Extradosed Bridge Midas

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EXTRADOSED BRIDGE Contents: 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

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

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EXTRADOSED BRIDGE

II. III. IV. V. VI. VII.

Case Study Modeling Initial Cable Forces Construction Stage Analysis Nonlinear Effects Results

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Extradosed Bridge

I. Introduction

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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

EXTRADOSED BRIDGE I.

Introduction

III. IV. V. VI. VII.

Modeling Initial Cable Forces Construction Stage Analysis Nonlinear Effects Results

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Extradosed Bridge

II. Case Study

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a. Bridge Information Bird’s Eye View

Extradosed Bridge

II. Case Study

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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=168m

Extradosed Bridge

II. Case Study

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a. Bridge Information Sectional Elevation

Preliminary Design

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)

Optimum Design of Bridge 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)

Extradosed Bridge

II. Case Study

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a. Bridge Information Side Perspective

Transverse section – Main Bridge

Transverse section – Connected Bridge

Extradosed Bridge

II. Case Study

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b. Construction Methods 1) Construction method of EXTRADOSED PSC BOX GIRDER Bridge

Construction Methods

F.S.M

Full Staging Method

F.C.M

Free Cantilever Method

Characteristics of the Construction Method Name

Restrictions

Duration

F.S.M

Restrictions by the bottom conditions are crucial, depending on the supporting system.

F.C.M

Slow construction due to Less restrictions by the bottom forward construction stage condition. method

Economic

Constructability

Economical efficiency is Construction is fast due to There are plenty of international determined by the height of the the lumped pouring method. bridges constructed by this method. supporting. Lower pier is more Easy to construct cost-effective 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

Extradosed Bridge

II. Case Study

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b. Construction Methods

FSM Low cost of equipment, simple method of construction Cost effective for level ground and low bridges Fast construction, stable supports during construction

FCM 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. High construction fee compared with F.S.M

Extradosed Bridge

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b. Construction Methods FSM Extradosed Bridge - Sequential Construction Stages in midas Civil (1/2)

1st Construction Stage: Model and activate side span temporary supports by Elastic link and Support

2nd Construction Stage: Remove side span temp. supports, and activate temp. supports of main span

3rd Construction Stage : Activate the main tower and place the diagonal tension-cables in order

Extradosed Bridge

II. Case Study

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b. Construction Methods FSM Extradosed Bridge - Sequential Construction Stages in midas Civil (2/2)

4th Construction Stage: Complete diagonal Tension Cables, and remove temp. supports of main span

5th Construction 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

Extradosed Bridge

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b. Construction Methods FCM Extradosed Bridge - Sequential Construction Stages in midas Civil (1/2)

1st Construction Stage: Construct Main Pier and Pylon

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2nd ~9th Construction Stage: Employ F/T Seg. Construct Diagonal cables

10th Construction Stage: FSM construction for Side Span and apply Pylon1girder Time Load as 255 days

Extradosed Bridge

II. Case Study

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b. Construction Methods FCM Extradosed Bridge - Sequential Construction Stages in midas Civil (2/2)

11th Construction Stage: Connect Key Seg. of Main Span

12th Construction Stage: Completion of Construction

Design Condition ① Structure: 3 span continuous EXTRADOSED P.S.C BOX Bridge ③ Dimension: L = 60.0 + 105.0 + 60.0 = 225.0 m ⑤ Thickness: H = 2.50 m (equal section)

② Grade: Excellant

④ Bridge Width: B = 23.74 m (4 lanes both way) 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

Extradosed Bridge

II. Case Study

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c. Structural Analysis Comparison

F.C.M:

Dead Load

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

Extradosed Bridge

II. Case Study

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c. Structural Analysis Comparison 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. 

Tendon Primary

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

Support

62,950 kN-m

Total : -23,940 kN-m

80,620 kN-m

Total :

-920 kN-m

Extradosed Bridge

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c. Structural Analysis Comparison  Tendon Secondary Moment is decided by placement and the amount of tendon. F.S.M. Tendon Secondary

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

Support

23,200 kN-m

Total :

-40 kN-m

38,940 kN-m

Total : 8,670 kN-m

5,500 kN-m

Total : 4,580 kN-m

Extradosed Bridge

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c. Structural Analysis Comparison  Creep Secondary Moment behaves similar to the case of Dead Load. Creep Secondary

 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

Support

-16,950 kN-m

Total : -17,690 kN-m

0 kN-m -35,730 kN-m

Total : 8,670 kN-m Total : -31,150 kN-m

Extradosed Bridge

II. Case Study

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c. Structural Analysis Comparison  Shrinkage Secondary Moment shows similarity in both method.

Shrinkage

 Similar to Creep Secondary moment the total sum of positive moment F.C.M. shows

Secondary

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

Support

-13,230 kN-m

Total : -30,920 kN-m

-15,060 Kn-m

Total : -46,210 kN-m

Extradosed Bridge

II. Case Study

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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

Upper limit stress (MPa)

Bottom limit stress (MPa)

F. S. M

F. C. M

Extradosed Bridge

II. Case Study

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d. Economic Comparison & Conclusion

Cost effective

 For applying F.S.M. there has been 10% reduction of the construction Cost.  F.C.M has a long term of construction since it requires accuracy of managing

Construction

Camber and several Seg. Construction stage.  Applying F.S.M workability increases and construction time can reduce

EXTRADOSED BRIDGE I. II.

Introduction Case Study

IV. V. VI. VII.

Initial Cable Forces Construction Stage Analysis Nonlinear Effects Results

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Extradosed Bridge

III. Modeling

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a. Section Definition

Draw section shape using CAD Database

Import CAD file through SPC

Import section properties

Extradosed Bridge

III. Modeling

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b. Bridge Wizard FCM Bridge Wizard

FSM Bridge Wizard

Extradosed Bridge

III. Modeling

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b. Bridge Wizard & Manual Modeling Cable Stayed Bridge Wizard

Manual modeling Using Node/Element tab

EXTRADOSED BRIDGE I. Introduction II. Case Study III. Modeling V. Construction Stage Analysis VI. Nonlinear Effects VII. Results

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Extradosed Bridge

IV. Initial Cable Force

a. Ideal State

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Extradosed Bridge

IV. Initial Cable Force

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b. Methods

1. Simple supported Beam Bridge segment is a simple beam supported by cables. 2. Continuous Beam Main girder is a continuous supported beam with inclined stay cables (Pendulum Rule).

Extradosed Bridge

IV. Initial Cable Force

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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).

Extradosed Bridge

IV. Initial Cable Force

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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.

EXTRADOSED BRIDGE I. II. III. IV.

Introduction Case Study Modeling Initial Cable Forces

VI. Nonlinear Effects VII. Results

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Extradosed Bridge

V. Construction Stage (CS) Analysis

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.

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Extradosed Bridge

V. Construction Stage (CS) Analysis

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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 specified as “External Force” type and obtain results

Extradosed Bridge

V. Construction Stage (CS) Analysis

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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

Extradosed Bridge

V. Construction Stage (CS) Analysis

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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.

EXTRADOSED BRIDGE I. II. III. IV. V.

Introduction Case Study Modeling Initial Cable Forces Construction Stage Analysis

VII. Results

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Extradosed Bridge

VI. Nonlinear Effects

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a. P-∆ Effects  Considered for both construction stage and final stage.  Can’t be run with Tension Only Cable Element in Final Stage Analysis.

Construction Stage

Final Stage

Extradosed Bridge

VI. Nonlinear Effects

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b. Large Deformations  Considered for main span length generally longer than 600m.  Considered for both construction stage and final state.

Construction Stage

Final State

EXTRADOSED BRIDGE I. II. III. IV. V. VI.

Introduction Case Study Modeling Initial Cable Forces Construction Stage Analysis Nonlinear Effects

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Extradosed Bridge

VII. Results

a. Deformation

Pylons Pylon construction tolerance is as shown:

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Extradosed Bridge

VII. Results

a. Deformation

Pylons Pylon maximum lateral deformation = 13.249mm < 38mm => OK

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Extradosed Bridge

VII. Results

a. Deformation Bridge Deck Bridge deck tolerance is as shown:

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Extradosed Bridge

VII. Results

a. Deformation Bridge Deck Maximum bridge deck deformation = 9.9mm < L/5000 = 20mm => OK

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Extradosed Bridge

VII. Results

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b. Camber Computation : Construction Camber Construction Camber

Construction Camber is shown as the net displacement results in Midas Civil

Extradosed Bridge

VII. Results

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b. Camber Computation : Manufacture Camber Manufacture Camber

To see real displacement in the results, check “Initial Tangent Displacement for Erected Structures” option in CS Analysis Control Data.

Extradosed Bridge

VII. Results

b. Camber Computation Camber results of Deck

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Extradosed Bridge

VII. Results

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c. Cable Forces & Stresses

Truss Forces

Truss Stresses

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