ISOMAT DOCUMENTATIE

PROF. THANASIS C. TRIANTAFILLOU UNIVERSITY OF PATRAS

DEPARTMENT OF CIVIL ENGINEERING STRUCTURAL MATERIALS LABORATORY

STRENGTHENING AND SEISMIC RETROFITTING OF REINFORCED CONCRETE STRUCTURES WITH

FIBER-REINFORCED POLYMERS (FRP)

PATRAS, GREECE

2005

iii

page

PREFACE i

CONTENTS iii

CHAPTER 1 – INTRODUCTION 1

1.1 General 1

1.2 Structure of the book 3

CHAPTER 2 – MATERIALS AND TECHNIQUES 5

2.1 Materials 5

2.1.1 General 5

2.1.2 Fibers 5

2.1.3 Matrix 7

2.1.4 Composite materials 7

Example 2.1 9

2.1.5 Adhesives 10

2.2 Strengthening systems 11

2.2.1 Wet lay-up systems 11

2.2.2 Prefabricated elements 12

2.3 Basic strengthening technique 13

CHAPTER 3 – BASIS OF DESIGN 15

3.1 General 15

3.2 Material constitutive laws 15

3.2.1 Calculation of resistance – full composite action 15

3.2.2 Calculation of resistance - debonding 17

3.2.3 Serviceability limit state 17

3.3 Bond at the FRP – concrete interface 17

3.3.1 General, behavior 17

3.3.2 Analytical model 19

Example 3.1 20

CONTENTS

iv

page

CHAPTER 4 – FLEXURAL STRENGTHENING 21

4.1 General 21

4.2 Initial situation 22

4.3 Ultimate limit state – failure modes 23

4.4 Ultimate limit state - calculations 25

4.4.1 Full composite action 25

4.4.2 Loss of composite action 27

4.5 Ductility considerations 30

4.6 Summary of design calculations – ultimate limit state 31

4.7 Example 32

4.8 Servicability limit state 34

4.9 Columns 35

CHAPTER 5 – SHEAR STRENGTHENING 39

5.1 General 39

5.2 Shear carried by FRP 41

5.3 Summary of design procedure 44

Example 5.1 45

Example 5.2 47

Example 5.3 47

5.4 Beam-column joints 48

CHAPTER 6 – CONFINEMENT 51

6.1 General 51

6.2 Behavior and constitutive modeling of FRP-confined concrete 52

6.2.1 Behavior 52

6.2.2 Design model 54

Example 6.1 58

6.3 Chord rotation and ductility 58

Example 6.2 63

6.4 Lap-splices 64

6.4.1 Behavior and design 64

Example 6.3 66

6.4.2 Effect of lap-splices on chord rotation 67

6.5 Rebar buckling 68

Example 6.4 69

v

page

6.6 General comments on FRP-jacketed columns 69

CHAPTER 7 – DETAILING AND PRACTICAL EXECUTION 71

7.1 General 71

7.2 Detailing 71

7.2.1 Flexural strengthening 71

7.2.2 Shear strengthening 73

7.2.3 Confinement 74

7.3 Practical execution 76

CHAPTER 8 – DURABILITY 79

8.1 General 79

8.2 Temperature effects 79

8.3 Moisture 79

8.4 UV light exposure 80

8.5 Alcalinity and acidity 80

8.6 Galvanic corrosion 81

8.7 Creep, stress rupture, stress corrosion 81

8.8 Fatigue 81

8.9 Impact 82

REFERENCES 83

APPENDIX – THE PROGRAM Composite Dimensioning 87

i

This document is based on the book by Prof. Thanasis C. Triantafillou “Strengthening of

Reinforced Concrete Structures with Fiber Reinforced Polymers” (in Greek), published in 2003,

and covers basic design aspects of strengthening and seismic retrofitting of concrete with

advanced composite materials. This relatively new strengthening/retrofitting technique offers, in

many cases, several advantages compared with traditional techniques, but is rather unknown to

many designers, especially with respect to the relevant calculations. It is this gap that the present

document intents to fill, through explanatory text (including simple examples) and a simple to use

software package – Composite Dimensioning – described in the Appendix and included in the

accompanied CD.

PREFACE

INTRODUCTION

STRENGTHENING AND SEISMIC RETROFITTING OF RC STRUCTURES WITH FRP T. C. Triantafillou

1

1.1 General

The issue of upgrading the existing civil engineering infrastructure has been one of great importance for over 15 years or so. Deterioration of bridge decks, beams, girders and columns, buildings, parking structures and others may be attributed to ageing, environmentally induced degradation, poor initial design and/or construction, lack of maintenance, and to accidental events such as earthquakes. The infrastructure’s increasing decay is frequently combined with the need for upgrading so that structures can meet more stringent design requirements (e.g. increased traffic volumes in bridges exceeding the initial design loads), and hence the aspect of civil engineering infrastructure renewal has received considerable attention over the past few years throughout the world. At the same time, seismic retrofit has become at least equally important, especially in areas of high seismic risk.

Recent developments related to materials, methods and techniques for structural strengthening and seismic retrofitting have been enormous. One of today’s state-of-the-art techniques is the use of fiber reinforced polymer (FRP) materials or simply composites, which are currently viewed by structural engineers as “new” and highly promising materials in the construction industry. Composite materials for strengthening of civil engineering structures are available today mainly in the form of: (a) thin unidirectional strips (with thickness in the order of 1 mm) made by pultrusion, (b) flexible sheets or fabrics, made of fibers in one or at least two different directions, respectively (and sometimes pre-impregnated with resin). Central to the understanding of composites bonded to concrete is the fact that stresses in these materials are carried only by the fibers, in the respective directions.

The reasons why composites are increasingly used as strengthening materials of reinforced concrete members may be summarized as follows: immunity to corrosion; low weight (about ¼ of steel), resulting in easier application in confined space, elimination of the need for scaffolding and reduction in labor costs; very high tensile strength (both static and long-term, for certain types of FRP materials); stiffness which may be tailored to the design requirements; large deformation capacity, which results in substantial member ductility; and practically unlimited availability in FRP sizes and FRP geometry and dimensions. Composites suffer from certain disadvantages too, which are not to be

CHAPTER 1

INTRODUCTION

INTRODUCTION


2

neglected by engineers: contrary to steel, which behaves in an elastoplastic manner, composites in general are linear elastic to failure (although the latter occurs at large strains) without any yielding or plastic deformation, leading to reduced (but generally adequate) ductility. Additionally, the cost of materials on a weight basis is several times higher than that for steel (but when cost comparisons are made on a strength basis, they become less unfavorable). Moreover, some FRP materials, e.g. carbon and aramid, have incompatible thermal expansion coefficients with concrete. Finally, their exposure to high temperatures (e.g. in case of fire) may cause premature degradation and collapse (some epoxy resins start softening at about 50-70 oC). Hence FRP materials should not be thought of as a blind replacement of steel (or other materials) in structural intervention applications. Instead, the advantages offered by them should be evaluated against potential drawbacks, and final decisions regarding their use should be based on consideration of several factors, including not only mechanical performance aspects, but also constructability and long-term durability.

Composites have found their way as strengthening materials of reinforced concrete (RC) members (such as beams, slabs, columns etc.) in many thousands of applications worldwide, where conventional strengthening techniques may be problematic (e.g. steel plating or steel jacketing). For instance, one of the popular techniques for upgrading RC elements has traditionally involved the use of steel plates epoxy-bonded to the external surfaces (e.g. tension zones) of beams and slabs. This technique is simple and effective as far as both cost and mechanical performance is concerned, but suffers from several disadvantages (Meier 1987): corrosion of the steel plates resulting in bond deterioration; difficulty in manipulating heavy steel plates in tight construction sites; need for scaffolding; and limitation in available plate lengths (which are required in case of flexural strengthening of long girders), resulting in the need for joints. Replacing the steel plates with FRP strips provides satisfactory solutions to the problems described above. Another common technique for the strengthening of RC structures involves the construction of reinforced concrete (either cast in-place or shotcrete) jackets (shells) around existing elements. Jacketing is clearly quite effective as far as strength, stiffness and ductility is concerned, but it is labour intensive, it often causes disruption of occupancy and it provides RC members, in many cases, with undesirable weight and stiffness increase. Jackets may also be made of steel; but in this case protection from corrosion is a major issue, as is the rather poor confining characteristics of steel-jacketed concrete. The conventional jackets may be replaced with FRP in the form of sheets or fabrics wrapped around RC members, thus providing substantial increase in strength (axial, flexural, shear, torsional) and ductility without much affecting the stiffness.

INTRODUCTION


3

1.2 Structure of the book

In this document the aim is to give an overview of the main applications of composites as externally bonded reinforcement (EBR) of concrete structures and to present guidelines for the design. Following a general description of materials and techniques related to the application of composites as external reinforcement of concrete members in Chapter 2, the document contains several chapters, with each of them devoted to one particular aspect of strengthening with externally bonded FRP. Chapter 3 deals with the basis of design with FRP and the three following chapters deal with the design and structural behaviour of concrete members strengthened in flexure (Chapter4), shear (Chapter 5) as well as through confinement (Chapter 6). Naturally, these chapters are followed by detailing and practical execution rules (Chapter 7) and various issues regarding environmental effects and durability (Chapter 8). The Appendix describes the use of the program Composite Dimensioning for the dimensioning of RC members strengthened in flexure, shear or through confinement.

INTRODUCTION


4

MATERIALS AND TECHNIQUES


5

This chapter provides general information on FRP materials used in concrete strengthening and on the basic technique for their application. 2.1 Materials 2.1.1 General

The selection of materials for different strengthening systems is a critical process. Every system is unique in the sense that the fibers and the binder components are designed to work together. This implies that a binder for one strengthening system will not automatically work properly for another. Furthermore, a binder for the fibers will not necessarily provide a good bond to concrete. Hence, only systems that have been tested extensively on reinforced concrete structures shall be used in strengthening with composites. Today there are several types of composite material strengthening systems, which are summarised below:

• Wet lay-up systems • Systems based on prefabricated elements • Special systems, e.g. automated wrapping, prestressing, near-surface mounted

bars, mechanically attached laminates, etc. These systems correspond to several manufacturers and suppliers, and are based

on different configurations, types of fibers, adhesives, etc. In the following sections the three main components, namely adhesives, matrices and fibers of a composite material strengthening system will be discussed briefly. 2.1.2 Fibers

Fibers have a diameter in the order of 5-25 µm and constitute the primary load-carrying elements (parallel to their axis) in a composite material system. Main properties of the fibers are the high tensile strength and the linear elastic behavior to failure (Fig. 2.1). Basic properties of the most common fibers used in FRP strengthening systems are given in Table 2.1 (Feldman 1989, Kim 1995). It should be noted that properties listed in

CHAPTER 2




6

this table correspond to monotonic loading and do not account for environmental degradation and/or sustained loading effects (see Chapter 8). Fig. 2.1 Typical uniaxial tension stress-strain diagrams for different fibers and comparison with

steel.

Table 2.1 Typical properties of fibers (Feldman 1989, Kim 1995).

Material Elastic modulus (GPa)

Tensile strength (MPa)

Ultimate tensile strain (%)

Carbon High strength Ultra high strength High modulus Ultra high modulus Glass E AR S Aramid Low modulus High modulus

215-235 215-235 350-500 500-700

70-75 70-75 85-90

70-80

115-130

3500-4800 3500-6000 2500-3100 2100-2400

1900-3000 1900-3000 3500-4800

3500-4100 3500-4000

1.4-2.0 1.5-2.3 0.5-0.9 0.2-0.4

3.0-4.5 3.0-4.5 4.5-5.5

4.3-5.0 2.5-3.5

Carbon fibers are normally either based on pitch or PAN, as raw material. Pitch

fibers are fabricated by using refined petroleum or coal pitch that is passed through a thin nozzle and stabilised by heating. PAN fibers are made of polyacrylonitrile that is carbonised through burning. The pitch base carbon fibers offer general purpose and high strength/elasticity materials. The PAN-type carbon fibers yield high strength materials and high elasticity materials. The density of carbon fibers is 1800-1900 kg/m3. Glass fibers for continuous fiber reinforcement are classified into three types: E-glass fibers, S-glass and alkali resistant AR-glass fibers. E-glass fibers, which contain high amounts of

σ (MPa)

ε

Mild steel

0.02 0.04

2000

6000

4000

Glass

Aramid

High modulus Carbon

0 0

High strength Carbon



7

boric acid and aluminate, are disadvantageous in having low alkali resistance. S-glass fibers are stronger and stiffer than E-glass, but still not resistant to alkali. To prevent glass fiber from being eroded by cement-alkali, a considerable amount of zircon is added to produce alkali resistance glass fibers; such fibers have mechanical properties similar to E-glass. An important aspect of glass fibers is their low cost. The density of glass fibers is 2300-2500 kg/m3. Aramid fibers were first introduced in 1971, and today are produced by several manufacturers under various brand names (Kevlar, Twaron, Technora). The structure of aramid fiber is anisotropic and gives higher strength and modulus in the fiber longitudinal direction. Aramid fibers respond elastically in tension but they exhibit non-linear and ductile behaviour under compression; they also exhibit good toughness, damage tolerance and fatigue characteristics. The density of aramid fibers is 1450 kg/m3. 2.1.3 Matrix

The matrix for a structural composite material is typically a polymer, of thermosetting type or of thermoplastic type, with the first being the most common one. Recent developments have resulted in matrices based on inorganic materials) (e.g. cement-based). The function of the matrix is to protect the fibers against abrasion or environmental corrosion, to bind the fibers together and to distribute the load. The matrix has a strong influence on several mechanical properties of the composite, such as the transverse modulus and strength, the shear properties and the properties in compression. Physical and chemical characteristics of the matrix such as melting or curing temperature, viscosity and reactivity with fibers influence the choice of the fabrication process. Hence, proper selection of the matrix material for a composite system requires that all these factors be taken into account.

Epoxy resins, polyester, vinylester and phenolics are the most common polymeric matrix materials used with high-performance reinforcing fibers. They are thermosetting polymers with good processibility and good chemical resistance. Epoxies have, in general, better mechanical properties than polyesters and vinylesters, and outstanding durability, whereas polyesters and vinylesters are cheaper. Phenolics have a better behavior at high temperatures. 2.1.4 Composite materials

Advanced composites as strengthening materials consist of a large number of small, continuous, directionalized, non-metallic fibers with advanced characteristics, bundled in the matrix (Fig. 2.2). Depending on the type of fiber they are referred to as CFRP (carbon fiber based), GFRP (glass fiber based) or AFRP (aramid fiber based); when



8

different types of fibers are used, the material is called “hybrid”. Typically, the volume fraction of fibers in advanced composites equals about 50-70% for strips and about 25-35% for sheets. Given also that the elastic modulus of fibers is much higher than that of the matrix, it becomes clear that the fibers are the principal stress bearing components, while the matrix transfers stresses among fibers and protects them. Different techniques are used for manufacturing (e.g. pultrusion, hand lay-up), detailed descriptions of which are outside the scope of this document. As externally bonded reinforcement for the strengthening of structures, advanced composite materials are made available in various forms, which are described in Section 2.2.

Fig. 2.2 Magnified cross section of a composite material with unidirectional fibers.

Basic mechanical properties of composites may be estimated if the properties of the constituent materials (fibers, matrix) and their volume fractions are known. Details about the micromechanics of composite materials are not considered here. However, for the simple – yet quite common - case of unidirectional fibers, one may apply the “rule of mixtures” simplification as follows: mmfibfibf VEVEE +≈ (2.1) mmfibfibf VfVff +≈ (2.2) where: fE = elastic modulus of fiber-reinforced material in fiber direction fibE = elastic modulus of fibers mE = elastic modulus of matrix fibV = volume fraction of fibers mV = volume fraction of matrix = 1- fibV ff = tensile strength of fiber-reinforced material in fiber direction

FiberMatrix



9

fibf = tensile strength of fibers mf = tensile strength of matrix

At this point we should note that since fibE / mE >>1 and fibf / mf >>1, the above equations

are approximately valid even if the second terms in the right parts are omitted. In case of prefabricated strips the material properties based on the total cross-

sectional area can be used in calculations and are usually supplied by the manufacturer. In case of in-situ resin impregnated systems, however, the final composite material thickness and with that the fiber volume fraction is uncertain and may vary. For this reason the properties of the total system (fibers and matrix) and the actual thickness should be provided based on experimental testing. Note that manufacturers sometimes supply the material properties for the bare fibers. In this case a property reduction factor

1r should apply, to be provided by the supplier of the strengthening system. The above is better explained in the following example.

Example 2.1

Material supplier Χ provides unidirectional carbon sheets, with a weight of 260 g/m2. Fiber properties are as follows: fibE = 230 GPa, fibf = 3500 MPa. The nominal thickness of the sheet, fibt , is calculated based on the fiber material density, say fibρ = 2000 kg/m3, as follows: fibρ : fibρ x fibt = 260, hence fibt = 0.13 mm. We assume that after resin impregnation, the composite material reaches a thickness of 0.3 mm, implying a volumetric fraction of fibers equal to fibV = 0.13/0.3 = 43%. If the tensile strength and the elastic modulus of the composite material were measured experimentally, the results would be lower than 0.43x230 GPa and 0.43x3500 MPa, respectively, say by 10% (hence 1r = 0.9): 89 GPa και 1355 ΜPa. Therefore, the composite material properties to be used in calculations should be one of the following: (a) fE = 89 GPa, ff = 1355 MPa, ft = 0.3 mm, or (b) fE = 0.9x230 GPa, ff = 0.9x3500 MPa, ft = 0.13 mm. In a real application the amount of impregnating resin could, in general, be different from that suggested by the supplier, hence the real thickness of the composite will not be equal to 0.3 mm. But what is of interest in the calculations is typically the product fE ft or, sometimes, the product ff ft , hence the above two solutions (a) and (b) are equivalent. The advantage of solution (a) is that the properties provided by the supplier are quite close to those expected in-situ and the disadvantage is that those properties are “hypothetical”. On the other hand, the advantage of solution (b) is that the material provided by the supplier is accompanied by a set of properties, which could be combine



10

with the proper reduction factor (0.9 in our example) to yield the properties of the in-situ applied composite.

2.1.5 Adhesives

The purpose of the adhesive is to provide a shear load path between the concrete surface and the composite material, so that full composite action may develop. The most common type of structural adhesives is epoxy, which is the result of mixing an epoxy resin (polymer) with a hardener. Other types of adhesives may be based on inorganic materials (mainly cement-based). Depending on the application demands, the adhesive may contain fillers, softening inclusions, toughening additives and others.

When using epoxy adhesives there are two different time concepts that need to be taken into consideration. The first is the pot life and the second is the open time. Pot life represents the time one can work with the adhesive after mixing the resin and the hardener before it starts to harden in the mixture vessel; for an epoxy adhesive, it may vary between a few seconds up to several years. Open time is the time that one can have at his/her disposal after the adhesive has been applied to the adherents and before they are joined together.

Fig. 2.3 Effect of temperature on elastic modulus of polymers (Triantafillou 2004).

Another important parameter to consider is the glass transition temperature, Tg. Most synthetic adhesives are based on polymeric materials, and as such they exhibit properties that are characteristic for polymers. Polymers change from relatively hard, elastic, glass-like to relatively rubbery materials at a certain temperature (Fig. 2.3). This temperature level is defined as glass transition temperature, and is different for different polymers.

Glass-like

Rubbery Viscous flow



11

Typical properties for cold cured epoxy adhesives used in civil engineering applications are given in Table 2.2 (fib 2001). For the sake of comparison, the same table provides information for concrete and mild steel too. Table 2.2 Typical properties of epoxy resins and comparison with concrete and

steel (fib 2001).

Property (at 20 °C) Epoxy adhesive

Concrete Mild steel

Density (kg/m3) 1100 – 1700 2350 7800 Elastic modulus (GPa) 0.5 - 20 20 - 50 205 Shear modulus (GPa) 0.2 – 8 8 - 21 80 Poisson´s ratio 0.3 – 0.4 0.2 0.3 Tensile strength (MPa) 9 - 30 1 - 4 200 - 600 Shear strength (MPa) 10 - 30 2 - 5 200 - 600 Compressive strength (MPa) 55 - 110 25 - 150 200 - 600 Tensile strain at break (%) 0.5-5 0.015 25 Approximate fracture energy (Jm-2) 200-1000 100 105-106 Coefficient of thermal expansion (10-6/°C) 25 - 100 11 - 13 10 - 15 Water absorption: 7 days - 25 °C (% w/w) 0.1-3 5 0 Glass transition temperature (°C) 50 - 80 --- ---

Alternative materials to epoxies may be of the inorganic binder type. These

materials are based on cement in combination with other binders (e.g. fly ash, silica fume, metakaolin), additives (e.g. polymers) and fine aggregates. In this case the adhesive also plays the role of the matrix in the composite material, hence it must be designed such that compatibility with the fibers (textiles) will be maximized. General requirements for inorganic binders are high shear (that is tensile) strength, suitable consistency, low shrinkage and creep and good workability. 2.2 Strengthening systems

Different systems of externally bonded FRP reinforcement exist, related to the constituent materials, the form and the technique of the FRP strengthening. In general, these can be subdivided into “wet lay-up” (or “cured in-situ”) systems and “prefab” (or “pre-cured”) systems. In the following, an overview is given of the different forms of these systems (e.g. ACI 1996, fib 2001). Basic techniques for FRP strengthening are given in Section 2.3. 2.2.1 Wet lay-up systems • Dry unidirectional fiber sheet (Fig. 2.4) and

semi-unidirectional fabric (woven or knitted),



12

where fibers run predominantly in one direction partially or fully covering the structural element. Installation on the concrete surface requires saturating resin usually after a primer has been applied. Two different processes can be used to apply the fabric: - the fabric can be applied directly into the resin which has been applied uniformly

onto the concrete surface - the fabric can be impregnated with the resin in a saturator machine and then

applied wet to the sealed substrate • Dry multidirectional fabric (woven or

knitted), Fig. 2.5, where fibers run in at least two directions (e.g. 0ο and 90ο or ± 45ο with respect to the member axis). Installation requires saturating resin. The fabric is applied using one of the two processes described above.

• Resin pre-impregnated uncured unidirectional sheet or fabric, where fibers run predominantly in one direction. Installation may be done with or without additional resin.

• Resin pre-impregnated uncured multidirectional sheet or fabric, where fibers run predominantly in two directions. Installation may be done with or without additional resin.

• Dry fiber tows (untwisted bundles of continuous fibers) that are wound or otherwise mechanically placed onto the concrete surface. Resin is applied to the fiber during winding.

• Pre-impregnated fiber tows that are wound or otherwise mechanically placed onto the concrete surface. Product installation may be executed with or without additional resin.

2.2.2 Prefabricated elements • Pre-manufactured cured straight strips, which are installed through the use of

adhesives. They are typically in the form of thin ribbon strips or grids that may be delivered in a rolled coil. Normally strips are pultruded. In case they are laminated, also the term laminate instead of strip may be used.

Σχ. 2.5

Σχ. 2.4



13

• Pre-manufactured cured shaped shells, jackets or angles, which are installed through the use of adhesives. They are typically factory-made curved or shaped elements or split shells that can be fitted around columns or other elements.

The suitability of each system depends on the type of structure that shall be strengthened. For example, prefabricated strips are generally best suited for plane and straight surfaces (e.g. bottom of beams and slabs), whereas sheets or fabrics are more flexible and can be used to plane as well as to convex surfaces (e.g. sides of beams, column wrapping). 2.3 Basic strengthening technique

Fig. 2.6 Examples for the application of the basic FRP strengthening technique.

Hand lay-up of CFRP strip

Hand lay-up of carbon fiber sheets

Flexural strengthening of bridge deck using CFRP strips

Column wrapping using CFRP fabric

Strengthening of cooling tower with carbon fiber sheets



14

The basic FRP strengthening technique, which is most widely applied, involves the

manual application of either wet lay-up (so-called hand lay-up) or prefabricated systems by means of cold cured adhesive bonding. Common in this technique is that the external reinforcement is bonded onto the concrete surface with the fibres as parallel as practically possible to the direction of principal tensile stresses. Typical applications of the hand lay-up and prefabricated systems are illustrated in Fig. 2.6.

Apart from the basic technique there is a number of special techniques with rather limited applicability: automated wrapping, prestressed FRP, in-situ fast curing using heating device, near-surface-mounted bars, mechanical fastening etc. The description of these not so common techniques falls outside the scope of this document.

BASIS OF DESIGN


15

3.1 General

The design of RC members strengthened with FRP follows the philosophy of the relevant design codes (e.g. Eurocodes 2 and 8) and involves the verification for the ultimate and serviceability limit states, with proper modifications to account for the contribution of FRP. 3.2 Material constitutive laws

This section describes briefly the material constitutive laws in uniaxial loading and gives data on FRP material safety factors. 3.2.1 Calculation of resistance – full composite action

For concrete and steel (“existing” materials) the design values for strength are calculated by dividing the representative value of strength kX with the material safety factor mγ . If the limit state verification is performed in terms of strength (“forces”), as representative value is taken the mean value divided by a reliability coefficient (1.0, 1.2, 1.35), which depends on the quantity and reliability of available material data. If the verification is performed in terms of deformations (e.g. displacements, rotations), the representative value is taken as the mean value. In each of the above cases the safety factor mγ ( cγ and sγ for concrete and steel, respectively) depends on the level of reliability for material strength data. For the concrete compressive strength cckcd /ff γ= , where ckf = representative strength and cγ = safety factor for concrete. For steel reinforcement sykyd /ff γ= , where ykf = representative value of yield stress and sγ = safety factor for steel.

The strength of composite materials (“added” materials) is represented by the characteristic value if the safety verification is performed in terms of strength, or by the mean value if the safety verification is performed in terms of deformations. Their behavior in uniaxial tension is assumed linear elastic to failure, according to eq. (3.1); failure is defined at a (design) stress ffkfd /ff γ= : fdfff fE ≤ε=σ (3.1)

CHAPTER 3

BASIS OF DESIGN

BASIS OF DESIGN


16

The elastic modulus of FRP is determined by dividing the representative values of strength to ultimate strain, fukfkf /fE ε= . The design stress-strain curves for concrete, steel and FRP are summarized in Fig. 3.1.

Σχ. 3.1 Design stress – strain curves.

At this point we should point out that that the in-situ tensile strength of FRP is lower than that measured in a uniaxial tension test, due to stress concentrations, complex multiaxial states of stress, several layers, environmental degradation effects etc. All these reduction factors may be taken into account by assuming that FRP reaches failure at an effective strain fueε , which is less than the mean ultimate strain fumε determined through testing. On the basis of the above, the design value of the effective strength for FRP, fdef , is given as follows:

fdef

fk

fum

fuefde f

ff η=

γεε

= (3.2)

More details on the effective strain fueε will be given in the sections where this strain plays an important role (e.g. shear strengthening, confinement).

Table 3.1 FRP material safety factors, fγ .

FRP type Application type A(1) Application type B(2)

CFRP 1.20 1.35

AFRP 1.25 1.45

GFRP 1.30 1.50 (1) Application of prefab FRP systems under normal quality control conditions. Application

of wet lay-up systems if all necessary provisions are taken to obtain a high degree of quality control on both the application conditions and the application process.

(2) Application of wet lay-up systems under normal quality control conditions. Application of any system under difficult on-site working conditions.

0.2% 0.35%

σc

εc

c

ckfγ

α

concrete

σr

εr

ffd FRP

fyd Steel

εyd εfu

Ef

BASIS OF DESIGN


17

Values for the FRP material safety factor are suggested in Table 3.1 (fib 2001). Note that these values are still a topic of current research and are subject to further refinements.

3.2.2 Calculation of resistance - debonding

In many cases fracture of the FRP is not reached due to premature bond failure at the FRP-concrete interface (see next chapter for details). Debonding is mainly caused due to high interfacial shear stresses and is observed as shearing through the concrete, due to the lower strength of the latter compared to that of epoxy resins. When debonding controls failure, the material safety factor concerns the substrate and should be taken as

b,fγ = 1.5.

3.2.3 Serviceability limit state

The elastic modulus of FRP for the serviceability limit state should be taken equal to that for the ultimate limit state. 3.3 Bond at the FRP – concrete interface

The full composite action between FRP and concrete can only be achieved through high quality epoxy adhesives. Bond failure is a critical phenomenon, which should be accounted for carefully in the safety verifications. This requires a good understanding of bond mechanics and the development of appropriate bond modeling, as described in the following. 3.3.1 General, behavior

The behavior of the bond between externally bonded FRP and concrete can be analyzed in bond tests, such as the one illustrated in Fig. 3.2, which represents, in a simplified manner, the state of stress and strain near cracks (see Fig. 3.3). In the vicinity of cracks (e.g. Fig. 3.3), the FRP carries a tension force fN (Fig. 3.2), which is transferred through shearing in the substrate. Of particular practical interest is the relationship between the mean shear stress bτ at the FRP-concrete interface (equal to

fbf b/N l in Fig. 3.2, where fb the width of FRP) and the slip fs . This relationship depends on many factors, including the concrete strength, the type of adhesive, the FRP characteristics (e.g. thickness, elastic modulus) and the bond length. A typical shear

BASIS OF DESIGN


18

stress – slip curve is plotted in Fig. 3.4, along with others for deformed and smooth steel rebars, which are provided for the sake of comparison.

Fig. 3.2 Simplified FRP-concrete bond test (e.g. Zilch et al 1998, Bizindavyi and Neale 1999). Fig. 3.3 Cracking in RC beam and possible debonding (the arrows indicate the crack

propagation).

Fig. 3.4 Σχέσεις τάσης συνάφειας – ολίσθησης (Zilch et al. 1998).

Contrary to the case of embedded steel rebars, an important characteristic of the FRP-concrete bond is that FRP fracture rarely precedes debonding. The force in the

crack propagation

crack propagation

0

2

4

6

8

10

0,0 0,2 0,4 0,6 0,8 1,0

bond stress τb (MPa)

embedded steel bar∅ 12 mm (deformed)

embedded steel bar∅ 12 mm (smooth)

CFRP strip tf = 1.2 mm

slip sf (mm)

adhesiveFRPslip sf

concrete

Nf

Nf

Nc

Bond length bl

debonding

BASIS OF DESIGN


19

Bond length bl max,bl

Nfa,max

Nfa

FRP to cause debonding, that is the maximum anchorable force, faN , increases with the bond length bl , until this length reaches a limiting value, beyond which the maximum anchorable force remains practically unchanged, equal to max,faN (Fig. 3.5).

Fig. 3.5 Anchorable force – bond length relationship. 3.3.2 Analytical model

For FRP-concrete interfaces, the anchorable force – bond length relationship shown in Fig. 3.5 can be described analytically as follows (Holzenkämpfer 1994, Neubauer and Rostásy 1999): if max,bb ll ≥ : ffctmfbc1max,fafa tEfbkkcNN == (N) (3.3a)

if max,bb ll < :

−=

max,b

b

max,b

bmax,fafa 2NN

l

l

l

l (N) (3.3b)

ctm2

ffmax,b fc

tE=l (mm) (3.4)

with

1

400b1

bb

2125.1k

fb

f

≥+

−

= (3.5)

where b/bf should be taken no less than 0.33, ck = concrete compaction coefficient, equal to 1.0 for normal compaction or equal to 0.67 for poor compaction (e.g. faces not in contact with the formwork during casting), fb = width of FRP (mm), b = width of RC

BASIS OF DESIGN


20

member cross section (mm), ctmf = mean tensile strength of concrete (MPa), fE = elastic modulus of FRP (MPa) and ft = thickness of FRP (mm). Moreover, 1c = 0.64 (or 0.50, if the characteristic value of max,faN is to be calculated) and 2c = 2.0.

In terms of stresses, the above model results in the following equations for the FRP design stress ( fffadfd tb/N=σ ) corresponding to debonding:

if max,bb ll ≥ : f

fctm

b,f

bcfd t

Efkk5.0γ

=σ (MPa) (3.6a)

if max,bb ll < :

−

γ=σ

max,b

b

max,b

b

f

fctm

b,f

bcfd 2

tEfkk5.0

l

l

l

l (MPa) (3.6b)

Example 3.1

Consider an FRP strip with width fb = 50 mm, thickness ft = 1.2 mm, elastic modulus

fE = 180 GPa and tensile strength ff = 3000 MPa, epoxy-bonded on a concrete member with a width b = 100 mm (Fig. 3.6). The mean tensile strength of concrete is assumed

ctmf = 1.9 MPa.

Eq. (3.4) gives that ( ) ( )9.122.1180000max,b ××=l = 238 mm and from eq. (3.5)

400501

100502125.1

kb+

−

= = 1.22 > 1,

hence from eq. (3.3a) we calculate 2.11800009.15022.10.164.0N max,fa ×××××= = 25010 Ν≈ 25 kN, corresponding to a stress in the FRP equal to 25010/(50x1.2) = 417 MPa [it is worth noting here that if the strip reached its tensile capacity the respective force would be Nf = 3000x(50x1.2)/1000 = 180 kN, that is about 7 times higher than that causing].

In terms of stresses, the design stress in the FRP at debonding (assuming a bond length at least equal to 238 mm) is given by eq. (3.6) (with material safety factor γf,b = 1.5) σfd = 217 MPa.

50 mm

100 mm

bl

faN

Σχ. 3.6

FLEXURAL STRENGTHENING


21

4.1 General

Reinforced concrete members, such as beams and columns, may be strengthened in flexure through the use of strips or sheets epoxy-bonded to their tension zones, with the direction of fibers parallel to that of high tensile stresses (member axis). The concept is illustrated in Fig. 4.1. Flexural strengthening of columns is, in general, more difficult to achieve, due to the requirements for anchorage of the FRP through the joints. The latter is easy to construct if the width of beams is smaller than that of columns (hence sufficient space is available to bond strips, Fig. 4.2b), but requires small FRP cross sections placed near the column corners if the column and the beams have similar dimensions (Fig. 4.2c).

The analysis for the ultimate limit state in flexure may follow well-established procedures for reinforced concrete structures, provided that: (a) the contribution of external FRP reinforcement is taken into account properly (linear elastic material); and (b) special consideration is given to the issue of bond between the concrete and the FRP.

Fig. 4.1 Flexural strengthening of beams.

CHAPTER 4




22

(b) (a) (c) Fig. 4.2 Flexural strengthening of columns with maximum moment at the ends requires proper

anchorage of the external reinforcement. (a) Incorrect application, (b) continuity of the FRP through the slab, (c) continuity of the FRP through the joint.

4.2 Initial situation

The effect of the initial load prior to strengthening should be considered in the calculation of the strengthened member. Based on the theory of elasticity and with oM the service moment (no load safety factors are applied) acting on the critical RC section during strengthening, the strain distribution of the member can be evaluated. As oM is typically larger than the cracking moment crM , the calculation is based on a cracked section (Fig. 4.3). If oM is smaller than crM , its influence on the calculation of the strengthened member may easily be neglected.

Based on the transformed cracked section, the neutral axis depth ox can be solved from:

)xd(A)dx(A)1(bx21

o1ss2o2ss2o −α=−−α+ (4.1)

where 1sA = area of tension steel, 2sA = area of compression steel, 1d = distance of tension steel centroid to extreme tension fiber, 2d = distance of compression steel centroid to extreme compression fiber, d = static depth, h = height of cross section, b = width of cross section and css E/E=α = ratio of steel elastic modulus to concrete elastic modulus. The concrete strain coε at the extreme compression fiber is calculated as follows:



23

2oc

ooco IE

xM=ε (4.2)

where 2oI is the moment of inertia of the transformed cracked section:

2o1ss

22o2ss

3o

2o )xd(A)dx(A)1(3

bxI −α+−−α+= (4.3)

Based on strain compatibility, the strain oε at the extreme tension fiber can be derived as

follows:

o

ocoo x

xh −ε=ε (4.4)

The strain oε determined by eq. (4.4) is the initial strain at the level of FRP when

strengthening takes place. Fig. 4.3 Strain distribution in rectangular cross section subjected to moment oM at the time of

strengthening. 4.3 Ultimate limit state – failure modes

The failure mechanisms of RC members strengthened with FRP in flexure are descrived schematically in Fig. 4 (Triantafillou and Plevris 1992, Matthys 2000, fib 2001, Teng et al. 2001). Calculations for each failure mechanism are given in the following section.



24

Fig. 4.4 Failure mechanisms for RC beam strengthened in flexure.

FRP fracture

steel yields 2

concrete crushing steel yields 1

concrete crushing no steel yielding 3

debonding at outermost crack 4

debonding at intermediate flexural crack 5

debonding at intermediate shear crack 6

Shear failure at FRP end, causing peeling-off 7



25

4.4 Ultimate limit state - calculations

Mechanisms (1), (2) and (3) in Fig. 4.4 are based on composite action between concrete and FRP and can be analyzed using standard procedures, whereas the other mechanisms involve some kind of debonding or peeling-off and will be analyzed separately. 4.4.1 Full composite action (1) Steel yielding, concrete crushing

Yielding of the longitudinal steel reinforcement followed by crushing of the concrete in the compression zone is the most desirable failure mechanism. The design bending moment capacity may be calculated based on equilibrium and strain compatibility as follows (Fig. 4.5): (a) (b) (c) Fig. 4.5 Cross section analysis at the ultimate limit state. (a) Geometry, (b) strain distribution, (c)

internal force distribution.

Calculation of neutral axis depth, x : fdfyd1s2sd2scd AfAfAbxf σ+=+ψα (4.5) where ψ =0.8, cdf = design strength of concrete, ydf = design value of tension steel yield stress, fA = cross section area of FRP, 2sdf = design stress in the top steel

εs2

εο εf

εc=εcu=0.0035

x

εs1

d2

bf

h

tf

b

d

Af

As1

As2

ψαfcd

δGx As2fsd2

Afσfd

As1fyd



26

reinforcement and fdσ = design stress in the FRP. Based on strain compatibility, 2sdf and fdσ are calculated as follows:

−ε=

xdxEf 2

cs2sd (4.6)

ε−

−ε=σ ocffd x

xhE (4.7)

In the above expression cuc ε=ε is the ultimate strain in the concrete (=0.0035) and oε is the initial strain given by eq. (4.4). Note that 2sdf should not be taken higher than ydf .

Design bending moment capacity:

( ) ( ) ( )[ ]2G2sd2sGfdfGyd1sRd

Rd dxfAxhAxdfA1M −δ+δ−σ+δ−γ

= (4.8)

where Gδ =0.4, Rdγ = safety factor for the calculation of the resistance in an existing member (in general ≥γRd 1, but in the case of flexure Rdγ =1).

For the equations given above to be valid, the following assumptions should be checked: (a) yielding of tensile steel reinforcement and (b) straining of the FRP is limited to the limiting strain, lim,fε (corresponding to fracture or debonding):

s

ydc1s E

fx

xd≥

−ε=ε (4.9)

lim,focf xxh

ε≤ε−−

ε=ε (4.10)

where cuc ε=ε .

(2) Steel yielding, FRP fracture

The failure mechanism involving steel yielding / FRP fracture is theoretically possible. However, it is quite likely that premature FRP debonding will precede FRP fracture and hence this mechanism will not be activated. For the sake of completeness we may state here that the analysis for this mechanism may be done along the lines of the previous section. Equations (4-5) – (4-8) still apply, with the following modifications:

cuε is replaced by cε ; fdσ is replaced by fdef ; and ψ, δG are provided by the following expressions:



27

≤ε≤ε

−

≤ε

ε−ε

=ψ

0035.0002.0if3000

21

0.002if12

10005.01000

cc

ccc

(4.11)

( )

( )( )

≤ε≤−εε+−εε

≤εε−ε−

=δ

0035.0002.0if230002000

2430001000

0.002if100064

10008

ccc

cc

cc

c

G (4.12)

The resisting moment can be obtained by solving eqs. (4.5) – (4.8) (with the above modifications) for the three unknowns, x , cε and RdM .

(3) Concrete crushing

Being a brittle failure mechanism, concrete crushing is not acceptable. Non-activation of this mechanism is achieved by limiting the area of FRP below certain limits. More details are provided in Section 4.5, which describes ductility requirements. 4.4.2 Loss of composite action (4) Debonding at outermost crack

Using the analytical model described in Section 3.3 one can calculate the bond length required to prevent debonding. Consider, for example, the beam in Fig. 4.6a, with a moment diagram as shown in Fig. 4.6b (note the application of the shift rule, resulting shift of the diagram by la ). The force distribution in the tension steel ( sdN ) and in the FRP ( fdN ) is provided in Fig. 4.6c. As an approximation, the total tensile force (in steel and FRP), sdN + fdN , equals z/MSd , where z = 0.95 d = lever arm.

Based on Fig. 4.6c, the FRP anchorage length is calculated beyond the location (section A) where the total tension force envelope z/MSd intersects the line corresponding to the maximum force carried by the steel only, yd1sRsd fAN = . At this location the FRP tension force is fadN and the corresponding anchorage length is bl . The anchorable force (design value) fadN can be estimated based on internal force equilibrium as follows:

+≈

εε

+=ff

s1sfad

fff

1ss1sfad

Sd

EAEA

1NEAEA

1Nz

M (4.13)



28

Equation (4.13) was derived on the assumption that 1/ f1s ≈εε .

Fig. 4.6 Anchorage of FRP.

It is clear that the force fadN is limited by max,fadN [eq. (3.3a), with safety factor b,fγ ] and that sufficient space should be provided for the anchorage length bl . If this is not the case, section A must be re-positioned (in the direction where the bending moment decreases, that is towards the support), Fig. 4.6d-f, so that fadN will be reduced to

max,fadN or so that a lower bl will be required (as seen in Fig. 3.5, a small reduction in

fadN results in substantial reduction in bl ). If the anchorage length is still not adequate, then the FRP width should be increased and the thickness decreased, or mechanical anchorages should be provided.

(5) Debonding at intermediate flexural crack

The analytical model described in Section 3.3 applies here too, provided that a proper correction is made to account for the fact that the true state of stress and strain at the concrete-FRP interface near vertical cracks in a real beam is not identical to that in the experimental setup of Fig. 3.2. Detailed finite element analyses as well as experimental evidence suggest that the maximum shear stress at the interface is much lower than the one found in the test setup. Based on the literature, it is proposed here to modify the model of Section 3.3.2 by increasing the debonding force by 150%. Hence,

MSd

la

Myd

bl

(b)

(a)

Α

la

MSd

Myd

bl

NSd , NRd

NRsd = As1fyd Nfad,max

NRfd

MSd/z

Α

(d)

(f)

(e)

NSd , NRd

NRsd = As1fyd

Nfad NRfd

(c)

MSd/z

Nsd

Nfd



29

the FRP strain corresponding to debonding in the vicinity of flexural cracks (where the shear force is practically zero) is calculated as follows:

if max,bb ll ≥ : ff

ctm

b,f

bcflfl,b,f tE

fkk5.0γ

α=ε (4.14a)

if max,bb ll < :

−

γα=ε

max,b

b

max,b

b

ff

ctm

b,f

bcflfl,b,f 2

tEfkk5.0

l

l

l

l (4.14b)

where 5.2fl =α .

The calculations for the resisting moment are performed as in the above case (2), with fl,b,fffd E ε=σ .

(6) Debonding at intermediate shear crack

The statements made above apply here too, except that the increase o fthe debonding force is about 100% compared with the experimental setup. Hence, the FRP strain corresponding to debonding in the vicinity of shear cracks is:

if max,bb ll ≥ : ff

ctm

b,f

bcshflshfl,b,f tE

fkk5.0γ

α=ε −− (4.1a)

if max,bb ll < :

−

γα=ε −−

max,b

b

max,b

b

ff

ctm

b,f

bcshflshfl,b,f 2

tEfkk5.0

l

l

l

l (4.15b)

where 2shfl =α − .

The calculations for the resisting moment are performed as in the above case (2), with shfl,b,fffd E −ε=σ .

(7) FRP end shear failure – peeling-off

Investigations by several researchers (e.g. Oehlers 1992, Ziraba et al. 1994, Jansze 1997, Raoof and Hassanen 2000), have indicated that when externally bonded plates stop at a certain distance from the supports (as is typically the case in strengthening applications) a nearly vertical crack might initiate at the plate end (plate end crack) and then grow as an inclined shear crack (Fig. 4.7). However, by virtue of internal stirrups, the shear crack may be arrested and the bonded-on plate separated from the concrete at the level of the longitudinal reinforcement in the form of spalling (Fig. 4-10 right). The latter failure mode is also called concrete peeling-off, and is attributed to a critical



30

combination of shear and vertical tensile stresses at the plate end. A simple, yet reliable and conservative approach for the verification of FRP end shear failure involves the following checks: c,Rdend,Sd V4.1V ≤ (4.16)

Rdend,Sd M32M ≤ (4.17)

where end,SdV and end,SdM is the acting shear force and bending moment (design values) at the FRP end, c,RdV is the member shear resistance neglecting the contribution of

stirrups and RdM is the moment resistance [minimum value calculated based on

mechanisms (1), (2), (5) and (6)]. It is noted that the verification of (4.17) is rather easy to achieve, e.g. by adjusting the FRP end. However, is (4.16) is not satisfied, then the member should be strengthened near the FRP ends in shear (see next chapter).

Fig. 4.7 FRP end shear.

4.5 Ductility considerations

The basic ductility requirement is to ensure activation of a failure mechanism that involves steel yielding, thereby securing a minimum curvature ductility factor ( φµ ). This implies that the tensile strain in the FRP at the ultimate limit state, c,fuε , must exceed a minimum value, min,fε ; at the same time, this strain is limited by either the FRP ultimate strain (at fracture), fuε , or by the strain corresponding to debonding (but not necessarily at the critical cross section for flexural failure). Relevant to the above is Fig. 4.8.

The minimum FRP strain at the ultimate limit state, min,fε , corresponding to a given curvature ductility factor, φµ , is given as follows:

ocuy

ydmin,f dh

hx

hd

ε−ε−

−

µε=ε φ (4.18)



31

where yx is the neutral axis depth at yielding of the steel reinforcement.

Fig. 4.8 Strain distribution at critical cross section.

A last point to be made here is that large ductility values are not always achievable,

especially when the FRP quantity is controlled by serviceability, in which case the member is under-designed in terms of strength. 4.6 Summary of design calculations – ultimate limit state

A summary of the verifications for the ultimate limit state is provided next: 1. Determine the resisting moment for the member before strengthening ( Rd,oM ). 2. From the service moment oM prior to strengthening determine the initial strain oε at

the extreme tension fiber. 3 Calculate the required FRP area fA (corresponding to RdM ) for cases (1), (2) and

(6) [or (5), in the absence of shear force] at the critical section, based on eqs. (4.5)-(4.12). Note that these equations with cuc ε≤ε and ),min( shfl,b,ffulim,ff −εε=ε≤ε describe three failure modes simultaneously (steel yielding – concrete crushing, steel yielding – FRP fracture, steel yielding – debonding at intermediate crack). As an approximation, lim,fε may taken equal to 0.004-0.005. Next follows the ductility verification.

4. Calculate the anchorage length and finalize the FRP configuration based on the anchorage verification [mechanism (4)].

5. Verify failure mechanism (7) (FRP end shear failure). If not satisfied, shear strengthening is required (see next chapter).

εcu

εf,min

εyd

εo

εfu

xlim

d h

εfu,c ≤ εfu

εf

εsu

ΑΒ

Zone Α : steel yielding – FRP failure (fracture or debonding)

Zone Β : steel yielding – concrete crushing



32

6. Verify the shear resistance of the member (given that the flexural resistance has been increased). If not satisfied, shear strengthening is required.

4.7 Example

Consider the simply supported T-beam of Fig. 4.9 at a span of 5 m, under a uniformly applied vertical load. Materials: cdf = 13.5 MPa, ctmf = 2.2 MPa, ydf = 435 MPa. Assuming an acting moment SdM = 203 kNm, design the appropriate strengthening system. Consider CFRP with thickness ft = 1.1 mm, width 80 mm, elastic modulus fE = 150 GPa and ultimate strain (design value) fuε = 0.01. The service moment during strengthening is oM = 47 kNm. Rdγ = 1.

Geometric data: 1sA = 940 mm2, 2sA = 400 mm2, h = 500 mm, d = 450 mm, 1d =

50 mm, 2d = 40 mm and b = 1200 mm. The ratio css E/E=α equals 200/29 = 6.9. Solving eq. (4.1)-(4.4) we find oε = 0.00066.

Assuming 1kc = and 1kb ≈ , eq. (4.14a) for debonding near the mid-span (where the moment is maximum and the shear equals zero) gives:

003.01.1150000

2.25.1

0.15.05.2fl,b,f =×

××=ε , hence ,limfε = min(0.01, 0.003) = 0.003,

which is the FRP strain at the critical section (mid-span) for the ultimate limit state (debonding).

Next, with RdM = 203 kNm (and Rdγ = 1) from eq. (4.5) – (4.12) we calculate x = 104 mm, cε = 0.00071 and fA = 245 mm2. Each strip has a cross section area equal to 88 mm2, hence the use of 3 strips is required, with a total cross section area of 264 mm2, which corresponds to RdM = 206 kNm, x = 105 mm and cε = 0.00071. These strips will be placed one next to the other, in order to avoid multiple layers.

The next step is the verification of the end anchorage (Fig. 4.10), which results in a total length of strips equal to 4.10 m.

Finally, the FRP end shear calculations give:

=

−= 45.0

2565V end,Sd 133.25 kN, =

−××=

245.0

2545.065M end,Sd 66.54 kNm

Assuming for the problem that Rdτ = 0.26 ΜPa, 1.4 c,RdV = 1.4 Rdτ max(1, 1.6- d)min(2, 1.2+1.4 lρ ) dbw =

1.4x0.26x1.15x1.2024x0.25x0.25x0.45x103 = 56.62 kN

250

150

50

3Φ20

2Φ16

500

1200

Fig. 4.9

40



33

It is concluded that (4.17) is satisfied but (4.16) is violated, hence the ends should be strengthened in shear for a shear force equal to 133.25 – 56.62 = 76.63 kN (according to the procedure described in Chapter 5).

kN11.71N1502642009401N7.408 fadfad =⇒

××

+≈

kN20.481.1

1500002.25.1

0.10.15.0264.0N max,fad =

××××=

m2.0mm6.1932.22

1.1150000max,b →=

××

=l

Fig. 4.10 Verification of anchorage.

(a)

Α

MSd

m40.0a ≈l

(b)

203 kNm

NSd , NRd

NRsd = As1fyd = 408.7 kΝ

Nfad=71.11 kN

(c)

MSd/z

203/0.95d=475 kN

1.35 m

(d)

Α

m40.0a ≈l

m20.0b =l MSd

(e)

203 kNm

NSd , NRd

NRsd = As1fyd = 408.7 kΝ

(f)

MSd/z 475 kN

1.35+0.50 m

Nfad,max=48.20 kN



34

4.8 Servicability limit state

Calculations to verify the serviceability limit state may be performed according to a linear elastic analysis and considering that the concrete does not sustain tension (Fig. 4.11).

Fig. 4.11 Linear elastic analysis of cracked section.

From the equilibrium of forces and strain compatibility, the depth of the neutral axis ex is obtained from the following:

εε

+−α+−α=−−α+ ec

offe1ss2e2ss

2e x1hA)xd(A)dx(A)1(bx

21 (4.19)

( ) ( ) ( ) ( )dh

xxd

Adhx

dxA1

3x

hbx21

ME

e

e1ss2

e

2e2ss

ee

kcc

−−

α−−−

−α+

−

=ε (4.20)

where cff E/E=α and kM is the characteristic value of the acting moment. The last two equations can be solved for the unknown ex and cε .

The moment of inertia of the cracked section is given by:

2eff

2e1ss

22e2ss

3e

2 )xh(A)xd(A)dx(A)1(3

bxI −α+−α+−−α+= (4.21)

whereas that of the uncracked section may be approximated as follows (for rectangular cross sections):

12bhI

3

1 ≈ (4.22)



35

Regarding stress verification, apart from limiting stresses in the concrete and steel, it is required to limit the stress in the FRP, fσ , under the rare load combination, as follows:

fkoe

ecff f

xxh

E η≤

ε−

−ε=σ (4.22)

where the reduction coefficient η < 1 accounts for the poor behavior of some composites (e.g. GFRP) under sustained loading. Based on creep rupture tests (e.g. Yamaguchi et al. 1998), indicative values of η are 0.8, 0.5 and 0.3 for CFRP, AFRP and GFRP, respectively. Note that as the design is often governed by the serviceability limit state, relative low FRP strains at service load may be expected, so that FRP creep rupture is typically not of concern.

The verification of deflections and crack widths is performed in analogy to the case of reinforced concrete members (e.g. fib 2001). 4.9 Columns

The analysis of cross sections where bending develops in combination with an axial force is performed according to the principles presented above, the basic difference being the addition of one more term in the force and moment equilibrium equations: SdN in the right part of eq. (4.5) and ]x)2/h[(N GSd δ− in the right part of eq. (4.8), where SdN is the acting axial force (design value). Furthermore, the contribution of FRP in carrying compression should be neglected. Assuming that debonding is prevented (e.g. through proper anchorage inside slabs or joints, Fig. 4.2b-c, the failure mechanism will be one of the following: • yielding of tension steel ( syd1s E/f≥ε ), concrete crushing ( cuc ε=ε ) • yielding of tension steel ( syd1s E/f≥ε ), debonding or FRP fracture

[ ),min( shfl,b,ffulim,ff −εε=ε=ε ] • concrete crushing ( cuc ε=ε )

The bending moment – axial force interaction at failure is best demonstrated through the so-called interaction diagrams, such as those given in Fig. 4.12a-b. Those diagrams have been constructed for various equivalent geometric ratios of steel and FRP reinforcement, eqρ , defined as:

s

ftot,ftot,s

s

ffseq E

Ebd

Abd

AEE

+=ρ+ρ=ρ (4.23)

where 2s1stot,s A2A2A == (symmetrically placed steel reinforcement) and

ftot,f A2A = (symmetrically placed FRP reinforcement). Moreover, for the sake of



36

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

ν d=N

Sd /

bhf cd

µd=MSd / bh2fcd

ρeq=0,012 ρeq=0,014 ρeq=0,016 ρeq=0,018 ρeq=0,020 ρeq=0,022

C16/20S400b/h=1d1/h=0,10Ef=180 GPaEs=200 GPa

ρeq=0,024

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,600,0

0,2

0,4

0,6

0,8

1,0

ν d=N

Sd /

bhf cd

µd=M

Sd / bh2f

cd

ρeq=0,006 ρ

eq=0,007

ρeq=0,008 ρeq=0,009 ρeq=0,010

C16/20S400b/h=1d1/h=0,10Ef=180 GPaEs=200 GPa ρeq=0,011

ρeq=0,012

simplicity it has been assumed that min,fε =0.008. The interaction diagrams in Fig. 4.12

show that the effectiveness of FRP in increasing the flexural capacity decreases substantially as the axial load increases. (a) (b) Fig. 4.12 Axial force – bending moment interaction diagrams for square cross sections (b=h)

under uniaxial bending. Concrete C16/20, steel S400, d1/h=0.10, Ef =180 GPa. (a) As,tot=0.006, (b) As,tot=0.012.

As a general conclusion one may state that flexural strengthening of columns is not

always feasible (and easy as in the case of beams); and certainly the FRP contribution is of rather low effectiveness, unless the axial load is kept at low levels (e.g. dν < 0.2).



37



38

SHEAR STRENGTHENING


39

5.1 General

Shear strengthening of RC members using FRP may be provided by bonding the external reinforcement (typically in the form of sheets) with the principal fiber direction as parallel as practically possible to that of maximum principal tensile stresses, so that the effectiveness of FRP is maximized (see Fig. 5.1 for the dependence of the FRP elastic modulus on the fiber orientation). For the most common case of structural members subjected to lateral loads, that is loads perpendicular to the member axis (e.g. beams under gravity loads or columns under seismic forces), the maximum principal stress trajectories in the shear-critical zones form an angle with the member axis which may be taken roughly equal to 45o. However, it is normally more practical to attach the external FRP reinforcement with the principal fiber direction perpendicular to the member axis (Fig. 5.2). Photographs of typical applications are shown in Fig. 5.3.

Fig. 5.1 Dependence of FRP elastic modulus on fiber orientation.

CHAPTER 5

SHEAR STRENGTHENING

φ

E

90ο60ο30οφ

SHEAR STRENGTHENING


40

Fig. 5.2 Shear strengthening of: (a)-(h) beams, (i)-(k) columns and shear walls.

FRP sheet or fabric

(a)

(f)

Wrapped of U-shaped strips or sheets

sf bf

bf

sf

(i) (j) (k)

(b)

tf B

Α

C (c) (d)

E (g)

F (h)

D (e)

SHEAR STRENGTHENING


41

Fig. 5.3 Shear strengthening (a) of beam end with CFRP, (b) of column with GFRP. 5.2 Shear carried by FRP

At the ultimate limit state in shear, the fibers crossing a diagonal crack are activated and carry tension in analogy to internal stirrups, Fig. 5.4.

Fig. 5.4 Contribution of FRP to shear resistance (Triantafillou 1998).

If shear strengthening is achieved with strips of thickness ft and width fb (measured perpendicular to the axis of the strips), at a spacing fs (parallel to the member axis), the design shear carried by the FRP, f,RdV , may be calculated from the following expression:

( ) αsinαcotcotds

b2t V d,feff

fff,Rd +θσ= (5.1)

where fd = height of FRP crossed by the shear crack, measured from the longitudinal steel reinforcement (equals 0.9 d in the case of fully wrapped members, e.g. Fig. 5.2g, k), θ = angle of diagonal crack with respect to the member axis (assumed equal to 45ο, based on the classical Mörsch-Ritter truss analogy), α = angle between principal fiber

(a) (b)

α θ

df d

≈ 0.1d

Inclined crack

Α

Β

SHEAR STRENGTHENING


42

orientation and longitudinal axis of member, d,feσ = design value of mean stress in the FRP crossing the shear crack, in the principal fiber direction (“effective” stress).

Note that the differences between eq. (5.1) and that for the contribution of internal stirrups to shear resistance ( s,RdV ) are: use of ffbt2 instead of swA (cross section area of stirrups), fs instead of hs (spacing of stirrups) and d,feσ instead of ywdf (yield stress of stirrups).

For the most common case of continuous sheets or fabrics (instead of equally spaced strips) α= sinsb ff and eq. (5.1) gives: ( ) αα+θσ= 2

d,fefff,Rd sincotcotd2t V (5.2) Furthermore, for the typical case where the FRP is applied with the fibers perpendicular to the member axis (α = 90ο), we obtain: θσ= cotd2t V d,fefff,Rd (5.3)

The exact calculation of the effective stress d,feσ is not a straightforward task. In approximation, this stress varies linearly with the crack opening, which may be taken as minimum at point A in Fig. 5.4 and maximum at point B. Hence the stress increases linearly up to a maximum value, max,fdσ , which, in approximation, controls failure of the FRP material. On the basis of the above assumptions, one may write:

max,fdf

max,fdfd,fe d9.0d5.01D σ

−=σ=σ (5.4)

The value of max,fdσ at the ultimate limit state in shear depends on the definition of

failure, which can be one of the following: FRP fracture

Fracture of the FRP is most likely the case in fully wrapped and properly anchored jackets (e.g. Fig. 5.2g-k). In this case fdemax,fd f=σ (5.5) where fdef is the design value of FRP strength given by eq. (3.2) (note that this is lower than the tensile strength of jacket in uniaxial tension). As a first estimate, we may consider that the strength reduction coefficient, eη , for determining fdef is 0.80.

SHEAR STRENGTHENING


43

FRP debonding For open-type jacketing (e.g. U-shaped or side-bonded, Fig. 5.2c-e or Fig. 5.2b,

respectively), fracture of the jacket is not likely to occur (except for the case of Fig. 5.2e, where anchorage conditions are slightly improved). In this case debonding of the FRP is expected to be the dominant failure mode (Fig. 5.5), which can be described with the analytical model presented in Section 3.3.2. This model can be adopted with 1kc = ,

1kb = and an empirical coefficient shα (in analogy to flα and shfl−α described in Section 4.4.2):

if max,bb ll ≥ : f

fctm

b,fshmax,fd t

Εf5.0γ

α=σ (5.6a)

if max,bb ll < :

−

γα=σ

max,b

b

max,b

b

f

fctm

b,fshmax,fd 2

tEf5.0

l

l

l

l (5.6b)

where 25.1sh =α ,

α

=sindf

bl for U-shaped (three-sided) jacket (5.7a)

α

=sin2df

bl for two-sided jacket (5.7b)

ctm2

ffmax,b fc

tE=l (5.8)

Fig. 5.5 Debonding of FRP strips used for shear strengthening.

SHEAR STRENGTHENING


44

Note that in the case of U-shaped (three-sided) jackets the best-anchored part of the FRP is that at the maximum crack opening, with a bonded length αsin/df (Fig. 5.6a), where in the case of two-sided jackets the best-anchored part of the FRP is at the middle of the shear crack (Fig. 5.6b); hence the factor 2 in eq. (5.7b).

(a) (b)

Fig. 5.6 Bond length of (a) U-shaped FRP jacket, (b) two-sided FRP.

The improved anchorage shown in Fig. 5.2e, where the FRP end is rolled around a rod and inserted into grooves is an interesting solution, which may be considered of effectiveness in between that for open (Fig. 5.2c) and closed (Fig. 5.2g-k) jackets. This case could be treated using the expressions for U-shaped jackets [eq. (5.6)-(5.7a], with

max,fdσ increased by approximately 30%. Limiting strain

Some researchers have proposed that the effective strain in the FRP be limited to a maximum value, in the order of 0.006, to maintain the integrity of concrete and secure activation of the aggregate interlock mechanism. With this limitation, max,fdσ should not be taken higher than 0.006 fE . 5.3 Summary of design procedure

The contribution of FRP to shear resistance is provided through the term f,RdV in the well-known equation for the design shear resistance:

( )maxRd,f,Rds,RdcRd,Rd

Rd V,VVV min1V ++γ

= (5.9)

where c,RdV shear resistance of member without stirrups (“concrete contribution”),

max,RdV maximum shear resistance determined from crushing of the diagonal concrete struts and Rdγ = safety factor (>1) for the determination of the shear resistance in existing members ( Rdγ =1.20).. The FRP contribution f,RdV in eq. (5.9) is given by eq.

SHEAR STRENGTHENING


45

(5.1) or (5.2) for FRP in the form of strips at equal spacing or continuous jackets, respectively, with d,feσ calculated from eq. (5.4), in which max,fdσ is determined as follows: • For closed, properly anchored jackets (e.g. columns or shear walls):

the minimum of the value given by eq. (5.5) and 0.006 fE . • For open jackets (U-shaped or two-sided): the minimum of the value given by eq. (5.5), (5.6) and 0.006 fE .

At this point we should mention that the shear resistance of RC members under

cyclic (e.g. seismic) loading depends on the target ductility factor: high values of ductility result in reduced shear resistance (e.g. Moehle et al. 2001), which affects (reduces) the terms of eq. (5.9), but not the one regarding the FRP contribution ( f,RdV ). Hence the reduced shear capacity due to cycling does not affect the equations presented above.

Finally it should be noted that if shear strengthening is provided by means of equally spaced strips, the spacing should be such that the shear crack intersects at least two strips, that is max,ff ss ≤ = ( )d9.0,dmin5.0 f (for θ= 45ο and α = 90ο). Example 5.1

Consider the T-beam of Fig. 5.7, with b = 250 mm, height h = 500 mm and static depth d = 460 mm. The mean tensile strength of concrete is assumed ctmf = 2 MPa. Determine the required CFRP thickness for an additional shear resistance f,RdV = 75 kN. We assume the following properties for the CFRP: thickness of one layer = 0.12 mm, elastic modulus fE = 230 GPa, effective design tensile strength fdef =2560 MPa. The jacket will be applied according to the configuration shown in Fig. 5.2c (U-shaped). Eq. (5.5): max,fdσ = 2560 MPa Eq. (5.7α): fd = 310 mm, α = 90ο, bl = 310 mm The problem will be solved trying different numbers of layers, in order to illustrate their relative effectiveness in carrying shear. Jacket with one layer:

250

150

40

3Φ20

2Φ16

500

1200

Fig. 5.7

SHEAR STRENGTHENING


46

Eq. (5.8): =××

=22

12.0230000max,bl 83 mm < bl

Eq. (5.6a): =×

×=σ12.0

23000025.15.025.1max,fd 815 MPa

We take max,fdσ = min(2560, 815, 0.006×230000) = 815 MPa.

Eξ. (5.4): =×=×

××

−=σ=σ 81562.08154609.03105.01D max,fdfd,fe 505 MPa

Eq. (5.3): =××××= −3

f,Rd 105053100.122 V 37.6 kN The above value is the shear force carried by a one-layered jacket. This value is quite low, hence we try three layers:

Eq. (5.8): ( )=

×××

=22

12.03230000max,bl 144 mm < bl

Eq. (5.6a): =×

××=σ

12.032300002

5.15.025.1max,fd 471 MPa


Eq. (5.4): =×=×

××


Eq. (5.3): ( ) =×××××= −3

f,Rd 1029231012.032 V 65.2 kN < 75 kN

Next we try four layers:

Eq. (5.8): ( )=

×××

=22

12.04230000max,bl 166 mm < bl

Eq. (5.6a): =×

××=σ

12.042300002

5.15.025.1max,fd 408 MPa


Eq. (5.4): =×=×

××


Eq. (5.3): ( ) =×××××= −3

f,Rd 1025331012.042 V 75.3 kN > 75 kN OK

SHEAR STRENGTHENING


47

Hence the jacket should be made with four layers. Example 5.2

Consider the T-beam of Example 5.1.

Design an appropriate shear strengthening system for an additional shear f,RdV = 75 kN, based on carbon fiber strips at constant spacing. The strips may be assumed fully anchored in the compression zone (Fig. 5.2h). We assume that the strips have a width fb = 40 mm, thickness ft = 1.4 mm, elastic modulus fE =120 GPa and effective design strength fdef =1360 MPa. Eq. (5.5): max,fdσ = 1360 MPa We take max,fdσ = min(1360, 0.006×120000) = 720 MPa.

d9.0df = Eq. (5.4): =×=σ=σ 7205.0D max,fdfd,fe 360 MPa Calculation of spacing:

Eq. (5.1): 3

ff,Rd 103604609.0

s401.42 V −××××

××= > 75 kN ⇒ fs < 223 mm

2074609.05.0s max,f =××= mm. Finally we propose the use of strips at a spacing of

200 mm. Example 5.3

Consider a column of rectangular cross section, 250x400 mm, with a static width of 365 mm. Design a CFRP jacket for an additional shear f,RdV = 100 kN corresponding to strong axis bending. We assume the following properties for the CFRP: thickness of one layer = 0.12 mm, elastic modulus fE = 230 GPa, effective design tensile strength fdef =2560 MPa. The jacket will be applied according to the configuration shown in Fig. 5.2i (full wrapping).

250

150

40

3Φ20

2Φ16

500

1200

Fig. 5.8

365 mm

Fig. 5.9

SHEAR STRENGTHENING


48

Eq. (5.5): max,fdσ = 2560 MPa We take max,fdσ = min(2560, 0.006×230000) = 1380 MPa. Eq. (5.4): =×=σ=σ 13805.0D max,fdfd,fe 690 MPa Required number of layers: Eq. (5.2): ( ) ≥××××××= −3

f,Rd 106903659.012.0n2 V 100 kN ⇒ ≥n 1.84 Hence we need two layers (they correspond to f,RdV =108.8 kN). 5.4 Beam-column joints

Typical shear failures of (exterior) beam-column joints are shown in Fig. 5.10. Studies on joints strengthened with FRP in shear demonstrated that even very thin FRP jackets (e.g. 2-3 layers of carbon fiber sheets with layer thickness in the order of 0.12 mm) properly anchored outside the joints can provide an increase in shear capacity by well above 80-100% (Antonopoulos 2001, Antonopoulos and Triantafillou 2002, Antonopoulos and Triantafillou 2003). This is feasible provided that the sheets will be made of fibers primarily in the beam direction, but if possible, also in the column (Fig. 5.11).

(a) (b) Fig. 5.10 Shear failure of exterior joints: (a) Hyogo-ken Nanbu earthquake, Japan, 1995. (b)

Kalamata earthquake, Greece, 1986 (fib 2003).

SHEAR STRENGTHENING


49

(a) (b)

Fig. 5.11 Typical configurations for shear strengthening of beam-column joints and anchorage

outside the joint. (a) Exterior joint, (b) Interior joint.

The substantial increase in shear capacity of beam-column joints is demonstrated schematically in Fig. 5.12, which gives load-displacement loops for non-strengthened as well as strengthened (with two layers of 0.12 mm thick carbon fiber sheets) joints under cyclic loading (Antonopoulos and Triantafillou 2003).

(a) (b) Fig. 5.12 Load-displacement loops for poorly detailed (lack of stirrups) beam-column joints. (a)

Non-strengthened specimen, (b) Strengthened specimen, which shows a 70% increase in shear strength.

An approximate and simple method to account for the contribution of FRP to the

shear resistance of joints is to assume that the fibers in the beam direction are activated up to a strain equal to 0.004.

-50 -40 -30 -20 -10 0 10 20 30 40 50-60-50-40-30-20-10

0102030405060

F22

P (k

N)

δ (mm)-50 -40 -30 -20 -10 0 10 20 30 40 50

-60-50-40-30-20-10

0102030405060

C1

P (k

N)

δ (mm)

P, δ P, δ

SHEAR STRENGTHENING


50

CONFINEMENT


51

6.1 General

Confinement is generally applied to members in compression (Fig. 6.1), with the aim of enhancing their load carrying capacity or, in cases of seismic upgrading, to increase their ductility. FRP, as opposed to steel that applies a constant confining pressure after yielding, has an elastic behavior up to failure and therefore exerts a continuously increasing confining action. The confining stresses applied by the FRP result in one or more of the following: 1. Increase of concrete compressive strength and deformability (ultimate strain). 2. Increase of chord rotation after flexural yielding of columns (that is, increase of

ductility). 3. Increase of bond strength at lap-splices, hence prevention of lap-splice failures. 4. Delay of rebar buckling in compression zones with poor detailing (inadequate

spacing of stirrups). Each one of the above is briefly described in the following sections.

(a) (b) Fig. 6.1 Confinement of columns with FRP jackets: (a) CFRP, fibers in the horizontal direction,

(b) helically applied GFRP.

CHAPTER 6

CONFINEMENT

CONFINEMENT


52

ft lσ

Dfσ fσ

σc

6.2 Behavior and constitutive modeling of FRP-confined concrete 6.2.1 Behavior

Consider a concrete cylinder (Fig. 6.2a) with diameter D , fully wrapped with an FRP jacket with thickness ft and elastic modulus fE (in the direction of the fibers, that is circumferentially).

(a) (b)

Fig. 6.2 (a) Axially loaded column. (b) Lateral stresses due to confinement.

The lateral stresses lσ (in the radial direction, due to dilation of the concrete) exerted in the jacket (equal but of opposite sign act on the concrete) are calculated as follows:

ffffff

ff E

21E

Dt2

Dt2

ερ=ε=σ=σl (6.1)

where fσ and fε = FRP tensile stress and strain, respectively, and fρ = volumetric ratio of FRP. The result of confining stresses lσ is control of lateral expansion and hence increase of deformability, until the tensile stress fσ (corresponding strain fε ) in the FRP reaches its tensile strength fdef (corresponding strain fueε ); at this point the jacket fractures (Fig. 6.3) and the member fails. Of course the mechanism described above is possible only provided that premature debonding of the FRP (at its ends) will not occur.

Note here that the circumferential tensile strength of the jacket is, in general, lower than the tensile strength of FRP measured in a uniaxial tension test. This is attributed to the multiaxial state of stress in the FRP, stress concentrations, the use of many layers, the quality of application etc., and may be taken into account through the reduction factor

eη , with values in the of 0.7-0.9: fdefde ff η= (6.2)

CONFINEMENT


53

Fig. 6.3 Tensile fracture of FRP jacket in the circumferential direction when the tensile stress fσ

reaches the design FRP strength fdef .

Fig. 6.4 Compressive stress-strain curves for concrete confined with FRP.

The stress-strain relationship for concrete confined with FRP is given schematically in Fig. 6.4. On the basis of experimental support, one may draw the following conclusions: • The stress-strain curve is approximately bilinear, with change of slope at a strain

( 002.0co ≈ε ) corresponding to the peak stress for unconfined concrete ( cf ). • Jackets of very low thickness increase only the ultimate strain ccuε (curve a in Fig.

6.4). • Jackets of low thickness result in confined concrete strength ccf which corresponds

to strain ccε lower than that at ultimate ( ccuε ) (curve b in Fig. 6.4). • For a given type of FRP, the strength ccf and ultimate strain ccuε of confined

concrete increase with the thickness of the jacket.

tf increases Compressive stress

fcc=σccu

fc

Compressive strain

Unconfined concrete

σc

εc

εccu εco

(εcc, fcc)

(εccu, σccu) a

b

εcu

CONFINEMENT


54

• For jackets of equal thickness but with different types of fibers (e.g. carbon versus glass) the confined strength ccf increases with the jacket strength fdef (carbon is better than glass in this case), whereas the ultimate strain ccuε increases with the jacket strength fdef but also, mainly, with its ultimate strain fueε (glass is better than carbon in this case).

• For jackets of equal stiffness (expressed by the product ff tE ), the confined strength

ccf increases with the ultimate strain of FRP fueε . 6.2.2 Design model

As far as the design of FRP jackets for confinement is concerned, typically we aim at calculating the required thickness ft (for a given type of FRP) for a target confined strength ccdf (design value) and/or for a target ultimate strain ccuε . The international literature on FRP-concrete confinement models is vast. One of these models is described next (fib 2001). The model applies to columns with rectangular cross section (dimensions b and d, db ≥ ), rounded at the corners with a radius cr . cdccuudsec,ccd fEf ≥ε= (6.3)

( )[ ] ( )( )

c

Mdsec,

EE

1

Mdsec,cudsec,

udsec,cMdsec,d2d1ccu EEE

EEE151002.0

−

−−

−αα+=ε (6.4)

f

fde

cd

c

cudsec,

Ef

002.01

fE21

EE

−+

= (6.5)

( )[ ]151002.0fE

d2d1

cdd2d1Mdsec, −αα+

αα= (6.6)

254.1f

2f

94.71254.2cd

b,ud

cd

b,udd1 −

σ−

σ+=α ll (6.7)

cd

b,ud2

d2 f8.0

bd4.1

bd6.01 lσ

+−

−=α (6.8)

fdef

fb,ud fdt2

α=σl (6.9)

In the above expressions cE = initial modulus of elasticity for concrete

[ 3/1ckc )8f(950005.1E +××= ] and fα = confinement effectiveness coefficient for the

CONFINEMENT


55

specific jacket used, depending on: (a) the cross section geometry (aspect ratio, radius at corners, Fig. 6.5), (b) the degree of concrete coverage (Fig. 6.6b) and (c) the fiber orientation with respect to the member axis (Fig. 6.6c). Specificallly: 1asnf ≤α×α×α=α (6.10)

Shape coefficient: ( ) ( )bd3

r2dr2b1

AA1A3

db1AA 2

c2

c

g

sg

22

g

en

−+−−≈

−

′+′−==α (6.11)

Coverage coefficient: 2

f

g

s

2f

s d2s1

AA1

d2s1

′−≈

−

′−

=α (6.12)

Fiber orientation coefficient: ( )2f

atan1

1β+

=α (6.13)

where gA = area of cross section, sA = cross section area of longitudinal steel, fs′ = clear space between strips, for the case of partial coverage (Fig. 6.6a), d = smallest dimension of the cross section (or diameter, in the case of circular columns) and fβ = fiber orientation with respect to member axis (Fig. 6.6b). For circular cross sections nα =1, for fully covered members sα =1 and for fibers in the direction perpendicular to the member axis aα =1.

Fig. 6.5 Confinement of rectangular cross sections is achieved by rounding the corners.

rc

b'=b-2rc

b

d'=d-2rc d

Confined concrete

Αe

CONFINEMENT


56

d,udlσ

b

b,udlσ d

(a) (b)

Fig. 6.6 Confinement (a) with equally spaced strips, (b) with helically applied fibers.

Other confinement models found in the international literature are much simpler,

typically in the form:

m

cd

ud1

cd

ccdf

k1ff

σ+= l (6.14)

n

cd

ud2cuccu f

k

σ+ε=ε l (6.15)

In eqs. (6.14)-(6.15) udlσ is the mean confining stress (at failure of the jacket), approximately equal to (Fig. 6.7):

Fig. 6.7 Mean confining stress in each direction of rectangular cross section.

α+α=σ+σ

= fdef

ffdef

fd,udb,ud

ud fbt2f

dt2

21

2ll

lσ

( ) ( )fdefffded,fb,ff ft

bddbf

21 +

α=ρ+ρα= (6.16)

βf

fs′ 2/sd f′−

fb

Confined concrete

CONFINEMENT


57

where b,udlσ and b,udlσ are the mean confining stresses in the direction of sides b and d, respectively. In eq. (6.16) b,fρ and d,fρ is the volumetric ratio of FRP in each direction: d/t2 fb,f =ρ and b/t2 fd,f =ρ .

Typical values found in the international literature for the empirical constants in eqs. (6.14) – (6.15) are as follows: 1k = 2.15, m = 1, 2k = 0.02 or 0.04 for carbon or glass fibers, respectively, and n = 1. Alternatively, 1k = 2.6, m = 2/3, 2k = 0.015 (regardless of the type of fibers) and n = 0.5. The ultimate strain of unconfined concrete is may be taken equal to cuε = 0.0035.

If the full constitutive law in uniaxial compression is of interest (e.g for column analysis under the combination of axial load and bending moment), the model of Lam and Teng (2003), described in Fig. 6.8, may be adopted.

( ) 2

ccd

22c

cccd f4EEE ε

−−ε=σ if tc0 ε≤ε≤ (6.17a)

c2cdcd Ef ε+=σ if ccuct ε≤ε≤ε (6.17b) where

( )2c

cdt EE

f2−

=ε (6.18)

ccu

cdccd2

ffEε−

= (6.19)

Fig. 6.8 Stress-strain model for unconfined and FRP-confined concrete.

Finally, one may rely on the simpler, but not so accurate for the case of FRP-

confined concrete, models described in Eurocodes 2 or 8.

Compressive stress

fccd

fcd

Compressive strain

Unconfined concrete

σcd

εc

εccu εco=0.002 εcu = 0035 εt

Ec

FRP-confined concrete E2

CONFINEMENT


58

Example 6.1

Consider a concrete column of rectangular cross section, with unconfined strength

cdf = 20 ΜPa and elastic modulus cE = 33.5 GPa. The column is to be jacketed with either CFRP or GFRP, aiming at increasing the compressive strength to ccdf = 35 MPa and the ultimate strain to ccuε = 0.025: (a) For CFRP we assume fE = 230 GPa, fdf = 2590 MPa, thickness of one layer = 0.12 mm. (b) For GFRP we take fE = 70 GPa, fdf = 1400 MPa and thickness of one layer 0.17 mm. Finally we assume that the tensile strength of the jacket is reduced by 5% with respect to tension testing specimens (that is

eη =0.95). For CFRP fdefde ff η= = 0.95×2590 = 2460 MPa and for GFRP fdef = 0.95×1400 = 1330 MPa. The results for the required fiber sheet thickness and the corresponding number of layers are calculated in Table 6.1, based on the analytical model of eq. (6.3) – (6.9), for three different cross sections. The results given in this table verify if the aim of confinement is to increase strength then the required CFRP is much less than GFRP, whereas the opposite is the case if the aim is to increase deformability.

Table 6.1 Required fiber sheet thickness for various types of cross sections.

Required thickness of fiber sheet ft (mm) [in () the corresponding number of layers]

Carbon fibers Glass fibers

Cross

section

(b , d σε m)

cr

(cm)

gA

(cm2)

fα (effectiveness)

for fccd = 35 MPa

for εccu = 0.025

for fccd = 35 MPa

for εccu = 0.025

2

896.5

0.50

0.39 (4)

0.31 (3)

0.82 (7)

0.12 (1)

2

1246.5

0.32

0.74 (7)

0.56 (5)

1.56 (13)

0.22 (2)

4

886.2

0.64

0.31 (3)

0.24 (2)

0.64 (6)

0.10 (1)

6.3 Chord rotation and ductility

According to the philosophy of the upcoming version of Eurocode 8, of outmost importance in seismic retrofitting is the increase of a member’s (column) chord rotation

b=0.3

d=0.3

0.3

0.3

0.5

0.25

CONFINEMENT


59

at failure uθ (Fig. 6.9a), which is more or less equivalent to increasing the ductility. The ductility may be quantified through the member chord rotation ductility factor,

yu / θθ=µθ , or through the curvature ductility factor, yu / φφ=µφ , where: yθ = chord rotation at yielding, uφ = curvature at failure and yφ = curvature at yielding. Note that, essentially, the chord rotation ductility factor θµ member (relative end) displacement ductility factor, yu∆ ∆/∆=µ , where u∆ and y∆ the relative displacement of member ends at ultimate and yielding, respectively (Fig. 6.9). In the above definitions “failure” is considered when either there is an abrupt fall in the member’s response (e.g. load – displacement curve) or the response parameter (e.g. force) has been reduced by 20% with respect to its peak (Fig. 6.9b).

(a) (b) (c) Fig. 6.9 (a) Lateral loading of RC member. (b) Load-displacement diagram. (c) Curvature.

uθ can be calculated from the simple expression:

( )

−φ−φ+θ=θ

s

plplyuyu L

L5.01L (6.20)

where sL = shear span (distance from base of column to the point where the bending moment is zero, equal to the ratio of moment to shear at the column end) and plL = plastic hinge length. The chord rotation at yielding, yθ , is not affected by FRP jacketing and equals: For beams or columns:

bc

yy

s

Vsyy d

f

f13.0

Lh5.110013.0

3zaL

φ+

++

+φ=θ (6.21)

For shear walls:

P

Pu 0.2Pu

∆y ∆u

P

∆y ∆u

Ls

θu

uφ

Lpl

yφ

CONFINEMENT


60

bc

yy

sVsyy d

f

f13.0

hL125.11002.0

3zaL

φ+

−++

φ=θ (6.22)

where bd = mean diameter of tension steel rebars, h = height of cross section, yf = yield stress of longitudinal steel (MPa) and cf = concrete strength (ΜPa). The above material data are taken as mean values of in-situ assessed properties, divided by a data reliability factor (1.0, 1.2, 1.35), as per Eurocode 8. The term zaV is the tension shift of the bending moment diagram la for shear cracking at 45ο and expresses the effect of tension forces shifted by la to the member’s flexural deformations. The coefficient Va , which multiplies the internal force lever arm z at the end cross section, equals 0 if the shear force at flexural yielding, syMy L/MV = , is less than the shear cracking force crV , or 1 otherwise. Note that the shear cracking force may be taken as the shear resistance of the member without shear reinforcement, c,RV , as calculated by Eurocode 2 with a safety factor 1c =γ .

The plastic hinge length plL may be estimated from the following expression:

bc

yspl d

f

f24.0h17.0L1.0L ++= (6.23)

where yf and cf are in ΜPa. The curvatures yφ και uφ are calculated based on section analysis at yielding and failure. uφ is calculated as uccuu x/ε=φ , where ux = depth of compression zone at failure and ccuε = ultimate strain of concrete, as provided by the confinement model, e.g. eq. (6.15) (it is this term that is mainly affected by the properties of the FRP jacket!).

The chord rotation uθ (or the curvature at failure uφ ) can increase by jacketing the

RC member at its critical regions (member ends), Fig. 6.10, where strains in concrete and steel are expected to be high. In these regions the confinement exerted by the FRP increases the ultimate strain of concrete (in addition to delaying rebar buckling and bond failure at lap-splices) and hence the ductility (Fig. 6.11).

Fig. 6.10 FRP wrapping at member ends aiming at increased ductility.

CONFINEMENT


61

(a) (b) Fig. 6.11 Load-displacement loops for RC column of 0.25x0.50 m cross section under cyclic

loading. (a) Unretrofitted member. (b) Member retrofitted with two layers of carbon sheet (thickness of each layer = 0.12 mm) at 0.60 m of the column base.

In summary, the design of FRP jackets for a given chord rotation at failure uθ (which

is introduced in the compliance criteria for the performance levels specified in Eurocode 8) requires the expression of uθ in terms of the jacket properties. This is achieved through the following steps: • Determine the plastic hinge length plL from eq. (6.23). • Calculate the yield curvature yφ , based on cross section analysis. • Calculate the chord rotation at yielding from eq. (6.21) or (6.22). • Solve eq. (6.20) for the required jacket characteristics.

An alternative approach for relating the FRP jacket characteristics to the ultimate chord rotation (mean value) at flexural failure of beams or columns designed according to old provisions for seismic design is based on the use of the following empirical relationship (Εurocode 8):

( ) ( )( ) ( )dc

fdefxf

c

ywsx 100f

fff35.0

s225.0

cum 25.125h

Lf,01.0max,01.0max3.0016.0 ρ

ρα+αρ

ν

ωω′

=θ (6.24)

where: ω = mechanical reinforcement ratio of tension longitudinal reinforcement (including any longitudinal reinforcement between the tension and compression flanges), ω′ = mechanical reinforcement ratio of compression longitudinal reinforcement,

cbhf/Ν=ν = normalized axial force (compression taken as positive, b = width of compression zone, h = cross section side parallel to the loading direction),

hwswsx sb/A=ρ = transverse steel ratio parallel to the direction x of loading,

C4_XB Load v Deflection

-250

-200

-150

-100

-50

0

50

100

150

200

250

-120 -80 -40 0 40 80 120

Deflection mm

Load

kN

C4_XB Load v Deflection

Load v Deflection C2X Control

-250

-200

-150

-100

-50

0

50

100

150

200

250

-120 -80 -40 0 40 80 120

Deflection mm

Load

kN

Load v Deflection C2X Control

P P

∆ ∆

CONFINEMENT


62

fxρ = geometric ratio of FRP parallel to the direction x of loading,

hs = spacing of stirrups,

ywf = yield stress of stirrups,

dρ = geometric ratio of diagonal reinforcement, if any,

fα = effectiveness coefficient for confinement with FRP, and α = effectiveness coefficient for confinement with stirrups, equal to

−

−

−=α ∑

oo

2i

o

h

o

hhb6b

1h2s1

b2s1 (6.25)

In eq. (6.25) ob and oh are the dimensions of confined concrete core to the centerline of the stirrups and ib is the centerline spacing of longitudinal rebars supported by stirrups. It is strongly recommended that if the stirrup ends are not bent towards the concrete core (≥ 135ο at corners, ≥ 90ο on the sides), the confinement provided by stirrups should be neglected (α = 0).

The corresponding to eq. (6.24) formula for the mean value of the plastic part of the ultimate chord rotation ( yu

plu θ−θ=θ ) is:

( ) ( )( ) ( ) ( )dc

fdefxf

c

ywsx 100f

fff35.0

s2.0c

3.0plum 275.125

hLf

,01.0max,01.0max25.00145.0 ρ

ρα+αρ

ν

ωω′

=θ (6.26)

For shear walls designed according to old seismic design code provisions the right part of eq. (6.24) και (6.26) should be multiplied by 0.625 and 0.6, respectively (0.016 and 0.0145 are replaced by 0.01 and 0.0087).

A careful examination of eq. (6.24) and (6.26) reveals that the contribution of FRP lies only in the exponent of 25.

Another alternative approach to deal with the design of FRP jackets for a target ductility is to use the following simple but highly conservative equation proposed by Tastani and Pantazopoulou (2002):

3.11.0f

4.123.1cd

ud∆ ≥

−

σ+=µ=µ θ

l (6.27)

udlσ in eq. (6.27) is the confining stress at the ultimate limit state, given e.g. by eq. (6.9), which neglects the contribution of stirrups. Note that the use of eq. (6.9) in rectangular columns applies with d taken as the cross section dimension perpendicular to the plane of bending. The application of this approach is illustrated in the next example.

CONFINEMENT


63

Example 6.2

(a) (b)

Fig. 6.12 (a) Loading of column and (b) retrofitting for ductility.

Consider a column with cross section 0.30x0.40 m, subjected to strong axis bending (Fig. 6.12). The column edges are rounded at a radius cr = 25 mm; the concrete strength is 11 ΜPa; and the carbon fiber sheets to be used have an elastic modulus 230 GPa, tensile strength 3000 MPa and thickness 0.12 mm (one layer). We assume that the FRP strength reduction coefficient is eη = 0.90. The objective is to design the jacket (that is to calculate the required number of layers) for a target displacement (or chord rotation) ductility factor )(∆ θµ=µ = 4. Tensile strength of the jacket: 0.90×3000 = 2700 MPa. Confinement effectiveness coefficient, eq. (6.11): 1195Ag = cm2, 25.15A s = cm2.

48.0

119525.15111953

2535122

n =

−××

+−=α

From eq. (6.27):

−××

+= 1.011

2700300

t248.04.123.14

f

hence mm40.0t f =

Longitudinal reinforcement: Φ18, 350fyd = ΜPa

3 m

CONFINEMENT


64

that is 0.40/0.12 = 3.3 4 layers (if repeated with 12.04t f ×= mm, the calculations give 75.4=µθ ).

6.4 Lap-splices 6.4.1 Behavior and design

FRP jackets in regions with straight lap-spliced rebars provide confinement which increases the friction between lap-splices and prevents slippage (typically this is not of concern in lap-splices with 180ο hooks, in which case slippage is not activated). The improved behavior in FRP-confined lap-spliced regions has been demonstrated in many studies, including those of Ma and Xiao (1997), Saadatmanesh et al. (1997), Seible et al. (1997), Restrepo et al. (1998), Osada et al. (1999), Haroun et al. (2001) etc. Typical results are shown in Fig. 6.13.

(a) (b) Fig. 6.13 Cyclic loading response of column with rectangular cross section: (a) unretrofitted

member, (b) member retrofitted at lap-splices (Saadatmanesh et al. 1997).

Fig. 6.14 State of stress at lap-splice (friction mechanism).

sbcsb pfAF lτ==

sl Bond stress lµσ=τb

Lateral stress lσ Diagonal struts

CONFINEMENT


65

According to the friction model of Fig. 6.14 and the possible failure patterns of Fig. 6.15 (details are omitted), it can be shown that lap-splice failures may be prevented using fiber sheets with a thickness ft as follows:

( ) sfdec

ydb,mins

s

Rdf fpdb

fA1bdt

l

l

l

µ+α

−

γ= (6.28)

where bA = cross section area and diameter of one spliced rebar, sl = available lap-splice length, ,minsl = lap-splice length required to prevent slippage, cp = perimeter of crack at lap-splice failure (Fig. 6.15b,c), ydf = yield stress of longitudinal rebars, b and d = dimensions of rectangular cross section, µ = friction coefficient, fdef = effective FRP jacket strength in circumferential direction and Rdγ = safety factor. An additional condition to met in order to prevent lap-splice failure according to Seible et al. (1997) is that the radial concrete strain should be kept below a critical value, in the order of 0.001-0.002. Hence, fdef in eq. (6.28) should exceed the value ffde E0015.0f ×≤ (6.29)

(a) (b) (c) Fig. 6.15 (a) Column confinement at lap-splice region. (b) Cracking of circular section in the

tension zone due to bond failure and definition of critical crack path. (γ) Similarly for rectangular columns.

sl pc=(s/2)+2(db+c) ≤ 22 (db+c)

c db

s

pc=(πD’/2n)+2(db+c) ≤ 22 (db+c) (wide spacing)

D’

c db

n lap-splices

CONFINEMENT


66

Closing this section we should point out that the effect of FRP confinement at lap-spliced rebars is favorable only for the corner rebars (in rectangular cross sections), where confining stresses are substantial due to rounding of the corners. Example 6.3

Consider the column of Fig. 6.12a (0.30x0.40 m cross section) with Φ16 rebars and

ydf = 230 ΜPa, under lateral loading which causes bending with respect to either the strong or the weak axis. We assume that the radius at column edges is cr = 25 mm and that the concrete cover is c = 30 mm. The concrete strength is 11 ΜPa, the friction coefficient is taken µ = 1.4, the lap-splice length is sl = 0.25 m and min,sl = 0.40 m. Assuming that confinement at the lap-splice region is provided with carbon fiber sheets with elastic modulus fE = 230 GPa, tensile strength 2600 ΜPa and thickness of one layer 0.12 mm, determine the required number of layers to prevent lap-splice failure. Take Rdγ = 1.5. (a) Strong axis bending Critical crack path: ( ) ( )[ ] ( ){ } mm136301822,301822/220minpc =+++= .

Rebar cross section area: ( ) 22b mm2004/16A =×π= .

( ) ( ) MPa345345,2600min2300000015.0,2600minffde ==×= .

From Example 6.2, 48.0=α mm.

Required jacket thickness: ( ) mm28.05003454.113640030048.0

2302004.0

25.014003005.1t f =

××××+×

××

−×××

= .

Required number of layers: 0.28/0.12 = 2.33 3 layers.

(b) Weak axis bending

d

b

220 Fig. 6.16a

d

b

150 Fig. 6.16b

CONFINEMENT


67

The calculations are as above, but note that FRP jacketing will prevent lap-splice failure only at the corner rebars. 6.4.2 Effect of lap-splices on chord rotation

The effect of lap-splices on chord rotation is taken into account by computing the yield chord rotation yθ and the plastic part of the ultimate chord rotation pl

uθ with ω′ twice as high compared to that outside the lap-splice region. The same applies for yφ and yM . Moreover, if min,ss ll < , then pl

uθ , uθ , yM and yφ should be computed by multiplying the yield stress of longitudinal rebars by min,ss / ll . Moreover, the 2nd term in eq. (6.21) – (6.22) should be multiplied by the ratio of the reduced yield moment to that outside the lap-splice region. Finally, the right part of eq. (6.26) should be multiplied by min,sus / ll .

For lap-splices without FRP jacketing:

bc

ymin,s d

f

f3.0=l (6.30)

b

cc

ywsx

y,minsu d

ff

f5.1405.1

f

ρα+

=

l

l (6.31)

where

n

nh2s1

b2s1 restr

o

h

o

h

−

−=αl (6.32)

n = total number of longitudinal rebars in the column perimeter and restrn = number of rebars supported at corners of stirrups or by cross ties.

For lap-splices with FRP jacketing at a height at least equal to 2 sl /3:

bc

ymin,s d

f

f2.0=l (6.33)

b

cc

fdefxf,

ymin,su d

ff

f5.1405.1

f

ρα+

=

l

l (6.34)

where f,lα = 4/n (because confinement is effective only in the vicinity of the four corner rebars). Note here that in order to avoid accounting for the FRP contribution twice in the

CONFINEMENT


68

Εi

0.04

fs

fu Εs

Strain

Stress

correction for pluθ , fα in the power of 25 in eq. (6.26) should be taken as zero. Finally, all

strength parameters in the above equations are given in MPa. 6.5 Rebar buckling

According to Priestley et al. (1996), in columns with Vd/M > 4 (M and V is the maximum acting bending moment and shear force, respectively, and d is the cross section dimension parallel to the plane of bending) and the ratio of stirrup spacing to rebar diameter bh d/s exceeds a critical value, buckling of the longitudinal rebars is likely to occur due to high axial strains. Such buckling may be delayed when the FRP confining jacket has a thickness equal to:

ffds

2s

f EE4dnf45.0tα

= (6.35)

where n = total number of longitudinal rebars in the cross section, sf = stress in the rebars at a strain equal to 0.04 and dsE = “double” modulus of rebars, defined as follows (Fig. 6.17):

( )2is

isds

EE

EE4E

+= (6.36)

Fig. 6.17 Definition of steel moduli.

In eq. (6.36) sE = secant modulus from stress sf to uf (strength of steel) and iE =

initial modulus of rebars. Finally, in eq. (6.35) the quantity 0.45 2sf / dsE may be taken

CONFINEMENT


69

approximately (and conservatively) equal to 40 MPa. Hence, with the introduction of the safety factor we have:

ff

Rdf End10tα

γ= ( fE in MPa) (6.37)

Example 6.4 Consider a column with 0.30x0.40 m cross section (Fig. 6.18) and 10 longitudinal rebars Φ18. The radius at the rounded edges is assumed cr = 25 mm and Rdγ = 1.5. For carbon fiber sheets with fE = 230 GPa and thickness of one layer equal to 0.12 mm, the required sheet thickness to delay rebar buckling is:

mm54.048.023000040010105.1t f =

××××

=

which implies 0.54/0.12 = 4.5 5 layers. 6.6 General comments on FRP-jacketed columns

It must be made clear that FRP jacketing in RC columns: (a) increases the axial load capacity (strength), if the predominant loading is axial and (b) increases substantially the deformability (ductility, chord rotation) and/or the shear resistance, if the predominant loading is lateral (seismic forces). Contrary to the case of steel jacketing, the stiffness is not affected by FRP jacketing, implying that very flexible structures (e.g. buildings with pilotis) may remain vulnerable and may require stiffening in addition to strengthening, as per the structural analysis results.

Under the condition that the intervention does not aim to increase the stiffness (or the flexural resistance!), any given seismic excitation will provide (through the structural analysis) (a) the target chord rotation (or ductility) and (b) the design shear (accounting for capacity design, that is flexural yielding before shear cracking). The required thickness of FRP jackets should be determined as the maximum given by the calculations for chord rotation, shear resistance, delay or rebar buckling and prevention of lap-splice failures.

rebars

Φ18, S500s

Fig. 6.18

CONFINEMENT


70

DETAILING AND PRACTICAL EXECUTION


71

7.1 General

This chapter summarizes basic detailing and practical execution rules for the application of composites as externally bonded reinforcement. 7.2 Detailing

Detailing rules are summarized here for the three basic cases: (a) flexural strengthening, (b) shear strengthening and (c) confinement. 7.2.1 Flexural strengthening

According to the fib bulletin 14 (2001), the following rules should be respected (for beam strengthening): • Maximum spacing between strips )h5,2.0min( l= ,

where l = span length and h = total depth (in the case of cantilevers 0.2 should be replaced by 0.4).

• Minimum distance to the edge of the beam should equal the concrete cover of the internal longitudinal reinforcement.

• Lap joints of strips should be avoided; they are absolutely not necessary, because FRP can be delivered in the required length. Nevertheless, if needed, lap joints should be made in the direction of the fibers with an overlap that will ensure tensile fracture of the FRP prior to debonding at the lap joint.

• Crossing of strips is allowed (e.g. strengthening of two way slabs) with bonding in the crossing area.

• If strips or sheets are to be applied in several layers, the maximum number or layers should not exceed 3 or 5 for prefabricated strips or in-situ cured sheets, respectively.

• In the case of applying FRP strips over supports of continuous beams or slabs, the strips should be anchored at a distance in the order of 1 m in the compression zone (Fig. 7.2).

CHAPTER 7


≥ cover

)h5.0,2.0min( l≤

Fig. 7.1



72

• Anchoring of FRP (especially if the strips are staggered) can be ensured by applying

bonded FRP “stirrups” that enclose the longitudinal strips at their ends (Fig. 7.3, 7.4). The use of such stirrups is strongly recommended. Note that these stirrups are not considered to be part of the shear reinforcement but are responsible to keep the longitudinal strips in their position and to prevent peeling-off.

Fig. 7.3 Flexural strengthening with possible end anchorages.

≥ 1 m Shift rule

FRP

Fig. 7.2 FRP bonding above internal support.

A

A

Section A - A



73

Fig. 7.4 Improved anchorage at FRP strip ends using transverse FRP. 7.2.2 Shear strengthening • In the case of strengthening T-beams, externally bonded FRP should be anchored in

the compression zone (e.g. Fig. 7.5).

Fig. 7.5 Typical configurations for the anchorage of FRP “ties” in the compression zone.

• If anchorage in the compression zone is not

possible, placement of sheets inside grooves at the top of the web is strongly recommended (Fig. 7.6). The rods inside the grooves could be non-metallic (e.g. FRP); if shear strengthening is provided with CFRP sheets and the rods are made of steel, the use of excessive resin inside the groove should ensure the non-contact between carbon and steel (due to the potential of galvanic corrosion).

• Minimum permissible radii at corners of rectangular cross sections are in the order of 20 mm for carbon or glass fibers and 10 mm for aramid fibers.

Rod, filling of the groove with epoxy 150 mm

Fig. 7.6



74

• Shear strengthening of columns between partial height infill walls should be done along the full column height, not just in the free part (Fig. 7.7).

WRONG CORRECT

Fig. 7.7 Shear strengthening of column between partial height infill walls.

• Full wrapping of columns with several pieces

of FRP along the height should be done with the lap joints in different sides (Fig. 7.8).

7.2.3 Confinement • Rounding of the corners in columns should be done at the maximum possible radius

(typically determined by the concrete cover). • Overlapping of the jacket’s ends in rectangular cross

sections (Fig. 7.9) should be such that fracture of the FRP would occur prior to debonding. Typical minimum lap lengths are in the order of 200 mm for carbon fiber sheets with a nominal thickness about 0.12-0.14 mm.

• The maximum number of superimposed layers should be in the order of 15 or according to the material supplier’s recommendation.

• When jacketing is applied at column ends for ductility, a 15 mm gap is recommended to allow for unrestraint rotation of the end cross section as well as to prevent damage of the FRP in compression (Fig. 7.10).

• Concerning the application of FRP on rectangular columns or pier walls with large aspect ratio, the FRP does not actually confine the internal concrete structure if just applied to the surface. In order to achieve confinement, the jacket need to be constrained on both sides along the length through the use of dowels or bolts or spike anchors (Fig. 7.11) that anchor the jacket to the existing structure, thereby

Fig. 7.9

gap

Fig. 7.10

Fig. 7.8



75

creating shorter distances. Spike anchors provide a low cost solution, which has been tested with very good results for the attachment of FRP jackets at the reentrant corners of L-shaped cross section columns, Fig. 7.12 (Karantzikis et al. 2005).

Fig. 7.11 FRP anchorage using spike anchor.

(a) (b) (c) Fig. 7.12 Fixing the jacket at reentrant corner: (a) typical configuration, (b) spike anchors, (c)

photograph of anchors at reentrant corner.

• As in the case of columns strengthened in shear, full wrapping with several pieces of

FRP along the height should be done with the lap joints in different sides (Fig. 7.8). • When jackets are provided to prevent lap-splice failures (e.g. at the bottom of

columns), the FRP should extend at a height equal to at least 2/3 of the lap splice. 7.3 Practical execution

FRP materials used in strengthening and/or seismic retrofitting are typically in the form of (a) 1.0-1.5 mm thick and 50-100 mm wide strips made of carbon fibers, or (b) sheets with a nominal thickness of 0.1-0.6 mm made of carbon, glass and (more rarely)

Predrilled hole filled with resin

First layer

Spike anchor

Final layerConcrete



76

aramid fibers. Bonding on concrete surfaces is achieved with two-part epoxy adhesives. Details about specific systems as far as material properties and practical execution are concerned are given by the supplier of the strengthening system. In this section we provide general rules, applicable to most of the commercially available systems. • The concrete should be sound and free from serious imperfections (e.g. cavities,

wide cracks, protrusions), roughened (e.g. by means of sand blasting or water jet blasting) and made laitance and contamination free. Surface moisture in excess of 4% requires the use of special resins. Typical surface preparation steps are given in Fig. 7.13.

(a) (b) (c)

Fig. 7.13 Surface preparation: (a) Grinding, (b) cleaning και (c) leveling.

• Use of prefabricated strips requires a

minimum substrate tensile strength equal to approximately 1.5 MPa (measured in-situ through pull-off testing, Fig. 7.14).

• Selection of the appropriate resin should be made on the basis of in-situ temperature and humidity requirements. Application of resins at very low temperatures may require local heating.

• FRP strips should be cut to proper size using an electric or manual saw. Depending on the type of strips, cleaning (e.g. with acetone) or removal of a surface veil may be required prior to bonding. Handling of strips by workers should be performed with care (the use of gloves is strongly recommended).

Fig. 7.14 In-situ testing of substrate strength.



77

Resin

Strip with resin in trapezoidal configuration

Air

Plastic roller

(a) (b)

Prepared substrate

• Bonding of strips should be followed by the application of pressure using a plastic roller, to remove entrapped air and excess resin (Fig. 7.15-7.16).

Fig. 7.15 (a) Application of resin on concrete and FRP, (b) application of pressure during

rolling.

Resin application on strip. Placement of strip.

Use of roller. Removal of excess resin.

Fig. 7.16 Steps for the application of strips.

• Sheets should be applied with special care to ensure that wrinkles are avoided and that the fibers are as straight as practically possible. Impregnation of sheets with resin is achieved using a plastic roller (Fig. 7.17)



78

(a) (b) (c) (d) (e) Fig. 7.17 In-situ impregnation of sheet: (a) Prime, (b) placement of first layer of sheet, (c)

impregnation of sheet on concrete. (d) Pre-impregnation of sheet and (e) application of pre-impregnated sheet.

• The average thickness of resin layer between strips and the concrete substrate

should be in the order of 1.5 mm. The resin used to impregnate sheets must have an appropriate viscosity and used at the proper quantity, to ensure full impregnation without entrapped air.

• Application of mortar plastering directly on the FRP can be made possible by providing a rough surface through the application of a certain quantity of sand (in the order of 1 kg/m2) directly on the last layer of resin prior to its hardening.

• Last, but certainly not least, the FRP strengthening system should be applied by properly trained and qualified personnel.

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8.1 General

This chapter provides a brief overview of the durability of FRP-based strengthening systems with regard to a number of factors, namely: • Temperature effects • Moisture • Ultraviolet light exposure • Alkalinity and acidity • Galvanic corrosion • Creep, stress rupture, stress corrosion • Fatigue • Impact 8.2 Temperature effects

As reported already in Chapter 2, high temperatures, in the order of 60-80 °C, cause a dramatic degradation of properties in resins (matrix material in FRPs, adhesive at the FRP-concrete interface). Much higher temperatures, such as those developed during fire, result in complete resin decomposition; hence FRPs during fire cannot carry any stresses. The decomposition of glass, carbon and aramid fibers starts at about 1000 oC, 650 oC and 200 oC, respectively. Experimental results have shown that CFRP jackets suffer substantial strength reduction at temperatures exceeding approximately 260 oC. Hence, an FRP strengthening system without special fire protection measures should be considered as ineffective during (and after) fire. Fire protection may be provided using either standard mortar plastering (with a minimum thickness of at least 40 mm, according to the JSCE 2001 guidelines), special mortars or gypsum-based boards. 8.3 Moisture

FRP materials are, in general, highly resistant to moisture. Occasionally, extremely prolonged exposure to water (either fresh or salt) may cause problems with some fiber/resin combinations. The resin matrix absorbs water, which causes a slight reduction

CHAPTER 8

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in strength and the glass transition temperature. However, most structural adhesives (high quality epoxy resins) are extremely resistant to moisture (Blaschko et al. 1998). As far as the fibers are concerned, the high susceptibility of aramid to moisture deserves special attention; carbon fibers are practically unaffected, whereas glass fibers have an intermediate behavior.

At this point it is worth pointing out that full jacketing of RC with FRP provides a moisture/vapor/air barrier which increases the longevity of members by protecting them from harsh conditions (e.g. chlorides, chemicals). On the hand, in case of poor concrete conditions, the encapsulation is at risk if the member is exposed to extreme climate cycling and/or excessive moisture. Applications of FRP to a structural member that is at risk of water pooling should not involve fully encapsulating the concrete. Good internal and surface concrete conditions, proper surface preparation, adequate concrete substrate exposure and proper application of an adequate FRP system may substantially reduce this risk. 8.4 UV light exposure

UV light affects the chemical bonds in polymers and causes surface discoloration and surface microcracking. Such degradation may affect only the matrix near the surface exposed to UV, as well as some types of fibers, such as aramid (Ahmad and Plecnik 1989); carbon and glass fibers are practically unaffected by UV. Anti-UV protection may be provided by surface coatings or special acrylic or polyurethane – based paints. 8.5 Alcalinity and acidity

The performance of the FRP strengthening over time in an alkaline or acidic environment will depend on both matrix and the reinforcing fiber. Carbon fibers are resistant to alkali and acid environment, glass fibers can degrade and aramid displays an intermediate behavior. However, a properly applied resin matrix will isolate and protect the fibers and postpone the deterioration. Nevertheless RC structures located in high alkalinity combined with high moisture or relative humidity environments should be strengthened using carbon fibers. 8.6 Galvanic corrosion

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The contact of carbon fibers with steel may lead to galvanic corrosion, a problem which is not of concern in the case of glass or aramid fibers. 8.7 Creep, stress rupture, stress corrosion

In general, creep strains in composite materials loaded parallel to the fibers are very low. CFRP does not creep, the creep of GFRP is negligible, but that of AFRP cannot be neglected. Hence, the creep behavior of CFRP - or GFRP - plated RC members is governed primarily by the compressive creep of concrete (e.g. Plevris and Triantafillou 1994). As AFRP creeps itself, long-term deformations increase considerably in the case of AFRP-strengthened elements. However, it should be born in mind that in (the very common) case when FRP strengthening systems are designed for additional loads (beyond the permanent ones), creep is not of concern.

Another important issue regarding time-effects is the poor behavior of GFRP under sustained loading. Glass fibers exhibit premature tensile rupture under sustained stress, a phenomenon called stress rupture. Hence the tensile strength of GFRP drops to very low values (as low as 20%) when the material carries permanent tension.

Stress corrosion occurs when the atmosphere or ambient environment is of a corrosive nature but not sufficiently so that corrosion would occur without the addition of stress. This phenomenon is time, stress level, environment, matrix and fiber related. Failure is deemed to be premature since the FRP fails at a stress level below its ultimate. Carbon fiber are relatively unaffected by stress corrosion at stress levels up to 80% of ultimate. Glass and aramid fibers are susceptible to stress corrosion. The quality of the resin has a significant effect on time to failure and the sustainable stress levels. In general, the following order of fibers and resins gives increasing vulnerability either to stress rupture or to stress corrosion: carbon-epoxy, aramid-vinylester, glass-polyester. We may also state that, in general, given the stress rupture of GFRP and the relatively poor creep behaviour of AFRP, it is recommended that when the externally bonded reinforcement is to carry considerable sustained load, composites with carbon fibres should be the designer’s first choice. 8.8 Fatigue

In general, the fatigue behavior of unidirectional fiber composites is excellent, especially when carbon fibers are used, in which case the fatigue strength of FRP is even higher than that of the steel rebars (e.g. Kaiser 1989, Deuring 1993, Barnes and Mays 1999).

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8.9 Impact

The strength of composites under impact loading is highest when aramid fibers are used (hence the use of these materials in bridge columns that may suffer impact loading due to vehicle collision) and lowest in the case of carbon fibers. Glass gives intermediate results.

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REFERENCES

American Concrete Institute (1996), State-of-the-art Report on Fiber Reinforced

Plastic Reinforcement for Concrete Structures, ACI Report 440R-96, Detroit, Michigan. Antonopoulos, Κ. (2001), Strengthening of RC Beam-Column Joints with FRP

Materials, Ph.D. Dissertation, University of Patras, Department of Civil Engineering (in Greek).

Ahmad, S. H. and Plecnik, J. M. (1989), Transfer of Composites Technology to Design and Construction of Bridges, Report of the California State University.

Antonopoulos, C. P. and Triantafillou, T. C. (2002), “Analysis of FRP-Strengthened RC Beam-Column Joints”, Journal of Composites for Construction, ASCE, 6(1), 41-51.

Antonopoulos, C. P. and Triantafillou, T. C. (2003), “Experimental Investigation of FRP-Strengthened RC Beam-Column Joints”, Journal of Composites for Construction, ASCE, 7(1), 39-49.

Barnes, R. A. and Mays, G. C. (1999), “Fatigue performance of concrete beams strengthened with CFRP plates”, Journal of Composites for Construction, ASCE, 3(2), 63-72.

Bizindavyi, L. and Neale, K. W. (1999), “Transfer lengths and bond strengths for composites bonded to concrete”, Journal of Composites for Construction, ASCE, 3(4), 153-160.

Blaschko M., Nierdermeier R. and Zilch, K. (1998), “Bond failure modes of flexural members strengthened with FRP”, Proceedings of Second International Conference on Composites in Infrastructures, Saadatmanesh, H. and Ehsani, M. R., eds., Tucson, Arizona, 315-327.

Deuring, M. (1993), Strengthening of RC with Prestressed Fiber Reinforced Plastic Sheets. EMPA Research Report 224, Dübendorf, Switzerland (in German).

Eurocode 2: Design of Concrete Structures – Part 1-1: General rules and rules for buildings. ENV 1992-1-1, Comité Européen de Normalisation, Brussels, Belgium, 1991.

Eurocode 8: Design of Structures for Earthquake Resistance – Part 3: Assessment and Retrofitting of Buildings, prEN 1998-3:2005, Comité Européen de Normalisation, Brussels, Belgium.

Feldman, D. (1989), Polymeric Βuilding Μaterials, Elsevier Science Publishers Ltd., UK.

Federation International du Beton – fib (2001), Externally Βonded FRP Reinforcement for RC Structures, Bulletin 14, Lausanne.

Federation International du Beton – fib (2003), Seismic Assessment and Retrofit of Reinforced Concrete Buildings, Bulletin 24, Lausanne.

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Haroun, M. A., Mosallam, A. S., Feng, M. Q. and Elsanedeby L. L. (2001) “Experimental investigation of seismic repair and retrofit of bridge columns by composite jackets”, Proceedings of the International Conference of FRP composites in Civil Engineering, J.-G. Teng, ed., Hong Kong, 839-848.

Holzenkämpfer, P. (1994), Ingenieurmodelle des verbundes geklebter bewehrung für betonbauteile. Dissertation, TU Braunschweig (In German).

Jansze, W. (1997), Strengthening of Reinforced Concrete Members in Bending by Externally Bonded Steel Plates, PhD Dissertation, TU Delft, The Netherlands.

Japan Society of Civil Engineers (2001), Recommendations for Upgrading of Concrete Structures with use of Continuous Fiber Sheets, Concrete Engineering Series 41.

Karantzikis, M., Papanicolaou, C. G, Antonopoulos, C. P. and Triantafillou, T. C. (2005), “Experimental Investigation of Non-Conventional Confinement for Concrete using FRP”, Journal of Composites for Construction, ASCE, December 2001.

Kaiser, H. (1989), Strengthening of Reinforced Concrete with CFRP Plates, Ph.D. Dissertation, ETH Zürich (in German).

Kim, D.-H. (1995), Composite Structures for Civil and Architectural Engineering, E & FN Spon, London.

Lam, L., and Teng, J. G. (2003), “Stress-strain model for FRP-confined concrete for design applications”, Proceedings of 6th International Symposium on Fibre-Reinforced Polymer (FRP) Reinforcement for Concrete Structures, Ed. K. H. Tan, Singapore, 1, 99-110.

Ma, R. and Xiao, Y. (1997), “Seismic retrofit and repair of circular bridge columns with advanced composite materials”, Earthquake Spectra, 15(4), 747-764.

Matthys, S. (2000), Structural Behaviour and Design of Concrete Members Strengthened with Externally Bonded FRP Reinforcement, Doctoral Thesis, Ghent University.

Moehle, J., Lynn, A., Elwood, K. and Sezen, H. (2001), Gravity Load Collapse of Building Frames During Earthquakes, PEER Report: 2nd US-Japan Workshop on Performance-based Design Methodology for Reinforced Concrete Building Structures, PEER Center, Richmont, CA.

Neubauer, U. and Rostásy, F. S. (1999), “Bond failure of concrete fibre reinforced polymer at inclined cracks – experiments and fracture mechanics model”, Proceedings of the 4th International Conference on Fibre Reinforced Polymer Reinforcement for Concrete Structures, Eds. C. W. Dolan, S. H. Rizkalla and A,. Nanni, ACI, Michigan, USA, 369-382.

Oehlers, D. J. (1992), “Reinforced concrete beams with plates glued to their soffits”, Journal of Structural Engineering, ASCE, 118(8), 2023-2038.

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Osada, K., Yamaguchi, T. and Ikeda, S. (1999), “Seismic performance and the retrofit of hollow circular reinforced concrete piers having reinforcement cut-off planes and variable wall thickness”, Transactions of the Japan Concrete Institute, 21, 263-274.

Plevris, N. and Triantafillou, T. C. (1994), “Time-dependent behaviour of RC members strengthened with FRP laminates”, Journal of Structural Engineering, ASCE, 120(3), 1016-1042.

Priestley, M. J. N., Seible, F. and Calvi, G. M. (1996), Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York, USA.

Raoof, M. and Hassanen, M. A. H. (2000), “Peeling failure of reinforced concrete beams with fibre-reinforced plastic or steel plates glued to their soffits”, Proceedings of the Institution of Civil Engineers: Structures and Buildings, 140, 291-305.

Restrepo, J. I., Wang, Y. C., Irwin, R. W. and DeVino, B. (1988) “Fibreglass/epoxy composites for the seismic upgrading of reinforced concrete beams with shear and bar curtailment deficiencies”, Proceedings 8th European Conference on Composite Materials, Naples, Italy, 59-66.

Saadatmanesh, H., Ehsani, M. R. and Jin, L. (1997) “Repair of earthquake-damaged RC columns with FRP wraps”, ACI Structural Journal, 94(2), 206-215.

Seible, F., Priestley, M. J. N., Hegemier, G. A. and Innamorato, D. (1997) “Seismic retrofit of RC columns with continuous carbon fiber jackets”, Journal of Composites for Construction, ASCE, 1(2), 52-62.

Tastani, S. and Pantazopoulou, S. (2002), “Design of seismic strengthening for brittle RC members using FRP jackets”, Proceedings of 12th European Conference on Earthquake Engineering, London, Paper 360.

Teng, J. G.; Chen, J. F.; Smith, S. T. and Lam, L. (2001), FRP Strengthened RC Structures, John Wiley & Sons Inc.

Triantafillou, T. C. (1998), “Shear strengthening of reinforced concrete beams using epoxy-bonded FRP composites”, ACI Structural Journal, 95(2), 107-115.

Τriantafillou, T. C. (2004), Structural Materials, Papasotiriou Bookstores (in Greek). Triantafillou, T. C. (2004), Strengthening and Seismic Retrofitting of RC Structures

with Fiber Reinforced Polymers (FRP), Papasotiriou Bookstores (in Greek). Triantafillou, T. C. and Plevris, N. (1992), “Strengthening of RC beams with epoxy-

bonded fibre-composite materials”, Materials and Structures, 25, 201-211. Yamaguchi, T., Nishimura, T., and Uomoto, T. (1998), “Creep model of FRP rods

based on fibre damaging rate”, Proceedings of 1st International Conference on Durability of Fibre Reinforced Polymer (FRP) Composites for Construction, Eds. B. Benmokrane and H. Rahman, Sherbrooke, Canada, 427-437.

Zilch, K., Niedermeier, R. and Blaschko, M. (1998), Bericht über versuche zum verstärken von betonbauteilen mit CFK (Test report on retrofitting concrete members with

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CFRP). Versuchsbericht Nr. 1310, Technische Universität München, Lehrstuhl für Massivbau (In German).

Ziraba, Y. N., Baluch, M. H., Basunbul, I. A., Sharif, A. M., Azad, A. K. and Al-Sulaimani, G. J. (1994), “Guidelines towards the design of reinforced concrete beams with external plates”, ACI Structural Journal, 91(6), 639-646.

THE PROGRAM Composite Dimensioning 87

This Appendix gives information on the use of the program Composite Dimensioning, which may be used for the dimensioning of concrete members strengthened with FRP in flexure, shear or through confinement. The program makes use of the composite materials provided by ISOMAT S.A, a major producer of chemicals and mortars for construction in Greece. The company also delivers the following composite materials products: MEGAWRAP-200 (unidirectional carbon fabric), MEGAPLATE THR-3000 and MEGAPLATE HM-250 (prefabricated carbon fiber plates). The program may also be used with user-specified properties for the composite materials. It runs on PCs operating under Windows 98, 2000, Me και XP and may be installed as follows: • Double click the “setup” icon. • Click “ΟΚ”. • Click “setup”. Upon starting, the program displays its introductory window: By clicking “OK” the following window allows the user to choose one of the following three options: FLEXURAL STRENGTHENING, SHEAR STRENGTHENING, CONFINEMENT.

The Program

Composite Dimensioning



First the type of cross section is selected (Beam or Column) and then the cross section geometry is defined, followed by selection of concrete class or design strength, material data for composite materials (pre-selected products or user-defined elastic modulus, limiting strain) and data for the longitudinal reinforcement. Next, the user defines the moment oM acting in the critical section during strengthening (initial situation) and the axial force oN , in the case of columns. Finally a selection of the target moment capacity RdM (and axial force

RdN in the case of columns) in the critical section at the ultimate limit state is made. By clicking “Solve” a new window appears, which gives the results in terms of the FRP

cross section area ( fA ), the resisting moment ( o,RdM ) of the unstrengthened cross section and the degree of strengthening.


If needed, the user may click on

“Strain profile”, in order to obtain the strain in the cross section both during strengthening (initial situation) and after strengthening, at the ultimate limit state. Moreover, the failure mode is provided. After selecting “Return”, a click on “Input FRP dimensions” opens a new window where the user inputs the width fb and thickness ft of FRP strips (or sheets). Next, the “Solve” button yields the required number of strips and the corresponding cross section area.


Finally the user has two options (apart from exiting the program): (a) “Return without

Solving”, which displays again the window of results, or (b) “Return with Solving”, which displays the window of results updated with new values for fA and RdM (as well as the updated degree of strengthening), those corresponding to the specific FRP geometry chosen.

SHEAR STRENGTHENING

First the user selects the type of jacket, that is the FRP anchorage conditions. A “Closed jacket” is typically the case in columns/shear walls (with full access) or beams with fully anchored FRP in the compression zone, whereas an “Open jacket” is typically the case in T-beams strengthened with U-shaped sheets. Next the cross section geometry is defined, followed by selection of concrete class or design strength and material data for composite materials (elastic modulus, design strength and effective strength). In the following the use of either continuous jacketing or strips (of width fb ) at equal spacing ( fs ) is specified and, finally, the shear to be carried by the FRP, f,RdV , is introduced.


By clicking “Solve” the required total fiber sheet thickness ft is calculated.

Α click on “Input FRP dimensions” opens a new window where the user inputs the thickness

fibt of each layer of sheet to be used in shear strengthening. Next, the “Solve” button yields the required number of layers and the corresponding total thickness of the fiber sheet, ft .

Finally the user has two options (apart from exiting the program): (a) “Return without Solving”, which displays again the window of results, or (b) “Return with Solving”, which displays the window of results updated with new values for ft and f,RdV , those corresponding to the number of layers calculated.


CONFINEMENT The type of cross section (rectangular or circular) is selected first and the cross section

geometry is defined, followed by selection of concrete class or design strength and material data for composite materials (elastic modulus, design strength and effective strength). Next the user inputs the data regarding the existing stirrups (strength of steel, spacing, cross section of ties in each direction, concrete cover) and defines the solution requirements, which can be one of the following: (a) increase the concrete strength and/or the ultimate strain, e.g. for columns where axial loading is predominant; (b) increase the displacement ductility factor ∆µ (equal to the chord rotation ductility factor θµ ), for columns subjected to lateral (seismic) loading causing bending either in the strong or in the weak axis (that is parallel to either the larger or the smaller side of the cross section.


At this point we must emphasize that use of eq. (6.27) is made, which gives quite conservative results (thicker jackets). By clicking “Solve” the required total fiber sheet thickness ft is calculated.

For increase in strength and/or ultimate strain: Apart from the thickness ft , the strength of concrete d1ccf confined with the existing stirrups is also calculated in this case. Moreover, for a given target confined concrete strength the corresponding ultimate strain is calculated and vice-versa. Note that if the user specifies both a target strength and a target ultimate strain, the thickness ft returned by the program is the one corresponding to the maximum of these two cases (hence the ultimate strain and strength values “after strengthening” correspond to this thickness). For increase in ductility:


Next, as in the case of shear strengthening, a click on “Input FRP dimensions” opens a new window where the user inputs the thickness fibt of each layer of sheet to be used for confinement. The “Solve” button yields the required number of layers and the corresponding total thickness of the fiber sheet, ft .

Finally the user has two options (apart from exiting the program): (a) “Return without

Solving”, which displays again the window of results, or (b) “Return with Solving”, which displays the window of results updated with new values for ft and ∆µ (or ccuε and ccdf , depending on the requirements), those corresponding to the number of layers calculated.

OTHER INFORMATION ABOUT THE PROGRAM

By clicking “Options” on the data entry form, the user may specify its data, printing details, and, for the case of “Flexural strengthening”, whether a failure mode that would not involve “Steel yielding” would be acceptable or not. Finally, “Print” gives a printout of all the input and output parameters.


TECHNICAL DATA SHEETS OF ISOMAT’S PRODUCTS Finally, by clicking “Product’s Data Sheets” on the data entry form, a new form is

presented in which all relative to repairing and strengthening issues products of ISOMAT could be presented. The products are divided by the use, as those related to substrate preparation (mortars or epoxy resins) and those related to FRP application (fabrics/plates or epoxy resins). The technical data sheets are in .pdf format so the user should have already install Acrobat Reader.

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