Cable stayed bridges non linear effects

Cable-Stayed Bridges - SteelSamuel Beckett Bridge, Dublin, Ireland Courtesy Santiago Calatrava... Cable-Stayed Bridges - SteelSteel Pylon Design – Second Order Effects 0.80 1.00 1.20 Eul

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Cable Stayed Bridges

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Presentation Layout

1 Introduction

2 Cable-Stayed Bridges - Steel

Theory & Examples Theory & Examples

3 Cable-Stayed Bridges - Concrete

Theory & Examples

4 Cable-Stayed Bridges - Composite

Examples

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1 Introduction

• Cable Stayed Bridges – Non Linearity

Geometric Non Linear (GNL) – Large Displacement Material Non Linear (MNL) – Moment Curvature

• Cable Stayed Bridges – Static Linear Analysis

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• BS 5400 Part 3: Clause 10

• First Principle Approach

Steel Pylon Design – Second Order Effects

• Perry Robertson Failure Criteria

• First Principle Approach

0

2

2 4

P dx

y d

E y

σ σ

σ η σ

σ η

( 2

) 1

(

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0.80 1.00 1.20

Euler Failure Curve Mean Axial Stress Perry Robertson Failure Curve

BS 5400 Part 3 Curve A

BS 5400 Part 3 Curve B

BS 5400 Part 3 Curve C

BS 5400 Part 3 Curve D

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0.00 0.20 0.40 0.60 0.80

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Samuel Beckett Bridge, Dublin, Ireland

Courtesy Santiago Calatrava

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Strabane Footbridges, Northern Ireland

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0.80 1.00 1.20

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0.80 1.00 1.20

BS 5400 Part 3 Curve A

BS 5400 Part 3 Curve B

BS 5400 Part 3 Curve C

0.00 0.20 0.40 0.60 0.80

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Analysis A = ULS DL + SDL + Wind Analysis B = ULS DL + SDL + Wind + Back-Stay Imbalance Analysis C = ULS DL + SDL Wind + Construction Tolerance Analysis D = ULS DL + SDL Wind + Back-Stay Imbalance + Constr Tol.

2.5

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0.0 0.5 1.0 1.5 2.0

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Analysis A = ULS DL + SDL + Wind Analysis B = ULS DL + SDL + Wind + Back-Stay Imbalance Analysis C = ULS DL + SDL Wind + Construction Tolerance Analysis D = ULS DL + SDL Wind + Back-Stay Imbalance + Constr Tol.

2.5

0.0 0.5 1.0 1.5 2.0

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Boyne Bridge, Meath / Louth, Ireland

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Dublin Eastern Bypass, Ireland

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Dublin Eastern Bypass, Ireland

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Taney Bridge, Ireland

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Taney Bridge, Ireland

Tower Design

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Pylon Design – Critical Loadcase & Location

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Second Order Effects – Bending Moments

First order First & second order Structure

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• Implications for Taney Bridge

• Methods and Codes

Second Order Effects – Investigation

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• Simple Cantilever Strut

• Methods and Codes

• Cable-Stay Bridge Design - Example

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• Elastic theory – Closed Form Solution

• Numerical Geometric Non-Linear Analysis

Second Order Effects – Methods & Codes

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BS 5400 Slenderness Upper Limit Upper Slenderness Limit

FIP Upper Slenderness Limit Taney Pylon - No Cables

Slenderness Definition – BS 5400 / EC 2 / FIP

BS 5400 Slenderness Upper Limit Upper Slenderness Limit

for FIP Equilibrium Method

Taney Pylon

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Taney Bridge – Free Standing Tower

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• Elastic theory – closed form solution

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x M dx

x w

Elastic Theory – Closed Form Solution

) ( )

( )

x w d EI

x Q dx

x w

2 2 4

4

= +

Deflection Equation:

Second Order

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• Numerical geometric non-linear analysis

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• Incremental load application

• Iterative techniques – equilibrium maintained

Numerical Geometric Non-Linear Analysis

• Stiffness revision

• Load – deformation path history

• Structural analysis packages

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• BS5400 Part 4

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y

e y

e y ix

tx

h

l h

l

Nh M

2

u e add l

e = ψ

γ

φε ψ

e y

add

h

l h

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• BS5400 Part 4

• Eurocode 2

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Three Methods

• Numerical Non-Linear Analysis

Eurocode 2

• Linear Second Order Analysis - Reduced Stiffness

• Curvature Estimation Methods

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Linear second order analysis with reduced stiffness

• Reduced stiffness

Eurocode 2

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• Total bending moment

• Buckling load factor

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• BS5400 Part 4

• Eurocode 2

• FIP / CEB

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• Step 1 – First Order Eccentricity at ULS ULS ULS ULS

N

M

Max Rd

e e

ty Eccentrici e

arg L e

e

Rd ULS

Rd d

dM EI

ty Eccentrici Small

dM EI

y Eccentrcit e

arg L

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• Step 4 – Second Order Moment





x w N M

1 2

λ

x w N

M Sd Sd

Rd ULS

Sd ULS compared with e

N M

e + 2

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Curvature Estimation Methods

0 5000 10000

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Simple Example – Cantilever Strut

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• Variation of slenderness ratio

Simple Example – Cantilever Strut

• Low first order moment (slenderness = 26)

- varying axial load 5000kN – 35000kN

• High first order moment (slenderness = 26)

- varying axial load 5000kN – 35000kN

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10

12

BS5400 Part 4 Moment 1st Order Elastic Theory FIP

Numerical NL Analysis Eurocode 2

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Numerical NL Analysis Eurocode 2

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Summary Low First Order Moment

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4 5 6

Summary High First Order Moment

0 1 2 3

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BS5400 (Reduced) FIP & Elastic Theory

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• Determine Buckling Factor, λ

• Determine First Order Eccentricity

Taney Bridge Pylon Design

• Determine First Order Eccentricity

• Application of Codes and Methods

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Taney Bridge Pylon Design

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Taney Bridge Buckling Factor

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Gross properties E ST I G E ST I G 13.5 1.08

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Cable-Stayed Span

Buckling Mode Shape 1

Anchor Span

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Anchor Span

T IT LE:

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30 35 40 45

Taney Bridge First & Second Order Moments

0 5 10 15 20 25

-8 00 00

-6 00 00

-4 00 00

-2 00 00

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FIP (Taney) Numerical NL Analysis (Taney) EC2 (Taney)

BS5400 (Taney)

First & Second Order Moments

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• Low first order moment & buckling factor λ > 3

Recommendation: Use EC2 or FIP

• High first order moment & buckling factor λ > 3

First & Second Order Moments

• High first order moment & buckling factor λ > 3

Recommendation: Use EC2 / FIP / BS 5400

• Buckling factor λ < 3

Recommendation: Curvature Methods Recommendation: Curvature Methods // Geometric & Material Non

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Second Order Effects – Extradosed Bridges

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4 Cable-Stayed Bridges- Composite

Monastery Road Bridge, Dublin, Ireland

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Waterford Footbridge, Ireland

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Waterford Footbridge, Ireland

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Narrow Water Bridge, Ireland / Northern Ireland

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New Wear Bridge, Sunderland

Courtesy TECHNIKER / SPENCE

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Thank You

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Thank You

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