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Determining Slipping Stress of PrestressingStrands in Confined Sections

ARTICLE in ACI STRUCTURAL JOURNAL NOVEMBER 2012

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Mohamed K. ElBatanouny

Wiss Janney Elstner Associates Inc.

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Paul Ziehl

University of South Carolina

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Availablefrom: Mohamed K. ElBatanounyRetrieved on: 17 August 2015
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Title no. 109-S66

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 109, No. 6, November-December 2012.MS No. S-2010-340.R1 received November 18, 2011, and reviewed under Institute

publication policies. Copyright 2012, American Concrete Institute. All rightsreserved, including the making of copies unless permission is obtained from the

copyright proprietors. Pertinent discussion including authors closure, if any, will bepublished in the September-October 2013ACI Structural Journalif the discussion isreceived by May 1, 2013.

ACI Structural Journal/November-December 2012 767

Determining Slipping Stress of Prestressing Strands in

Confined Sections

by Mohamed K. ElBatanouny and Paul H. Ziehl

Development length and slipping stress of prestressing strandssubjected to confining stress is not well-quantified and the appro-

priateness of the ACI 318-11 equation under such conditions canbe questioned. In 1992, a test was performed on nineteen 14 in.

(356 mm) square prestressed concrete piles with a clamping forceapplied during testing under lateral load. The findings indicatedthat the ACI 318-11 equation for development length of prestressingstrands may not be suitable when used for sections subjected toconfining stress. In this study, a modified equation that accounts forthe effect of concrete confinement is discussed and compared to the

published 1992 results and the ACI 318-11 equation. The moment

strength of the sections is also compared using moment-curvatureanalysis by comparing three different slipping values: 1) thoseobtained from experimental results; 2) the ACI 318-11 equation;and 3) the modified equation.

Keywords:confining stress; development length; moment capacity; slipping.

INTRODUCTIONThe use of precast, prestressed concrete piles in bridge

construction is common in the United States; however,the performance of such units under seismic loading isnot entirely clear. The behavior of the connection betweenprestressed piles and cast-in-place (CIP) reinforced concretecaps is particularly not well-understood. Current South

Carolina Department of Transportation (SCDOT) connec-tion details1,2 require the plain embedment of the pile intothe bent cap one pile diameter with a construction toleranceof 6 in. (152 mm). Plain embedment requires no specialdetailing to the pile end or the embedment region and nospecial treatment of the pile surface, such as rougheningor grooving. The ductility and moment capacity of suchconnections is of interest because this short embedmentlength is often much less than the length required for devel-opment of the full tensile strength of the prestressing strandswithin the embedded region.

Generally, the development length of prestressing strandsis calculated from ACI 318-11, Eq. (12-4).3 In the case of

piles embedded in CIP caps, the embedment length is usuallyfar less than the development length. Therefore, the strandsare predicted to slip at a level of stress less than their nominalcapacity. This stress is referred to as the slipping stress.

The ACI 318-11 equation was developed for the case ofsuperstructure elements not subjected to confining stress.Therefore, the application of this equation to substructureelements having significant confining stress may not beappropriate. A pile embedded in a CIP cap is subjected tothe shrinkage of the confining concrete in the cap, whichcreates confining stress (also known as clamping force)on the pile, which serves to enhance the bond betweenthe prestressing strand and the surrounding concrete. This

leads to a decrease in the development length and an asso-ciated increase in the slipping stress of the prestressing

strand.4,5This effect became very apparent during the testingof a series of precast concrete piles embedded in CIP bentcaps at the University of South Carolina Structures Labora-tory.5Because the embedment length of the piles was muchless than the development length of prestressing strands, thestrands were expected to slip prior to achieving the nominalcapacity. Significant differences were found between theexperimental results and those predicted by ACI 318-11,Eq. (12-4).5

Shahawy and Issa4discussed the findings of a significant

experimental investigation related to the effect of confine-ment from CIP caps to prestressed concrete piles withemphasis on the resulting behavior under lateral load. Theresults showed that the development length of prestressingstrands was enhanced due to confining stress. They concludedthat using the ACI 318-11 equation without consideration ofconfinement will lead to very conservative values.

This study makes use of the experimental results reportedby Shahawy and Issa4to investigate the appropriateness ofa potential modification to the ACI 318-11 equation.5Thetheoretical slipping stress calculated from the modifiedequation and ACI 318-11, Eq. (12-4), are compared.

The calculation of the moment strength of piles in seismic

regions is a critical issue. A moment-curvature analysis

6

wasperformed to calculate the moment strength of the sectionsusing the modified equation and the ACI 318-11 equation.These were then compared to calculated moments usingmeasured slipping stress values from the Shahawy andIssa4study. Furthermore, finite element models were createdto investigate the value and distribution of the confiningstress due to shrinkage for use in the modified equation.

RESEARCH SIGNIFICANCESeveral important investigations have addressed the suit-

ability of ACI 318-11, Eq. (12-4), for development length7,8;however, only a few have considered the effect of confine-ment.4,5The ACI 318-11 equation for calculating the devel-opment length of prestressing strands was derived forunconfined sections and does not account for the effect ofconfinement. To account for the effect of confinement, apotential modification to the ACI 318-11 equation is devel-oped and described. The results from the modified equationare compared to published experimental results that directlyaddressed the effect of confinement for the developmentlength of prestressing strands.

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Mohamed K. ElBatanounyis a Graduate Research Assistant in the Department of

Civil & Environmental Engineering at the University of South Carolina, Columbia,

SC. He received his BS from Helwan University, Cairo, Egypt, in 2008, and his MS

from the University of South Carolina in 2010.

ACI memberPaul H. Ziehlis an Associate Professor in the Department of Civil &

Environmental Engineering at the University of South Carolina. He received his PhD

from the University of Texas at Austin, Austin, TX. He is a member of ACI Committees

335, Composite and Hybrid Structures, and 437, Strength Evaluation of Existing

Concrete Structures.

SUMMARY OF EXPERIMENTAL RESULTS4

Test specimensNineteen 14 in. (356 mm) square prestressed concrete pile

specimens with 8.5 in. (13 mm) diameter prestressing strandswere tested in this study. The specimens were 12 ft (3.66 m)

long and were cut from 80 ft (24.4 m) long prestressedconcrete piles. Number 5 (No. 16) gauge steel was usedas spiral reinforcement that varied in pitch depending onlocation. The end sections of the full-length piles wereprovided with more spiral reinforcement than the interiorsections (middle sections), as shown in Fig. 1. Four embed-ment lengths of 36, 42, 48, and 60 in. (914, 1067, 1219,and 1524 mm) were used in this study. Cores with diametersof 6 in. (152 mm) were taken from the specimens to deter-mine the concrete compressive strength. A summary of theexperimental program is provided in Table 1.

Test procedure and analytical studyThe experimental investigation was designed to simu-

late the behavior of a CIP cap. A steel test frame was usedto restrain the pile cap against translation and rotation. Aninitial test was conducted to assess the value of confiningstress exerted from the shrinkage of the cap. A CIP cap wascast with a pile embedded in its center for the initial test. TheCIP cap had a cross section of 42 x 54 in. (1.1 x 1.4 m) witha depth of 48 in. (1219 mm). The pile was instrumented withvibrating wire strain gauges spaced at 12 in. (305 mm) alongthe embedment length (48 in. [1219 mm]). A schematic of

this confining stress test is shown in Fig. 2. After 28 days, theprincipal strains were measured with a resulting maximumvalue of 245 . Using a conservative value for the Youngsmodulus of 3.6 106 psi (24,800 MPa), the maximumconfining stress was calculated to be 880 psi (6.1 MPa).

The authors4 of this study assumed that this valuewould approach zero at the ends of the embedment lengthfollowing a parabolic distribution of a maximum measuredvalue of 245 at a depth of 30 in. (762 mm); therefore,Fig. 1Details of test specimens.4

Table 1Details of test program4

Specimen number Section fc, ksiMeasured steel stress

at failure, ksi fse*,ksi Embedment length, in. Transfer length, in.

Available flexural

bond length, in.

A-1E End 7.10 256 162 36 26.9 9.10

A-2E End 5.84 263 178 36 29.6 6.40

A-3I Interior 6.59 254 161 36 26.9 9.10

A-4I Interior 5.60 153 164 36 27.3 8.70

B-1E End 6.70 262 173 42 28.8 13.2

B-2E End 6.45 261 172 42 28.6 13.4

B-3E End 5.98 257 169 42 28.1 13.9

B-4E End 7.80 260 168 42 28.0 14.0

B-5E End 6.48 263 174 42 29.0 13.0

B-6I Interior 6.48 259 169 42 28.2 13.8

C-1E End 6.96 260 168 48 28.0 20.0

C-2E End 6.50 258 166 48 27.6 20.4

C-3I Interior 7.76 262 170 48 28.3 19.7

C-4I Interior 6.50 258 165 48 27.5 20.5

C-5I Interior 6.50 260 170 48 28.4 19.6

C-6E End 6.50 258 167 48 27.8 20.2

D-1E End 7.20 262 169 60 28.2 31.8

D-2I Interior 6.50 261 172 60 28.6 31.4

D-3E End 6.50 260 170 60 28.3 31.7

*Effective prestressing stress back calculated from Shahawy and Issa4data.Embedment length minus transfer length.

Notes: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.

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21000

3

d

ss se ps

b

Lf f f

d= + (1b)

2. A modification to Eq. (1a), as proposed by Shahawy and

Issa.4 The proposed modification incorporates an average

bond stress term in the second part of the equation, as shown

in Eq. (2a). The Shahawy and Issa4equation is rearranged

as Eq. (2b), which can be used to calculate slipping stress.

The calculated average bond stress (psi) is uave, which can be

calculated using Eq. (3). In this equation, Pis the resisting

steel strength based on the strand slipping stress at failure

(lb); T is the resisting concrete strength, which is assumed

to be zero at ultimate due to cracking (lb); leis the available

embedment length (in.); and dbis the nominal strand diam-

eter (in.).

( )3000 4

ps sese

d b b

ave

f ffL d d

u

= + (2a)

44 1

3000

d ave

ss ave se ps

b

L uf u f f

d

= +

(2b)

( )avee b

P Tul d=

(3)

Fig. 2Confining stress test setup.4

Fig. 3Lateral loading test setup with applied clamping force.4

an average confining stress was computed to be 525 psi(3.6 MPa). Using this average confining stress value as anupper limit, a clamping force of 200 kips (888 kN) wasapplied to the upper and lower faces of the embedmentlength of the pile specimens to represent the confining stress.This clamping force was applied using post-tensioningthread bars, as shown in Fig. 3. The lateral faces of the pileembedment length were not subjected to confinement. Theconfining stress varied with embedment length, resulting in

397, 340, 298, and 238 psi (2.74, 2.34, 2.05, and 1.64 MPa)for embedment lengths of 36, 42, 48, and 60 in. (914, 1067,1219, and 1524 mm), respectively. The highest appliedconfining stress value was taken to be 75% of the averageconfining stress measured in the initial test.

A hydraulic jack placed at 6 ft (1.84 m) from the face ofthe supporting frame was used to apply lateral load on thepiles in increments of 3 kips (13.3 kN) up to a load of 18 kips(80.1 kN); thereafter, the load increments were much smalleruntil failure was achieved. At each load step, cracks weremarked and displacements and strains were recorded. Detailsof the test setup are shown in Fig. 3.

The piles were next analyzed using a nonlinear mate-

rial model. The time-dependent effects due to load history,temperature history, creep, shrinkage, and relaxation ofsteel were considered in the computer program.4 Theprogram4 was used to calculate the structural responsethrough the elastic and inelastic range up to ultimate load.At each load step, nonlinear equilibrium equations using thedisplacement formulation of the finite element method werederived for the geometry and material properties.4

Findings of Shahawy and Issa4

The effect of transverse reinforcement was examined andtransverse reinforcement was found to have a slight effectin terms of the moment capacity of the piles. The ulti-

mate moment of the piles cut from the end sections wasslightly higher than those of the piles cut from the middlesections by approximately 6%, as shown in Table 2. Theexperimental slipping stress of the prestressing strands wasdetermined by measuring the strain along the length of thestrand at various levels of load until failure. The measuredslipping stress determined by this method is presented inTable 2. For development length, the embedment lengthof the piles was compared to the theoretical developmentlength required to obtain the same slipping stress usingthree different equations:

1. The ACI 318-11 equation3 for development lengthof prestressing strands, which is shown in Eq. (1a). This

equation divides the development length into two parts:1) transfer length; and (2) flexural bond length. In this equa-tion, Ld is the development length (in.), which is equal tothe embedment depth of the pile;fseis the effective stress ofprestressing strand (psi);fpsis the nominal flexural strengthof the prestressing strand (psi); and dbis the nominal diam-eter of the prestressing strand (in.). The slipping stress canbe calculated by rearranging the ACI 318-11 equation, asshown in Eq. (1b). The nominal flexural strength of theprestressing strand,fps, is renamed as the slipping stress,fss(psi), for clarity.

( )3000 1000ps sese

d b b

f ffL d d

= + (1a)

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3. An equation proposed by Zia and Mostafa,8as shown

in Eq. (4a). Their approach used the same parameters

used in calculating the development length of prestressing

strands, with the exception of two terms: fsi, which is the

stress in prestressing steel at transfer (ksi), and fc, whichis the compressive stress of concrete at the time of initial

prestressing (ksi). The effective stress of the prestressing

strand, fse, and the nominal flexural strength of the

prestressing strand,fps, should be used (ksi).

( )1.5

4.6 1.25si

d b ps se b

c

fL d f f d

f= +

(4a)

3.680.8 1.2

d siss se ps

b c b

L ff f f

d f d= + +

(4b)

Comparisons between these three approaches are

summarized in Table 2. The comparisons indicate that

the ACI 318-11 equation is conservative when confining

stress is applied to the concrete section. The Zia and

Mostafa8 proposed equation (Eq. (4b)) was more conser-

vative than the ACI 318-11 equation. The Shahawy and

Issa4proposed equation (Eq. (2b)) has a good match with the

experimental data. However, this equation uses the slipping

stress of the strand as an input. More detailed discussion isprovided in the following sections.

HISTORY OF ACI 318-11 EQUATIONThe expression for the development length of prestressing

strands found in ACI 318-11 was proposed by Mattock9and

members of ACI Committee 423.10The expression dividesthe development length into two parts: transfer length andflexural bond length. To develop the expression for transferlength,11results of a study by Hanson and Kaar12and Kaar etal.13were used. They stated a value for average transfer bondstress ut = 400 psi (2.76 MPa). For flexural bond length,another approach was used based on the definition of generalbond slip introduced by Janney.14Janney14stated that whenthe peak of the high bond stress wave reaches the transferlength, general bond slip occurs and leads to a reduction inthe frictional resistance resulting from the Hoyer effect.15

Hanson and Kaar12agreed with Janneys14explanation, butthey did not state a value for the average flexural bond stress.

Due to the difficulty of codifying this concept, Mattock9andthe members of ACI Committee 42310 used the data ofHanson and Kaars12 beam tests to formulate an approachbased on an average flexural bond stress. They constructeda straight-line relationship by subtracting the estimatedtransfer length from the embedment length of the strand. Theincrease in strand stress due to flexure was determined to bethe difference between the strand stress at the load causingslip and the effective stress due to prestressing. The use ofa constant slope for the flexural bond length implies a valueof average flexural bond stress ufb= 140 psi (0.96 MPa).

5Itis worth noting that the assumption of average flexural bondstress was made to simplify the approach and makes it easier

to codify. The expressions for transfer length and flexuralbond length are shown in Eq. (5) and (6), respectively.

Table 2Shahawy and Issa4test results and calculated slipping stresses

Specimen number Embedment length, in.Theoretical ultimate

moment, kip-in.Measured ultimate

moment, kip-in.Measured steel stress

at failure, ksi

Slipping stress, ksi

Eq. (1b) Eq. (2b) Eq. (4b)

A-1E 36 1560 1840 256 180 256 167

A-2E 36 1460 1800 263 190 263 177

A-3I 36 1530 1550 254 180 254 166

A-4I 36 1440 1550 253 181 253 167

B-1E 42 1530 1620 262 199 262 182

B-2E 42 1520 1870 261 199 261 183

B-3E 42 1480 1760 257 197 257 180

B-4E 42 1600 1560 260 196 260 179

B-5E 42 1520 1840 263 200 263 185

B-6I 42 1520 1600 259 197 259 181

C-1E 48 1550 1510 260 208 260 190

C-2E 48 1520 1690 258 206 258 188

C-3I 48 1600 1760 262 209 262 190

C-4I 48 1520 1660 258 206 258 188

C-5I 48 1520 1690 260 210 260 192

C-6E 48 1520 1700 258 207 258 189

D-1E 60 1570 1730 262 233 261 210

D-2I 60 1520 1730 261 235 261 212

D-3E 60 1520 1620 260 233 260 210

Notes: 1 in. = 25.4 mm; 1 kip-in. = 0.11298 kN-m; 1 ksi = 6.895 MPa.

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7.36 3000

ps se se se

t b b

t t

A f f fL d d

o u u

= = =

(5)

( ) ( )7.36 1000

ps se ps se

fb b b

fb

f f f fL d d

u

= =

(6)

where Lt is transfer length (in.);Lfbis flexural bond length(in.); o is the strand perimeter (o= 4/3 * * db [in.]);andApsis the strand cross-sectional area (Aps= 0.725 * *db

2/4 [in.2]).

EFFECT OF CONFINEMENT ON EFFECTIVETRANSFER LENGTH

Transfer length in the absence of confinement is a functionof diameter, effective prestress, and average transfer bondstress. Mechanisms contributing to the value of averagetransfer bond stress can be categorized into three groups:adhesion, friction, and mechanical interlock.11 Adhesionis destroyed by the relative slip between the strand and the

surrounding concrete and the contribution of mechanicalinterlock in the average transfer bond stress can be neglecteddue to unwinding.16

Frictional bond stress is developed as a result of the radialcompressive stresses, which are attributed to the Hoyereffect,15 where longitudinal contraction results in radialexpansion of the tendon. This Poissons expansion inducescompression perpendicular to the steel-concrete interface. Inthe absence of confinement, the value of the average transferbond stress is assumed to be ut= 400 psi (2.76 MPa). Whenconfinement occurs, it is convenient to represent the effectas an increase in the apparent bond stress. It should be notedthat confinement does not change the transfer length itself.

Rather, confinement decreases the potential for slipping ofthe strands within the transfer zone.To account for this behavior, a new term referred to as the

effective transfer length (Lte) is proposed. This term takesinto account both the unconfined average transfer bond andthe increase in bond stress due to confinement. The value ofthe resulting apparent bond stress is determined by addingthe average transfer bond stress (400 psi [2.76 MPa]) to theaverage bond stress that is due to confinement. The averagebond stress due to confinement is calculated by multiplyingthe confining stress by the coefficient of friction between thesteel and concrete (). The resulting average bond stress isshown in Eq. (7).

400tc cavu = + (7)

where utc is the average confined bond stress within thetransfer zone (psi); cav is the average confining stressapplied to the prestressed concrete section; and is the coef-ficient of friction between the steel and concrete (generallytaken as = 0.417).

EFFECT OF CONFINEMENT ONFLEXURAL BOND LENGTH

For the confined flexural bond stress ufbc (psi), the sameapproach was used, assuming that the confining stress would

only affect the friction stress. Due to the reduction in stranddiameter resulting from the increase in strand stress in the

average flexural bond stress zone, the Hoyer effect15 isreduced and ufbis implied in the ACI 318-11 equation to beequal to 140 psi (0.96 MPa).5The reduction of the Hoyereffect15leads to a decrease in the frictional forces resultingfrom the confining stress. A ratio between the average transferbond stress and the average flexural bond stress was usedto decrease the effect of the confining stress, where ut/ufb=2.86. Therefore, Eq. (8a) is introduced to assess the averageflexural bond stress, including the effect of confining stress.

Another reason to use this factor is the fact that microcrackswill form in the pile/bent-cap system at higher levels of load(average flexural bond stress only appears after cracking14),causing the confining stress from the shrinkage of the bentcap to decrease. In the test program considered, however, theconfining stress is not expected to decrease, as it was appliedto the specimens permanently via a clamping force.4There-fore, for the test program considered, the reduction factor of2.86 was neglected, as presented in Eq. (8b).

1402.86

cav

fbcu

= + (8a)

140fbc cavu = + (8b)

POTENTIAL MODIFICATION TO ACI 318-11EQUATION (ACCOUNTING FOR CONFINEMENT)Replacing the average flexural bond stress term in the

expression of flexural bond stress given in Eq. (6) by theconfined flexural bond stress will modify the equation toaccount for confining stress. In the cases where confiningstress is present, the values of both confined transfer bondstress (Eq. (7)) and confined flexural bond stress (Eq. (8a))

are greater than those of the average transfer bond stress andaverage flexural bond stress, respectively, thereby decreasingthe development length (Eq. (9a)) and increasing the slippingstress of prestressing strands (Eq. (9b)). It is noted that theeffect of confinement does not change the transfer length.Rather, it reduces the potential for slipping of the strandsdue to an increase in the apparent bond stress. The first partof the equation represents the effective transfer length, whilethe second part represents the flexural bond length, whereLdcis the confined development length (in.). Equations (7)and (8a) are used to define the values for confined transferbond stress and confined flexural bond stress, respectively.

7.36 7.36

ps sese

dc b b

tc fbc

f ffL d d

u u

= +

(9a)

7.36 tc fbcd

ss fbc se ps

b tc

u uLf u f f

d u

= + (9b)

MOMENT-CURVATURE ANALYSISA detailed moment-curvature analysis was conducted

using a numerical program.6Using the compressive strength

data in Table 1, each of the 19 piles was modeled accordingto its material properties. Two concrete material models were

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used in the analysis: unconfined concrete for the cover andconfined concrete for the core of the section where lateralreinforcement surrounds the concrete. The confined concretestress-strain curve differs from the unconfined concretestress-strain curve according to the percentage of transversereinforcement in the section. This is accounted for withinthe numerical program through use of the Mander18confinedconcrete model.

Slipping stress of prestressing strandsThe slipping stress of a prestressing strand is affected

by the embedment length in the pile-to-cap connection.Considering the ACI 318-11 equation (Eq. (12-4)), as shownin Table 2, it is predicted that the strands will not developtheir full tensile capacity (fpu=270 ksi [1860 MPa]) due toinsufficient development length. Three slipping stress valueswere investigated in the modeling of each pile:

1. The experimentally determined slipping stress obtainedfrom the experiments performed by Shahawy and Issa4;

2. The slipping stress as calculated from the ACI 318-11equation (Eq. (1b) of this paper), knowing the value ofdevelopment length and effective prestressing stress calcu-

lated from the results of Shahawy and Issa4; and3. The slipping stress as calculated from Eq. (9b), which

accounts for the effect of confinement. Within this equation,the confined transfer bond stress and confined flexural bondstress are calculated using Eq. (7) and (8b), respectively,where the average confining stress is acquired by averagingthe applied confining stresses and distributing it over the fourfaces of the pile. As the value of confining stress changesaccording to the different development lengths used in thisstudy, the values of the confined transfer and flexural bondstresses will change accordingly, as shown in Table 3.

The three slipping stress values calculated for each pilewere incorporated in the numerical models, and moment-

curvature plots were generated to examine the differencesin moment capacity for each specimen. The analysis in eachmodel is terminated when the strands reach the maximumallowable strain.

CONFINING STRESSThe confining stress described in this paper was intro-

duced using a known force and was therefore calculated andused in Eq. (9b); however, for design purposes, this confiningstress will be exerted from the shrinkage of the CIP bent capcast around the embedded pile. Therefore, an equation forthe estimation of the confining stress for purposes of designhas been developed and is described in the following.5

The equation uses Lams equations for the calculation ofstresses in thick-walled cylinders. For this equation, ideal-

ized circular geometries are modeled for both the pile andbent cap for simplicity. In Eq. (10), cis the confining stress(psi); do and Do are the least dimensions (in.) of the pileand bent cap, respectively; and Ep, vpand EBC, vBCare theYoungs modulus (psi) and Poissons ratio of the pile andbent cap, respectively.

( )

( )2 2

0 0

2 2

0

1

* 1

o c

o sh p

p

c

o o

BC p

BC po

dD v

E

d D d d v v

E ED d

= ++ +

(10)

where sh is the shrinkage strain at a given time, calcu-lated in accordance with ACI 209R-92.19 In this paper,the shrinkage strain can be calculated as sh= t/(35 + t) (sh)u, where t is the time in days and (sh)uis the ultimateshrinkage strain (780 ). The value of ultimate shrinkagegiven in ACI 209R-9219is only applicable for cases wherethe reinforcement of the bent cap is minimal. For othercases, the effect of reinforcement on the shrinkage strainshould be considered.

The confining stress from the Shahawy and Issa4 initialtest was calculated using Eq. (10), with dimensions andmaterial properties taken from the Shahawy and Issa4experi-ment. A finite element model was created to assess the accu-racy of the equation in predicting the confining stress at agiven strain.20The results are described in the Results andDiscussion section.

Effect of creepAn analytical creep model was used to assess the

effect of creep on the confining stress. A restrained creepmodel21,22was used to model creep in the pile, as the pileshave spiral reinforcement, which will affect the creep, while

an unrestrained creep model23was used to model creep inthe cap, as it did not have any reinforcement. A daily basedcreep analysis was performed and, as expected, the effect ofcreep decreased the value of the confining stress. To incor-porate creep in the confining stress equation, an approxima-tion was introduced to simplify the approach by introducingcreep as a reduction factor (Rcr). The value ofRcris definedin the following. This simplification was done due to thecomplexity of dealing with two time-dependent variables:shrinkage and creep. In Eq. (11), the confining stress calcu-lated from Eq. (10) is reduced by the creep effect and isreferred to as the average confining stress cav. The averageconfining stress cavshould be calculated and used in Eq. (7)and Eq. (8a) or (8b).

( )1cav c cr R = (11)

RESULTS AND DISCUSSIONResults related to confining stress, slipping stress, moment

capacity, and development length are discussed in this section.

Confining stressThe confining stress due to shrinkage of the bent cap

in the Shahawy and Issa4 initial test was calculated using

Eq. (10), which does not account for creep, and Eq. (11),where Rcr was calculated using a daily-based shrinkage/

Table 3Relation between embedment lengthand confinement

Embedmentlength, in.

Confiningstress, psi

cav,psi

utc

(Eq. (7)),psi

ufbc

(Eq. (8a)),psi

ufbc

(Eq. (8b)),psi

36 397 199 479 168 220

42 340 170 468 164 208

48 297 149 460 161 200

60 238 119 448 157 188

Notes: 1 in. = 25.4 mm; 1 psi = 0.006895 MPa.

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creep analysis to be 20%. The results from Eq. (11) werethen compared to a finite element model, which uses theactual rectangular geometry of the pile and bent cap from theShahawy and Issa4test. Using Eq. (10), the confining stresswas significantly overpredicted with a value of 1230 psi(8.5 MPa). The average confining stress (accounting forcreep) calculated using Eq. (11) was more reasonably esti-mated with a value of 980 psi (6.8 MPa). This compares tothe maximum measured confining strain by Shahawy andIssa4of 880 psi (6.1 MPa), which is 90% of the calculatedaverage confining stress by Eq. (11). This is considered tobe a reasonable match when consideration is given to theuncertainty involved with the material properties used inEq. (10) and (11). From the finite element model using theactual rectangular geometry for both the pile and the bentcap, the average confining stress was found to be 907 psi

(6.3 MPa). This value compares favorably and is within 3%of the measured confining stress value.

The aforementioned confining stresses represent themaximum value of the confining stress acting over theembedment length of the pile. Shahawy and Issa4reported anaverage value of the confining stress to be 525 psi (3.6 MPa)by assuming a parabolic distribution of confining stress alongthe embedment length. For design purposes, a proposedsimplification is to assume that the value of the confiningstress varies linearly over the embedment length, where theminimum value is zero (at the soffit) and the maximum valueis calculated using Eq. (11). Therefore, a recommendedapproach is to use one-half of the confining stress value

calculated using Eq. (11) due to the assumed linear distri-bution. The confining stress for purposes of design would

therefore be 490 psi (3.4 MPa), which compares favorablywith the average confining stress value reported by Shahawyand Issa4(within 7%).

Slipping stressWhen sufficient development length is provided, slipping

of the strands should not occur and the strands will reachtheir nominal tensile capacity fpu. In the study by Shahawyand Issa,4 the available development length (embedmentlength) was less than the theoretical value required by theACI 318-11 equation. This condition therefore predicts slip-ping prior to reaching the nominal tensile capacity of thestrands. The measured steel stress at failure as reported inShahawy and Issa4(fps; Table 1, Column 4) is compared tothe theoretical values calculated with the ACI 318-11 equa-tion (Eq. (1b)) and the modified equation (Eq. (9b)), which

accounts for confining stress. The results are shown inTable 4. The ratios (in percentage) between slipping stresscalculated from the ACI 318-11 equation, experimental slip-ping stress, and the modified equation are listed. Overall,a better match is achieved with the modified equation(Eq. (9b)). The slipping stress from Eq. (9b) was calculatedtwice using both Eq. (8a) and (8b). There is a better matchwith the experimental results when Eq. (8b) is used to calcu-late the confined flexural bond stress because this equation ismore representative for the study discussed.

Moment capacityThe moment capacity of the piles is dependent on the slip-

ping stress andfpsof the prestressing strands. Using the threeslipping stress values discussed previously, the values of

Table 4Results of slipping stresses

Specimen number Ld, in. Experimentalfss, ksifss(ACI 318-11)

(Eq. (1b)), ksi Ratio*, %fss(Eq. (9b)), ksi

(ufbc[ Eq. (8a)]) Ratio, %

fss(Eq. (9b)), ksi

(ufbc[Eq. (8b)]) Ratio, %

A-1E 36 256 180 70 194 76 204 80

A-2E 36 263 190 73 204 78 213 81

A-3I 36 254 180 71 194 76 204 80

A-4I 36 253 181 71 195 77 205 81

B-1E 42 262 199 76 214 82 225 86

B-2E 42 261 199 76 213 82 224 86

B-3E 42 257 197 77 211 82 222 87

B-4E 42 260 196 75 210 81 222 85

B-5E 42 263 200 76 215 82 225 86

B-6I 42 259 197 76 211 82 223 86

C-1E 48 260 208 80 223 86 236 91

C-2E 48 258 206 80 221 86 235 91

C-3I 48 262 209 80 224 86 237 91

C-4I 48 258 206 80 221 86 234 91

C-5I 48 260 210 81 225 86 237 91

C-6E 48 258 207 80 222 86 235 91

D-1E 60 262 233 89 249 95 264 101

D-2I 60 261 235 90 250 96 265 102

D-3E 60 260 233 90 249 96 264 102

*Ratio between slipping stress from ACI 318-11 equation (Eq. (1)) and experimental slipping stress.Ratio between slipping stress from modified ACI 318-11 equation (Eq. (9b)) usingufbcfrom Eq. (8a) and experimental slipping stress.Ratio between slipping stress from modified ACI 318-11 equation (Eq. (9b)) usingufbcfrom Eq. (8b) and experimental slipping stress.

Notes: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.

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Table 5Ultimate moments for different slipping stresses using moment-curvature analysis and requireddevelopment length to achieve experimental slipping stress

Specimennumber Ld, in.

Theoretical ultimatemoment, kip-in.

Calculated moment, kip-in. Development length

Using experimentalslipping stress

Using ACI 318-11(Eq. (1b)) slipping stress

Using Eq. (9b)slipping stress

ACI 318-11(Eq. (1a)), in. Eq. (9a), in.

A-1E 36 1560 1540 1250 1360 74.2 52.2

A-2E 36 1500 1490 1280 1380 72.2 51.5

A-3I 36 1530 1520 1240 1350 73.2 51.5

A-4I 36 1480 1470 1220 1330 72.2 51.0

B-1E 42 1540 1530 1350 1450 73.2 54.1

B-2E 42 1530 1520 1350 1440 73.2 54.0

B-3E 42 1510 1490 1320 1410 72.2 53.3

B-4E 42 1580 1560 1360 1480 74.2 54.6

B-5E 42 1530 1520 1350 1450 73.2 54.1

B-6I 42 1530 1510 1340 1440 73.2 53.9

C-1E 48 1550 1540 1400 1490 74.2 56.3

C-2E 48 1530 1520 1380 1470 73.9 56.0

C-3I 48 1580 1560 1440 1510 74.2 56.4

C-4I 48 1530 1510 1380 1460 73.8 55.9

C-5I 48 1530 1520 1400 1470 73.2 55.7

C-6E 48 1530 1510 1390 1470 73.2 55.6

D-1E 60 1560 1550 1500 1560 74.2 59.0

D-2I 60 1530 1520 1480 1520 73.2 58.4

D-3E 60 1530 1520 1480 1520 73.2 58.2

Notes: 1 in. = 25.4 mm; 1 kip-in. = 0.11298 kN-m.

ultimate moment are calculated and summarized in Table 5.As the embedment length increases, the average momentcapacity for each embedment length increases in all cases.However, the moment capacity as calculated using the modi-fied equation (Eq. (9b)) compares favorably with the onescalculated using the experimental slipping stress.

Figure 4 shows a moment-versus-curvature plot forSpecimen D-2I (60 in. [1524 mm] embedment). The ratiosbetween the moment capacities calculated using the proposedequation (Eq. (9b)) and the one using experimental slipping

stress for embedment lengths of 36, 42, 48, and 60 in. (914,1067, 1219, and 1524 mm) are 91%, 95%, 97%, and 100%,

respectively. If the ACI 318-11 equation (Eq. (1b)) is usedfor calculating moment capacity and compared to the valuescalculated using experimental slipping stress, the ratios are82%, 88%, 92%, and 97%, respectively. Figure 5 showsthe average calculated moment capacity versus embedmentlength for the different models.

Development lengthThe development length required to reach the measured

experimental slipping stress was calculated using the

ACI 318-11 equation (Eq. (1a)) and the modified equation(Eq. (9a)), as shown in Table 5. Using the embedment length

Fig. 4Moment versus curvature for Specimen D-2I (60 in.[1524 mm] embedment).

Fig. 5Average ultimate moment versus embedment depth.

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as a benchmark, the results obtained from the modified equa-tion (Eq. (9a)) provide a better match than those obtainedwith the ACI 318-11 equation (Eq. (1a)).

Design recommendation and limitationsThe confining stress is a function of shrinkage; therefore,

it is predicted that the value of confining stress will continueto increase with time. At higher levels of confining stress,microcracks may form to relieve the high stress, which leads

to a drop in the magnitude of the confining stress. Therefore,an upper limit of 750 psi (5.2 MPa) is proposed to take intoaccount the effect of microcracking at high levels of confine-ment. This value is partially based on an ongoing laboratoryinvestigation, where piles are plainly embedded in CIP bentcaps and tested under reverse lateral cyclic loading to checkthe moment capacity and ductility of the connection.24,25Thisupper-limit value is assumed to be the maximum confiningstress acting on the embedded end of the pile. A simplifiedequation (Eq. (12)) is proposed by substituting this upper-limit value in Eq. (9a).5

5000 1800

ps sese

dc b b

f ff

L d d

= + (12)

The results from the actual pile-to-CIP-bent-cap connec-tions show that Eq. (12) has a better comparison with theexperimental results than the ACI 318-11 equation5; however,the use of Eq. (12) with the data described in this paper is notappropriate, as the confining stress was artificially simulatedwith steel plates for the Shahawy and Issa4study.

The ACI 318-11 equation is more conservative than themodified equation. Therefore, it is not recommended thatthe modified equation approach be used in practice in theabsence of further investigation and verification. The results

presented in this study are limited to the use of 0.5 in.(13 mm) low-relaxation seven-wire prestressing strands.The appropriateness of using Eq. (12) with a different stranddiameter requires further investigation.

SUMMARY AND CONCLUSIONSThe appropriateness of ACI 318-11, Eq. (12-4), for the

calculation of development length for prestressing strandsin confined sections was studied. A modified equationwas developed and introduced in this paper to account forconfinement. The experimental results of Shahawy andIssa4 were used to develop a moment-curvature analysis.The results were compared to calculated results from the

ACI 318-11 equation and the modified equation. The conclu-sions of this study can be drawn as follows:

1. Confining stress affects the bond between prestressingstrands and concrete by increasing the effective averagebond stress within the transfer zone and the average flexuralbond stress. This enhances (increases) the stress required tocause slipping.

2. Equation (9a) was developed for calculating develop-ment length in cases where confining stress takes place. Onesuch case occurs when precast piles are embedded in CIPbent caps.

3. A better fit to the published experimental data wasobtained for confined sections with Eq. (9b) than with the

ACI 318-11 equation (Eq. (1b)). The results of both equationsare conservative when compared to the experimental results.

4. The difference between the modified equation and theACI 318-11 equation becomes more significant as shorterembedment lengths are used in the pile/bent-cap system.

5. The embedment length of prestressed piles in CIP bentcaps has a notable effect on the slipping stress of prestressingstrands and the moment capacity of the section.

6. The modified equation (Eq. (9a) and (9b)) provideda reasonable fit to the experimental data described in thispaper. Further consideration is recommended prior to imple-mentation of these equations for purposes of design. Amongother items, it is recommended that confining stresses bemonitored in field applications.

ACKNOWLEDGMENTSThe authors wish to express their gratitude and sincere appreciation to

the South Carolina Department of Transportation (SCDOT) and the Federal

Highway Administration (FHWA) for financial support. The opinions, find-

ings, and conclusions expressed in this paper are those of the authors and

not necessarily those of SCDOT or FHWA.

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