MIDAS 2013 Indonesia Workshop - Cable Stayed Bridge

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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

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1. Introduction

Cable Stayed Bridge Designing

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Regular Analysis Process for Cable Stayed Bridge

Final Stage

Analysis

Backward

Construction

Stage

Analysis

Forward

Construction

Stage

Analysis

Other

Structural

Analysis

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1. Introduction

Cable element:

① Truss

② Tension only truss

③ Hook

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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

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1. Introduction

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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

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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

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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 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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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

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③ Define Boundary Conditions

Boundary -> Elastic Link

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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④ Define Loads

Load -> Static Load Cases

a) Name -> Self Weight b) Type -> Dead Load

c) Add

d) Name -> Additional Load e) Type -> Dead Load

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③ Define Boundary Conditions

Load -> Self Weight

a) Load Case Name -> Self Weight b) Self Weight Factor -> Z -> -1

c) Add

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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

Unknown Load Factor

• Run the linear analysis

• Unknown Load Factor

• Cable Force Tuning

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

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4. Unknown Load Factor

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Define unit pretension loads for cables

Load -> Static Load Cases

a) Name -> Tension 1 b) Type -> USER

c) Description -> Cable 1 – Unit Pretension

d) Add

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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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Run Analysis

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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) Factor all 1

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Unknown Load Factor

Result -> Cable Control -> Unknown Load Factor

a) Item Name -> bending moment b) Load Comb -> LCB1

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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

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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

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Unknown Load Factor

Unknown Load Factor Result

a) Make Load Combination -> Bending moment

b) Generate Excel File c) Ok

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Unknown Load Factor

b) Generate Excel File c) Ok

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Unknown Load Factor

b) Name -> bending moment

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Unknown Load Factor

Result -> Force -> Beam Diagram

a) Load Case-> Bending moment b) Apply

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Unknown Load Factor

Unknown Load

Factor Result

a)

Generate

Excel File

Constraint Result Value

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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

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Result Item

a)

Name -> Moment

b)

Group -> Beam

c)

Type -> Beam Force -> My

d)

x- Axis -> +DX

e)

Add

f)

Close

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5. Cable Load Tuning

Pretension

force for

cable

Red line -

is the

range

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Step 1 •Cable Stayed Bridge Modeling, input dead load

Step 2 • Increase the cable stiffness while reduce the pylon and girder stiffness against bending moment

Step 3 • Generate load conditions for dead load for main girder and the pretension loads for cables.

Step 4 • Run Analysis

Step 5 • Use the cable force result as the initial pretension force of the cable

Step 6 • Change the cable element type from truss to cable, use pretension to input their initial pretension force

Step 7 • Run Analysis

Step 8 • Use the cable force result to modify the initial pretension load again

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6. Bending Energy Method

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Bending moment of tower and girder

Result -> Force -> Beam Diagram

a) Load Case-> Bending moment b) Apply

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Cable force

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Cable force

Result -> Result Table -> Truss -> Force

a) Load Case-> CLB1

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Change element’s type

Node/Element -> Change Parameters

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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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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Run Analysis

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Bending moment of tower and girder

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Cable force

Result -> Force -> Truss

a) Load Case-> CLB1 b) Apply

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Cable force

Pretension load comparison

Element Result

Pretension load

Δ

relative error

33 2230.72

2237.59

6.87 0.31%

34 1890.90

1896.10

5.20 0.28%

35 1501.43

1506.77

5.34 0.36%

36 2476.35

2485.37

9.02 0.36%

37 2477.92

2485.37

7.45 0.30%

38 1503.00

1506.77

3.77 0.25%

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Construction

Stage Analysis

Backward

Construction

Stage Analysis

Forward

Construction

Stage Analysis

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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

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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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Boundary -> Elastic Link

a) Boundary Group Name -> Temporary Link (Tower)

b) Options -> Add c) Type -> Rigid

d) 2 node -> Node 5, 26 e) Apply

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Define Construction Loads

Load -> Static Load -> Specified Displacement of Support

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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Load -> Static Load -> Nodal Load

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

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Define Construction Stages

Stage Num

Duratio n

Element Boundary Load

Active Age Deactivated Active Deactivated Active Active day Deactivated Stage1 30 Stage1 10

Fixed Support (Tower) & Temporary Support

(Tower)

Self Weight First

Stage2 30 Stage2 10

Hinge Support (Tower) & Temporary

Bent

Stage3 30

Stage4 30 Stage4 10 Pretension Load 4 Last Stage4-1 30 Temporary Bent Stage5 30 Stage5 10 Stage6 30 Stage6 10 Pretension Load 3 Last Stage7 30 Derrick Crane 2 First Derrick Crane 1 Stage7-1 30 Stage7 10 Pretension Load 2 Last

Stage8 30 Stage8 10 Stage9 30 Stage9 10 Pretension Load 1 Last Stage10 30 Derrick Crane 3 First Derrick Crane 2

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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

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Construction Stages Analysis Control

Analysis -> Construction Stages Analysis Control

a) Final stage -> Last Stage

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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

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Lack of Fit Force

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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

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10. Forward Construction Analysis

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11. Other structure analysis

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Case CS…”

Moving Load Linear Truss Element Consider geometrical stiffness the elastic

catenary Cable Elements and Beam

Elements

Settlement Same Same

Dynamic Analysis Same Same

Temperature Load equivalent truss

element Same

Other Static Load equivalent truss

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