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Determining Slipping Stress of Prestressing Strands in Confined Sections ARTICLE in ACI STRUCTURAL JOURNAL · NOVEMBER 2012 Impact Factor: 0.96
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2 AUTHORS: Mohamed K. ElBatanouny
Paul Ziehl
Wiss Janney Elstner Associates Inc.
University of South Carolina
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Available from: Mohamed K. ElBatanouny Retrieved on: 17 August 2015
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title no. 109-S66
Determining Slipping Stress of Prestressing Strands in Confined Sections by Mohamed K. ElBatanouny and Paul H. Ziehl Development length and slipping stress of prestressing strands subjected to confining stress is not well-quantified and the appropriateness of the ACI 318-11 equation under such conditions can be questioned. In 1992, a test was performed on nineteen 14 in. (356 mm) square prestressed concrete piles with a clamping force applied during testing under lateral load. The findings indicated that the ACI 318-11 equation for development length of prestressing strands may not be suitable when used for sections subjected to confining stress. In this study, a modified equation that accounts for the 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-curvature analysis by comparing three different slipping values: 1) those obtained from experimental results; 2) the ACI 318-11 equation; and 3) the modified equation. Keywords: confining stress; development length; moment capacity; slipping.
INTRODUCTION The use of precast, prestressed concrete piles in bridge construction is common in the United States; however, the performance of such units under seismic loading is not entirely clear. The behavior of the connection between prestressed piles and cast-in-place (CIP) reinforced concrete caps is particularly not well-understood. Current South Carolina Department of Transportation (SCDOT) connection details1,2 require the plain embedment of the pile into the bent cap one pile diameter with a construction tolerance of ±6 in. (±152 mm). Plain embedment requires no special detailing to the pile end or the embedment region and no special treatment of the pile surface, such as roughening or grooving. The ductility and moment capacity of such connections is of interest because this short embedment length is often much less than the length required for development of the full tensile strength of the prestressing strands within the embedded region. Generally, the development length of prestressing strands is calculated from ACI 318-11, Eq. (12-4).3 In the case of piles embedded in CIP caps, the embedment length is usually far less than the development length. Therefore, the strands are predicted to slip at a level of stress less than their nominal capacity. This stress is referred to as the “slipping stress.” The ACI 318-11 equation was developed for the case of superstructure elements not subjected to confining stress. Therefore, the application of this equation to substructure elements having significant confining stress may not be appropriate. A pile embedded in a CIP cap is subjected to the shrinkage of the confining concrete in the cap, which creates confining stress (also known as “clamping force”) on the pile, which serves to enhance the bond between the prestressing strand and the surrounding concrete. This leads to a decrease in the development length and an associated increase in the slipping stress of the prestressing ACI Structural Journal/November-December 2012
strand.4,5 This effect became very apparent during the testing of a series of precast concrete piles embedded in CIP bent caps at the University of South Carolina Structures Laboratory.5 Because the embedment length of the piles was much less than the development length of prestressing strands, the strands were expected to slip prior to achieving the nominal capacity. Significant differences were found between the experimental results and those predicted by ACI 318-11, Eq. (12-4).5 Shahawy and Issa4 discussed the findings of a significant experimental investigation related to the effect of confinement from CIP caps to prestressed concrete piles with emphasis on the resulting behavior under lateral load. The results showed that the development length of prestressing strands was enhanced due to confining stress. They concluded that using the ACI 318-11 equation without consideration of confinement will lead to very conservative values. This study makes use of the experimental results reported by Shahawy and Issa4 to investigate the appropriateness of a potential modification to the ACI 318-11 equation.5 The theoretical slipping stress calculated from the modified equation 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 analysis6 was performed to calculate the moment strength of the sections using the modified equation and the ACI 318-11 equation. These were then compared to calculated moments using measured slipping stress values from the Shahawy and Issa4 study. Furthermore, finite element models were created to investigate the value and distribution of the confining stress due to shrinkage for use in the modified equation. RESEARCH SIGNIFICANCE Several important investigations have addressed the suitability of ACI 318-11, Eq. (12-4), for development length7,8; however, only a few have considered the effect of confinement.4,5 The ACI 318-11 equation for calculating the development length of prestressing strands was derived for unconfined sections and does not account for the effect of confinement. To account for the effect of confinement, a potential modification to the ACI 318-11 equation is developed and described. The results from the modified equation are compared to published experimental results that directly addressed the effect of confinement for the development length of prestressing strands. 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 rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the September-October 2013 ACI Structural Journal if the discussion is received by May 1, 2013.
767
long and were cut from 80 ft (24.4 m) long prestressed concrete piles. Number 5 (No. 16) gauge steel was used as spiral reinforcement that varied in pitch depending on location. The end sections of the full-length piles were provided with more spiral reinforcement than the interior sections (middle sections), as shown in Fig. 1. Four embedment lengths of 36, 42, 48, and 60 in. (914, 1067, 1219, and 1524 mm) were used in this study. Cores with diameters of 6 in. (152 mm) were taken from the specimens to determine the concrete compressive strength. A summary of the experimental program is provided in Table 1.
Mohamed K. ElBatanouny is 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 member Paul H. Ziehl is 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 specimens Nineteen 14 in. (356 mm) square prestressed concrete pile specimens with 8.5 in. (13 mm) diameter prestressing strands were tested in this study. The specimens were 12 ft (3.66 m)
Test procedure and analytical study The experimental investigation was designed to simulate the behavior of a CIP cap. A steel test frame was used to restrain the pile cap against translation and rotation. An initial test was conducted to assess the value of confining stress exerted from the shrinkage of the cap. A CIP cap was cast with a pile embedded in its center for the initial test. The CIP cap had a cross section of 42 x 54 in. (1.1 x 1.4 m) with a depth of 48 in. (1219 mm). The pile was instrumented with vibrating wire strain gauges spaced at 12 in. (305 mm) along the embedment length (48 in. [1219 mm]). A schematic of this confining stress test is shown in Fig. 2. After 28 days, the principal strains were measured with a resulting maximum value of 245 me. Using a conservative value for the Young’s modulus of 3.6 × 106 psi (24,800 MPa), the maximum confining stress was calculated to be 880 psi (6.1 MPa). The authors4 of this study assumed that this value would approach zero at the ends of the embedment length following a parabolic distribution of a maximum measured value of 245 me at a depth of 30 in. (762 mm); therefore,
Fig. 1—Details of test specimens.4 Table 1—Details of test program4 Section
fc′, ksi
Measured 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
Specimen number
*
4
Effective prestressing stress back calculated from Shahawy and Issa data. Embedment length minus transfer length. Notes: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa. †
768
ACI Structural Journal/November-December 2012
an average confining stress was computed to be 525 psi (3.6 MPa). Using this average confining stress value as an upper limit, a clamping force of 200 kips (888 kN) was applied to the upper and lower faces of the embedment length of the pile specimens to represent the confining stress. This clamping force was applied using post-tensioning thread bars, as shown in Fig. 3. The lateral faces of the pile embedment length were not subjected to confinement. The confining 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 applied confining stress value was taken to be 75% of the average confining stress measured in the initial test. A hydraulic jack placed at 6 ft (1.84 m) from the face of the supporting frame was used to apply lateral load on the piles in increments of 3 kips (13.3 kN) up to a load of 18 kips (80.1 kN); thereafter, the load increments were much smaller until failure was achieved. At each load step, cracks were marked and displacements and strains were recorded. Details of the test setup are shown in Fig. 3. The piles were next analyzed using a nonlinear material model. The time-dependent effects due to load history, temperature history, creep, shrinkage, and relaxation of steel were considered in the computer program.4 The program4 was used to calculate the structural response through the elastic and inelastic range up to ultimate load. At each load step, nonlinear equilibrium equations using the displacement formulation of the finite element method were derived for the geometry and material properties.4 Findings of Shahawy and Issa4 The effect of transverse reinforcement was examined and transverse reinforcement was found to have a slight effect in terms of the moment capacity of the piles. The ultimate moment of the piles cut from the end sections was slightly higher than those of the piles cut from the middle sections by approximately 6%, as shown in Table 2. The experimental slipping stress of the prestressing strands was determined by measuring the strain along the length of the strand at various levels of load until failure. The measured slipping stress determined by this method is presented in Table 2. For development length, the embedment length of the piles was compared to the theoretical development length required to obtain the same slipping stress using three different equations: 1. The ACI 318-11 equation3 for development length of 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 equation, Ld is the development length (in.), which is equal to the embedment depth of the pile; fse is the effective stress of prestressing strand (psi); fps is the nominal flexural strength of the prestressing strand (psi); and db is the nominal diameter of the prestressing strand (in.). The slipping stress can be calculated by rearranging the ACI 318-11 equation, as shown in Eq. (1b). The nominal flexural strength of the prestressing strand, fps, is renamed as the slipping stress, fss (psi), for clarity.
Ld =
(
)
f ps - fse fse db + db 3000 1000
ACI Structural Journal/November-December 2012
(1a)
Fig. 2—Confining stress test setup.4
Fig. 3—Lateral loading test setup with applied clamping force.4 fss = 1000
Ld 2 + f ≤ f ps db 3 se
(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 Issa4 equation 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, P is 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); le is the available embedment length (in.); and db is the nominal strand diameter (in.).
Ld =
(
)
f ps - fse fse db + db 3000 4uave
fss = 4uave
Ld 4uave + 1fse ≤ f ps db 3000
uave =
(P - T ) ple db
(2a)
(2b)
(3) 769
Table 2—Shahawy and Issa4 test results and calculated slipping stresses Slipping stress, ksi
Specimen number
Embedment length, in.
Theoretical ultimate moment, kip-in.
Measured ultimate moment, kip-in.
Measured steel stress at failure, 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.
3. An equation proposed by Zia and Mostafa,8 as 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′, which is 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). Ld =
1.5 fsi db - 4.6 + 1.25 f ps - fse db fc′
(4a)
Ld f 3.68 - 1.2 si + + fse ≤ f ps db fc′ db
(4b)
fss = 0.8
(
)
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 conservative than the ACI 318-11 equation. The Shahawy and Issa4 proposed 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 is provided in the following sections. 770
HISTORY OF ACI 318-11 EQUATION The expression for the development length of prestressing strands found in ACI 318-11 was proposed by Mattock9 and members of ACI Committee 423.10 The expression divides the development length into two parts: transfer length and flexural bond length. To develop the expression for transfer length,11 results of a study by Hanson and Kaar12 and Kaar et al.13 were used. They stated a value for average transfer bond stress ut = 400 psi (2.76 MPa). For flexural bond length, another approach was used based on the definition of general bond slip introduced by Janney.14 Janney14 stated that when the peak of the high bond stress wave reaches the transfer length, general bond slip occurs and leads to a reduction in the frictional resistance resulting from the Hoyer effect.15 Hanson and Kaar12 agreed with Janney’s14 explanation, but they did not state a value for the average flexural bond stress. Due to the difficulty of codifying this concept, Mattock9 and the members of ACI Committee 42310 used the data of Hanson and Kaar’s12 beam tests to formulate an approach based on an average flexural bond stress. They constructed a straight-line relationship by subtracting the estimated transfer length from the embedment length of the strand. The increase in strand stress due to flexure was determined to be the difference between the strand stress at the load causing slip and the effective stress due to prestressing. The use of a constant slope for the flexural bond length implies a value of average flexural bond stress ufb = 140 psi (0.96 MPa).5 It is worth noting that the assumption of average flexural bond stress was made to simplify the approach and makes it easier to codify. The expressions for transfer length and flexural bond length are shown in Eq. (5) and (6), respectively. ACI Structural Journal/November-December 2012
Aps ∗ fse
fse f Lt = = ∗ db = se ∗ db 7.36 ∗ ut 3000 So ∗ ut
L fb =
(f
ps
- fse
)d = (f
7.36 ∗ u fb
b
ps
- fse
1000
)d
b
(5)
(6)
where Lt is transfer length (in.); Lfb is flexural bond length (in.); So is the strand perimeter (So = 4/3 * p * db [in.]); and Aps is the strand cross-sectional area (Aps = 0.725 * p * db2/4 [in.2]). EFFECT OF CONFINEMENT ON EFFECTIVE TRANSFER LENGTH Transfer length in the absence of confinement is a function of diameter, effective prestress, and average transfer bond stress. Mechanisms contributing to the value of average transfer bond stress can be categorized into three groups: adhesion, friction, and mechanical interlock.11 Adhesion is destroyed by the relative slip between the strand and the surrounding concrete and the contribution of mechanical interlock in the average transfer bond stress can be neglected due to “unwinding.”16 Frictional bond stress is developed as a result of the radial compressive stresses, which are attributed to the Hoyer effect,15 where longitudinal contraction results in radial expansion of the tendon. This Poisson’s expansion induces compression perpendicular to the steel-concrete interface. In the absence of confinement, the value of the average transfer bond stress is assumed to be ut = 400 psi (2.76 MPa). When confinement occurs, it is convenient to represent the effect as an increase in the apparent bond stress. It should be noted that confinement does not change the transfer length itself. Rather, confinement decreases the potential for slipping of the 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 takes into account both the unconfined average transfer bond and the increase in bond stress due to confinement. The value of the resulting apparent bond stress is determined by adding the average transfer bond stress (400 psi [2.76 MPa]) to the average bond stress that is due to confinement. The average bond stress due to confinement is calculated by multiplying the confining stress by the coefficient of friction between the steel and concrete (m). The resulting average bond stress is shown in Eq. (7). utc = 400 + m ∗ s cav
(7)
where utc is the average confined bond stress within the transfer zone (psi); scav is the average confining stress applied to the prestressed concrete section; and m is the coefficient of friction between the steel and concrete (generally taken as m = 0.417). EFFECT OF CONFINEMENT ON FLEXURAL BOND LENGTH For the confined flexural bond stress ufbc (psi), the same approach was used, assuming that the confining stress would only affect the friction stress. Due to the reduction in strand diameter resulting from the increase in strand stress in the ACI Structural Journal/November-December 2012
average flexural bond stress zone, the Hoyer effect15 is reduced and ufb is implied in the ACI 318-11 equation to be equal to 140 psi (0.96 MPa).5 The reduction of the Hoyer effect15 leads to a decrease in the frictional forces resulting from the confining stress. A ratio between the average transfer bond stress and the average flexural bond stress was used to decrease the effect of the confining stress, where ut /ufb = 2.86. Therefore, Eq. (8a) is introduced to assess the average flexural bond stress, including the effect of confining stress. Another reason to use this factor is the fact that microcracks will 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 bent cap to decrease. In the test program considered, however, the confining stress is not expected to decrease, as it was applied to the specimens permanently via a clamping force.4 Therefore, for the test program considered, the reduction factor of 2.86 was neglected, as presented in Eq. (8b). m ∗ s cav 2.86
(8a)
u fbc = 140 + m ∗ s cav
(8b)
u fbc = 140 +
POTENTIAL MODIFICATION TO ACI 318-11 EQUATION (ACCOUNTING FOR CONFINEMENT) Replacing the average flexural bond stress term in the expression of flexural bond stress given in Eq. (6) by the confined flexural bond stress will modify the equation to account for confining stress. In the cases where confining stress is present, the values of both confined transfer bond stress (Eq. (7)) and confined flexural bond stress (Eq. (8a)) are greater than those of the average transfer bond stress and average flexural bond stress, respectively, thereby decreasing the development length (Eq. (9a)) and increasing the slipping stress of prestressing strands (Eq. (9b)). It is noted that the effect of confinement does not change the transfer length. Rather, it reduces the potential for slipping of the strands due to an increase in the apparent bond stress. The first part of the equation represents the effective transfer length, while the second part represents the flexural bond length, where Ldc is the confined development length (in.). Equations (7) and (8a) are used to define the values for confined transfer bond stress and confined flexural bond stress, respectively. Ldc =
f ps - fse fse ∗ db + ∗ db 7.36 ∗ utc 7.36 ∗ u fbc
fss = 7.36 ∗ u fbc ∗
Ld utc - u fbc + fse ≤ f ps db utc
(9a)
(9b)
MOMENT-CURVATURE ANALYSIS A detailed moment-curvature analysis was conducted using a numerical program.6 Using the compressive strength data in Table 1, each of the 19 piles was modeled according to its material properties. Two concrete material models were 771
Table 3—Relation between embedment length and confinement Embedment length, in.
Confining stress, psi
scav, 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.
used in the analysis: unconfined concrete for the cover and confined concrete for the core of the section where lateral reinforcement surrounds the concrete. The confined concrete stress-strain curve differs from the unconfined concrete stress-strain curve according to the percentage of transverse reinforcement in the section. This is accounted for within the numerical program through use of the Mander18 confined concrete model. Slipping stress of prestressing strands The 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 shown in Table 2, it is predicted that the strands will not develop their full tensile capacity (fpu = 270 ksi [1860 MPa]) due to insufficient development length. Three slipping stress values were investigated in the modeling of each pile: 1. The experimentally determined slipping stress obtained from the experiments performed by Shahawy and Issa4; 2. The slipping stress as calculated from the ACI 318-11 equation (Eq. (1b) of this paper), knowing the value of development length and effective prestressing stress calculated from the results of Shahawy and Issa4; and 3. 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 bond stress are calculated using Eq. (7) and (8b), respectively, where the average confining stress is acquired by averaging the applied confining stresses and distributing it over the four faces of the pile. As the value of confining stress changes according to the different development lengths used in this study, the values of the confined transfer and flexural bond stresses will change accordingly, as shown in Table 3. The three slipping stress values calculated for each pile were incorporated in the numerical models, and momentcurvature plots were generated to examine the differences in moment capacity for each specimen. The analysis in each model is terminated when the strands reach the maximum allowable strain. CONFINING STRESS The confining stress described in this paper was introduced using a known force and was therefore calculated and used in Eq. (9b); however, for design purposes, this confining stress will be exerted from the shrinkage of the CIP bent cap cast around the embedded pile. Therefore, an equation for the estimation of the confining stress for purposes of design has been developed and is described in the following.5 The equation uses Lamés equations for the calculation of stresses in thick-walled cylinders. For this equation, ideal772
ized circular geometries are modeled for both the pile and bent cap for simplicity. In Eq. (10), sc is the confining stress (psi); do and Do are the least dimensions (in.) of the pile and bent cap, respectively; and Ep, vp and EBC, vBC are the Young’s modulus (psi) and Poisson’s ratio of the pile and bent cap, respectively. Do ∗ e sh sc =
do E BC
do ∗ s c ∗ 1 - vp Ep
(
)
D 2 + d0 2 d * o2 + vBC + 0 ∗ 1 - v p 2 Do - d0 Ep
(
)
(10)
where esh is the shrinkage strain at a given time, calculated in accordance with ACI 209R-92.19 In this paper, the shrinkage strain can be calculated as esh = t/(35 + t) × (esh)u, where t is the time in days and (esh)u is the ultimate shrinkage strain (780 me). The value of ultimate shrinkage given in ACI 209R-9219 is only applicable for cases where the reinforcement of the bent cap is minimal. For other cases, the effect of reinforcement on the shrinkage strain should be considered. The confining stress from the Shahawy and Issa4 initial test was calculated using Eq. (10), with dimensions and material properties taken from the Shahawy and Issa4 experiment. A finite element model was created to assess the accuracy of the equation in predicting the confining stress at a given strain.20 The results are described in the Results and Discussion section. Effect of creep An analytical creep model was used to assess the effect of creep on the confining stress. A restrained creep model21,22 was used to model creep in the pile, as the piles have spiral reinforcement, which will affect the creep, while an unrestrained creep model23 was used to model creep in the cap, as it did not have any reinforcement. A daily based creep analysis was performed and, as expected, the effect of creep decreased the value of the confining stress. To incorporate creep in the confining stress equation, an approximation was introduced to simplify the approach by introducing creep as a reduction factor (Rcr). The value of Rcr is defined in the following. This simplification was done due to the complexity of dealing with two time-dependent variables: shrinkage and creep. In Eq. (11), the confining stress calculated from Eq. (10) is reduced by the creep effect and is referred to as the average confining stress scav. The average confining stress scav should be calculated and used in Eq. (7) and Eq. (8a) or (8b). s cav = s c ∗ (1 - Rcr )
(11)
RESULTS AND DISCUSSION Results related to confining stress, slipping stress, moment capacity, and development length are discussed in this section. Confining stress The 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/ ACI Structural Journal/November-December 2012
Table 4—Results of slipping stresses Specimen number
Ld, in.
Experimental fss, ksi
fss (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)) using ufbc from Eq. (8a) and experimental slipping stress. ‡ Ratio between slipping stress from modified ACI 318-11 equation (Eq. (9b)) using ufbc from Eq. (8b) and experimental slipping stress. Notes: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.
creep analysis to be 20%. The results from Eq. (11) were then compared to a finite element model, which uses the actual rectangular geometry of the pile and bent cap from the Shahawy and Issa4 test. Using Eq. (10), the confining stress was significantly overpredicted with a value of 1230 psi (8.5 MPa). The average confining stress (accounting for creep) calculated using Eq. (11) was more reasonably estimated with a value of 980 psi (6.8 MPa). This compares to the maximum measured confining strain by Shahawy and Issa4 of 880 psi (6.1 MPa), which is 90% of the calculated average confining stress by Eq. (11). This is considered to be a reasonable match when consideration is given to the uncertainty involved with the material properties used in Eq. (10) and (11). From the finite element model using the actual rectangular geometry for both the pile and the bent cap, 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 the maximum value of the confining stress acting over the embedment length of the pile. Shahawy and Issa4 reported an average value of the confining stress to be 525 psi (3.6 MPa) by assuming a parabolic distribution of confining stress along the embedment length. For design purposes, a proposed simplification is to assume that the value of the confining stress varies linearly over the embedment length, where the minimum value is zero (at the soffit) and the maximum value is calculated using Eq. (11). Therefore, a recommended approach is to use one-half of the confining stress value calculated using Eq. (11) due to the assumed linear distribution. The confining stress for purposes of design would ACI Structural Journal/November-December 2012
therefore be 490 psi (3.4 MPa), which compares favorably with the average confining stress value reported by Shahawy and Issa4 (within 7%). Slipping stress When sufficient development length is provided, slipping of the strands should not occur and the strands will reach their nominal tensile capacity fpu. In the study by Shahawy and Issa,4 the available development length (embedment length) was less than the theoretical value required by the ACI 318-11 equation. This condition therefore predicts slipping prior to reaching the nominal tensile capacity of the strands. The measured steel stress at failure as reported in Shahawy and Issa4 (fps; Table 1, Column 4) is compared to the theoretical values calculated with the ACI 318-11 equation (Eq. (1b)) and the modified equation (Eq. (9b)), which accounts for confining stress. The results are shown in Table 4. The ratios (in percentage) between slipping stress calculated from the ACI 318-11 equation, experimental slipping 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 calculated twice using both Eq. (8a) and (8b). There is a better match with the experimental results when Eq. (8b) is used to calculate the confined flexural bond stress because this equation is more representative for the study discussed. Moment capacity The moment capacity of the piles is dependent on the slipping stress and fps of the prestressing strands. Using the three slipping stress values discussed previously, the values of 773
Table 5—Ultimate moments for different slipping stresses using moment-curvature analysis and required development length to achieve experimental slipping stress Calculated moment, kip-in.
Development length
Specimen number
Ld, in.
Theoretical ultimate moment, kip-in.
Using experimental slipping 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.
Fig. 4—Moment versus curvature for Specimen D-2I (60 in. [1524 mm] embedment).
Fig. 5—Average ultimate moment versus embedment depth.
ultimate moment are calculated and summarized in Table 5. As the embedment length increases, the average moment capacity for each embedment length increases in all cases. However, the moment capacity as calculated using the modified equation (Eq. (9b)) compares favorably with the ones calculated using the experimental slipping stress. Figure 4 shows a moment-versus-curvature plot for Specimen D-2I (60 in. [1524 mm] embedment). The ratios between the moment capacities calculated using the proposed equation (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 used for calculating moment capacity and compared to the values calculated using experimental slipping stress, the ratios are 82%, 88%, 92%, and 97%, respectively. Figure 5 shows the average calculated moment capacity versus embedment length for the different models.
774
Development length The 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 ACI Structural Journal/November-December 2012
as a benchmark, the results obtained from the modified equation (Eq. (9a)) provide a better match than those obtained with the ACI 318-11 equation (Eq. (1a)). Design recommendation and limitations The confining stress is a function of shrinkage; therefore, it is predicted that the value of confining stress will continue to 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 into account the effect of microcracking at high levels of confinement. This value is partially based on an ongoing laboratory investigation, where piles are plainly embedded in CIP bent caps and tested under reverse lateral cyclic loading to check the moment capacity and ductility of the connection.24,25 This upper-limit value is assumed to be the maximum confining stress acting on the embedded end of the pile. A simplified equation (Eq. (12)) is proposed by substituting this upperlimit value in Eq. (9a).5 Ldc =
f ps - fse fse ∗ db + ∗ db 5000 1800
(12)
The results from the actual pile-to-CIP-bent-cap connections show that Eq. (12) has a better comparison with the experimental results than the ACI 318-11 equation5; however, the use of Eq. (12) with the data described in this paper is not appropriate, as the confining stress was artificially simulated with steel plates for the Shahawy and Issa4 study. The ACI 318-11 equation is more conservative than the modified equation. Therefore, it is not recommended that the modified equation approach be used in practice in the absence 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 strand diameter requires further investigation. SUMMARY AND CONCLUSIONS The appropriateness of ACI 318-11, Eq. (12-4), for the calculation of development length for prestressing strands in confined sections was studied. A modified equation was developed and introduced in this paper to account for confinement. The experimental results of Shahawy and Issa4 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 conclusions of this study can be drawn as follows: 1. Confining stress affects the bond between prestressing strands and concrete by increasing the effective average bond stress within the transfer zone and the average flexural bond stress. This enhances (increases) the stress required to cause slipping. 2. Equation (9a) was developed for calculating development length in cases where confining stress takes place. One such case occurs when precast piles are embedded in CIP bent caps. 3. A better fit to the published experimental data was obtained for confined sections with Eq. (9b) than with the ACI 318-11 equation (Eq. (1b)). The results of both equations are conservative when compared to the experimental results. ACI Structural Journal/November-December 2012
4. The difference between the modified equation and the ACI 318-11 equation becomes more significant as shorter embedment lengths are used in the pile/bent-cap system. 5. The embedment length of prestressed piles in CIP bent caps has a notable effect on the slipping stress of prestressing strands and the moment capacity of the section. 6. The modified equation (Eq. (9a) and (9b)) provided a reasonable fit to the experimental data described in this paper. Further consideration is recommended prior to implementation of these equations for purposes of design. Among other items, it is recommended that confining stresses be monitored in field applications. ACKNOWLEDGMENTS
The 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, findings, and conclusions expressed in this paper are those of the authors and not necessarily those of SCDOT or FHWA.
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1. SCDOT Bridge Design Manual, South Carolina Department of Transportation, Columbia, SC, 2006, pp. 19.1-19.22. 2. “SCDOT Seismic Design Specifications for Highway Bridges, Version 2.0,” South Carolina Department of Transportation, Columbia, SC, 2008, 153 pp. 3. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp. 4. Shahawy, M. A., and Issa, M., “Effect of Pile Embedment on the Development Length of Prestressing Strands,” PCI Journal, V. 37, No. 6, 1992, pp. 44-59. 5. ElBatanouny, M. K.; Ziehl, P. H.; Larosche, A.; Mays, T.; and Caicedo, J. M., “Bent-Cap Confining Stress Effect on the Slip of Prestressing Strands,” ACI Structural Journal, V. 109, No. 4, July-Aug. 2012, pp. 487-496. 6. “XTRACT Program,” v3.0.8, TRC/Imbsen Software Systems, Rancho Cordova, CA, 2007. 7. Deatherage, J. H.; Burdette, E. G.; and Key Chew, C., “Development Length and Lateral Spacing Requirements of Prestressing Strands for Prestressed Concrete Bridge Girders,” PCI Journal, V. 39, No. 1, Jan.-Feb. 1994, pp. 70-83. 8. Zia, P., and Mostafa, T., “Development Length of Prestressing Strands,” PCI Journal, V. 22, No. 5, Sept.-Oct. 1977, pp. 54-65. 9. Mattock, A. H., “Proposed Redraft of Section 2611—Bond of the Proposed Revision of Building Code Requirements for Reinforced Concrete (ACI 318-56),” ACI Committee 323 Correspondence, 1962. 10. Bennett, W. B. Jr., “Preliminary Draft of the Proposed Revision of Section 211—Bond and Anchorage of the Tentative Recommendations for Prestressed Concrete,” Letter to the Members of ACI Committee 423, 1963. 11. Tabatabai, H., and Dickson, T. J., “The History of the Prestressing Strand Development Length Equation,” PCI Journal, V. 38, No. 6, Nov.Dec. 1993, pp. 64-75. 12. Hanson, N. W., and Kaar, P. H., “Flexural Bond Tests of Pretensioned Prestressed Beams,” ACI JOURNAL, Proceedings V. 55, No. 1, Jan. 1959, pp. 783-802. 13. Kaar, P. H.; La Fraugh, R. W.; and Mass, M. A., “Influence of Concrete Strength on Strand Transfer Length,” PCI Journal, V. 8, No. 5, Oct. 1963, pp. 47-67. 14. Janney, J. R., “Nature of Bond in Pretensioned Prestressed Concrete,” ACI JOURNAL, Proceedings V. 50, No. 5, May 1954, pp. 717-736. 15. Hoyer, E., and Friedrich, E., “Beitrag zur frage der haftspannung in eisenbetonbauteilen (Contribution to the Question of Bond Stress in Reinforced Concrete Elements),” Beton und Eisen 38, 1939, pp. 107-110. 16. Stocker, M. F., and Sozen, M. A., “Investigation of Prestressed Concrete for Highway Bridges, Part V: Bond Characteristics of Prestressing Strand,” Bulletin 503, University of Illinois Engineering Experiment Station, Urbana, IL, 1970, 119 pp. 17. PCI Design Handbook: Precast and Prestressed Concrete, sixth edition, Precast/Prestressed Concrete Institute, Chicago, IL, 2004, 736 pp. 18. Mander, J. B.; Priestley, M. J. N.; and Park, R., “Theoretical StressStrain Model for Confined Concrete,” Journal of Structural Engineering, ASCE, V. 114, 1988, pp. 1804-1826. 19. ACI Committee 209, “Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures (ACI 209R-92) (Reapproved 1997),” American Concrete Institute, Farmington Hills, MI, 1992, 48 pp.
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20. Dassault Systèmes, ABAQUS Analysis User’s Manual V. 6.9, ABAQUS Inc., Dassault Systèmes, Providence, RI, 2009. 21. Bažant, Z. P., “Prediction of Concrete Creep Effects Using AgeAdjusted Effective Modulus Method,” ACI JOURNAL, Proceedings V. 69, No. 4, Apr. 1972, pp. 212-219. 22. Dilger, W. H., “Creep Analysis of Prestressed Concrete Structures Using Creep-Transformed Section Properties,” PCI Journal, V. 27, No. 1, 1982, pp. 99-118.
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23. Comité Euro-International du Béton, “CEB-fib Model Code 1990,” Thomas Telford Services, Ltd., London, UK, 1993, 437 pp. 24. ElBatanouny, M. K., “Determining Slipping Stress of Prestressing Strands in Piles Embedded in CIP Caps,” MS thesis, University of South Carolina, Columbia, SC, Dec. 2010, 90 pp. 25. Larosche, A., “The Connection Behavior of Precast Prestressed Piles to Cast-in-Place Bent Caps,” MS thesis, University of South Carolina, Columbia, SC, May 2011, 130 pp.
ACI Structural Journal/November-December 2012
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