transverse
diaphragms
and unbonded
CFrP posttensioning
in box-beam
bridges
Nabil F. Grace,
Elin A. Jensen,
Tsuyoshi Enomoto,
Vasant A. Matsagar,
Eslam M. Soliman,
and Joseph Q. Hanson
Longitudinal cracking in deck slabs over shear keys is a
common distress in prestressed concrete box-beam highway bridges. These cracks can be initiated by a drastic thermal gradient and are further propagated as a result of traffic
loads. Longitudinal cracks can also develop because of
differential rotation between the adjacent box beams due to
eccentric application of the service load.1 In addition, longterm neglect of preventive maintenance, improper handling during production and construction, and inadequate
shear-key performance can cause longitudinal cracks in
concrete deck slabs.2 Furthermore, the longitudinal cracks,
combined with the excessive relative vertical displacements
between the adjacent box beams, lead to failure of the shear
key.3
Editor’s quick points
n Carbon-fiber-reinforced-polymer (CFRP) strands alleviate many
construction challenges when used as transverse posttensioning in box-beam bridges.
n The use of unbonded transverse post-tensioning of CFRP
strands for replacement of strands that are damaged or deteriorated is considered.
n The results of testing of a model using transverse, post-tensioned CFRP strands are presented.
The longitudinal cracks may compromise the waterproofing action of the deck and allow water and chemicals to
penetrate through the concrete, causing steel corrosion and
eventually reducing the serviceability and longevity of the
bridge.4 Corroded steel may cause additional cracking and
can lead to spalling of the concrete in the surrounding area.
The use of transverse post-tensioning force has been
considered a viable method of preventing the development of longitudinal cracks in the deck slab of box-beam
bridges. Furthermore, the misalignment of the transverse
post-tensioning ducts due to differential cambers in
adjacently placed box beams poses a great construction
challenge. Alternatively, carbon-fiber-reinforced-polymer
S p r i n g 2010 | PCI Journal
109
Deck-slab longitudinal reinforcement
(no. 3 steel bars) at 6 in. spacing
Oval-shaped duct 4.5 in. 6 in.
for transverse post-tensioning
Styrofoam
m
Hanger bar (no. 4 steel bar) Top reinforcement (no. 4 steel bars)
6 in.
6 in.
in.
Bottom reinforcement (no. 4 steel bars)
7.5 ft
5 in.
7.5 ft
Deck-slab transverse reinforcement
(no. 3 steel bars) at 6 in. spacing
CFCC 1 7 0.67 in. diameter strands
Stirrups (no. 3 steel bars) at 5 in.
spacing
7.5 ft
7.5 ft
6 in.
in.
6 in.
31 ft
32 ft
Figure 1. This diagram shows the longitudinal section of the bridge model. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m; no. 3 = 10M; no. 4 = 13M.
(CFRP) strands have advantages over the conventional
steel strands, such as greater longitudinal axial strength,
less thermal expansion, and less density.5 Because they
are noncorrosive, CFRP strands are considered suitable
for prestressed concrete bridges in moderate to aggressive
environments.6 The use of unbonded CFRP strands for
transverse post-tensioning has been successfully implemented in the field with the construction of the Bridge
Street Bridge, the first three-span CFRP prestressed concrete highway bridge in the United States.7
Another major issue in current construction practice for
side-by-side box-beam bridges is the replacement of
damaged or deteriorated exterior or interior beams. In
prestressed concrete highway bridges, a high-impact load
on the fascia box beams is potentially induced by collision
of overheight vehicles.8 Damage resulting from a collision by an overheight vehicle may require replacement of
the entire superstructure when individual beams cannot
practically be replaced. In side-by-side precast, prestressed
concrete box-beam bridges, replacing a damaged beam is
challenging when bonded transverse post-tensioning steel
strands are used. The use of unbonded transverse post-tensioning strands could be an alternative to using the bonded
strands in side-by-side box-beam bridges.
To address these problems, the Michigan Department of
Transportation (MDOT) funded an extensive experimental
investigation as conducted on a half-scale, 30-deg-skew,
precast, prestressed concrete side-by-side box-beam bridge
model. The bridge model was constructed, instrumented,
and tested using unbonded, transverse post-tensioned
CFRP strands. Strain- and load-distribution tests were conducted to evaluate the effect of the level of transverse posttensioning forces and the number of diaphragms on the
behavior of the bridge model in the transverse direction.
This paper presents the details of the construction, experimental test procedures, discussions of the test results, and
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conclusions on the bridge model. Noncorrosive unbonded
carbon-fiber-composite-cable (CFCC) strands were examined and recommended for their use as transverse posttensioning strands. The results of this research investigation quantify the influence of the level of transverse posttensioning force and the number of transverse diaphragms
on improving the deformation response of side-by-side
box-beam bridges.
In addition, a practical and simple approach for the replacement of a damaged beam was proposed and successfully implemented. Currently, MDOT is scheduling the
deployment of the results of this investigation in a twospan, box-beam bridge that will be constructed in 2010
over highway M-39 in Michigan.
Experimental investigation
A half-scale, 30-deg-skewed, precast, prestressed concrete
side-by-side box-beam bridge model was designed and
constructed in the Center for Innovative Materials Research
at Lawrence Technological University. The bridge model
consisted of four precast, prestressed concrete box beams
designated as B-1, B-2, B-3, and B-4. The box beams were
placed side by side to form full-depth female-to-female keyways that facilitated the construction of the shear keys.
In addition, five transverse diaphragms were provided at
an equal spacing of 7.5 ft (2.3 m) according to MDOT
specifications.9 A 3-in.-thick (75 mm) reinforced deck slab
was placed over the box beams. The span of the bridge
model was 31 ft (9.5 m). Figures 1 and 2 show the longitudinal and cross-section details of the bridge model.
Bridge-model construction
The top and bottom reinforcement for each box beam
consisted of four no. 4 (13 M) deformed steel reinforcing
bars. In addition, three 0.5-in.-diameter (13 mm), seven-
Individual box
beam
Deck-slab longitudinal
reinforcement
(no. 3 steel bars) at 6 in. spacing
Deck-slab transverse
Top steel
reinforcement
reinforcement
(no. 4 steel bars)
Shear
1.88
2 in.
key
1.5 in.
in.
in.
in.
3 in.
Stirrups (no. 3 steel bars) at 5 in. spacing
Deck
slab
5.25 in.
1 in.
B-1
11 in.
B-4
B-3
B-2
6 in.
in.
2.75 in.
1.94 in.
Bottom pretensioning steel
strands
Bottom steel
reinforcement
(no. 4 steel bars)
1 in.
18 in.
CFCC 1 7 0.67-in.-diameter strands
6.25 ft
Figure 2. This drawing illustrates the cross section of the bridge model. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m; no. 3 = 10M; no. 4 = 13M.
wire steel prestressing strands were provided. The stirrups
protruded 1.5 in. (38 mm) from the top surface of the box
beams to achieve composite action between the box beams
and deck slab.
To simulate differential camber commonly observed in the
field, different levels of prestressing forces were applied
to the individual box beams. The two exterior box beams
were prestressed with an average force of 20 kip/strand
(90 kN/strand), while the two interior box beams were
prestressed with an average force of 25 kip/strand (111
kN/strand).
To account for potential differential camber between the
adjacent box beams, an oval-shaped duct was introduced at
each transverse diaphragm to accommodate the unbonded
transverse post-tensioning CFCC strands rather than the
traditional circular duct. The oval-shaped ducts were created
by inserting aluminum tubes at the appropriate transverse
diaphragm locations. Pieces of 5-in.-deep (127 mm), 10-in.wide (250 mm) Styrofoam were used to create the hollow
portion within the cross section of the box beams and were
placed at the midheight of the box-beam cross section.
The box beams were cast from concrete with average 28day compressive strength of 6300 psi (43 MPa). Styrofoam
gaskets were attached at the ends of each transverse duct
between the adjacent box beams to avoid the possible leakage of shear-key grout into the ducts.
The 3-in.-thick (75 mm) cast-in-place concrete deck slab
was reinforced with no. 3 (10M) deformed steel reinforc-
Table 1. Characteristics of CFCC strands and steel reinforcement
Grade
Nominal
diameter,
in.
Effective
crosssectional
area, in.2
Linear
density,
lb/in.
Minimum
yield
strength,
ksi
Breaking
load, kip
CFCC seven-wire strands*
n.a.
0.67
0.23
16.2
n.a.
78.4
Nonprestressing steel no.
4 bar
60
0.5
0.2
8.0
60
18.0
90
29,000
9
270
0.5
0.153
6.24
229.5
41.3
250
27,000
1
0.375
0.11
4.512
60
9.9
90
29,000
9
Seven-wire steel prestressing strands
Steel stirrups, no. 3 bars
60
Tensile
strength,
ksi
Tensile
modulus,
ksi
0.34
22.3
Elongation
at break
1.5
* Data are from Tokyo Rope Mfg. Co. Ltd., CFCC Quality Report (2007).
Note: CFCC = carbon-fiber-composite cable; n.a. = not applicable. 1 in. = 25.4 mm; 1 lb = 4.448 N; 1 kip = 4.448 kN; 1 ksi = 6.895 MPa;
no. 3 = 10M; no. 4 = 13M.
PCI Journal | S p r i n g 2010
111
Cracked deck slab (C) In this phase, the concrete
deck slab and the shear keys were partially cracked, simulating the longitudinal cracks developed in the deck over
the shear keys. The longitudinal cracks were initiated by
applying a single point load to individual beams while partially restraining the other three beams.
Damaged-beam replacement (R) This phase
involved the replacement of an assumed damaged exterior
box beam with a new box beam, new shear key, and portion
of a reinforced deck slab tied to the existing concrete deck
slab. The replacement procedure involved several steps:
1.
A full-depth cut was made in the exterior shear key
C-C (Fig. 4) between box beams B-3 and B-4.
2.
Horizontal 0.75-in.-diameter (19 mm), 12-in.-deep
(300 mm) holes were drilled into the deck slab using
an electric hammer drill to accommodate the new
concrete deck slab’s transverse reinforcement.
3.
The new exterior beam B-5 was placed adjacent to
box beam B-3, and the shear key between the two
beams was grouted.
4.
The test program was conducted in three distinct phases
similar to what a highway box-beam bridge might experience during its service life span.
The concrete deck slab’s longitudinal reinforcement
was placed and tied at an equal spacing of 6 in. (150
mm) center to center, and its transverse reinforcement was placed in the holes with a high-performance
epoxy resin.10
5.
Uncracked deck slab (UC) The uncracked concrete
deck-slab phase was used as a reference phase for the investigation. This phase simulated a typical newly constructed
highway bridge without any longitudinal cracks. Both loadand strain-distribution tests were conducted at this phase.
The deck-slab formwork was then constructed, followed by casting of the deck slab with the same mixture proportions used for casting the original concrete
deck slab.
Three major tests were conducted on the bridge model:
transverse strain distribution, load distribution, and ulti-
Figure 3. This photo depicts the general view of the precast, prestressed concrete
box-beam bridge model.
ing bars spaced at 6 in. (150 mm) center-to-center in the
longitudinal and transverse directions. The deck slab was
cast using concrete with a 28-day average compressive
strength of 4600 psi (32 MPa). The CFRP reinforcement
used for transverse post-tensioning was 0.67-in.-diameter
(17 mm) CFCC seven-wire strands. Table 1 shows the
mechanical properties of the CFCC strands and steel reinforcement. Figure 3 shows the completed bridge model.
Test program
Centerline
Four at 22.5 in.
= 7.5 ft
Four at 22.5 in.
= 7.5 ft
18.5 in.
30 deg
Two at 19 in.
= 38 in.
18.5 in.
9
8
7
6
5
4
3
2
1
C
B
Shear-key
locations
A
Strain gauges in the
transverse direction
Figure 4. This diagram shows the shear-key locations and strain-gauge layout on the deck slab. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m.
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B-1
80 kip
40 kip
20 kip
B-2
B-4
B-3
80 kip
40 kip
20 kip
15 kip
80 kip
40 kip
20 kip
80 kip
40 kip
20 kip
80 kip
40 kip
20 kip
Figure 5. The load-distribution test applies transverse post-tensioning forces at five diaphragms. Note: 1 kip = 4.448 kN.
mate load. Following are the procedures used during the
tests.
Transverse-strain-distribution test The straindistribution test was conducted by applying different levels
of transverse post-tensioning forces at different diaphragms
using unbonded CFCC strands. This test was conducted
during the uncracked-deck-slab phase only. The transverse
strains were monitored using 27 strain gauges installed on
the top surface of the deck slab at the shear-key locations
and oriented in the transverse direction (Fig. 4).
Two unbonded CFCC strands provided transverse posttensioning forces at each diaphragm.
Four levels of transverse post-tensioning forces were
selected: 0 kip, 20 kip, 40 kip, and 80 kip (0 kN, 90 kN,
180 kN, and 360 kN). These forces were applied at each
diaphragm and were distributed equally between the two
CFCC strands. These transverse post-tensioning force
levels were varied along with number of diaphragms
receiving the forces (three to five diaphragms). In the
three-diaphragm case, the transverse post-tensioning forces
were applied at the midspan and end diaphragms. In the
four-diaphragm case, the transverse post-tensioning forces
were applied at the quarter-span and end diaphragms. In
the five-diaphragm case, the transverse post-tensioning
forces were applied at all five diaphragms.
Load-distribution test The load-distribution test was
conducted by applying a single point load of 15 kip (67 kN)
on each box beam at the midspan for different arrangements
of the transverse post-tensioning forces. This load level
was selected to avoid potential cracking problems. The corresponding deflections were recorded using linear-motion
transducers attached at the midspan of all box beams.
Figure 5 shows the arrangement of the load-distribution
test for the case of five diaphragms. The load-distribution
test was conducted on all three phases of the test program.
Ultimate-load test The ultimate-load test was conducted to determine the ultimate flexural load-carrying
capacity of the bridge model and to evaluate the response of
the unbonded transverse post-tensioning CFCC strands up
to failure of the bridge model. A transverse post-tensioning
force of 80 kip (360 kN) was applied at all five diaphragms
before testing. The bridge model was loaded eccentrically
at the midspan of box beam B-2 using a two-point loading
frame (Fig. 6).
The transverse post-tensioning forces were monitored
during the test using load cells attached to the dead end of
the CFCC strands. Four linear-motion transducers were
also installed at the midspan of each box beam to monitor
the corresponding deflections. Five loading and unloading
cycles were conducted before failure by increasing and
releasing the applied load at a rate of about 15 kip/min (67
kN/min).
Experimental results
and discussion
The results of the load- and strain-distribution tests were
used to evaluate the effect of the level of transverse
post-tensioning forces and number of diaphragms that the
force was applied to on the behavior of the bridge model
in the transverse direction. In addition, the results of the
ultimate-load test were used to evaluate the response of the
unbonded transverse post-tensioning arrangement during
catastrophic failure.
Strain-distribution test
Effect of transverse post-tensioning force
level on strains It was observed that by increasing the
levels of the transverse post-tensioning forces, the transverse strains increased proportionally at all points located
along the transverse diaphragms (Fig. 7). For example,
PCI Journal | S p r i n g 2010
113
B-1
40 kip
40 kip
B-2
B-3
P
B-5
Linear-motion transducers
Load cell
Strain gauges
40 kip
40 kip
Two-point loading frame
40 kip
40 kip
7.5 ft
31 ft
40 kip
40 kip
40 kip
40 kip
6.25 ft
Figure 6. The experimental-setup ultimate-load test of the bridge model included a two-point loading frame, linear-motion transducers, and strain gauges. Note: AASHTO
LRFD = The American Association of State and Highway Transportation Officials' AASHTO LRFD Bridge Design Specifications. 1 ft = 0.305 m; 1 kip = 4.448 kN.
Figure 7. This graph shows the transverse strains along shear key A-A for transverse post-tensioning forces at five diaphragms.
for the case of five diaphragms, point A-9 (Fig. 4), located
on the midspan diaphragm, experienced transverse strains
of -192 × 10-6, -94 × 10-6, and -56 × 10-6 due to transverse
post-tensioning forces of 80 kip, 40 kip, and 20 kip (360
kN, 180 kN, and 90 kN), respectively. Similar behavior was
observed in the cases of three and four diaphragms.11 The
linear relation between the transverse post-tensioning forces
and the corresponding transverse strains indicated an elastic
behavior of the deck-slab concrete.
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Effect of number of diaphragms on strains
As expected, for the case of five diaphragms the points
located over the transverse diaphragms experienced higher
transverse strains relative to those located between the diaphragms (Fig. 8), where the spacing between the transverse
post-tensioning forces was 7.5 ft (2.3 m). For instance,
point A-5, located over the quarter-span diaphragm, experienced a transverse strain of -87 × 10-6 due to a transverse
post-tensioning force of 80 kip (360 kN) applied at each
of the four diaphragms. Alternatively, point A-3, located
between the quarter-span and end diaphragms, experienced
Distance from bridge end, mm
3000
2500
2000
1500
1000
0
500
0
100
80 kip
80 kip
80 kip
80 kip
AB - axis
C- axis
AASHTO LRFD limit
80 kip
180
160
140
Centerline
120
100
80
60
40
Distance from bridge end, in.
80 kip
80 kip
200
-6
3500
10
4000
Transverse strain
4500
0 300
20
80 kip
C
40 kip
40 kip
B
Transverse strain gauges
A
80 kip
9
80 kip
80 kip
8
7
6
5
4
3
2
1
Figure 8. This graph shows the transverse strain distribution for a transverse post-tensioning force of 80 kip applied at five diaphragms. Note: AASHTO LRFD = The American Association of State and Highway Transportation Officials' AASHTO LRFD Bridge Design Specifications. 1 kip = 4.448 kN.
insignificant transverse strain due to the same arrangement
of transverse post-tensioning forces.
Similar behavior was observed when 20 kip and 40 kip (90
kN and 180 kN) transverse post-tensioning forces were applied.12 This was attributed to the nonuniform distribution
of the transverse post-tensioning forces along the span of
the bridge model, resulting in high local transverse strains
in the regions near the diaphragms. In the case of four
diaphragms (Fig. 9), where the transverse post-tensioning
forces were applied to the quarter-span diaphragms at
a spacing of 15 ft (4.6 m), low transverse strains were
observed at the midspan region, and high transverse strains
were observed at the end and quarter-span diaphragms. In
general, the bridge model experienced the highest transverse strains near the transverse post-tensioning force locations, and the transverse strains decreased as the distance
from the transverse post-tensioning forces increased.
Comparison with AASHTO LRFD recommendations The American Association of State Highway
and Transportation Officials’ (AASHTO’s) AASHTO
LRFD Bridge Design Specifications recommend a minimum transverse prestress of 0.25 ksi (1.7 MPa) developed
due to transverse post-tensioning forces,13 herein called
the AASHTO LRFD specifications limit. However, the
AASHTO LRFD specifications did not provide further
details about the region or the area at which the limit should
be maintained. To compare the measured transverse strains
with the AASHTO LRFD specifications limit, it was converted to an equivalent limit of 62 × 10-6 and compared with
the measured strains at the deck slab (Fig. 7).
It was observed that at least eight points experienced
transverse strains below 62 × 10-6 for each arrangement of
the transverse post-tensioning forces (Fig. 8). Furthermore,
all of the 27 points experienced transverse strains less than
that of the AASHTO LRFD specifications limit when the
transverse post-tensioning force of 20 kip (90 kN) was applied. This was mainly because of the nonuniform distribution of the transverse post-tensioning forces along the span
or inadequate levels of transverse post-tensioning forces.
Similar trends were observed for the transverse strains
when the same transverse post-tensioning force levels were
applied through three and four diaphragms.
Load-distribution test
Effect of level of transverse post-tensioning
forces The loaded beam always experienced the largest
deflection, and the deflection in the other beams decreased
as distance from the loaded beam increased. This was true
PCI Journal | S p r i n g 2010
115
Distance from bridge end, mm
4000
3500
3000
2500
2000
1500
1000
0
500
-100
80 kip
80 kip
80 kip
A-axis
B-axis
C-axis
AASHTO LRFD limit
80 kip
180
160
140
120
100
80
60
40
-200
20
0
Transverse strain
10
0
-6
4500
-300
Distance from bridge end, in.
Centerline
80 kip
80 kip
C
40 kip
40 kip
B
A
Transverse strain gauges
80 kip
80 kip
9
8
7
6
5
4
3
2
1
Figure 9. This graph shows the transverse strain distribution for a transverse post-tensioning force of 80 kip applied at four diaphragms. Note: AASHTO LRFD = The American Association of State and Highway Transportation Officials' AASHTO LRFD Bridge Design Specifications. 1 kip = 4.448 kN.
in both the cracked and repaired phases (Fig. 10 and 11).
It was observed that the differences in these deflections
decreased as the level of transverse post-tensioning forces
increased. For instance, when box beam B-4 was loaded
in the cracked phase and different levels of the transverse
post-tensioning forces were applied at all five diaphragms,
the differences in deflection between box beams B-1 and
B-4 were 0.22 in., 0.05 in., 0.04 in., and 0.03 in. (5.59 mm,
1.27 mm, 1.02 mm, and 0.76 mm) for the transverse posttensioning forces of 0 kip, 20 kip, 40 kip, and 80 kip (0 kN,
90 kN, 180 kN, and 360 kN), respectively.
observed in the cracked phase, when transverse post-tensioning forces of 0 kip, 20 kip, 40 kip, and 80 kip (0 kN,
90 kN, 180 kN, 360 kN) were applied to five diaphragms,
were 0.42 in., 0.34 in., 0.33 in., and 0.30 in. (10.67 mm,
8.64 mm, 8.38 mm, and 7.62 mm) for the loaded exterior
beam B-4 and 0.36 in., 0.32 in., 0.31 in., and 0.29 in. (9.14
mm, 8.13 mm, 7.87 mm, and 7.37 mm) for the loaded
interior beam B-2. This clearly shows that increasing the
transverse post-tensioning forces significantly improved
the load distribution among the adjacent beams in the
cracked and repaired phases.
Similarly, the differences in deflections in the repaired
phase were 0.17 in., 0.05 in., 0.05 in., and 0.03 in. (4.32
mm, 1.27 mm, 1.27 mm, and 0.76 mm) for the same levels
of the transverse post-tensioning forces. Moreover, the
deflection of box beams B-3 and B-5 was reduced in the
beam-replacement phase compared with the cracked-deckslab phase (Fig. 10). This is attributed to increased stiffness
caused by beam replacement and repair of the shear key
and deck slab.
In addition, it could be deduced that applying a transverse
post-tensioning force of 40 kip (180 kN) is adequate to
hold the adjacent beams to act as a unit when the bridge
model was subjected to the vertical load. However, it did
not satisfy the AASHTO LRFD specifications limit of 0.25
ksi (1.7 MPa).
Furthermore, the deflections of the loaded interior beams
were lower than that of the loaded exterior beam regardless of the level of transverse post-tensioning force and the
phase of the bridge model (Fig. 10 and 11). The deflections
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Effect of number of diaphragms Figures 12 and
13 show the effect of the number of transverse diaphragms
on the deflection of the bridge model. The number of diaphragms did not affect the differences in deflection between
the loaded beam and the far exterior box beam in the
uncracked-deck-slab phase. However, for the cracked and
beam-replacement phases, the three- and five-diaphragm
Width = 75 in.
Figure 10. This graph shows the deflection of the bridge model while loading beam B-4 at different levels of transverse post-tensioning force. Note: C = cracked deck slab;
R = damaged beam replacement; P = load; TPT = transverse post-tensioning. 1 kip = 4.448 kN.
Figure 11. This graph shows the deflection of the bridge model while loading beam B-2 at different levels of transverse post-tensioning force. Note: C = cracked deck slab;
P = load; TPT = transverse post-tensioning; UC = uncracked deck slab. 1 kip = 4.448 kN.
PCI Journal | S p r i n g 2010
117
Width = 75 in.
Figure 12. This graph shows the deflection of the bridge model while loading beam B-1 with a different number of diaphragms. Note: C = cracked deck slab; P = load;
TPT = transverse post-tensioning; UC = uncracked deck slab. 1 kip = 4.448 kN.
Width = 75 in.
Figure 13. This graph shows the deflection of the bridge model while loading beam B-3 with a different number of diaphragms. Note: C = cracked deck slab; P = load;
R = damaged beam replacement; TPT = transverse post-tensioning. 1 kip = 4.448 kN.
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Deflection, mm
104 kip, 10.55 in.
B-1
B-2
B-3
Loading points
B-5
Deflection sensor at beam B-2
80 kip
80 kip
31 ft
14 in.
80 kip
80 kip
6.25 ft
Load, kN
Load, kip
80 kip
11.5 kip, 27.04 in.
Deflection, in.
Figure 14. This graph shows the load-deflection response of beam B-2 for different loading and unloading cycles. Note: 1 ft = 0.305 m; 1 kip = 4.448 kN.
cases resulted in lower differences in deflections compared
with the four-diaphragm case. Typically, the differences
in deflections between box beams B-1 and B-4, when box
beam B-1 was loaded in the uncracked phase, were 0.06 in.,
0.04 in., and 0.03 in. (1.52 mm, 1.02 mm, and 0.76 mm),
corresponding to a transverse post-tensioning force of 80
kip (360 kN) applied to three, four, and five diaphragms,
respectively.
However, the differences in deflections between box
beams B-1 and B-4 in the cracked phase were 0.05 in.,
0.06 in., and 0.04 in. (1.27 mm, 0.52 mm, and 1.02 mm),
corresponding to the similar arrangement of transverse
post-tensioning. Therefore, the five-diaphragm case outperformed the three-diaphragm case in terms of effectively
distributing the applied vertical load, especially in the
cracked and the repaired phases of the bridge model.
the ultimate load cycle, it was observed that all box beams
deflected simultaneously regardless of the levels of the
applied load until the complete failure of the bridge model
occurred.14
Failure mode The mode of failure was a typical ductile
flexural failure for the entire bridge model. The failure
started by initiation and propagation of the flexural tensile
cracks at the soffit of the box beams in the midspan region.
This was followed by yielding of the bottom reinforcement,
which resulted in large deformation of the bridge model
near the area of constant load. The yielding of the bottom
reinforcement was followed by crushing of the deck-slab
concrete across the entire width of the bridge model near
the midspan (Fig. 15). All four box beams failed simultaneously, which demonstrated the effectiveness of the unbonded transverse post-tensioning arrangement in forcing the
bridge model to act as one unit.
Ultimate-load test
Load-deflection response The bridge model was
loaded eccentrically at the midspan of box beam B-2 with
different loading and unloading cycles. Figure 14 shows
the load-deflection response for box beam B-2. The ultimate load-carrying capacity of the bridge model was 104
kip (462 kN), and the corresponding deflection for beam
B-2 was 10.55 in. (268 mm). The maximum deflection
observed for box beam B-2 was 27.04 in. (687 mm). During
When the unbonded CFCC strands used for transverse
post-tensioning were removed, it was clear that none of
the CFCC strands experienced any permanent deformation
or even rupture during the ultimate-load test, even after
complete failure of the bridge model. In addition, it was
observed that the strands located at the midspan diaphragm
experienced the largest increase in transverse post-tensioning force.
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•
The proposed approach for the replacement of a damaged beam using unbonded transverse post-tensioning
CFCC strands was successfully implemented. The
replacement of the damaged beam and reconstruction
of the deck slab and shear key restored the behavior
of the bridge model by reducing the deflection of box
beams B-3 and B-5. The effect was pronounced at
larger numbers of transverse diaphragms and higher
levels of transverse post-tensioning forces.
•
The failure mode was ductile flexural failure for the
entire bridge model (all four box beams). No differential deflection was observed between the adjacent box
beams, and no rupture of any unbonded CFCC strands
used for transverse post-tensioning was observed after
the complete failure. The unbonded transverse posttensioning arrangement, coupled with the concrete
deck slab, distributed the applied eccentric load in the
transverse direction until the complete failure of the
bridge model.
•
The use of unbonded CFCC strands is suitable for
transverse post-tensioning applications in side-byside box-beam bridge systems. The combination of
unbonded CFCC strands and transverse diaphragms
facilitates the replacement of damaged box beams
and allows restoration of strength in box-beam
bridges.
•
The use of oval-shaped ducts to accommodate
unbonded CFCC strands used for transverse posttensioning can overcome the misalignment problem
resulting from differential camber between adjacent
box beams.
Figure 15. This photo shows the failure of the bridge model.
The bottom strand experienced a larger increase in the
transverse post-tensioning force than the top strand within
the same diaphragm. The largest increase in the transverse
post-tensioning force of 2.29 kip (10.2 kN) was observed
at the bottom strand located at the midspan diaphragm.
This increase was about 9% above the transverse posttensioning level, which corresponded to an elongation of
8%. However, the strand was still only stressed to 54% of
its ultimate guaranteed capacity.
Conclusion
From the tests conducted on the half-scale, 30-deg-skewed,
precast, prestressed concrete side-by-side box-beam bridge
model, the following results and conclusions are presented:
•
•
•
120
Increasing the levels of transverse post-tensioning
forces proportionally increases the transverse strains for
all points located along the post-tensioned diaphragms.
The linear relation between the level of the transverse
post-tensioning forces and the corresponding transverse
strains reflects the elastic behavior of the concrete.
Increasing the number of transverse diaphragms,
spaced at 7.5 ft and 15 ft (2.29 m and 4.57 m), has an
insignificant influence on transverse strain developed
on the region between the diaphragms. The low transverse strains indicate a nonuniform distribution of the
transverse post-tensioning forces along the entire span
of the bridge. None of the arrangements of transverse
post-tensioning satisfied the minimum transverse
prestress of the AASHTO LRFD specifications limit
along the entire length of the bridge.
The level of transverse post-tensioning forces and the
number of transverse diaphragms did not significantly
affect the load-distribution behavior of the bridge
model in the uncracked-deck-slab phase. However,
significant improvement of the load-distribution behavior was observed in the cracked-deck-slab phase.
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Acknowledgment
The experimental program presented in this paper was
conducted at the Center for Innovative Materials Research
(CIMR) at Lawrence Technological University in Southfield, Mich., through the generous support of the Michigan
Department of Transportation (MDOT) and the Federal
Highway Administration (FHWA) (contract number 20040105). The support and comments provided by the MDOT
research committee are gratefully appreciated.
References
1.
New York State Department of Transportation (NYSDOT). 1992. Modifications of the Current Shear Key
and Tendon System for Adjacent Beam Prestressed
Concrete Structures. Engineering Instruction 92-010:
pp. 1–6. Albany, NY: NYSDOT.
2.
Gilbertson, G., U. Attanayake, T. M. Ahlborn, and H.
Aktan. 2006. Prestressed Concrete Box-Beam Bridge
Performance: Condition Assessment and Design
Analysis. 06-2432: pp. 22–23. Washington, DC:
Transportation Research Board.
3.
Huckelbridge, A. A., H. El-Esnawi, and F. Moses.
1995. Shear Key Performance in Multibeam Box
Girder Bridges. Journal of Performance of Constructed Facilities, V. 9, No. 4 (November): pp. 271–285.
4.
Fam, A. Z., S. H. Rizkalla, and G. Tadros. 1997. Behavior of CFRP for Prestressing and Shear Reinforcements of Concrete Highway Bridges. ACI Structural
Journal, V. 94, No. 1 (January–February): pp. 77–86.
5.
American Concrete Institute (ACI) Committee 440.
2003. Guide for the Design and Construction of
Concrete Reinforced with FRP Bars. ACI 440.1R-03.
Farmington Hills, MI: ACI.
6.
Grace, N. F., and S. B. Singh. 2003. Design Approach
for Carbon Fiber-Reinforced Polymer Prestressed
Concrete Bridge Beams. ACI Structural Journal, V.
100, No. 3, (May–June): pp. 365–376.
7.
Grace, N. F., F. C. Navarre, R. B. Nacey, and W.
Bonus. 2002. Design-Construction of Bridge Street
Bridge—First CFRP Bridge in the United States.
PCI Journal, V. 47, No. 5 (September–October): pp.
20–35.
8.
Maryland State Highway Administration (MDSHA).
2001. Maryland Study, Vehicle Collision with Highway Bridges. Baltimore, MD: MDSHA.
9.
Michigan Department of Transportation (MDOT)
Design Manual. 2006. Prestressed Concrete Box Beam
Details and Post-Tensioning Details. MDOT Bureau of
Highway Development, Lansing, MI: MDOT.
14. Grace, N., E. Jensen, V. Matsagar, M. Bebawy, E.
Soliman, and J. Hanson. 2008. Use of Unbonded
CFCC for Transverse Post-tensioning of Side-by-Side
Box-Beam Bridges. pp. 265–272. Construction and
Technology Division of MDOT, Lansing, MI.
10. MDOT. 2007. Materials Source Guide. Lansing, MI:
MDOT.
11. Hanson, J. Q. 2008. Effect of Level of Transverse
Post-Tensioning Forces on the Behavior of Sideby-Side Box-Beam Bridges Using Unbonded CFRP
Strands. M.Sc. thesis. Lawrence Technological University, Southfield, MI.
12. Soliman, E. M. 2008. Effect of Number of Diaphragms on the Behavior of Side-by-Side Box-Beam
Bridges Using Unbonded Transverse Post-Tensioning
CFRP Strands. M.Sc. thesis. Lawrence Technological
University, Southfield, MI.
13. American Association of State Highway and Transportation Officials (AASHTO). 2005. AASHTO LRFD
Bridge Design Specifications, 3rd Edition—2005 Interim Revisions. 3rd ed. Washington, DC: AASHTO.
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About the authors
Nabil F. Grace is a University
Distinguished Professor, dean of
Engineering, and the director of the
Center for Innovative Materials
Research at Lawrence Technological University in Southfield, Mich.
Elin A. Jensen is an associate
professor and associate dean of
engineering for Lawrence
Technological University.
Tsuyoshi Enomoto is engineer,
manager for the Carbon Fiber
Cable Department of the New
Business Development Division
of the Tokyo Rope Manufacturing
Co. Ltd. in Tokyo, Japan.
Vasant A. Matsagar is a postdoctorate research fellow for the
Department of Civil Engineering
at Lawrence Technological
University.
Synopsis
This paper presents the effects of the number of
transverse diaphragms and the level of transverse
post-tensioning forces using unbonded carbon-fiberreinforced-polymer (CFRP) strands on the behavior of
side-by-side box-beam bridges. An experimental program, consisting of load- and strain-distribution tests,
was conducted on a half-scale, 30-deg-skew, side-byside box-beam bridge model. The bridge model was
tested under three different phases: uncracked deck
slab, cracked deck slab, and replaced beam.
An ultimate-load test was conducted to evaluate the
response of the unbonded transverse post-tensioning
arrangement up to failure of the bridge model. The
experimental results show that increasing the level of
transverse post-tensioning forces generally improved
the flexural behavior of the bridge model. Moreover,
the different arrangements of the transverse posttensioning forces had insignificant influence on the
transverse strains developed in the region between
the diaphragms. From the results of the ultimate-load
test, it was evident that the unbonded transverse posttensioning arrangement coupled with the deck slab
uniformly distributed the applied eccentric load in the
transverse direction until complete flexural failure of
the bridge model occurred.
Keywords
Eslam M. Soliman is a research
assistant for the Department of
Civil Engineering at Lawrence
Technological University.
Bridge, box beam, camber, carbon-fiber-reinforced
polymer, CFRP, load, strain, unbonded transverse
post-tensioning.
Review policy
Joseph Q. Hanson is a research
assistant for the Department of
Civil Engineering at Lawrence
Technological University.
This paper was reviewed in accordance with the
Precast/Prestressed Concrete Institute’s peer-review
process.
Reader comments
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editor-in-chief Emily Lorenz at elorenz@pci.org or
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