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PTI JOURNALDecember 2012 • V. 8 • No. 2

JOURNAL OF THE POST-TENSIONING INSTITUTE

PTI JOURNAL | December 2012 1

PTI JOURNALPTI JOURNAL STAFF

EDITOR-IN-CHIEF MIROSLAV F. VEJVODA

GRAPHIC DESIGNER & EDITOR KELLI R. SLAYDEN

ADVERTISING JEFFREY D. PONDER

MANAGER BARRY M. BERGIN

EDITORS CARL R. BISCHOF

KAREN CZEDIKDENISE WOLBER

GRAPHIC DESIGNER RYAN M. JAY

EDITORIAL DATA

The PTI JOURNAL is published

semi-annually by the Post-

manuscripts and reader

are accepted pending review by the PTI Editorial Review Board.

Direct all correspondence to: Editor-in-Chief, PTI JOURNAL

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DECEMBER 2012 • V. 8 • NO. 2

5 DIFFERENT BOUNDARY CONDITIONS

20 STRUCTURAL EFFICIENCY FROM A SUSTAINABILITY PERSPECTIVE CAROL HAYEK AND SALEEM KALIL

26 FLAT PLATES

43 KENNETH B. BONDY

49 THE TOWER, 3900 WEST ALAMEDA BOULEVARD, BURBANK, CA KENNETH B. BONDY

52 PTI COMMITTEE NEWS, ACI NEWS, PTI DOCUMENTS

5, 20,

p. 26, S

2 December 2012 | PTI JOURNAL

RASHID AHMEDBRETT ALAMILLO JAMES L. BEICKER

KENNETH B. BONDY JAMES R. CAGLEY

TOMMASO CICCONE GUY CLOUTIER

SERGIO P. DALMAU MARC DUCOMMUN

RICHARD ELKINS JEFF FEITLER

TRAVIS GILPIN MARK HASELTON PAUL HOHENSEE BRUCE JENSEN

TERRY JOHNSON RATTAN L. KHOSA ANDY D. KOCHIS

CARY KOPCZYNSKI DAWN KORI

JIM LUKE

PRESIDENT LARRY KRAUSER

VICE PRESIDENT MARC KHOURY

ANDY LYNAM DAN MACLEAN

DAVID B. MARTIN ANDREW MICKLUS JR.

TED MUMFORD HARLEY NETHKEN DAVID PATTRIDGECARRICK PIERCE RUSSELL L. PRICE

JOSÉ LUIS QUINTANADANNY RAINES

STEVE ROSSDOUGLAS J. SCHLEGEL

GUIDO SCHWAGERPETE SCOPPA

TODD STEVENSBOB SWARD

BEN TNGGREG TOMLINSON

MERRILL R. WALSTAD CURTIS WOLFE JR.

EXECUTIVE DIRECTOR THEODORE L. NEFF

TECHNICAL AND

CERTIFICATION DIRECTOR MIROSLAV F. VEJVODA

MEMBER SERVICES

COORDINATOR MICHELLE J. STERN

LEAD ACCOUNTANTSTACEY A. CLEMENT

CERTIFICATION PROGRAMS COORDINATOR

TRACEY M. BALES

MARKETING COORDINATOR JEFFREY D. PONDER

EDITOR &

GRAPHIC DESIGNER KELLI R. SLAYDEN

PTI STAFF

GUY CLOUTIERNORRIS HAYES

GREG HUNSICKERNEEL KHOSA

MARC KHOURY

CHAIR LARRY KRAUSER

RASHID AHMED ASIT BAXI

JAMES L. BEICKER KENNETH B. BONDY

JAMES R. CAGLEY

CHAIR CARY KOPCZYNSKI

VICE CHAIRJAMES R. CAGLEY

SECRETARY MIROSLAV F. VEJVODA

JOHN CRIGLERCAROL HAYEK

DON KLINE DOUGLAS SCHLEGEL MERRILL WALSTAD

EDGAR ZUNIGA

THOMAS MATHEWSHARLEY NETHKENMERILL WALSTADJACK WELBORN

CURTIS WOLFE JR.


NOTES FROM THE EDITOR'S DESK

EDITORIAL

Dear Reader:We are happy to present you with the second issue of

the PTI JOURNAL published in the 2012 calendar year. The economic downturn of recent years delayed our goal to consistently publish the JOURNAL twice a year, but now we are back on our track to provide the JOURNAL semi-annually to our readers and authors. This is a great medium to share your research and significant post-tensioned struc-tures with a wide readership in the always exciting field of post-tensioning.

“PT TREASURES”With this issue, we are starting a new column that may

be of great interest—“PT Treasures.” This column will show-case pioneering or otherwise significant structures built in the “good old days.” It is important to remind ourselves from time to time that it takes imagination and a little bit of courage to propose new methods and new applications, and to push the conventional ways just a little further. Such an approach not only provides us with great satisfaction but it also opens new opportunities and stimulates the imagina-tion of others.

The Tower is the first project selected for this column and it is not by chance. This post-tensioned concrete tower, completed in 1988, opened up options for architects, engi-neers, and owners by demonstrating that tall post-tensioned concrete structures in the most severe seismic conditions are not only safe and superior in performance, but also econom-ical. As a result, similar structures today are becoming more common in these demanding conditions.

Post-tensioning is the prevalent and indispensable reinforcement used in concrete bridges, from small cast-

in-place bridges to major segmental bridges. Most bridges use grouted post-tensioning tendons—both internal and external. The post-tensioning system suppliers and bridge contractors work in many states and have to adapt to the local practices and specifications that prevail in each indi-vidual state. These sometimes very different requirements make the work more difficult, may lead to interpretation difficulties, and can be more costly.

With the publication of the PTI/ASBI M50.3-12, “Guide Specification for Grouted Post-Tensioning,” an important step was made in the direction of making the requirements more uniform across the different states. A team of PTI and ASBI, supported by the FHWA and local post-tensioning system suppliers, is presenting this new specification to the major state DOTs where most post-tensioned concrete bridges are built. This industry-initiated discussion is bringing the major stakeholders together with the common goal of improving the construction of the infrastructure. At the same time, the new edition of the PTI M55.1-12, “Specification for Grouting of Post-Tensioned Structures,” is presented and discussed, thus including all aspects of post-tensioning construction. Last but not least, the new M50.3-12 specification requires field personnel certification that goes beyond current practices. Recognizing the key role of field personnel certification, some DOTs are planning on adopting these certification requirements. Many contractors have already certified many of their workforce, as the avoidance of problems through knowledge and anticipation is the best insurance.

Miroslav F. VejvodaEditor-in-Chief

2013 PTI Convention

www.post-tensioning.org

Save the date

May 5-7, 2013 • Scottsdale, AZ

• Technical Sessions

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• Networking Events

• 2013 PTI Awards Dinner

• Industry Trade Show


TECHNICAL PAPER

REHABILITATION OF UNBONDED

DIFFERENT BOUNDARY CONDITIONS

In Phase-I, a total of six unbonded post-tensioned (PT) slab specimens were tested. Three were simply supported two-way slabs with two-way post-tensioning (Specimens PTS-1, PTS-2, and PTS-6), whereas three other one-way slabs were tested with different boundary conditions (Specimens PTS-3, PTS-4, and PTS-5). The specimens were loaded to develop extensive cracks. Each of the specimens was then repaired with carbon fiber-reinforced polymer (CFRP) sheets using two different patterns. In Phase-II, the repaired specimens (PTS-1CR, PTS-2CR, PTS-3CR, PTS-4CR, PTS-5CR, and PTS-6CR) were tested again to reach their ultimate loads. The Phase-I and Phase-II research focused on the study of cracking patterns, reinforcing bar strains, tendon stresses, as well as the pressure-deflection and ultimate strength behavior of unbonded PT slabs. The investigation was also extended to the repair of these slabs with CFRP and the evaluation of the efficiency of CFRP repair of unbonded PT slabs. The research revealed that proper placement of CFRP sheets effectively restrained crack opening and crack growth and increased the flexural strength, stiffness, and deflection capacity of unbonded PT slabs, whereas there were modest increases in tendon stress.

Boundary conditions; carbon fiber-reinforced poly-mers; post-tensioned concrete; rehabilitation; repair; slabs; strengthening; unbonded tendons.

INTRODUCTIONIn recent decades, a large number of structures, which

have aged, were built with one- and two-way PT. In most cases, the PT tendons were unbonded (PTI 2011). Some of the problems that existing buildings and infrastructures with

unbonded post-tensioning face today are excess loading, inadequate maintenance, and a lack of periodic repair and strengthening (PTI 2011). Some form of external reinforce-ment is needed to repair and strengthen these structurally deficient buildings and infrastructures. Many of the slabs can also be repaired or retrofitted by using external PT tech-niques and fiber-reinforced polymer (FRP) composites. The external post-tensioning, however, is often challenging for one-way slabs, due to the obstruction of one-way beams, and for two-way slabs, due to the limited clear story height of office and residential buildings. Replacing old strands with new internal strands is more difficult and cumbersome, even though the new strands are smaller. An addition of new tendons and a new layer of concrete could be an option; however, this makes the structure heavier, which contradicts the design philosophy of prestressed structures—namely, the pursuit of relatively light, crack-free, long-span struc-tures. An FRP repairing and retrofitting system, particularly a carbon FRP (CFRP) system, is a suitable and convenient solution embracing such a philosophy. The FRP system saves time and costs. Also, it does not require significant alteration to the original floor slabs.

A handful of research programs on flexural and shear strengthening of the prestressed concrete members using FRP composites have been conducted in recent decades (for example, Meier and Kaiser 1991; Chakrabarti 1995; Chakrabarti et al. 2002; Di Ludovico et al. 2005; Chakrab-arti 2005a, 2005b; Rosenboom et al. 2007; Ibrahim Ary and Kang 2012a; Kang and Ibrahim Ary 2012b). All of these tests focused on the study of bonded pre-tensioned and unbonded PT concrete beams. In particular, only limited research was conducted on unbonded PT slabs with FRP (Michaluk et al. 1998; Chakrabarti et al. 2007, 2009). Therefore, the behavior of unbonded PT members strengthened with FRP remains poorly understood, and standard configurations and formal procedures are yet to be established. Given this gap, an extensive experimental

PTI JOURNAL, V. 8, No. 2, December 2012. Received and reviewed under Institute journal publication policies. Copyright ©2012, Post-Tensioning Institute. All rights reserved, including the making of copies unless permission is obtained from the Post-Tensioning Institute. Pertinent discussion will be published in the next issue of PTI JOURNAL if received within 3 months of the publication.


research program was conducted on the application of CFRP for the rehabilitation of unbonded, PT one- and two-way slabs and repaired slabs using CFRP in this study.

The objectives of this experimental research are 1) to observe the general behavior of unbonded PT slabs before and after the application of CFRP with different boundary conditions; 2) to understand the relationship between internal reinforcement (mild steel and unbonded PT tendons) and externally bonded CFRP; 3) to observe and record crack propagation, strain, pressure, and deflec-tion during testing; and 4) to quantitatively compare the ultimate strength of nonrepaired and repaired slabs.

MATERIALSQuality concrete with a design compressive strength

of 5000 psi (34.5 MPa) was used. Concrete mixtures were prepared according to ASTM C-94. The slabs were cured in their forms for 24 hours and then removed and continuously cured for at least 28 days. The concrete was proportioned using portland cement and fly ash with a water-cementitious material ratio (w/cm) of 0.34 (weight per volume ratio), resulting in a slump of about 3 in. (76 mm). The average concrete compressive strength of at least three specimens measured on the test date for each specimen is indicated in Table 1. The average measured concrete strength was 5690 psi (39.2 MPa), which is typical for PT slabs. Quarter-inch diameter seven-wire

strands were used in each direction of the two-way slabs and in the span direction of one-way slabs. These were Grade 270 ASTM A-416 strands with a specified ultimate strength fpu of 270 ksi (1860 MPa) and cross-sectional area Aps of 0.036 in.

2 (23.2 mm2). The individual prestressing strands were inserted through 9/32 in. (7 mm) inner diam-eter plastic tubes. This process eliminated any bonding between the strands and the concrete.

Two different types of non-prestressed mild steel were used: 1) welded wire mesh (WWM) produced in accor-dance with ASTM A-185; and 2) ASTM A-615 deformed reinforcing bars. For the tension mild steel of two-way slabs, the WWM with a specified yield strength of 60 ksi (414 MPa) was used, whereas Grade 60 No. 3 (db = 3/8 in. [9.5 mm]) reinforcing bars were used as tension reinforce-ment of the one-way slabs.

For strengthening, CFRP sheets were used. Three different types of CFRP sheet materials were applied: 1) CF130 high tensile carbon; 2) CF530 high-modulus carbon; and 3) CF160 high-modulus carbon. All the material properties indicated in Table 2 were obtained from the manufacturer (Structural Group, Inc. 2002). The second type (CF530) had measured values of ultimate tensile strength fu,frp of 580 ksi (4000 MPa) and modulus of elasticity Efrp values of 54,000 ksi (372,300 MPa). The first and second types had the same material properties, whereas the third type (CF160) with an ultimate strength

Table 1—Summary of steel reinforcement and measured concrete strength for specimens

SpecimensPT tendons per unit width

Aps, in.2/in. (mm2/mm)

Tensile mild steel per unit width Aps, in.

2/in. (mm2/mm)Compressive mild steel per unit width Aps, in.

2/in. (mm2/mm)fc′,

psi (MPa)

PTS-1, PTS-1CR16-1/4 in. strands

each way 0.00554 (0.14)

4 x 4-4/4 WWM0.01 (0.254)

6 x 6-10/10 WWM0.0024 (0.06) 5931 (40.9)


each way 0.00554 (0.14)

6 x 6-10/10 WWM0.0024 (0.06)

6 x 6-10/10 WWM0.0024 (0.06) 5963 (41.1)

PTS-3, PTS-3CR16-1/4 in. strands in span direction 0.00554 (0.14)

25-No. 3 at top and 9-No. 3 at bottom

each fixed end 0.0265 (0.673)

6 x 6-10/10 WWM0.0024 (0.06) 5726 (39.5)

PTS-4, PTS-4CR16-1/4 in. strandsin span direction 0.00554 (0.14)



6 x 6-10/10 WWM0.0024 (0.06) 5959 (41.1)

PTS-5, PTS-5CR16-1/4 in. strandsin span direction0.00554 (0.14)



6 x 6-10/10 WWM0.0024 (0.06) 5362 (37)


each way 0.00554 (0.14)

6 x 6-10/10 WWM0.0024 (0.06)

6 x 6-10/10 WWM0.0024 (0.06) 5223 (36)

Note: WWM is welded wire mesh; fc′ is concrete compressive strength; concrete pouring dates are different.


Fu,frp of approximately 7.14 kips/in. (1.6 kN/mm) had twice the thickness of the first type (CF130) with an Fu,frp of approximately 3.57 kips/in. (0.8 kN/mm). The ulti-mate strengths fu,frp in Table 2 were calculated as Fu,frp times the unit width of 1 in. (25.4 mm), divided by the CFRP thickness (for example, 0.0058 in. [0.146 mm] for CF130; 0.0115 in. [0.292 mm] for CF160 per ply, where the thick-ness of the CFRP impregnated with epoxy [saturant] was used). The design strengths in Table 2 were determined as the average ultimate strength minus three standard devia-tions of the measured values of fu,frp.

TEST SPECIMENSAn experimental program was divided into two phases:

1) Phase-I; testing control specimens of three two-way PT slabs and three one-way PT slabs; and 2) Phase-II; testing the same specimens after repairing using CFRP sheets. Table 3 summarizes the dimensions and boundary condi-tions of each specimen. Six control slabs were nonrepaired specimens labeled as PTS (Post-Tensioned Slab Specimen). Of these six, three were two-way slabs (PTS-1, PTS-2, and PTS-6) and three were one-way slabs (PTS-3, PTS-4, and PTS-5). Note that testing of PTS-6 (additional two-way slab specimen) was planned and conducted after the completion of testing of the first four specimens, and that all the damaged specimens were repaired with CFRP sheets and retested. The six repaired slabs were labeled as CR (for

example, PTS-1CR; Post-Tensioned Slab No. 1 with CFRP Repair). The two-way slab specimens (PTS-1, PTS-2, and PTS-6) were simply supported on four sides of the slab. The one-way slab specimens had three different boundary conditions on two span ends: 1) PTS-3 and PTS-3CR had fixed conditions on both ends; 2) PTS-4 and PTS-4CR were simply supported on one end and fixed on the other end; and 3) PTS-5 and PTS-5CR were simply supported one-way slabs. The test installations to achieve the desig-nated boundary conditions are as shown in Fig. 1 and 2.

Specimens TypeTensile modulus of

elasticity, ksi (MPa)Design tensile strength,

ksi (MPa)Ultimate tensile

strength*, ksi (MPa)PTS-1CR, PTS-2CR CF130 high tensile carbon 33,000 (227,600) 550 (3790) 620 (4280)

PTS-5CR, PTS-6CR CF530 high modulus carbon 54,000 (372,400) 550 (3790) 580 (4000)

PTS-3CR, PTS-4CR CF160 high tensile carbon 33,000 (227,600) 510 (3520) 620 (4280)*Provided by manufacturer’s design guide (Structural Group, Inc., 2002).Note: CF160 (7.14 kips/in.;1.6 kN/mm) has twice the thickness of CF130 (3.57 kips/in.; 0.8 kN/mm).

Table 3—Dimensions for test specimensSpecimens l1 lc1 l2 lc2 Boundary condition

PTS-1, PTS-1CR, PTS-2, PTS-2CR,

PTS-6, and PTS-6CR9 ft 0.5 in. (2756 mm) 8 ft 10 in. (2692 mm) 9 ft 0.5 in. (2756 mm) 8 ft 10 in. (2692 mm) Pin-pin

PTS-3, PTS-3CR 10 ft 8 in. (3251 mm) 8 ft 8 in. (2642 mm) 8 ft 8 in. (2642 mm) 8 ft 8 in. (2642 mm) Fixed-fixed

PTS-4, PTS-4CR 9 ft 10 in. (2997 mm) 8 ft 9 in. (2667 mm) 8 ft 8 in. (2642 mm) 8 ft 8 in. (2642 mm) Fixed-pin

PTS-5, PTS-5CR 8 ft 10 in. (2692 mm) 8 ft 10 in. (2692 mm) 8 ft 8 in. (2642 mm) 8 ft 8 in. (2642 mm) Pin-pinNotes: l1 is slab length in span or one direction; lc1 is support center-to-support center length in span or one direction; l2 is slab length in transverse or other direction; and lc2 is support center-to-support center length in transverse or other direction.

Fig. 1—Fixed-fixed condition (PTS-3).


Slab thickness was 3 in. (76 mm) for all specimens. The two-way slabs (PTS-1, PTS-1CR, PTS-2, PTS-2CR, PTS-6, and PTS-6CR) had a footprint of 9 ft 0.5 in. x 9 ft 0.5 in. (2.76 x 2.76 m) (Fig. 3) and were internally reinforced using mild steel and unbonded PT tendons in each direction as indicated in Table 1. The clear span length in each prin-cipal direction was 8 ft 10 in. (2.7 m) for PTS-1, PTS-1CR, PTS-2, PTS-2CR, PTS-6, and PTS-6CR (Fig. 4). Mild steel

wire mesh measuring 7 x 7 ft (2.13 x 2.13 m) was placed at the compression surface of each slab, mainly to prevent damage during transportation (Fig. 5). The amount of mild steel, which varied for each specimen, is provided in Table 1. Two different sizes of the WWM mild steel were used (Fig. 6): 1) 4 x 4 – 4/4 with cross-sectional areas As of 0.01 in.

2 (6.45 mm2) per unit inch width; and 2) 6 x 6 – 10/10 with an As of 0.0024 in.

2 (1.55 mm2) per unit inch width. The WWM

Fig. 2—Pin-support portion of PTS-4.

Fig. 3—Test setup for two-way slabs under uniformly distributed area loads or pressure. (Note: 1 ft = 305 mm; 1 in. = 25.4 mm.)

Fig. 4—Draped tendon profiles for test specimens. (Note: 1 ft = 305 mm; 1 in. = 25.4 mm.)

Fig. 5—Tendon and mild steel layout for PTS-6.


of 6 x 6 – 10/10 was placed as compression reinforcement at the bottom of the two-way slabs.

The one-way slabs (PTS-3, PTS-3CR, PTS-4, PTS-4CR, PTS-5, and PTS-5CR) had various foot-prints depending on the support boundary conditions as indicated in Table 3 and Fig. 4. Twenty-five No. 3 (db = 3/8 in. [9.5 mm]) tension bars were placed at a spacing of 4 in. (102 mm) in the span direction of the one-way slabs (Fig. 7), and nine No. 3 bars were placed as tension reinforcement at a spacing of 11 in. (280 mm) at the fixed end of the one-way slabs. Additionally, the 6 x 6 – 10/10 bottom wire meshes were used for all one-way slab

specimens to prevent cracks during installation of the specimens. Overall, the amount of bonded steel was deter-mined to obtain the balanced failure mode (this was done to see whether or not CFRP is effective even with a small degree of steel yielding), and the number of tendons was determined not to make any initial cracks due to excessive camber under applied PT forces.

Figure 4 shows the draped tendon profiles used for the specimens. Figures 8 and 9 show the PT reinforcement layout plan for the specimens. A total of 16 post-tensioning tendons were placed in each direction of the two-way slabs and in the span direction of the one-way slabs (Fig. 5 and 10). The spacing of uniformly distributed tendons was 6 in. (152 mm) for the two-way slabs; thus, the cross-sectional area of the tendons per unit width was 0.006 in.2/in. (0.15 mm2/mm). For the one-way slab, two tendons were grouped with a spacing of 2.25 in. (57 mm) between each tendon, and the two-tendon group was then uniformly distributed with a spacing of 12 in. (305 mm) between the groups (Fig. 9 and 10). PT tendons were stressed to approximately 0.7fpu before transfer (that is, jacking stress fpj), resulting in approximately 0.65fpu after transfer (that is, initial stress fpi). Note that the initial stress fpi is almost the same as the effective stress fpe in this research, as there are minor long-term changes in tendon stress. After

Fig. 6—Welded wire mesh (WWM) mild steel used for two-way slabs.

Fig. 7—No. 3 deformed mild steel used for one-way slabs. (Note: 1 ft = 305 mm; 1 in. = 25.4 mm.)

Fig. 8—Tendon layout for two-way slabs.


the Phase-I test was completed, each of the six specimens was repaired with CFRP and high-strength adhesive (epoxy) in accordance with ACI 440.2R-02 recommenda-tions (Fig. 11 and 12). Prior to placing the CFRP sheet, the substrate was cleaned and primer was applied: a steel coarse brush attached to the hand drill was used to smooth and remove concrete deposit from the top. This method provided strong bond between concrete surface and CFRP. Then, the slabs were physically repaired (for

example, filling cracks and applying sealer). The two-way slabs were repaired using two different FRP-strengthening schemes: 1) a diagonal scheme; and 2) an orthogonal scheme. Two plies of CFRP fabric sheets were placed for both schemes. The diagonal scheme, which was used for PTS-2CR, is shown in Fig. 13, and the orthogonal scheme, which was used for PTS-1CR and PTS-6CR (parallel to slab edges), is shown in Fig. 14. The one-way slabs (PTS-3CR, PTS-4CR, and PTS-5CR) were strengthened with straight CFRP sheets in the slab top (note that loading is applied from the bottom) and in the bottom tension zone over a quarter of the clear span at the support (Fig. 15). Details of CFRP materials are given in Table 2.

TEST SETUP AND TESTINGTwo-way, simply supported, PT slabs were tested

under uniformly distributed area loads or pressure. The

Fig. 9—Tendon layout for one-way slabs. (Note: 1 ft = 305 mm; 1 in. = 25.4 mm.)

Fig. 10—Tendon and mild steel layout for PTS-3 and PTS-4.

Fig. 11—Diagonal scheme for CFRP attachment (PTS-2CR).

Fig. 12—Orthogonal scheme for CFRP attachment (PTS-1CR).


loading frame is shown in Fig. 3 and 16. The area loads or pressure were applied upward by using a hydraulic water bag (the top of the slab at midspan was referred to as the tension side). The water pressure was gradually increased at approximately 1 psi (7 kPa) increments. One-way PT

slabs were also subjected to uniformly distributed area load (water pressure), which was exerted vertically upward.

The control slabs were loaded to the ultimate (Phase-I); however, the slabs were not loaded to a point where they could become unrepairable for safety. Phase-I testing stopped when the slabs reached one of the following three criteria: 1) when excessive cracks were visually observed; 2) when the deflection in the slab reached close to L/120, where L is the span length; and 3) when the PT stress reached nearly 75 to 85% (0.75fpu to 0.85fpu) of the ulti-mate tensile strength. It was intended that the specimens would not completely fail during the Phase-I testing. The point of excessive cracking was close to the threshold of either of the other two criteria.

The same criteria were used for the repaired slabs (Phase-II), except for the first criteria. At the time the Phase-II test was stopped, the slabs were deemed semi-elastic. No crushing of concrete occurred until the ulti-mate stage. As noted previously, the cracked slabs (all six specimens) were then repaired with CFRP sheets and tested again. The same criteria to determine the ultimate load were used for the repaired slabs.

During the testing, all readings were taken using an automated data recording system. The test measurements included pressure, deflection, strain (in mild steel), and a change in PT forces. The applied pressure was monitored by the pressure gauge. The displacement gauges used to measure the deflection were linear variable differential transformers (LVDTs) with 4 in. (100 mm) of travel. Strain gauges were mounted in the mild steel at the midspan of the slab. Load cells were placed behind the anchor plates of the unbonded PT tendons to record the PT forces and stresses, and the increments of those forces and stresses during the PT and external loading. The strain gauges were attached at midspan of the slab.

TEST RESULTS AND DISCUSSIONCracking

The compression (bottom) surface of each of the test specimens was not accessible for observation of cracks while testing was in progress. After the first crack appeared in the tension (top) surface, additional cracks were marked and recorded (Fig. 17). As expected, diagonal cracking patterns were observed in the two-way control slabs (PTS-1, PTS-2 and PTS-6). Since the square panel with the same reinforcing details in two principal directions was tested, the crack patterns were symmetrical with respect to both principal axes (Fig. 17 and 18). The symmetric

Fig. 13—Diagonal scheme for CFRP attachment (PTS-2CR). (Note: 1 ft = 305 mm.)

Fig. 14—Orthogonal scheme for CFRP attachment (PTS-1CR and PTS-6CR). (Note: 1 ft = 305 mm; 1 in. = 25.4 mm.)


cracks observed from the two-way slabs indicate that the area load/pressure was quite uniformly applied on the slabs. For the one-way control slabs (PTS-3, PTS-4, and PTS-5), flexural cracks were focused on the tension (top) surface at the location where positive moment was the largest (for example, midspan for PTS-3 at approxi-mately 3 ft 9 in. (1.14 m) from the simply supported end for PTS-4) (Fig. 19). After the test, the bottom surfaces of the slabs were examined. Almost no cracking was observed

on the bottom surface of the control or repaired two-way slabs (that is, no concrete crushing was noted). In the first phase of testing of control specimens, the loads were not applied to the collapse level for safety reasons. It is noted that special safety precautions are essential in the testing of

Fig. 15—CFRP attachment for PTS-3CR and PTS-4CR. (Note: 1 ft = 305 mm.)

Fig. 16—Water pressure loading test frame.

Fig. 17—Crack patterns (PTS-1).


an unbonded PT system. Also, the use of a hydraulic water bag warrants further precautions.

For the repaired slabs (PTS-CR specimens), cracks were not visible on the tension (top) surface during testing, as the surface was covered by CFRP. In some of the exposed areas, the old cracks opened up. No debonding of the CFRP sheets was observed at the ultimate loading stage.

The comparison of deflection values between control (nonrepaired) and repaired specimens is shown in Table 4 and Fig. 20 to 25. In general, the control slabs behaved linearly during the initial stages of loading. A hairline

crack (tension crack) for any one test slab was defined as the first crack which appeared on the top of the slab and corresponding pressure was defined as pressure at first cracking (Table 5). Once the two-way slabs cracked under approximately 2 to 4 psi (0.014 to 0.028 MPa) pressure, they exhibited reduced flexural stiffness as evidenced by the pressure-deflection relationships shown in Fig. 20, 21, and 25. The second stage of the linear behavior of cracked elastic slabs continued until approximately 4.5 to 6.5 psi (0.031 to

Fig. 18—Crack patterns (PTS-6).

Fig. 19—Crack patterns (PTS-3 and PTS-4). (Note: 1 ft = 305 mm; 1 in. = 25.4 mm.)

SpecimenExternal water

pressure, psi (MPa)

Measured deflection ∆,

in. (mm)

repaired

non-repaired

ΔΔ

PTS-1 5.2 (0.0359) 0.45 (11.5) 1

PTS-1CR 5.2 (0.0359) 0.40 (10.3) 0.9

PTS-2 5.2 (0.0359) 0.31 (7.9) 1

PTS-2CR 5.2 (0.0359) 0.20 (5.1) 0.64

PTS-3 5.2 (0.0359) 0.85 (21.6) 1

PTS-3CR 5.2 (0.0359) 0.6 (15.2) 0.71

PTS-4 5.2 (0.0359) 1.52 (38.6) 1

PTS-4CR 5.2 (0.0359) 1.05 (26.8) 0.69

PTS-5* 5.2 (0.0359) 2 (50.8) 1

PTS-5CR 5.2 (0.0359) 0.69 (17.5) 0.34

PTS-6 5.2 (0.0359) 0.45 (11.4) 1

PTS-6CR 5.2 (0.0359) 0.39 (9.8) 0.86*Excessive cracking.


0.045 MPa) pressure was applied. As the flexural tensile cracks increased in number and width, the pressure-deflec-tion curves started to show trilinearity and slope reduction. Subsequently, a significantly reduced stiffness was noted. This trilinear pressure-deflection behavior was similar for each two-way slab specimen. The strength of PTS-1 with a larger amount of mild steel was greater than that of PTS-2 by approximately 25%.

Similar behavior was noted for the one-way slabs. The boundary condition affected the pressure-deflection behavior. As the number of simple supports changed from 0 to 1 to 2, the stiffness and load-carrying capacity were reduced. Testing of PTS-5 with two simple supports was stopped due to excessive cracking. The curves of the PTS-3 and PTS-4 specimens also became nonlinear rather than trilinear, while PTS-5 exhibited a distinctly bilinear

Fig. 20—Pressure-deflection relationship (PTS-1 and PTS-1CR).





pressure-deflection relationship. This indicates that the initial stiffness of unbonded PT slabs can be improved by increasing the fixity of the end supports. This point is especially important in terms of the serviceability of such slender PT members. Thus, in order to minimize floor vibrations, etc., application of restrained boundary condi-tions is highly recommended.

After the Phase-I testing of control specimens and release of water pressure, it was noticed that the residual deflections were negligible due to the restoring force provided by the PT tendons. These measurements are also noteworthy in that unbonded PT structures possess a high elastic deformation-restoring capability even after consider-able concrete damage. Therefore, there was no additional

Fig. 24—Pressure-deflection relationship (PTS-5 and PTS-5CR). Fig. 25—Pressure-deflection relationship (PTS-6 and PTS-6CR).

cr u

Specimen Pressure at first cracking Pcr, psi (MPa) Ultimate pressure Pu, psi (MPa)u

cr

PP

_ repaired

_ non-repaired

u

u

PP

PTS-1 6.35* (0.044) 6.5 (0.045) 1.02 NAPTS-2 4.8* (0.033) 5.2 (0.036) 1.08 NAPTS-3 5.65* (0.04) 6.5 (0.045) 1.15 NA

PTS-4 4* (0.028) 5.4 (0.037) 1.35 NA

PTS-5 2* (0.021) 4.17 (0.029) 2.09 NAPTS-6 3.5* (0.024) 5.5 (0.044) 1.57 NA

PTS-1CR N/A 9.2 (0.063) N/A 1.42PTS-2CR N/A 9.8 (0.068) N/A 1.88PTS-3CR N/A 10.9 (0.075) N/A 1.68PTS-4CR N/A 7.9 (0.055) N/A 1.46PTS-5CR N/A 7.48†(0.052) N/A 1.79PTS-6CR N/A 8.88 (0.061) N/A 1.61

*Based on visual observation.†Testing was prematurely stopped for safety reason; thus, 10% of last measured value was added. Note: N/A is not available.


step related to zeroing slab deflection before applying CFRP sheets. All LVDTs were removed prior to the applica-tion of CFRP sheets on the surface of specimens, and then the LVDTs were reinstalled. At this point, initial midspan deflections were reset to zero.

The deflection profiles for the strengthened slabs primarily show essentially linear or slightly nonlinear behavior without sharp turning points, whereas the load-carrying capacity was considerably increased (by approxi-mately 17 to 88%) (Table 5). For the two-way slabs, the stiffness was recovered up to that of the control slabs. For the repaired one-way slabs, the stiffness also became equiva-lent to that of the original one-way slabs or even superior to the nonrepaired slabs with simple support (PTS-3CR, PTS-4CR, and PTS-5CR). In particular, the simply supported PTS-5CR had less deflection at the ultimate load of PTS-5 even after excessive cracking. At the pressure level around the yielding point of the control specimen, the repaired slab’s deflection was much smaller than the nonre-paired slab’s deflection (see Fig. 24), indicating that use of CFRP sheets effectively increases the flexural resistance of unbonded PT slabs.

In terms of ductility capacity, there were no consistent trends between the nonrepaired and repaired specimens. If significantly smaller reinforcing bar amounts are present, the failure mode would have been more ductile. More studies need to be developed to achieve ductile failure mode, and/or a strength reduction factor should be applied to the brittle mode of failure.

Stresses in PT and nonprestressed mild steelUnlike bonded prestressed or conventionally rein-

forced concrete members, the prestressing strands in the unbonded PT members never reach their ultimate strength fpu. This is because the ultimate strength fpu of unbonded tendons is not dependent on the localized strain at the flex-ural critical section but depends on the total member elon-gation, number of spans, span-depth ratio, and loading type (ACI 318-08; Kang and Wallace 2008). Just before loading of the slabs, the PT forces in the strands were recorded. The average effective stress (in this case before external loading) was normally kept between 65 and 70% of the ultimate strength of the strands. As the loading increased, the tendon stress increased nonlinearly. The rate of tendon stress increase was very small (approximately 0.005% of fpe) before concrete cracking, but it became increasingly larger as the slab deflection increased until the ultimate load. Figure 26 shows a representative result for PT force varia-tion against an external pressure.

On the other hand, as the slabs were loaded and started to crack heavily, the stress in the mild steel started to increase and became close to yield stresses (Fig. 27); however, no significant yielding was observed from the strain gauge data (Fig. 27). For example, strain in the wire mesh of PTS-1

Fig. 26—Tendon load variation with increasing pressure (PTS-3).

Fig. 27—Reinforcing bar strain variation with increasing pressure (PTS-3).


started to increase as the external loading was increased and reached a maximum strain of approximately 0.002 at an external pressure on the slab of 6.5 psi (0.045 MPa). The stresses of the wire mesh in the two-way slabs nearly reached the yield stress near the ultimate load, but it cannot be said that the nonlinear pressure-deflection behavior is attrib-uted to the yielding of the mild steel. Rather, the nonlinear behavior was related to the significant concrete cracking. Note that the nonlinear behavior of the tendons was modest, as it was kept within the elastic range.

The stresses of the reinforcing bars in the one-way slabs were greater than those of the wire mesh in the two-way slabs. For instance, the average stress at the ultimate load was 52.5 ksi (362 MPa) and 55.6 ksi (383 MPa) for PTS-1 and PTS-2, respectively, whereas the average was 56 ksi (386 MPa) and 61 ksi (421 MPa) for PTS-3 and PTS-4, respectively. This may be due in part to the larger width of the damaged region that formed in the one-way slab than in the two-way slab; however, the degree of bonded steel yielding was limited for the specimens.

As noted, the cracked slabs were repaired with CFRP sheets and tested again. The ultimate loads of the test specimens strengthened with CFRP sheets were always higher than the ultimate loads of the non-repaired speci-mens (Table 5). The flexural strength of the slabs strength-ened with CFRP composite materials increased by 42%, 88%, and 61% for PTS-1CR, PTS-2CR, and PTS6CR (two-way slabs), respectively, and by 68%, 46% and 79% for PTS-3CR, PTS-4CR, and PTS-5CR (one-way slabs), respectively. Interestingly, however, the stress increases in PT tendons in the repaired specimens at ultimate loading

stage were always lower in comparison to those in the control specimens by approximately 10 to 65% (Table 6). This was the case even though the maximum deflections of the repaired specimens were larger than those of the control specimens. Note that the testing of the non-repaired control specimens was stopped when the tendon stress reached the criteria of 0.75fpu to 0.8fpu or other criteria were reached. This means that the total elongation of the tendon was larger when the concrete cracked heavily such that the plastic concrete deformation (that is, opening of cracks) at the level of the tendons was substantial. On the other hand, the cracks were stitched by the CFRP reinforcement externally bonded to the concrete top surface. After the repair, the slab concrete behaved like an elastic solid and, in this case, the tendon stress increase in the CFRP-repaired slab was not as much as that in the slab without CFRP at the same given deflection. As a result, the components of tension were produced primarily by the CFRP composite materials under bending. This experimental finding is of value and demonstrates another benefit of using CFRP for unbonded PT structures, as the CFRP strengthening not only provides the additional strength but also leads to the decrease in the tendon stress increase.

The increased strength with respect to the nonrepaired strength varied from 42 to 88% for two-way slabs and from 46 to 79% for one-way slabs. The larger increase in strength was attributed to the larger amount of CFRP used for strengthening (refer to Tables 2 and 5). The critical yield line pattern developed in the control specimens could not propagate further because of the presence of the CFRP across the crack lines. Again, at the time the testing was completed, the CFRP-repaired slabs remained in an essen-tially elastic condition. This is due to the perfectly linear strain-stress behavior of the carbon fibers, which had not

SpecimenApplied pressure,

psi (MPa)

Measured average PT forces, lb (kN)∆F = Fu – Fe ,

lb (kN) e

FFΔ

, %Fe FuPTS-1 6.5 (0.045) 6900 (30.8) 7101 (31.7) 201 (0.897) 2.9

PTS-1CR 9.2 (0.063) 6920 (30.89) 7001 (31.25) 81 (0.362) 1.2PTS-2 5.2 (0.036) 6931 (30.94) 7128 (31.82) 197 (1.027) 2.8

PTS-2CR 9.8 (0.068) 6910 (30.85) 7013 (31.3) 103 (0.879) 1.5PTS-3 6.5 (0.045) 6892 (30.77) 7122 (31.8) 230 (1.46) 3.3

PTS-3CR 10.9 (0.075) 6920 (30.89) 7068 (31.55) 148 (0.661) 2.1PTS-4 5.4 (0.037) 6588 (29.41) 7033 (31.4) 445 (1.987) 6.8

PTS-4CR 7.9 (0.054) 6546 (29.22) 6601 (29.47) 55 (0.246) 0.8Notes: Fe is effective tendon force; Fu is tendon force at ultimate load.


been ruptured throughout the testing. Also, rigid plate movement along the crack line did not happen. Concrete did not crush at the bottom surface along the yield lines. Overall, it was verified that effective placement of CFRP increased the load-carrying capacity of unbonded PT slabs. The quantity of the CFRP sheets used for the specimens was sufficient and adequate for increasing the flexural strength by about 42 to 88% without concrete crushing. Further-more, it was concluded that the CFRP placement patterns of both the diagonal and orthogonal schemes were effective for two-way unbonded PT slabs.

SUMMARY AND CONCLUSIONS1. Nonlinear behavior was observed from pressure-

deflection relationships of unbonded PT one- and two-way slabs under uniformly distributed pressure or area loads. This was due to the considerable tensile cracks that occurred at the high moment region. However, as anticipated, the tendon stress increase was only approximately 0.8 to 6.8% of the effective stress.

2. While the deflection was much higher for CFRP-repaired slabs, the unbonded tendon stress increases were lower than those in the control specimens by approximately 10 to 65%. This indicates that a total elongation of the tendons is much higher when large crack opening occurs, rather than when a large deflection occurs.

3. The PT concrete slabs repaired with CFRP fabric and bonded to the tension surfaces gained considerable strength. Flexural capacity of the slabs strengthened with CFRP composite materials increased by approximately 40 to 90% for two-way slabs (PTS-1CR, PTS-2CR, and PTS6CR) and approximately 50 to 80% for one-way slabs (PTS-3CR, PTS-4CR, and PTS-5CR).

4. As such, the slabs repaired with properly designed CFRP schemes showed sufficiently larger load-carrying capac-ities than the nonrepaired slabs. Both orthogonal and diagonal two-layer placement schemes used in this study were effective, as the CFRP fibers were perpendicular to the crack lines.

5. The measured pressure-deflection relationships between the control PT slabs and repaired slabs also indicate better serviceability conditions (for example, stiffness and crack restraint) for the repaired slabs even after substantial damage. The behavior of the CFRP-repaired slabs was essen-tially linear or slightly nonlinear. No fiber tensile failure, debonding, or concrete crushing was observed.

6. The quantity of used CFRP sheets was sufficient and adequate for increasing the flexural strength by approxi-mately 42 to 88% without concrete crushing.

7. The results from this study indicate that different end supports of one-way slabs caused large variations in perfor-mance. The fixed-fixed condition (PTS-3 and PTS-3CR) shows a 68% increase in ultimate strength due to CFRP repair, whereas the fixed-pin condition (PTS-4 and PTS-4CR) shows a 46% increase. As the degree of fixity at the ends decreased, the stiffness and load-carrying capacity (ultimate strength) increased by the CFRP sheets were reduced.

An alternate CFRP retrofitting system that can be employed is to use CFRP laminated strips or CFRP prestressed strips. These retrofitting methods for prestressed or PT concrete structures should also be considered as future studies. Although promising outcomes have been reported by this study, the CFRP systems applied to unbonded PT slabs may not be considered as a generally applicable repair system until further verifications are undertaken on the ductility of CFRP-repaired PT slabs with overstressed or ruptured steel reinforcement.

The work presented in this paper was funded by a NASA grant (FAR-NASA-2002) and, in part, by a U.S. DOT–RITA grant (DTRT06-G-0016/OTCREOS10.1-21). The authors would like to acknowledge laboratory staff L. Sanchez and research assistants M. Busciano, V. Dao, and H. Hong at California State University, Fullerton, CA, and Y. Huang at the University of Oklahoma, Norman, OK, for their assis-tance. The views expressed are those of authors and do not necessarily represent those of the sponsors.

REFERENCESACI Committee 318, 2011, “Building Code Require-

ments for Structural Concrete (ACI 318-11) and Commen-tary,” American Concrete Institute, Farmington Hills, MI, 503 pp.

ACI Committee 440, 2002, “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI 440.2R-02),” American Concrete Institute, Farmington Hills, MI, 45 pp.

ASTM International, 2008, “American Society for Testing and Materials Annual Book of ASTM Standards,” West Conshohocken, PA.

Chakrabarti, P. R., 1995, “Ultimate Stress for Un-Bonded Post-Tensioning Tendons in Partially Pre-Stressed Beams,” ACI JOURNAL, Proceedings V. 92, No. 6, Nov.-Dec., pp. 689-697.

Chakrabarti, P. R.; Miller, D.; and Bandyopadhayay, S., 2002, “Application of Composites in Infrastructure—


Parts I, II, and III (a brief report on materials and construc-tion),” Proceedings ICCI-2002, The Third International Conference on Composites in Infrastructure, June 10-12, 2002, San Francisco, CA.

Chakrabarti, P. R., 2005a, Retrofitting and Repairing of Heavily Cracked Un-bonded Post-Tensioned Structural Systems, ACI SP-225, American Concrete Institute, Farm-ington Hills, MI, 2005.

Chakrabarti, P. R., 2005b, “Repairing and Retrofitting of Post-Tensioned Beams,” Concrete International, Amer-ican Concrete Institute, Farmington Hills, MI, Feb. 2005, pp. 45-48.

Chakrabarti, P. R.; Kim, U.; Hong, H., Busciano, M.; and Dao, V., 2007, “Repair Systems for Post-Tensioned Slabs with Composite Materials,” Proceedings ASCE/SEI Structures Congress 2007, May 16-19, 2007, Long Beach, CA.

Chakrabarti, P. R.; Kim, U.; Busciano, M.; and Dao, V., 2009, “Repair Systems for Un-Bonded Post-Tensioned One & Two Way Slabs with CFRP,” Proceedings of the 5th Inter-national Structural Engineering and Construction Conference (ISEC-5), Sept. 21-27, 2009, Las Vegas, NV.

Di Ludovico, M.; Nanni, A.; Prota, A.; and Cosenza, E., 2005, “Repair of Bridge Girders with Composites: Experi-mental and Analytical Validation,” ACI Structural Journal, V. 102, No. 5, Sept.-Oct., pp. 639-648.

Kang, T. H.-K., and Wallace, J. W., 2008, “Stresses in Unbonded Tendons of Post-Tensioned Flat Plate Systems under Dynamic Excitation,” PTI Journal, V. 6, No. 1, Feb., pp. 31-44.

Ibrahim Ary, M., and Kang, T. H.-K., 2012a, “Shear-Strengthening of Reinforced & Prestressed Concrete Beams Using FRP: Part I—Review of Previous Research,” Interna-tional Journal of Concrete Structures and Materials, V. 6, No. 1, Mar., pp. 41-48.

Kang, T. H.-K., and Ibrahim Ary, M., 2012b, “Shear-Strengthening of Reinforced & Prestressed Concrete Beams Using FRP: Part II—Experimental Investigation,” Interna-tional Journal of Concrete Structures and Materials, V. 6, No. 1, Mar., pp. 49-57.

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Michaluk, C. R.; Rizkalla, S. H.; Tadros, G.; and Benmokrane, B., 1998, “Flexural Behavior of One-Way Concrete Slabs Reinforced by Fiber-Reinforced Plastics Reinforcements,” ACI Structural Journal, V. 95, No. 3, May-June, pp. 353-365.

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Uksun Kim is an Associate Professor and Chair of civil engineering at California State University, Fullerton, CA. He received his BS from Yonsei University, Seoul, Korea; his MS from Michigan State University, East Lansing, MI; and his PhD from the Georgia Institute of Technology, Atlanta, GA. His research interests include seismic design of building systems with steel joist girders, partially restrained connec-tions and concrete-filled tubes, and seismic rehabilitation of prestressed building systems. He is a licensed professional engineer in Washington and a LEED AP.

PTI Fellow Thomas H.-K. Kang is an Assistant Profes-sor at Seoul National University, Seoul, Korea. Before that, he was an Assistant Professor at the University of Oklahoma, Norman, OK. He received his BS from Seoul

National University and his PhD from the University of California, Los Angeles, Los Angeles, CA. He is a member of PTI Committee DC-20, Building Design. His research interests include design and rehabilitation of post-tensioned buildings and systems. He is a licensed professional engi-neer in California.

Pinaki R. Chakrabarti is a Professor of civil engineering at California State University, Fullerton, CA, He received his BE from Calcutta University, India; his MS from the University of Minnesota, Twin Cities, MN; and his PhD from Rutgers University, Piscataway, NJ. His research interests include admixtures, prestressed concrete, and seis-mic retrofit with composites. He is a licensed professional engineer and structural engineer in California.


TECHNICAL PAPER

STRUCTURAL EFFICIENCY FROM A SUSTAINABILITY PERSPECTIVE

BY CAROL HAYEK AND SALEEM KALIL

A practical approach to evaluate structural efficiency is presented, taking into consideration various structural alternatives applied to a high-rise building located in central London, UK. The study focuses on the choice of the slab system between conventional reinforced and bonded post-tensioned concrete and tackles the sustainability triple bottom line: environmental, social, and economic. The environmental impact is assessed using European factors restricted to embodied energy and embodied carbon dioxide (CO2); the social impact is assessed using a ranking scheme considering construction time, material usage, and indoor and outdoor factors. The results show that the post-tensioned concrete option contributed to the project’s sustainability goals and led to considerable savings of approximately 25% on the overall slab’s embodied energy and embodied carbon while presenting an economical solution and social benefits.

INTRODUCTIONConstruction material, construction activity, and the

operability of a building impact our quality of life in many ways. As population levels around the world continue to rise and more building structures are required, the construction impact is set to increase. To fully assess the effect of buildings on the environment, it is important to assess the impact of the construction phase in addition to the impact of the operational phase. There has been tremendous focus on the operational phase, given the fact that it accounts for approximately 90% of the environmental impact. However, as buildings become more environmentally efficient during the operation phase, the impact of the construction phase and, consequently, the structural efficiency, become essential.

This study aims to evaluate structural efficiency over the building’s life cycle through a practical approach, covering the sustainability triple bottom line: environmental, social, and economic. The focus is on slab construction for bonded post-tensioned and conventional reinforced concrete slab options with an emphasis on the construction phase. The comparison is carried out on an actual project—Strata SE1—a high-rise building in London designed with stringent sustainability requirements. The evaluation of structural efficiency examines material selection, quantity, construction time, and architectural features and how they translate into the environment and social well-being.

PROJECT DESCRIPTIONThe project is a multi-

unit residential building (482 ft tall) with 41 post-tensioned flat slabs designed using European standards with a central core and only two internal columns. The building has several unique features, with offset columns and wind turbines housed at the top of the tower and resting on a post-tensioned transfer slab. It is the world’s first building with wind turbines destined to supply a portion of the building’s operational energy.

For the structural slab design, the following objectives were put in place:

• Structural performance: Frame a solution that simplifies forming, routing of mechanical services, and architectural layout flexibility; reach the thinnest achievable slab thickness for spans of 31 ft; and frame



a solution that controls deflection and cracks to meet cladding requirements and tolerances. Deflection was set to 0.4 in. on all the façade elements and to L (span)/360 internally.

• Construction: Achieve a fast construction schedule and stay below budget.

• Sustainability: Optimize use of resources, mini-mize carbon footprint, and reduce social impact of the construction work.

STRUCTURAL SLAB OPTIONS Given the slab layouts and the sustainability goals set for the

project, it was decided from the start that an in-place concrete frame would work better than a steel frame. The main reasons behind this assessment were the curved slab edges, which could be formed easily and economically with concrete; advantages of concrete, such as acoustic isolation, resilience, and thermal mass properties (Schokker 2010); and lateral stability capacity. Therefore, only the following in-place concrete options were considered for the comparative analysis:

• PT: Flat-slab post-tensioned concrete with a bonded system (bonded post-tensioning is common in UK building construction);

• RC1: Flat-slab reinforced concrete; and• RC2: Slab with drop beams all in reinforced

concrete.A detailed design for all three options was performed

following the same assumptions to allow for a fair compar-ison. Given the project location, the structures were designed according to the British code to meet equivalent service-ability, ultimate state, and deflection limits. Table 1 shows the material quantity rates per square foot of slab. Non-prestressed reinforcement rates represent all conventional reinforcement needed, including detailing requirements, such as trim bars around openings and bars at slab edges. The overall slab area shown in the table is the exact value from the built project accounting for all recesses, openings, and so on.

The roof slab supporting the wind turbine is excluded from the aforementioned quantities. Its quantities do not affect the analysis, as the overall material quanti-ties are driven by the typical 40 stories. The roof slab is very specific to the loads induced by the wind turbines. It involves concentrated wind loads and moments trans-ferred by the turbines to the slab.

PROJECT CONSTRUCTION SCHEDULEConstructing a high-rise on a very tight site in London,

where the Strata project is located, comprises many challenges. One of the main focuses is to reduce disruptions to nearby communities and businesses and complete the construction work as fast as possible. It is therefore vital to adopt a construc-tion system that speeds up the construction schedule.

Structural frame designEstimates of the construction time of the three

concrete options were computed. The estimates for each option were based on same concrete strength, loadings,

Structure type

Structural item Unit PT RC1 RC2

Average slab area ft2 6781 6781 6781Overall area ft2 271,272 271,272 271,272

Slab thickness in. Approximately 8 (200 mm)Approximately 10 (260 mm) 8.3*

Non-prestressed reinforcement rate lb/ft2 2.38 4.42 3.99PT strand rate lb/ft2 0.72 0 0

PT ducts rate (0.43 ft/ft2) lb/ft2 0.12 0 0PT anchors (0.01 pc/ft2) lb/ft2 0.08 0 0

*Value represents equivalent slab thickness. It is based on slab of 7.1 and 23.6 in. (180 and 600 mm) deep beams placed along long spans and perimeter to control deflection.


deflection control, and forming and labor resources. The floor cycles came out at 5, 6.5, and 8.5 days for the PT, RC1, and RC2 options, respectively. Consequently, for the 40 stories, RC1 yields a total increase of 60 working days with respect to the PT option and RC2 yields an increase of 140 working days with respect to PT. With additional forming and labor resources consisting of an entire slab forming set and back-propping, the floor cycle for the RC options can be improved; however, this additional forming adds—in addition to its cost—an environmental impact caused by the extra formwork material, its mobilization, and more waste. Time savings for the PT option is due to less material and hence less installation time and labor, stressing of the tendons and, consequently, faster deshoring. The actual floor cycle achieved for the PT slab was 4.5 days on average, yielding even greater time savings.

On job sites, as trades are interlinked, efficient coor-dination and control of the work to minimize errors and enhance information-sharing significantly improve the construction workflow and deadlines. It is hard to quan-tify the related savings, but the project was completed 12 weeks ahead of the estimated schedule.

Structural detailingWhile the choice of the structural frame has a major

impact on the construction time period, small improve-ments from thorough detailing can also help in reducing the construction time. A simple example is the construction requirement for this project to avoid complicated, skewed blockouts at the PT anchor locations and the slabs’ curved edges. Skewed blockouts require more labor and material and, most importantly, would lead to increased friction losses at the anchor and higher risk of damage to the post-tensioning tendons. With efficient detailing, these blockouts were avoided at no extra cost or resources. Every anchor would have necessitated approximately 2 additional minutes for installation or, alternatively, more labor cost. This seems negligible, but when counting 2000 anchors required for the project, this amounts to 67 hours; therefore, this saved the site approximately 1.5 weeks on the PT trade schedule.

MATERIAL AND ENVIRONMENTAL RATESThe overall material quantity for the 40 stories is listed

in Table 2 along with the unit rates of embodied energy and embodied CO2.

The environmental factors listed are taken from the ICE report (Hammond and Jones 2008), which is based on life-cycle inventory (LCI) cradle-to-gate and 40% recycled content for steel. This reference focuses on energy and carbon dioxide factors without representation of other greenhouse gases. It was used due to its comprehensive database on concrete slab material and application to the UK market. The LCI approach was deemed satisfactory given the scarcity and variability of data on life-cycle assessment (LCA) or cradle-to-grave; the use of the same material type in all options; and the abundance of cradle-to-gate values, which are docu-mented by the material manufacturers (Sweet 2010). In addition, for database consistency, the wire and galva-nized sheet rates used herein for PT strands and duct are from virgin material, as no other values are given in the ICE source. However, PT strand and ducts can have up to 95% recycled content. The results are, therefore, very conservative and the reality would yield higher savings in the PT option.

ENVIRONMENTAL IMPACTThe cumulative environmental impact of the concrete

stories is shown in Fig. 1. The results point out that PT records the lowest embodied energy at 25,200 GJ and embodied CO2 at 3101 tons. An estimated 6393 GJ in energy and 797 tons in CO2 is added by using RC1 versus PT—an increase of approximately 25% in the overall embodied energy and CO2. Between PT and RC2, the environmental differences are not as pronounced; PT saves approximately 5% in energy and CO2. RC2, however, does not benefit from a simplified formwork that a flat slab presents. The existence of drop beams in RC2 requires elaborate formwork, more workmanship, changes to mechanical services distribution, and reduced layout flexibility.

The results can be extrapolated to determine the LCA of the concrete slabs. The transport, construction process, and demolition phases to cover gate-to-grave are estimated to add between 10 and 20% to the LCI results (Kawai et al. 2005; Guggemos and Horvath 2005; Nielsen 2008). Due to lack of a coherent database, more research is needed to obtain reliable numbers.

It is important to note that per Table 3, concrete alone accounts for 56% on average of the embodied energy of the slabs and 72% of total embodied CO2.

Moreover, as the three options involve cast-in-place concrete solid slabs and would benefit from the concrete’s


thermal mass properties, the environmental impact of the operational phase of the building is expected to be comparable for all the options. The savings in energy and carbon dioxide that resulted from the structural frame choice, therefore, would come at no extra burden to the overall building’s LCA.

SOCIAL IMPACT Human science is taking an increasing role in the built

environment (Frank et al. 2003). Several studies discuss the social impact of construction and buildings on quality of life (Gangolells et al. 2009; Gilchrist and Allouche 2005). In this study, the social impact is assessed through a ranking scheme that gives a practical comparison of various

structural slab options during construction and operability phases. The approach considers the effect of the construc-tion time period, reduced nuisances reflected by material quantities and material type, and architectural features for indoor and outdoor impact, as shown in Table 4.

During the construction work, a wide array of social discomfort can occur (Gauzin-Muller 2002), such as air pollution, dirt and dust, noise, vibration, traffic, parking problems, and disruption to nearby businesses. These can be directly related to material quantity, type, and construction time:

Material typeOverall material weight, U.S. ton Embodied

energy, MJ/lbEmbodied CO

2,

lbCO2/lbPT RC1 RC2

Concrete C32/40 (1:1.5:3) 13,886 18,052 14,581 0.50 0.159Non-prestressed reinforcement (bar and rod) 322 601 543 11.2 1.71

PT strand (wire) 97 0 0 16.3 2.83PT duct (galvanized sheet) 17 0 0 17.7 2.82PT anchors (general steel) 12 0 0 11.1 1.77

Embodied energy, % Embodied CO2, %

Material item PT RC1 RC2 PT RC1 RC2

Concrete C32/40 56 58 55 71 74 71Non-prestressed reinforcement (bar and rod) 29 42 45 18 26 29

PT strand (wire) 13 0 0 9 0 0PT duct (galvanized sheet) 2 0 0 2 0 0PT anchors (general steel) 1 0 0 1 0 0

Fig. 1—Total embodied energy and carbon dioxide.


• Using less of the same material leads to less disrup-tion, reduced pollution, trucking, traffic conges-tion, deliveries, and waste. Because all options use concrete and reinforcement, based on the material quantities of Table 4, the options rank: 1) PT; 2) RC2; and 3) RC1.

• A faster construction cycle yields less disrup-tion and helps alleviate the negative nuisances of construction sites. The options rank: 1) PT; 2) RC1; and 3) RC2 in terms of time savings. The PT option saved the community approximately 3 months of construction time and all related disruptions.

During the operational phase, improving indoor living conditions has a direct impact on economic and social bene-fits from increased productivity to better health. The average person spends 87% of their time indoors (Kleipis et al. 2001); thus, their well-being depends largely on the condi-tions of the interior spaces in terms of lighting, air quality, acoustics, sight openness (visual), and thermal comfort.

• Concrete has clear benefits for the aforementioned factors (applicable to all three options).

• Architecturally, a flexible and open indoor layout that a flat-slab system provides would contribute to better visual and living comfort. While both PT and RC1 options are based on flat slabs, RC2 includes drop beams. Such beams would lower the layout flexibility and restrain the view.

• Outdoors, efficient structures that reduce unnec-essary building height stemming from pure floor thickness also help the environment with a lesser shadowing effect, less cladding material, and all its repercussions in energy consumption. The slab thicknesses in Table 1 show that RC1 and RC2 would have yielded increases of 7.9 and 52.5 ft in overall building height, respec-

tively. A smaller building would also consume less energy in terms of its heating, cooling, and overall operation.

For the overall social impact, a weighted scoring scheme could be used by assigning an importance factor to each item. For Strata, the PT option ranks first in all categories, as summarized in Table 5.

ECONOMIC IMPACTAs with any project, cost-effectiveness plays an

important role in deciding on an optimal solution. When comparing overall cost impact, however, a holistic approach is needed to cover both direct and indirect cost.

Direct cost estimates for the three options were done according to UK unit prices from 2008 to 2009. The prices for PT, RC1, and RC2 yield 6.9£/ft2, 7.2£/ft2, and 7.8£/ft2, respectively, which include material and placement costs for concrete, non-prestressed reinforcement, PT strands, ducts, anchors, and formwork.

Further savings for the PT option came from indirect cost, such as reduced columns and foundation material due to the lighter concrete weight, savings in cladding material from the lowered building height, and the fast construc-tion schedule.

CONCLUSIONSThe concept of sustainability is at the forefront of many

aspects of our daily lives, and the area of construction is no exception. The United Nations World Commission on Environment and Development (Brundtland 1987) defines sustainability as “meeting the needs of the present without compromising the ability of future generations to meet their own needs.”

This study shows that building sustainable structures can be achieved without compromising social well-being, structural performance, or cost. The comparison between PT and RC structures indicates that structural efficiency

Table 4—Slab parametersMaterial item* Unit PT RC1 RC2

Material weight U.S. ton 14,334 18,652 15,124 Increase in material weight U.S. ton — 4318 790

Main material type — Concrete Concrete ConcreteIncrease in construction time Days — 60 140

Increase in building height Foot — 7.9 52.5 Structural slab configuration — Flat Flat Drop beams

*Increases shown in RC1 and RC2 columns are with respect to PT option.


contributes to a building’s overall sustainability assess-ment. For the Strata project, the use of PT slabs saved approximately 25% in embodied energy (6400 GJ) and embodied carbon (797 tons of CO2) and yet it is the most economical solution. The results are based on structural efficiency alone and through an LCI of the slabs. On the social impact, the proposed ranking scheme shows that PT also has the best score for indoor living, outdoor living, and reduced construction disruption. This demonstrates that when structural efficiency is assessed at the design stage, it can result in considerable sustainability benefits. When deciding which structure type and material to use on a given building, the earlier sustainability factors are integrated into the decision-making process, the greater the possibilities of reaching sustainable solutions.

REFERENCESBrundtland, U. N., 1987, Our Common Future (Brundt-

land Commission Report)—General Assembly Resolution 42/187, Oxford University Press.

Frank, L.; Engelke, P.; and Schmid, T., 2003, Health and Community Design: The Impact of the Built Environment on Physical Activity, Island Press.

Gangolells, M.; Casals, M.; and Gasso, S. E., 2009, “A Methodology for Predicting the Severity of Environmental Impacts Related to the Construction Process of Residential Buildings,” Building and Environment, V. 44, pp. 558-571.

Gauzin-Muller, D., 2002, Sustainable Architecture and Urbanism: Concepts, Technologies, Examples, Birkhauser.

Gilchrist, A., and Allouche, E., 2005, “Quantification of Social Costs Associated with Construction Projects: State-of-the-Art Review,” Tunnelling and Underground Space Technology, V. 20, No. 1, pp. 89-104.

Guggemos, A., and Horvath, A., 2005, “Comparison of Environmental Effects of Steel- and Concrete-Framed Buildings,” Journal of Infrastructure Systems, ASCE, V. 11, No. 2, pp. 93-101.

Hammond, G., and Jones, C., 2008, Inventory of Carbon and Energy (ICE), University of Barth.

Kawai, K.; Sugiyama, T.; Kobayashi, K.; and Sano, S., 2005, “Inventory Data and Case Studies for Environ-mental Performance Evaluation of Concrete Structure Construction,” Journal of Advanced Concrete Technology, V. 3, No. 3, pp. 435-456.

Kleipis, N.; Nelson, W.; Ott, W.; Robinson, J.; Tsang, A.; Switzer, P. et al., 2001, “The National Human Activity Survey: A Resource for Assessing Human Exposure to Pollutants,” Journal of Exposure Analysis and Environmental Epidemiology, V. 11, pp. 231-252.

Nielsen, C., 2008, “Carbon Footprint of Concrete Buildings Seen in the Life Cycle Perspective,” Proceedings of the NRMCA 2008 Concrete Technology Forum, Denver, CO.

Schokker, A., 2010, The Sustainable Concrete Guide—Strategies and Examples, U.S. Green Concrete Council, Washington, DC, 89 pp.

Sweet, A., 2010, An Environmental Comparison of Framing Options in Multi-Story Building Construction, CCL, UK.

Social factor PT RC1 RC2

Construction phaseReduced negative

social impacts 1 3 2

Faster construction cycle 1 2 3

Operational phaseIndoor impact 1 1 2

Outdoor impact 1 2 3Total points (lower is better) 4 8 10

Restore PT Structures!NEW! — PTI DC80.3-12/ICRI 320.6, Guide for Evaluation and Repair of Unbonded

Post-Tensioned Concrete Structures

This publication familiarizes readers with procedures, tests, equipment, and other aspects of the evaluation and repair of post-tensioned structures.

Order in hard copy or digital format at www.post-tensioning.org/bookstore.php.


TECHNICAL PAPER

ASSESSMENT OF SECONDARY EFFECTS IN

The research was focused on determining the secondary, or hyperstatic, moment of post-tensioned concrete flat plate buildings of different dimensions, as well as investigating the secondary column axial forces induced by post-tensioning. The primary purpose of this research was to develop design charts regarding the secondary moment to aid practicing engineers in the preliminary design of post-tensioned flat plates. Prac-ticing engineers in the post-tensioned building construction industry often struggle to calculate the secondary moment of indeterminate structures because of the interrelation of many different variables, including the degree of post-tensioning and restraints, post-tensioning steel profile, and member sizes. The design aid charts produced contain the secondary moment for these provided building sizes. The other purpose of this research was to investigate the effect of post-tensioning on column axial forces and to determine the possibility of differential column shortening, which may occur at exterior building locations in very tall buildings. This paper describes the methods used in completing the aforementioned charts and analyzes the data and trends found throughout the project.

Balanced moment; column axial force; flat plates; post-tensioned concrete; primary moment; secondary moment.

INTRODUCTIONPrestressed concrete encompasses both pre-tensioned

and post-tensioned concrete structures, which both use high-strength materials as a means to counteract the stress of gravity loads that are placed on a structure. There are different areas of implementation for pre-tensioned and post-tensioned concrete; however, the focus of this research

is on cast-in-place post-tensioned concrete slabs. Post-tensioning is used for many reasons, including economy and building efficiency as well as the reduction of deflec-tion and cracking it provides. The use of post-tensioning can reduce the depth of slabs and story height, as well as improve the installations of “heating and electrical ducts, plumbing risers, and wall and partition surfaces” (Nilson et al. 2009). Post-tensioned flat plates have already been widely implemented into the design of both residential and commercial structures (Foutch et al. 1990).

This research uses the idea of the application of equiva-lent or balanced loads as a way to describe the effect of post-tensioning on the structures, that is, the load balancing method (Lin and Burns 1981). The load balancing method can be especially useful for analysis of indeterminate struc-tures such as continuous beams and two-way slabs. In post-tensioned flat plate construction, post-tensioning tendons with variable eccentricity are used to apply such balanced loads throughout the length of the slabs. Different loads can be achieved by different tendon profiles. Free-body diagrams are important tools to visually display the loads applied through post-tensioning, both axially along the tendon and vertically countering the applied loads. With slabs that use tendon eccentricity at the ends, forces at the ends of the beams or slabs may create end moments, although it is not typical for relatively thin two-way slabs.

Many different tendon profiles can be chosen for different building scenarios, and the choice depends on the necessary balanced loads. In buildings with slabs that stretch across multiple columns or supports, the shape of the tendon can be variable along the entire length of the span to best balance the applied loads. If uniformly distributed loads are being applied, the best tendon profile is typically a second-order parabolic shape. It is always important to consider not only the loads involved in the design, but also the economic aspect of the different tendon profiles, quantities of unbonded post-tensioning



tendons and bonded reinforcing bars, and slab thickness and span length (Kang and Wallace 2008).

In cast-in-place post-tensioned flat plate construction, the slab is restrained against vertical deformation at the support, and such a restraint causes secondary moments in the slab as well as secondary axial forces in the column, both of which should be considered in the design. However, determination of the induced secondary moments is very cumbersome during the preliminary design stage because of the interrelation of many different variables, including the degree of post-tensioning and restraints, post-tensioning steel profile, and member sizes. The objectives of this research are to determine the secondary moment of post-tensioned concrete flat plates, to provide design aid charts regarding this secondary moment, and to investigate the effect of the forces induced by post-tensioning on the columns as an axial force. The purpose of this paper is to describe the methods used in completing this research, to provide a summary of the data collected, and to analyze the data found throughout the project to draw conclusions about certain characteristics of post-tensioned flat plate design.

METHODOLOGYThis research was completed in two main portions,

the first involving the determination of secondary, or hyperstatic, slab moments (Msec) in indeterminate struc-tures; and the second focusing on the secondary effects of post-tensioning on column axial forces. The process for conducting this research involved using a finite element program for both portions of the research.

The secondary moment (Msec) is defined as the moment due to reactions induced by prestressing (with a load factor of 1) according to ACI 318-08 (Section 18.10.3) (ACI Committee 318 2008). In monolithic concrete construction, as the columns constrain transla-tion—deflection and rotation of the slab that are caused by post-tensioning—additional reactions are developed in the columns and these additional column axial forces and moments generate hyperstatic (or secondary) moments and shears in the slab (Alaami and Bommer 1999). There are two methods to determine the Msec value: 1) the direct method; and 2) the indirect method. In the direct method, the column reactions due to post-tensioning can be first obtained by imposing balanced loads on the slabs, and then these column reactions are separately applied to each slab at the top and bottom to determine the secondary moment Msec. In the indirect method, which was used in this research, first the balanced moment Mbal in the concrete generated

by the post-tensioning forces was found for model build-ings of different dimensions. Next, the primary moment (Mp = ePe) was found by evaluating the eccentricities e of the placement of the tendons at certain locations and the effective post-tensioning forces Pe. Finally, from this information, the secondary moment Msec was calculated as (Mbal – Mp). Both the direct and indirect methods would yield the same solution when using the Equivalent Frame Method (refer to ACI 318-08 Sections 13.7 and 18.12.1) (Alaami and Bommer 1999).

For the second portion of the research, the column axial forces induced solely by post-tensioning were found and then analyzed to consider other effects, including differential column shortening. A detailed step-by-step procedure is provided in the following sections.

Model buildingsA total of 96, 3-bay by 3-bay, two-story model build-

ings were created in a structural analysis program SAP2000 (CSI 2009) as shown in Fig. 1 and Tables 1 and 2 (refer to Fig. 2 for notation and directions). The selected dimen-sions of the buildings are typical of those used in actual post-tensioned flat plate construction (PTI Committee DC-20 2010). The dimensions were input to the program, including the story height, bay width, number of bays in each direction, and number of stories. Fixed joint restraints were defined for the bottom of the columns. The concrete used was assumed to have a compressive strength of 5000 psi. For each dimension provided, three trials were used to explore the effect of different column sizes. Keeping all other variables consistent, only the column

Fig. 1—Office flat plate buildings with 20 x 25 ft slab panels.


sizes were changed from 20 x 20 in. to 24 x 24 in. and 28 x 28 in. The slab-beam sections were defined to function as equivalent slab-beams, using a length l2 reaching the full transverse span with a thickness h, as provided, and a width depending on the location of the slab-beam and the tributary area. The interior slab-beams were defined with a width equivalent to the transverse width of the bay, while exterior slab-beams received half of this width plus half of the column transverse width (refer to Fig. 2). The equivalent slab-beams were applied in both directions. The end offsets were defined as half the distance of the column width, embedded halfway into the column, giving the slab-beams a rigid-zone factor of 1. The column stiffness was not reduced, as the stiffness of torsional elements (refer to Section 13.7.2.3 of ACI 318-08) is likely to be significantly higher than that of nonprestressed concrete flat plates due to the in-plane (membrane) constraints provided by the post-tensioning. This was shown from previous experi-mental studies (Kang 2004; Kang and Wallace 2005) and also is commonly used at both the service limit and ulti-mate limit states (under gravity loads) in practice (PTI Committee DC-20 2010; also refer to Section 4.3.1 of PTI DC20.9-11 [PTI Committee DC-20 2011]). Figure 1 shows a sample of one of the buildings within the program.

First, the gravity loads were determined for each building model and applied as trapezoidal loads along the

modelsBay width in

transverse direction (x-direction), ft

Slab span length in longitudinal direction

(y-direction), ftSlab thickness,

in.

20

25 7.527 830 8.5

25

25 7.527 830 8.5

30

25 8.527 8.530 8.5

35

25 1027 1030 10

building modelsBay width in

transverse direction (x-direction), ft

Slab span length in the longitudinal direction

(y-direction), ftSlab thickness,

in.

20

21 5.524 6.527 7.530 832 8.5

25

21 724 727 7.530 832 8.5

28

21 7.524 7.527 7.530 832 8.5

30

21 824 827 830 832 8.5

Fig. 2—Model building plan.


length of each slab-beam to account for accurately shaped tributary areas, which can be seen in Fig. 3. For buildings of different bay widths in the two principal directions, the longer bay direction has a trapezoidal gravity load, whereas the load distribution of the shorter bay is triangular (Fig. 3). If the span lengths along both principal directions are equal, the tributary areas are also equal for the slab-beams in each of these directions (Fig. 4).

A dead load was applied based on a unit weight of concrete of 150 lb/ft3 for both the office and residential buildings. A sustained dead load of 30 lb/ft2 and a live load of 50 lb/ft2 were also applied to the office buildings, while a sustained dead load of 10 lb/ft2 and a live load of 55 lb/ft2 were applied to the residential buildings. These loads are commonly used in practice (PTI Committee DC-20 2010). Figures 3 and 4 show the loads applied to the building using the load distribution caused by the tribu-tary areas. To determine the factored gravity moments Mu, load factors of 1.2 and 1.6 were used for the combined dead

loads (sustained dead load in addition to the self-weight of the concrete) and the live loads, respectively, considering only the factored gravity load combination.

Balanced moments due to post-tensioningThe next step involved finding the balanced moment

Mbal due to post-tensioning. For this part, the buildings were again created in SAP2000 (CSI 2009) using the same methods previously discussed. This time, the balanced loads ωbal induced by post-tensioning were applied instead of the factored gravity loads. The balanced loads were determined by analyzing the tendon profiles. Parabolic tendon profiles were used, as can be seen in Fig. 5. Also, horizontal end forces due to post-tensioning were applied at the perimeter of each floor (Fig. 5).

The number of tendons was determined to meet ACI 318 flexural and minimum precompression require-ments. The tendon starts at the center of gravity of the concrete slab (c.g.c.) at the exterior. Specified clear covers governed the eccentricities of the tendon at the peak of the parabolic shape. The distance from the slab bottom to the lowest point in the parabolic center of gravity of the pressing force (c.g.s.) curve in the exterior span was 1.75 in. (Fig. 5). This point is located in the middle of the exterior span. The highest point of the c.g.s. curve can be

Fig. 3—Gravity load distribution based on tributary area for model buildings with rectangular panels.

Fig. 4—Gravity load distribution based on tributary area for model buildings with square panels.


found over the interior column centerline, 1.5 in. from the top of the slab. The distance from the soffit to the lowest c.g.s. for the interior span is 1.25 in. The tendon c.g.s values used are based on typical practice (PTI Committee DC-20 2010) and consistent with those in Chapter 6 of PTI DC20.9-11.

Another important aspect of parabolic tendon profiles is the presence of inflection points along the length of the tendon. In this profile, two can be found in each span. These changes in curvature create both upward and downward forces due to post-tensioning. The change in direction of the force at the inflection points of the tendon is illustrated in Fig. 5. To provide a smooth transition between the changes in positive and negative curvature, the inflection points must be located at specific locations that satisfy the following conditions (refer to Fig. 6 for derivation and notation).

a b

a bl l

=(1)

c d

c dl l

= (2)

where a, b, c, and d are the vertical distances between the c.g.s. and the inflection point as shown in Fig. 5, and la, lb, lc, and ld are the lengths of portions of the span considered as shown in Fig. 5. These conditions were based on the basic geometry of the tangential force at the location of the inflection points. The heights and lengths shown in Fig. 5 are dependent on one another in the determination of the inflection points. The geometrical conditions ensured that the length of the slab span and the thickness of the slab were both considered accurately, as well as ensured that the angles shown in Fig. 6 were equal. Although many different scenarios related length between inflection points and distance between inflection point and maximum and minimum heights of the tendon in a way that satisfied the tangential force equilibrium, typical tendon profiles influenced the final choice of inflection point location. In this study, the inflection points were located at 8 and 92% of the length of the span (~ l2/12), with the lowest point of the tendon at the exact center of the span, for both the interior and exterior spans.

The balanced loads applied through post-tensioning involved upward and downward uniformly distributed

Fig. 5—Tendon profile and balanced loads induced by post-tensioning.

Fig. 6—Free body diagram of tendon at exterior half of exte-rior span.


forces of differing magnitudes due to the presence of these inflection points. An example of the loads induced by post-tensioning can be seen in Fig. 5. The placement of the inflection points at these specific positions resulted in a smooth transition between positive and negative curvature as well as an equilibrium of vertical balanced loads acting on the concrete slab within a given floor. The uniform downward load applied by each tendon at the left-hand edge of the exterior span (refer to Fig. 5 or 6) was found using Eq. (3), while the uniform upward load was found using Eq. (4).

sin tandownward e a e a ea

aP P P

l⎛ ⎞

ω = θ ≈ θ = ⎜ ⎟⎝ ⎠2

(3)

sin tanuplift e b e b eb

bP P P

l⎛ ⎞

ω = θ ≈ θ = ⎜ ⎟⎝ ⎠2 (4)

where Pe is the total effective stress of tendons,

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