Pile and Pile Cap Connection

July-August 2001 

Behavior of Precast, Prestressed Concrete Pile to Cast-in-Place Pile Cap Connections Kent A. Harries, Ph.D. Assistant Professor Department of Civil and Environmental Engineering University of South Carolina Columbia, South Carolina

Michael F. Petrou, Ph.D. Associate Professor Department of Civil and Environmental Engineering University of South Carolina Columbia, South Carolina

This investigation studied the capacity of square pile-to-pile cap connections where the precast, prestressed pile is simply embedded in the castin-place pile cap. Both experimental and analytical results are presented. It is shown that the plain embedment can develop the flexural capacity of the pile without distress to the pile cap or connection region provided that a sufficient embedment length is furnished. Equations for determining the required embedment length are provided. For design purposes, it is recommended that a plain embedment length equal to the width of the embedded pile be used.

P

iles, particularly those embedded in soft soils, may be subjected to large lateral deflections in the event of an earthquake. The lateral deflections can result in high local curvature and moment demands at various locations along the pile length as shown in Fig. 1. Of particular concern is the behavior at the pile-to-pile cap interface. At this location, very high moment demands result from the assumed fixity of the pile-to-pile cap connection. In order for this behavior to occur as assumed, the connection must be able to transmit lateral forces to the pile and remain essentially rigid. For this discussion, it is assumed that the pile cap may translate but not rotate. If rotation is permitted, the demands on the connection are reduced. 82

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Severe pile damage has been observed in past earthquakes.1,2 Pile design for seismic loading assumes that the pile can develop and maintain its moment capacity through large deformation demands. Indeed, significant research1,2 has shown that welldetailed precast, prestressed piles can develop and maintain large moments. Although a pile may be detailed to resist large forces, it is also necessary that the pile-to-pile cap connection be able to transfer these forces. There are only a few published investigations which report the behavior of the pileto-pile cap connection. These studies are summarized further on in this paper. The objective in designing the pileto-pile cap connection is to provide a connection capable of developing the moment demands on the pile while remaining essentially rigid. Conservatively, this requires the connection to be able to develop the theoretical capacity of the pile while remaining elastic. In this paper, the specific case of precast, prestressed piles embedded in cast-in-place pile caps is considered.

Fig. 1. Bending of long piles due to horizontal ground motion (adapted from Joen and Park,1 1990).

PILE EMBEDMENT DETAILS There are a number of options for detailing pile-to-cap connections. Fig. 2 shows the connection detail currently used by the South Carolina Department of Transportation (SCDOT). It is reported that this detail costs close to $800 per pile to fabricate. The objective of the study presented here was to address this issue and determine if less expensive details could provide adequate lateral load resisting capacity. There are a variety of details proposed and used in the embedment region of piles in cast-in-place pile caps. Fig. 3 shows a number of these details which are described as follows: A. No treatment; the pile is simply embedded in the pile cap. B. Roughening the exterior of the pile (using a rotary or chipping hammer, for instance) to provide additional mechanical bond between the pile and pile cap. C. Grooving (cut or cast in place) the pile surface to provide additional mechanical bond. D. Embedding vertical dowels in the driving head of the pile (after driving). July-August 2001

Fig. 2. Pile anchorage detail required by SCDOT.

E. Drilling horizontal dowels through the pile. F. Confining the immediate embedment region with hoop or square spiral reinforcement. G. Confining the immediate embedded region with round spiral reinforcement. H. Exposing the strands and embedding them in the cast-in-place concrete. Often, the wires will be

“broomed” (separated) or twisted open to form an annular space (a so-called “olive” anchorage) to improve their development. Typically, embedments will include a combination of these details. For example, the SCDOT detail shown in Fig. 2 incorporates Details B, D, and G. Each additional detail has an associated cost in terms of both money and time. 83

Studies of Pile Embedment Details Joen and Park1 reported tests of six pile-to-pile cap connection types. The piles were tested under combined axial load and reversed cyclic lateral loads. The axial load was kept constant at 0.2Ag f c′ for all tests. All piles tested were 16 in. (406 mm) octagonal piles. Two specimens were provided with a 32 in. (813 mm) embedment having Details B and G (see Fig. 3). Another two specimens had 24 in. (610 mm) embedments with Details G and H (exposed strand left straight). A fifth specimen had a 36 in. (914 mm) embedment with Details G and H (exposed strand provided with an “olive” anchorage). The final specimen was provided with only a 2 in. (51 mm) embedment and Details D and G. The theoretical capacity of the pile was obtained in each test and only the sixth detail showed significant distress to the pile cap and the embedment region, which led to a significant decay of the load-deflection response of the pile.1 Sheppard2 summarized the results of both experimental and post-earthquake

field investigations. Two embedment details were presented as being adequate for the pile-to-pile cap connection to behave in a desirable manner. The first suitable detail is H; the second is D. It is implied that confining Detail G is also provided. Curiously, the details presented by Sheppard show minimal embedment of the pile, similar to the sixth specimen described by Joen and Park. 1 As such, it would appear that the details recommended by Sheppard may be inadequate for severe seismic loading. No experimental results concerning this aspect are reported by Sheppard.

is adequate to develop the theoretical moment capacity of the pile. Note that the scope of this study is restricted to driven precast, prestressed piles embedded in cast-in-place pile caps. There are two proposed models, namely, Mattock and Gaafar 3 and Marcakis and Mitchell,4 for determining the capacity of the pile-to-pile cap connection. Both models assume that a rigid body (pile) is embedded in a cast-in-place concrete monolith (pile cap). Both models are based on the mobilization of an internal moment arm between bearing forces Cf and Cb as shown in Fig. 4. Mattock and Gaafar3

PLAIN PILE-TO-PILE CAP EMBEDMENT The objective of this study is to investigate the behavior of a plain embedment (Detail A in Fig. 3). In this detail, the capacity of the pile is developed along the length of the embedment. The pile-to-pile cap connection should be designed such that it

A parabolic distribution of bearing stresses is assumed for Cb, and Cf is computed by a uniform stress equal to 0.85f c′. The bearing stresses are distributed over the width of the embedded pile, b. Following these assumptions and calibrating the calculated stresses against experimental data, the required embedment length, Le, may be determined from:

Fig. 3. Proposed pile embedment details. 84

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0.66

 b′  Vu = 54 fc′  b ′ 0.66β1bLe Vu = 54 fc′ b  β1bLe  b    0.58 − 0.22 β   0.58 − 0.22 β11  ( psi units) a  ( psi units) 0.88 + a   0.88 + Le − c   Le − c  (1a) (1a) 0.66

 b′  Vu = 4.5 fc′  b ′ 0.66β1bLe Vu = 4.5 fc′ b  β1bLe  b    0.58 − 0.22 β   0.58 − 0.22 β11  (MPa units) a  (MPa units) 0.88 + a  0.88 + Le − c   Le − c  (1b) (1b) where a is the shear span of the pile (distance from pile cap to assumed point of zero moment) and β1 is the concrete stress block factor defined in ACI 319-99, Section 10.2.7.3.5 It is suggested that the shear span be increased by an amount equal to the concrete cover, c, to account for possible spalling of the soffit of the pile

cap as shown in Fig. 4. The value of b′ is given by Mattock and Gaafar as the width of the element into which (in this case) the pile is embedded. This value is intended to account for the spreading of the compressive stresses away from the embedment as indicated in Fig. 4(b). For a single pile in a pile cap, this value is taken as the width of the pile cap. For a pile group, this value may be conservatively taken as the pile spacing. Marcakis and Mitchell4 Using slightly different assumed stress distributions shown in Fig. 4(b), Marcakis and Mitchell4 proposed the following expression for determining the required embedment length, Le. This expression has also been calibrated against experimental data: 0.85 fc′ b ′( Le − c) Vu = 3.6e 1 + Le − c (consistent units)

(2)

point of zero moment to the center of the effective embedment as shown in Fig. 4(b). Marcakis and Mitchell define b ′ based on a “strut-and-tie” approach as being the effective width to the assumed “tie” steel, limited by a value of 2.5b [see Fig. 4(b)]. Eq. (2) has been adopted in Chapter 6 of the PCI Design Handbook6 for the design of embedded structural steel haunches or brackets in precast concrete. The same method has also successfully been applied to the design of moment-resisting connections for steel beams embedded in concrete core walls 7 and may be reasonable extended to the embedment of any essentially rigid body in a concrete embedment.

EXPERIMENTAL PROGRAM The objective of this experimental program is to demonstrate that no special details are needed when embedding prestressed piles into castin-place pile caps provided that the embedment length is sufficiently long.

where e is the eccentricity from the

Fig. 4. Analytical methods for determining capacity of embedment. July-August 2001

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Fig. 5. Prestressed concrete pile [18 in. (450 mm) square] used in present study.

The pile-to-pile cap connection must be adequate to develop the probable moment capacity of the embedded pile without significant deterioration. The connection must remain stiff enough so that rotation of the pile within the embedment does not contribute significantly to the overall drift of the pile-to-pile cap assembly. Additionally, the deterioration of the connection region should not allow the expected hinging of the pile to migrate into the embedded region. In this program, piles are embedded into cast-in-place pile caps. The embedded portions of the piles are not prepared in any particular way; they are simply placed within the pile cap forms and the pile cap concrete Fig. 6. Detail of 24 in. (610 mm) embedment.

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is placed around them. No dowels or confinement reinforcement beyond that provided by the cast-in-place pile cap are provided. Pile Details Two 18 in. (450 mm) square by 18 ft (5.49 m) long piles were fabricated simultaneously in the 40 ft (12.2 m) prestressing bed located in the University of South Carolina Structures Laboratory. These piles were prepared for an ongoing study of strand slippage.8 The piles used in this study had the lowest observed strand end slip of all 22 piles available to this experimental program. The 28-day concrete compressive strength of the Type I ready-mixed

concrete was 6700 psi (46.2 MPa). The piles were prestressed with eight 1/2 in. (12.7 mm) diameter low-relaxation strands. Each strand had an initial prestressing force of 31 kips (138 kN), equivalent to 0.75fpu. The strands were released 43 hours after casting when the concrete compressive strength was 4500 psi (31 MPa). The strands were confined with W6 (0.276 in.) plain wire spiral. The strand layout and spiral details are shown in Fig. 5. The predicted nominal moment capacity of the piles corresponding to an axial load of 200 kips (890 kN) is 285 ft-kips (386 kN-m). All predictions presented in this paper were made using the plane section analysis program RESPONSE-2000.9 Pile Cap Details Each pile was embedded in a 7 x 3 x 7 ft (2.14 x 0.92 x 2.14 m) castin-place pile cap. Each pile cap was reinforced with No. 7 bars on the top and bottom and No. 3 ties at 6 in. (152 mm) spacing in the transverse direction and through the depth of the pile cap (see Fig. 6). The concrete compressive strength and primary reinforcing details of each pile cap was different for each test. The details of the first pile test are representative of what may be expected in the field in South Carolina. The details for the second test were purposely selected to represent very poor in situ conditions. Pile cap data are provided PCI JOURNAL

in Table 1. Embedment Details The embedment length of Pile No. 1 was selected to be 24 in. (610 mm), the value desired by the SCDOT. The embedment length of Pile No. 2 was 18 in. (457 mm). This value was felt by the SCDOT to be the minimum acceptable embedment length. Required embedment lengths calculated from Eqs. (1) and (2) are shown in Table 1. Based on current practice, and assuming typical pile cap material properties and details, an embedment length of approximately 12 in. (305

Table 1. Pile cap and embedment details and requirements. Specimen

Primary steel

Concrete Embedment Required embedment length compressive length strength provided Eq. (1) Eq. (2)

Pile No. 1

6 - No. 7 bars top and bottom

5000 psi (34.5 MPa)

24 in. (610 mm)

12.4 in. (316 mm)

11.9 in. (303 mm)

Pile No. 2

4 - No. 7 bars

3000 psi

18 in.

14.0 in.

14.8 in.

mm) is required to develop the 285 ft-kip (386 kN-m) capacity of the piles used. These calculations are based on a shear span (a in Fig. 4) equal to 12 ft (3.66 m). Based on these calcula-

tions, it is expected that the embedment lengths provided are sufficient to develop the piles used. A photograph of the embedment region of Pile No. 1 prior to casting the pile cap is shown

0.1f c′ Ag

Fig. 7. Test setup to simulate seismic loading of pile-to-pile cap assembly. July-August 2001

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in Fig. 6. Test Setup The pile-to-pile cap assembly was tested as a cantilever beam in the horizontal position. The test setup is shown in Fig. 7. Each pile-to-pile cap assembly was tested under constant axial load and reversed cyclic lateral load. The 200 kip (890 kN) axial load, equal to 0.092Ag f c′, was applied using a load following mechanism that does not impose secondary moment effects on the column. The axial load was kept constant throughout the test using a regulated hydraulic power supply. The reversed cyclic lateral loads were applied at a distance of 146 in. (3.7 m) from the soffit of the pile cap. This loading is representative of a pile having a shear span of 146 in. (3.7 m) or point of fix-

ity approximately 24 ft (7.3 m) below the pile cap soffit. This shear span was thought to be typical of partially exposed 18 in. (457 mm) piles [see Fig. 1(a)]. Shorter piles will place less demand on the embedment region and longer 18 in. (457 mm) piles are not common. Pile deflections were recorded at the point of application of the lateral load. Load History and Experimental Observations The lateral load is cycled three times at each load or displacement level. The load-deflection response of each pile is shown in Fig. 8. The predicted pile moment capacity of 285 ft-kips (386 kN-m) is shown as a horizontal dotted line. The piles were cycled at two elastic load levels; ±7 kips (±85 ft-kips) and ±14 kips (±170 ft-kips)

0.1f c′ Ag

0.1f c′ Ag

Fig. 8. Applied load versus deflection responses for piles tested. 88

[(±31 kN (±115 kN-m) and ±62 kN (±230 kN-m)]. In each test, the piles were first observed to crack at the pile-to-pile cap interface at an applied load of 13.9 kips (62 kN), corresponding to an applied moment of 169 ft-kips (230 kNm) at the crack location. The predicted load to cause cracking of the piles is 136 ft-kips (185 kN-m). Loading continued to the “yield” load level. Yielding was defined as a significant change in the load-deflection response of the pile. The yield displacement, δ, was found to be approximately 1 in. (25.4 mm), corresponding to a pile drift of 0.7 percent. The applied load to cause a deflection of δ = 1 in. was 20.2 kips (90 kN) or 246 ft-kips (332 kN-m) and 17.8 kips (79 kN) or 217 ft-kips (293 kN-m) for Pile No. 1 and No. 2, respectively. The predicted moment to cause significant nonlinearity of the pile section response is 240 ft-kips (326 kN-m). At this load, cracks were observed in the piles at approximately 12 and 26 in. (305 and 660 mm) from the pile cap soffit. Beyond yield, the piles were cycled three times each to displacements equal to 1.5δ, 2δ and 3δ. Pile No. 2 was also cycled to 2.5δ in sequence. No lateral or axial load capacity decay or stiffness degradation was noted through these cycles as can be seen in Fig. 8. The peak load values recorded during testing were 24.9 kips (111 kN) or 303 ft-kips (410 kN-m) and 21.5 kips (96 kN) or 262 ft-kips (354 kN-m) for Pile No. 1 and No. 2, respectively. While attempting the initial cycle to 4δ, Pile No. 1 experienced a flexural failure due to crushing of the extreme compression concrete (see Fig. 9). At this point, the axial capacity of the pile was affected. The axial load regulator was unable to sustain the 200 kip (890 kN) axial load without further driving the compressive failure. The final monotonic load response to a peak deflection of approximately 5 in. (127 mm), corresponding to a 3.4 percent drift, is shown in Fig. 8(a). Pile No. 2 was cycled once at 3.5δ and twice at 4δ before failing while being pushed to 5δ for the first time. In this case, the failure appeared to be PCI JOURNAL

rupture of at least one of the strands. After testing, the pile was broken off from the pile cap and no strand ruptures were evident. It is believed, in this case, that the loud noise and accompanying decrease in lateral load that occurred on the cycle to 5δ may have resulted from the catastrophic slipping of a strand. Two views of Pile No. 2 near the end of testing are shown in Fig. 10. Pile No. 2 behaved somewhat differently from Pile No. 1. Most of the deflection of Pile No. 2 was accounted for by the significant opening of the crack at the pile-to-pile cap interface as shown in Fig. 10(a). The deflection of Pile No. 1, on the other hand, derived from the more uniform opening of cracks at the interface and at 12 and 16 in. (305 and 406 mm) from the pile-to-pile cap interface. It is believed that this differing behavior is entirely due to the piles and is not related to the pile-to-pile cap connections. Pullout Test It is possible that piles may experience tensile loads during a seismic event. It is clearly undesirable for the pile to separate from the pile cap in these instances. The question arises as to whether the cyclic loads imposed on the embedment region causes a

Fig. 9. Pile No. 1 [24 in. (610 mm) embedment] at displacement of +5 in. (127 mm) (3.4 percent drift).

“ratcheting” induced degradation of the embedment region resulting in the possibility of the pile pulling out of the pile cap. To test this hypothesis, an ad hoc pullout test was devised. After the completion of the reversed cyclic load tests, Pile No. 1 was fitted with a collar and an attempt was made to remove the pile from the pile cap. A direct axial tension of 75 kips (334 kN) was applied to the pile. There was no evidence of distress or movement of the pile away from the pile cap at this load. This test was not repeated for

(a) Pile No. 2 [18 in. (457 mm) embedment] at displacement of -4.5 in. (114 mm) (3.1 percent drift).

Pile No. 2 since it was assumed that a strand had been ruptured.

SUMMARY OF EXPERIMENTAL RESULTS Each pile behaved very much as was expected. Observed cracking, yielding, and ultimate capacities were very close to those predicted for the 18 in. (457 mm) piles. There was no observable damage to the embedment region in either test. Pile curvature data measured relative to the pile cap indicated that neither rotation of the pile cap nor

(a) Pile No. 2 [18 in. (457 mm) embedment] at displacement of +5.5 in. (140 mm) (3.8 percent drift).

Fig. 10. Pile No. 2 near end of test. July-August 2001

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rotation of the embedment region had a significantly measurable effect on the recorded deflections of the pile. In essence, the pile cap provided the desired rigid end condition for the cantilevered pile. It is clear that the 24 and 18 in. (610 and 457 mm) embedments provided were sufficient to develop the capacity of the piles with no special embedment details. This conclusion was expected based on past research of embedded members in cast-in-place concrete.3,4,7 For practical reasons, it is not believed that embedment lengths shorter than 18 in. should be specified. The SCDOT expects the tolerance on embedment lengths to be ±6 in. (±152 mm). Similarly, embedment lengths longer than 24 to 30 in. (610 to 762 mm) are also impractical without significantly affecting the design and construction of pile caps. For instance, pile caps in South Carolina have been standardized to be 36 in. (914 mm) deep, making the longest practical embedment length approximately 30 in. (762 mm). Application to Other Pile Sizes The experimental program has indicated that practical construction issues

are more likely to control the specified embedment length than are capacity requirements. Fig. 11 shows curves generated from Eqs. (1) and (2) for the moment capacity of the embedment for varying embedment lengths and square pile sizes. Figs. 11(a) and (b) show the capacity to embedment length relationships for piles having a shear span of 12 ft (3.66 m) [similar to Fig. 1(a)], while Figs. 11 (c) and (d) show the similar relationship for piles having a short shear span of 4 ft (1.22 m) [Fig. 1(b)]. Note that for all calculations shown in Fig. 11, the concrete compressive strength, f c′, of the pile cap has been assumed to be 5000 psi (34.5 MPa), the load spreading factor [see Fig. 4(b)] is 2 (thus b′ = 2b) and 3 in. (76 mm) of concrete cover has been assumed. Both Eqs. (1) and (2) yield similar results. Eq. (2) tends to result in slightly more conservative embedment capacity values. The calculated embedment capacities are lower for shorter shear spans, where the shear-to-moment ratio at the pile-to-pile cap interface is high [see Figs. 11(c) and (d)]. As the shear span increases, the embedment capacity in-

f c′

f c′

f c′

f c′

creases at a decreasing rate. For the geometry shown in Fig. 11, increasing the shear span beyond 12 ft (3.66 m) has little effect on the capacity of the embedment. Fig. 12 shows the same results from Eqs. (1) and (2) for 18 and 36 in. (457 and 914 mm) square piles. Superimposed on these relationships is the range of probable pile moment capacities. Based on the data shown in Figs. 11 and 12, it is proposed that providing a minimum embedment length equal to the width of the pile will conservatively result in an embedment having sufficient capacity to develop the pile. Furthermore, such an embedment may reasonably be assumed to provide a rigid end condition for the top of the pile. Certainly, the pile embedment requirement may be significantly reduced for piles having a long shear span. Additional Embedment Details The inclusion of additional embedment details, such as those discussed previously and shown in Fig. 3, will increase the capacity of the embedment to some extent. For instance, the method for designing embedded steel

Fig. 11. Embedment capacity predictions of varying pile sizes having varying embedment lengths. 90

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haunches contained in the PCI Design Handbook6 includes guidance for determining the additional embedment capacity resulting from the inclusion of horizontal dowels [see Fig. 3(e)]. It is felt, however, that these additional details will not significantly enhance the capacity of the embedment even though they may be beneficial in providing post-failure continuity in the event of extremely large lateral deflections of the pile.

bedment region. It is not believed that this discussion can be extended beyond prestressed concrete piles. For instance, it is not advocated that the analyses presented here are applicable to large caissonto-pier cap connections despite the geometric similarities. No analysis or experiments of other pile shapes or sizes has been carried out. Data from embedment tests on smaller embedded sections6 having a width less than 12 in. (305 mm) do correlate well with the presented equations.

Application to Other Pile Shapes The previous discussion applies to square piles. It is felt, however, that the discussion may be extended to other typical pile shapes using the projected pile width in place of the square pile dimension b. It is cautioned, however, that unlike square piles, round or octagonal piles will develop bearing forces directed radially from the embedment. This may result in greater deterioration of the pile cap and em-

Strand Development Length In this study, it has been assumed that the design capacity of the pile-topile cap embedment is based on developing the capacity of the pile. Implicit in this assumption is that the capacity of the pile is actually attainable at the pile-to-pile cap interface. This requires full development of the prestressing strand at this location.

With relatively short embedment lengths this may not be possible.8 It has been suggested that a pile should have an embedment length equal to the strand development length to ensure that the capacity of the pile is available at the face of the pile cap.10 It is felt that the provision of an embedment length equal to the strand development length is impractical in most cases because it would result in very deep pile caps. Note that the maximum moment demand on a pile may not occur at the pile-to-pile cap interface1 (see Fig. 1), in which case full development of the strand at the face of the pile cap may be unnecessary. The embedment calculations proposed here will result in a conservative pile cap design. This is desirable because it leads to a “weak pile, strong pile cap” behavior that permits easier inspection and repair in the event of damage from an earthquake.

CONCLUSIONS aND recommendations

f c′

f c′

Fig. 12. Comparison of embedment capacity and pile capacity. July-August 2001

Based on the results of this investigation, the following conclusions and recommendations can be made. These conclusions apply to square prestressed piles smaller than 36 in. (914 mm) embedded in cast-in-place pile caps. 1. The simple plain embedment of a precast, prestressed pile into a cast-inplace pile cap can be designed to develop the required capacity of the pile. 2. The required plain embedment length may be conservatively determined from either Eqs. (1) or (2). Eq. (2) is proposed in Chapter 6 of the PCI Design Handbook6 for the design of embedded steel haunches or brackets in precast concrete. This is analogous to the embedment of precast, prestressed piles in cast-in-place pile caps. 3. Conservatively, the required embedment length to develop the flexural capacity of a pile may be taken as the width of the pile. A minimum absolute embedment length of 12 in. (305 mm) is recommended. 4. Due to the prestressing strands not being developed at the pile-to-pile cap interface, the flexural capacity of the pile may not be available at this location. This condition must be in91

vestigated by the designer. 5. The pile-to-pile cap embedment length proposed here should be interpreted as the minimum embedment required to attain the theoretical capacity of the pile. The flexural capacity at the pile-to-pile cap interface is determined from the flexural capacity of the pile, which is affected by the strand development length provided at this location.

This investigation was funded by the South Carolina Department of Transportation (SCDOT). The authors would like to thank the entire staff of the USC Structures Laboratory for their assistance in preparing the piles, pile caps, and assisting with the tests; and SMI-Owen Steel for assisting with the fabrication of the reaction frame.

Special Projects Engineer at SCDOT, Jeff Mulliken, a Project Engineer at the LPA Group in Columbia, South Carolina, and Lewis Ryan of United Contractors in Chester, South Carolina. Their assistance is greatly appreciated. Lastly, the authors wish to thank the PCI JOURNAL reviewers for their helpful and constructive comments.

ACKNOWLEDGMENTS

The authors would also like to acknowledge Terry Koon, the Seismic

The opinions, findings, and conclusions ex-

pressed in this paper are those of the authors and do not necessarily reflect those of the South Carolina Department of Transportation.

REFERENCES 1. Joen, P. H., and Park, R., “Simulated Seismic Load Tests on Prestressed Concrete Piles and Pile-Pile Cap Connections,” PCI JOURNAL, V. 35, No. 6, November-December 1990, pp. 42-61. 2. Sheppard, D. A., “Seismic Design of Prestressed Concrete Piling,” PCI JOURNAL, V. 28, No. 2, March-April 1983, pp. 21-49 3. Marcakis, K., and Mitchell, D., “Precast Concrete Connections with Embedded Steel Members,” PCI JOURNAL, V. 25, No. 4, July-August 1980, pp. 88-116. 4. Mattock, A. H., and Gaafar, G. H., “Strength of Embedded Steel Sections as Brackets,” ACI Journal, V. 79, No. 2, MarchApril 1982, pp 83-93. 5. ACI Committee 318, “Building Code Requirements for Struc-

tural Concrete (ACI 318-99),” American Concrete Institute, Farmington Hills, MI, 1999. 6. PCI Design Handbook: Precast and Prestressed Concrete, Fifth Edition, Precast/Prestressed Concrete Institute, Chicago, IL, 1999. 7. Harries, K. A., Mitchell, D., Cook, W. D., and Redwood, R. G., “Seismic Response of Steel Beams Coupling Reinforced Concrete Walls,” ASCE Journal of the Structural Division, V. 119, No. 12, December 1992, pp. 3611-3629. 8. Wan, B., Petrou, P., Harries, K. A., and Hussein, A. A., “‘Top Bar’ Effect in Prestressed Concrete Piles,” submitted for publication to ACI Structural Journal. 9. Bentz, E. C., and Collins, M. P., “RESPONSE-2000 Reinforced Concrete Sectional Analysis Using the Modified Compression Field Theory Computer Program, Release 1.0.0.1,” University of Toronto, Toronto, Ontario, Canada.

10. Shahawy, M.A., and Issa, M., “Effect of Pile Embedment on the Development Length of Prestressing Strands,” PCI JOURNAL, V. 37, No. 6, November-December 1992, pp. 44-59.

APPENDIX – NOTATION a = shear span of pile taken as distance from pile cap soffit to point of zero moment b′ = effective width of concrete compression block b = width of pile, also bearing width of the embedment

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c = depth of concrete cover Cf = resultant bearing (compressive) force in embedment e = eccentricity from midspan of beam to center of embedment f c′ = specified concrete compressive strength Le = embedment length of pile inside pile cap Vu = shear force on pile xb = length of compression block at back of embedment

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xf = length of compression block at front of embedment β1 = ratio of average concrete compressive strength to maximum stress δ = deflection at yield stress of pile

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