Cable Stayed BridgesModeling and AnalysisVidish A. Iyer Structural Engineer and CAE consultant at Midas IT

What kind of bridge type can midas Civil handle?Conventional Bridge Staged Segmental Bridge Cable-stayed Bridge & Suspension Bridge CONTENTS Click to edit Master subtitle style WHAT TYPE

Modeling and Analysis

Vidish A Iyer

Structural Engineer and CAE consultant at Midas IT

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CONTENTS Click to edit Master subtitle style ABOUT MIDAS IT

What is midas Civil?

CONTENTS

Click to edit Master subtitle style WHAT IS MIDAS CIVIL ?

What kind of bridge type can midas Civil handle?

Conventional Bridge

Staged Segmental Bridge

Cable-stayed Bridge & Suspension Bridge

CONTENTS

Click to edit Master subtitle style WHAT TYPES OF BRIDGES CAN IT HANDLE ?

Click to edit Master subtitle style

MODELING PHILOSOPHY

INITIAL SIZING

• Aside from loadings , Pylon and Deck Geometry and orientation are usually driven

by cost and aesthetics

• Backstay forces are maximum when live load is on main span and lowest when it is

on side spans

• Backstays usually get largest stress variations among all cables

Three main modeling methods

• Spine Beam Model

• Multi-Scale Model

• Meshed Finite Element model

INITIAL MODELING

• Most common modeling method

• Bridge is modeled using beam , truss elements and links

• Deck Sections can be modeled using equivalent section

properties

SPINE BEAM MODELING

Cables can be modeled as tension trusses with sag effect considered through the Earnst Formula :

CABLE MODELING

• Use of different elements for modeling bridge

• Used to capture more accurate and localized results

MULTI-SCALE MODELING

• More realistic structural response Accurate representation of local and

global responses.

• Usually quite cumbersome to model entire bridge using this , so only

certain critical portions are modeled and analyzed

MESHED FINITE ELEMENT MODELING

SUPPORT SYSTEMS FOR CONVENTIONAL BRIDGES

ANALYSIS PHILOSOPHY

Basic Philosophy :

final model.

considering time-dependant effects

METHODOLOGY

Three Basic Methods :

1 Continuous Beam Method

2 Bending moment envelope method

3 Influence Matrix Method

OPTIMUM CABLE FORCE FOR FINAL STATE MODEL

• Stay cable locations idealized as support points

• Helps eliminate creep in vertical direction at nodal locations

CONTINUOUS BEAM METHOD

A matrix of influence coefficients can be made to reflect the effect of loading

in one or more cables on the rest of the structure :

INFLUENCE MATRIX / UNKNOWN LOAD FACTOR METHOD

CABLE FORCE TUNING

The cable pretension (or Load Factor) from the unknown load factor method might not be practical or might exceed the cable force tolerance limit

Backward Analysis :

Forward Analysis :

are not considered

CONSTRUCTION STAGING

ITERATION PROCESS

Initial cable forces at the time of installation

Lack-of-Fit Force table

LACK OF FIT FORCE

Lack of Fit Force in Truss

Lack of Fit Force in Beam

• Camber Calculation is one of the many requirements for such bridges

CAMBER

CONSTRUCTION CAMBER

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

Construction Camber

MANUFACTURE/FABRICATION CAMBER

Manufacture Camber

To see real displacement in the results, check

“Initial Tangent Displacement for Erected Structures” option in CS Analysis Control Data.

3 Major Nonlinear Effects :

• Sag Effect of cables

• P-Delta effects ( 2 nd order )

• Large deformation ( 3 rd order )

NONLINEAR EFFECTS

SAG EFFECTS

Cable element treated as

equivalent truss with

effective stiffness given by

the formula shown below

Cable element is transformed into elastic catenary element

• For short to medium span bridges deflections

limited to live load effects

• For long span bridges , these should be

considered for both construction and final

stage calculations

2 nd ORDER EFFECTS

• In general , no hard and fast rule to decide when 3 rd order

theory should be used

• For short span bridges, Virlogeux et al (1994 ) suggest that

dead load distribution be analyzed as first order and second

order checks be done for live load computation

• Wang et al (2003) suggest that for main spans beyond 600 m ,

LINEAR VS P-DELTA VS NONLINEAR

PROJECT APPLICATIONS

Ironton-Russell Bridge

Overall bridge length 1,900 ft

between Ironton and Russell

Cost of construction $110 Million

Number of elements and element types used

Truss (Cable): 70Beam: 2088Shell: 2730

Type of analysis

Construction Stage Analysis with Time-Dependent EffectsUnknown Load Factor Analysis

Year of completion 1989 (Health Monitoring, 2005)Cost of construction $30 Million

Number of elements and element types used

Truss (Cable): 52Beam: 484Shell: 13312

Cable Tension Optimization

Overall bridge length 400 m

Number of elements and element types used

Truss: 56 (Stay cables)Beam: 582 (Deck and Tower)

type of analysis

Static AnalysisVehicle Load Optimization Time History Analysis

TU Delft / Movares Research Project on Train-Structure Interaction

Cost of construction $ 20 Million

Number of elements and element types used

Truss (Cable): 104Beam: 4063Shell: 2288

Type of analysis

Static AnalysisVehicle Load OptimizationEigenvalue Analysis

Korabelny Farvater Bridge

Overall bridge length 120 m

Truss: 10Beam: 903Shell: 637

Lazarevsky Bridge

Co., Ltd

Cost of construction $ 2.4 Billion

Number of elements and element types used

Truss (Cable): 176Beam: 1653

Incheon 2ndBridge – 5thLongest Cable Stayed Bridge

Overall bridge length 1600 m

City, Hong Kong, China

Number of elements and element types used

Truss (Cable): 224Beam: 1638

Construction Stage Analysis with Time-Dependent Effects

Cable Tension Optimization

Stonecutters Bridge – 3rd Longest Cable Stayed Bridge

midasCivil 41/138

between Nantong and Changshu

Designer

Jiangsu Province Communications Planning and Design Institute

Cost of construction $750 MillionNumber of elements

and element types used

Truss (Cable): 272Beam: 760

Thermal AnalysisBuckling Analysis

Sutong Bridge – 2nd Longest Cable Stayed Bridge

THANK YOU !