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  • FEDERAL UNIVERSITY OF MINAS GERAIS

    STRUCTURAL ENGINEERING DEPARTMENT

    Elayne Marques Silva

    Probabilistic Assessment of Serviceability of FRP-

    Reinforced Concrete Beams

  • Silva, Elayne Marques. S586p Probabilistic assessment of serviceability of FRP-reinforced concrete beams [manuscrito] / Elayne Marques Silva. - 2017. xvi, 105 f., enc.: il.

    Orientadora: Sofia Maria Carrato Diniz. Coorientadora: Sidnea Eliane Campos Ribeiro

    Dissertação (mestrado) Universidade Federal de Minas Gerais, Escola de Engenharia. Apêndices: 86-105. Bibliografia: f. 82-85.

    1. Engenharia de estruturas - Teses. 2. Confiabilidade (Engenharia)- Teses. 3. Momentos de inércia - Teses. 4. Método de Monte Carlo – Teses. 5. Plástico reforçado por fibras - Teses. I. Diniz, Sofia Maria Carrato. II. Ribeiro, Sidnea Eliane Campos. III. Universidade Federal de Minas Gerais. Escola de Engenharia. IV. Título.

    CDU: 624(043)

  • FEDERAL UNIVERSITY OF MINAS GERAIS

    STRUCTURAL ENGINEERING DEPARTMENT

    “PROBABILISTIC ASSESSMENT OF SERVICEABILITY OF FRP-REINFORCED

    CONCRETE BEAMS”

    Elayne Marques Silva

    Dissertation presented to the Graduate

    Program in Structural Engineering of the

    Structural Engineering Department of the

    Federal University of Minas Gerais, being

    part of the requirements for the “Master in

    Structural Engineering” degree.

    Examination committee:

    _____________________________________________

    Prof. Sofia Maria Carrato Diniz – (Advisor)

    DEEs – Structural Engineering Department – UFMG

    _____________________________________________

    Prof. Sidnea Eliane Campos Ribeiro – (Co-advisor)

    DEMC – Department of Materials and Construction - UFMG

    _____________________________________________

    Prof. José Márcio Fonseca Calixto

    DEEs – Structural Engineering Department – UFMG

    _____________________________________________

    Prof. Sebastião Salvador Real Pereira

    DEEs – Structural Engineering Department – UFMG

    Belo Horizonte, August 2017.

  • i

    1. ACKNOWLEDGEMENTS

    I would like to thank God for giving me the strength and knowledge to carry out this research.

    I would like to thank my advisor Prof. Sofia Maria Carrato Diniz for believing in me and for

    her guidance in this research. I am so grateful to Sofia for sharing her vast and invaluable

    research experience and directing me in all stages of this work. My deep gratitude to my co-

    advisor, Prof. Sidnea Eliane Campos Ribeiro, for her interest in my work.

    A special “thank you” goes to Prof. José Márcio Fonseca Calixto, for his excellent lectures.

    I also would like to thank CAPES for the financial support provided.

  • ii

    2. ABSTRACT

    Reinforced concrete (RC) structures are often subjected to deicing salts or in a marine

    environment; as such, a major problem in the durability of these structures is the corrosion of

    reinforcing steel. In this light, Fiber Reinforced Polymers (FRP), as noncorrosive materials,

    provide a promising prospect for use as reinforcement in concrete construction. FRP

    reinforcement may offer not only greater durability but also higher resistance and,

    consequently, potential gains throughout the lifecycle of the structure. Although the use of

    FRP bars as structural reinforcement shows great promise in terms of durability, the

    characteristics of this material led to new challenges in the design of FRP-RC components.

    Due to differences between the mechanical properties of steel and FRP, the reliability of FRP-

    reinforced concrete (RC) beams shall be assessed. While a reasonable body of knowledge has

    been gathered regarding the reliability of FRP-RC beams with respect to ultimate limit states,

    the same is not true for serviceability of such beams. Since FRP is characterized by higher

    values of strength and lower Young’s modulus compared to steel, this implies that the design

    of FRP-RC structures will be influenced almost exclusively by serviceability limit states. In

    this study, a contribution to the development of semiprobabilistic design recommendations for

    FRP-RC beams, with respect to the serviceability limit state, is reported. Numerous equations

    have been proposed for computing the effective moment of inertia of FRP-RC members. This

    research also aims to select an equation for the calculation of the effective moment of inertia

    for FRP-RC beams assessed in this study. Since most of the variables involved in the problem

    (mechanical properties of concrete and FRP, geometric characteristics, model error, loads,

    etc.) are random, serviceability is established in probabilistic terms. In this context, Monte

    Carlo simulation is used in the probabilistic description of beam deflections, and in the

    computation of the probability of failure of designed beams with respect to the limit state of

    excessive deflections. Large probabilities of failure are found for this serviceability limit state

    according to current design recommendations. Suggestions are presented on simple, but

    effective ways to circumvent this limitation.

    Keywords: FRP, FRP-Reinforced Structures, Durability, Beams, Effective Moment of Inertia, Design

    Codes, Deflections, Serviceability Limit State, Reliability, Probability, Monte Carlo Simulation.

  • iii

    3. TABLE OF CONTENTS

    ACKNOWLEDGEMENTS ........................................................................................................ i

    ABSTRACT ............................................................................................................................... ii

    TABLE OF CONTENTS .......................................................................................................... iii

    LIST OF FIGURES .................................................................................................................. vii

    LIST OF TABLES .................................................................................................................... ix

    ACRONYMS ............................................................................................................................ xi

    NOTATION ............................................................................................................................. xii

    1. INTRODUCTION ............................................................................................................... 1

    1.1 STATEMENT OF THE PROBLEM .............................................................................. 1

    1.2 OBJECTIVES ................................................................................................................. 3

    1.3 ORGANIZATION .......................................................................................................... 4

    2. MECHANICAL PROPERTIES OF MATERIALS ............................................................ 6

    2.1 CONCRETE ................................................................................................................... 6

    2.2 FIBER-REINFORCED POLYMERS (FRP) ................................................................. 8

    2.2.1 Tensile behavior of FRP bars ............................................................................... 8

    2.2.2 Compressive behavior of FRP bars .................................................................... 10

    2.2.3 Shear behavior of FRP bars ................................................................................ 10

    2.2.4 Density ................................................................................................................ 10

    2.2.5 Creep rupture of FRP bars .................................................................................. 11

    2.3 SUMMARY OF THE CHAPTER ............................................................................... 11

  • iv

    3. DESIGN CONSIDERATIONS FOR FRP-REINFORCED CONCRETE BEAMS ........ 12

    3.1 GENERAL DESIGN CONSIDERATIONS ................................................................ 12

    3.2 ACI-440 recommendations for flexural design ............................................................ 13

    3.2.1 Strength reduction factors ................................................................................... 16

    3.2.2 Minimum FRP reinforcement ............................................................................. 17

    3.2.3 Design material properties .................................................................................. 18

    3.2.4 Serviceability ...................................................................................................... 19

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