-clic loading produced tension of 6 f,;'psi in the concrete at midspan, fatiguefracture of the strands occurred at about3 million cycles of repetitive loading.These specimens included a control

girder with draped strands. Therefore,blanketing did not cause fatigue ofstrands.

7. Use of ties to confine the concretein the stress transfer region of blanketedstrands in one specimen did not provideany substantial improvement in the be-havior of that specimen.

In view of the findings of the abovetest series, the original double de-velopment requirement for blanketedstrands of the 1971 ACI Code was mod-ified in the 1983 Code edition, allowingthat in pretensioned members designedfor zero tension in the concrete underfull service load conditions, the de-velopment length for dehonded strandsneed not he doubled.

For Further details on the effect ofblanketing strand, see Refs. 4, 5 and 16.

*The following comment by Dr. Alex Aswad ofStanley Structures in private correspondence withthe authors may be of interest:

'I reviewed the PCA report in 1978 before itspublication ... Rabbat et al did not use AASHTOlosses; instead, they assumed a smaller 'flat value.'IfAASHTO losses were used, the calculated bottomtension would have been 8.9 yI psi (0.74 y]^MPa)."

In the above mentioned review Dr. Aswad alsoexpressed the opinion that the three girders de-signed for zero tension in the concrete under ser-vice load conditions actually had bottom tensionapproximately equal to 3 5,7 psi (0.25 ^^ f,' MPa). Itshould additionally be noted that in the Kaar-Magu ra tests,' a bottom tension of 2.4 V7' psi(0.20 y f, MFa) under the full design service loadhad been allowed.

7. PERMISSIBLE CONCRETE STRESSES INPRESTRESSED CONCRETE FLEXURAL MEMBERS

In this section the current ACT Codeprovisions and their significance arediscussed together with some resultsfrom an industry survey. Lastly, thebackground and evaluation of the Codeprovisions on allowable concretestresses are brought into focus.

ACI Code ProvisionsThe current AC! Code provisions2

concerning permissible concretestresses in prestressed concrete flexuralmembers are given below:

Section 18.4.1 -- Stresses in concreteimmediately after prestress transfer

50

(before time-dependent prestress los-ses) shall not exceed the following:*

(a) Extreme fiber stress incompression ........... 0,6of^;

(b) Extreme fiber stress intension except aspermitted in (c) ......... 3 \^ f:i

(c) Extreme fiber stress intension at ends of simply _supported members ..... 6 f7r

Where computed tensile stresses ex-ceed these values, bonded auxiliaryreinforcement (nonprestressed or pre-stressed) shall be provided in the tensilezone to resist the total tensile force inconcrete computed with the assumptionof an uncracked section.

Section 18.4.2 — Stresses in concreteat service loads (after allowance for allprestress Iosses) shall not exceed thefollowing:

(a) Extreme fiber stress incompression........... 0.45f^

(b) Extreme fiber stress intension inprecompressed tensilezone.................. 6 ^.f

(c) Extreme fiber stress intension in precompressedtensile zone of members(except two-way slabsystems), where analysisbased on transformedcracked sections and onbilinearmoment-deflectionrelationships show thatimmediate and long-timedeflections comply withrequirements of Section9.5.4, and where coverrequirements complywith Section 7.7.3.2 ..... 12 YIT

Section 18.4.3 — Permissible stressesin concrete of Sections 18.4.1 and 18.4.2may be exceeded if shown by test or

`Metric (SI) conversion factors:1.0 psi = o.0068 5 MPa I.0 = 0.083 v fC'h4 Pa.

analysis that performance will not beimpaired.

Significance of the Code Provisions

The tension stress limits of 3 v f,';and 6 4 f,, refer to tensile stress at loca-tions other than the precompressed ten-sile zone (that portion of the membercross section in which flexural tensionoccurs under dead and live loads). If thetensile stress exceeds the applicablelimiting value, the total force in the ten-sion zone should be calculated andhonded auxiliary reinforcement pro-vided to resist this force. For designpurposes, such steel is assumed to act ata stress of 60 percent of its yield stress,but not at a stress greater than 30 ksi.

The service load stress limits applyafter all losses have occurred and whenthe full service load acts. The allowableconcrete tensile stress of 6 V' f,' has beenestablished mostly on the basis of ex-perience with test members and actualstructures. Use of this stress limit, ratherthan a lower value or zero, requires thatthere be a sufficient amount of bondedreinforcement in the precompressedtension zone to control cracking, that theamount of concrete cover over the rein-forcement be sufficient to avoid corro-sion, and that unusually corrosive con-ditions not be encountered.

Bonded reinforcement may consist ofbonded prestressed or nonprestressedtendons, or of bonded reinforcing bars,well distributed over the tension zone.In all flexural members where the pre-stressing tendons are not bonded, theminimum bonded reinforcement re-quirements of Section 18.9 must be fol-lowed. Unbonded construction, whichis invariably post-tensioned, is beyondthe scope of the broader investigation ofwhich this study forms a part. Whether,in bonded construction, the allowablestress limits of 6 f,' (or 12 ,), 0.45ffand/or 0.60 ff, can be exceeded, and aux-iliary reinforcement used to carry the en-

PCI JOURNAUSeptember-October 1986 51

tire tension and/or the excess compressionforce, is not clear from the Code.

The Code neither specifically allows,nor expressly forbids, such practice. Theauthors are not sure as to whether suchpractice is amenable to mechanizedplant precasting. The added cost ofproduction may outweigh any potentialadvantages that might exist. Also, theanticipated service load behavior of(partially prestressed) members thatmay be designed following the abovepractice must be preascertained, basedon such experimental information andperformance record as may he available.

The allowable concrete stresses of theACI Code are also significant in thatthey lead directly to the practice of de-bonding of tendons. Two methods are inpopular use for limitation of compres-sive and tensile concrete stresses nearthe ends of pretensioned prestressedconcrete members. Some of the preten-sioned reinforcement may be "harped,"that is, deflected upward near the endsof the members; or bond to the concretemay be prevented for some of the pre-tensioned reinforcement in the end re-gions.

Harping or draping of strands in pre-tensioned beams can present problemsfor designers, fabricators, and inspectorsin some plants. The tensioning proce-dure is time consuming, expensive andleaves doubt as to the actual prestresslevel obtained throughout the length ofthe strand. Relevant aspects of the prac-tice of debonding have already beendiscussed at length.

Some Results From IndustrySurveys

In response to the question, "Do theauxiliary reinforcement provisions ofSection 18.4.1 cause any hardship?", 8respondents answered yes, 39 answeredno. Comments from those with affirma-tive answers were as follows:

1. How far from the end does Section18.4.1(c) stop and Section 18.4.1(b) start

applying? We use Section 18.4.1(c) fulllength with no problems.

2. It may be more appropriate to pro-vide tension reinforcement based on aforce-distance from centroid relation-ship instead of force only.

3. Taking the "total tensile force withreinforcement" per Section 18.4.1 maybe too conservative.

4. Allow an increase in top fiber ten-sion at ends of simply supported mem-bers.

Comments from those with negativeanswers included the following:

1. 3 fi t should he changed to 4 fL T

at release.2. Investigate whether a higher allow-

able stress can be achieved.3. Section 18.4.1 should include the

following item: allowable tension underdead load only — zero.

4. Section 18.4.1(b) — increase to5 . Justification:

fr _ 7.5_1 5 1.5 eft = 5 f

5. Cracking can and will result if aux-iliary reinforcement is not used whenneeded.

6. The auxiliary reinforcement re-quirement is not a problem for doubletees.

In response to the question, "Arethere any other ACI Code requirements[other than those specifically cited inthe survey] relative to double teescausing difficulties?" the following an-swers of interest to the current discus-sion were received:

1. Section 18.4.1(a) — We frequentlyallow initial compression stressesgreater than 0.60ff 1 . Often I feel wrap-ping of strands is more detrimental thanis the higher compression stress, espe-cially in a thin stemmed member. I seeno problem in allowing an initial stressequal to 0.70f. Losses are not appreci-ably affected.

2. Section 18.4.1(a) and 18.4.2(a) -The ACI Code should stipulate additionof reinforcing steel if allowable corn-

52

pression stress in the concrete is ex-ceeded. It does so in the case of tension[Section 18.4.1(c) ]. This eliminates thenecessity to drape strands. Sometimeswe use this practice because the Codedoes not forbid it. However, some de-signers do not agree.

3. Release stresses of Section 18.4.1for compression are too conservative. Aflat factor of safety of 1000 psi or 1200psi (6.9 or 8.3 MPa) is preferable.

4. An allowable compressive stress of0.60 f,' is too restrictive; suggest using0.70f,.

5. The effects of a compressive stressat release greater than 0.60f f i should beinvestigated. What, for example, wouldhappen if the stress were 0.70f?

6. We don't believe that a maximumtensile stress is needed. We often designfor camber and let stress go over 1000psi (6.9 MPa).

7. Lack of acceptance of 12 , 7 allow-able stress by conservative consultingengineers.

Background and Evaluation ofCode Provisions

A chapter on prestressed concrete wasincluded for the first time in the 1963edition of the ACI Code. The chapterwas based on recommendations byACI-ASCE Committee 423 on pre-stressed concrete. 17 The chapter in-eluded the following allowable stressesin concrete.

(a) Temporary stresses immediatelyafter transfer, before losses due tocreepand shrinkage, shall not exceed the fol-lowing.

1. Compression ......... 0.60 f^^2. Tension stresses in

members withoutauxiliary reinforcement(unprestressed orprestressed) in thetension zone .......... 3 v fOWhere the calculated tensionstress exceeds this value, rein-forcement shall be provided to

resist the total tension force inthe concrete computed on theassumption of an uncrackedsection.

(b) Stresses at design loads, after al-lowance for all prestress losses, shall notexceed the following:

1. Compression ......... 0.45fc2. Tension in the

precompressed tensionzone: Members notexposed to freezingtemperatures nor to acorrosive environment,which contain bondedprestressed orunprestressedreinforcement locatedso as to control cracking

All other members .... 0These values may be exceededwhen not detrimental to properstructural behavior as providedin Section .. .

In his discussion of Ref. 17, T. Y. Linwrote:"

"As an example of the dangerous er-rors contained in these allowable stress-es, let us consider the temporary stress-es allowed. ... Here tension in theconcrete is limited to 3 for singleelements.... A recently completed in-vestigation at the University of Califor-nia proved definitely that the strengthand behavior of beams at transfer cannotbe simply described by stresses but aredependent upon a number of factors,such as the shape of the section, theamount and location of prestress, etc."

In its closure to the discussion of Ref.17, Committee 423 wrotc:1

"The specific (allowable) stress val-ues ... were chosen after a thoroughstudy of all pertinent data. During thelast year before publication of the re-port, numerous comments were re-ceived and some modifications made inthe allowable stresses. It is a fact that thevalues published reflect the very best anwhich agreement could be obtained."

PCI JOl1RNAL1September-October 1986 53

"In reference to some of Lin's remarksabout allowable stresses, it should hereaffirmed that the (proposed) provi-sions ... are intended to be advisoryrather than intransigent, Special cir-cumstanccs may dictate a downward re-vision of certain values. Liberalizationmay be indicated in other instanceswhere sufficient supporting data can besubmitted, including analytical studies,test results, or performance records. Inthe latter case, the burden of proofshould fall upon those who wish to de-viate from the generally accepted val-ues."

Specifically on the limit 0.60f,,, asapplicable to pretensioned members,the Committee wrote;

"Here, production had preceded de-sign recommendations, and the stress of0.60 f f r had already been widely estab-lished in the pretensioning industry. Noill effect had been reported in regard tostrength and performance. Only camberproved difficult to control for certainbuilding members."

The authors would also like to recordhere their belief that the choice of0.60 ff, must have been dictated origi-nally by a desire not to go too far into theinelastic range of stresses. The elasticlimit is usually at a stress of about halfthe compressive strength. The stress 0.6J' ( is beyond, but not too far beyond, thatlimit.

On the 6 limit on tension stressesat full service load, Committee 423wrote: "This is another instance inwhich the pretensioning industry formany years had followed a standard ofproduction that had given satisfactoryresults."

Section 18,4.2 of ACT 318-83, in itspresent form, first became part of the1971 edition of the ACI Code. The useof a tensile stress limit of 12 V ff waspermitted to obtain improved serviceload deflection characteristics, particu-larly when a substantial part of the liveload is of a transient nature. It should beemphasized that an allowable tensile

stress of 12 N! f , calculated on the basisof an untracked cross section, is a nomi-nal stress only, since its value is wellabove any reasonable estimate of themodulus of rupture of the concrete. Ifthis stress limit is used, the concreteprotection for the reinforcement must beincreased 50 percent above its usualvalue, according to the Code, and anexplicit check made of service load de-flections.

The 6 Vf, limit on initial tensionstresses, applicable to the ends of sim-ply supported members only, was intro-duced into the 1977 edition of the ACICode in an effort to mitigate hardshipsfaced by the hollow-core industry. Theindustry had difficulty in satisfying the3 stress limit at the ends of hollow-core planks. Draping of strands is not apractical solution for such shallowmembers. Debonding of strands is notan economically viable solution either.The use of auxiliary reinforcement is notpractical in view of the extrusion pro-cess of manufacture. The industry alsoproduced evidence that a relaxation ofthe 3 stress limit only for the endsof simply supported members would notadversely affect performance.

Whether the 3,1 ,' i or the 6 . -, limitapplies should be fairly obvious in mostdesign situations. The sole exception tothat is where dehonded strands are usedat the ends of simply supported mem-bers. In checking the stresses where thedebonding ends, a strict reading of theCode would appear to indicate use ofthe 3 y+ lirnit. If the debonding is overa significant length, it should not be dif-ficult to satisfy this stricter stress limit,because the dead load moments wouldrelieve some of the extreme tensionfiber stresses. If the debonding is over avery short length, so that benefit fromthe dead load stresses does not obtain,use of the 6 ,' J^, stress limit would ap-pear to be justified.

The allowable tensile stresses of3 ^f,, and 6 VTare obviously related tothe modulus of rupture which, accord-

54

L,MPa

I i

0 2 4 6 8 10f,MPo

20 4060801001400 + 10 fe 10

// a

a 1200 f, = I I.V 8w-` f -0.94

IOOQ

XMP/16 aci

800-

600 //^^C

, :ec400 ~

2200 ° 7 doys

0 28 days0 95 day s

00 20cS0 600 odoo 14000 0

Cylinder Strength f, , psi0 20 40 60 80 100 120 140

f, , psi

Fig. 4. Modulus of rupture as a function of concrete strength?'

ing to the Code, for normal weight con-crete is [Eq. (9-9), Section 9.5.2.3]:

fr =7.5 tif,'+

According to the recently published"State-of-the-Art Report on High-Strength Concrete" by AC! Committee363,21 the values reported by various in-vestigators for the modulus of rupture ofboth lightweight and normal weighthigh strength concretes fall in the rangeof 7,5 „I f,' to 12 y+ f,' where both themodulus of rupture and the compressive

strength are expressed in psi. The foI-lowing equation was recommended21 forthe prediction of the tensile strength ofnormal weight concrete, as measured bythe modulus of rupture (Fig. 4):

fr = 11 .7 `I fcfor 3000 psi c fe <12,000 psi

The reader should consult lief. 22 forfurther valuable background informa-tion on the ACI Code provisions con-cerning allowable stresses in pre-stressed concrete flexural members.

PCI JOURNALJSeptember-October 1986 55

REFERENCES1. Ghosh, S. K., and Fintel, M., "Exceptions

of Precast, Prestressed Members toMinimum Reinforcement Requirements(of American Concrete Institute StandardACI 318-83)," PCISFRAD Project No. 2,Prestressed Concrete Institute, Chicago,Illinois, 1986, 204 pp.

2. ACI Committee 318, "Building CodeRequirements for Reinforced Concrete(ACI 318-83)," American Concrete In-stitute, Detroit, Michigan, 1983, 111 pp.

3. Martin, L. D., and Scott, N. L., "De-velopment of Prestressing Strand inPretensioned Members," ACI Journal,Proceedings V. 73, No. 8, August 1976,pp. 453-456.

4. Kaar, P. H., and Magura, D. D., "Effect ofStrand Blanketing on Performance ofPretensioned Girders," PCI JOURNAL,V. 10, No. 6, December 1965, pp. 20-34.Also PCA Development DepartmentBulletin D97.

5. Horn, D. G., and Preston, H. K. (for PCICommittee on Bridges), "Use of De-bonded Strands in Pretensioned BridgeMembers," PCI JOURNAL, V. 26, No. 4,July-August 1981, pp. 42-58.

6. Hanson, N. W., and Kaar, P. H., "FlexuralBond Tests of Pretensioned PrestressedBeams,"ACI Journal, Proceedings V. 55,No. 7, January 1959, pp. 783-802. AlsoPCA Development Department BulletinD28.

7. ACI Committee 318, "Commentary onBuilding Code Requirements for Rein-fiorced Concrete (ACI 318R-83)," Ameri-can Concrete Institute, Detroit, Michi-gan, 1983, 155 pp.

8. Zia, P., and Mostafa, T., "DevelopmentLength of Prestressing Strands," PCIJOURNAL, V. 22, No. 5, September-October 1977, pp. 54-65.

9. Chosh, S. K., and Fintel, M., "Summaryof Responses to a Questionnaire onMinimum Reinforcement Requirementsfor Prestressed Concrete Members."To be published in November-Decem-ber 1986 PCI JOURNAL.

10. Janney, J. R., "Nature of Bond in Preten-sioned Prestressed Concrete," ACI Jour-nal, Proceedings V. 50, No. 9, May 1954,pp. 717-736. Also PCA DevelopmentDepartment Bulletin D2.

11. Janney, J. R., Hognestad, E., and

McHenry, D., "'Ultimate FlexuralStrength of Prestressed and Convention-ally Reinforced Concrete Beams," ACIJournal, Proceedings V. 52, No. 6, Feb-ruary 1956, pp. 601-620. See alsoPCA Development Department Bulle-tin D7.

12. Kaar, P. H., LaFraugh, R. W., and Mass,M. A., "Influence of Concrete Strengthon Strand Transfer Length," PCI JOUR-NAL, V. 8, No. 5, October 1963, pp.47-67. Also PCA Development Depart-ment Bulletin D71.

13. Anderson, A. R., and Anderson, R. G.,"An Assurance Criterion for FlexuralBond in Pretensioned Hollow CoreUnits," ACI Journal, Proceedings V. 73,No. 8, August 1976, pp. 457-464.

14. Furr, H. L., Sinno, R., and Ingram, L. L.,"Prestress Loss and Creep Camber in aHighway Bridge With Reinforced Con-crete Slab on Pretensioned PrestressedConcrete Beams," Research Report 69-3,Texas A&M University, College Station,Texas, 1969, 144 pp.

15. Dane, J., III, and Bruce, R. N., Jr.,"Elimination of Draped Strands in Pre-stressed Concrete Girders," Civil En-gineering Department, Tulane Univer-sity, New Orleans. Submitted to theLouisiana Department of Highways,State Project No. 736-01-65, TechnicalReport No. 107, 1975.

16. Rabbat, B. G., Kaar, P. H., Russell, H. G.,and Bruce, R. N., Jr., "Fatigue Tests ofPretensioned Girders With Blanketedand Draped Strands," PCI JOURNAL, V.24, No. 4, July-August 1979, pp. 88-114.

17. ACI-ASCE Committee 423 (323), "Ten-tative Recommendations for PrestressedConcrete," ACI Journal, Proceedings V.54, No. 7, January 1958, pp. 546-578.

18. Lin, T. Y., Discussion of Ref. 17, ACIJournal, Proceedings V. 54, Part 2, Sep-tember 1958, pp. 1232 -1233.

19. ACI-ASCE Committee 423 (323), Clo-sure to Discussion of Ref. 17, ACI Jour-nal Proceedings V. 54, Part 2, September1958, pp. 1232-1233.

20. ACI Committee 363, "State-of-the-ArtReport on High-Strength Concrete,"ACIJournal, Proceedings V. 81, No. 4, July-August 1984, pp. 364-411.

21. Can'asquillo, R. L., Nilson, A. H., and

56

Slate, F. O_, "Properties of High Strength 22. Jenny, D. P., "Current Status of PartialConcrete Subjected to Short-Term Prestressing for Prestressed ConcreteLoads," ACI Journal, Proceedings V. Products in North America," PCI78, No_ 3, May-June 1981, pp. 171- JOURNAL, V. 30, No. 1, January-Feb-178. ruary 1985, pp. 142-152.

APPENDIX - NOTATION

db = nominal diameter of strand, in.= specified compressive strength

of concrete, psi= compressive strength of concrete

at time of initial prestress, psiJpx = stress in prestressed reinforce-

ment at nominal strength, ksif,,„ = specified tensile strength of pre-

stressing strand, ksiJr = modulus of rupture of concrete,

psif^ = effective stress in prestressed re-inforcement (after allowance forall losses), ksi

fg3 = initial stress in prestressed rein-forcement, ksi

Ie = development length of prestress-ing strand, in.

Ir = distance from end of memberto section under consideration,in.

Ia = flexural bond length of prestress-ing strand, in.

Ir = transfer length of prestressingstrand, in.

u0, = average bond stress of prestress-ing strand within flexural bondlength, in.

NOTE: Discussion of this paper is invited. Please submit yourcomments to PCI Headquarters by May 1, 1987.

PCI JOURNALJSeptember-October 1986 57