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.
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.
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.
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
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
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
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.
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
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.
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.
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
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
” 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
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
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
Width: 44 m;
Bridge type: semi-harp (asymmetric);
Pylon type: twin pylon (H-frame), single plane
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
Fernandez Casado, Spain;
(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.
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
Finite Element Model
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
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
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.`