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PTI JOURNALDecember 2012 • V. 8 • No. 2
JOURNAL OF THE POST-TENSIONING INSTITUTE
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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
38800 Country Club Drive
Farmington Hills, MI 48331 Phone: (248) 848-3184
Fax: (248) 848-3181 Web: www.post-tensioning.org
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
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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.
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PTI JOURNAL | December 2012 3
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
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2013 PTI Convention
www.post-tensioning.org
Save the date
May 5-7, 2013 • Scottsdale, AZ
• Technical Sessions
• Committee Meetings
• Networking Events
• 2013 PTI Awards Dinner
• Industry Trade Show
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PTI JOURNAL | December 2012 5
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.
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6 December 2012 | PTI JOURNAL
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)
PTS-2, PTS-2CR16-1/4 in. strands
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)
26-No. 3 at top and 9-No. 3 at bottom
each fixed end 0.0276 (0.7)
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)
27-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) 5362 (37)
PTS-6, PTS-6CR16-1/4 in. strands
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.
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PTI JOURNAL | December 2012 7
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).
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8 December 2012 | PTI JOURNAL
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.
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PTI JOURNAL | December 2012 9
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.
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10 December 2012 | PTI JOURNAL
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).
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PTI JOURNAL | December 2012 11
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.)
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12 December 2012 | PTI JOURNAL
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).
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PTI JOURNAL | December 2012 13
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.
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14 December 2012 | PTI JOURNAL
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).
Fig. 21—Pressure-deflection relationship (PTS-2 and
PTS-2CR).
Fig. 22—Pressure-deflection relationship (PTS-3 and
PTS-3CR).
Fig. 23—Pressure-deflection relationship (PTS-4 and
PTS-4CR).
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PTI JOURNAL | December 2012 15
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.
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16 December 2012 | PTI JOURNAL
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).
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PTI JOURNAL | December 2012 17
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.
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18 December 2012 | PTI JOURNAL
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—
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PTI JOURNAL | December 2012 19
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.
Meier, U., and Kaiser, H., 1991, “Reprinted from Advanced
Composite Materials in Civil Engineering Structures,” Proceedings
MT Div/ASCE/Las Vegas, Jan. 31, pp. 224-229.
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.
PTI Committee DC-20, 2011, “Guide for Design of Post-Tensioned
Buildings (PTI DC20.9-11),” Post-Tensioning Institute, Farmington
Hills, MI, 74 pp.
Rosenboom, O.; Hassan, T. K.; and Rizkalla, S., 2007, “Flexural
Behavior of Aged Prestressed Concrete Girders Strengthened with
Various FRP Systems,” Construction and Building Materials,
Elsevier, V. 21, pp. 764-776.
Structural Group, Inc., 2002, “Wabo®-M-Brace Composite
Strengthening System Engineering Design Guidelines,” May, Hanover,
MD.
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.
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20 December 2012 | PTI JOURNAL
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
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.
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PTI JOURNAL | December 2012 21
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.
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22 December 2012 | PTI JOURNAL
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
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PTI JOURNAL | December 2012 23
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.
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24 December 2012 | PTI JOURNAL
• 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.
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PTI JOURNAL | December 2012 25
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.
-
26 December 2012 | PTI JOURNAL
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
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.
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PTI JOURNAL | December 2012 27
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.
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28 December 2012 | PTI JOURNAL
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.
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PTI JOURNAL | December 2012 29
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.
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30 December 2012 | PTI JOURNAL
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.
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PTI JOURNAL | December 2012 31
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,