1. Modeling of Cable Stayed Bridges

Design of Cable Stayed Bridges

Dr. Naveed Anwar Executive Director, AIT Consulting Affiliated Faculty, Structural Engineering Advance Topics in Bridge Engineering, SET, AIT Director, ACECOMS

•

Introduction, Brief History/Development of Cable Stayed Bridges

•

Major Cable Stayed Bridges in World

•

Basic Components and types of Cable Stayed Bridges

•

•

–

Cable Arrangement Types

–

Pylon Types

–

Deck Types

–

Substructure Types

Key Challenges •

Design Challenges

•

Material Challenges

•

Construction Challenges

Behavior of Cable Stayed Bridges –

Load Path

–

Static behavior

–

Dynamic Response

•

Modeling and Analysis

•

Seismic Effects

•

Wind Effects

•

Bridges in Bangkok Advance Topics in Bridge Engineering, SET, AIT

Dr. Naveed Anwar

Advance Topics in Bridge Engineering, SET, AIT

Advance Topics in Bridge Engineering, SET, AIT Dr. Naveed Anwar

Suspension bridge-drawing by Faust Vrančića in Machinae novae, 1595

A diagram of one of the earliest known suspension bridges in the world, built in 1430, at Chushul, south of Lhasa in Tibet. The image was taken by an Indian spy working for the Survey of India in 1878, and published by Waddell in 1905





•

•

A cable-stayed bridge, one of the most modern bridges, consists of a continuous strong beam (girder) with one or more pillars or towers in the middle. Cables stretch diagonally between these pillars or towers and the beam –

•

These cables support the beam

The cables are anchored in the tower rather than at the end




•

Appropriate for medium span bridges (200 to 800 m)

•

Requires less cable then a suspension bridge

•

Can be constructed out of identical pre-cast concrete sections

•

Faster to build

• •

Cable-stayed bridges look futuristic, but the idea for them goes back a long way. Stability Conditions –

–

To prevent sideways and vertical movements of the tower/pylon and deck under asymmetrical live loading Possible to maintain stability of the whole structure by resisting only the horizontal and vertical components of the forces generated


Parallel Attachm ent Pattern

Radial Attachm ent Pattern Advance Topics in Bridge Engineering, SET, AIT Dr. Naveed Anwar



pros •

•

•

Construction method is simple (cantilever method)

cons •

Typically built for larger spans

•

Simple to design (as opposed to the suspension bridge)

•

May require pier, or at least a tower on either side of the site More susceptible to damage by wind forces (also weak in torsion). Although cheaper than suspension bridges, can be more expensive for short spans (as opposed to truss bridges)


•

•

Many things to think about mathematically: –

Horizontal distance from tower to point of attachment

–

Height of point of attachment above bridge level

–

Stretched length of cable

–

Angle between cable and tower

Experiments to consider: –

Cable needs to be tested to see how its stretch varies with the angle to the vertical •

an experiment to determine how much a length of cable stretches when it supports a mass


•

The tower of the bridge forms the vertical side of the right triangle. –

–

•

The distance between the points of attachment of preceding cables on the tower should be equal Likewise, the points of attachment of the cables on the beam of the span should be equidistant.

You can calculate the length of the remaining cables after the first cable has been installed by applying the proportionality concept or the Pythagorean theorem.


•

•

•

The tower is responsible for absorbing and dealing with compression forces Tension occurs along the cable lines

Tension

This works because a moving load is not applied evenly across the bridge, and as it moves one set or the other of the diagonals will find itself in tension

Compression



Rank

N a me

L o cat i o n

1

RusskyBridge

Vladivostok, Eastern Bosphorus Strait

2

SutongBridge

Suzhou, Nantong

3

StonecuttersBridge

RamblerChannel

4

E’dong Bridge

5

Tatara Bridge

6

Pont de Normandie

Huangshi

Co untry

L o n g e sts p a n

Russia

1,104 m

2012

2

People's Republic of China

1,088 m

2008

2

HongKong (PRC) People's Republic of China

Seto Inland Sea Le Havre

Japan France

7

JingyueBridge

Jingzhou


8

Incheon Bridge

Incheon

South Korea

9

Jiaxing-ShaoxingS eaBridge

10

Zolotoy Bridge

Hangzhou Bay


Vladivostok


1,018 m

Russia

C o mp l et ed

2009

926 m 890 m 856 m

800 m 780.29 m 737 m

2

2010

2

1999 1995

816 m

Py lo ns

2 2

2010 2009 2013 2012

2 2 multi pylon 2

Rank

1

N a me

RusskyBridge

L o c at i o n

Vladivostok, Eastern Bosphorus Strait

Co untry

L o n g e sstp a n

Russia

1,104 m

Russky Bridge, Vladivostok, Russia Dr. Naveed Anwar

C o mp l et ed

2012

Py lon s

2

Rank

2

N a me

SutongBridge

L o c at i o n

Suzhou, Nantong

Co untry


Sutong Bridge, China Dr. Naveed Anwar

L o n g e sstp a n

1,088 m

C o mp l et ed

2008

Py lon s

2

Rank

3

N a me

StonecuttersBridge

L o c at i o n

RamblerChannel

Co untry

HongKong (PRC)

Stonecutters Bridge, Hong Kong Dr. Naveed Anwar

L o n g e sstp a n

1,018 m

C o mp l et ed

2009

Py lon s

2

Rank

N a me

4

E’dong Bridge

L o c at i o n

Huangshi

Co untry


E’dong Bridge, China Dr. Naveed Anwar

L o n g e sstp a n

926 m

C o mp l et ed

2010

Py lon s

2

Rank

N a me

5

Tatara Bridge

L o c at i o n

Seto Inland Sea

Co untry

Japan

Tatara Bridge, Japan Dr. Naveed Anwar

L o n g e sstp a n

890 m

C o mp l et ed

1999

Py lon s

2

Rank

6

N a me

Pont de Normandie

L o c at i o n

Le Havre

Co untry

France

L o n g e sstp a n

856 m

Pont de Normandie Bridge, France Dr. Naveed Anwar

C o mp l et ed

1995

2

Py lon s

Rank

7

N a me

JingyueBridge

L o c at i o n

Jingzhou

Co untry


Jingyue Bridge, China Dr. Naveed Anwar

L o n g e sstp a n

816 m

C o mp l et ed

2010

Py lon s

2

Rank

8

N a me

Incheon Bridge

L o c at i o n

Incheon

Co untry

South Korea

Incheon Bridge, South Korea Dr. Naveed Anwar

L o n g e sstp a n

800 m

C o mp l et ed

2009

2

Py lon s

Rank

N a me

9

Jiaxing-ShaoxingS ea Bridge

L o c at i o n

HangzhouBay

Co untry


Jiaxing-Shaoxing Sea Bridge, China Dr. Naveed Anwar

L o n g e sstp a n

780.29 m

C o mp l et ed

2013

Py lon s

multi pylon

Rank

10

N a me

Zolotoy Bridge

L o c at i o n

Vladivostok

Co untry

Russia

Zolotoy Rog Bridge, China Dr. Naveed Anwar

L o n g e sstp a n

737 m

C o mp l et ed

2012

Py lon s

2

Coalbrookdale, UK


Gi-Lu bridge, Taiwan

Dr. Naveed Anwar

Zakim Bridge, Boston, MA

Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

Mixed Systems

Dr. Naveed Anwar





Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar


Ra n k

1

Dec kl engt h 2,460metres

Na m e MillauV iaduct

2 3 4

2,252metres 1,688metres 1,596 meters

Rio-AntirioB ridge SutongBridge Stonecutters Bridge

5

1,552 metres

ErqiY angtze River Bridge

6 7 8

1,495 metres 1,320metres 1,312metres

General Rafael UrdanetaBr idge IncheonBridge TataraB ridge

9

1,272metres

RusskyBridge

10 11 12 13 14

1,246metres 1,177metres 1,170 metres 1,158 metres 1,121metres

Shanghai YangtzeRiverBridge TingKauB ridge Meiko-ChuoBridge Third Nanjing Yangtze Bridge SecondNanjingYangtzeBridge

15

1,105metres

QingzhouB ridge

16

1,096metres

E’dong Bridge

17

1,082metres

18

1,074metres

Zhengzhou Yellow River Road Rail Bridge XupuB ridge

19

1,056metres

JintangB ridge

20

1,040metres

AnqingB ridge

21

1,020 metres

Tsurumi Tsubasa Bridge




Dr. Naveed Anwar

Rama IX Bridge

Dr. Naveed Anwar

Single Plane Bridge

•

Construction materials used: Cables

•

RC

Pylons

Steel

Dimensions: Main span Total length


Steel

Piers

450 m 781.20 m

Largestcabledia.

167mm

Deckdepth

4.00m

Deckwidth

33.00m

Clearancebelow

41m


Rama VIII Bridge

Single Pylon Bridge Cables

steel

Piers

reinforcedconcrete

Pylons

reinforced concrete

Longest Span – 300m

Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

•

Longest span - 326 m and 398 m


Dr. Naveed Anwar

•

Longest Span – 500m


• • •

•


Cable Arrangement Types Pylon Types Deck Types Substructure Types

•

•

Cables are usually either arranged in a single-plane or two-plane system Single-plane is commonly employed with a divided road deck, and requires only a narrow pylon and pier Single Plane

•

In the two-plane system the cable can either be arranged to hang vertically or slope towards the top of the tower or pylon

Two Plane


Parallel Attachm ent Pattern

Radial Attachm ent Pattern Advance Topics in Bridge Engineering, SET, AIT Dr. Naveed Anwar

Radial : cables connect evenly throughout the deck, but all converge on the top of the pier

Harp : cables are parallel, and evenly spaced along the deck and the pier

Fan : a combination of radial and harp types

Star-shaped : cables are connected to two opposite points on the pier


•

•

Similar to that used for normal prestressing work May comprise of: –

–

multi-strand cable made up of cold drawn wires single strand cable (mono-strand cable) consisting of parallel wires

•

•

Diameters in the range 40-125 mm are typical Protection against corrosion is a major concern


Polyethylene duct Protective grout

Prestressing wire

Parallel wires

Polyethylene duct

S- section wires

Cement grout

Trapezoidal section wires Round wire

Spacer Strand

Locked Cables


Strands

•

•

•

•

Main tensile elements made out of High tensile prestressing steel and standardized structural steel for anchorages Zink or other corrosion protective coating on prestressing Steel and Structural steel components High density polyethylene protective cover Filling material such as wax and grease for protection of free length and anchorages


•

Usually the cable has a pin type joint to the Pylon

•

Have either swaged or filled sockets

•

The deck-to-cable connection is usually of the 'free' type accommodate adjustment

•

to

Cable Anchorages in Pylon are usually expensive


Bottom Anchorage


Upper Anchorage

•

Durability

•

Wide size range

•

Easiness of Installation

•

Unitary Stressing(Strand by Strand)

•

•

•

Adjustable anchorages for full stay stressing or distressing Force checking or monitoring at any time Replacement of stay as a whole or strand by strand individually

•

Ability to damper Installation

•

Longer Fatigue Life(2 million cycles) Advance Topics in Bridge Engineering, SET, AIT

Dr. Naveed Anwar

•

•

May be fabricated from –

steel plate,

–

precast concrete elements

–

occasionally in in-situ concrete

Various design options are available to produce good aesthetic effects SingleTower

A-Frame Tower


TwinTower

Diamond Tower

Dr. Naveed Anwar

•

Generally has a hollow box cross section

•

Provides torsional resistance across the deck width

•

May be assembled in precast concrete elements, steel plate or girders, or made in in situ concrete


•

•

Various methods in practice include: –

Erect on temporary props

–

Free cantilever with progressive placing

–

Balanced cantilever

–

Push-out

Method of erection is influenced by: –

–

the stiffness of the pylon cable anchorage system viability of installing temporary supports

–

maximum unsupported spans permitted by the design

–

case of transporting materials


Dr. Naveed Anwar

Dr. Naveed Anwar


Dr. Naveed Anwar

Dr. Naveed Anwar

• • •


Design Challenges Material Challenges Construction Challenges

•

A cable-stayed bridge is a highly redundant, or statically indeterminate structure.

•

The permanent load condition includes

•

•

•

•

•

–

All structural dead load

–

All Superimposed dead

–

All prestressing effects

–

All secondary moments and forces.

It is the load condition when all permanent loads act on the structure. There are an infinite number of possible combinations of permanent load conditions for any cable-stayed bridge. The designer can select the one that is most advantageous for the design when other loads are considered. Construction stage analysis checks the stresses and stability of the structure in every construction stage, starts from this selected final condition backwards. However, if the structure is of concrete or composite, creep and shrinkage effect must be calculated in a forward calculation starting from the beginning of the construction. Advance Topics in Bridge Engineering, SET, AIT

Dr. Naveed Anwar

•

•

•

•

•

Live-load stresses are mostly determined by evaluation of influence lines. The stress at a given location in a cable-stayed bridge is usually a combination of several force components. In lieu of the combined influence lines, some designs substitute P, M, and K with extreme values, i.e., maximum and minimum of each. Such a calculation is usually conservative but fails to present the actual picture of the stress distribution in the structure. Vibrations, resonance effects of moving trucks can be greatly amplified in cable stayed bridges


•

•

Differential temperature between various members of the structure, especially that between the cables and the rest of the bridge, must be considered in the design. Black cables tend to be heated up and cooled down much faster than the towers and the girder, thus creating a significant temperature difference. –

•

Light-colored cables, therefore, are usually preferred.

Orientation of the bridge toward the sun is another factor to consider. –

One face of the towers and some group of cables facing the sun may be warmed up while the other side is in the shadow, causing a temperature gradient across the tower columns and differential temperature among the cable groups.


•

Most cable-stayed bridges are relatively flexible with long fundamental periods in the range of 3.0 s or longer. –

•

In the transverse direction, the towers are similar to a high-rise building. –

•

•

Their seismic responses are usually not very significant in the longitudinal direction. Their responses are also manageable.

Experience shows that, except in extremely high seismic areas, earthquake load seldom controls the design. On the other hand, because most cable-stayed bridges are categorized as major structures, they are usually required to be designed for more severe earthquake loads than regular structures.


•

High-strength concrete

•

High-strength steel cables

•

Rubber bearings

•

Precast concrete


•

Highly Skilled tasks

•

Availability of heavy equipment

•

High level of precision and sophistication

•

Previous experience is often essential

•



•

The Dead load of deck is primary loading

•

Lateral loads due wind

•

Aero elastic loading due to wind –

Resonance, Flutter, Vortex shedding

•

Seismic load and amplification

•

Expansion due temperature change –

•

Cable elongation effects

Traffic/ Truck load is less important –

Generally uniformly distributed load is considered


T

C C

W P? P


+- Dx +dL +- dy

-dL -dL Deck Free to Move

Dy

Dy


Main Span – StayForceDiagram


BackSpan

– Stay Force Diagram

•

Depending on the type of bearing or supports used, the dynamic behavior of the structure can be quite different. –

–

If very soft supports are used, the girder acts like a pendulum. Its fundamental frequency will be very low. Stiffening up the supports and bearings can increase the frequency significantly.


•

•

Modeling of Cables –

Consider the Nonlinearity due to profile and material

–

Consider the Pre-Tension and multiple stressing

–

Consider the Partial Fixity at Anchors

Modeling of Deck –

–

The extent of deck model and level of detail Global Model and Local Models


•

•

•

Modeling of Pylons –

Modeling the Flexibility and Stability

–

Partial construction loading and unbalanced conditions

Modeling of Expansion Joint –

Accommodating Large Moments

–

Transfer of large forces

Modeling of Foundations –

Foundations are often under water

–

Very large loads and moments

–

Modeling Water waves, collision etc



•

The towers are the struts for the bridge. They receive all of the compressive forces.

•

These members have to be thick enough resist buckling, flexure, and oscillation.

•

•

•

They have to withstand minor changes as a result of live loads and temperature changes. The main job of the towers is to withstand the forces that are exerted on it by the cables. Depends upon the height and mode of erection and may be: –

shop-fabricated in steel as complete units

–

Made up from cellular or box girder sections

–

In situ concrete either cast lift-by-lift or slip-formed


•

•

•

All of the tension forces in the bridge is transferred to the main cable through the suspenders The cables need to allow vibration and be resistant to corrosion Generally spun in place from individual galvanized wires, or positioned similar to the method used for cable-stayed bridges

•

The wire or stands are compacted together and then bound in galvanized wire and coated with weather- resistant paint to aid corrosion protection



•

Model as Load

•

Model as Element with or without Tendon Loads


•

Model as Element


•

•

•

•

Click Draw Frame Element Tools Select Tendon or Cable from “Line Object Type”

Draw Element in Model Specify Parameters Cable

Tendon


•

•

106

Special 2D elements to capture the Non-Linear behavior Various NL Links are used in modeling including –

Multi-Linear Elastic

–

Multi-Linear Plastic

–

Damper

–

Gap

–

Hook

–

Rubber Isolators

–

Friction Isolators



CE 72.90 - Advanced Topics in Bridge Engineering – June 2013, Dr. Naveed Anwar

Moving load analysis of cable stayed bridge

Dr. Naveed Anwar

Construction stage analysis of cable stayed bridge

Dr. Naveed Anwar


•

The modal analysis determines the inherent natural frequencies of vibration

•

Each natural frequency is related to a time period and a mode shape

•

Time Period is the time it takes to complete one cycle of vibration

•

The Mode Shape is normalized deformation pattern

•

The number of Modes is typically equal to the number of Degrees of Freedom

•

The Time Period and Mode Shapes are inherent properties of the structure and do not depend on the applied loads

Ad vanc e Topic s in Br id ge Eng in eeri ng , SET, AIT CE 72.90 - Advanced Topics in Bridge Engineering – June 2013, Dr. Naveed Anwar

ACECOMS, AIT

First mode (f1 = 0.40 Hz)

Second mode (f2 = 0.64 Hz)

Fourth mode ( f4 = 1.00 Hz).



•

•

•

•

•

For each mode of free vibration, corresponding Time Period is obtained. For each Time Period and specified damping ratio, the specified Response Spectrum is read to obtain the corresponding Acceleration For each Spectral Acceleration, corresponding velocity and displacements response for the particular degree of freedom is obtained The displacement response is then used to obtain the corresponding stress resultants The stress resultants for each mode are then added using some combination rule to obtain the final response envelop


ACECOMS, AIT

Design Spectral Acceleration Vs Time Period Ad vanc e Topic s in Br id ge Eng in eeri ng , SET, AIT CE 72.90 - Advanced Topics in Bridge Engineering – June 2013, Dr. Naveed Anwar

ACECOMS, AIT

•

•

Input needed for Response Spectrum Analysis –

Mass and stiffness distribution

–

A Specified Response Spectrum Curve

–

The Response Input Direction

–

The Response Scaling Factors

–

The modes to be included

Output From Response Spectrum Analysis –

Unsigned displacements, stress resultants and stresses etc.


ACECOMS, AIT

•

•

•

The full dynamic equilibrium equation is solved for each time step on the acceleration-time curve The History of the deformations resulting from previous time step calculation is considered in computing the response for the current time step The time-history analysis is in-fact a piece wise solution of the entire force histogram


ACECOMS, AIT

0.1

Cliff Station from 1989 Loma Preita, USA 0

-0.1 0

10

20

30

40

Time (sec) 0.05

CUIP Station from 1985 Michoacan, Mexico 0

-0.05 0

10

20

30

40

50

60

Time (sec)

Ad vanc e Topic s in Br id ge Eng in eeri ng , SET, AIT

CE 72.90 - Advanced Topics in Bridge Engineering – June 2013, Dr. Naveed Anwar

ACECOMS, AIT

Internal dampers:


External dampers:



Dr. Naveed Anwar

Deformation Due to Time Ave raged aerodynamic for ce Stress Due to Wind Induced P ressure or Forc e

Static Effects

Torsiona l Divergence (nega tive stiff ness) Static Instability

Late ral Buckli ng

Due to Atmospheric Turbulence

Forced Vibration

Buffe rting (random vibration)

Limited Amplitude Response Due to Body induced Turbulence (Wake)

Dynamic Effects

Vortex Excitation Galloping

Wake Gallopi ng

Dynamic Instability (negative damping)

Tor siona l Flu tter Coupled Flutter Rain Induced Vibrations

Classification of Wind Effects Dr. Naveed Anwar

Divergent Amplitude Response

Dr. Naveed Anwar

Metrology

Aerodynamics

Theory of Structures

Material science, codes, regulations

Wind

Loading on the Structure

Structural Respose

Check Safety/ Serviceability

Influence of Deformation on Loading Aeroelasticity

CE 72.32 - Design of Tall Buildings - January 2013, Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar

WindTunnelTests Dr. Naveed Anwar

Dr. Naveed Anwar

Dr. Naveed Anwar


•

•

•

•

•

Seismic and aerodynamics have contradictory demands on the structure. For aerodynamic stability a stiffer structure is preferred but for seismic design, except if the bridge is founded on very soft soil, a more flexible bridge will have less response. Some compromise between these two demands is required. A device that connects the girder and the tower, which can break at a certain predetermined force will help in both events. Under aerodynamic actions, it will suppress the onset of the vibrations as the connection makes the structure stiffer. Under seismic load, the connection breaks at the predetermined load and the structure becomes more flexible. This reduces the fundamental frequency of the bridge.



Thank You

Dr. Naveed Anwar Executive Director, AIT Consulting Affiliated Faculty, Structural Engineering Advance Topics in Bridge Engineering, SET, AIT Director, ACECOMS

1. Modeling of Cable Stayed Bridges

Recommend Documents