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midas Civil Cable Stayed Bridge

2

Introduction

Problem Statement

Preliminary Design

Determination of Cable Force

Optimization of Deck

Construction Stage Modeling

Cable Tension Forces in Construction Stages

Time Dependent Material Effect

Non Linear Effect

Dynamic Analysis

Post Processsing

Wind Load Analysis

Contents:

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1. Introduction

midas Civil Cable Stayed Bridge

Cable Stayed Bridge

Wheel Load

Cable Supports

Tension In cables

Flexure In Deck

Axial Load in Pylon

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Stiffness of the cable is dependent on : 1. Load Applied

2. Tension Applied

P1 P1 P2 P2

Cable Stayed Bridge

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Cable Stiffness can be determined as per the following two techniques: 1. Equivalent Truss Method 2. . Elastic Catenary Cable

Cable Stayed Bridge

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Cable Bridges are highly indeterminate structures:

Cable Stayed Bridge

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Change of Cable Stiffness with Pretension High Indeterminacy

Difficult Analysis

Cable Stayed Bridge

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Cable Shape and pretension are in turn dependent on the load applied on the cable.:

Geometric Non Linear Analysis

Cable Stayed Bridge

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2. Problem Statement

midas Civil Cable Stayed Bridge

Problem Statement:

100 m 200 m 100 m

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2. Design Process

midas Civil Cable Stayed Bridge

Steps of Design : Determination of Cable Forces for Fully

Constructed Model

Check for Resisting Moments of Deck and Pylon Section

Change the Deck and Pylon Sections

Construction Stage Analysis

Non Linear Analysis

Dynamic Analysis

Preliminary Design

Check for Final Design

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Preliminary Design 1. Deck, Pylon Cross section. 2. Diameter of Cables. 3. Height of Pylons

3. Preliminary Design

midas Civil Cable Stayed Bridge

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Determination of Cable Forces 1. Use the unknown Load factor.

4. Determination of Cable Tension

midas Civil Cable Stayed Bridge

What is Unknown Load Factor ? Ans: It is a feature with which you can calculate the cable pretension force that would satisfy certain constraints in terms of displacements, bending moments etc.

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4. Determination of Cable Tension

midas Civil Cable Stayed Bridge

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5. Optimization

midas Civil Cable Stayed Bridge

Check the Design forces for the deck, pylon and cables and modify.

Bridging Your Innovations to Realities Cable Stayed Bridge

6. Forward Construction Stage Analysis

Modeling of Structure

Defining Structure Groups

Defining Loads under Load Group

Defining Boundary under Boundary Groups

Generation of Construction Stages

Defining Construction Stage Data

Construction Stage Analysis Control

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Bridging Your Innovations to Realities Cable Stayed Bridge

6. Forward Construction Stage Analysis

Implication with Forward Construction Stage Analysis

New Tendons

S Stage 10

Stage 11

More Pretension is required

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Bridging Your Innovations to Realities Cable Stayed Bridge

6. Forward Construction Stage Analysis

Lack of Fit Force: It calculates the additional pretension required for cable installation

midas Civil

Bridging Your Innovations to Realities Cable Stayed Bridge

7. Unknown Load Factor With Time Dependent Materials

The material Properties changes with time and the cable pretension force depends on the creep. The unknown load factor can take that into consider and the program can perform iterations to find the pretension in the cable which will include the time dependent effect.

Construction Stage

Construction Stage

Unknown Load Factor

Check

End

Unit Pretension loading

Set constraints and calculate unknown load factor by step

Using influence coefficient to reanalyze construction stage

[Iterative analysis procedure

to calculate unknown load factor]

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8. Eigen Value Analysis

midas Civil Cable Stayed Bridge

Analysis -> Eigen Value Analysis Control

Ritz Vectors Unlike the natural eigenvalue modes, load dependent Ritz vectors produce more reliable results in dynamic analyses with relatively fewer modes. The Ritz Vectors are generated reflecting the spatial distribution or the characteristics of the dynamic loading.

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9. Eigen Value Analysis

midas Civil Cable Stayed Bridge

To convert the final stage Cable forces to be used for determining cable stiffness for the Eigen Value Analysis

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9. Eigen Value Analysis

midas Civil Cable Stayed Bridge

Step 2: Eigen Value Analysis Results A) Natural modes (or mode shapes) B) Natural periods (or frequencies) C) Modal participation factors. D) Effective modal mass.

Eigenvalue analyses must precede dynamic analyses such as Modal Time History analysis or Response spectrum analysis.

The response spectrum analysis uses the natural periods from the eigenvalue analysis.

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10. Time History Analysis

midas Civil Cable Stayed Bridge

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Linear Case

Non Linear Case

R(x,xa) : Viscous Damping Fs(x): Variable Stiffness

10. Time History Analysis

midas Civil Cable Stayed Bridge

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Input Non Linear Links

Define Time History Load Case

Perform Non Linear Time History Analysis

Check the Results

Define Properties of Non linear Links

10. Time History Analysis

midas Civil Cable Stayed Bridge

Procedure of Eigenvalue Analysis:

Time Forcing Function

Ground Acceleration

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10. Time History Analysis

midas Civil Cable Stayed Bridge

Step 1: Defining Properties of Non Linear Links Model -> Boundaries -> General Link Properties

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Base Isolators: Lead Rubber Bearing Isolator Friction Pendulum System Isolator

Base Isolators Provided in midas Civil

Viscoelastic Damper Gap Hook Hysteresis System Base Rubber isolator Friction Pendulum System isolator

10. Time History Analysis

midas Civil Cable Stayed Bridge

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10. Time History Analysis

midas Civil Cable Stayed Bridge

Step 2: Define Time History Load Case Load -> Time History Analysis Data -> Time History Load Case

Transient: Time history analysis is carried out on the basis of loading a time load function only once. This is a common type for time history analysis of earthquake loads. Periodic: Time history analysis on the basis of repeatedly loading a time load function, which has a period identical to End Time. This type is applicable for machine vibration loads.

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10. Time History Analysis

midas Civil Cable Stayed Bridge

Step 2: Define Time History Load Case Load -> Time History Analysis Data -> Time History Load Case

Order in Sequential Loading: Select a time history analysis condition previously defined, which precedes the time history analysis condition currently being defined. The Analysis Type and Analysis Method for the current time history analysis condition must be consistent with those for the preceding load condition

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10. Time History Analysis

midas Civil Cable Stayed Bridge

Damping Method: the damping method can be one of : 1. Modal 2. Element Mass & Stiffness Proportional 3. Strain Energy Proportional

For Element Mass & Stiffness Proportional the relevant has to be provided in : Model -> Properties -> Group Damping: Element Mass and Stiffness Proportional

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The user can select the time history function from the list of various database earthquake or can generate its own:

Load -> Time History Analysis Data -> Time Forcing Function

10. Time History Analysis

midas Civil Cable Stayed Bridge

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Rotational angle about GCS Z-axis signifying the direction of the horizontal component of the ground acceleration. Sign convention is (+) in the counter-clockwise direction and (-) in the clockwise direction, with reference to the X-axis.

Select the Earthquake for X,Y and Z direction

Load -> Time History Analysis Data -> Ground Acceleration

10. Time History Analysis

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The user can do the time history analysis with Moving loads using this feature. The user needs to define the moving loads as Dynamic Nodal Loads.

Load -> Time History Analysis Data -> Dynamic Nodal Loads

10. Time History Analysis

midas Civil Cable Stayed Bridge

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Load -> Time History Analysis Data -> Multiple Support Excitation

In a structure with multiple supports, different time history forcing functions in terms of ground acceleration can be applied to different supports at varying times.

10. Time History Analysis

midas Civil Cable Stayed Bridge

Thanks