Abstract

Complex

structures such as bridges need proof of performance over the desired life

time, prior to the beginning constructions stages, as structural failure can be

avoided. Among the most complex civil engineering constructions we find

cable-stayed bridges, which are the most advanced bridge designs up to this

point. Alongside the development of the cable-stayed bridge the finite element method,

a method of structural behaviour prediction, has been developed.

The

aim of the present project si to find the most adequate model of a cable-stayed

bridge that can be compared, in terms of its structural system, with the

cable-stayed bridge located within the Basarab Overpass, Bucharest, Romania.

This thesis will be conducting two-dimensional finite element analysis with the

aid of Oasys GSA software, as well as a three-dimensional finite element analysis

with the aid of ANSYS Structures software and MIDAS Civil software.

A

comparison between the two-dimensional and the three-dimensional models will be

conducted, with the consideration of variable materials and element sizes. This

study will respect the structural system present in the Basarab Overpass’

cable-stayed bridge. Following the

outcome of the analysis described above, the finale design model will be

compared to the real life bridge in order to determine if material costs could

have been diminished.

Introduction

Today, one of the most important parts of the Civil

Engineering industry is based on the design and analysis stages of a project.

With the development of technology and the construction field, more and more

complex structures are made; construction that are based on complex geometrical

shapes and concepts as well as ingenious materials combinations. These complex

constructions (e.g. cable-stayed bridges) involve a huge increase in terms of manpower,

technical expertise, tools, machines and most importantly cost. Therefore, any miscalculation,

wrong use of materials or perplexity of the construction phases can conclude

with a structural failure of the construction. Those types of mistakes have

consequences, both time and money wise, which are unacceptable and can, lead to

project failure. On top of that, structures such as dams, nuclear power plants,

refineries are of immense concern. Failure of such structures would have

disastrous outcomes. To make sure such catastrophes don’t occur, prevention

measures may be taken before even starting the construction process. To ensure

more accurate structures, analysis and modelling tools have been created in

order to foreseen failure scenarios, diminish errors and choose best fitting

materials before construction starts. The modelling and analytical tools are

required to ensure the best suiting design outcome for the wanted lifetime of

the structure at hand. Nonetheless, modelling and analysing help diminish time

and costs in the eventuality of unforeseen design changes.

Since the introduction of the structural analysis, this

stage has seen multiple changes in method and application. Rudimental

structural analysis includes methods such as moment distribution method, joint

method, elasticity method which have had immense contributions to the engineering

industry. Although, the technological advancement enabled the creation of

powerful electronic computational devices have lead to more complex analytical

methods.

Today, two of the most frequent and efficient structural

analysis methods are the numerical method and matrix method; methods that

involve a high degree of accuracy. The most commune analytical tool is the

Finite Element Analysis. The matrix method is rather similar to the numerical

method, such that it is based on the use of matrices; only that it is used to analyse

structures that involve more complex elements (e.g. frameworks). With the aim

of the finite element analysis, a mathematical model is created; model that

simulates the real life behaviour of the structure analysed. The FEA would

examine the non-linear behaviour, the dynamic response and stability of the

structure. In order for the FEA model to

have such high accuracy, various material and geometrical parameters are taken

into account.

Literature Review

Finite element analysis of cable-stayed bridges (Kajita T.,

Cheung Y.K. 1973) presents the analysis of a cable stayed bridge in which the

deck is divided into shall elements an treated as a three dimensional system.

In terms of the stayed-cables, are assumed to behave as springs.

Construction and Design of Cable-Stayed Bridges (Walter Podolny,

Jr., Ph.D. and John B. Scalri, Sc.D.) presents the technical attributes of

cable-stayed bridges along side of the construction requirements and stages implied by such s structure.

Finite Element Procedures (Klaus-Jurgen Bathe, 2014) consists

of theoretical information describing the implementation and use of finite element

analysis. It presents a vast number of techniques that help the implementation

of the finite element method.

Dead Load Analysis of Cable-Stayed Bridges (Tao. Zhanf

and ZhiMin Wu., 2011) describes an optimization method of varied load with the

aim of approximating the forces present within the cables, in order to achieve

the ideal state. Consequently, the

idealized cable forces are used to perform the construction stage analysis.

Comparison between three types of cable-stayed bridges

using structual optimization (Olaf Sarhang Zadeh, 2012) analyses the behaviour

of stayed-cables, using finite element analysis, in order to achieve the

optimal design in terms of material use.

Finite Element Analysis

The finite element analysis is a numerical method and is

a branch of solid mechanics and it is used for solving multi-physics problems. This

method of analysis has applications in fields such as: structural analysis, fluid

dynamics, thermal analysis or solid mechanics.

The main area of application for finite element analysis

(FEA) is the linear analysis of solid structures. It is also recognized as the

first FEA application and it is also the base point of the finite element

method (FEM). The standard interpretation for a finite element analysis solution

of solids is known as the displacement method.

FEA has been introduced as a method of finding the approximate

solution for problems with an indefinite number of equations and unknown

variables; problems that would be virtually impossible to solve. The FEM tries to approximate the outcomes of

the analysed body by dividing the body into smaller segments with virtually the

same properties; this is done using a mesh to delimitate the boundaries of the

divisions. Consequently, the properties calculated gathered from the small

sections are extrapolated onto the whole analysed body. In order to solve complex structures that are

dependent of an indefinite number of variables the aid of big computational is necessary.

Hence, FEA of structures such as bridges is to be carried out with the help of computer

software.

Cable-Stayed Bridges

Overview

The cable-stayed bridge is one of the most advanced

solutions of its kind although it has been developed over a long time span. The

first approach of what we call today cable-stayed bridge has been designed over

400 years ago by Veranzio, a Venetian engineer. Veranzio design consisted in a

bridge with more diagonal chain-stays (Kavangh, 1973). Although, the popularity

of the cable-stayed bridge rise in the 19th century when elements from both

suspension bridge design and cable-stayed bridge design were combined; such

designs can be seen in the Albert Bridge, the Brooklyn Bridge or Bath (Victoria

Bridge). In the early 20th century the cable-stayed bridge has seen a decrease

in its application as most large gaps were solved using suspension bridges and

smaller gaps were approached by construction fixed reinforced concrete bridges.

In the late 20th century we see a new age of the cable-stayed bridges as

technologies advances; using combinations of steel and concrete and using larger

machines allows cable-stayed bridge designs for large and medium spans.

The modern approach at this type of bridge design consists

of structural steel or reinforced concrete decking, towers that are connected

to each in-between using tension members. These characteristics give cable-stayed

bridges two strong advantages over other design solutions; aesthetic design and

efficient use of materials. Today, the solution of the cable-stayed bridge is

due to Western European engineers’ research on acquiring the highest structural

performance from modern material combinations (Troitsky, 1972). In the past few decades the cable-stayed

bridge design has been used frequently for medium span solutions. Nevertheless,

recent advancements in the construction and civil engineering fields will enable

more frequent use of cable-stayed bridges for long span approaches.

In order for this modern advance structures to have such

outstanding structural performance, the use of modelling and analysis is needed

to eliminate most of the uncertainties and flows in the initial design. Therefore,

traffic loading, wind loading and earthquake effects upon the structure must be

taken into account and simulated with the use of FEA.

Structural characteristics

Overview

Cable-stayed bridges are based on a structural system

which consists of three main elements: deck, pylons and cables. An orthotropic decking

is placed on top of continuous girders, which consequently are supported by

diagonal strayed-cables connected from the girders to the main piers. In the

approach of cable-stayed bridges, pylons form the main load-bearing structure.

In these types of bridges, the load acting onto the deck is transferred to the girders

than the cables in tension take the load to the pylons that subsequently dissipate

the load into the ground. In terms of static horizontal forces, cable-stayed

bridges balance them in order to control pylon heights and keep them within a

reasonable range. Due to the way the load is transferred between the members of

the bridge, this design has a low centre of gravity which enables a high

earthquake resistance.

Deck

This is the roadway element of the cable-stayed bridge

and its main load comes from traffic such as train, trams or vehicles. It can

be made out of structural steel, reinforced concrete or even a composite

steel-concrete. As this is directly connected to weight it can impact the

entire construction not only in terms of load and time but also in terms of

cost. Therefore, the choice of material for this part of the bridge is crucial.

The most commonly used approach in modern era for the deck is choosing a

composite steel-concrete solution. This gives the best outcome in terms of

structural performance and weight.

Pylon

The pylon is the element of the bridge that dissipates

the weight and live load, acting upon the bridge, into the ground. This is usually

made out of reinforced-concrete and can have various shapes such as A-frame,

single pylon, trapezoidal pylon or twin pylon. The shape of the pylons is chosen

upon considering factors such as length, aesthetics or stayed-cables type.

There are three main bridge systems in terms of pylon position and shape: single

plane system, two-vertical plane system and two-inclined plane system.

Cables

These elements transfer the dead load of the acting upon

the deck to the pylons. Usually these members are post tensioned in order to ameliorate

lateral deflection of pylons and vertical deflection the deck. Today, four

major types of stayed-cables are used: parallel-wire cables, locked coil

cables, stranded cables and parallel-bar cables. Depending on the arrangement

of the stayed-cables in between the bridge deck and the pylons, there are five

main systems of bridges: mono system, harp system, fan system, semi-harp system

and star system. Abbreviations such as asymmetric cable-stayed bridges can be

seen.

Basarab Overpass and the

Cable- Stayed Bridge

History & Overview

Basarab Overpass is the largest and

most complex infrastructure project in Romania for the last 20 years. This

project was meant to reduce the traffic within the canter of Bucharest and

complete the road ring of Bucharest’s city centre. This project has had a

rather long span of completion, starting in 2004 and finishing in 2011. This

structure consists of 4 main parts: Grozavesti Viaduct, the 120 m arched bridge

over the River Dambovita, the Orchidea Viaduct and the most outstanding, the

cable-stayed bridge over the rail tracks converging from the main train station

in Bucharest.

” The Basarab Viaduct

makes up the highway and tramway junction between the Titulescu Avenue– the

Orquídeas Highway- the Grozavesti Bridge – Vasile Milea Avenue (for the

tramways and the Grozavesti Highway, thus closing the main circulation ring

road in northwest Bucharest.

The idea for this passage dates from

1930, but by 1940, only the metal Basarab Bridge had been achieved, which covered

a length of approximately 100 metres above the railway lines.

Today, the new passage is being

executed as an arch over the places where the old city quarters came into

being.

Its history begins in 1863 when Mr

Effingham Grant, Secretary to the British Consul in Bucharest, married thedaughter

of Ana Golescu (the daughter of a Romanian noble), constructed the first

foundry in Bucharest, near the “Earth barrier”. During this time,

Grant cultivated orchids on the patio of his house and these were the only

orchids in Bucharest at the time, this lead to the Basarab highway being

renamed to “The Orchid Highway”.

Nowadays, the Basarab Bridge is not

only an arch across time and history, but will probably become one of the

city’s emblems. Romanian philately has issued a special series of stamps

depicting the Basarab Bridge.

The arch bridge over the River

Dambovita is 124 metres long and its pylons are supported on footings on top of

40-metre deep columns. The arches have a 180-metre front.

Between the two bridges, unique

structures in Romania, the highway and tramway traffic operates along a 1,500-metre

long pre-stressed concrete viaduct, including the access ramps that employed an

innovating tensioning method and which, just like the bridges, includes an

advanced seismic protection system, applied here for the first time in Romania.

The Basarab Bridge connects the

north and south of Bucharest and facilitates the traffic in the area, thus

completing the main movement ring road in the northwest of the city.

Because of its construction, the

Basarab Bridge becomes the largest intermodal point in Romania, joining tramway

lines on the surface and below it, trolleybus lines, metro lines, two railway

stations, as well as bus stations for national and international transport. ” – Ciudad FCC: Basarab

Viaduct

Location

This structure is located near the Northern Train

Station. As mentioned above the largest and most impressive part, the cable

stayed bridge passes over the train tracks converging from the main train

station in Bucharest (North-West).

Specification of the

cable-stayed bridge

Length: 365

m;

Width: 44 m;

Bridge type: semi-harp (asymmetric);

Pylon type: twin pylon (H-frame), single plane

system;

Pylon height: 80 m;

Pylon foundations: pile

(diameter – 1.5 m, depth – 36 m)

Number of cables: 30 (on each pylon).

This cable-stayed bridge includes stair access to the

metro station and also a tram line and station in between the strayed-cables,

having roadways in each direction separated by the tram line.

Members involved in the

cable-stayed bridge project

Beneficiary: Mayor

of Bucharest;

Designer: Carlos

Fernandez Casado, Spain;

Contractor: BBR

(Grup FCC), Coifer-Martifer.

Social Impact & Outcome

This project was an outstanding one. The cable-stayed

bridge has been declared the widest bridge in Europe, of its kind, and the only

one that has access to a metro station, a tram station and accommodates vehicle

traffic as well. Also, it helped reduce the traffic in the city centre by 40%.

Although, this project has led to the demolition of 25 buildings and it has exited

the budget with 140 million Euros after it had been estimated that the

construction will not exceed 60 million Euros.

Solution

The project’s biggest design problem has been passing

over the train tracks converging towards the train station. In the end the most

suitable approach in passing over the train tracks has was the construction of

a cable-stayed bridge as this was the only solution that did not require the

main train station in Bucharest to temporary be closed. This is due to the

position of the twin pylon which could was able to be placed outside the train

tracks.

Methodology

Introduction

Finite Element Model

Future Work

Analysis of a two dimensional model will be conducted,

using Oasys GSA software. Several materials and element sizes will be verified

for the same structural system used in the design of cable-stayed bridge present

in the Bucharest Overpass.

Three-dimensional models of all main elements (decking,

cables, tower) of the above bridge will

be simulated in MIDAS Civil and Ansys Structures. With the finial goal of

constructed a full three dimensional model of the cable-stayed bridge of

interest.

A third stage will be carried out to compare data

obtained from both two and three dimensional models to find the most ideal

design model for the location and requirements imposed by the whole Basarab

Overpass project.

Gantt Chart

Referencing

Tao. Zhang and ZhiMin

Wu. Dead Load Analysis of Cable-Stayed Bridge. In International Conference

on Intelligent Building and Management (CSIT’11), pages

270 – 274, 2011.

Pownuk A., (1999), “Optimization

of mechanical structures using interval analysis”, Computer Assisted Mechanics

and Engineering Sciences, Polish Academy of Sciences.

M. Venkata Rama Rao (MArch, 2004),

“Analysis of cable stayed bridges by fuzzy-finite element modelling”,

pp. 18 – 28.

Revista Constructiilor (Jan. –

Feb. 2013), “Pasajul rutier suprateran Basarab” (in Romanian), p. 47.

Walther, Rene, (1988), “Cable

Stayed Bridges”, Thomas Telford, London.

Kavanagh, T.C., Discussion of

“Historical Developments of Cable-Stayed Bridges” by Podolony and

Fleming, Journal of the Structural Division, ASCE, Vol.99, No. ST 7, Proc.

Paper 9826, July 1973.

Klaus-Jurgen Bathe (2014), “Finite

Element Proceures”, 2nd edition, K.J. Bathe, Watertown, MA.

Adevraul (Assesed: 10/11/2017),

“Pasajul Basarab, cel mai lat pod urban din Europa” (in Romanian),

Available at: adevarul.ro.

Troitsky. M.S. DSC, “Cable-Stayed Bridges: Theory and Design”,

Crosby Lockwood Staples, London, 1972.

Ciudad FCC (Assessed: 12/1/2017), “Ciudad FCC: Basarab Viaduct”,

Available at: http://www.ciudadfcc.com/en.

Kulpa Z., Pownuk A., Skalna I.,

(1998) Analysis of linear mechanical structures with uncertainties by means of

interval methods. Computer Assisted Mechanics and Engineering Sciences, vol. 5,

pp.443 – 477.

Rump, S. M. (1990). ”

Rigorous Sensitivity Analysis for Systems of Linear and Nonlinear Equations,

“Mathematics of Computations, Vol. 54,

190, pp. 721-736.`