Reinforced Concrete Beams Strengthened with Side Near Surface Mounted FRP: A parametric study based on finite element analysis

with Side Near Surface Mounted FRP:

A parametric study based on finite element analysis

Rewan Eredini

Civil Engineering, masters level 2016

Luleå University of Technology

Department of Civil, Environmental and Natural Resources Engineering

II

Forward

This report is the result of my master thesis of 30 credits as a final step in the Master Programme in Civil Engineer- ing at Luleå University of technology (LTU). The work is carried out in affiliation with Department of Civil, Environmental and Natural Resources Engineering, Division of Structural and Fire Engineering.

The work has been performed at LTU in collaboration with associate senior lecturer Gabriel Sas and PhD-student Cristian Sabau as supervisors and Professor Lars Bernspång as examiner.

I would like to express my gratitude to Gabriel and Cristian for letting me be a part of the project and the support provided. I would also like to thank Oskar Seth for the ideas to the thesis and Lars Bernspång for the support.

Finally, I would like to thank Dobromil Pryl at Červenka consulting for feedback on my work with Atena Many thanks to my family for believing in me and providing the support from the day I was born.

Luleå, November 2016

Rewan Eredini

Abstract

III

Abstract

Most of the today’s concrete structures are older than ten years, and the need to strengthening existing structures is growing steadily. This is due to various reasons such as degradation due to ageing, environmentally induced degradation, poor initial design or construction and lack of maintenance, to name a few. Among the benefits of strengthening existing structures are; less impacts on the environmental and financial benefits. Therefore, there is a need to find alternative ways to strengthen concrete structures more effectively.

For the past decades, several different strengthening methods have been studied. Two examples are externally bonded reinforcement (EBR) and near surface mounted reinforcement (NSM). The outcome of these studies has shown a significant enhancement to the structures. Steel plates and rebar have been used to strengthen concrete structures and have shown good increases in flexural capacity. For this purpose, resins have been used to imple- ment the steel plates and rebar, e.g. shotcrete and epoxy. Due to the weight of steel and its sensitivity to corrosion, new materials have been sought. A promising material for this use is the fiber reinforced polymers (FRP). There are several types of FRP such as, carbon fiber reinforced polymer (CFRP), glass fiber reinforced polymer (GFRP) and aramid fiber reinforced polymer (AFRP). These new material has shown a better performance, due to their light weight, resistance to corrosion, etc.

NSM and EBR perform extremely well in practice as long as sufficient anchorage is provided. However, a prema- ture debonding has been observed by several researchers. This report will study an alternative method to reinforce existing concrete structures called “Side Near Surface Mounted Reinforcement (S-NSMR)” in association with a project run by Gabriel Sas at Luleå University of Technology. This is compared to Bottom Near Surface Mounted Reinforcement (B-NSM), which is a well-established method. It is assumed that the fiber utilisation will increase in NSM applied on the side of the beam. If this hypothesis is proven correct, the proposed method will also solve a major constrain in the utilisation of the NSM technique. In certain cases, the bottom of a beam is not fully acces- sible for strengthening using bottom Applied NSM techniques due to e.g. partition walls or beam-column joints.

To test the effect of S-NSMR seven concrete beams, one reference beam with no fiber reinforcement and two sets of three, for S-NSMR and B-NSMR respectively with different CFRP-rebar length, were tested in the laboratory.

An analytical calculation has also been carried out. In this thesis, a parametric study is performed with FEM software Atena.

The thesis begins with a study of the failure phenomena occurring in the earlier mentioned strengthening method.

A benchmark model is then modelled with a good comparison to the experimental results. An idealised model of the steel reinforcement in the concrete beam is used according to Eurocode 2. Material parameters in concrete are calculated according to Atena theory documents. The influence of creep and shrinkage are considered by reducing the elastic modulus of concrete by 25 %, reducing the tensile strength by 50 % and fracture energy accordingly.

Thereafter, three additional parameters were chosen to continue the parametric study with Atena, 1) CFRP with E- modulus 160 GPa, 2) two different position in cross-section height of S-NSM and 3) five shorter CFRP-rebar each 100 mm smaller than the previous rebar. The behaviour of the two reinforcing types is then compared.

The first parameter is, CFRP with a smaller E-modulus. It could be observed that all beams lost their stiffness, especially after yielding of the steel reinforcement. A small improvement in ductility could also be observed. The utilisation rate of CFRP increased by 13-16% in the case of S-NSM and 18-20% in the case of B-NSM.

The second parameter is, different position of CFRP along the height of the beams cross-section in S-NSM beams.

The positions of the CFRP was lowered in two steps. In each case an increase in stiffness and a decrease in ductility

could be observed. However, the increase of the stiffness was still smaller than the stiffness in the B-NSM, in all

cases. The failure mode changed from a ductile (concrete crushing) type to a more brittle kind (peeling-off con-

crete), due to large flexural cracks at the end of the CFRP-rebar.

IV The utilisation rate of CFRP-rebar, is decreased in each S-NSM beam except for S-NSM 2 with the height 25 mm.

The reduction in the utilisation rate of the CFRP is 7-32 % and in S-NSM 2 with the height H25mm showing an increased in utilisation rate by 7 %.

The third is parameter, different length of CFRP-rebar. In the case of S-NSM, the failure mode changed from a ductile failure mode to a brittle failure mode. The utilisation rate decreased with the decrease in CFRP length. In three of five cases, the S-NSM shows a higher ultimate load-displacement relation, and in all five cases the maxi- mum tensile strains in the CFRP were higher in S-NSM than B-NSM. Even though the stiffness in the S-NSM is lower than the B-NSM, it would be more preferable to use the S-NSM than B-NSM, because of its higher ultimate load and lower displacements.

Keywords: Side near surface mounted reinforcement, Bottom near surface mounted reinforcement, Parametric

study, FEM-analysis, Atena, Carbon fiber reinforced polymer

Sammanfattning

V

Sammanfattning

De flesta av dagens betong konstruktioner är äldre än 10 år. Förstärknings behovet av dessa konstruktioner ökar för varje dag. Detta beror på av nedgraderingen av betongens bärförmåga som är orsakad av bl.a. åldring, miljö- mässiga påverkningar, bristfällig dimensionering, fel vid uppbyggnad eller dåligt underhåll. Förstärkning av befint- liga konstruktioner är fördelaktigt både ekonomiskt och miljömässigt. Därför finns det ett behov av att hitta alternativa metoder till att förstärka befintlig betong konstruktioner på ett effektivare sätt.

Flera förstärknings metoder har undersökts under de senaste decennierna t.ex. ” externally bonded reinforcement (EBR)” och ”near surface mounted reinforcement (NSMR)”. Dessa två metoder har visat en markant ökning av bärförmåga hos konstruktioner som metoderna applicerats på. Till en början använde stål plåtar och armering som förstärkning material som visade en god ökning i bärförmågan. Vid förstärkningen användes olika typer av lim t.ex.

epoxi och ibland göts ett extra lager av betong. Det finns dock några nackdelar med att använda stål armering, då den är känsligt för korrosion, dels pga. av miljön och dels av epoxi limmet. Vilket ledde till fortsatt sökning av material, så som ”fiber reinforced polymers (FRP)”. Några fiberarmerade material typer som använts är, kolfiber (CFRP), glasfiber (GFRP) och aramid fiber (AFRP). Användningen av dessa material har visat goda resultat samt fördelar så som att ha lättare vikt och vara resistenta mot korrosion.

NSM och EBR har visat väldigt bra resultat vid tidigare användning. Dock så har flera forskare uppmärksammat ett förtidigt brott vid förbindelsen mellan befintlig betong element och förstärknings material. Denna rapport a

”baserat” på ett projekt anordnad av Gabriel Sas, biträdande universitet lektor, på Luleås tekniska universitet kommer undersöka en alternativ metod att förstärka befintliga konstruktioner ”Side Near Surface Mounted Reinforcement (S-NSMR)”, sidmonterade yt-nära förstärkningar.

Denna metod kommer att jämföras med en tidigare etablerad metod kallad ”Bottom near surface mounted rein- forcement (B-NSM)”. Hypotesen är, att utnyttjandegraden av kolfiber kommer att öka med den nya metoden. Ifall hypotesen stämmer kommer den alternativa metoden, S-NSMR, att lösa en stor begräsning av NSM användningen.

Speciellt i de fall där botten delen av betong konstruktioner inte är fullt tillgänglig för förstärkning pga. skiljeväggar och balk-pelare skarvar.

Sju betongbalkar testades för att undersöka effekten hos S-NSMR, varav en referens balk utan fiber förstärkning, tre förstärkta balkar av varje förstärknings metod, d.v.s. tre S-NSMR och tre B-NSMR balkar, där längderna på fiber stavarna varierade. I detta examensarbete kommer en parameter studie att utföras med finit element pro- grammet Atena.

Examensarbetet började med en förstudie om olika brottsfall som kan ske med fiber förstärkta konstruktioner. En förankrad modell programmerades med god jämförelse av experimental resultaten. Inga tester hade gjorts på stål armering, därför användes en generell spänning-töjning samband enligt Eurocode2. För att ta hänsyn till krypning och krympning, minskades elasticitets modul med 25 %, draghållfastheten med 50 % och specifika energin med 50 %.

Därefter valdes tre olika parametrar till fortsatta studien med Atena. En hållfasthet på CFRP med E-modulus 160 GPa, två nya positioneringar av CFRP i balkarnas tvärsnittshöjd i S-NSM och fem nya längder på kolfibern. Däref- ter jämfördes resultaten från båda förstärknings metoder.

Den första parametern som användes var kolfiber av ett mindre hållfasthet. Resultatet blev en mindre styv balk, speciellt efter stål armeringen hade nått sin flyttgräns. Det kunde också noteras att utnyttjandegraden av kolfibern hade ökat med 13-16% i S-NSM balkar och 18-20% B-NSM balkar.

Den andra parametern var olika positioneringar av CFRP i balkarnas tvärsnittshöjd i S-NSM balkarna. Utöver

referens balkarna två andra höjder testades, först sänktes höjden med 13-15 mm sedan ytterligare 10 mm. I varje

sänkning av höjden, en ökning av styvheten kunde noteras och en minskning av böjbarheten. Trots ökningen av

VI styvheten, uppnåddes inte samma styvhet som i B-NSM balkarna. Brotts mekanism ändrades dock från betong- kross till lossning av betong lager i botten av balkarna (peeling-off concrete), pga. böjsprickor i änden av kolfiber armeringen. Utnyttjandegraden av CFRP minskade i alla undersökta fallen förutom S-NSM 2 balken med tvär- snittshöjden på 25 mm. Utnyttjande graden i CFRP minskade med 7-32 % och i S-NSM 2 med tvärsnittshöjden H25mm ökade med 7 %.

Den tredje parametern var olika längder på kolfiberstavarna. I S-NSM balkarna ändrades brottmekanismen från betong kross till separation av betonglager i botten på balkarna. Utnyttjandegraden av kolfibern armeringen minskades med förkortningen av längden. I tre av fem fall visade S-NSM högre brottlast än B-NSM. Och i alla undersökta fallen högre töjningar i CFRP kunde noteras i S-NSM balkarna än B-NSM.

Nyckelord: Side near surface mounted reinforcement, Bottom near surface mounted reinforcement, Parameter

studies, FEM-analysis, Atena, kolfiber

Notations and Abbreviations

VII

Notations and Abbreviations

Notations

Latin upper case letters

A Coefficient of thermal expansion [1/K]

A

Concrete cross-section area (m2)

A

Steel reinforcement cross-section area (m2)

A

Total steel reinforcement area (m2)

E Elastic modulus of steel plate (N/m2)

E

Young´s modulus of concrete (N/m2)

E

Young´s modulus of steel reinforcement (N/m2)

F

Compressive strength (N/m2)

F

Tension strength (N/m2)

G

Fracture energy (N/m)

H

The height of CFRP in reference beams (mm)

H

The first height, chosen as parameter (mm)

H

The second height, chosen as parameter (mm)

L Beam length (mm)

L

Span length (mm)

L

Distance from support to the end of CFRP (mm)

L

Length of carbon fibre reinforced polymer (CFRP) (mm)

L

Distance from support to point loads (mm)

D Diameter (mm)

P Point load

N

Number of stirrups (-)

X

Distance between stirrups (mm)

VIII Latin lower case letters

a

Aggregate size (m)

a

Distance from the end of beams to supports (mm)

a

Distance between point-loads (mm)

c/c Distance between the grooves, B-NSM (mm)

i

Tension stiffening factor (-)

f

Onset of crushing (N/m2)

f

Mean cubic compressive strength (N/m2)

f

Characteristic compressive strength of concrete (N/m2)

f

Reduction of compressive strength (-)

f

Yield strength of the reinforcement (N/m2)

h Height (mm)

h

Height, upper part of S-NSM (mm)

h

Height, lower part of S-NSM (mm)

k

First distance from the edge of B-NSM to the grooves (mm) k

Second distance from the edge of B-NSM to the grooves (mm)

t

Height of the grooves, S-NSM, (mm)

t

First groove width B-NSM (mm)

t

Second groove width (mm)

w Width (mm)

w

Critical compressive displacement (m)

x,y,z Coordinates (m)

Greek lower case letters

α

, ε

Tension stiffening parameter (-)

ε

Strain in the concrete (-)

ε

Plastic strain in concrete (-)

ε

Strains in steel reinforcement at ultimate load (-)

Notations and Abbreviations

IX

ε

Strains in steel reinforcement at yielding (-)

υ Poisson ratio

σ

Compressive stress in the concrete (N/m2)

χ Factor that account for openings (-)

µm/m Micro-meter/meter

Abbreviations

AFRP Aramid fiber reinforced polymers

B Bottom near surface mounted, in graphs

B-NSM Bottom near surface mounted

C Carbon fibre reinforced polymer, in graphs

CFRP Carbon fibre reinforced polymer

Cod1 Crack opening displacement, perpendicular to x-axis Cod2 Crack opening displacement, perpendicular to y-axis Cod3 Crack opening displacement, perpendicular to x-y axis

EBR Externally bonded reinforcement

FEM Finite element model

FEM-initial Initial data used in FEM

FEM-reduced value Reduced data, Ft, Gf and E-module FEM-Sh-LC FEM-shrinkage as load case,

FRP Fibre reinforced polymer

FTG Full tensor gravity gradient

FTG FTG side near surface mounted (1,2,3) strains in CFRP mean value FTG-S(1,2,3)S-Mean FTG side near surface mounted 1 strains in steel reinforcement mean value

GFRP Glass fiber reinforced polymers

LVDT Linear variable differential transformer

LVDT-S Linear variable differential transformer side near surface mounted

X LVDT-B Linear variable differential transformer bottom near surface mounted

MD-S(1,2,3) Displacement in Side near surface mounted (1,2,3) Middle

MEAN Mean value

Mid Middle

MSC Mid strain CFRP

MSC-B(1,2,3)-FEM-Mid Strains in CFRP Bottom near surface mounted (1,2,3), in finite element model MSC-S(1,2,3)-FEM-Mid Strains in CFRP Side near surface mounted (1,2,3), in finite element model

MSS Mid strain steel reinforcement

MSS-S1-FEM-Mid Strains in steel reinforcement Side near surface mounted 1, in finite element model

Ref Reference beam

RC Reinforced concrete

S Side near surface mounted, in graphs

S-NSM Side near surface mounted

XI

FORWARD ... II ABSTRACT ... III SAMMANFATTNING ... V NOTATIONS AND ABBREVIATIONS ... VII

1 INTRODUCTION ... 13

1.1 Background ... 13

1.2 Hypothesis and research questions ... 14

1.3 Goal and objectives ... 14

1.4 Limitations ... 14

1.5 Scientific approach ... 14

1.6 Structure of thesis ... 15

2 LITERATURE REVIEW ... 16

2.1 Concrete structures ... 16

2.2 Strengthening progression ... 16

2.3 External bonded reinforcement ... 16

2.4 Near surface mounted reinforcement (NSM) ... 16

2.5 Bottom near surface mounted reinforcement (B-NSMR) ... 17

2.6 Side near surface mounted reinforcement (S-NSM) ... 18

2.7 Failure modes of flexural-strengthened beams NSM and EBR with FRP ... 18

3 ANALYSIS WITH FEM ... 21

3.1 Geometry ... 21

3.2 Conditions ... 22

3.3 Material models ... 24

3.4 Initial material models ... 28

3.5 Influence of shrinkage and creep... 29

3.6 Mesh sensitivity analysis ... 30

3.7 Mesh size ... 34

3.8 FEM compared to experimental test ... 34

4 PARAMETRIC STUDY... 51

4.1 Results ... 52

5 ANALYSIS AND DISCUSSION ... 81

5.1 Benchmark model ... 81

5.2 Different CFRP qualities ... 81

5.3 Different heights of CFRP ... 81

5.4 Different lengths of CFRP ... 82

6 CONCLUSIONS AND FUTURE WORK ... 84

6.1 Conclusions ... 84

6.2 Future work ... 85

XII

7 REFERENCES ... 86

APPENDIX 1. BEAM SCHEMATIC ... 87

APPENDIX 2. DIMENSION OF S-NSM AND B-NSM ... 88

APPENDIX 3. RESULTS FROM CUBE TESTS ... 90

APPENDIX 4. DIFFERENT CFRP QUALITIES, CRACK BEHAVIOUR ... 91

APPENDIX 5. DIFFERENT POSITIONS IN HEIGHT OF CFRP, CRACK BEHAVIOUR ... 92

APPENDIX 6. DIFFERENT LENGTHS OF CFRP, STRAINS ... 95

APPENDIX 7. DIFFERENT LENGTHS OF CFRP, CRACK BEHAVIOUR ... 100

Introduction

13

1 Introduction

1.1 Background

Since the invention of cement, concrete structures have gradually increased around the world. Concrete has become world's most used building material. The common design age of concrete structures is 50-100 years accord- ing to Eurocode 2 (SS-EN_1992-1-1_2005).

In the 1970s, most of the concrete structures in Sweden were younger than 25 years and half of them were younger than ten years, (Tjälsten, et al., 2011). Studies of existing buildings have shown a reduction of performance regard- ing load bearing capacity, aesthetics, function and stability. Instead of building new construction, reparations and maintenance on existing structures have been favourable due to financial benefits. Studies have proven that FRP (Fibre Reinforced Polymer) has a significant influence on the results regarding flexural and shear capacity. FRP comes in different types and shapes; two examples are carbon fibre rebar and carbon fibre laminate, (Tjälsten, et al., 2011). Other types of fiber have also been used for this purpose, e.g. Glass fiber reinforced polymers (GFRP), and Aramid firber reinforced polymers (AFRP).

The need for reinforcement of concrete structures is increasing. Due to the concrete structures, like bridge decks, beams, girders, columns, and building, etc. are continuously degrading. This is closely linked to the ageing, envi- ronmentally induced degradation, poor initial design or construction and lack of maintenance. Another reason for the need of reinforcement could be changed in society, like the increase in traffic volumes, which exceeds the initial design loads of bridges, (Triantafillou, et al., 2001).

Several different approaches have been performed to strengthen concrete structures with fibre reinforced polymers.

Externally bonded FRP reinforced structures have performed extremely well in practice. However, a premature debonding has been observed by several researchers. Another strengthening method that has been more popular over the years is near surface mounted reinforced concrete. This method can be used to flexural strengthen con- crete slabs against tensile forces. One advantage of this method is the surrounding concrete providing protection from mechanical and environmental damages, (Hassan, et al., 2003).

This report aims to investigate an alternative method for strengthening reinforced concrete beams in flexural,

using fiber reinforced polymers (FRP) applied as side bonded near surface mounted reinforcement (S-NSMR). The

NSM strengthening technique was first introduced to overcome the debonding problems of externally bonded

reinforcement (EBR). However, the NSM technique also has certain limitations. Although tests have shown a

better utilisation of the fibers when applied as NSM, the bond loss is not resolved.

14 1.2 Hypothesis and research questions

NSM bars applied traditionally at the bottom of beams debond due to loss of tensile strength (Fig 1b) or shear strength (Fig 1a). It is expected that the fibre utilisation will increase if the NSMs are applied on the side of the beam, see Fig 1c, due to confinement effects of the surrounding concrete. If this hypothesis is proven correct, the proposed method will also solve a major constraint in the utilisation of the NSM technique. In certain cases, the bottom of a beam is not fully accessible for strengthening using bottom applied NSM technique due to e.g. parti- tion walls or beam-column joints.

 How does the CFRP strengthening affect the failure mode of reinforced concrete beams?

 How does the CFRP quality affect the failure mode of reinforced concrete beams?

 How does changing the position of CFRP influence the utilisation rate of CFRP?

 How does changing the position of the CFRP influence the behaviour of the beam?

 How does the length of CFRP in S-NSM affect the failure modes and the utilisation rate compared to B- NSM?

Figure 1-1: Classical NSMR strengthening (a, b) and the proposed S-NSMR method (c)

1.3 Goal and objectives

The goals and objectives of this thesis are to study an alternative way of applying near surface mounted reinforce- ment. Thereafter, perform a parametric study in which the improvement of ultimate capacity and the utilisation rate of CFRP is to be evaluated and analysed. This will be done by replicating the test results with finite element modelling (FEM) software Atena.

1.4 Limitations

It is chosen not to include the interface (epoxy) in the models for the carbon fibre reinforced beams. Because the failure in the experimental test was either concrete crushing following by bond-slip in the interface-concrete or peeling-off concrete.

For the same reason, it was chosen not to use any bond-slip model, between the CFRP and the concrete in the models. CFRP are designed with perfect connections.

The designed beams were well reinforced in shear with stirrups. Therefore, the focus will be on the flexural behav- iour.

1.5 Scientific approach

Initially, a study was performed based on the literature that followed with the Atena software. Continuous contact

with the software developers Dobromil Pryl was held during the studies to get familiar with the software, discuss

issues with the approach and modelling of the structure and evaluating and controlling the results.

Introduction

15

Thereafter a literature study was performed to become more familiar with strengthening mechanism, failure modes and structural behaviour.

1.6 Structure of thesis 1. Introduction

This chapter describes the background and the aim of this master thesis. The hypothesis and research questions that need to be answered are listed in this chapter. The goals and objectives, as well as the limitations of the work and the scientific approach to the work, are presented.

2. Literature review

This chapter explains the different approach of reinforcing concrete structures with FRP, NSM, B-NSM, S-NSM and different failure modes that may happen in flexural reinforced structures.

3. Analysis with FEM

In the FEM analysis, the modelling approach is explained, the geometry of the tested beams are drawn for illustra- tions. Different conditions regarding the structures are presented, and the approach and meaning of them are explained. The material, boundary conditions and loading are described. Also, a sensitivity study made on material parameters regarding the shrinkage and creep of the concrete and mesh size are presented. The results from the final models are compared with the experimental results firmly to establish a final model for the parametric study.

4. Parametric study

A description of three different parameters is presented, and the parametric study is performed. Thereafter, the results from the parametric study are presented.

5. Analysis and discussion

The results from the parametric study are analysed and discussed.

6. Conclusion and future work

In this chapter conclusions on parametric study are made regarding research hypothesis and questions. Thereafter some recommendations for future studies are presented.

7. Appendix

In the appendixes beam schematics, and results from the cube tests are presented. Graphs of load-displacements,

load-strains are shown for the parameter with different lengths and at last, the overall cracking behaviour of all

studied parameters are presented.

16

2 Literature review

2.1 Concrete structures

Concrete structures have high compressive strength and very poor tensile strength. A concrete structure without any reinforcement will crack and fail when a relatively small tensile load is applied. The failure is brittle and occurs very sudden. Therefore, concrete structures are usually reinforced with steel bars. This improves the structures capacity and ductility. This kind of reinforcement is regularly done before the concrete is cast. Concrete structures have a long service life, and it is common that the use and demand of a certain structure change over time. The structure may have to carry larger loads or meet new standards. In some cases, it is essential to repair a structure because of accidents, errors made in design or construction phase. Moreover, ageing, environment or poor maintenance contributes to the degradation of the structure, (Täljsten, et al., 2003).

2.2 Strengthening progression

During the last decades, several different strengthening methods have been used. Some of the traditional strength- ening methods are increasing cross-sectional area, post-stressing, casting new concrete cover, etc. New methods were developed in the middle of 1970s; steel plates were glued on the concrete surface of the structures. This method has frequently been used in USA, Japan and in Europe, (Täljsten, et al., 2011).

This method comes with some crucial disadvantages, such as corrosion, self-weight of the steel, requiring expensive machinery for the field installations. Another problem is the weight of steel plates that requires applying outer pressure to the plate during the construction until hardening of the epoxy is achieved. Furthermore, it has been proven that steel plate is vulnerable to corrosion, especially at the steel-epoxy interface, (Mohamed, 2002).

After decades of extensive research, new materials have been discovered to strengthen reinforced concrete (RC).

This new material is called fibre-reinforced polymer (FRP). In the beginning, the structures were externally bonded with FRP-laminates. This new method has been extensively used worldwide. However, a premature debonding has been observed by several researchers, (Hassan, et al., 2003). Recently, near surface mounted reinforcement (NSM), a method that dates back to 1950s in Europe, has attracted an increasing amount of research as well as practical application. This method is based on cutting grooves into the concrete cover, to later glue in FRP with epoxy, paste or cement. It is even possible to use steel bars with this method. However, it is preferable to use fibre reinforced polymer due to its resistance to corrosion, ease and speed of installation due to its lightweight and a reduced groove size due to the higher tensile strength. Which outlast the steel bars, (L. De Lorenzis a, 2006).

2.3 External bonded reinforcement

Externally bonded reinforcement with FRP is simply based on bonding the FRP laminates on the structure surface.

The most crucial disadvantages are that the laminates are exposed to the environmental impact, like accidents, fire, etc. since the FRP laminates and the resins are very sensitive to heat.

2.4 Near surface mounted reinforcement (NSM)

Near surface mounted reinforcement dates back to the early 1940s. In this method steel reinforcement was placed in grooves in concrete cover or in additional concrete cover, which is cast onto the structure. The steel bars are then placed in grooves in the concrete structure and then the grooves are mortared. Another method has been, to use steel bars, fastened to the surface of the structure and covered with shotcrete. This method comes with some disadvantages; it is often difficult to achieve a good bond to the original structure and in some cases, it is hard to cast concrete around the steel reinforcement. New adhesive that were developed in the 1960s, such as epoxy, improved the bonding mechanism of the steel reinforcement. However, due to the steel reinforcement’s sensitivity to corrosion, an additional concrete cover is still needed. As a protection layer, steel reinforcement was coated with epoxy. A method that has shown over time to not be optimal. Epoxy coated steel reinforcement are not always corrosion resistant for various reasons, (Rayo, 2008).

CFRPs are resistant to corrosion, which eliminates the need of thick concrete cover. CRFP can be custom made

for the current purpose, and furthermore, the lightweight of the CFRP laminates makes them easy to install.

Literature review

17

Another advantage is that both epoxy and high-quality cement mortar can be used for the installation of CFRP, (Täljsten, et al., 2003).

Compared to externally bonded FRP reinforcement, the NSM system has some advantages, (L. De Lorenzis a, 2006).

 The amount of site installation work may be reduced, as surface preparation other than grooving is no longer required (e.g., plaster removal is not necessary; irregularities of the con- crete surface can be more easily accommodated; removal of the weak laitance layer on the concrete surface is no longer needed);

 NSM reinforcement is less prone to debonding from the concrete substrate

 NSM bars can be more easily anchored into adjacent members to prevent debonding failures;

this feature is particularly attractive in the flexural strengthening of beams and columns in rigidly-jointed frames, where the maximum moments typically occur at the ends of the member

 NSM reinforcement can be more easily pre-stressed

 NSM bars are protected by the concrete cover and so are less exposed to accidental impact and mechanical damage, fire, and vandalism; this aspect makes this technology particularly suitable for the strengthening of negative moment regions of beams/ slabs

 The aesthetic of the strengthened structure is virtually unchanged.

2.5 Bottom near surface mounted reinforcement (B-NSMR)

Since the invention of the near surface mounted reinforcement many studies have been carried out, e.g. Täljsten, et al., 2003; L. De Lorenzis a, 2006; and Al-Mahmoud, et al., 2009. Proving that NSMR is an effective method. A different approach has been taken to apply reinforced polymers, for example, pre-stressed and standard carbon fibre reinforcement, etc.

However, near surface mounted reinforcement has some limitations. The width of a beam to be strengthened can limit the number of bars that can be used due to the needed groove width spacing between adjacent grooves. A problem that can occur is debonding due to stress overlapping. This contributes to a limit of rebar to be used, (Hosen, et al., 2015).

Figure 2-1 Different options for applying FRP as NSM (L. De Lorenzis a, 2006)

18 2.6 Side near surface mounted reinforcement (S-NSM)

A study by, (Hosen, et al., 2015) on S-NSM method compared steel bars with CFRP. Their results indicated that the CFRP beams showed better improvement compared to the steel reinforcement; the first cracking load was increased and the ultimeate loads were higher. However, this improvement is dependent on the dimension of the bars used for strengthening.

2.7 Failure modes of flexural-strengthened beams NSM and EBR with FRP

The failure mode of RC with NSM CFRP is depended on different parameters. For regular RC beams, the failure mode varies from the rupture of tensile reinforcement to concrete crushing. This is dependent on the ratio of tensile reinforcement and concrete compressive strength.

Two types of rupture are possible for NSM systems. These are pull-out and peeling off. In the case of pull-out the failure occurs when, FRP bar is longer than the cracked span length of the beam at ultimate stage, (Al-Mahmoud, et al., 2009). This is a sudden failure and as results are splitting of the cracked concrete surrounding the groove.

The second failure type is peeling-off concrete, which occurs when the acting load causes cracks reaching the end of the FRP bars. Even this case is a sudden failure and as a result, the concrete covering the groove from the end of the bar peels-off, (Al-Mahmoud, et al., 2009).

Figure 2-2: Concrete peeling-off mechanism (Al-Mahmoud, et al., 2009)

The most usual failure mode in externally bonded RC in flexural member has been due to peeling-off concrete.

The weakest link has been the concrete layer near the surface. The following four different failure modes closely linked to the length of the FRP are presented by (Triantafillou, et al., 2001), see Figure 2-3, and the description of the different failure modes below.

Figure 2-3: Bond failure modes of a concrete member with EBR, (Triantafillou, et al., 2001)

Literature review

19

Mode 1: peeling-off in an uncracked anchorage zone

The FRP may peel-off in the anchorage zone as a result of bond shear fracture through the concrete.

Mode 2: peeling-off caused at flexural cracks

Flexural (vertical) cracks in the concrete may propagate horizontally and thus cause peeling-off of the FRP in regions far from the anchorage.

Mode 3: peeling-off caused at shear cracks

Shear cracking in the concrete generally results in both horizontal and vertical opening, which may lead to FRP peeling-off. However, in elements with sufficient internal (and external) shear reinforcement (as

well as in slabs) the effect of vertical crack opening on peeling-off is negligible Mode 4: peeling-off caused by the unevenness of the concrete surface

The unevenness or roughness of the concrete surface may result in localized debonding of the FRP, which

may propagate and cause peeling-off.

20 Figure 2-4: Bond failure modes of NSM systems, (L. De Lorenzis a, 2006)

Debonding is another common failure mode, which occurs in different ways. Bond failure at the bar-epoxy inter-

face, epoxy-concrete interface, splitting of epoxy cover, concrete cover separation, and secondary debonding failure

mechanisms, (L. De Lorenzis a, 2006).

Analysis with FEM

21

3 Analysis with FEM

The main goal of this thesis is to perform a parametric analysis; it is needed to create a finite element model which is reasonably good in comparison with the laboratory test. The modelling is done in the finite element program called Atena 2D engineering, version (5.1.3). Same basic material parameters for concrete, steel reinforcement, etc.

will be used for all models. The only differences will be the length and position of carbon fibre reinforced polymer and small geometrical differences. At the time of the experimental test age of the beams was 180 + days. Therefore, the influence of ageing is considered. A recommendation from Cervenka documentation-troubleshooting has been considered; this will be presented with more details in the coming subchapters.

3.1 Geometry

Solid with four nodal elements is used due to the effect of bending and shear forces occurring while loading the beams. The beams are modelled fully due to no symmetry in the carbon fibre reinforcement. The beams consist of five volumes, designed as macro-elements. The first macro-element is the beam to be analysed. The other four macro-elements are steel plates used to transfer the loads to the beam and from the beam to supports.

Figure 3-1: Principle drawing of the reference beam in Atena

The steel reinforcement in compression and tension are modelled as discrete bars with a vertical anchorage of 100 mm, and the shear reinforcement is modelled as smeared reinforcement (vertical lines, Figure 3-1), assigned with 1D-properties. Thus, they take only axial forces, see Appendix Beam Schematic for the full detailed reference drawing used for ordering the beams from the manufacturer.

The proposed approach of S-NSM and B-NSM are illustrated in the figures below, with notation of difference in geometrical values. The exact values for the three different beams are presented in Appendix 2.

Figure 3-2: Proposed approach of the CFRP reinforced beams, i) S-NSM and ii) B-NSM

1

2 3

4 5

1 2

X

Y

22 Figure 3-3: Cross-section of NSM types, i) S-NSM and ii) B-NSM

3.2 Conditions Boundary condition 3.2.1

All beams are simply supported.

Figure 3-4: Principal drawing of the reference beam with boundary conditions Loading

3.2.2

The beams are loaded with two point loads. The applied loads are prescribed displacement in the negative y- direction. The total prescribed displacement is 0.6 mm in each load step, which was chosen to represent the same loading pattern as the laboratory test. The 20 first steps in the analysis were loaded with ¼ of 0,6 mm. This was done to achieve a more precise first cracking behaviour in the concrete beams.

Monitoring points and cuts 3.2.3

Several different monitoring points are modelled. First monitor was to measure the mid-displacement and was placed in the middle of the bottom part of the beam. Second monitor was placed at supports to measure the reaction in the supports and one more measuring the strains in the reinforcement, in the middle of the beam.

Figure 3-5: Monitoring points placed at described positions above

Atena engineering offers a very useful feature called “cuts”. This can be defined as a single straight line, an arc, or a polygon consisting of straight lines or arcs, along which scalar quantities can be evaluated and displayed. This feature is used to evaluate stresses, strains, etc. in the concrete.

1 2

X

Y

1 2

3

2 X 8 9 1 4 5 3

Y

Analysis with FEM

23

Numerical method 3.2.4

Atena Engineering offers two different solution parameters, Newton-Raphson and Arc Length. The difference between these solutions parameters is 1), Newton-Raphson is used in cases of displacement control (pre- or post- peak) or nominal force loading (dead weight, 100% service load, etc.), and 2), Arc Length is used in cases of force loading up to failure. However, the laboratory tests were performed with displacement control, thus the use of Newton-Raphson, (Červenka, et al., 2014).

Newton-Raphson is a method based on the concept of incremental step by step analyses. The applied load is gradually increased. In each load step the out of balance forces are calculated and differentiated with the minus internal forces at the end of the previous load step. Four different convergence criteria are set, the first criteria are to check the deformation changes during the last step, the second checks the norm of the out-of-balance force, the third checks out-of-balanced forces regarding maximum components and the fourth checks out-of-balance energy.

For the first three parameters the values of the convergence limits are set by default to 0.01 and for the fourth to 0,0001, (Červenka, et al., 2014).

The numerical method is modified by increasing the number of iteration from 40 to 60. Increasing the possibility of reaching convergence. However, this affects only a few steps in the process. Since most of the steps in the analysis reaches convergence below 40 iterations. Conditional break criteria are also changed. This change only limits the running of the model. As mentioned earlier the convergence limits of the four different parameters is set as default values to 0,01 and 0,0001. The limitation made here is that the analysis will stop running when the convergence error reaches 10*0,01 meaning 10% and 0,0001*1000 also 10%. An assumption made in some cases is that, if a step does not reach convergence limited to 1 % followed be more than ten steps converged is accepted as a small error. “A single step with an error about 2% is absolutely no problem in most cases”, (Pryl & Červenka, 2015).

Figure 3-6: Modified Newton-Raphson method, ( Č ervenka, et al., 2014) Cracking behaviour

3.2.5

The crack width will be evaluated as crack opening displacement (cod). Atena provides three different crack

directions, thus cod1, cod2 and cod3. In a material point, there can be up to 3 cracks in mutually perpendicular

planes. Thought the modelling is performed in 2D, the cracks in X and Y directions can be seen as lines. However,

for the cracks parallel to X-Y planes the cracks are displayed as circles, cod1 are cracks perpendicular to the x-axis,

cod2 are cracks perpendicular to y-axis and cod3 are cracks perpendicular to X-Y axis. The size of cracks will be

based on the scalars provided by the software in element nodes. These values are an average of all integration

points.

24 3.3 Material models

In this sub-chapter the material behaviour, calculation, etc. are presented for the reader. For a broader purpose and limitations done on the material properties. Which may have different effects on the material behaviour, contrib- uting to the results achieved in this study. The mode of procedure of material properties are based on the software Atena material design, access to information regarding the material properties, etc.

Concrete 3.3.1

In Atena software, there is a modified model “CC3DNonLinCementitious2” for concrete that is used in this project as material. This material is formulated to combine tensile (fracturing) and compressive (plastic) behaviour.

The model is based on the classical orthotropic smeared crack formulation and crack band model. Using the Rankine failure criterion for exponential softening, while it can be used as rotated or fixed crack model. “The hardening/softening plasticity model is based on Menétrey-Willam failure surface. The model uses return mapping algorithm for the integration of constitutive equations”, (Červenka, et al., 2014). This algorithm is based on recur- sive substitution, and it consents for the two models to be developed and formulated independently.

According to (Červenka, et al., 2014), “The algorithm can handle cases when failure surfaces of both models are active, but also when physical changes such as crack closure occur. The model can be used to simulate concrete cracking, crushing under high confinement, and crack closure due to crushing in other material directions.”

The material property for the concrete material used are based on the cubic tests performed in the laboratory, see Appendix 3. The tests were performed 130 days after the casting of the cubes. A total of 12 cubes were casted and tested. The mean value of the compressive strength, f

was calculated to 62,6 MPa. This mean value is then transformed to a cylindrical mean compressive strength according to, (Červenka, et al., 2014) defined as,

𝐹

= −0,85 ∗ 𝑓

(1)

The tensile strength is calculated according to the equation below,

𝐹

= 0,24𝑓

(2)

The tensile strength is influenced by the cracking of the concrete. A model based on crack-opening law and frac- ture energy is used to predict the crack propagation in the concrete. This fracture energy is the amount of energy needed to produce a crack with zero stress in the concrete, see Figure 3-7. The following equation is defined by, (Červenka, et al., 2014), for this purpose.

𝐺

= 0,000025𝐹

(3)

Figure 3-7: Exponential crack opening law, ( Č ervenka, et al., 2014)

Analysis with FEM

25

Figure 3-8: Compressive hardening/softening, ( Č ervenka, et al., 2014)

The elastic modulus E c has a significant influence on the stiffness behaviour of the beam; higher values give stiffer beam and lower values a less stiff beam. The E-modulus is dependent on the stress and strain relation, Hook’s law.

However due to non-linear relation in concrete, (Červenka, et al., 2014), has defined the initial elastic modulus as,

𝐸

= (6000 − 15,5𝑓

)√𝑓

(4)

The compressive hardening/softening is derived with the help of “return mapping algorithm”, see (Červenka, et al., 2014). The final equation is as following,

𝜀

= 𝐹

𝐸

(5)

It also depends on the onset of nonlinear behaviour according to (Červenka, et al., 2014) defined as,

𝑓

= 𝑚𝑖𝑛 {−2.1𝐹

; 2

3 𝐹

} (6)

The critical compressive displacement defines the end of the softening curve, therefore, the plastic displacement w d . A default value of 0.5 mm is set in the software. Which was defined by Van MIER (1986) by experiments, Cervenka et al. (2014). The slope of the curve is defined by the points at maximum stress and the limit compres- sive strain at zero stress, see Figure 3-9.

Figure 3-9: Softening displacement law in, ( Č ervenka, et al., 2014)

26 Figure 3-10: Tension stiftning ( Č ervenka, et al., 2014)

As the beams to be analysed consists of steel reinforcement, the tension stiffening has to be included in the mate- rial model. This is due to the reinforcement preventing the full development of cracks in the concrete. Therefore, the concrete contributes to the stiffness of the reinforcement. To include this in Atena, a tension stiffening factor ac

is defined to include the relative minimum tensile stress in the cracked concrete. However, this is set to a default value of 0,4 in Atena software.

It is important to take into account the reduction of the compressive strength after crack occurring in the concrete.

Therefore, a factor c is defined. The strength reduction is parallel to the fracture direction, (Červenka, et al., 2014).

Up to date, different results are presented by researchers e.g., Collins; Vecchio and (DYNGELAND 1989). A default value is chosen in Atena c=0,8.

Following results were obtained using equations explained above.

Table 3-1: Initial concrete parameters Concrete parameters

E

3.980E+04 [MPa]

f

-5.325E+01 [MPa]

f

 3.786E+00 [MPa]

υ  0.200 [-]

G

 9.465E-05 [MN/m]

f

ε

 -1.338E-03 [-]

w

 -5.000E-04 [m]

C 0.8 [-]

Analysis with FEM

27

Figure 3-11: Idealised and design stress-strain diagrams for reinforcing steel (tension and compression), (SS-EN-1992-1-1, 2004)

Reinforcement 3.3.2

Two different approaches are used to model reinforcement, discrete- and smeared reinforcement. Shear reinforce- ment is modelled as smeared reinforcement, which is calculated as a ratio of the cross section of the beam As/Ac.

Bending reinforcement is modelled as discrete bars. The smeared reinforcement is calculated according to Equation 7, derived by, (Pryl & Červenka, 2015).

2 ∗ 𝐴

𝐿 ∗ 𝑤

(7)

Table 3-2: Smeared reinforcement

Variable Amount of shear reinforcement Units

N

52 [bars]

X

(distance between stirrups) 75 [mm]

D 10 [mm]

L 3,995 [mm]

A

 799000 [mm

]

A

 8168,141 [mm

]

A

/A

 0,0102 [%]

Each beam is reinforced with two bars in tension and two bars in compression. No tests were performed to deter- mine the reinforcement behaviour. Therefore, a theoretical behaviour was used. The bending reinforcement is of type S500 with a diameter of 16 mm. This gives a theoretical yield strength of 500 MPa, E-module of 200 GPa and tensile strain of 2,5 ‰. An idealised design of stress and strain has been used according to EC2 and Annex C, where k is 1,08 and ε

is 5 %.

Steel plates 3.3.3

Steel plates used as supports and under point loads have been replicated with exact dimensions. The material

behaviour is assumed to be linearly elastic. So the material called “plane stress elastic isotropic” was chosen in

Atena. Table 3-3 shows material parameters used. The connection between the steel plates and concrete beams are

designed as perfect connection.

28 Table 3-3: Steel Plates used as load transfer

Steel plates Value Unit

E 200 [GPa]

µ 0.3 [-]

Ρ

2.300E-02 [MN/m

]

Α 1.200E-05 [1/K]

Carbon fibre reinforced polymer 3.3.4

In this study carbon fibre reinforced polymer are used as discrete bars. The cross-section area is 100 mm

in all cases. However, the length of the bars varies in each case. These are presented in Appendix 2. The CFRP has an elastic modulus of 210 GPa and tensile strength of 3300 MPa with a tensile strain of 14 ‰. Due to the high tensile strength, it is assumed that failure will not be the rupture of the CFRP-bars. Therefore, they are designed as linear-elastic (stress-strain law) in the FEM modules.

Epoxy 3.3.5

Based on the test results and material properties of concrete, CFRP and epoxy, it is assumed that the failure will occur as a flexural failure, concrete crunching/tensile failure, yielding of the steel bars, debonding as peeling-off concrete at the end of CFRPs. Therefore, a design of the interface is excluded, and CFRP is introduced as rein- forcement bars with perfect connection.

3.4 Initial material models

Concrete parameters defined above are used in Atena as a first step to compare FEM-results with experimental test results. The initial stiffness seems to be much higher than the laboratory test. The first concrete cracks appear at a load of 20,59 kN while in the laboratory test it was approximately 7,25 kN. The maximum load (at yielding of reinforcement) is overestimated by 2,72 %, and the displacement (at yielding of reinforcement) is underestimated by 38,35 %, see Figure 3-12 and Table 3-4. Equation eight is used to calculate the percentage increase in different cases if no other options are presented.

( 𝐍𝐞𝐰 𝐯𝐚𝐥𝐮𝐞 − 𝐎𝐥𝐝 𝐯𝐚𝐥𝐮𝐞𝐬

𝐎𝐥𝐝 𝐕𝐚𝐥𝐮𝐞𝐬 ) ∗ 100 (8)

Figure 3-12: Load Vs Displacement, Reference beam 0

20 40 60 80 100

0 5 10 15 20 25 30 35 40 45 50 55 60

Lo ad [ kN ]

Displacement [mm ]

Reference beam

FEM

Ref

Analysis with FEM

29

3.5 Influence of shrinkage and creep

The influence of shrinkage depends on different variables in the concrete beams; the ambient humidity, tempera- ture, mixture proportions, material properties, curing conditions and the geometry of the element affect the magnitude of free shrinkage strain, (Kaklauskas, et al., 2009). However, structures with steel reinforcement are restraint to shrinkage, which leads to compressive stresses in the reinforcement and tensile stresses in the concrete.

These strains and stresses are dependent on the symmetry of the reinforcement in the concrete structure. This means that the stresses and strain will be non-uniformly distributed within the height of the section if the beams are not reinforced symmetrically, (Kaklauskas, et al., 2009). To account for the creep, the E-modulus of the con- crete is reduced by 25 %.

Three different approaches are provided in Atena to account for shrinkage, (Pryl & Červenka, 2015) 1. Reduction of the tensile strength (and/or fracture energy) of the concrete by ½-1/10.

2. Application of shrinkage as initial strain (constant volume reduction throughout the whole struc- ture/volume). Recommended values are 150-450 microstrains.

3. Performing a detailed analysis using the Creep analysis module .

The first and second method will be tested to evaluate the most consistent method compared to the laboratory test.

The third option is eliminated due to the advanced approach and time consuming.

In the first case the tensile strength and fracture energy were reduced by 50 % and to account for the creep E- modulus of the concrete is reduced by 25 %. For case two an initial strain of 450 microstrains is added as applyied load. However, in both cases the ultimate load was approximately the same and the displacements were underestimated by 23-37 %, see Table 3-4. The results between the two methods do not differ much. As stated before, the symmetry of the reinforcement has a significant influence on the stress distribution along the cross- section of the beams, and CFRP-reinforced beams are reinforced non-symmetrically. Therefore, the first option is chosen.

Figure 3-13: Comparison of different cases regarding reduction of concrete strength, (FEM-reduced value= reduced Ft, Gf and E-module, FEM-initial= no changes in data, FEM-Sh-LC= shrinkage as load case, Ref= reference beam)

Table 3-4: Theoretical calculations compared with loads at failure at laboratory Ultimate load

[kN]

Ultimate deflection [mm]

Laboratory/FEM [Ultimate-load]

Laboratory/FEM [Deflection]

Laboratory 69,92 26

Initial values 71,82 16,4 1,027 0,631

Reduced Ft-Gf and Ec 69,84 19,78 0,999 0,761

Shrinkage as load case 70,14 20 1,003 0,769

0 20 40 60 80 100

0 5 10 15 20 25 30 35 40 45 50 55 60

Lo ad [ kN ]

Displacement [mm]

Reference beam

FEM-reduced values FEM-Initial

FEM-Sh-LC

Ref

30 The summarised parameters in Table 3-5 are chosen to continue with in the coming FEM-models. The chosen method is to reduce the tensile strength and fracture energy by half and the E-modulus by 25 %.

Table 3-5: Chosen value to continue the study with Concrete parameters

E

3.0E+04 [MPa]

f

-5.325E+01 [MPa]

f

 1,980E+00 [MPa]

υ  0.200 [-]

G

 4,730E-05 [MN/m]

f

ε

 -1.780E-03 [-]

w

 -5.0000E-04 [m]

C 0.8 [-]

3.6 Mesh sensitivity analysis

A mesh sensitivity analysis is performed with three different mesh sizes. Thus, the analyses is performed in 2D, the ratio of the finite elements for the different meshes are chosen to 1:1 (width: height). The compared mesh sizes are 30:30, 25:25 and 20:20 mm. A comparison as percentage in ultimate load and displacement, is performed be- tween the different meshes and the experimental results. The increase in percentage is calculated according to the equations 8 and 9.

( 𝐌𝐞𝐬𝐡 𝟐𝟓: 𝟐𝟓 − 𝐌𝐞𝐬𝐡 𝟑𝟎: 𝟑𝟎

𝐌𝐞𝐬𝐡 𝟑𝟎: 𝟑𝟎 ) ∗ 100 (9)

( 𝐌𝐞𝐬𝐡 𝟐𝟎: 𝟐𝟎 − 𝐌𝐞𝐬𝐡 𝟐𝟓: 𝟐𝟓

𝐌𝐞𝐬𝐡 𝟐𝟓: 𝟐𝟓 ) ∗ 100 (10)

Side near surface mounted reinforcement (S-NSM) 3.6.1

In this subchapter results from mesh sensitivity analysis are presented. The mesh, 30:30 is performed at first and later decreased by 5 mm in two steps. Thus, mesh 25:25 and 20:20 explained above. At first, the results are pre- sented as a percentage of increase or decrease in ultimate load and displacements, compared to previous mesh.

S-NSM 1

When decreasing the mesh size from 30:30 mm to 25:25 the ultimate load increases by 4 % and the displacements by 6,5 %. Moreover, when decreasing the mesh size from 25:25 mm to 20:20 mm, the ultimate load increases by 1,74 % and the displacement increases by 12,44 %.

Compared to the experimental tests all mesh sizes underestimated the ultimate load and displacement. The mesh

size of 30:30 mm underestimated the ultimate load by 6,71 % and displacement 16,96 %. The mesh size of 25:25

mm underestimated the ultimate load by 3.01 % and displacement by 11,55 %. The mesh size of 20:20 underes-

timated the experimental results the least, the ultimate load was underestimated by 0,54 % and the displacement

by 1,32 %.

Analysis with FEM

31

Figure 3-14: Mesh analysis of side near surface mounted beam 1 S-NSM 2

When decreasing the mesh size from 30:30 mm, the ultimate load and displacement are decreased by 2,85 % and 9,19 %. While changing the mesh size from 25:25 to 20:20 the ultimate load and displacement increased by 8,54

% and 23,8 %.

Compared to the experimental results, mesh size 30:30 mm underestimates the ultimate load and displacement by 8,91 % and 13,78 %. The mesh size 25:25 shows a bigger difference, underestimating the ultimate load and displacement by 11,51 % and 21,70 %. The most promising mesh is the mesh size 20:20 which underestimates the experimental results by 4 % of the ultimate load and 2 % of the displacement at ultimate load, see Figure 3-15.

Figure 3-15: Mesh analysis of side near surface mounted beam 2 S-NSM 3

When decreasing the mesh size from 30:30 mm to 25:25 the ultimate load is increased by 4,24 % and the displacement is decreased by 2,35 %. When decreasing the mesh size further to 20:20 an increase can be noted in both ultimate load and displacement, 3,06 % and 12,38 %, compared to mesh size 25:25.

Compared to the experimental results all mesh sizes underestimated both the ultimate load and displacements.

The mesh size 30:30 underestimates the ultimate load by 10,82 % and displacement by 10,45 %, mesh size 25:25 underestimated the results by 7,04 and 12,56 % and the mesh size 20:20 underestimated the ultimate load and displacement by 5 % and 3 %, see Figure 3-16.

0 25 50 75 100 125 150 175 200

0 10 20 30 40 50 60 70 80

Lo ad [ kN ]

Displacement [mm]

S-NSM 1

S1 20:20 mm S1-30:30 mm S1-25:25 mm LVT mean

0 25 50 75 100 125 150 175 200

0 10 20 30 40 50 60 70 80

Lo ad [ kN ]

Displacement [mm]

S-NSM 2

S2-25:25 mm

S2-20:20mm

S2-30:30 mm

LVDT- mean

32 Figure 3-16: Mesh analysis of side near surface mounted beam 3

Bottom near surface mounted reinforcement (B-NSM) 3.6.2

The same process is performed to compare results from different mesh sizes with experimental results for bottom near surface mounted CFRP.

B-NSM 1

Reducing the mesh size from 30:30 mm to 25:25 mm, the ultimate load decreases by 5,99 % and displacement increased by 13,10%. When reducing the mesh further from 25:25 mm to 20:20 mm the ultimate load and displacement increases by 3,55 % and 0,18 %.

However, when the results above are compared with the experimental results, all mesh sizes show a higher ultimate load and displacement except for the displacement of mesh 25:25 mm. The mesh size 30:30 show a higher ulti- mate load and displacement by 7,30 % and 10,63 %, the mesh size 25:25 mm show a very small difference, a higher value of 0,87 % in ultimate load and a lower displacement of 3,87 %. Moreover, the mesh size 20:20 gave a higher value in both ultimate load and displacement by 10 % and 10 %, see Figure 3-17.

Figure 3-17: Mesh analysis of bottom near surface mounted beam 1 0

25 50 75 100 125 150 175 200

0 10 20 30 40 50 60 70 80

Lo ad [ kN ]

Displacement [mm]

S-NSM 3

S3-30:30 mm S3-25:25 mm LVDT Mean S3-20:20 mm

0 25 50 75 100 125 150 175 200

0 10 20 30 40 50 60

Lo ad [ kN ]

Displacement [mm]

B-NSM 1

20:20 mm

25:25 mm

30:30 mm

LVDT-B1-Mean

Analysis with FEM

33 B-NSM 2

Reducing the mesh size from 30:30 mm to 25:25 mm, the ultimate load is increased by 3,42 and displacement is decreased by 0,39 %. When reducing the mesh size further from 25:25 mm to 20:20 mm the ultimate load and displacement are decreased by 2,57 % and 5,18 % respectively.

When the results above are compared with the experimental results, all mesh sizes show a higher ultimate load and smaller displacement. The mesh size 30:30 show a higher ultimate load by 2,85 % and smaller displacement by 0,33 %, the mesh size 25:25 mm show a higher value of 6,37 % in ultimate load and a smaller displacement of 0,73 %. The mesh size 20:20 gave a higher value in ultimate load with a value of 3,64 % and a smaller displace- ment by 5,86 %, see Figure 3-18.

Figure 3-18: Mesh analysis of bottom near surface mounted 2 B-NSM 3

Reducing the mesh size from 30:30 mm to 25:25 mm, the ultimate load is decreased by 0,39 % and displacement is decreased by 6,45 %. When reducing it further from 25:25 mm to 20:20 mm the ultimate load and displace- ment are increased by 3,82 % and 8,89 % respectively.

When the results above are compared with the experimental, all mesh sizes show a higher ultimate load and displacement. The mesh size 30:30 show a higher ultimate load by 8,19 % and a higher displacement by 7,60 %, the mesh size 25:25 mm show a higher value of 7,76 % in ultimate load and displacement of 0,66 %. The mesh size 20:20 gave a higher value in ultimate load with a value of 3 % and a higher displacement by 8 %.

Figure 3-19: Mesh analysis bottom near surface mounted 3 0

25 50 75 100 125 150 175 200

0 10 20 30 40 50 60 70

Lo ad [ kN ]

Displacement [mm]

B-NSM 2

30:30 mm 25:25 mm 20:20 mm LVDT Mean

0 25 50 75 100 125 150 175 200 225

0 10 20 30 40 50 60

Lo ad [ kN ]

Displacement [mm]

B-NSM 3

30:30 mm

20:20 mm

25:25 mm

LVDT_3