Modelling of Cable stayed bridge by AIT

Advance Topics in Bridge Engineering, SET, AIT
Dr. Naveed Anwar
Executive Director, AIT Consulting
Affiliated Faculty, Structural Engineering
Director, ACECOMS
Design of Cable Stayed Bridges

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar

Dr. Naveed Anwar
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
Suspension bridge-drawing
by Faust Vrančića in
Machinae novae, 1595

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
Parallel Attachment Pattern
Radial Attachment Pattern

Dr. Naveed Anwar
pros
• Construction method is simple
(cantilever method)
• Typically built for larger spans
• Simple to design (as opposed to the
suspension bridge)
cons
• 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)

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
• 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.

Dr. Naveed Anwar
• The tower is responsible for absorbing
and dealing with compression forces
• Tension occurs along the cable lines
• 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
Tension
Compression

Dr. Naveed Anwar
Rank Name Location Country Longest span Completed Pylons
1 Russky Bridge
Vladivostok, Eastern
Bosphorus Strait
Russia 1,104 m 2012 2
2 Sutong Bridge Suzhou, Nantong
People's Republic
of China
1,088 m 2008 2
3 Stonecutters Bridge Rambler Channel Hong Kong (PRC) 1,018 m 2009 2
4 E’dong Bridge Huangshi
People's Republic
of China
926 m 2010 2
5 Tatara Bridge Seto Inland Sea Japan 890 m 1999 2
6 Pont de Normandie Le Havre France 856 m 1995 2
7 Jingyue Bridge Jingzhou
People's Republic
of China
816 m 2010 2
8 Incheon Bridge Incheon South Korea 800 m 2009 2
9 Jiaxing-Shaoxing Sea Bridge Hangzhou Bay
People's Republic
of China
780.29 m 2013
multi
pylon
10 Zolotoy Bridge Vladivostok Russia 737 m 2012 2

Dr. Naveed Anwar
Russky Bridge, Vladivostok, Russia
1 Russky Bridge
Vladivostok, Eastern
Bosphorus Strait
Russia 1,104 m 2012 2

Dr. Naveed Anwar
Sutong Bridge, China
2 Sutong Bridge Suzhou, Nantong
People's Republic of
China
1,088 m 2008 2

Dr. Naveed Anwar
Stonecutters Bridge, Hong Kong
3 Stonecutters Bridge Rambler Channel Hong Kong (PRC) 1,018 m 2009 2

Dr. Naveed Anwar
E’dong Bridge, China
4 E’dong Bridge Huangshi
China
926 m 2010 2

Dr. Naveed Anwar
Tatara Bridge, Japan
5 Tatara Bridge Seto Inland Sea Japan 890 m 1999 2

Dr. Naveed Anwar
Pont de Normandie Bridge, France
6 Pont de Normandie Le Havre France 856 m 1995 2

Dr. Naveed Anwar
Jingyue Bridge, China
7 Jingyue Bridge Jingzhou
China
816 m 2010 2

Dr. Naveed Anwar
Incheon Bridge, South Korea
8 Incheon Bridge Incheon South Korea 800 m 2009 2

Dr. Naveed Anwar
Jiaxing-Shaoxing Sea Bridge, China
9 Jiaxing-Shaoxing Sea Bridge Hangzhou Bay
China
780.29 m 2013
multi
pylon

Dr. Naveed Anwar
Zolotoy Rog Bridge, China
10 Zolotoy Bridge Vladivostok Russia 737 m 2012 2

Dr. Naveed Anwar
Coalbrookdale, UK

Dr. Naveed Anwar
Gi-Lu bridge, Taiwan

Dr. Naveed Anwar
Zakim Bridge, Boston, MA

Dr. Naveed Anwar
Mixed Systems

Dr. Naveed Anwar
Rank Deck length Name
1 2,460 metres Millau Viaduct
2 2,252 metres Rio-Antirio Bridge
3 1,688 metres Sutong Bridge
4 1,596 meters Stonecutters Bridge
5 1,552 metres Erqi Yangtze River Bridge
6 1,495 metres General Rafael Urdaneta Bridge
7 1,320 metres Incheon Bridge
8 1,312 metres Tatara Bridge
9 1,272 metres Russky Bridge
10 1,246 metres Shanghai Yangtze River Bridge
11 1,177 metres Ting Kau Bridge
12 1,170 metres Meiko-Chuo Bridge
13 1,158 metres Third Nanjing Yangtze Bridge
14 1,121 metres Second Nanjing Yangtze Bridge
15 1,105 metres Qingzhou Bridge
16 1,096 metres E’dong Bridge
17 1,082 metres
Zhengzhou Yellow River Road Rail
Bridge
18 1,074 metres Xupu Bridge
19 1,056 metres Jintang Bridge
20 1,040 metres Anqing Bridge
21 1,020 metres Tsurumi Tsubasa Bridge

Dr. Naveed Anwar
Rama IX Bridge

Dr. Naveed Anwar
Single Plane Bridge
• Construction materials used:
Cables Steel
Piers RC
Pylons Steel
• Dimensions:
Main span 450 m
Total length 781.20 m
Largest cable dia. 167 mm
Deck depth 4.00 m
Deck width 33.00 m
Clearance below 41 m

Dr. Naveed Anwar
Rama VIII Bridge
Single Pylon Bridge
Cables steel
Piers reinforced concrete
Pylons reinforced concrete
Longest Span – 300m

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

Dr. Naveed Anwar
Single Plane
Two Plane
• 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
• In the two-plane system the cable can
either be arranged to hang vertically or
slope towards the top of the tower or
pylon

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

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
Parallel wires
StrandsLocked Cables
Polyethylene duct
Protective grout
Prestressing wire
Polyethylene duct
Cement grout
Spacer
Strand
Round wire
Trapezoidal section wires
S- section wires

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
• 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 to
accommodate adjustment
• Cable Anchorages in Pylon are
usually expensive

Dr. Naveed Anwar
Bottom Anchorage Upper Anchorage

Dr. Naveed Anwar
• 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)

Dr. Naveed Anwar
Single Tower Twin Tower
A-Frame Tower Diamond Tower
• May be fabricated from
– steel plate,
– precast concrete elements
– occasionally in in-situ concrete
• Various design options are available to
produce good aesthetic effects

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

Dr. Naveed Anwar
• 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

• Design Challenges
• Material Challenges
• Construction Challenges

Dr. Naveed Anwar
• 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.

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

Dr. Naveed Anwar
• 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.

Dr. Naveed Anwar
• Most cable-stayed bridges are relatively flexible with long fundamental periods in
the range of 3.0 s or longer.
– Their seismic responses are usually not very significant in the longitudinal direction.
• In the transverse direction, the towers are similar to a high-rise building.
– 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.

Dr. Naveed Anwar
• High-strength concrete
• High-strength steel cables
• Rubber bearings
• Precast concrete

Dr. Naveed Anwar
• Highly Skilled tasks
• Availability of heavy equipment
• High level of precision and sophistication
• Previous experience is often essential
• <watch any of Mega Structure programs in Discovery>

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
W
T
CC
P
P ?

Dr. Naveed Anwar
Dy
-dL-dL
Dy
+- dy
+dL
+- Dx
Deck Free to Move

Dr. Naveed Anwar
Main Span – Stay Force Diagram Back Span – Stay Force Diagram

Dr. Naveed Anwar
• 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.

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
• Model as Load
• Model as Element
with or without Tendon Loads

Dr. Naveed Anwar
• Model as Element

Dr. Naveed Anwar
• Click Draw Frame Element Tools
• Select Tendon or Cable
from “Line Object Type”
• Draw Element in Model
• Specify Parameters
Tendon
Cable

Advance Topics in Bridge Engineering, SET, AIT106 Advance Topics in Bridge Engineering, SET, AIT
CE 72.90 - Advanced Topics in Bridge Engineering – June 2013, Dr. Naveed Anwar
• 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

Dr. Naveed Anwar
Moving load analysis of cable stayed bridge

Dr. Naveed Anwar
Construction stage analysis of cable stayed bridge

ACECOMS, AITCE 72.90 - Advanced Topics in Bridge Engineering – June 2013, 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

Dr. Naveed Anwar
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

Design Spectral Acceleration Vs Time Period

• 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.

• 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

0 10 20 30 40
Time (sec)
-0.1
0
0.1
Acceleration(g)
Cliff Station from 1989 Loma Preita, USA
0 10 20 30 40 50 60
Time (sec)
-0.05
0
0.05
Acceleration(g)
CUIP Station from 1985 Michoacan, Mexico

Dr. Naveed Anwar
Internal dampers:

Dr. Naveed Anwar
External dampers:

Dr. Naveed Anwar
Classification of Wind Effects
Static
Effects
Deformation Due to Time Averaged aerodynamic force
Stress Due to Wind Induced Pressure or Force
Static Instability
Torsional Divergence (negative stiffness)
Lateral Buckling
Dynamic
Effects
Forced Vibration
Bufferting (random
vibration)
Due to Atmospheric
Turbulence
Limited Amplitude
Response
Due to Body induced
Turbulence (Wake)
Vortex Excitation
Dynamic Instability
(negative damping)
Galloping
Divergent Amplitude
Response
Wake Galloping
Torsional Flutter
Coupled Flutter
Rain Induced Vibrations

CE 72.32 - Design of Tall Buildings - January 2013, Dr. Naveed Anwar
Wind
Loading on
the Structure
Structural
Respose
Check Safety/
Serviceability
Influence of Deformation
on Loading
Metrology Aerodynamics Theory of Structures
Material science,
codes, regulations
Aeroelasticity

Dr. Naveed Anwar
Wind Tunnel Tests

Dr. Naveed Anwar
Wind Tunnel Test on a Bridge Section Model
To check its Aerodynamic Stability

Dr. Naveed Anwar
The Rach Mieu Cable-stayed Bridge
(Vietnam)

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.

Dr. Naveed Anwar
Executive Director, AIT Consulting
Affiliated Faculty, Structural Engineering
Director, ACECOMS
Thank You

Modelling of Cable stayed bridge by AIT

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