MASTER'S THESIS

Finite Element Analysis of Post-TensionedConcrete Trough Bridges

Jaime Tomás Ordiales2015

Master of Science in Engineering TechnologyCivil Engineering

Luleå University of TechnologyDepartment of Civil, Environmental and Natural Resources Engineering

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Acknowledgements

The investigation work presented in this thesis has been performed during the period September 2013 to March 2014. The research has been developed at the Division of Structural and Construction Engineering at Luleå University of Technology and with the cooperation of Trafikverket.

First of all, I would like to thank Lennart Elfgreen for giving me the opportunity of doing this thesis at LTU. I also want to thank him and Jonny Nilimaa technical advice, recommendations and supervision, which played an indispensable role in the finalizing of this thesis.

I am also indebted to my parents, friends and all those who in one

way or another participated and helped me in the preparation and performing of this inquiry. Jaime Tomás Ordiales June 2013 Luleå, Sweden

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Abstract (English)

The demands on civil structures have increased during recent years. Many structures are required to carry higher loads and larger traffic flows than what they originally were designed for. Also many structures have grown old and have suffered deterioration, so that they do not any longer fulfill the safety requirements. If a structure is no longer able to satisfy the safety level, that structure should be replaced, repaired or strengthened. The purpose of this thesis is to investigate a suitable strengthening method for railway concrete trough bridges - a bridge type quite common in Sweden. The goal is study the benefits of the method and to discuss when it is preferable to strengthen a bridge instead of replacing it. There are a few strengthening methods, which can be used. In our case the method studied is internal unbonded post-tensioning. This seems to be a very promising strengthening method. Internal unbonded post-tensioning may be defined as a prestress introduced by tendons located inside the deck of a bridge. The main advantages using this technique are (1) the method is economic; (2) both flexural and shear strength can be increased without the penalty of increased dead load; (3) the tendons can be made fully replaceable; (4) no traffic restrictions are required on the bridge being strengthened; and (5) the method can be applied to both new and existing structures. In order to study this strengthening method a finite element study was performed. The results were discussed and compared with the results of a laboratory and a field study performed by Jonny Nilimaa. The studies were successful and proved that internal unbonded post-tensioning increases the flexural and the shear capacity, improves the cracking performance and decreases the internal strains of the structure.

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Sammanfattning (Svenska)

Kraven på bärverk i transportsektorn har ökat under senare år. Det finns

önskemål på många konstruktioner att de skall kunna bära högre laster

och härbergera större trafikflöden än vad de ursprungligen

dimensionerades för. Alla konstruktioner bryts successivt ned i samband

med att de blir äldre. Med tiden kan de då komma att inte längre

uppfylla gällande krav på bärförmåga och säkerhet utan måste repareras,

förstärkas eller bytas ut.

Målet med detta examensarbete är att undersöka en förstärkningsmetod

för trågbroar av betong - en i Sverige vanlig brotyp. Metoden går ut på

att föra in icke vidhäftande kablar genom borrade håll i betongplattan

och därefter efterspänna kablarna.

De huvudsakliga fördelarna med metoden är: (1) den är ekonomisk, (2)

såväl böj- som tvärkraftskapaciteten ökar utan att egenvikten höjs, (3)

kablarna är utbytbara, (4) trafiken behöver inte inskränkas på bron under

förstärkningsarbetet och (5) metoden kan användas för såväl nya som

befintliga konstruktioner.

För att studera metoden har en finit elementanalys genomförts.

Resultaten har diskuterats och jämförts med provningar som utförts av

Jonny Nilimaa i såväl laboratorium som i fält

Studierna var lyckosamma och gav som resultat att icke vidhäftanande

efterspänd armering ökar böj- och tvärkraftskapaciteten, ökar

sprickmotståndet i plattan och minskar töjningarna i konstruktionen

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Resumen (Español)

Actualmente los requerimientos a los que están sometidos las estructuras

civiles han ido aumentando a lo largo de los años. Muchas estructuras

tienen que soportar mayores cargas y mayores flujos de trafico. Muchas

veces incluso mayores de las cargas y flujos para los que fueron

diseñadas. Además muchas de estas estructuras se han hecho viejas y han

sufrido un gran deterioro, por lo que dejan de cumplir los niveles de

seguridad. Si una estructura deja de cumplir los niveles de seguridad

estructural esta debe ser reforzada, reparada o remplazada.

El propósito de esta tesis es investigar un método para reforzar puentes

ferroviarios de hormigón. Mas específicamente puentes de canal, ya que

son muy comunes en Suecia. La meta de la tesis es estudiar los

beneficios del método elegido y discutir si son lo suficiente beneficiosos

para el puente o es preferible remplazarlo.

Hay pocos métodos de refuerzo que pueden ser utilizados en estos

puentes. El método elegido en nuestro caso es postensado interno sin

adherencia. Este método parece ser bastante prometedor y se basa en

presforzar la estructura añadiendo tendones en el interior de la losa del

puente.

Las mayores ventajas de esta técnica son: (1) es económica; (2) la

resistencia a flexión y a cortante puede ser incrementada sin un aumento

del peso propio de la estructura; (3) los tendones son fácilmente

reemplazables; (4) no son necesarias restricciones de trafico par a su

colocación; y (5) el método puede ser aplicado igualmente a estructuras

nuevas o estructuras ya existentes.

Para estudiar este método se hizo un estudio de elementos finitos por

ordenador. Los resultados obtenidos fueron analizados y comparados con

un estudio de laboratorio y otro de campo ambos hechos por Jonny

Nilimaa.

Los estudios fueron satisfactorios y probaron que el método de

postensado interno aumenta la capacidad a flexión y a cortante, mejora la

fisuración y disminuye los esfuerzos internos de la estructura.

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Table of content

1. Introduction .................................................................................... 1 1.1 Background .................................................................................................................................... 1 1.2 Research topic and purpose ................................................................................................... 2 1.3 Research Questions .................................................................................................................... 3 1.4 Limitations ............................................................................................................................................. 3

2. Strengthening of Structures ............................................................ 5 2.1 Strengthening ............................................................................................................................... 5

2.1.1 Condition of the structure ...................................................................................................... 5 2.1.2 Reasons, Requirements and objectives ............................................................................. 5 2.1.3 Strengthening Method ............................................................................................................. 6

2.2 Main types of strengthening ................................................................................................... 7 2.2.1 Adding material to the structure ........................................................................................ 7 2.2.2 Post-tensioning: .......................................................................................................................... 9 2.2.3 Strengthening with composite components: .............................................................. 12

3. Theory .......................................................................................... 15 3.1. Prestressing in concrete ....................................................................................................... 15

3.1.1 Methods of prestressing: ...................................................................................................... 15 3.1.2 Advantages of prestressing ................................................................................................. 16 3.1.3 Position of the prestressing tendons. ............................................................................. 16 3.1.4 Applications of prestressing: .............................................................................................. 18

3.2 Shear failure ............................................................................................................................... 20 3.2.1 Shear failure in sections with no shear reinforcement .......................................... 21 3.2.2 Development of Flexure-Shear cracks ........................................................................... 24

3.3 Finite element method ........................................................................................................... 27 3.3.1 Introduction to the finite element method .................................................................. 27 3.3.2 Finite element mesh ............................................................................................................... 28

4. Finite element study ..................................................................... 29 4.1 Test specimen ............................................................................................................................ 29 4.2 Laboratory work ...................................................................................................................... 32 4.3 Computer Study ........................................................................................................................ 33

4.3.1 2D Study ...................................................................................................................................... 33 4.3.2 3D Study ...................................................................................................................................... 35

5. Results .......................................................................................... 39 5.1 Laboratory study ...................................................................................................................... 39 5.2. 2D study ..................................................................................................................................... 40

5.2.1 Cracking: ..................................................................................................................................... 42 5.3. 3D study ...................................................................................................................................... 44

5.3.1 Failure Load and Deformations ....................................................................................... 44 5.3.2 Strains........................................................................................................................................... 48 5.3.3 Stresses in the post-tensioning tendons ........................................................................ 54 5.3.4 Cracks ........................................................................................................................................... 57

5.4. Resume ........................................................................................................................................ 59

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6. Analysis and Conclusions ............................................................... 61

7. Further research............................................................................ 65

8. References .................................................................................... 67

9. About the author .......................................................................... 69

1.Introduction

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<20 years

20-50 years

50-100 years

>100 years

Introduction 1

1.1 Background

Nowadays transportation has become a really important part of

everybody’s life. During the last 50 years the need of transportation has

increased a lot. According to the Community of European Railway and

Infrastructure Companies (CER) and the International Union of Railways

(UIC), since 1970 goods transportation has increased by 185 % and

transport of people by 145 % in the European Union (García San Martin,

2011). Therefore the requirements for civil structures have increased. As

a result, many civil structures are now required to carry higher loads and

larger traffic flows than their original design load. Additionally,

throughout the years many civil structures have become old and they

have suffered important deterioration that makes those structures not

fulfilling their safety level any more. The safety level is a minimum level

of performance. If any structure is not able to satisfy the safety level, that

structure should be replaced, repaired or strengthened.

A survey performed in 2004 by the European Railway Bridge

Demography showed an overview of the actual European railway

network (Bell, 2004). There are almost 50000 concrete bridges in Europe

and almost 3000 in Sweden. There are a big group of bridges that have

become old, over 50 years, see Figure 1.1., also many of them were

designed to carry lower loads than the actual required ones.

Figure 1.1 - Age of concrete bridges in a) Europe b)Sweden

<20 years

20-50 years

50-100 years

>100 years

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The Theoretical service life of bridges is normally 100 years. But

according to Mattsson and Sundquist (2008) the average age at

demolition due to severe deterioration process and/or reduced load-

bearing capacity was 68 years. Therefore this group of bridges needs

accurate inspections and many times maintenance, repair or even

upgrading to accommodate the requirements to keep the safety level. If

the safety level is not achieved by the previously mentioned methods, the

bridge has to be replaced by a new one.

Besides, many times new traffic conditions produce the increasing of the

loads acting over the bridge and make the need of upgraded it. According

Mattsson and Sundquist (2008) the annual maintenance and repair costs

were on average about 1% of the new construction cost, therefore

increasing the service life of a bridge will create a economic gain for the

Railway Administrations. Moreover there are some strengthening

methods that do not produce any traffic restrictions, thus it does not

represent any cost.

1.2 Research topic and purpose

The purpose of this thesis is to study one proper method of strengthening

railway trough bridges. The method chosen is called internal unbonded

post-tensioning. It consists in place steel or a composite strands or bars,

called tendons, within the deck of a bridge and prestress the bars with an

axial load. The axial load counteracts with the internal stresses caused by

the normal actions and improves the behaviour of the structure.

The method of internal post-tensioning was studied at Lulea University

of technology, see Nilimaa, (2012). A laboratory investigation was

performed at LTU and also one bridge in Haparanda was post-tensioned

in a joint research programme between LTU and Trafikverket.

The conclusion of both studies was that post tensioning is a good

strengthening method for the bearing capacity and also in the flexural

capacity but it was not possible to analyse if post tensioning really

improves the shear capacity. Thus, a computer study has been performed

with a finite element computer program (ATENA) to study the

performance of post-tensioning in shear and it will be described in the

thesis.

1.Introduction

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1.3 Research Questions

Is the FEM a good method for study the behaviour of post-tensioned

concrete bridges?

What is the effect of changing the vertical position of the prestressing

tendons?

How does different spacing between prestressing tendons affect to the

results?

What effects have post-tensioning in shear and flexural capacity?

Does the Eurocodes estimate the method of post-tensioning properly?

1.4 Limitations

The main limitation was the lack of knowledge on the shear failure.

Shear has been a tough issue over the years in concrete structures. For

decades many tests have been performed to study this phenomenon in

order to try to solve the riddle that shear is. Researchers have become

more knowledgeable about shear and what the most influences are.

Despite all these research efforts over last century not only one model is

accepted for describe the real influence of the shear failure as for flexure.

There are different explanations of how to calculate the shear distribution

of concrete members all over the world. The reason is that shear failure

is a complicated mechanism, dependent on many factors.

Another limitation was the computer used for the study. The power of

the computer limited the accuracy of the finite element study.

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2.Strengthening of structures

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Strengthening of Structures 2

2.1 Strengthening

According to the English dictionary of the Cambridge University

strengthening is to make something stronger or more effective. In

engineering, strengthening is a tool for repair and upgrading. After

strengthening the resistance of the structures must always exceed the

loads acting on it and it have to fulfil the safety level. In cases when

strengthening is needed it is important to determine the condition of the

structure as well as reasons, requirements and objectives for

strengthening and finally the method for strengthening.

2.1.1 Condition of the structure

The condition of the existing bridge is an important consideration. If the

bridge is in bad condition, then future maintenance and safety problems

might override the benefits of the reduced capital costs of strengthening

and provide justification for bridge replacement. The strength and

condition of the sub-structure must not be ignored and strengthening

should not proceed without giving due consideration to the capacity of

the bridge piers, abutments and foundations. Thus, the condition of the

bridge must be checked before taking the decision of repair, strengthen

or replace the bridge. (Daly & Witarnawan, 1997).

2.1.2 Reasons, Requirements and objectives

In response to increased traffic flow, the requirements for bridges have

increased. Many bridges are now required to carry higher loads and

larger traffic flows than their original design load. Additionally,

throughout the years many civil bridges have become old and have

suffered deterioration that makes many bridges not fulfilling their safety

level any more. If any structure is not able to satisfy the safety level, that

structure should be replaced, repaired or strengthened.

As a result, bridge owners are faced with the choice of restricting traffic

or carry out rehabilitation. When this is combined with the growing

Jaime Tomas Ordiales

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competition for the funding of infrastructure projects, there is great

pressure to keep bridges in service and minimising capital and

maintenance expenditure. Bridge strengthening as an alternative to

complete replacement can provide an effective and economic solution in

appropriate situations. In particular, traffic management costs can be

considerably reduced especially in cases where rehabilitation can avoid

the closure of the railway. (Daly & Witarnawan, 1997).

2.1.3 Strengthening Method

The selection of an appropriate method for strengthening bridge depends

on a number of different factors: The type of structure, the magnitude of

the strength increase required and the associated costs. Strengthening

costs would certainly be lower than bridge replacement. It is important to

consider, not only the initial capital costs of the strengthening project,

but also the maintenance costs associated with the future in-service

behaviour. The difficulties associated with traffic management and the

costs arising from traffic delays should be considered in the economic

justification. In some cases, this may limit the use of certain methods of

strengthening.

Depending on the bridge configuration and the expected service life of

the bridge after strengthening, other factors might need to be considered

before a particular scheme is adopted. The durability, inspectability and

replaceability of components of the rehabilitated bridge are very

important aspects. For some strengthening systems, the ability to monitor

the behaviour of the strengthened bridge might need to be considered.

The aestetics of the bridge after strengthening is an important

consideration and should not be ignored.

Many strengthening techniques have general applicability, but some may

be specific to particular bridge types and configurations. The decision to

adopt a particular scheme is based on the consideration of a wide range

of parameters. (Daly & Witarnawan, 1997).

2.Strengthening of structures

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2.2 Main types of strengthening

Some of the main strengthening methods for concrete bridges are

explained in this section. The main objective of these methods is to

increase the load capacity of a structure by changing the structural

system, adding material to the structure, prestressing the structure or

adding composite components.

2.2.1 Adding material to the structure

2.2.1.1 Concrete jacketing:

Concrete jacketing is a strengthening technique, which aims at increasing

the size of the existing reinforced concrete sections by adding

reinforcement and concrete. By increasing the concrete area, the

structural resistance will also be increased and a higher capacity can be

obtained. This technique could be performed by next methods:

1. Conventional Concrete: Adding concrete around the part of the

structure to be strengthened with additional steel reinforcement

anchored to the existing section, see figure 2.1. It has some

inconvenient: It needs formwork and it needs a long time owing to

the curing time

2. Sprayed Concrete (Shotcrete): It consists in projecting concrete on

to the surface. It is projected pneumatically by a spray gun. It does

not need formwork and is useful to strengthen large areas in a

relatively short time. Some inconvenient are that there are a large

loss of sprayed materials. So this technique it is not suitable for

small areas due to the big costs.

3. Pre-Packet Aggregate Grouting: Pumping of cementitious grout

into washed/graded coarse aggregates placed with properly

anchored reinforcement around the part of the structure to be

strengthened in a tightly sealed formwork. It is one of the best

ways of jacketing a concrete member with a dense mix and a good

surface finish.

One problem of this method is that it makes the structure larger

decreasing the space for the traffic, in adition it causes stiffness

modifications, and subsequently alteration of the dynamic characteristics

of the whole structure (Vandoros & Dritsos, 2008; Chhabra, 2004).

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Figure 2.1 - Applying concrete jacketing (Conventional concrete) to

a concrete column. (Chhabra, 2004).

2.2.1.2 Plate Bonding:

This method consists in increasing the load capacity or the stiffness of

concrete structures by adding additional reinforcement to the external

faces of a structural member. The steel plates are bonded to the surface

by adhesives and anchors. Due to the stiffness and strength of the steel,

compared to the concrete, strengthening components require relatively

small additional material. The success of the technique relies heavily on

the physical properties of the material used to attach the reinforcement

and the long durability of the reinforcement material. Using this method

is possible to reduce the deflection, increase the load capacity, the

flexural strength and the resistance to shear.

The main disadvantages of this plate bonding are the appearance of the

surface and corrosion. This method can also be developed with Fibre

Reinforced Polymer (FRP) plates, which provides a better appearance to

the structure and does not suffer of corrosion (Shaw, (1997)).

2.Strengthening of structures

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2.2.2 Post-tensioning:

Post-tensioning is a method of strengthening concrete or other materials

with high-strength steel or composite strands or bars, typically

denominated tendons. The aim of post-tensioning is to counteract the

internal stresses caused by the normal actions with the application of an

axial load to increase the flexural capacity of a beam and improving the

cracking performance. It can also have a beneficial effect on shear

capacity. The Post-Tensioning Institute tried to explain the concept of

post-tensioning as a series of wooden blocks with holes drilled through

them, into which a rubber band is threaded. If one holds the ends of the

rubber band, the blocks will sag. Post-tensioning can be demonstrated by

placing wing nuts on either end of the rubber band and winding the

rubber band so that the blocks are pushed tightly together. If one holds

the wind nuts after winding the blocks will remain straight. The tightened

rubber band is comparable to a post-tensioning tendon that has been

stretched by hydraulic jacks and is held in place by wedge-type

anchoring devices. (Post-tensioning institute, 2000).

Main Advantages of Post-Tensioning:

The method is economic. It is cheaper to install than methods,

which require reconstruction of the bridge deck.

Both flexural and shear strength can be increased without the

penalty of increased dead load.

The tendons can be made fully replaceable. The tendons can be

removed to carry out a close examination. If corrosion or any

other damage is detected a new tendon can be installed.

No traffic restrictions are required on the bridge being

strengthened.

Main disadvantages:

Application of the method is very dependent on the existing

condition of the bridge. Concrete of poor quality should not be

over-stressed and where the condition of the concrete is suspect,

due to corrosion, deterioration or impact damage. The post-

tensioning should be applied with care as it requires to drill holes.

The main alternatives for post-tensioning are external unbonded post-

tensioning and Internal unbonded post-tensioning. Post-tensioning can

also be internal bonded if you fill the holes with concrete after

prestressing.

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2.2.2.1 External unbonded post-tensioning

In this method, prestressing tendons are located on the external surface of

the member to be strengthened, see figure 2.2. Anchor heads are

positioned at the ends of these tendons. Hydraulic jacks are used to post-

tension the member. This method could be performed either with Carbon

Fibre Reinforced Polymers (CFRP) (Bennitz et al., 2012) or steel

tendons (Daly & Witarnawan, 1997)

Some inconvenient of using this method are:

The tendons, being external, are more susceptible to corrosion and

can be susceptible to contamination by bird and bat droppings.

Where tendons need to be installed below the bottom flange, the

decreased headroom is a distinct disadvantage. If the bridge is

over a road, high vehicles passing under bridge can damage the

tendons.

If this method is performed with CFRP tendons. An especial

anchorage device must be used because of the weakness of the

CFRP bars in transversal direction. Some of them were developed

and studied by LTU. (Bennitz, 2008).

Figure 2.2 - Concrete bridge strengthened using external unbonded

post-tensioning. (Chhabra, 2004).

2.Strengthening of structures

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2.2.2.2 Internal unbonded post-tensioning

The method of internal unbonded post-tensioning consists in placing the

post tensioning tendons within the structure. Normally these tendons are

made of steel but also composite tendons could be used. In order to place

the tendons, first of all, it is necessary to drill holes through the structure.

It is important beware with the internal reinforcement of the structure

when drilling. Those holes are drilled using the technique of core

drilling. According (Bennitz, 2012) this technique was suitable in

concrete bridges. Finally, the tendons are placed in the holes, pre-

stressed with hydraulic jacks and anchored to the lateral part of the

bridge with anchor plates and anchor wedges, see figure 2.3.

Since the tendons are inside the structure some of the inconvenients of

the external post-tensioning are solved (Nilimaa, 2013).

Figure 2.3 - Concrete trough bridge strenthened using internal

unbonded post-tensioning in Haparanda (Nilimaa, 2013).

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2.2.3 Strengthening with composite components:

Fibre Reinforced Polymer (FRP) consist in high tensile continuous

fibres, typically glass, aramid or carbon oriented in a desired direction

within a protective matrix. Epoxy is the most used matrix. By varying

the constituents and their mechanical properties, FRPs with a wide range

of properties can be obtained. FRP can increase shear, flexural,

compression capacity and ductility of the structure.

FRP strengthening is a fast effective and aesthetical method to strength

concrete structures and it can be used almost in the same strengthening

methods as steel (Jacketing of concrete structures, surface bonding, post-

tensioning).

FRP is also used in post-tensioning techniques, due to its high ultimate

strength, a modulus of elasticity similar than prestressing steel and linear

elastic behaviour until the point of failure, see figure 2.4. In addition it is

not affected by fatigue or corrosion (Bennitz, 2011).

Figure 2.4. - Representative constitutive models for prestressing steel

and CFRP tendons (Bennitz, 2011).

However, the creep-rupture behaviour of CFRP imposes an upper limit

2.Strengthening of structures

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on the effective prestress. Thus CFRP should not work over the 70%

over the ultimate capacity. Even with this limit, CFRP can sustain

prestressing forces comparable to the forces that the steel is able to resist.

Recently a new technique was introduced to reduce some problems of

externally bonded reinforcements as damage from collision, fire and

temperature, ultraviolet rays. This technique is Near Surface Mounted

(NSM) Reinforcement which consists of placing the FRP reinforcing

bars or strips into grooves pre-cut into the concrete cover in the tension

region of the reinforced concrete member and bonded to the three sides

of the groove using high-strength epoxy adhesive or cementitious grout.

The application of NSM FRP reinforcement does not requires surface

preparation work as in the case of externally bonded FRP reinforcement.

In addition, the NSM FRP strengthening technique is also very efficient

and practical for flexural strengthening of slabs and beams in the

negative moment regions and protects FRP bars from damage (El-Hacha

& Rizkalla, 2004).

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3.Theory

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Theory 3

3.1. Prestressing in concrete

Prestressed concrete is a method for overcoming concrete's natural

weakness in tension. Where internal stresses are induced to counteract

external stresses. The concept of prestressing was invented years ago

when metal brands were wound around wooden pieces to form barrels.

The metal brands were tighten under tensile stress which creates

compression between the staves allowing them to resist internal liquid

pressure. The fundamental aim of prestressed concrete is to limit tensile

stresses and hence flexural cracking, in the concrete under working

conditions.

Prestressing is a method in which a compression force is applied to the

reinforced concrete section. Those zones of the member ultimately

required to carry tensile stresses under working load conditions are given

an initial compressive stress before the application of working loads so

that the tensile stresses developed by these working loads are balanced

by induced compressive strength, see figure 3.1.

3.1.1 Methods of prestressing:

There are two basic methods of applying pre-stress to a concrete

structure.

Pre-tensioning consist in apply a tensile force to high tensile steel

tendons and place them inside concrete before casting. Then,

after the concrete hardened, the tension force is released.

Therefore, the tendon tries to shrink back to the initial length but

the concrete resists it through the bond between them, thus,

compression force is induced in concrete. Pretension is usually

done with precast members.

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Post-tensioning is the application of a compressive force to the

concrete after hardening. Commonly, metal or plastic ducts are

placed inside the concrete before casting. After the concrete

hardened and had enough strength, the tendon was placed inside

the duct, stressed, and anchored against concrete. Grout may be

injected into the duct later. This can be done either as precast or

cast-in-place

3.1.2 Advantages of prestressing

The use of prestressed concrete offers different advantages over ordinary

reinforced concrete. These advantages can be briefly listed as follows:

Decreases the cracks in the concrete elements.

Allows reduced beam depths achieving the same strength.

It will recover better from overloading than any other material.

Prestressed concrete will suffer less deflection.

A more efficient usage of steel and enables the economic use of

high tensile steels and high strength concrete.

Lighter elements permit the use of longer spanning members

3.1.3 Position of the prestressing tendons.

3.Theory

Page 17

The prestressing tendons could be placed in different positions within the

beam.

Central prestressing: The tendons coincide with the beam axis and

central compressive forces load the beam-ends, see figure 3.1. In

figure 3.1. P/A is the compressive stress caused by prestressing

and is uniform in the cross section. M/Z is the stress caused by the

bending moment and causes tension in the bottom and

compression in the top. The result is a cross section with smaller

tensile stresses. Central prestressing does not generate any extra

bending moment.

Figure 3.1 - Loading case for prestressing in the central part of the

beam and stress diagrams. (Caprani, 2006).

Eccentric prestressing: The tendons are placed in the tension area

instead of the member axis. Eccentric prestressing generates the

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same stresses than the central prestressing including an extra

moment, which provides better results see figure 3.2. In figure

3.2. P/A is the compressive stress caused by prestressing which is

uniform in the cross section. Pe/Z is the stress caused by the extra

bending moment produced by the eccentricity, which causes

compression in the bottom and tension in the top. M/Z is the stress

caused by the bending moment and causes tension in the bottom

and compression in the top. The eccentricity produce reduce the

compression in the top and increase it in the bottom of the beam

avoiding tensile stresses. The minimum required prestressing

force, to avoid tensile stresses, becomes smaller with increasing

the eccentricity (Hartsuijker & Welleman, 2011).

Figure 3.2 - Loading case for eccentric prestressing and stress

diagrams. (Caprani , 2006).

3.1.4 Applications of prestressing:

Typical applications of prestressing in building and construction are:

3.Theory

Page 19

Structural components for integration with ordinary reinforced

concrete construction, e.g. floor slabs, columns, beams.

Structural components for bridges.

Water tanks

Construction components e.g. piles, wall panels, frames, window

mullions, power poles, fence posts, etc.

The construction of relatively slender structural frames.

Major bridges and other structures.

• Offshore Platforms

• Nuclear Power Plants

• Repair, Rehabilitations and Strengthen

Jaime Tomas Ordiales

Page 20

3.2 Shear failure

Shear and torsion have been a tough issue over the years in concrete

structures. For decades many tests have been performed to study this

phenomenon in order to try to solve the riddle that shear is. Researchers

have become more knowledgeable about shear and what the most

influences are. Despite all these research efforts over last century not

only one model is accepted for describe the real influence of the shear

failure as for flexure. There are different explanations of how to calculate

the shear distribution of concrete members all over the world. The

reason is that shear failure is a complicated mechanism, dependent on

many factors. (Rúnar, 2011).

The shear failure, best known as diagonal tensile failure has next

characteristics:

There is not only one type of shear failure.

It is difficult to predict.

The failure is sudden and catastrophic.

The study of its behaviour is completely different to the flexure

one.

The cracks are inclined and have larger width than the flexure

ones, see figure 3.3.

Figure 3.3 - Typical shear failure in simple supported beams.

3.Theory

Page 21

When determining the shear strength of concrete, we have the two

following cases:

With Shear Reinforcement: If beams are equipped with shear

reinforcement or stirrups, it is well known to predict the shear

resistance of the web crushing with the truss analogy developed

by Ritter and Morsch that is based on the lower-bound theory of

plasticity. The upper bound solution is used to minimize the

strengthening effect of the stirrups (Braestrup, 2009).

Without Shear Reinforcement: When there is no shear

reinforcement in place, the shear transfer mechanism is the only

thing responsible for forming the shear resistance. That’s where

Eurocode 2 lacks the support of an adequate theory and uses

instead totally empirical procedures. (Collins et al., 2007)

3.2.1 Shear failure in sections with no shear reinforcement

In concrete beams subjected to both flexural and shear loading (bi-axial

loading) a field of diagonal tensile strains is created similar to figure 3.4

These inclined strains are proportional to the shear “V” force and to the

flexural “M” moment.

Figure 3.4 - Trajectories of principal stresses in a homogeneous

Isotropic rectangular beam. (Giraldo, 2003).

Jaime Tomas Ordiales

Page 22

Since the low tensile strength of concrete compared with steel, one

concrete element tend to fail in perpendicular direction to the tensile

trajectories i.e. following tensile trajectories from figure 3.4 as it is

shown in 3.5.

Figure 3.5 - Development of cracks according the trajectories of

principal stresses in a homogeneous isotropic rectangular beam.

(Giraldo, 2003).

It is possible to determine regions where high and low shear forces are

combined with low and high flexural moments, in order to, determine the

magnitude and direction of the diagonal strains. Analysing these regions,

it is possible to explain the two main different ways of diagonal cracking

in concrete beams produced by shear. The first one is web-shear cracking

and the other is flexure-shear cracking.

Web-Shear cracking appears in zones where there are low flexural

stresses and high shear ones, the cracking is controlled by the

shear, thus there are no vertical cracks. The diagonal stresses will

incline approximately 45 degrees and the magnitude will be the

same as the shear stress with a maximum in the neutral axis.

Therefore, the diagonal cracking will appear close to the neutral

axis as is shown in figure 3.6 Web-shear appears when the

principal tensile stresses exceed the tensile strength of the

concrete.

3.Theory

Page 23

Figure 3.6 - Web-Shear Cracking (Giraldo, 2003).

Flexure-Shear cracking appears in zones with high flexural

stresses combined with high shear stresses, the situation is

completely different. If the structure is designed properly in

bending, cracking will be initiated by flexural cracking and

propagates in a vertical direction from the most tensile side to the

flexural reinforcement. When flexural cracking occurs, the shear

stresses in the concrete above the crack are increased and the

crack develops when the combined shear and tensile stress

exceeds the tensile strength of the concrete. Therefore the cracks

propagate diagonally towards the compression zone of the

member, see figure 3.7. This type of cracking is the most common

in reinforced concrete structures.

Figure 3.7 - Flexure-Shear Cracking (Giraldo, 2003).

Jaime Tomas Ordiales

Page 24

3.2.2 Development of Flexure-Shear cracks

Flexural cracking accepted in the design of structures because it does not

affect the structural resistance, but diagonal cracking must be controlled.

It affect the behaviour of the structure and its failure mode.

When flexure-shear cracking appears it propagates immediately

throughout the transversal section of the element. After that the collapse

is sudden and unpredictable (Giraldo, 2003).

The development of flexure-shear cracks is a rather complex issue. In

figure 4.1 is shown the typical diagonal failure in reinforced concrete.

The purpose is to analyse the forces acting in that section.

Figure 3.9 - Components of shear resistance for cracked reinforced

concrete (Giraldo, 2003).

First the external shear forces are: Vext=R1-P1 . This shear force should be

equilibrate with internal forces:

Vcz: Shear force of the uncracked concrete (Concrete in the

compression zone).

Va: Agregate interlock across flexural cracks

Vd: Dowelling action of tensile reinforement

Arch action depending on l/h

3.Theory

Page 25

Many investigators have tried to determine the contribution from each of

these elements of beam action to shear resistance. It was concluded by

some that after inclined cracks developed the contribution from each of

Vd, Va, and Vcz is altered between 15-25% ; 33-55% ; and 20-40% (Ziara

1993) and (Kien & Park, 1996).

The internal shear force is: Vint=Vcz+Vay+Vd

From the equilibrium of vertical forces: Vext=Vint Vext=Vcz+Vay+Vd

If moments are taken from the “a” point the internal and external

moments are:

𝑀𝑎,𝑒𝑥𝑡 = 𝑅1 × 𝑥𝑎 − 𝑃1 × (𝑥𝑎 − 𝑥1)

𝑀𝑎,𝑖𝑛𝑡 = 𝑇 × 𝑧 + 𝑉𝑑 × 𝑝 − 𝑉𝑎 × 𝑚

Where “p” is the projection of the diagonal crack and “m” is the distance

between Va and “a”.

Equilibrium: Mext=Mint

𝑀𝑎,𝑒𝑥𝑡 = 𝑇 × 𝑧 + 𝑉𝑑 × 𝑝 − 𝑉𝑎 × 𝑚

If Vd and Va are neglected in order as the crack width is increasing. A

small mistake is committed and next equation is obtained.

𝑇 =𝑀𝑎,𝑒𝑥𝑡 − 𝑉𝑑 × 𝑝 + 𝑉𝑎 × 𝑚

𝑧 ≅

𝑀𝑎,𝑒𝑥𝑡

𝑧

Finally is possible to conclude that the diagonal cracking produces a

redistribution of the internal stresses (Giraldo, 2003):

Before cracking, the average of shear stresses in “a” has a value of

Vext/bwd. After cracking the external shear forces is resisted by

Va,Vd, and Vcz. As the external stresses increase both Vd and Va

decrease making the shear stress increase in the uncracked

concrete zone.

Jaime Tomas Ordiales

Page 26

The diagonal crack reaches the neutral axis and propagates to the

compressive zone. Thus, “C” performs in a smaller area (b*y)

compared to the initial area. Therefore the diagonal cracking have

increased the compression stresses in the concrete.

Before the diagonal cracking the tensile force in the reinforcement

“T” in “b” is only due to a flexural moment in “b” and is

proportional to its value. After the cracking the value of “T” is

due to the moment in “a” and is also proportional to it. As the

moment in “a” is larger than the moment in “b”, the appearance of

cracks has produced a sudden increase of stresses in “b”.

3.Theory

Page 27

3.3 Finite element method

3.3.1 Introduction to the finite element method

All the physical phenomena encountered in engineering mechanics are

modelled by differential equations, and usually the problem addressed is

too complicated to be solved by classical analytical methods. The finite

element method is a numerical approach by which general differential

equations can be solved in an approximate manner.

The differential equation or equations, which describe the physical

problem considered, are assumed to hold over a certain region. Which

could be 2D or 3D. The main characteristic of finite element method is

that instead of seeking approximations over an entire region, the region is

divided into smaller parts and the approximation is carried out over each

small part, called element. Although the variable varies in a non-linear

manner over the whole region, it may be a good approximation to

assume that the variable varies in a linear fashion over each element. The

set of all elements is called finite element mesh.

After choosing the type of approximation to be applied over each

element, the behaviour of each element can be determined. It can be done

because the approximation made over each element is quite simple.

Having determined the behaviour of all elements, these elements are then

patched together, using some specific rules, to form the whole region,

which eventually enables us to obtain an approximate solution for the

behaviour of the entire body.

As the finite element method is a numerical means of solving general

differential equations, it can be applied to various physical phenomena.

For example: heat conduction, torsion of elastic shafts, diffusion,

groundwater flow, and elastic behaviour of one, two and three-

dimensional bodies, including beam and plate analysis.

As it was mention before, the finite element method can be applied to

arbitrary differential equations. Furthermore, arbitrary geometries of

bodies consisting of arbitrary materials can be analysed. Thus, the finite

element method today presents one of the most powerful approach for

solving differential equations that occur in engineering, physics and

mathematics.

Jaime Tomas Ordiales

Page 28

The emergence of the finite element method took place in the early

1960s and since then its use has spread to virtually all fields of

engineering. In practise finite element programs are often used to analyse

different problems. There are many computer programs available today

for almost all the fields of engineering (Ottosen & Petersson, 1992).

3.3.2 Finite element mesh

The first step in an finite element analysis is to select the type of

elements and the finite element mesh. Obviously, the accuracy increases

with smaller element size for a given type of element. Thus, some times

is important to use smaller elements where the function varies rapidly.

This means that is really important to have a physical knowledge of the

problem in order to get a realistic analysis. Actually, the decision on

element types and size is more delicate than that. Every analysis involves

the use of resources. Some times we are only interested in the behaviour

in local regions, while for others we only want a general response of the

whole region. Additionally some simplifications may be introduced

when the problem is defined. As engineers we must use our judgement in

order to obtain that optimum choice for element type and element and

element mesh which balances the requirement of reliable results with that

of cost effectiveness.

The ratio between the largest and smallest dimension of an element is

called the aspect ratio and in a good finite element mesh, it should be

close to the unity. In order to increase the computational efficiency,

symmetry properties should be used whenever possible. That symmetry

involves geometry and also loading and material data. (Ottosen &

Petersson, 1992).

5.Finite element study

Page 29

Finite element study 4

The study developed in this thesis is a computer study based on the

laboratory work performed by Jonny Nilimaa at LTU in 2013 (Nilimaa,

2013). In which, the strengthening method of internal unbonded post-

tensioning was applied on a scaled replica of a trough concrete bridge. In

order to complement this study, a computer analysis with a finite element

program was performed. The program chosen for this study was Atena,

which is a finite element program, specialized in concrete and reinforced

concrete structures.

The purpose of this study is to investigate the behaviour of a railway

concrete trough bridge after applying the method of internal unbonded

post-tensioning. Therefore the load capacity, the shear capacity, the

cracking behaviour and the stresses in the bridge are going to be

checked.

Two different computer studies were performed doing this thesis and

both are described in section 4.3. The results are shown in section 5.2

and they are going to be compared with the results from the laboratory

study mention before and with the results from the Eurocodes.

4.1 Test specimen

The specimen used in the study were based in the drawings of an existing

railway trough bridges from 1950’s but reduced to a scale 1/3. The real

length of the bridge was 4.5 meters and the real width was also 4.5

meters. This scaled replica was also used in the laboratory work

performed before this thesis. The test setup is shown in figure 4.1.

The internal reinforcement of the bridge consisted of deformed steel bars

with diameters of 6, 8 and 10 mm and it is shown in figure 4.2.The

bridge does not contain any stirrups but some deformed reinforcement

bars are bent up at the junction between the slab and the girders. These

bars actually function as a kind of shear reinforcement, enhancing the

shear resistance in the section.

Jaime Tomas Ordiales

Page 30

Figure 4.1 - Test setup, cross sectional view, in [mm], (Nilimaa,

2013).

Figure 4.2 - Transverse reinforcement placed within the specimen.

(Nilimaa, 2013).

5.Finite element study

Page 31

The concrete class was C30/37. The concrete compressive and tensile

strength were tested in the laboratory and the results are shown in table

4.1. The same concrete properties were also used in the computer study.

Table 4.1 - Concrete properties used in both studies. B1. Non

prestressed specimen. B2. Prestressed specimen. (Nilimaa, 2013).

In case of post-tensioning, straight prestressing strands were used with a

diameter of 9.6mm and a tensile strength of 1860 MPa. Rectangular

plates (100x120x15 mm) were used as anchor plates and cylinder-wedge

anchor was also used.

Jaime Tomas Ordiales

Page 32

4.2 Laboratory work

The purpose of this laboratory work was to upgrade a railway concrete

trough bridge by the method of internal unbonded post-tensioning.

In this study two specimens were tested until failure, with a constant

deformation. One of the specimens was unstrengthened and used as

reference and the other one was post-tensioned. The lengths of the

specimens are shown in figure 4.1 and 4.2. In the post-tensioned

specimen three prestressing tendons were placed in the vertical central

line of the deck (55 mm from the bottom of the deck) and aligned in the

transverse direction. One of the tendons was located at the longitudinal

mid-section, while the remaining two were located at 375 mm on each

side of the centre, see figure 4.3.

Figure 4.3 - Tendon distribution within the deck in the prestressed

specimen (Nilimaa, 2013).

The specimens were prepared with plastic ducts before casting. The steel

tendons were placed in the ducts and anchored. Hydraulic jacks were

used for the post-tensioning applying a effective prestress of 744 MPa.

Both specimens were subjected to two deformations applied by a

hydraulic jack at the midpoint of the transverse steel profile as it is

shown in figure 4.1. Loading was conducted until failure at a constant

deformation rate of 0,01 mm/s. The two longitudinal steel profiles

obtained equal loading P/2 at their midspan and the load on the concrete

deck was assumed to be distributed with a magnitude of P/2L.

5.Finite element study

Page 33

4.3 Computer Study

The finite element study was performed in order to study the method of

post-tensioning in concrete trough bridges. Two different studies were

performed in this thesis. A two-dimensional study performed in Atena

2D and a three-dimensional study performed in Atena 3D.

4.3.1 2D Study

The Two-dimensional study was performed in Atena 2D. In which a 2D

specimen of a reinforced concrete trough bridge was modelled, see figure

4.4.

The aims of the two dimensional study were to show the development of

the cracks within the deck and to also study how affects to change the

vertical position of the tendons inside the deck.

Three different simulations were performed. The first simulation was

performed without any prestressing force and used as reference. In the

second one, the specimen was post-tensioned with three prestressing

tendons in the middle of the beam as in the laboratory study, see figure

4.3. Finally in the last simulation the specimen was post-tensioned with

only three prestressing tendons at the bottom of the beam.

Figure 4.4 - 2D specimen of the transversal section of a concrete

trough bridge.

Step 1, Transversal reinforced beam Reinforcements: Stress, Tau xy, <0.000E+00;0.000E+00>[MPa]

X

Y

Jaime Tomas Ordiales

Page 34

4.3.1.1 Modelling and Meshing.

The first step in the computer study was to model the specimen and to

choose the materials. The specimen modelled consisted in the cross

section of the bridge. Only half of the bridge was modelled taking

advantage of the symmetry, see figure 4.4. The specimen had the same

lengths as the ones used in the previous laboratory study, see figure 4.1

and 4.2. Three different types of materials were chosen. First for the steel

plates at the supports and for the load beam the material chosen was

called PlaneStressElasticIsotropic. It had an elastic modulus of 210 GPa

and a poisson’s ratio of 0,3. For prestressing tendons and for the

reinforcement bars the material choosed was an expecific material used

in Atena. The reinforcement bars had an elastic modulus of 200 Gpa and

σy of 560 Mpa and the prestressing tendons an elastic modulus of 210

Gpa and σy of 1860 Mpa. Finally, for the concrete, the material chosen

was SBetamaterial and the values of table 3.1 were used for its

characteristics.

Atena 2D produces an automatic meshing after choosing some

parameters, the element size, mesh type and type of cuadrilateral

elements. In our study case a mixed mesh type was chosen with CCQ10

cuadrilateral elements with an element size of 5 mm. The element size

and mesh type was chosen after plenty of simulations choosing the

combination which gave the most accurate results considering the

limitation of the computer power.

To finish the modelling part, the same reinforcement used in the

laboratory study was added to the specimen, see figure 4.2.

4.3.1.2 Loading

At the support and at the surface where symmetry was applied some

boundary conditions must be place. The specimen was supported with a

steel plate. Thus, a restriction of displacement in the y-direction was

added at the bottom surface of this steel plate. Since only a symmetric

half of the bridge was analysed, it was necessary to enforce the axis of

symmetry along the side where the symmetry was applied. This means

that the horizontal x-displacements in one surface should be equal to

zero.

5.Finite element study

Page 35

The simulations were loaded with a prescribed deformation of 0,25 mm

per step in the negative direction of y-axis. The load was placed in the

middle of the load line beam. In the second simulation a presstressing

force was applied in the middle of the deck before the vertical

deformation. A total tensile force of 126 KN was applied to the specimen

i.e. 42 KN in each of the 3 tendons placed in the bridge (3*42 KN) and

the area elected for the tendons was three times the Area of one tendon.

Finally in the last simulation the same presstressing force was applied

but in this case at the lower part of the deck, 20 mm from the bottom part

of the deck.

4.3.2 3D Study

The Three-dimensional study was performed in Atena 3D. In which a 3D

specimen of a reinforced concrete trough bridge was modelled, see figure

4.5. The modelled specimen was the same than the one used in the

laboratory work, see figure 4.1 and 4.2. The 3D study was used to verify

the validity of the finite element method used in the thesis for study the

behaviour of the bridge and also to complement the laboratory study

performed before this thesis. Also the influence of changing the spacing

between tendons and the cracking performance of the specimen were

checked.

Figure 4.5 - Concrete trough bridge modelled with Atena 3D.

Three different simulations were performed. The first simulation was

performed without any prestressing force, only with a vertical prescribed

deformation. In the second one the specimen was prestressed with three

prestressing tendons as in laboratory, see figure 4.3, and then the same

vertical prescribed deformation used before was applied. In the last

Jaime Tomas Ordiales

Page 36

simulation the specimen was prestressed with only two prestressing

tendons.

4.3.2.1 Modeling.

The first step in the computer study is to model the specimen and to

choose the materials. In order be able to do the most accurate study as

possible and taking into account that the specimen is symmetric, only a

quarter of the bridge was modelled with the measures of figure 4.1 and

4.2, see figure 4.6. Three different types of materials were chosen. For

the steel plates at the supports and for the load beams the material chosen

was 3DElasticisotropic with an elastic modulus of 210 GPa and a

poisson’s ratio of 0,3. For tendons and reinforcement the chosen material

was an expecific material used in Atena for the reinforcement, with a

Elastic modulus of 200 GPa and σy 550 MPa. Finally for concrete the

material chosen was 3DNonlinearCementitious2 and the values of table

3.1 was used for its characteristics.

Figure 4.6 - Quarter of the concrete trough bridge used in the 3D

study after modelling.

After choosing the materials, five macro-elements were modelled

according with the data of figure 4.1 and all of them related with each

respective material. Finally the reinforced was placed within the structure

according to figure 4.2.

5.Finite element study

Page 37

4.3.2.2 Meshing

After modelling the next step in the definition of the numerical model is

the mesh generation. The finite element mesh quality has a very

important influence on the quality of the analysis results, the speed, and

memory requirements. As it was model only one quarter of the structure

a more accurate mesh can be applied. In Atena 3d, each macro-element

can be meshed independently. In our case it was applied a tetrahedral

mesh for all the macro-elements and with a global element size of 0,0275

m, see figure 4.5. The element size and mesh type was chosen after

plenty of simulations choosing the combination which gave the most

accurate results considering the limitation of the computer power. The

study was performed with an ordinary laptop. The study would have

been more accurate if a more powerful computer had been used.

Figure 4.7 - Quarter of the concrete trough bridge used in the 3D

study after meshing.

Jaime Tomas Ordiales

Page 38

4.3.2.3 Loading

As it was mention before symmetry was applied in the specimen,

therefore at the surfaces where symmetry was applied some boundary

conditions must be place and also at the supports. A restriction of

displacement in the y-direction was added at the bottom surface of the

steel plate from the support. Also it was necessary to enforce the axis of

symmetry along the sides in which symmetry was applied. This means

that the horizontal x-displacements in one surface and z-displacements in

the other should be equal to zero.

All the three-dimensional simulations were loaded with a prescribed

deformation of 0,25 mm per step in the negative direction of y-axis. This

load was placed on the top of the load line beam. In the case of the two

simulations in which post-tensioning were applied, a prestressing force

was applied before the vertical deformation. In the simulation with three

tendons, this prestressing force consisted in a tensile force of 21 KN

applied in the tendon which is in the middle of the specimen and a tensile

force of 42 KN in the tendon which is located in one side because of the

symmetry properties applied before. Finally achieving a total

presstressing force of 126 KN. And in the simulation with two tendons a

force of 63 KN was applied in the tendon, because of symmetry again the

same force of 126 KN is achieve as in the other simulation.

5.Results

Page 39

Results 5

5.1 Laboratory study

The maximum load that the structure was able to resist, the failure load,

according to the laboratory study was 344 KN for the unstrengthened

specimen and 380 KN for the strengthened specimen.

The deflections at the mid-span during the tests, for both specimens are

shown in figure 5.1. According to the figure, the deformations are larger

at the unstrengthened specimen than the strengthened with lower loads.

Figure 5.1 - Deflection-Load curves from the laboratory study at the

mid-span. B1. Unstrengthened specimen. B2 Strengthened specimen.

Jaime Tomas Ordiales

Page 40

5.2. 2D study

Three simulations were performed in the 2D study with the ATENA 2D

in order to study the how affects varying the vertical position of the

tendons inside the deck, see chapter 4.2. The failure load calculated for

each specimen was 281 KN for the untrengthened specimen, 310 KN for

the specimen strengthened in the middle of the deck and 334 KN for

specimen strengthened at the bottom of the deck specimen. Figure 5.2,

5.3 and 5.4 shows the deflection in the mid-span during the experiment

for each test. The deflection at mid-span follows more or less the same

pattern for the three specimens. The highest load capacity is achieved

applying eccentricity.

Figure 5.2 - Deflection-Load at mid-span for the specimen without

post-tensioning.

[m]

[MN]

-1.0

69E-0

2-1

.050E-0

2

-1.0

15E-0

2

-9.8

00E-0

3

-9.4

50E-0

3

-9.1

00E-0

3

-8.7

50E-0

3

-8.4

00E-0

3

-8.0

50E-0

3

-7.7

00E-0

3

-7.3

50E-0

3

-7.0

00E-0

3

-6.6

50E-0

3

-6.3

00E-0

3

-5.9

50E-0

3

-5.6

00E-0

3

-5.2

50E-0

3

-4.9

00E-0

3

-4.5

50E-0

3

-4.2

00E-0

3

-3.8

50E-0

3

-3.5

00E-0

3

-3.1

50E-0

3

-2.8

00E-0

3

-2.4

50E-0

3

-2.1

00E-0

3

-1.7

50E-0

3

-1.4

00E-0

3

-1.0

50E-0

3

-7.0

00E-0

4

-3.5

00E-0

4

0.0

00E+

00

-2.813E-01-2.500E-01

-2.000E-01

-1.500E-01

-1.000E-01

-5.000E-02

0.000E+00M2: Deflection

M1:

Load

5.Results

Page 41

Figure 5.3 - Deflection-Load at mid-span for the specimen with post-

tensioning in the centre of the deck.

Figure 5.4 - Deflection-Load at mid-span for the specimen with post-

tensioning in the bottom part of the deck.

[m]

[MN]

-9.7

46E-0

3

-9.4

50E-0

3

-9.1

00E-0

3

-8.7

50E-0

3

-8.4

00E-0

3

-8.0

50E-0

3

-7.7

00E-0

3

-7.3

50E-0

3

-7.0

00E-0

3

-6.6

50E-0

3

-6.3

00E-0

3

-5.9

50E-0

3

-5.6

00E-0

3

-5.2

50E-0

3

-4.9

00E-0

3

-4.5

50E-0

3

-4.2

00E-0

3

-3.8

50E-0

3

-3.5

00E-0

3

-3.1

50E-0

3

-2.8

00E-0

3

-2.4

50E-0

3

-2.1

00E-0

3

-1.7

50E-0

3

-1.4

00E-0

3

-1.0

50E-0

3

-7.0

00E-0

4

-3.5

00E-0

4

0.0

00E+

00

-3.102E-01-2.750E-01

-2.200E-01

-1.650E-01

-1.100E-01

-5.500E-02

0.000E+00M2: Deflection

M1:

Load

[m]

[MN]-9

.449E-0

3

-9.1

00E-0

3

-8.7

50E-0

3

-8.4

00E-0

3

-8.0

50E-0

3

-7.7

00E-0

3

-7.3

50E-0

3

-7.0

00E-0

3

-6.6

50E-0

3

-6.3

00E-0

3

-5.9

50E-0

3

-5.6

00E-0

3

-5.2

50E-0

3

-4.9

00E-0

3

-4.5

50E-0

3

-4.2

00E-0

3

-3.8

50E-0

3

-3.5

00E-0

3

-3.1

50E-0

3

-2.8

00E-0

3

-2.4

50E-0

3

-2.1

00E-0

3

-1.7

50E-0

3

-1.4

00E-0

3

-1.0

50E-0

3

-7.0

00E-0

4

-3.5

00E-0

4

3.9

64E-0

5

-3.350E-01-3.000E-01

-2.400E-01

-1.800E-01

-1.200E-01

-6.000E-02

0.000E+00M2: Deflection

M1:

Load

Jaime Tomas Ordiales

Page 42

5.2.1 Cracking:

Another purpose of the 2D study was to see the development of the

cracks within the structure in the prestressed specimen. The cracking in

the 2D post-tensioned specimen is shown in figures 5.5-5.7 for different

load values. Clearly the specimen suffers from flexure-shear cracking.

The cracks start from flexural cracking, see figure 5.5, and propagates in

a vertical direction until up to the centre of the beam. Then the cracks

propagate diagonally towards the compression zone of the member, see

figure 5.6. Finally in the figure 5.7 we can see a large diagonal crack

close to produce shear failure.

Figure 5.5 - Cracks in the post-tensioned specimen. Step 12 of the

simulation. Load of 110 KN.

Step 12, Transversal reinforced beam Scalars:iso-areas, Basic material, in nodes, Crack Width, Cod1, <0.000E+00;1.059E-06>[m] Cracks: in elements, openning: <4.192E-09;1.040E-06>[m], Sigma_n: <2.490E+00;2.698E+00>[MPa], Sigma_T: <-7.723E-03;3.867E-02>[MPa] Reinforcements: Cable Force, Force, <1.266E-01;1.266E-01>[MN]

X

Y

0.000E+00

9.000E-08

1.800E-07

2.700E-07

3.600E-07

4.500E-07

5.400E-07

6.300E-07

7.200E-07

8.100E-07

9.000E-07

9.900E-07

1.059E-06

5.Results

Page 43

Figure 5.6 - Cracks in the post-tensioned specimen. Step 25 of the

simulation. Load of 310 KN.

Figure 5.7 - Cracks in the post-tensioned specimen. Step 45. Load of

275 KN.

Step 25, Transversal reinforced beam Scalars:iso-areas, Basic material, in nodes, Crack Width, Cod1, <-1.261E-06;7.444E-05>[m] Cracks: in elements, openning: <-5.027E-07;1.331E-04>[m], Sigma_n: <-2.046E+00;2.697E+00>[MPa], Sigma_T: <-2.700E+00;2.506E+00>[MPa] Reinforcements: Cable Force, Force, <1.484E-01;1.484E-01>[MN]

X

Y

-1.261E-06

0.000E+00

7.000E-06

1.400E-05

2.100E-05

2.800E-05

3.500E-05

4.200E-05

4.900E-05

5.600E-05

6.300E-05

7.000E-05

7.444E-05

Step 45, Transversal reinforced beam Scalars:iso-areas, Basic material, in nodes, Crack Width, Cod1, <-1.164E-06;1.389E-03>[m] Cracks: in elements, openning: <-2.402E-06;1.673E-03>[m], Sigma_n: <-1.291E+01;2.660E+00>[MPa], Sigma_T: <-2.677E+00;2.700E+00>[MPa] Reinforcements: Cable Force, Force, <1.895E-01;1.895E-01>[MN]

X

Y

-1.164E-06

1.500E-04

3.000E-04

4.500E-04

6.000E-04

7.500E-04

9.000E-04

1.050E-03

1.200E-03

1.350E-03

1.389E-03

Jaime Tomas Ordiales

Page 44

5.3. 3D study

Three simulations were performed in the 3D study with the ATENA 3D,

see chapter 4.3. As a result of these simulations, failure loads,

deformations, strains and stresses for each specimen were calculated and

are shown in next figures. Comparing the two first simulations, it was

possible to verify the validity of the finite element method used in this

thesis to complement the laboratory study. Then analysing the third

simulation, the influence of changing the spacing between tendons and

finally the cracking performance of the specimen were also checked.

5.3.1 Failure Load and Deformations

The failure load calculated at the 3D study was 369 KN for the

untrengthened specimen, 417 KN for the strengthened specimen with

three post-tensioning tendons and also 417 KN for the strengthened

specimen with two post-tensioning tendons. Figure 5.8, 5.9, 5.10 shows

the deformations in the mid-span of the deck during the experiment for

each test.

5.Results

Page 45

Figure 5.8 - Load-Deflection curve at mid-span in the non-

prestressed specimen.

Load

Deflection [m]

0,00E+00 1,50E-03 3,00E-03 4,50E-03 6,00E-03 7,50E-03 9,00E-03 1,05E-02 1,20E-02 1,43E-02

Load [

MN

]

0,00E+00

1,00E-02

2,00E-02

3,00E-02

4,00E-02

5,00E-02

6,00E-02

7,00E-02

8,00E-02

9,00E-02

1,00E-01

1,10E-01

1,20E-01

1,30E-01

1,40E-01

1,50E-01

1,60E-01

1,70E-01

1,80E-01

1,90E-01

2,00E-01

2,10E-01

2,20E-01

2,30E-01

2,40E-01

2,50E-01

2,60E-01

2,70E-01

2,80E-01

2,90E-01

3,00E-01

3,10E-01

3,20E-01

3,30E-01

3,40E-01

3,50E-01

3,63E-01

Jaime Tomas Ordiales

Page 46

Figure 5.9 - Load-Deflection curve at mid-span in the prestressed

specimen (2º simulation with three post-tensioning tendons).

Load

Deflection [m]

3,07E-04 1,50E-03 3,00E-03 4,50E-03 6,00E-03 7,50E-03 9,00E-03 1,05E-02 1,20E-02 1,37E-02

Load [

MN

]

9,11E-02

9,90E-02

1,08E-01

1,17E-01

1,26E-01

1,35E-01

1,44E-01

1,53E-01

1,62E-01

1,71E-01

1,80E-01

1,89E-01

1,98E-01

2,07E-01

2,16E-01

2,25E-01

2,34E-01

2,43E-01

2,52E-01

2,61E-01

2,70E-01

2,79E-01

2,88E-01

2,97E-01

3,06E-01

3,15E-01

3,24E-01

3,33E-01

3,42E-01

3,51E-01

3,60E-01

3,69E-01

3,78E-01

3,87E-01

3,96E-01

4,05E-01

4,17E-01

5.Results

Page 47

Figure 5.10 - Load-Deflection curve at mid-span in the prestressed

specimen (3º simulation with two post-tensioning tendons).

Jaime Tomas Ordiales

Page 48

5.3.2 Strains

Figures 5.11-5.16 show the strain curves for transverse tensile and

compressive reinforcement at the mid-span in each specimen. Applying

post-tensioning the strains in the reinforcement has reduced.

Figure 5.11 - Strain in tensile reinforcement in the mid-span of the

bridge in the unstrengthened specimen.

Load

Strain [None]

0,00E+00 3,00E-04 6,00E-04 9,00E-04 1,20E-03 1,50E-03 1,80E-03 2,10E-03 2,40E-03 2,65E-03

Load [

MN

]

0,00E+00

1,00E-02

2,00E-02

3,00E-02

4,00E-02

5,00E-02

6,00E-02

7,00E-02

8,00E-02

9,00E-02

1,00E-01

1,10E-01

1,20E-01

1,30E-01

1,40E-01

1,50E-01

1,60E-01

1,70E-01

1,80E-01

1,90E-01

2,00E-01

2,10E-01

2,20E-01

2,30E-01

2,40E-01

2,50E-01

2,60E-01

2,70E-01

2,80E-01

2,90E-01

3,00E-01

3,10E-01

3,20E-01

3,30E-01

3,40E-01

3,50E-01

3,60E-01

3,70E-01

5.Results

Page 49

Figure 5.12 - Strain in tensile reinforcement in the mid-span of the

bridge in the strengthened specimen.

Load

Strain [None]

4,58E-05 2,50E-04 5,00E-04 7,50E-04 1,00E-03 1,25E-03 1,50E-03 1,75E-03 2,00E-03 2,25E-03 2,50E-03 2,72E-03

Load [

MN

]

9,11E-02

9,90E-02

1,08E-01

1,17E-01

1,26E-01

1,35E-01

1,44E-01

1,53E-01

1,62E-01

1,71E-01

1,80E-01

1,89E-01

1,98E-01

2,07E-01

2,16E-01

2,25E-01

2,34E-01

2,43E-01

2,52E-01

2,61E-01

2,70E-01

2,79E-01

2,88E-01

2,97E-01

3,06E-01

3,15E-01

3,24E-01

3,33E-01

3,42E-01

3,51E-01

3,60E-01

3,69E-01

3,78E-01

3,87E-01

3,96E-01

4,05E-01

4,17E-01

Jaime Tomas Ordiales

Page 50

Figure 5.13 - Strain in tensile reinforcement in the mid-span of the

bridge in the strengthened specimen with two tendons.

5.Results

Page 51

Figure 5.14 - Strain in compressive reinforcement in the mid-span of

the bridge in the unstrengthened specimen.

Load

Strain [None]

-4,33E-04 -3,50E-04 -3,00E-04 -2,50E-04 -2,00E-04 -1,50E-04 -1,00E-04 -5,00E-05 0,00E+00

Load [

MN

]

0,00E+00

1,00E-02

2,00E-02

3,00E-02

4,00E-02

5,00E-02

6,00E-02

7,00E-02

8,00E-02

9,00E-02

1,00E-01

1,10E-01

1,20E-01

1,30E-01

1,40E-01

1,50E-01

1,60E-01

1,70E-01

1,80E-01

1,90E-01

2,00E-01

2,10E-01

2,20E-01

2,30E-01

2,40E-01

2,50E-01

2,60E-01

2,70E-01

2,80E-01

2,90E-01

3,00E-01

3,10E-01

3,20E-01

3,30E-01

3,40E-01

3,50E-01

3,60E-01

3,70E-01

Jaime Tomas Ordiales

Page 52

Figure 5.15 - Strain in compressive reinforcement in the mid-span of

the bridge in the strengthened specimen with three tendons.

Load

Strain [None]

-6,07E-04 -5,40E-04 -4,80E-04 -4,20E-04 -3,60E-04 -3,00E-04 -2,40E-04 -1,80E-04 -9,62E-05

Load [

MN

]

9,11E-02

9,90E-02

1,08E-01

1,17E-01

1,26E-01

1,35E-01

1,44E-01

1,53E-01

1,62E-01

1,71E-01

1,80E-01

1,89E-01

1,98E-01

2,07E-01

2,16E-01

2,25E-01

2,34E-01

2,43E-01

2,52E-01

2,61E-01

2,70E-01

2,79E-01

2,88E-01

2,97E-01

3,06E-01

3,15E-01

3,24E-01

3,33E-01

3,42E-01

3,51E-01

3,60E-01

3,69E-01

3,78E-01

3,87E-01

3,96E-01

4,05E-01

4,17E-01

5.Results

Page 53

Figure 5.16 - Strain in compressive reinforcement in the mid-span of

the bridge in the strengthened specimen with two tendons.

Jaime Tomas Ordiales

Page 54

5.3.3 Stresses in the post-tensioning tendons

The stresses of the post-tensioning tendons in each specimen are shown

in Figure 5.17-19.

Figure 5.17 - Tendon located at the mid-span of the bridge in the

specimen with three tendons.

Load

Tendom stress [MPa]

5,80E+02 6,60E+02 7,15E+02 7,70E+02 8,25E+02 8,80E+02 9,35E+02 9,90E+02 1,04E+03 1,10E+03

Load [

MN

]

9,11E-02

9,90E-02

1,08E-01

1,17E-01

1,26E-01

1,35E-01

1,44E-01

1,53E-01

1,62E-01

1,71E-01

1,80E-01

1,89E-01

1,98E-01

2,07E-01

2,16E-01

2,25E-01

2,34E-01

2,43E-01

2,52E-01

2,61E-01

2,70E-01

2,79E-01

2,88E-01

2,97E-01

3,06E-01

3,15E-01

3,24E-01

3,33E-01

3,42E-01

3,51E-01

3,60E-01

3,69E-01

3,78E-01

3,87E-01

3,96E-01

4,05E-01

4,17E-01

5.Results

Page 55

Figure 5.18 - Tendon off-center of the bridge (not at the midspan) in

the specimen with three tendons.

Jaime Tomas Ordiales

Page 56

Figure 5.19 - Tendon off-center of the bridge (not at the midspan) in

the specimen with two tendons.

5.Results

Page 57

5.3.4 Cracks

Figure 5.20-5.22 show the largest cracks for different loading in the

unstrengthened specimen and in the strengthened specimen with three

tendons. The specimens of Figure 5.20 and 5.21 are loaded with almost

the same force around 369 KN which is the load capacity for the

unstrengthen specimen and the one in figure 5.22 is loaded with 417 KN

which is the load capacity of the strengthened specimen. The cracking

performance had improve a lot comparing these figures.

Figure 5.20 - Larger cracks for the unstrengthened specimen in step

68 with a load of 369 KN. Cracks width between 3 and 6 mm.

Jaime Tomas Ordiales

Page 58

Figure 5.21 - Larger cracks for the strengthened specimen in step 26

with a load of 371 KN. Cracks width between 0,1 and 0,3 mm.

Figure 5.22 - Larger cracks for the strengthened specimen in step 60

with a load of 414 KN. Cracks width between 0,5 and 4 mm.

5.Results

Page 59

5.4. Resume

Table 5.1 show the load capacities for each study, the maximum load that

corresponds to the shear and flexural capacity calculated according to

Eurocode 2, the calculations are given in Nilimaa (2012) and also the

load capacity from the Laboratory study and from the FE study for the

non prestressed specimen and for the prestressed specimen with three

tendons.

Table 5.1 - Load capacity in each study.

Eurocode Lab FEM study

Shear

Cap.

Flexural Cap.

Non prestressed specimen 258 294 344 369

Prestressed specimen 286 356 380 414

Jaime Tomas Ordiales

Page 60

6.Analysis and conclusions

Page 61

Analysis and Conclusions 6

As a result of the laboratory study and the FE study, internal unbonded

post-tensioning seems to be a really good strengthening method for

concrete trough bridges. The load capacity has increased after post-

tensioning according to table 5.4. The deformations were reduced in the

slabs and the strain levels significantly decreased after prestressing. For

the load capacity of the unstrengthened specimen the deformations were

reduced over a 60% at the mid-span and the strains in the tensile

reinforcement also were reduced over a 15%, which indicate that higher

loads are required before yielding. Thus a higher flexural capacity is

achieved.

One of the objectives was to study how the vertical position of the

tendons within the deck affects to the final results of the strengthening

method. Therefore a 2D study was performed varying the height of the

tendons inside the deck. According with chapter 4.1 and the results from

the 2D study, see figures 5.1, 5.2 and 5.3 clearly the strengthening

method provides a higher capacity, almost 25 kN more, when the

position of post-tensioning tendons is closer to the bottom flange.

Despite this result most of the times it is really difficult or even

impossible to place the post-tensioning tendons in the bottom part of the

deck because of the internal tensile reinforcement of the bridge,

especially in old bridges. So it is preferable to place the tendons in the

centre of the slab although worse results are achieved. Clearly, the 2D

study is not accurate enough to study the behaviour and the capacity of

the bridge but is enough to compare how affect the different position of

the tendons and to see the development of the cracking. In the 2D

experiment the bridge was modelled as a simple supported beam

however in the 3D the complete bridge could be modelled and studied.

Other objective of the thesis was to verify the validity of the finite

element method comparing the three dimensional study performed in

Atena 3D with the laboratory work performed by Jonny Nilimaa at LTU.

Comparing the deflection-load curves from laboratory, see figure 5.1,

with the ones from the 3D study, see figure 5.5 and 5.6, it is possible to

conclude that the curves are really similar and follow the same pattern.

The results of the laboratory study and the computer study fits good,

Jaime Tomas Ordiales

Page 62

however the computer study is a bit more optimistic than the laboratory

one. The load capacity is almost 30 KN higher for both specimens and

the deflections lower in both of the specimens. The reason of these

discrepancies could be that the finite element mesh was not accurate

enough. Probably using smaller element size the results from both

studies would be the same. In this case, it was not possible to use a more

accurate mesh because of the limitation of the computer power. Other

reason could be that the prescribed deformation applied in the laboratory

work was not properly distributed along the load lines, therefore the

loads concentrated in some points producing a different behaviour than

in the FE analysis in which the prescribed deformation was perfectly

distributed. Despite this difference using the finite element method is a

good complement for study the behaviour of post-tensioned concrete

bridges.

Another objective of the study was to investigate how post-tensioning

affect the shear behaviour. As it was shown in the 2D study, see chapter

5.2.2, the structure clearly suffers of flexure-shear cracking, the cracks

start from flexural cracking and propagates in a vertical direction until

the tensile reinforcement. Then the cracks propagate diagonally towards

the compression zone of the member. Therefore large cracks appear in

the external parts of the line loads caused by shear see figures 5.20, 5.21

and 5.22. Also these figures show how the cracks decrease applying

post-tensioning to the structure. All the models were affected by flexure-

shear cracks but those cracks were almost ten times smaller in the post-

tensioned specimen than in the non post-tensioned one for the failure

load of the unstrengthened specimen. In addition, these cracks were still

smaller in the post-tensioned specimen than the non post-tensioned one

for their respective failure load, see figures 5.20, 5.21, 5.22. The shear

capacity was increased, decreasing the internal strains and improving the

cracking performance.

The specimens failed in flexure in contrast to what indicated Eurocode 2.

It predicted that the specimen should failed in shear, see table 5.1. The

Eurocode 2 is very conservative regarding to the shear capacity.

Eurocode 2 predicted a shear capacity of at least 100 KN lower than the

real shear capacity. Probably due to the lack of knowledge on the shear

failure as was mention in chapter 3.2.

The last objective of the thesis was to study how affects varying the

spacing between post-tensioning tendons within the structure. As it was

mention before two simulations were performed varying the spacing

between tendons with the same prestressing force, 126 KN. The first one

6.Analysis and conclusions

Page 63

with a spacing of 375 mm using three tendons and the second one with a

spacing of 750 mm using two tendons. Almost the same results were

achieved for both simulations, the same load capacity and also the same

strains and stresses, see figures from chapter 5.3.1, 5.3.2 and 5.3.3.

Therefore in this case it is preferable to use only two tendons with a

larger spacing. Thus a tendon would be saved achieving a much more

economic strengthening method. However Eurocode 2 assumed that the

post-tensioning force disperses with an angle of 33.7° in concrete

therefore the spacing length should be in this case only of 265 mm.

Jaime Tomas Ordiales

Page 64

7.Further research

Page 65

Further research 7

The main objective of this thesis was study a good strengthening method

for old railway trough concrete bridges. Finally internal unbonded post-

tensioning seems to be a really good method as it was shown before. It

clearly increase the load capacity of old bridges. However there is a large

lack of knowledge of this method and large limitations from the

Eurocodes. Therefore much more research should be performed in order

to finally really understand and predict the real behaviour of the method

of post-tensioning in old bridges. The Eurocodes are really conservative

do not predict its behaviour.

Different research work could be performed, combining the laboratory

work, fieldwork with the computer studies using finite element analysis

as in this thesis.

Jaime Tomas Ordiales

Page 66

Annex

Page 67

References 8

Braestrup, M. (2009). Structural Concrete Beam Shear - Still a Riddle?

ACI Special Publication , 265, 327-344.

Bell B. (2004), “D1.2 European Railway Bridge Demography”,

European FP 6 Integrated project “Sustainable Bridges”, Assessment for

Future Traffic Demands and Longer Lives,

<http://www.sustainablebridges.net>, (Oct. 10, 2012).

Bennitz, A. (2011). Externally unbonded post-tensioned CFRP tendons:

a system solution. Luleå: Luleå tekniska universitet. (Doctoral thesis /

Luleå University of Technology).

Bennitz A., Schmidt J.W., Nilimaa J., Täljsten B., Goltermann P. and

Ravn D.L. (2012a), “Reinforced concrete T-beams externally prestressed

with unbonded carbon fiber-reinforced polymer tendons”, ACI Structural

Journal, Vol. 109, No. 4, pp. 521–530.

Bennitz, A., (2008). “Mechanical anchorage of prestressed CFRP

tendons: theory and tests. Lulea ”: Lulea University of Technology, 293.

Bennitz A., Täljsten B. and Danielsson G. (2012b), “CFRP strengthening

of a railway concrete trough bridge: a case study”, Structure &

Infrastructure Engineering, Vol. 8, No. 9, pp. 801–816.

Blanksvärd T. (2009). “Strengthening of concrete structures using

mineral-based composites” Lulea university of Technology.

Caprani C. (2006/7) “Civil Engineering Design (1) Prestressed Concrete”

Chhabra Y. (2004) “Bridge Rehabilitation Techniques” The D S Brown

Company. Singapore

Collins, M., Bentz, E., Sherwood, E., & Xie, L. (2007). An adequate

theory for the shear strength of reinforced concrete structures.

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Page 68

Daly A.F and Witarnawan W. (1997) “Strengthening of bridges using

external post-tensioning” EASTS '97, Seoul

El-Hacha R., Rizkalla S.H. (2004). “Near-Surface-Mounted Fiber-

Reinforced Polymer Reinforcements for Flexural Strengthening of

Concrete Structures” ACI Structural Journal v, 101, No, 5, September-

October 2004.

Garcia San Martin,L. (2011). “Life Cycle Assessment of Railway

Bridges”. Stockholm : Royal Institute of Technology (KTH).

Giraldo Bolivar O. (2003). “Estructuras de hormigón 1” University of

Colombia

Hartsuijker C., Welleman J.W. (2001) “Engineering Mechanics: Volume

2: Stresses, Strains, Displacements”

Nilimaa J (2013) “Upgrading Concrete Bridges Post-tensioning for

higher loads” Lulea University of Technology.

Ottosen N. and Petersson, H. (1992) “Introduction to the finite element

method” University of Lund

Post-tensioning institute webpage (2000), “What is post-tensioning”

Retrieved from http://www.dsicanada.ca/uploads/media/DSI-

USA_What_is_Post-Tensioning_us_02.pdf.

Strengthening (n.d.) In Cambridge University online dictionary.

Retrieved from http://dictionary.cambridge.org.

Rúnar Birgisson S. (2011), “Shear resistance of reinforced concrete

beams without stirrups” , thesis, Reykjavik University.

Shaw M. (1997) “Structural Strengthening with external plate bonding”

Sika limited, Welwyn Garden City, Herts AL7 1BQ

Vandoros K.G. & Dritsos S.E. (2008), “Concrete jacket construction

detail effectiveness when strengthening RC columns”, Construction and

Building Materials, Vol. 22, No. 3, March 2008, pp. 264-276.

Annex

Page 69

About the author

Jaime Tomas Ordiales was born in

Pola de Siero, Spain on October

19st, 1989. He made his primary

and secondary studies at his

hometown, Pola de Siero. He was

always interested in engineering,

therefore he studied

industrial/structural engineering in

the city of Gijon at the University

of Oviedo. He specialized in

structures and construction.

He spent a year and a half in

Luleå, Sweden, studying at LTU,

Luleå University of Technology,

performing his last year of his

degree and this thesis. After that he

has been doing an internship in an

Engineering company back in

Spain.