quaderni del dottorato

Università degli Studi di Brescia
Dipartimento di Ingegneria Civile, Architettura,
Territorio, Ambiente e di Matematica
quaderni del dottorato
1
Ph.D. Thesis, Ph.D course in Materials for Engineering, University of Brescia
Supervisors:
Prof. Giovanni A. Plizzari
University of Brescia
Prof. Fausto Minelli
University of Brescia
Prof. Gustavo J. Parra-Montesinos
University of Michigan
Antonio Conforti
Ph.D. in Materials for Engineering
University of Brescia
Via Branze 43, 25123
Brescia (Italy)
[email protected]
[email protected]
Antonio Conforti
Shear Behavior of Deep and Wide-Shallow
Beams in Fiber Reinforced Concrete
Copyright © MMXIV
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I edizione: aprile 2014
Ai miei cari Bruno e Giuliano
ACKNOWLEDGMENTS
In these few lines I would like to thank and express my appreciation and gratitude
to all the people who, though in different ways, significantly contributed and
supported me during my PhD.
Firstly, I wish to express my appreciation to Professor Giovanni Plizzari who
guided me during my doctoral course and provided me with his useful and
important suggestions.
I would like to thank Professor Fausto Minelli as well. Thanks for helping me with
important engineering advices and your continuous support.
I would like also to express my special appreciation to Professor Gustavo J. Parra
Montesinos for his help, advices and important suggestions. Thanks also for giving
me the possibility of working at the University of Michigan.
Thanks also to Professor Pedro Serna for helping me during my stay at Universitat
Politècnica de València.
I want to express my special thanks to all friends who supported me during my
stay in the United States of America, particularly: Paolo Bianchi, Rishi Moudgil,
/àm Xuân Thái, Monthian Setkit, Brad Bodensteiner. Special thanks go also to
Stephen Klenke and his wonderful family Carey, Abby and Lucy.
Doverosi ringraziamenti vanno anche alla Prof. Laura Depero, a tutti i tecnici di
laboratorio e ai miei colleghi, tra i quali ringrazio in modo particolare l'Ing. Luca
Facconi. Rendo grazie inoltre a tutti i "tesisti" che mi hanno aiutato, ovvero: Ing.
Carlo Vezzoli; Ing. Francesco Bianchi; Ing. Bonomelli Mauro; Ing. Francesco
Bianchi; Ing. Andrea Tinini e l'Ing. Marco Galuppi.
Altresì, vorrei ringraziare i miei genitori Giovanni e Pierangela, mia sorella
Giuliana e i miei nonni: Domenica, Lucia e Rocco. In particolare ringrazio
tantissimo mia nonna Domenica. Ringrazio inoltre mio zio Giulio e mia zia Silvana.
Grazie per essermi sempre accanto sia nei momenti belli che in quelli brutti della
mia vita. Non per ultimo ringrazio anche il mio nonnino Bruno che ogni giorno mi
protegge da lassù.
Quisiera también dar las gracias a una magnífica familia española, la familia
Cuenca Asensio. Gracias Dolores, Esteban y Natalia por preocuparos por mí y por
mimarme como a un niño todas las veces que voy a España.
Finalmente, un gracias de todo corazón va a ti Fani! Gracias por todo lo que has
hecho por mí en estos años! Gracias por haber estado siempre a mi lado y por ser
una persona tan especial.
v
ABSTRACT
The behavior and design of reinforced concrete members subjected to shear
remains an area of much concern in spite of the vast number of experiments that
have been carried out to assess the shear capacity of structural members.
Consequently, design codes are frequently changed and are generally becoming
more stringent, so that structures designed several decades ago typically do not
comply with the requirements of current codes.
In fact, there are many parameters which affect the shear strength of a reinforced
concrete element without transverse reinforcement: shear-span-to-effective-depth
ratio, size of the element (better known as size effect), presence or absence of axial
load (tensile or compression), longitudinal reinforcement ratio, concrete
compressive strength, loading conditions, coarse aggregate size, shape of the cross
section and the distribution of longitudinal reinforcement along the beam depth.
Therefore, incorporating the influence of all these parameters in a formulation that
can be applied in the design is rather complicated.
The International Shear Workshop held in Salò, Italy, in 2010 provided an
opportunity to discuss the new approaches and verify how they meet or diverge
from one another. Moreover, it is of essential importance to recognize the effects
that new models may determine in the field and for structural design and
applications. In the workshop, both the shear behavior of reinforced concrete (RC)
and fiber reinforced concrete (FRC) elements has been discussed. In fact, fiber
reinforced concrete is now a material widely recognized by the international codes,
such as in the Model Code 2010.
Several reports published over the past twenty-five years confirm the effectiveness
of steel fibers as shear reinforcement. Fibers are used to enhance the shear capacity
of concrete or to partially or totally replace stirrups in RC structural members. This
relieves reinforcement congestion at critical sections such as beam-column junctions
in seismic applications. Fiber reinforcement may also significantly reduce
construction time and costs, especially in areas with high labor costs, and possibly
even labor shortages, since stirrups involve relatively high labor input to bend and
fix in place. Fiber concrete can also be easily deployed in thin or irregularly shaped
sections, such as architectural panels, where it may be very difficult to place
stirrups. This is of essential significance for many secondary structural elements in
which a minimum conventional reinforcement is not required for equilibrium.
The present PhD thesis intends to be a further contribution to the knowledge of
shear behavior of structural elements made of concrete and fiber reinforced
concrete.
Firstly, an extensive literature survey on the structural typology discussed in this
PhD thesis, RC beams and RC wide-shallow beams will be presented. This
vii
literature review will also address the material fiber reinforced concrete and its
possible structural applications, including its use as shear reinforcement.
Afterwards, an experimental campaign on RC deep beams will be presented, where
nine full-scale structural elements have been made and tested with the aim of
evaluating the influence of the element size on the shear strength of fiber reinforced
concrete beams.
Particular attention will be placed on two specific experimental campaigns
regarding the shear behavior of wide-shallow beams (WSBs) in both reinforced
concrete and fiber reinforced concrete (with steel fibers or synthetic fibers), in
which thirty wide-shallow beams have been tested. The main purpose of this
research has been the study of the shear behavior of wide-shallow beams, as well as
the role of the width on the shear strength.
The experiments have been also studied numerically by means of the finite element
program VecTor2 based on the Modified Compression Field Theory (MCFT) and
the Disturbed Stress Field Model (DSFM). An interesting numerical study on the
size effect influence on the shear strength of fiber reinforced concrete elements will
be presented, discussed and compared with the experimental results obtained from
the experimental campaign on deep beams.
Finally, in order to summarize the main experimental tests done at the University of
Brescia on reinforced concrete elements critical in shear, the last chapter will
present the overall University of Brescia’s shear database. This shear database
consists of ninety-one elements, in which sixty-two are beams and twenty-nine
wide-shallow beams, both in RC and FRC.
viii
SOMMARIO
Il comportamento strutturale di travi in calcestruzzo armato soggette a
sollecitazioni taglianti continua ad essere materia di vivace dibattito all’interno
della comunità scientifica. Conseguentemente le formulazioni sulla resistenza a
taglio presenti nelle diverse normative vigenti sono in continua evoluzione e in
generale tendono a divenire sempre più severe.
Molti sono infatti i parametri che influenzano la resistenza a taglio di un elemento
in calcestruzzo armato privo di rinforzo trasversale: la snellezza a taglio, la
dimensione dell’elemento (più noto come effetto scala), la presenza o meno di
azione assiale (trazione o compressione), la percentuale di armatura longitudinale
tesa, la resistenza a compressione del calcestruzzo, le condizioni di carico, le
dimensioni degli aggregati, la forma della sezione trasversale e la distribuzione
dell’armatura longitudinale all’interno della sezione. Inserire l’influenza di tutti
questi parametri in una formulazione che sia applicabile nella progettazione è
pertanto alquanto complicato.
Ad ottobre 2010, l’Università degli Studi di Brescia ha organizzato un Workshop
internazione sulla tematica del taglio e del punzonamento (Recent Developments
on Shear and Punching Shear in RC and FRC Elements), che ha costituito
un’importante opportunità di discussione sul nuovo Model Code 2010 e sui più
recenti sviluppi della ricerca a riguardo. Sono state inoltre analizzate le implicazioni
che questo documento porterà nel mondo della progettazione, sia nelle strutture in
calcestruzzo ordinario, che in quelle in calcestruzzo armato fibrorinforzato (Fiber
Reinforced Concrete, FRC), materiale ampiamente documentato e riconosciuto dal
nuovo Model Code 2010. Infatti, molti contributi scientifici, pubblicati negli ultimi
venticinque anni, hanno sperimentalmente confermato l’efficacia delle fibre come
rinforzo a taglio. Le fibre migliorano la capacità portante, la duttilità a taglio e
possono sostituire, parzialmente o totalmente, l’armatura trasversale. Questo
permette di ridurre la congestione dell’armatura nelle sezioni critiche, in primis
nodi trave-colonna nelle applicazioni sismiche. Il rinforzo fibroso può altresì
ridurre il tempo e il costo di costruzione, soprattutto in aree in cui il costo del
lavoro è significativo e in tutti i casi in cui la disposizione delle staffe è onerosa se
non estremamente difficoltosa (si pensino a profili di sezione complessa nella
prefabbricazione o a pannelli sottili), risultando spesso non rispettosa dei valori
minimi di ricoprimento richiesti.
Il presente lavoro di ricerca intende costituire un ulteriore contributo sullo studio
del comportamento a taglio di elementi strutturali in calcestruzzo armato e
calcestruzzo fibrorinforzato.
Innanzitutto, un’approfondita indagine bibliografica sulle tipologie strutturali
trattate in questa tesi, ovvero travi altre e travi in spessore verrà presentata. Tale
ix
ricerca bibliografica tratterà anche il materiale calcestruzzo fibrorinforzato e le sue
possibili applicazioni strutturali, tra cui il suo uso come rinforzo a taglio.
In seguito, ampio spazio sarà dedicato alla campagna sperimentale svolta su travi
alte, dove nove elementi strutturali in scala reale sono stati realizzati e testati col
fine di valutare l’influenza della dimensione dell’elemento sulla resistenza a taglio
di elementi in calcestruzzo fibrorinforzato.
L’attenzione verrà poi posta su due specifiche campagne sperimentali riguardanti il
comportamento a taglio di travi in spessore (Wide-Shallow Beams, WSBs) sia in
calcestruzzo armato che in calcestruzzo fibrorinforzato (con fibre di acciaio o fibre
sintetiche), nelle quali trenta travi in spessore sono state realizzate e testate
sperimentalmente.
I risultati sperimentali sono poi stati studiati anche numericamente grazie
all’utilizzo del programma ad elementi finiti VecTor2 basato sulla Modified
Compression Field Theory (MCFT) e sulla Disturbed Stress Field Model (DSFM). A
seguire, uno studio numerico sull’influenza dell’effetto scala sulla resistenza a
taglio di elementi in calcestruzzo fibrorinforzato verrà presentato, discusso e
confrontato con i valori sperimentali ottenuti dalla campagna sperimentale sulle
travi alte.
Infine, con lo scopo di riassumere e sintetizzare tutte le campagne sperimentali
svolte presso l’Università degli Studi di Brescia sul comportamento a taglio di
elementi strutturali in calcestruzzo armato e fibrorinforzato, il database delle prove
di taglio dell’Università degli Studi di Brescia verrà presentato. Tale database è
composto da novantuno elementi strutturali in calcestruzzo armato e calcestruzzo
armato fibrorinforzato.
x
RESUMEN
El comportamiento estructural de vigas de hormigón armado sometidas a
solicitaciones de cortante continúa siendo materia de debate en la comunidad
científica. Por tanto, las formulaciones para determinar la resistencia a cortante
presentes en las distintas normativas vigentes están en continua evolución y, en
general, tienden a ser cada vez más severas.
De hecho, muchos son los parámetros que influencian la resistencia a cortante de
un elemento de hormigón armado sin armadura transversal: la esbeltez a cortante,
la dimensión del elemento (más conocido como efecto tamaño), la presencia o no de
axil (tracción o compresión), el porcentaje de armadura longitudinal traccionada, la
resistencia a compresión del hormigón, las condiciones de carga, el tamaño máximo
de árido, la forma de la sección transversal y la distribución de la armadura
longitudinal en el interior de la sección. Tener en cuenta la influencia de todos estos
parámetros en una formulación que sea aplicable en el proyecto es, por tanto,
complicado.
En octubre de 2010, la Università degli Studi di Brescia organizó un Workshop
internacional tratando la temática del cortante y el punzonamiento (Recent
Developments on Shear and Punching Shear in RC and FRC Elements), que
constituyó una importante oportunidad de discusión sobre el nuevo Código
Modelo 2010 (Model Code 2010) y sobre los más recientes y destacados resultados
de investigación publicados hasta ese momento. En consecuencia, se ha analizado
la influencia que este documento tendrá en el mundo del proyecto, ya sea en las
estructuras de hormigón convencional como en las de hormigón reforzado con
fibras (Fiber Reinforced Concrete, FRC), siendo este último material ampliamente
documentado y reconocido por el Código Modelo 2010 (Model Code 2010). De
hecho, muchas contribuciones científicas, publicadas en los últimos 25 años, han
confirmado experimentalmente la eficacia de las fibras como refuerzo a cortante.
Las fibras mejoran la capacidad portante, la ductilidad a cortante y pueden
sustituir, parcial o totalmente, la armadura transversal. Esto permite reducir la
congestión de armadura en las secciones críticas, en nudos viga-columna en las
aplicaciones sísmicas. Además, el refuerzo con fibras puede reducir el tiempo y el
coste de construcción, sobretodo en las áreas cuyo coste de mano de obra es
significativo y en todos los casos donde la disposición de los estribos es costosa o
extremadamente difícil (sea el caso de perfiles de sección compleja en
prefabricación o paneles delgados), no respetando, a menudo, los valores mínimos
de recubrimiento requeridos.
El presente trabajo de investigación pretende constituir una posterior contribución
al estudio del comportamiento a cortante de elementos estructurales de hormigón
armado y hormigón reforzado con fibras.
xi
En primer lugar, se presentará un profundo estudio bibliográfico sobre las
tipologías estructurales tratadas en esta tesis doctoral, es decir, vigas altas y vigas
planas. Tal estudio bibliográfico tratará también el hormigón reforzado con fibras
como material y sus posibles aplicaciones estructurales, así como su uso como
refuerzo a cortante.
Después, se dedicará buena parte de la tesis a la campaña experimental
desarrollada sobre vigas altas, donde nueve elementos estructurales en escala real
fueron fabricados in situ y posteriormente ensayados con el fin de evaluar la
influencia de la dimensión del elemento sobre la resistencia a cortante de elementos
de hormigón reforzado con fibras.
Posteriormente, se prestará atención específica sobre dos campañas experimentales
relativas al comportamiento a cortante de vigas planas (Wide-Shallow Beams,
WSBs) tanto de hormigón armado como de hormigón reforzado con fibras (con
fibras de acero o fibras sintéticas), en las cuales treinta vigas planas fueron
producidas y ensayadas experimentalmente.
Posteriormente, los resultados experimentales fueron analizados también
numéricamente mediante el software de elementos finitos VecTor2 basado en la
Modified Compression Field Theory (MCFT) y en la Disturbed Stress Field Model
(DSFM). A continuación, un estudio numérico sobre la influencia del efecto tamaño
sobre la resistencia a cortante de elementos de hormigón reforzado con fibras será
presentado, discutido y comparado con los valores experimentales obtenidos de la
campaña experimental sobre vigas altas.
Finalmente, con el objetivo de resumir y sintetizar todas las campañas
experimentales llevadas a cabo en la Università degli Studi di Brescia sobre el
comportamiento a cortante de elementos estructurales de hormigón armado y de
hormigón reforzado con fibras, se presentará la base de datos de los ensayos de
cortante realizados en la Università degli Studi di Brescia. Esta base de datos está
compuesta de noventa y uno elementos estructurales de hormigón armado y
hormigón armado reforzado con fibras.
xii
CONTENTS
CONTENTS
1.
2.
INTRODUCTION ..................................................................................................... 3
1.1
Statement of problems and aim of the research .............................................. 3
1.2
Organization of the Thesis ................................................................................. 5
LITERATURE SURVEY ............................................................................................ 7
2.1
Fiber reinforced concrete.................................................................................... 7
2.1.1
2.1.2
2.1.3
2.1.4
2.2
Reinforced concrete deep beams in shear ...................................................... 24
2.2.1
2.2.2
2.3
3.
Size effect for RC elements ......................................................................... 24
Size effect for FRC elements ....................................................................... 32
Reinforced concrete wide-shallow beams in shear ...................................... 36
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.4
Material properties ........................................................................................ 7
Fiber geometries and types ........................................................................ 12
Use of fibers as shear reinforcement ......................................................... 13
Structural application of fiber reinforced concrete ................................. 22
Introduction ................................................................................................. 36
Width-to-effective depth ratio (b/d).......................................................... 39
Size effect for wide-shallow beams ........................................................... 43
Support width .............................................................................................. 45
Transverse stirrup configuration............................................................... 48
References .......................................................................................................... 54
EXPERIMENTAL PROGRAM ON DEEP BEAMS ............................................ 63
3.1
Introduction ....................................................................................................... 63
3.2
Material and specimen geometry ................................................................... 64
3.3
Test set-up and instrumentation ..................................................................... 69
3.4
Experimental results and discussion .............................................................. 73
3.5
International code previsions for RC deep beams........................................ 85
3.6
Concluding remarks ......................................................................................... 91
3.7
Future research .................................................................................................. 92
3.8
References .......................................................................................................... 94
4.
EXPERIMENTAL PROGRAM ON WIDE-SHALLOW BEAMS..................... 95
4.1
Introduction ....................................................................................................... 95
4.2
Steel fiber reinforced concrete wide-shallow beams .................................... 95
4.2.1
4.2.2
4.2.3
4.2.4
4.3
Polypropylene fiber reinforced concrete wide-shallow beams ................ 118
4.3.1
4.3.2
4.3.3
4.3.4
5.
Materials ....................................................................................................... 97
Test set-up and instrumentation ............................................................. 101
Experimental results and discussion ...................................................... 103
Concluding remarks ................................................................................. 117
Geometry and material properties .......................................................... 119
Instrumentation set-up and loading modalities.................................... 128
Experimental results ................................................................................. 131
Concluding remarks ................................................................................. 145
4.4
International code previsions for RC wide-shallow beams ...................... 146
4.5
Future research ................................................................................................ 153
4.6
References ........................................................................................................ 156
NUMERICAL ANALYSES ................................................................................... 157
5.1
Introduction ..................................................................................................... 157
5.2
Deep beams: comparison between numerical and experimental results 158
5.2.1 Modeling of materials ............................................................................... 159
5.2.1.1
Concrete........................................................................................... 159
5.2.1.1.1 Tension softening for PC ...................................................... 160
5.2.1.1.2 Tension softening for FRC .................................................... 160
5.2.1.2
Longitudinal reinforcement .......................................................... 165
5.2.2
5.2.3
6.
Modeling of beam geometry .................................................................... 166
Comparison of numerical and experimental results ............................ 168
5.3
Size effect for RC and FRC members by finite element analyses (FEA) .. 175
5.4
Concluding remarks ....................................................................................... 184
5.5
References ........................................................................................................ 185
SHEAR DATABASE ............................................................................................. 187
6.1
University of Brescia’s shear database ......................................................... 188
6.1.1
RC and FRC beams ................................................................................... 188
CONTENTS
6.1.2
6.2
7.
RC and FRC wide-shallow beams ........................................................... 193
References ........................................................................................................ 196
CONCLUSIONS .................................................................................................... 197
Shear behavior of deep and wide-shallow beams
in fiber reinforced concrete
1. INTRODUCTION
1.
INTRODUCTION
1.1 Statement of problems and aim of the research
The shear behavior of structural elements in reinforced concrete continues to be a
topic of great interest within the international scientific community. In fact, despite
the large number of scientific papers published in the last decades, there is still no
consensus concerning mechanisms of shear transfer and the best way to model
structural elements subjected to shear without transverse reinforcement. Therefore,
it remains a need to establish design and analysis methods that provide realistic
assessments of the strength, stiffness and ductility of structural elements subjected
to shear loading.
However, recent attempts to provide a broadly acknowledged design procedures
for shear (especially with regard to members with little or no shear reinforcement)
can be outlined in the final draft of fib Model Code (2012), referred to in the
following as MC2010: four different approximation levels are proposed for
designing shear members, incorporating statements and models well recognized
such as the Modified Compression Field Theory (MCFT) (Vecchio et al., 1986).
In addition, the International Shear Workshop held in Salò (Italy) (fib Bulletin 57,
2010), provided an opportunity to assess and analyze the shear behavior of
reinforced concrete elements, aside from discuss the new shear approaches and
verify how they meet or diverge from one another. This workshop has given new
ideas for future research and to further harmonize the various shear rules of
international codes, towards an unified approach to solve the long standing
problem that already in 1964 Kani, one of the pioneers of modern research on shear,
called "The riddle of shear failure".
Moreover, in the shear workshop, both the shear behavior of reinforced concrete
(RC) and fiber reinforced concrete (FRC) elements have been discussed. In fact,
fiber reinforced concrete is now an innovative material widely recognized by the
international codes, as well as in the Model Code 2010. Fiber reinforced concrete, as
defined in the Model Code 2010, is a composite material characterized by a cement
matrix and discrete fibers (discontinuous), where the matrix is made of concrete or
mortar and fiber can be made of steel, polymers, carbon, glass or natural materials.
Fibers can be used to improve both the behavior at Serviceability Limit State (they
can reduce crack spacing and crack width) and Ultimate Limit State (they can
partially or totally substitute conventional reinforcement).
Research on structural application of fiber reinforced concrete have been mainly
focused on the use of fibers as shear reinforcement. In fact, a significant number of
reports published over the past thirty years (Cuenca, 2012; Dinh et al., 2010; Choi et
al., 2007; Minelli, 2005) have been confirmed the effectiveness of steel fibers as shear
3
reinforcement since they enhance the shear capacity of concrete and allow to
partially or totally replace stirrups in reinforced concrete structural members
(reducing construction time and costs). This is very important also in seismic
application because relieves reinforcement congestion at critical sections such as
beam-column junctions. Therefore, many studies produced a number of
experimental researches on the shear resistance of Steel Fiber Reinforced Concrete
(SFRC) and also defined new equations for predicting the ultimate shear strength of
SFRC beams.
Even though these studies can be certainly considered a good advancement for
understanding the shear behavior of SFRC members, many of them are
characterized by tests on beams of special geometry with a limited range of crucial
parameters and conditions being investigated (concrete class, fiber geometry,
content and composition, size, longitudinal and transverse reinforcing ratio). In
addition, most of the experiments are characterized to study only classical beams
and not other kind of structural elements, as shallow-wide beams, which are widely
used in residential buildings.
In this respect, the present PhD thesis focuses on the study of shear behavior of
structural elements made of concrete (RC) and fiber reinforced concrete (FRC).
Thus, it intends to be a further contribution to the knowledge of shear behavior of
structural elements. The results of three experimental campaigns on both reinforced
concrete and fiber reinforced concrete beams under shear loading tested at the
University of Brescia will be presented, focusing on the size effect issue and the
shear behavior of wide-shallow beams (as well as the role of the width on the shear
strength). With the first regard, nine full scale beams, having a height varying from
500 to 1500 mm, were tested for investigating the effect of steel fibers on size effect.
Concerning the shear behavior of wide-shallow beams (WSBs), thirty shallow
beams with different width, fiber content and type (steel or polypropylene fibers)
and, also, minimum amount of classical shear reinforcements, were tested for
evaluating the shear response of typical structural members utilized in residential
buildings. Results show that a relatively low volume fraction of fibers can
significantly increase shear bearing capacity and ductility. The latter determines
visible deflection and prior warning of impending collapse, which is not possible in
plain concrete beams (without transverse reinforcement). The size effect issue is
substantially limited and it is observed that, with a fairly tough FRC composite, it is
possible to completely eliminate this detrimental effect. Shallow beams do not show
the typical brittle failure also without any shear reinforcement and the effect of
fibers is even more prominent than in deep beams.
Moreover, a number of numerical analyses on reinforced concrete deep beams by
the finite element program VecTor2 based on the Modified Compression Field
Theory (MCFT) and the Disturbed Stress Field Model (DSFM) will be presented.
Finally, in order to summarize the main experimental tests done at the University of
4
1. INTRODUCTION
Brescia on reinforced concrete elements subjected to shear, the overall University of
Brescia’s shear database will be presented. This shear database consists of ninetyone elements, in which sixty-two are beams and twenty-nine wide-shallow beams,
both in RC and FRC.
1.2 Organization of the Thesis
The present PhD thesis is divided into seven chapters:
Chapter 1 underline the statement of problem and the aim of research.
Chapter 2 reports a literature review focused on the structural typology discussed
in this PhD thesis, namely deep beams and wide-shallow beams. An overview of
both fiber reinforced concrete material and the shear behavior of reinforced
concrete elements made of this material is presented as well.
Chapter 3 is devoted to an experimental campaign on fiber reinforced concrete
(FRC) beams under shear loading tested at the University of Brescia, where nine
full scale beams, having a height varying from 500 to 1500 mm, have been tested for
investigating the effect of steel fibers on key-parameters influencing the shear
response of concrete members, with special emphasis on FRC toughness and size
effect. All tested members contained no conventional shear reinforcement.
Chapter 4 is focused on two experimental campaigns on wide-shallow beams in
reinforced concrete and fiber reinforced concrete under shear loading tested at the
University of Brescia for studying the shear behavior of wide-shallow beams (as
well as the influence of the width on the shear strength) and evaluate the possibility
to substitute the minimum conventional transverse reinforcement required by
Eurocode 2 with fibers. This section has been organized as follows:
Section 4.1: Sixteen experimental tests on reinforced concrete (RC) and steel fiber
reinforced concrete (SFRC) wide-shallow beams (all having depth of
250 mm) with two different widths, fiber content and, also, minimum
amount of classical shear reinforcements will be presented.
Section 4.2: Fourteen experimental tests on wide-shallow beams both in reinforced
concrete (RC) and polypropylene fiber reinforced concrete (PFRC)
characterized as having different width and depth, fiber content and,
also, minimum amount of classical shear reinforcements will be
discussed.
5
Chapter 5 focuses in the numerical nonlinear analyses of reinforced concrete and
fiber reinforced beams by the program VecTor2 (VT2). Several numerical analyses
will be presented in order to model and discuss the shear behavior of RC and FRC
deep beams contained in the Chapter 3. Moreover, other specific numerical
analyses will be presented in order to study the size effect influence on the shear
behavior of RC and FRC elements by Finite Element Analyses (FEA).
Chapter 6 reports the overall University of Brescia's shear database, consisting of
ninety-one elements, both in reinforced concrete and fiber reinforced concrete.
Chapter 7 summarizes the main conclusions of this PhD thesis.
6

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