Transverse Design of Adjacent Precast Prestressed Concrete Box Girder Bridges

18 Pages·2011·3.05 MB·English

Transverse Design of
Adjacent Precast Prestressed
Concrete Box Girder Bridges
Ahmed EI-Remaily
American and japanese design and detailing
Research Assistant
practices of prestressed concrete box girder
University of Nebraska-Lincoln
Omaha, Nebraska bridges are compared. A new precast,
prestressed box girder bridge design suitable to
U.S. practice is proposed. The design is based
on requiring the deck to act as a rigid assembly
of longitudinal and transverse members. This is
consistent with japanese practice and fulfills the
intent of several state DOT initiatives. The
proposal advocates quarter-point diaphragms
Maher K. Tadros, Ph.D., P.E. with relatively large amounts of transverse post
Cheryl Prewett Professor tensioning. A design chart and recommended
of Civil Engineering
details are provided for bridges up to 80 ft (24
University of Nebraska-Lincoln
Omaha, Nebraska m) long. The amount of post-tensioning was
found to be unaffected by bridge span length.
Also, a comparison with the requirements of the
AASHTO LRFO provisions is given. A fully
Takashi Yamane
worked numerical design example is included to
Chief Engineer
Kyokuto Corporation demonstrate the proposed design procedure.
Hiroshima, Japan
Precast, prestressed concrete box girders are widely used
in short and medium span bridges in North America.
Based on the National Bridge Inventory, Dunker and
Rabbat showed the change in percentage of the eight most
common prestressed concrete bridge types built in the
Uruted States during the period 1950 to 1989 (see Fig. 1).'
Gary Krause, Ph.D., P.E.
Stringer and multiple box sections are the most prevalent
Associate Professor
types of prestressed concrete bridges. Each system ac
of Civil Engineering
University of Nebraska-Lincoln counted for about one-third of all prestressed concrete
Omaha, Nebraska bridges constructed in the United States during 1979 to 1989.
96 PCI JOURNAL
en
Q)
Q
·'.a: 40
m-
Q)
...
Q)
CJ
c
0
0 30
'a
Q)
en
-en
...
Q)
en
-
!
a. 20
0
fie
10
om-~~~~----~~~~9------9----==~=-----~----~
50-54 55-59 60-64 65-69 70-74 75-79 80-84 85-89
Year Built
-Stringer/multi-beam or girder __._Box beam or girders -multiple
---tr-Siab ~Tee beam
""""*--Continuous stringer/multi-beam or girder ~Box beam or girders -single or spread
-...-Continuous box beam or girders -multiple ~Continuous box beam or girders - single or spread
Fig. 1. Percentages of prestressed concrete bridge types built during 1950 to 1989 (Ref.1 ).
Compared with other types of pre category of prestressed concrete grouted shear keys and, in some states,
stressed concrete highway bridges, tee bridge.1 are provided with a nominal amount of
and single/spread box structures have In adjacent box girder bridges, full-width transverse post-tensioning as
the highest deficiency percentages. boxes are placed butted against each shown in Fig. 2. In most applications,
However, since their introduction, no other as shown in Fig. 2. Adjacent box a 2 in. (50.8 mm) non-structural wear
major structural improvements have girder bridges are widely used in most ing surface is added. In a few cases,
been made to the system. Therefore, parts of the United States for spans up however, a 5 to 6 in. (127 to 152 mm)
there is definitely good reason to im to 100 ft (30.5 m) due to ease of erec structurally composite concrete over
prove these bridge types and thus con tion, shallow superstructure depth, and lay is used.
tinue and let grow the already excel aesthetic appeal. The girders are gen Recent surveys of adjacent box
lent reputation and performance of this erally connected at their interfaces by girder bridges have revealed frequent
July-August 1996 97
~
Girder length: 81' -6" :
Elevation
~
I
" "
" " I
~----------------------------------- ----------J..,
r---
Girder center - I I
-r- --- -- -------- -- - -- ·- ·
I I
---------------------------------------------------~,
J
Transv:rse
post-tensioning
Plan
Section between diaphragm .....e ---.--____,.~ . Section through diaphragm
52' -2"
1'-2" 24'- 11" 24' -11" 1'-2"
270k - ~" dia.
post-tensioning strand
12@ 48" = 48'-0" (576")
Typical Cross Section
Fig. 2. Elevation, plan and typical cross section of precast box girder bridges in the United States. Note: 1 ft = 0.305 m;
1 in.= 25.4 mm.
longitudinal cracking in the grout keys ment corrosion. This is particularly cient consideration of the structural
and reflective cracking in the overlay prevalent in bridges without relatively behavior of a bridge.2 Both shear and
over these keys. In some cases, water thick composite concrete overlays or bending must be transferred at the
and deicing chemicals have penetrated inadequate transverse post-tensioning. transverse joint between girders in
through the cracks, causing concrete Martin and Osborn related the prob order to control both translational and
staining and spalling and reinforce- lem of reflective cracking to insuffi- rotational deformation.
98 PCI JOURNAL
20 Girder length: 17 600 20
.. lr
l~
Tran~verse post-tensioning
t_A
4 300 4200
17 ()()() 300
Elevation
11200
600 600
10000
Curb (CIP)
Wearing surface
(50-80mm)
Transverse post-tensioning
Cast-in-place concrete I
(at diaphragm location)
I
I
13 = 10 140
B- B
A-A
Cross Section
Fig. 3. Precast, pretensioned concrete box girder bridge system for simple short span. Note: 1 m = 3.28 ft; 100 mm = 3.94 in.
A few state DOTs, e.g., Michigan, are similar to those in the United combines the performance require
use a combination of heavy struc States, except for size and shape of the ments for a Japanese bridge with the
turally composite topping and a large longitudinal joint between the girders simplicity of American construction
amount of transverse post-tensioning. and the amount of transverse post-ten practices. The proposed design in
Composite topping is not a structurally sioning.3 Cast-in-place (CIP) concrete volves provision of post-tensioned
efficient solution because it does not is placed in relatively wide and deep transverse diaphragms at quarter
control differential rotation of the box, joints between girders, as shown in points of the bridge span.
nor is it an economical solution be Figs. 3 and 4, as opposed to narrow The diaphragms would be made
cause a composite concrete topping mortar-grouted joints in the United continuous in the space between the
costs about four times as much as a States. Higher levels of post-tension boxes through deep blockouts filled
thin layer of bituminous concrete. ing are used in Japan than is the gen with grout. Post-tensioning is provided
In reviewing the practices in other eral practice in the United States. based on bridge width and loading, as
countries, it was found that cases of In the following sections, various suming the bridge consists of an as
longitudinal cracking are seldom re design approaches of typical precast, sembly of rigidly connected stringers
ported in Japanese adjacent box girder prestressed concrete box girder and diaphragms. A preliminary design
bridges. Cross-sectional shapes and bridges are discussed. A proposed de chart has been developed for simple
design criteria for box girders in Japan sign is also presented. The design span bridges of common width and
July-August 1996 99
170 560
Transverse GlB 100 1m80 180 -100
post-tensioning c
A
::::: :::::: :::: ::: :::::::: :;::::: :::::::
:::: :::::::: :::::: ::;::::: : I' ,,,,
v %s:}:::'::::::~ :: ;:::}:::::::::::::;;:': : ::::::,:;;::::::; H:tk:: :::::::::@::::::;;:::::::: : :::}:::::::::::;:{:::::::::: :: :::::;m::':::::4::}:::: ::::'::::::::::':::::::::' ::::::::: ::::;::;:;::::::::: : <:::::::::::::::I:lt: :::::;:::::::: : I::::::::::: :::::::::: : ~}::::::::::;u::::::::::::'::::: \] ~
B - B
A - A
Cross Section
Transverse post -tensioning
Detail C
Fig. 4. Transverse post-tensioning arrangement for Japanese box girder bridges. Dimensions are in millimeters.
Note: 100 mm = 3.94 in.
material properties using AASHTO 2. Is a waterproofing material or terms of percentage of respondents.
HS-25 live loading. membrane used over the longitudinal The survey data also indicated that 62
joints? percent of the respondents used
3. Is skew limited for the use of pre strands as the transverse tie material
RECENT STUDIES
stressed box beam bridges? while 38 percent used rods. The num
In 1992, the PCI Committee on 4. Are shear keys grouted after ten ber of transverse ties varied largely
Bridges formed a Subcommittee on sioning the ties? from state to state. Fig. 6 reveals that
Reflective Cracking in Adjacent Box 5. Is there a problem with differen the number of transverse ties is se
Beam Bridges to study the problem. tial camber between adjacent bands? lected quite arbitrarily.
The subcommittee's report (1995) in 6. Are there any problems with un Case Western Reserve University
dicated that at least two national sur even sealing of the beam ends for investigated the performance of shear
veys had been conducted with the goal skewed bridges? keys in adjacent box beam bridges in
of isolating the causes of reflective 7. What material is used for trans 1993.5 The five test bridges showed
cracking.4 The following are specific verse ties? differential deflections between 0.08
questions the committee identified as 8. What spacing is specified for and 0.8 in. (2 and 20 mm), which indi
most pertinent to its investigation: transverse ties? cated shear key fracture along part or
1. Are there any problems with The results of the survey for the first all of the bridge length. The large dif
leakage at the joints between beams? six questions are shown in Fig. 5 in ferential deflection resulted in leakage.
100 PCI JOURNAL
The test structures also showed a
satisfactory load distribution among 80
beams after the shear key partially
70
fractured. Mild steel lateral ties were
found to be ineffective in resisting dif 60
ferential deflections. The study sug
.t~.iA. ) 50
gested either moving the shear key
~
=
down to the neutral axis of the beam 40
u~...
or using a stronger epoxy grout in the
~ 30
existing shear key. ~
West Virginia DOT investigated 20
several high volume, heavily loaded
10
bridges that had joint failure and top
ping cracking.• The investigators con 0 ..
cluded that vertical shear failure in the ".'C"". l .'"5S ' ~E i..5Ci. l
keys was most likely the result of in .'.".. (E!)! u'" Ccl)
adequate grout installation and trans ~a ~
verse tie force. The ties used for the ::c:>
failed joints were 1 in. (25.4 rom) di Item Considered
ameter A36 rods spaced at the third
points along the span with an approxi Fig. 5. Survey summary.
mately 400 ft-lb (542.3 N-m) torque.
As a result of this investigation, the
West Virginia DOT changed its prac
12
tice as follows: Number ofTr , sverse Ties
1. A pourable epoxy is used instead I --None '_-- Three I
of a non-shrink grout in the shear key. 10 +-------t---------i---1 _ ··-··Four
2. The surfaces to be grouted are ...
"'
sand-blasted. .~.. 8 ................... ..
~ ..... ...... ...... ~
3. Post-tensioned high strength ties .0.=.0. .......... ::-.. ,.~~·
are used. ... 6
I , "'
In Oregon, the practice for adjacent .eQ~ .... ........ "'
....
box beams is to begin erection at ei ::s 4
z
ther one of the exterior beams or at the .
center of the bridge.• After the first ' ................. .. .,.
2 ....
two adjacent beams are in place, the _ -··-. . +! -.. .... ........
..
transverse tie rods are installed and the :
0
nuts are tightened. The sequence con
20 20-40 40-60 60-80 80- 100
tinues by placing a beam, installing
the appropriate number of tie rods, and Span (ft)
tightening the nuts each time.
After all the beams in a span are in Fig. 6. Number of transverse ties. Note: 1 ft = 0.305 m.
stalled, the bottoms of the shear keys
are sealed with a backer rod and the
keys are filled with grout. The keys sium ammonium phosphate grouted the transverse shear force to be re
are sandblasted in the precasting plant specimens displayed an exceptionally sisted by the joint for the appropriate
to remove laitance and enhance bond. higher failure load than the non-shrink values of span and {3, where f3 is given
The area around the shear keys should grout specimens. This result encour by the following formula:
be kept moist for 24 hours prior to in aged the use of magnesium ammo
stalling the grout. The grout should be nium phosphate for keyway grouting
kept moist for a minimum of 72 hours applications to eliminate some of the
following the installation. problems encountered with keyways.67
·
Gulyas, Wirthlin, and Champa un The Ontario Bridge Design Code as in which
dertook a labor~ory study to compare sumes that the transfer of load from b = half width of bridge
non-shrink grouts and magnesium am one beam to another takes place L = span of bridge
monium phosphate mortars.6 Compos mainly through transverse shear and Dx =longitudinal flexural rigidity per
ite grouted keyway specimens were that the transverse flexural rigidity is unit width
tested in vertical shear, longitudinal equal to zero.'·8 Charts such as those Dxy =longitudinal torsional rigidity
shear, and direct tension. The magne- shown in Fig. 7 are used to determine per unit width
July-August 1996 101
For this design, five diaphragms are
provided at a spacing equal to one
I I I
~ \ width, 2b = 1 2.5 m I 1\.\ width. 2b = 15.0 m f-- fourth of the span. This number was
chosen based on a parametric study
300 . \ ' v- ~ " 0.2 \ 1\ v-~ = 0.2-rr-- that was done to determine the appro
l\ / v-~ = 0.5 .I\ \ / v--~ = 0.5_- r- priate number of diaphragms.
~ _'.I \ ~ L . ~ = 1.0 ' \ 'I/ 1/ ~~ = 1.0_ - For spans up to 100 ft (30.5 m), by
! 200 \ ' / \ / ~ = 1.5 \'I1 \ \ lv V'v // _,-~ ~ 1.5- -- aunsidn gth frievee adt iqapuharrtaegrm pso, intwtso, daitf ftheree enntidasl
~i Il.\.', VK\ /' \ rl3 = 2.0 ~.\\ v '~ IX.. r ~ = 2I. 0- dine.f l(e0c.t5io mn mis ),l iwmhitiecdh tios laens sa cthcaenp t0ab.0l2e
"CD' ./ " \\I X )\ '- !
~"c~:' 100 1\ ,~"\.. 1 ~'".. 1' . . .... ....... .-....... ........., "."."_' \ ~~ ~...... !\..... ...'...-.." :i"- -"-. . -'--.Ji...!.. .. -- atrwemqoou uiarnte tts.h TeJ ehesens dutsrs aean nosdvf eotrhnsreee eap tdo tishatep- themrnaisdgidmolnes ,,
...... ~ :""'o r- I f"""o" ~-- ing than a five-diaphragm arrange
I ment. However, the corresponding dif
I
I ferential deflection may become
0
0 10 20 30 40 50 10 20 30 40 50 unacceptable, which defeats the main
purpose of transverse post-tensioning.
Span (m) Span (m)
Although the proposed five
diaphragm system provides a good
Fig. 7. Ontario Code design chart (Ref. 4). Note: 1 kN/m = 0.0685 kips per ft;
1 m = 3.28 ft. balance between performance and
economy, an additional parametric
study may produce a more optimum
The Ontario Code also requires that The amount and location of post solution. Parameters to be considered
adjacent box beam bridges be pro tensioning for the diaphragms are de should include speed of construction,
vided with a reinforced concrete struc termined by the flexural design. The tolerance to differential deflection be
tural slab of at least 5.9 in. (150 mm) design is primarily based on the work tween girders, and maximum accept
thickness capable of providing the ing stress method with the flexural able post-tensioning force.
shear transfer between the units. Be strength checked. A shear check is
cause of this provision, the bridges do usually waived in standard design.
Precast Section Modification
not have to rely on a grouted shear key Fig. 4 shows a typical transverse post
A minor change in concrete dimen
to transfer loads. tensioning arrangement for a Japanese
sions is recommended to allow for the
box girder bridge.
placement of grout between girders at
JAPANESE PRACTICE the diaphragm locations. The modified
PROPOSED DESIGN precast section is shown in Fig. 9. The
Four to seven equally spaced di
I in. (25 mm) side pockets are pro
aphragms, including end diaphragms, Prior to describing the details of the
vided with internal blackouts on the
are commonly provided for box girder proposed design, the design methodol
forms, as shown in Figs. 9 and A 1.
bridges in Japan.9 About 6.7 in. (170 ogy is discussed.
The proposed change thus does not re
mm) of clear spacing in the longitudi
quire any modification of existing
nal joint between girders is used in
Design Methodology steel forms.
Japan to provide for adequate toler
ance of differential camber between The proposed design involves provi
Member Force Analysis
girders. Box girders and diaphragms sion of rigid post-tensioned transverse
are integrated by cast-in-place con diaphragms. The diaphragms serve as Grid analysis is used to determine
crete between adjacent girders and the primary wheel load transfer mecha the member forces. The bridge deck is
post-tensioning. All highway bridge nism between adjacent boxes. Without modeled as a series of beam elements,
decks in Japan are covered with a 2 to diaphragms, each box must be designed representing the girders, connected
3 in. (50 to 80 mm) concrete or as to carry a full set of wheel loads with with another series of crossing beam
phaltic concrete wearing surface. out contribution from adjacent boxes. elements, representing the diaphragms.
Because of the built-in integrity, su As a result, large differential deflec The joints between elements allow for
perimposed dead and live loads are dis tions between girders will take place transmission of shear, bending, and
tributed over the entire bridge system in and reflective cracking could be ex torsion. •
both the longitudinal and transverse di pected [see Fig. 8(a)]. However, if the It is important to select realistic
rections. The member forces in the box box girders are fully connected, the properties of the girder elements to ob
girders and the diaphragms are com load is distributed over the entire bridge tain valid results. For example, it may
puted by modeling the bridge deck as a width and the deflected shape becomes be important to consider shear defor
slab or a gridwork of beam elements. a smooth curve [see Fig. 8(b)]. mations if the girders are relatively
102 PCI JOURNAL
deep and the diaphragm spacing is rel Table 1 (a). Geometric properties needed for grid analysis.
atively small. The geometric properties
Section type I Geometric properties
needed for the grid analysis are sum I--
marized in Tables l(a) and l(b). Diaphragm A =ah
I
Side rails and live loads are the main I= ah'/!2
causes of transverse bending moments -r-- 1= kha'
I
generated in the diaphragms. The live
load positions are chosen so that maxi
mum positive and maximum negative
h
moments are produced. The live load
is placed over the center of the deck
for maximum transverse positive mo
ment at midspan. For maximum trans
verse negative moment at the same lo -~I. -I
cation, the load is placed as close to the
bridge railing as is allowed.'0 This con a
cept is in general agreement with the
results of Gallt's analytical study at the
University of Kentucky."
Box section A and I are obtained
,. ., from Ref. 14.
Design and Detailing
h To obtain 1, the section
It is suggested that the diaphragms dimensions are
be post-tensioned. Designing the di simplified as shown in
aphragm as a non-prestressed rein -r-- the opposite figure.
forced concrete member is impractical D =
1 kha'- k,h,ai
because of the difficulty of projecting
a
a!
reinforcement and splicing it between
girders. Also, the absence of precom
pression would result in possible
--
cracking and leakage. The post
tensioning force should have no ec
centricity because the diaphragm ex
hi
periences significant alternating posi
tive and negative moments.
For working stress design, concrete
Note: h and h, are the longer sides.
stresses due to loads and post-tension A =cross-sectional area; I= moment of inertia; J =torsional inertia; k and k, are given in Table I (b).
ing forces are calculated and the total
stresses are checked against allowable Table 1 (b). Torsional parameter k for rectangular cross section.
stress limits. Tensile stress is not per
h/a
mitted because the diaphragm is a I 1.5 2 2.5 3 4 6 10
or h,la,
composite of both precast and grout
k or k, 0.141 0.196 0.229 0.249 0.263 0.281 0.299 0.312
components, and cracking of the inter
face should be avoided. Flexural
strength should also be checked.
The design chart shown in Fig. 10 is
Design Charts
obtained by dividing the required ef
Construction
The four standard AASHTO-PCI fective post-tensioning force for the
The construction process after erect box depths, 27, 33, 39 and 42 in. (686, midspan diaphragm by the spacing be
ing the girders consists of the follow 838, 991 and 1067 mm), were ana tween diaphragms and then taking the
ing steps: lyzed for three bridge widths of 28, 52 average of the spans analyzed. The
1. Girders are placed and post and 84ft (8.53, 15.85 and 25.6 m). For transverse post-tensioning should con
tensioning ducts are aligned. each combination of section depth and sist of one tendon near the top and an
2. Tendons are inserted through the bridge width, three different spans other near the bottom in order to pro
diaphragms. were considered. Appropriate span vide sufficient flexural strength.
3. Grout is poured between the ranges were considered for each sec The required post-tensioning force
girders. tion depth. The required transverse for the quarter-point diaphragms was
4. When the specified grout strength post-tensioning force was found to be found to be similar to the midspan di
is reached, transverse post-tensioning almost linearly proportional to the aphragm. It is recommended, there
is applied. span length. fore, to use the same post-tensioning
July-August 1996 103
Wheel load
Differential
'
/ deflection
v
----------· i---------- '
I I
I
II I
II I
,_---------_II,I _---------_:I
(a) Deflected shape of unconnected boxes
Wheel load
-----·
---------- -----------:
~----------
,_----------··-----------··-----------·:------_____ 1: ---________ ,, ___ --------
(b) Deflected shape of fully connected boxes
Fig. 8. Schematic of deflected shape of box girder bridge.
force for the quarter-point diaphragms continuously supported over the abut (1.72 MPa), applied to the diaphragm
as for the midspan diaphragm. The end ments. For the end diaphragms, it is cross-sectional area, in order to main
diaphragms, however, have almost no recommended to use a minimum ef tain adequate stiffness at the ends of
bending moments because they are fective post-tensioning stress of 250 psi the bridge.
Table 2. Incremental cost analysis. Cost Analysis
Post-tensioning and grout Materials Unit cost Cost To determine the impact on construc
Subtracting post-tensioning tion cost, a comparison between a con
130 lbs $2 -$260
(270k 1h in. diameter strand) ventional American design and the pro
Adding grout 22.2 cu ft $50 + $1110 posed design is made in Table 2. The
proposed design requires grout and in
Adding post-tensioning
( 150k 1/• in. diameter bar) 1700 lbs $2 + $3400 creased transverse post-tensioning.
The longitudinal joint between the
Total - - + $4250
diaphragms now no longer serves any
= =
Incremental construction cost of proposed design $4250/(80 x 52) $1.02 per sq ft
structural purpose. To make this com
Note: I fl = 0.305 m; I lb = 0.4536 kg. parison, five 1h in. (12.7 mm) diame-
104 PCI JOURNAL
ter strands, one per diaphragm, are as
sumed to be used for transverse "ties"
in the standard design. They are re
placed with the much heavier trans
verse post-tensioning in the proposed II
II
design.
•
The calculation is made by subtract ,.--
ing the amount of tranverse ties from 3"
~£1
the proposed transverse post-tension
ing to determine the incremental cost. 42"
The additional cost of the proposed
l-3d3"
design is only $1.02 per sq ft. This is a •
very modest increase in cost consider L-
ing the projected substantial improve I. ..I
48"
ment in durability.
Original Precast Section
COMPARISON WITH
AASHTO LRFD
The AASHTO LRFD Specification
states that the use of transverse mild ll1." 46" 1.."I I
steel rods secured by nuts should not
be considered sufficient to achieve full 2" dia. duct-
transverse flexural continuity unless
demonstrated by test or experience.'2
To make the boxes act together, t I t
40"
AASHTO LRFD recommends a mini
mum average effective post-tensioning
pressure of 250 psi (1.72 MPa). How
ever, it does not specify the contact
area over which this prestressing force
L 2"
.. I
should be introduced. In double-tee 48"
applications, for example, it is obvious
that the flange area is to be used. In
adjacent box applications, it is not Modified Precast Section at Diaphragm
clear whether it should be the top
shear key area, the diaphragm-to
diaphragm contact area or the full
girder side face. Also, it does not spec
ify the spacing between diaphragms
nor the diaphragm size. Three differ
ent interpretations are compared
2" dia. post-tensioning duct
below for the box type used in the de
sign example.
If the post-tensioning is to be applied
~8"
over the whole contact area between
boxes, the required post-tensioning
force per diaphragm is equal to 42 x 20
X 12 X 0.25 = 2520 kips (11.2 MN). If
only the shear key area is to be consid
ered, the required post-tensioning force
is 6 X 20 X 12 X 0.25 = 360 kips (1600
kN) per diaphragm.
Note that if the diaphragm area is
Plan
used in the calculation, the required
post-tensioning force is 8 x 42 x 0.25
= 84 kips (374 kN) per diaphragm.
The value obtained by analysis, as
shown in Appendix A, is 202 kips Fig. 9. Comparison of precast concrete sections. Note: 1 in. = 25.4 mm.
July-August 1996 105