MIDAS 2013 Indonesia Workshop - Cable Stayed Bridge

Tongji University Chen Xin

Introduction Basic Steps for Modeling Cable Stay Bridge Finding Cable Pretension Forces

Unknown Load Factor Cable Tuning Bending energy method Construction Stage Analysis

Unknown Load Factor In construction stages Lack of Fit Force Moving load analysis Buckling analysis

Dynamic analysis Other structural analysis

Part 3. Design midas Civil

Cable Stayed Bridge

1. Introduction

Cable Stayed Bridge Designing

The Requisites for Design: 1. Cable Tension Force for Designing Cable 2. Axial Press and Bending Moments for Designing Deck 3. Axial Force and Bending Moments for Designing Pylon midas

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1. Introduction

Regular Analysis Process for Cable Stayed Bridge

Final Stage Analysis

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Backward Construction Stage Analysis

Forward Construction Stage Analysis

Other Structural Analysis

Part 3. Design midas Civil

Cable Stayed Bridge

1. Introduction

Cable element: ① Truss ② Tension only truss

③ Hook ④ Cable

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1. Introduction

A cable element is automatically transformed into:  An equivalent truss element in the case of a linear analysis

 An elastic catenary cable element in the case of a geometric nonlinear analysis

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Part 3. Design midas Civil

Cable Stayed Bridge

1. Introduction

equivalent truss element

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Part 3. Design midas Civil

Cable Stayed Bridge

1. Introduction

elastic catenary cable element

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1. Introduction

Different analysis method for cable type element:  Static load linear analysis Equivalent truss element  Static load nonlinear analysis(Nonlinear analysis control ON) Elastic catenary cable element  Construction stage analysis include time dependent effect Equivalent truss element

 Construction stage analysis include nonlinear analysis Elastic catenary cable element  Moving load analysis or settlement analysis Truss element taken geometric stiffness at the final stage into consider

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Part 3. Design midas Civil

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1. Introduction

Cable type element used in different structure:  Suspension Bridge’s Main Cable and Hangers Cable element taken large displacement into consider is recommended  Large Span Cable Stayed Bridge (main span over 1,000m ) Cable element taken large displacement into consider is recommended  Medium Span Cable Stayed Bridge Equivalent truss element is recommended

 Arch Bridge’s Hanger Truss element is recommended

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Part 3. Design midas Civil

Cable Stayed Bridge

2. Basic Steps for Modeling Cable Stay Bridge

① Define Material and Section Properties ② Build Nodes and Elements ③ Define Boundary Conditions

④ Define Loads

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2. Basic Steps for Modeling Cable Stay Bridge

① Define Material and Section Properties

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Cable Model 1

Part 3. Design midas Civil

Cable Stayed Bridge

2. Basic Steps for Modeling Cable Stay Bridge

② Build Nodes and Elements

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2. Basic Steps for Modeling Cable Stay Bridge

② Build Nodes and Elements

Node/Element -> Create Elements

a)

Element type -> Truss

b)

Material Name -> Cable

c)

Sectiona Name -> Cable

d)

Nodal Connectivity -> Select 1,34 and

3,34 and 7,34 and 9,34 and 35,13 and 35,15 and 35,19 and 35,21

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2. Basic Steps for Modeling Cable Stay Bridge

③ Define Boundary Conditions

Boundary -> Define Support

a)

Options -> Add

b)

Support Type -> D-all and R-all

c)

Model view window Select Node 22, 23

-> Apply d)

Support Type -> Dy, Dz, Rx and Rz

e)

Model view window Select Node 1, 21

-> Apply

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2. Basic Steps for Modeling Cable Stay Bridge

③ Define Boundary Conditions

Boundary -> Elastic Link

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a)

Options -> Add

b)

Type -> General

c)

SDx -> 500000

d)

SDy -> 1000000

e)

SDx -> 1000

f)

2 node -> Node 5, 26

g)

Apply

h)

2 node -> Node 17, 27

i)

Apply

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2. Basic Steps for Modeling Cable Stay Bridge

④ Define Loads Load -> Static Load Cases

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a)

Name -> Self Weight

b)

Type -> Dead Load

c)

Add

d)

Name -> Additional Load

e)

Type -> Dead Load

f)

Add

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2. Basic Steps for Modeling Cable Stay Bridge

③ Define Boundary Conditions

Load -> Self Weight

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a)

Load Case Name -> Self Weight

b)

Self Weight Factor -> Z -> -1

c)

Add

d)

Close

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Part 3. Design midas Civil

Cable Stayed Bridge

2. Basic Steps for Modeling Cable Stay Bridge

③ Define Boundary Conditions

Load -> Element beam loads

a)

Load Case Name -> Additional Load

b)

Value -> w -> -3

c)

Model view window Select Element

1to20 -> Apply

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3. Cable Pretension Force

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3. Cable Pretension Force

Unknown Load Factor • Run the linear analysis • Unknown Load Factor • Cable Force Tuning

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Bending Energy Method • Change element’s stiffness • Run the analysis • Input the tension force to the initial pretension force • Run the nonlinear analysis • Modify the initial pretension force base on the result

Part 3. Design midas Civil

Cable Stayed Bridge

4. Unknown Load Factor

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Part 3. Design midas Civil

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4. Unknown Load Factor

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Part 3. Design midas Civil

Cable Stayed Bridge

4. Unknown Load Factor

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Part 3. Design midas Civil

Cable Stayed Bridge

4. Unknown Load Factor

Unknown Load Factor

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4. Unknown Load Factor

Define unit pretension loads for cables Load -> Static Load Cases a)

Name -> Tension 1

b)

Type -> USER

c)

Description -> Cable 1 –

Unit Pretension

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d)

Add

e)

Create the Tension 2-4

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4. Unknown Load Factor

Input unit pretension loads for cables Load -> Temp./Prestress -> Pretension Load a)

Load Case Name -> Tension 1

b)

Options-> Add

c)

Pretension Load -> 1 tonf

d)

Model view window Select Element

33,34 -> Apply e)

Define unit pretension loads for element

34,39 and 35,38 and 36,37

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4. Unknown Load Factor

Cable Model 2 Run Analysis

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Part 3. Design midas Civil

Cable Stayed Bridge

4. Unknown Load Factor

Load combinations for dead loads and unit loads Result -> Load Combination a)

Name -> LCB1

b)

Active -> Active

c)

Type-> Add

d)

Load Cases and Factor -> Self

Weight, Additional Load, Tension 1, Tension 2, Tension 3, Tension 4

e)

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Factor all 1

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4. Unknown Load Factor

Unknown Load Factor Result -> Cable Control -> Unknown Load Factor a)

Item Name -> bending moment

b)

Load Comb -> LCB1

c)

Constraints -> Add

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4. Unknown Load Factor

Unknown Load Factor Unknown Load Factor Constrant a)

Constraint Name -> Elemernt 6

b)

Constrain Type -> Beam Force

c)

Element ID -> 6

d)

Point -> J-end

e)

Component -> My

f)

Equality/Inequality Condition ->

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4. Unknown Load Factor

Unknown Load Factor Result -> Cable Control -> Unknown Load Factor a)

Constrains -> Element 5,

Element 6, Element 8, Node 34 b)

Object function type -> Linear

c)

Sign of unknowns -> Both

d)

Select Tension 1 to Tension 4 to

unknown e)

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Get Unknown Load Factors

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4. Unknown Load Factor

Unknown Load Factor Unknown Load Factor Result a)

Make Load Combination ->

Bending moment b)

Generate Excel File

c)

Ok

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4. Unknown Load Factor

Unknown Load Factor Unknown Load Factor Result a)

Make Load Combination ->

Bending moment b)

Generate Excel File

c)

Ok

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4. Unknown Load Factor

Unknown Load Factor Unknown Load Factor Result a)

Make Load Combination ->

Bending moment b)

Name -> bending moment

c)

OK

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4. Unknown Load Factor

Unknown Load Factor

Result -> Force -> Beam Diagram

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a)

Load Case-> Bending moment

b)

Apply

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4. Unknown Load Factor

Unknown Load Factor Unknown Load Factor Result

a) Generate Excel File

Constraint Result Value

Modify tension value

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Influence Matrix

Part 3. Design midas Civil

Cable Stayed Bridge

5. Cable Load Tuning

Define Structure Groups

Tree Window -> Group a)

Structure Group -> NEW -> Beam

b)

Model Window Select Element 1to20

c)

Drag the group to the model window

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5. Cable Load Tuning Result -> Cable Load Control -> Cable Load Tuning

Click “…”

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5. Cable Load Tuning Result -> Cable Load Control -> Cable Load Tuning

Result Item a) Name -> Moment

b) Group -> Beam c) Type -> Beam Force -> My d) x- Axis -> +DX

e) Add f)

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Close

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5. Cable Load Tuning Result -> Cable Load Control -> Cable Load Tuning

Pretension force for cable

Red line is the range you define

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Green Line – Influence line Blue Line – Calculation Result Base on the cable force

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6. Bending Energy Method Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 9

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•Cable Stayed Bridge Modeling, input dead load • Increase the cable stiffness while reduce the pylon and girder stiffness against bending moment • Generate load conditions for dead load for main girder and the pretension loads for cables. • Run Analysis • Use the cable force result as the initial pretension force of the cable • Change the cable element type from truss to cable, use pretension to input their initial pretension force • Run Analysis

• Use the cable force result to modify the initial pretension load again • Run Analysis again

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6. Bending Energy Method

Cable Model 3

Increase the cable stiffness while reduce the pylon and girder stiffness against bending moment midas

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Part 3. Design midas Civil

Cable Stayed Bridge

6. Bending Energy Method

Bending moment of tower and girder

Result -> Force -> Beam Diagram

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a)

Load Case-> Bending moment

b)

Apply

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6. Bending Energy Method

Cable force

Result -> Force -> Truss

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a)

Load Case-> CLB1

b)

Apply

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6. Bending Energy Method

Cable force

Result -> Result Table -> Truss ->

Force a)

Load Case-> CLB1

b)

OK

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6. Bending Energy Method

Change element’s type Node/Element -> Change Parameters

midas

a)

Parameter type -> Element Type

b)

Mode -> From -> Truss -> To ->Cable

c)

Select Element 33, 40 -> Pretension ->2237 tonf -> Apply

d)

Select Element 35, 39 -> Pretension -> 1896 tonf ->Apply

e)

Select Element 36, 38 -> Pretension -> 1507 tonf ->Apply

f)

Select Element 35, 39 -> Pretension -> 2485 tonf ->Apply

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Part 3. Design midas Civil

Cable Stayed Bridge

6. Bending Energy Method

Input unit pretension loads for cables Load -> Temp./Prestress -> Pretension Load a)

Load Case Name -> Pretension Load

b)

Options-> Add

c)

Select Element 33, 40 -> Pretension

Load ->2237 tonf -> Apply d)

Select Element 35, 39 -> Pretension

Load -> 1896 tonf ->Apply

e)

Select Element 36, 38 -> Pretension

Load -> 1507 tonf ->Apply f)

Select Element 35, 39 -> Pretension

Load -> 2485 tonf ->Apply

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6. Bending Energy Method

Change the cable stiffness and the pylon and girder stiffness back to normal

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6. Bending Energy Method

Cable Model 4 Run Analysis

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Part 3. Design midas Civil

Cable Stayed Bridge

6. Bending Energy Method

Bending moment of tower and girder

Result -> Force -> Beam Diagram

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a)

Load Case-> Bending moment

b)

Apply

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6. Bending Energy Method

Cable force

Result -> Force -> Truss

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a)

Load Case-> CLB1

b)

Apply

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6. Bending Energy Method

Cable force

Element 33 34 35 36 37 38 39 40

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Pretension load comparison Result Pretension load Δ 2230.72 2237.59 6.87 1890.90 1896.10 5.20 1501.43 1506.77 5.34 2476.35 2485.37 9.02 2477.92 2485.37 7.45 1503.00 1506.77 3.77 1892.47 1896.10 3.63 2232.29 2237.59 5.30

relative error 0.31% 0.28% 0.36% 0.36% 0.30% 0.25% 0.19% 0.24%

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7. Construction Stage Analysis

Backward Construction Stage Analysis

Construction Stage Analysis Forward Construction Stage Analysis

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Part 3. Design midas Civil

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7. Construction Stage Analysis

Forward Construction Stage Analysis

Unknown Load Factor to calculate the initial pretention force

Lack of Fit Force to calculate the initial pretension force

Nonlinear Forward Construction Analysis midas

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Part 3. Design midas Civil

Cable Stayed Bridge

7. Construction Stage Analysis

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7. Construction Stage Analysis

Define Structure Groups, Boundary Groups, Load Groups

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Cable Model 5-1

Part 3. Design midas Civil

Cable Stayed Bridge

7. Construction Stage Analysis

Define Temporary boundaries

Boundary -> Point Spring Supports

a)

Boundary Group Name -> Temporary

Bent b)

Options -> Add

c)

Type -> Linear

d)

SDy, SDz, SRx, SRz -> 10000000

e)

SDx, Sry -> 0

f)

Model view window Select Node 2, 4 ,

18, 20-> Apply

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Cable Stayed Bridge

2. Basic Steps for Modeling Cable Stay Bridge

Define Temporary boundaries

Boundary -> Elastic Link

a)

Boundary Group Name -> Temporary

Link (Tower)

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Civil

b)

Options -> Add

c)

Type -> Rigid

d)

2 node -> Node 5, 26

e)

Apply

f)

2 node -> Node 17, 27

g)

Apply

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Cable Stayed Bridge

7. Construction Stage Analysis

Define Construction Loads Load -> Static Load -> Specified Displacement of Support

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a)

Load Case Name -> Jack Up

b)

Load Group Name -> Jackup Load

c)

Options -> Add

d)

Displacement -> Dz -> 0.01

e)

Model view window Select Node 1, 21

f)

Apply

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Cable Stayed Bridge

7. Construction Stage Analysis

Define Construction Loads Load -> Static Load -> Nodal Load

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a)

Load Case Name -> Derrick Crane

b)

Load Group Name -> Derrick Crane 1

c)

Options -> Add

d)

Fz -> -80 tonf

e)

Select Node 6, 16 -> Apply

f)

Load Group Name -> Derrick Crane 2

g)

Select Node 8, 14 -> Apply

h)

Load Group Name -> Derrick Crane 3

i)

Select Node 10, 12 -> Apply

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7. Construction Stage Analysis

Define Construction Stages

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Cable Model 5-2

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Cable Stayed Bridge

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7. Construction Stage Analysis

Define Construction Stages Stage Num

Duratio n Active

Element Age

Stage1

30

Stage1

10

Stage2

30

Stage2

10

Stage3 Stage4 Stage4-1 Stage5 Stage6 Stage7 Stage7-1 Stage8 Stage9 Stage10

30 30 30 30 30 30 30 30 30 30

Stage4

10

Stage11

30

Stage12

30

Stage12-1 Stage13

30 30

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Civil

Boundary Deactivated

Active Fixed Support (Tower) & Temporary Support (Tower) Hinge Support (Tower) & Temporary Bent

Deactivated

Active

Load Active day

Self Weight

First

Pretension Load 4

Last

Pretension Load 3 Derrick Crane 2 Pretension Load 2

Last First Last

Pretension Load 1 Derrick Crane 3

Last First

Deactivated

Temporary Bent Stage5 Stage6 Stage7 Stage8 Stage9 Stage11

10 10 10 10 10 10

Derrick Crane 1

Derrick Crane 2 Derrick Crane 3

Elastic Link (Tower)

Temporary Support (Tower) Jackup Load Additional Load

First First

Part 3. Design midas Civil

Cable Stayed Bridge

7. Construction Stage Analysis

Define Construction Stages 1 Define Construction stage -> Add -> Compose Construction Stage a)

Name -> Stage 1

b)

Duration -> 30 days

c)

Save Result -> Stage

d)

Element -> Group list -> Stage 1 ->

Age -> 10 ->Add e)

Boundary -> Group list -> Fixed

Support (Tower) & Temporary Link (Tower) ->Add f)

Load -> Group list -> Self Weight -

>Add g) midas

Apply

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7. Construction Stage Analysis

Construction Stages Analysis Control

Cable Model 5-3

Analysis -> Construction Stages Analysis Control a)

Final stage -> Last Stage

b)

Analysis option -> Include P-Delta Effect Only/Include Nonlinear Analysis -> Accumulative stage

c)

Cable pretension force control -> External Force

d)

OK

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Part 3. Design midas Civil

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7. Construction Stage Analysis

Construction Stages Analysis Control

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Cable Model 5-3

Part 3. Design midas Civil

Cable Stayed Bridge

7. Construction Stage Analysis

Run Analysis

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Cable Stayed Bridge

8. Unknown Load Factor In construction stages

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Cable Stayed Bridge

8. Unknown Load Factor In construction stages

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Cable Stayed Bridge

8. Unknown Load Factor In construction stages

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Cable Stayed Bridge

8. Unknown Load Factor In construction stages

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8. Unknown Load Factor In construction stages

Use the pretension force of the final stage for the pretension load add in the construction stage

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9. Lack of Fit Force

Construction Stages Analysis Control

Cable Model 6

Analysis -> Construction Stages Analysis Control a)

Final stage -> Last Stage

b)

Analysis option -> Include Nonlinear Analysis -> Accumulative stage

c)

Cable pretension force control -> Internal Force

d)

Initial Tangent Displacement for Erected Structures -> Lack of Fit Force Control -> Lack of Fit Force

e)

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OK

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Cable Stayed Bridge

9. Lack of Fit Force

Run Analysis

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9. Lack of Fit Force

Bending moment of the final stage

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Part 3. Design midas Civil

Cable Stayed Bridge

9. Lack of Fit Force

Pretension load for construction stage

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9. Lack of Fit Force

Lack of Fit Force Result -> Result Tables -> Construction stage -> Lack of Fit Force -> Truss/Beam

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Part 3. Design midas Civil

Cable Stayed Bridge

10. Forward Construction Analysis

Use the construction stage pretension force we get in the Lack of Fit Force Model and input them into the pretension force for the forward construction model

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10. Forward Construction Analysis

Construction Stages Analysis Control

Analysis -> Construction Stages Analysis Control a)

Final stage -> Last Stage

b)

Analysis option -> Include Nonlinear Analysis -> Accumulative stage

c)

Cable pretension force control -> External Force

d)

OK

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Cable Model 7

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Cable Stayed Bridge

10. Forward Construction Analysis

Run Analysis

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10. Forward Construction Analysis

Bending moment at the final stage

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10. Forward Construction Analysis

Tension of the cable

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11. Other structure analysis

Analysis -> Construction Stages Analysis Control a)

Final stage -> Last Stage

b)

Analysis option -> Include Nonlinear Analysis -> Accumulative stage

c)

Cable pretension force control -> External Force

d)

Convert Final Stage Member Forces to Initial Forces for Post C.S. ->Truss and Beam

e)

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OK

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11. Other structure analysis Final Stage Load

Do not chose ”Post

Case

CS…”

Moving Load

Linear Truss Element

Chose“PostCS…”

Consider geometrical

stiffness the elastic catenary Cable Elements and Beam Elements Settlement

Same

Same

Dynamic Analysis

Same

Same

Temperature Load equivalent truss element

Same

equivalent truss element

Same

Other Static Load

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Civil

Notes

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