Finite Element Modelling of Bosporus Suspension Bridge

Eighteenth Postgraduate Student Conference on MSc Dissertations 2011-12

Department of Civil & Structural Engineering, University of Sheffield, 2012

FINITE ELEMENT MODELLING OF BOSPORUS BRIDGE

Farhad Huseynov

Candidate MSc(Eng) Structural Engineering

ABSTRACT The Bosporus Bridge is one of the two permanent transportation connections between

Europe and Asia in Istanbul. It carries the main arterial transportation link of the city, namely O-1

motorway. Any broken link due to the bridge failure would totally ruin the whole transportation system

in the city. Due to importance and complexity of the Bosporus Bridge, in this particular study, special

care was given to understand the real behavior of the structure by developing a sophisticated FE model

of the structure. Details of the structural components, geometric nonlinearities with cable sagging and

stress stiffening are the main factors affecting the vibration characteristics of the bridge. Sometimes, to

define these properties accurately from the first attempt is impossible during the modelling process.

Producing a sophisticated 3-D FE model of the Bosporus Suspension Bridge requires too much time

and a lot of effort. To facilitate the modelling process, initially two 2-D FE models were produced to

adopt the correct properties. Then the results obtained from the 2-D FE models were confirmed to be

accurate by comparing them with the experimental data available from the past studies. Afterwards, the

same properties were defined to develop a sophisticated 3-D FE model of the Bosporus Bridge. Since

the computer processing capacity is limited, modelling the bridge in three dimensions with all the

structural components is an impossible job. To overcome this issue, degrees of freedom were reduced

by introducing the equivalent super elements for the towers and the suspended deck structure.

1 INTRODUCTION

Istanbul, being the largest and commercial city

of Turkey, is situated on the NW shore of Sea of

Marmara and is divided, between two continents

Europe and Asia, by 22km long and minimum of

1km wide stretch of water, namely Bosporus

strait, which links the Black Sea with the Sea of

Marmara. One of the two permanent

transportation links between two parts of the city

is provided by the Bosporus Bridge, which

carries the main transportation link of the city,

namely O-1 motorway. Any broken link due to

the bridge failure would totally ruin the whole

transportation system in the city. Due to its

importance and complexity, remarkable

theoretical works were carried out by Brownjohn

et al. (1989), Erdik & Uckan (1989), Dumanoglu

(1985), Kosar (2003) and Apaydin (2010) and

full scale dynamic tests were performed by

Tezcan et al. (1975) and Brownjohn et al. (1989)

to estimate the dynamic characteristics of the

Bosporus Bridge.

In this particular study, special care was given to

understand the real behavior of the Bosporus

Bridge by developing a sophisticated FE model

of the structure that contains the detailed

structural components and geometric

nonlinearity with cable sagging and stress

stiffening which are the main factors affecting

the bridge vibration characteristics.

In Bosporus Bridge side spans are not connected

to cables and are carried by piers. Apart from the

small mass contribution to towers, they do not

have any significant influence on the bridge

behavior. Thus the side spans were excluded in

the FE model.

To understand the factors affecting the bridge

behavior, a sophisticated 3-D FE model was

analyzed both for static and modal analysis

under different cases where the cable strains,

mass of the structure and boundary conditions

were changed.

Finally, to validate the accuracy of the FE

models natural frequencies and mode shapes

obtained from the current study were compared

with the experimental data available form the

past studies

2 DESCRIPTION OF THE BOSPORUS

BRIDGE

Bosporus Bridge, which is located between

Ortakoy and Beylerbeyi villages in Istanbul, was

designed as a gravity anchored suspension

bridge, made of steel with hollow towers, and

inclined hangers, carrying the shallow box deck

structure. It consists of one main span and two

side spans. Only the main span was designed as a

suspended structure which is spanning 1074 m

over the Bosporus strait and is carried by cables

and hangers that transfer the load to the massive

towers, having 165m height on each end. Side

spans, each 231m and 255m long on Ortakoy

and Beylerbeyi sides, respectively was designed

independent of the cable and are carried by piers.

When the bridge was opened to traffic (in 1973)

it was accounted the first bridge connection

between Europe and Asia and had the 4th longest

suspension bridge span. However at the present

it is the 19th longest suspension bridge span in

the world ranking

Geometric and material properties play an

important role in the modeling process. To

achieve an accurate FE model, geometric and

material properties were calculated from the

design drawings as tabulated in table 1.

Bridge

Major

Parts

Mo

du

lus

of

Ela

stic

ity

(G

Pa)

Po

isso

n's

rati

o

Mass

per

un

it

vo

lum

e (

ton

/m3)

Are

a (

m2)

Mo

men

t o

f

Inert

ia-

Iyy (

m4)

Mo

men

t o

f

Inert

ia-

Izz

(m4)

Main

Cable193 0.3 7.8 0.205 3.34E-03 3.34E-03

Backstay

Cable193 0.3 7.8 0.219 3.82E-03 3.82E-03

Hanger 162 0.3 7.8 0.0021 3.51E-07 3.51E-07

Deck 205 0.3 12.76 0.851 1.238 63.61

Tower 205 0.3 10.7 1.36 9 271

Table 1: Geometric and material properties of

the Bosporus Bridge

3 FINITE ELEMENT MODELLING OF

BOSPORUS BRIDGE

Suspension bridges are the complex structures

with large dimensions. Details of the structural

components, geometric nonlinearities with cable

sagging and stress stiffening are the main factors

affecting the vibration characteristics of the

bridge. Sometimes, to define these properties

accurately from the first attempt is impossible

during the modelling process. Producing a

sophisticated 3-D FE model of the Bosporus

Suspension Bridge requires too much time and a

lot of effort. To facilitate the modelling process,

in the first stage, two 2-D FE models were

produced to adopt the correct properties. The

first 2-D FE model was restrained in the vertical

plane and the second one in the horizontal plane

which provide vertical and lateral modes,

respectively. Then the results obtained from the

2-D FE models were confirmed to be accurate by

comparing them with the experimental data

available from the past studies. Afterwards, the

same properties were defined to develop a

sophisticated 3-D FE model of the Bosporus

Suspension Bridge.

3.1 2-D FE Modelling

Two 2-D FE models of the bridge were produced

using ANSYS commercial software. The first

model restricts the vibration in the vertical plane,

so that allowed degrees of freedom are

translations in longitudinal (UX) and vertical

(UY) directions, and rotation about Z-axis

(ROTZ), whereas the second 2-D FE model

allows vibration to take place only in the

horizontal plane, so that allowed degrees of

freedom are translations in longitudinal (UX)

and lateral (UZ) directions, and rotation about Y-

axis (ROTY). Otherwise, modelling of the

elements is completely similar for both 2-D FE

models.

2-D suspended deck structure model was

produced in ANSYS using BEAM 4, 3-D elastic

beam element. Keypoint coordinates were

extracted from the design drawings and the

material and geometric properties were defined

similar to the values tabulated in table 1. Then,

elements were meshed with the size of 500 mm

and the two ends of the suspended deck structure

were restrained to move only in the longitudinal

direction (UX).

Cables were divided into different segments

based on the hanger connection points and taking

the advantage of long geometry, were modeled

as straight lines using LINK 10 element. Key

option 3 were activated as zero using KEYOPT

command to define the cables as tension only

elements. Sectional and material properties were

defined in accordance with the design drawings

as tabulated in table 1.

To calculate the initial strains for each cable

element, horizontal component of tension force

was calculated using the

d

WxLH

8

2

(1)

formula where H, W, L and d is the horizontal

component of tension force, total weight of the

suspended structure, length of the main span and

sag of the cable, respectively. Based on the

calculated horizontal component of tension force

and the angle of inclination of each cable

segment, the initial strains were calculated for

each cable element. Finally, cables were meshed

in a way that each cable segment formed one

element and boundary conditions were defined

as fixed at the tower saddles and pinned in the

anchorages.

Hangers were modeled as inclined lines using

LINK 8 element. The keypoint coordinates were

already defined by the cable and the deck

elements. Geometric and material properties

were defined in accordance with the design

drawings as provided in table 1.

The vertical component of tension force in each

hanger element was calculated by assuming that

the single hanger element carries it is own self-

weight and the half weight of the deck structure

between two adjacent hangers. Then the resultant

tension force was calculated based on the hanger

inclination as a result initial strain values of each

hanger elements were obtained

Towers were modeled with the same principals

used in deck modelling. 3-D elastic beam

element (BEAM 4) was used to model the tower

elements. Geometric and material properties

were defined in accordance with the design

drawings. Finally, elements were meshed with

500 mm size and bottom of the towers were

defined as a fixed support.

3.1.1 2-D FE Model Analysis

To verify the accuracy of the properties defined

in 2-D FE models, the results obtained from the

modal analysis were compared with the

experimental data carried out at the Bosporus

Bridge by Brownjohn et al. (1989)

2-D FE model restrained in the vertical plane

V Mode 1: Theoretical frequency: 0.124 Hz

Experimental frequency: 0.129 Hz









2-D FE model restrained in the horizontal plane

L Mode 1: Theoretical frequency: 0.069 Hz










Comparison of the results obtained from the 2-D

FE models and the experimental data assured

that the input data used to produce the 2-D FE

models represents the real behavior of the

bridge. Therefore, similar properties were used

to develop a sophisticated 3-D FE model for the

Bosporus Bridge

3.2 3-D FE Modelling

Representation of cables and hangers by finite

elements in 3-D FE model is same as 2-D FE

model that is by LINK 10 and LINK 8 elements,

respectively, except that the full six degrees of

freedom are allowed at each node. However, the

major difference in 3-D FE modelling is that the

suspended box deck structure and the towers are

now modeled by SHELL 63 elements, having six

degrees of freedom at each node instead of the

BEAM 4 elements used in 2-D FE models. Since

the computer processing capacity is limited,

modelling the towers and the suspended deck

structure with all the details is an impossible job.

Therefore, equivalent super elements were

introduced for the suspended box deck and the

tower structures.

To develop a sophisticated 3-D FE model with

the less degree of freedom the equivalent deck

section was designed. To achieve more realistic

3-D FE model of the bridge, the equivalent deck

element had to be designed in a way that it

represents the actual properties of the original

deck section. To do so, the real behavior of the

original deck structure was needed. Therefore, a

box deck section of 17.9m long was modeled in

ANSYS to obtain the original deck structure

1

X

Y

Z

3-D BOSBORUS SUSPENSION BRIDGE FE MODEL

AUG 23 2012

23:40:07

DISPLACEMENT

STEP=1

SUB =1

FREQ=.123842

DMX =.011059

1

X

Y

Z


AUG 23 2012

23:40:41

DISPLACEMENT

STEP=1

SUB =2

FREQ=.161966

DMX =.016092

1

X

Y

Z


AUG 23 2012

23:56:09

DISPLACEMENT

STEP=1

SUB =2

FREQ=.201773

DMX =.0134

1

XY

Z


AUG 24 2012

00:06:51

DISPLACEMENT

STEP=1

SUB =1

FREQ=.069158

DMX =.011647

1

XY

Z


AUG 24 2012

00:07:11

DISPLACEMENT

STEP=1

SUB =2

FREQ=.19726

DMX =.012216

1

X

Y

Z


AUG 23 2012

23:40:59

DISPLACEMENT

STEP=1

SUB =3

FREQ=.228401

DMX =.012858

1

X

Y

Z


AUG 23 2012

23:41:14

DISPLACEMENT

STEP=1

SUB =4

FREQ=.281435

DMX =.011627

1

XY

Z


AUG 24 2012

00:07:22

DISPLACEMENT

STEP=1

SUB =3

FREQ=.316247

DMX =.023133

1

XY

Z


AUG 24 2012

00:07:34

DISPLACEMENT

STEP=1

SUB =4

FREQ=.319302

DMX =.023697

1

XY

Z


AUG 24 2012

00:07:46

DISPLACEMENT

STEP=1

SUB =5

FREQ=.407279

DMX =.015198

properties. Based on this, a rectangular

equivalent box deck section was designed as 2m

deep with 15mm thick top and bottom plates and

12 mm thick side plates. Then using the

equivalent box deck section elements the whole

suspended deck structure was modeled in

ANSYS.

The suspend deck structure connects to the

towers by the rocker bearings which have a great

impact on bridge mode shapes and frequencies.

Therefore, two A-frame rocker bearings were

modeled at each end of the suspended deck

structure using BEAM 4 element. Geometric

quantities of a single frame element were

calculated in accordance with the design

drawings and COMBIN 7 revolution joint

element was assigned at the end of each BEAM

4 element to work as pin connection in the

longitudinal direction.

The towers were modeled as hollow sections.

Keypoint coordinates were extracted from the

design drawings and the same cross sectional

dimensions that were used in the design

drawings were adopted for the tower model. The

areas were defined with four or six keypoints and

SHELL 63 element was assigned with the six

degrees of freedom at each node. To reduce the

degrees of freedom, towers were modeled

without any stiffeners. Instead, equivalent

thickness for main plates was calculated as 30

mm.

3.2.1 3-D FE Model Analysis

To understand the factors affecting the bridge

behavior, a sophisticated 3-D FE model was

analyzed under different cases both for static and

modal. The cases that were analyzed are as

follows;

Bridge model with;

Case1: Different boundary conditions,

Case 2: Additional mass.

Case1: Bridge model with different boundary conditions

A-frame rocker bearings were designed to allow

the movement only in the longitudinal direction

but resist the lateral and the vertical translations.

However, throughout the bridge service life there

was a significant increase in traffic load in

Istanbul, for which the bridge was not designed.

This issue raises a concern that the rocker

bearings at the end of the suspended deck

structure might be jammed in due to overloading.

To understand the impact of the different

boundary conditions in terms of the bridge

behavior, different cases were analyzed which

are as follows;

Case 1: All the rockers free to move in

longitudinal direction

Case 2: Both rockers are restricted to move in

the longitudinal direction at ORTAKOY side

Case 3: One of the rockers is restricted to move

in the longitudinal direction at ORTAKOY side

Case 4: All the rockers are restricted to move in

the longitudinal direction

The results showed that depending on the

boundary conditions, the first vertical mode

shape might be symmetric or antisymmetric. In

case one where the rockers were allowed to

move freely in the longitudinal direction, the first

vertical mode shape was obtained as symmetric

with 0.125 Hz frequency, however, analyses

results for cases 2,3 or 4, where the rockers

either on one side or on both sides restricted to

move in the longitudinal direction, provided the

first vertical mode antisymmetric. This shows

that throughout the bridge service life, the first

vertical mode shape might change from

symmetric to antisymmetric shape depending on

the boundary conditions.

Case 2: Bridge Model with additional mass

Suspension bridges are the important structures

with long term service life. To maintain the

integrity of the bridge, careful inspection and

proper maintenance is compulsory. Sometimes,

during the maintenance works such as a road

restoration, an extra weight might be added to

the dead weight of the structure. To understand

the importance of the change in bridge mass, in

terms of the bridge dynamic behavior, the model

was analyzed in two cases. In the first case,

bridge mass was defined in accordance with the

design stage whereas in the second case, 1tons/m

extra distributed mass was added to the dead

weight of the structure. Each case was analyzed

both for static and modal analysis

The analyses results showed that the single

noded asymmetric torsional mode shape

appeared at two slightly different mode

frequencies (0.467 Hz and 0.472 Hz) in case 2

(model with the different mass) whereas only one

single noded asymmetric torsional mode shape

was observed in case 1. Besides, the model with

the extra mass experienced the 3rd lateral mode

(frequency: 0.309 Hz) with both lateral and

torsional deformation however, in the first case

no such behavior was observed in the analysis.

Overall, comparison of the modal analyses for

different cases showed that the bridge behavior

is sensitive to changes in the bridge mass and the

boundary conditions.

4 MODEL VALIDATION

As a last step, to validate the accuracy of the

foregoing FE models, the analyses results

obtained from the current study were compared

with experimental data available from the past

studies.

Due to the importance of the Bosporus Bridge,

remarkable theoretical works and full scale

dynamic tests were carried out by Brownjohn et

al. (1989) and Tezcan et al. (1975) to estimate

the dynamic characteristics of the Bosporus

Bridge. The first dynamic test was carried out by

Tezcan et al. (1975) using the ambient vibration

measurements in 1973. Due to the limitations on

the equipment used, only four vertical and one

torsional modes were identified between 0.2-05

Hz. However, later in 1987 Brownjohn et al.

(1989) carried an ambient vibration survey in the

Bosporus Bridge where the vertical, lateral and

torsional modes between 0-1.1 Hz were

identified. Using these experimental data,

comparison were carried out for each vertical

lateral and torsional modes obtained from the

foregoing FE models.

4.1 Comparison of Experimental and

Analytical Results for Vertical Modes

Analysis results obtained both from 2-D and 3-D

FE models have shown that the predicted vertical

modes are quite close to the experimental results.

Table 2 tabulates results obtained both from the

current analytical and the past experimental

studies.

2-D FE

Model

3-D FE

Model

Bro

wn

joh

n

et

al.

Tezcan

et

al.

2-D 3-D

0.124 0.125 A 1 2 0.129 - 4 3

0.162 0.163 S 2 3 0.16 - 1 2

0.202 0.182 A 1 3 0.18 - 11 1

0.228 0.227 S 2 3 0.217 0.233 5 5

0.281 0.281 A 3 4 0.277 0.282 1 1

0.371 0.366 S 4 5 0.362 0.357 2 1

0.453 0.444 A 5 6 0.446 0.44 2 1

0.561 0.543 S 6 7 0.544 - 3 0

0.665 0.636 A 7 8 0.637 - 4 0

0.775 0.728 S 8 9 0.739 - 5 1

0.9 0.833 A 9 10 0.83 - 8 0

0.9 0.833 A 9 10 0.852 - 5 2

1.032 0.938 S 10 11 0.959 - 7 2

Vertical Mode

Theoretical

frequency (Hz)

Sy

mm

etr

y

Percent

difference

No

des

An

tin

od

es

Experimental

results

Table 2 Comparison of experimental and

analytical results for vertical modes


Analytical Results for Lateral Modes

Comparison between experimental and analytical

results is not simple for lateral modes. Among

the 9 modes identified during the experimental

test, only 4 modes (1st, 2nd, 5th and 7th modes)

have appreciable movement of deck structure.

However, in other modes, the towers moved in

lateral direction together with main cables

thereby the deck moved comparatively little

(Brownjohn, et al., 1989). Similar behavior was

observed during the analysis for both 2-D and

3-D FE models. Table 3 shows theoretical

frequencies, obtained from 2-D and 3-D FE

models, and the experimental frequencies.

Looking at the last two columns, percent

differences show that the theoretical frequencies

are still close to the experimental frequencies.

2-D FE

Model

3-D FE

Model2-D 3-D

0.069 0.070 S 0 1 0.07 1 0

0.197 0.203 A 1 2 0.209 6 3

0.3163 0.2999 S 0 1 0.284 10 5

0.3193 0.306 A 1 2 0.294 8 4

0.4073 0.398 S 2 3 0.365 10 8

- 0.456 S 0 2 0.382 - 16

0.524 0.495 S 2 3 0.44 16 11

0.533 0.552 S 2 3 0.525 2 5

0.746 0.737 A 3 4 0.762 2 3

Theoretical

frequency (Hz)

Ex

peri

men

tal

freq

uen

cy

-

Bro

wn

joh

n e

t al.

Lateral Mode

Sy

mm

etr

y

No

des

An

tin

od

es

Percent

difference


analytical results for lateral modes


Analytical Results for Torsional Modes

Table 4 (next page) shows the frequency

comparison for torsional modes. There is a good

agreement between experimental and theoretical

frequencies except that experimental results

show two single noded asymmetric torsional

modes however, only one single noded

asymmetric torsional mode was obtained from

3-D FE model.

Theoretical

frequency (Hz)

Percent

difference

3-D FE Model

Bro

wn

joh

n

et

al.

Tezcan

et

al.

3-D

0.327 S 0 1 0.324 0.331 1

0.484 S 1 2 0.474 - 2

0.484 S 1 2 0.492 - 2

0.631 S 2 3 0.649 - 3

0.842 A 3 4 0.877 - 4

Torsional Mode

Sy

mm

etr

y

No

des

An

tin

od

es

Experimental

frequency (Hz)


analytical results for torsional modes

5 CONCLUSIONS

Comparison of analytical and experimental

results assures that the procedures followed

during the modelling process, particularly

replacing the box deck section with the

equivalent box element, are the reliable

approaches and provide the accurate results.

Thus it can be concluded that the models

discussed so far represent the real behavior of

the Bosporus Bridge. However, the calibration of

the model still might need some extra work to

achieve better results. As already discussed

previously, the bridge model is sensitive to

several factors. By tuning these factors, the

accuracy of the model could be slightly

improved. Therefore, the following

recommendations are proposed for further

studies.

First of all, its worths to mention that the

boundary conditions for the FE models were

defined in accordance with the bridge initial

condition which possibly changed throughout the

bridge service life. Thus defining the related

properties after detailed inspection to represent

the current condition would enhance the

accuracy of the model

Besides, the mass of the structure is another

important factor that could be improved by

calculating the bridge mass in detail and defining

the model in accordance.

REFERENCES

Apaydin, N. M., 2010. Earthquake Performance

Assessment and Retrofit Investigation of Two

Suspenion Bridges in Istanbul. Soil Dynamics

and Earthquake Engineering, Volume 30, pp.

702-710.

Brownjohn, J., Blakeborough, A., Dumanoglu,

A. A. & Severn, R. T., 1989. Ambient Vibration

Survey of the Bosporus Suspension Bridge.

Earthquake Engineering and Structural

Dynamics, Volume 18, pp. 263-83.

Dumanoglu, A. A., 1985. Asynchronous Seismic

Analysis of Modern Suspension Bridges- Part I:

Free Vibration, s.l.: University of Bristol.

Department of Civil Engineering.

Erdik, M. & Uckan, E., 1989. Ambient vibration

survey of the Bogazici Suspension Bridge,

Istanbul- Turker: Department of Earthquake

Engineering Kandilli Observatory and

Earthquake Research Institute, Bogazici

University.

Kosar, U., 2003. System Identification of

Bogazici Suspension Bridge, MSc Thesis,

Istanbul, Turkey: Department of Earthquake

Engineering, Bogazici University.

Tezcan, S., Ipek, M. & Petrovski, J., 1975.

Forced Vibration Survey of Istanbul Bogazici

Suspension Bridge, Skopje, Yugoslavia: Institute

of Earthquake Engineering and Engineering

Seismology.

Finite Element Modelling of Bosporus Suspension Bridge

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