C:Documents and SettingsMilan.U-DNEVNOJ-SOBIDesktopprint 293

Mira Vasic

Design procedures for the use

o f E B F R P i n s h e a r

strengthening of reinforced

concrete beams.

Italy | 2011

Design Procedures for the Use of EB FRP in Shear Strengthening of Reinforced Concrete Beams

Erasmus Mundus Programme

ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS I

DECLARATION

Name: Mira Vasić

Email: [email protected]

Title of the

Msc Dissertation:

Design procedures for the use of EB FRP in shear strengthening of reinforced

concrete beams

Supervisor(s): Prof. Carlo Pellegrino

Year: 2011

I hereby declare that all information in this document has been obtained and presented in accordance

with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I

have fully cited and referenced all material and results that are not original to this work.

I hereby declare that the MSc Consortium responsible for the Advanced Masters in Structural Analysis

of Monuments and Historical Constructions is allowed to store and make available electronically the

present MSc Dissertation.

University: University of Padova

Date: September 2nd, 2011

Signature: ___________________________



II ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS III

ACKNOWLEDGEMENTS

I would like to exspress my acknowledge to European Commission and SAHC consortium for

providing me financial support in terms of Erasmus Mundus scholarship and making continuation of

my education in European Union possible.

I would like to give my gratitude to Prof. Carlo Pellegrino from University of Padova for being excellent

tutor and making work on this thesis enjoyable and very productive study, but also for guiding and

advicing me in my future cariere. Many thank to ing. Tommaso D'Antino who has been very helpful

during this research.

I want to present acknowledgment to all professors that gave us lectures during first seven months at

Politecnical University of Barcelona and made this SAHC course precious professional experience.

Special thank to Prof. Pere Roca for taking care of us while staying in Barcelona, organizing trips to

Tarragona and Palma de Mallorca and being supervisor for my coleagues and me during our work on

Tarragona Aqueduct.

On the other hand, I want to say thanks to coleagues that I met during my staying in Spain. All of you

changed my life and made this year amasing as it was, in one way or another. Guys, thank you for all

moments that we shared and all things that you have thougth me.

I also want to give a special thanks to flatmates with whome I shared rooms, flats or hotels in last year.

Thank you for learning me important life lesons and making me being a better person. I am particulary

greateful to my dear greek friends and coleagues, Evina and Thanasi, thank you for each 'gelato' and

'spritz', but also for being so good company in Padova.

I would like to thank to my family for endless support that they were giving me every day on Skype, but

more important also 'offline'. Dad, mom, brow and sisters...Thank you. Sincerely thanks to all my

friends in Serbia and world wide who didn't gave up on me even being thousand kilometers away,

especialy to you Jelena. Also I want to thank to Ivan Ignjatović for supporting me and believing in me.

At last but not the least, I would like to thank to my A. G. for finding me and making things perfect,

giving me all his love...Thank you for beeing you.



IV ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS V

ABSTRACT

The aim of this work is assessment and analysis of the reliability of the most well-known design

models, available for the prediction of the contribution of fiber reinforced polymer (FRP) systems to the

shear capacity of strengthened reinforced concrete beams. In this study, current analytical

formulations for basic shear design and shear strengthening design are presented in detail and main

problems and lacks, being the motivation of this work, are highlighted.

The research is based on the comparison of previous experimental studies with both current design

guidelines and design models recently proposed by several authors, considering also various

recommendations for the angle of inclination of shear cracks. Assessment of design procedures was

done using probabilistic aproach, and several descriptive statistical measures, such as the average

(AVG) and the coefficient of variation (CoV), have been obtained from database, regarding different

strengthening schemes. A more detailed analysis of reduced database was made, considering only U-

jacketed configurations with transversal steel.

Because of its good performance, a detailed investigation on Pellegrino and Modena (2008) model

has been made and in order to predict better results, modification of this model has been proposed.



VI ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS VII

Titolo

della Tesi di Master:

Procedure di Calcolo per l’Uso di EB FRP nel Rinforzo a Taglio di Travi in

Cemento Armato

ESTRATTO

Lo scopo del presente lavoro consiste nella valutazione e nell’analisi dell’affidabilità dei più noti

modelli di calcolo disponibili per la previsione del contributo dei sistemi di rinforzo in materiale

composito (FRP) per la resistenza a taglio di travi in cemento armato. In tale studio sono presentate in

dettaglio le attuali formulazioni analitiche per il progetto a taglio senza rinforzo e per il progetto a taglio

di elementi rinforzati con FRP, e sono evidenziati principali problemi e carenze.

La ricerca è basata sul confronto di precedenti studi sperimentali con gli attuali codici normativi e

modelli di calcolo, recentemente proposti da diversi autori, considerando anche l’inclinazione

dell’angolo delle fessure a taglio. La valutazione delle procedure di progetto è stata effettuata usando

diverse misure statistiche, come la media (AVG) ed il coefficiente di variazione (CoV), ottenuti dal

database, con riferimento a diversi schemi di rinforzo. È stata condotta un’analisi più dettagliata su un

database ridotto, considerando solo la configurazione di rinforzo a U con armatura trasversale.

Date le buone prestazioni, è stato studiato in dettaglio il modello di Pellegrino e Modena (2008) e, al

fine di predire migliori risultati, è stata proposta una lieve modifica di tale modello.



VIII ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS IX

Naslov

Master Disertacije:

Proračun otpornosti na smicanje greda ojačanih FRP laminatima

REZIME

Cilj ovog rada je procena pouzdanostii najpoznatijih modela za proračun udela sistema ojačanja greda

putem/pomoću polimera armiranih vlaknim (FRP sistema) u nosivosti na smicanje armiranobetonskih

greda. U ovoj studiji, detaljno su objašnjene važeće analitičke formulacije za proračun nosivosti na

smicanje neojačanih/klasičnih i ojačanih greda, a takođe su istaknuti glavni problemi i nedostaci ovih

procedura, što je ujedno i (primarni cilj) ovog rada.

Istraživanje je bazirano na poređenju dosadašnjih, u literaturi dostupnih eksperimentalnih ispitivanja

greda ojačanih FRP sistemima sa važećim standardima, ali i sa modelima koji su u skorije vreme

predloženi od strane više autora; sa posebnim osvrtom na različite preporuke propisa za vrednost ugla

smičuće prsline. Za analizu ovih proračunskih modela, korišćen je probabilistički pristup u okviru koga

su su prosečna vrednost i koeficijent varijacije, dobijene obradom baze podataka za različite šeme

ojačanja. Detaljno je analizirana baza podataka i redukovana na podatke koji se odnose samo na U-

konfiguracije ojačanja.

S obzirom na relativno dobre rezultate poređenja eksperimentalnih i teorijskih rezultata dobijenih

upotrebom modela Pelegrina i Modene (2008), ovaj model je detaljno analiziran, i u cilju njegovog

poboljšanja određene modifikacije su predložene u ovom radu.



X ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS XI

TABLE OF CONTENT

1. INTRODUCTION 1

1.1 Motivation and objectives of the study 1

1.2 Outline of the study 2

2. CURRENT ANALYTICAL FORMULATIONS 3

3. REVIEW OF CURRENT DESIGN GUIDELINES FOR NON-STRENGTHENED

STRUCTURES 9

3.1 EUROCODE 2 (2004) 9

3.2 ACI 318M-08 (2008) 11

3.3 fib MC10 (2010) 11

4. REVIEW OF CURRENT DESIGN GUIDELINES FOR STRENGTHENED STRUCTURES 13

4.1 fib - TG 9.3 (2001) 13

4.2 CNR-DT200 (2004) 15

4.3 ACI 440.2R (2008) 18

4.4 fib ’09 - draft 2009 20

5. RECENT DESIGN MODEL PROPOSALS 23

5.1 Chen and Teng (2003a) 23

5.2 Carolin and Täljsten (2005) 26

5.3 Pellegrino and Modena (2008) 27

5.4 Bukhari et al. (2010) 29

5.5 Modifi and Chaallal (2011) 30

6. METHODOLOGY FOR ANALYZING EXPERIMENTAL VS THEORETICAL VALUES 33

6.1 Database Description 33

6.2 The Total Shear Strength 40

6.3 Analyzed design procedures 40

6.4 General statistical analysis procedures 41



XII ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS

7. RESULTS AND DISCUSSION 43

7.1 Assessment of Pellegrino and Modena (2008) model and its improvement 43

7.2 Results obtained using the DB 50

7.3 Results obtained using the RDB 51

8. CONCLUSIONS 55

8.1 Model of Pellegrino and Modena 55

8.2 Basic codes 55

8.3 Angle inside basic code 55

8.4 Models 56

8.5 U-jacketing with transversal steel configuration 56

8.6 General conclusions 56

9. REFERENCES 57



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS XIII

LIST OF FIGURES

Figure 1 - Lateral view of FRP shear strengthening (CNR-DT200 2004) 3

Figure 2 - Cross section of FRP strengthened members (CNR-DT200 2004 3

Figure 3 - FRP Shear contribution according to CNR (Barros, Dias and Lima 2007) 5

Figure 4 - Failure modes of beams by Pellegrino and Modena in (2002) and (2006) 6

Figure 5 - Notation for angles of shear cracks and FRP fiber orientation according to fib ‘01 (2001) 13

Figure 6 - Notation for shear strengthening using FRP strips (CNR-DT200 2004) 15

Figure 7 - Illustration of the dimensional variables used in shear-strengthening recommendations of ACI 440.2R (American Concrete Institute (ACI) Committee 440 2008) 19

Figure 8 - Chen and Teng notation for a general shear strengthening scheme (Chen, Teng and Chen, RC beams shear-strengthened with FRP: shear resistance contributed by FRP 2010) 24

Figure 9 - Fiber alignment and crack angle, Carolin and Taljsten (2005) 26

Figure 10 - Shape of the fracture surface of “U-jacketed” (a) and side-bonded beams (b) 27

Figure 11 - Forces acting in the cross section of “U-jacketed” (a) and side-bonded beams (b) 28

Figure 12 - U-jacketed configurations without (graphs a and b) and with transversal reinforcement graphs c and d) 45

Figure 13 - Side bonded configurations without (graphs a and b) and with transversal reinforcement graphs c and d) 46

Figure 14 - Best prediction results in general overview: U-jacketed configurations without and with transversal steel and side bonded configurations without and with transversal steel (graphs a,b,c and d, respectively) 50



XIV ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS XV

LIST OF TABLES

Table 1 - Experimental Database 35

Table 2 - Continuation of Table 1 36




Table 6 - Design procedures for analyzing DB 40

Table 7 - Comparison of results for Modena and Pellegrino model 44

Table 8 - Values for Coefficient of Variation (CoV) obtained from DB 47

Table 9 - Values for the Average (AVG) obtained from DB 48

Table 10 - Results from RDB for θ=45°and θ=36° 52

Table 11 - Results from RDB for θ=var and θ=35/45° 53



XVI ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS 1

1. INTRODUCTION

Necessity for structural strengthening may be induced by variety of reasons, such as ageing, lack of

maintenance, damages due to accidental or natural causes, degradation caused by poor initial

construction conditions or bad quality of used material; but also with other problems related to upgrading

or rehabilitation of existing reinforced concrete (RC) structures.

In last two decades, development of materials that will replace those used in traditional techniques of

strengthening, such as steel and concrete, resulted in experimental investigation of their application,

efficiency and safety of techniques, durability, properties of material itself and compatibility with other

materials.

As one of the methods that has been widely accepted all over the world, bonding of fiber reinforced

polymer (FRP) composites with a suitable epoxy adhesive, has shown to be applicable to many types of

RC structures. Currently, the use of this modern material may be in general classified as axial (confining),

flexural and shear strengthening. Many efforts are made in proposing design recommendations regarding

flexural strengthening and have been experimentally confirmed in the past. On the other hand, the shear

behaviour of RC beams strengthened with FRP is still not well understood and interpreted in current

design guidelines and models.

1.1 Motivation and objectives of the study

Since the usage of FRP in building retrofit has shown as an effective technique, the field of its application

is continuously growing. The result in last decade is implementation of experimentally based analytical

models for design, detailing and installations of FRP strengthening systems into design guidelines and

codes. The intent of the assessment of existing recommendations and models is to verify their validity,

safety and quality of their predictions.

This work reviews not only the recommendations for shear strengthening analysis produced by the

Fèderation Internationale du Bèton, fib buletin 14 (2001) and fib bulletin – draft (2009), the Italian National

Research Council (CNR-DT200 2004) and the American Concrete Institute ACI440 (2008); but also

models recently proposed by several groups of authors: Chen and Teng (2003a), Carolin and Täljsten

(2005), Pellegrino and Modena (2008), Bukhari et al. (2010), and Modifi and Chaallal (2011). This study

also addresses the main lacks of design procedures for strengthening of RC beams with FRP, such as

non considering the interaction between the external FRP and internal transversal steel reinforcement, or

assuming the constant angle of diagonal crack with respect to the member axis, and to be equal to 45°.

Since many scientists such as Pellegrino and Modena (2002), Barros (2007) and Colotti (2011) have



2 ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS

pointed out strong influence of these parameters to the efficiency of the shear strengthening rehabilitation

technique, further investigation in this field and improvement of codes and models is necessary in order to

obtain more sophisticated results.

1.2 Outline of the study

This work is a critical review of current guidelines and recently proposed models, regarding weaknesses of

shear strengthening design procedures.

A description of the basis of the current codes for non-strengthened structures and their design procedure

are presented in Chapter 3.

In Chapter 4, a description of the analytical approach of the current design guidelines is given, while

recently proposed models by several authors and their proposed equations are presented in Chapter 5.

Collected data base of an experimental investigation on reinforced concrete (RC) rectangular beams

strengthened in shear with externally bonded FRP is presented. Methodology for analyzing experimental

vs. theoretical values and general statistical procedure used in this study is explained in Chapter 6.

Finally, a comparison between different basic codes and models was performed within the objective of

study. Results are given and discussed in Chapter 7. In this chapter are also given results, discussion and

proposal of modified Pellegrino and Modena model.

At the end, in Chapter 8, conclusions considering basic codes, models, angles of shear cracks and

general conclusions are summarized.




2. CURRENT ANALYTICAL FORMULATIONS

Shear strengthening is performed by applying one or more layers of FRP material externally bonded to the

surface of the member to be strengthened (Figure 1). External FRP reinforcement can be applied in a

discontinuous fashion, with gaps between following strips, or continuously, with strips next to each other.

Figure 2 shows three FRP strengthening configurations: side bonding, U-wrapped, and completely

wrapped beams.

Figure 1 - Lateral view of FRP shear strengthening (CNR-DT200 2004)

Figure 2 - Cross section of FRP strengthened members (CNR-DT200 2004)

Many doubts and uncertainties regarding the reliability of parameters used in guidelines are addresses by

scientist during last few years of research. One of them is the approach in which the shear strength of a

member is determined by adding individual contributions of concrete, steel and FRP:

�� = �� + �� + �� (1)




This simple adding of force components and independency between them is one of the assumptions that

have shown as inadequate interpretation of strengthened member behaviour, since it eliminates

contribution of FRP (��) in nominal shear strength. Several models for strengthened structures propose

equations for contribution of FRP composites (��), which configures in equation (1), while for

contributions of concrete (��) and steel (��) they recommend usage of current guidelines for non-

strengthened structures.

Most of the equations that predict contribution of FRP are not calibrated taking into account different

approaches of basic codes, which is consequence of individual interpretation of these codes by scientists

who are proposing models. Current basic codes for nonstrengthened structures, Eurocode 2, ACI 318M-

08 and fib MC10 have different approaches to shear design procedure regarding contributions of steel and

concrete, but also the angle of shear crack.

Lima and Barros (2011) performed reliability analysis of the collected experimental data and concluded

that the orientation of the critical shear crack �� may be quite different from the suggested value

recommended by the design codes. This indicated that �� depends on the existing conventional shear

reinforcement in the strengthened beam. This fact is one more direct implication for the FRP contribution

to the shear resistance, since it supports the unreliable predictions obtained in many cases with the

studied formulations proposed by guidelines.

The program of experiment performed by a group of authors (Barros, Dias and Lima (2007)) included four

series of shear reinforced concrete beams. During comparison of experimental and theoretical data,

several different values for angle of shear crack were considered (Figure 3 - FRP Shear contribution

according to CNR ). Although using various values of the critical shear crack, each series was constituted

by beams with only strips or FRP sheet as shear reinforcement and in this way failed in considering steel

and FRP reinforcement interaction.




Figure 3 - FRP Shear contribution according to CNR (Barros, Dias and Lima 2007)

On the other hand, these authors (Barros, Dias and Lima 2007) were analyzing problems with parameters

that are involved in design procedure, but they did not consider the computation of interacting

contributions of FRP and steel to the nominal shear strength of beams. Usually, experimental values were

compared with analytical ones, considering only contribution of FRP as independent component:

��,�� = �� + �� (2)

��,�� = �� + �� + ��,�� (3)

��,�� = ��,�� − ��,�� (4)

Where ��,�� is the shear resistance of the non-strengthened reference control tested beam, ��,�� is the

shear resistance of the strengthened tested beam and ��, �� and ��,�� are, respectively, the concrete,

stirrup and FRP contribution to the global shear resistance.

In this study, a total shear resistance of beams will be analyzed, as it is in details explained in section 6.2.




Another observation that impacts on reliability of models is not taking into account interaction between

FRP and steel. Comparison of experimental tests and current analytical models, performed by Pellegrino

and Modena (2008), has shown that the interaction between an external FRP and an internal transverse

steel reinforcement, which is not considered in some actual code recommendations, strongly influences

the efficiency of the shear strengthening rehabilitation technique.

In addition, one of the reasons why the shear behaviour of RC beams strengthened with FRP is not well

understood is that most of the tests in past have been carried out on simply supported beams without

steel stirrups, but models for both configurations with and without steel are based on these experiments.

Experimental observations of Pellegrino and Modena in (2002) and (2006) have shown different typical

failure modes of beams for different initial conditions – types of reinforcement and FRP strengthening

configurations (Figure 4).

Figure 4 - Failure modes of beams by Pellegrino and Modena in (2002) and (2006)




These authors concluded from experimental results that for U-jacketed beams, both with internal steel

stirrups (Figure 4a) and without (Figure 4b), peeling-off of the FRP with the concrete cover occures in a

lateral triangular portion above the principal diagonal crack from bearing location to the load point. On the

other hand, for side-bonded beams, with same initial steel reinforcement (with internal steel stirrups -

Figure 4c and without - Figure 4d), this peeling-off occures above the principal diagonal crack.

Analyzing a computational model for shear interaction between FRP strips and steel stirrups, a

group of authors (G. Chen, J. Teng, et al., Interaction between Steel Stirrups and Shear-Strengthening

FRP Strips in RC Beams 2010) concluded that the maximum shear contributions of steel stirrups and FRP

may not be reached simultaneously, so that their combined contribution may be less than the sum of the

respective peak values of �� and ��. Also, in the evaluation of shear strength, the simultaneous use of

these maximum values is an unconservative approach. For accurate evaluation of the shear resistance

they recommended the determination of the maximum value of the combined contribution of steel stirrups

and FRP strips.

The parameters that have the greatest influence on the shear behavior of RC members strengthened with

EB FRP and the role of these parameters in current design codes were deeply analyzed by Modifi and

Chaallal (2011). One of them is cracking angle, for which they concluded that should be implemented in

calculation of �� and proposed their design equation (this proposal will be disscused later on).

Finally, main questions that are result of state of art and will be analyzed in this study are:

1. Are the approaches recommended by current basic codes still valid when strengthening is

applied?

2. Do the current recommendations for shear crack angle θ, both in basic codes and models for

strengthened structures have impact on results?

3. Does the presence of transverse internal steel or external FRP have any effect on the shear

design procedure?







3. REVIEW OF CURRENT DESIGN GUIDELINES FOR NON-STRENGTHENED

STRUCTURES

As a remark, it has to be said that the equations reviewed in this study are presented in the units

of the codes, unless otherwise specified. The names and symbols of the used variables correspond to the

ones used in the codes, models or articles investigated and have been explained in details or if it possible

illustrated with figures.

3.1 EUROCODE 2 (2004)

For the design of shear reinforcement, Eurocode (2004) recommends the variable strut inclination method.

In this method, it is assumed that the shear force is entirely resisted by a truss consisting of concrete

struts acting in compression equilibrated by shear reinforcement in tension. Limiting values for the angle of

the concrete compression struts to the longitudinal axis of the beam are:

21,8∘ ≤ ≤ 45∘ (5)

Indicated by:

1 ≤ �� ≤ 2,5 (6)

The effective crushing strength of concrete is:

��,� � = !�" ∙ $" ∙ 0,9 ∙ ' ∙ () ∙ *��/(cot + tan )

(7)

For *�1 ≤ 60345 6) = 0,6

For *�1 ≥ 60345 6) = 0,9 − *�1/200 > 0,5

!�" = 1

a) For members not requiring design shear reinforcement, the design value for the shear

resistance is given by:

�� = 9:;<��,�; ��,� �> (8)




��,� = ?@��,� ∙ A ∙ (100 ∙ B) ∙ *�1)) CD + A) ∙ E��F ∙ $" ∙ ' (9)

With a minimum of:

��,��G� = H6�G� + A) ∙ E��I ∙ $" ∙ ' (10)

Where *�1 is in [MPa], d in [mm]

A = 1 + J200' ≤ 2,0 (11)

B) = K�L$" ∙ ' ≤ 0,02 (12)

6�G� = 0,035 ∙ AC/N ∙ *�1)/N

(13)

Where K�L is the area of the tensile reinforcement and $" is the smallest width of the cross-section in the

tensile area [mm]. The recommended value for @��,� is 0,18/γc, and for k1 is 0,15.

b) For members with inclined shear reinforcement, the design value for the shear resistance is

given by:

�� = 9:;<��,�; ��,� �> (14)

And shear reinforcement in tension capacity is:

��,� = K�"O ∙ 0,9 ∙ ' ∙ *P"� ∙ (�� + �� Q) ∙ O:; Q (15)

In equations (7) and (15), represents the angle of shear cracks, and it is recommended by Eurocode 2

to be assumed equal to 45° unless a more detailed calculation is made.




Equation (14) shows that the variable angle truss model is an idealisation in which whole shear force is

assumed to be resisted by the stirrups. In reality, part of the shear force is resisted by ��, which is not

constant as assumed in equation (9).

3.2 ACI 318M-08 (2008)

Design of cross sections subject to shear should be based on nominal shear strength computed by:

�� = �� + �� (16)

Where �� is nominal shear strength provided by concrete, and calculated as:

�� = 0,17 ∙ S ∙ T*′� ∙ $" ∙ ' (17)

�� is nominal shear strength provided by shear reinforcement, and calculated for:

a) Member where used shear reinforcement is perpendicular to axis of member

�� = KV ∙ ' ∙ *P�O (18)

Where KV is the area of shear reinforcement within spacing O.

b) Member where inclined stirrups are used as shear reinforcement:

�� = KV ∙ ' ∙ (sin ! + cos !) ∙ *P�O (19)

Where ! is the angle between inclined stirrups and longitudinal axis of the member, and s is measured in

direction parallel to longitudinal reinforcement.

From equation (19) it can be observed that ACI 318M-08 (2008) assumes angle of shear cracks to be

equal to = 45°, and reliability of this approach will be analyzed in further study of this document.

3.3 fib MC10 (2010)

The design shear resistance of a web or slab shall be determined as:

�� = 9:;<��,� + ��,�; ��,� �> (20)




��,� � = A� ∙ *�1Z� ∙ $" ∙ 0,9 ∙ ' ∙ �� + �� !1 + (�� )N (21)

Where is the selected inclination of the compression stresses; ! is the inclination of the stirrups relative

to the beam axis, so the design shear resistance provided by the stirrups may be calculated as:

��,� = K�"O" ∙ 0,9 ∙ ' ∙ *P"� ∙ (cot + cot !) ∙ sin ! (22)

The design shear resistance attributed to the concrete can be taken as:

��,� = AV ∙ T*�1Z� ∙ $" ∙ 0,9 ∙ ' (23)

Where the value of T*�1 shall not be taken as greater than 8 MPa.

fib MC10 proposes three levels of approximation in terms of complexity, effort and level of detail. In this

study, considering available data on experimental results that will be analyzed, first level will be used:

Level I Approximation:

= 45° or = 36° (in case of early design stages) A� = 0,5 ∙ [ 30*P1\) CD ≤ 0,5 (24)

for B" = 0

AV = 2001000 + 1,3 ∙ 0,9 ∙ ' ≤ 0,15 (25)

for B" ≥ 0,08 ∙ T�]^�_^

AV = 0,15

(26)




4. REVIEW OF CURRENT DESIGN GUIDELINES FOR STRENGTHENED

STRUCTURES

Current guidelines are truss-model based, and adopted notation to define the main geometric properties

of FRP shear reinforcement is given in figures and has been reviewed for each guideline.

4.1 fib - TG 9.3 (2001)

Provisions of fib - TG 9.3 (2001) on shear strengthening of RC beams are based on the regression of

experimental results carried out by Triantafillou and Antonopoulos (2000). The shear capacity of a

strengthened element according to (fib task group 9.3 2001) should be calculated as follows:

�� = min (�� + �"� + �� , ��,N) (27)

Where �� and �"� are designed values of concrete and transversal steel, respectively and can be

calculated according to current basic codes for nonstrengthened structures.

Figure 5 - Notation for angles of shear cracks and FRP fiber orientation according to fib ‘01 (2001)

�� is the FRP contribution, and is given by:

�� = 0,9 ∙ a��,� ∙ b�c ∙ B� ∙ $" ∙ ' ∙ (cot + cot !) ∙ sin ! (28)

Where a��,� is design value of effective FRP strain. In this model, the effective strain is governed by the

FRP strengthening configuration and the FRP material type. The guideline states that the effective strain

is a function of the axial rigidity of FRP(b�c ∙ B�) and the compressive strength of concrete as follows:




a) in case of FRP fully wrapped configuration

a��,� = 0,17 ∙ d *��N CDb�c ∙ B�ef,Cf ∙ a�c (29)

b) in case of Side or U-shaped FRP jackets

a��,� = 9:; g0,65 ∙ d *��N CDb�c ∙ B�ef,hi ∙ 10jC ; 0,17 ∙ d *��N CDb�c ∙ B�ef,Cf ∙ a�ck (30)

Where b�c is elastic modulus of FRP in the principal fibre orientation in [GPa]; *�� is cylindrical

compressive strength of concrete in [MPa]; B� is FRP reinforcement ratio, which is for continuously

bonded shear reinforcement of thickness �� ($" is minimum width of the concrete cross section over the

effective depth) equal to:

B� = 2 ∙ �� ∙ sin ! /$" (31)

Or for FRP reinforcement in the form of strips or sheets of width $" at spacing O� is equal to:

B� = H2 ∙ ��/$"I ∙ H$�/O�I (32)

Where $" is minimum width of cross section over the effective depth; ' is effective depth of cross section; ! is the angle between principal fiber orientation and longitudinal axis of member; is the angle of

diagonal crack with respect to the member axis and is assumed to be equal to 45°.




4.2 CNR-DT200 (2004)

The Italian CNR-DT200 (2004) guidelines provisions are based on a research study by Monti et al. (2003)

and in Figure 6, notation used in this code is given. Shear capacity of FRP strengthened members can be

evaluated as follows:

�� = 9:;<��,�� + ��,� + ��,�; ��,� �> (33)

Figure 6 - Notation for shear strengthening using FRP strips (CNR-DT200 2004)

Where ��,�� and ��,� represent concrete and steel contribution to the shear capacity according to the

current building code, and ��,� is the FRP contribution to the shear capacity. In this guideline, the FRP

contribution related to each of the FRP strengthening configurations is given by:

a) In case of FRP side bonding configuration

��,� = 1Z�� ∙ 9:;l0,9 ∙ '; ℎ"n ∙ *�� ∙ 2 ∙ �� ∙ O:; QO:; ∙ o�p� (34)

b) In case of FRP U-wrapped or completely wrapped configuration

��,� = 1Z�� ∙ 0,9 ∙ ' ∙ *�� ∙ 2 ∙ �� ∙ (�� + �� Q) ∙ o�p� (35)




Where the partial factor is assumed to be Z�� = 1,20, d is the member effective depth, ℎ" is the

crossection depth, *�� is the effective FRP design strength, �� is the thickness of the adopted FRP

system, β is the fibers angle with respect to the member longitudinal axis, θ represents the angle of shear

cracks (to be assumed equal to 45° unless a more detailed calculation is made), and o� and p� are FRP

width and spacing, respectively, measured orthogonally to the fiber direction. For FRP strips installed one

next to each other, the ratio o� / p� shall be set equal to 1.0.

Effective FRP design strength:

a) FRP side bonding

*�� = *�� ∙ q�G�,�r9:;l0,9 ∙ '; ℎ"n d1 − 0,6 ∙ J s�rq�G�,�reN (36)

q�G�,�r = q�G� + l�r (37)

q�G� = 9:;l0,9 ∙ '; ℎ"n − l� ∙ sin Q (38)

l�r = O�*��/b� ∙ sin Q (39)

b) U-wrap configurations

*�� = *�� ∙ u1 − 13 ∙ l� ∙ sin Q9:;l0,9 ∙ '; ℎ"nv (40)

c) Completely wrapped members

*�� = *�� ∙ u1 − 16 ∙ l� ∙ sin Q9:;l0,9 ∙ '; ℎ"nv + 12 ∙ (w� ∙ *�� − *��) ∙ u1 − l� ∙ sin Q9:;l0,9 ∙ '; ℎ"nv (41)

w� = 0,2 + 1,6 ∙ x�$" (42)




0 ≤ x�$" ≤ 0,5 (43)

Where x� is the corner radius of the section to be wrapped, and $" is the width of the member. The second

term of equation (41) shall be considered only when it is greater than zero. The optimal bonded length le,

may be estimated as follows:

s� = J b� ∙ ��2 ∙ *�� (44)

Where b� and �� are Young modulus of elasticity and thickness of FRP, respectively, and *�� is the

average tensile strength of the concrete.

The specific fracture energy Γz1, of the FRP – concrete interface may be expressed as follows (forces in

[N], lengths in [mm]):

Γz1 = 0,03 ∙ A{T*�1 ∙ *�� (45)

Where *�1 is the characteristic strength of concrete, A{ is a geometric coefficient depending on both width

of the strengthened beam $ and width of the FRP system $�; and A{ can be written as follows:

A{ = | 2 − $�$1 + $�400 (46)

Where $�/$ ≥ 0.33 (if $�/$ < 0.33, the value for kb corresponding to {�{ = 0.33 is adopted). For

laminate/sheet end debonding it is assumed that the provided bond length is equal to or larger than the

optimal bonded length, the ultimate design strength *�� can be calculated as follows:

*�� = 1Z�,� ∙ TZ� J2 ∙ b� ∙ Γz1�� (47)




Where the partial factor is Z�,� = 1,20 (for FRP debonding failure mode and strengthening system with

certification of each component as well as the final product to be applied to a given support) and Z� = 1,5

(partial factor for concrete).

For external FRP reinforcement in the form of discrete strips, strips width, wf (mm), and center-

to-center spacing between strips, pf (mm), shall not exceed the following limitations, respectively:

50 mm ≤ wf ≤ 250 mm, and wf ≤ pf ≤ min{0.5 ⋅ d,3 ⋅ wf ,wf + 200 mm}.

4.3 ACI 440.2R (2008)

The American Concrete Institute (American Concrete Institute (ACI) Committee 440 2008) guideline is

based on a research study by Khalifa (1998). In the ACI code, the total shear strength can be calibrated

as:

�� = �� + �� + �� (48)

Where �� is the reduction factor, and has value 0,95 for completely wrapped configuration and value 0,85

for three and two-opposite side schemes.

While contributions of steel �� and concrete ��, can be calculated using the current code for

nonstrengthened structures, the FRP contribution is given by:

�� = K�V ∙ *�� ∙ (sin ! + cos !) ∙ '�O� (49)

While:

K�V = 2 ∙ ; ∙ �� ∙ o� (50)

*�� = a�� ∙ b�� = K�V ∙ *�� ∙ (O:; ! + ��O !) ∙ '�O� (51)




Where K�V is area of FRP shear reinforcement with spacing O�; *�� is effective stress in the FRP; ! is the

angle between principal fiber orientation and longitudinal axis of member; '� is effective depth of FRP

flexural reinforcement; b� is tensile modulus of elasticity of FRP; a�� is effective strain level in FRP

reinforcement attained at failure. In Figure 7, an illustration of used variables is given.

Figure 7 - Illustration of the dimensional variables used in shear-strengthening recommendations of ACI

440.2R (American Concrete Institute (ACI) Committee 440 2008)

The effective-strain limit for full-wrap FRP systems is based on limiting the crack opening to ensure proper

aggregate interlocking of the concrete, whereas the effective strain for the bonded U-wraps and side-

bonded FRP systems is calculated based on the FRP-to-concrete bond mechanism as follows:

a) For completely wrapped members

a�� = 0,004 ≤ 0,75 ∙ a�� (52)

b) For two and three side wrappes

a�� = AV ∙ a�� ≤ 0,004 (53)

The bond-reduction coefficient AV can be computed from:




AV = A) ∙ AN ∙ �� 11900 ∙ a�� ≤ 0,75 (54)

�� = 23300 H; ∙ �� ∙ b�If,h� ≤ 0,75 (55)

A) = [*�� 27\N CD (56)

For U-wraps:

AN = '�V − �� '�V (57)

For two sides bonded:

AN = '�V − 2�� '�V (58)

As it can be observed from equation (49), ACI uses 45°- truss-angle analogy without variation of the

shear crack angle �x. And the shear strength provided by the FRP reinforcement is determined by

calculating the force resulting from the tensile stress in the FRP across the assumed crack.

4.4 fib ’09 - draft 2009

In this draft of new fib ’09 code for strengthened structures, side-wrapped section are allowed only for

near surface melted (NSM) reinforcement.

The shear capacity of a beam without shear reinforcement is calculated according to the formula:

�� = 9:;<��,� + ��; ��,� �> (59)

Where ��,� is determined according to paragraph 6.2.2 in (Eurocode, 2004). It is here suggested that a

crack angle of 45 ° is used.




The shear capacity of a beam with shear reinforcement is calculated according to the formula:

�� = 9:;<��,� + ��; ��,� �> (60)

Where ��,� is determined according to paragraph 6.2.2 in (Eurocode, 2004). It is here suggested that the

crack angle of 35 ° is used.

Shear contribution from FRP:

�� = K� ∙ a�� ∙ b� ∙ �� ∙ sin Q� (61)

a) Completely wrapped section (W):

The effective length, �� can be determined as:

�� = q ∙ (cot ! + cot Q�) (62)

The effective strain, a�� in the fibres is limited to:

a�� = 9:; �a�{,�a�c,�� (63)

Where:

a�{,� = J 2 ∙ ��b� ∙ �� (64)

�� = 0,003 ∙ A{ T*�1 ∙ *�� (65)

A{ = | 2 − o�O�1 + o�400 (66)

Where o�/O� ≥ 0.33 (if o�/O� < 0.33, the value for kb corresponding to "�� = 0.33 is adopted). For

laminate/sheet end debonding assuming that the provided bond length is equal to or larger than the:




a�c,� = a�c/Z� (67)

b) U-wrapped section:

�� = '�� ∙ (cot ! + cot Q�) (68)

'�� = 9:; � q'� − s�� (69)

'�� = J b� ∙ ��2 ∙ *�� (70)

Although fib ’09 – draft (2009) is based on equations of Eurocode 2 as basic code, for the purpose of this

research, it is also combined with fib MC10 (2010) as the other models for strengthened structures.




5. RECENT DESIGN MODEL PROPOSALS

In order to understand better the interaction between internal transverse steel and external FRP

reinforcement and the effect of these two components on concrete-cracking patterns and influence of

crack angle, a brief review of recent design proposals was made. They were used for comparison with

data obtained by following current guidelines recommendation and as result, their deficiencies are

highlighted.

The researchers define the contribution of the FRP to the shear strength as the product between the

effective stress in FRP, the area of the FRP, partial reduction factors that intend to take into account the

quality of material and/or workmanship quality, and a geometrical factor depending on the type of

strengthening system used, as well as fiber inclination with respect to the beams longitudinal axis. In

general, the scientists are in agreement about the type and relevance that these parameters have in the

prediction performance of a model, but the way that these parameters are defined is not the same, and in

general, important differences can be found. The main difference appears in the evaluation of the

stresses/strains in fibers.

In a previous work, several scientists (Barros, Dias and Lima 2007) (Sas, et al. 2009) (Gonzales 2010)

based on the results of the same database, had already verified that none of the analytical formulations

predicts with enough accuracy the contribution of the FRP systems for the shear strengthening of RC

beams. In the present work this type of appraisal is extended to a larger set of models, recently published

in reputed journals and conference proceedings.

The models presented in this section are used to calculate the contribution of the FRP only for the

strengthening configurations for which they were devised. It should be remembered that proposed models

do not give any recommendations for RC members strengthened with a full-wrap configuration.

For the sake of relevancy, all the equations are presented using the same notation as in the original

formulation. A detailed notation list is added after every equation individually.

5.1 Chen and Teng (2003a)

An extensive work performed by Chen and Teng resulted in one of the most widely used shear models.

The general design equation (71) is based on the truss model theory, with the remark that discrete FRP

strips were modeled as equivalent continuous FRP sheets/plates and a reduction factor for the stress is

used instead of strain, as in the other models. Since the writers of the model considered continuous

sheets as a special case of strips, proposed equations are established in terms of strips.




Figure 8 - Chen and Teng notation for a general shear strengthening scheme (Chen, Teng and Chen, RC

beams shear-strengthened with FRP: shear resistance contributed by FRP 2010)

This model proposes equation for contribution of FRP ��:

�� = 2 ∙ *�� ∙ �� ∙ o�� ∙ ℎ��,� ∙ (cot + cot Q) ∙ sin QO�� (71)

Where *�� is the average (or effective) stress in the FRP intersected by the critical shear crack at the

ultimate limit state, Q is the angle between principal fiber orientation and longitudinal axis of member and

θ is the angle of diagonal crack with respect to the member axis.

Taking the non-uniformity of stresses in the FRP intersected by the critical shear crack into consideration,

the average stress in the FRP at the ultimate limit state, *��,� can be defined as:

*��,� = �� ∙ E��,� � (72)

In which E��,� � is the maximum stress in the FRP and �� the stress distribution factor.

E��,� � = 9:; �� *��,c

0,427 ∙ Q" ∙ Q� ∙ Jb�� ∙ T*′�� (73)




�� = ��ℎ��,�sin Q *�x � − �5�A��Oℎ��,�2 sin Q *�x O:'� ps5��O��

�� (74)

The effective height of the FRP ℎ��,� is expressed as:

ℎ��,� = q{ − q� (75)

Where q� and q{ are the coordinates of the top and bottom ends of the effective FRP, which may be

expressed as:

q� = '��,� (76)

q{ = 0,9 ∙ ' − (ℎ − '��) (77)

In which '��,� is the distance from the compression face to the top edge of the FRP, h is the height of the

beam, and '�� is the distance from the compression face to the lower edge of the FRP (thus, '��,� = ℎ

for U jackets). The lower end of the effective FRP is taken to be at the centroid of the steel tension

reinforcement if the FRP terminates at the base of the RC beam (ℎ = '�� in Eq. (77)) for simplification of

expressions. This means that the effective lower end is (h-d) above the actual lower edge of FRP. For

consistency, the lower end of the effective FRP is also taken to be (h-d) above the actual lower edge if the

FRP terminates above the base. This treatment is again conservative.

Q� = � 1 :* S ≥ 1sin �S2 :* S < 1� (78)

S = �� (79)




�� = Jb�� ∙ ��T*′� (80)

q{ = Q" = J2 − o�/HO� ∙ sin QI1 + o�/HO� ∙ sin QI 0,9 ∙ ' − (ℎ − '��) (81)

Although reviewed by authors Chen and Teng in 2010 (RC beams shear-strengthened with FRP: shear

resistance contributed by FRP) and compared with modified model, it was concluded by themselves that

the original model of Chen and Teng (2003a) is more suitable for the use in design considering its overall

accuracy and simpler form.

5.2 Carolin and Täljsten (2005)

Figure 9 - Fiber alignment and crack angle, Carolin and Taljsten (2005)

The design model is based on the superposition principle of the shear contributions of the strengthening

and the strut and tie model.

Contribution of FRP strengthening to total shear strength, �� has been suggested by Carolin and Täljsten

as:

�� = � ∙ a� ∙ b� ∙ �� ∙ q ∙ (cos sin !) ∙ sin Q (82)

Where � is a reduction factor that considers linear elastic material (� = 0,6), a� is critical strain in fibers, b�

is modulus of elasticity of fibres, �� is thickness of fibres, and q is the length of a vertical tension tie in the




truss, for steel stirrups normally expressed by the internal lever arm or 0.9d. The variables !, Q and are

angles considering crack inclination, fiber direction and the difference between them, respectively.

5.3 Pellegrino and Modena (2008)

Based on their own and experimental results of other investigations on the interaction between an external

FRP and an internal transverse steel reinforcement, Pellegrino and Modena proposed a new analytical

model. This model describes the shear capacity of RC beams strengthened according to the most

common schemes, taking into account interaction between FRP and transversal steel.

Figure 10 - Shape of the fracture surface of “U-jacketed” (a) and side-bonded beams (b)

They assumed the external FRP strains equal to those of internal stirrups, and obtained the FRP shear

contribution �� from the rotational equilibrium of the forces �� and �� operating in the FRP and concrete

surface respectively, at failure (Figure 11):

�� = 2 ∙ ;� ∙ �� ∙ �� ∙ o� ∙ a�� ∙ b� ∙ ℎ�O� (83)

Where ;� is the number of layers, �� is the thickness of FRP (one layer), o� is the width of FRP, b� is the

elastic modulus of FRP in the principal fiber orientation, ℎ� is the vertical distance from the top edge of the

FRP shear reinforcement to the bottom of concrete crossection, O� is the spacing of FRP strips and a�� is

effective strain:

a�� = 2 ∙ *�� ∙ K� ∙ cosN w ∙ $�,V;� ∙ �� ∙ �� ∙ b� ∙ ℎ� − s�ℎ� ∙ $� (84)




Where w is the angle characterizing the conventional roughness of the interface, which is by these authors

assumed to be equal to 79°, according to the calibration process based on the experimental ultimate

shear capacities.

Figure 11 - Forces acting in the cross section of “U-jacketed” (a) and side-bonded beams (b)

A new formulation for the contribution of the transversal steel, modified with respect to that proposed by

the EC2 (CEN 2004) code for nonstrengthened RC structures, is also proposed for FRP shear-

strengthened beams. This was done assuming variable amplitude for the diagonal crack and in the

presence of an external FRP reinforcement, the maximum stress in the internal transverse steel is equal

to its yield value only if the effective FRP strain is higher than the steel yield stress.

Therefore, the formulation for the steel contribution in the presence of an external FRP reinforcement is

proposed as:

�� = ?! ∙ BV �1 − �'� ∙ cot ∙ 9:;Ha�� ∙ b�; *PIF ∙ $" ∙ ' (85)

Where ! is taken as 0,75; BV is the transverse steel ratio, *P is the yield stress of the transverse steel, c is

the depth of the neutral axis, and d is the effective depth.




5.4 Bukhari et al. (2010)

A group of authors is proposing shear strength of beams without internal stirrups strengthened with FRP

only, ��,z�� as:

��,z�� = @ ∙ q� ∙ $" ∙ b� ∙ (cot + cot Q) ∙ sin Q (86)

� = 9:;�B ∙ a��,) ; B∗ ∙ a��,N� (87)

a) For side wrap:

a��,) = 0,7 ∙ �40,25 B ∙ b�/*�N CD ¡jf,¢£ ∙ 10jC ≤ 0,1 ∙ a�c ≤ 0,004 (88)

b) For U wrap:

a��,) = 0,8 ∙ �29,14 B ∙ b�/*�N CD ¡jf,¤�£ ∙ 10jC ≤ 0,1 ∙ a�c ≤ 0,004 (89)

And:

a��,N = 9:; ¥a�c2 ; 0,64 ∙ J *��b�� ∙ �� ; 0,004¦ (90)

B�∗ = B� ∙ H'� − ; ∙ s�� /3I/q� (91)

Where B� is FRP shear reinforcement ratio, n=0 for fully wrapped sections, 1 for U wrap and 2 for side

wrap, q� = 0,9'� and s�� is the anchorage length required to develop full anchorage capacity which is

taken as:

s�� = 0,7 ∙ Jb� ∙ ��*�� (92)




5.5 Modifi and Chaallal (2011)

A new design approach has been proposed for calculating the shear contribution of FRP by these two

authors, taking into account the effect of transverse steel on the EB FRP contribution in shear. They

proposed equation for contribution of FRP ( ��), taking into account a variable crack angle:

�� = BV ∙ b� ∙ a�� ∙ $ ∙ '� ∙ (cot + cot !) ∙ sin ! (93)

Where BV is FRP shear reinforcement ratio, b� is the elastic modulus of FRP in the principal fiber

orientation, $ is cross section width, '� is FRP effective depth ! is the angle between principal fiber

orientation and longitudinal axis of member and θ is the angle of diagonal crack with respect to the

member axis.

It should be noted that in the case of a continuous FRP sheet, the FRP width, wf, and the spacing, sf, can

be assumed equal to 1. The effective strain, a�� can be calculatted using formulation:

a�� = 0,31 ∙ Q� ∙ Q� ∙ Q" ∙ J T*′�� ∙ b� ≤ ac� (94)

Where *′� is compressive strength of concrete, and coefficient Q� (cracking modification factor) is:

a) For U-jackets:

Q� = 0,6TB� ∙ b� + B� ∙ b�

b) For side bonded FRP:

Q� = 0,43TB� ∙ b� + B� ∙ b� (95)

Where Q� is a decreasing coefficient (FRP effective anchorage length ratio) which represent the effect of

FRP sheets having an anchorage length shorter than �� and it is Q� = 1 for S ≥ 1 or Q� = (2 − S) ∙ S for S < 1. While:




S = �� (96)

�� is the maximum available bond length, calculated as '�/ sin ! for U-jackets or 2 ∙ '�/ sin ! for side

plates. And �� is effective bond length in mm, calculated as:

�� = Jb� ∙ ��2 ∙ *�� (97)

Q" = J2 − o�/O�1 + o�/O� (98)







6. METHODOLOGY FOR ANALYZING EXPERIMENTAL VS THEORETICAL

VALUES

In this chapter, the general methodology that will be used in this study for comparison between the

experimental values of different test carried out on concrete beams strengthened by FRP and the values

predicted by the equations of the studied codes and recently proposed models is presented.

Firstly, evaluation of the codes and models is made using the total database improved during the

execution of this document. Later on, evaluation of best predictions is made using reduced database,

considering only U-jacketed configuration with transversal steel. Total value of the theoretical shear

strength (concrete, steel and FRP contribution) is compared, distinguishing the presence of transversal

steel reinforcement and the type of strengthened scheme used in the tested specimens.

It should be pointed out that all formulations used in analysis of data base, both from guidelines

and recent models are treated without partial factors of safety in order to gain representative theoretical

values, comparable with testing results.

6.1 Database Description

The use of databases (DBs) with modern statistical analysis and data-mining software packages provides

the basis for registering, sharing and manipulating results from a large number of experimental tests

performed worldwide by different researchers. This kind of approach, used in the present work, is

particularly suitable for the study of complex phenomena (such as the shear behaviour of RC beams

strengthened with FRP) in which the number of variables involved is large and their relative importance is

not yet known.

Relevant data was collected from experimental programs carried out in recent years in the context of

shear strengthening with FRP, and an extended database was obtained. Using this data, the performance

of different design guidelines was appraised by means of comparing the behaviour of the FRP shear

systems predicted by analytical formulations with those registered experimentally.

To assess the accuracy of the theoretical predictions obtained with analytical formulations, presented in

chapters 3 and 4, a DB containing 225 experimental results of RC beams strengthened with externally

bonded FRP was collected from published literature, and previously compiled DBs (Sas, et al. 2009)

(Gonzales 2010) were upgraded. Afterwards, a reduced data base (RDB) was obtained, keeping only

results from U-jacketed configurations with transversal steel, since this is the most used case in practical

application of FRP strengthening systems.

The database (Table 2 to 5) contains values from experiments performed on 30 beams with T cross

sections and 194 beams with rectangular cross sections. For calculating the predictions of each individual




model, the material properties obtained from tests and reported in the original papers have been

considered. No partial safety factors have been adopted in the calculations of the predictions.

The database was divided in groups in order to study the accuracy of the codes for different strengthening

schemes. DB contains data of 36 and 27 tested U-jacketed configurations with and without transversal

steel, respectively. Tested side bonded configurations with transversal steel are 49, while without

transversal reinforcement are 16. Fully wrapped configurations are 22 in DB, and the rest of data are

‘’control samples’’ without FRP reinforcement, which are 69 in this DB. Total number of tests in RDB is 27.

In all beams with transversal reinforcement, inclination of the stirrups relative to the beam axis is 90°.




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ppor

tR

150,

025

00,

0018

820

0000

400

35,0

03,

21S

1,00

010

050

4515

0000

2400

94,0

Csu

ppor

tR

70,0

110

0,00

000

2000

0040

030

,00

2,90

--

--

--

-8,

2S

1 a

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4090

2350

0033

0021

,8S

1 b

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4090

2350

0033

0019

,5S

2 a

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4090

2350

0033

0024

,1S

2 b

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4090

2350

0033

0021

,1S

3 a

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4090

2350

0033

0021

,4S

3 b

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4090

2350

0033

0018

,8S

1 45

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4045

2350

0033

0022

,3S

2 45

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4045

2350

0033

0023

,7S

3 45

supp

ort

R70

,011

00,

0000

020

0000

400

30,0

02,

90S

0,07

760

4045

2350

0033

0020

,4TR

30

A1

supp

ort

R15

0,0

300

0,00

000

2000

0050

022

,60

2,40

--

--

--

-50

,8TR

30

A2

supp

ort

R15

0,0

300

0,00

000

2000

0050

022

,60

2,40

S0,

200

11

9023

3600

1400

79,9

TR 3

0 A

3su

ppor

tR

150,

030

00,

0000

020

0000

500

22,6

02,

40S

0,20

01

145

2336

0014

0099

,9TR

30

A4

supp

ort

R15

0,0

300

0,00

000

2000

0050

022

,60

2,40

S0,

200

11

6023

3600

1400

97,0

TR 3

0 A

5su

ppor

tR

150,

030

00,

0000

020

0000

500

22,6

02,

40S

0,20

01

145

2336

0014

0081

,1TR

30

AR

supp

ort

R15

0,0

300

0,00

000

2000

0050

022

,60

2,40

S0,

200

11

9023

3600

1400

92,6

TR 3

0 B

1su

ppor

tR

150,

030

00,

0031

420

0000

500

22,6

02,

40-

--

--

--

118,

1C

W 1

cont

inue

R15

0,0

305

0,00

838

2000

0035

027

,50

2,73

--

--

--

-17

5,0

CW

2*

cont

inue

R15

0,0

305

0,00

838

2000

0035

027

,50

2,73

S0,

165

11

9022

8000

3790

214,

0C

O 1

cont

inue

R15

0,0

305

0,00

000

2000

0046

020

,50

2,25

--

--

--

-48

,0C

O 2

cont

inue

R15

0,0

305

0,00

000

2000

0046

020

,50

2,25

U0,

165

125

5090

2280

0037

9088

,0C

O 3

cont

inue

R15

0,0

305

0,00

000

2000

0046

020

,50

2,25

U0,

165

11

9022

8000

3790

113,

0C

F 1

cont

inue

R15

0,0

305

0,00

000

2000

0043

050

,00

4,07

--

--

--

-93

,0C

F 2

cont

inue

R15

0,0

305

0,00

000

2000

0043

050

,00

4,07

U0,

165

11

9022

8000

3790

119,

0C

F 3

*co

ntin

ueR

150,

030

50,

0000

020

0000

430

50,0

04,

07S

0,16

51

190

2280

0037

9013

1,0

CF

4co

ntin

ueR

150,

030

50,

0000

020

0000

430

50,0

04,

07R

0,16

51

190

2280

0037

9014

0,0

BT

1su

ppor

tT

150,

040

50,

0000

020

0000

460

35,0

03,

21-

--

--

--

90,0

BT

2su

ppor

tT

150,

040

50,

0000

020

0000

460

35,0

03,

21U

0,16

51

190

2280

0037

9015

5,0

BT

3*su

ppor

tT

150,

040

50,

0000

020

0000

460

35,0

03,

21S

0,16

51

190

2280

0037

9015

7,5

BT

4su

ppor

tT

150,

040

50,

0000

020

0000

460

35,0

03,

21U

0,16

512

550

9022

8000

3790

162,

5B

T 5

supp

ort

T15

0,0

405

0,00

000

2000

0046

035

,00

3,21

S0,

165

125

5090

2280

0037

9012

1,5

BT

6*su

ppor

tT

150,

040

50,

0000

020

0000

460

35,0

03,

21U

0,16

51

190

2280

0037

9022

1,0

SW

3-1

supp

ort

R15

0,0

305

0,00

838

2000

0035

019

,30

2,16

--

--

--

-12

6,5

SW

3-2

*su

ppor

tR

150,

030

50,

0083

820

0000

350

19,3

02,

16S

0,16

51

190

2280

0037

9017

7,0

SW

4-1

supp

ort

R15

0,0

305

0,00

838

2000

0035

019

,30

2,16

--

--

--

-10

0,0

SW

4-2

*su

ppor

tR

150,

030

50,

0083

820

0000

350

19,3

02,

16S

0,16

51

190

2280

0037

9018

0,5

SO

3-1

supp

ort

R15

0,0

305

0,00

000

2000

0046

027

,50

2,73

--

--

--

-77

,0S

O 3

-2su

ppor

tR

150,

030

50,

0000

020

0000

460

27,5

02,

73U

0,16

512

550

9022

8000

3790

131,

0S

O 3

-5su

ppor

tR

150,

030

50,

0000

020

0000

460

27,5

02,

73U

0,16

51

190

2280

0037

9016

9,5

SO

3-4

supp

ort

R15

0,0

305

0,00

000

2000

0046

027

,50

2,73

U0,

165

11

9022

8000

3790

144,

5S

O 4

-1su

ppor

tR

150,

030

50,

0000

020

0000

460

27,5

02,

73-

--

--

--

65,0

SO

4-2

supp

ort

R15

0,0

305

0,00

000

2000

0046

027

,50

2,73

U0,

165

125

5090

2280

0037

9012

7,5

SO

4-3

supp

ort

R15

0,0

305

0,00

000

2000

0046

027

,50

2,73

U0,

165

11

9022

8000

3790

155,

0

Kha

lifa

and

Nan

ni (

2000

)

Kha

lifa

and

Nan

ni (

2002

)

STE

EL

RE

INF

OR

CE

ME

NT

Aut

hors

Spe

cim

en

FR

P

Kha

lifaa

et

al.

(199

9)

Cha

alla

l et

al.

(199

8)

Tria

ntaf

illou

(1

998)

GE

OM

ETR

IC C

HA

RA

CTE

RIS

TIC

SE

XP.R

ES

CO

NC

RE

TE

Mod

ena

et a

l. (1

999)

Taer

we

et a

l. (1

997)

Sta

tic

sche

me

Table 1 - Experimental Database




Cro

ss

Sec

tion

Web

Th

ickn

ess

Dep

thTr

ansv

ersa

l R

einf

orce

men

t R

atio

Ela

stic

M

odul

usTe

nsile

S

tren

gth

Com

pres

sive

S

tren

gth

Tens

ile

Str

engt

hS

tren

gthe

ning

C

onfig

urat

ion

One

Lay

er

Thic

knes

s

FR

P S

hear

R

einf

orce

men

t S

paci

ng

FR

P S

hear

R

einf

orce

men

t F

abric

Wid

th

Fib

er

Orie

ntat

ion

You

ng's

M

odul

usTe

nsile

S

tren

gth

She

ar

Str

engt

h

(R,

T)

bw

Hρ

wE

sf y

f ck

f ctm

(U,

S,

R)

t frp

sfr

p (

pfr

p)

wfr

p (

bf)

βfr

pE

frp

f frp

Vn

,te

st

mm

mm

-M

Pa

MP

aM

Pa

MP

am

mm

mm

m°

MP

aM

Pa

kNTR

30

C1

supp

ort

R15

0,0

300

0,00

000

2100

0054

822

,82

2,41

--

--

--

-74

,7TR

30

C2

supp

ort

R15

0,0

300

0,00

000

2100

0054

822

,82

2,41

S0,

165

11

9023

3600

4490

119,

0TR

30

C3

supp

ort

R15

0,0

300

0,00

000

2100

0054

822

,82

2,41

S0,

165

11

9023

3600

4490

112,

8TR

30

C4

supp

ort

R15

0,0

300

0,00

000

2100

0054

822

,82

2,41

S0,

165

11

9023

3600

4490

140,

0TR

30

D1

supp

ort

R15

0,0

300

0,00

335

2100

0054

826

,06

2,64

--

--

--

-16

1,5

TR 3

0 D

10su

ppor

tR

150,

030

00,

0033

521

0000

548

26,0

62,

64S

0,16

51

190

2336

0044

9019

3,0

TR 3

0 D

2su

ppor

tR

150,

030

00,

0033

521

0000

548

26,0

62,

64S

0,16

51

190

2336

0044

9021

3,3

TR 3

0 D

20su

ppor

tR

150,

030

00,

0033

521

0000

548

26,0

62,

64S

0,16

51

190

2336

0044

9023

8,3

TR 3

0 D

3su

ppor

tR

150,

030

00,

0033

521

0000

548

26,0

62,

64S

0,16

51

190

2336

0044

9016

1,4

TR 3

0 D

4su

ppor

tR

150,

030

00,

0033

521

0000

548

26,0

62,

64S

0,16

51

190

2336

0044

9020

8,8

TR 3

0 D

40su

ppor

tR

150,

030

00,

0033

521

0000

548

26,0

62,

64S

0,16

51

190

2336

0044

9021

2,0

B 1

supp

ort

R30

0,0

300

0,00

000

1960

0039

538

,00

3,39

--

--

--

-11

2,0

C 1

supp

ort

R30

0,0

300

0,00

000

1960

0039

537

,20

3,34

U0,

167

11

9023

0000

3400

165,

0C

2su

ppor

tR

300,

030

00,

0000

019

6000

395

41,0

03,

57U

0,16

71

190

2300

0034

0022

8,5

C 3

supp

ort

R30

0,0

300

0,00

000

1960

0039

541

,10

3,57

U0,

167

11

9023

0000

3400

237,

5T4

S2

supp

ort

T14

0,0

400

0,00

202

2100

0052

028

,60

2,81

--

--

--

-20

1,3

T4S

2-C

45su

ppor

tT

140,

040

00,

0020

221

0000

520

29,4

02,

86U

0,11

050

5045

2300

0034

0021

9,1

T1-T

2su

ppor

tR

150,

020

00,

0000

020

5000

467

34,2

83,

17-

--

--

--

59,9

T3su

ppor

tR

150,

020

00,

0000

020

5000

467

34,2

83,

17S

0,13

01

190

2300

0035

0060

,8T4

supp

ort

R15

0,0

200

0,00

000

2050

0046

734

,28

3,17

S0,

130

11

9023

0000

3500

60,8

T5su

ppor

tR

150,

020

00,

0000

020

5000

467

34,2

83,

17U

0,13

01

190

2300

0035

0097

,7T6

supp

ort

R15

0,0

200

0,00

000

2050

0046

734

,28

3,17

U0,

130

11

9023

0000

3500

91,1

RE

F 1

supp

ort

R25

0,0

450

0,00

101

2000

0050

013

,30

1,68

--

--

--

-10

5,0

RE

F 2

supp

ort

R25

0,0

450

0,00

101

2000

0050

013

,30

1,68

--

--

--

-93

,5S

S 9

0su

ppor

tR

250,

045

00,

0010

120

0000

500

13,3

01,

68S

0,22

030

015

090

3900

0030

0010

2,5

SS

45

supp

ort

R25

0,0

450

0,00

101

2000

0050

013

,30

1,68

S0,

220

424

150

4539

0000

3000

101,

0S

F 9

0su

ppor

tR

250,

045

00,

0010

120

0000

500

13,3

01,

68S

0,22

01

190

3900

0030

0011

2,5

US

90

supp

ort

R25

0,0

450

0,00

101

2000

0050

013

,30

1,68

U0,

220

300

150

9039

0000

3000

95,0

US

60

supp

ort

R25

0,0

450

0,00

101

2000

0050

013

,30

1,68

U0,

220

346

150

6039

0000

3000

111,

0U

S 9

0(2)

supp

ort

R25

0,0

450

0,00

101

2000

0050

013

,30

1,68

U0,

220

300

150

9039

0000

3000

89,5

R1

supp

ort

R18

0,0

500

0,00

000

2050

0050

055

,94

4,39

--

--

--

-12

4,1

C1

supp

ort

R18

0,0

500

0,00

000

2050

0050

055

,94

4,39

S0,

055

11

4523

4000

4500

246,

7C

2su

ppor

tR

180,

050

00,

0000

020

5000

500

59,2

64,

56S

0,05

51

145

2340

0045

0025

7,2

C3

supp

ort

R18

0,0

500

0,00

000

2050

0050

048

,72

4,00

S0,

055

11

9023

4000

4500

260,

6C

5su

ppor

tR

180,

050

00,

0000

020

5000

500

59,2

64,

56S

0,05

51

145

2340

0045

0033

4,3

P0

supp

ort

R13

0,0

450

0,00

145

2100

0055

038

,00

3,39

--

--

--

-22

0,0

P0-

bis

supp

ort

R13

0,0

450

0,00

145

2100

0055

038

,00

3,39

--

--

--

-22

0,0

PC

1su

ppor

tR

130,

045

00,

0014

521

0000

550

38,0

03,

39R

0,43

020

040

9010

5000

1400

355,

0P

C2

supp

ort

R13

0,0

450

0,00

145

2100

0055

038

,00

3,39

R0,

430

250

4090

1050

0014

0031

0,0

PC

3su

ppor

tR

130,

045

00,

0014

521

0000

550

38,0

03,

39R

0,43

030

040

4510

5000

1400

291,

0P

C4

supp

ort

R13

0,0

450

0,00

145

2100

0055

038

,00

3,39

R0,

430

350

4045

1050

0014

0026

4,0

B -

1su

ppor

tR

150,

020

00,

0000

018

2000

582

30,5

02,

93-

--

--

--

39,2

B -

2su

ppor

tR

150,

020

00,

0000

018

2000

582

35,4

03,

23S

0,16

71

190

2300

0034

0050

,5B

- 3

supp

ort

R15

0,0

200

0,00

000

1820

0058

233

,50

3,12

S0,

167

11

9023

0000

3400

63,6

B -

4su

ppor

tR

150,

020

00,

0000

018

2000

582

31,5

02,

99S

0,16

71

190

2300

0034

0058

,6B

- 5

supp

ort

R15

0,0

200

0,00

000

1820

0058

231

,00

2,96

S0,

167

11

9023

0000

3400

60,3

B -

6su

ppor

tR

150,

020

00,

0000

018

2000

582

33,7

03,

13S

0,16

71

190

2300

0034

0080

,8B

- 7

supp

ort

R15

0,0

200

0,00

000

1820

0058

234

,40

3,17

U0,

167

11

9023

0000

3400

68,5

B -

8su

ppor

tR

150,

020

00,

0000

018

2000

582

35,4

03,

23U

0,16

71

190

2300

0034

0085

,8

CO

NC

RE

TEF

RP

EXP

.RE

S

Sta

tic

sche

me

Aut

hors

Dia

gana

et

al.

(200

3)

Adh

ikar

y an

d M

utsu

yosh

i (2

004)

Ta¨lj

sten

(20

03)

Pel

legr

ino

and

Mod

ena

(200

2)

Mon

ti et

al.

(200

3)

Spe

cim

en

Don

aton

e et

al.

(200

3)

Den

iaud

and

Che

ng

(200

3)

GE

OM

ETR

IC C

HA

RA

CTE

RIS

TIC

SS

TEE

L R

EIN

FO

RC

EM

EN

T

Adh

ikar

y et

al.

(200

3)

Table 2 - Continuation of Table 1




Cro

ss

Sec

tion

Web

Th

ickn

ess

Dep

thTr

ansv

ersa

l R

einf

orce

men

t R

atio

Ela

stic

M

odul

usTe

nsile

S

tren

gth

Com

pres

sive

S

tren

gth

Tens

ile

Str

engt

hS

tren

gthe

ning

C

onfig

urat

ion

One

Lay

er

Thic

knes

s

FR

P S

hear

R

einf

orce

men

t S

paci

ng

FR

P S

hear

R

einf

orce

men

t F

abric

Wid

th

Fib

er

Orie

ntat

ion

You

ng's

M

odul

usTe

nsile

S

tren

gth

She

ar

Str

engt

h

(R,

T)

bw

Hρ

wE

sf y

f ck

f ctm

(U,

S,

R)

t frp

sfr

p (

pfr

p)

wfr

p (

bf)

βfr

pE

frp

f frp

Vn

,te

st

mm

mm

-M

Pa

MP

aM

Pa

MP

am

mm

mm

m°

MP

aM

Pa

kNU

Nb

supp

ort

R15

0,0

350

0,00

328

2060

0062

141

,03

3,57

--

--

--

-18

6,0

ST1

bsu

ppor

tR

150,

035

00,

0032

820

6000

621

41,0

33,

57R

0,12

01

190

7590

036

0024

2,0

ST2

bsu

ppor

tR

150,

035

00,

0032

820

6000

621

41,0

33,

57R

0,12

01

190

7590

036

0027

0,0

ST3

bsu

ppor

tR

150,

035

00,

0032

820

6000

621

41,0

33,

57R

0,12

01

190

7590

036

0027

9,0

SB

S0

0Lsu

ppor

tT

95,0

220

0,00

000

2050

0053

027

,00

2,70

--

--

--

-36

,1S

B S

0 1L

supp

ort

T95

,022

00,

0000

020

5000

530

27,0

02,

70U

0,06

61

190

2310

0036

5059

,3S

B S

0 2L

supp

ort

T95

,022

00,

0000

020

5000

530

27,0

02,

70U

0,06

61

190

2310

0036

5068

,5S

B S

1 0L

supp

ort

T95

,022

00,

0038

116

5000

420

27,0

02,

70-

--

--

--

92,9

SB

S1

1Lsu

ppor

tT

95,0

220

0,00

381

1650

0042

027

,00

2,70

U0,

066

11

9023

1000

3650

95,7

SB

S1

2Lsu

ppor

tT

95,0

220

0,00

381

1650

0042

027

,00

2,70

U0,

066

11

9023

1000

3650

105,

1A

1su

ppor

tR

150,

025

00,

0018

820

6000

303

30,5

02,

93-

--

--

--

141,

0A

2su

ppor

tR

150,

025

00,

0018

820

6000

303

30,5

02,

93R

0,16

710

030

9024

9000

3635

170,

0A

3su

ppor

tR

150,

025

00,

0018

820

6000

303

30,5

02,

93R

0,16

715

030

9024

9000

3635

162,

0B

asu

ppor

tR

150,

025

00,

0134

020

6000

228

30,0

02,

90-

--

--

--

66,0

Bb

supp

ort

R15

0,0

250

0,01

340

2060

0022

830

,00

2,90

R1,

270

4020

9020

500

260

120,

0B

csu

ppor

tR

150,

025

00,

0134

020

6000

228

30,0

02,

90R

1,27

080

2090

2050

026

010

4,0

L1su

ppor

tR

150,

025

00,

0134

020

6000

228

17,8

02,

05-

--

--

--

64,0

L2su

ppor

tR

150,

025

00,

0134

020

6000

228

17,8

02,

05R

1,20

050

2590

5300

112

90,0

L3su

ppor

tR

150,

025

00,

0134

020

6000

228

17,8

02,

05R

1,20

010

025

9053

0011

273

,0R

1su

ppor

tR

180,

050

00,

0000

021

0000

515

65,0

04,

85-

--

--

--

126,

0R

2su

ppor

tR

180,

050

00,

0000

021

0000

515

67,0

04,

95-

--

--

--

124,

0R

3su

ppor

tR

180,

050

00,

0000

021

0000

515

47,0

03,

91-

--

--

--

103,

0R

4su

ppor

tR

180,

050

00,

0000

021

0000

515

53,0

04,

23-

--

--

--

119,

0R

5su

ppor

tR

180,

050

00,

0000

021

0000

515

46,0

03,

85-

--

--

--

125,

014

5su

ppor

tR

180,

050

00,

0000

021

0000

515

67,0

04,

95S

0,05

51

145

2340

0045

0024

7,0

20su

ppor

tR

180,

050

00,

0000

021

0000

515

59,0

04,

55S

0,05

51

145

2340

0045

0015

4,0

245a

supp

ort

R18

0,0

500

0,00

000

2100

0051

571

,00

5,14

S0,

055

11

4523

4000

4500

257,

024

5bsu

ppor

tR

180,

050

00,

0000

021

0000

515

53,0

04,

23S

0,05

51

145

2340

0045

0030

5,0

245R

asu

ppor

tR

180,

050

00,

0000

021

0000

515

67,0

04,

95S

0,05

51

145

2340

0045

0030

6,0

245R

bsu

ppor

tR

180,

050

00,

0000

021

0000

515

47,0

03,

91S

0,05

51

145

2340

0045

0025

1,0

245R

Fsu

ppor

tR

180,

050

00,

0000

021

0000

515

53,0

04,

23S

0,05

51

145

2340

0045

0029

1,0

345

supp

ort

R18

0,0

500

0,00

000

2100

0051

571

,00

5,14

S0,

055

11

4523

4000

4500

334,

034

5Fsu

ppor

tR

180,

050

00,

0000

021

0000

515

54,0

04,

29S

0,05

51

145

2340

0045

0034

4,0

Rsu

ppor

tR

180,

040

00,

0015

721

0000

515

45,0

03,

80-

--

--

--

237,

029

0su

ppor

tR

180,

040

00,

0015

721

0000

515

46,0

03,

85S

0,05

51

190

2340

0045

0029

8,0

390

supp

ort

R18

0,0

400

0,00

157

2100

0051

546

,00

3,85

S0,

055

11

9023

4000

4500

298,

0ZC

4su

ppor

tR

152,

422

8,6

0,00

000

2060

0040

043

,80

3,73

--

--

--

-46

,1Z4

-90

supp

ort

R15

2,4

228,

60,

0000

020

6000

400

43,8

03,

73S

1,50

012

740

9016

5000

2800

73,7

Z4-4

5su

ppor

tR

152,

422

8,6

0,00

000

2060

0040

043

,80

3,73

S1,

500

127

4045

1650

0028

0082

,2Z4

-Fab

supp

ort

R15

2,4

228,

60,

0000

020

6000

400

43,8

03,

73S

1,00

01

190

1650

0028

0053

,6ZC

6(2)

supp

ort

R15

2,4

228,

60,

0000

020

6000

400

43,8

03,

73-

--

--

--

42,9

Z6-9

0su

ppor

tR

152,

422

8,6

0,00

000

2060

0040

043

,80

3,73

S1,

500

127

4090

1650

0028

0063

,9Z6

-Fab

supp

ort

R15

2,4

228,

60,

0000

020

6000

400

43,8

03,

73S

1,00

01

190

1650

0028

0051

,2

Spe

cim

en

GE

OM

ETR

IC C

HA

RA

CTE

RIS

TIC

SS

TEE

L R

EIN

FO

RC

EM

EN

TC

ON

CR

ETE

FR

PE

XP.R

ES

Sta

tic

sche

me

Car

olin

and

Tä

ljste

n (2

005)

Iann

irube

rto

and

Imbi

mbo

(20

04)

Aut

hors

Zhan

g an

d H

su

(200

5)

Bou

ssel

ham

an

d C

haal

lal

(200

5)

Cao

et

al.

(200

5)





Cro

ss

Sec

tion

Web

Th

ickn

ess

Dep

thTr

ansv

ersa

l R

einf

orce

men

t R

atio

Ela

stic

M

odul

usTe

nsile

S

tren

gth

Com

pres

sive

S

tren

gth

Tens

ile

Str

engt

hS

tren

gthe

ning

C

onfig

urat

ion

One

Lay

er

Thic

knes

s

FR

P S

hear

R

einf

orce

men

t S

paci

ng

FR

P S

hear

R

einf

orce

men

t F

abric

Wid

th

Fib

er

Orie

ntat

ion

You

ng's

M

odul

usTe

nsile

S

tren

gth

She

ar

Str

engt

h

(R,

T)

bw

Hρ

wE

sf y

f ck

f ctm

(U,

S,

R)

t frp

sfr

p (

pfr

p)

wfr

p (

bf)

βfr

pE

frp

f frp

Vn

,te

st

mm

mm

-M

Pa

MP

aM

Pa

MP

am

mm

mm

m°

MP

aM

Pa

kNA

10_C

supp

ort

R15

0,0

300

0,00

000

2060

0057

437

,60

3,37

--

--

--

-50

,2A

10_S

supp

ort

R15

0,0

300

0,00

126

2060

0054

037

,60

3,37

--

--

--

-84

,7A

10_M

supp

ort

R15

0,0

300

0,00

000

2060

0054

037

,60

3,37

U0,

167

190

2590

3900

0030

0061

,0A

12_C

supp

ort

R15

0,0

300

0,00

000

2060

0057

437

,60

3,37

--

--

--

-58

,3A

12_S

supp

ort

R15

0,0

300

0,00

251

2060

0054

037

,60

3,37

--

--

--

-10

7,5

A12

_Msu

ppor

tR

150,

030

00,

0000

020

6000

540

37,6

03,

37U

0,16

795

2590

3900

0030

0089

,8B

10_C

supp

ort

R15

0,0

150

0,00

000

2060

0057

149

,50

4,04

--

--

--

-37

,0B

10_S

supp

ort

R15

0,0

150

0,00

251

2060

0054

049

,50

4,04

--

--

--

-60

,3B

10_M

supp

ort

R15

0,0

150

0,00

000

2060

0054

049

,50

4,04

U0,

167

8025

9039

0000

3000

55,6

B12

_Csu

ppor

tR

150,

015

00,

0000

020

6000

571

49,5

04,

04-

--

--

--

37,9

B12

_Ssu

ppor

tR

150,

015

00,

0050

320

6000

540

49,5

04,

04-

--

--

--

79,6

B12

_Msu

ppor

tR

150,

015

00,

0000

020

6000

540

49,5

04,

04U

0,16

740

2590

3900

0030

0071

,6S

B-S

0-0L

supp

ort

T15

2,0

406

0,00

000

2000

0047

025

,00

2,56

--

--

--

-81

,2S

B-S

0-0,

5Lsu

ppor

tT

152,

040

60,

0000

020

0000

470

25,0

02,

56U

0,06

01

190

2310

0036

5010

2,4

SB

-S0-

1Lsu

ppor

tT

152,

040

60,

0000

020

0000

470

25,0

02,

56U

0,10

71

190

2310

0036

5012

0,0

SB

-S0-

2Lsu

ppor

tT

152,

040

60,

0000

020

0000

470

25,0

02,

56U

0,10

71

190

2310

0036

5012

1,7

SB

-S1-

0Lsu

ppor

tT

152,

040

60,

0037

816

5000

420

25,0

02,

56-

--

--

--

262,

8S

B-S

1-0,

5Lsu

ppor

tT

152,

040

60,

0037

816

5000

420

25,0

02,

56U

0,06

01

190

2310

0036

5028

2,0

SB

-S1-

1Lsu

ppor

tT

152,

040

60,

0037

816

5000

420

25,0

02,

56U

0,10

71

190

2310

0036

5025

5,0

SB

-S1-

2Lsu

ppor

tT

152,

040

60,

0037

816

5000

420

25,0

02,

56U

0,10

71

190

2310

0036

5026

7,2

SB

40su

ppor

tR

150,

025

00,

0000

020

7000

500

54,3

04,

30-

--

--

--

45,3

SB

40R

supp

ort

R15

0,0

250

0,00

000

2070

0050

054

,30

4,30

R0,

281

100

1090

6500

030

0058

,0S

B41

supp

ort

R15

0,0

250

0,00

000

2070

0050

053

,70

4,27

--

--

--

-68

,0S

B41

Rsu

ppor

tR

150,

025

00,

0000

020

7000

500

53,7

04,

27R

0,51

510

010

9065

000

3000

89,5

RS

4NR

supp

ort

R25

0,0

450

0,00

101

2060

0050

021

,00

2,28

--

--

--

-22

5,4

RS

3NR

supp

ort

R25

0,0

450

0,00

134

2060

0050

021

,00

2,28

--

--

--

-31

3,6

RS

2NR

supp

ort

R25

0,0

450

0,00

201

2060

0050

021

,00

2,28

--

--

--

-43

1,2

RS

4Wsu

ppor

tR

250,

045

00,

0010

120

6000

500

21,0

02,

28R

0,19

11

190

3920

0030

0049

0,0

RS

3Wsu

ppor

tR

250,

045

00,

0013

420

6000

500

21,0

02,

28R

0,19

11

190

3920

0030

0064

6,8

RS

2Wsu

ppor

tR

250,

045

00,

0020

120

6000

500

21,0

02,

28R

0,19

11

190

3920

0030

0058

8,0

RS

3Usu

ppor

tR

250,

045

00,

0013

420

6000

500

21,0

02,

28U

0,19

11

190

3920

0030

0053

9,0

RS

2Usu

ppor

tR

250,

045

00,

0020

120

6000

500

21,0

02,

28U

0,19

11

190

3920

0030

0056

8,4

RS

3Ssu

ppor

tR

250,

045

00,

0013

420

6000

500

21,0

02,

28S

0,19

11

190

3920

0030

0040

1,8

RS

2Ssu

ppor

tR

250,

045

00,

0020

120

6000

500

21,0

02,

28S

0,19

11

190

3920

0030

0047

0,4

CO

N-3

supp

ort

R25

0,0

250

0,00

000

2000

0055

034

,70

3,19

--

--

--

-62

,5C

P3-

VW

supp

ort

R25

0,0

250

0,00

000

2000

0055

134

,70

3,19

S0,

200

11

9023

5000

3550

154,

0C

P3-

1VS

supp

ort

R25

0,0

250

0,00

000

2000

0055

234

,70

3,19

S0,

200

100

5090

2350

0135

5094

,5C

S3-

VW

supp

ort

R25

0,0

250

0,00

000

2000

0055

434

,70

3,19

S0,

200

11

9015

8000

3160

108,

0C

S3-

DW

supp

ort

R25

0,0

250

0,00

000

2000

0055

534

,70

3,19

S0,

200

11

4515

8000

3160

110,

0S

B-C

supp

ort

R75

,018

00,

0027

920

6000

500

27,4

02,

73-

--

--

--

40,8

SB

-U1

supp

ort

R75

,018

00,

0027

920

6000

500

27,4

02,

73U

0,11

060

2090

2310

0036

5065

,0S

B-U

2su

ppor

tR

75,0

180

0,00

279

2060

0050

027

,40

2,73

U0,

110

6020

9023

1000

3650

45,9

SB

-F1

supp

ort

R75

,018

00,

0027

920

6000

500

27,4

02,

73R

0,11

060

2090

2310

0036

5066

,1S

B-F

2su

ppor

tR

75,0

180

0,00

279

2060

0050

027

,40

2,73

R0,

110

6020

9023

1000

3650

66,7

MB

-Csu

ppor

tR

150,

036

00,

0111

720

6000

500

27,4

02,

73-

--

--

--

149,

9M

B-U

1su

ppor

tR

150,

036

00,

0111

720

6000

500

27,4

02,

73U

0,22

012

040

9023

1000

3650

154,

9M

B-U

2su

ppor

tR

150,

036

00,

0111

720

6000

500

27,4

02,

73U

0,22

012

040

9023

1000

3650

159,

8M

B-F

1su

ppor

tR

150,

036

00,

0111

720

6000

500

27,4

02,

73R

0,22

012

040

9023

1000

3650

236,

4M

B-F

2su

ppor

tR

150,

036

00,

0111

720

6000

500

27,4

02,

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6.2 The Total Shear Strength

Total shear strength of the RC beams has been considered in the comparison, because it is necessary to

observe behaviour and capacity of whole element (beam), and not contribution of each component

separately. Although the models presented in the studied literature refer only to the FRP contribution to

the total capacity, many scientist are pointing out interaction between steel, concrete and FRP which

cannot be discarded. The experimental values of the shear strength have been directly obtained from the

tests performed on each FRP strengthened beam.

6.3 Analyzed design procedures

For assessment of DB, predictions of total shear strength have been obtained by combining basic model

codes and models for strengthened structures.

Estimation of contribution of FRP (�*) is made according to models for FRP strengthening reviewed in

chapter 4 of this document, while contributions of concrete, steel and effective crushing strength of

concrete are estimated according to basic model codes reviewed in chapter 3, as given in Table 6.

Table 6 - Design procedures for analyzing DB

As it has been explained earlier in chapter 2, the angle of shear crack θ may have significant influence on

prediction of models, so different values of this angle have been considered. Since most of the basic

codes (EC2, ACI 318 and fib 2010) recommend the usage of value θ=45°, this value of angle was firstly

analyzed. Eurocode 2 also recommends the variable angle with limits of 21,8°≤ θ≤ 45°, so this was

second case in which various values of angle were taken in order to maximize contribution of steel and

concrete and used while combining models for strengthened structures with EC2. New model code fib

2010 recommends usage of not only θ=45°, but also θ=36°, so this was considered as third case. Since

draft of new code for strengthened structures fib ’09 - draft (2009) recommends θ=45° in case of elements

without transversal reinforcement and θ=35° for elements with transversal steel, this case was also

considered while combining models for strengthened structures with fib MC10 (2010).

Basic code for V Rd,c ; V Rd,s ; V Rd,max Models for V f With transversal steel Without transversal steel

EC2 (2004) Chapter 4 VRd = min {VRd,s + Vf ;VRd,max } VRd = min {VRd,c + Vf ;VRd,max }

fib MC10 (2010) Chapter 4 VRd = min {VRd,c + VRd,s + Vf ;VRd,max } VRd = min {VRd,c + Vf ;VRd,max }




6.4 General statistical analysis procedures

The performance of FIB, ACI, CNR design models and recent model proposals was appraised using the

collected data registered in the DB. For each design model, the obtained values of ��,�§�¨ were compared

with ��,�� , and a factor ©, corresponding to ��,��/��,�§�¨, was evaluated. On the performed analysis, ��,�§�¨ is the design value of the global shear resistance predicted by the design model and ��,�� is the

shear resistance obtained based on experimental results. In each plot of results, a line © = 1.0 establishes

the division between safe (conservative) and unconservative predictions.

The main descriptive statistical measures analyzed in this study are percentage of conservative

predictions, the average (AVG), the standard deviation (std) and the coefficient of variation (CoV). In

further study, CoV and AVG will be taken as main parameters, since they are both indicators of accuracy.

The average (AVG) represents a global safety factor associated with the design procedure. A coefficient

of variation (CoV) is calculated and interpreted analyzing a single variable. The formulation of the CoV is

the ratio of the standard deviation to the mean value, and it aims to describe the dispersion of the variable

in a way that does not depend on the variable's measurement unit. For higher values of CoV, the

dispersion in the variable is greater. The advantage of the CoV is that it is unitless. This allows CoV to be

compared to each other in ways that other measures, like standard deviations or root mean squared

residuals, cannot be.







7. RESULTS AND DISCUSSION

It should be pointed out once more that in this study, the total shear strength of element is considered.

This is done by taking into account the fact that the influence of the steel and shear contributions

estimated by the respective codes does not allow having a clear understanding of the predictions given for

the individual FRP contribution. In addition, as it was stated before, the scope of this document is to study

the equations for FRP systems due to their more recent development and need of validation.

*notification: since guideline fib ‘09 (2009) does not recognize difference between U-jacketed and side

bonded configurations, all data of side bonded configurations were in case of fib treated as U-jacketed

and shown in previous figures.

7.1 Assessment of Pellegrino and Modena (2008) model and its improvement

Analyzing recently proposed models for strengthening of RC structures (explained in details in chapter 5

of this study), author found model of Pellegrino and Modena specially interesting cause it distinguishes

from other models by taking into account interaction between the internal steel and external FRP and

considering variable angle θ. Results predicted by this model are very good comparing to other models

and codes. In order to improve this model, author of this study analyzed different parameters that are

configuring in equations proposed by Pellegrino and Modena (2008). As a result, a different value of the

angle characterizing the conventional roughness of the interface is proposed in this study.

Originally, Pellegrino and Modena have proposed their model (Pellegrino and Modena, An Experimentaly

Based Analytical Model for the Shear Capacity of FRP-strenghtened Reinforced Concrete Beams 2008) in

which this angle was assumed to be equal to w=79°, according to the calibration process based on the

experimental ultimate shear capacities obtained in their experimental investigation. After considering

several values of this angle, author of this study has found an optimal value w=75°, which gives

improvement of Pellegrino and Modena model in 21 out of 24 cases considering different basic model

code and angle of shear crack, θ. The main descriptive statistical measures are summarized in Table 7,

regarding percentage of conservative predictions, the average (AVG), the standard deviation (std) and the

coefficient of variation (CoV). It can be noticed that modification of this angle from w=79° to w=75°,

improves model not only in sense of CoV, but also in sense of AVG.

Model of Pellegrino and Modena will be analyzed in further study as two cases: firstly with original value w=79° for angle characterizing the conventional roughness of the interface and secondly, as modified

model, with w=79°.




Table 7 - Comparison of results for Modena and Pellegrino model

Model Conservative

Standard

Deviation AVG CoV

EC2 (2004) θ=45° 88,9% 0,51 1,39 0,37

EC2 (2004) θ=45° (φ=75°) 51,9% 0,37 1,08 0,34

fib MC10 (2010) θ=45° 96,3% 1,10 1,92 0,57

fib MC10 (2010) θ=45° (φ=75°) 63,0% 0,71 1,40 0,51

EC2 (2004) θ=36° 88,9% 0,51 1,39 0,37

EC2 (2004) θ=36° (φ=75°) 51,9% 0,37 1,08 0,34

fib MC10 (2010) θ=36° 96,3% 1,10 1,92 0,57

fib MC10 (2010) θ=36° (φ=75°) 63,0% 0,71 1,40 0,51

EC2 (2004) θ=var 88,9% 0,51 1,39 0,37

EC2 (2004) θ=var (φ=75°) 51,9% 0,37 1,08 0,34

fib MC10 (2010) θ=35/45° 96,3% 1,10 1,92 0,57

fib MC10 (2010) θ=35/45° (φ=75°) 63,0% 0,71 1,40 0,51

EC2 (2004) θ=45° 86,1% 0,69 1,54 0,45

EC2 (2004) θ=45° (φ=75°) 72,2% 0,39 1,18 0,33

fib MC10 (2010) θ=45° 80,6% 0,65 1,50 0,43

fib MC10 (2010) θ=45° (φ=75°) 75,0% 0,44 1,26 0,35

EC2 (2004) θ=36° 80,6% 0,57 1,40 0,41

EC2 (2004) θ=36° (φ=75°) 66,7% 0,32 1,08 0,29

fib MC10 (2010) θ=36° 75,0% 0,45 1,26 0,36

fib MC10 (2010) θ=36° (φ=75°) 69,4% 0,34 1,09 0,31EC2 (2004) θ=var 66,7% 0,36 1,13 0,31

EC2 (2004) θ=var (φ=75°) 33,3% 0,25 0,94 0,26

fib MC10 (2010) θ=35/45° 75,0% 0,43 1,24 0,35

fib MC10 (2010) θ=35/45° (φ=75°) 66,7% 0,33 1,07 0,31

EC2 (2004) θ=45° 79,6% 0,29 1,16 0,26

EC2 (2004) θ=45° (φ=75°) 26,5% 0,29 0,87 0,33

fib MC10 (2010) θ=45° 89,8% 0,69 1,53 0,45

fib MC10 (2010) θ=45° (φ=75°) 51,0% 0,43 1,09 0,40

EC2 (2004) θ=36° 79,6% 0,29 1,16 0,26

EC2 (2004) θ=36° (φ=75°) 26,5% 0,29 0,87 0,33

fib MC10 (2010) θ=36° 89,8% 0,69 1,53 0,45

fib MC10 (2010) θ=36° (φ=75°) 51,0% 0,43 1,09 0,40

EC2 (2004) θ=var 79,6% 0,29 1,16 0,26

EC2 (2004) θ=var (φ=75°) 26,5% 0,29 0,87 0,33

fib MC10 (2010) θ=35/45° 89,8% 0,69 1,53 0,45

fib MC10 (2010) θ=35/45° (φ=75°) 51,0% 0,43 1,09 0,40

EC2 (2004) θ=45° 87,5% 0,60 1,47 0,41

EC2 (2004) θ=45° (φ=75°) 62,5% 0,23 1,05 0,22

fib MC10 (2010) θ=45° 81,3% 0,42 1,32 0,32

fib MC10 (2010) θ=45° (φ=75°) 68,8% 0,25 1,09 0,23

EC2 (2004) θ=36° 87,5% 0,51 1,38 0,37

EC2 (2004) θ=36° (φ=75°) 43,8% 0,21 0,98 0,22

fib MC10 (2010) θ=36° 68,8% 0,27 1,13 0,24

fib MC10 (2010) θ=36° (φ=75°) 43,8% 0,19 0,94 0,20

EC2 (2004) θ=var 62,5% 0,34 1,18 0,29

EC2 (2004) θ=var (φ=75°) 56,3% 0,23 0,97 0,24

fib MC10 (2010) θ=35/45° 68,8% 0,26 1,11 0,23

fib MC10 (2010) θ=35/45° (φ=75°) 37,5% 0,19 0,92 0,21

U-JACKETING WITHOUT TRANSVERSAL REINFORCEMENT

U-JACKETING WITH TRANSVERSAL REINFORCEMENT

SIDE BONDING WITHOUT TRANSVERSAL REINFORCEMENT

SIDE BONDING WITH TRANSVERSAL REINFORCEMENT



ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS

In general, combining model of Pellegrino and Modena (both original and modified version) with EC2 for

non-strengthened structures gives the best predictions in case where angle of shear crack is used as

θ=var. Improvement in behaviour of this model with m

observed graphically. In Figure

(upper and lower graphs, respectively) are given.

a.

c.

Figure 12 - U-jacketed configurations without

Also, a comparison between experimental and theoretical

configurations without and with transversal reinforcement (upper and lower graphs, respectively).


MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS


strengthened structures gives the best predictions in case where angle of shear crack is used as

Improvement in behaviour of this model with modification of angle w from 79°

Figure 12, U-jacketed configurations without and with transversal reinforcement

d lower graphs, respectively) are given.

b.

d.

jacketed configurations without (graphs a and b) and with transversal reinforcement

c and d)

Also, a comparison between experimental and theoretical values is given in Figure 13


MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS 45


strengthened structures gives the best predictions in case where angle of shear crack is used as

79° to 75° can be also

jacketed configurations without and with transversal reinforcement

and with transversal reinforcement graphs

13 for side bonded




a.

c.

Figure 13 - Side bonded configurations

7.2 Results obtained using the

The database was divided in five groups in order to study the accuracy of the codes for the different

strengthening schemes. U-jacketed and side bonded configurations, both with and without transversal

steel are considered as separated four groups. Also, i

wrapped configuration and for that reason that scheme is analyzed as unique group, without

distinguishing presence of transversal steel. However, the lack of data regarding completely wrapped

beams is understandable when it is considered that in real applications, strengthening a concrete beam in

this fashion is not practical.

In Table 8, values for the coefficient of variation (CoV) obtained from DB

model codes, models for strengthened structures and angles of shear crack

values of average (AVG) are also given.




b.

d.

configurations without (graphs a and b) and with transversal reinforcement

graphs c and d)

Results obtained using the DB


jacketed and side bonded configurations, both with and without transversal

steel are considered as separated four groups. Also, it has to be said that there are not enough test for the



understandable when it is considered that in real applications, strengthening a concrete beam in

of variation (CoV) obtained from DB are summarized regarding

model codes, models for strengthened structures and angles of shear crack θ. In Table 9

values of average (AVG) are also given.




without (graphs a and b) and with transversal reinforcement


jacketed and side bonded configurations, both with and without transversal

t has to be said that there are not enough test for the



understandable when it is considered that in real applications, strengthening a concrete beam in

are summarized regarding basic

, corresponding




Table 8 – Values for Coefficient of Variation (CoV) obtained from DB

Model Code ACI318

Angle θ 45° 36° var (45 - 21.8) 45° 36° 35/45° 45°

fib '01 (2001) 0,23 0,20 0,56 0,61 0,54 0,61

CNR-DT 200 (2004) 0,29 0,22 0,37 0,45 0,35 0,45

ACI440 (2008) 0,48

fib '09 - draft (2009) 0,43 0,42 0,43 0,29 0,50 0,29

Chen and Teng (2003a) 0,55 0,54 0,50 0,75 0,73 0,75

Carolin and Täljsten (2005) 0,21 0,30 0,75 0,32 0,26 0,32

Pellegrino and Modena (2008) 0,37 0,37 0,37 0,57 0,57 0,57

Pellegrino and Modena φ=75° 0,34 0,34 0,34 0,51 0,51 0,51

Bukhari et al.(2010) 0,47 0,44 0,37 0,67 0,65 0,67

Modifi and Chaallal (2011) 0,49 0,45 0,35 0,68 0,65 0,68

fib '01 (2001) 0,59 0,45 0,39 0,47 0,35 0,34

CNR-DT 200 (2004) 0,62 0,49 0,38 0,37 0,28 0,27

ACI440 (2008) 0,37

fib '09 - draft (2009) 0,54 0,52 0,53 0,26 0,45 0,49

Chen and Teng (2003a) 0,71 0,59 0,29 0,55 0,54 0,54




Bukhari et al.(2010) 0,76 0,65 0,37 0,55 0,44 0,43


fib '01 (2001) 0,27 0,37 0,76 0,60 0,58 0,60

CNR-DT 200 (2004) 0,39 0,36 0,29 0,54 0,51 0,54

ACI440 (2008) 0,46

Chen and Teng (2003a) 0,52 0,59 0,78 0,62 0,63 0,62




Bukhari et al.(2010) 0,50 0,48 0,46 0,69 0,68 0,69


fib '01 (2001) 0,38 0,30 0,49 0,44 0,34 0,34

CNR-DT 200 (2004) 0,62 0,50 0,26 0,45 0,35 0,34

ACI440 (2008) 0,23

Chen and Teng (2003a) 0,55 0,44 0,40 0,28 0,30 0,30




Bukhari et al.(2010) 0,66 0,52 0,24 0,37 0,28 0,28


fib '01 (2001) 0,92 0,83 0,44 0,61 0,54 0,53

CNR-DT 200 (2004) 0,84 0,74 0,48 0,54 0,52 0,53

ACI440 (2008) 0,51

fib '09 - draft (2009) 0,61 0,54 0,53 0,38 0,45 0,45

COMPLETE WRAPPING

EC2 (2004) fib MC10 (2010)








Table 9 - Values for the Average (AVG) obtained from DB

Model Code ACI318

Angle θ 45° 36° var (45 - 21.8) 45° 36° 35/45° 45°

fib '01 (2001) 1,14 0,96 0,66 2,32 1,99 2,32

CNR-DT 200 (2004) 1,28 1,10 0,78 1,65 1,36 1,65

ACI440 (2008) 1,67

fib '09 - draft (2009) 0,75 0,76 0,75 0,93 0,72 0,93

Chen and Teng (2003a) 1,96 1,85 1,61 3,03 2,81 3,03




Bukhari et al.(2010) 1,76 1,63 1,34 2,67 2,39 2,67


fib '01 (2001) 1,78 1,30 0,83 1,64 1,29 1,25

CNR-DT 200 (2004) 1,82 1,33 0,84 1,35 1,05 1,02

ACI440 (2008) 1,28

fib '09 - draft (2009) 0,91 0,84 0,92 0,93 0,75 0,72

Chen and Teng (2003a) 2,77 2,02 1,14 1,89 1,84 1,83




Bukhari et al.(2010) 2,99 2,17 1,23 1,93 1,54 1,50


fib '01 (2001) 0,94 0,81 0,59 1,93 1,70 1,93

CNR-DT 200 (2004) 1,44 1,35 1,12 1,93 1,78 1,93

ACI440 (2008) 1,42

Chen and Teng (2003a) 0,92 0,82 0,66 1,19 1,06 1,19




Bukhari et al.(2010) 1,62 1,51 1,30 2,42 2,22 2,42


fib '01 (2001) 1,26 0,95 0,72 1,41 1,11 1,08

CNR-DT 200 (2004) 2,14 1,63 1,02 1,47 1,20 1,17

ACI440 (2008) 1,07

Chen and Teng (2003a) 1,47 1,10 0,80 1,12 1,06 1,06




Bukhari et al.(2010) 2,02 1,48 0,99 1,39 1,09 1,06


fib '01 (2001) 2,54 1,90 1,09 1,79 1,43 1,40

CNR-DT 200 (2004) 2,57 1,90 1,18 1,05 0,99 1,07

ACI440 (2008) 1,05

fib '09 - draft (2009) 1,79 1,43 1,40 1,09 0,89 0,87

COMPLETE WRAPPING

EC2 (2004) fib MC10 (2010)








Since basic codes, EC2 (2004) and fib MC10 (2010) are conceptually different in sense that EC2 does not

take into account contribution of both steel and concrete in presence of transversal steel, while fib MC10

does, it was expected gaining different results. It can be observed that for configurations with transversal

steel (U-jacketed and side bonded) and wrapped configurations, in general fib MC10 gives better

predictions, considering both values for CoV and AVG. This indicates once more that both contributions of

concrete and steel should be taken into account, also in presence of steel reinforcement.

In these cases, with presence of transversal steel or wrapped configurations, combination of fib MC10 with

models using angels θ=45° and θ=36° gives better predictions than combination of EC2 with models and

same angels, respectively. Combining EC2 with models and usage of θ=var still gives better results than

combining fib MC10 with models and usage of θ=35/45°, and more over it gives, in general, the best

results considering different basic codes and angels.

As for the angle inside the basic code, θ=var gives the best prediction in case of EC2 as basic code, while

in case of fib MC10 it is not very clear which angle is the most appropriate. On the other hand, taking into

account both values for CoV and AVG, for configurations with transversal steel θ=35/45° gives best

predictions and for configurations without transversal steel θ=36°. This means that in case of EC2 angle

should be taken into account as variable in order to maximize contribution of steel and concrete.

If we analyze values for CoV and AVG in terms of models for strengthened structures, in general, Italian

code CNR-DT200 (2004) and model of Pellegrino and Modena (2008) give good results.

In the overall comparison, considering also modified Pellegrino and Modena model, this model in general

gives the best predictions.



a.

c.

Figure 14 - Best prediction results in general overview: U

transversal steel and side bonded configurations without and with transversal steel (

In Figure 14, graphs are given for best predictions of models, considering different strengthening

configurations.




b.

d.

Best prediction results in general overview: U-jacketed configurations without and with

transversal steel and side bonded configurations without and with transversal steel (graphs a,b,c and d

respectively)

, graphs are given for best predictions of models, considering different strengthening




jacketed configurations without and with

graphs a,b,c and d,

, graphs are given for best predictions of models, considering different strengthening




7.3 Results obtained using the RDB

As it was explained before, the most used configuration in practical application is U-jacketed configuration

with transversal steel. Because of this, a Reduced Data Base (RDB) has been made and analyzed. In

Table 10 and Table 11 the main descriptive statistical measures obtained from this analysis are

summarized regarding percentage of conservative predictions, the average (AVG), the standard deviation

(std) and the coefficient of variation (CoV).

In general, usage of basic model code fib MC10 (2010) gives better predictions than usage of EC2,

although still usage of EC2 with θ=var gives the best results considering angle inside basic codes.

It can be observed that design models fib MC10 + fib ’09 – draft with θ=45° and EC2 + modified model of

Pellegrino and Modena (2008) with θ=45° and w=75° give the best predictions, both having the lowest

CoV=0,26. However, a second type of comparison is performed, in which values for AVG were compared

for both models. It has been shown that in overall, modified model of Pellegrino and Modena has value of

AVG closer to one, which makes this prediction more accurate.




Table 10 - Results from RDB for θ=45°and θ=36°

(U-jacketed configurations with transversal steel)

Model Conservative

Standard

Deviation AVG CoV

EC2 (2004) + fib '01 (2001) 91,2% 1,05 1,78 0,59

EC2 (2004) + CNR-DT 200 (2004) 88,9% 1,13 1,82 0,62

EC2 (2004) + fib '09 - draft (2009) 25,0% 0,49 0,91 0,54

ACI318 (2008) + ACI440 (2008) 83,3% 0,47 1,28 0,37

fib MC10 (2010) + fib '01 (2001) 86,1% 0,78 1,64 0,47

fib MC10 (2010) + CNR-DT 200 (2004) 80,6% 0,49 1,35 0,37

fib MC10 (2010) + fib '09 - draft (2009) 30,6% 0,24 0,93 0,26

EC2 (2004) + Chen and Teng (2003a) 94,4% 1,96 2,77 0,71

EC2 (2004) + Carolin and Täljsten (2005) 83,3% 0,68 1,48 0,46

EC2 (2004) + Pellegrino and Modena (2008) 86,1% 0,69 1,54 0,45

EC2 (2004) + Pellegrino and Modena φ=75° 72,2% 0,39 1,18 0,33

EC2 (2004) + Bukhari et al.(2010) 94,4% 2,27 2,99 0,76

EC2 (2004) + Modifi and Chaallal (2011) 94,4% 1,96 2,64 0,74

fib MC10 (2010) + Chen and Teng (2003a) 86,1% 1,05 1,89 0,55

fib MC10 (2010) + Carolin and Täljsten (2005) 80,6% 0,40 1,21 0,33

fib MC10 (2010) + Pellegrino and Modena (2008) 80,6% 0,65 1,50 0,43

fib MC10 (2010) + Pellegrino and Modena φ=75° 75,0% 0,44 1,26 0,35

fib MC10 (2010) + Bukhari et al.(2010) 88,9% 1,06 1,93 0,55

fib MC10 (2010) + Modifi and Chaallal (2011) 86,1% 0,92 1,77 0,52

EC2 (2004) + fib '01 (2001) 79,4% 0,59 1,30 0,45

EC2 (2004) + CNR-DT 200 (2004) 75,0% 0,65 1,33 0,49

EC2 (2004) + fib '09 - draft (2009) 19,4% 0,43 0,84 0,52

fib MC10 (2010) + fib '01 (2001) 80,6% 0,46 1,29 0,35

fib MC10 (2010) + CNR-DT 200 (2004) 69,4% 0,29 1,05 0,28

fib MC10 (2010) + fib '09 - draft (2009) 19,4% 0,34 0,75 0,45

EC2 (2004) + Chen and Teng (2003a) 91,7% 1,19 2,02 0,59




EC2 (2004) + Bukhari et al.(2010) 94,4% 1,42 2,17 0,65








θ=45°

θ=36°




Table 11 - Results from RDB for θ=var and θ=35/45°

(U-jacketed configurations with transversal steel)

Model Conservative

Standard

Deviation AVG CoV

EC2 (2004) + fib '01 (2001) 23,5% 0,32 0,83 0,39

EC2 (2004) + CNR-DT 200 (2004) 19,4% 0,32 0,84 0,38

EC2 (2004) + Chen and Teng (2003a) 75,0% 0,33 1,14 0,29




EC2 (2004) + Bukhari et al.(2010) 75,0% 0,46 1,23 0,37


EC2 (2004) + fib '09 - draft (2009) 25,0% 0,48 0,92 0,53

fib MC10 (2010) + fib '01 (2001) 80,6% 0,43 1,25 0,34

fib MC10 (2010) + CNR-DT 200 (2004) 66,7% 0,28 1,02 0,27

fib MC10 (2010) + fib '09 - draft (2009) 19,4% 0,35 0,72 0,49







θ=var°

θ=35/45°







8. CONCLUSIONS

This work reviews current knowledge on structural behaviour of reinforced concrete (RC) beams

strengthened with composite materials in terms of shear. Performed statically oriented study is

addressing main lacks of building codes recommendations and gives important imputes for further

research in field of the use of FRP in shear strengthening of RC structures.

8.1 Model of Pellegrino and Modena

• This model gives very good predictions in terms of CoV and AVG, since it takes into account

interaction between steel, concrete and FRP.

• It also shows good results while combining both with EC2 (2004) and fib MC10 (2010).

• Modification of the angle characterizing the conventional roughness of the interface w=79° to w=75°, improves model not only in sense of CoV, but also of AVG.

8.2 Basic codes

• For configurations with transversal steel and wrapped, fib MC10 (2010) in general gives better

predictions than EC2 (2004).

• In further investigation, different levels of approximation regarding fib MC10 (2010) should be

analyzed.

• In general, combining fib MC10 (2010) with models using angels θ=45° and θ=36° gives better

predictions than combining EC2 (2004) with models and same angles, respectively.

• Combining EC2 (2004) with models and usage of θ=var still gives better results than combining fib

MC10 (2010) with models and usage of θ=35/45°, and in general, the best results considering

different basic codes.

8.3 Angle inside basic code

• In case of EC2 (2004) as basic code, θ=var gives the best predictions.

• In case of fib MC10 (2010), the best predictions are θ=35/45° and θ=36° for configurations with

and without transversal steel, respectively.




8.4 Models

• In general, the Italian code CNR-DT200 (2004) and model of Pellegrino and Modena (2008) give

good results

• In the overall comparison, modified Pellegrino and Modena model gives the best predictions.

8.5 U-jacketing with transversal steel configuration

• In general, fib MC10 (2010) gives better predictions than EC2 (2004)

• Considering angle inside basic codes, EC2 (2004) with θ=var gives the best results.

• Combining EC2 (2004) with modified model of Pellegrino and Modena (2008), considering θ=var

and w=75° give the best predictions.

8.6 General conclusions

• In general, usage of EC2 (2004) θ=var gives the best predictions, which indicated great impact of

value of shear crack angle to model predictions.

• Combining EC2 (2004) with modified model of Pellegrino and Modena (2008), considering θ=var

and w=75° in general gives the best predictions for configurations with transversal steel.

• Since model that takes into account interaction between FRP and transversal steel gives (in

general) best predictions, it is proved that this interaction cannot be discarded in design

procedure.




9. REFERENCES

fib task group 9.3. Externally Bonded FRP Reinforcement for RC Structures (FIB bulletin draft ), 2009.

American Concrete Institute (ACI) Committee 318. "Shear and Torsion." In Building Code Requirements

for Structural Concrete (ACI 318M-08) and Commentary, 167-168. Farmington Hills, MI: American Concrete Institute, 2008.

American Concrete Institute (ACI) Committee 440. "Shear Strengthening." In Guide for the Design and

Construction of Extrenaly Bonded FRP Systems for Strengthening Concrete Structures (ACI 440.2R-08), 34-36. Farmington Hills, MI: American Concrete Institute, 2008.

Barros, J, S Dias, and J Lima. "Efficacy of CFRP-based techniques for the flexural and shear strengthening of concrete beams." Cement & Concrete Composites 29, 2007: 203-217.

Bukhari, I A, R L Vollum, S Ahmad, and J Sagaseta. "Shear strengthening of reinforced concrete." Magazine of Concrete Research 62, 2010: 65-77.

Carolin, A, and B Täljsten. "Theoretical study on strengthening for increased shear bearing capacity." Journal of Composites for Construction 9, 2005: 497-506.

CEN. Eurocode 2: Design of Concrete Structures — Part 1-1: General Rules and Rules for Buildings (ENV

1992-1-1). Brussels: Comite Europeen de Normalisation, 2004.

Chen, G M, J G Teng, and J F Chen. "RC beams shear-strengthened with FRP: shear resistance contributed by FRP." Magazine of Concrete Research 62, No. 4, 2010: 301–311.

Chen, G M, J G Teng, J F Chen, and O A Rosenboom. "Interaction between Steel Stirrups and Shear-Strengthening FRP Strips in RC Beams." Journal of Composites for Construction, Vol. 14, 2010: 498-509.

Chen, J F, and J G Teng. "Shear capacity of FRP-strengthened RC beams: FRP debonding." Construction and Building Materials 17, 2003a: 27–41.

CNR-DT200. Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening

Existing Structures. Materials, RC and PC Structures, Masonry Structures (CNR- DT 200/2004). Rome: Italian Research Italian Council, Advisory Committee on Technical Recommendations for Construction, 2004.

Colloti, V, and R N Swamy. "Unified analytical approach for determining shear capacity of RC beams strengthened with FRP." Engineering Structures 33, 2011: 827–842.

fib task group 9.3. Externally Bonded FRP Reinforcement for RC Structures (FIB bulletin 14). Lausanne: International Federation for Concrete, fib, 2001.

Gonzales, J. Assesment of Current Standards for Evaluation of Shear FRP Strengthening of Concrete

Beams. Master's Thesis, Padova: University of Padova, 2010.

International Federation for Concrete, fib. "Model Code." 2010.




Lima, J, and J Barros. "Reliability analysis of shear strengthening externally bonded FRP models." Structures and Buildings, 2011: 43-56.

Modifi, A, and O Chaallal. "Shear Strengthening of RC Beams with EB FRP: Influencing Factors and Conceptual Debonding Model." Journal of Composites for Constructions, 2011: 62-74.

Pellegrino, C, and C Modena. "An Experimentaly Based Analytical Model for the Shear Capacity of FRP-strenghtened Reinforced Concrete Beams." Mechanics of Composite Materialsrials, Vol. 44, No. 3,, 2008: 231-244.

Pellegrino, C, and C Modena. "Fiber-Reinforced Polymer Shear Strengthening of Reinforced Concrete Beams: Experimental Study and Analytical Modeling." ACI Structural Journal, V. 103, No. 5,, 2006.

Pellegrino, C, and C Modena. "FRP Shear Strengthening of RC Beams with Transverse Steel Reinforcement." Journal of Composites for Construction Vol. 6, No. 2,, 2002: 1-8.

Sas, G, B Täljsten, J Barros, J Lima, and A Carolin. "Are Available Models Reliable for Predicting the FRP Contribution to the Shear Resistance of RC Beams?" Journal of Composites for Constructions, 2009: 514-534.