2
I.
Introduction
II.
Case Study
a. Bridge Information
b. Construction Methods
c. Structural Analysis Comparison
d. Economic Comparison
III. Modeling
a. Section Property Definition
b. Bridge Wizard
IV. Initial Cable Forces
a. Ideal State
b. Methods
c. Cable Tuning with ULF
Contents:
V. Construction Stage (CS) Analysis
a. Backward CS Analysis
b. Forward CS Analysis
1) Using Backward CS Analysis results
2) Using Lack of fit force
3) Using Unknown load factor
VI. Nonlinear Effects
a. P-∆ Effects
b. Large Deformations
VII. Results
a. Deformation
b. Camber Computation
1) Construction Camber
2) Manufacture Camber
c. Cable Forces and Stresses
II.
Case Study
III. Modeling
IV. Initial Cable Forces
V. Construction Stage Analysis
VI. Nonlinear Effects
VII. Results
Benefits with Extradosed Bridge
Ordinary prestressed girder bridge with internal or external tendons having cables installed
outside and above the main girder and deviated by short towers located at supports.
=>Construction & appearance
: Cable Stayed Bridge
=>Structural properties & design specifications
: PSC girder bridge
Reduced girder depth
=>
Reduced self weight
of the structure
Longer spans possible with the use of cables
=>
H/L
of extradosed bridges:
1/15 to 1/35
=>
H/L
of box girder bridges:
1/15 to 1/17
Lower main tower
=>
H/L
of extradosed bridges:
1/15
=>
H/L
of cable stayed bridges:
1/5
=>
Smaller stress variation
in stay cables
=>
Reduced fatigue failure
of stay cables
I.
Introduction
III. Modeling
IV. Initial Cable Forces
V. Construction Stage Analysis
VI. Nonlinear Effects
VII. Results
a. Bridge Information
a. Bridge Information
Location Total Length: L=1085m Road expansion: B=30m, L=692m Main Bridge: B=24m, L=225m Connection Bridge: B=15m, L=168ma. Bridge Information
Cable arrangements FAN arrangement Harp arrangement Number of Cables 7 lines on one side (0.6”-27) (0.6”-29) (0.6”-31) Main Tower Height H=10,12,14m L=105.0m (L/8~L/12) Section Uniformed section H=2.5m L=105.0m (L/30~L/60) Cable arrangement:FAN arrangement (one sided) Number of Cables: 7 lines (0.6”-29EA) Height of the Main Tower:
H=12.0m (L/8.75)
Section: Uniformed Section 2.5m(L/40) Optimum Design of Bridge
P relim in ar y Desig n Sectional Elevation
a. Bridge Information
Side Perspective
b. Construction Methods
Name
Characteristics of the Construction Method
Restrictions Duration Economic Constructability
F.S.M
Restrictions by the bottom conditions are crucial, depending on the supporting system.
Construction is fast due to the lumped pouring method.
Economical efficiency is determined by the height of the supporting. Lower pier is more cost-effective
There are plenty of international bridges constructed by this method. Easy to construct
F.C.M Less restrictions by the bottom
condition.
Slow construction due to forward construction stage method
Cost-effective if higher pier or if there is limited space underneath the bridge. For instance, bridge over rail road, bridge over the sea.
Construction management is complicated due to having measurements of each stage
1) Construction method of EXTRADOSED PSC BOX GIRDER Bridge
Construction Methods
F.S.M
F.C.M
Full Staging Method
b. Construction Methods
FSM
FCM
Low cost of equipment, simple method of construction Cost effective for level ground and low bridges
Fast construction, stable supports during construction
Little effect of supporting conditions
Possible for constructing long suspension bridge without heavy duty equipment Accuracy of the construction can be enhanced by the correction of errors at each construction stage.
Precise construction and management needed due to changes in the structural system by each construction stage.
b. Construction Methods
FSM Extradosed Bridge - Sequential Construction Stages in midas Civil (1/2)
1stConstruction Stage: Model and activate side span temporary supports by Elastic link and Support
2ndConstruction Stage: Remove side span temp. supports, and activate temp. supports of main span
b. Construction Methods
FSM Extradosed Bridge - Sequential Construction Stages in midas Civil (2/2)
4thConstruction Stage: Complete diagonal Tension Cables, and remove temp. supports of main span
5thConstruction Stage : Pavement and Finishing => Completion of Construction
Design Condition
① Structure: 3 span continuous EXTRADOSED P.S.C BOX Bridge ② Grade: Excellent
③ Dimensions: L = 60.0 + 105.0 + 60.0 = 225.0 m ③ Bridge Width: B = 23.740 m (4 lanes both way) ⑤ Thickness: H = 2.50 m (equal section) ⑥ Inclination: S = (±) 0.5 %
⑦ Plane surface alignment: R = ∞ ⑧ Construction method: F.S.M (Full Staging Method ) ⑨ Prestress construction: Post-Tensioning Method
b. Construction Methods
FCM Extradosed Bridge - Sequential Construction Stages in midas Civil (1/2)
1stConstruction Stage: Construct Main Pier and Pylon
`
2nd~9thConstruction Stage: Employ F/T Seg. Construct Diagonal cables
b. Construction Methods
FCM Extradosed Bridge - Sequential Construction Stages in midas Civil (2/2)
11thConstruction Stage: Connect Key Seg. of Main Span
12thConstruction Stage: Completion of Construction
Design Condition
① Structure: 3 span continuous EXTRADOSED P.S.C BOX Bridge ② Grade: Excellant
③ Dimension: L = 60.0 + 105.0 + 60.0 = 225.0 m ④ Bridge Width: B = 23.74 m (4 lanes both way) ⑤ Thickness: H = 2.50 m (equal section) ⑥ Inclination: S = (±) 0.5 %
⑦ Plane surface alignment: R = ∞(Straight line) ⑧ Construction method: FCM (Free Cantilever Method) ⑨ Prestress construction: Post-Tensioning Method
c. Structural Analysis Comparison
Dead Load
F.C.M: Maximum negative moment on supports are relatively greater than Maximum positive moment in the middle point. The moments are concentrated to the supports. F.S.M: The moment of the supports and the middle point are relatively balanced.
Moment after 10,000 days
Method F. S. M F. C. M Dead Load ` Mid-point 255,900 kN-m 22,540 kN-m Support -384,800 kN-m -531,500 kN-m
c. Structural Analysis Comparison
Tendon Primary
For F.C.M construction Cantilever Tendon is added on the upper part to resist excessive negative moment.
(Efficient to place internal tendon especially bottom tendon)
For F.S.M. construction it is difficult to place certain tendon at the negative and positive moment.
Comparing the sum of moment F.C.M. shows more efficient aspect on Positive and Negative moment.
Moment after 10,000 days
Method F. S. M F. C. M
Tendon Primary
Mid-Point -70,400 kN-m Total : -21,560 kN-m -57,830 kN-m Total : -30,270 kN-m
c. Structural Analysis Comparison
Tendon Secondary
Tendon Secondary Moment is decided by placement and the amount of tendon. F.S.M. shows efficiency in both positive and negative moment.
However, in the total sum F.C.M. shows efficiency in analysis.
Moment after 10,000 days
Method F. S. M F. C. M
Tendon Secondary
Mid-Point 33,390 kN-m Total : 11,830 kN-m 38,940 kN-m Total : 8,670 kN-m
c. Structural Analysis Comparison
Creep Secondary
Creep Secondary Moment behaves similar to the case of Dead Load.
In the total sum of positive moment F.C.M. shows efficiency but, in the negative moment since the Creep Secondary acts F.S.M. show efficiency.
Moment after 10,000 days
Method F. S. M F. C. M
Creep Secondary
Mid-Point 4,639 kN-m Total : 16,469 kN-m 0 kN-m Total : 8,670 kN-m
c. Structural Analysis Comparison
Shrinkage Secondary
Shrinkage Secondary Moment shows similarity in both method.
Similar to Creep Secondary moment the total sum of positive moment F.C.M. shows efficiency but, in the negative moment since the Creep Secondary acts F.S.M. show efficiency.
Moment after 10,000 days
Method F. S. M F. C. M
Shrinkage Secondary
Mid-point 9,980 kN-m Total : 26,449 kN-m 9,177 Kn-m Total : 17,847 kN-m
c. Structural Analysis Comparison
Conclusion of Stress analysis
Structural analysis shows that on the final combination both Method of construction has similar results.
For stress aspect F.S.M. shows greater and conservative. However since the placement of Continuity Tendon is functioned to greater section force, it is inefficient for placing tendon.
Special Loads (D + CF + LI + PS1 + PS2 + CRSH2 + SD) Method F. S. M F. C. M Upper limit stress (MPa) Bottom limit stress (MPa)
d. Economic Comparison & Conclusion
Cost effective For applying F.S.M. there has been 10% reduction of the construction Cost.
Construction
F.C.M has a long term of construction since it requires accuracy of managing Camber and several Seg. Construction stage.
I.
Introduction
II.
Case Study
IV. Initial Cable Forces
V. Construction Stage Analysis
VI. Nonlinear Effects
VII. Results
a. Section Definition
Database
Draw section shape using CAD
Import CAD file through SPC
Import section properties
b. Bridge Wizard
FSM Bridge Wizard FCM Bridge Wizard
b. Bridge Wizard & Manual Modeling
Cable Stayed Bridge WizardManual modeling
I.
Introduction
II.
Case Study
III. Modeling
V. Construction Stage Analysis
VI. Nonlinear Effects
VII. Results
b. Methods
1. Simple supported Beam
Bridge segment is a simple beam supported by cables.
2. Continuous Beam
b. Methods
3. Unit Load Method
Unit load cases equal to the number of fixed ideal moment points (for dead load) are defined. Xi is the
unknown to be multiplied to the unit load to achieve the ideal moment distribution.
4. Additional Constraint Method
Extension of Unit load method to time dependent effects and non-linear effects.
5. Unknown Load Factor
User defined displacement/reaction/force constraint. Using vector and matrix calculations the cables’
forces are adjusted to satisfy the constrained condition(s).
c. Cable Tuning with ULF
Importance of Cable Tuning
ULF calculates the value of cable pretension for a particular constraint. That cable pretension (or Load
Factor) might not be practical or might exceed the cable force tolerance limit. Thus force can be adjusted
using Cable Tuning.
Procedure
1. Use Unknown Load Factor to
calculate the cable pretension (or
Load Factor).
2. Adjust the cable pretension (or load
factor) using the table or bar graph.
3. Select the result item for which the
effects of the cable pretension are to be
checked.
4. Produce the results graph for the result
item selected from step 3.
5. Save the adjusted pretension forces in
a load combination or apply the new
pretension forces to the cables directly
using the pre-programmed buttons.
I.
Introduction
II.
Case Study
III. Modeling
IV. Initial Cable Forces
VI. Nonlinear Effects
VII. Results
a. Backward CS Analysis
Significance
Cable prestress, introduced during
the construction of cable-stayed
bridge, could be calculated by
Backward CS Analysis from the
final stage.
Limitations
Does not consider Time Dependent
Effects and Non-Linearity Effects.
b. Forward CS Analysis
1) Using Backward CS Analysis Results (Preferred for Multiple Pretension Loads for single cable)
Obtain cable pretension load using unknown load
factor and cable tuning after final stage analysis
Perform Backward CS Analysis applying the
pretension load obtained from last step
Obtain cable forces in each CS after performing
Backward construction stage analysis
Apply cable forces as Pretension Loads in each
construction stage
Perform CS analysis with cable pretension force
b. Forward CS Analysis
2) Using lack of fit force (No time dependent effects considered)
Obtain initial pretension load using Unknown Load
Factor on final stage
Fine tune the cable forces using “Cable Force
Tuning”
Apply initial prestress force to cables for
construction stage analysis
Turn on “Lack of fit force Control” option in
construction stage analysis control
Perform construction stage analysis to obtain
jacking forces of cables at each construction stage
b. Forward CS Analysis
3) Using Unknown Load Factor (Not suitable for Cables)
Perform CS analysis with self weight and unit
pretension load
Calculate Unknown Load Factor for the stages of
cable force activation
Perform iterative analysis using Unknown Load
Factor to modify the cable forces
Further modify cable pretension load using cable
tuning
Check the jacking forces of cables at each CS in
results > forces > truss forces.
I.
Introduction
II.
Case Study
III. Modeling
IV. Initial Cable Forces
V. Construction Stage Analysis
VII. Results
a. P-∆ Effects
Considered for both construction stage and final stage.
Can’t be run with Tension Only Cable Element in Final Stage Analysis.
b. Large Deformations
Considered for main span length generally longer than 600m.
Considered for both construction stage and final state.
I.
Introduction
II.
Case Study
III. Modeling
IV. Initial Cable Forces
V. Construction Stage Analysis
VI. Nonlinear Effects
a. Deformation
Pylons
Pylon construction
tolerance is as shown:
a. Deformation
Pylons
Pylon maximum lateral deformation
= 13.249mm < 38mm => OK
a. Deformation
Bridge Deck
a. Deformation
Bridge Deck
b. Camber Computation : Construction Camber
Construction Camber is shown as the
net displacement results in Midas Civil
Manufacture Camber
To see real displacement in the results, check
“Initial Tangent Displacement for Erected Structures”
option in CS Analysis Control Data.
b. Camber Computation
c. Cable Forces & Stresses
Bridging Your Innovations to Realities
