Finite Element Modelling of Bosporus Bridge.pdf

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I

Declaration

I Farhad Huseynov declare that this dissertation study is my own work and that all the sources

that I have used or quoted have been acknowledged by means of complete references.

________________________

Farhad Huseynov 31.08.2012

Signature Date



II

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 dissertation study special care was given to understand the real behavior of the

structure. The purpose of this research was to develop a sophisticated FE model with less

uncertainty that provides with a clearer understanding and higher confidence in estimating the

real behavior of the Bosporus Bridge.

To develop a FE model commercial software, namely ANSYS V12.1 was used which is a FE

modelling package that numerically solves wide range of mechanical problems. There are two

methods available to use ANSYS. The first method is by means of Graphical User Interface,

which is so called GUI and the second one is by means of script files. For this particular work,

second option was used to produce the FE models.

Dimensions of the structural components play an important role in the modelling process.

To develop an accurate FE model, dimensions have to be adopted as correct as possible. The

Bosporus Suspension Bridge was designed more than 40 years ago as a result softcopy of the

design drawings is not available. Therefore, the bridge major parts (towers, cables hangers and

the suspended box deck section) and overall shape were redrawn in accordance with the

design drawings using the AutoCAD software to get more accurate coordinates for the model.

Details of the structural components, geometric nonlinearities, cable sagging and stress

stiffening and profile of the deck structure 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. Besides, in terms

of computer processing capacity, analyzing a 3-D FE model takes longer time compared to a 2-D

FE model. To facilitate the modelling process, initially 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 2-D FE models were confirmed to be accurate by comparing them



III

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 offreedom were reduced by introducing the equivalent super elements for the towers and the

suspended deck structure which are explained in detail in the related sections. The 3-D FE

model was divided into 4 major parts being cables, hangers, towers and the suspended deck

structure and was modeled separately. Then all the parts were combined together and

imported into ANSYS to develop a complete model. The model were analyzed both for static

and modal analysis. Finally the results obtained from the 3-D analytical model was compared

with the experiment data available from the past studies and was ensured that a sophisticated

3-D FE model works properly without any major warnings and represents the real behavior of

the Bosporus Bridge.



IV

Acknowledgement

First and foremost, I would like to thank to my supervisor, Prof. James Brownjohn for the

valuable guidance and advice. This thesis would not have been possible without his help,

support and patience. Besides, I would like to thank to a PhD student, Rahi Rahbari, for his good

advice and friendship who never hesitated to share his knowledge and experience despite his

many other academic and professional commitments.

Last but not least I would like to thank my family. They were always supporting me and

encouraging me with their best wishes.



V

Contents

Declaration ...................................................................................................................................... I

Abstract .......................................................................................................................................... II

Acknowledgement ........................................................................................................................ IV

Contents ......................................................................................................................................... V

Figure List ..................................................................................................................................... VII

Table List ....................................................................................................................................... IX

1 Introduction ........................................................................................................................... 1

2 Background ............................................................................................................................ 2

2.1 Principal Dimensions and Quantities ............................................................................. 5

3 FINETE ELEMENT MODELLING ............................................................................................... 6

3.1 Dimensions ..................................................................................................................... 7

3.1.1 Suspended Deck Structure ..................................................................................... 7

3.1.1.1 Longitudinal Parts .............................................................................................. 8

3.1.1.2 Main Diaphragm .............................................................................................. 10

3.1.2 Cables ................................................................................................................... 11

3.1.3 Hangers ................................................................................................................ 11

3.1.4 Towers .................................................................................................................. 12

3.1.5 Bridge Profile ........................................................................................................ 133.2 2-D FE Model ................................................................................................................ 14

3.2.1 Deck Modelling .................................................................................................... 14

3.2.2 Cable Modelling ................................................................................................... 14

3.2.3 Hanger Modelling ................................................................................................. 16

3.2.4 Tower modelling .................................................................................................. 17

3.2.5 Complete 2-D FE Model of the Bridge ................................................................. 17

3.2.6 2-D FE Model Analysis .......................................................................................... 17

3.3 3-D FE Model ................................................................................................................ 20

3.3.1 Equivalent Super Element for Suspended Deck Structure ................................... 20

3.3.1.1 Modelling of the Original Box Deck Section..................................................... 20

3.3.1.2 Equivalent Plate Element ................................................................................. 25

3.3.1.3 Equivalent Box Deck Element .......................................................................... 28



VI

3.3.1.4 Complete 3-D FE Model of the Suspended Deck Structure ............................. 31

3.3.2 Equivalent Super Element for Towers ................................................................. 32

3.3.3 Complete 3-D FE Model of the Bridge ................................................................. 33

3.3.4 3-D FE Model Analysis .......................................................................................... 34

3.3.4.1 Bridge Model with Different Cable Strains ...................................................... 34

3.3.4.2 Bridge Model with Additional Mass ................................................................. 38

3.3.4.3 Bridge Model with Different Boundary Conditions ......................................... 42

4 Model Validation .................................................................................................................. 45

4.1 Comparison of Experimental and Analytical Results for Vertical Modes .................... 45

4.2 Comparison of Experimental and Analytical Results for Lateral Modes...................... 46

4.3 Comparison of Experimental and Analytical Results for Torsional Modes .................. 47

5 Conclusion ............................................................................................................................ 48

6 References ........................................................................................................................... 49

7 Appendix A ........................................................................................................................... 50

8 Appendix B ........................................................................................................................... 51

9 Appendix C ........................................................................................................................... 53



VII

Figure List

Figure 3-1 Example of original deck section drawing.....................................................................7

Figure 3-2 Example of deck section drawn by AutoCAD................................................................8

Figure 3-3 Deck section divided into 5 main parts......................................................................8

Figure 3-4 Standard upper deck plate drawn by AutoCAD.........................................................8

Figure 3-5 Standard side unit drawn by AutoCAD........................................................................9

Figure 3-6 Standard footway plate drawn by AutoCAD..............................................................9

Figure 3-7 Standard side plate drawn by AutoCAD.....................................................................9

Figure 3-8 Standard bottom flange plate drawn by AutoCAD...................................................10

Figure 3-9 Standard diaphragm drawn by AutoCAD..................................................................10

Figure 3-10 Arrangement of uncompacted cables (Brown & Parsons, 1975).............................11

Figure 3-11 Towers Drawn by AutoCAD.....................................................................................12

Figure 3-12 Side plates labels.......................................................................................................12

Figure 3-13 Suspended deck structure and cable profile.............................................................13

Figure 3-14 Arrangement of cables and hangers.........................................................................13

Figure 3-15 2-D FE model.............................................................................................................17

Figure 3-16 Analysis Results from 2-D FE model restrained on the vertical plane......................18

Figure 3-17 Analysis Results from 2-D FE model restrained on the horizontal plane.................19

Figure 3-18 Original deck section keypoint locations..................................................................20

Figure 3-19 Model of the original deck Section...........................................................................21

Figure 3-20 Diaphragms...............................................................................................................21

Figure 3-21 Complete meshed section (mesh size 500mm)........................................................22

Figure 3-22 Deformed shape of the original deck section for vertical bending...........................22

Figure 3-23 Deformed shape of the original deck section due Lateral bending..........................23



VIII

Figure 3-24 Deformed shape of the original deck section due to torsion...................................23

Figure 3-25 Equivalent Plate........................................................................................................24

Figure 3-26 Deformed shape of equivalent plate under different loading conditions................26

Figure 3-27 Deformed shape of the equivalent box deck due to vertical bending (1st

Case)....28

Figure 3-28 Deformed shape of equivalent box deck due to lateral bending (1st Case)............28

Figure 3-29 Deformed shape of equivalent box deck due to torsion (1st

Case)..........................29

Figure 3-30 Deformed shape of equivalent box deck due to vertical bending (2nd Case)...........29

Figure 3-31 Deformed shape of equivalent box deck due to lateral bending (2nd

Case).............30

Figure 3-32 Deformed shape of equivalent box deck due to torsion (2nd

Case)..........................30

Figure 3-33 Complete 3-D FE model of the Bridge.......................................................................32



IX

Table List

Table 3-1 Tower structure plate thicknesses...............................................................................12

Table 3-2 Strain values for main cables........................................................................................15

Table 3-3 Strain values for hanger elements................................................................................16

Table 3-4 Equivalent plate displacements obtained for different arrangements........................26

Table 3-5 Equivalent box deck element displacements obtained for different arrangements....28

Table 3-6 Comparison of vertical mode shapes and frequencies between case 1,2 and 3..........34

Table 3-7 Comparison of lateral mode shapes and frequencies between case 1,2 and 3...........35

Table 3-8 Comparison of Torsional mode shapes and frequencies between case 1,2 and 3.......36

Table 3-9 Comparison of vertical mode shapes and frequencies between case 1 and 2.............38

Table 3-10 Comparison of lateral mode shapes and frequencies between case 1 and 2............39

Table 3-11 Comparison of torsional mode shapes and frequencies between case 1 and 2........40

Table 3-12 Comparison of vertical mode shapes and frequencies between

case 1, 2, 3 and 4.......................................................................................................42

Table 3-13 Comparison of lateral and torsional mode shapes and frequencies

between case 1, 2, 3 and 4......................................................................................43

Table 4-1 Comparison of Experimental and Analytical results for vertical modes.......................45

Table 4-2 Comparison of Experimental and Analytical results for lateral modes........................46

Table 4-3 Comparison of Experimental and Analytical results for torsional modes....................46



1

1 Introduction

Suspension bridges are the structures with the large dimensions and long service life.

Throughout the history of the suspension bridges, their behavior under different dynamic

loadings such as wind, earthquake and traffic loads was always a matter of concern. Before

1930s, suspension bridges were designed to resist only the static loadings however failure of

the Tacoma Narrows Bridge in 1940 gave a clue to researchers that the suspension bridges are

vulnerable to dynamic loading. To understand the behavior of suspension bridges under

dynamic loadings many remarkable theoretical and experimental studies were carried out by

different authors. Major advances have been achieved through the advances in computer

process capacity and the use of Finite Element (FE) Method. Ambient field measurements were

carried out for the Bosporus suspension bridge in Istanbul and data collected was compared

with already developed analytical model. It was proven that an accurate FE model is a useful

tool to simulate the real behavior of the existing suspension bridges (Brownjohn, et al., 1989).

Furthermore, a precise FE model can be helpful in regular inspections and modifications.

(Merce, et al., 2007)

Long span suspension bridges are very flexible and lightly damped structures. Throughout

their service life, traffic load may significantly change their dynamic behavior and affect the

fatigue life of the bridge. In fact 80-90% of steel structures failures are related to fatigue and

fracture. Therefore, British standards recommend FE method as an accurate method for fatigue

stress analysis in suspension bridges. (Chan, et al., 2003)



2

2 Background

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. For centuries, it was a challenging task for the communities to provide a

permanent crossing over the Bosporus strait. It is believed that the very first idea of a bridge

crossing the Bosporus dates back to the ancient times as recorded by the Greek writer

Herodotus in his histories. Once an engineer named Mandrocles designed a boat type bridge

(480 BCE) that stretched across the Bosporus, linking Asia to Europe, so that Darius I, the king

of the Achaemenid Empire (also called Darius the Great) move his army into position in the

Balkans to overcome the Macedon (Pericles, 1987). However, after that, till the half of the 20th

century no permanent link existed over the Bosporus and the transportation between two

parts of the city was provided by ferries but, following the rapid development in the city,

permanent link became mandatory. Although several engineering solutions were proposed

before 1950s, due to several reasons none of them drew a serious attention. Later with the

increase in demand on transportation, government started to give a serious consideration on

this issue and in 1956 feasibility study was performed by De Leuw Cather where it was

concluded that a permanent crossing is feasible and economically viable. The report was

accepted by government and following this several design proposals were presented bydifferent international companies mainly based in US by 1960. Unfortunately, later due to the

political issues in Turkey the project was postponed. Meanwhile the amount of traffic was

continuously increasing and after a while ferries could not cope up with the amount of traffic

and long delays become an issue. Thus in 1967, after a very careful assessment, mainly

considering its economical sides, Turkey government included the construction of the Bosporus

Bridge in its forthcoming 5 year plan of highway construction programme. (Brown & Parsons,

1975)



3

Prior to 1960 all the existing major suspension bridges had been built in USA but by 1966,

with the completion of Forth Road and Severn Bridges, UK experience was also available in the

market. Therefore, companies invited for tendering were both from USA and UK. British

structural engineering company, Freeman Fox and Partners, presented their preliminary

proposal in 1967 and formal agreement was made with them in January 1968 (Brown &

Parsons, 1975). Bosporus Bridge was designed as gravity anchored suspension bridge made of

steel with hollow towers, and inclined hangers, carrying the shallow box deck structure which is

located between the villages of Ortakoy and Beylerbeyi.

The Bosporus Bridge consists of one main span and two side spans. Only the main span was

designed as 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. The Construction

of the bridge was performed by the Turkish company, namely “Enka Construction & Industry

Co.” along with the contractors which are “Cleveland Bridge & Engineering Co. Ltd.” (UK) and

“Hochtief AG” (Germany). The Construction started in 20th of February 1970 with the big

ceremony and finished in 30th

of October 1973. When the bridge was opened to traffic 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. (General Directorate of Highways, Turkey, 1973)

The bridge total width consists of 8 lanes. Each direction has 3 lanes for daily vehicle traffic

and additional one emergency lane and one for pedestrians. After four years the bridge had

been opened f or use, the pedestrians’ walk over the bridge was prohibited. Previously, they

could walk over the bridge reaching in it through the elevators inside the towers. Recently,

pedestrians are allowed to walk over the bridge only one day in a year (usually in October)

during the “Intercontinental Istanbul Eurasia Marathon”. Visitors to Istanbul in October can

sign up for the Marathon and have a chance to enjoy the view from the bridge.



4

The Bosporus Bridge reaches its 40 years of service life in 2013. As per maintenance

schedule, the bridge has to go through a full maintenance programme every 40 years where all

the hangers are needed to be replaced. Therefore, the bridge is planned to be closed for the

vehicular traffic for a year in early 2013 to carry out the maintenance works.

The traffic intensity is continuously increasing in Istanbul. As a result, both Bosporus Bridge

and Fatih Sultan Mehmet Bridge, which is the second bridge spanning the Bosporus, are

exposed to heavy traffic load for which they were not designed. To overcome this issue, the

Turkish government started to consider the construction of the third bridge over the Bosporus

strait in early 2010. Following this, in 29th

of May 2012 it was officially announced that the “IC

Ictas-Astaldi” consortium was awarded a contract for the “Northern Marmara Highway Project”

which includes the third bridge construction over the Bosporus. The site was located between

the Poyraz and Garipce villages and expected completion date is planned by the end of 2015.

The cost of the project was estimated as 4.5 billion Turkish Liras which is equivalent to 2.5

billion USD. (Exchange rate based on the Central Bank of Turkish Republic: 1 USD-1.8 TL. 26th of

August 2012)

The Bosporus Bridge is one of the two continuous transportation connections between

Europe and Asia in Istanbul. It carries the 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

special care was given by many researchers to understand the real behavior of the structure. In

this particular dissertation study, two 2-D FE models and a sophisticated 3-D FE Model of the

Bosporus Suspension Bridge will be developed using ANSYS V12.1 commercial software. The

purpose of this research is to develop a model with less uncertainty that provide with a clearer

understanding and higher confidence in estimating the real behavior of the Bosporus Bridge.



5

2.1 Principal Dimensions and Quantities (General Directorate of Highways, Turkey,

1973)

Total length of a bridge : 1 560 m

Main Span length : 1 074

Approach Spans (Ortakoy) : 231 m

(Beylerbeyi) : 255

Clearance over the sea : 64 m

Height of the towers : 165 m

Design Loads

Live load : 1.33 tons/m

Wind Load : 45 m/s

Ground acceleration : 0.1 g

Main cable sagging : 93 m

Tension in the main cables : 15 400 tons/cable

Some Manufacturing quantities

Excavation : 63 000 m3

Concrete : 71 000 m3

Concrete reinforcement : 4 000 tons

Steel : 17 000 tons

Cables : 6 000 tons

Cost of the bridge : 191 785 265 TL (Turkish Lira)

23 213 666 USD



6

3 FINETE ELEMENT MODELLING

Suspension bridges are the complex structures with large dimensions. Details of the

structural components, geometric nonlinearities, cable sagging and stress stiffening and profile

of the deck structure are the main factors affecting the vibration characteristics of the bridge

(Apaydin, 2010). 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. Besides, in terms of

computer processing capacity, analyzing a 3-D FE model takes longer time compared to 2-D FE

model. Thus, to facilitate the modelling process, initially, 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, same properties

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

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 in all models the side spans were excluded in the model. The procedures

followed to produce both 2-D and 3-D FE models later will be covered in detail in the related

sections.

To develop the FE models commercial software, namely ANSYS V12.1 were used which is a

FE modelling package that numerically solves wide range of mechanical problems. There are

two methods available to use ANSYS. The first is by means of Graphical User Interface, which is

so called GUI and the second is by writing the script files. For this particular work, second

option was used to produce the FE models. Additionally, there are no predefined set of units

specified in ANSYS. It is the responsibility of the user to adopt the consistent set of units. The

units defined within the script files are as follows;

-Length (keypoint coordinates) - in mm -Area-in mm2 -Mass- in tons

-Density- in tons/mm3 -Force- in Newton -Modulus of Elasticity- in MPa

-Second Moment of Area- in mm4



7

Dimensions of the structural components play an important role in the modelling process.

To develop an accurate FE model, dimensions have to be adopted as correct as possible. The

Bosporus Bridge was designed more than 40 years ago as a result softcopy of the design

drawings is not available. Therefore, the bridge major parts (towers, cables, hangers and the

suspended box deck section) and overall profile of the bridge were redrawn in accordance with

the design drawings using the AutoCAD software to get more accurate coordinates for the

models.

3.1 Dimensions

Due to the absence of the softcopy of the bridge design drawings, bridge major parts and

overall profile of the structure were redrawn using the AutoCAD software as described in the

below sections

3.1.1 Suspended Deck Structure

Suspended deck structure consists of 60 box girders, each of 17.9 m long, 33.4m wide and

3m deep. Each box section is made up of 22 stiffened plates. 2 types of stiffeners were used

which are V shaped 6mm thick pressed through members for upper deck plates and single

sided bulb flat (S.S.B.F) stiffeners for elsewhere in the deck structure. Diaphragms are placed at

every 4475 mm apart along the length of the deck structure to prevent local buckling.

Figure 3-1 Example of original deck section drawing



8

Figure 3-2 Example of deck section drawn by AutoCAD

3.1.1.1 Longitudinal Parts

Box deck section was divided into 5 main parts as shown in the figure below and was drawn

separately using the AutoCAD software.

Figure 3-3 Deck section divided into 5 main parts

Part 1

Part 1 consists of 10 plates each of 2470mm wide and 17900mm long, stiffened with 6mm

pressed V shaped stiffeners and 12mm thick diaphragm plate which connects to the main

diaphragm and forming the upper part of the deck structure.

Figure 3-4 Standard upper deck plate drawn by AutoCAD



9

Part 2

Part 2 plays and important role in

deck section. It connects the upper

and lower deck and footway section. It

is made up of 2 plates, each of 9mm

thick and 17900mm long, stiffened

with 150x8x17750 S.S.B.F stiffeners

and 6mm thick diaphragm plate that

connects to the main diaphragm.

Figure 3-5 Standard side unit drawn by AutoCAD

Part 3

Part 3 is a footway section which consists of 3 plates, each of 8mm, 10mm and 12mm thick

and stiffened with 150x8x17750 S.S.B.F stiffeners and 8mm thick diaphragm plate

Figure 3-6 Standard footway plate drawn by AutoCAD

Part 4

Part 4 is bottom side section of

the deck structure which is made

up of 9mm thick and 17900mm

long plate, stiffened with

150x8x17750 S.S.B.F stiffeners and

9 mm thick diaphragm plate that

connects to the main diaphragm

Figure 3-7 Standard side plate drawn by AutoCAD



10

Part 5

Part 5 consists of 7 plates, each of 9mm thick and 17900mm long welded together and

stiffened with 150x8x17750 S.S.B.F stiffeners and 9mm thick diaphragm plate which is

connected to the main diaphragm and forming the bottom deck section

Figure 3-8 Standard bottom flange plate drawn by AutoCAD

3.1.1.2 Main Diaphragm

Main diaphragm is made up of 6mm plate and stiffened with 2 types of stiffeners. In the

horizontal direction, 150x8 S.S.B.F stiffeners were provided and in the vertical direction, 75x6

flat stiffeners were used to achieve the required resistance. After all, the main diaphragms are

connected to the main deck diaphragm plates using 16mm black bolts.

Figure 3-9 Standard diaphragm drawn by AUTOCAD



11

3.1.2 Cables

The cables are built up from parallel wires, each 5mm in diameter. Initially, the main span

cables were designed to have 10414 wires (82 strands each having 127 wires) and both side

spans 11176 wires (88 strands each having 127 wires). However, during the tendering the

number of strands in the main cables was reduced to 19, each having 448 wires and an

additional 4 strands each of 192 wires, in the backstays. The final arrangement of cables for

main span and backstays became as shown in Figure 3-10 (Brown & Parsons, 1975)

Figure 3-10 Arrangement of uncompacted cables (Brown & Parsons, 1975)

After compaction the diameter of the main cables and the backstays became approximately

511mm and 528mm, respectively.

3.1.3

Hangers

The suspended deck structure is connected to the cables with the inclined hangers. Each

hanger is built up from single spiral galvanized wire strand with the approximate diameter of

52mm. The type of connections both with cables and suspended deck structure is pinned in

longitudinal direction. (Brown & Parsons, 1975)



12

3.1.4 Towers

The towers, being 165 m high, are made up from hollow steel

sections. Each tower has two columns which are connected by three

portal beams. Cross section dimensions and plate thicknesses

change over the height. Cross section dimension is 7000x5200 mm

at the bottom and 7000x3000mm at the top of the towers.

Table 3-1 tabulates the plate thicknesses for each plate (shown in

figure 3-12) along the height of the tower. To get an accurate

keypoint coordinates, the towers were drawn in three dimensions

using the AutoCAD software as shown in figure 3-11

Table 3-1 Tower structure plate thicknesses

Figure 3-12 Side plates labels

SectionHeight

(mm)

Plate A

(mm)

Plate B

(mm)

Plate C

(mm)

Plate E

(mm)

1 25000 5570X224677/

4423.5X22800X22

200X

100X15

2 19500 5570X224423.5/

4156X22800X22

200X

100X15

3 19500 5570X224156/

3888.5X22800X22

200X

100X15

4 19500 5570X223888.5/

3621.5X20800X22

200X

100X15

5 19500 5570X223621.5/

3354X20 800X22200X

100X15

6 19500 5570X223354/

3087X20800X22

200X

100X15

7 19500 5570X223087/

2819.5X20800X22

200X

100X15

8 18500 5570X222819.5/

2566X20800X22

200X

100X15

Figure 3-11 Towers

Drawn by AutoCAD



13

3.1.5 Bridge Profile

Bridge profile was derived in accordance with the design drawings. Deck shape was drawn

in a way that it forms a part of a circle in the vertical plane with the radius of 17900 m. All the

cable coordinates was calculated assuming it is catenary element under dead-load conditions.

Figure 3-13 Suspended deck structure and cable profile

Figure 3-14 Arrangement of cables and hangers



14

3.2 2-D FE Model

As already mentioned, because it is faster and easier to develop a 2-D FE model compared

to a sophisticated 3-D FE model, initially, two 2-D FE models of the bridge were produced using

ANSYS commercial software. First model restricts the vibration in the vertical plane, so thatallowed 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, which will be explained in detail in the sections below, is completely

similar for both 2-D FE models.

3.2.1

Deck Modelling

2-D suspended deck structure model was produced in ANSYS using BEAM 4, 3-D elastic

beam element. Keypoint coordinates were extracted from AutoCAD drawing, showing the

overall shape of the bridge, into EXCEL spreadsheet, to make them more accessible. Real

constants were assigned based on the provided axial area of steel, second moment of area for

vertical bending and second moment of area for lateral bending values which are 0.851 x 106

mm2, 1.238 x 1012 mm4 and 63.61 x 1012 mm4, respectively (The factors were attributed to

Dumanoglu (1985)). Materials were defined as linear isotropic with the Modulus of Elasticity of

205 x 103 MPa and Poisson’s ratio of 0.3. Based on the provided box deck structure’s mass,

10.84 tons/m, the equivalent density was calculated as 1.276 x 10-8 tons/mm3 (The factors were

attributed to Brown & Parsons (1975)). Finally, elements were meshed with the size of 500 mm

and two ends of the deck structure were restrained to move only in the longitudinal direction

(UX).

3.2.2

Cable Modelling

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. Each cable element was labeled, using NUMSTR command, from 1001 to 1030

for west side and from 10001 to 10030 for east side, starting from the centerline of the main



15

span towards the towers. Backstay cables were labeled as 1031 and 10031 for Ortakoy and

Beylerbeyi side, respectively. Modulus of Elasticity, Poisson’s ratio and density were defined as

193 x 103 MPa, 0.3 and 7.8 x 10-9 tons/mm3, respectively. Area of main span and backstay

cables were defined as 2.05x105 and 2.19x10

5 mm

2, respectively. Cables were meshed in a way

that each cable segment formed one element.

To calculate the initial strains for each cable element, horizontal component of tension

force was calculated using the H= WxL2/(8xd) formula as described below;

W=142.64 Total weight of the suspended structure calculated along the length (KN/m)

L=1074 Length of main span (m)

d=93 The sag in the cable (m)

H=221140 Total horizontal component of tension force for pairs of cables (KN)

Based on the calculated total horizontal component of tension force and angle of inclination

of each segment, initial strains were calculated as follows;

T=H/cosθ Tension in each segment=Horizontal component of tension/ cosine of the angle

σ=T/A Stress in the cross section= Tension force/ Area

ε=σ/E Strain=Stress/Modulus of Elasticity

Table A-1 provided in Appendix A shows the list of strain values calculated for each cable

elements. For simplification, seven different strain values, from 0.002802 to 0.002955, were

used to define the initial strains in main span cable elements as shown in the below table

Line Number Cable

Strain

Values

West Side East Side

From To From To

1001 1011 10001 10011 0.002802

1012 1015 10012 10015 0.002825

1016 1019 10016 10019 0.002847

1020 1023 10020 10023 0.002876

1024 1026 10024 10026 0.002906

1027 1028 10027 10028 0.0029321029 1030 10029 10030 0.002955

Table 3-2 Strain values for main cables

The initial strain values for backstays will be calculated later during the static analysis which

will be explained in later sections.

Boundary conditions were defined as fixed at tower saddles and pinned in anchorages.



16

3.2.3 Hanger Modelling

Hangers were modeled as inclined lines using LINK 8 element. The keypoint coordinates

were already defined by cable and deck elements. Each hanger element was labeled, using

NUMSTR command, from 2001 to 2059 for west side and from 20001 to 20059 for east side,

starting from the centerline of the main span towards the towers. The Modulus of Elasticity,

Poisson’s ratio and density was assigned as 162x103 MPa, 0.3 and 7.8x10

-9 t/mm

3, respectively.

Area of each hanger was defined as 2.1x103 mm2. The vertical component of tension force in

each hanger was calculated by assuming that single hanger element carries it is own self-weight

and half weight of the deck structure between two adjacent hangers. Then the resultant

tension force was calculated based on the hanger inclination and initial strain values were

obtained as follows;

T=V/cos(θ) Resultant tension force=Vertical component of tension force/cosine of the angle

σ=T/A Stress in section= Tension force/Area

ε=σ/E Strain=Stress/Modulus of Elasticity

Table B-1 in Appendix B shows the strain values calculated for each hanger element. For

simplification, seven different strain values, from 0.001408 to 0.002810, were used to define

the initial strains in hanger elements as shown in the below table

Line Number Hanger

strain

Values

West Side East side

From To From To

2001 2029 20001 20029 0.001540

2030 2031 20030 20031 0.001473

2032 2035 20032 20035 0.001450

2036 2041 20036 20041 0.001430

2042 2047 20042 20047 0.001417

2048 2058 20048 2058 0.0014082059 - 20059 - 0.002810

Table 3-3 Strain values for hanger elements



17

3.2.4 Tower modelling

Towers were modeled with the same principals used in deck modelling. 3-D elastic beam

element (BEAM 4) was used to model the elements. The real constants were assigned based on

the provided axial area of steel, second moment of area for vertical bending and second

moment of area for lateral bending values which are 1.36 x 106 mm2, 9 x 1012 mm4 and 271 x

1012

mm4, respectively (The factors were attributed to Dumanoglu (1985)). The Modulus of

elasticity, Poisson’s ratio and equivalent density were assigned as 205 x 103 MPa, 0.3 and 1.07 x

10-8

t/mm3, respectively. Elements were meshed with 500 mm size and bottom of the towers

were defined as a fixed support.

3.2.5

Complete 2-D FE Model of the Bridge

The complete 2-D FE model of the bridge was generated by combining the script files

written for each main part of the bridge and inserting them into ANSYS.

Figure 3-15 2-D FE model

3.2.6 2-D FE Model Analysis

To complete the model, backstay initial strain values are needed to be defined. They were

obtained by trial and error approach during the static analysis. The backstay initial strain values

were defined in a way that, deflection in the longitudinal direction at the top of the towers

becomes negligible. Several values were tried and the initial strains for the backstays were

adopted as 3.068x10-3

and 3.003x10-3

for Ortakoy and Beylerbeyi sides, respectively. Finally,

each 2-D FE model was analyzed both for static and modal analysis. To verify the accuracy of

the properties defined within the script files, the results obtained from the modal analysis were

compared with the experimental data available from the past studies. The validation of 2-D FE

model later will be covered in detail under “Model Validation” chapter, however, for

illustration purposes; figure 3-16 and 3-17 sequentially compare the vertical and lateral mode

shapes and frequencies of the first five modes with the ambient vibration test results carried

out for the Bosporus Bridge by Brownjohn et al.(1989).

X

Y

Z



18

Static Analysis

Maximum Displacement-1394 mm

2-D FE model Restrained in the Vertical Plane

Vertical Modes

V Mode 1: Theoretical frequency: 0.124 Hz

Experimental frequency: 0.129 Hz









Figure 3-16 Analysis Results from 2-D FE model restrained on the vertical plane

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z



19

2-D FE model Restrained in the Horizontal Plane

Lateral Modes

L Mode 1: Theoretical frequency: 0.069 Hz










Figure 3-17 Analysis Results from 2-D FE model restrained on the horizontal plane

Comparison of the results obtained from the 2-D FE models and the experimental data

assures 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 as described in detail in the below sections.

XY

Z

XY

Z

XY

Z

XY

Z

XY

Z



20

3.3 3-D FE Model

Representation of cables and hangers by finite elements in 3-D FE model is same as the 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. Therefore, in this chapter steps to model the hangers

and the cables will not be covered. 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 process capacity is limited, modelling the towers and the suspended deck

structure with all the details is an impossible job. Therefore, necessary actions should be taken

to reduce the degrees of freedom for the towers and the suspended deck structure. To

overcome this issue, equivalent super elements are now introduced and will be discussed in

the below sections.

3.3.1

Equivalent Super Element for Suspended Deck Structure

To develop a sophisticated 3-D FE model with the less degree of freedom the equivalent

deck structure was designed. To achieve more realistic 3-D FE model of the bridge, the

equivalent deck element should be designed in a way that it represents the actual properties of

the original deck structure. To do so, the real behavior of the deck structure is needed.

Therefore, a box deck section of 17.9m long was modeled in ANSYS to understand the real

behavior of the original deck structure.

3.3.1.1 Modelling of the Original Box Deck Section

To develop a model in ANSYS keypoint coordinates were exported from already drawn

AutoCAD drawing into Excel spreadsheets to make them more accessible. The box deck section

was divided into 6 main areas and the keypoint locations were defined as shown in Figure 3-18

(Next page). Each area was modeled separately within the different script files and later

combined together to generate the whole model of the original deck section.



21

X

Y

Z

Figure 3-18 Original deck section keypoint locations

Taking the advantage of the symmetric section, keypoints are labeled in a way that only

loop command (*DO) were used to define the areas for the model, which made the modelling

process faster and simpler. The model was developed in accordance with the design drawings

only with the minor differences. S.S.B.F type stiffeners were modeled with the exact

dimensions but as flat stiffeners. In the design drawing gap was provided between V-shaped

stiffeners and a diaphragm plate to avoid stress concentration in the weld connection which

was excluded in the model. Additionally, at the end of the deck section extra diaphragm was

provided to prevent local buckling and provide smooth stress distribution. Except that, the

model includes all the necessary details from the design drawings, including the horizontal and

the vertical stiffeners for the main diaphragms. All the areas were modeled with SHELL 63

element and meshed with the size of 500mm. The materials are defined as linear isotropic with

the Modulus of Elasticity of 205 GPA and Poisson’s ratio of 0.3. Density for all elements is

defined as zero to exclude the self-weight of the structure.

Figure 3-19 Model of the original deck Section



22

X

Y

Z

Figure 3-20 Diaphragms

To calculate the properties of the box deck section all the nodes at 17900mm in Z direction

were fixed and force was applied at the other end of a section as shown in the figure 3-21.

Point loads were applied at two keypoints coinciding with hanger connection. Each point load

was assigned as 1000KN and the direction was depending on the type of the required

displacement.

Figure 3-21 Complete meshed section (mesh size 500mm)



23

1

MN

MX X

Y

Z

-

-49.266-43.708

-38.15-32.591

-27.033-21.475

-15.917-10.359

-4.8.757818

AUG 24 2012

13:20:31

NODAL SOLUTION

STEP=1SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =49.292

SMN =-49.266

SMX =.757818

1

MN MX

X

Y

Z

-

-49.266-43.708

-38.15-32.591

-27.033-21.475

-15.917-10.359

-4.8.757818

AUG 24 2012

13:21:22

NODAL SOLUTION

STEP=1SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =49.292

SMN =-49.266

SMX =.757818

1

MN

MX X

Y

Z

-

-1.131

-.991962

-.852722

-.713483

-.574243

-.435004

-.295764

-.156525

-.017285

.121954

AUG 24 2012

14:02:17

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UX (AVG)

RSYS=0

DMX =1.329

SMN =-1.131

SMX =.121954

1

MN

MX

XY

Z

-

-1.131

-.991962

-.852722

-.713483

-.574243

-.435004

-.295764

-.156525

-.017285

.121954

AUG 24 2012

14:04:47

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UX (AVG)

RSYS=0

DMX =1.329

SMN =-1.131

SMX =.121954

Vertical Displacement

For the vertical displacement, the point load of 2000KN was applied in the negative

Y-direction and the maximum vertical displacement was obtained as 48.4mm from the analysis.

Figure 3-22 Deformed shape of the original deck section due vertical bending

Based on the obtained displacement the second moment of area for vertical bending (Ixx)

was calculated as follows;

Lateral Displacement

For lateral displacement 2000KN load was applied in the negative X-direction and themaximum lateral displacement was obtained as 1.1mm from the analysis.

Figure 3-23 Deformed shape of the original deck section due lateral bending



24

1

MN

MX

X

Y

Z

-

-27.474-21.369

-15.263-9.158

-3.0533.053

9.15815.263

21.36927.474

AUG 24 2012

14:23:05

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =27.476

SMN =-27.474

SMX =27.474

1

MN

MXX

Y

Z

-

-27.474-21.369

-15.263-9.158

-3.0533.053

9.15815.263

21.36927.474

AUG 24 2012

14:39:44

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =27.476

SMN =-27.474

SMX =27.474

Based on the obtained displacement the second moment of area for lateral bending (Iyy)

was calculated as follows;

Torsional Deformation

For torsional deformation, coupled load each 1000KN was applied in the positive and

negative Y-direction and the deflection at the point load location was obtained as +/-23.1 mm.

Figure 3-24 Deformed shape of the original deck section due to torsion

Based on the obtained displacement, torsional constant (J) was calculated as follows;



25

1

X

Y

Z

1

X

Y

Z

1

X

Y

Z

1

X

Y

Z

1

X

Y

Z

AUG 24 2012

15:35:12

A-E-L-K-N

U

ROT

F

3.3.1.2 Equivalent Plate Element

The equivalent plate element was modeled in ANSYS to fit with the original deck section

properties. The problems were encountered while matching the relatively similar properties in

original deck section for the equivalent plate, which will be covered in detail later in this

section. As a starting point in producing the equivalent plate, the width (b) of the plate was

taken as 28 m, the distance between the hanger points, and the length equal to the original

deck section length as 17.9 m. Areas were defined with 4 keypoints and SHELL 63 element was

assigned with the six degrees of freedom at each node. Plate was meshed with the size of

15 000mm which divided the plate area into four rectangular elements. The same principals,

used in the original deck section analysis, were applied for the equivalent plate. 1000KN point

loads were assigned at one end of a section, at two keypoints which are 28m apart and thick

diaphragm plate was attached to provide the uniform stress distribution. Nodes at the otherend of a section were fixed to behave as a cantilever. Initially, the material properties were

defined as linear isotropic with the Modulus of Elasticity of (Ex) 205GPa and Poisson’s ratio (ν)

of 0.3.

Figure 3-25 Equivalent Plate



26

To make the model ready for the analysis, thickness of the plate had to be defined, which

was the challenging part. To get an idea about the approximate thicknesses that would satisfy

each property of the original deck section (Ixx, Iyy, J), the equivalent thicknesses for each

property were estimated by following observations.

For bending about X-axis, the corresponding Ixx value for the equivalent plate is “b*hb3/12”

where the hb is the equivalent thickness for the bending about X-axis and was calculated as 548

mm. The equivalent plate was analyzed with the same thickness for bending about X-axis and

the displacement was obtained as 48.5 mm, which is same with the displacement obtained for

the original deck section. Referring now to second moment of area for the lateral bending (Iyy)

the corresponding quantity for equivalent plate is “hL *b3/12” where the hL is the equivalent

thickness for the bending about Y-axis and was calculated as 9.3mm. The equivalent plate was

analyzed with the thickness of 9mm and the displacement was obtained as 2.7mm, which is

very close to 1.1mm obtained for the original box section. Looking now to the last property

obtained for the original deck section, which is the torsional constant (J), the standard

expression of the torsional constant for solid rectangular sections is equal to

”

(

) “. For a thin rectangular solid section the

expression simplifies to “b*ht3/3”, where the ht is the equivalent thickness for torsion and

calculated as 744mm. The equivalent plate was again analyzed with the thickness calculated

for torsion and the displacement was obtained as 11.7 mm, which was still close to the value

obtained for the original deck section. Above observation shows that the equivalent

thicknesses corresponding to each property vary significantly and it is impossible to satisfy all

three properties together. Later, to extend the observation further, the equivalent plate was

modeled with the linear orthotropic material properties and different cases were tried. A trial

and error approach was used where the Modulus of Elasticity in Y-axis (Ey), In-plane Shear

Modulus (Gxy) and the thickness of the section (h) were changed. To match the properties of

the equivalent plate with the original deck section, displacement was taken as the commonproperty. Several analyses were carried out and the displacement values obtained from the

analysis were compared with the original deck section displacements as shown in Table 3-4.

The second row from the bottom, highlighted, has the closest displacement values, however,

not all the properties are satisfied as accurate as required. Displacement due to torsion varies

by 29 mm (~230%) from the displacement obtained for the original box deck section.



27

1

MN

MXX

Y

Z

-48.89-43.457

-38.025-32.593

-27.161-21.729

-16.297-10.864

-5.4320

AUG 24 2012

16:46:19

NODAL SOLUTION

STEP=1SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =48.896

SMN =-48.89

1

MN

MX XY

Z

-1.223

-1.087

-.951256

-.815362

-.679468

-.543575

-.407681

-.271787

-.135894

0

AUG 24 2012

16:47:26

NODAL SOLUTION

STEP=1SUB =1

TIME=1

UX (AVG)

RSYS=0

DMX =1.432

SMN =-1.223

1

MN

MX

X

Y

Z

-52.107-40.528

-28.948-17.369

-5.795.79

17.36928.948

40.52852.107

AUG 24 2012

16:48:43

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =52.115

SMN =-52.107

SMX =52.107

Figure 3-26 shows the deformed shape of equivalent plate under different loading

combinations.

EY

(GPa)

GXY

(GPa)

H

(mm)

Vertical

displacement (mm)

Lateral displacement

(mm)

Torsional

displacement (mm)

required obtained required obtained required obtained

205 1.3 530 48.4 57.49 1.1 1.87 23.1 59.09

205 1.4 530 48.4 57.48 1.1 1.73 23.1 59

205 1 530 48.4 57.524 1.1 2.42 23.1 59.337

205 1 600 48.4 40 1.1 2.21 23.1 45.73

205 2 600 48.4 39.96 1.1 1.14 23.1 45.02

205 2 550 48.4 51.53 1.1 1.25 23.1 54.12

205 2 560 48.4 48.9 1.1 1.22 23.1 52.11

50 2 560 48.4 195.65 1.1 1.29 23.1 127.76

Table 3-4 Equivalent plate displacements obtained for different arrangements

Figure 3-26 Deformed shape of equivalent plate under different loading conditions

Above discussed observations show that it is not possible to design an equivalent plate

element in ANSYS with all the required properties. To achieve more accurate properties an

equivalent box deck element is now introduced which will be covered in detail in the next

section.



28

3.3.1.3 Equivalent Box Deck Element

To get more accurate equivalent super element for the suspended deck structure, the

rectangular equivalent box deck section was designed using ANSYS. The same principles that

were used to model the original box deck section were applied for the equivalent box section.

The width of the equivalent box section was defined as 28m and the length equal to the

original box deck section length, 17.9m. To understand the contribution of diaphragms to

section resistances (except from preventing local buckling), two different cases are modeled. In

the first case, diaphragms are placed 4475mm apart similar with the original deck section and

in the second case, spacing of diaphragms was reduced to half as 2237.5mm. The thickness for

the inner diaphragms was assigned as 20mm and the outer diaphragm, which was placed at the

end of a section to provide a smooth stress distribution, was modeled with the thicker

dimension. The areas were defined with 4 keypoints and SHELL 63 element was assigned withthe six degrees of freedom at each node. Same boundary conditions and loading scenarios that

were used for the equivalent plate were defined for the equivalent box deck section. Areas

were meshed with the size of 5567 mm and the material properties were defined as linear

isotropic with the Modulus of elasticity (Ex) of 205GPa and Poisson’s ratio of 0.3. Again, to

match the section properties, displacement was taken as a common property. Trial and error

approach was used to match the properties of the equivalent box section with the original box

deck section, where the thickness of the bottom and top plates (t1), the thickness of the side

plates (t2) and the height of the section (H) were changed. Table 3-4 shows the results obtained

for different arrangements where the last row, highlighted, had the closest displacement

values. Based on the analysis results, the equivalent box deck section was designed 2m deep

with 13 mm and 12 mm thick plates for the upper and bottom plates, and side plates,

respectively.



29

1

MN

MXX

Y

Z

-55.506-49.339

-43.172-37.004

-30.837-24.67

-18.502-12.335

-6.1670

AUG 24 2012

17:53:17

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =55.515

SMN =-55.506

1

MN

MXX

Y

Z

-55.506-49.339

-43.172-37.004

-30.837-24.67

-18.502-12.335

-6.1670

AUG 24 2012

17:53:49

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =55.515

SMN =-55.506

1

MN

MXX

Y

Z

-1.054-.937085

-.819949-.702814

-.585678-.468542

-.351407-.234271

-.1171360

AUG 24 2012

17:55:46

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UX (AVG)

RSYS=0

DMX =1.872

SMN =-1.054

1

MN

MX XY

Z

-1.054-.937085

-.819949-.702814

-.585678-.468542

-.351407-.234271

-.1171360

AUG 24 2012

17:56:08

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UX (AVG)

RSYS=0

DMX =1.872

SMN =-1.054

top/bottom

plates

thickness

(mm) t1

Side

plates

thickness

(mm) t2

Section

Height

(mm) H

Vertical

Displacement

(mm)

Lateral

Displacement

(mm)

Torsional

Displacement (mm)

requir-

ed

obtain

-ed

requir-

ed

obtain-

ed

requir-

ed

Obtain-

ed

16 6 2250 48.3 48.53 1.1 1.04 23.3 20.06

16 6 2000 48.3 59.08 1.1 1.05 23.3 24.4

15 8 2000 48.3 56.46 1.1 1.08 23.3 23.5

14 10 2000 48.3 55.97 1.1 1.13 23.3 23.48

14 12 2000 48.3 53.77 1.1 1.118 23.3 22.62

16 12 2000 48.3 48.91 1.1 1 23.3 20.4

15 12 2000 48.3 51.2 1.1 1.05 23.3 21.44

Table 3-5 Equivalent box deck element displacements obtained for different arrangements

1st Case: 4475mm Diaphragm Spacing


Vertical displacement was obtained as -51.2mm

Figure 3-27 Deformed shape of the equivalent box deck due to vertical bending ( 1st

Case)

Lateral displacement

Lateral displacement was obtained as -1.05 mm

Figure 3-28 Deformed shape of the equivalent box deck due to lateral bending ( 1st

Case)



30

1

MN

MX

X

Y

Z

-21.443-16.678

-11.913-7.148

-2.3832.383

7.14811.913

16.67821.443

AUG 24 2012

17:58:08

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =21.519

SMN =-21.443SMX =21.443

1

MN

MX

X

Y

Z

-21.443-16.678

-11.913-7.148

-2.3832.383

7.14811.913

16.67821.443

AUG 24 2012

17:58:40

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =21.519

SMN =-21.443SMX =21.443

1

MN

MXX

Y

Z

-55.478-49.314

-43.15-36.985

-30.821-24.657

-18.493-12.328

-6.1640

AUG 24 2012

18:19:24

NODAL SOLUTION

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =55.487

SMN =-55.478

1

MN

MXX

Y

Z

-55.478-49.314

-43.15-36.985

-30.821-24.657

-18.493-12.328

-6.1640

AUG 24 2012

18:20:02

NODAL SOLUTION

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =55.487

SMN =-55.478

Torsion

The displacement due to torsion was obtained as +/- 21.4 mm

Figure 3-29 Deformed shape of the equivalent box deck due to torsion (1st

Case)

2nd Case: Diaphragms with 2237.5mm spacing

To understand the contribution of diaphragms to section resistances except from

preventing local buckling, the same equivalent box deck section was analyzed with the reduced

diaphragm spacing. The results showed that the diaphragms do not have any extra contribution

to section resistances. They are only designed to prevent local buckling and provide uniform

stress distribution.


Vertical displacement was obtained as -51.3 mm

Figure 3-30 Deformed shape of the equivalent box deck due to vertical bending (2nd

Case)



31

1

MN

MXX

Y

Z

-1.055-.938005

-.820755-.703504

-.586253-.469003

-.351752-.234501

-.1172510

AUG 24 2012

18:24:55

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UX (AVG)

RSYS=0

DMX =1.871

SMN =-1.055

1

MN

MX XY

Z

-1.055-.938005

-.820755-.703504

-.586253-.469003

-.351752-.234501

-.1172510

AUG 24 2012

18:25:13

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UX (AVG)

RSYS=0

DMX =1.871

SMN =-1.055

1

MN

MX

X

Y

Z

-21.406-16.649

-11.892-7.135

-2.3782.378

7.13511.892

16.64921.406

AUG 24 2012

18:26:32

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =21.482

SMN =-21.406

SMX =21.406

1

MN

MX

X

Y

Z

-21.406-16.649

-11.892-7.135

-2.3782.378

7.13511.892

16.64921.406

AUG 24 2012

18:26:45

NODAL SOLUTION

STEP=1

SUB =1

TIME=1

UY (AVG)

RSYS=0

DMX =21.482

SMN =-21.406

SMX =21.406

Lateral Displacement

Lateral Displacement was obtained as -1.06 mm

Figure 3-31 Deformed shape of equivalent box deck due to lateral bending (2nd

Case)

Torsional Displacement

Displacement due to torsion was obtained as -/+21.4 mm

Figure 3-32 Deformed shape of the equivalent box deck due to torsion (2nd

Case)

3.3.1.4 Complete 3-D FE Model of the Suspended Deck Structure

The suspended deck structure was modeled using the equivalent box deck sections. The

keypoint coordinates were extracted from 3-D AutoCAD drawing into EXCEL, to make them

more accessible. The areas were defined with four or six keypoints and SHELL 63 element was

assigned with six degrees of freedom at each node and meshed with the size of 5567mm. The

similar material properties and dimensions which were used for equivalent box section were

assigned for the suspended deck structure elements. Diaphragms are located with variable

spacing up to 4475mm apart and modeled as weightless elements. The weight of the

suspended structure was assigned by defining the equivalent density for upper, bottom and



32

side plates. The weight per meter of the original box deck section was provided as 10.84

tons/m. Based on this, the equivalent density was calculated as 1.226E-8 tons/mm3.

Boundary Conditions

The suspend deck structure connects to the towers by the rocker bearings which have agreat 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 obtained as following

Area= 16x104 mm

2

Izz= 60.4 x 106 mm4

Iyy=42.35 x 106 mm

4

At the end of each BEAM 4 element COMBIN 7 revolution joint element was assigned to

work as pin connection in the longitudinal direction.

3.3.2

Equivalent Super Element for Towers

Another challenging task encountered during the 3-D FE modelling was producing an

accurate model for the towers. As already been mentioned, modelling the towers with all the

details, in terms of computer processing capacity, would be an impossible job to analyze.

Therefore, the equivalent structure for the towers had to be designed with the less degrees of

freedom. The same approach used in developing the equivalent super element for the

suspended deck structure is a convenient approach, however, it requires the in detail modelling

of at least one tower structure which is obviously too complicated and time consuming.

Therefore, a new approach was introduced at this point and explained step by step as

described below.

The towers were modeled as hollow sections. Keypoint coordinates were extracted from3-D AUTOCAD drawing into EXCEL spreadsheet to make them more accessible. 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. Materials were modeled as linear isotropic with the

Modulus of Elasticity of 205 GPa and Poisson’s ratio of 0.3. The diaphragms were modeled with



33

the thickness of 60mm as weightless elements. The weight of the towers was assigned by

defining the equivalent density for main plates, which was calculated as 1x10-8 tons/mm3. In

the original design drawings opening was provided on the diaphragm plates for the elevator

shaft which was excluded in the model. Besides that, to reduce the degrees of freedom, towers

were modeled without any stiffeners. Instead, equivalent thickness was adopted for the main

plates by trial and error approach during the static analysis. Several different thicknesses were

tried in a way that, using the similar cable strain values that were defined during the 2-D FE

modelling, longitudinal deflection at the top of the towers becomes negligible. 30 mm

thickness end up with 0 mm deflection at the top of the towers in the longitudinal direction

hence was taken as the equivalent thickness for the tower model.

3.3.3 Complete 3-D FE Model of the Bridge

The complete 3-D FE model of the bridge was produced by combining the script files for the

different parts and importing them into ANSYS

Figure 3-33 Complete 3-D FE model of the Bridge

X

Y

Z



34

3.3.4 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 analysis and discussed in detail in the

next sections. The cases that were analyzed are as follows;

Bridge model with;

Case 1: Different cable strains,

Case2: Different mass,

Case 3: Different boundary conditions.

3.3.4.1

Bridge Model with Different Cable StrainsAs already mentioned in the previous chapters, each cable and hanger elements have their own

strain values. However, to simplify the model 7 strain values were defined both for the cable

and the hanger elements within the script file. To verify this simplification, the model was

analyzed both with correct strains and with 7 different strain values. Besides that, to

understand the influence of the initial strains on the bridge behavior, strain values were

modified slightly that would provide less static deflection. To summarize, the bridge model was

analyzed both for static and modal analysis for three different cases which are as follows;

1.

Correct strain values for each cable and hanger elements

2.

Seven different values for both cable and hanger elements

3.

Modified strains for case 2 that would provide less static deflection

Tables from 3-6 to 3-8 shows the natural frequencies and the mode shapes for vertical, lateral

and torsional modes of each case. Looking at case 1 and case 2, results show that the

difference between the relevant mode frequencies is negligible for all modes, thus using 7

different strain values for the cable and the hanger elements is a reliable simplification.

Referring now to case 3, the least static deflection that was possible to achieve is 1129 mm

which is very close to the previously achieved static deflection (1395mm- Case 2). Therefore,

there was no significant change in the natural frequencies which ensures that the initial strain

values already calculated and defined within the script files are close to reality.



35

X

Y

Z

X

Y

Z

.

.

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

.

.

X

Y

Z

.

.

X

Y

Z

-

.

.

X

Y

Z

-

.

.

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

1st Case (Correct strains) 2

nd Case (7 different strains) 3

rd Case (modified strains for case 2)

Static Analysis

Max. Static deflection: 1390 mm Max. Static Deflection: 1395 mm Max. Static Deflection: 1129 mmModal Analysis- Vertical Modes

V Mode 1: 0.125 Hz V Mode 1: 0.125 Hz V Mode 1: 0.125 Hz


V Mode 3: 0.227 Hz V Mode 3: 0.227Hz V Mode 3: 0.227 Hz

V Mode 4: 0.280 Hz V Mode 4:0.281 Hz V Mode 4: 0.281 Hz


Table 3-6 Comparison of vertical mode shapes and frequencies between case 1,2 and 3

X

Y

Z

-

.

.

X

Y

Z



36

XY

Z

XY

Z

XY

Z

XY

Z

XY

Z

XY

Z

XY

Z

XY

Z

XY

Z

XY

Z

1st

Case

(Correct strains for both cables and hangers)

2nd

Case (7 different strains for both cables

and hangers)

3rd

Case

(modified strains for case 2)

Modal Analysis- Lateral Modes

L Mode 1: 0.070 Hz L Mode 1: 0.070 Hz L Mode 1: 0.070 Hz





Table 3-7 Comparison of lateral mode shapes and frequencies between case 1,2 and 3

XY

Z

XY

Z

XY

Z

XY

Z

XY

Z



37

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

1st

Case

(Correct strains for both cables and hangers)

2nd

Case (7 different strains for both cables

and hangers)

3rd

Case

(modified strains for case 2)

Modal Analysis- Torsional Modes

T Mode 1: 0.326 Hz T Mode 1: 0.327 Hz T Mode 1: 0.327 Hz




T Mode 5: 1.042 Hz T Mode 5:1.043 Hz T Mode 5: 1.043 Hz

Table 3-8 Comparison of Torsional mode shapes and frequencies between case 1,2 and 3

X

Y

Z

X

Y

Z

X

Y

Z



38

3.3.4.2 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 load 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, by defining a

new equivalent density for the deck structure which was calculated as 1.3946x10-8

ton/mm3.

Each case was analyzed both for static and modal analysis and the results are tabulated in

tables 3-9 to 3-11.

The analyses results show that the vertical modes are the least affected mode due to the

extra mass added to the dead weight of the structure. No significant variations were observed

except slight change in the mode frequencies by up to 3% difference. Looking now to lateral

modes, slight variations (up to 5%) were observed here as well. However, the major difference

is, the model with the extra mass experiences the 3rd

lateral mode (frequency: 0.309 Hz) with

both lateral and torsional deformation as shown in table 3-10.

Similar to vertical and lateral modes, the torsional mode also displayed a slight change in

mode frequencies. However, the main difference is that single noded asymmetric mode shape

appears 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. Overall, comparison of the modal analysis for case 1 and 2 shows that the

bridge behavior is sensitive to changes in bridge mass and any modifications that could change

the dead weight of the structure should be taken into account.



39

X

Y

Z

-

1st Case 2nd Case (Different Mass)

Static Analysis

Maximum Displacement: 1395 mm Maximum Displacement: 1821 mm

Modal Analysis – Vertical Mode

V Mode 1: 0.125 Hz V Mode 1: 0.124 Hz

V Mode 2: 0.163 Hz V Mode 2: 0.158 Hz

V Mode 3: 0.227 Hz V Mode 3: 0.221 Hz

V Mode 4: 0.281 Hz V Mode 4: 0.277 Hz

V Mode 5: 0.366 Hz V Mode 5: 0.359 Hz

Table 3-9 Comparison of vertical mode shapes and frequencies between case 1 and 2

X

Y

Z

-

X

Y

Z

-

X

Y

Z

-X

Y

Z

-

X

Y

Z

-X

Y

Z

-

X

Y

Z

-X

Y

Z

-X

Y

Z

-

X

Y

Z

-X

Y

Z

-



40


Modal Analysis – Lateral Mode

L Mode 1: 0.070 Hz L Mode 1: 0.068 Hz

L Mode 2: 0.203 Hz L Mode 2: 0.194 Hz

L Mode 3: 0.300 Hz (Fig. above is in horizontal

below is in vertical plane)

L Mode 3: 0.309 Hz (Fig. above is in horizontal

below is in vertical plane)

L Mode 4: 0.306 Hz L Mode 4: 0.318 Hz

L Mode 5: 0.398 Hz L Mode 5: 0.389 Hz

Table 3-10 Comparison of lateral mode shapes and frequencies between case 1 and 2

XY

Z

-

XY

Z

-

XY

Z

-

XY

Z

-

XY

Z

-

XY

Z

-

XY

Z

-

XY

Z

-

XY

Z

-

XY

Z

-

X

Y

Z

-

X

Y

Z

-



41

X

Y

Z

-

X

Y

Z

-

T Mode 2: 0.467 Hz


Modal Analysis – Torsional Mode

T Mode 1: 0.327 Hz T Mode 1: 0.321 Hz

T Mode 2: 0.484 Hz T Mode 3: 0.472 Hz

T Mode 3: 0.631 Hz T Mode 4: 0.615 Hz

T Mode 4: 0.842 Hz T Mode 5: 0.815 Hz

T Mode 5: 1.043 Hz T Mode 6: 1.015Hz

Table 3-11 Comparison of torsional mode shapes and frequencies between case 1 and 2

X

Y

Z

-

X

Y

Z

-

X

Y

Z

-

X

Y

Z

-

X

Y

Z

-

X

Y

Z

-

X

Y

Z

-

X

Y

Z

-

X

Y

Z

-



42

3.3.4.3 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

Tables 3-12 and 3-13 tabulate the results obtained both from static and modal analysis for

cases one to four, respectively. From the modal analysis first four mode shapes and the

corresponding frequencies are provided for each vertical, lateral and torsional mode.

Looking at the static analysis, results show that there are no significant changes in static

displacements and all the obtained values are very close. However, the modal analyses provide

some interesting results which worth’s to mention. For vertical mode, the results show that

depending on the boundary conditions, the first 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 is 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, provide 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.

Referring now to the lateral mode, analyses results show that the boundary conditions mostly

influence the second mode where around 10% increase was observed in mode frequencies.

Apart from this, there is no remarkable change in lateral modes. The torsional mode is the least

influenced mode due to the change in boundary conditions. Some of the mode frequencies

were changed slightly by up to 1%. .



43

X

Y

Z

-

: :

=

=

=

=

X

Y

Z

-

: :

=

=

=

=

X

Y

Z

-

: :

=

=

=

=

X

Y

Z

-

: :

=

=

=

=

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Y

Z

-

: :

=

=

=.

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Y

Z

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: :

=

=

=.

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Y

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-

: :

=

=

=.

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Y

Z

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: :

=

=

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Y

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-

: :

=

=

=.

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X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

= =

=.

=.

X

Y

Z

-

: :

=

=

=.

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X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

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X

Y

Z

-

: :

=

=

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X

Y

Z

-

: :

=

=

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X

Y

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: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

1st Case 2

nd Case 3

rd Case 4

th Case

Static Analysis

Max. Displacement: 1395 mm Max. Displacement: 1395 mm Max. Displacement: 1395 mm Max. Displacement: 1366 mm

Modal Analysis- Vertical Mode

V Mode 1: 0.125 Hz V Mode 1: 0.162 Hz V Mode 1: 0.162 Hz V Mode 1: 0.164 Hz




Table 3-12 Comparison of vertical mode shapes and frequencies between case 1, 2, 3 and 4



44

X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

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Y

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-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

X

Y

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-

: :

=

=

=.

=.

X

Y

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-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

X

Y

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

XY

Z

-

: :

=

=

=.

=.

1st

case 2nd

Case 3rd

Case 4th

Case

Modal Analysis- Lateral Mode

L Mode 1: 0.070 Hz L Mode 1: 0.070 Hz L Mode 1: 0.071 Hz L Mode 1: 0.086 Hz



Modal Analysis- Torsional Mode

T Mode 1: 0.327 Hz T Mode 1: 0.327 Hz T Mode 1: 0.327 Hz T Mode 1: 0.327 Hz



Table 3-13 Comparison of lateral and torsional mode shapes and frequencies between case 1, 2, 3 and 4



45

4 Model Validation

So far, the procedures followed to develop 2-D and 3-D FE models of the Bosporus

Suspension Bridge and different type of analysis that were performed to understand the bridge

dynamic behavior, were covered in the previous chapters. As a last step, to validate the

accuracy of the foregoing FE models, the analysis results will be 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 ambient vibration measurements in 1973, just before the bridge was

opened to traffic. 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 past available results,

comparison were carried out for each vertical and lateral modes available from 2-D and 3-D FE

models and torsional mode available from 3-D FE model and reported in the below sections.

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 4-1 tabulates results obtained

both from current analytical and past experimental studies. The last two columns compare

sequentially 2-D and 3-D FE model analysis results with experimental studies.

Experimental studies carried out by Brownjohn et al. (1989) showed that the bridge

experiences its first vertical asymmetrical mode at two slightly different frequencies, one above

and one below the first symmetric mode. A Possible explanation given by the authors

(Brownjohn, et al., 1989) was that bridge had a dual character between two bearing conditions

and it was presumable changing depending on the traffic intensity. Accordingly, in the previous

sections, the analyses were carried out for similar cases where it was shown that the first



46

vertical asymmetric mode might appear before or after the first vertical symmetric mode

depending on the boundary conditions.

Vertical Mode

Theoretical

frequency (Hz)Symmetry Nodes Antinodes

Experimental frequency

(Hz)

Percent

difference (%)

2-D FE

Model

3-D FE

Model

Brownjohn

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 10.453 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

Table 4-1 Comparison of Experimental and Analytical results for vertical modes

4.2 Comparison of Experimental and Analytical Results for

Lateral Modes

Comparison between experimental and analytical results is not simple for lateral modes.

Among the 9 modes identified during the 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 4-2 (next page) shows theoretical frequencies, obtained from 2-D and 3-D

FE models, and the experimental frequencies. Looking at last two columns, percent differences

show that the theoretical frequencies are still close to the experimental frequencies.



47

Lateral Mode

Theoretical


Experimental

frequency-

Brownjohn et al.

Percent

difference (%)

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 - - - 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

Table 4-2 Comparison of Experimental and Analytical results for lateral modes

4.3 Comparison of Experimental and Analytical Results for

Torsional Modes

Table 4-3 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. Similar behavior was observed during the

modal analysis where 3-D FE model was analyzed with extra mass. It worth’s to mention that

the bridge FE models were developed based on the design stage and there is no solid

information available whether the mass changed throughout its service life.

Torsional Mode

Theoretical


Experimental

frequency (Hz)

Percent

difference (%)

3-D FE Model

Brownjohn

et al.

Tezcan

et al. 3-D

0.327 S 0 1 0.324 0.331 1

0.484 A 1 2 0.474 - 2

0.484 A 1 2 0.492 - 2

0.631 S 2 3 0.649 - 3

0.842 A 3 4 0.877 - 4

Table 4-3 Comparison of Experimental and Analytical results for torsional modes



48

5 Conclusion

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 such as

strains in the cables, mass of the structure, boundary conditions and etc. 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 worth’s 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.



49

6 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.

Brown, W. C. & Parsons, M. F., 1975. Bosporus Bridge, Part I, History and Design. s.l., Institution

of Civil Engineers.

Chan, T. H., Guo, L. & Li, Z. X., 2003. Finite Element Modeling for Fatigue Stress Analysis of

Large Suspension Bridges. Journal of Sound and Vibration, Volume 261, pp. 443-464.

Dumanoglu, A. A., 1985. Asynchronous Seismic Analysis of Modern Suspension Bridges- Part I:Free Vibration, s.l.: University of Bristol. Department of Civil Engineering.

General Directorate of Highways, Turkey, 1973. Record book: Istanbul Bogazici Koprusu

(Bosporus Suspension Bridge), Istanbul: KGM matbaasi.

Merce, R. N. et al., 2007. Finite Element Model Updating of a Suspension Bridge Using ANSYS

Software. Miami, Florida, U.S.A, Inverse Problems, Design and Optimization Symposium.

Pericles, G., 1987. Darius in Scythia: The Formation of Herodotus' Sources and the Nature of

Darius' Campaign. American Journal of Ancient History, 12(ISSN 0362-8914), pp. 97-147.

Tezcan, S., Ipek, M. & Petrovski, J., 1975. Forced Vibration Survey of Istanbul Bogazici

Suspension Bridge, Skopje, Yugoslavia: Institute of Earthquake Engineering and Engineering

Seismology.



50

7 Appendix A

3-D FE Model 2-D FE ModelCable

strain

Values

Line Number (from CL towards the towers)

West Side East side West East

1 31 101 131 1001 10001 2.795E-03

2 32 102 132 1002 10002 2.795E-03

3 33 103 133 1003 10003 2.796E-03

4 34 104 134 1004 10004 2.797E-03

5 35 105 135 1005 10005 2.798E-03

6 36 106 136 1006 10006 2.800E-03

7 37 107 137 1007 10007 2.802E-03

8 38 108 138 1008 10008 2.805E-03

9 39 109 139 1009 10009 2.807E-03

10 40 110 140 1010 10010 2.811E-03

11 41 111 141 1011 10011 2.814E-03

12 42 112 142 1012 10012 2.818E-03

13 43 113 143 1013 10013 2.822E-03

14 44 114 144 1014 10014 2.827E-03

15 45 115 145 1015 10015 2.832E-03

16 46 116 146 1016 10016 2.838E-03

17 47 117 147 1017 10017 2.844E-03

18 48 118 148 1018 10018 2.850E-03

19 49 119 149 1019 10019 2.857E-03

20 50 120 150 1020 10020 2.864E-03

21 51 121 151 1021 10021 2.871E-03

22 52 122 152 1022 10022 2.879E-03

23 53 123 153 1023 10023 2.888E-03

24 54 124 154 1024 10024 2.897E-03

25 55 125 155 1025 10025 2.906E-03

26 56 126 156 1026 10026 2.916E-03

27 57 127 157 1027 10027 2.927E-03

28 58 128 158 1028 10028 2.938E-03

29 59 129 159 1029 10029 2.949E-03

30 60 130 160 1030 10030 2.961E-03Table A-1 Main span cable strain values



51

8 Appendix B

3-D FE Model 2-D FE ModelCable strain

ValuesLine Number (from CL towards the towers)

West Side East side West East

201 301 401 501 2001 20001 1.543E-03

202 302 402 502 2002 20002 1.543E-03

203 303 403 503 2003 20003 1.543E-03

204 304 404 504 2004 20004 1.543E-03

205 305 405 505 2005 20005 1.543E-03

206 306 406 506 2006 20006 1.543E-03

207 307 407 507 2007 20007 1.543E-03

208 308 408 508 2008 20008 1.543E-03

209 309 409 509 2009 20009 1.543E-03

210 310 410 510 2010 20010 1.543E-03

211 311 411 511 2011 20011 1.543E-03

212 312 412 512 2012 20012 1.543E-03

213 313 413 513 2013 20013 1.543E-03

214 314 414 514 2014 20014 1.543E-03

215 315 415 515 2015 20015 1.543E-03

216 316 416 516 2016 20016 1.543E-03

217 317 417 517 2017 20017 1.543E-03

218 318 418 518 2018 20018 1.543E-03

219 319 419 519 2019 20019 1.543E-03

220 320 420 520 2020 200201.543E-03

221 321 421 521 2021 20021 1.543E-03

222 322 422 522 2022 20022 1.543E-03

223 323 423 523 2023 20023 1.543E-03

224 324 424 524 2024 20024 1.543E-03

225 325 425 525 2025 20025 1.543E-03

226 326 426 526 2026 20026 1.543E-03

227 327 427 527 2027 20027 1.520E-03

228 328 428 528 2028 20028 1.492E-03

229 329 429 529 2029 20029 1.493E-03

230 330 430 530 2030 20030 1.472E-03231 331 431 531 2031 20031 1.473E-03

232 332 432 532 2032 20032 1.457E-03

233 333 433 533 2033 20033 1.456E-03

234 334 434 534 2034 20034 1.445E-03

235 335 435 535 2035 20035 1.446E-03

236 336 436 536 2036 20036 1.436E-03



52

237 337 437 537 2037 20037 1.437E-03

238 338 438 538 2038 20038 1.430E-03

239 339 439 539 2039 20039 1.430E-03

240 340 440 540 2040 20040 1.424E-03

241 341 441 541 2041 20041 1.424E-03

242 342 442 542 2042 20042 1.420E-03

243 343 443 543 2043 20043 1.420E-03

244 344 444 544 2044 20044 1.416E-03

245 345 445 545 2045 20045 1.417E-03

246 346 446 546 2046 20046 1.414E-03

247 347 447 547 2047 20047 1.414E-03

248 348 448 548 2048 20048 1.411E-03

249 349 449 549 2049 20049 1.411E-03

250 350 450 550 2050 20050 1.410E-03

251 351 451 551 2051 20051 1.410E-03

252 352 452 552 2052 20052 1.408E-03

253 353 453 553 2053 20053 1.408E-03

254 354 454 554 2054 20054 1.407E-03

255 355 455 555 2055 20055 1.407E-03

256 356 456 556 2056 20056 1.406E-03

257 357 457 557 2057 20057 1.406E-03

258 358 458 558 2058 20058 1.405E-03

259 359 459 559 2059 20059 2.809E-03

Table B-1 Hanger elements strain values



9 Appendix C

Main

Span

Cables 3.32

Cable wrapping 0.08

Cable bands 0.11

Handropes 0.02

Protective treatment 0.01

Hangers and sockets 0.16

Suspended box steel work 8.02

Roadway surfacing 2.25

Footway surfacing 0.08

Parapets and crash

barriers 0.2

Services 0.22

Protective treatment 0.07

Total design dead load 14.54

Table C-1 Dead load of the main span measured along the length (tons/m) (Brown & Parsons,

1975)

Finite Element Modelling of Bosporus Bridge.pdf

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