423.5R-99 State-of-the-Art Report on Partially Prestressed ... · PARTIALLY PRESTRESSED CONCRETE...

ACI Committee RCommentaries ardesigning, executdocument is inteare competent limitations of itswho will accept rmaterial it contadisclaims any aprinciples. The Indamage arising the

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Partially prestressed contion of prestressed and nconcrete falls between thcrete and fully prestresseservice loads. When fleunder service loads, the

ACI 423.5R-99

Sarah L. BKenneth B

Robert N. Dale Buck

Ned H. Bu

Gregory P.Jack Chris

Todd Chris

Steven R.

Thomas E

Charles W

Apostolos

Mark W. F

Martin J. F

Catherine Clifford Fr

*Subcommi

State-of-the-Art Report onPartially Prestressed Concrete

Reported by Joint ACI-ASCE Committee 423

eports, Guides, Standard Practices, ande intended for guidance in planning,ing, and inspecting construction. Thisnded for the use of individuals whoto evaluate the significance and content and recommendations and

esponsibility for the application of theins. The American Concrete Institutend all responsibility for the statedstitute shall not be liable for any loss orrefrom.

his document shall not be made ints. If items found in this document arerchitect/Engineer to be a part of thets, they shall be restated in mandatoryporation by the Architect/Engineer.

423.5R

crete construction uses prestressed, or a combina-onprestressed, reinforcement. Partially prestressede limiting cases of conventionally reinforced con-d concrete, which allows no flexural tension underxural tensile stresses and cracking are allowedprestressed members have historically been called

partially prestressed. This report is presented as an overview of the currentstate of the art for partial prestressing of concrete structures. Researchfindings and design applications are presented. Specific topics discussedinclude the history of partial prestressing, behavior of partially prestressedconcrete members under static loads, time-dependent effects, fatigue, andthe effects of cyclic loadings.

Keywords: bridges; buildings; concrete construction; corrosion; cracking;crack widths; cyclic loading; deflections; earthquake-resistant structures;fatigue; partially prestressed concrete; post-tensioning; prestressing; pre-stress losses; shear; stresses; structural analysis; structural design; time-dependent effects; torsion.

Ward N. Marianos, Jr.*Chairman

Henry Cronin, Jr.Secretary

illington William L. Gamble H. Kent Preston. Bondy Hans R. Ganz Denis C. Pu

Bruce, Jr.* J. Weston Hall Julio A. Ramirez*

ner Mohammad Iqbal Ken B. Rear

rns* Francis J. Jacques Dave Rogowsky

Chacos* Daniel P. Jenny Bruce W. Russell

tiansen Paul Johal David H. Sanders

topherson Susan N. Lane Thomas Schaeffer*

Close Les Martin* Morris Schupack

. Cousins Alan H. Mattock* Kenneth W. Shushkewich

. Dolan* Gerard J. McGuire Khaled S. Soubra

Fafitis Mark Moore* Richard W. Stone

antozzi Antoine E. Naaman* Patrick Sullivan

radua Kenneth Napior Luc R. Taerwe

W. French* Thomas E. Nehil H. Carl Walker

eyermuth Mrutyunjaya Pani Jim J. Zhao

Paul Zia*

ttee preparing report (Michael Barker contributed to writing Chapters 4 and 5 of this report).

CONTENTSChapter 1—Introduction, p. 423.5R-2

1.1—Historical perspective

1.2—Definition

1.3—Design philosophy of partial prestressing

ACI 423.5R-99 became effective December 3, 1999.Copyright 2000, American Concrete Institute.All rights reserved including rights of reproduction and use in any form or by any

means, including the making of copies by any photo process, or by electronic ormechanical device, printed, written, or oral, or recording for sound or visual reproduc-tion or for use in any knowledge or retrieval system or device, unless permission inwriting is obtained from the copyright proprietors.

-1

423.5R-2 ACI COMMITTEE REPORT

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1.4—Advantages and disadvantages of partial prestressing

1.5—Partial prestressing and reinforcement inde1.6—Report objective

Chapter 2—Partially prestressed members under static loading, p. 423.5R-5

2.1—Behavior2.2—Methods of analysis2.3—Cracking2.4—Deflections2.5—Shear and torsion

Chapter 3—Time-dependent behavior, p. 423.5R-123.1—Prestress losses3.2—Cracking3.3—Deflections3.4—Corrosion

Chapter 4—Effects of repeated loading (fatigue), p. 423.5R-15

4.1—Background4.2—Material fatigue strength4.3—Fatigue in partially prestressed beams4.4—Prediction of fatigue strength4.5—Serviceability aspects4.6—Summary of serviceability

Chapter 5—Effects of load reversals, p. 423.5R-205.1—Introduction5.2—Design philosophy for seismic loadings5.3—Ductility5.4—Energy dissipation5.5—Dynamic analyses5.6—Connections5.7—Summary

Chapter 6—Applications, p. 423.5R-286.1—Early applications6.2—Pretensioned concrete components6.3—Post-tensioned building construction6.4—Bridges6.5—Other applications

Chapter 7—References, p. 423.5R-307.1—Referenced standards and reports7.2—Cited references

Appendix—Notations, p. 423.5R-36

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CHAPTER 1—INTRODUCTION1.1—Historical perspective

Application of prestressing to concrete members imparcompressive force of an appropriate magnitude at a suitlocation to counteract the service-load effects and modithe structural behavior of the members. Although the ccept of prestressed concrete was introduced almost conrently in the U.S. and in Germany before the turn of the 2century (Lin and Burns 1981), its principle was not fuestablished until Freyssinet published his classical st

s

ableesn-ur-th

dy

(Freyssinet 1933). Freyssinet recognized that as the loaa prestressed member is increased, flexural cracks wappear in the tensile zones at a certain load level, whicreferred to as the transformation load. Even though cracks would close as the load was reduced and the struwould recover its original appearance, Freyssinet advocavoiding cracks under service load so that the concwould behave as a homogeneous material.

A different design approach, however, was proposedvon Emperger (1939) and Abeles (1940). They suggeusing a small amount of tensioned high-strength steecontrol deflection and crack width while permitting highworking stresses in the main reinforcement of reinforcconcrete. Most of the early work in support of this desconcept was done by Abeles (1945) in England. Based ostudies, Abeles determined that eliminating the tensile stand possible cracking in the concrete is unnecessary in mdesigns. Abeles also realized that prestress can be applcounteract only part of the service load so that tensile stror even hairline cracks, occur in the concrete under service load. Abeles did specify that under dead load ono flexural tension stress should be allowed at any memface where large flexural tensile stresses occurred umaximum load, so as to ensure closure of any cracks may have occurred at maximum load. Additional bondand well-distributed nonprestressed reinforcement couldused to help control cracking and provide the requistrength. Abeles termed this design approach as “partprestressed concrete.” Therefore, the design approach acated by Freyssinet was then termed as “fully prestresconcrete.” In actual practice, nearly all prestressed conccomponents designed today would be “partially prestressas viewed by Freyssinet and Abeles.

Interest in partial prestressing continued in Great Britainthe 1950s and early 1960s. Many structures were desigby Abeles based on the principle of partial prestressing, examinations of most of these structures around 1revealed no evidence of distress or structural deterioraas discussed in the technical report on Partial Prestressingpublished by the Concrete Society (1983). Partiaprestressed concrete design was recognized in the FirstReport on Prestressed Concrete published by the Institutionof Structural Engineers (1951). Provisions for partprestressing were also included in the British Standard Codeof Practice for Prestressed Concrete (CP 115) in 1959. In thacode, a permissible tensile stress in concrete as high aspsi (5.2 MPa) was accepted when the maximum workload was exceptionally high in comparison with the lonormally carried by the structure. Presently, the British C(BS 8110) as well as the Model Code for Concrete Structure(1978), published by CEB-FIP, defines three classesprestressed concrete structures:

Class 1—Structures in which no tensile stress is permiin the concrete under full service load;

Class 2—Structures in which a limited tensile stress is pmitted in the concrete under full service load, but there isvisible cracking; and

423.5R-3PARTIALLY PRESTRESSED CONCRETE

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Class 3—Structures in which cracks of limited wid(0.2 mm [0.008 in.]) are permitted under full service loaCalculations for Class 3 structures would be based onhypothetical tensile stress in the concrete assuminguncracked section. The allowable values of the hypothetensile stress vary with the amount, type, and distributiothe prestressed and nonprestressed reinforcement.

Elsewhere in Europe, interest in partial prestressing developed in the 1950s and 1960s. In the mid-1950s, mprestressed concrete structures in Denmark, especbridges, were designed using the partial prestressing conTheir performance was reported as satisfactory after 25 yof service (Rostam and Pedersen 1980). In 1958, thepartially prestressed concrete bridge in Switzerla(Weinland Bridge) was completed near Zurich. Provisifor partial prestressing were introduced in SIA Standard 1issued by the Swiss Society of Engineers and Archit(1968), and since 1960, more than 3000 bridges have designed according to this concept with highly satisfacresults (Birkenmaier 1984). Unlike the British Code aCEP-FIP Model Code, the limit of partial prestressing in Swiss Code was not defined by the hypothetical tenstress. Instead, it was defined by the tensile stress inprestressed and nonprestressed reinforcement, calculated using the cracked section. Under full servload, the allowable stress in the nonprestresreinforcement was 22,000 psi (150 MPa), and in railrbridges, the stress increase in the prestressed reinforcewas not to exceed 1/20 of the tensile strength. This valuetaken as 1/10 of the tensile strength in other structures. Itrequired, however, that the concrete be in compression wthe structure supported only permanent load.

In the U.S., the design of prestressed concrete in the 1950s was largely based on the Criteria for Prestressed Concrete Bridges (1954) published by the Bureau of PubRoads, which did not permit tensile stress and crackinconcrete under service loads. The ACI-ASCE Joint Comtee 323 report (1958), however, recognized that “compfreedom from cracking may or may not be necessary atparticular load stage.” For bridge members, tensile stwas not allowed in concrete subjected to full service loFor building members not exposed to weather or corroatmosphere, a flexural tension stress limit of 6√f ′c psi* wasspecified with the provision that the limit may be exceedif “it is shown by tests that the structure will behave propeunder service load conditions and meet any necesrequirements for cracking load or temporary overloaThus, partial prestressing was permitted in that first deftive design guide for prestressed concrete, and desigwere quick to embrace the idea. When the balanced design concept was published by Lin (1963), it provideconvenient design tool and encouraged the practical apption of partial prestressing.

In 1971, the first edition of the PCI Design Handbook waspublished. Design procedures allowing tension stresses

* In this report, when formulas or stress values are taken directly from U.S. codesand recommendations, they are left in U.S. customary units.

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illustrated in that guide. The second edition (1978) mentiothe term “partial prestressing,” and by the third edition (19design examples of members with combined prestressednonprestressed reinforcement were included. Presently,318 permits a tensile stress limit of 12√f ′c psi withrequirements for minimum cover and a deflection cheSection 18.4.3 of ACI 318 permits the limit to be exceededthe basis of analysis or test results. Bridge design guidelinrecommendations, however, did not follow the developmuntil the publication of the Final Draft LRFD Specificationsfor Highway Bridges Design and Commentary (1993), eventhough most bridge engineers had been allowing tensiotheir designs for many years.

The concept of partial prestressing was developed hcentury ago. Over the years, partial prestressing has accepted by engineers to the extent that it is now the noway to design prestressed concrete structures. Bennwork (1984) provides a valuable historical summary of development of partially prestressed concrete.

1.2—DefinitionDespite a long history of recognition of the concept

partial prestressing, both in the U.S. and abroad, therebeen a lack of a uniform and explicit definition of the ter“partial prestressing.” For example, Lin and Burns (19state: “When a member is designed so that under the woload there are no tensile stresses in it, then the concresaid to be fully prestressed. If some tensile stresses wproduced in the member under working load, then itermed partially prestressed.” On the other hand, Naa(1982a) states: “Partial prestressing generally implies a cbination of prestressed and nonprestressed reinforcemboth contributing to the resistance of the member. The ato allow tension and cracking under full service loads wensuring adequate strength.” According to Nilson (198“Early designers of prestressed concrete focused on the plete elimination of tensile stresses in members at noservice load. This is defined as full prestressing. As expence has been gained with prestressed concrete construit has become evident that a solution intermediate betwfull prestressed concrete and ordinary reinforced concoffers many advantages. Such an intermediate solutiowhich a controlled amount of concrete tension is permiat full service, is termed partial prestressing.”

A unified definition of the term “partial prestressingshould be based on the behavior of the prestressed meunder a prescribed loading. Therefore, this report defpartial prestressing as: “An approach in design and constion in which prestressed reinforcement or a combinatioprestressed and non-prestressed reinforcement is usedthat tension and cracking in concrete due to flexure allowed under service dead and live loads, while serviceity and strength requirements are satisfied.”

For the purposes of this report, fully prestressed concis defined as concrete with prestressed reinforcement anflexural tension allowed in the concrete under service loConventionally reinforced concrete is defined as concwith no prestressed reinforcement and generally, ther


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flexural tension in concrete under service loads. Partprestressed concrete falls between these two limiting cServiceability requirements include criteria for crack widtdeformation, long-term effects (such as creep and shage), and fatigue.

By the previous definition, virtually all prestressed cocrete that uses unbonded tendons is “partially prestresas codes require that a certain amount of bonded reinfment be provided to meet strength requirements. Mosttensioned members used in routine applications sucbuilding decks and frames, and bridges spanning to appimately 100 ft (30 m) will allow flexural tension under fuservice load. The addition of nonprestressed reinforcemeused only in special situations, such as unusually long sor high service loads, or where camber and deflection cois particularly important.

1.3—Design philosophy of partial prestressingThe basic design philosophy for partial prestressing is

different from that of conventionally reinforced concretefully prestressed concrete. The primary objective is to vide adequate strength and ductility under factored loadto achieve satisfactory serviceability under full service lo

By permitting flexural tension and cracking in concrethe designer has more latitude in deciding the amount ofstressing required to achieve the most desirable strucperformance under a particular loading condition. Therefpartial prestressing can be viewed as a means of provadequate control of deformation and cracking of a stressed member. If the amount of prestressed reinforceused to provide such control is insufficient to develop required strength, then additional nonprestressed reinfoment is used.

In the production of precast, pretensioned concrete mbers, serviceability can be improved by placing additiostrands, as this is more economical than placing reinforbars. When this technique is used, the level of initial stress in some or all of the strands is lowered. This is auseful technique to keep transfer stresses below the mmum values prescribed by codes. At least for purposeshear design, the ACI Building Code treats any member effective prestress force not less than 40% of the testrength of the flexural reinforcement as prestressed con

1.4—Advantages and disadvantages of partial prestressing

In the design of most building elements, the specified load often exceeds the normally applied load. This isaccount for exceptional loading such as those due to imextreme temperature and volume changes, or a peakload substantially higher than the normal live loads. using partial prestressing, and by allowing higher flextension for loading conditions rarely imposed, a more enomical design is achieved with smaller sections and reinforcement.

Where uniformity of camber among different membersa structure is important, partial prestressing will enabledesigner to exercise more control of camber differential

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multispan bridges, camber control is important in improvriding comfort as a vehicle passes from one span to the The relatively large mild steel bars used in partially pstressed members result in a transformed section that csignificantly stiffer than a comparable section that resolely on prestressing strand, thus reducing both cambedeflection.

Nonprestressed reinforcement used in partially prestremembers will enhance the strength and also control cformation and crack width. Under ultimate load, a partiaprestressed member usually demonstrates greater duthan a fully prestressed member. Therefore, it will be ababsorb more energy under extreme dynamic loading suan earthquake or explosion.

Because mild steel does not lose strength as rapidly astressing strands at elevated temperature, it is someadded to prestressed members to improve their fire-rtance rating. See Chapter 9 of the PCI Design Handbook(1992) and Design for Fire Resistance of Precast Pstressed Concrete (1989) for more information.

Partial prestressing is not without some disadvantaUnder repeated loading, the fatigue life of a partially pstressed member can be a concern. In addition, durabila potential problem for partially prestressed membbecause they can be cracked under full service load. Rstudies (Harajli and Naaman 1985a; Naaman 1989; andman and Founas 1991), however, have shown that fastrength depends on the range of stress variation of the s(refer to Chapter 4) and that durability is related more to coer and spacing of reinforcement than to crack width, so tconcerns can be addressed with proper design and detof the reinforcement (Beeby 1978 and 1979).

1.5—Partial prestressing and reinforcement indexes

Several indexes have been proposed to describe the eof prestressing in a structural member. These indexeuseful in comparing relative performances of members mwith the same materials, but caution should be exerciseusing them to determine absolute values of such thingdeformation and crack width. Two of the most common inces are the degree of prestress λ, and the partial prestressinratio (PPR). These indexes are defined as

(1-1)

where

Mdec = decompression moment (the moment that produzero concrete stress at the extreme fiber of a secnearest to the centroid of the prestressing fowhen added to the action of the effective prestalone);

MD = dead-load moment; and

ML = live-load moment

and

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whereMnp = nominal moment capacity provided by prestress

reinforcement; andMn = total nominal moment capacity.

In the previous expressions, all moments are computecritical sections. This report will generally use the PPR todescribe the extent of prestressing in flexural members. tests, studies, and examples described in this report usconcern members with PPR < 1, and the members are prtensioned unless otherwise noted.

Characterizing the total amount of flexural reinforcemein a member is also important. This will be done with treinforcement index ω

(1-3)

where

andAps = area of prestressed reinforcement in tension zo

in.2 (mm2);As = area of nonprestressed tension reinforcement, 2

(mm2);A′s = area of nonprestressed compression reinfor

ment, in.2 (mm2);b = width of compression face of member, in. (mm)d = distance from extreme compression fiber to ce

troid of nonprestressed tension reinforcement, (mm);

dp = distance from extreme compression fiber to cetroid of prestressed reinforcement, in. (mm);

f ′c = specified compressive strength of concrete, (MPa);

fps = stress in prestressed reinforcement at nomstrength, psi (MPa); and

fy = yield strength of nonprestressed reinforcement,(MPa).

1.6—Report objectiveThe objective of this report is to summarize the state of

art of the current knowledge as well as recent developmin partial prestressing so that engineers who are not expenced in prestressed concrete design will have a bunderstanding of the concept.

PPRMnp

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CHAPTER 2—PARTIALLY PRESTRESSED MEMBERS UNDER STATIC LOADING

2.1—BehaviorThere are a number of investigations on the behavio

partially prestressed concrete beams under static loa(Abeles 1968; Burns 1964; Cohn and Bartlett 1982; Ha1985; Harajli and Naaman 1985a; Shaikh and Branson 1Thompson and Park 1980a; and Watcharaumnuay 1984)following results were observed for beams having the sultimate resistance in flexure but reinforced with variocombinations of prestressed and nonprestressed reinforce

• Partially prestressed beams show larger ultimate detions, higher ductility, and higher energy absorption thfully prestressed beams;• Partially prestressed beams tend to crack at lower levels than fully prestressed beams. Average crack sing and crack widths are smaller. The stiffness of ptially prestressed beams after cracking is larger;• For a given reinforcement index ω, the moment-curva-ture relationship is almost independent of the ratio oftensile reinforcement areas (prestressed versus nostressed);• Changing the effective prestress in the prestressingdons does not lead to any significant change in the mate resistance and curvature of flexural members; a• A decrease in effective prestress leads to an increayield curvature and a decrease in curvature ductility.

2.2—Methods of analysisSeveral methods can be followed to analyze parti

prestressed concrete members subjected to bending. In of assumptions, purpose, and underlying principles, theyidentical to those used for reinforced and prestresconcrete (Nilson 1976, Naaman and Siriaksorn 19Siriaksorn and Naaman 1979, Al-Zaid and Naaman 19and Tadros 1982).

2.2.1 Linear elastic analysis—In the elastic range obehavior, the analysis must accommodate either a crackan uncracked section subjected to bending, with or withprestress in the steel. The usual assumptions of plane distribution across the section, linear stress-strain relatiand perfect bond between steel and concrete remain apble. Linear elastic analysis under service loads assuminuncracked section is used for prestressed concrete. InU.S., the design of reinforced concrete is predominabased on strength requirement, but a linear elastic anaunder service loads is also necessary to check servicealimitations such as crack widths, deflections, and fatigue

Prestressed concrete beams can act as crackeuncracked sections, depending on the level of loadingcontrast to reinforced concrete, the centroidal axis of cracked section does not coincide with the neutral axis pof zero stress (Fig. 2.1). Moreover, the point of zero stress donot remain fixed, but moves with a change in applied loWhen the effective prestress tends toward zero, the poizero stress and the centroidal axis tend to coincide. Generaequations have been developed to determine the zero point based on satisfying equilibrium, strain compatibility, astress-strain relations (Nilson 1976; Naaman and Siriak1979; Siriaksorn and Naaman 1979; and Al-Zaid and Naa


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1986). They usually are third-order equations with respecmember depth. Although they can be solved iteratively, chtables, and computer programs have been developed forsolution (Tadros 1982, Moustafa 1977). These equat

provide unified treatment for cracked reinforced, prestreand partially prestressed sections.

Fig. 2.1—Assumed stress or strain distribution in linelastic analysis of cracked and uncracked sections (Naa1985).

2.2.2 Strength analysis—At ultimate or nominal momenresistance, the assumptions related to the stress and distributions in the concrete, such as the compression bin ACI 318, or the stress and strain in the steel (such as ying of the reinforcing steel) are identical for reinforced, pstressed, and partially prestressed concrete (Fig. 2.2). Thecorresponding analysis is the same and leads to the nomoment resistance of the section. Numerous investigahave shown close correlation between the predicted (bon ACI 318) and experimental values of nominal momeThe ACI 318 analysis, however, resulted in conservapredictions of section curvatures at ultimate load, leadinerroneous estimates of deformations and deflections (Wet al. 1978, Naaman et al. 1986). To improve the predicof nominal moment and curvature, either a nonlinear simplified nonlinear analysis may be followed.

Simplified nonlinear analysis—In the simplified nonlinearanalysis procedure (also called pseudo-nonlinear analythe actual stress-strain curve of the steel reinforcemeconsidered while the concrete is represented by the ACcompression block. A solution can be obtained by solvtwo nonlinear equations with two unknowns, namely stress and the strain in the prestressing steel at nommoment resistance (Naaman 1977, Naaman 1983b).

Nonlinear analysis—The best accuracy in determininnominal moments and corresponding curvatures is achithrough a nonlinear analysis procedure (Cohn and Ba1982, Naaman et al. 1986, Harajli and Naaman 19Moustafa 1986). Nonlinear analysis requires as inpuaccurate analytical representation of the actual stress-scurves of the component materials (concrete, reinforsteel, and prestressing steel). Typical examples can be in two references (Naaman et al. 1986, Moustafa 1986)

n

Fig. 2.2—Assumed strain distribution and forces in: (nonlinear analysis; (b) approximate nonlinear analysand (c) ultimate strength analysis by ACI Code (Naam1985).

2.3—CrackingPartially prestressed concrete permits cracking under

vice loads as a design assumption. To satisfy servicearequirements, the maximum crack width should be equal smaller than, the code-recommended limits on crack wid

The maximum allowable crack widths recommendedACI Committee 224 (1980) for reinforced concrete membcan be used, preferably with a reduction factor for stressed and partially prestressed concrete memberselect the reduction factor, consideration should be givethe small diameter of the reinforcing elements (barsstrands), the cover, and the exposure conditions.

Only a few formulas are used in the U.S. practice to precrack widths in concrete flexural members. Because thetors influencing crack widths are the same for reinforcedpartially prestressed concrete members, existing formfor reinforced concrete can be adapted to partially stressed concrete. Five formulas (ACI 224 1980; Gerand Lutz 1968; Nawy and Potyondy 1971; Nawy and Hu1977; Nawy and Chiang 1980; Martino and Nilson 1979;Meier and Gergely 1981) applicable to partially prestrebeams are summarized in Table 2.1 (Naaman 1985). The var

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able tensile stress in the reinforcing steel fs should be replacedby the stress change in the prestressing steel after decomsion ∆fps. The ACI 318 formula initially developed bGergely and Lutz (1968) for reinforced concrete couldused as a first approximation for partially prestressed ccrete. Meier and Gergely (1981), however, suggested a mified form (shown in Table 2.1) for the case of prestresseconcrete. This alternate formula uses the nominal strathe tensile face of the concrete (instead of the stress insteel), and the cover to the center of the steel dc. Both thestress in the steel and the clear concrete cover are foundthe controlling variables in the regression equation deriby Martino and Nilson (1979). The two prediction equatioproposed by Nawy and Huang (1977) and Nawy and Ch(1980) contain most of the important parameters found incracking behavior of concrete members except the concover, which is accounted for indirectly. Moreover, they based on actual experimental results on prestressed antially prestressed beams.

As pointed out by Siriaksorn and Naaman (1979), ladifferences can be observed in predicted crack widdepending on the prediction formula used. Harajli and Nman (1989) compared predicted crack widths with obsercrack widths from tests on twelve partially prestressed ccrete beams. They considered the three prediction equarecommended by Gergely and Lutz (1968), Nawy and H

es-

-d-

athe

bed

gete

ar-

es

ng (1977), and Meier and Gergely (1981). Although nonthe three equations gave sufficiently good correlation wexperimental data for all conditions, the following obsertions were made (Fig. 2.3):

• The Gergely and Lutz equation gave a lower predicin all cases (Fig. 2.3(a)); • The Meier and Gergely equation gave the worst colation (Fig. 2.3(c)); and • The Nawy and Huang equation gave a higher predicin most cases (Fig. 2.3(b)).

Although more experimental data are needed to imprthe accuracy of crack-width prediction equations availablU.S. practice, there is sufficient information to judge if tserviceability, with respect to cracking or crack width unshort-term loading, is satisfactory for a partially prestresmember. The effects of long-term loading and repetiloading (fatigue) on the crack widths of partially prestresmembers need to be further clarified. A research investion provided an analytical basis to deal with the prob(Harajli and Naaman 1989); however, the proposed metology is not amenable to a simple prediction equation can be easily implemented for design.

(1) (1) Same equation

(2) (2) Multiply by 220

Table 2.1—Crack width prediction equations applicable to partially prestressed beams (Naaman 1985)

Source Equation* with U.S. system, (in., ksi) Equation* with SI system, (mm., N/mm2)

Gergely and Lutz (1968)ACI Code (1971, 1977, and 1983)ACI Committee 224 (1980)

Multiply expression by 0.1451

fs = tensile stress in reinforcing steel

dc = concrete cover to center of closest bar layerAb = concrete tensile area per barβ = ratio of distances from tension face and steel centroid to neutral axis

Note: ACI Committee 224 recommends multiplication factor of 1.5 when strands, rather than deformed bars, are used nearest to beam tensile face.

Nawy and Potyondy (1971)

Nawy and Huang (1977)Nawy and Chiang (1980) Multiply expression by 0.1451

At = area of concrete tensile zoneΣO = sum of perimeters of bonded reinforcing elements ∆fps = net stress change in prestressing steel after decompression

α =

Martino and Nilson (1979)d′c= concrete clear cover

Meier and Gergely (1981) C1, C2 = bond coefficientsFor reinforcing bars: C1 = 12; C2 = 8.4For strands: C1 = 16; C2 = 12εct = nominal concrete tensile strain at tensile face

*In the formulas shown, fs can be replaced by ∆fps when applied to partially prestressed concrete.

Wmax 7.6 10 5 – βfs× dcAb3=

Wmax 1.44 104– fs 8.3–( )×= 5.31 104– fs 57.2–( )×=

Wmax α 10 5– β At

ΣO--------∆fps×=

5.85 if pretensioning

6.51 if post-tensioning

Wmax 14 10 5– d′c fs 0.0031+×= 2 10 5– d′c fs 0.08+×=

Wmax C1εctdc =

Wmax C2εctdc Ab3=

-d-ns-

2.4—DeflectionsFully prestressed concrete members are assumed

uncracked and linearly elastic under service loads. Instantashort-term deflections are determined using gen


e

t ofn-rchers ins. Thean

pre-ts as-ctionend-r theat thete ofros’ma-n theen-

who ofgr and cur-

edloadon-nts a

Fig. 2.3—Comparison of observed and theoretically predictcrack widths (Naaman 1985).

onsert

tia s o

rs sseriz

son83art982n obeef th

iedre- the1).ndder

achf thehearnge

tingage,rcesbothd it to

principles of mechanics. To compute short-term deflecticustomary U.S. practice is to use the gross moment of inIg for pretensioned members, or the net moment of inerInfor members with unbonded tendons, and the moduluelasticity of concrete at time of loading or transfer Eci.Several approaches proposed by various researchecompute short-term and long-term deflections in prestreor partially prestressed uncracked members are summain Table 2.2 (Branson and Kripanarayanan 1971; Bran1974; Branson 1977; Naaman 1982a; Naaman 19Branson and Trost 1982a; Branson and Trost 1982b; M1977; Tadros et al. 1975; Tadros et al. 1977; Dilger 1and Moustafa 1986). Although no systematic evaluatiocomparison of these different approaches has undertaken, for common cases they lead to results osame order.

The widely accepted concept of the effective momeninertia Ieff, initially introduced by Branson (1977) for reiforced concrete, has been examined by several reseaand modified accordingly to compute the deflectioncracked prestressed and partially prestressed membermodified effective moment of inertia is defined (Naam1982a) as

(2-1)

whereIg = gross moment of inertia, in.4 (mm4);Icr = moment of inertia of cracked section, in.4 (mm4);Mcr = cracking moment, in.-k (mm-N);Mdec = decompression moment, in.-k (m-N); andMa = applied moment, in.-k (m-N).

Although there is general agreement for the use of thevious expression, substantial divergence of opinion existo the computation of Icr and Mdec. The computation difference is whether the moment of inertia of the cracked seshould be computed with respect to the neutral axis of bing or with respect to the zero-stress point, and whethedecompression moment should lead to decompression extreme concrete fiber or whether it should lead to a stazero curvature in the section. The discussion of Tadpaper (1982) by several experts in the field is quite infortive on these issues. A systematic comparison betweevarious approaches, combined with results from experimtal tests, is given in work by Watcharaumnuay (1984), observed that the use of Icr with respect to the neutral axisbending is preferable, while the use of Mdec as that causindecompression at the extreme concrete fiber, is easieleads to results similar to those obtained using the zerovature moment.

Ieff I cr Mcr Mdec–( ) Ma Mdec–( )⁄( )3 +=

Ig Icr–( ) Ig≤

,ia

f

toded

a;in;rne

d

2.5—Shear and torsion2.5.1 General—Nonprestressed and fully prestress

concrete (tensile stress in the concrete under full service is zero) are the two limiting cases of steel-reinforced ccrete systems. Partially prestressed concrete represecontinuous transition between the two limit cases. A unifapproach in design to combined actions including partial pstressing would offer designers a sound basis to makeappropriate choice between the two limits (Thurlimann 197

The equivalent load concept provides a simple aefficient design of prestressed concrete structures uncombined actions (Nilson 1987). For example, this approallows the designer to calculate the shear component oprestress anywhere in the beam, simply by drawing the sdiagram due to the equivalent load resulting from a chain the vertical alignment of the tendon (Fig. 2.4). Thatequivalent load, together with the prestressing forces acat the ends of the member through the tendon anchormay be looked upon as just another system of external foacting on the member. This procedure can be used for statically determinate and indeterminate structures, anaccounts for the effects of secondary reactions due


Table 2.2—Deflection prediction equations for prestressed and partially prestressed beams (from Naaman 1985)

SourceShort-term instantaneous

deflectionLong-term or additional long-term

deflection Remarks

ACI 435 (1963)∆t is obtained from elastic

analysis using Ft, Ect, and Ig.

Long-term deflection obtained by integrating curvatures with due

account for creep effects and prestress losses with time.

• Uncracked section; and• No provisions for As and A′s.

ACI Code Section 9.5 (1971, 1977, and 1983)

∆t shall be obtained from elastic analysis using Ig for

uncracked sections.

∆add shall be computed, taking into account stresses under sustained load, including effects of creep, shrinkage,

and relaxation.

• No provisions for partialprestressing (cracking, Asand A′s).

Branson et al. (1971, 1974, and 1977)

∆t is obtained from elastic analysis using Ect and Ig.

whereCCU = ultimate creep coefficient of concrete;η = F/Ft;kr = 1/(1 + As/Aps); andKCA = age at loading factor for creep

• Uncracked section;• kr is applicable only when

(∆t)Ft + G is a camber; and• Ft = initial prestressing force

immediately after transfer.

Naaman (1982 and 1983)

∆t is obtained using Ig and the predicted elastic modulus at

time of loading Ec (t).

The long-term deflection is estimated from:

whereφ1(t) = midspan curvature at time t;φ2(t) = support curvature at time t;φ(t) = M/[Ece(t) × I]; andEce(t) = equivalent modulus

• Uncracked section;• The pressure line is assumed

resulting from the sustainedloadings;

• The profile of the pressureline is assumed parabolic;

• Prestress losses must beestimated a priori;

• Design chart is provided forthe equivalent modulus; and

• As and A′s are accounted forthrough It and neutral axis ofbending.

Bronson and Trost (1982)

For cracked members, the short-term deflection is

computed using Ieff modified for partial prestressing.

Long-term deflection is not addressed but it is assumed that for a given ∆t, the

earlier method is applicable.• Cracked members.

Martin (1977)∆t is obtained from elastic analysis using Ect and Ig.

• kr = same as Branson;• Uncracked section; • Design values of λ1 and λ2

were recommended; and• The method is adopted in

PCI Design Handbook.

Tadros et al. (1975 and 1977)

∆t is obtained from elastic analysis using Ec(t) and Ig.

The long-term deflection is obtained by integrating the curvatures modified by a creep recovery parameter and a relaxation reduction factor that are

time-dependent.

• Uncracked sections; and • For common loading cases,

only the curveatures at thesupport and midspansections are needed.

Dilger (1982)

∆t is obtained from long-term deflection expression at initial loading time. The age adjusted effective modulus and a creep transformed moment of inertia

are used.

The long-term deflection is obtained by integrating the curvature along the member. The time-dependent curvature is modified by the effect of an equivalent force acting at the centroid of the prestressing steel due to creep and shrinkage strain.

Itr = transformed moment of inertia;Mc = moment due to equivalent transformed force; andEca(t) = age adjusted modulus

• Uncracked sections; and• A relaxation reduction factor

is used.

Moustafa (1986)∆t is obtained from nonlinear analysis using actual material

properties.

The nonlinear analysis takes both creep and shrinkage into account, using ACI creep and shrinkage

functions and a time step method.

• A computer program isavailable from PCI toperform the nonlinearanalysis.

∆add η 1 1 η+2

------------- krCcu+–=

∆t( )FtkrCCU ∆t( )G KCA+ + krCCU ∆t( )SD

∆ t( ) φ1 t( ) l2

8--- φ2 t( ) φ1 t( )–[ ] l2

48------+=

∆add λ1 ∆i( )G λ2 ∆i( )Fi+=

λ1 krEci

Ec

------α=

α 2 1.2As′ As⁄–( ) 0.6≥=

λ2 ηλ 1=

φ t( ) φiCc t( ) Mc

I tr Eca t( )--------------------–=


r s eete

aed

r to

onarettrites

rceuc

asnt

houtsionsto theent.res-ion,

inls, as face the

loadhis

rce-

on- thelained

andinal

1987);

prestressing, as well. This approach allows the designetreat a prestressed concrete member as if it wanonprestressed concrete member. The prestressing sttreated as mild (passive) reinforcement for ultimaconditions, with a remaining tensile capacity of (fps – fpe),where fps is the stress in the reinforcement at nominstrength, and fpe is the effective stress in the prestressreinforcement (after allowance for all losses).

Most codes of practice (ACI 318; AASHTO BridgeDesign Specifications, Eurocode 2; and CSA Design of Con-crete Structures for Buildings) use sectional methods fodesign of conventional beams under bending, shear, andsion. Truss models provide the basis for these sectidesign procedures that often include a term for the conccontribution (Ramirez and Breen 1991). The concrete conbution supplements the sectional truss model to reflect results in beams and slabs with little or no shear reinfoment and to ensure economy in the practical design of smembers.

In design specifications, the concrete contribution hbeen taken as either the shear force or torsional mome

toal is

l

cracking, or as the capacity of an equivalent member wittransverse reinforcement. Therefore, detailed expreshave been developed in terms of parameters relevant strength of members without transverse reinforcemThese parameters include the influence of axial compsion, member geometry, support conditions, axial tensand prestress.

Fig. 2.4—Equivalent loads and moments produced by prestressing tendons (NilsonP = prestressing force.

r-le-t-h

at

2.5.2 Shear—The following behavioral changes occurpartially prestressed members at nominal shear levesome of the longitudinal prestressing steel in the tensionof the member is replaced by mild reinforcement, butsame total flexural strength is maintained:

• Due to the lower effective prestress, the external required to produce inclined cracking is reduced. Tresults in an earlier mobilization of the shear reinfoment; and• After inclined cracking, there is a reduction in the ccrete contribution. The reduction is less significant asdegree of prestressing decreases. This can be expas follows:

•The addition of mild reinforcement results in increase in the cross-sectional area of the longitu


ss

ionck thre-.erthire resaam t t

bg

tiothetir

fon re a

onea

eairrua

libr

fth

theer

urad td H

forenpre

a-n

el ckitrule rs

re th

ctood

russdes

hin-hear onlye is thick-nsted bytion.sionnantthan pro-

st tor-outerross

thin-

retete

flowonsle toto

y thetress-l ten-ue

pre-exter- the

ionsroms the addi- ofas

con-beeneim

m-r has

tension reinforcement and the reinforcement stiffneand•The increase in stiffness of the longitudinal tensreinforcement delays the development of the craing pattern, so that the cracks are narrower andflexural compression zone is larger than in fully pstressed members of comparable flexural strength

These behavioral changes are well documented in a sof shear tests carried out by Caflisch et al. (1971). In series of tests, the only variable was the degree of presting. The cross sections of the prestressing steel and theforcing steel were selected so that all the beams had the flexural strength. These tests also showed that for the sexternal load, a higher degree of prestressing delaysonset of diagonal cracking and results in a decrease instirrup forces. The decrease in stirrup forces canexplained by the fact that a higher degree of prestressinthe web of the member results in a lower angle of inclinaof the diagonal cracks. The lower angle of inclination of cracks leads to the mobilization of a larger number of srups.

In ACI 318, a cursory review of the design approach shear indicates that partially prestressed members cadesigned following the same procedure as for fully pstressed members. In ACI 318, it is assumed that flexureshear can be handled separately for the worst combinatiflexure and shear at a given section. The analysis of a bunder bending and shear using the truss approach clindicates that, to resist shear, the member needs both stand longitudinal reinforcement. The additional longitudintension force due to shear can be determined from equium conditions of the truss model as (V cot θ), where V is theshear force at the section, and θ is the angle of inclination othe inclined struts with respect to the longitudinal axis of member.

In the shear provisions of ACI 318, no explicit check of shear-induced force in the longitudinal reinforcement is pformed (Ramirez 1994). The difference between the flexstrength requirements for the prestress reinforcement anultimate tensile capacity of the reinforcement can be usesatisfy the longitudinal tension requirement. The 1994 AASTO LRFD Bridge Design Specifications, in the section shear design, includes a check for longitudinal reinforcemThese recommendations are based on a modified comsion field theory (Vecchio and Collins 1986).

2.5.3 Torsion—ACI 318 includes design recommendtion for the case of torsion or combined shear and torsioprestressed concrete members. These provisions modbehavior of a prestressed concrete member before craas a thin-walled tube and after cracking using a space-model with compression diagonals inclined at an angθaround all faces of the member. For prestressed membeθcan be taken equal to 37.5 degrees if the effective presting force is not less than 40% of the tensile strength ofprestressed reinforcement. For other cases, θ can be takenequal to 45 degrees. This approach is based on the workried out in the 1960s and 1970s by European investigaled by Thurlimann (1979). This work proposed a meth

;

-e

iessss-in-mee

heheeinn

-

rbe-nd ofm

rlyps

li-

e

-lheto-

t.s-

inthengss

, ss-e

ar-rs

supported by the theory of plasticity, in which a space twith variable inclination of compression diagonals provia lower-bound (static) solution.

This procedure is representative of the behavior of twalled tubes in torsion. For these members, the sstresses induced by torsion can be determined usingequilibrium relationships. Because the wall of the tubthin, a constant shear stress can be assumed across itsness. In the longitudinal direction, equilibrium conditiodictate that the torsion-induced shear stresses be resisa constant shear flow around the perimeter of the secFor other sections before cracking, the strength in torcan be computed from the elastic theory (de Saint-Ve1956) or from the plastic theory (Nadai 1950). Rather using these more complex approaches, an approximatecedure is used in ACI 318 based on the concept that mosion is resisted by the high shear stresses near the perimeter of the section. In this approach, the actual csection before cracking is represented by an equivalentwalled tube with a wall thickness t of

(2-2)

where Acp = area enclosed by outside perimeter of conccross section, and Pcp = outside perimeter of the concrecross section. While the area enclosed by the shearpath, Ao, could be calculated from the external dimensiand wall thickness of the equivalent tube, it is reasonabapproximate it as equal to 2Acp/3. Cracking is assumed occur when the principal tensile stress reaches 4√f ′c . For pre-stressed members, the cracking torque is increased bprestress. A Mohr’s Circle analysis based on average ses indicates that the torque required to cause a principasile stress equal to 4√f ′c is the corresponding cracking torqof a nonprestressed beam times

(2-3)

where fpc in psi is the average precompression due to stress at the centroid of the cross section resisting the nally applied loads or at the junction of web and flange ifcentroid lies within the flange.

In ACI 318, the design approach for combined actdoes not explicitly consider the change in conditions fone side of the beam to the other. Instead, it considerside of the beam where shear and torsional effects aretive. After diagonal cracking, the concrete contributionthe shear strength Vc remains constant at the value it hwhen there is no torsion, and the torsion carried by thecrete is taken as zero. The approach in ACI 318 has compared with test results by MacGregor and Ghon(1995).

In the AASHTO LRFD Specifications, the modified copression field theory proposed for members under shea

t 0.75 Acp

Pcp

--------=

1fpc

4 fc′-------------+


eous

oragepre-pre-

ep ofthodspre-

loss-ss duetime-ns—-

ingre-

barscrete thanr is as arizedg par-p ofe and overared in

waslues-n be

ain the

e-n uce

asal andd by

ndd totiallyer the

lly loads985)g theate of and

ts

n itupe foCce

te p

ine ietefoalsinn

thilire

bsid

tur inotaver

t ed

).

been extended to include the effects of torsion. Similar toACI 318 procedure, the AASHTO approach concentratethe design of the side of the beam where the shear andsional stresses are additive.

As in the case of shear, torsion leads to an increase itensile force on the longitudinal reinforcement. The longdinal reinforcement requirement for torsion should be suimposed with the longitudinal reinforcement requirementbending that acts simultaneously with the torsion. In A318, the longitudinal tension due to torsion can be reduby the compressive force in the flexural compression zonthe member. Furthermore, in prestressed beams, thelongitudinal reinforcement, including tendons at each stion, can be used to resist the factored bending momentthe additional tension induced by torsion at that section.

ACI 318 and AASHTO Specifications recognize that,many statically indeterminate structures, the magnitudthe torsional moment in a given member will depend ontorsional stiffness. Tests have shown (Hsu 1968) that whmember cracks in torsion, its torsional stiffness immediaafter cracking drops to approximately 1/5 of the value becracking, and at failure can be as low as 1/16 of the vbefore cracking. This drastic drop in torsional stiffneallows a significant redistribution of torsion in certaindeterminate beam systems. In recognizing the reductiotorsional moment that will take place after cracking in case of indeterminate members subjected to compatibinduced torsion, ACI 318R states that a maximum factotorsional moment equal to the cracking torque canassumed to occur at the critical sections near the facesupports. This limit has been established to control the wof the torsional cracks at service loads.

CHAPTER 3—TIME-DEPENDENT BEHAVIOR3.1—Prestress losses

The stress in the tendons of prestressed concrete strucdecreases continuously with time. The total reductionstress during the life span of the structure is termed “tprestress loss.” The total prestress loss consists of se

components, which are generally grouped into instantanand time-dependent losses.

Instantaneous losses are due to elastic shortening, anchseating, and friction. They can be computed for partially stressed concrete in a manner similar to that for fully stressed concrete.

Time-dependent losses are due to shrinkage and creconcrete and relaxation of prestressing steel. Several meare available to determine time-dependent losses in stressed concrete members: lump-sum estimate of totales, lump-sum estimates of separate losses (such as loto shrinkage or creep), and calculation of losses by the step method. Because the numerical expressiodescribed, for instance, in the AASHTO’s Standard Specifications for Highway Bridges or the PCI Design Handbook(1992)—for the first two methods were developed assumfull prestressing, they are not applicable to partially pstressed members.

The combined presence of nonprestressed reinforcingand a lower level of prestress in partially prestressed conshould lead to smaller time-dependent prestress lossesfor fully prestressed concrete. Another significant factothat a partially prestressed member can be designedcracked member under sustained loading. A computetime-step analysis of the concrete and steel stresses alontially prestressed sections shows that the effect of creeconcrete on the stress redistribution between the concretsteel tends to counteract the effect of prestress lossestime. This is particularly significant for members that cracked under permanent loads. The result is illustrateFig. 3.1 (Watcharaumnuay and Naaman 1985), which derived from the analysis of 132 beams with various vaof the partially prestressed ratio (PPR) and the reinforcement index ω. While time-dependent prestress losses ca14% for uncracked fully prestressed sections, they remlow for cracked sections up to relatively high values ofPPR. Fig. 3.1 also shows that for uncracked sections, timdependent prestress losses decrease with a decrease iPPR.Creep redistribution of force to reinforcing steel may redthe precompression in the concrete.

An investigation under NCHRP Project 12-33 haddressed prestress losses in partially prestressed normhigh-strength concrete beams. This work was describeNaaman and Hamza (1993) and was adopted in the FinalDraft LRFD Specifications for Highway Bridge Design aCommentary (Transportation Research Board 1993). It lelump-sum estimates of time-dependent losses for parprestressed beams that are assumed uncracked unddesign sustained loading. These are summarized in Table 3.1and can be used as a first approximation in design.

heontor-

the-r-rIed ofotalc-lus

oftsn alyreues

ofety-de ofth

nder

Fig. 3.1—Typical stress change in prestressing steel aof service life for sections cracked and uncracked unpermanent loads (Watcharaumnuay and Naaman 1985

3.2—CrackingCrack widths in reinforced and cracked partia

prestressed concrete members subjected to sustainedare known to increase with time. Bennett and Lee (1reported that crack widths increase at a fast rate durinearly stages of loading then tend toward a slow steady rincrease. This is not surprising because deflections

es

lal


Table 3.1—Time-dependent losses, ksi (LRFD Bridge Design Specifications 1994)

Type of beam section Level

For wires and strands withfpu = 235, 250, or 270 ksi For bars with fpu = 145 or 160 ksi

Rectangular beams and solid slab

Upper bound 29.0 + 4.0 PPR19.0 + 6.0 PPR

Average 26.0 + 4.0 PPR

Box girder Upper bound 21.0 + 4.0 PPR15.0

Average 19.0 + 4.0 PPR

I-girder Average 19.0 + 6.0 PPR

Single-T, double-T, hollow core, and

voided slab

Upper bound

Average

33.0 1.0 0.15fc′ 6.0–

6.0-------------------– 6.0PPR+

39.0 1.0 0.15fc′ 6.0–

6.0-------------------– 6.0PPR+

31.0 1.0 0.15fc′ 6.0–

6.0-------------------– 6.0PPR+

33.0 1.0 0.15fc′ 6.0–

6.0-------------------– 6.0PPR+

se

odessef ali

ngio

re

threa

88reinlethoamd

eBar

fu w

w

naone

n

post-

me-ially

sedchersdros88;89).od toplyckedn is withromime

ndms

camber increase with time. Crack widths, however, repreonly localized effects, and their relative increase with timenot proportional to the increase of deflections.

No studies have been reported where an analytical mof crack width increase with time was developed. An invtigation by Harajli and Naaman (1989), however, discusin Chapter 4 of this report, has led to the development omodel to predict the increase in crack width under cycfatigue loading. The model accounts for the effect of chain steel stress due to cyclic creep of concrete in compressthe increase in slip due to bond redistribution, and concshrinkage.

3.3—DeflectionsSeveral experimental investigations have dealt with

time-dependent deflection of partially prestressed concmembers (Bennett and Lee 1985; Bruggeling 1977; Jittawand Tadros 1979; Lambotte and Van Nieuwenburg 19Abeles 1965; and Watcharaumnuay and Naaman 19Deflections and cambers in partially prestressed concmembers are expected to vary with time similarly to reforced or fully prestressed concrete. When positive deftion (opposite to camber) is present, in all cases deflection in partially prestressed beams falls between thof reinforced concrete and fully prestressed concrete be(Fig. 3.2). A limited experimental study by Jittawait anTadros (1979) also seems to confirm this observation.

A study of the long-term behavior of partially prestressbeams has been conducted at the Magnel laboratory in gium (Lambotte and Van Nieuwenburg 1986). Twelve ptially prestressed beams with PPR of 0.8, 0.65, and 0.5 wereeither kept unloaded or were loaded with an equivalent service load. For the unloaded beams, increased cambertime was generally observed for PPR = 0.8; for PPR = 0.65,the camber reached a peak value and then decreasedtime, resulting in a practically level beam; and for PPR = 0.5,the initial camber decreased with time, resulting in a fidownward deflection. For the loaded beams, deflectiwere observed in all cases and increased with time. Thobservations are illustrated in Fig. 3.3. After 2 years of load-ing, the ratio of additional deflection to the initial deflectio

s

del--

llith

ith

lsse

was about 1.25 for pretensioned members and 1.5 for tensioned members.

Several analytical investigations have dealt with the tidependent deflections of prestressed and partprestressed beams assumed to be uncracked (Table 2.2). Theevaluation of deflections for cracked, partially prestresmembers has been conducted by several resear(Branson and Shaikh 1985; Ghali and Tadros 1985; Taet al. 1985; Ghali and Favre 1986; Al-Zaid et al. 19Elbadry and Ghali 1989; Ghali 1989; and Founas 19Watcharaumnuay and Naaman (1985) proposed a methdetermine time- and cyclic-dependent deflections in simsupported, partially prestressed beams in both the craand uncracked state. The time-dependent deflectiotreated as a special case of cyclic deflection. Comparedthe time-step method where the deflection is obtained fthe summation of deflection increments over several t

ntis

el-d

cen,te

eteit

6;5).te-c-ese

Fig. 3.2—Long-term deflections of fully prestressed apartially prestressed (cracked and uncracked) bea(Naaman 1982); 1 in. = 25.4 mm.


ine9889ll

ee anh i

n tran

io

nd

n

e

oxi-

at

oef-tees.

etterin assedgents.ions,stedssedber intratedams usedheseaused the

ilitystud-achst ofted. thanssingakingivid-mall,ively wire

rur

ra

intervals, this method leads to the deflection at any time t andcycle N directly. The method satisfies equilibrium and stracompatibility. Using a slightly different approach, thmethod proposed by Watcharaumnuay and Naaman (1was generalized by Al-Zaid et al. (1988) and Founas (19and was extended to include composite beams as wenoncomposite beams.

In dealing with time-dependent deflections, several timdependent variables should be determined. These includprestressing force, the moment of inertia of the section, the equivalent modulus of elasticity of the concrete. Texpression for the effective moment of inertia describedEq. (2-1) can be used. In this expression, however, Mcr andIcr are time-dependent variables because they depend ovalue of the prestressing force and the location of the neuaxis (zero stress point along the section), both of which vwith time. The equivalent modulus of elasticity of the cocrete depends on the variation of creep strain with time.

The following method can be used to estimate deflectat any time t in a cracked, simply supported beam

(3-1)

where

∆ t( )KDM

Ece t( )Ieff t( )-----------------------------

KFF t( )Ece t( )Ieff t( )-----------------------------+=

KD, KF = constants depending on type of loading asteel profile;

M = sustained external moment at midspan;

F(t) = prestressing force at time t;

Ieff (t) = effective moment of inertia of cracked sectioat time t; and

Ece(t) = equivalent elastic modulus of concrete at timt.

The eqivalent elastic modulus of concrete can be apprmated by the following equation

(3-2)

where

t = time or age of concrete;

tA = age of concrete at time of loading;

Ec(t) = instantaneous elastic modulus of concretetime t;

and

Cc (t - tA) = creep coefficient of concrete at time t whenloaded at time tA.

Several expressions are available to predict the creep cficient of concrete. The recommendations of ACI Commit209 (1982) can be followed in most common application

Ece t( )Ec t( )

1 Cc t tA–( )+--------------------------------=

g

5)),as

-thed

en

thealry-

n

3.4—CorrosionThe reinforcement in a fully prestressed member is b

protected against corrosion than the reinforcement partially prestressed member. Cracks in partially prestrebeams are potential paths for the passage of corrosive aAlthough corrosion also occurs along uncracked sectcracking can facilitate corrosion. Abeles (1945) suggethat corrosion of the prestressing steel in partially prestremembers can be mitigated by requiring that the memfaces that are cracked under full service load becompression under permanent (dead) loads. He demonsthe effectiveness of this strategy in the behavior of bepartially prestressed using small-diameter wires that werein the roof of an engine shed for steam locomotives. Tbeams successfully resisted a very corrosive atmosphere cby the mixture of smoke and steam ejected onto them fromfunnels of the locomotives.

Limiting the size of crack widths to reduce the probabof corrosion has been common practice in design. Later ies (ACI 222R-89), however, move away from this approby pointing out that corrosion is due to many causes, mowhich can proceed with or without cracking to be activaCorrosion in prestressing steels is much more seriouscorrosion in nonprestressed reinforcing steels. Prestresteel is generally stressed to over 50% of its strength, mit susceptible to stress corrosion, and the diameter of indual prestressing steel wires is relatively small. Even a suniform corrosive layer or a corroded spot can progressreduce the cross-sectional area of the steel and lead tofailure.

n

Fig. 3.3(a)—Variation with time of midspan deflection founloaded specimens (Lambotte and Van Nieuwenb1986); 1 in. = 25.4 mm.

Fig. 3.3(b)—Variation with time of midspan deflection fospecimens under service loading (Lambotte and VNieuwenburg 1986); 1 in. = 25.4 mm.


ndak

n

ro, franrind t-m-

hadeon

m.0io

ob

oadsACIpar- thanpre-

eas-ue asths

allye is a

ritish the torit-

full- psice load and

Corrosion is mostly an electrochemical problem ashould be treated accordingly. Precautions should be tto prevent or to reduce prestressing steel corrosion.

ACI 423.3R addresses the historical causes of corrosiounbonded tendons. The Post-Tensioning Manual (Post-Ten-sioning Institute 1990) provides guidance for corrosion ptection for bonded and unbonded tendons. Occasionallypretensioned concrete, epoxy-coated prestressing sthave been specified for corrosive environments. High cutemperatures, however, could adversely affect the bonepoxy-coated strand. Guidelines for the Use of Epoxy-Coaed Strand (PCI Ad Hoc Committee 1993) contains recomendations for its use.

Lenschow (1986) reported that crack widths less t0.004 to 0.006 in. (0.1 to 0.15 mm), which develop unmaximum load, will heal under long-term compressiCrack widths that increase to less than 0.01 in. (0.3 munder rare overload (every 1 to 3 years) can reduce to 0to 0.006 in. (0.1 to 0.15 mm) under sustained compressKeeping crack widths under such limits should avoid prlems with corrosion.

hemb

tigu arac

y bmin, aer Thho

ues vicaadinaue s

upuent thens firck

ssioens

reamaan

theo 550vior

ackshe

cyclicuct- per-

ntalird-. Thewith. One m)twocon- hadof the

heber ofs MPa) thelightthere per-g.ird- flex-94% thatsuredment-

CHAPTER 4—EFFECTS OF REPEATEDLOADING (FATIGUE)

4.1—BackgroundTwo major requirements should be considered w

designing members subjected to repeated loads: mestrength and serviceability. The static strength and fastrength of the member should exceed loads imposedadequate serviceability requirements (deflection and ccontrol) should be provided.

The fatigue strength of a member is affected primarilthe stress range (difference between maximum and mum stress), the number of load applications or cyclesthe applied stress levels. The fatigue life of a membdefined as the number of load cycles before failure. higher the stress range imposed on the member, the sthe fatigue life.

Reliability analyses indicate that the probability of fatigfailure of reinforcement in partially prestressed beamhigher on average than failure by any other common serability or ultimate limit state criterion (Naaman 1985, Nman and Siriaksorn 1982). Fatigue can be a critical loacondition for partially prestressed concrete beams bechigh stress ranges can be imposed on the member in thvice-load range (Naaman and Siriaksorn 1979).

Partially prestressed concrete beams generally crackfirst application of live load (Naaman 1982b). Subseqapplications of live load cause the cracks to reopen adecompression load (when the stress at the extreme tface is zero), which is less than the load that causedcracking. To maintain equilibrium in the section after craing, the neutral axis shifts toward the extreme comprefiber. This shift generates higher strains (stresses) in the treinforcement.

Under repeated loads, the larger stress changes (cby opening and closing of the cracks) cause fatigue dain the constituent materials, bond deterioration,

en

in

-ordsgof

nr.)

04n.-

nerendk

yi-

ndiserter

ise--gseer-

onteilest-nile

tedged

increased crack widths and deflections under service l(Naaman 1982b; Shakawi and Batchelor 1986; and Committee 215 1974). The increase in crack widths in tially prestressed beams, however, has been smallerthat generated in similarly loaded, precracked, fully stressed beams (Harajli and Naaman 1984).

Because the proportion of dead to total load often incres as the span length increases, the significance of fatiga critical limit state tends to diminish as span lengincrease (Freyermuth 1985).

Abeles demonstrated the practicability of using partiprestressed concrete members when fatigue resistancserious consideration (Abeles 1954). He persuaded BRailways to consider the use of partial prestressing inreconstruction of highway bridges over the LondonManchester line, when it was electrified around 1950. Bish Railways financed extensive cyclic loading tests of scale members, which were designed to allow 550(approximately 8√f ′c or 3.8 MPa) tension under full serviload and 50 psi (0.34 MPa) compression under deadonly. These members were cracked under static loadwere then subjected to 3 million cycles of load producingdesign range of stress, 50 psi (0.34 MPa) compression tpsi (3.8 MPa) tension at the flexural tension face. Behawas satisfactory, with essentially complete closure of crand recovery of deflection after 3 million cycles of load. Tstrength under static loading was not decreased by the loading. Many relatively short-span bridges were constred using such partially prestressed members and theyformed satisfactorily.

Recently, Roller et al. (1995) conducted an experimeprogram including four full-size, pretensioned, bulb-tee gers made with high-strength concrete and pretensionedgirders were 70 ft (21.3 m) long and 54 in. (1.4 m) deep a concrete compressive strength of 10,000 psi (69 MPa)of the four test girders with a simple span of 69 ft (21.0was subjected to cyclic (fatigue) flexural loading using point loads spaced 12 ft (3.66 m) apart at midspan. A crete deck 10 ft (3.05 m) wide and 9.5 in. (250 mm) thickbeen cast on the girder to represent the effective flange composite girder in a bridge.

During the cyclic flexural loading, the upper limit of tload produced a midspan tensile stress at the extreme fithe lower flange equal to 6√f ′c . The lower limit of the load waselected such that a steel stress range of 10,000 psi (69would be produced. After each million cycles of loading,girder was tested statically to determine its stiffness. Sreductions in stiffness and camber were observed, but was no significant change in prestress loss. The girderformed satisfactorily for 5 million cycles of fatigue loadinAfter completion of the long-term fatigue load test, the ger was tested under static load to determine its ultimateural strength. It developed an ultimate moment equal to of the ultimate moment capacity of a companion girderhad been under long-term sustained load. The meamoment capacity also exceeded the calculated mocapacity by 7.5% based on the AASHTO Standard Specifications for Highway Bridges.


bothrop-960,

215

f 20,The

hot-4).essent

s-d in

entorage(ACIt al.ire

ers.e-ngedngesnts of. The the

to

s onion.om-

es,tresster

axi-

eev

or t

re

zioouonreanl ian

dbyul

si

4.2—Material fatigue strengthThe fatigue resistance of a structural concrete memb

directly related to the fatigue properties of its componmaterials (Naaman 1982b). Therefore, the fatigue behaof the constituent materials should be investigated first.

Fatigue of concrete—The applied stress range limit fconcrete recommended by ACI 215 (1974) is given byformula

(4-1)

wherefcr = maximum recommended stress range for concf ′c = specified concrete compressive strength; andfmin = minimum applied stress.

Concrete can sustain a fluctuating stress between and 50% of its static strength for approximately 10 millcycles in direct compression, tension, or flexure withfailure (Norby 1958; Gylltoft 1978; McCall 1958; Stelsand Cernica 1958; and Hilsdorf and Kesler 1966). Concstresses resulting from service loads are generally smthan this magnitude (Shahawi and Batchelor 1986). Coquently, concrete fatigue failure generally will not controthe case of repetitively loaded partially prestressed be(Naaman 1982b; Harajli and Naaman 1984; and Ben1986).

Fatigue of reinforcement—Fatigue failure of underreinforceprestressed concrete beams is believed to be governed fatigue failure of the steel reinforcement (Warner and Hbos 1966a).

fcr 0.4fc′ fmin 2⁄–=

Tests have been conducted on ordinary reinforcement,in-air and embedded in concrete, to determine its fatigue perties. These tests have yielded varying results (Rehm 1Soretz 1965). For straight deformed bars, ACI Committee(1974), Model Code for Concrete Structures (CEB-FIP 1978),FIP Commission on Model Code (1984), and Ontario High-way Bridge Design Code (Ministry of Transportation andCommunications 1983) recommend stress range limits o22, and 18 ksi (138, 152, and 124 MPa), respectively. lowest stress range found to cause fatigue failure in arolled bar is 21 ksi (145 MPa) (ACI Committee 215 197ACI 343R recommends limiting the reinforcement strrange in terms of the minimum stress and reinforcemdeformation geometry

(4-2)

whereff = safe stress range, ksi;fmin = minimum applied stress, ksi; andr/h = ratio of base radius-to-height of rolled-on tran

verse deformation (a value of 0.3 can be usethe absence of specific data).

The fatigue strength of prestressing reinforcemdepends upon the steel type (bar, wire, strand), anch(unbonded post-tensioned reinforcement), extent of bond Committee 215 1974), and steel treatment. Paulson e(1983) conducted fatigue tests (in-air) of 50 seven-wstrand samples obtained from six different manufacturAll of the strands conformed with ASTM A 416 requirments. The minimum stresses applied in the tests rafrom 75 to 165 ksi (517 to 1138 MPa), and the stress ravaried from 22 to 81 ksi (152 to 559 MPa). A significavariation was observed in results from even two samplethe same product produced by the same manufacturereffect of the end grips dominated the fatigue curves inregion of long-life, low-stress-range.

The following relationship was found to lie above 9597.5% of the failure points

(4-3)

whereN = number of cycles; andfsr = maximum stress range for a fatigue life of N cy-

cles, ksi.The researchers did not find the effect of minimum stres

fatigue life great enough to warrant inclusion in the equatThe FIP Commission on Prestressing Steel (1976) rec

mends a stress range of 15% of fpu with a minimum appliedstress not greater than 75% of fpu for a fatigue life of 2 mil-lion cycles. For the same fatigue life of two million cyclhowever, Naaman (1982b) recommends a reduced srange of 10% fpu with a minimum applied stress not greathan 60% of fpu to better correlate with test results (Fig. 4.1).The following equation can be used to predict other mmum safe stress ranges

ff 21 0.33fmin 8 r h⁄( )+–=

Nlog 11 3.5 fsrlog–=

r isntior

he

te;

eront

tellerse-nmsett

thes-

ng
Fig. 4.1—Comparison of observed fatigue life of prestresstrands with existing data (Harajli and Naaman 1985a).


n

co

n

tatiig

rm

omsoseanttdtehee -mc

peo

thee-

rst thetiallyignif-ary

ma-6b).-

f theict-

ingtionsro-

ireed toith aide a

n in8);

(4-4)

wherefsr = maximum safe stress range for a fatigue life ofN

cycles;fpu = specified tensile strength of the prestressi

strand; andNf = number of cycles to failure.

The endurance limit (stress range for which the reinforment will not fail for an infinite number of cycles) has nbeen found for prestressing steel (Naaman 1982b); howea fatigue life of 2 million cycles is considered to be sufficiefor most applications.

The previous discussion applies to pretensioned straFor post-tensioned tendons, two more levels of fatigstrength have to be considered: the strand/duct assemblythe tendon anchorages. For the strand/duct assembly, frefatigue may govern if high contact stresses between strand corrugated steel duct are combined with small relamovements at cracks. Under such circumstances, the fatstrength of the strand/duct assembly can drop to as low14,300 psi (100 MPa). Fatigue strengths of anchorages athe order of 14,300 psi (100 MPa), according to FIP Comission on Prestressing Steel and Systems (1992).

Designers typically place tendon anchorages away frareas with high stress variations and avoid fatigue probleat the anchorages. A similar approach normally will nwork to avoid fretting fatigue because maximum stresoften occur at sections with maximum tendon curvature maximum contact stresses between strand and duct. Frefatigue between strand and duct, however, can be avoideusing thick-walled plastic ducts rather than corrugated sducts (Oertle 1988). With a thick-walled plastic duct, tstrand reaches fatigue strengths comparable to thosstrand in air. Fig. 4.2 shows the fatigue performance of tendons with steel and plastic ducts in simply supported beaunder four-point loading. In the specimen with a steel du50% of the tendons failed at a fatigue amplitude of 25,000(175 MPa); in contrast, only 18% of the tendons in the spimen with a plastic duct failed at a fatigue amplitude 39,400 psi (275 MPa).

fsr fpu⁄ 0.123 Nf 0.87+log–=

llrths

sigr S

dadif

g

e-tver,nt

ds.ue

Fig. 4.2—Fatigue resistance of post-tensioned tendosteel duct and in thick-walled plastic duct (Oertle 1981 ksi = 6.9 MPa.

ycr

s

nia

p ie

singtigue

m-x tostab-ree

n of, one

e-f the theseent to

4.3—Fatigue in partially prestressed beamsTo illustrate the relative importance of fatigue for partia

prestressed beams compared with that for ordinary reinfoor fully prestressed beams, Naaman (1982b) analyzed concrete beams, identical except for the partially prestrereinforcement ratio (PPR = 0, 0.72 and 1.0). Note that PPR= 0 represents an ordinary reinforced beam; PPR = 1.0 rep-resents a fully prestressed beam; and PPR = 0.72 representa partially prestressed beam. All of the beams were desto provide the same ultimate moment capacity. Mateproperties and relevant data are given by Naaman andaksorn (1979).

For each beam, computed stress ranges in ordinary anstressed steel were plotted with respect to the applied loexcess of the dead load) varying from zero to the spec

andtingndveue

ase in

-

m

live load (Fig. 4.3). For the same type of beam section, effect of the PPR was plotted with respect to the reinforcment stress range due to the application of live loads (Fig.4.4). The discontinuity in the plots corresponds with ficracking of the concrete in the beams. It is evident fromfigures that higher stress ranges are associated with parprestressed sections. Thus, fatigue problems are more sicant in partially prestressed sections than in their ordinreinforced or fully prestressed counterparts.

tsd

ing byel

of

st,sic-f

edeeed

edl

iri-

re-(ind

4.4—Prediction of fatigue strengthThe studies described have a common conclusion sum

rized by Naaman (1982b) and Warner and Hulsbos (196The critical limit state (fatigue failure) of partially prestressed concrete beams is generally due to failure oreinforcement. The fatigue life of the member can be preded from the smaller of the fatigue lives of the reinforcsteel or the prestressing steel. Many of these investigahave indicated that in-air test results of reinforcement pvide a good indication of the member fatigue life.

Naaman therefore recommends using Eq. (4-4) or Fig. 4.1to estimate the fatigue life of stress-relieved seven-wstrand for the appropriate stress range. A strand subjecta minimum stress less than 60% of its tensile strength wstress range of 10% of the tensile strength should provfatigue life of approximately two million cycles.

For ordinary reinforcement, Naaman recommends uEq. (4-2) to determine safe stress ranges that provide falives in excess of 2 million cycles.

ACI Committee 215 (1974) and Venuti (1965) recomend conducting a statistical investigation of at least si12 reinforcement samples at appropriate stress levels to elish the fatigue characteristics of the material. At least thstress levels are required to establish the finite-life portiothe S-N diagram: one stress level near the static strengthnear the fatigue limit, and one in between.

The choice of the PPR and relative placement of the reinforcment have a significant effect on the fatigue response omembers. Naaman (1982b) states that proper selection ofvariables can maintain the stress ranges in the reinforcemwithin acceptable limits.


, and
Fig. 4.3—Typical comparison of stress changes in steel for reinforced, prestressedpartially prestressed beams (Naaman 1982a).
sent-tiguethodfatiguesteel Naa-both

o cal-age,teel.m-

ssed,dthsdings

reterete thecks. ofls
Fig. 4.4—Typical stress changes in steel at different leve
prestressing (Naaman 1982a).

Balaguru (1981) and Balaguru and Shah (1982) have preed a method and a numerical example for predicting the faserviceability of partially prestressed members. The mecompares the stress ranges in the beam constituents to the limits of each individual component (concrete, prestressing and nonprestressing steel) using the equations derived byman and Siriaksorn (1979) to calculate stresses for uncracked and cracked sections.

Naaman and Founas (1991) also presented models tculate the structural responses that account for shrinkstatic and cyclic creep, and relaxation of prestressing sFor any time t and cycle N, the models can be used to copute stresses, strains, curvatures, and deflections.

4.5—Serviceability aspectsIn a cracked concrete member, whether nonprestre

partially prestressed, or fully prestressed, the crack wiand deflections generally increase under repeated loa(Naaman 1982b).

The increase in crack widths and deflections in concmembers is mostly attributed to the cyclic creep of concand bond deterioration accompanied by slip betweenreinforcement and concrete on either side of existing craACI Committee 224 (1980) notes that 1 million cyclesload can double the crack widths.

of


dearibrssrisndnt.are

asDin ks

ndss o89teesio

avre

centrencr

ceimearc

nda

nt

e

acknd

ilarent

ationar-

t the

tialcon-982)dthssive

s ofulad the

tedtion

andings

load0%

989,

Harajli and Naaman (1989) developed an analytical mofor cyclic slip and stresses to compute crack widths in ptially prestressed concrete beams. In the analysis, equilum was assumed between the reinforcement bond streand the concrete tensile stresses in a concrete tensile pjoining two successive cracks. In addition, a local bostress-slip relationship was assumed for the reinforceme

The results of the analyses were in agreement compwith the experimental results shown in Fig. 4.5 and 4.6 formonotonic and cyclic loading, respectively. Agreement walso obtained with tests conducted by Lovegrove and El (1982) for which the steel stresses ranged from 7 to 43(48 to 297 MPa).

The analytical models were also useful in predicting trein the crack patterns in terms of growth and mechanismgrowth. From the analyses, Harajli and Naaman (19attributed increased crack widths to increases in sstresses caused by cyclic creep of concrete in compresand bond redistribution between cracks.

They indicated that partially prestressed beams hsmaller crack spacings and less crack growth than fully pstressed beams subjected to fatigue loads. The presenordinary reinforcement in prestressed beams helps to cocracking in static and fatigue tests. Ordinary reinforcemreduces the increased steel stresses attributed to cyclic of concrete. In addition, it minimizes bond redistribution.

Crack widths were observed to be a function of reinforment stress and crack spacing. In tests that generated scrack spacings (3 to 4.5 in., [76 to 114 mm]), a nearly linrelationship was observed between crack widths and reinfoment stress (Fig. 4.7). To estimate the crack spacing acs andcrack width W the following equations were given

(4-5)

(4-6)

(4-7)

whereacs = crack spacing, in. (mm);At = effective area of concrete tension zone surrou

ing all reinforcementhaving the same centroid the reinforcement, in.2 (mm2);

P = sum of the perimeters of all tension reinforcemein. (mm);

W = crack width at the first loading cycle;WN = crack width at the Nth loading cycle;So = slip of the reinforcement at the first cycle;So,N = slip of the reinforcement at the Nth cycle;B = distance ratio at the first cycle;BN = distance ratio at the Nth cycle;fso = steel stress at the primary crack at the first cyclfso,N = steel stress at the primary crack at cycle N;N = number of load cycles; andEs = modulus of elasticity of steel.

acs 1.20At P⁄=

W 2SoB=

WN 2So N, BN fso N, fso–( )acsBN Es⁄[ ]+=

eep

-ilarre-

-s

,

Tests by Shahawi and Batchelor (1986) indicated a simlinear relationship between crack width and reinforcemstress. They recommend the use of the FIP-CEB equ(Eq. 4-8) for predicting the maximum crack widths in ptially prestressed beams subjected to fatigue

(4-8)

whereWmax = maximum crack width, mm; andfs = change in steel stress from decompression aextreme tensile fiber, MPa.

The previous FIP-CEB equation accounts for pardebonding, but does not consider cyclic creep of the crete. Balaguru (1981) and Balaguru and Shah (1developed an equation to estimate maximum crack withat incorporates the effects of cyclic creep and progresdeterioration of flexural stiffness. Comparing the resultthis equation with those of the FIP-CEB crack width formusing data by Bhuvasorakul (1974), Balaguru determinefollowing ratios of maximum crack width after N cycles toinitial maximum crack width: Wmax,N / Wmax = 2.45 (experi-mental) = 1.003 (FIP-CEB) = 2.15 (Balaguru). He attributhe disparity in the result obtained by the FIP-CEB equato the lack of consideration of cyclic creep of concrete.

Wmax fs 10 3–×=

l-i-esm

d

i

f)ln

e- ofolt

Fig. 4.5—Comparison of observed and predicted crwidths for monotonically tested beams (Harajli aNaaman 1989); 1 ksi = 6.9 MPa; 1 in. = 25.4 mm.

;

4.6—Summary of serviceabilityIn all types of concrete members, crack widths

deflections generally increase under repeated load(Naaman 1982b). These increases occur during earlystages and then generally stabilize until approximately 9of their fatigue life. Researchers (Harajli and Naaman 1


er of
Fig. 4.6—Comparison of observed and predicted crack width increases with numbloading cycles (Harajli and Naaman 1989); 1 in. = 25.4 mm.
shiess firs

fors oce

arykince co

avts o

ts toivenentedns inding

n.

s of load-roundove-

s canmilar

Shahawi and Batchelor 1986) show a nearly linear relationbetween maximum crack width and reinforcement strDeflections can increase to twice the static deflection of theload cycle.

The importance of correct reinforcement detailing crack control should be emphasized. Pretensioned wirenonprestressed bars can be placed near the tensile fahelp limit crack widths according to the report Partial Pre-stressing (Concrete Society 1983). The presence of ordinreinforcement in prestressed beams helps to control cracin static and fatigue tests. Ordinary reinforcement reduthe increased steel stresses attributed to cyclic creep ofcrete. In addition, it minimizes bond redistribution.

Balaguru (1981) and Balaguru and Shah (1982) hderived a refined approach that incorporates the effec

p.t

r to

gsn-

ef

cyclic creep of the concrete and tension stiffening effecestimate maximum crack widths and deflections at a gload cycle. Naaman and Founas (1991) also presmodels to compute stresses, strains, and deflectiopartially prestressed beams for static and cyclic loaincorporating effects of shrinkage, creep, and relaxatio

CHAPTER 5—EFFECTS OF LOAD REVERSALS5.1—Introduction

Cyclic load reversals can result from dynamic effectearthquake, shock, wind, or blast loadings. Earthquakeings are imparted to the base of the structure through gmotion, whereas wind loadings transmit forces to the abground portions of the structure. Shock or blast loadinginvolve both of these effects: air overpressure forces si


rajli
Fig. 4.7—Crack width variation versus reinforcing steel stress at different PPR (Haand Naaman 1985); 1 ksi = 6.9 MPa, 1 in. = 25.4 mm.
ith

feerrontetury

onabtru ataondo thclanom

mt worrg

ctu

ired

ccor-rns as

con-

and

s they

aterovid-uatege

uired

and thetion,Parktili-ent duc-stic

ateially

to wind loadings and ground motions accompanying eburied, air, or contact blasts.

5.2—Design philosophy for seismic loadingsIn design for seismic effects, the primary concern is sa

of the occupants (Bertero 1986), and a secondary conceconomics. Even for an earthquake with reasonable pbility of occurrence; however, it is not possible to guarawith absolute certainty complete life safety and no strucdamage. The Federal Emergency Management Agenctheir document NEHRP 1997 Recommended Provisi(1998), give minimum requirements to provide “reasonand prudent life safety.” To achieve these objectives, stures should be proportioned to resist design forces withquate strength and stiffness to limit damage to acceplevels. Design forces are determined by using a respmodification coefficient R to reduce the forces obtaineassuming that the structure responds linear elastically tground motion. The reduction factor accounts for reduced strength demand due to a number of effects, ining energy dissipation through hysteretic damping lengthening of the structural period as the structure becinelastic.

In simplistic terms, there are two basic options in seisdesign: (1) make the structure strong enough so that irespond elastically; or (2) permit the structure to definelastically while ensuring adequate ductility and enedissipation capacity. The second option permits the stru

er

tyn isba-eal

, inslec-

de-blese-,theeud-des

icill

myre

to be designed for considerably lower forces than requfor the first option.

Designing partially prestressed concrete structures in adance with the second approach, raises the same concefor the case of designing with conventional reinforced crete; that is, the designer must ensure:

• Ductility at plastic hinges; and • Adequate energy dissipation through damping hysteresis.

This chapter concentrates on these characteristics arelate to partially prestressed concrete.

5.3—DuctilityDuctility allows the redistribution of forces in indetermin

systems and ensures gradual rather than brittle failure, ping a warning to the occupants before collapse. If adeqductility is not provided at the critical regions (plastic hinzones), the member will be unable to develop the reqinelastic rotation.

Ductility is usually expressed for structural members systems in terms of a deformation ductility ratio, wheredeformation is described in terms of displacement, rotaor curvature (Naaman et al. 1986, Thompson and 1980a, Giannini et al. 1986). Deflection and rotation ducties give an indication of drift (ratio of lateral displacemto height) and are used in structural analysis. Curvaturetility is used to define member or section behavior at plahinges.

The ductility ratio is defined as the ratio of the ultimdeformation to the yield deformation. In the case of part


tili-.53 and

fer- theheell.har-l oft tobers

s ofgor77),t al.zenrial975,ioneissercted ofndwithns),sing

iveourt ofns

hined

s for.

tive

held

ed ass

as

t inhe

innteral

iel86

Thsses

anatn,

seienrvntity lafirstiolti-

prethatt o

ess de onf a

ore b

ret

ity

prestressed concrete structures, the definition of ydeformation can be quite arbitrary (Naaman et al. 19Thompson and Park 1980a; Giannini et al. 1986). section contains both prestressed and nonprestrereinforcement that can have different yield stressprestressing steel does not have a definite yield point,reinforcement located in different layers will yield different member deformations. The yield deformatiotherefore, can be defined in many ways.

Among numerous investigations on partially prestresconcrete, there has not been a consistent definition of ydeformation (Fig. 5.1). Cohn and Bartlett’s study (1982) opartially prestressed concrete assumed that the yield cuture corresponded to yielding of ordinary reinforcemeThis approach gives a relatively high value of ductilbecause the prestressing reinforcement yields at a mucher deformation. Thompson and Park (1980a) defined yield as the intersection of the tangent to the elastic porof the load-deformation curve and a horizontal line at umate load. In Park and Falconer’s study (1983) on stressed piles, the yield deformation was taken at intersection of the secant from zero to 75% of the ultimmoment capacity and the postelastic slope. Naaman e(1986) defined the yield deformation as the intersectionthe secant from zero to the proportional limit of the prestring steel and the postelastic slope. Although these latterinitions give slightly different results, they are all basedthe ductility of the member section rather than yielding oparticular component in the cross section.

Local section ductility demands can be much msevere than overall deflection ductilities of frames. TestsMuguruma et al. (1980) on partially prestressed conc

frames indicated that the ratios of section curvature ducties to deflection ductilities of the frame were 1.24 and 1for partially prestressed concrete systems with bondedunbonded tendons, respectively.

Fig. 5.1—Definitions of yield for determination of ductil(Naaman et al. 1986).

5.3.1 Factors affecting ductility—Numerous investiga-tions have been conducted to determine the effect of difent parameters on ductility. Generally, factors that affectductility of ordinary-reinforced concrete sections affect tductility of partially prestressed concrete sections as wEffects of anchorage, bond, transfer lengths, grouting, cacteristics of high-strength prestressing steels, and leveprestressing are additional parameters uniquely importanprestressed and partially prestressed concrete mem(Bertero 1986).

Investigations were conducted to determine the effectthe reinforcement ratio (Cohn and Ghosh 1972; MacGre1974; Scott et al. 1982; and Park and Thompson 19concrete confinement (Park and Falconer 1983; Scott e1982; Burns 1979; Kent and Park 1966; Wight and So1975; Sheikh and Uzumeri 1982; and Sheikh 1982), matestrengths and stress-strain properties (Wight and Sozen 1Wang 1977), section geometry, ratio of compressreinforcement (Park and Thompson 1977, Burns and S1962), PPR, and axial load (Lin and Burns 1981). Anothinvestigation by Thompson and Park (1980a) was conduto determine the effects of the content and distributionlongitudinal reinforcement, transverse reinforcement, aconcrete cover. Naaman et al. (1986) analyzed beams four types of sections (rectangular, T, I, and box sectiofive different concrete strengths, three types of prestressteel, four levels of PPR, and seven reinforcing indexes ω.For the rectangular and T-sections, five levels of effectprestress fpe/fpu were analyzed, and in selected cases, flevels of compression reinforcement ratios and the effecconfinement were investigated. The following observatiowere made from the parametric evaluation:• Reinforcement index—Section ductility decreases wit

increasing ω because of the significant reduction ultimate curvatures associated with increasreinforcement ratios (Fig. 5.2 and 5.3).

• Effective prestress—When the effective prestress wadecreased, it led to an increase in ultimate curvaturereinforcing indices ω greater than approximately 0.12It also led to an increase in yield curvature irrespecof the reinforcement index. Fig. 5.2 illustrates theinfluence of effective prestress on ductility factor or tratio of these two quantities. The increase in yiecurvature tended to dominate the results and causreduction in ductility with decreased effective prestreirrespective of the reinforcing indices. This effect wmore significant for fully prestressed beams.

• Partially prestressed ratio—A decrease in PPR led toan increase in both ultimate and yield curvatures, buterms of ductility, there was no consistent trend. Teffect of PPR on ductility became negligible withincreased concrete compressive strengths.

• Transverse reinforcement—Increases in concreteconfinement resulted in corresponding increasessectional ductility irrespective of the reinforcemeindex. This effect was also observed in tests by sev

d;

eed;d

dld

a-.

rg-tn

-eeal.f-f-

ye


a end

tdidesth%

fod Ithag

gthh-

eheof

T-

ction

ratioscribessed

testsi andman

onman

on
other investigators (Watanabe et al. 1980; Mugurumal. 1982b; Iyengar et al. 1970; Okamoto 1980; aHawkins 1977).
• Concrete strength—For high values of reinforcemenindex (ω > 0.25), the concrete compressive strength not have a significant effect on ductility. For low valuof ω (< 0.25), however, the use of higher-strengconcrete reduced section ductility as much as 30particularly in cases of low PPR (ordinary reinforcedconcrete). This trend was also more pronounced rectangular sections as compared with box, T- ansections. Tests by Muguruma et al. (1983) indicate high-strength concrete is effective in improvinductility, but that the consequences of high-strentendon fracture and brittle compressive failure of higstrength concrete should be considered.

• Section geometry—The section geometry did not havan appreciable effect on ductility, provided that tductility index was expressed as a function

,

r-t

reinforcement index ω (computed using the web for sections).

Naaman et al. (1986) found the reinforcement index ω tobe an excellent independent variable for describing seductility, as it is proportional to c/dctf (c = distance fromextreme compression fiber to neutral axis; and dctf = depthto centroid of tensile steel). Based on the reinforcementand concrete compressive strength, it can be used to deall three types of systems: reinforced concrete, prestreconcrete, and partially prestressed concrete.

Based on the results of analysis and experimental on twelve partially prestressed concrete beams (HarajlNaaman 1984) described in the previous chapter, Naa

Fig. 5.2—Typical variation of curvature ductility as functiof effective prestress in steel from analytical study (Naaet al. 1986).

tFig. 5.3—Comparison of analytical results with predictiequations (Naaman et al. 1986); γ = ratio of compression-to-tension steel force at ultimate; and 1 ksi = 6.9 MPa.

TEE REPORT

litdeud5 heeinen

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et al. developed prediction equations for sectional ductiand plastic rotation as a function of the reinforcement inω. Three equations were derived for both the sectional dtility and plastic rotation to give upper limit, lower limit, anaverage values for ranges of reinforcement index of 0.00.3 (Fig. 5.3). The upper and lower limits accommodate teffects of parameters described previously, other than rforcement index ω which were shown to have an effect oductility. For example, Naaman et al. suggest the lowbound equation be used to describe cases with high-streconcrete, low effective prestress, and high PPR. The upper-bound equations are suggested for cases with normal streconcrete, high effective prestress, and low PPR. The equationsare given as follows

Curvature ductility ratio Plastic rotation (radians)

Upper bound (5-1)

Lower bound (5-2)

Average (5-3)

1ω 0.045–-----------------------

1.05 ω–850ω 35–-------------------------

LP

dctf 2⁄--------------

11.94ω 0.086–---------------------------------- 1.05 1.65ω–

1300ω 40–-------------------------------

LP

dctf 2⁄--------------

11.5ω 0.075–----------------------------- 1.07 1.58ω–

1050ω 45–-------------------------------

LP

dctf 2⁄--------------

yxc-

to

n-

r-gth

gth

whereω = reinforcement index;dctf = depth to centroid of tensile force in steel; andLp = equivalent plastic hinge length.

In Fig. 5.4, the equations are compared with the resultsseveral investigations (Kent and Park 1966; Corley 196Mattock 1964; Mattock 1967; Harajli and Naaman 1985Bishara and Brar 1974; and Baker and Amarakone 196The equations show fairly good correlation with the resu(assuming a plastic hinge length Lp of dctf /2), and are recom-mended by Naaman et al. for use as a first approximationthe design and detailing of ordinary reinforced, fully prestressed or partially prestressed members.

In a discussion of this work, Loov et al. (1987) recommespecifying c/d rather than ω to ensure ductility, as is done inthe Standards Association of Australia’s Draft Unified Con-crete Structure for Buildings (1984) and the CSA’s Designof Concrete Structures for Buildings. The use of c/d ensuresconsistent ductility demands from sections independentgeometry and concrete compressive strength. To accomdate this, Naaman et al. also provided the expressionsterms of c/dctf, valid for c/dctf between 0.08 and 0.42:

wherec = depth to neutral axis from extreme compressio

fiber;dctf = depth to centroid of tensile force in steel; andLp = equivalent plastic hinge length.

Thompson and Park (1980a) agreed with a form of c/d asa measure of the ductility in an investigation in which moment-curvature relation was developed applicable to ornary reinforced, prestressed, and partially prestressed concbeams, and verified with experimental tests on symmetricareinforced (prestressed and ordinary reinforced) rectangubeam-column assemblies subjected to cyclic load reversThe model was subsequently used to conduct a paramestudy. Their recommendations are as follows:

• Effect of prestressing steel content—ACI 318 limits theprestressing steel content by requiring ωp ≤ 0.36 β1,where β1 is a parameter used to modify the neutral axdepth c to determine the depth of the equivalenrectangular stress block a. Although the code limits theprestressing steel content, ACI 318 allows this valuebe exceeded if the additional reinforcement is nconsidered in the flexural strength calculation. Althougthis can result in sufficient ductility for gravity loading, ican be insufficient for seismic loading. To ensuadequate ductility, one can limit ωp to less than 0.2(rather than 0.3 for the case of β1 = 0.85). Alternatively,rather than using the previous equation, one can alimit a/h ≤ 0.2 (a = depth of rectangular stress block; anh = depth of section). This provides a given amount

Curvature ductility ratio Plastic rotation (radians)

Upper bound (5-4)

Lower bound

(5-5)

Average (5-6)

10.73c d⁄ ctf 0.053–-------------------------------------------- 1.86 0.73c d⁄ ctf–

621c dctf⁄ 42–-----------------------------------------

LP

dctf 2⁄--------------

11.42c d⁄ ctf 0.102–-------------------------------------------- 1.86 1.28c d⁄ ctf–

949c dctf⁄ 50–-----------------------------------------

LP

dctf 2⁄--------------

11.095c d⁄ ctf 0.087–----------------------------------------------- 1.88 1.15c d⁄ ctf–

766c dctf⁄ 53–-----------------------------------------

LP

dctf 2⁄--------------

423.5R-24 ACI COMMIT

Fig. 5.4—Comparison of prediction equations wiexperimental results (Naaman et al. 1986).


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ductility by specifying the location of the neutral axindependent of tendon positions. This relationship been adopted by FIP (Cement and Concrete Associaof England 1977) and the Standards Association of NZealand’s Code of Practice for General StructuraDesign and Design Loading for Buildings (1980).• Effect of prestressing steel distribution on ductility—Sections with only one tendon have reduced momcapacity as the concrete in compression deterioraThompson and Park (1980a) recommend the use of at two grouted tendons (one near the top and one neabottom of the section) for seismic loading, and suggelocating a third tendon towards the center of the sectThe use of unbonded tendons was generally not recmended for primary earthquake-resistant membbecause of lack of information on the performance of anchorages (Muguruma 1986). In cases where partprestressed beams are designed with nonprestressedforcement in the extreme fibers providing at least 80%the seismic resistance, however, they indicated thatprestress can be provided by one or more groutedunbonded tendons in the middle third of the beam deThe centrally located prestressing steel is recommenbecause it can delay cracking and enhance strength out much reduction in ductility. Studies at the NationInstitute of Standards and Technology (NIST) and as of the National Science Foundation Precast SeisStructural Systems (PRESSS) program (Cheok and 1990) have explored the use of unbonded prestresreinforcement through the connections. In the studieNIST, central post-tensioning was used in conjunctwith mild steel reinforcement at the top and bottomthe beam-column interface. The central post-tensionmaintained integrity of the joint, while energy dissipatiwas accommodated with the mild steel reinforcementstudy by Priestley and Tao (1993) proposed the uslightly stressed, unbonded prestressing steel throughjoint (nonlinear-elastic concept). The system offers ducbehavior through crack opening at the interface, whmaintaining a “self-restoring” force. Because the strado not yield, they work to bring the connection back tooriginally undeformed position. This system has bestudied further with other proposed connection systeas part of the PRESSS program (Cheok and Lew 199• Effect of transverse reinforcement on ductility—Thedegree of confinement provided by the transverse reinfoment to the compression regions significantly increaductility. The confinement enhances the performance ofconcrete within the core and also inhibits buckling of compression reinforcement (Park and Thompson 19Park and Paulay 1975; and Thompson 1975). Thompand Park recommend that the stirrups be spaced lessd/4 or 6 in. (150 mm).• Effect of cover thickness—For ductility, Thompson andPark suggest that the cover be made as small as posbecause loss of cover under cyclic loads causes a retion in capacity. The effect of cover spalling on membstrength is not as great for deeper members where cis a smaller percentage of member depth.

Holding all other parameters constant, ductility decreawith an increase in reinforcement index. ACI 318 givemaximum value for the reinforcement index of ω ≤ 0.36 β1.Maintaining this limit would give section ductilities on th

n

ts.ste

d.-

s

order of 1.5 to three. With Park’s suggested limit of 0.2, dtilities in excess of four or five can be obtained. TestsMuguruma et al. (1982a) indicate that if the sections docontain compression reinforcement, ω < 0.2 can give ductil-ities of only about three. If the reinforcement index is matained at less than 0.1, ductilities in excess of 10 caachieved (Naaman et al. 1986).

Tests by Nakano and Okamoto (1978) on beam-colsubassemblages indicated that even when tension reinfment is adequate (for example, ω < 0.15 to provide ductilityof five), hoop reinforcement (> 0.5%) is required to provthe required deflection ductility. Okamoto (1980) carried similar tests on eleven simply supported beams and ninetilever beams and reached similar conclusions.

in-

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r

5.3.2 Special cases Compression members—Relatively little information is

available on partially prestressed concrete columns (Be1986). Tertea and Onet (1983) analyzed 20 columns different PPR ranging from zero to 100%. As observed in beam tests, curvature ductility of columns improved withaddition of nonprestressed reinforcement. Curvature duty factors of 3.9, 6.1, and 9.8 corresponded with PPR of 100,50, and 0%. Irrespective of the degree of prestressing,umn ductilities improved with increased confinement.

Tests by Park and Falconer (1983) on prestressed found that the curvature ductility increased with reduced al load levels and increased confinement by spiral reinfoment. They discourage the use of hard-drawn reinforwire for spirals as it commenced fracture at displacemductility factors of four to six. They recommend requirithe wire to have high fracture strains.

Shear—Beams should be proportioned to ensure ducflexural behavior and to avoid brittle shear behavior (Ber1986). To accomplish this objective, the FIP Commiss(Cement and Concrete Association of England 1977) recmends assuming material overstrengths on the order ofin calculating the design shear force from the plastic hmoments. The New Zealand Code of Practice for GeneraStructural Design and Design Loading for Buildings (Stan-dards Association of New Zealand 1980) recommneglecting the concrete contribution to shear resistance wthe axial compression is less than 0.1 f ′c .

Muguruma et al. (1983) determined that concrete retance to shear can be improved by prestressing. Experimwere conducted on 7 x 10 in. (180 x 250 mm) simply sported beams with span lengths of 7.22 ft. (2.20 m) to intigate shear in prestressed beams. The flexural scracking load was found to increase in direct proportionthe increase in flexural cracking load (due to an increasprestressing). Muguruma (1986) suggests in the desigpartially prestressed concrete beams that the concrete cbution to shear resistance can be increased by the sheacorresponding to the decompression moment at the crsection. This effect is taken into consideration in ACI 31

Beam-column joints—Beam-column joints should bdesigned and detailed so that the plastic-hinge zones ibeams can develop their full plastic capacities. Muguru(1986) indicates that there are no differences in joint de


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for ordinary reinforced or partially prestressed systeexcept that the prestressing tendons do not bond to thecrete as well as ordinary deformed reinforcement. Reseon the performance of bond between tendons and concrejoints (Muguruma and Tominaga 1972) has indicated tendons undergo bond deterioration at early load staTendon slip causes a reduction in energy dissipation capby pinching the hysteresis loops.

Park’s investigation of beam-column subassemblawith grouted post-tensioned tendons (Applied TechnoloCouncil 1981) recommended minimizing the possibility failure in the joint. To avoid this type of failure, the hingzones should be displaced away from the beam-coluinterface. This can be accomplished by haunching beams, adding additional reinforcement at the interfaceusing cruciform shapes (Bertero 1986). Displacing the hifrom the interface has the added advantage of locatingfailure in a region in which nonprestressed reinforcemenlocated, increasing ductility and energy dissipation. Displing the hinge further into the beam results in increased sat the interface when the hinge reaches its capacity produces increased ductility demands relative to hingethe interface when subjected to similar drift levels. Uspost-tensioned tendons through the joint core at middecan reduce the amount of required joint shear reinforment as it serves to maintain integrity of the joint (Park aThompson 1977).

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5.4—Energy dissipationEnergy dissipation can be attributed to viscous and hys

etic damping described separately below. Energy dissipaof prestressed concrete is as little as 0.15 times that of ventional reinforced concrete of comparable size astrength (Bertero 1986).

5.4.1 Viscous damping—In a 1978 state-of-the-art repoby Hawkins (1977) on seismic resistance of prestressedprecast structures, a thorough review of the researchdamping was presented. Tests by Penzien (1964) indicthat the level of prestress and concrete strength affects ding by affecting cracking. Decreases in cracking causreduction in damping.

Tests by Spencer (1969) on centrally prestressed beindicated that damping ratios were not frequency dependDamping ratios tended to increase with end rotations prestress. Spencer also found damping to be higherbeams loaded in uniform shear rather than uniform momand attributed this result to the higher effects of interfshear and bond slip in the case of uniform shear loading

Tests by Brondum-Nielsen (1973) on centrally prestresbeams indicated damping decreased with increased preslevels, which is the opposite of what Spencer observed. ues of damping obtained by Nakano (1965) from tests ofscale four-story frames were 1% before cracking, 3%cracking, and 7% before inelastic behavior.

5.4.2 Hysteretic behavior—The energy dissipation (areenclosed within the force-deformation hysteresis loopsprestressed concrete members is lower than thatreinforced concrete members designed to develop sim

strengths (Thompson and Park 1980b). Prestressed comembers can achieve significant elastic recoveries evlarge deformations (Schoeder 1977) because of the itensile stress in the strand due to prestressing. In erecoveries, the strand unloads its tensile force and is caof achieving large recoveries. The member will not achsignificant energy dissipation unless the prestressing yields, the concrete crushes, or the nonprestressed defobar yields (Nakano 1965; Blakeley and Park 1973b; Gu1965; Blakeley and Park 1971; and Bertero 1973). addition of nonprestressed reinforcement in partiprestressed concrete members has been shown to promarked improvement in energy dissipation characteri(Thompson and Park 1980b, Inomata 1986). This is eviin Fig. 5.5, which shows typical hysteresis loops cyclically loaded fully prestressed, ordinary reinforced, partially prestressed concrete members. In additionreducing the strength degradation, the presencelongitudinal nonprestressed reinforcing steel improductility by acting as compression reinforcement (Park Thompson 1977, Inomata 1986). As mentioned previouCheok and Lew (1990) have investigated the use of ligprestressed unbonded reinforcement. The performancthe PRESSS connections has the advantage of a restoring force (nonlinear-elastic system). The stiffnreduction compared with that of a monolithic counterpcan compensate for the reduced energy dissipation. Hconnections (Cheok and Lew 1991) have been investigthat combine the nonlinear elastic system with elementsyield or dissipate energy.

Thompson and Park (1980a, 1980b) developed ideamoment-curvature relations for partially prestresconcrete sections by combining relations obtainedBlakeley (1971) and Blakeley and Park (1973a) prestressed concrete and by Ramberg and Osgooreinforced concrete (Iwan 1973). The idealized hyster

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Fig. 5.5—Moment-curvature idealizations for prestressereinforced, and partially prestressed concrete (Thompsand Park 1980b); α = ratio of strength of reinforcedconcrete component to total strength of partially prestressconcrete system; and β = ratio of strength of prestressedconcrete component to total strength of partially prestressconcrete system.


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curves agree with those obtained experimentally from on beam-column subassemblages. Fig. 5.6 through 5.8 showthe idealized and experimental moment-curvarelationships for fully prestressed, reinforced, and partprestressed members subjected to cyclic loading.

In the fully prestressed member (Fig. 5.6), the energy dissipation capacity of the member increased (although still considerable elastic recovery) after the beam-moment caty had been reached and crushing of the concrete hadmenced. The compression steel in the beam was nominthe significant degradation in the strength and stiffnessattributed to the reduction in the sectional area when the concrete crushed.

After the beam-moment capacity had been reachedcrushing of the concrete had commenced for the parprestressed member (Fig. 5.8), the energy dissipation capaity of the partially prestressed member was considergreater than that observed for the fully prestressed memFor this particular test, the beneficial effect of the nonstressed longitudinal steel in the compression zone obeam plastic hinge region was evident from the stmoment-curvature relations. The strength degradationnot large because after concrete crushing commencenonprestressed steel was able to carry some of the comsion previously carried by the cover concrete and therehelped maintain the internal lever arm (Thompson and 1980b).

Similar findings were obtained by Muguruma et (1982a, 1982b), who tested 24 partially prestressed (etric) beams with various levels of prestress, and alsNakano and Okamoto (1978), who tested 21 partially stressed (symmetric) beams subjected to cyclic-load reve

Confining the concrete has a marked benefit on the ducof partially prestressed concrete and also improves the hetic behavior. Closely spaced stirrup ties or spirals in the ing regions enhance ductility and energy dissipationconfining the concrete compression zone, reducing stiffdegradation, and inhibiting buckling of the compression s

Fig. 5.6—Comparison of idealized and experimentmoment-curvature relations for prestressed concrete sect(Thompson and Park 1980b).

alion

Fig. 5.7—Comparison of idealized and experimenmoment-curvature relations for reinforced concrete sect(Thompson and Park 1980b).

sts

relly

ithaci-om- andasver

andlly-bly

Fig. 5.8—Comparison of idealized and experimentmoment-curvature relations for partially prestressed concrete section (Thompson and Park 1980b).

5.5—Dynamic analysesGiannini et al. (1986) presented an analytical investiga

on the seismic behavior of fully prestressed and partiallystressed concrete. The influences of the fundamental pPPR, and seismic intensity were considered. The respwas obtained in the form of time histories and peak valuterms of displacements, curvatures, local strains (in thestituents), forces, and dissipated energy.

Partially prestressed concrete seems to coupleadvantages of fully prestressed concrete with those of ordreinforced concrete in resisting loads. Fully prestreconcrete has a tendency to greater strain and deformdemands than ordinary reinforced concrete. After a stimpulse, the displacements of the reinforced concretepartially prestressed concrete systems tended to damwhereas those of the fully prestressed concrete systenot. The analysis showed that fully prestressed conresists the design seismic intensity, but for greintensities, it rapidly approaches collapse. Fully prestreconcrete structures, however, can behave better forintensity seismic excitation.

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Similar conclusions were obtained from a studyThompson and Park (1980b). They used the ideamoment-curvature relations (discussed previously) to duct a nonlinear dynamic analysis of ordinary reinforfully prestressed, and partially prestressed concrete sdegree-of-freedom systems. Displacements of fully stressed concrete systems are larger than those of orreinforced and partially prestressed concrete sysbecause of the reduced energy dissipation associatedprestressing.

Fully prestressed systems also undergo a signifreduction in stiffness after cracking that counteractsincreased displacements under dynamic loading. The rtion in stiffness causes a reduction in the effective periovibration that can reduce the displacement response. Uthe combination of both of these effects, the analysescate that fully prestressed frames will have, on averagegreater maximum lateral displacements than reinforcedcrete systems designed to have the same strength, vdamping ratio, and initial stiffness (Thompson and P1980b).

Similar analytical studies have been conducted as pthe NSF PRESSS program (Palmieri et al. 1996, El Shet al. 1999) that indicated systems incorporating unbopost-tensioned connections experienced moderate incin displacements in comparison with those expected monolithic concrete frame systems. An advantage ounbonded post-tensioned connections was the reductresidual drift associated with the nonlinear elastic behaof the system in comparison with the permanent sydeformations associated with the inelastic response oordinary reinforced frames.

Fully prestressed concrete members can be detailaccommodate increased displacements in a ductile mahowever, these higher displacements can result in gnonstructural damage and P-delta effects. An advantausing full prestressing and partial prestressing is the retion in residual displacements due to the self-restoring nof these systems. The addition of nonprestressed reinment can reduce these deflections.

5.6—ConnectionsResults of tests (Berg and Degenkolb 1973; Elliott 1

Kunze et al. 1965; Sutherland 1965; Ozaka 1968; FIP 1FIP 1974; Arya 1970; and Architectural Institute of Ja1970) and observations on the past performance ofstressed concrete in earthquakes indicate that mosstressed concrete members perform well. Most failuresbeen found to occur in connections between elements.

Several investigations have been conducted to studperformance of connections between fully prestressedpartially prestressed concrete precast elements. As menpreviously, ductile connection concepts have been testpart of the PRESSS program. French et al. (1989a, 19Amu and French (1985), Hafner and French (19Jayashankar and French (1987), and Tarzikhan and F(1987) investigated post-tensioned, welded, bocomposite, threaded coupler, and tapered-threaded

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connections. The most viable alternatives were continupost-tensioned connections displacing the plastic-hiregion from the beam-column interface, and taperthreaded splice connections that emulate the performanmonolithically cast beam-column connections. It was asuggested that advantage be taken of composite abetween the beam and the slab.

5.7—SummaryIf members are detailed properly, it is possible to ens

ductile behavior in fully prestressed and partially prestresconcrete beams (Applied Technology Council 1981).

Ordinary reinforced concrete has an advantage in enedissipation characteristics. Prestressed concrete haadvantage in its ability to reach large displacements only a small loss in load-carrying capacity and almost cplete recovery of displacements. Joint performanceimproved by the use of continuous prestressed stthrough the joint.

Partially prestressed concrete couples the advantagprestressed concrete with those of ordinary reinforced crete (Giannini et al 1986). The sections can be detailethat energy dissipation and deformation demands are osame order as those of ordinary reinforced concrete. Parprestressed concrete also offers the possibility of calibrathe subsequent yielding of both prestressed and nonstressed of reinforcement to optimize stiffness and enedissipation properties (Giannini et al 1986).

A recommended design concept is to balance all or pathe gravity loads, satisfy serviceability criteria with drapor blanketed prestressing strands, and place sufficient prestressed reinforcement in the section to meet the addal requirements for seismic design strength, ductility, energy dissipation (Hawkins 1977; Inomata 1986; aThompson and Park 1980b). Stirrup ties should be locatehinging regions to prevent bar buckling, confine concrand increase shear strength (Park and Thompson 1977and Paulay 1975).

CHAPTER 6—APPLICATIONS6.1— Early applications

Partial prestressing has been used in the desigstructures since the early 1950s. In 1952, partially prestrebeams with post-tensioned cables were first used in theof a freight depot at Bury St. Edmunds, England (Ben1984). Lower concrete tensile stresses were specinitially, but with successful experience and an increasamount of test data, the permissible fictitious tensile strewere increased to 750 psi (5.2 N/mm2) for pretensioning and650 psi (4.5 N/mm2) for post-tensioning (Bennet 1984Other early applications of partial prestressing includeddevelopment of a concrete mast for overhead power and structures designed to withstand mining collapse; both applications, the most severe design load was usuatemporarily unbalanced load (Bennet 1984).


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6.2—Pretensioned concrete componentsIn the early 1980s, a survey was conducted among th

tensioned, precast-concrete plants in the U.S. and C(Jenny 1985) concerning the use of partial prestressing industry. Sixty-five plants responded to the survey. Fouthe plants manufactured only bridge girders, and partialstressing was rarely considered in their production. Thevey revealed, however, that there was a general familwith partial prestressing and the concept was used for ming special design situations rather than as a routine prtion standard. Only seven of the 61 remaining plresponding to the survey indicated that they did not aany product to exceed a nominal tensile stress of 6√f ′c psi(√f ′c /2 MPa) for certain members, such as stemmed uinverted tees, spandrel beams, hollow-core slabs, or col(Jenny 1985).

The nominal stress levels reported by the plants wereto 12√f ′c psi (√f ′c /1.6 to √f ′c MPa) for stemmed units; 7to 12√f ′c psi (√f ′c /1.6 to √f ′c MPa) for beams; 7.5 to 9√f ′cpsi (√f ′c /1.6 to √f ′c /1.33 MPa) for hollow-core slabs; a7.5√f ′c psi (√f ′c /1.6 MPa) for columns. Reasons for desiing these members with a nominal tensile stress greate6√f ′c psi (√f ′c /2 MPa) were to meet special design loareduce camber, save steel and lower the cost, reducrequired concrete strength at release, and achieve comtive span-depth ratios (Jenny 1985).

6.3—Post-tensioned building construction The majority of post-tensioned building construction

the U.S. is based on the use of unbonded tendons in cotion with code-specified minimum amounts of bonded nprestressed reinforcement. Maximum design tensile strrange from 6 to 12√f ′c psi (√f ′c /2 to √f ′c MPa) (Feyermuth1985). For designs where durability considerations dogovern, service-load nominal tensile stress levels of to12√f ′c psi (√f ′c /2 to √f ′c MPa) are now routine for one-wapost-tensioned systems. According to Feyermuth, “Theof partial prestressing, especially as applied to flat slabsreduced the incidence of significant cracking problempost-tensioning buildings. This results from lower prestlevels, inducing proportionately smaller elastic and cshortening movements, and the presence of bonded nostressed reinforcement to control crack widths” (1985).

In the design of office and hotel structures, the use of pprestressing is often cost-effective. Post-tensioned beamwell as one-way slabs, designed to an extreme nominalstress in tension between 6 and 12√f ′c psi (√f ′c/2 and √f ′cMPa) have performed well in practice. The use of partprestressed design is especially effective when cedesignated areas of a building are required to have a hdesign live load than the majority of the floor area. The 1Peachtree Tower (shown in Fig. 6.1) is a 27-story, cast-inplace concrete office building located in Atlanta, Ga. Theis 5 in. (127 mm) thick, conventionally reinforced, asupported by post-tensioned beams 14 in. (356 mm) wid22 in. (559 mm) deep. By allowing the nominal tensile stin the beams to reach 10√f ′c psi (√f ′c/1.2 MPa) under servicloads, economy was achieved by reducing the overall nu

s, theeti-

nnc-

n-ses

of tendons and by reducing the overall height of the structowing to the shallower beam depths.

For two-way flat-plate designs, ACI 318 limits the streat column locations as calculated by the equivalent framethod or other approximate methods to 6√f ′c ( √f ′c /2MPa). This is in recognition of the gross approximationthe actual strains in the vicinity of the column. Higher alloable stresses, however, are permitted in conjunction more precise analytical procedures.

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6.4—BridgesPrestressed concrete bridges designed to permit cra

under service loads are still rare in the U.S., even thoughcommon to allow flexural tension in extreme fibers unservice load. The primary concerns about bridge membeing cracked under service loads have to do with fatand durability. Partially prestressed concrete bridges hbeen built in Europe and Japan.

Taerwe (1990) has described a number of partially stressed concrete bridges constructed in Belgium. Thighway bridges were designed according to the Class 2ditions described in Chapter 1 of this report. As of 1990,bridges described by Taerwe (built between 1965 and 1performed satisfactorily.

The Kannonji Viaduct in Japan was completed in 1(Soda and Kazuo 1994). The bridge has a total lengt2464 ft (751 m), with an average span length of 92 ft (28The bridge superstructure units are continuous for threfour spans each. It was designed to allow flexural cracunder service loads at midspan but not over interior suppFour other partially prestressed concrete highway bridalso have been constructed in Japan (Soda and Kazuo 1

AASHTO’s Standard Specifications for Highway Bridgdoes not currently allow service load cracking in prestreconcrete bridges. AASHTO, however, has adopted a l


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and resistance-factor design specification for highway bres (AASHTO LRFD Bridge Design Specifications) that dospecifically address partially prestressed concrete. Thislead to a wider use of partially prestressed concrete for hway bridges in the U.S.

6.5—Other applicationsDolan* reports that the prismatic beams on the Walt D

ney World Monorail were designed for tensile stressesnearly 12√f ′c psi (√f ′c MPa) for certain load combinationThe beams were precast and post-tensioned to providetinuity. Reinforcing bars were used to control cracking atcontinuity joint.

Partial prestressing also has applications in nuclear-tainment structures, cylindrical shells, and rectangular wvessels. In the 1960s, the first prestressed concrete conment structures for nuclear reactors were partially pstressed in the vertical direction only with nonprestresreinforcement in the circumferential (hoop) direction of tcylinder and in the dome. Two examples are the containmstructures at R.E. Ginna and H.B. Robinson Unit 2 nucstations (Ashar et al. 1994). Similarly, partial prestressinused vertically in the walls of cylindrical shell and rectanglar water-storage structures. If these structures are deswith restrained bases, high negative or positive vertbending moments, or both, will be present. An economdesign can be produced when a small amount of verticalstressing in the range of 200 psi (1.4 MPa) is provided nonprestressed reinforcement is added to resist any netural tensile stresses. These high bending moments oonly at one point in the wall. Therefore, the economyachieved by not overreinforcing the entire height of wThis method of design has been used since the 19†

CHAPTER 7—REFERENCES7.1—Referenced standards and reportsAmerican Concrete Institute222R Corrosion of Metals in Concrete318 Building Code Requirements for Structural Co

crete and Commentary343R Analysis and Design of Reinforced Concr

Bridge Structures423.3R Recommendations for Concrete Members

stressed with Unbonded TendonsASTMA 416 Standard Specification for Uncoated Sev

Wire Stress-Relieved Strand for PrestresConcrete

American Association of State Highway and TransportaOfficials (AASHTO)AASHTO/ Bridge Design SpecificationsLRFDAASHTO Standard Specification for Highway Bridges

* April 16, 1991 corresponence from Charles W. Dolan to Paul Zia.† October 26, 1995 correspondence from Steven R. Close to Nick Marianos.

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The reports and standards listed above were the latestions at the time this document was prepared. Because documents are revised frequently, the reader is advisecontact the proper sponsoring group if it is desired to refethe latest version.

AASHTO444 N. Capitol Street NWSuite 249Washington D.C. 20001

American Concrete InstituteP.O. Box 9094Farmington Hills, Mich. 48333-9094

ASTM100 Barr Harbor DriveWest Conshohocken, PA 19428

7.2—Cited referencesAbeles, P. W., 1940, “Saving Reinforcement by Prestr

ing,” Concrete and Constructional Engineering, V. 35, 3 pp.Abeles, P. W., 1945, “Fully and Partially Prestress

Reinforced Concrete,” ACI JOURNAL, Proceedings V. 41,No. 3, Jan., pp. 181-214.

Abeles, P. W., 1954, “Static and Fatigue Tests on PartPrestressed Concrete Constructions,” ACI JOURNAL, V. 51,No. 12, Dec., 361 pp.

Abeles, P. W., 1965, “Studies of Crack Widths and Demation Under Sustained and Fatigue Loading,” PCI Journal,V. 10, No. 6, Dec., pp. 43-52.

Abeles, P. W., 1968, “Preliminary Report on Static aSustained Loading Tests,” PCI Journal, V. 13, No. 4, Aug.,pp. 12-32.

ACI Committee 209, 1982, “Prediction of Creep, Shrinage, and Temperature Effects in Concrete StructurDesigning for Creep and Shrinkage, SP-76, B. B. Goyal,ed., American Concrete Institute, Farmington HilMich., pp. 193-300.

ACI Committee 215, 1974, “Considerations for DesignConcrete Structures Subjected to Fatigue Loading,” JOURNAL, V. 71, No. 3, Mar., pp. 97-121.

ACI Committee 224, 1980, “Control of Cracking in Cocrete Structures,” Concrete International, V. 2, No. 10, Oct.,pp. 35-76.

ACI-ASCE Joint Committee 323, 1958, “Tentative Reommendations for Prestressed Concrete,” ACI JOURNAL,Proceedings V. 54, No. 7, Jan., pp. 545-578.

Al-Zaid, R. Z., and Naaman, A. E., 1986, “Analysis Partially Prestressed Composite Beams,” Journal of Struc-tural Engineering, ASCE, V. 112, No. 4, Apr., pp. 709-725

Al-Zaid, R. Z.; Naaman, A. E.; and Nowak, A. S., 198“Analysis of Partially Prestressed Composite Beams unSustained and Cyclic Fatigue Loading,” Journal of Struc-tural Engineering, ASCE, V. 114, No. 2, Feb., pp. 269-29

Amu, O. O., and French, C. W., 1985, “Moment ResistConnections in Precast Structures Subjected to Cyclic eral Loads,” Structural Research Report No. 87-07,Deptartment of Civil and Mineral Engineering, Universof Minnesota, Minneapolis, Minn.

Applied Technology Council, 1981, Proceedings, Work-


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shop on Design of Prefabricated Concrete BuildingsEarthquake Loads, Los Angeles, Calif., Apr.,

Architectural Institute of Japan, 1970, Design Essentialin Earthquake Resistant Buildings, Elsevier Co., New Yorkpp. 186-200.

Arya, A. S., 1970, “Use of Prestressed Concrete in Equake Resistance Structures,” Proceedings, Fourth Symposium on Earthquake Engineering, Roorkee, India, Nov.

Ashar, H.; Naus, D.; and Tan, C.P., 1994, “PrestreConcrete in U.S. Nuclear Power Plants (Part 1),” ConcreteInternational V. 16, No. 5, May, pp. 30-34.

Baker, A. L. L., and Amarakone, A. M. N., 1964,, “Ineltic Hyperstatic Frame Analysis,” Proceedings, InternationalSymposium on the Flexural Mechanics of Reinforced crete, SP-12, American Concrete Institute, FarmingHills, Mich., pp. 85-142.

Balaguru, P. N., 1981, “Analysis of Prestressed ConBeams for Fatigue Loading,” PCI Journal, V. 26, No. 3,May-July, pp. 70-94.

Balaguru, P. N., and Shah, S. P., 1982, “Method of dicting Crack Widths and Deflections for Fatigue LoadinFatigue of Concrete Structures, SP-75, S. P. Shah, eAmerican Concrete Institute, Farmington Hills, Mich., 153-175.

Beeby, A. W., 1978, “Corrosion of Reinforcing SteeConcrete and its Relation to Cracking,” Structural Engi-neer, London, V. 56A, No. 3, Mar., pp. 77-81.

Beeby, A. W., 1979, “The Prediction of Crack WidthsHardened Concrete,” Structural Engineer, London, V. 57A,No. 1, Jan., pp. 9-17.

Bennet, E. W., 1984, “Partial Prestressing—An HistoOverview,” PCI Journal, V. 29, No. 5, Sept.-Oct., pp. 104-11

Bennett, E. W., 1986, “Partially Prestressed Concrete Mbers: Repeated Loading,” Partial Prestressing, From Theoto Practice, NATO ASI Series, V. 1, Martinus Nijhoff Pulishers, Dordrecht, The Netherlands, pp. 135-149.

Bennett, E. W., and Lee, K. H., 1985, “Deflection of Ptially Prestressed Beams under a Combination of LTime and Short-Time Loading”, Deflections of ConcretStructures, SP-86, G. M. Sabnis, Ed., American ConcInstitute, Farmington Hills, Mich., pp. 185-214.

Berg, G. V., and Degenkolb, H. J., 1973, “Engineering sons from the Managua Earthquake,” Managua, NicaraguaEarthquake, Dec. 1972, Earthquake Engineering ReseaInstitute, Oakland, Calif., Nov., pp. 761-763.

Bertero, V. V., 1973, “Experimental Studies ConcernReinforced, Prestressed, and Partially Prestressed CoStructures and their Elements,” Resistance and UltimaDeformability of Structures Acted on by Well DefinRepeated Loads, IABSE, Lisbon.

Bertero, V. V., 1986, “Partially Prestressed ConcMembers for Earthquake-Resistant Design and Constion,” Partial Prestressing, from Theory to Practice, NATOASI Series, V. 1, Martinus Nijhoff Publishers, DordrecThe Netherlands, pp. 151-188.

Bhuvasorakul, T., 1974, “Performance of Members Rforced with Smooth Welded Wire Fabric Under Static Repeated Loads,” PhD thesis, Oklahoma State Universit

Birkenmaier, M., 1984, “Developments in the DesignPartial Prestressing,” Partial Prestressing, from Theory Practice, NATO ASI Series, Martinus Nijhoff PublisherDordrecht, The Netherlands.

Bishara, A. G., and Brar, G. S., 1974, “Rotational Ca

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ity of Prestressed Concrete Beams,” Journal of the Struc-tural Division, ASCE, V. 100, No. ST9, Sept., pp. 1881895.

Blakeley, R. W. G., 1971, “Ductility of Prestressed Cocrete Frames under Seismic Loading,” PhD thesis, Unisity of Canterbury, Christchurch, New Zealand.

Blakeley, R. W. G., and Park, R., 1971, “Seismic Retance of Prestressed Concrete Beam-Column AssembACI JOURNAL, V. 68, No. 9, Sept., pp. 677-692.

Blakeley, R. W. G., and Park, R., 1973a, “ResponsePrestressed Concrete Structures to Earthquake MotioNew Zealand Engineering, V. 28, No. 2, Feb., pp. 42-54.

Blakeley, R. W. G., and Park, R., 1973b, “Prestressed Ccrete Sections With Seismic Loadings,” Journal of the Struc-tural Division, ASCE, V. 99, No. ST8, Aug., pp. 1717-1742

Branson, D. E., 1974, “The Deformation of Non-Compite and Composite Prestressed Concrete Members,” Deflec-tions of Concrete Structures, SP-43, American ConcretInstitute, Farmington Hills, Mich., pp. 83-128.

Branson, D. E., 1977, Deformation of Concrete Structures, McGraw-Hill, New York.

Branson, D. E., and Kripanarayanan, K. M., 1971, “Lof Prestress, Camber, and Deflections of Non-Compoand Composite Prestressed Concrete Structures,” PCI Jour-nal, V. 16, No. 5, Sept.-Oct. pp. 22-52.

Branson, D. E., and Shaikh, A. F., 1985, “DeflectionPartially Prestressed Members,” Deflections of ConcreteStructures, SP-86, G. M. Sabnis, Ed., American ConcrInstitute, Farmington Hills, Mich., pp. 323-363.

Branson, D. E., and Trost, H., 1982a “Unified Procedufor Predicting the Deflection and Centroidal Axis Locatiof Partially Cracked Nonprestressed and Prestressed crete Members,” ACI JOURNAL, V. 79, No. 2, Mar.-Apr., pp119-130.

Branson, D. E., and Trost, H., 1982b “Application of theEffective Method in Calculating Deflections of Partially Pstressed Members,” PCI Journal, V. 27, No. 5, Sept.-Oct.

Brondum-Nielsen, T., 1973, “Effect of Prestress on Damping of Concrete,” Resistance and Ultimate Deformability of Structures Acted on by Well Defined RepeaLoads, IABSE, Lisbon.

Bruggeling, A. S. G., 1977, “Time Dependent Deflectof Partially Prestressed Beams,” Report No. 5-77-1, Depart-ment of Civil Engineering, Delft Technical University, Ma16 pp.

Bureau of Public Roads, 1954, Criteria for PrestressedConcrete Bridges, U.S. Department of Commerce, Wasington, D.C.

Burns, N. H., 1964, “Moment Curvature Relationship Partially Prestressed Concrete Beams,” PCI Journal, V. 9,No. 1, Feb., pp. 52-63.

Burns, N. H., and Siess, C. P., 1962, “Loading Deformtion Characteristics of Beam-Column Connections in Rforced Concrete,” Civil Engineering Studies, StructuResearch Series, Bulletin No. 234, University of Illinois,Urbana, 261 pp.

Burns, V. V., 1979, “Inelastic Behavior of Structural Ements and Structures,” Proceedings, NSF Workshop (Dec2-4), University of Illinois at Chicago, pp. 96-167.

Caflisch, R.; Krauss, R.; and Thurlimann, B., 197“Beige-und Schubversuche and Teilweise VorgespanBetonbalken, Serie C.,” Bericht 6504-3, Institut fur Baustik, ETH, Zurich.


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CEB-FIP; 1978, Model Code for Concrete Structure,Paris, 348 pp.

Cement and Concrete Association, 1977, Recommendations for the Design of Aseismic Prestressed Concrete Stures, London, Nov., 28 pp.

Cheok, G. S., and Lew, H. S., 1990, “Performance of Scale Model Precast Concrete Beam-Column ConnecSubjected to Cyclic Inelastic Loads,” NISTIR 4433, NIST,Gaithersburg, Md.

Cheok, G. S., and Lew, H. S., 1991, “Performance of Scale Model Precast Concrete Beam-Column ConnecSubjected to Cyclic Inelastic Loads — Report No. 2,” NIS-TIR 4589, NIST, Gaithersburg, Md.

Cohn, M. Z., and Bartlett, M., 1982, “Nonlinear FlexuResponse of Partially Prestressed Concrete Sections,”Jour-nal of the Structural Division, ASCE, V. 108, No. ST12Dec., pp. 2747-2765.

Cohn, M. Z., and Ghosh, S. K., 1972, “The Flexural Dtility of Reinforced Concrete Sections,” Publications, Inter-national Association for Bridge and Structural EngineerZurich, V. 32-II, pp. 53-83.

Corley, W. G., 1966, “Rotational Capacity of ReinforcConcrete Beams,” Journal of the Structural Division,ASCE, V. 92, No. ST5, Oct., pp. 121-146. (See also PBulletin D108.)

CSA Committee A23.3, 1984, Design of Concrete Structures for Buildings, CAN3-A23.3-M84, Canadian StandarAssociation (CSA), Rexdale, Ontario, Canada, 281 pp.

de Saint-Venant, 1956, “Memoires presentes par dsavants a I’Academie des Sciences de I’Institut ImperiaFrance,” V. 14 (Second Series), Paris.

Dilger, W. H., 1982, “Creep Analysis of Prestressed Ccrete Structures Using Creep-Transformed Section Prties,” PCI Journal, V. 27, No. 2, Jan.-Feb., pp. 98-118.

Elbadry, M. M., and Ghali, A., 1989, “ServiceabilDesign of Continuous Prestressed Concrete StructuPCI Journal, V. 34, No. 1, Jan-Feb, pp. 54-91.

Elliott, A. L., 1972, “Hindsight and Foresight on the Pformance of Prestressed Concrete Bridges in the Fernando Earthquake,” PCI Journal, V. 17, No. 2, Mar.-Apr., pp. 8-16.

El-Sheikh, M. T.; Sause, R.; Pessiki, S.; and Lu, L-1999, “Seismic Behavior and Design of Unbonded PTensioned Precast Concrete Frames,” PCI Journal, V. 44,No. 3, May-June, pp. 54-69.

Emperger, F. V., 1939, “Reinforced Concrete with Adtions of High-Strength Pretensioned Steel,” Forschingsar-beiten auf dem Gebiete des Eisenbetons, H. 47, WilhelmErnest und Sohn, Berlin.

European Committee for Standardization (CEN), 19“Eurocode 2 (EC2): Design of Concrete Structures, PaGeneral Rules and Rules for Buildings,” Brussels, Belg

Federal Emergency Management Agency, 1998, NEHRPRecommended Provisions for Seismic Regulations forBuildings and Other Structures, Part 1 — Provision(FEMA 302), Part 2—Commentary (FEMA 303), BuildiSeismic Safety Council, Feb.

FIP Commission on Model Code, 1984, “Recommentions for Practical Design of Reinforced and PrestreConcrete Structures Based on the CEB-FIP Model C(MC78),” Federation Internationale de la Precontra(FIP), London, England.

FIP Commission on Prestressing Steel and Systems,

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“Report on Prestressing Steels: Types and Properties,” eration Internationale de la Precontrainte (FIP), LondEngland, Aug.,18 pp.

FIP Commission on Prestressing Steel and Systems, 1“Recommendations for Acceptance of Post-Tensioning Stems (Draft Version),” Federation Internationale de la Pcontrainte (FIP), London, England, March 10, 21 pp.

FIP Commission on Seismic Structures, 1970, “Repothe FIP Commission on Seismic Structures,” Proceedings,Sixth Congress of FIP (Prague), Federation Internatiode la Precontrainte (FIP), London, England, pp. 91-95.

FIP Commission on Seismic Structures, 1974, “Repothe FIP Commission on Seismic Structures,” Proceedings,Seventh Congress of FIP (New York), Federation Internanale de la Precontrainte (FIP), London, England, pp. 64

FIP-CEB Joint International Committee, 1970, “Recomendations for the Design and Construction of ConcStructure,” Cement and Concrete Association, LondEngland, June, 80 pp.

Founas, M, 1989, “Deformation and Deflections of PartiPrestressed Concrete T-Beams under Static and RaAmplitude Fatigue Loading,” PhD thesis, Department of CEngineering, University of Michigan, 402 pp.

French, C. W.; Amu, O.; and Tarzikhan, C., 1989a, “Cnections between Precast Elements—Failure Outside nection Region,” Journal of Structural Engineering, ASCE,V. 115, No. 2, Feb., pp. 316-340.

French, C. W.; Hafner, M.; and Jayashankar, V., 198“Connections between Precast Elements—Failure WiConnection Region,” Journal of Structural Engineering,ASCE, V. 115, No. 12, Dec., pp. 3171-3192.

Freyermuth, C. L., 1985, “Practice of Partial Prestresfor Continuous Post-Tensioned Structures in North Amica,” PCI Journal, V. 30, No. 1, Jan.-Feb., pp. 154-172.

Freyssinet, E., 1933, “New Ideas and Methods,” Scienceet Industrie, Jan. (See also in Trauvaux, Apr.-May 1966, pp.607-622.)

Gergely, P., and Lutz, L. A., 1968, “Maximum CraWidth in Reinforced Concrete Flexural Members,” Causes,Mechanisms and Control of Cracking in Concrete, SP-20,R. E. Philleo, ed., American Concrete Institute, FarmingHills, Mich., pp. 87-117.

Ghali, A., 1989, “Stress and Strain Analysis in PrestresConcrete,” PCI Journal, V. 34, No. 6, Nov.-Dec., pp. 80-95

Ghali, A., and Favre, R., 1986, Concrete StructuresStresses and Deformations, Chapman and Hall, London anNew York, 352 pp.

Ghali, A., and Tadros, M.K., 1985, “Partially PrestresConcrete Structures,” Journal of Structural Engineering,ASCE, V. 111, No. 8, Aug, pp. 1846-1865.

Giannini, R.; Menegotto, M.; and Nuti C., 1986 “Inflence of Prestressing on Seismic Response of StructurNumerical Study,” Partial Prestressing, from Theory tPractice, NATO ASI Series, V. 2, Martinus Nijhoff Publishers, Dordrecht, The Netherlands, pp. 255-274.

Guyon, Y., 1965, “Energy Absorption of Prestressed Ccrete,” Proceedings, 3WCEE, New Zealand, V. III, Jan., pIV.216-IV.223.

Gylltoft, K., 1978, “Fatigue Tests of Concrete SleepeReport No. 1978:13, Division of Structural Engineering, Uversity of Lulea, Sweden, 26 pp.

Hafner, M., and French, C. W., 1986, “Moment ResisConnections between Precast Elements Subjected to C


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Lateral Loads,” Structural Research Report No. 87-09,Department of Civil and Mineral Engineering, University Minnesota, Minneapolis, Minn.

Harajli, M. H., 1985, “Deformation and Cracking of Patially Prestressed Beams Under Static and Cyclic FatLoading,” PhD thesis, Department of Civil EngineerinUniversity of Michigan.

Harajli, M. H., and Naaman, A. E., 1984, “Deformatioand Cracking of Partially Prestressed Concrete Beams uStatic and Cyclic Fatigue Loading,” Report No. UMEE84R1, Department of Civil Engineering, University Michigan.

Harajli, M. H., and Naaman, A. E., 1985a, “Static aFatigue Tests on Partially Prestressed Beams,” Journal ofStructural Engineering, ASCE, V. 111, No. 7, July, pp1602-1618.

Harajli, M. H., and Naaman, A. E., 1985b, “EvaluationUltimate Steel Stress in Partially Prestressed Flexural Mbers,” PCI Journal, V. 30, No. 5, Sept.-Oct.

Harajli, M. H., and Naaman, A. E., 1985c “Evaluationthe Inelastic Behavior of Partially Prestressed ConcBeams,” Report No. UMCE 85-2, Dept. of Civil Engineering, University of Michigan, 191 pp.

Harajli, M. H., and Naaman, A. E., 1989, “Cracking Partially Prestressed Beams under Static and Cyclic FaLoading,” Cracking in Prestressed Concrete Structures, SP-113, G. T. Halvorsen, and N. H. Burns, eds., American Ccrete Institute, Farmington Hills, Mich., pp. 29-54.

Hawkins, N. M., 1977, “Seismic Resistance of Prestresand Precast Concrete Structures —Part I,” PCI Journal, V. 22,No. 6, Nov.-Dec., pp. 80-110.

Hilsdorf, H. K., and Kesler, C. E., 1966, “Fatigue Strenof Concrete Under Varying Flexural Stresses,” ACI JOUR-NAL, Proceedings V. 63, No. 10, Oct., pp. 1059-1075.

Hsu, T.C., 1968, “Torsion of Structural Concrete Behavof Reinforced Concrete Rectangular Members,” Torsion ofStructural Concrete, SP-18, G. P. Fisher, ed., AmericaConcrete Institute, Farmington Hills, Mich., pp. 261-306.

Inomata, S., 1986, “Partially Prestressed Concrete uCyclic Actions—Analytical Moment-Curvature Model,Partial Prestressing, From Theory to Practice, NATO ASISeries, V. 2, Martinus Nijhoff Publishers, Dordrecht, TNetherlands, pp. 193-204.

Institution of Structural Engineers., 1951, First Report onPrestressed Concrete, London, 285 pp.

Iyengar, K. T. S. R.; Desayi, P.; and Reddy, K. N., 19“Stress-Strain Characteristics of Concrete Confined in SBinder,” Magazine of Concrete Research, V. 22, Sept., pp.173-184.

Iwan, W. D., 1973, “A Model for the Dynamic Analysis oDeterioration Structures,” (Paper 222) Presented at the World Conference on Earthquake Engineering, heldRome, Italy.

Jayashankar, V., and French, C. W., 1987, “An InteMoment Resistant Connection between Precast ElemSubjected to Cyclic Lateral Loads,” Structural ResearchReport No. 87-10, Department of Civil and Mineral Engneering, University of Minnesota, Minneapolis, Minn.

Jenny, D. P., 1985, Current Status of Partial Prestresfor Pretensioned Concrete Products in North America,” PCIJournal, V. 30, No. 1, Jan.-Feb., pp. 142-152.

Jittawait, J., and Tadros, M. K., 1979, “Deflection of Ptially Prestressed Concrete Members,” Research Report,

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d

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er

,el

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-

Department of Civil Engineering, West Virginia UniversityKent, D. C., and Park, R., 1966, “Flexural Members w

Confined Concrete,” Journal of the Structural Division,ASCE, V. 97, No. ST5, Oct., pp. 121-146 (see also PBulletin D108).

Kunze, W. E.; Sbarounis, J. A.; and Amrhein, J. E., 19“Behavior of Prestressed Concrete Structures During Alaskan Earthquake,” PCI Journal, V. 10, No. 2, Apr., pp.80-91.

Lambotte, H., and Van Nieuwenburg, D., 1986, “LonTerm Behavior of Partially Prestressed Beams,” Partial Pre-stressing, From Theory to Practice, NATO ASI Series, V. 2,Martinus Nijhoff Publishers, Dordrecht, The Netherlands

Lenschow, R. J., 1986, “Partial Prestressing and RepeLoads Related to Random Dynamic Loading,” Partial Pre-stressing, from Theory to Practice, NATO ASI Series, V. 2,Martinus Nijhoff Publishers, Dordrecht, The Netherlanpp. 221-229.

Lin, T. Y., 1963, “Load-Balancing Method for Design anAnalysis of Prestressed Concrete Structures,” ACI JOUR-NAL, Proceedings V. 60, No. 6, June, pp. 719-742.

Lin, T. Y., and Burns, N. H., 1981, Design of PrestressedConcrete Structures, 3rd Edition, John Wiley & Son, N.Y.

Loov, R. E., 1987, Reader Comments on “AnalysisDuctility in Partially Prestressed Flexural Members,” by E. Naaman; M. H. Harajli; and J. K. Wight, PCI Journal, V.32, No. 1, Jan.-Feb., pp. 141-145.

Lovegrove, J. M., and El Din, S., 1982, “Deflection aCracking of Reinforced Concrete under Repeated Loaand Fatigue,” Fatigue of Concrete Structures, SP-75, S. P.Shah, ed., American Concrete Institute, Farmington HMich., pp. 133-152.

MacGregor, J. G., 1974, “Ductility of Structural Elments,” Handbook of Concrete Engineering, First Edition,M. Fintel, ed., Prentice Hall, New York.

MacGregor, J. G., and Ghoneim, M. G., 1995, “DesignTorsion,” ACI Structural Journal, V. 92, No. 2, Mar.-Apr.,pp. 211-218.

Martin, L. D., 1977, “A Rational Method for EstimatinCamber and Deflections,” PCI Journal, V. 22, No. 1, Jan.-Feb. pp. 100-108.

Martino, N. E., and Nilson, A. H., 1979, “Crack Widths Partially Prestressed Concrete Beams,” Report No. 79-3,Department of Structural Engineering, Cornell UniversIthaca, New York, 86 pp.

Mattock, A. H., 1964, “Rotational Capacity of HinginRegion in Reinforced Concrete Beams,” Proceedings, Inter-national Symposium on Flexural Mechanics of ReinforConcrete, SP-12, American Concrete Institute, FarmingHills, Mich., pp. 143-181. (See also PCA Bulletin D101.)

Mattock, A. H., 1967, Discussion on “Rotational Capacof Concrete Beams,” Journal of Structural Division, ASCE,V. 93, No. ST-2, Apr., pp. 519-522.

McCall, J. T., 1958, “Probability of Fatigue Failure Plain Concrete,” ACI JOURNAL, Proceedings V. 55, No. 2,Aug., pp. 221-231.

Meier, S. W., and Gergely, P., 1981, “Flexural Crack Wiin Prestressed Concrete Beams,” Journal of the StructuralDivision, ASCE, V. 107, No. ST2, Feb., pp. 429-433.

Ministry of Transportation and Communications, 198Ontario Highway Bridge Design Code, Downsview,Ontario, Canada.

Moustafa, S. E., 1977 “Design of Partially Prestres


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gi-

ears,

.80,ete

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“Onno-, p

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edity,

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-

Flexural Members,” PCI Journal, V. 22, No. 3, May-June.Moustafa, S. E., 1986, “Nonlinear Analysis of Reinforc

and Prestressed Concrete Members,” PCI Journal, V. 31,No. 5, Sept-Oct.

Muguruma, H., 1986 “Seismic Problems of PPC BuildiStructures with Special Reference to Basic ResearcJapan,” Partial Prestressing, From Theory to Practic,NATO ASI Series, V. 2, Martinus Nijhoff Publishers, Dodrecht, The Netherlands, pp. 231-254.

Muguruma, H., and Tominaga, H., 1972, “DeformatiCharacteristics of Prestressed Lightweight Concrete BeColumn Assemblies under Seismic Force,” Proceedings,18th National Symposium on Bridge and Structural Enneering, Japan, pp. 123-136.

Muguruma, H.; Watanabe, F.; and Fujii, M., 1983, “ShBehavior of Prestressed Reinforced Concrete BeamTransactions, Japan Concrete Institute, V. 5, pp. 225-230

Muguruma, H.; Watanabe, F.; and Fukai, S., 19“Behavioor of Class 3 Partially Prestressed ConcrBeam under Reversed Cyclic High Over-Load,” Proceed-ings of FIP Symposium on Partial Prestressing (Buchar-est), Federation Internationale de la Precontrainte (FLondon, Sept., pp. 118-127.

Muguruma, H.; Watanabe, F.; and Fukai, S., 1983, “OnClass 3 Prestressed Concrete Member with High StreConcrete,” (in Japanese), Proceedings, Annual Meeting ofJapan Concrete Institute, Tokyo, June, pp. 449-452.

Muguruma, H.; Watanabe, F.; and Nasu, T., 1982a, the Fundamental Behaviors of a PPC Beam under Motonic and Cyclic High Overload,” Journal, Japanese Prestressed Concrete Engineering Association, V. 24, Sept.101-108.

Muguruma, H.; Watanabe, F.; and Tanaka, H., 198“Improving the Flexural Ductility of Prestressed Concreby Using High Yield Strength Lateral Hoop Reinforcment,” Journal, Japanese Prestressed Concrete EngineeAssociation , V. 24, Sept., pp. 109-123.

Naaman, A. E., 1977, “Ultimate Analysis of Prestressand Partially Prestressed Sections by Strain CompatibilPCI Journal, V. 22, No. 1, Jan.-Feb., pp. 32-51.

Naaman, A. E., 1982a, Prestressed Concrete Analysis aDesign, McGraw Hill, N.Y, 670 pp.

Naaman, A. E., 1982b, “Fatigue in Partially PrestresBeams”, Fatigue of Concrete Structures, SP-75, S. P. Shahed., American Concrete Institute, Farmington Hills, Micpp. 25-46.

Naaman, A. E., 1983a, “Time-Dependent DeflectionPrestressed Beams by the Pressure-Line Method,” PCIJournal, V. 28, No. 2, Mar.-Apr., pp. 98-119.

Naaman, A. E., 1983b, “An Approximate Nonlinear DesProcedure for Partially Prestressed Concrete Beams,” Com-puters and Structures, V. 17, No. 2, pp. 287-293.

Naaman, A. E., 1985, “Partially Prestressed ConcrReview and Recommendations,” PCI Journal, V. 30, No. 6,Nov-Dec, pp. 30-71.

Naaman, A. E., 1989, “Fatigue of Reinforcement in Ptially Prestressed Beams,” Proceedings, ASCE StructuresCongress, San Francisco, Volume on Structural MateriaF. Orofino, ed., May, pp. 377-381.

Naaman, A. E., and Founas, M., 1991, “Partially Pstressed Beams under Random Amplitude Fatigue Loing,” Journal of Structural Engineering, ASCE V. 117, No.12, Dec., pp. 3742-3761.

n

-

”

,

h

-

p.

,

g

”

:

.

-

Naaman, A. E., and Hamza, A. M., 1993, “PrestreLosses in Partially Prestressed High Strength ConcBeams,” PCI Journal, V. 38, No. 3, May-June, pp. 98-114.

Naaman, A. E.; Harajli, M. H.; and Wight, J. K., 198“Analysis of Ductility in Partially Prestressed ConcreFlexural Members,” PCI Journal, V. 31, No. 3, May-June,pp. 64-87.

Naaman, A. E., and Siriaksorn, A., 1979, “ServiceabiliBased Design of Partially Prestressed Beams: Part 1—Alytical Formulation,” PCI Journal, V. 24, No. 2, Mar.-Apr.,pp. 64-89.

Naaman, A. E., and Siriaksorn, A., 1982 “Reliability Partially Prestressed Beams at Serviceability Limit StatePCI Journal, V. 27, No. 6, Nov.-Dec., pp. 66-85.

Nadai, A., 1950, Theory of Flow and Fracture of Solids,McGraw-Hill, New York.

Nakano, K., 1965, “Experiments on Behavior of Prstressed Concrete Four-Story Model Structure on LatForce,” Proceedings, 3WCEE, New Zealand, V. III, Jan.pp. IV.572-IV.590.

Nakano. K., and Okamota, S., 1978, “Test Results Beam-Column Assemblies,” Proceedings, 8th FIP Congress,London, May, pp. 58-69.

Nawy, E. G., and Chiang, J. Y., 1980, “ServiceabilBehavior of Post-Tensioned Beams,” PCI Journal, V. 25,No. 1, Jan.-Feb., pp. 74-95.

Nawy, E. G., and Huang, P. T., 1977 “Crack and Defltion Control of Pretensioned Prestressed Beams,” PCI Jour-nal, Vol. 22, No. 3, May-June, pp. 30-47.

Nawy, E. G., and Potyondy, J. G., 1971, “Flexural Craing Behavior of Pretensioned Prestressed Concrete I- anBeams,” ACI JOURNAL, V. 68, No. 5, May, pp. 355-360.

Nilson, A. H., 1976, “Flexural Stresses After Cracking Partially Prestressed Beams,” PCI Journal, V. 21, No. 4,July-August, pp. 72-81.

Nilson, A. H., 1987, Design of Prestressed Concret,John Wiley & Son, N.Y.

Nordby, G. M., 1958, “Fatigue of Concrete—A Review Research,” ACI JOURNAL, Proceedings V. 55, No. 2, Aug.,pp. 191-219.

Oertle, J., 1988, “Reibermudung einbetonierter Spannbel (Fretting Fatigue of Bonded Post-Tensioning TendonReport No. 166, thesis, Institute for Structural EngineerinETH, Zurich, Switzerland, 213 pp.

Okamoto, S., 1980, “Experimental Study on the Ductilof PPC Beams,” Proceedings, FIP Symposium on PartiaPrestressing (Bucharest), Federation Internationale dPrecontrainte (FIP), London, Sept., pp. 128-149.

Ozaka, T., 1968, “Report on Behavior of Concrete Strtures During the Tokachioki Earthquake,” Journal, JapanPrestressed Concrete Engineering Association, V. 10, NDec.

Palmieri, L.; Saqan, E.; French, C.; and Kreger, M., 19“Ductile Connections for Precast Concrete Frame SystemMete A. Sozen Symposium: Tribute from his Students, SP-162, J. K. Wight, and M. E. Kreger, eds., American ConcrInstitute, Farmington Hills, Mich., pp. 313-356.

Park, R., and Falconer, T. J., 1983, “Ductility of Prstressed Concrete Piles Subjected to Simulated SeiLoading,” PCI Journal, V. 28, No. 5, Sept.-Oct., pp. 111144.

Park, R., and Paulay, T., 1975, Reinforced Concrete Structures, John Wiley & Sons, New York.


stslum

“A

ng

93

re-

24

icDe.

ed,

f a

hece

d

B.ten

Pre

stnt:rk,

hee tog-

ss-ng

ar-

ed

e-

al

,

lity-Com-

rder

rete

teelg

ine

80,ign

per-

arth-, and.

sis

andn; T. A. S.

e-essed,

cttion,”

re-ers,”

dges

andSub-rtng,

re-r-

rio,

Park, R., and Thompson, K. J., 1977, “Cyclic Load Teon Prestressed and Partially Prestressed Beam-CoJoints,” PCI Journal, V. 22, No. 5, Sept.-Oct., pp. 84-111.

Paulson, C. Jr.; Frank, K. H.; and Breen, J. E., 1983,Fatigue Study of Prestressing Strand,” Research Report No.300-1, Center for Transportation Research, Bureau of Eneering Research, University of Texas at Austin.

PCI Ad Hoc Committee on Epoxy-Coated Strand, 19“Guidelines for the Use of Epoxy—Coated Strand”, PCIJournal, V. 38, No. 4, July-Aug., pp. 26-32.

Penzien, J., 1964, “Damping Characteristics of Pstressed Concrete,” ACI JOURNAL, Proceedings V. 61, No.9, Sept., pp. 1125-1148.

Post-tensioning Institute, 1990, Post-Tensioning Manual,Phoenix, Ariz.

Precast/Prestressed Concrete Institute, 1989, Design forFire Resistance of Precast Prestressed Concrete (MNL-189), 2nd Edition, Chicago, Ill.

Precast/Prestressed Concrete Institute, 1992, PCI DesignHandbook, 4th Edition, Chicago, Ill.

Priestley, M. J. N., and Tao, J. R., 1993, “The SeismResponse of Precast-Prestressed Frames with Partially onded Tendons,” PCI Journal, V. 38, No. 1, Jan.-Feb., pp58-69.

Ramirez, J.A., 1994, “Strut-Tie Design of PretensionMembers,” ACI Structural Journal, V. 91, No. 5, Sept.-Oct.pp. 572-578.

Ramirez, J.A., and Breen, J.E., 1991, “Evaluation oModified Truss-Model Approach for Beams in Shear,” ACIStructural Journal, V. 88, No. 5, Sept.-Oct., pp. 562-571.

Rehm, G., 1960, “Contributions to the Problem of tFatigue Strength of Steel Bars for Concrete Reinforment,” Preliminary Publication, 6th Congress of the IABSE(Stockholm), International Association for Bridge anStructural Engineering, Zurich, Switzerland, pp. 35-46.

Roller, J. J.; Russell, H. G.; Bruce, R. N.; and Marin,T., 1995, “Long-Term Performance of Prestressed, Presioned High-Strength Concrete Bridge Girders,” PCI Jour-nal, V. 40, No. 6, Nov-Dec, pp. 48-59.

Rostam, S., and Pedersen, E. S., 1980, “Partially stressed Concrete Bridges, Danish Experience,” Proceed-ings, Symposium on Partial Prestressing, BuchareICCPDC-INCERC, V. 1, pp. 361-376. (See also repriReport R129, Lyngby, Technical University of Denma1980.)

Schroeder, A. B., 1977, “The Influence of Bond on tTransfer of Cyclically Reversing Shear Across a ConcretConcrete Interface,” MSCE thesis, University of Washinton, Seattle.

Scott, B. D.; Park, R.; and Priestley, M. N., 1982, “StreStrain Behavior of Concrete Confined by OverlappiHoops at Low and High Strain Rates,” ACI JOURNAL, Pro-ceedings V. 79, No. 1, Jan.-Feb., pp. 13-27.

Shahawi, M., and Batchelor, B., 1986, “Fatigue of Ptially Prestressed Concrete,” Journal of Structural Engi-neering, ASCE, V. 112, No.3, Mar., pp. 524-537.

Shaikh, A. F., and Branson, D. E., 1970, “Non-TensionSteel in Prestressed Concrete Beams,” PCI Journal, V. 15,No. 1, Feb., pp. 14-36.

Sheikh, S. A., 1982, “A Comparative Study of Confinment Models,” ACI JOURNAL, Proceedings V. 79, No. 4,July-Aug., pp. 296-306.

Sheikh, S. A., and Uzumeri, S. M., 1982, “Analytic

n

i-

,

-

b-

-

-

-

,

Model for Concrete Confinement in Tied Columns,” Jour-nal of the Structural Division, ASCE, V. 108, No. ST12Dec., pp. 2703-2722.

Siriaksorn, A., and Naaman, A. E., 1979, “ServiceabiBased Design of Partially Prestressed Beams, Part 2: puterized Design and Evaluation of Major Parameters,”PCIJournal, V. 24, No.3, May-June, pp. 40-60.

Soda, N., and Kazuo I., 1994, “PRC Continuous GiBridge with Double-Tee Section—Kannonji Viaduct,” Pre-stressed Concrete in Japan, Japanese Prestressed ConcEngineering Association, Tokyo.

Soretz, S., 1965, “Fatigue Behavior of High-Yield SReinforcement,” Concrete and Constructional Engineerin,London, V. 60, No. 7, July, pp. 272-280.

Spencer, R. A., 1969, “Stiffness and Damping of NCyclically Loaded Prestressed Members,” PCI Journal, V.14, No. 3, June, pp. 39-52.

Standards Association of Australia, 1984, Draft UnifiedConcrete Structures Code, BD/2/84-11.

Standards Association of New Zealand (NZA), 19Code of Practice for General Structural Design and DesLoading for Buildings, (NZA 4203).

Stelson, T. E., and Cernica, J. N., 1958, “Fatigue Proties of Concrete Beams,” ACI JOURNAL, Proceedings V. 55,No. 2, Aug., pp. 255-259.

Sutherland, N. M., 1965, “Prestressed Concrete Equake-Resistant Structures: Development, PerformanceCurrent Research,” Proceedings, 3WCEE, New Zealand, VIII, Jan., pp. IV-463-507.

Swiss Society of Engineers and Architects, 1968, SIAStandard 162, Switzerland.

Tadros, M. K., 1982, “Expedient Service Load Analyof Cracked Prestressed Concrete Sections,” PCI Journal, V.27, No. 6, Nov-Dec., pp. 86-111 (see also discussionsclosure by H. Bachmann; E. W. Bennett; D. E. BransoBrondum-Nielsen; A.S.G. Bruggeling; S. E. Moustafa;H. Nilson; A. S. Prasada Rao; S. Natarajan; G.Ramaswaym; and A. F. Shaikh; PCI Journal, Nov-Dec.1983, pp. 137-158).

Tadros, M. K.; Ghali, A.; and Dilger, W. H., 1975, “TimDependent Prestress Loss and Deflection in PrestrConcrete Members,” PCI Journal, V. 20, No. 3, May-Junepp. 86-98.

Tadros, M. K.; Ghali, A.; and Dilger, W. H., 1977, “Effeof Non-Prestressed Steel on Prestress Loss and DeflecPCI Journal, V. 22, No. 2, Mar.-Apr., pp. 50-63.

Tadros, M. K.; Ghali, A.; and Meyer, A. W., 1985, “Pstress Loss and Deflection of Precast Concrete MembPCI Journal, V. 30, No. 1, Jan-Feb, pp. 114-141.

Taerwe, L., 1990, “Partially Prestressed Concrete Briin Belgium,” Annales des Travaux Publics De Belgique No.5, Brussels.

Tarzikhan, C., and French, C. W., 1987, “Welded Composite Connections between Precast Elements jected to Cyclic Lateral Loads,” Structural Research RepoNo. 87-08, Department of Civil and Mineral EngineeriUniversity of Minnesota, Minneapolis, Minn.

Tertea, I., and Onet, T., 1983, “Ductility of Partially Pstressed Concrete,” International Symposium on Nonlineaity and Continuity in Prestressed Concrete, PreliminaryPublication, V.1, University of Waterloo, Waterloo, OntaJuly, pp. 235-250.

The Concrete Society, 1983, Partial Prestressing, Techni-


sn-

e-on

ns

,”

d

ry

s-b

y-AC

ig

.

onteo,

e

le

daen--

e-oa

me

o

-

ve

rete

ion

tmentur-e

ion

en-t

ion

en-

cks

ked

at

e or

at

rete

ing

pre-

inal

in

cingplica-

nt

cal Report No. 23, London.Thompson, K. J., 1975, “Ductility of Concrete Frame

Under Seismic Loading,” Ph.D. thesis, University of Caterbury, Christchurch, New Zealand.

Thompson, K. J., and Park, R., 1980a, “Ductility of Prstressed and Partially Prestressed Concrete Beam SectiPCI Journal, V. 25, No. 2, Mar.-Apr., pp. 46-70.

Thompson, K. J., and Park, R., 1980b, “Seismic Respoof Partially Prestressed Concrete,” Journal of the StructuralDivision, ASCE, Aug., pp. 1755-1775.

Thurlimann, B., 1971, “A Case for Partial PrestressingStructural Concrete Symposium Proceedings, University ofToronto, May, pp. 253-301.

Thurlimann, B., 1979, “Torsional Strength of Reinforceand Prestressed Concrete Beams—CEB Approach,” Con-crete Design: U.S. and European Practices, SP-59, Ameri-can Concrete Institute, Farmington Hills, Mich., 346 pp.

Transportation Research Board, 1993, Final Draft LRFDSpecification for Highway Bridge Design and Commenta,NCHRP 12-33, Washington, D.C.

Vecchio, J., and Collins, M.P., 1986 “Modified Compresion Field Theory for Reinforced Concrete Elements Sujected to Shear,” ACI Journal, V. 83, No. 2, Mar.-Apr., pp.219-231.

Venuti, W. J., 1965, “A Statistical Approach to the Analsis of Fatigue Failure of Pre-stressed Concrete Beams,” JOURNAL, Proceedings V. 62, Nov., pp. 1375-1394.

Wang, F.; Shah, S. P.; and Naaman, A. E., 1978, “HStrength Concrete in Ultimate Strength Design,” Journal ofthe Structural Division, ASCE,V. 104, No. ST11, Nov., pp1761-1773.

Wang, P. T., 1977, “Complete Stress-Strain Curve of Ccrete and its Effect on Ductility of Reinforced ConcreMembers,” PhD thesis, University of Illinois at Chicag257 pp.

Warner, R. F., and Hulsbos, C. L., 1966a, “Fatigue Propties of Prestressing Strand,” PCI Journal, V. 11, No. 1, Feb.,pp. 32-52.

Warner, R. F., and Hulsbos, C. L., 1966b, “ProbabFatigue Life of Prestressed Concrete Beams,” PCI Journal,V. 11, No. 2, Apr., pp. 16-39.

Watanabe, F.; Muguruma, H.; Tanaka, H.; and KatsuS., 1980, “Improving the Flexural Ductility of ConcretBeams by Using High Yield Strength Lateral Hoop Reiforcement,” Proceedings, FIP Symposium on Partial Prestressing (Bucharest), Federation Internationale dePrecontrainte (FIP), London, Sept. pp. 398-406.

Watcharaumnuay, S., 1984, “Deflection of Partially Prstressed Concrete Beams Under Sustained and Cyclic Ling,” PhD thesis, University of Illinois at Chicago.

Watcharaumnuay, S., and Naaman, A. E., 1985, “Tiand Cyclic Dependent Deflections in Partially PrestressConcrete Beams,” Report No., Department of Civil Engi-neering, University of Michigan.

Wight, J. K., and Sozen, M. A., 1975, “Strength DecayRC Columns Under Shear Reversals,” Journal of the Struc-tural Division, ASCE, V. 101, No. ST5, May, pp. 10531065.

APPENDIX—NOTATIONSa = depth of equivalent rectangular compressi

stress blockacs = crack spacing

s,”

e

-

I

h

-

r-

,

la

d-

ed

f

Acp = area enclosed by outside perimeter of conccross section

Aps = area of prestressed reinforcement in tenszone

As = area of nonprestressed tension reinforcemenA′s = area of nonprestressed compression reinforceAt = effective area of concrete tension zone s

rounding all reinforcementhaving the samcentroid as reinforcement

b = width of compression face of memberB = distance ratio at first loading cycleBN = distance ratio at the Nth loading cyclec = depth to neutral axis from extreme compress

fibercN = depth of neutral axis after Nth cycle of loadingc2 = constantCc(t–tA) = creep coefficient of concrete at time t when

loaded at time tAd = distance from extreme compression fiber to c

troid of nonprestressedtension reinforcemendc = cover to center of reinforcing steeld′c = concrete clear coverdctf = depth to centroid of tensile force in steelde = depth to centroid of nonprestressed tens

reinforcementdmax,N = maximum deflection after Nth cycledp = distance from extreme compression fiber to c

troid of prestressed reinforcementer,n = average strain in concrete between the cra

after N cycles of loadinges,n = steel strain at crack calculated using crac

section elastic analysis afterN cycles of loadingEc(t) = instantaneous elastic modulus of concrete

time tEce(t) = equivalent elastic modulus of concrete at timtEci = elastic modulus of concrete at time of loading

transferEi(t) = instantaneous elastic modulus of concrete

time tEN = cyclic modulus of elasticity after N cyclesEs = modulus of elasticity of steelfc′ = concrete compressive strengthfcr = maximum recommended stress range for concff = safe stress rangefmin = minimum applied stress (in concrete or reinforc

steel, as applicable)fpc = average precompression in concrete due to

stress at centroid of cross-sectionfpe = effective stress in prestressing steelfps = stress in prestressed reinforcement at nom

bending strengthfpu = ultimate strength of the prestressing steelfs = tensile stress in reinforcing steel, or change

steel stress from decompressionfso = steel stress at primary crack at first cyclefso,N = steel stress at primary crack at cycle Nfsr = maximum recommended stress range in reinfor

steel (prestressedor nonprestressed, as apble)

fy = yield strength of nonprestressed reinforcemeF = prestressing forceF(t) = prestressing force at time th = depth of member


o

n a

an

pro ofingre

se

nt

s- in

-

of

ed

e-

d

t

h1 = distance from neutral axis to tension faceh2 = distance from neutral axis to centroid

reinforcementIcr = moment of inertia of cracked sectionIeff(t) = effective moment of inertia of cracked sectio

time tIeN = effective moment of inertia after N cyclesIg = gross moment of inertiaKD, KF = constants depending on type of loading

steel profileLp = equivalent plastic hinge lengthM = sustained external moment at midspanMa = applied momentMD = dead load momentMdec = decompression moment (moment which

duces zero concrete stressat extreme fibersection, nearest to centroid of the prestressforce, when added to action of effective pstress alone)

Mcr = cracking momentML = live-load momentMn = total nominal moment capacityMnp = moment capacity provided by prestres

reinforcementN = number of load cyclesNf = number of cycles to failureP = sum of perimeters of all tension reinforcemePcp = outside perimeter of concrete cross sectionPPR = partial prestressing ratioQ = applied load

f

t

d

- a

-

d

Qser = applied service loadr/h = ratio of base radius to height of rolled-on tran

verse deformation (value of 0.3 may be usedabsence of specific data)

So = slip of reinforcement at first cycleSo,N = slip of reinforcement at Nth cyclet = time or age of concretetA = age of concrete at time of loadingVc = concrete contribution of shear strengthW = crack width at the first loading cycleWN = crack width at the Nth loading cycleWmax = maximum crack widthWmax,N = maximum crack width after N cyclesZ = slope of descending portion of concrete com

pression curveβ1 = parameter relating neutral axis depth to depth

equivalent rectangular compression block∆fps = change in stress in prestressing steel∆(t) = deflection at time tλ = degree of prestressε = strain (in general)ρ = reinforcement ratio of tensile nonprestress

reinforcementρ′ = reinforcement ratio of compressive nonpr

stressed reinforcementρp = reinforcement ratio of tensile prestresse

reinforcementΣo = sum of perimeters of all tension reinforcemenω = reinforcing indexωp = reinforcing index for prestressing steel

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