Transverse

post-tension-
ing design
and detailing
of precast,
prestressed
concrete
adjacent-
box-girder
bridges
Kromel E. Hanna,
George Morcous,
and Maher K. Tadros

Precast concrete adjacent-box-girder bridges are the most

prevalent box-girder system for short- and medium-span
bridges (which typically span from 20 ft to 127 ft [6.1 m to
38.7 m]), especially on secondary roadways. These bridges
consist of multiple precast concrete box girders that are
butted against each other to form the bridge deck and
superstructure.

Editor’s quick points There is new interest in using these bridges for rapid
construction under the Federal Highway Administration
n  This paper presents a review of various transverse design and (FHWA) Highways for Life program. Adjacent box gird-
detailing practices for adjacent-box-girder bridges. ers are generally connected using partial- or full-depth
grouted shear keys along the sides of each box. Transverse
n  Design charts were developed for various combinations of span ties are usually used in addition to the grouted shear keys,
length, bridge width, skew angle, and girder depth using the and they may vary from a limited number of threaded rods
latest loading from AASHTO LRFD Bridge Design Specifications to several post-tensioned tendons. In some cases, no top-
to update the information in section 8.9 of the PCI Precast ping is applied to the structure, while in other cases a non-
Prestressed Concrete Bridge Design Manual, which was based composite topping or a composite structural slab is added.
on an earlier version of the AASHTO standard specifications.
Bridges built with adjacent precast, prestressed concrete
n  This research was funded by PCI through the Daniel P. Jenny box girders have several advantages:
Fellowship.

160 Fall 2 0 0 9 | PCI Journal

 2-in.-thick overlay
Waterproofing membrane

Noncomposite superstructure system with shear keys

5-in.-thick cast-in-place concrete

composite deck slab

Composite superstructure system with shear keys

5-in.-thick cast-in-place concrete
composite deck slab

Post-tensioned tie or threaded rod

Composite superstructure system with shear keys and transverse post-tensioning

Figure 1. Adjacent-box-girder bridges incorporate various practices in the design and detailing of transverse connecting systems. Note: 1 in. = 25.4 mm.

• ease and speed of construction because of eliminat- between adjacent units, resulting in reflective cracks in the
ing concrete forming and placing operations (for wearing surface.
example, the Arbor Rail Line Bridge in Nebraska
City, Neb., was erected and opened to traffic within The development of these longitudinal cracks over the
72 hr)1 shear keys jeopardizes the durability and structural behav-
ior of adjacent-box-girder bridges.2,3 In most cases, the
• a shallow superstructure depth, which is often neces- cracking leads to leakage, which allows chloride-laden wa-
sary to maintain the required vertical clearance (for ter to penetrate the sides and bottoms of the girders, caus-
example, an interstate bridge in Colorado has a span- ing corrosion of the steel reinforcement. In addition, the
to-depth ratio of 39) load distribution among the girders is adversely affected
because the loaded girders are required to carry more load
• low construction cost compared with I-girder bridges than the design load.3
and other competing systems
These deficiencies have led to severe deterioration and
• hollow portions inside the box girders that reduce the premature replacement of several bridges. On December
self-weight of the girders and provide space for gas 27, 2005, the east-side fascia girder of the Lakeview Drive
lines, water pipes, telephone ducts, storm drains, and Bridge over Interstate 70 in Washington, Pa., failed near
other utilities midspan and fell to the highway below. Inspection of
the bridge revealed heavy spalling and corrosion of the
• improved bridge aesthetics because of the flat soffit strands on the bottom flange of the failed noncomposite
and slender superstructure prestressed concrete box girder. Additional corrosion was
revealed on other box girders, and the bridge was subse-
• high torsional stiffness, which is ideal for curved- quently removed from service.4
bridge construction
A similar failure occurred in a railroad bridge in Nebraska
Bridges constructed using box girders have been in service in 2007. Unfortunately, public attention focuses on the few
for many years and have generally performed well. How- failed cases and not on the many successful examples.
ever, a recurring problem is cracking in the grouted joints

PCI Journal | Fa l l 2009 161

 Current practice In Korea, transverse connection is achieved by using mid-
depth shear keys fully filled with cast-in-place concrete in
Adjacent-box-girder bridges incorporate various prac- addition to heavy transverse post-tensioning similar to the
tices in the design and detailing of transverse connecting Japanese practice. The choice of a mid-depth shear key is
systems. Figure 1 shows three configurations. The first is based on a detailed analysis and full-scale testing.7
a noncomposite system with a nonstructural overlay as the
riding surface applied directly to the top flange of the adja- The state of Oregon has developed empirical transverse
cent box girders. This system depends only on the grouted design and detailing procedures for adjacent box girders
shear key to provide the shear-transfer mechanism between that have demonstrated satisfactory performance over sev-
adjacent box girders. eral years. The developed system is based on using trans-
verse threaded ties at several locations according to the
The second is a thick, reinforced cast-in-place concrete span length; grouted, partial-depth shear keys; and recesses
slab anchored to the supporting box girders using shear as 1/4 in. (6 mm) chamfer at the bottom edges of the girder
connectors to act as a composite superstructure system. to prevent spalling due to stress concentration.

The third system is a typical transverse connection made The results of research conducted by the West Virginia
between the adjacent box girders using a post-tensioning DOT on several bridges that had joint fracture and topping
tie or a threaded rod. This transverse connection system cracks revealed that vertical shear failure in the key was
can be used in conjunction with the composite or noncom- due to poor grouting and inadequate transverse tie force.8
posite systems to prevent differential deflection. As a result of this study, the West Virginia DOT follows
certain guidelines:
According to the Ministry of Transportation of Ontario’s
(MTO’s) Ontario Highway Bridge Design Code,5 the • Post-tensioned high-strength ties are used.
general design philosophy of adjacent-member systems
assumes that the entire load between adjacent members is • A pourable epoxy is used instead of a nonshrink grout
transferred by transverse shear, and the transverse flexural in the shear key.
rigidity is completely ignored.
• The surfaces to be grouted are sandblasted.
Also, grouted shear keys are considered inadequate to
transfer the shear force, and therefore a structural concrete Before 1992 in New York state, depths of shear keys were
slab of a minimum thickness of 5.9 in. (150 mm) is re- about 12 in. (300 mm) from the tops of the precast con-
quired. The transverse shear force is determined as a func- crete girders.9 Transverse tendons applying a compressive
tion of the bridge width-to-span ratio, longitudinal flexural force of 30 kip (133 kN) were used across the width of a
rigidity, and longitudinal torsional rigidity. bridge. Spans up to 50 ft (15 m) long had no transverse
tendons, but those from 50 ft to 75 ft (23 m) long had one
Some states’ departments of transportation (DOTs) com- transverse tendon at the center. For those longer than 75 ft,
bine the use of a structural concrete slab and transverse tendons were used only at the outer quarter points.
post-tensioning. This is based on the assumption that both
shear and flexure forces must be transversely transferred The bridge continuity in transverse direction was ensured
at the joints between adjacent members to control both by using a 6-in.-thick (150 mm), cast-in-place concrete
translational and rotational deformations.6 deck slab reinforced with welded-wire reinforcement. A
survey in 19908 indicated that 54% of such bridges built
In Japan, adjacent box girders are designed using sections from 1985 to 1990 had developed longitudinal cracks over
and design criteria similar to those used in the United the shear keys. In 1992, two major changes were adopted
States. However, longitudinal joints are detailed differ- in New York state’s design standards:
ently and transverse post-tensioning is significantly higher.
Cast-in-place concrete is placed in full-depth joints that • Shear keys were placed at almost the full depth of the
are 6.7 in. (170 mm) wide and 22 in. (560 mm) deep. After precast concrete box girders.
grouting, post-tensioning is applied through several ducts
located at different elevations. All box girders are covered • The number of transverse tendons was increased to
with a 2-in.-thick to 3-in.-thick (50 mm to 75 mm) asphalt- three for spans less than 50 ft (15 m) and five for
concrete wearing surface. Using the Japanese practice, longer spans.
longitudinal cracking and concrete deterioration has rarely
been reported. El-Remaily et al.6 give details of the post- Since the changes were adopted, more than 100 bridges
tensioning arrangement and joint dimensions used. have been built statewide. In 1996, a survey was con-
ducted to evaluate the effectiveness of implemented design
changes. The survey indicated that only 23% of the bridges

162 Fall 2 0 0 9 | PCI Journal

built from 1993 to 1996 experienced longitudinal cracks. shear key from its position in the upper third of the gap
This indicated the effectiveness of applying transverse closer to the midheight of the box-girder section. His ex-
post-tensioning to reduce cracking of the deck slab.9 perimental program included testing the current shear-key
design against the proposed one while incorporating dif-
The Ohio DOT constructed a high-performance concrete ferent grout materials such as nonshrink grout, magnesium
(HPC) adjacent-box-girder bridge.10 This bridge was ammonium phosphate mortar, and epoxy resin mortar in
constructed as a replacement for a three-span bridge. The both of the designs. The test specimens were loaded gradu-
bridge used an experimental shear key at mid-depth of the ally until failure.
cross section. The girders were tightened together using
nonprestressed threaded rods located transversely through El-Esnawi observed that the static-load capacity was
diaphragms at the ends and quarter points of the bridge. almost tripled from the current shear-key design with the
same grouting material. He reported that magnesium am-
The shear keys were grouted after tightening the transverse monium phosphate was sensitive to carbonated concrete
bars. The area above the shear key was filled with sand and surfaces, and it was difficult to provide a carbonate-free
a sealant to further guard against leakage. After construct- contact surface to prevent the chemical reaction with mag-
ing the entire bridge width, the bridge was subjected to an nesium ammonium phosphate. The research also revealed
eccentric load of 120 kip (534 kN) using four Ohio DOT that epoxy grout was a strong grouting material that had
trucks filled with gravel. The researchers reported that the excellent adhesion with concrete. However, its preparation
deflection profiles in the transverse direction showed that had many difficulties and its long-term behavior under dif-
all of the girders were working together. In addition, while ferent temperature changes was questionable.
subjecting the bridge to eccentric load, the deflection on
the loaded side was greater than that on the opposite side Annamalai et al.15 conducted an experimental program to
of the bridge width. investigate the effect of transverse post-tensioning on the
behavior of small assemblies. The parameters studied were
Miller et al.11 and Hlavacs et al.12 studied the performance the number and thickness of shear keys and the level and
of nonshrink grout and epoxy in shear keys. Nonshrink distribution of the prestressing. They concluded that post-
grout in shear keys close to the top edge of the girder tensioning significantly improved the shear strength of
experienced cracks before any load was applied. The grouted shear-key connections, and post-tensioned grouted
researchers reported that these cracks developed because of shear-key connections exhibited a high degree of mono-
temperature stresses. The use of epoxy grout made it pos- lithic action.
sible to prevent cracking under either temperature or load
effects, but the coefficient of its thermal expansion was Assemblies with three keys showed higher rigidity than
two to three times greater than that of concrete. specimens with two keys. Assemblies with a 1-in.-thick
(25 mm) joint were found to have significantly higher
Gulyas et al.13 compared the behavior of nonshrink grout shear strengths than specimens with 2-in.-thick (50 mm)
with the behavior of magnesium ammonium phosphate joints for the same prestress level. The connections without
mortars in the shear keys. The researchers tested the shear keys and with a prestress of 800 psi (5520 kPa) had
component material in assemblies using different types of nearly the same shear strength as connections with shear
tests, such as vertical shear, direct tension, and longitudinal keys and no prestress. Prestress in combination with shear
shear tests. The vertical shear test was intended to simulate keys provided superior performance. The shear strength
the action of a vehicle wheel load on one member and no was not significantly influenced by the distribution of
wheel load on the adjacent member. The direct tension test prestress along the height of the specimen.
attempted to simulate the transverse shortening of the pre-
cast concrete member due to shrinkage and also to simulate Stanton and Mattock16 tested the strength of welded con-
the drying shrinkage that can occur in the keyway grout. nectors acting alone and with grout keys. The experimental
program involved six specimens. Each specimen consisted
The longitudinal shear tests were performed in the direc- of two 6-in.-thick (150 mm) reinforced concrete slabs
tion parallel to the keyway to simulate the action of the joined together at their edges using a 5-ft-long (1.5 m)
prestressed concrete member shortening because of creep shear key.
and shrinkage while the grout would not shorten to the
same degree. In all tests, the magnesium ammonium phos- Stanton and Mattock concluded that the forces from the
phate–grouted assembles displayed an exceptionally higher wheel loads were transferred through the shear key. The
failure load than the nonshrink grout composite assemblies. steel connectors carried shear forces induced before grout-
ing because of differential camber, and tension forces be-
In an attempt to overcome the problems associated with cause of shrinkage. They concluded that the strength of the
the failure of the shear keys, El-Esnawi14 suggested a new shear key was affected by inclined cracking in the parts of
shear-key design. The new design proposed moving the the member flanges above and below the shear key rather

PCI Journal | Fa l l 2009 163

 than by failure of the grout itself. They recommended the midspan. The joints were grouted using relatively low-
use of transverse post-tensioning to improve the behavior strength, high-shrinkage grout.
of transverse connections.
In both bridge models, it was found that the moment
Huckelbridge et al.3 conducted a total of six field tests on resisted by each outer slab was about 33% greater than the
three bridges with noncomposite topping and two field moment resisted by the middle slab. Martin and Osburn
tests with composite cast-in-place concrete decks. One of concluded that a properly grouted shear key and either
the bridges was tested before and after repairing a severely transverse tie rods or welded connectors are an effective
deteriorated joint. way to transfer shear between adjacent members.

They reported that a relative displacement between the El-Shahawy19 investigated the behavior of the transverse
girders of more than 0.001 in. (0.025 mm) indicated failure connections in the double-tee bridges. He tested a half-
in the shear key. The magnitude of relative displacement scale bridge model consisting of three 30-ft-long (8.2
experienced by each bridge depended on the actual length m) double-tees. The transverse connections consisted of
of the fracture, stiffness of the girders, and magnitude and V-shaped joints between the girders filled with nonshrink
proximity of the wheel load to the failed joint. Relative portland cement grout and transverse post-tensioning
displacements between 0.003 in. and 0.02 in. (0.075 mm strands. The developed stresses due to transverse post-
and 0.50 mm) were observed at joints that indicated at least tensioning strands were equal to 150 psi (1030 kPa) at the
partially fractured shear keys. The results also revealed that middle portion and 300 psi (2070 kPa) at the ends.
tie bars had little to no impact on shear-key performance.
The behavior of the transverse connection was investigated
Issa et al.17 tested a total of 36 full-scale specimens for by conducting several punching-shear tests on the deck
vertical shear, direct tension, and flexural capacity. Four slab followed by a load-distribution test across the entire
different grout materials were used to construct the shear bridge width. The results from all tests indicated that the
keys in the specimens. The grout materials were set grout, selected level of transverse prestressing satisfied the design
set 45 for normal temperatures, set 45 for hot weather, and requirements. It was also concluded that transverse post-
polymer concrete. tensioning helped the slab achieve monolithic behavior.

Polymer concrete was found to be the best material for According to the AASHTO LRFD Bridge Design Speci-
transverse joints in terms of strength, bond, and mode of fications,20 the use of transverse mild-steel rods secured
failure. However, they recommended the use of set grout in by nuts is not sufficient to achieve full transverse flexural
transverse deck joints due to its ease of use and satisfactory continuity. Section 5.14.4.3.3d recommends a minimum
performance and polymer concrete in the joints subjected effective post-tensioning pressure of 250 psi (1720 kPa)
to excessive stresses or when quick repair is required. through the shear key. There is neither a rational justifica-
tion for this value nor an adequate explanation regarding
Martin and Osburn18 tested two precast, prestressed the area over which this pressure is applied when different
concrete–slab bridge models. Each model consisted of shear keys are used.
three adjacent precast, prestressed concrete slabs that were
connected by two different types of transverse connections. The PCI subcommittee on adjacent-member bridges
The precast, prestressed concrete slabs had a cross sec- conducted a survey on the current practices in the design
tion of 8 in. × 36 in. (200 mm × 910 mm), a length of 18 ft and construction of adjacent-box-girder bridges in United
(5.5 m), and a span of 16 ft (4.9 m). States and Canada.9 This survey indicated that 29 states and
3 provinces are currently using adjacent-box-girder bridges.
Each bridge model was tested by loading the two outer
slabs cyclically at midspan by equal concentrated loads of Most of these transportation agencies have experienced
16 kip (71 kN), which was intended to simulate American premature reflective cracks in the wearing surface on the
Association of State Highway and Transportation Officials bridges built in the late 1980s and early 1990s. These
(AASHTO) HS-20 wheel loads. agencies have emphasized the importance of eliminating
these cracks that allow the penetration of water and deic-
In the first bridge model, the slabs were joined together by ing chemicals and lead to the corrosion of reinforcing steel
tie rods at the third point of the span, and the tie rods were in the sides and bottoms of concrete box girders. The states
tensioned to 12 kip (53 kN). The joints were grouted using and provinces have recommended preventive actions based
high-strength, nonshrink grout. on the lessons learned in the past two decades:

In the second bridge model, the slabs were joined together • Cast-in-place concrete deck on top of the adjacent
with three welded connectors located at both supports and box girders can prevent water leakage and uniformly
distribute the loads on adjacent box girders.

164 Fall 2 0 0 9 | PCI Journal

 Standard section Diaphragm section

Grout 8.0 in.

A
2.0 in.
7.5 in.

7.5 in.

A 2.0 in.
Section A-A
Transverse post-tensioning:
threaded bars through
ducts in girders

Figure 2. The transverse diaphragms are made continuous across the entire width of the bridge using grouted full-depth shear keys and post-tensioning tendons. Source:
Figure 8.9.3-1. PCI Bridge Design Manual Steering Committee, Precast Prestressed Concrete Bridge Design Manual (Chicago, IL: PCI, 2003). Note: 1 in. = 25.4 mm.

• Nonshrink grout or the appropriate sealant instead dimensional tolerances that result in inadequate seal-
of the conventional sand-cement mortar in the shear ing of the shear keys.
keys should be used in addition to blast cleaning of
key surfaces prior to grouting. Also, a few states have PCI method
recommended the use of full-depth shear keys due to
their superior performance over the traditional top- PCI’s Precast Prestressed Concrete Bridge Design
flange keys. Manual21 method was developed by El-Remaily et al.6 and
is reported in section 8.9 of the manual. In this method,
• Transverse post-tensioning is recommended to the post-tensioning force required to achieve adequate
improve load distribution and minimize differential stiffness in the transverse direction to keep differential
deflections among adjacent box girders. Adequate deflection within the acceptable limit (0.02 in. [0.50 mm])
post-tensioning should be applied after grouting the is calculated.
shear keys to minimize the tensile stresses that cause
longitudinal cracking at these joints. This method assumes that post-tensioned transverse dia-
phragms are the primary mechanism for the distribution of
• End diaphragms should be used to ensure proper wheel loads across the bridge. Five diaphragms are provid-
seating of adjacent box girders, and intermediate ed in each span: one at each end, one at midspan, and one
diaphragms should be used to provide the necessary at each quarter point. Without diaphragms, each box girder
stiffness in the transverse direction. must be designed to carry a full set of wheel loads without
contribution from adjacent box girders. As a result, a large
• Wide bearing pads under the middle of the box and differential deflection between adjacent girders will take
sloped bearing seats that match the surface cross slope place and reflective cracking is generally expected. How-
are recommended to eliminate the rocking of the box ever, if the box girders are transversely connected using
while grouting the shear keys. diaphragms, the loads are distributed over the entire bridge
width, and the deflected shape becomes a smooth curve.
• Adequate concrete cover and corrosion-inhibiting The transverse diaphragms are made continuous across the
admixtures should be used in the concrete to resist the entire width of the bridge using grouted, full-depth shear
chloride-induced corrosion of reinforcing steel. keys and post-tensioning tendons (Fig. 2).

• It is recommended to eliminate the use of welded To determine the required amount of post-tensioning, the
connections between adjacent box girders and to avoid bridge is analyzed using a grid model. A series of longitu-

PCI Journal | Fa l l 2009 165

 Centerline of the diaphragms
L

Skew angle

L/4
Centerline of the box

Figure 3. This drawing shows the grid analysis model. Note: L = span length; W = bridge width.

dinal girder elements located at the centerline of each box Transverse post-tensioning force is calculated so that
girder is used to represent the box girders, and a series of diaphragm concrete stresses due to both loads and post-
transverse girder elements located at the ends and quarter tensioning are within the allowable limits (compression =
' '
points is used to represent the diaphragms (Fig. 3). The 0.6 f c where f c is specified compressive strength of con-
joints between elements allow the transmission of shear, crete and tension is 0). Tensile stresses are not permitted
bending, and torsion. The weight of barrier rails and live in the diaphragm in order to prevent possible cracking at
loads are the main source of transverse bending moments the interface between precast concrete components and the
generated in the diaphragms. This is because self-weight, grout at shear-key locations. Also, post-tensioning force is
deck weight, and wearing-surface weight are considered applied concentrically in the transverse direction because
uniform on all of the elements and therefore do not gener- diaphragms experience significant alternating positive and
ate any differential movements. negative bending moments under different loading condi-
tions.

The design chart currently available in the PCI bridge

design manual was developed for the AASHTO standard
48 in.
box girders in Fig. 4 and Table 1, assuming mild skew
angles (that is, less than 15 deg), average span lengths, and
H = 27 in., 33 in., 39 in., and 42 in.

AASHTO HS-25 truck loading with impact.6 New charts

3 in. need to be developed to accommodate the cases of highly
skewed bridges with different span lengths and using the
AASHTO LRFD specifications truck and lane loads in ad-
5.5 in. dition to dynamic load allowance.20

5 in. 5 in. Updated design charts

and design equation
3 in. 5.5 in.
The updated design charts were developed using the same
PCI method for the four standard AASHTO box girders in
Fig. 4 and Table 1. For each girder, several combinations
of bridge width, span length, and skew angle were con-
sidered. The AASHTO LRFD specifications for truck and
Figure 4. This drawing shows the American Association of State Highway and lane live loads (HL-93) and dynamic load allowance (33%
Transportation Officials’ standard box girder used for developing the design charts for truck load only) were applied in addition to 0.48 kip/ft
currently available in the PCI Precast Prestressed Concrete Bridge Design Manual. (7.0 kN/m) for the self-weight of a solid concrete barrier.20
Note: H = height of box girder. 1 in. = 25.4 mm.

166 Fall 2 0 0 9 | PCI Journal

Table 1. Box beam properties

Type Height H, in. Area A, in.2 Ybottom Moment of inertia I, in.4

BI-48 27 692.5 13.37 65,941

BII-48 33 752.5 16.33 110,499

BIII-48 39 812.5 19.29 168,367

BIV-48 72 842.5 20.78 203,088

Note: Ybottom = distance from bottom of girder to center of gravity. 1 in. = 25.4 mm.

Figure 5 shows the effective post-tensioning force versus charts. This is mainly due to the use of the AASHTO
bridge width for the four standard box girders, assuming LRFD specifications on live-load and dynamic-load al-
a 0 deg skew angle and a span-to-depth ratio of 30. This lowance. This increase varies depending on the box-girder
graph indicates that for any girder depth, the wider the depth and the bridge width, and it is more noticeable in
bridge, the higher the required post-tensioning force. It also narrow bridges than in wide bridges. It should be noted
indicates that the required force is higher in shallower gird- that the PCI bridge design manual values correspond to a
ers than in deeper girders for the same bridge width. This skew angle of 15 deg and average span length, while the
is mainly to compensate for the reduction in the transverse proposed values correspond to a skew angle of 0 deg and a
stiffness due to the use of shallower diaphragms. Each line span-to-depth ratio of 30.
in Fig. 5 has two different curvatures. The first curvature
represents the relationship when the negative moment Figure 7 shows the required post-tensioning force versus
controls the design, which occurs in the relatively narrow bridge width for a 0 deg skew angle and span-to-depth
bridge widths (up to 52.0 ft [15.9 m]). The second curva- ratios of 30 and 40. Although the effect of the span-to-
ture represents the relationship when the positive moment depth ratio was evaluated for the four standard box girders,
controls the design, which occurs in wider bridges. only the lines for the 27-in.-deep and 42-in.-deep (690 mm
and 1070 mm) box girders were plotted for clarity. This
Figure 6 shows the PCI bridge design manual design plot indicates that the span-to-depth ratio has an insignifi-
chart superimposed over the updated design chart. This cant and variable effect on the required post-tensioning
graph indicates a significant increase in the required post- force per unit length. As the span-to-depth ratio increased,
tensioning force (up to 40% in some cases) in the updated the required prestressing force increased when the design

16

14
Post-tensioning force, kip/ft

12

10

8
Box girder depth
6
76 in.
4 33 in.
39 in.
2
42 in.
0
20 28 36 44 52 60 68 76 84 92

Bridge width, ft

Figure 5. This graph shows the effect of bridge width on post-tensioning force at the midspan diaphragm for the four standard box girders assuming a 0 deg skew angle
and a span-to-depth ratio of 30. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m; 1 kip = 4.448 kN.

PCI Journal | Fa l l 2009 167

 16

14
Post-tensioning force, kip/ ft

12

10

6 Box girder length

27 in. (PCI bridge design manual)

4
27 in. (Updated chart)
42 in. (PCI bridge design manual)
2
42 in. (Updated chart)

0
20 30 40 50 60 70 80 90

Bridge width, ft

Figure 6. This graph compares the Precast Prestressed Concrete Bridge Design Manual design chart with updated charts showing the effect of bridge depth on post-
tensioning force. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m; 1 kip = 4.448 kN.

was positive-moment controlled, and decreased when the the required post-tensioning force is minimal, especially
design was negative-moment controlled. This effect was on deep girders that usually correspond to longer spans.
more noticeable in the shallow girders. For shallow girders used in short-span bridges, as the skew
angle increased the required post-tensioning force also
Figure 8 shows the effect of skew angle on the required increased.
post-tensioning force at the midspan diaphragm for a
bridge width of 52 ft (16 m) and a span-to-depth ratio of
30. Figure 8 indicates that the impact of the skew angle on

16

14
Post-tensioning force, kip/ft

12

10

8 Box girder depth

27 in. (L/D = 40)
6
27 in. (L/D = 30)
4
42 in. (L/D = 40)
2 42 in. (L/D = 30)

0
20 28 36 44 52 60 68 76 84 92
Bridge width, ft

Figure 7. This graph shows the effect of the span-to-depth ratio on post-tensioning force at the midspan diaphragm for a 0 deg skew angle and span-to-depth ratios equal
to 30 and 40. Note: D = depth; L = span. 1 in. = 25.4 mm; 1 ft = 0.305 m; 1 kip = 4.448 kN.

168 Fall 2 0 0 9 | PCI Journal

 16

14
Post -tensioning force, kip/ft

12

10

8
Box girder depth
6
27 in.
4 33 in.

2 39 in.
42 in.
0
0 5 10 15 20 25 30 35 40 45
Skew angle, deg

Figure 8. This graph shows the effect of the bridge skew angle on post-tensioning force for the midspan diaphragm for a bridge width of 52 ft and a span-to-depth ratio of
30. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m; 1 kip = 4.448 kN.

Figures 5, 7, and 8 indicate that the bridge width and box- a span-to-depth ratio of 30 and a skew angle of 0 deg and
girder depth are the most important parameters in deter- should be corrected using Fig. 7 and 8, respectively, when
mining the required post-tensioning force per unit length of different span-to-depth ratios or skew angles are used.
the bridge. Therefore, the designer should first estimate the
force based on the bridge width and girder depth using the Data from the grid analysis were used to develop a simpli-
proposed design chart (Fig. 5). These values correspond to fied design equation for calculating the required post-
Calculated force using simplified equation, kip/ft

16

14

12

10

0
0 2 4 6 8 10 12 14 16
Estimated force using grid analysis, kip/ft

Figure 9. This graph compares the post-tensioning force estimated using grid analysis with the proposed equation. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m;
1 kip = 4.448 kN.

PCI Journal | Fa l l 2009 169

 Span = 120 ft
30 ft 30 ft 30 ft 30 ft

Elevation
52 ft

Cross section 3 ft 6 in.

Figure 10. This drawing illustrates the bridge geometry for the design example. Note: 1 in. = 25.4 mm; 1 ft = 0.305 m.

tensioning force P (kip/ft) for the intermediate diaphragm estimate of the required transverse post-tensioning force in
per unit length of the bridge. The following equation was most of the cases, with an average deviation of 7.7%.
developed by fitting the data points obtained from the grid
analysis of all cases. The first part of the equation repre- Design example
sents the relationship when the negative moment controls
the design, which occurs in smaller bridge widths (up to The provided design example illustrates the design steps of
52.0 ft [15.9 m]). The second part of the equation repre- the single-span bridge (Fig. 10).
sents the relationship when the positive moment controls
the design, which occurs in wider bridges. These relation- Bridge data
ships were assumed to be linear to eliminate sophisticated
formulations. Figure 10 shows the cross section and the elevation of the
bridge.
⎛ 0.9W ⎞ ⎛ 0.2W ⎞
PP== ⎜ −1.0⎟ K L K S ≤ ⎜ + 8.0⎟ K L K S Span = 120 ft (37 m)
⎝ D ⎠ ⎝ D ⎠
Width = 52 ft (16 m)
where
Depth = 42 in. (1070 mm) (AASHTO LRFD
D = box depth specifications standard box girder)

W = bridge width Skew = 15 deg

KL = correction factor for span-to-depth ratio Concrete strength

⎛ L ⎞ Precast concrete f c' = 6000 psi (41 MPa)

= 1.0 + 0.003⎜ − 30 ⎟
⎝D ⎠
Grout f c' = 6000 psi (41 MPa)
KS = correction factor for skew angle more than 0 deg
Box girder section properties
= 1.0 + 0.002θ
Area A = 842.5 in.2 (543,600 mm2)
L = bridge span
Moment of inertia I = 203,088 in.4 (8.453 × 1010 mm4)
θ = skew angle
Diaphragm section properties
To evaluate the accuracy of the simplified equation in
fitting the analysis data, the post-tensioning force values The cross section of the diaphragms is rectangular. The
obtained using the equation were compared with those depth of the diaphragm is equal to the depth of the box
obtained using the grid analysis for several combinations girder (42 in. [1070 mm]), and the width is 8 in. (200 mm)
of bridge width and depth. Span-to-depth ratio and skew
angle were kept constant to evaluate the accuracy of the A = 336 in.2 (216,800 mm2)
basic equation without any correction factors. Figure 9
shows that the simplified equation provides a conservative I = 49,392 in.4 (1.68 × 1010 mm2)

170 Fall 2 0 0 9 | PCI Journal

Loading ⎛ 187 12 1000 21 ⎞ P 1000
( )( )( ) ( )
f bot = − ⎜ ⎟+ ≤ 3600
⎝ 49,392 ⎠ 336
Dead load: curb and railing w = 0.48 kip/ft (7.0 kN/m)

Live load: HL-93 truck and lane load Pdiaphragm ≤ 890 kip (3959 kN)

Impact factor for truck load = 33% Based on the previous calculations, the total required
transverse post-tensioning force per diaphragm is 324 kip
Calculation of the required (1440 kN). The total required transverse post-tensioning
transverse post-tensioning force force per foot of the bridge is 324/30, which equals 10.8
using working stresses analysis kip/ft (158 kN/m).

The grid analysis was used to get the member forces. According to section 5.14.4.3.3d of the AASHTO LRFD
Moments of the midspan diaphragm were used for design specifications and using the area of the full-depth verti-
calculations. The live-load positions were chosen to give cal shear key as the contact area, the minimum required
the maximum positive and maximum negative moments. transverse post-tensioning force per diaphragm is equal to
Allowable compressive strength due to effective prestress 0.25(8)(42 - 2), or 80 kip (360 kN). This is low because
plus maximum load was calculated using the following it represents only 25% of the force calculated using the
equation. updated PCI method. If the entire side of the box is used
as the contact area, the minimum required transverse
0.6 f c' = 0.6(6000) = 3600 psi (24,800 kPa) post-tensioning force per diaphragm is 0.25(30)(12)(42),
or 3780 kip (16,800 kN). This is extremely high because
Tension is not permitted. These stresses must be checked it is 10 times the force calculated using the updated PCI
for both the maximum positive and maximum negative method.
load cases:
Calculation of the required
• Positive-moment load case: the unfactored maximum transverse post-tensioning force
positive moment is 147 kip-ft (199 kN-m). using the developed equation

⎛ 147 12 1000 21 ⎞ P 1000

( )( )( ) ( ) From the proposed equation, the required transverse post-
f bot = − ⎜ ⎟+ ≥0 tensioning force is calculated as follows.
⎝ 49,392 ⎠ 336

⎛ L ⎞
where KL = 1.0 + 0.003⎜ − 30 ⎟
⎝D ⎠
Pdiaphragm ≥ 252 kip (1121 kN) ⎛ 120 12 ⎞
= 1.0 + 0.003⎜
( ) − 30⎟ = 1.013
fbot = stress in bottom of diaphragm ⎝ 42 ⎠

⎛ 147 12 1000 21 ⎞ P 1000 Ks = 1.0 + 0.002θ = 1.0 + 0.002(15) = 1.03

ftop = − ⎜
( )( )( ) (
≤ 3600
)
⎟+
⎝ 49,392 ⎠ 336 The required post-tensioning force:
⎛ ⎞ ⎛ ⎞
Pdiaphragm ≤ 958 kip (4381 kN) P = 0.9W − 1.0 K K ≤ 0.2W + 8.0 K K
⎜⎝ D ⎟⎠ L S ⎜⎝ D ⎟⎠ L S
ftop = stress in top of diaphragm
⎛ 0.9 52 12
( )( ) ⎞ ⎛ 0.2 52 12 ⎞
( )( )
• Negative-moment load case: the unfactored maximum =⎜
42
( )(
− 1.0⎟ 1.013 1.03 ≤ ⎜ )
42
+ 8.0⎟ 1.013 1( )(
negative moment is 187 kip-ft (254 kN-m). ⎝ ⎠ ⎝ ⎠
⎛ 0.9 52 12
( )( ) ⎞ ⎛ 0.2 52 12
( )( ) ⎞
⎛ 187 12 1000 21 ⎞= ⎜ P 1000
( )( )( ) ( )
42 ≥ 0
( )( )
− 1.0⎟ 1.013 1.03 ≤ ⎜
42
( )(
+ 8.0⎟ 1.013 1.03 )
ftop = − ⎜ ⎟ +⎝ ⎠ ⎝ ⎠
49,392 336
⎝ ⎠
= 12.9 ≤ 11.5 ∴ P = 11.5 kip/ft (168 kN/m)
Pdiaphragm ≥ 324 kip (1441 kN)
Pdiaphragm = 11.5(30) = 345 kip (1535 kN)

PCI Journal | Fa l l 2009 171

 Required prestressing strands Acknowledgments

Two tendons will be used in each diaphragm. The required The authors acknowledge the invaluable support of the
area of post-tensioning force Aps is calculated by dividing PCI subcommittee on Adjacent Member Bridges led by
the required force Pdiaphragm by the effective prestress f s' , Kevin Eisenbeis and the financial and technical support of
which is assumed to be 55% of the ultimate strength of the PCI through the Daniel P. Jenny Fellowship.
strands fpu.
References
Aps = 345/(0.55 × 270) = 2.32 in.2 (15.0 mm2)
1. Hennessey, S. A., and K. A. Bexten. 2002. Value
Try six 0.6-in.-diameter strands at each tendon. The total Engineering Results in Successful Precast Railroad
area is 2.604 in.2 (16.80 mm2), which is acceptable. Bridge Solution. PCI Journal, V. 47, No. 4 (July–
August): pp. 72–77.
Conclusion
2. Kahl, S. 2005. Box-Beam Concerns Found under the
Based on the results of the parametric study and the com- Bridge. C&T Research Record, No. 102 (September):
parison of the updated design chart with the existing PCI pp. 1–4.
bridge design manual design chart, several conclusions are
made: 3. Huckelbridge, A. A., H. El-Esnawi, and F. Moses.
1995. Shear Key Performance in Multi-Beam Box
• The latest AASHTO LRFD specifications for live- Girder Bridges. Journal of Performance of Construct-
load and dynamic-load allowance cause a significant ed Facilities, V. 9, No. 4 (November): pp. 271–285.
increase (up to 40% in some cases) in the required
transverse post-tensioning force for adjacent-box- 4. Naito, C., R. Sause, I. Hodgson, S. Pessiki, and C.
girder bridges. Desai. 2006. Forensic Evaluation of Prestressed Box
Beams from the Lake View Drive Bridge over I-70.
• The bridge width and girder depth have the most Advanced Technology for Large Structural Systems
significant effect on the required transverse post- (ATLSS) report no. 06-13.
tensioning force. For any girder depth, an increase in
the bridge width is accompanied by a higher post- 5. Ministry of Transportation of Ontario (MTO). 1995.
tensioning force. Also, the required force is higher in Ontario Highway Bridge Design Code. 1995. MTO.
shallower girders than in deeper girders for the same
bridge width. 6. El-Remaily, A., M. K. Tadros, T. Yamane, and G.
Krause. 1996. Transverse Design of Adjacent Precast
• Span-to-depth ratio has a variable effect on the Prestressed Concrete Box Girder Bridges. PCI Jour-
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As the span-to-depth ratio increases, the required
prestressing force also increases when positive mo- 7. Nam, J. W., H. J. Kim, J. H. Kim, S. H. Nam, S. B.
ment controls the design, and less prestressing force is Kim, and K. J. Byun. 2008. International Perspec-
required when negative moment controls. This effect tive: Overview and Application of Precast Prestressed
is more noticeable in the shallow girders. Box-Beam Bridges in Korea. PCI Journal, V. 53, No.
4 (July–August): pp. 83–107.
• Skew angle has a minimal effect on the required trans-
verse post-tensioning force, especially on deep girders 8.  CI Bridges Committee. 2008. Reflective Cracking
P
that usually correspond to longer spans. For shallow in Adjacent Box Girder Bridge Superstructures. Sub-
girders used in short-span bridges, greater skew angles committee on Adjacent Box Beam Bridges, October.
require more transverse post-tensioning force.
9. Lall, J., S. Alampalli, and E. F. Dicocoo. 1998.
• The simplified design equation provides the required Performance of Full-Depth Shear Keys in Adjacent
transverse post-tensioning force per unit length of the Prestressed Box Beam Bridges. PCI Journal, V. 43,
bridge as a function of its width and box-girder depth No. 2 (March–April): pp. 72–79.
and accounts for the span-to-depth ratio and skew
angle using correction factors. The average deviation 10. Greuel, A., T. M. Baseheart, B. T. Rogers, R. A.
of the values calculated using the simplified equation Miller, and B. M. Shahrooz. 2000. Evaluation of a
and the grid analysis results is 7.7%. High Performance Concrete Box Girder Bridge. PCI
Journal, V. 45, No. 6 (November–December): pp.
60–71.

172 Fall 2 0 0 9 | PCI Journal

11. Miller, R. A., G. M. Hlavacs, T. Long, and A. Greuel. Notation
1999 Full-Scale Testing of Shear Keys for Adja-
cent Box Girder Bridges. PCI Journal, V. 44, No. 6 A = area
(November–December): pp. 80–90.
Aps = required area of post-tensioning force
12. Hlavacs, G. M., T. Long, R. A. Miller, and T. M.
Baseheart. 1997. Nondestructive Determination D = depth
of Response of Shear Keys to Environmental and
Structural Cyclic Loading. Transportation Research fbot = stress in bottom of diaphragm
Record, No. 1574 (November): pp. 18–24.
f c' = specified compressive strength of concrete
13. Gulyas, R. J., G. J. Wirthlin, and J. T. Champa.
1995. Evaluation of Keyway Grout Test Methods for fpu = ultimate strength of the strand
Precast Concrete Bridges. PCI Journal, V. 40, No. 1
(January–February): pp. 44–57. f s' = effective prestress

14. El-Esnawi, H. H. 1996. Evaluation of Improved Shear ftop = stress in top of diaphragm
Key Designs for Multi-Beam Prestressed Concrete
Box Girder Bridges. PhD thesis. Case Western Re- H = height
serve University, Cleveland, Ohio.
I = moment of inertia
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Behavior of Post-tensioned Grouted Shear Key Con- KL = correction factor for span-to-depth ratio
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Multi-Beam Bridge Superstructures. TRB report
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PCI Journal | Fa l l 2009 173

 About the authors differential displacement and rotation of adjacent box
girders. The reflective cracking and leakage allow
Kromel E. Hanna, PhD, is a chloride-induced corrosion of reinforcing steel and
Post-Doctoral Fellow for the prestressing strand and premature deterioration of the
Civil Engineering Department at bridge superstructure.
the University of Nebraska–Lin-
coln in Omaha, Neb. This paper presents a review of the various practices
in the transverse design and detailing of adjacent-box-
girder bridges. The basis for calculating the transverse
George Morcous, PhD, P.E., is an post-tensioning force according to PCI’s Precast Pre-
assistant professor for the stressed Concrete Bridge Design Manual is discussed.
Construction Systems Depart- Design charts and equations were developed for vari-
ment at the University of Nebras- ous combinations of span length, bridge width, skew
ka–Lincoln. angle, and girder depth using the latest loading from
AASHTO LRFD Bridge Design Specifications. These
aids may be viewed as an update to the information
Maher K. Tadros, PhD, P.E., is a in section 8.9 of the PCI bridge design manual, which
Leslie D. Martin Professor of was based on an earlier version of the AASHTO stan-
Civil Engineering at the Univer- dard specifications.
sity of Nebraska–Lincoln.
Keywords

Adjacent box girder, bridge deterioration, grid analy-

Synopsis sis, longitudinal joint, rapid construction, shear key,
transverse design.
Precast, prestressed concrete adjacent box girders are
widely used in short- and medium-span bridges. Rapid Review policy
construction and low construction cost are the main
attractions of this system. Also, the continuous flat This paper was reviewed in accordance with the
soffit and relatively high span-to-depth ratio make this Precast/Prestressed Concrete Institute’s peer-review
system aesthetically pleasing. process.

However, reflective cracking and leakage have been Reader comments

reported along the longitudinal joints between adjacent
box girders in a number of bridges. The cracking Please address any reader comments to PCI Journal
and leakage are mainly due to inadequate design and editor-in-chief Emily Lorenz at elorenz@pci.org or
detailing of the transverse connection between adja- Precast/Prestressed Concrete Institute, c/o PCI Journal,
cent box girders, which eventually leads to excessive 209 W. Jackson Blvd., Suite 500, Chicago, IL 60606. J

174 Fall 2 0 0 9 | PCI Journal