DANIEL P. JENNY RESEARCH FELLOWSHIP

Strength Design ofPretensioned Flexural ConcreteMembers at Prestress Transfer

Panya NoppakunwijaiPh.D. CandidateCivil Engineering DepartmentUniversity of Nebraska-LincolnOmaha, Nebraska

Maher K.Tadros, Ph.D., RE.Cheryl Prewett Professor

Departments of Civil Engineeringand Construction Systems

University of Nebraska-LincolnOmaha, Nebraska

Zhongguo (John) Ma,Ph.D., P.E.Assistant ProfessorCivil and Environmental EngineeringDepartmentUniversity of Alaska-FairbanksFairbanks, Alaska

Robert F. Mast, P.E.Senior Principal

BERGERJABAM Engineers Inc.Federal Way, Washington

This paper presents a rational method for thedesign of pretensioned flexural concrete membersdue to the effects of prestress transfer. Conditions atprestress transfer often control the level of prestressthat can be placed in pretensioned flexural members. The level of prestress significantly influencesthe maximum span capability. It is proposed thatthe flexural design of pretensioned, prestressedconcrete members for the effects of prestress transfer be based on strength design criteria. In practice,the proposed method will generally lead to higherprestress levels than the empirical limit of 0.6 fgiven in AC! 318-99 Building Code and AASHTOStandard Specifications for Highway Bridges. Satisfying the current 0.6 f limit often results in excessive strand debonding or necessitates drapingstrand at member ends. Debonding results inweakening of shear strength and poses possibledurability concerns. Another significant advantageof the proposed strength design approach is that it

automatically and rationally allows for calculationof any top bonded reinforcement required to maintam strength at transfer with controlled tensioncracking. The current method directs the designengineer to use an uncracked section analysis of analready cracked section to calculate the bondedreinforcement area.

34 PCI JOURNAL

The main reason for setting permissible stress limits due to unfactored loads in prestressed

concrete flexural members is to ensurethat serviceability criteria are met.These criteria include deflection, camber control, crack control, and fatigue,if applicable. In addition, the allowable extreme fiber compressive stressat transfer appears to be an indirectway of checking that concrete will not“crush” due to prestress transfer.

Extreme fiber tension stress limitsat transfer and at service are a meansto check whether cracking takes placeand if any measures are needed tocontrol crack width. However, to beconsistent with current design practice, the compression stress limitshould be based on a strength designapproach, while the tension limit isrelated to serviceability at unfactoredload levels.

This paper presents the results of atheoretical and experimental researchprogram for conditions due to transferof prestress in precast, pretensionedflexural members. The main objecfives of this study are to:

1. Establish a simplified strengthdesign method.

2. Recommend appropriate loadfactors.

3. Determine the correlation, if any,between the new strength designand working stress design limitsgiven in current codes.

4. Investigate various serviceabilityeffects.

5. Develop relevant design criteria.

A further objective of this researchproject is to develop a semi-empiricalformula for compressive stress limitsas a more justifiable substitute for thecurrent O.6f limit given in ACI 318-99 Building Code and AASHTO Standard Specifications for HighwayBridges.1’2It is anticipated that a moreappropriate allowable compressivestress formula will be used for a transitional period until design engineersand computer software developers become familiar with the strength designprocedure.

To overcome excessive compressive stresses at member ends, designengineers sometimes resort todebonding the strands near memberends. However, such debonding is be-

lieved to contribute to bond slippage,reduction of shear resistance, and corrosion of the strands because of moisture penetration along the “sleeved”or debonded length of strand at themember end. This practice could significantly reduce the level of anchorage of the strands at the beam bearingwhen the beam’s end zone acts as atied arch as the applied load approaches the ultimate capacity of thebeam.

Strands are depressed in double teesand other products to control memberend stresses. However, for double tees,the stems are narrow and the strandsare often pushed down from the topafter stressing, rather than being helddown during stressing as is commonpractice in bridge beams.

This operation is not as safe askeeping all the strands straight. Thedevice used to push strands downfrom the top of the member is oftenpulled out after prestress transfer. Thevertical hole created in this operationis then filled with grout. This locationbecomes vulnerable to moisture andsalt penetration which can cause premature corrosion of the strands.

Today, many design engineers tendto believe that allowable compressivestress limits in the code are intended toguard against concrete crushing. However, it is more rational to use an ultimate strength calculation to protectagainst concrete crushing.3’4

The description of the strength design procedure is given using eithercommercially available column designsoftware, such as PCACOL.5Alternatively, a designer-developed spreadsheet may be used for the strength design calculations described in thispaper.

The prestress force just beforetransfer, the self-weight moment andthe section geometry are input. Theoutput is the required concrete compression strength and area of bondedreinforcement. It is shown that in thisdesign procedure, a design engineercan select a suitable fj and solve forthe corresponding area of top tensionreinforcement.

To test this approach, an experimental program was undertaken. Invertedtee members were pretensioned to alevel as high as 0.84f. Their perfor

mance was observed for severalmonths before additional dead loadswere applied. Prestress loss and camber growth with time were found to bepredictable with available calculationmethods.

A parametric study was conductedto determine an equivalent allowablecompressive stress limit for sectionsdesigned using the proposed strengthdesign method. An accurate relationship could not be found. However, ithas been observed that the equivalentallowable compression varies from 0.6

fj the current code limit, to 0.75 fj

depending on section shape and the effect of prestress relative to self-weightmoments.

H ISTORICALBACKGROUND

The Prestressed Concrete Institute(PCI) issued the first specification6forbonded pretensioned, prestressed concrete on October 7, 1954. In this specification, the maximum allowable compression at the time of transfer ofprestressing was 0.5 f’ for bridgemembers and 0.55 f’ for buildingmembers. No explanation was givenon the justification of these limits orwhy they were related to f’ the specified compressive strength of concrete,rather than the compressivestrength of concrete at the time of initial prestress.

Following publication of the firstPCI specification in the 1957 Proceedings of the World Conference on Prestressed Concrete, there was a discussion on the “Criteria for PrestressedConcrete Bridges,” by E. L. Erickson,7who at the time was chief of theBridge Division, Bureau of PublicRoads (BPR). Erickson’s paper gavethe reasoning that led to the adoptionof the allowable compression 0.60 flimit as the following:

“It should be noted that the allowable concrete stresses are based onthe strength at the time ofprestressingand not the 6 x 12 in. cylinder strengthat 28 days.

There seems to be considerable difference of opinion among authoritiesas to the maximum allowable stresseswhich may be imposed temporarily,i.e., before creep and shrinkage takesplace. For the maximum temporary

January-February 2001 35

concrete compressive stress, HajnaiKonyi would allow 0.45 f, Dobellprefers 0.50 whereas Holley wouldallow 0. 60f provided the stress wasreally temporary, i.e., provided it wasreduced to 0.40 f before creep andshrinkage took place. Simpson wouldalso permit 0.60f provided it wasshortly reduced to 0.50 f. Siess disapproves the use of 0.60f even as atemporary stress.

He gives three reasons: First, concrete strengths vary as much as 15percent; second, the ultimate for sustained loads is perhaps only 90 percent of that for instantaneous loads;and third, some allowance should bemade for a variation from the assumedeccentricity of the prestress force.

Dean points out that a higher temporary concrete stress should be allowed for pretensioned concrete thanfor post-tensioned construction. Hereasons that in the former case, themaximum compressive concretestress under dead load alone is always at the ends of the beam where itis comparatively harmless, whereasin the post-tensioned beam withdraped tensioning elements it is morenearly uniform.

The value of 0.55f adopted in thecriteria for post-tensioned construction is slightly more conservative thanHolley ‘s and Simpson’s figures andwould give a little more allowance forsustained load, variation in concretestrength, and eccentricity in the prestressing procedure as suggested bySiess.

For pretensioned construction, aslightly higher value (0.60ff’,) wasadopted. Mr. Dean, Bridge Engineerof the Florida Highway Department,points out that the high compressionin pretensioned construction only occurs at the ends. Furthermore, onewould expect better control in thecasting yard where pretensioning isdone than in the case of post-tensioning which is usually done as a fieldoperation.”

The earliest versions of the PCIBuilding Code8 (1961) upgraded therelease strength limit to 0.6 f’1. Thislimit was kept unchanged by the AdASCE Committee 323 (now ACIASCE 423, Prestressed Concrete), andthe 1963 ACT 318 Building Code.

The issue of allowable compressivestress for prestress transfer has become a restrictive factor in the moderndesign of pretensioned flexural members. Much of the cost-effectiveness ofprecast concrete members results froma daily production cycle of a long-linepretensioning bed.

The requirement for artificially highconcrete strengths at transfer may hinderthis cycle. When overnight strengths arenot achieved, precast concrete producersmust delay, or cancel, production in thatpretensioning bed for that thy.

As a result, some precast producershave exceeded the allowable compression limit of 0.6f without any apparent detrimental effects. Also, a PCIStandard Design Practice Report, prepared jointly by the PCI Technical Activities Council and the PCI Committee on Building Code,9 indicates thatno problems have been reported by allowing compression to go as high as0.75f.

PROPOSED STRENGTHDESIGN FOR

PRESTRESS TRANSFERThe strength design for prestress

transfer can be approached in a manner similar to that for non-prestressedreinforced concrete. The member canbe treated as a “reinforced concretecolumn” subjected to moment combined with axial compression forceequal to the force in the prestressingsteel just before prestress transfer.

The incremental “compression” inthe “reinforcement” at the compression face of the section is equivalent tothe strain and stress reduction in theprestressing steel. This reduction isgenerally known in current design,using unfactored loads, as elastic prestress loss. Thus, the prestressing steeland the concrete share in resisting theeffects of the applied moment andaxial compression.

A load factor of 1.2 is applied tothe prestress force in prestressingsteel just before prestress transfer, P1.This is the same load factor used inthe design of post-tensioned memberanchorage zones (see ACI 318-99,’

Section 9.2.8).A load factor of 0.8 or 1.2 is applied

to the self-weight moment, Mg, due to

the uncertainty of lifting locations.When the members are handled atpick-up points located somewhat inward from their theoretical supportpoints, the moment due to self-weightshould be accounted for. The load factor of 1.2 is used when the memberself-weight effect is opposite to theprestress force moment, which is thecommon practice. However, if themember weight moment is in the samedirection as the prestress force moment, the factor should be 0.80.

This situation is encountered whenthe lifting points are beyond the member ends, using for example structuralsteel ledges or strong backs. A strengthreduction, 4,, of 0.7, is applied to thenominal axial capacity, P,, and bendingmoment capacity, M. This is the samevalue used for tied columns.

At this time, it may be too conservative for this application as concretestrength is known because cylindersare tested just before prestress is transferred. Thus, the “applied” loads aretemporary and the compressive prestressing force is internally induced,having a self-relieving ability. Untilfurther results are available, = 0.7should provide a conservative solution.

It is interesting to note that a verysimilar approach has already been introduced in Australian practice, according to Reference 10 which refersto the Australian Code, AS 3600. Inthe Australian Code, the corresponding load factors are 1.15 and 0.8, andthe corresponding strength reductionfactor is 0.6. The prestress force usedthere is the jacking force rather thanthe force just before transfer as recommended here.

This appears to be a minor difference, and it is fortunate that the Australian practice was brought to the authors’ attention just before publicationof this paper. It is unclear, however,whether the Australian practice advocates, as the proposed method givenherein, total elimination of crackedsection service load analysis, even ifthe member top fiber stresses exceedthe modulus of rupture.

In calculating the strength of thecross section subjected to axial compression and bending, equilibrium andstrain compatibility conditions are satisfied. The following commonly used

36 PCI JOURNAL

Internal Effects Loads effects

Fig. 1. Proposed strength design diagram for prestress transfer.

assumptions are made:1. Plane sections normal to the axis

of bending remain plane afterbending.

2. Concrete has no tensile strength.3. The ACI 318 equivalent rectangu

lar compressive stress block is

a = depth of equivalent rectangular stress block

= area of tension reinforcementA’ = area of “compression rein

forcement”b = width of compression face of

member

f’, = compressive strength of concrete at time of initial prestress

f3 = calculated stress in tension reinforcement

f’ = calculated stress in “compression reinforcement”

(1) Mg = moment due to self weightP1 = prestress force immediately

after prestress release= strength reduction factor

Using Eqs. (1), (2), (3) and (4), onewhere

d = effective depth of sectiond’ = distance from extreme com

__________ __________________________

pression fiber to centroid of“compression reinforcement,”i.e., prestressing steel

= tension reinforcement strain= “compression reinforcement”

Once the values of c, £‘ and areknown, the stresses in each layer of

______ ____________

the reinforcing steel can be computed,

f5’ = s E andf e E. The equilibrium conditions require that:

A

________

hdd

b

0.85f

O.8Mg or l.2Mg

) )l.2P1

6

0.85fba +Af; —

0.85fbaQ. — d’) —

0.8MAf3(d—d’)=

g

where

(3)

(4)used.

4. The ultimate concrete compressive strain is equal to 0.003.

Fig. 1 shows the proposed strengthdesign diagram for prestress transfer atthe member ends. The standard assumptions are used. A rectangularcompressive stress block with constantintensity of 0.85 f’ and depth a = f3 cis assumed, where c is the neutral axisdepth, and /31 varies from 0.85 forf =

4000 psi (27.6 MPa) to 0.65 forf8000 psi (55.2 MPa).

The strain compatibility conditionsprovide for the following relationship:

E(c_dt)

0.003

= (.4__ 0.003

can solve for a, fif’f and As’. However, the equations provide for fourunique relationships only.

The design engineer can theoretically find an unlimited number of acceptable solutions. Therefore, one ofthe five unknowns must be assumed.

For example, if no top tension reinforcement is desirable, one can set A’= 0, and obtain the corresponding f,which will be relatively high. If onewants to have a relatively low releasestrength, the design engineer can setthe stress at that desired strength andobtain a relatively large requiredbonded tension reinforcement.

COMPARISON WITHWORKING STRESSDESIGN RESULTS

An example of a rectangular section, 16RB40, from the PCI DesignHandbook11 is used for the comparison. The beam span is 30 ft (9.14 m).Twenty-two Grade 270 ksi (1860MPa) low-relaxation, 0.5 in. (12.7mm) diameter strands with an eccen

Table 1. Summary of stresses in a rectangular beam, 1 6RB40.

strain

Transfer section at release Midspan at release

Load f, [psi (MPa)] f,, [psi (MPa)] J [psi (MPa] f [psi (MPa)]

P/A 959 (6.6) 959 (6.6) 959 (6.6) 959 (6.6)

Fe/S -1869 (-12.9) 1869 (12.9) -1869 (-12.9) 1869 (12.9)

M915 55 (0.4) -55 (-0.4) 211 (1.5) -211 (-1.5)

Total Stresses -855 (-5.9) 2773 (19.1) -699 (-4.8) 2617 (18.0)

Notes: 1. Positive sign is compression and negative sign is tension.2. P/A and Pe/S are the stresses due to prestressing.3. M5 /S is the stress due to self-weight of precast rectangular beam.4. 1 ksi = 6.9 MPa.

January-February 2001 37

Fig. 2.Comparison between

strength and working stressdesign.

tricity of 13 in. (330 mm) are used inthe member.

It is assumed that the jacking stressjust before prestress transfer is equalto 0.75(270) = 202.5 ksi (1395 MPa)and the initial prestress loss for working stress design is equal to 20.25 ksi(139.6 MPa) at transfer. The requiredconcrete release strength based onworking stress design, using both ACT318-99 and the PCI Design Handbook,will be compared to that determinedby the proposed strength designmethod.

The allowable compression at transfer is limited to 0.6f in ACT 318-99and to 0.7f in the PCI Design Handbook. The allowable tension withoutadded reinforcement is limited to6’J (O.SJ) in both ACT 318-99and the PCI Design Handbook. Theworking stresses at a section located adistance equal to the transfer length,25 in. (635 mm) from the memberend, and at midspan at release aresummarized in Table 1.

The total compressive stress of 2773psi (19.1 MPa) at the extreme bottomfibers, fb’ at the transfer section controls the working stress design. A concrete strength of 4622 psi (31.9 MPa)would be required according to ACT3 18-99, and 3961 psi (27.3 MPa)would be required according to thePCI Design Handbook. Because thetensile stress of 855 psi (5.9 MPa) atthe top fiber, J, at transfer exceeds thelimit of 6J (0.5 ), it is assumedthat the member is cracked, and re

quires top bonded reinforcement.Top bonded reinforcement is de

signed to carry the tensile force determined using an uncracked sectionanalysis at a stress of 0.6 but notmore than 30 ksi (207 MPa). An areaof 2.15 sq in. (1389 mm2) of Grade 60(414 MPa), reinforcing steel would berequired using both ACT 318-99 andthe PCI Design Handbook.

The same example beam is workedout using the proposed strength designmethod. A spreadsheet program wasdeveloped. In this example, the program was used to calculate the requiredconcrete strength for an assumed areaof the top bonded reinforcing steel, A.The area, A, of the top reinforcementwas varied from 1.29 to 5.78 sq in.(830 to 3726 mm2).

The results show that a concretestrength of 3811 psi (26.3 MPa) is required by the strength design method,when the same amount of reinforcement as that required in the workingstress design method, 2.15 sq in. (1389mm2), is used. The required concretestrength of 3811 psi (26.3 MPa) wouldcorrespond to an equivalent compressive stress limit of 0.73 f’ by theworking stress design method, asshown in Fig. 2.

One of the major advantages of thestrength design approach is that itleads to a rational method for sizingtop bonded reinforcement, as opposed to the arbitrary working stressdesign method now used. Fig. 2demonstrates that the demand for

concrete strength at transfer can bereduced by the design through an increase in the amount of top bondedreinforcement.

Using strain compatibility, the stressin the top reinforcement at nominalstrength level can be determined. Inthis example, the calculated steelstress ranges from 30 ksi (207 MPa),when A is 5.78 sq in. (3726 mm2), to60 ksi (414 MPa) when A is 1.29 sqin. (830 mm2), as shown in Fig. 2.

Obviously, the grade of top bondedreinforcement must meet the calculatedstress requirement shown in Fig. 2. Forexample, if Grade 60 (414 MPa) steelis used, the minimum amount of topbonded reinforcement should be 1.29sq in. (830 mm2).

Another simple method to verify thestrength design is by using commercially available computer programs forthe design of the compression member, of which PCACOL is an example.An interaction diagram for this example “column” is shown in Fig. 3. Themark, +1, in the figure represents theload effects due to axial force combined with bending moment.

In this example problem, the mark ismatched with the interaction diagram.This indicates that the results from thespreadsheet program and PCACOLare consistent. Additional design examples of the proposed method are included in Appendix B.

Control of Top Fiber Cracking

The stress at the top fiber of the sec

Strength Design at Transfer Span 30 ftRequired

f1(ksi)5

4.5. ACI 3 18-99 (O.6f1)

f56Oks4 A PCI Handbook (O.7f1)

O.73f, Strength Design3.5 f=40 j 16RB40

f5=30 ksi3 .2

0 1 2 3 4 56A5(m)

Required compressive strength, f’d, and top reinforcement, A5

Note: I in = 25.4 mm; I ksi =6.9 MPa

38 PCI JOURNAL

tion in the preceding example exceedsthe modulus of rupture of concrete,7.5 JJ (0.62 ,T ). However, thestrength design approach proposedherein does not directly establish theadequacy of top tension bonded reinforcement for crack control.

The current code provisions alsofail to directly relate the empiricallycomputed amount of bonded reinforcement to crack width or spacing.The reinforcement area is calculatedas if the section were uncracked, withthe steel stress limited to an arbitrary30 ksi (207 MPa) to control cracking.

The most rigorous approach is toanalyze a cracked section subjected tothe combined effects of unfactoredprestress and self-weight. An analysisof cracked prestressed concrete sections is described in detail in Reference 12.

Using that method for the above example, the depth of the neutral axiscan be found to vary from 24.66 to28.52 in. (626 to 724 mm) and thecorresponding steel stress to varyfrom 12.03 to 7.21 ksi (83 to 50 MPa)if the top reinforcement is varied from1.29 to 5.78 sq in. (830 to 3726 mm2)(see Fig. 4). The same range of reinforcement area is shown in Fig. 2 tocorrespond to a steel stress of 60 to 30ksi (414 to 207 MPa) at nominalstrength levels.

The PCI Design Handbook rectangular and inverted tee sections, andthe standard NU (Nebraska University) inverted tee’3 sections were investigated using the cracked sectionanalysis of Reference 11. Table 2 presents a summary of the level of steelstress after cracking. Note that in allcases, the steel area used in the analysis was the area corresponding to theone producing a stress of 60 ksi (414MPa) at nominal strength levels.

Values of steel stresses at unfactored bond levels in all cases werebelow the current ACT Code limit of30 ksi (207 MPa). Therefore, it is recommended that if a maximum steelstrain of 0.0021 and a steel stress of(0.0021)(29000) = 60 ksi (414 MPa)are used in the strength designmethod, there is no need to perform aservice load cracked section analysisor to check for crack control for steelgrades not greater than Grade 60.

Fig. 3. PCACOL interaction diagram for prestress transfer. Note: 11 kip-ft = 1.356 kN-m, 1 ft = 0.3048 m.

Fig. 4. Cracked section analysis of 1 6RB40.

16RB40: Span =30 ft.

P (kip)

1600

1200

800

400

-400

kip 4.44 kN,

Cracked Section Analysis

40‘ 36

30 30.

20

c1 12

6

0 I I I 00 1 2 3 4 5 6 7

Area of top reinforcement, A (in2)

steel stress neutral axis

Note: I in 25.4 mm; I ksi 6.9 MPa

January-February 2001 39

Approximate Equivalent AllowableStress for Pretensioned Members

An effort was made to establish thecompressive stress limit at unfactoredload levels that would produce comparable results to the proposed strengthdesign method. The objective is togive design engineers an alternativelimit to the 0.6 f’ currently used,while still permitting them to use thefamiliar allowable (working) stress design procedures.

Standard double tee, rectangular andinverted tee cross sections were chosen to represent geometry variation.For comparison purposes, the PCI Design Handbook rectangular and doubletee sections, and NU inverted tee sections were used in the study.

The analysis indicated that the geometry of a member cross section isone of the most important parameters.The stress limits for the NU invertedtee sections varied from 0.66 f’1 to

0.67 fj, while the values for the PCIrectangular sections varied from 0.69f to 0.70 f. The values for the PCIdouble tee sections were the highest,namely, 0.73 fj to 0.76f.

For simplification purposes, it isrecommended that the limit 0.6f be

0.6 + jf 0.75f (5)

Yb = distance between section centroid and extreme bottom fiber

h = overall depth of memberIn the rectangular example previ

ously given, Eq. (5) produces an allowable stress limit equal to (0.6 +

0.5/5) f’j = 0.7 f, compared to 0.73

f by the strength design approach.This shows that the proposed for

mula is more conservative than thetheoretically more rigorous strengthdesign method. Results of the parametric study for the proposed formulaare summarized in Appendix C.

EXPE RI ME NTAL.PROG RAM

One of the tasks of this project wasto conduct experiments to determinethe impact of creep of concrete undervery high compressive stress levels induced by prestress. To achieve thisgoal, two simply supported invertedtee specimens with a cast-in-placecomposite topping were designed, produced and tested at the University ofNebraska Structures Laboratory (seeFig. 5). They are referred to here asSpecimens 1 and 2.

Design of Specimens

The specimens were designed tohave a total length of 33 ft (10.06 m),a span length of 32 ft (9.75 m) and aspan-to-depth ratio of 32. Section di-

Table 2. Summary of steel stress after cracking.

No. of [ Neutral

Section strands A [sq in. (mm2)] e [in. (mm)] axis [in. (mm)]

- 5 0.52 (335) j_600(152) 8.20 (208)

8 0.72 (465) 7.25 (184) 10.76 (273)

1.03 (665) 9.00229) 2.85 (326)

12RB16

12RB20

12RB24

12RB28

12RB32

12RB36

16RB24

16RB28

I6RB32

16RB36

replaced with the following formula:

12 1.23 (794)

13 1.53 (987)

1.81 (1168)

140(903)13 j

Steel stress

f [ksi (MPa)1

-

15.99(110)

16.40 (113)

_22 (124)

18.25(126)

18.45 (127)

10.50 (267) 15.14 (385)

12.31 (313) 17.31 (440)

where

13 1.71 (1103)

18 2.07 (1335)

20 2.46(1587)

16RB40 22

281128 13

14.00 (35)_4 19.49 (495) 19.00 (131)

9.08(231) 12.82 (326) 17.97 (124)

11.08 (28i)j 14.77 (375) 18.29 (126)

12.33 (313) 17.26 (438)

2.82 (1819) 15.82 (402)

1.94 (1252) 9.09(231)

18.89 (130)

14.10 (358) 19.44(494)

21.64(550)

15.18 (386)

19.20 (132)

19.35 (133)

14.73 (374)

21.02(534)

281T44 20 2.78 (1794)

281T60 28 3.58 (2310)

341T24 17 2.68 (1729)

341T40 30 4.27 (2755) j341T60 42 5.55 (3581)

401T20 4 - 18 2.18 (1406)

401T32 30 3.91 (2523)

5.47 (3529)

15.45 (107)

24.25 (616) 17.45 (120)

32.36 (822) 20.05 (138)

8.03 (204) 13.33 (339) 14.66 (101)

13.92 (354) 22.45 (570) 17.58 (121)

22.07 (561) 32.54 (827) 20.37 (140)

6.74(171) 10.37 (263)

11.27(286) 17.45 (443)

16.36(113)

17.39(120)401T40 38 14.47 (368) 22.98 (584) 16.17(111)401T48

____

40 6.05 (3903) 17.68 (449) 26.27 (667) 19.30 (133)401T52 48 6.52 (4206) 19.32 (491) 28.39 (721) 19.77 (136)

NU-1T300 22 0 1.39 (35) 8.27 (210) —

NU-1T400 22 0 - 2.60 (66) 8.27(210) —

— NU-1T500 22 0.22 (142) 1 3.99 (101)

_________

NU-1T600 22 0.47 (303)

NU-1T700 22 0.73 (471)

NU-1T800

NU-1T900 122 0.97 (626) 8.74 (222)

22 1.20 (774) 10.44 (265)

Notes: M5 is assumed equal to zero.1 in. = 25.4 mm, 1 ksi = 6.9 MPa.

_______

10.43(265) 19.31 (133)

5.50(140) I 11.95 (304) 21.77 (150)

7.08 (180) 13.89 (353) 21.82(150)

15.95 (405.) 1.37 (147) -

18.08 (459) 20.83 (144)

Fig. 5. The inverted tee specimens with cast-in-place composite topping.

40 PCI JOURNAL

Fig. 6. Inverted tee cross section. Note: 1 in. 25.4 mm.

mensions and reinforcement detailsare shown in Fig. 6. Stirrups (#3 U-bars) at 2 in. (51 mm) spacing wereused in the bottom flange only for 3 ft(914 mm) from each member end.This confinement at member ends wasused to control member end splittingcracks at the time of prestress transfer.

In designing the specimens, it wasassumed that the initial prestress losswas 10 percent and the final loss was20 percent of the prestress just beforetransfer. The strand tension beforetransfer was set at 0.75 f115, or 202.5ksi (1396 MPa).

These losses were later calculated inmore detail, using the method in Reference 14, and compared with themeasured quantities. Note, however,that the specimens were designed tohave significantly higher compressivestresses of 0.85 f’ at member endsand 0.71 f at midspan. This stress isless conservative than a design usingthe recommended equivalent stresslimit formula:

(0.6 + Yb’ 5h)f = (0.6 + 2.34 /40)f= 0.66f

A summary of the member stressesat the transfer point and midspan ascompared to the allowable code limitis shown in Table 3.

Specimen Constructionand Materiak

The specimens were prestressedusing Grade 270 (1860 MPa), 0.5 in.(12.7 mm) diameter, low-relaxationseven-wire strands. A total of ninestrands were used for each specimen.

The average elongation of strandsduring prestressing was measured to

check the jacking force. The jackingforces were 74 and 77 percent of270 ksi (1862 MPa) for Specimens 1and 2, respectively. After jacking ofthe strands was completed, theheight of the form was adjusted toprovide the correct eccentricity ofthe strands.

Ready mixed concrete was supplied.Concrete with Type HI cement for the

::.‘....:.:::....

4.o- -

41

:!•::•, :.

0.765’12.00”

#3 stirrups —... —— 3.00’

0.5’dia.Grade27O,

,,“l.75’spacing

________

/

_________________________

— o.ss —

1.625’ — I

______

R5.75e

R25’_.J’ I

:.i

3.25’

9.50’ #3 stips Jfor end 3 ft. only

Table 3. Summary of stresses for inverted tees.

Transfer point at release

f, = 5874 psi (40 MPa) Midspan at release

Load f, [psi (MPa)] f,, [psi (MPa)] f [psi (MPa)j fb [psi (MPa)J

P/A 3403 (23.5) 3403 (23.5) 3403 (23.5) 3403 (23.5)

Fe/S 1849 (12.7) -4253 (-29.3) 1849 (12.7) -4253 (-29.3)

Md./S -259 (-1.8) 594(4.1) -1088 (-7.5) 2501 (17.2)

Total stresses 4993 (34.4) -255 (-1.8) 4164 (28.7) 1651 (11.4)= 0.85f

CurrentAASHTO limit 0.6f = 200 wo/rft. 3500(24.1) 3500 (24.1)

and 3500(24.1) 576 w/rft.ACT 318 limit

Notes: 1. Positive sign is compression and negative sign is tension.2. P/A and Pe/S are the stresses due to prestressing.3. is the stress due to precast IT beam self-weight.4. IS is the stress due to deck self-weight.5. 1 ksi = 6.9 MPa.

January-February 2001 41

precast portion of Specimen 1 wasplaced on March 12, 1999, and concrete with Type I cement for Specimen 2 was placed on August 2, 1999.Burlap soaked with water was used tocure the freshly cast concrete.

One day after concrete placement,the side forms were removed in orderto install mechanical demec gauges onthe specimen. The demec gauges wereattached to the concrete surface tomonitor the change in the concretestrain with time (see Fig. 7). The relative displacement of the gauge pointswas measured with an accuracy of 4.0x I 0 of the concrete strain. A total of

Fig. 7.Strain gauge

attached to concretesurface.

148 demec gauges were used for eachspecimen, as shown in Fig. 8.

Concrete placement for the toppingconcrete of Specimens I and 2 was doneon June 4, 1999 and December 17,1999, respectively. The ages of the precast members of Specimens 1 and 2were 84 and 137 days, respectively.These relatively long periods were usedto determine if any detrimental creep effects or unpredictable cambers takeplace. Cylinders were prepared in accordance with ASTM C31-87. They werekept in the same environmental condition as the specimens, and their compressive strengths are listed in Table 4.

TEST RESULTSDiscussed below is concrete stress

at transfer, camber, and the transversestrain effect.

Concrete Stress at Transfer

Prestress losses due to steel relaxation and elastic shortening at midspanof the specimens were calculated.They were found to be 11.78 and12.64 percent of the jacking force forSpecimens 1 and 2, respectively. Theactual concrete stresses at transferwere 0.79f and 0.84f for Specimens 1 and 2, respectively.

Variation of strain with time is attributed to creep and shrinkage of theconcrete, and relaxation in the steel. Acomparison between the calculatedconcrete strain and the measured concrete strain at midspan (Level A) isshown in Figs. 9 and 10. There appears to be good agreement betweenthe theoretical and measured concretestrain in both specimens.

Camber

The stresses in the concrete and prestressing steel vary continually withtime due to the effects of creep and

:i 44

Fig. 8. Demec gauge location for Specimens 1 and 2.Note: 1 ft = 0.3048 m, 1 in. 25.4 mm.

42 PCI JOURNAL

Table 4. Measured concrete strength.

shrinkage of concrete and stress relaxation of steel. The measured unitweight of concrete was 150 and 147 lbper cu ft (2400 and 2355 kg/rn3) forSpecimens 1 and 2, respectively.

A comparison between the theoretical’4 and the measured camber afterreleasing the strands is shown inFigs. 11 and 12. The measured camber at midspan immediately afterprestress transfer was 1.18 and 1.38in. (35 and 30 mm) for Specimens 1and 2, respectively.

These values are in agreement -withthe calculated values of 1.17 and 1.24in. (29.7 and 31.5 mm) for Specimens1 and 2, respectively. The time-dependent camber was calculated based onlinear elastic analysis, and was plottedat 81 days for Specimen I and at 128days for Specimen 2 before castingthe deck.

The relatively high initial compression in relationship to the concretestrength could still be reasonably estimated using the straight-line elasticanalysis. The calculated camber immediately after prestress transfer was stillpredictable by linear elastic analysis,within the reasonable margins of error.It was possible to fairly accurately predict time-dependent camber usingavailable creep prediction methods andthe usual assumption of linear proportionality of creep strain to elastic strain.

Transverse Strain Effect

The transverse strain, due to highcompressive stress at the ends of thebeams, was also monitored after release. Near the ends of the specimens,a possible increase in transverse tensile strain with time had been mentioned as a possible concern due to thehigh compressive stress at prestresstransfer. After the strands were released, a total of 30 demec gaugeswere installed at the bottom surface at

both ends of Specimen 2, as shown inFig. 13.

Note that it was not possible to install the demec gauges before releasing the prestress. The transverse strainmeasurement was monitored immediately after prestress release. It was ob

served that no sign of splitting or anymicrocracking occurred at the bottomsurface of the specimen.

The highest transverse strain occurred at the time of prestress transfer.Beyond that time, compression (ratherthan tension) strain increments, due tocreep and shrinkage, developed withtime. The average measured strain atboth ends is plotted in Fig. 14. Notethat the transverse strain near themember ends actually diminished,rather than increased with time. Thismay be attributed to the effects ofshrinkage and reduction of prestresswith time.

Although not specifically mentionedin ACT 318, some design engineers be-

Strength at transfer Strength at time of deck placement[psi (MPa)l [psi (MPa)]

Specimen Specified Actual Specified Actual

1 5870(40 MPa) 5900 (41 MPa) 7000 (48 MPa) 10780 (74 MPa)

2 5870 (40 MPa) 5600 (39 MPa) 7000 (48 MPa) 6200 (43 MPa)

Strain

0.0000

-0.0005

-0.0010

-0.0015

-0.0020

0 14 28 42 56 70 84 98 112 126 140

Time (thys)

...... measured • calculatedi

Fig. 9. Concrete strain vs. time for Specimen 1.

Strain

0 14 28 42 56 70 84 98 112 126 140

Time (days)

measured • calculated

Fig. 10. Concrete strain vs time for Specimen 2.

January-February 2001 43

lieve that limiting the compressivestress at transfer to 0.6 f would prevent members from having “too muchcreep deformation, too much prestressloss, and excessive transverse strain(dilation).”

Based on the test results of the inverted tee specimens, no negative im

pact was detected due to the prestresslevels used in the test when significantly exceeding the allowable concrete compressive stress limit at transfer, and even the limits correspondingto the proposed strength design approach. There are two reasons why design engineers should not be unneces

sarily alarmed when they calculatehigh compressive stresses in the concrete due to prestress transfer:

1. Compared to externally loadedcolumns, bonded pretensioned prestress is an internal system of forcesthat has some degree of self-adjustingcapability. High concrete compressivestress and strain result in high prestress losses, which in turn cause a reduction in concrete compression.

2. Another factor that tends to exaggerate the effects on concrete fromprestress transfer is the conventionallinear concrete stress-strain relationship. It is recognized that nonlinearanalysis may be unattractive to manydesign engineers. A study by Huo andTadros,3 titled “Allowable Compression Strength of Concrete at PrestressRelease,” compares accurate nonlinearbehavior with approximate linearstress analyses.

In that paper, it is shown that a linear analysis significantly overestimates the concrete and steel stresses.Thus, a linear analysis may give thefalse impression that a member isoverstressed when in fact a more accurate nonlinear analysis would showthis is not the case.

CONCLUSIONSBased on this analytical and experi

mental study, the following conclusions can be drawn:

1. The authors propose that the allowable compression stress limit requirement at prestress transfer beeliminated for pretensioned concretemembers. The factor of safety usingworking stress design can vary significantly with such parameters as reinforcement ratio, concrete strength, and

Fig. 13. Demec gauge locations for transverse strain of Specimen 2 at bottom of beam. Note: 1 ft = 0.3048 m, 1 in. = 25.4 mm.

PCI JOURNAL

camber(in.) 2.5 (mm.)

50

40

30

2010

0 14 28 42 56 70 84 98 112 126 140

-

. measured i caicuJ

Time (days)

Fig. 11. Midspan camber of Specimen 1.

camber(in.) 2.5

2

1.5

0.5

0

(mm.)

50

403020

10

0 14 28 42 56 70 84 98 112 126 140

Time (days)

measured • calculated

Fig. 12. Midspan camber of Specimen 2.

North South

-I

11”

H

32ft

section geometry. Using a constant allowable concrete compressive stress attransfer cannot be justified as the basisfor controlling compression failure.

2. The authors further propose that analternative approach using the strengthdesign method presented in this paperbe adopted to replace the working stressdesign approach. The proposed strengthdesign approach can be applied usingcommercially available column designsoftware or a design spreadsheet. Theinput is the prestress just before transfer,factored by a 1.2 load factor, and theself-weight moment factored by either a1.2 or 0.8 factor, whichever is more critical. Also, the section dimensions andprestressing steel are input. The program output is the concrete strength f,area of top bonded reinforcement A5,and stress in the top bonded reinforcement f5. Since there are an unlimitednumber of acceptable solutions, the design engineer has the option to choose

f and obtain the required correspondingf5, then check that the correspondingstress is less than 60 ksi (414 MPa).

3. As a transitional measure, to convert from the working stress approachto the strength design method, thisstudy has furnished a semi-empiricalallowable compressive stress limit thatis a more realistic substitute for the 0.6f’, limit. In the proposed limit, the coefficient 0.6 should be replaced with0.6 + yI5h 0.75. This formula wasbased on curve-fitting the strength design results for highly prestressedmember ends of various cross-sectional geometries.

4. The strength design method provides a more uniform factor of safetyagainst concrete crushing than doesthe working stress approach. It is expected that this new method will havesignificant benefits for designing precast/prestressed concrete structures.This approach allows the prestress tobe released at a lower concretestrength than culTently permitted andthus a more rapid production cyclewould result. The demand for debonding or draping of strands at memberends would be reduced. The cost ofaccelerated curing would be minimized. Alternatively, more prestressing could be introduced into a member, thus increasing its external loadcarrying capacity.

Fig. 14. Transverse strain of Specimen 2.

5. The proposed strength design approach provides for adequate safetyagainst concrete crushing at prestresstransfer. As a by-product of the analysis, the area of bonded reinforcementat the top of the member can be found.Thus, the need for empirically calculating the steel area as is done in current codes is eliminated. If such reinforcement is found to be needed for agiven member, it is recommended thatits strain be limited to 60 ksi (414MPa)/E5 or 0.0021. That limit wouldcurtail the steel stress at unfactoredload levels to less than the 30 ksi (207MPa) limit specified in the codes,without requiring any need to performa complicated cracked section stressanalysis.

RECOMMENDATIONS1. The current ACT 3 18-99 Code

provisions should be revised asgiven in Appendix D.

2. The current ASSHTO StandardSpecifications for Highway Bridgesrequires that in precast, prestressedconcrete members, the extreme fiberstress in tension not exceed the limitof 7.5 (0.62 ‘JI ). For compositemembers, this limit should bewaived at the extreme top fiber ofprecast, prestressed concrete members. Bonded reinforcement can beused when the extreme fiber stress intension of precast composite bridgemembers exceeds the limit of 6(0.50J ). A direct result of this isthat a satisfactory design can be accomplished when using the strengthdesign analysis approach with the

serviceability criteria requirements.3. The load factors and strength

reduction factor proposed in thispaper appear to be conservative.The 20 percent fluctuation of applied prestress force appears to betoo high because the accuracy of thejacking force can be measured. Inaddition, the strength reduction factor = 0.7 is low because the eccentricity of strand can be controlled. However, the load factor of0.8 or 1.2 for self-weight momentmay be reasonable. Therefore, further study, based on the theoreticaland experimental program, of theload factors and strength reductionfactor is still needed, in order to refine these recommendations.

ACKNOWLEDGMENTThis research was performed under

Project No. SPR-PL-1(037) P527,funded by the Nebraska Department ofRoads and under a Daniel P. JennyResearch Fellowship awarded to thefirst author from the Precast/Prestressed Concrete Institute. Additionalsupport was provided by the Centerfor Infrastructure Research at the University of Nebraska-Lincoln, Omaha,Nebraska.

The authors are grateful tO the manyindividuals who contributed technicalcomments and guidance throughoutthe various stages of this project. Theyinclude Alex Aswad, Neil Hawkins,Paul Johal, Donald Logan, Leslie Martin, George Nasser, Alan Mattock,Basile Rabbat, Bruce Russell, SteveSeguirant and Irwin Speyer.

1EZpEStrain

0.00000

-0.00005

-0.00010

-0.00015

-0.00020

-0.000250 14 28 42 56 70 84 98 112 126 140

Time (days)

(Note: negative is compressive strain)

January-February 2001 45

REFERENCES

1. ACT Committee 318, “Building Code Requirements for Structural Concrete (ACI 3 18-99) and Commentary (ACT 318R-99),” American Concrete Institute, Farmington Hills, MI,1999, 391 pp.

2. AASHTO, Standard Specfications for Highway Bridges, 16thEdition, American Association of State Highway and Transportation Officials, Washington, D.C., 1996.

3. Huo, X., and Tadros, M. K., “Allowable Compressive Strengthof Concrete at Prestress Release,” PCI JOURNAL, OpenForum Section, V. 42, No. 1, January-February 1997, pp. 95-99.

4. Huo, X., Savage, J. M., and Tadros, M. K., “Reexamination ofService Load Limit Compressive Stress in Prestressed Concrete Members,” ACI Structural Journal, V. 92, No. 2, March-April 1995, pp. 199-210.

5. PCACOL, “Design and Investigation of ReinforcedConcrete Column Sections,” Computer Software Version3.0, Developed by Portland Cement Association, Skokie, IL,1999.

6. PCI’s First Specifications for Pretensioned Bonded Prestressed Concrete Products, First Edition, Prestressed Concrete Institute, P.O. Box 495, Lakeland, FL, 1954.

7. Erickson, E. L., Criteria for Prestressed Concrete Bridges,

Bureau of Public Roads, U.S. Department of Commerce, U.S.Government Printing Office, Washington, D.C., 1954.

8. PCI Committee (Lin, T. Y., Bryan, Ross H., Edwards, HarryH., Gerwick Jr., Ben C., Schupack, Morris, Speyer, Irwin J.,and Verna Jr., Peter J.), Prestressed Concrete Building CodeRequirements, Prestressed Concrete Institute, P.O. Box 495,Lakeland, FL, 1961.

9. PCI Technical Activities Council and PCI Committee onBuilding Code, “PCI Standard Design Practice,” PCI JOURNAL, V. 41, No. 4, July-August 1996, pp. 31-43.

10. Warner, R. F., Rangan, B. V., Hall, A. S., and Faulkes, K. A.,Concrete Structures, Addison Wesley Longman Australia PtyLimited, Sydney, Australia, 1998, pp. 197-202.

11. PCI Design Handbook — Precast and Prestressed Concrete, FifthEdition, PrecastlPrestressed Concrete Institute, Chicago, IL, 1998.

12. Mast, R. F., “Analysis of Cracked Prestressed Concrete Sections,”PCI JOURNAL, V.43, No.4, July-August 1998, pp. 80-91.

13. Kamel, R., and Tadros, M. K., “The Inverted Tee ShallowBridge System for Rural Areas,” PCI JOURNAL, V. 41, No.5, September-October 1996, pp. 28-43.

14. Tadros, M. K., Ghali, A., and Meyer, A. W., “Prestress Lossand Deflection of Precast Members,” PCI JOURNAL, V. 38,No. 1, January-February 1985, pp. 114-141.

APPENDIX A - NOTATION

a = depth of equivalent rectangular stress blockA = cross-sectional area

= area of tension reinforcementA5’ = area of “compression reinforcement,” i.e., prestress

ing steelb = width of compression face of memberc = distance from extreme compression fiber to neutral

axisd effective depth of sectiond’ = distance from extreme compression fiber to centroid

of compression reinforcemente = eccentricity of prestress force from centroid of section

E = modulus of elasticity of concreteE5 = modulus of elasticity of prestressing steelE3 = modulus of elasticity of nonprestressed steel

E’ = modulus of elasticity of compression reinforcement

fb = stress in bottom fiber of cross section= stress in top fiber of cross section

f’ specified compressive strength of concrete at service

f’ = specified compressive strength of concrete at time ofinitial prestress

f = specified tensile strength of prestressing tendons

f = specified yield strength of non-prestressedreinforcement

= calculated stress in tension reinforcement= calculated stress in compression reinforcement, i.e.

reduction in tensile stress in prestressing steelh = overall depth of memberK = coefficient of allowable concrete compressive stress

at prestress releaseL = span lengthMg moment due to self weight of member

nominal moment strength

M5d= moment due to superimposed dead loadM51 = moment due to superimposed live load

M = factored moment

P = effective prestress force after all prestress losses= prestress force immediately after prestress release

P, = nominal axial load strength

Yb = distance between section centroid and extremebottom fiber

S = section modulus

13i = equivalent stress block factor= concrete strain= tension reinforcement strain= compression reinforcement strain

= concrete strain at ultimate= strength reduction factor

46 PCI JOURNAL

APPENDIX B - DESIGN EXAMPLESEXAMPLE 1

Given:8DT24: Span = 44 ft (13.4 m),f= 5000 psi (34.5 MPa),

superimposed DL load = 10 psf (0.48 kPa), superimposedLL load = 90 psf (4.31 kPa).

Determine strand pattern and strength at transfer.

(a) Current DesignAccording to the PCI Design Handbook, Fifth Edition:

Use a draped strand pattern, eight strands, eç 9.15 in.(232 mm) and e 14.40 in. (366 mm), as shown in Fig. BI.

The requiredf is based on the compression at transfer atmidspan.

P Pe M0.6f=_L + _L -

A Sb 5b

223.07 223.07 x 14.4= xl000+ xl000

401 12241213.9

— xl0001224

f = 3648 psi (25.2 MPa)

(b) Proposed DesignA straight strand pattern will be attempted. The strand

pattern is shown in Fig. B2.The top strands are fully tensioned. They are intended to

control the conditions at transfer at the member end.Use ten strands, ee = e = 8.75 in. (222 mm).

(1) Check strength:M 6199 kip-in. (700 kN-m)M = 5579 kip-in. (630 kN-m)

(2) Check tensile stress at final condition:

247.9 247.9 x 8.75= xl000 + xl000—

401 12241213.9

xl000— 232.3

xl000—1224 1224

2090.9

1224=

— 499 psi (3.44 MPa) (tension)

499 < 12Jöö = 848 psi (5.85 MPa) ok.

(3) Check conditions at transferBecause strands are straight, only the section at transfer

point needs to be checked.P1 = 0.75 x 270 x 10 x 0.153 = 309.8 kips (1378 kN)1.2P1 = 371.8 kips (1654 kN)Self-weight moment at transfer point from member end:Mg = 219 kip-in. (24.74 kN-m)0.8 Mg = 175.2 kip-in. (19.79 kN-m)Compression member is designed for axial force = 371.8

kips (1654 kN) and bending moment = 1.2 P1e —0.8 Mg= (371.8 x 8.75 — 175.2)/12 kips = 256.5 kip-ft (348 kN-m)

L—1ee = 9.15 in. ec = 14.4 in.

F44 ft

Fig. B1. Draped strand. Note: 1 ft 0.3048 m, 1 in. = 25.4 mm.

8 ft.

Fig. B2. Straight strand. Note: 1 ft = 0.3048 m, 1 in. = 25.4 mm.

2”

2”2”2”2

January-February 2001 47

Using these applied loads, input any commercially available computer program for design of compression member;PCACOL is one such example.

Enter section geometry, compression “reinforcement” A2’= 8 x 0.153 = 1.224 sq in. (790 mm2), at bottom fibers andtension reinforcement A2 = 2 x 0.153 = 0.306 sq in. (197mm2) at 2 in. (51 mm) from top fibers. Also, input the factored loads P = 371.8 kips (1654 kN) and M 256.5 kip-ft(348 kN-m).

Solve forf through trial and adjustment. Fig. B3 showsa typical interaction diagram, output with Trial No. 1 using

f = 3000 psi (20.68 MPa) and Trial No. 2,f = 3230 psi(22.27 MPa). In Trial No. 2, the design strength matches therequired strength.

It is interesting to note that if “Current Design” for releasestrength is used, the requiredf will be as follows:

P. Re M0.6f=—- + ——

— _LA Sb Sb

278.84 278.84 x 8.75= xl000+ xl000

401 1224— 219.01

x 10001224

f = 4183 psi (28.84 MPa)

The above value is significantly higher than that requiredby the proposed strength design method.

Fig. B3.Interaction diagram.

Note: 1 kip 4.448 kN,1 kip-ft = 1.356 kN-m.

EXAMPLE 2

Given:401T52: Span = 48 ft (14.63 m),f = 3500 psi (24.13

MPa).Determine strand pattern and strength at transfer.

(a) Current DesignAccording to the PCI Design Handbook, Fifth Edition:

Use 48 strands, e = 17.62 in. (448 mm), as shown inFig. B4.

The requiredf is determined based on compression at release at midspan.

fb=-—A Sb Sb

— 1338.4 1338.4 x 17.62— xl000+ xl000

1504 15,497

5415.6xl000

15,497

= 2062 psi

0.6f = 2062 psi (14.22 MPa)

f’1 = 3437 psi (23.7 MPa)

A total of 12 strands, 25 percent of total, were debonded.The new prestress is 1003.8 kips (6920 kN), the new ec

centricity is 17.28 in. (439 mm) and the stresses at transferare determined:

P (kip)

200

4

annvw

40G I

-300 -200 -100-

20

M.

3

(k-ft;

48 PCI JOURNAL

P. Re Mgfb---

1003.8 1003.8 x 17.28= xl000+ xl000

1504 15,497

— 899.4x 1000

15,497

= 1729 psi (11.92 MPa)

F Re Mgft =— + —‘—- —

A Sb 5h

— 1003.8 1003.8 x 17.28— xl000— xl000

1504 15,497

899.4— xl000

15,497

-678 psi (-4.67 MPa) (high)

Since the tensile stress exceeds the limit, 6J5 = 351psi (2.42 MPa), reinforcement is required to resist the totaltensile force, as follows:

(h)ft+f,,

678(52)

678+ 1729= 14.63 in. (372 mm)

T =

2= 14.63(678)(24)

2= 119, 030 lb (529 kN)

Using reinforcement withL = 60 ksi (414 MPa):0.6(60) = 36 ksi (248 MPa), use 30 ksi (207 MPa)A (or top mild steel reinforcement) = 3.97 sq in. (2561

mm2) (use 7 No. 7 bars Grade 60). EXAMPLE 3

Given:

Fig. B4.Bonded strand.

Fig. B5.No debonding.

(b) Proposed DesignA total of three /2 in. (12.7 mm) diameter fully preten

sioned strands were added at the top fiber. No debonding atthe member ends would be required, as shown below (seeFig. B5).

Check conditions at transfer:Because the strands are straight, only the section at the

transfer point needs to be checked.= 5 1(0.153) = 7.803 sq in. (5034 mm2)

P = 0.75 x 270 x 7.803 = 1580 kips (7028 kN)1.2P1 = 1896 kips (8433 kN)Eccentricity, e = 14.99 in. (381 mm)Mg = 899.4 kip-in. (102 kN-m)0.8 Mg =719.5 kip-in. (81 kN-m)

Design a compression member subjected to axial force=1896 kips (8433 kN) and bending moment:

l.2Pje - O.8Mg = (1896 x 14.99 - 719.5)/12= 2274.8 kip-ft (3084 kN-m)

NU1 100 [43.3 in. (1100 mm) deep]: Span = 130 ft (39.62 m)Use 58 strands, eç = 9.04 in. (230 mm)Determine strength at release when a total of 12 strands

were draped as high in the web as possible, as shown in Fig.B6.

(a) Current DesignThe required f4.’j is determined based on compression at

prestress transfer at transfer point.

fb=±-A Sb 5b

1617.3 1617.3 x 9.04= xl000+ xl000

694.1 93221157.6

xl0009322

= 3774 psi (26.02 MPa)

0.6f = 3774 psi

= 6290 psi (43.37 MPa)

Using these applied loads, input PCACOL. The requiredconcrete strength is 3500 psi (24.13 MPa).

January-February 2001 49

Fig. B6.Strand pattern atmember end for

NU1 100.

(b) Proposed DesignCheck conditions at transfer:A3 = 58(0.153) = 8.874 sq in. (5725 mm2)P1 = 0.75 x 270 x 8.874 1797 kips (7993 kN)1.2P 2156.4 kips (9592 kN)Eccentricity, e 9.04 in. (230 mm)Mg= 1157.6 kip-in. (131 kN-m)0.8 Mg =926.8 kip-in. (105 kN-m)Design compression member subjected to axial force= 2156.4 kips (9592 lcN) andBending moment = 1.2P1e - O.8Mg

=(2156x 9.04—926)/121547 kip-ft (2097 kN-m)

Using these applied loads, input PCACOL. The strengthrequired is 5730 psi (39.51 MPa).

APPENDIX C - PARAMETRIC ANALYSIS FOR APPROXIMATEEQUIVALENT COMPRESSIVE STRESS LIMIT

C.1 Assumptions for Developing a Semi-EmpiricalWorking Stress Design (WSD)

The following assumptions were used to establish the coefficient K in Kf, where K is the allowable concrete compressive stress at prestress transfer. Effort was made to establish values of K that produce equivalent results to thestrength design approach being proposed.

• Use either Grade 60 mild steel reinforcement, As,, with29,000 ksi (200 GPa) or low relaxation, 270 ksi

(1860 MPa), strand; with = 28,500 ksi (197 GPa) isused when service load tensile stress limit at top fiber isgreater than 6J (0.5

• Prestress immediately before transfer is equal to 75 percent of 270 ksi (1860 MPa). Only the end section is considered while the self-weight moment is ignored.

• For working stress design, elastic loss is assumed equal to10 percent of initial prestress.

C.2 Selected ParametersThe standard double tee, rectangular and inverted tee sec

tions were chosen to represent geometry variations. PCI Design Handbook rectangular and double tee sections were

Table Cl. Kvalue for rectangular section.

used. Service load stress at bottom fibers of 2450 psi (16.89MPa) was assumed for rectangular and double tee sections.NU inverted tee sections were used in the study. The maximum number of strands that can be accommodated in thestandard NU inverted tee, 22, was used in the bottom flange.Microsoft Excel Spreadsheet program was developed andused for computation. All runs were verified with the PCACOL software.

C.3 Proposed FormulaAn approximate formula was developed to determine the

K value at the end section of the pretensioned member:

K = 0.6 + (Yb’ 5h) 0.75 (5)

Based on Eqs. (3) and (4), the K values range from 0.66 to0.76. Double tee sections with the highest strand eccentricity allow for the greatest K value, while the inverted tee sections require the smallest K value.

C.4 Tables of ResultsTables Cl, C2 and C3 show a comparison between the K

value based on strength design and the proposed formula.

Rectangular No. of A A5 d’ d e A h Sb Yb fb fsection strand (sq in.) (sq in.) (in.) (in.) (in.) (sq in.) (in.) (in.3) (in.) (psi) (psi) K 0.6 + (JYbI5h)12RB20 8 1.224 0.459 4.547 18.5 5.453 240 20 800 10 2450 3517 0.70 - 0.70

12RB24 10 1.53 0.427 5.878 22.5 6.122 288 24 1152 12 2450 3530 0.69 0.70

12RB28 12 1.836 0.404 7.186 26.5 6.814 336 28 1568 14 2450 3536 0.69 0.70

12RB32 13 1.989 0.671 7.491 30.5 8.509 384 32 2048 16 2450 3493 0.70 0.70

12RB36 15 2.295 0.641 8.817 34.5 9.183 432 36 2592 18 2450 3508 0.70 0.70

16RB24 13 1.989 0.671 5.619 22.5 6.381 384 24 1536 12 2450 3513 0.70 0.70

16RB32 18 0.695 8.003 30.5 7.997 512 - 32 2731 16 2450 3522 0.70 0.70

16RB36 20 3.06 0.854 8.817 34.5 9.183 576 36 3456 18 2450 3508 0.70 0.70

16RB40 22 3.366 1.016 9.626 38.5 10.374 640 40 4267 20 2450 3495 0.70 0.70

*Kjs based on strength design. Note: 1 in. = 25.4 mm. 12RB20: 12 in. wide; 20 in. deep.

50 PCI JOURNAL

Table C2. K value for double tee section.

No. of A, d’ d e A h Sb Yb ib f,strands (sq in.) (in.) (in.) (in.) (sq in.) (in.) (in.3) (in.) (psi) j (psi) K 0.6 + (Ybf5h)

1_r2 142 1252 — 240 463 401 24 1224 iT15 2450 3376 073 07422_j3.366 15.38 32.0 5.83 567 32 2615 21.21 2450 3376 0.73 0.73

14 T2.142 12.65 24.0 5.12 449 24 1264 17.77 1 2450 3335 O.73j 0.75

14212.99 26.0 7.30 L62_TiW7 20.292450 3237 0.76 0.76

22 3.366 15.55 32.0 6.43 615 32 27iT98 2450 t3333 0.741 034

___________

3.06 13.97 — 28.0 6.24 640 28 1 2205 f_20.21 2450 3353 0.73 0.74

22 2 142 15 31Z 300 7 63 928 30 2615 22 94 2450 3311i074 07522 2.142 15.52 32.0 f23 690 32 2840 22.75 2450 3339 0.73 0.74

APPENDIX D - PROPOSED CODE CHANGE

Change Submittal:Subject: Modifications of ACT 318 Code wording and

equations that currently permit stress limits in flexural pretensioned concrete members as a method of design for prestress transfer force.

Current Sections Affected: 18.4.1, 18.4.2, R18.4.1,R18.4.2.

Reason: Permit the strength design theory to be the primary method of design of pretensioned flexural members atprestress transfer. Allowable tensile stress of 6 will beretained if the member is desired to be uncracked in the topfibers at prestress transfer. Another design requirement includes the design of top bonded reinforcement. If the member is allowed to crack, this can be achieved through thestrength design approach given here. An approximate alternative to the strength design method is the compressivestress limit formula given in Section 18.4.2.

Proposed Code Change:Add a new Section 18.4.1 and renumber Section 18.4.1 to

Section 18.4.2, Section 18.4.2 to Section 18.4.3 and Section18.4.3 to Section 18.4.4.

18.4.1 — The requirement of Section 18.4.2. except Section 18.4.2 (a) and (b). may be waived if a strength analysisis performed based on the assumptions that Section 10.2 issatisfactorily completed. For the strength analysis, the required strength U according to Section 9.2. shall be basedon a combination of 1 .2P,. and either 1 .2Mg or 0.8M

4). according to Section 9.3. shall be 0.7. If required. theamount of bonded tension reinforcement placed near themember extreme tension fibers may be obtained using thisstrength design approach. If the bonded tension reinforcement stress at the strength level is not greater than 60 ksi,the equivalent unfactored load reinforcement stress shouldbe expected to be below the stress that causes unacceptabletop fiber cracks.

18.4.1 — Strcooco in concrete immcdiatoly aftcr prentreriotranofcr (before time dcpcndcnt prentrcIm loonc3) ohall notexceed the following: 18.4.2 — In lieu of the more accuratestrength design approach. the following working stress analysis. using unfactored loads, should give satisfactory results:

(a) Extreme fiber stress in compression at ends of simplytiinnnrtM mmhr

but not greater than 0.75f....(0.6 + YbI5h)fci

(b) Extreme fiber stress in compression except as permitted in (a) 0.60f

1g{c Extreme fiber stress in tension except as permitted3JF

Extreme fiber stress in tension at ends of simplysupported members 6

Proposed Commentary Change:Add a new Sections R 18.4.1 and renumber Section R

18.4.1 to Section R 18.4.2.

R.18.4.1: — Studies in Reference 18.X1, have demonstrated the validity of the strength design method of preten

Double teesection8DT24

8DT32

10DT24

10DT26

10DT32

12DT28

12DT30

12DT32

Note: 1 ft= 0.3048 m, 1 in. = 25.4 mm. 10DT32: 10 ft wide; 32 in. deep.

Table C3. Kvalue for inverted tee section.

Inverted tee No. of A3 A d’ d e A h S

section strands (sq in.) (sqin.) (in.) (in.)(in.) (sq in.) (in.) (in?)

1T300 22 3.366 0.095 2.756T9.81 1.394 171J_11.8l 368

1T400 22 3.366 0.545 2.756 1351 2.604 196.1 j15.75 666

— 1T500 j 22 3.366 0.945 2.756 117.69 3.994 T 220.9Ti69

1T600 22 3.366 J 1.267 2.756 21.62 5.504 245.7] 23.62 1445

- 1T700 22 1 3.366 1.536 2.756 25.56 7.084 270.5 27.56 1904

- 1T800 22 3.366 1.778 2.756 29.50 8.744 295.31.50 2396

1T900 22 3.366 1.984 2.756 33.43 fio.444 320.1 35.43 2927

Note: 1 in. = 25.4 mm. 1T500 mm deep; 600 mm bottom flange width.

Yb fb

(in.) (psi) (psi) . K I 0.6 + (ybI5h)4.15 5907 8777 0.671 0.66

5.36 J 5528 8325 0.66 0.66

- 6.75 5155 j7S7 0.66 0.66

8.26J_4833 J1 0.67[ 0.679.84 J4550 6766 0.67 j 0.67

11.50J4316 6351 10.681 0.67

13.20 1 4106 5985 0.691 0.67

whichever is more critical, and the strenuth reduction factor

January-February 2001 51

sioned concrete members at prestress transfer. The load factor 1.2 applied to the prestress force P. just before prestresstransfer, is consistent with the factor used for strength design of post-tensioning anchorage zone. The strength reduction factor = 0.7 is consistent with that used for tiedcolumns. Both factors may be too conservative for this application as P1 is known with high precision and concretestrength is normally tested for prestress transfer. Further, theprestressin reinforcement is in tension and there is no possibility of reinforcement buckling under factored loads, as isthe case of reinforcement in tied columns. Additional studies may produce further refinement of these factors.

Reference 18.X1 studies have shown that if the stress inbonded tension reinforcement at factored load is below0.0021(29000 = 60 ksi. which is the yield point of Grade60 steel, the corresponding stress at unfactored load level isfound to be in the range of 15 to 22 ksi, which is below thatcausing unacceptable cracking.

Interestingly, it was discovered near the completion ofthis report that a very similar concept is being promoted inAustralia. See Reference 18.X2. The Australian Code. AS3600 Clause 8.1.4.2, already accepts strength design for prestress transfer in lieu of allowable compressive stress. InAustralia, the load factors used are 1.15 for prestress force.and either 1.2 or 0.8 for member self-weight. The strengthreduction factor is 0.6. These factors confirm the reasonableness of the factors recommended herein. It is unclear.

however, how the tension reinforcement stress due to factored loads is utilized for crack control.

Add a new Section R18.4.2 (a) and (b)R.18.4.2: (a) and (b) — The formula for allowable com

pression is equivalent to using 0.7 f for rectangular and I-shape sections, approximately 0.65 f for inverted tee and0.75f for double tee members. The proposed coefficientswere based on correlation with strength design results for alarge number of common pretensioned concrete membershapes and levels of prestress. For post-tensioned concretemembers, it is recommended that the compression stresslimit of 0.60f at ends of member should be retained.

Renumber Commentary R18.4.1(b) and (c) to read:R.18.4.l(c) and R18.4.1(d)

Add new References 18.X1 and 18.X2:References

18.X1. Noppakunwijai. P.. Tadros, M.K., Ma, Z., andMast. R.F., “Strength Design of Pretensioned FlexuralMembers at Prestress Transfer.” PCI JOURNAL. V.46.No.1. January-February 2001. pp. 34-52.

18.X2. Warner, R.F., Rangan. B.V., Hall, A.S.. andFaulkes, K.A., Concrete Structures. Addison Wesley Longman Australia Pty Limited. Sydney. Australia, 1998. pp.197-202.

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