47189_1248369986_773
TRANSCRIPT
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1. Introduction
Located almost at the center of the Honshu-Shikoku
Bridge Onomichi-Imabari Route (Nishiseto Expressway
or popularly called Shimanami Kaido), the Tatara
Bridge is the worlds longest cable stayed bridgemeasuring 1 480 m in total length and 890 m in center
span, linking Ikuchijima Island in Hiroshima Prefecture
and Ohmishima Island in Ehime Prefecture. The Third
Construction Bureau of the Honshu-Shikoku Bridge
Authority placed orders for design, fabrication and
erection of the bridge in January 1994 and the IHI-
Yokogawa-NKK-Takigami-Matsuo Specified Construction
Joint Venture was put in charge of the Ohmishima
Island (Ehime Pref.) side of the bridge.
This paper provides general information on the design
of the Tatara Bridge.
2. Outline of the Tatara Bridge
The Tatara Bridge is the worlds longest cable stayed
bridge, whose 890 m center span is longer than that of
the Normandy Bridge in France by 34 m. Fig. 1
shows the general arrangement of the Tatara Bridge,while the main tower and the main girder section are
shown in Fig. 2 and Fig. 3, respectively. The section
distribution is shown in Fig. 4. The main tower is 220
m high and designed as an inverted Y shape. It has a
cross-shaped section with corners cut for higher wind
stability and better landscaping.
The main girder section consists of three spans, 270
m, 890 m, and 320 m, and measures 1 480 m in total
length. As either side span is shorter than the center
span, PC girders are installed at each end of both side
span sections as counterweight girders to resist negative
Design of Tatara Bridge
YABUNO Masashi : Design Department, Bridge & Road Construction Division,
Logistics Systems & Structures
FUJIWARA Toru : Manager, Planning & Development Department, Honshu-
Shikoku Bridge Authority
SUMI Kazuo : Manager, Bridge Maintenance Section, Naruto Operation
Office, Honshu-Shikoku Bridge Authority
NOSE Takashi : Manager, Overseas Project Department, Bridge & Road
Construction Division, Logistics Systems & Structures
SUZUKI Masanao : Manager, Design Department, Bridge & Road Construction
Division, Logistics Systems & Construction
The Tatara Bridge is the worlds longest steel-concrete hybrid cable stayed bridge. It measures 1 480 m intotal length and 890 m in the center span. The side spans consist of steel and prestressed concrete (PC) girders.
IHI, as one of the joint venture member companies, received the order for design, fabrication, and erection of
the Ohmishima Island side of the bridge in 1994. The bridge design is described.
1 480 000
890 00050 000 170 00050 000
105 500
PC girder
1 312 000
Steel girder
T.P.+0.000
T.P.-33.000
T.P.+44.460
Ikuchijima Island side
(Hiroshima Pref.)
39000
25 000
T.P.+6.000 N.H.H.W.L. T.P.+2.200
T.P.+47.661
T.P.+46.215 T.P.+28.200
T.P.+226.000
25 000
19000
T.P.-13.000
Ohmishima Island side
(Ehime Pref.)
T.P.+44.135
T.P.+6.000T.P.+46.215
T.P.+226.000
62 500
PC girder
270 000 50 000
M M M K K MM
3P P3 4P2PP11A P2
(Note) T.P. : Mid-tide in Tokyo Bay (unit : m)N.H.H.W.L : Nearly highest tide level (unit : m)
Fig. 1 General arrangement (unit : mm)
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reaction. This cable stayed bridge thus uses a steel and
PC connection girder.
The bridge has a total width of 30.6 m, including a
road for motorized bicycles and pedestrians (hereafter
called sidewalk) and a girder height of 2.7 m. It uses
flat box girders attached with fairings to ensure wind
stability. Cables installed in 21 levels were two-plane
multi-fan cables (maximum cable length: about 460 m).
Cables of the bridge have indented surfaces in the
polyethylene cable coating, similar to dimples on a golfball, to resist vibration caused by both windy and rainy
weather (rain vibration) (Fig. 5).
The outline of the erection is illustrated in Fig. 6.
The main girders were erected in a balancing method,in which girders for the main span and side spans are
erected alternately block by block, up to the seventh
level. Then, about 100 m long steel girders were
25 00043 000
12 000 12 000
17 000 8 5008 500
T.P.+226.000
T.P.+45.400
T.P.+46.215
T.P.+38.500
32 500
15 420
3000
3000
6000
19000
32500
2500
36900
220000
180600
6 0006 000
C1C42
C41
C40
C39
C38
C37
C36
C35
C3
4
C33
C32
C31
C30
C29
C28
C27
C26
C25
C24
C23
C22
C43 C4
4
C45 C4
6
C47 C4
8
C49 C5
0
C51 C5
2
C53 C5
4
C55 C
56
C57 C
58
C59
C60
C61
C62
C63
C2
C3 C4
C5 C
6
C7 C
8
C9
C10
C11 C
12
C13
C14
C15
C16
C17
C18
C19
C20
C21
C84
C83
C82
C81
C80
C79
C78
C77
C
76
C75
C74
C73
C72
C71
C70
C69
C68
C67
C66C
65
C64
25 000
2P 3P
43 000
T.P.+6.000
12 000 12 000
17 000
T.P.+226.000
T.P.+45.400
T.P.+46.215
T.P.+38.500
N.H.H.W.L.T.P.+2.200
32 500
15 420
3000
3000
6000
39000
32500
2500
36900
220000
180600
T.P.+6.000
T.P.-33.000
T.P.-13.000
N.H.H.W.L.T.P.+2.200
Fig. 2 General arrangement (main tower) (unit : mm)
2 500 2 5002 245 2 245295
9 500
6 380 6 380
2700
9 040
21 8004 400 4 400
Center distance of cable anchor points 23 000
30 600
Road forbicycles
andpedestrians
Road formotorizedbicycles
Road forbicycles
andpedestrians
Road formotorizedbicycles
9 500260260295
1% 2%
Shikoku-bound lane Honshu-bound lane
2% 1%
Cross section of steel girder
Diaphragm section Lateral rib section
2 500 2 5002 245 2 245
295
9 500
21 8004 400 4 400
Center distance of cable anchor points 23 000
30 600
1 0001 000 9 500
260
260
295
2700
Shikoku-bound lane Honshu-bound lane
Cross section of PC girder
Side span section Supporting point
1% 2% 2% 1%
Fig. 3 General arrangement (main girder section) (unit : mm)
Fig. 5 Indent of cable surface
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4
2
890 000
30 000 2222 000 28 000
28 000 22 000
9 000108 000
= 80 000
4 20 000
= 80 000
19 20 000 = 380 000 19 20 000 = 380 000 2 000 13 000
11 000
9 000 16 000
170 000
5 500 Steel girders 1 312 000
161616
16
19
19
19
19
14
16
1212 14141413 1111 10
320
320
240
6
3202408
320
240
8
22
22
22
22
15
25025
25025
25025
25025
20022
20022
20022
20022
16016
17016
20022
20022
200192001925025 20019 1901923022
16
16 14 14 12
250 000 60 00060 000 40 00040 00060 00060 000 60 00060 000
60 000 20 00020 000 20 00020 00032 000 21 000 21 021 000 14 000 32 500
32 00010 500
1622
50 00050 000
1 480 000
2PP11A P2
CL
2221201918171615
JIGEDCBA
141312
BCD
1110987654321
Interval of cableanchor points
Side span length
EGIJLMLJIHN
Fig. 4 Section distribution (unit : mm)
Section number
Section classification
Sectional changelength
Steel plate deckflat rib
Steel plate deck thickness
Steel plate deck trough rib
External web platethicknessExternal webplate flat rib
Internal web platethickness
Lower flange thickness
Lower flange trough rib
Internal webplate flat rib
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altogether erected as a single large block with floating
cranes to the PC girder section.
The length of the large girder block in the side span,
which is about 100 m, was determined and designed
to be self-supporting as a single beam. It is the first
time in the world that both balancing erection and largeblock erection were used for erection of girders. For
the center span, the work of main-girder cantilever
erection using traveler cranes was conducted block by
block for both work areas.
3. Basic design conditions
3.1 Design conditions
The Joint Venture started its detailed design work in
January 1994 and continued for about one and a half
years. Table 1 shows the design specifications, while
Table 2 shows a list of quantities used in the design.
3.2 LoadsTable 3 and 4 show design loads and combinations of
loads, respectively.
4. General structural analysis
4.1 Analytical procedure
The general structural analysis flowchart is shown in
Fig. 7. To begin with, cable prestress was determined
by infinitesimal deformation analysis to finalize the
condition of the final profile. Then, sectional force
analysis was conducted for each loading case by
linearized finite displacement analysis using this
completed system model in which initial internal forcewas set under this condition of the final profile. Then,
sectional force, displacement and reaction were
calculated and the results were edited for use in design
of each member.
4.2 Analytical model
4.2.1 Modeling of main girders
A three-dimensional skeleton model was used for
analysis of the overall structure (Fig. 8). It is a fishbone
model in which each girder is a single road and virtual
members are extended to cable anchor points. During
modeling, the axial centers of girders were placed at
the middle point between the diagram center and theshear center so as to allow it to be used also as a
dynamic analysis model.
4.2.2 Modeling of main tower
Cable length was taken into consideration for analysis
of the main tower by creating a main tower model in
which virtual members are extended from the axial
center of the tower to cable anchor points (Fig. 9). In
reality, even though the target points of cables for the
center span and the side spans are set on the axial line
of the main tower with some deviation from each other,
they are sometimes designed as identical in structural
analysis. In this case, it is easy, in analysis, to makebending moment of the main tower zero by balancing
the horizontal components of cable tension in the final
profile. But if we try to manage an actual bridge with
this tension and balance horizontal components of force,
bending moment will occur in the tower and can slopethe tower due to misaligned setting of target points in
the actual structure and the defective consequence will
appear in the form of camber errors in girder.
Item Description
Route 317 (Onomichi-Imabari route)
Tatara Bridge
Three-span continuous composite cable stayed bridge
L = 1 480
L = 270 + 890 + 320
B live load (Specifications for Highway Bridges)Feb. 1994
Category 1, Class 3
V= 80
4 lanes (9.5 m 2) + sidewalk (2.5 m 2)
2.0 straight line
1.0 straight line
A = 300, R = 600
Straight line to a plane
A = 539.838, R = 599.700
0.65 grade to straight line
0.325 parabola
26 m from nearly highest tide level(T.P.+2.200+26.000)
Inverted Y shape with steel slits (base designedas a trapezoidal structure with the bottom sideshorter than the topside)
H= 220 (T.P. + 226.000)
Base : 12TT 8.5LL, Top : 6TT 6LL
(LL : direction of bridge axis; TT : directionperpendicular to bridge axis)
Steel girder section: 3-cell steel box girderPC girder section: 3-cell PC box girder
H= 2.7(at the center of the bridge of the standard part)
Total width : 30.6, Outside web interval : 21.8,Cable anchoring width : 23.0
Two-plane multi-fan 21-level non-grout PWS(strand f 7 mm)
Asphalt pavement
Steel girder section : 65, PC girder section : 75
30
Steel girder section : Steel plate deck,PC girder section : PC slab
Fixing block method
Web-mounting square column anchoring method
SS400, SM490Y, SM570
SS400, SM490Y
sck= 24{sck= 240}
s= 640
{s= 6 400}
(Note) F : FIX
M : MOVE
(N/mm2
){kgf/cm2}
( N/mm2)
{kgf/cm2}
1A
F
F
M
P1
F
M
M
P2
F
M
M
P3
F
M
M
4P
F
F
M
2P
F
F
K= 2 000 t/m
3P
F
F
K= 2 000 t/m
Table 1 Design specification
Cross grade
Road name
Bridge name
Bridge type
Bridge length (m)
Span length (m)
Design live load
Road specification
Design speed (km/h)
Number of lanes
Under clearance (m)
Main tower
Main girder
Cable shape
Deck slab type
PC girder member standarddesign strength
Cable strand allowablestress
Vertical direction
Direction of bridge axis
Direction perpendicular to bridge axisSupportingconditions
Pavement
Anchoringmethod
Main steelmembers
Horizontalalignment
Verticalalignment
Roadway (%)
Sidewalk (%)
Side span (%)
Shape
Tower height (m)
Sectional dimension (m)
Girder height (m)
Girder width (m)
Type
Main tower side
Main girder side
Main tower
Main girder
Roadway (mm)
Sidewalk (mm)
Shape
Center span (%)
Side span on the 1A side (m)
Center span
Side span on the 4P side (m)
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0.607
0.607
0.009
0.000
0.000
0.000
0.007
0.002
0.001
0.000
0.000
0.004
0.005
0.010
0.000
0.009
0.016
0.004
0.030
0.021
0.011
0.000
0.000
0.002
0.000
0.134
0.740
0.113
0.004
0.117
0.002
0.003
0.001
0.000
0.005
0.122
2.532
0.005
0.183
0.073
2.793
0.023
0.033
0.008
0.002
0.003
0.003
0.001
0.072
2.865
1.219
12.501
12.501
0.193
0.004
0.009
0.001
0.141
0.035
0.024
0.005
0.006
0.086
0.106
0.206
0.008
0.188
0.332
0.074
0.620
0.440
0.218
0.007
0.001
0.041
0.007
2.753
15.254
2.325
0.078
2.403
0.038
0.052
0.011
0.009
0.109
2.513
52.164
0.109
3.768
1.500
57.541
0.473
0.673
0.155
0.045
0.059
0.055
0.018
1.477
59.018
25.121
16 401
16 401
285
6
14
2
209
52
36
8
9
127
157
305
12
278
492
109
917
651
323
10
2
61
10
4 075
20 476
3 441
116
3 557
56
77
16
13
162
3 719
11 476
24
829
330
12 659
104
148
34
10
13
12
4
325
12 984
37 179
910
910
19
0
1
1
13
3
2
0
3
8
9
18
0
20
31
0
72
31
18
1
0
2
0
252
1 162
476
16
492
0
0
0
1
1
492
3 387
6
274
0
3 667
28
32
8
0
0
0
0
68
3 735
5 389
8 902
8 902
148
3
8
1
115
28
19
3
6
69
82
159
6
160
260
41
496
356
164
5
1
32
5
2 167
11 069
1 763
58
1 821
28
38
8
7
81
1 902
5 756
12
418
165
6 351
52
74
17
5
6
6
2
162
6 513
19 484
7 499
7 499
137
3
6
1
94
24
17
5
3
58
75
146
6
118
232
68
421
295
159
5
1
29
5
1 908
9 407
1 678
58
1 736
28
39
8
6
81
1 817
5 720
12
411
165
6 308
52
74
17
5
7
6
2
163
6 471
17 695
Steel girder
Steel girder - subtotal
Base structures of accessories A
Base structures of accessories B
Drainage A
Access door
Rail for maintenance vehicle A
Rail for maintenance vehicle B
Supporting member in girder A
Supporting member in girder B
Bridge light base
Maintenance gangway
Safety fencing for vehicles A (median strip)
Safety fencing for vehicles B (shoulder)
Safety fencing for vehicles B2 (shoulder integrated)
Fairings A (shop attachment)
Fairings B (field attachment)
Fairings C (PC)
Sidewalk (1) (shop installation)
Sidewalk (2) (shop installation)
Handrailing of sidewalk
NTT supporting (1)
NTT supporting (2) (PC)
Chugoku Electric Power Co. supporting (1)
Chugoku Electric Power Co. supporting (2) (PC)
Main girder accessories - subtotal
Main girder related - total
Cable
Socket
Cable - subtotal
Anchor block for main tower
Anchor block for main girders
Shim plate
Cable cover
Cable attachments - subtotal
Cable related - total
Main tower
Remaining materials for erection of main tower
Welding of main tower
Fixing block
Main tower proper - subtotal
Connecting corridor
Accessories for internal tower
Accessories for external tower
Accessories of tower top
Cable waterproofing pipe
Obstacle light
Tower-attached management equipment
Accessories of main tower - subtotal
Main girder
Main girder
accessories
Cable
Cable
attachments
Main tower
Main tower
accessories
Grand total of Tatara Bridge
Main tower related - total
(Note) The mass of steel per square meter was calculated based on the effective width of 20.6 m.
Mass ofsteel/m2
(t/m2)
Mass ofsteel/m(t/m)
Total of entireTatara Bridge
work (t)
IHI portion
(t)
Phase 1work - total
(t)
Phase 2work - total
(t)RemarksItem
Table 2 Amount of quantity
Calculated assuming steel girder length is 1 312 m
Calculated assuming bridge length is 1 480 m
Total for steel girder section
Calculated assuming bridge length is 1 480 m
Calculated assuming tower height is 220 m
Calculated assuming bridge length is 1 480 m
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11.01
17.05
1.00
1.10
0.36
13.47
19.51
3.13
0.43
3.56
0.00
0.14
0.24
0.18
0.04
0.60
4.16
0.03
0.18
0.05
0.06
0.20
0.52
0.15
0.02
0.17
0.03
0.10
0.13
0.82
18.45
24.49
63.91
92.14
1.10
65.01
93.24
3.46
0.35
0.25
4.06
0.14
0.460.16
0.17
0.93
0.11
0.21
0.18
0.04
0.54
5.53
0.05
0.06
0.20
0.31
0.15
0.02
0.17
0.00
0.48
71.02
99.25
Input
waves
Accessories
Vehicle live load
Management road live load
Seismic live load
Applicable standard
Bridge
surface work
Pavement
Ground
covering
Handrail
of safety
fence
Bridge surface work - subtotal
Accessories - subtotal
Managementfacilities
Utility
Road section
Sidewalk section
Cable anchor points
Subtotal
Median strip
ShoulderInside of sidewalk
Outside of sidewalk
Subtotal
Median strip
Shoulder
Inside and outside of sidewalk
Safety fence against falling objects
Subtotal
Drainage device
Maintenance vehicle rail
Road lights
Fire hydrants
Electric equipment
Subtotal
Chugoku Electric Power Co.
NTT
Subtotal
Rail for maintenance vehicles inside girders
Cable attachments
Subtotal
Short-cycle spectra
Long-cycle spectra
Long-cycle time history waveform
Vertical spectra
Hyogoken Nambu Earthquake
Purpose
For design
For design
For check
For design
For check
B live load (Feb. 1994, Specifications for Highway Bridges)
Superstructure design standard 2.3.2
L (EQ) = 1/2 [L* (H) ]
L* (H) : p2 (equivalent distribution) of main load and sub load was provided to the entire bridge.
Acceleration response spectra for Tatara Bridge substructure design
Design acceleration response spectra of the seismic design standard
Earthquake waveform for checking of superstructure of Tatara Bridge
One half of both long-cycle and short-cycle spectra
Seismic motion (spectra) observed at the Kobe Marine Meteorological Observatory
Accessories
Bridge
proper
Table 3 Design loads
Dead load strength (tf/m/Br)
Dead loads - total
Bridge proper
Sidewalk
Fairing (including inspection road)
Erection reinforcement
Subtotal
Completed system Remarks
PC section included in the bridge proper
Steel girder PC girder
Live loads
Onomichi-Imabari Route Wind Resistance Design Standard and its Commentaries (fourth plan), May 1994
Wind load
Seismic force
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P + Li + T+ SD + E
P + W+ T+ SD + E
P + W+ T+ SD + E
P + EQ + L (EQ) + T+ SD + E
P = D + PS + PT+ CR + SH+ CW
Li = L + I
L (EQ) : live load during earthquakeFor temperature during a storm (+15C), both cases with and without its
influence should be considered and extracted.
P
P + Li + SD
P + Li + T+ SD
P + Li + W+ SD
P + EQ + L ( EQ ) + T+ SD
(Note) EQ : Seismic load
SD : Movement of supporting point
I : Impact coefficient
Li : Live load (including impact)
CW: Counterweight
PT : Prestress inside PC girder
CR : Creep
L (EQ) : Live load during earthquake
E : Fabrication/erection error load
W: Wind load
T : Temperature
L : Live load
P : Main load
SH: Dry shrinkage
PS : Prestress
P = D + PS + PT+ CR + SH+ CW
Li = L + I
L (EQ) : live load during earthquake
SD should take a value 50% reduced.
1
2
3
4
1
2
3
4
5
1.00
1.50
1.40
1.50
Allowable bending
compression stress
N/mm2 {kgf/cm2}
Allowable
tensile stress
N/mm2 {kgf/cm2}
Remarks
Remarks
Additional factorof
allowable stress
Additional factor
of
allowable stress
Members appliedSteel structure section
PC girder section
Maingirder
Maintower Cable Support
1.00
1.00
1.15
1.50
1.50
14 {140}
14 {140}
16 {161}
21 {210}
21 {210}
{ 0}
{ 0}
{ 5}
{25}
{30}
0
0
0.5
2.5
3.0
Table 4 Combinations of loads
Static analysis
Li, T, SD, W, L (EQ)
Creep and dry shrinkageanalysis
CR, SH
Seismic responseanalysis
EQ
Determination of PS
Calculation of cable
prestress (PS)
Loading of dead loads (D2)
excluding PC girder dead load (D1)
Preparation of simple
beam PC girder model
Loading of PC girder
dead load (D1)
Preparation of two
dimensional skeleton
Loading calculation of
counterweight (CW)
Main tower buckling analysis
Main girder buckling analysis
Skeleton analysis for floor
arrangement system
To design of each
members section
To PC girder
section design
FEM analyses forindividual reviews, such
as cable fixing points
Summation of sectional force, displacement and reaction of completed system
(ordinary time, storm and earthquake)
Determination of final profile (D1
+ D2
+ PS + CW)
Summation of sectional force, displacement, reaction, acceleration, and response
amplitude of erected system (ordinary time, storm and earthquake)
To member check, erection reinforcement
and erection machinery and equipment
Erected system seismicresponse analysis
(at the time of balancing erection)
(at the time of cantilever erection)
Gust response analysis atthe erection stage
(at the time of balancing erection)
(at the time of cantilever erection)
Analysis of erection
stage
(all erection step)
Preparation of twodimensional final profilemodel for erection stage
Preparation of 3D erection stage model
Fig. 7 Flowchart of analysis
Analysis of final profile Analysis of erection stage
Preparationoffinalprof
ilemodel
Analysisofsectionalforc
e
forfinalprofile
Individual
analyses
Section
design
Preparation of 3D skeleton for the entire bridge
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For ordinary bridges, such an impact is not so
influential and causes no practical damage, but the
Tatara Bridge is very long and its girder rigidity is
relatively soft and thus any slight error in target points
will give a serious impact on the girder camber shape.
In order to reduce the influence of such minor error in
target points on the model, prestress was determined
and the actual structure of the bridge was precisely
simulated in the initial modeling stage in which the final
profile is generated. Then, the deviation of target points
was reflected on the model.
4.2.3 Cable modelingA cable is converted to a rod model, with its sectional
area alone being considered. The bending rigidity of
the cable is ignored. Converted modulus of elasticity
Eeq by the equation of H. J. Ernst, as shown below, is
used to consider reduction of rigidity by the influence
of cable sag.
..........................(1)
E0 : Modulus of elasticity of a straightcable (2.0 105 N/mm2)
g : Unit volumetric weight of cable
= w/A (N/mm3)
E
L E+
0
2 20
31
12
Eeq =
L : Horizontal projection length of cable
(mm)
s : Tensile stress of cable = T/A (N/mm2)
w : Weight per unit length of cable
(N/mm)
T : Cable tension (N)A : Cable sectional area (mm2)
Note that the value ofT is the value when the final
profile is prepared (when prestress was studied, T= (D
+ PS) given in the basic design was used). When the
loading was calculated for each loading case after
determination of the final profile model, cable tension
T = (D2 + PS) determined in the detail design phase
was used to set Eeq (where D, PS, and D2 represent
dead load, cable prestress and dead loads other than
PC girder dead load).
4.3 Cable prestress (PS)
When cable prestress for the Tatara Bridge wasdetermined, the following points were considered.
(1) Bending moment of steel girders should be reduced
and made uniform.
(2) The main tower should have no displacement in
the direction of bridge axis in the condition of (D2+ PS) (bending moment of the main tower M
0).
(3) There should be no void of cable tension.
(4) Cable section should be uniform.
(5) Girders sectional force at the center of the center
span should be reduced (axial force N= 0, M
small).The bending moment at the PC girder section due to
the dead load of PC girders (D1) is extremely large
compared with the steel girder section and adjustment
of such bending moment by means of cable prestressing
alone is not realistic. Therefore, it was decided that no
improvement of bending moment of PC girders by
means of cable prestressing would be made. The
counterweight CWfor the PC girder section was excluded
from the conditions used for determination of cable
prestress because of the following reasons.
(1) The counterweight itself is effective against
reaction, but its impact on the final profile is smalland therefore may be ignored when determining
prestress.
(2) The counterweight CWwas to be determined so
as to satisfy the negative reaction check method,
but if the counterweight CW is to be involved in
determination of prestress, it will require a
convergent calculation with the entire analysis,
complicating the setting conditions of the
counterweight CW and requiring a convergent
calculation for the final profile. Thus, the entire
analysis can be very complicated.
(3) In case the unit weight of the counterweight orthe range of counterweights CW to be driven
changes for some reason, it will become unclear
about for which final profiles cable prestress was
Point of intermediate member
Cable
Main girder
Panel point at fixing position
(Note) A : Sectional areaI : Inertia moment of sectionJ : Torsion modulus
Pin structure
Direction of bridge axis
Virtual member( A, I, J= )
2P
1A
3P
4P
R side (north side)
L side (south side)
Fig. 8 Skeleton model for analysis
Center span
Towerwall
Tower shaft
Virtual member
Cable
Cable
Horizontal
Fixing pointof cable strand
Side span Center spanSide span
Modeling
(a) Main tower fixing point structure (b) Main tower fixing point model
Fig. 9 Modeling of main tower
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set. Thus, it is desirable not to relate the
counterweight CW to determination of cable
prestress.
The relative rigidity method was therefore used for
calculations to determine cable prestress.
4.4 PC girder deadweight loading for compositecable stayed bridge
For a steel and PC composite cable stayed bridge, the
difference of girder dead loads is so large that it becomes
difficult to make uniform the bending moment of all
girders by cable prestress. The major role of PC girders
used for part of the side spans of the Tatara Bridge
is to serve as a counterweight. Then, there are two
options, whether we should make the dead load of PC
girders, which are part of the girders, influence the
final profile or not influence it by taking the PC girders
merely as counterweights. Which method is favorable
should be reviewed depending on the structuralcharacteristics or conditions of each bridge.
For the Tatara Bridge, the dead load of PC girders
at the side spans (D1) was not loaded on the final profile
model, but the structural design of the bridge was made
by combining the values obtained from analysis with
a simple beam PC girder model with the analysis of
the final profile model. In conclusion, in our model
calculation, rigidity alone is present in the entire bridge
model, girders are those with no deadweight, and the
PC girders are treated completely as counterweights.
4.5 Fabrication/erection error load (E)
1/2 000 of the tower height for error of inclination ofthe tower and 5% of working stress for main girders
and cables are generally allowed for in a basic design
with regard to fabrication and erection error loads. But
as the error of inclination of the tower ended up being
within 5% of working stress, 5% of working stress was
allowed for as fabrication/erection error in the detail
design.
5. Seismic design
5.1 Seismic analysis
Design and design check were carried out by two seismic
analytical methods: spectral response analysis, which
is one of the mode analysis techniques, and time historyresponse analysis, which is a time-domain analysis
using mode analysis. Load combinations used in the
design are shown by the following equation.
..............(2)
D : Dead load
CW : Counterweight
L(EQ) : Live load during earthquake
SD : Influence of supporting point
movementPS : Prestress
EQ : Influence of earthquake
T : Influence of temperature change
E : Fabrication/erection error
The safety factor of allowable stress is 1.5 for
earthquake. Seismic analytical cases are shown in Table
5.
5.2 Results of seismic analysis
5.2.1 Results of spectral response analysis
Cross section design of major structural parts, or main
girders, main tower and cables, was not based on any
condition in case an earthquake occurs. Of bearing,reaction in the direction perpendicular to bridge axis
was largest in an earthquake. Movement of the supporting
points in the direction of bridge axis and the direction
perpendicular to bridge axis was greatest in an
earthquake. Therefore, the values of bearing movement
and those of expansion devices for the earthquake case
were used as the standard.
D PS CW EQ L EQ
T SD E
+ + + + +
+ +
( )
AnalysisNo.
Analytical method Input wave Input method
Input direction
Bridge axis VerticalPerpendicularto bridge axis
Calculation of groundspring
Kurushima Method
Aseismic Method
Aseismic Method
Aseismic Method
Kurushima Method
Response spectral analysis(CQC method)
A short-cycle spectra
B long-cycle spectra
C long-cycle time history
D long-cycle time history
E Spectra observed fromthe Hyogoken Nanbu
Earthquake
Same phase(multiple point
simultaneous input)
Same phase(multiple point
simultaneous input)
Same phase(multiple point
simultaneous input)
Same phase(multiple point
simultaneous input)
Phasal difference
Response spectral analysis(CQC method)
Time history responseanalysis
Time history responseanalysis
Response spectral analysis(CQC method)
1
2
3
4
5
(Note) Ground spring was calculated based on the following standards:- Kurushima Method: Kurushima Bridge Steel Foundation Aseismic Calculation Method (proposed)- Aseismic Method: Honshu-Shikoku Bridge Authority Aseismic Design Standard (February 1977)
Table 5 Earthquake analysis cases
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5.2.2 Results of time
history response
analysis
Sectional force, displacement
and acceleration of major
structural components, or maintower, main girders and cables,
were generally smaller in value
than those obtained from the
analysis of spectral response.
This fact confirmed safety from
the design viewpoint. Bearing
reaction and movement were
also confirmed to be below the design value by the
results of time history response analysis.
6. Wind resistant design
Wind resistant design was carried out in accordance withthe Onomichi-Imabari Route Wind Resistant Design
Standard and its Commentaries (fourth draft), May
1994, Honshu-Shikoku Bridge Authority. Various wind
tunnel tests were also conducted, which will be reported
some other time.
6.1 Wind resistant design for completed system
6.1.1 Design wind resistance
Wind load to be applied to girders and cables:
PD = 1/2 m2 r Uz2 CD An ......................(3)
Wind load to be applied to the tower
PD = 1/2 m3 r Uz2 CD An ....................(4)
Where
Uz = m1 U10 ..............................................(5)
m1 = (Z/10)1/7 ............................................(6)
m2 : Corrective coefficient for gust
response for girders and cables
m3 : Corrective coefficient for gust
response for the main tower
Z : Average elevation
r : Air density (1.225 N s2
/m4
)CD : Drag coefficient
An : Projected area
Note that design standard wind speed U10 is 37 m/s
(29 m/s during erection). See Table 6 for drag coefficient
and Table 7 for corrective coefficient for gust response.
6.1.2 Wind load application
(1) Wind load in the direction perpendicular to bridge
axis
q For girders, all loads were applied to the
effective projected area at the windward side.
w For the tower, the wind load was applied to
the axial line of the tower block each at thewindward and leeward side.
e For cables, wind loads working on the cables
were applied as intensive loads half by half
equally to each cable fixing point of the girder
side and the tower side.
In applying wind loads in the direction
perpendicular to the bridge axis, it was known
from wind tunnel tests that quartering wind near
around a horizontal deflection angle of 35 degrees
prevails. So, the load in the direction of thebridge axis was simultaneously applied in order
to take quartering wind into consideration. At
this time, the strength against wind load in the
direction of the bridge axis used was 50% of
total strength.
(2) Wind load in the direction of bridge axis
q For girders, wind loads in the direction of
bridge axis were uniformly applied.
w For the tower, wind loads calculated assuming
all sections including the tower blocks and
horizontal members are effective were uniformly
applied.e For cables, wind loads were caused to work
on cables by considering the slope of the cables
and applied half by half equally to each cable
fixing point at the girder side and the tower side
as intensive loading.
(3) Displacement
In designing structural components, such as
bearings and expansion devices, for which
displacement would be a major issue, the total
strength against wind load in the bridge axial
direction and 50% strength against wind load in
the direction perpendicular to bridge axis weresimultaneously applied.
6.2 Wind resistant design for erection system
For wind loads to be applied to the bridge during
Drag coefficient
CD
1.2
0.6
1.2
1.3
1.8
1.3
1.8
1.0
0.3
0.7
Remarks
Wind tunnel
test value
Wind resistant
design standard
Schematic diagram
Upperpart
Lowerpart
Table 6 Drag coefficient
Subject structure
Windward
Perpendicular to bridge axis
Cable
Bridge axis
Lower part of the lee side
Upper part
Lower part
Horizontal beam at the lower part
Intermediate horizontal beam at the upper part
Upper part of the lee side
Maintower
Maingirder
Perpendicularto bridge axis
Bridge axis
For design of girders For design of towers
Directionperpendicularto bridge axis
1.90
1.90
1.90
1.65
1.65
1.65
Directionof bridge axis
Directionperpendicularto bridge axis
Directionof bridge axis
1.35
1.35
1.50
1.35
1.35
1.50
Before cable erection
(1.80)
m2
m2
m3
Table 7 Corrective coefficient for Gust responce
Main girderCable
Main tower
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erection, the two conditions that were considered very
susceptible to wind load, or the maximum overhang
condition immediately before center span closing, and
the maximum balancing condition before large side-span
block erection, were studied to determine appropriate
wind loads.6.2.1 Maximum balancing condition
When cables are installed to the seventh level, the
bridge would look like a balancing toy. As it was
important to ensure stability of the bridge under such
a condition against wind, wind tunnel tests were
conducted, which indicated that excessive negative
reaction would occur at the diagonal bent by gust
response. Subsequent analytical study lead to re-
examination of the erection procedure to reduce negative
reaction at the diagonal bent. To be specific, large
main-girder blocks in side spans were erected at the
lower first and second level cables under the side spans.No tension was given until the system became stabilized
so as not to generate negative reaction at the diagonal
bent.
6.2.2 Maximum cantilever condition
The maximum cantilever erection of the center span
goes to about 430 m, the largest ever in the world. How
to stabilize the cantilever against wind load had been
one of the earliest issues. Before commencement of the
design work by the Joint Venture, various wind tunnel
tests were conducted to work on the issue. Major points
of focus were identified as follows.
(1) Characteristics of local wind were studied by awind tunnel test using a model formed after the
local topography. It was found that quartering wind
with very hard turbidity is likely to blow because
of the influence of the mountains behind the Tatara
Bridge.
(2) The maximum cantilever span length is 430 m
and its primary natural frequency is about 16 sec.
If this condition is handled by a conventional
vibration-damping device, the device would have
to be very big and could not be manufactured
because of its size.
With these points in mind, analyses and windtunnel tests were conducted to work on the design
of sections and vibration control during actual
erection. The following points were actually
reviewed.
q Erection machinery was converted into a model,
which was used in an erection system wind force
test. Then, detailed data, such as aerodynamic
coefficient, necessary for design work were
obtained.
w Gust response analysis of the maximum
cantilever erection system was conducted and the
gust response coefficient for the main girdererection stage was newly established to be 2.0
(while it is 1.9 for the final profile).
e Considering the effect of quartering wind on
reduction of wind speed and spatial correlation
of quartering wind, it was confirmed that the
safety factor of allowable stress is 1.7, and that
the first horizontal bending mode would be
satisfied.
rAs an extra vibration-damping countermeasure,a tie-down plan to connect sinkers under the
water and girders was checked by wind tunnel
tests and analyses, which confirmed the
effectiveness of the method and indicated a
possibility of reducing both girder horizontal
displacement and bending moment of girders at
the bases of the towers to about 60% compared
with the case of no such plan.
t It was finally decided that no special
countermeasure would be taken because of the
special characteristics of wind direction and
speed, low reproduction probability and theproven fact that the first horizontal mode would
be satisfied.
7. Check of stability of main girdersagainst buckling
In case axial compressive stress in the bridge axial
direction prevails for a long-span cable stayed bridge
with flattened box girder, such as the Tatara Bridge,
it is essential to study stability against whole buckling.
One of the standard methods to evaluate stability
against whole buckling is use of the stability inspection
equation using effective buckling length (Le), as givenin the Specifications for Highway Bridges (SHB).
But if this method is applied to variable sectional
members, as seen in main girders of a cable stayed
bridge, the effective buckling length at the center span
where axial compressive strength level is low becomes
too long and the resultant design would have to be
made based on a practically unassumable buckling
length. Then, uneconomical cross sections could result.
Today, thanks to the improved capability of computers,
in some cases, elastoplastic analysis of an entire system
with residual stress and initial irregularity taken into
consideration is conducted to carry out stabilityinspection. For the Tatara Bridge, the Bridge Planning
Committee for the Tatara Bridge (hereafter called
Tatara Committee) of the Honshu-Shikoku Bridge
Authority decided to carry out elastoplastic analysis
for an entire system and also carried out buckling
experiments using an entire system model. It was
ultimately found that the experiment results have a
good agreement with the elastoplastic analysis results
for buckling modes and buckling load capacity and
confirmed the validity of the analysis.
These reports indicated that critical points in terms
of buckling are the same members whose effectivebuckling length was found shortest by the buckling
analysis. For the Tatara Bridge, the sectional design
that satisfies the stability inspection equation given in
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the SHB by using their effective buckling length was
used only for members whose effective buckling length
was shortest, located near the main tower.
When the effective buckling length was calculated,
the effective shearing modulus method (Ef method)
was used. As a result, the effective buckling length forthe main girders (Le) turned out to be 34.9 m, almost
twice (40 m) the cable fixing interval. This value was
rounded off to 35 m and the stability inspection equation
was applied only to the main girders near the towers.
Fig. 10 shows the portions to which the buckling stability
inspection was conducted. For allowable stress relative
to local buckling, values given by the block model
approach were used.
8. Design of main tower
8.1 Design outline of main tower
The design of the main tower was developed based onsupplementary review, including FEM, in addition to
the use of the sectional force used in the whole bridge
analysis. The major components to be designed were
as follows.
(1) The tower anchor frame and the base of the
tower
(2) Tower blocks
(3) Crossing zone and knuckle parts
(4) Lower horizontal beam (horizontal beam at the
level of the road)
(5) Upper and intermediate horizontal beam
(6) Cable anchorThe major design points of the tower are as follows.
q The shape of the main tower is an inverted Y
with a cut-off corner section, which was found
to be excellent in wind resistance by the wind
tunnel tests. Corner cut-off is different between
the lower part of the tower and the upper part.
The corner cut-off for the lower part is effective
in controlling the vortex induced vibration. The
corner cut-off for the upper part is designed to
provide a section effective against galloping.
w For the cross section of the main tower, as
ease of production and erection was consideredimportant, a single chamber box section was
adopted. A three-chamber section divided by
vertical diaphragms had to be used for the
crossing zone and knuckle of the lower horizontal
members and the cable anchor in the upper part
for unavoidable structural reasons.
e The tower blocks were designed as block
members for the axial force and two-directional
bending. Since the in-plane effective buckling
length is close to the out-plane effective buckling
length, the bi-axial bending stability inspection
equation was adopted.r Since the large blocks for the lower part were
to be assembled on the ground, each block volume
was determined to be 160 tons considering the
lifting capability of companies. Single member
erection blocks for the upper parts were
determined to be less than 145 tons each so that
they could be handled by cranes to be set up at
the site.
t Blocks were all connected by friction joints
using high tensile bolts (HTB). The steel plates
were to be designed as 50% metal touch. Large
block interfaces and horizontal members weredesigned as 100% high tensile bolts to absorb
production and erection errors.
8.2 Effective buckling length of main tower
The effective buckling length of the main tower was
determined based on the values calculated from the
three methods as follows.
(1) The effective buckling length of all members
was calculated based on Pcr(buckling load) of the
primary mode.
(2) The effective buckling length was calculated
based on Pcrof the primary mode of each member.
(3) Inflection points of a mode in which each memberbuckles were selected from the mode diagram and
the effective buckling length was calculated using
the mode diagram.
8.3 Design of crossing zone and knuckle
At a crossing zone of a conventional rectangular cross-
section, flange forces of horizontal members are
transmitted to the webs of the tower blocks as shear
via the diaphragms of the crossing zones. But since the
Tatara Bridge has a single-chamber 12-angle cross
section with cut-off corners, stress would not smoothly
transmit. For stress of webs of horizontal members,
smooth stress transmission would not be realized dueto the small width of the webs in the tower blocks.
Thus, internal webs were extended for the crossing
zones of the horizontal members to turn the cross section
near the crossing zones into a three-chamber shape for
positioning stays of horizontal members (Fig. 11). In
terms of calculation, the plate thickness of the internal
web and the external web was converted as a single
plate so that the cross-section is interpreted as a single-
chamber rectangular shape and the Okumura-Ishizawa
Method was used to carry out simple design. Then, the
3D FEM analysis was used to check the design before
finally determining the plate thickness.For the Tatara Bridge, knuckle points of the tower
blocks were aligned with the line of the girder edge
for the appearance and thus there is a clearance of
The stability inspection equation was applied only to this range.
The minimum effective buckling
length was used.
Fig. 10 Check for buckling stability of main girder
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compression check was conducted since it was
impossible to ignore stress in the direction
perpendicular to the bridge axis caused by cable
fixing.
r For the cable anchor, square column anchors
were used at the outside of external web plates.The detailed structure was determined after
fatigue testing and FEM analysis.
t Composite girders play a pivotal role in
connecting PC girders to steel box girders. Rear
face fixing, a composite girder system with
proven performance from the Ikuchi Bridge
experience, was used. For backing concrete, high-
fluidity concrete was cast in-situ to realize
downsizing of blocks, use of smaller erection
cranes, and reduction in site work.
9.2 Design of wide stiffened plates
At the center cell of the Tatara Bridge, the intervalof web plates is 9.04 m and that of lateral ribs is 2.5
m. They are sufficiently wide compression-stiffened
plates with an aspect ratio (a) of 0.277. The SHB,
however, assumes compression stiffened plates of about
2 in aspect ratio and defines a level of stiffness of
stiffened plates that makes the buckling mode become
nodes at the lateral rib positions. According to the
regulation of compression-stiffened plates in the
superstructure design standard of HSBA, the definition
of the SHB is used as an applicable specification. But
for such wide compression-stiffened plates as used for
the Tatara Bridge, the required stiffness for a stiffenedplate would be so large that it would be a large cross-
section of unrealistic size.
The Tatara Committee then came up with the Tatara
Bridge Design Procedure (draft), based on which wide
stiffened plates were designed for longitudinal and
lateral stiffeners and allowable stress of local buckling
was calculated using the block model approach. For
longitudinal ribs of the Tatara Bridge, closed section
ribs (U ribs) were to be used both at the steel plate
deck side and the bottom flange side and thus the load
capacity curve in the Buckling Design Guideline (Japan
Road Association) that is almost equal to the StandardLoad Capacity Curve (V) in the SBH (Feb. 1994, Japan
Society of Civil Engineers) was used for ultimate
strength of effective stiffeners used in the block model
approach. Since steel plate decks are supported at cable
fixing points and loaded by in-plane compression in the
direction of bridge axis and the direction perpendicular
to bridge axis, they were given bi-axial buckling checks.
9.3 Longitudinal ribs
Trough ribs (320 240 8) were used for all
longitudinal ribs at the steel plate deck side and almost
all other longitudinal ribs except for those of bottom
flanges around the center of the center span. Ribsmeasuring 320 240 6 were used for some bottom
flanges near the center of the center span. Since
longitudinal ribs form part of the main girders of the
bridge, axial compressive force acts on them due to
horizontal components of cable tension. Therefore, it
is necessary to check longitudinal ribs for their resistance
to local buckling.
For 8-mm-thick trough ribs, blocks composed of deck
plates and trough ribs were put to load capacity teststo confirm that no local buckling will occur. Based on
the results of buckling tests and elastoplastic analysis,
a structural arrangement in which another row of bolts
is added only to splice plates at one side, as shown in
Fig. 14, was applied to reduce the stress concentration
immediately before the splices so as not to reduce load
capacity at joints. For 6-mm-thick trough ribs, elastic
buckling analysis was made to set allowable stress with
regard to local buckling to 167 N/mm2 {1 700 kgf/cm2}.
9.4 Design of cable anchor
Web plate fixing square column anchors were used for
cable fixing. Where stress was expected to intensify,the results of large fatigue tests, conducted in an earlier
stage of design, as well as other reviews including FEM
analysis were used to determine shapes of elements,
such as the fillet shape of bearing plates used for cable
fixing assemblies. The structure of the cable anchor is
shown in Fig. 15.
The following points were reviewed in designing the
section of the cable anchor.
(1) Structure of bearing plate (FEM analysis)
(2) Stress check at anchor and the area near it (FEM
analysis)
(3) Load sharing ratio of vertical component of cabletension (grid analysis)
(4) Main girder in-plane bending stress distribution
(FEM analysis)
A - A
AA
75
5
Fig. 14 Joint of longitudinal rib (unit : mm)
Fig. 15 Cable anchor (main girder)
Deck plate
Diaphragm
Bottom flange External web plate
Internalstrengtheningweb
Internalstrengtheningflange
Internalstrengtheningstructure
Anchorflange
Anchor rib
Auxiliary rib
Squarecolumnanchor
Bearing plate
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is large. As a proactive safety measure against huge
earthquakes, it was confirmed that if friction of this
bearing is considered as attenuation, response
displacement decreases to about 20%.
According to this review, stoppers in the bridge axial
direction, which were to be installed in the basic designstage, were canceled in the detailed design stage based
on the assumption that frictional force of bearings will
work in the case of anomalies or earthquakes. It is
therefore a matter-of-course that movement was
calculated at the design seismic level assuming that
they were ordinary movable bearing shoes and that no
frictional force is expected.
Acknowledgment
The authors acknowledge the staff of Third Construction
Bureau of the Honshu-Shikoku Bridge Authority andthe members of the Tatara Committee for their guidance
and cooperation in planning, designing, fabrication and
erection of the Tatara Bridge construction work. In
particular, the authors wish to thank Prof. Toshiyuki
Kitada of Osaka City University for his valuable
comments on application of wide stiffened plate design
for main girders and Prof. Chihiro Miki of Tokyo
Institute of Technology for his valuable instructions on
detailed review of fatigue of steel plate decks.
The authors feel that all our hard work in solving
numeral technological difficulties and developing safety
measures for work instantly turns into a heart-warmingsatisfaction the moment we see the beautiful shape of
the Tatara Bridge located at the middle of the
Shimanami Kaido (Fig. 17).
REFERENCES
(1) T. Fujiwara and A. Moriyama : Wind-Proof
Design on the Tower of Tatara Bridge, Honshi
Technical Report Vol.19 No.74 Apr. 1995 pp.24-
37
(2) M. Kitagawa, R. Toriumi and H. Katsuchi :
Study on Large Scale Wind Tunnel Test of TataraBridge, Honshi Technical Report Vol.19 No.20
Jan. 1996 pp.38-45
(3) H. Akiyama, R. Toriumi and Y. Ohtani : Large
Scale Wind Tunnel Test of the Tatara Bridge (2nd
report) Gust Response in Complicate Topography,
Honshi Technical Report Vol.21 No.83 July 1997pp.30-36
(4) N. Hirahara : Erection of Superstructure of Tatara
Bridge (Report I) Tower Erection and Large Block
Erection of Deck at Tower, Honshi Technical
Report Vol.21 No.84 Oct. 1997 pp.33-40
(5) N. Hirahara and T. Murata : Erection of
Superstructure of Tatara Bridge (Report II)
Erection of Steel Girder and Cables, Honshi
Technical Report Vol.22 No.88 Oct. 1998 pp.28-
37
(6) T. Nose, T. Murata and M. Yabuno : Precision
Control during Balancing Erection for Tatara Bridge,Proceedings of the 54th Annual Conference of the
Japanese Society of Civil Engineers, 1-(A) Sep.
1999 pp.724-725
Fig. 17 View of Tatara Bridge