Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Structures

Transcription

1 CNR Advisory Committee on Technical Recommendations or Construction NATIONAL RESEARCH COUNCIL ADVISORY COMMITTEE ON TECHNICAL RECOMMENDATIONS FOR CONSTRUCTION Guide or the Design and Construction o Externally Bonded FRP Systems or Strengthening Existing Structures Materials, RC and PC structures, masonry structures CNR-DT 200/2004 ROME CNR July 13th, 2004

2 This document is subject to copyright. No part o this publication may be stored in a retrieval system, or transmitted in any orm or by any means electronic, mechanical, recording, or otherwise without the prior written permission o the Italian National Research Council. The reproduction o this document is permitted or personal, noncommercial use.

3 CONTENTS 1 FOREWORD PUBLIC HEARING SYMBOLS MATERIALS INTRODUCTION CHARACTERISTICS OF COMPOSITES AND THEIR CONSTITUENTS Fibers used in composites Types o ibers available in the market and their classiication Glass ibers Carbon ibers Aramid ibers Other types o ibers Technical characteristics o yarn Non-impregnated abrics Technical characteristics o non-impregnated abrics Matrices Epoxy resins Polyester resins Other types o resins Technical data sheet o the resin Adhesives and bonding principles Technical data sheet o the adhesive FRP STRENGTHENING SYSTEMS Mechanical properties o FRP strengthening systems Pre-cured systems Mechanical characteristics Technical data sheets or pre-cured systems Wet lay-up systems Determination o laminate cross sectional area Mechanical characteristics Technical data sheets or wet lay-up systems Pre-impregnated systems QUALITY CONTROL Level 1: Physical-mechanical properties Level 2: Long-term properties ACCEPTANCE CRITERIA i

4 2.5.1 Selection and testing o materials: tasks and responsibilities o proessionals TRANSPORTATION, STORAGE AND HANDLING BASIS OF DESIGN FOR FRP STRENGTHENING BASIC REQUIREMENTS DURABILITY REQUIREMENTS GENERAL PRINCIPLES OF THE STRENGTHENING DESIGN General Partial actors and design loads Properties o FRP materials Design capacity PARTIAL FACTORS Partial actors γ m or FRP materials Partial actors γ Rd or resistance models SPECIAL DESIGN PROBLEMS AND RELEVANT CONVERSION FACTORS Environmental conversion actor η a Conversion actors or long-term eects η l Impact and explosive loading Vandalism STRENGTHENING LIMITATIONS IN CASE OF FIRE STRENGTHENING OF REINFORCED AND PRESTRESSED CONCRETE STRUCTURES DEBONDING MECHANISMS Failure mechanisms due to debonding Fracture energy Ultimate design strength or laminate/sheet end debonding (mode 1) Ultimate design strength or intermediate debonding (mode 2) Interacial stress or serviceability limit state FLEXURAL STRENGTHENING Introduction Analysis at ultimate limit state Introduction Strain in the structure prior to FRP strengthening Flexural capacity o FRP-strengthened members Flexural capacity o FRP-strengthened members subjected to bending moment and axial orce Failure by laminate/sheet end debonding Analysis at serviceability limit state Design assumptions ii

5 Stress limitation Delection control Crack control Ductility SHEAR STRENGTHENING Introduction Strengthening conigurations Shear capacity o FRP strengthened members Shear capacity Eective FRP design strength Limitations and construction details TORSIONAL STRENGTHENING Introduction Strengthening conigurations Torsional capacity o FRP strengthened members Torsional capacity Limitations and construction details CONFINEMENT Introduction Axial capacity o FRP-conined members under concentric or slightly eccentric orce Coninement lateral pressure Circular sections Square and rectangular sections Ductility o FRP-conined members under combined bending and axial load FLEXURAL STRENGTHENING OF PRESTRESSED CONCRETE MEMBERS Use o FRP or prestressed concrete members Design at ultimate limit state Design at serviceability limit state DESIGN FOR SEISMIC APPLICATIONS Introduction Design objectives Selection criteria or FRP strengthening Strategies in FRP strengthening Removal o all brittle collapse mechanisms Removal o all storey collapse mechanisms Enhancement o the overall deormation capacity o a structure Increasing o the local rotational capacity o RC members Capacity design criterion iii

6 4.7.3 Saety requirements Ductile members and mechanisms Combined bending and axial load Chord rotation Brittle members and mechanisms Shear Lap splices Buckling o longitudinal bars Joints INSTALLATION, MONITORING, AND QUALITY CONTROL Quality control and substrate preparation Evaluation o substrate deterioration Removal o deective concrete, restoring o concrete substrate and protection o existing steel reinorcement Substrate preparation Recommendations or the installation Humidity and temperature conditions in the environment and substrate Construction details Protection o the FRP system Quality control during installation Semi-destructive tests Non destructive tests Personnel qualiication Monitoring o the strengthening system NUMERICAL EXAMPLES STRENGTHENING OF MASONRY STRUCTURES INTRODUCTION Scope Strengthening o historical and monumental buildings FRP strengthening design criteria Strengthening Rationale SAFETY EVALUATION Structural modelling Veriication criteria Saety veriications EVALUATION OF DEBONDING STRENGTH General considerations and ailure modes Bond strength at ultimate limit state Bond strength with stresses perpendicular to the surace o bond...85 iv

7 5.4 SAFETY REQUIREMENTS Strengthening o masonry panels Strengthening or out-o-plane loads Simple overturning Vertical lexural ailure Horizontal lexural ailure Strengthening or in-plane loads In-plane combined bending and axial load Shear orce Lintel and tie areas Design o lintels Design o tie areas STRENGTHENING OF STRUCTURAL MEMBERS WITH SINGLE OR DOUBLE CURVATURE Arches Arch scheme Arch-pier scheme Single curvature vaults: barrel vaults Double curvature vaults: domes Membrane-type stresses Flexural-type stresses Double curvature vaults on a square plane CONFINEMENT OF MASONRY COLUMNS Design o axially loaded conined members Coninement o circular columns Coninement o prismatic columns DESIGN FOR SEISMIC APPLICATIONS Design objectives Selection criteria or FRP strengthening INSTALLATION, MONITORING, AND QUALITY CONTROL Quality control and substrate preparation Evaluation o substrate deterioration Removal and reconstruction o deective masonry support Recommendations or the installation Humidity and temperature conditions in the environment and substrate Construction details Protection o FRP systems Quality control during installation Semi-destructive tests v

8 Non destructive tests Personnel qualiication Monitoring o the strengthening system APPENDIX A (MANUFACTURING TECHNIQUES AND STRESS-STRAIN RELATIONSHIP OF ORTHOTROPIC LINEAR ELASTIC MATERIALS) MANUFACTURING TECHNIQUES Pultrusion Lamination MECHANICAL BEHAVIOR OF COMPOSITES Eect o loading acting on directions other than that o material symmetry Failure criteria MECHANICAL CHARACTERIZATION TESTS FOR FIBER-REINFORCED MATERIALS APPENDIX B (DEBONDING) FAILURE DUE TO DEBONDING BOND BETWEEN FRP AND CONCRETE Speciic racture energy Bond-slip law SIMPLIFIED METHOD FOR DEBONDING DUE TO FLEXURAL CRACKS (MODE 2) AT ULTIMATE LIMIT STATE APPENDIX C (STRENGTHENING FOR COMBINED BENDING AND AXIAL load OF REINFORCED CONCRETE MEMBERS) FLEXURAL CAPACITY OF FRP STRENGTHENEND MEMBERS SUBJECTED TO COMBINED BENDING AND AXIAL LOAD APPENDIX D (CONFINED CONCRETE) CONSTITUTIVE LAW OF CONFINED CONCRETE APPENDIX E (EXAMPLES OF FRP STRENGTHENING DESIGN) GEOMETRICAL, MECHANICAL, AND LOADING DATA INCREASE OF APPLIED LOADS DESIGN OF FLEXURAL REINFORCEMENT DESIGN OF SHEAR REINFORCEMENT CONFINEMENT OF COLUMNS SUBJECTED TO COMBINED BENDING AND SLIGHTLY ECCENTRIC AXIAL FORCE CONFINEMENT AND FLEXURAL STRENGTHENING OF COLUMNS SUBJECTED TO COMBINED BENDING AND AXIAL FORCE WITH LARGE ECCENTRICITY vi

9 11 ACKNOWLEDGEMENTS vii

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11 1 FOREWORD It is a common eeling, among those involved in research and design activities in the ield o strengthening with iber-reinorced composites, that Italy is getting a worldwide reputation, both or the value o its contribution in improving the knowledge in this ield as well as or the presence o a peculiar and important building heritage. This includes those o historical and architectural relevance as well as more recent masonry, reinorced concrete, prestressed concrete, and steel structures. Most o the latter structures are now over 30 years old and in need o urgent structural remedial works. The main international initiatives or the identiication o design guidelines to address these needs are well known. It is worth mentioning the Japanese (JSCE 1997), the American (ACI ), as well as the European guidelines (FIP-CEB 2001). For the sake o completeness, the study report entitled Non-metallic reinorcements in RC structures, approved by the Italian National Research Council (CNR) in January 1999 will also be included. All the aorementioned documents deal with structures made out o reinorced concrete. The purpose o this guideline is to provide, within the ramework o the Italian regulations, a document or the design and construction o externally bonded FRP systems or strengthening existing structures. A guideline, by its nature, is not a binding regulation, but merely represents an aid or practitioners interested in the ield o composites. Nevertheless, the responsibility o the operated choices remains with the designer. The document deals with the ollowing topics: - Materials - Basic concepts on FRP strengthening - Strengthening o reinorced and prestressed concrete structures - Strengthening o masonry structures Speciic guidelines or the strengthening o reinorced and prestressed concrete structures as well as masonry structures or construction subjected to earthquakes according to the most recent national and international design codes are provided. The irst topic includes a summary o the several advantages and some disadvantages o FRP materials. It also includes an Appendix (Appendix A) where notions on the mechanical characterization o composite materials are presented. The peculiar dierences between FRPs as compared to traditional materials (such as their anisotropic behaviour) as well as emphasis to their constitutive laws are highlighted. The remaining topics are approached according to the usual style o technical documents published by CNR. The approach o the Eurocodes is adopted; statements are divided between Principles and Application Rules. Each statement is marked by a progressive numbering, with the principles being marked by the label (P). Principle statements include the ollowing: - General statements and deinitions o mechanical-structural nature. - Recognized needs and/or analytical models accepted by the scientiic community, whose value is universally deemed to be pre-eminent with respect to possible alternatives, unless otherwise explicitly stated. Application Rules are procedures o widely recognized value, ollowing the Principles and satisying their needs. 1

12 The document contains our more Appendices: - Appendix B includes a section on the ailure modes due to debonding and a section on the constitutive law or bond between FRP and concrete substrate. - Appendix C on the design o FRP-reinorced concrete columns under combined bending and axial orces. - Appendix D on conined concrete. - Appendix E containing numerical examples on FRP strengthening o reinorced concrete members. This Technical Document has been prepared by a Task Group whose members are: AIELLO Pro. Maria Antonietta ASCIONE Pro. Luigi BARATTA Pro. Alessandro BASTIANINI Ing. Filippo BENEDETTI Pro. Andrea BERARDI Ing. Valentino Paolo BORRI Pro. Antonio BRICCOLI BATI Pro. Silvia CERONI Ing. Francesca CERSOSIMO Ing. Giuseppe COSENZA Pro. Edoardo CREDALI Dott. Lino DE LORENZIS Ing. Laura FAELLA Pro. Ciro FANESI Ing. Elisabetta FEO Pro. Luciano FORABOSCHI Pro. Paolo FRASSINE Pro. Roberto GIACOMIN Ing. Giorgio GRANDI Ing. Alberto IMBIMBO Pro. Maura LA TEGOLA Pro. Antonio LAGOMARSINO Pro. Sergio LUCIANO Pro. Raimondo MACERI Pro. Franco MAGENES Pro. Guido MANFREDI Pro. Gaetano MANTEGAZZA Dott. Giovanni MARTINELLI Ing. Enzo MODENA Pro. Claudio MONTI Pro. Giorgio MORANDINI Ing. Giulio NANNI Pro. Antonio NIGRO Pro. Emidio OLIVITO Pro. Renato Sante PASCALE Pro. Giovanni PECCE Pro. Maria Rosaria PISANI Pro. Marco Andrea POGGI Pro. Carlo PROTA Ing. Andrea - University o Lecce - University o Salerno - Università Federico II - Napoli - University o Bologna - University o Bologna - University o Salerno - University o Perugia - University o Firenze - University o Sannio - Benevento - Interbau S.r.l.- Milano - University Federico II - Napoli - Ardea S.r.l. - Casalecchio (BO) - University o Lecce - University o Salerno - Polytechnic o Milano - University o Salerno - IUAV - Venezia - Polytechnic o Milano - Maxor - Quarto d Altino (VE) - Sika Italia S.p.a. - Milano - University o Cassino - University o Lecce - University o Genova - University o Cassino - University Tor Vergata - Roma - University o Pavia - University Federico II - Napoli - Ruredil S.p.a. - Milano - University o Salerno - University o Padova - University La Sapienza - Roma - Mapei S.p.a. - Milano - University Federico II - Napoli - University Federico II - Napoli - University o Calabria - Cosenza - University o Bologna - University o Sannio - Benevento - Polytechnic o Milano - Polytechnic o Milano - University Federico II - Napoli 2

13 REALFONZO Pro. Roberto ROSATI Pro. Luciano SACCO Pro. Elio SAVOIA Pro. Marco SPACONE Pro. Enrico - University o Salerno - University Federico II - Napoli - University o Cassino - University o Bologna - University o Chieti Coordinators: - or the chapter on Materials : FRASSINE Pro. Roberto, POGGI Pro. Carlo; - or the chapter on Basic notions on the strengthening design and special issues : MONTI Pro. Giorgio, NANNI Pro. Antonio; - or the chapter on Reinorced concrete and prestressed concrete structures : ASCIONE Pro. Luigi, MANFREDI Pro. Gaetano, MONTI Pro. Giorgio; - or the chapter on Masonry structures : BENEDETTI Pro. Andrea, SACCO Pro. Elio. General Coordinator: ASCIONE Pro. Luigi. Technical Secretariat: FEO Pro. Luciano, ROSATI Pro. Luciano. 1.1 PUBLIC HEARING Ater its publication, the document n.200/2004 was subject to public hearing between November 2004 and January Following the public hearing, some modiications and/or integrations have been made to the document including corrections o typos, additions o subjects that had not been dealt with in the original version, and elimination o others deemed to be not relevant. The updated document has been discussed and approved by the authors during the meetings held on March 2005 at the CNR headquarters in Rome. This Technical Document has been approved by the Advisory Committee on Technical Recommendation or Construction as a drat version on 13/07/04, and as a inal version on 26/04/2005; the latter document includes the modiications derived rom the public hearing. The members o the Advisory Committee on Technical Recommendation or Construction are: ANGOTTI Pro. Franco ASCIONE Pro. Luigi BARATTA Pro. Alessandro CECCOLI Pro. Claudio COSENZA Pro. Edoardo GIANGRECO Pro. Elio JAPPELLI pro. Ruggiero MACERI Pro. Franco MAZZOLANI Pro. Federico Massimo PINTO Pro. Paolo Emilio POZZATI Pro. Piero SOLARI Pro. Giovanni URBANO Pro. Carlo ZANON Pro. Paolo - University o Firenze - University o Salerno - University Federico II - Napoli - University o Bologna - University Federico II - Napoli - University Federico II - Napoli - University Tor Vergata - Roma - University Tor Vergata - Roma - University Federico II - Napoli - University La Sapienza - Roma - University o Bologna - University o Genova - Polytechnic o Milano - University o Trento 3

14 1.2 SYMBOLS General notations (.) c value o quantity (.) or concrete (.) cc value o quantity (.) or conined concrete (.) d design value o quantity (.) (.) value o quantity (.) or the iber-reinorced composite (.) k characteristic value o quantity (.) (.) mc value o quantity (.) or conined masonry (.) R value o quantity (.) as resistance (.) s value o quantity (.) or steel (.) S value o quantity (.) as demand Uppercase Roman letters A c area o concrete cross-section, net o steel reinorcement A area o FRP reinorcement A w area o FRP shear reinorcement A l overall area o longitudinal steel reinorcement A sw area o one stirrup leg A s1 area o steel reinorcement subjected to tension A s2 area o steel reinorcement subjected to compression E c Young s modulus o elasticity o concrete E Young s modulus o elasticity o FRP reinorcement E ib Young s modulus o elasticity o iber itsel E m Young s modulus o elasticity o matrix E s Young s modulus o elasticity o steel reinorcement F max,d design value o the maximum tensile orce transerred by FRP reinorcement to the concrete support F pd design value o the maximum anchorage orce transerred by FRP reinorcement bonded on a masonry structure in the presence o a orce perpendicular to the bonded surace area G a shear modulus o adhesive G c shear modulus o concrete I o moment o inertia o cracked and un-strengthened reinorced concrete section I 1 moment o inertia o cracked and FRP-strengthened reinorced concrete section I c moment o inertia o transormed section I moment o inertia o FRP reinorcement about its centroidal axis, parallel to the beam neutral axis M Rd lexural capacity o FRP-strengthened member M Sd actored moment M o bending moment acting beore FRP strengthening M 1 bending moment applied to the RC section due to loads applied ater FRP strengthening N Rcc,d axial capacity o FRP-conined concrete member N Rmc,d axial capacity o FRP-conined masonry N Sd actored axial orce P ib weight raction o ibers P m weight raction o the matrix T g glass transition temperature o the resin T m melting temperature o the resin T Rd torsional capacity o FRP-conined concrete member T Rd, FRP contribution to the torsional capacity T Rd,max torsional capacity o the compressed concrete strut 4

15 T Rd,s steel contribution to the torsional capacity T Sd actored torsion T x Yarn count in x direction V ib volumetric raction o ibers V Rd shear capacity o FRP-strengthened member V Rd,ct concrete contribution to the shear capacity V Rd,max maximum concrete contribution to the shear capacity V Rd,s steel contribution to the shear capacity V Rd, FRP contribution to the shear capacity V Rd,m masonry contribution to the shear capacity actored shear orce V Sd Lowercase Roman letters b width o FRP reinorcement d distance rom extreme compression iber to centroid o tension reinorcement bd design bond strength between FRP reinorcement and concrete (or masonry) bk characteristic bond strength between FRP reinorcement and concrete (or masonry) c concrete compressive strength (cylindrical) ccd design strength o conined concrete cd design concrete compressive strength ck characteristic concrete compressive strength ctm mean value o concrete tensile strength d design strength o FRP reinorcement dd design debonding strength o FRP reinorcement (mode 1) dd,2 design debonding strength o FRP reinorcement (mode 2) ed eective design strength o FRP shear reinorcement k characteristic strength o FRP reinorcement pd design debonding strength o FRP reinorcement mk characteristic compressive strength o masonry h mk characteristic compressive strength o masonry in the horizontal direction mcd characteristic compressive strength o FRP-conined masonry md design compressive strength o masonry h md design compressive strength o masonry in the horizontal direction mtd design tensile strength o masonry mtk characteristic tensile strength o masonry mtm mean value o the tensile strength o masonry vd design shear strength o masonry vk characteristic shear strength o masonry y yield strength o longitudinal steel reinorcement yd design yield strength o longitudinal steel reinorcement ywd design yield strength o transverse steel reinorcement l conining lateral pressure l,e eective conining pressure h section depth k e coeicient o eiciency or coninement k H coeicient o eiciency in the horizontal direction k V coeicient o eiciency in the vertical direction k α coeicient o eiciency related to the angle α o ibers respect to the longitudinal axis o conined member l b bond length optimal bond length l e 5

16 p b p s s t w x distance between layers o bars in the coninement o masonry columns spacing o FRP strips or discontinuous FRP U-wraps interace slip interace slip at ull debonding thickness o FRP laminate width o FRP laminate distance rom extreme compression iber to neutral axis Uppercase Greek letters Γ Fk characteristic value o speciic racture energy design value o speciic racture energy Γ Fd Lowercase Greek letters α E saety coeicient or abric stiness α saety coeicient or abric strength γ m partial actor or materials γ Rd partial actor or resistance models ε o concrete strain on the tension iber prior to FRP strengthening ε c concrete strain on the compression iber ε ccu design ultimate strain o conined concrete ε co concrete strain on the compression iber prior to FRP strengthening ε cu ultimate strain o concrete in compression ε strain o FRP reinorcement ε d design strain o FRP reinorcement ε d,rid reduced design strain o FRP reinorcement or conined members ε k characteristic rupture strain o FRP reinorcement ε dd maximum strain o FRP reinorcement beore debonding ε mcu ultimate compressive strain o conined masonry ε mu ultimate compressive strain o masonry ε s1 strain o tension steel reinorcement ε s2 strain o compression steel reinorcement ε yd design yield strain o steel reinorcement η conversion actor ν ib Poisson s ratio o ibers ν m Poisson s ratio o matrix ρ ib iber density ρ m matrix density σ c stress in the concrete σ stress in FRP reinorcement σ s stress in tensile steel reinorcement σ Sd stress normal to masonry ace acting on the bonded surace area between FRP reinorcement and masonry τ b,e equivalent shear stress at the adhesive-concrete interace φ u curvature at ultimate curvature at yielding φ y 6

17 2 MATERIALS 2.1 INTRODUCTION Continuous iber-reinorced materials with polymeric matrix (FRP) can be considered as composite, heterogeneous, and anisotropic materials with a prevalent linear elastic behavior up to ailure. They are widely used or strengthening o civil structures. There are many advantages o using FRPs: lightweight, good mechanical properties, corrosion-resistant, etc. Composites or structural strengthening are available in several geometries rom laminates used or strengthening o members with regular surace to bi-directional abrics easily adaptable to the shape o the member to be strengthened. Composites are also suitable or applications where the aesthetic o the original structures needs to be preserved (buildings o historic or artistic interest) or where strengthening with traditional techniques can not be eectively employed. There are also examples o applications o composite strengthening with discontinuous ibers and polymeric matrix as well as continuous ibers and inorganic matrix; the latter has been proven to be o particular interest. Such strengthening methodologies, however, will not be discussed in this document because available literature is not suicient to ensure reliable structural applications. This chapter reports the basic inormation on composite materials, their constituents (iber, matrix, and adhesive), and their physical and mechanical properties. Such inormation is necessary to know the pros and cons o iber-reinorced composite materials to make use o their advantages and mitigate, i possible, their disadvantages. This is o particular relevance to ensure durability o FRP strengthening applications where traditional materials such as concrete or masonry are coupled with high technology materials. The readers amiliar with the technological and mechanical properties o iber-reinorced composite materials may postpone the reading o Sections 2.2 and 2.3 and proceed to Section CHARACTERISTICS OF COMPOSITES AND THEIR CONSTITUENTS Composite materials exhibit the ollowing characteristics: They are made o two or more materials (phases) o dierent nature and macroscopically distinguishable. At least two phases have physical and mechanical properties quite dierent rom each other, such to provide FRP material with dierent properties than those o its constituents. Fiber-reinorced composites with polymeric matrix satisy both o the above characteristics. In act, they are made out o both organic polymeric matrix and reinorcing ibers, whose main characteristics are summarized in Table 2-1. As it can be seen, carbon ibers may exhibit values o Young s modulus o elasticity much larger than those o typical construction materials. Thereore, they are more eective rom a structural point o view. Potential problems with other materials used as support need to be careully evaluated by designers and practitioners. The matrix may be considered as an isotropic material, while the reinorcing phase, with the exception o glass iber, is an anisotropic material (dierent properties in dierent directions). The deining characteristics o FRP materials are as ollows: Geometry: shape and dimensions. Fiber orientation: the orientation with respect to the symmetry axes o the material; when random, the composite characteristics are similar to an isotropic material ( quasi- 7

18 isotropic ). In all other cases the composite can be considered as an anisotropic material. Fiber concentration: volume raction, distribution (dispersion). Thereore, composites are in most cases a non-homogeneous and anisotropic material. Table 2-1 Comparison between properties o ibers, resin, and steel (typical values) Young s Tensile Strain Coeicient o Density modulus strength at ailure thermal expansion E σ r ε r α ρ [GPa] [MPa] [%] 6 1 [ 10 C ] [ g 3 cm ] E-glass S-glass Carbon (high modulus) Carbon (high strength) Aramid Polymeric matrix Steel (yield) (ailure) To summarize FRP properties, it is convenient to recognize iber-reinorced composites in two categories, regardless o their production technology: Single-layer (lamina) Multi-layer (laminates) Laminates are materials composed o stacked layers (the lamina) whose thickness is usually o some tenths o a millimeter. In the simplest case, ibers are embedded only in the lamina s plane (there are no ibers arranged orthogonally to that plane). The size o laminates is intermediate between those o the ibers and those o engineering structures (Table 2-2). There is also a special class o multi-layer composites, so-called hybrid laminates, where each single lamina is made out o both dierent ibers (e.g., epoxy matrix composites with carbon and aramid ibers to get a sti and tough composite) or dierent materials (e.g., composites with alternate layers o epoxy resin with aramid and aluminium ibers). The main advantage o laminates is represented by the greater reedom o iber arrangement. Table 2-2 Size o iber composites with polymer matrix. representative dimensions pm nm μm mm m km Atom * * Polymer molecules * * Biological polymers * * Crystallites * * Spheroids * * Diameter o ibers * Thickness o FRP sheets * * * Thickness o FRP laminates * * Length o laminates * * * Structures * * * 8

19 Due to the anisotropic characteristics o FRP material, their mechanical properties depend on the choice o the reerence system. The main axes are usually chosen to be concurring with the symmetry axes o the material (natural axes). The case o a unidirectional FRP material is illustrated in Figure 2-1. Figure 2-1 Choice o axes or a unidirectional FRP material. The ratio between values o the properties o composite materials in dierent directions is named anisotropic ratio. Some values o the anisotropic ratio related to the main characteristics o interest in unidirectional laminates ( E i : Young modulus o elasticity; G ij : shear modulus; σ ri : ailure stress; α i : coeicient o thermal expansion) are shown in Table 2-3. Table 2-3 Anisotropic ratios o iber-reinorced unidirectional laminates (typical values). E 1 /E 2 E 1 / G 12 σ r1 /σ r2 α 1 /α 2 Silicon carbide/ceramic Boron/aluminium Silicon carbide/aluminium S-Glass/epoxy E-Glass/epoxy Boron/epoxy Carbon/epoxy Aramid/epoxy Composite materials can be stronger and stier (carbon FRP) than traditional construction materials. As a result, composites may become very attractive when the weight o the structure becomes an issue. FRP tensile strength and Young s modulus o elasticity can be up to our and two times that o traditional materials, respectively. This means that a composite material structure may weigh nearly hal o a traditional construction material structure o equal stiness. The nature o the phases o the composite determines the inal properties o FRP materials. To obtain a composite with high mechanical strength, using strong ibers is not enough. A good adhesion between matrix and ibers used as loading carrying component is also necessary. The adhesion is usually obtained through a third component applied in a very thin layer on the iber surace that makes them compatible with the organic matrix. Such surace treatment requires the presence o an intermediate phase between the matrix and the ibers, named interace, or interphase (Figure 2-2). The interphase is typically made o a very thin layer (oten a single-atom) placed directly on the iber that is essential or determining the inal properties o the material. Figure 2-2 Representation o phases in a FRP composite. 9

20 Structural ailures o FRP composites are oten due to lack o bond between matrix and ibers. Thereore, the FRP material manuacturer should take special care in choosing the most appropriate component to use to promote the bond Fibers used in composites The most common ibers used in composites are glass, carbon, and aramid. Their unique monodimensial geometry, in addition to being particularly suitable or the realization o composites, provides FRP laminates with stiness and strength higher than those o three-dimensional FRP shapes. This is due to the lower density o deects o mono-dimensional conigurations as opposed to that o three-dimensional members Types o ibers available in the market and their classiication Fibers are made o very thin continuous ilaments, and thereore, are quite diicult to be individually manipulated. For this reason, they are commercially available in dierent shapes (Figure 2-3). A brie description o the most used is summarized as ollows: Monoilament: basic ilament with a diameter o about 10 μm. Tow: untwisted bundle o continuous ilaments. Yarn: assemblage o twisted ilaments and ibers ormed into a continuous length that is suitable or use in weaving textile materials. Roving: a number o yarn or tows collected into a parallel bundle with little or no twist. Figure 2-3 Types o ibers. By combining a number o tows or yarns together, a tape is obtained, where tows or yarns can be simply arranged side by side or sewed or astened on a bearing. The classiication o ibers is directly taken rom that traditionally used or textile ibers. The ilaments used to produce yarns are basically characterized by their chemical composition or by their mass per unit length. The unit o linear mass or count (mass per unit length) according to ISO 2974:2000(E) is the TEX, equivalent to 1 g per km o iber. Another unit o linear mass, now obsolete, is the denier, equivalent to TEX. The technical name o iberglass ollows the rule o ISO 1139:1973(E) and ISO 2078:1993(E) and includes the ollowing members: A letter identiying the type o glass used A second letter identiying the type o iber used - C ( Continuous, or ilaments) 10

21 - D ( Discontinuous, or discontinuous ibers) A irst number identiying the nominal diameter (in μm) o the ilament A second number indicating the linear mass o the iber in TEX The direction and value o torsion (Figure 2-4), expressed in rpm (optional) The number o wires used to produce the twisted member (optional) A manuacturer label containing all the un-coded inormation necessary or the product characterization (optional) Negative torsion (S). Positive torsion (Z). Figure 2-4 Deinition o the two possible directions o torsion. Examples o labeling are listed in the ollowing: EC10 40: continuous ilament o E-glass, with a diameter o 10 μm and a linear mass o 40 TEX. EC9 34 Z 40: continuous ilament o E-glass, with a diameter o 9 μm and a linear mass o 34 TEX, twisted at 40 rpm. The letter Z indicates a torsion deined as positive according to ISO 1139:1973(E) (negative torsion is indicated with the letter S). EC9 34 Z 160 x 4 S 150: the letter x shows that the material is a wire containing a number o identical ilaments. The code preceding the x identiies the characteristics o the ilaments, while the ollowing number (4) represents the number o ilaments and the letter S a negative torsion, accomplished at 150 rpm. EC9 x 4 S 150: simpliied labelling o the previous ilament. Yarns commonly used or structural composites are reerred to as EC5 10 x 2 or SC5 4 x 2, depending whether the material is E-glass or S-glass, respectively. For carbon ibers, yarns are usually classiied by the symbol k, standing or thousands [e.g., a 1k yarn is made o 1000 ilaments (66.6 Tex), a 3k yarn (200 Tex) has 3000 ilaments, and so on]. Typical values are 0.5k, 1k, 3k, 6k, 12k, 18k, 24k, and 48k. In addition to yarns or rovings, ibers are also commercially available as abrics. In this case, ibers dispositions may be such as to provide a quasi-isotropic properties o the abric. In such materials the main direction is named warp while the orthogonal direction is named wet Glass ibers These are ibers commonly used in the naval and industrial ields to produce composites o medium-high perormance. Their peculiar characteristic is their high strength. Glass is mainly made o silicon ( SiO 2) with a tetrahedral structure ( SiO 4 ). Some aluminium oxides and other metallic ions are then added in various proportions (Table 2-4) to either ease the working operations or modiy some properties (e.g., S-glass ibers exhibit a higher tensile strength than E-glass). 11

22 Table 2-4 Typical composition o iberglass (% in weight). E-glass S-glass Silicon oxide Aluminium oxide Iron oxide Calcium oxide Magnesium oxide Sodium oxide Boron oxide Barium oxide Various The production technology o iberglass is essentially based on spinning a batch made o sand, alumina, and limestone. The constituents are dry mixed and brought to melting (about 1260 C) in a tank. The melted glass is carried directly on platinum bushings and, by gravity, passes through ad hoc holes located on the bottom. The ilaments are then grouped to orm a strand typically made o 204 ilaments. The single ilament has an average diameter o 10 μm and is typically covered with a sizing. The yarns are then bundled, in most cases without twisting, in a roving. The typical value o the linear mass or roving to be used in civil engineering applications is larger than 2000 TEX. Glass ibers are also available as thin sheets, called mats. A mat may be made o both long continuous or short ibers (e.g., discontinuous ibers with a typical length between 25 and 50 mm), randomly arranged (Figure 2-5) and kept together by a chemical bond. The width o such mats is variable between 5 cm and 2 m, their density being roughly 0.5 kg/m 2. Glass ibers typically have a Young modulus o elasticity (70 GPa or E-glass) lower than carbon or aramid ibers and their abrasion resistance is relatively poor; thereore, caution in their manipulation is required. In addition, they are prone to creep and have a low atigue strength. To enhance the bond between ibers and matrix, as well as to protect the ibers itsel against alkaline agents and moisture, ibers undergo sizing treatments acting as coupling agents. Such treatments are useul to enhance durability and atigue perormance (static and dynamic) o the composite material. FRP composites based on iberglass are usually denoted as GFRP. Discontinuous ibers. Discontinuous ibers mat. Figure 2-5 Fiberglass mat Carbon ibers Carbon ibers are used or their high perormance and are characterized by high Young modulus o elasticity as well as high strength. They have an intrinsically brittle ailure behavior with a relatively low energy absorption; nevertheless, their ailure strength are larger compared to glass and aramid ibers. Carbon ibers are less sensitive to creep rupture and atigue and show a slight reduction o the long-term tensile strength. 12

23 The crystalline structure o graphite is hexagonal, with carbon atoms arranged on a basically planar structures, kept together by transverse Van der Waals interaction orces, much weaker than those acting on carbon atoms in the plane (covalent bonds). For such reason, their Young modulus o elasticity and strength are extremely high in the iber directions and much lower in the transversal direction (anisotropic behavior). The structure o carbon ibers is not as completely crystalline as that o graphite. The term graphite ibers is however used in the common language to represent ibers whose carbon content is larger than 99 %. The term carbon ibers denotes ibers whose carbon content is between 80 and 95 %. The number o ilaments contained in the tow may vary rom 400 to The modern production technology o carbon ibers is essentially based on pyrolysis (e.g., the thermal decomposition in the absence o oxygen o organic substances), named precursors, among which the most requent are polyacrylonitrile ibers (PAN), and rayon ibers. PAN ibers are irst stabilized, with thermal treatments at C or 24 hrs, so their molecular structure becomes oriented in the direction o the applied load. As a second step, carbonization treatments at 1500 C in inert atmosphere to remove chemical components other than carbon are perormed. The carbonized ibers may then undergo a graphitization treatment in inert atmosphere at 3000 C, to develop a ully crystalline structure similar to that o graphite. FRP composites based on carbon are usually denoted as CFRP Aramid ibers Aramid ibers are organic ibers, made o aromatic polyamides in an extremely oriented orm. First introduced in 1971, they are characterized by high toughness. Their Young modulus o elasticity and tensile strength are intermediate between glass and carbon ibers (Figure 2-6 and Figure 2-7). Their compressive strength is typically around 1/8 o their tensile strength. Due to the anisotropy o the iber structure, compression loads promote a localized yielding o the ibers resulting in iber instability and ormation o kinks. Aramid ibers may degrade ater extensive exposure to sunlight, losing up to 50 % o their tensile strength. In addition, they may be sensitive to moisture. Their creep behavior is similar to that o glass ibers, even though their ailure strength and atigue behaviour is higher than GFRP. Figure 2-6 Stress-strain diagram or dierent reinorcing ibers The production technology o aramid ibers is based on high-temperature and high-speed extrusion o the polymer in a solution ollowed by ast cooling and drying. The ibers produced in this way 13

24 may undergo a hot orientation treatment through winding on ast rotating coils (post-spinning) to improve their mechanical characteristics. Aramid ibers are commercially available as yarns, roving, or abrics. FRP composites based on aramid ibers are usually denoted as AFRP. Figure 2-7 Comparison between FRPs and steel Other types o ibers Fibers as previously described are the most commonly used or the production o composite materials to be employed or application in the civil engineering ield. Alternative ibers such as boron ibers have high Young modulus o elasticity as well as good strength. In presence o high temperatures, dierent types o ibers may be used, such as ceramic ibers (e.g., alumina ibers and silicon carbide ibers), whose mechanical characteristics are reported in Table 2-5 along with those o boron ibers. Table 2-5 Properties o boron and ceramic ibers. Boron ibers Ceramic ibers Alumina (CFP)* SiC (CVD)** SiC (pyrolysis) Diameter [μm] ± Density [ g 3 cm ] Failure stress [MPa] Young s modulus [GPa] (*) Chemically Formed Processes (**) Chemical Vapour Deposition Technical characteristics o yarn Yarns are not available on the market as strengthening materials; instead, they are used as raw material or the production o abrics. Hereater, the structure o a typical technical data sheet or yarn is proposed. The international reerence standard is ISO 2113:1996(E). ISO 1889:1997 (E) can be used to determine the count o a yarn. A sample o any given length should be taken rom the abric and should be weighted; the count value is given by the ollowing ratio: 14

25 T x P 1000 = (2.1) L where T x is the count o the yarn, expressed in Tex [ g km ]; P is the weight o the sample, expressed in grams; and L is the length o the sample, expressed in meters. 2 The area A, in mm, o the cross-section o a ilament or bundle (yarn, tow, or roving), can be determined using the ollowing equation: Tx A = (2.2) ρ 1000 where ρ is the yarn density, expressed in g cm ; and T x is the count, expressed in TEX. The evaluation o such parameters may be useul or production quality control. 3 TECHNICAL DATA SHEET: yarn THE MANUFACTURER SHALL REPORT THE STATISTICAL VALUES NEEDED TO EVALUATE THE STRENGTH CHARACTERISTICS (E.G. SAMPLE MEAN, SAMPLE STANDARD DEVIATION, POPULATION, PERCENTILE, CONFIDENCE INTERVAL). Yarn description Commercial name, type o yarn, twisting, inishing, and any other inormation deemed necessary. Yarn characteristics property Measurement unit Test method Reerence standard iber diameter μm iber density g 3 cm no. o ilaments count Tex ISO1889:1997(E) type o inishing (size) inishing content % ISO1887:1995(E) ISO10548:2002(E) Young modulus o elasticity GPa ISO10618:1999(E) tensile strength (average and characteristic value) MPa ISO10618:1999(E) ailure strain % ISO10618:1999(E) moisture content % ISO3344:1997(E) Storage conditions Description Saety and handling Description Non-impregnated abrics The abric that is not impregnated with resin is named dry. The simplest abric is obtained start- 15

26 ing rom a roving and is named woven roving. Since the roving does not exhibit any twisting, the ilament is transversely compressed where wet and warp cross each other. The resulting abric is suitable to realize large products in size and thickness. Fabrics obtained directly rom the weaving o the yarns, being lighter and more compact, can be used or more speciic applications that require an optimization o the structural weight. A composite laminate obtained rom these abrics has a lower volumetric raction o ibers than a laminate made o unidirectional iber due to the crimp associated to weaving. The most used types o abric are plain, twill and satin. Plain ibers exhibit the stiest and most stable structure. The main disadvantages are the diiculty o impregnation with resin as well as the crimp o wet and warp. This latter characteristic implies a lower strengthening eectiveness on the plane o the laminate. The crimp or such abrics is about 10 %. Twill ibers and satin ibers are more lexible but relatively prone to be damaged during manipulation. The satin abric is intrinsically stier in the lamination plane, since its has the least crimp o ibers in both directions. Figure 2-8 shows the geometries o the most used abrics in current applications. The representation complies with the ollowing assumptions: Black or dashed box = wet yarn on top o warp yarn White box = wet yarn under warp yarn Plain Twill Satin Figure 2-8 Fabric examples. There are also multi-axial abrics, where the ibers are oriented in more than two directions. They can be made o woven yarns or simply sewn yarns. Finally, three-dimensional abrics are also available, where the presence o a second wet in a direction orthogonal to the plane provides the product with higher strength and special properties (e.g. the capability to inlate when they are impregnated with resin) Technical characteristics o non-impregnated abrics Fabrics or structural strengthening are commonly distributed as a dry product to be impregnated with special resins at the job site. They can be unidirectional, where the ibers are all oriented in the direction o the length and kept together by a light non-structural wet; bi-directional, made o a orthogonal wet-warp weaving, usually balanced (same ratio o ibers in the two directions); and multi-axial, where ibers are oriented in dierent directions. Dry iber manuacturers are required to provide material data sheets. The structure o a material data sheet is reported hereater or monoand bi-directional abrics; data sheets o commercially available abrics may also include other inormation or parts o those indicated. The suggested structure is exhaustive regarding the type and amount o inormation provided. 16

27 TECHNICAL DATA SHEET: non-impregnated abric THE MANUFACTURER SHALL REPORT THE STATISTICAL VALUES NEEDED TO EVALUATE THE STRENGTH CHARACTERISTICS (E.G. SAMPLE MEAN, STANDARD DEVIATION, POPULATION, PERCENTILE, CONFIDENCE INTERVAL). Fabric description Type o weave (plain, twill, satin, etc.), type o yarn (wet and warp), characteristics other than wet and warp (inishing, veil, wrapping, etc.), and any other inormation deemed necessary. Fabric characteristics ISO 3374:2000(E) Property Direction Measurement Test method o yarn unit Reerence standard yarn count warp Tex wet Tex ISO 1889:1997(E) yarn density g/cm 3 no. o yarns/cm warp n /cm wet n /cm ISO 4602:1997(E) mass (weight) total g/m 2 warp g/m 2 wet g/m 2 Young modulus o elasticity warp MPa or tensile stress wet MPa tensile strength warp [N] ISO 4606:1995(E) (textile glass) (mean and characteristic value) wet [N] ISO :1999(E) ailure strain warp % ISO 4606:1995(E) (textile glass) wet % ISO :1999(E) Characteristics o the yarn See the yarn technical data sheet. Storage conditions Description. Saety and handling Description. Indications or use as strengthening system The manuacturer may indicate other products to couple with the abric or the realization o the strengthening systems, such as impregnation resins, possible protective coatings, primer, putty, etc. Such inormation shall be accompanied by the results o compatibility tests perormed on the complete system (see Section 2.5). The general reerence standard is ISO 8099:1980. For multi-axial abrics, in addition to the general inormation concerning the type o yarn and other characteristics o the abric, the orientation o each layer o ibers should be reported as well. In the ollowing, examples concerning the determination o some characteristic parameters o the abrics used or structural strengthening are illustrated. 17

28 In cases where only the yarn count and geometry are provided, the mass o ibers per unit area in a given direction can be determined with the ollowing equation: p x T N 10 x = (2.3) where p x is the mass o the abric in the principal direction, expressed in g ; T x is the yarn count reerred in the principal direction, expressed in Tex [ g km ]; and N is the number o yarns per unit width in the principal direction [yarns/cm]. For example, given a unidirectional abric characterized by 3.8 yarns/cm and by a yarn count o 800 Tex, the resulting mass per unit area is: 2 m p x 800 [Tex] 3.8 [yarns/cm] = = 304 g / m 10 2 I it is necessary to evaluate the number o yarns arranged in a given direction per unit length in the orthogonal direction, ISO 4602:1997(E) can be applied: the yarns arranged in the orthogonal direction on a given abric strip (e.g., 10 cm wide) are counted, and the resulting number is varied proportionally to the chosen unit length Matrices Thermoset resins are the most commonly used matrices or production o FRP materials. They are usually available in a partially polymerized state with luid or pasty consistency at room temperature. When mixed with a proper reagent, they polymerize to become a solid, vitreous material. The reaction can be accelerated by adjusting the temperature. Thermoset resin have several advantages, including low viscosity that allows or a relative easy iber impregnation, good adhesive properties, room temperature polymerization characteristics, good resistance to chemical agents, absence o melting temperature, etc. Disadvantages are limited range o operating temperatures, with the upper bound limit given by the glass transition temperature, poor toughness with respect to racture ( brittle behavior), and sensitivity to moisture during ield applications. The most common thermosetting resins or civil engineering are the epoxy resin. Polyester or vinylester resins are also used. Considering that the material is mixed directly at the construction site and obtains its inal structural characteristics through a chemical reaction, it should always be handled by specialized personnel. Fiber-reinorced composite materials with thermoplastic polymeric matrices are also available but require installation techniques dierent rom thermosetting resin. Composite bars with thermoplastic matrix that may be bent at any time by means o special thermal treatment are currently being investigated Epoxy resins Epoxy resins are characterized by a good resistance to moisture, chemical agents, and have excellent adhesive properties. They are suitable or production o composite material in the civil engineering ield. The maximum operating temperature depends both on ormulation and reticulation temperature. For operating temperatures higher than 60 C, the resin should be suitably selected by taking into account the variations o its mechanical properties. There are usually no signiicant restrictions or the minimum operating temperature. The main reagent is composed o organic luids with a low molecular weight, containing a number o epoxy groups, rings composed by a oxygen atom and two carbon atoms: 18

29 Figure 2-9 Epoxy group. Such materials may be produced by the reaction o epichlorohydrin with amino compounds or acid compound o bisphenol A. The epoxy pre-polymer is usually a viscous luid, with viscosity depending on the polymerization degree. A reticulating agent (typically an aliphatic amine) is to be added to this mixture in the exact quantity to obtain the correct structure and properties o the crosslinked resin. The reaction is exothermic and does not produce secondary products. It can be carried out at both room and high temperatures, according to the technological requirements and the target inal properties. The chemical structure o the resin may be changed on the basis o the chemical composition o the epoxy prepolymer. The most commonly used epoxy resin in composite materials or civil applications is the diglycidylether o bisphenol A (DGEBA) Polyester resins Polyester resins have a lower viscosity compared to epoxy resins, are very versatile, and highly reactive. Their mechanical strength and adhesive properties are typically lower than those o epoxy resins. Unsaturated polyesters are linear polymers with a high molecular weight, containing double C=C bonds capable o producing a chemical reaction. The polymerization degree, and hence the molecule length may be changed; at room temperature the resin is always a solid substance. To be used, polyester resin has to be dissolved in a solvent, typically a reactive monomer, which reduces the resin viscosity and thereore aids the iber impregnation process. The monomer (typically styrene) shall also contain double C=C bonds, allowing cross-linking bridges between the polyester molecules to be created. The reaction is exothermic and no secondary products are generated. It is usually perormed at room temperature, according to technological requirements and target inal properties. The chemical structure o polyester resins may be adapted either by changing the acid and the glycol used in the polymer synthesis or by employing a dierent reactive monomer. The amily o polyester resins or composite materials is typically composed o isophthalic, orthophthalic, and bisphenolic resins. For both high temperatures and chemically aggressive environment applications, vinylester resins are oten used; they represent a compromise between the perormance o traditional polyester resins and that o epoxy resins Other types o resins The intrinsic limitations o thermosetting resins, in particular their poor toughness, their quite low operating temperatures, and their tendency to absorb moisture rom the environment, have recently led to the development o composites with a thermo-plastic matrix. Such resins have the capability o lowing ater heating at a high enough temperature, speciically, higher than T g (glass transition temperature) or amorphous materials and higher than T m (melting temperature) or semi-crystalline materials. The shape o each components may be modiied by simply heating the material at a suitable temperature (hot orming). Their use in the civil engineering ield is rather limited at present; however, applications o potentially remarkable relevance are currently being developed (e.g., reinorcing bars or concrete). In general, thermoplastic resins are tougher than thermosetting resin, and 19

30 in some instances have higher operating temperatures. In addition, they have a better resistance to environmental actors. The main limitation or their use is their high viscosity, which makes iber impregnation diicult, and requires complex and costly working equipment. Moreover, the use o inorganic matrices (cement-based, metallic, ceramic, etc.) or production o iber-reinorced composites or construction is rapidly growing. Even though they are not discussed in this document, their use is deemed possible when accompanied by suitable technical documentation and experimental validation to prove their eectiveness Technical data sheet o the resin The structure o a typical technical data sheet or resin is reported as an example (technical data sheets available on the market could report other inormation or only a portion o those indicated here). The suggested structure is exhaustive regarding type and amount o provided inormation. TECHNICAL DATA SHEET: resin Characteristics o unmixed resin property Resin description Commercial name, mono-or bi-component, pasty or luid consistency, use, and any other necessary inormation. Measurement unit Comp. A Comp. B Mixture Test method Reerence standard color viscosity at 25 C Pa s ISO 2555:1989(E) ISO 3219:1993(E) (1) thyxotropy index ASTM D (1) density g/cm 3 ISO 1675:1985(E) mixing ratio volume % weight storage conditions time months (sealed container) temperature C Notes (1) For non thyxotropic resins the Garner viscosimeter can be used; or thyxotropic resins the Brookield viscosimeter shall be used. Characteristics o mixed resin Mixing conditions: Description Application conditions: Description property Measurement Test method Notes unit Reerence standard pot lie (at 35 C) Pot lie (at 35 C) ISO 10364:1993(E) (2) At 5 C ISO 9396:1997(E) (3) gel time At 20 C min ISO 2535:2001(E) At 35 C ISO 15040:1999(E) % 20

31 minimum application temperature C exothermic peak Time min temperature C At 5 C ull cure time At 20 C min At 35 C ISO 12114:1997(E) ISO 12114:1997(E) (2) Pot lie (working lie) = maximum working time ater mixing o all components. (3) Gel time = time needed rom luid to gel appearance at predeined temperature conditions. Characteristics o cured resin property Measurement tempera- Cured 5 days Cured 1 hour Reerence standard Test Value Test method unit ture at 22 C at 70 C volume shrinkage --- ISO 12114:1997(E) coeicient o thermal expansion 10-6 C ISO :1999(E) ISO :1999(E) (DSC) glass transition C --- ISO :1999(E) (TMA) temperature ASTM E1640 (DMA) Young modulus o elasticity or tensile stress GPa ISO 527:1993(E) tensile strength MPa ISO 527:1993(E) ailure strain % ISO 527:1993(E) Storage conditions Descriptions Saety ad handling Description Adhesives and bonding principles The implementation o FRP-based structural strengthening (e.g., pultruded laminate) requires the use o adhesives. The choice o the most suitable adhesive as well as the type o surace treatment to be carried out prior to FRP application shall be made on the basis o available substrate and properties o the selected FRP system. Technical data sheets or FRP materials usually report the indications o the adhesive to be used as a unction o the structure to be strengthened. Even the application o dry abrics impregnated on-site might be considered as an assembling operation using adhesives. The type o surace treatment to be carried out prior to FRP application is important or the correct use o adhesives. For this reason, the rationale or a suitable substrate preparation that describes physical, chemical, and mechanical mechanisms o adhesion is presented. For a more comprehensive study, the reader is reerred to speciic literature on the subject. An adhesive is a material quite oten o a polymeric nature capable o creating a link between at least two suraces and able to share loads. There are many types o natural and synthetic adhesives (elastomers, thermoplastics, and mono- or bi-component thermosetting resins); the most suitable adhesives or composite materials are based on epoxy resins. Epoxy adhesives usually are bicomponent viscous mixture; once hardened, through a cross-linking chemical reaction, they become suitable or structural applications. 21

32 There are several advantages in the use o adhesive bonding compared to mechanical anchorage. They include the possibility o connecting dierent materials, providing greater stiness, uniorm distribution o loads, and avoiding holes dangerous or stress concentrations. On the other hand, adhesives are sensitive to environmental conditions, such as moisture, and are not appropriate when exposed to high temperatures (ire resistance). The ollowing three types o racture can be identiied or adhesive bonding (Figure 2-10). Cohesive racture: it takes place inside one o the materials orming the connection. The same material is thereore on both sides o the racture surace, which may be either smooth or rough. It is the ideal racture or adhesives. Adhesive racture: it takes place at the interace between adhesive and support when the adhesive strength is lower than that o the support. The racture surace is typically smooth. This type o racture highlights inaccurate applications. Mixed racture: it appears as both cohesive and adhesive ailure. The racture suraces are very irregular and characterized by coexistence o both materials. It appears or both weak and non-consolidated support (e.g., deteriorated masonry or concrete) and inaccurate adhesive applications. adhesive racture cohesive racture mixed racture Figure 2-10 Comparison between dierent types o racture. The eiciency o adhesion depends on many actors, such as surace treatment, chemical composition and viscosity o the adhesive, application technique, and hardening or cross-linking process o the adhesive itsel. Adhesion mechanisms primary consist o interlocking o the adhesive with the surace o the support with ormation o chemical bonds between polymer and support. As a result, adhesive strength is enhanced by surace treatments that improve interacial properties o the support by increasing the roughness o the surace to be strengthened. Several types o adhesive mechanisms are described in the literature and briely summarized hereater. Physical bond: it involves secondary bonds, such as Van der Waals orces, ionic bonds, and hydrogen bonds between molecules o the adhesive and those o the support. It is based on electrostatic and absorption theory, or which good adhesion is ensured when the adhesive is capable o wetting the support. To this end, the surace energy o the support Γ SV (energy per unit area) shall be higher than that o the adhesive Γ LV (Figure 2-11): or example, wetting properties o epoxy resins bonded to steel support are excellent; they are poor or other materials such as polyethylene. FLUID θ = contact angle θ = 0 complete wrapping 0 < θ < 180 partial wetting θ = 180 no wetting Figure 2-11 Adsorption theory and contact angle. 22

33 Chemical-covalent bond: it involves primary bonds (covalent bonds) between the molecules o the support and the adhesive (Figure 2-12). The racture implies breaking o such bonds. For this reason, coupling agents are oten used particularly in the case o glass ibers. Coupling agents link with the oxides o the surace support to react with the adhesive during cross-linking or causing diusive phenomena (see the ollowing item). Diusive or inter-diusive phenomena: ater diusion or inter-diusion o atoms or molecules across the interace, the bond between two suraces is generated (Figure 2-12). The described mechanism is typical or polymeric matrix composites, where the mobility o polymeric chains makes linking possible; in such a case, time is important to allow the adhesive reaching the inal strength. Mechanical interlock theory: the bond exploits the mutual creep resistance between locally permeated suraces; thereore, it is important to have irregular suraces to allow spreading o the adhesive, illing o the support pores, and cracks beore solidiication takes place (Figure 2-12). Electrostatic attraction Chemical reaction (covalent bond) Inter-diusion and Mechanical interlocking ormation o connections Figure 2-12 Adhesive mechanisms. The main objective o surace treatment is cleaning o the surace by removal o all possible surace contaminations, such as oxides, oreign particles, oil, laitance, dust, moisture, etc. The adopted treatment usually modiies the chemistry o the surace, enhancing the ormation o stronger bonds with the adhesive such to resist environmentally aggressive agents, which would degrade the adhesion over time. Finally, treatments should ensure adequate surace roughness. Other treatments such as solvents and sandblasting can be eectively employed. In some instances, prior to adhesive application, a layer o primer acting as a coupling agent is applied. The use o FRP pultruded laminate requires an additional cleaning o the laminate ace prior to bonding. In some cases, laminates have a protective ilm that prevents external contamination. Such ilms shall be removed beore the laminate is applied. Any surace treatment shall be carried out immediately beore FRP application takes place to avoid surace recontamination. Presence o moisture in the support shall be avoided during FRP application; the suraces o the support shall be perectly dry prior to application o the adhesive. In the ollowing o this document, recommendations to reduce the risk o ailures associated to bonding are presented. 23

34 Technical data sheet o the adhesive The most suitable adhesives or composite materials are those based on bi-component epoxy resins. Technical data sheets shall thereore include the chemical-physical properties o each single components as well as the adhesive properties. Because the ormer have already been listed in , the data sheet here reported only reers to the adhesive properties. TECHNICAL DATA SHEET: adhesive THE MANUFACTURER SHALL REPORT THE STATISTICAL VALUES NEEDED FOR THE EVALUATION OF CHARACTERISTIC PROPERTIES (E.G. SAMPLE MEAN, STANDARD DEVIATION, POPULATION, PERCENTILE, CONFIDENCE INTERVAL) Adhesive description Commercial name, mono- or bi-component, pasty or luid consistency, use, and any other inormation deemed useul. Bonding properties o the resin property shear strength (average and characteristic value) peeling strength (average and characteristic value) Measurement unit MPa kn/m Test temperature Cured 5 days at 22 C Value Cured 1 hours at 70 C Test method Reerence standard single lap shear ISO 4587:2003(E) loating-roller method ISO 4578:1997(E) Note: or external strengthening with FRP laminate an ISO standard (TC71/SC6N) Non-conventional strengthening o concrete - Test methods-part 2: Fiber strengthened polymer (FRP) sheets is under preparation, where two new tests are proposed to evaluate the bond on concrete: Test Method or direct pull-o strength o FRP sheets with concrete and Test Method or bond properties o FRP sheets to concrete. A similar pull-o test, Test method or direct tension pull-o test, is also proposed in the document ACI 440.3R-04 Guide Test Methods or Fiberreinorced Polymers or Reinorcing or Strengthening Concrete Structures by the American Concrete Institute. Such standards do not propose speciic tests or bond on steel. There is however a similar Japanese standard (JSCE- E Test methods or continuous iber sheets ), proposing also a lap shear strength test or FRP and steel The cited documents include also a shear strength test o the adhesive based on shear lap test. Storage conditions Descriptions Saety and handling Description 2.3 FRP STRENGTHENING SYSTEMS FRP systems suitable or external strengthening o structures may be classiied as ollows: Pre-cured systems (2.3.2): Manuactured in various shapes by pultrusion or lamination, pre-cured systems are directly bonded to the structural member to be strengthened. Wet lay-up systems (2.3.3): Manuactured with ibers lying in one or more directions as FRP sheets or abrics and im- 24

35 pregnated with resin at the job site to the support. Prepreg systems (2.3.4): Manuactured with unidirectional or multidirectional iber sheets or abrics pre-impregnated at the manuacturing plant with partially polymerized resin. They may be bonded to the member to be strengthened with (or without) the use o additional resins Mechanical properties o FRP strengthening systems In FRP materials, ibers provide both loading carrying capacity and stiness to the composite while the matrix is necessary to ensure sharing o the load among ibers and to protect the ibers themselves rom the environment. Most FRP materials are made o ibers with high strength and stiness, while their strain at ailure is lower than that o the matrix. Figure 2-13 shows the stress-strain relationship or iber, matrix, and the resulting FRP material. The resulting FRP material has lower stiness than ibers and ails at the same strain, ε, o the, max ibers themselves. In act, beyond such ultimate strain, load sharing rom ibers to the matrix is prevented. Figure 2-13 Stress-strain relationship o ibers, matrix and FRP. Table 2-6 summarizes mechanical properties o a pre-cured laminate compared to the average values o the corresponding ibers. The values o Young modulus o elasticity, E, and ultimate strength at ailure,, o the laminate are lower than those o the iber itsel, while the ultimate tensile strain is o the same order o magnitude or both materials. Table 2-6 Comparison between mechanical properties o a pre-cured laminate and ibers Pre-cured systems Modulus o elasticity [GPa] Ultimate strength [MPa] Ultimate strain [%] FRP E Fiber E ib FRP Fiber ib FRP ε u Fiber ε ib,u CFRP (low modulus) CFRP (high modulus) For FRP material made o unidirectional ibers, the mechanical behavior o the composite can be estimated using micro-mechanical models; or example, by using the rule o mixtures [eq. (6.5) in Appendix A]: E =V ib E ib + (1-V ib ) E m (2.4) V ib ib + (1-V ib ) m (2.5) where V ib is the volumetric raction o ibers (ratio between the volume o ibers and the overall volume o the composite), and E ib and E m are the Young modules o elasticity o ibers and ma- 25

36 trix, respectively. The rule o mixtures is based on the hypothesis o a perect bond between ibers and matrix; or unidirectional composites it provides accurate assessment o the modulus o elasticity. The same accuracy can not be obtained or ultimate strength. For design purposes, it is always preerable to rely upon experimental determination o the above mentioned values ( E and ), as discussed in the ollowing. For proper deinition o stiness and strength properties o FRP composites impregnated in-situ, geometrical (volumetric ratio or weight ratio between ibers and matrix) and mechanical characteristics o each components shall be available. For example, a unidirectional 100 mm wide abric (ibers area A ib = 70 mm ) impregnated with variable quantities o resin is considered. By dividing 2 the overall area o the impregnated abric, A (obtained as the sum o resin and ibers area), by the abric width, the thickness o the composite is obtained. The properties o each components are reported in Table 2-7. The importance o resin content on the mechanical properties in the iber direction, calculated using Equations (2.4) and (2.5), is summarized in Table 2-8. Table 2-7 Properties o components. Fibers Matrix E ib = 220 GPa E m = 3 GPa ib = 4000 MPa m = 80 MPa Table 2-8 Importance o iber volumetric raction on the FRP mechanical properties A ib A m A V ib E ε u F u E A [mm 2 ] [mm 2 ] [mm 2 ] [%] [GPa] [MPa] [%] [kn] [kn] Table 2-8 and Figure 2-14 reer to volumetric ractions o ibers ranging between 30 and 100 %.. Values o iber stiness and strength are remarkably larger than those o the matrix (Table 2-7). As a result, mechanical properties o FRP composite materials ( E and ) are mainly controlled by ibers, and the matrix contribution can be neglected. [MPa] (MPa) 4000 Fiber Fibre VV ib 100% FRP 70% 50% 30% ε ε Figure 2-14 Stress-strain relationship as a unction o the volumetric raction. When the above mentioned properties are reerred to the overall section o the composite, both Young modulus o elasticity and strength at ailure decrease as the resin content increases. The 26

37 same does not apply i one were to look at both ultimate orce, F u, and axial stiness ( E A ) whose variations (3-4 %) are negligible. In act, the reduction o E and are compensated by the increase o the overall cross-sectional area with respect to that o ibers only. The example shows that when evaluating FRP mechanical properties to be used or design, the resin volumetric raction needs to be available when reerring to stiness and ultimate strength o the composite. Alternatively, FRP axial stiness and ultimate orce at ailure, F u, calculated neglecting the matrix, shall be available. Such values do not take into account other relevant parameters associated to the composite manuacturing process that signiicantly aect the mechanism o collapse Pre-cured systems Mechanical characteristics Pre-cured composites are characterized by a unidirectional disposition o ibers that allows the use o the rule o mixtures to determine stiness and strength o the composite, since the volumetric ractions usually vary between 50 and 70 %. However, such values only represent an estimate (typically an overestimation) because other relevant parameters, such as adhesion properties between ibers and matrix, presence o manuacturing deects, voids, or ibers misalignment, are not taken into account. Reliable values o FRP mechanical properties shall be obtained with experimental testing to ensure determination o appropriate statistical parameters accounting or the adopted manuacturing process as well. The values provided by FRP manuacturers shall be based on criteria similar to those discussed in 2.4. In case o pre-cured systems, manuacturers typically provide mechanical characteristics reerred to the laminate cross-section having a well speciied size Technical data sheets or pre-cured systems Hereater, the structure o a typical data sheet or pre-cured composites (laminates, bars, grids, etc.) is proposed. As previously seen, technical data sheets available on the market can also include other inormation or report only a portion o those here indicated. The proposed structure is exhaustive regarding the type and amount o inormation given. TECHNICAL DATA SHEET: pre-cured composites (laminates, bars, grids) THE MANUFACTURER SHALL REPORT THE STATISTICAL VALUES NEEDED FOR THE EVALUATION OF THE CHARACTERISTIC STRENGTHS (E.G. SAMPLE MEAN, STANDARD DEVIATION, POPULATION, PERCENTILE, CONFIDENCE INTERVAL) Description Commercial name, type o iber, type o resin, manuacturing technology (pultrusion, lamination, etc.), and any other inormation deemed useul. Geometrical and physical properties property Measurement Test method Notes unit Reerence standard thickness (laminate) mm width mm length mm section geometry (bars, grids) % 27

38 nominal area (bars, grids) mm 2 nominal perimeter (bars, grids) mm (1) color density iber g/cm 3 matrix g/cm 3 ISO :2004(E) (2) iber content weight % volume % glass transition temperature o resin ( T g ) C maximum operating temperature C electrical conductivity S/m ISO 11667:1997(E) ISO :1999(E) (DSC) ISO :1999(E) (TMA) ASTM E1640 (DMA) (1) Value to be used in case o bars and grids o non circular cross section to compute bond length. (2) Value to be used to compute the weight raction o iber when the volume raction is known and vice versa. Properties property Measurement Test method Notes unit Reerence standard tensile Young modulus o elasticity GPa ISO 527-4,5:1997(E) tensile strength (average and characteristic value) MPa ISO 527-4,5:1997(E) strain at ailure % ISO 527-4,5:1997(E) compression Young modulus o elasticity (bars) GPa ISO 14126:1999(E) compressive strength (bars) (average and characteristic value) MPa ISO 14126:1999(E) compressive strain at ailure (bars) % ISO 14126:1999(E) creep ISO 899-1:2003(E) (3) relaxation (bars, grids) (4) bond: shear stress (bars, grids) Pull-out test (4) (3) The ISO 899-1:2003(E) standard is the general reerence standard or creep behavior o FRP materials, while the ISO standard (TC71/SC6N) Non-conventional strengthening o concrete - Test methods-part 1: Fiber strengthened polymer (FRP) bars and grids is under way or reinorcing FRP bars and prestressed grids, where a speciic test is proposed or FRP bars ( Test Method or creep ailure ). As an alternative, there is a test proposed in the document ACI 440.3R-04 Guide Test Methods or Fiber-reinorced Polymers or Reinorcing or Strengthening Concrete Structures named Test Method or creep rupture o FRP bars. (4) In the ISO standard (TC71/SC6N) concerning FRP bars and grids the ollowing two tests are proposed: Test method or bond strength by pull-out testing or bond, and Test Method or long-term relaxation or relaxation. Similar tests are included in the ACI 440.3R-04 document. Storage conditions Description Saety and handling Description Indications or use as strengthening system The manuacturer may indicate other products to couple with the pre-cured composite or the realization o the strengthening system, such as adhesives, possible protective coatings, primer, putty, etc. Such inormation shall be accompanied by compatibility test results perormed on the as-proposed system. 28

39 2.3.3 Wet lay-up systems In case o wet lay-up systems, inal thickness o the FRP laminate can not be estimated in a deterministic ashion. Thereore, it is recommended to reer to both mechanical and geometrical properties o dry abric according to the technical data sheets provided by FRP manuacturer Determination o laminate cross sectional area For the laminate cross sectional area, A rt, reerence shall be made to the technical data sheet provided by FRP manuacturer. Laminate cross sectional area per unit width can be expressed as ollows: A rt Tx N = 10 ρ ib (2.6) 2 where A rt is expressed in mm m, T x is the yarn count reerring to the principal direction expressed in TEX [g/km], N is the number o yarns per unit width reerring to the principal direction 3 expressed in [yarns/cm], and ρ is the iber density [ g cm ]. ib In case o abrics with the same number o ibers in two orthogonal directions (balanced abrics), laminate cross sectional area, A, may also be calculated as ollows: rt A rt t = (2.7) 2 p ρ ib where p t is the abric mass per unit area, expressed in 2 g m. In case o a unidirectional abric, A rt, may be evaluated as ollows: A rt p ρ t =. (2.8) ib Sometimes it is common to reer A rt to the thickness o an equivalent plate made o iber only. The equivalent thickness, t eq, expressed in mm, can be obtained as ollows: A 1000 rt t eq = (2.9) A disadvantage o this method is that dierent thickness values o the equivalent plate would be associated to the same unbalanced abric (e.g., a abric having dierent number o ibers in two orthogonal directions). Table 2-9 summarizes the parameters deemed necessary or the determination o the laminate cross sectional area or three dierent abrics as ollows: 1) unbalanced plain weave abric (abric A), 2) balanced plain weave abric (abric B), and 3) unidirectional abric (abric C). 29

40 Table 2-9 Property Measurement unit Fabric A Fabric B Fabric C Fabric mass g 2 m Fiber density g 3 cm no. o yarns/cm wet No/cm warp No/cm Count wet Tex warp Tex In case o unbalanced abric (abric A), Equation (2.6) yields: [ Tex] 4[ yarns cm] wet 67 mm A rt = = (area in wet direction) g [ cm ] m [ ] 8[ yarns cm] warp 200 Tex mm A rt = = (area in warp direction) g [ cm ] m For case B abric, cross sectional area can be written as ollows (both directions): 2 2 A 200 [Tex] 6 [ili/cm] mm = = [g/cm ] m rt 3 2 Alternatively, the same result can be obtained rom Equation (2.7) as ollows: A p t g/m 240 mm mm = = = m m rt 3 2 ρ ib g/cm Finally, or case C abric, Equation (2.8) provides: A p t g/m 304 mm mm = = = m m rt 3 ρ ib g/cm Mechanical characteristics Mechanical properties o wet lay-up systems cannot be determined by multiplying the cross sectional area, A rt, computed according to Equation (2.6), by both Young modulus o elasticity and ultimate iber or abric strength. In act, values reerring to ibers do not take into account the real geometry o the abric (weaving, wet-warp) that considerably aect the abric mechanical properties. Similarly, values o stiness and strength reerred to dry abric, when available, cannot be used directly or the determination o the same properties reerring to the inal composite. As a result, mechanical properties o wet lay-up systems can be determined using two dierent methods; both o them require inormation that shall be provided by FRP manuacturer/supplier. 30

41 Mode 1 Saety actors or both stiness, α E, and strength, α, can be introduced as ollows: where Aib Art A E = α E A ib E ib (2.10) = is calculated according to , and E ib is the Young modulus o elasticity or iber only, while the product A E reers to the axial stiness o the FRP ater impregnation. The saety actor, α E, shall be estimated by the FRP manuacturer/supplier and shall be determined on the basis o experimental tests carried out on composite samples corresponding to well-deined volumetric ractions. Such saety actors may take into account both resin type and strengthening geometry; however, quality o installation and nature o support can not be considered or the calibration o α E. Similarly: A = α A ib ib (2.11) Mode 2 Alternatively, FRP manuacturer/supplier may speciy characteristic values o the mechanical properties o the system considered applied to the structure to be strengthened, based on experimental investigations carried out on the inal system. In this case, it is possible to take into account all the parameters aecting the behavior o the inal system, including nature and geometry o the support Technical data sheets or wet lay-up systems A speciic technical data sheet can not be ormulated or wet lay-up systems; thereore, it is necessary to reer to properties o dry iber. The manuacturers/suppliers shall, however, provide the values o the saety actors, α E and α, with detailed inormation on the perormed experimental testing Pre-impregnated systems Pre-impregnated (prepreg) systems are impregnated directly at the manuacturer plant and delivered in rolls. Resin may receive pre-polymerization treatments. A pre-impregnated system is a thin sheet (0.15 mm typical thickness), lexible and moderately sticky, with detaching ilm (silicon paper or similar) applied on the suraces to preserve the system itsel rom external contamination. Storing shall be perormed under controlled moisture and temperature conditions; system cross linking shall occur at the time o application by means o thermal treatments. Mechanical characteristics and technical data sheets are identical to wet lay-up systems (2.3.3). 2.4 QUALITY CONTROL The qualiication process o FRP systems and the necessary experimental tests developed by the manuacturer shall be aimed to complete the ollowing: Ensure quality o products and compliance with published speciied values. Provide a statistically signiicant number o experimental results or physical and mechanical characteristics to be used or design. Provide, when possible, data on experimental tests related to long-term behavior o the FRP system. Qualiication tests regard physical and mechanical properties (stiness and strength) o composite materials, regardless o their particular application. Quality o installation as well as FRP monitoring over time is reported elsewhere. 31

42 Two qualiication levels or FRP systems can be identiied: Level 1: where physical and mechanical properties o composite are deined using statistical analysis on a large series o tests. Level 2: where long-term physical and mechanical properties o composite are deined. Both mechanical and physical qualiication tests shall be carried out by a certiied laboratory provided with the necessary equipment and experience in the characterization o composite materials. Each manuacturer shall provide the mechanical characteristics obtained with statistical analysis, including the characteristic values, percentile, sample mean, sample standard deviations, conidence intervals, and number o samples tested. Suitable saety actors should be employed on the basis o the adopted manuacturing technique Level 1: Physical-mechanical properties Table 2-10 summarizes the most common tests perormed on composite materials and the corresponding technical standards (ISO and ASTM). Property Table 2-10 Mechanical and physical characteristics o composites. Reerence standard ISO ASTM Mechanical properties Tensile Young modulus o elasticity 527-4, 5:1993(E) D , D , D Tensile strength 527-1, 4, 5:1993(E) D , D , D Tensile strain at ailure 527-1, 4, 5:1993(E) D , D , D Compression Young modulus o elasticity 14126:1999(E) D3410 Compressive strength 14126:1999(E) D3410 Compressive strain at ailure 14126:1999(E) D3410 Creep 899-1:2003(E) D Physical properties Density :2004(E) D Coeicient o thermal expansion :1999(E) E831, D696 Glass transition temperature (matrix) :1999(E) (DSC) :1999(E) E1356, E1640 (TMA) Fiber content 11667:1997(E) D3171, D2584 Samples shall be obtained either rom the manuacturing plant or realized in the laboratory using the same technique that will be used in the ield. The minimum number o samples shall be at least ive or each test to be carried out. Each FRP component may be qualiied according to Table 2-11 (abrics) and Table 2-12 (resins). 32

43 Table 2-11 Mechanical characteristics o abrics. Property ISO Reerence standard Product type Mechanical properties Tensile Young modulus o elasticity 4606:1995(E), :1999(E) abric Tensile strength 4606:1995(E), :1999(E) abric Tensile strain at ailure 4606:1995(E), :1999(E) abric Table 2-12 Mechanical and physical characteristics o resins (matrix and adhesive). Property Reerence standard Product ISO ASTM type Mechanical properties Tensile Young modulus o elasticity 527-1:1993 (E) D resin Tensile strength 527-1:1993 (E) D resin Tensile strain at ailure 527-1:1993 (E) D resin Compression Young modulus o elasticity 604:2002(E) D695 resin Compressive strength 604:2002(E) D695 resin Compressive strain at ailure 604:2002(E) D695 resin Shear strength 4587:2003(E) D adhesive Peeling strength 4578:1997(E) D adhesive Physical properties Viscosity 2555:1989(E), 3219:1993(E) D resin Thyxotropy index D resin Density 1675:1985(E) D resin Gel time 9396:1997(E), 2535:2001(E) 15040:1999(E) Pot lie 10364:1993(E) D D resin resin, adhesive Exothermic peak 12114:1997(E) D resin Time to ull cross-linking 12114:1997(E) D resin Volumetric shrinkage 12114:1997(E) D resin Coeicient o thermal expansion :1999(E) E831, D696 resin Glass transition temperature :1999(E) (DSC) :1999(E) (TMA) Level 2: Long-term properties Three dierent behaviors can be identiied over time, according to the ollowing: Chemical degradation phenomena. Environmental actors (e.g. reeze-thaw cycles). Load application: constant (creep) or variable (atigue). E1356, E1640 resin Tests shall be perormed on samples o suitable geometry depending upon the particular test to be carried out. For chemical degradation phenomena and environmental actors, tests are carried out on specimens that have been treated with thermal and/or environmental conditioning or a suitable time. Once conditioning is completed, mechanical and/or physical properties can be determined according to the provisions o ISO (or ASTM) standards (Table 2-10, 2-8, 2-9). 33

44 I the variation over time o a particular property is related to the chemical degradation o the material, its value at any given time may be estimated by applying the Arrhenius procedure (e.g., extrapolating the results o short-term high-temperature tests). It shall be noticed that the results obtained in such a way do not take into account the eect o stresses or environmental actors, such as extended exposure to ultraviolet rays, acids, alkali, salts etc. To evaluate the strength o FRP systems or particular environmental conditions, speciic standards must be reerenced. In some instances, a standard developed or the qualiication o other materials can be used (e.g., the eect o reeze-thaw cycles on the properties o the composite material or which the same conditioning procedure used or concrete may be adopted). Ater sample conditioning, the value o the property o interest can be obtained according to the standard reerence (Table 2-10, 2-8, 2-9). It is worth noting that the ISO EN (1 5) are particularly useul or aging cycles as well as or the evaluation o the long-term perormance o adhesive bond. Creep tests are deemed necessary or long-term behavior o FRP material subjected to a constant load according to ISO 899-1:2003(E); alternatively, the ASTM D can be used. Perormance under atigue shall be reerred to ISO (E) or ASSTM D ACCEPTANCE CRITERIA FRP materials to be used or structural strengthening shall undergo a series o controls to ensure appropriateness level o mechanical and physical characteristics. For construction materials, speciic standards are available or the determination o minimum values o physical and mechanical properties, test procedures, as well as acceptance criteria (6.3). Few items concerning the responsibility o manuacturers, designers, contractors, etc., are briely reported in the ollowing Selection and testing o materials: tasks and responsibilities o proessionals Manuacturers/suppliers: Production o FRP materials shall be subjected to a quality control program including ibers, matrices, adhesives, pre-cured composites and other constituents. Manuacturers shall provide test certiicates or each production lot in compliance with their published literature. Whenever possible, each production lot shall be marked to ensure traceability. I this is not the case, each lot shall be accompanied by labels or tags reporting all the inormation needed or their traceability. In addition to mechanical and physical characteristics, manuacturers/suppliers producing complete strengthening systems (ibers, resins, pre-cured or prepreg systems, adhesives and other components) can provide the mechanical properties o the complete system by indicating the type o substrate used. Such values shall be the results o experimental tests carried out either in the laboratory or in-situ. Complete strengthening systems certiied according to the previous item shall be indicated as Type-A applications, as opposed to Type-B applications: Type-A applications Type-B applications Strengthening system with certiication o each component as well as the inal product to be applied to a given support. Strengthening systems certiied or each component only. Designer: Designers shall clearly state the quality and characteristics (geometrical, mechanical, and 34

45 physical) o the each constituent o the selected strengthening system, speciying, i necessary, the minimum acceptance requirements. Designers shall speciy acceptance criteria or both selected strengthening systems and ield application. In the irst case, the designer indicates specimens to be taken rom the job site as well as the tests to be perormed. In the second case, the designer may indicate quality tests or FRP installation as suggested in and or reinorced concrete and masonry structures, respectively. Contractor/subcontractors: Shall obtain the material indicated by the designer through suppliers/manuacturers who guarantee the quality o their products. Shall make sure that the products are accompanied by technical data sheets, reporting both mechanical and physical characteristics, and possibly by laboratory test certiicates. Shall make sure that the products comply with the provisions indicated by the designer; i the material with the indicated requirements is not available, they shall agree with the designer upon viable alternatives. Construction manager: Shall make decisions as to the acceptance o products. Shall check the compliance o the material with the designer s provisions. Shall check the origin o the supplied material. Pultruded materials are typically marked by the manuacturer or their identiication. Other materials shall have labels or tags with the necessary inormation or their traceability. Shall check the mechanical and physical characteristics o products using the test certiicates provided by the manuacturer. Based upon the importance o the application, it may require experimental tests to evaluate both quality o materials and compliance with the values provided by the manuacturer. Such tests shall be carried out in laboratories o proven experience and appropriately equipped to characterize FRP materials. Acceptance criteria may be based on the maximum acceptable deviation o results rom the values obtained during production. In such a case, it is necessary to ensure that the test procedures are the same and that samples are obtained with the same production techniques. In some cases, tests may be required to evaluate both mechanical and physical properties o un-conditioned and conditioned specimens to take into account temperature and moisture variation. For Type-A applications, it is the decision o the construction manager to require acceptance tests or the installed system. For Type-B applications, the construction manager shall require a number o tests to ensure proper quality o both strengthened system and installation procedures as suggested in and or reinorced concrete and masonry structures, respectively. Test laboratories: Shall demonstrate experience in the experimental characterization o FRP materials. Shall be equipped with appropriate measurement devices and tests instrumentation. Shall carry out the experimental tests according to the procedures indicated in the speciic standards or FRP materials. Shall provide detailed test reports on test instrumentation and results. Shall own a quality manual and carry out experimental activities according to EN-ISO17025 General requirements or the competence o testing and calibration laboratories. Inspector: 35

46 I the FRP strengthened structure has to be tested, the inspector shall do the ollowing: Check the quality o the materials to be in compliance with the manuacturer speciications. Veriy that all materials used have been accepted by the construction manager. Check the results o experimental tests required by the construction manager, i available. 2.6 TRANSPORTATION, STORAGE AND HANDLING Transportation, storage, and handling o FRP material is undamental to ensure that properties o each components are not altered and compliance with saety laws and regulations is met. Transportation. Each component o the selected FRP system shall be suitably packaged and transported according to saety laws and regulations. Storage. To preserve properties o FRP material and ensure compliance with saety laws and regulations, FRP material shall be stored according to the recommendations provided by the supplier/manuacturer. To preserve properties o ibers and resins, storage shall be perormed under suitable temperature conditions (suggested range is C), in a dry environment (moisture less than 20 %), unless otherwise suggested by the manuacturer. Laminate and other preormed material may be damaged due to bending or improper stacking. Due to saety reasons, some constituents such as reactive reticulating agents, initiators, catalysts, solvents or surace cleaning, etc., shall be stored according to manuacturer requirements or oicial standards. Catalysts and initiators (typically peroxides) shall be stored separately rom other reagents to avoid any accidental contact leading to premature polymerization. The properties o non-polymerized resins can change over time and are aected by moisture and temperature conditions. The latter can also aect the mixture reactivity and the properties o polymerized resin. Manuacturers shall indicate the storage time (shel lie) that ensures that the properties o thermo-setting resins are maintained. Constituents exceeding their shel time or suering degradation or contamination shall not be used. All the constituents deemed unusable shall be disposed o according to the manuacturer speciications as well as the provisions o saety laws and regulations. Handling. The manuacturer shall provide the technical data sheet reporting all inormation relevant to saety (MSDS Materials Saety Data Sheet) or all the constituents o FRP material. Substances used in combination with thermoset resins are typically hardeners, crosslinkers, initiators (peroxides), and illers. Some potential dangers when using thermoset resins include: - Skin irritation and sensitization. - Inhalation o vapours o solvents, diluents, and monomers. - Fire or blast risk due to large concentrations o lammable substances in the air or contact with lames or sparks (including cigarettes). - Exothermal reactions between reagents that may cause ires or accidents to the personnel involved. - Presence o dusts rom working or handling FRP material. It is thereore necessary to adopt precautions when working with such products or with their constituents. The complexity o thermosetting resins and the associated materials require to all personnel a careul read o labels and MSDS to avoid risks o accidents. For handling o ibers or resins, the use o disposable gloves, work-suits, and protection glasses is suggested. Rubber or plastic gloves shall be solvent-resistant. In the presence o iber ragments, dusts or solvent vapours, or when mixing and applying resins, respiratory protection devices are needed, as speciically required by FRP manuacturers. The working site shall always be properly ventilated. 36

47 3 BASIS OF DESIGN FOR FRP STRENGTHENING (1)P The subject o this chapter regards FRP strengthening o existing reinorced and prestressed structures as well as masonry structures or which building code requirements are not met. The same principles also apply to existing structures made out o steel and timber, not included in this document. (2)P The ollowing is assumed: The choice and the design o the strengthening system are made by an appropriately qualiied and experienced engineer. The installation phase is carried out by personnel having the appropriate skills and experience. Proper supervision and quality control is provided during installation. Construction materials are used as speciied in the ollowing. (3)P The FRP strengthening system shall be designed to have appropriate strength, and meet serviceability and durability requirements. In case o ire, the strength o the selected FRP system shall be adequate to the required period o time. (4)P The FRP strengthening system shall be located in areas where tensile stresses are to be carried out. FRP composites shall not be relied upon to carry compressive stresses. 3.1 BASIC REQUIREMENTS (1)P Design o FRP strengthening system shall be perormed in compliance with the ollowing principles: The risks to which the structure can be subjected shall be accurately identiied, removed or attenuated. The strengthening coniguration shall not be very sensitive to the above risks. Strengthening systems shall survive the occurrence o acceptable localized damages. Strengthening systems collapsing without warning shall be avoided. (2)P The above deined basic requirements can be considered met i the ollowing are satisied: Suitable materials are chosen. Design is properly perormed, with a careul choice o the construction details. Quality control procedures are deined or design and construction relevant to the particular project. (3)P I FRP strengthening concerns structures o historical and monumental interest, a critical evaluation o the strengthening technique is required with respect to the standards or preservation and restoration. The actual eectiveness o the strengthening technique shall be objectively proven, and the adopted solution shall guarantee compatibility, durability, and reversibility. 3.2 DURABILITY REQUIREMENTS (1)P A strengthening application shall be designed such that deterioration over the design service lie o the strengthened structure does not impair its perormance below the intended level. Environmental conditions as well as the expected maintenance program need to be careully addressed. Durability is o undamental relevance and all the operators involved in the FRP-based strengthening processes shall pursue such requirement (2.5.1). 37

48 (2) To ensure durability to FRP strengthened members the ollowing shall be taken into account: Intended use o the strengthened structure. Expected environmental conditions. Composition, properties, and perormance o existing and new materials. Choice o the strengthening system, its coniguration, and construction details. Quality o workmanship and the level o control. Particular protective measures (e.g., ire or impact). Intended maintenance program during the lie o the strengthened structure. (3)P Special design problems (regarding environmental issues, loading, etc.) shall be identiied at the design stage to evaluate their relevance or a durability point o view, assign proper values o the conversion actors (3.5), and take the necessary provisions or protection o the adopted FRP system. (4) When conversion actors or a particular FRP system are not available, any possible reason o degradation o the adopted strengthening coniguration shall be accurately estimated. Such estimation can be accomplished through theoretical models, experimental investigations, experience on previous applications, or any combination o the above. 3.3 GENERAL PRINCIPLES OF THE STRENGTHENING DESIGN General (1)P Design with FRP composites shall be carried out both in terms o serviceability limit state (SLS) and ultimate limit state (ULS), as deined by the current building code. (2) Veriication o one limit state may be omitted provided that suicient inormation is available to prove that it is satisied by another one. (3)P Structures and structural members strengthened with FRP shall be designed to have design strength, R d, at all sections at least equal to the required strength, E d, calculated or the actored load and orces in such combinations as stipulated in the current building code. The ollowing inequation shall be met: E d R (3.1) d (4) The design values are obtained rom the characteristic values through appropriate partial actors dierent or each limit state as indicated in the current building code. Speciic partial actors or FRP materials are indicated in this document. (5) For structural applications using FRP to be carried out on single structural members, when conditions or upgrading are not met, it shall be proven that the adopted strengthening method is such to provide the structure with a signiicant level o saety with respect to the applied loads. Such applications are deined as ameliorations. For ameliorations, the level o saety shall be computed or each limit state both prior to and ater FRP application Partial actors and design loads (1)P When designing FRP strengthened members, the structure s service lie shall be in compliance with the requirements o the current building code. Thereore, the same partial actors or ex- 38

49 isting materials and the same design loads prescribed by the current building code or new constructions shall be adopted Properties o FRP materials (1)P The properties o FRP materials to be used or strengthening existing structures shall be determined through standardized laboratory tests, such as those indicated in the chapter on materials. (2)P Properties o the existing materials in the structure to be strengthened shall be obtained rom both on-site or laboratory tests and, when available, rom any additional source o inormation (original documents o the project, urther documentation obtained subsequently, etc) (3) Strength and strain properties o FRP materials used or strengthening, as well as those o existing materials (unless otherwise indicated in the current building code) are described by the corresponding characteristic values. The derivation o the characteristic value o a mechanical property through on-site tests shall take into account dispersion o test results, statistical uncertainty associated to the number o perormed tests, and previous statistical knowledge. (4) Only the stiness parameters (Young modulus o elasticity) o FRP materials as well as those o the existing materials are evaluated through the corresponding average values. (5) In case o FRP wet lay-up systems, the coeicients α E and α (Section ), or FRP Young modulus o elasticity and FRP tensile strength shall not be larger than (6) For the generic property o a FRP material, the design value, X d, can be expressed as ollows: X d X η γ k = (3.2) m where η is a conversion actor accounting or special design problems (3.5), X k is the characteristic value o the property being considered, and γ m is the partial actor o the material that takes into account the type o application (Table 3-2). (7) For the generic property o the existing material belonging to the structure to be strengthened, the design value X d can be determined through a series o on-site tests, according to the current building code (dividing the average value by a conidence actor); alternatively, the ollowing equation can be used: X η X = η = m (1 k V ) (3.3) γ γ k(n) d X n X m m where X k( n) is the characteristic value o the property X resulting rom the number n o on-site tests, and m X is the average value o the property X resulting rom the number n o tests. The value o k n is provided in Table 3-1 as a unction o the number n, while the coeicient o variation V X shall be assumed equal to 0.10 or steel, 0.20 or concrete, and 0.30 or masonry and timber. The value o the conversion actor η is typically assumed equal to 0.85 or concrete and 1.00 or steel, masonry, and timber. 39

50 Table 3-1 Values o k n or the determination o the characteristic value. n k n Design capacity (1) The design strength, R d, can be expressed as ollows: 1 R = R{ X ; a } (3.4) γ d d,i d,i Rd In Equation (3.4), R {} is a suitable unction or the speciic mechanical model being considered (e.g., lexure, shear, etc), and γ Rd is a partial actor covering uncertainties o the assumed model. The arguments o the unction R {} are typically the design values X d, i o the materials used or strengthening, or the existing materials, and the nominal values a d, i o the geometrical parameters involved in the model. (2)P As a rule, the FRP contribution to the strengthened member can not increase its capacity or more than 60 % o that o the unstrengthened member. Such limitation does not apply to exceptional or seismic loads. 3.4 PARTIAL FACTORS Partial actors γ m or FRP materials (1) For ultimate limit states, values to be assigned to the partial actors, γ m, indicated by γ or FRP materials, are suggested in Table 3-2, as a unction o the FRP ailure mode: Table 3-2 Partial actors, γ m, or materials and products. Failure mode Partial actor Type-A application (1) Type-B application (2) FRP rupture γ FRP debonding γ,d (1) Strengthening systems certiied according to the indications o Chapter 2 o (Section 2.5). (2) Strengthening systems uncertiied according to the indications o Chapter 2 (Section 2.5). (2) For serviceability limit state, a value o γ m = γ = 1.0 is assigned to all partial actors, except where otherwise indicated Partial actors γ Rd or resistance models (1) For ULS, values to be assigned to the partial actors γ Rd are reported in Table 3-3. Table 3-3 Partial actors γ Rd. Resistance model γ Rd Bending/Combined bending and axial load 1.00 Shear/Torsion 1.20 Coninement

51 3.5 SPECIAL DESIGN PROBLEMS AND RELEVANT CONVERSION FACTORS (1) Hereater, some reerence values to be assigned to the conversion actor η, (3.3.3(6)) that aects both durability and behavior o FRP materials are reported Environmental conversion actor η a (1)P Mechanical properties (e.g., tensile strength, ultimate strain, and Young modulus o elasticity) o FRP systems degrade under speciic environmental conditions such as alkaline environment, moisture, extreme temperatures, thermal cycles, reeze and thaw cycles, and ultraviolet radiations (UV). (2) Eects o alkaline environment. The water contained in the pores o concrete may cause degradation o the resin and the interace between FRP and support. The damage o the resin due to alkaline environment is typically more dangerous than that due to moisture. The resin shall complete its curing process prior to being exposed to alkaline environment. (3) Eects o moisture. The main eects o moisture absorption concern the resin; they can be summarized as ollows: plasticization, reduction o glass transition temperature, and strength and stiness (the latter less signiicant). The absorption o moisture depends on the type o resin, the composition and quality o the laminate, the thickness, the curing conditions, the resin-iber interace, and the working conditions. In a marine environment, where osmotic eects may cause the presence o air pockets in the resin, it is suggested to use protective coatings. (4) Eects o extreme temperatures and thermal cycles. The primary eects o temperature concern the viscous response o both resin and composite. As the temperature rises, the Young modulus o elasticity o the resin lowers. I the temperature exceeds the glass transition temperature, the perormance o FRP materials signiicantly decreases. In general, thermal cycles do not have harmul eects on FRP; however, they may cause micro-ractures in systems with high modulus resins. For typical temperature in civil inrastructures, undesired perormance can be avoided by choosing a system where the glass transition temperature is always higher than the maximum operating temperature o the structure or component being strengthened. (5) Eects o reeze and thaw cycles. In general, exposure to reeze and thaw cycles does not have an impact on FRP perormance, whereas it lowers the perormance o the resin as well as the iber-resin interace. For temperatures below 0 C, polymeric-based resin systems may improve their perormance by developing higher strength and stiness. The eects o the degradation induced by reeze and thaw cycles may be magniied by the presence o moisture. (6) Eects o ultraviolet radiations (UV). Ultraviolet radiations rarely degrade the mechanical perormance o FRP-based systems, although this may cause some resins to have a certain degree o brittleness and surace erosion. In general, the most harmul eect linked to UV exposure is the penetration o moisture and other aggressive agents through the damaged surace. FRP-based systems may be protected rom such damages by adding illers to the resin or by providing appropriate coatings. (7) Table 3-4 summarizes the values to be assigned to the environmental conversion actor η a, depending upon iber/resin type and exposure conditions. Such values represent conservative estimates based on the durability o dierent iber types. Values as reported in the table may be increased by 10 % (however, η a 1 shall always be satisied) whenever protective coatings are used. Such coatings need to be maintained on the strengthened structure or its entire lie and need to be 41

52 experimentally tested and proven to be eective in protecting the FRP system rom the environmental exposure. Table 3-4 Environmental conversion actor η a or dierent exposure conditions or FRP systems. Exposure conditions Type o iber/resin η a Glass/Epoxy 0.75 Internal Aramid/Epoxy 0.85 Carbon/Epoxy 0.95 Glass/Epoxy 0.65 External Aramid/Epoxy 0.75 Carbon/Epoxy 0.85 Glass/Epoxy 0.50 Aggressive environment Aramid/Epoxy 0.70 Carbon/Epoxy Conversion actors or long-term eects η l (1)P Mechanical properties (e.g., tensile strength, ultimate strain, and Young modulus o elasticity) o FRP-based systems degrade due to creep, relaxation, and atigue. (2) Eects o creep and relaxation. For FRP-based systems, creep and relaxation depend on both properties o resins and ibers. Typically, thermosetting resins (unsaturated polyesters, vinyl esters, epoxy, and phenolic resins) are less viscous than thermo-plastic resins (polypropylenes, nylon, polycarbonates, etc.). Since the presence o ibers lowers the resin creep, such phenomena are more pronounced when the load is applied transversely to the ibers or when the composite has a low volume ratio o ibers. Creep may be reduced by ensuring low serviceability stresses. CFRP, AFRP, and GFRP systems are the least, moderately, and most prone to creep rupture, respectively. (3) Fatigue eects. The perormance o FRP systems under atigue conditions need to be taken into consideration as well. Such perormance depends on the matrix composition and, moderately, on the type o iber. In unidirectional composites, ibers usually have ew deects; thereore, they can eectively delay the ormation o cracks. The propagation o cracks is also prevented by the action o adjacent ibers. (4) To avoid ailure o FRP strengthened members under continuous stress or cyclic loading, values o the conversion actor or long term eects, η l, are suggested in Table 3-5. In case o combined continuous or cyclic loading, the overall conversion actor may be obtained as the product o the pertaining conversion actors. Table 3-5 Conversion actor or long-term eects η l or several FRP systems at SLS. Loading mode Type o iber/resin η l Glass/Epoxy 0.30 Continuous Aramid/Epoxy 0.50 (creep and relaxation) Carbon/Epoxy 0.80 Cyclic (atigue) All

53 3.5.3 Impact and explosive loading (1) The behavior o FRP systems subjected to impact or explosive loading is not completely understood yet. First indications suggest choosing AFRP (more resistant to impact) and/or GFRP systems rather than CFRP Vandalism (1)P FRP composite materials are particularly sensitive to cuts and incisions produced by cutting tools. (2) Particular protection systems need to be carried out or FRP strengthened members open to the public where vandalism could be an issue. The saety o the structural member shall be checked, assuming that the FRP system is no longer in place. Design shall be veriied using the combination or quasi-permanent loads while the material partial actors at ULS shall be considered or exceptional loading. 3.6 STRENGTHENING LIMITATIONS IN CASE OF FIRE (1)P FRP materials are particularly sensitive to high temperatures that may take place during ire. When the room temperature exceeds the glass transition temperature o the resin (or the melting temperature in the case o semi-crystalline materials), both strength and stiness o the installed FRP system are reduced. In case o FRP applied as external reinorcement to concrete or masonry members, exposure to high temperature produces a ast degradation o the bond between the FRP system and the support. As a result, degradation o the strengthening eectiveness and debonding o FRP composite may take place. (2) With regard to ire exposure, mechanical properties o FRP strengthened members may be improved by increasing the thickness o protective coatings. It is suggested to employ coating capable o reducing the spreading o lames as well as smoke production. It is also recommended to employ protective coating systems provided with oicial certiicates. Further speciications on the application o protective coating systems are reported in sections and (3)P In order to prevent collapse o the FRP strengthened structure, as long as urther inormation on the actual behaviour o coatings and resins under ire exposure is not available, it is recommended to keep low the FRP contribution to the member capacity. (4) It is suggested that the combination or exceptional loading (ire), as deined by the current building code, takes as a reerence the situations hereater listed, where the design value o the eect o indirect thermal loading is indicated by the symbol E d. Exceptional loading with FRP strengthening still in place ( E d 0), when the strengthening system has been designed to withstand ire exposure. Applied loads need to be considered at SLS and load actors in compliance with requent loading conditions. In this case, all loads acting on the structure or the requent combination are to be considered. The member capacity, reduced to take into account the duration o ire exposure, shall be computed with the partial actors pertaining to exceptional situations, according to the current building code (or iber-reinorced composites γ = 1 ). Situation ollowing an exceptional event ( E d = 0), when the strengthening system is no longer in place. Applied loads need to be considered or quasi-permanent loading conditions. The member capacity, reduced to take into account the duration o ire exposure, shall be computed with the partial actors pertaining to exceptional situations. 43

54 4 STRENGTHENING OF REINFORCED AND PRESTRESSED CONCRETE STRUCTURES 4.1 DEBONDING MECHANISMS Failure mechanisms due to debonding (1)P When strengthening reinorced concrete members with FRP composites, the role o bond between concrete and FRP is o great relevance due to the brittleness o the ailure mechanism by debonding (loss o adhesion). According to the capacity design criterion, such a ailure mechanism shall not precede lexural or shear ailure o the strengthened member. (2)P The loss o adhesion between FRP and concrete may concern both laminates or sheets applied to reinorced concrete beams as lexural and/or shear strengthening. As shown in Figure 4-1, debonding may take place within the adhesive, between concrete and adhesive, in the concrete itsel, or within the FRP reinorcement (e.g. at the inteace between two adjacent layers bonded each other) with dierent iber inclination angles. When proper installation is perormed, because the adhesive strength is typically much higher than the concrete tensile strength, debonding always takes place within the concrete itsel with the removal o a layer o material, whose thickness may range rom ew millimeters to the whole concrete cover. Figure 4-1 Debonding between FRP and concrete. (3)P Debonding ailure modes or laminates or sheets used or lexural strengthening may be classiied in the ollowing our categories, schematically represented in Figure 4-2. Mode 1 (Laminate/sheet end debonding) Mode 2 (Intermediate debonding, caused by lexural cracks) Mode 3 (Debonding caused by diagonal shear cracks) Mode 4 (Debonding caused by irregularities and roughness o concrete surace) Figure 4-2 FRP lexural strengthening: debonding ailure modes (4) In the ollowing, reerence is made to Modes 1 and 2 only, since they are the most requent in ordinary situations. To mitigate the risk o occurrence o the remaining ailure modes, recom- 44

55 mendations on both support control and preparation, as reported in this document (Section 4.8), can be ollowed. (5) Further details on ailure modes due to debonding and criteria or design are provided in Appendix B Fracture energy (1)P Beore any lexural and shear design can take place, the evaluation o the maximum orce that may be transerred rom the concrete to the FRP, as well as the evaluation o shear and normal stresses at the concrete-frp interace is required. The ormer is necessary when designing at ULS; the latter when designing at SLS. (2)P With reerence to a typical bond test as represented in Figure 4-3, the ultimate value o the orce transerred to the FRP system prior to debonding depends on the length, l b, o the bonded area. The optimal bonded length, l e, is deined as the length that, i exceeded, there would be no increase in the orce transerred between concrete and FRP. F max l b l e t b Figure 4-3 Maximum orce transerred between FRP and concrete. (3) The optimal bonded length, l e, may be estimated as ollows: b le E t 2 ctm = [length in mm] (4.1) where E and t are Young modulus o elasticity and thickness o FRP, respectively, and ctm is the average tensile strength o the concrete. (4) The speciic racture energy, Γ Fk, o the FRP concrete interace may be expressed as ollows: Γ = 0 k [orces in N, lengths in mm] (4.2) Fk. 03 b ck ctm where ck is the characteristic strength o concrete. The value provided in Equation (4.2) is intended as a characteristic value (5th percentile); k b is a geometric coeicient depending on both width, b, o the strengthened beam and width, b, o the FRP system; and k b can be written as ollows: 45

56 k b b 2 = b b [length in mm] (4.3) where b b (i b b < 0. 33, the value or k b corresponding to b b = is adopted) Ultimate design strength or laminate/sheet end debonding (mode 1) (1) For laminate/sheet end debonding assuming that the provided bond length is equal to or larger than the optimal bonded length, the ultimate design strength, dd, can be calculated as ollows: dd 1 2 E Γ = γ γ t,d c Fk (4.4) where γ, d is the partial actor indicated in Table 3-2 (Section 3.4.1) and γ c is the partial actor or concrete. Equation (4.4) may be used or: Flexural strengthening ( ) Shear strengthening ( ) (2) For bond lengths, l b, shorter than the optimal bonded length, l e, the ultimate design strength shall be reduced according to the ollowing equation: dd,rid l l b b = dd e 2 l le (4.5) (3) When special anchoring devices are used (FRP transverse bars, U-wrap with FRP sheets, etc.), the maximum design strength must be evaluated directly with ad-hoc experimental tests Ultimate design strength or intermediate debonding (mode 2) (1)P To prevent ailure rom intermediate debonding mechanism, the stress variation Δ σ in the FRP system between two subsequent cracks should not exceed the limit Δ σ R. The latter value typically depends on the characteristics o bond between concrete and FRP (as deined in Appendix B), the distance between transverse cracks in the concrete, and the level o stress, σ, in the FRP reinorcement. (2) Alternatively, a simpliied procedure may be used. The maximum strength calculated in the FRP system at ULS shall be less than dd,2 : k dd,2 = kcr dd = γ γ,d cr Fk c 2 E Γ t (4.6) where k cr can be taken equal to 3.0 i speciic data are not available. 46

57 The corresponding value o the design strain, ε dd, in the FRP system can be calculated as ollows: dd,2 ε dd = (4.7) E Interacial stress or serviceability limit state (1)P For FRP-strengthened beams, stress concentrations (shear and normal stresses) take place at the interace between concrete and FRP close to transverse cracks in the concrete or to the ends o FRP reinorcement. Stress concentrations may cause cracks at the interace. (2)P Under service conditions, interacial cracks need to be avoided, especially when the strengthened member can be subjected to atigue and reeze/thaw cycles. For the analysis, a linear elastic behavior or both concrete and steel can be considered. (3) For rare or requent loading conditions, the equivalent shear stress, τ b, e, at the adhesiveconcrete interace, shall be smaller than the design bond strength, bd, between FRP reinorcement and concrete according to the ollowing equation: b,e bd τ (4.8) (4) The equivalent shear stress, τ b, e, may be deined as ollows: τ = k τ (4.9) b,e id m where: - k id represents a coeicient ( 1) accounting or shear and normal stresses close to the anchorage ends (Appendix B): ( ) 2/3 k = k + k (4.10) id σ τ - and the coeicients k σ and k τ can be calculated as ollows: k = k β t (4.11) σ τ M ( z=a) k = 1+ α a τ V ( z=a) a (4.12) - M ( z=a) is the moment acting on the section where FRP strengthening ends (Figure 4-4). - V ( z=a) is the shear orce acting on the section where FRP strengthening ends. 47

58 q z FRP a L Figure 4-4 Deinition o beam geometrical parameters. - α and β are two elastic parameters depending on the characteristics o the interace and the FRP: α = K1 E t (4.13) β b 2.30 K 4 E I 1 = 14 (4.14) where E, t, b, and I, represent Young modulus o elasticity, thickness, width, and moment o inertia (with respect to its centroidal axis parallel to b ) o the FRP reinorcement, respectively, and K 1 is the slope o the initial linear branch o τ-s diagram (Appendix B). K 1 is assumed to be equal to: K 1 1 = t G + t G a a c c (4.15) where G a and G c are the adhesive and concrete shear modulus, respectively, t a is the nominal thickness o the adhesive, and t c is the eective thickness o the concrete (typical values or t c are mm). - τ m is the average shear stress according to the Jourawski theory: τ m V t h x = (4.16) I n ( z=a) ( e) c - x e and I c are the distances rom the extreme compression iber to the neutral axis and the moment o inertia o the transormed section, respectively. n = E E is the modular ratio ( E c is the Young modulus o elasticity or the concrete corresponding to the considered load combination). - c (5) I end anchorage is provided using U-wrap, the eect o normal stresses can be neglected and the coeicient k σ in Equation (4.11) can be assumed equal to zero., is a unction o the characteristic tensile strength o the con- (6) The design bond strength, bd crete, ctk, as ollows: 48

59 bd γ ctk = k (4.17) b b where the partial actor γ b is taken equal to 1.0 or rare loading combinations, 1.2 or requent loading combinations, and the geometric coeicient k b 1 can be obtained rom Equation (4.3). (7) When computing anchorage stresses at SLS, reerence can be made to the stress corresponding to the increased load ollowing the application o FRP reinorcement. 4.2 FLEXURAL STRENGTHENING Introduction (1)P Flexural strengthening is necessary or structural members subjected to a bending moment larger than the corresponding lexural capacity. Only the case o uniaxial bending (e.g., when the moment axis coincides with a principal axis o inertia o the cross-section, in particular a symmetry axis) is addressed here. (2)P Flexural strengthening with FRP materials may be carried out by applying one or more laminates or one or more sheets to the tension side o the member to be strengthened Analysis at ultimate limit state Introduction (1)P Flexural design at ULS o FRP strengthened members requires that both lexural capacity, M Rd, and actored ultimate moment, M Sd, satisy the ollowing inequation: M Sd M (4.18) Rd (2)P ULS analysis o RC members strengthened with FRP relies on the ollowing undamental hypotheses: Cross-beam sections, perpendicular to the beam axis prior to delection, remain still plane and perpendicular to the beam axis ater delection. Perect bond exists between FRP and concrete, and steel and concrete. Concrete does not react in tension. Constitutive laws or concrete and steel are accounted or according to the current building code. FRP is considered a linear-elastic material up to ailure. (3) FRP strengthening is eective or low steel reinorcement ratios (e.g., steel yielded at ultimate); the rules hereater reported reer exclusively to this situation. (4)P It is assumed that lexural ailure takes place when one o the ollowing conditions is met: The maximum concrete compressive strain, ε cu, as deined by the current building code is reached. The maximum FRP tensile strain, ε d, is reached; ε d can be calculated as ollows: 49

60 ε ε = min η, ε k d a dd γ (4.19) where ε k is the characteristic strain at ailure o the adopted strengthening system; γ and η a are the coeicients deined in Table 3-2 and in Table 3-4, respectively; ε dd is the maximum strain due to intermediate debonding as deined in Section 4.1.4; and E is the FRP Young modulus o elasticity (generally the minimum value in Equation (4.19) corresponds to ε dd ). (5)P The shear capacity o the strengthened member shall be larger than the shear demand corresponding to the examined case. I deemed necessary, shear capacity shall be increased according to the provisions o Section 4.3. (6)P Because a member strengthened with FRP is generally loaded at the time o FRP application, the existing strain in the structure beore FRP strengthening takes place shall be taken into account Strain in the structure prior to FRP strengthening (1)P When FRP strengthening is applied to a member subjected to existing loads, the initial strain shall be evaluated when the applied moment due to the existing loads, M 0, is larger than the member cracking moment. I this is not the case, initial strain can usually be neglected. (2)P Design is carried out assuming a linear elastic behavior or all materials o the member being analyzed. (3)P Strains to be taken into account are those on compression, ε co, and tension side, ε o, where the FRP strengthening system is applied. They can be obtained on the basis o the linearity o the strain diagram as a unction o the mechanical and geometrical properties o the cross section Flexural capacity o FRP-strengthened members (1)P Member lexural capacity is carried out according to Section (2) The lexural analysis o FRP strengthened members can be carried out by using strain compatibility and orce equilibrium. The stress at any point in a member must correspond to the strain at that point; the internal orces must balance the external load eects. (3) With reerence to the simple situation shown in Figure 4-5, two types o ailure can be observed, depending on whether the ultimate FRP strain (region 1) or the ultimate concrete compressive strain (region 2) is reached. (4) When design alls in region 1, ailure is due to the rupture o the FRP system. Any strain diagram corresponding to such a ailure mode has its ixed point at the value o the FRP strain, ε d, as deined in Equation (4.19). The distribution o strains over the depth o the member must be linear to satisy the undamental hypotheses presented earlier in this chapter. They shall be calculated as ollows: - (FRP) ε = ε d 50

61 - (concrete in compression) ε x c = ( d + ε o) cu ( h x ) - (steel in compression) x d2 εs2 = ( εd + εo) ( h x ) - (steel in tension) d x εs1 = ( εd + εo) ( h x ) where all the symbols are shown in Figure 4-5, and ε cu represents the ultimate concrete compressive strain. In particular, the position x o the neutral axis is identiied by its distance rom the extreme compression iber o the member cross-section. As2 Α εc0 ε co d 2 x = =ξ ξ d 1 εcu ε εs2 ε σs2 σ s2 σc σ c h d As1 Α 2 M d 1 b b A A t εd ε s εy,d >ε yd ε d ε0ε o σs1 yd σ σ Figure 4-5 Failure mode o a RC member Strengthened with FRP Checking the value o the steel strain at ultimate is usually unnecessary because typical FRP systems present values o ultimate strain signiicantly smaller compared to that o steel. I the ultimate strain or steel according to the current building code is exceeded, this shall be taken into account when computing the position o the neutral axis and thereore the member lexural capacity. (5) When design alls in region 2, ailure is due to concrete crushing (strain equal to ε cu ) with yielding o steel in traction, while FRP strain has not reached its ultimate value. The distribution o strains over the depth o the member must be linear to satisy the undamental hypotheses presented earlier in this chapter. They shall be calculated as ollows: ε ε = ε0 εd x - (concrete in compression) εc = εcu x d2 - (steel in compression) εs2 = εcu x d x - (steel in tension) εs1 = εcu x All symbols used have been previously shown in Figure 4-5. cu - (FRP) ( h x) (6) For both ailure modes, the position x o the neutral axis is computed by means o the translational equilibrium equation along the beam axis as ollows: 51

62 0 = ψ b x + A σ A A σ (4.20) cd s2 s2 s1 yd where is equal to the design concrete compressive strength,, suitably reduced i it is neces- cd cd sary. The lexural capacity, M Rd, o the strengthened member can be calculated using the rotational equilibrium equation as ollows: 1 M = ψ b x ( d λ x) + A σ ( d d ) + A σ d Rd cd s2 s2 2 1 γ Rd (4.21) where the partial actor, γ Rd, should be assumed equal to 1.00 (Table 3-3, Section 3.4.2). In Equations (4.20) and (4.21), the non-dimensional coeicients ψ and λ represent the resultant o the compression stresses and its distance rom the extreme compression iber, respectively, divided by b x and by x, respectively. cd (7) I the steel is in its elastic phase, stresses may be obtained by multiplying the corresponding strain by the Young modulus o elasticity; otherwise they can be assumed equal to the yielding stress,. In both regions 1 and 2, the strain exhibited by tension steel bars is always larger than ε yd. yd (8) Because FRP materials have a linear elastic behavior up to ailure, their stress shall be taken as the product o the Young modulus o elasticity times the calculated strain. (9) To avoid the occurrence that existing steel reinorcing bars remain elastic at ultimate, the non-dimensional coeicient ξ = x d shall not exceed the limit value, ξ lim, provided as ollows: ξ lim ε cu = ε + ε cu yd (4.22) Flexural capacity o FRP-strengthened members subjected to bending moment and axial orce (1)P The principles introduced in Section , rom (1)P through (5)P, still apply. However, the presence o the axial orce, N Sd, needs to be taken into account when determining the member lexural capacity, M Rd. (2)P Strengthening eectiveness close to the beam-column intersections shall be ensured with suitable construction details. In addition, longitudinal ibers subjected to combined axial load and bending shall be properly anchored to avoid iber delamination and spalling o concrete. When evaluating the maximum strain using Equation (4.19), the value corresponding to the irst term in brackets shall be considered or design. (3) Items (2) to (9) o Section still apply to this case; the let-hand side term o Equation (4.20) is no longer equal to zero and shall be considered equal to the design actored axial load, N. Sd 52

63 (4) Alternatively, it shall be possible to evaluate the member lexural capacity due to combined axial load and bending according to the provisions o Appendix C Failure by laminate/sheet end debonding (1)P Laminate/sheet end debonding depends on a number o parameters such as location and type o cracks (shear or lexural cracks), uneven concrete surace, as well as stress concentration close to the anchorage zone. (2) The maximum distance a (Figure 4-6) to avoid debonding shall be computed by equating the ultimate design strength rom Equation (4.4), or lb le, to the stress calculated at ULS in the FRP system, at a distance a + lb rom the support. I the available bond length is l b < le, Equation (4.4) shall be replaced with Equation (4.5). (3) When the end o the FRP system is close to the member supports, where shear orces may induce inclined cracking, the moment to be taken into account in item (2) shall be evaluated by increasing the design moment as ollows: M = V a (4.23) where Sd a 1 = 0.9 d 1 cotα, α is the angle o existing transverse steel reinorcement, and d is the member eective depth (Figure 4-6). Sd 1 V is the actored shear orce, ( ) a l b a 1 Figure 4-6 Shiting o bending moment diagram. (4) When special anchoring devices used to avoid FRP debonding at the termination points are employed, it shall be permitted to neglect provisions o Such anchoring devices need to be guaranteed based on proper experimental tests. Experimental tests need to be conducted or the material intended or such application (adhesives and reinorcing ibers), or the speciic system used (transverse bars embedded in concrete, U-wrap with FRP sheets, etc.), or construction procedures as recommended by the manuacturer, or surace preparation, and or the expected environmental conditions Analysis at serviceability limit state Design assumptions (1)P This section deals with the ollowing serviceability limit states: Stress limitation (Section ) Delection control (Section ) 53

64 Crack control (Section ) Other serviceability limit states may be relevant in particular situations, even though they are not listed in this document. (2)P At SLS the ollowing items need to be checked: Stresses need to be controlled to avoid yielding o tensile steel and creep phenomena in both concrete and FRP. Delections should not attain excessive values such as to prevent the normal use o the structure, induce damage to non-structural members, and cause psychological disturbance to the users. Excessive cracking could signiicantly reduce the durability o structures, their unctionality, their aspect, and decrease bond perormance o the FRP-concrete interace. (3)P Design at SLS can be carried out considering all materials having a linear-elastic behavior or both uncracked and cracked transormed section conditions. Existing strain at the time o FRP installation shall be accounted or. The principle o superposition can be used or design. Design assumptions are as ollows: Linear-elastic behavior o all materials. Cross-beam sections, perpendicular to the beam axis prior to delection, remain still plane and perpendicular to the beam axis ater delection. Perect bond exists between steel and concrete, and concrete and FRP. (4)P The irst assumption allows one to assume a constant value or the Young modulus o elasticity o each material. The second implies the linearity o the strain diagram. The third, along with the irst, allows the deinition o the modular ratios n s = σ s σ c = E s E c and n = σ σ c = E E c. Such modular ratios are used to transorm the actual beam into an all-concrete beam. The stesses in the concrete can be deduced by the strains multiplying these ones by the Young modulus o elasticity, E c.the actual values o stresses in the steel and in the FRP are n s or n times, respectively, those evaluated in the concrete adjacent ibers. The values o the modular ratios shall be set to account or creep as well as short and long-term conditions. (5)P When designing at SLS it is necessary to evaluate the position o the neutral axis as well as the value o the moment o inertia or both cracked and uncracked conditions prior to and ater the installation o the FRP strengthening system. (6)P I deemed necessary, service stress due to thermal loads, creep, shrinkage, etc., shall be added to the stress given by the applied loads Stress limitation (1)P Stress at service in the FRP system, computed or the quasi-permanent loading condition, shall satisy the limitation σ η k, where k is the FRP characteristic strength at ailure and η is the conversion actor as suggested in Section 3.5. Service stress in concrete and steel shall be limited according to the current building code. (2) Assuming that M 0 is the bending moment acting on the member prior to FRP strengthening, and assuming that M 1 is the bending moment acting ater FRP strengthening, the stress due to the combined moment M = M 0 + M1 can be evaluated as ollows: 54

65 Stress in the concrete σ c = σ c0 + σ c1 s σ c0 = M 0 / W 0,c Stress in the steel: σ s = σ s0 + σ s1 i σ s0 = n s M 0 / W 0,s Stress in the FRP: i σ = n M 1 / W 1, s σ c1 = M 1 / W 1,c i σ s1 = n s M 1 / W 1,s where (see Figure 4-5): s - 0, c I0 x0 W = : modulus o resistance o RC members related to extreme concrete compression iber i 0, s 0 x0 s - 1, c I1 x1 - W I ( d ) = : modulus o resistance o RC members related to tension steel W = : modulus o resistance o RC strengthened members related to extreme concrete compression iber i - W 1, s I1 ( d x1 ) i - W I ( H x ) 1, = : modulus o resistance o RC strengthened members related to tension steel = : modulus o resistance o RC strengthened members related to FRP system 1 1 When the existing applied moment, M 0, is such to produce cracking in the concrete member, neutral axis determination as well as values o the moment o inertia I 0 and I 1 shall be calculated with reerence to cracked transormed section or both unstrengthened and strengthened conditions. Modular ratios used or design shall also take into account shrinkage and creep o concrete depending upon the perormed short or long term analysis Delection control (1)P Delections exhibited by FRP strengthened structures shall comply with current building code requirements. (2)P The adopted delection model shall simulate the real behavior o the structure. I deemed necessary, cracking shall be accounted or. (3)P The adopted delection model should take into account the ollowing: Creep and shrinkage o concrete. Concrete stiening between cracks. Existing cracks prior to FRP strengthening. Thermal loads. Static and/or dynamic loads. Appropriate concrete Young modulus o elasticity depending upon aggregate type and concrete curing at the time o loading. (4)P The superposition principle shall not be applied i delections are computed using non-linear analysis. (5) Delections or FRP strengthened beams can be perormed by integration o the curvature diagrams. Such diagrams can be computed with non-linear analyses by taking into account tension stiening o concrete. Alternatively, simpliied analyses are possible similarly to what used or traditional RC beams, provided that they are supported by suitable experimental basis. (6)P Existing strain prior to FRP strengthening can be accounted or by adding the delections related to dierent phases. 55

66 Crack control (1)P At SLS, crack width shall be checked to guarantee a proper use o the structure and to protect steel internal reinorcement. (2)P Crack width limitations or FRP strengthened structures shall satisy the requirements o the current building code. (3) At present no accurate and completely reliable models are available or crack width computation o FRP strengthened concrete structures. Several experiment-based ormulations are available in the literature. Such ormulations modiy the expressions used or traditional RC sections to take into account the presence o the external strengthening. Experimental evidences show that members strengthened with FRP have smaller but closer cracks. (4)P More reined and accurate models can be adopted when supported by ad-hoc experimental results Ductility (1)P For lexural members, ductility is a measure o the member capability o evolving in the plastic range; it depends on both section behavior and the actual ailure modes o the overall structural member. (2)P For FRP strengthened members, greater ductility is ensured when ailure takes place due to crushing o concrete. Collapse due to FRP rupture leads to brittle ailures. (3)P Regardless o the type o cross section, ductility is mainly controlled by the member ailure mode. It can be considered totally absent i debonding starts prior to any other ailure mechanism. 4.3 SHEAR STRENGTHENING Introduction (1)P Shear strengthening is deemed necessary when the applied actored shear orce is greater than the corresponding member shear capacity. The latter shall be determined considering the contributions o both concrete and steel transverse reinorcing bars when available. (2)P Shear strengthening shall be veriied at ULS only. (3)P In the ollowing o this document some speciic conigurations o FRP shear strengthening are considered. Other solutions are also possible, provided that their eectiveness is proven and their contribution to the shear capacity is quantiied Strengthening conigurations (1) Shear strengthening is realized by applying one or more layers o FRP material externally bonded to the surace o the member to be strengthened (Figure 4-7). External FRP reinorcement can be applied in a discontinuous ashion, with gaps between ollowing strips, or continuously, with strips next to each other. 56

67 β = 90 β 0 < β < 180 β Figure 4-7 Lateral view o FRP shear strengthening. (2) Design o FRP strengthening depends on both geometry (FRP thickness, width, and spacing) and the iber s angle with respect to the longitudinal axis o the member. (3) Figure 4-8 shows three FRP strengthening conigurations: side bonding, U-wrapped, and completely wrapped beams. Side bonding U-wrapped Completely wrapped Figure 4-8 Cross section o FRP strengthened members. (4) For U-wrap strengthening o rectangular or T-section, delamination o the end portions o FRP reinorcement can be avoided by using laminates/sheets and/or bars installed in the direction o the member longitudinal axis. In such a case, the behavior o U-wrap strengthening can be considered equivalent to that o a completely wrapped member, provided that the eectiveness oered by these devices is proven. (5) Shear strengthening may also be realized through the installation o FRP bars in dedicated slots made on the outer surace o the member to be strengthened as near-surace mounted reinorcement. Such type o strengthening is not dealt with in this document. I used, its eectiveness shall be supported by experimental evidence Shear capacity o FRP strengthened members Shear capacity (1) Shear capacity o FRP strengthened members can be evaluated as ollows: { } V = min V + V + V, V (4.24) Rd Rd,ct Rd,s Rd, Rd,max where V Rd, ct and V Rd, s represent concrete and steel contribution to the shear capacity according to the current building code, and V Rd, is the FRP contribution to the shear capacity to be evaluated as 57

68 indicated in the ollowing. Shear strength shall not be taken greater than V Rd, max. This last value denotes the ultimate strength o the concretet strut, to be evaluated according to the current building code. (2) In the case o a RC member with a rectangular cross-section and FRP side bonding coniguration, the FRP contribution to the shear capacity, V Rd,, shall be calculated as ollows: 1 sin w V = β min{ 0.9 d, h } 2 t γ sinθ p (4.25) Rd, w ed Rd where the partial actor γ Rd shall be assumed equal to 1.20 (Table 3-3, Section 3.4.2), d is the member eective depth, h w is the stem depth, ed is the eective FRP design strength to be evaluated as indicated in Section , t is the thickness o the adopted FRP system, β is the ibers angle with respect to the member longitudinal axis, θ represents the angle o shear cracks (to be assumed equal to 45 unless a more detailed calculation is made), and w and p are FRP width and spacing, respectively, measured orthogonally to the iber direction (Figure 4-9). For FRP strips installed one next to each other the ratio w p shall be set equal to 1.0. (3) In the same case o a RC member with a rectangular cross-section and U-wrapped or completely wrapped conigurations, the FRP contribution to the shear capacity shall be calculated according to the Moersch truss mechanism as ollows: 1 w V 0.9 d 2 t (cot θ cot β ) γ p = + (4.26) Rd, ed Rd where all symbols have the meaning highlighted in item (2). h d h w β p' w θ c b w t p p Figure 4-9 Notation or shear strengthening using FRP strips. (4) For completely wrapped members having circular cross-sections o diameter D when ibers are placed orthogonal to the axis o the member ( β = 90 ), the FRP contribution to the shear capacity,, shall be calculated as ollows: V Rd, 1 π V = D t cotθ (4.27) Rd, ed γ 2 Rd 58

69 p meas- (5) In all Equations (4.25) to (4.27), it is allowed to replace the term p with the term ured along the member longitudinal axis, where p = sin β. p Eective FRP design strength (1) Debonding o FRP may be caused by stress concentrations at the concrete-frp interace close to shear cracks. A simpliied procedure to take into account such phenomenon requires the introduction o the eective FRP design strength deined as the FRP tensile strength when debonding starts. (2) For FRP side bonding on a rectangular cross section, the eective FRP design strength can be calculated as ollows: ed z rid,eq = dd { dh} min 0.9, w z l eq rid,eq 2 (4.28) where dd represents the ultimate design strength, to be evaluated according to Equation (4.4) and item (5), d is the eective depth, and h w is the beam stem depth. Moreover: s z = z + l, z = min rid,eq rid eq rid { 0.9 d, hw } l sin β, l = sin β (4.29) e eq / E where l e is the eective bond length according to Equation (4.1), β is the ibers angle with respect to the member longitudinal axis, s is the ultimate debonding slip assumed to be equal to 0.2 mm (see Appendix B), and E is the FRP Young modulus o elasticity. (3) For U-wrap conigurations on a rectangular cross section, the eective FRP design strength can be calculated as ollows: dd ed 1 = dd l sin β e 1 3 min 0.9, { dh} w (4.30) (4) For completely wrapped members having rectangular cross sections, the eective FRP design strength can be calculated as ollows: 1 l sin β 1 l sin β = 1 + ( φ ) 1 e e ed dd R d dd 6 min{ 0.9 dh, w} 2 min{ 0.9 dh, w} (4.31) where d is the FRP design strength to be evaluated as in Section 3. Moreover: φ = c c r r, R b b (4.32) w w where c r is the corner radius o the section to be wrapped, and w b is the width o the member. The second term o Equation (4.31) shall be considered only when it is greater than zero. 59

70 (5) When calculating dd rom Equation (4.4), the k b coeicient according to Equation (4.3) shall be considered as ollows: or discrete FRP strips application, b = w and b = p ; or FRP systems installed continuously along the span length o the member it shall be permitted to consider b = b = min{ 0.9 d, hw } sin( θ + β ) sinθ where h w is the beam stem depth. (6) When special devices used to anchor the end portions o U-wrapped FRP systems are proven to be as eective as the completely wrapped strengthening coniguration, the eective FRP design strength can be computed rom Equation (4.31). I this is not the case, the eective FRP design strength shall be calculated according to Equation (4.30). (7) For completely wrapped members having circular cross-section o diameter D, when ibers are placed orthogonal to the axis o the member ( β = 90 ), the eective FRP design strength shall be calculated as ollows: = E ε (4.33) ed,max where E is the FRP Young modulus o elasticity, and ε, max represents FRP maximum allowable strain to be set equal to 0.005, unless a more detailed calculation is made Limitations and construction details (1) For U-wrapped and completely wrapped conigurations, a minimum 20 mm radius shall be provided when FRP sheets are installed around outside corners. (2) For external FRP reinorcement in the orm o discrete strips, strips width, w (mm), and center-to-center spacing between strips, p (mm), shall not exceed the ollowing limitations, respectively: 50 mm 250 mm w p min 0.5 d,3 w, w 200 mm. w, and { } TORSIONAL STRENGTHENING Introduction (1)P Strengthening or torsion is deemed necessary when the applied actored torsional moment is greater than the corresponding torsional capacity. The latter shall be determined considering the contributions o both concrete and steel transverse reinorcing bars when available. (2)P Torsional strengthening shall be veriied at ULS only. (3)P In the ollowing o this document some speciic conigurations o FRP torsional strengthening are considered. Other solutions are also possible, provided that their eectiveness is proven and their contribution to the shear capacity is quantiied Strengthening conigurations (1) Strengthening or torsion is realized by applying one or more layers o FRP material externally bonded to the surace o the member to be strengthened (Figure 4-7). External FRP reinorcement can be applied in a discontinuous ashion with gaps between ollowing strips, or continuously with strips next to each other. 60

71 (2) Design o FRP reinorcement depends on FRP thickness, width, and spacing. Fibers shall be arranged with an angle β = 90 with respect to the longitudinal axis o the member. (3) FRP shall be placed around the cross section as a completely wrapped system only (Figure 4-8). (4) Strengthening or torsion may also be realized through the installation o FRP bars in dedicated slots made on the outer surace o the member to be strengthened as near-surace mounted reinorcement. Such type o strengthening is not dealt with in this document. I used, its eectiveness shall be supported by experimental evidence Torsional capacity o FRP strengthened members (1)P The ollowing applies to prismatic members where an ideal ring-shaped resisting area can be identiied Torsional capacity (1) Torsional capacity o FRP strengthened members can be evaluated as ollows: { } T = min T + T, T (4.34) Rd Rd,s Rd, Rd,max where T Rd, s is the existing steel contribution to the torsional capacity according to the current building code, and T Rd, is the FRP contribution to the torsional capacity, to be evaluated as indicated in the ollowing. Torsional strength shall not be taken greater than. This last value T Rd, max denotes the ultimate strength o the concretet strut, to be evaluated according to the current building code. (2) The existing steel contribution to the torsional capacity, T Rd, s, can be calculated as ollows: A A sw l T = min 2 cot, 2 tan Rd,s B θ B θ e ywd e yd p ue (4.35) where A sw is a one-leg steel stirrup area, p is the stirrups spacing, B e is the area bounded by the polygon whose edges are the centers o gravity o the longitudinal steel bars, ywd is the design yield strength o transverse steel reinorcement, A 1 is the total area o existing steel longitudinal reinorcement, u e is the perimeter o the above mentioned polygon, yd is the design yield strength o the existing steel longitudinal reinorcement, and θ is the angle o the compressed struts with respect to the member longitudinal axis (the value θ = 45 can be assumed i a more accurate determination is not available). (3) T Rd, max in Equation (4.34) shall be calculated as ollows: T = 0.50 B h (4.36) Rd,max cd e s where cd is the design concrete compressive strength, and s h is set equal to 6 1 o the diameter o the maximum circle enclosed in the polygon whose edges are the centers o gravity o the existing 61

72 steel longitudinal reinorcement. (4) I Equation (4.35) shows that the minimum torsional capacity is due to the existing steel transverse reinorcement, the FRP contribution expressed in Equation (4.34) shall be calculated as ollows: 1 w T = Rd, 2 t b h ed cot θ (4.37) γ p Rd where the partial actor γ Rd shall be set equal to 1.20 (Table 3-3, Section 3.4.2); ed is the FRP design eective strength to be evaluated as in Section ; t is the thickness o the FRP strip or sheet; b and h are section width and depth, respectively; θ is the angle o the compressed struts with respect to the member longitudinal axis (the value θ = 45 can be assumed i a more accurate determination is not available); and w and p are width and center-to-center spacing o FRP strips measured orthogonally to the iber direction, respectively. For FRP strips applied one next to each other the ratio w p shall be set equal to 1.0. (5) I Equation (4.35) shows that the minimum torsional capacity is due to the existing steel longitudinal reinorcement, FRP strengthening shall not be perormed. (6) In case o combined torsion, T sd, and shear, V sd, the ollowing limitation shall be met: T T Sd Rd,max V V Sd + 1 (4.38) Rd,max where T Rd, max and V Rd, max are calculated according to Equations (4.36) and the requirements o the current building code, respectively. Because strengthening or shear and torsion are calculated separately, the overall strengthening area is given by the sum o the area deemed necessary or shear and torsional FRP strengthening Limitations and construction details (1) For U-wrapped and completely wrapped conigurations, a minimum 20 mm radius shall be provided when FRP sheets are installed around outside corners. (2) For external FRP reinorcement in the orm o discrete strips, strips width, w (mm), and center-to-center spacing between strips, p (mm), shall not exceed the ollowing limitations, respectively: 50 mm 250 mm w p min 0.5 d,3 w, w 200 mm. w, and { } CONFINEMENT Introduction (1)P Appropriate coninement o reinorced concrete members may improve their structural perormance. In particular, it allows the increase o the ollowing: Ultimate capacity and strain or members under concentric or slightly eccentric axial loads. Ductility and capacity under combined bending and axial load, when FRP reinorcements are present with ibers lying along the longitudinal axis o the member (Section and 62

73 Appendix C). (2)P Coninement o RC members can be realized with FRP sheets disposed along the member perimeter as both continuous or discontinuous external wrapping. (3)P The increase o axial capacity and ultimate strain o FRP-conined concrete depends on the applied coninement pressure. The latter is a unction o the member cross section and FRP stiness. (4)P The redistribution o vertical loads cannot rely upon the ductility o members under concentric or slightly eccentric axial load. (5)P FRP-conined members (FRP is linear-elastic up to ailure), unlike steel conined members (steel has an elastic-plastic behavior), exert a lateral pressure that increases with the transversal expansion o the conined members. (6)P A typical stress-strain ( σ ε ) diagram or compression tests carried out on FRP-conined specimens is reported in Figure Figure 4-10 Stress-strain relationship or FRP-conined concrete. (7)P For axial strain values, ε c, up to 0.2 %, the stress in the conined concrete is only slightly greater than that exhibited by unconined concrete. (8)P For axial strain values larger than 0.2 %, the stress-strain diagram is non linear and the slope o the corresponding σ ε curve gradually lowers up to a nearly constant value. In the linear branch o the diagram, the conined concrete gradually loses its integrity due to widespread cracks. (9)P Failure o RC conined member is attained by iber rupture. However, beyond a critical value o the axial strain, the FRP-conined member may be linked to a recipient with very lexible walls illed with incoherent material. Beyond that threshold it loses its unctionality since it can only carry small or negligible transverse orces. As a result, ailure o the FRP-conined RC member is said to be reached when FRP strain equal to 0.4 % is attained Axial capacity o FRP-conined members under concentric or slightly eccentric orce (1)P Coninement o RC member with FRP is necessary or structural members subjected to concentric or slightly eccentric axial loads larger than the corresponding axial capacity. 63

74 (2)P Good coninement can only be achieved by installing FRP ibers orthogonally to the member axis. (3)P When FRP reinorcement is spirally arranged around the member perimeter, the coninement eectiveness shall be properly evaluated. (4)P I the adopted FRP system is not initially prestressed, it exerts a passive coninement on the compressed member. The coninement action becomes signiicant only ater cracking o the concrete and yielding o the internal steel reinorcement due to the increased lateral expansion exhibited by the strengthened member. Prior to concrete cracking, FRP is practically unloaded. (5)P Design at ULS o FRP conined members requires that both actored design axial load, N Sd, and actored axial capacity, N Rcc,d, satisy the ollowing inequation: N Sd N (4.39) Rcc, d (6) For non-slender FRP conined members, the actored axial capacity can be calculated as ollows: 1 N = A + A (4.40) Rcc, d c ccd s yd γrd where the partial actor γ Rd shall be taken equal to 1.10 (Table 3-3, Section 3.4.2); A c and ccd represent member cross-sectional area and design strength o conined concrete as indicated in item (7), respectively; and A s and yd represent area and yield design strength o existing steel reinorcement, respectively. (7) The design strength, ccd, o conined concrete shall be evaluated as ollows: ccd cd l,e = + cd 2/ 3 (4.41) where cd is the design strength o unconined concrete as per the current building code, and 1, e is the eective coninement lateral pressure as deined in the ollowing section. The same relationship shall be used also to attain the second objective mentioned in Section (1)P. (8) The coninement is eective i , e cd > Coninement lateral pressure (1)P The eectiveness o FRP-conined members only depends on a raction o the coninement lateral pressure, 1, exerted by the system, namely eective coninement lateral pressure 1, e. (2) The eective coninement lateral pressure, 1, e, is a unction o member cross section and FRP coniguration as indicated in the ollowing equation: 64

75 l, e ke l = (4.42) where k e is a coeicient o eiciency ( 1), deined as the ratio between the volume, V c, e, o the eectively conined concrete and the volume, V c, o the concrete member neglecting the area o existing internal steel reinorcement. (3) The coninement lateral pressure shall be evaluated as ollows: 1 = ρ E ε (4.43) l d,rid 2 where ρ is the geometric strengthening ratio as a unction o section shape (circular or rectangular) and FRP coniguration (continuous or discontinuous wrapping), E is Young modulus o elasticity o the FRP in the direction o ibers, and ε d, rid is a reduced FRP design strain, deined in the ollowing item (9). (4) The coeicient o eiciency, k e, shall be expressed as: k = k k k e H V α (4.44) (5) The coeicient o horizontal eiciency, k H, depends on cross-section shape (see Sections and ). (6) The coeicient o vertical eiciency, k V, depends on FRP conigurations. For RC conined members with continuous FRP wrapping, it is assumed k V = 1. For RC conined members with discontinuous FRP wrapping (Figure 4-11), such as FRP strips installed with a center-to-center spacing o p and clear spacing o p, reduction in the coninement eectiveness due to the diusion o stresses (approximately at 45 ) between two subsequent wrappings shall be considered. unconined concrete Figure 4-11 Elevation view o circular member conined with FRP strips. Regardless o the section shape, the coeicient o vertical eiciency, k V, shall be assumed as ollows: k V p = 1 2 d min 2 (4.45) 65

76 where d min is the minimum cross-section o the member. (7) In case o discontinuous wrapping the net distance between strips shall satisy the limitation ' p d. min 2 (8) Regardless o the section shape, the eiciency coeicient, k α, to be used when ibers are spirally installed with an angle α with respect to the member cross-section, shall be expressed as ollows: k α 1 = (4.46) (tan α ) (9) The reduced FRP design strain, ε d, rid, shall be computed as ollows (see also Section 4.5.1, item (9)P): ε = min{ η ε / γ ; 0.004} (4.47) d,rid a k where η a and γ represent environmental conversion actor and partial actor as suggested in Table 3-4 and Table 3-2, respectively Circular sections (1)P FRP-coninement is particularly eective or a circular cross section subjected to both concentric or slightly eccentric axial loads. (2)P Fibers installed transversely to the longitudinal axis o the strengthened member induce a uniorm pressure that opposes the radial expansion o the loaded member. (3) The geometric strengthening ratio, ρ, to be used or the evaluation o the eective coninement pressure shall be expressed as ollows: 4 t b ρ = D p (4.48) where (Figure 4-11) t, b, and D is the diameter o the circular cross section. In case o continuous wrapping, 4 D. t p represent FRP thickness, width, and spacing, respectively, and ρ becomes (4) For circular cross sections, the coeicient o horizontal eiciency, k H, is equal to 1.0. (5) For circular sections, the dimension d min introduced in Equation (4.45) or the computation o the coeicient o vertical eiciency, is to be intended as the section diameter Square and rectangular sections (1)P FRP-coninement o members with square or rectangular cross sections produce marginal increases o the member compressive strength. Thereore such applications shall be careully vali- 66

77 dated and analyzed. (2)P Prior to FRP application, the cross section edges shall be rounded to avoid stress concentrations that could lead to a premature ailure o the system. (3) The corner radius shall satisy the ollowing limitation: r 20 mm (4.49) c (4) The strengthening geometric ratio, ρ, to be used or the evaluation o the eective coninement pressure shall be expressed as ollows: 2 t ( b+ d) b ρ = bd p (4.50) where t, b, and p represent FRP thickness, width, and spacing, respectively, while b and d are cross section dimensions o the rectangular member. In case o continuous wrapping, ρ becomes 2 t b + d b d. ( ) ( ) (5)P For rectangular cross sections, the eectively conined concrete area may be considered to be only a raction o the overall concrete cross section (Figure 4-12). The reason or such a behavior lies in the arch eect that orms within the concrete cross section. Such an eect depends on the values o the corner radius r c. unconined concrete Figure 4-12 Coninement o rectangular sections. (6) For rectangular cross sections, the coeicient o horizontal eiciency, k H, that takes into account the arch eect shall be expressed as ollows: k H 2 g 2 b' + d' = 1 (4.51) 3 A where b and d are the dimensions indicated in Figure 4-12, and A g is the cross section area. (7) The eect o FRP coninement shall not be considered or rectangular cross sections having b d > 2, or max { b, d} > 900 mm unless otherwise proven by suitable experimental tests. 67

78 4.5.3 Ductility o FRP-conined members under combined bending and axial load (1)P FRP-coninement may also be realized on concrete members under combined bending and axial load; coninement will result in a ductility enhancement while the member axial capacity can only be slightly increased. (2) Unless a more detailed analysis is perormed, the evaluation o the ultimate curvature o a FRP conined concrete member under combined bending and axial load may be accomplished by assuming a parabolic-rectangular approach or the concrete stress-strain relationship, characterized by a maximum strength equal to cd and ultimate strain, ε ccu, computed as ollows: l,e ε = (4.52) ccu cd where 1, e is the eective coninement pressure, and cd is the design strength o unconined concrete. (3) In Equation (4.52), the eective pressure is computed assuming a reduced FRP design strain as ollows: ε k ε = η 0.6 ε (4.53) d,rid a k γ (4) More accurate evaluation o ultimate curvature and lexural capacity o FRP strengthened members may be obtained with suitable concrete-conined models (Appendix D) capable o capturing the behavior described in and Figure FLEXURAL STRENGTHENING OF PRESTRESSED CONCRETE MEMBERS Use o FRP or prestressed concrete members (1) P The methods and criteria hereater apply to non-prestressed FRP systems used or strengthening prestressed concrete (PC) structures Design at ultimate limit state (1)P The evaluation o the lexural capacity o PC members subjected to a bending moment shall be carried out in the ollowing procedures similar to those described in or RC members, with the only changes speciied in the ollowing. The strain o prestressed reinorcement is equal to the algebraic sum o the strain o the concrete surrounding the tendon and the strain at the decompression limit, ε p. The latter represents the strain exhibited by existing tendons or an appropriate combination o internal orces such to produce zero stress in the concrete surrounding the tendons (Figure 4-13). The ultimate strain o prestressing tendons is equal to εp. I the concrete age is such to considered to have exhausted all long-term phenomena, the initial concrete strain, ε 0, is equal to the strain at the time o FRP installation. I long-term phenomena in the concrete can not be considered exhausted, the value o ε 0 is the algebraic sum o the previously computed value and the long-term strain developed in the concrete substrate ater FRP strengthening takes place. In the evaluation o such a long- 68

79 term strain, as well as or any loss o prestress, the presence o the strengthening system can be neglected. Figure 4-13 Failure mode o PC member strengthened with FRP. (2)P The attainment o the ultimate limit state shall be preceded by yielding o existing steel prestressing tendons. (3) For debonding-ailure mechanisms, reer to Sections 4.1 and Design at serviceability limit state (1)P Service stress limitations or concrete and steel shall satisy the requirements o the current building code. Service stress limitations or FRP material shall comply with FRP strengthening shall be neglected i temporarily compressed (e.g., due to creep o con- (2)P crete). 4.7 DESIGN FOR SEISMIC APPLICATIONS Introduction Design objectives (1)P It shall be permitted to strengthen RC and PC members with FRP composites when the structure does not meet the seismic requirements speciied in the current building code. (2)P This part o the document recognizes the provisions o the current building code as well as the indications provided in the most updated literature related to seismic constructions; particular importance is given to the ollowing: Evaluation o seismic saety. Saety requirements (veriication o limit states). Levels o seismic protection (magnitude o the associated seismic action). Methods o analysis. Veriication criteria (distinction between ductile and brittle members). Materials characteristics to be used or design. 69

80 Selection criteria or FRP strengthening (1) Type and size o selected FRP systems as well as the urgency o FRP installation shall take into account the ollowing: Common errors shall be eliminated. Major building irregularities can not be eliminated using FRP as a strengthening technique. A better resistance regularity can be obtained by strengthening a limited number o members. Enhancement o local ductility. Localized strengthening shall not reduce the overall ductility o the structure. (2)P FRP strengthening may be classiied as ollows: Strengthening or total or partial reconstruction o members. (3)P Design o FRP strengthening shall include the ollowing: Motivated choice o the intervention type. Selection o appropriate technique and/or materials. Preliminary design o the selected FRP strengthening system. Structural analysis taking into account the characteristics o the structure ater FRP strengthening. (4)P FRP strengthening o RC members is mainly aimed at the ollowing: Increase the member lexural capacity by using FRP material with ibers running in the axis direction o the strengthened member. Increase the member shear capacity by using FRP material with ibers running orthogonal to the direction o the axis o the strengthened member. Increase the ductility o end sections o beams and/or columns by using FRP material wrapped to the member cross section. Improve the eiciency o lap splices by using FRP material wrapped to the member cross section. Prevent buckling o steel longitudinal bars by using FRP material wrapped to the member cross section. Increase tensile capacity o beam-column joints by using FRP material installed with ibers located along the principal tensile stresses. (5)P Design o FRP-strengthened members shall be in compliance with the ollowing sections Strategies in FRP strengthening (1)P When using FRP material or strengthening RC members, the ollowing principles shall be taken into account: Removal o all brittle collapse mechanisms (Section ). Removal o all storey collapse mechanisms ( sot storey ) (Section ). Enhancement o the overall deormation capacity o the structure through one o the ollowing mechanisms (Section ): - Increasing the rotational capacity o the potential plastic hinges without changing their position (Section ). - Relocating the potential plastic hinges ollowing the capacity design criterion (hierarchy o resistance) (Section ). 70

81 Removal o all brittle collapse mechanisms (1)P Brittle collapse mechanisms to be removed as well as FRP strengthening methodologies are as ollows: Shear ailures shall be avoided; all members that present shear deiciency shall be strengthened. Failure due to loss o bond in steel overlapping areas; the areas where overlapping length o the longitudinal bars is not enough shall be conined with FRP wrapping. Failure due to buckling o steel longitudinal bars: areas where the ormation o plastic hinges is expected shall be conined with FRP wrapping when existing steel transverse reinorcement can not prevent the post-elastic buckling o compressed longitudinal bars. Failure due to tensile stresses on beam-column joint; FRP strengthening shall be applied Removal o all storey collapse mechanisms (1)P Storey collapse mechanisms usually start ollowing the ormation o plastic hinges at column top and bottom locations o structures with no vertical walls. In such a case, FRP strengthening can be perormed to enhance the column lexural capacity with the intent o precluding the ormation o plastic hinges. In no case is the removal o the storey collapse mechanisms allowed with the only intent o increasing storey displacements Enhancement o the overall deormation capacity o a structure (1)P The ultimate deormation capacity o a structure is a measure o its capability to sustain seismic orces. (2) The ultimate deormation capacity o a structure can be computed with non linear static analysis methods (push-over analysis). (3)P The ultimate deormation capacity o a structure depends on the plastic deormation capacity o each single resisting member (beams, columns, and walls) Increasing o the local rotational capacity o RC members (1) The deormation capacity o beams and columns may be measured through the rotation θ o the end section with respect to the line joining the latter with the section o zero moment (chord rotation) at a distance equal to the shear span: L V = M V. Such a rotation is also equal to the ratio o the relative displacement between the two above mentioned sections to the shear span. (2)P The deormation capacity o RC members in the plastic range is limited by the ailure o compressed concrete. FRP coninement increases the ultimate deormation o compressed concrete and enhances the ductility o the strengthened member Capacity design criterion (1)P The application o the capacity design criterion (hierarchy o resistance) implies the adoption o mechanisms such to prevent the ormation o all potential plastic hinges in the columns. In the weak column-strong beam situations, typical or structures designed or vertical loads only, columns are under-designed due to lack o longitudinal reinorcement. In such a case, it is deemed necessary to increase the column capacity under combined bending and axial load toward a strong column-weak beam situation. (2)P When FRP reinorcement is used to increase the lexural capacity o a member, it is important to veriy that the member will be capable o resisting the shear orces associated with the in- 71

82 creased lexural strength. I deemed necessary, shear strengthening shall be taken into account to avoid premature brittle collapse mechanisms Saety requirements Ductile members and mechanisms Combined bending and axial load (1) Flexural capacity o ductile members may be increased with FRP material. (2) FRP strengthening design o members subjected to bending or combined bending and axial load shall be perormed according to Sections 4.2 and 4.5. (3) When the member lexural capacity is increased, particular care shall be taken to properly anchor the adopted FRP reinorcement. (4) Longitudinal ibers used or strengthening RC members subjected to combined bending and axial load shall be properly conined to avoid iber delamination and concrete spalling under cyclic loads Chord rotation (1) The chord rotation o mono-dimensional members (mainly beams and columns) may be increased with FRP-coninement. (2) For the evaluation o the ultimate chord rotation, θ u, o members strengthened with FRP coninement, the ollowing relationship shall be used: 1 θu = θy + ( φu φy) L pl L γ el L pl v (4.54) where γ el is typically assumed equal to 1.5 or 1.0. Such values are only valid or secondary members (e.g., members whose stiness and resistance may be neglected in the response analysis, even though they should be able to carry the deormations o the structure under the design seismic loads preserving their supporting capacity against vertical loads). The remaining terms o Equation (4.54) have the ollowing meaning: - θ y represents the chord rotation exhibited by the end section when the steel is yielded: L V h d θ = φ φ y y + + y 3 LV b c y (4.55) where h is the section depth, d b is the (average) diameter o the longitudinal bars, and c and y are concrete compressive strength and steel yield longitudinal strength (in MPa), respectively, obtained rom in-situ tests o the existing materials and divided by a conidence actor to be set larger than 1 when there is no adequate level o knowledge o the existing structure. - φ u represents the ultimate curvature o the end section, evaluated by assigning at the concrete ul- 72

83 timate strain, ε ccu, the value deined in Section φ y represents the curvature exhibited by the end section when the steel is yielded. - L p1 represents the magnitude o the plastic hinge evaluated as ollows: b y d L = L + h+ (4.56) pl V c - L V represents the shear span o the member (distance between the maximum moment point and the point o zero moment) Brittle members and mechanisms Shear (1) For shear design o RC members strengthened with FRP the criteria o Section 4.3 shall apply; urther provisions as ollows shall be taken into account: Only U-wrapped or completely wrapped conigurations are allowed. FRP strengthening can only be installed with ibers orthogonal to the member longitudinal axis ( β = 90 ) Lap splices (1) Slip o existing steel reinorcement in RC columns at the locations o lap splice may be avoided by conining the member cross section with FRP. (2) For circular cross sections o diameter D, the thickness o the FRP conining the member cross section shall be evaluated as ollows: t D ( σ ) E l sw = (4.57) where: - σ sw represents the stirrup s tensile stress corresponding to a 1 % strain or the mortar injection pressure between the FRP reinorcement and the RC column, i present. - 1 represents the coninement pressure at the lap splice location extending or a length, L s, equal to: l A s y = ue 2( ) b + d + c Ls 2 n (4.58) where u e is the perimeter o the cross section within the polygon circumscribing the longitudinal bars having average diameter d b, n is the number o bars spliced along u e, and c is the concrete cover. (3) For rectangular sections bxd, Equation (4.57) shall be used by replacing D with { b, d} 73 max ; the eectiveness o the FRP coninement shall be reduced by the actor H k deined in Section

84 Buckling o longitudinal bars (1) Buckling o existing steel vertical reinorcement o RC columns may be avoided by conining the member cross section with FRP. (2) The thickness o such FRP coninement shall be evaluated as ollows: t n d y 10 nd = 4 E E E ds (4.59) where: - n represents the total number o existing steel longitudinal bars subjected to buckling. - y has been introduced in Section d represents the size o the cross section parallel to the bending plane. - E represents the Young modulus o elasticity o FRP reinorcement in the direction o existing steel vertical bars. - E ds represents a suitable reduced modulus deined as ollows: E = 4 E E s i ds 2 ( E + E s i ) (4.60) where E s and E i are the initial Young modulus and the tangent modulus o elasticity o existing steel vertical bars ater yielding, respectively Joints (1) Beam-column joints o RC members can be eectively strengthened with FRP only when FRP reinorcement is applied with the ibers running in the direction o principal tensile stresses and provided that FRP reinorcement is properly anchored. In any case, the maximum tensile strain or FRP reinorcement shall not be larger than 4 %. When FRP reinorcement is not properly anchored, FRP strengthening shall not be considered eective. 4.8 INSTALLATION, MONITORING, AND QUALITY CONTROL (1)P Several aspects inluence the eectiveness o FRP material used as externally bonded systems or strengthening RC members. In addition to those discussed in previous chapters, surace preparation and FRP installation will be dealt with in this section. The relative importance o each o these aspects depends on whether reerence is made to applications deined as bond-critical (lexure or shear) or contact-critical (coninement). For example, some tests on the quality o the substrate can be omitted or contact-critical applications (e.g., coninement by wrapping) or when the FRP system is properly anchored provided that its eectiveness is tested by an independent laboratory. (2)P Once FRP strengthening has been carried out, over time monitoring by non destructive or semi-destructive tests as listed in the ollowing sections shall be perormed to ensure the eectiveness o the proposed strengthening solution. (3)P This document describes the tests that can be carried out or quality control as well as over time monitoring o the FRP system. The type and number o tests to be perormed shall be linked to the importance o the application by taking into account the ollowing: 74

85 For strategic buildings or inrastructures, when their unctionality during seismic events is o undamental importance or civil protection or when their roles becomes relevant due to the consequences o a possible collapse. When FRP application concerns primary structural members (e.g., beams and columns) or secondary elements (e.g., loors). The extent o FRP application compared to the size o the structure. (4)P The numerical values indicated in the ollowing are to be understood as suggested values Quality control and substrate preparation (1)P Quality control o the support implies determination o concrete conditions, removal o any deteriorated or loose concrete, cleaning as well as protection rom corrosion o existing steel reinorcement, and inally substrate preparation or receiving the selected FRP reinorcement. (2)P When special devices are used to properly anchor the selected FRP system, testing o such devices shall be conducted in compliance with available standardization documents. Anchoring devices shall be installed according to the manuacturer/supplier speciications regarding both material used as well as surace preparation, environmental conditions, and sequence o each phase. The investigation shall also evaluate the eect o such parameters on the inal result Evaluation o substrate deterioration (1) Prior to FRP application, soundness o the concrete substrate shall be checked. In any case, 2 concrete compressive strength shall not be less than 15 N mm. FRP strengthening shall not be considered eective or concrete compressive strength less than N mm. (2) It is suggested to carry quality control tests on the entire area to be strengthened Removal o deective concrete, restoring o concrete substrate and protection o existing steel reinorcement (1) Concrete substrate may have undergone physical-chemical, physical-mechanical, or impactcaused deterioration. Deteriorated concrete shall be removed rom all damaged areas. (2) Removal o unsound concrete allows or assessment o existing steel reinorcing bars. Corroded steel bars shall be protected against urther corrosion so as to eliminate a possible source o deterioration o the restored concrete. (3) Once all deteriorated concrete has been removed, and suitable measures have been taken to prevent urther corrosion o existing steel reinorcement as well as all other phenomena causing concrete degradation (e.g., water leakage), concrete restoration using shrinkage-ree cement grouts shall be perormed. Roughness o the concrete surace larger than 10 mm shall be leveled with compatible epoxy paste; speciic illing material shall be used or unevenness larger than 20 mm. Also, cracks within solid concrete in the substrate wider than 0.5 mm shall be stabilized using epoxy injection methods beore FRP strengthening can take place Substrate preparation (1) Once the quality control o the substrate has been perormed, the deteriorated concrete has been removed, the concrete cross section restored, and the existing steel reinorcement has been properly treated, sandblasting o the concrete surace to be strengthened shall be perormed. Sandblasting shall provide a roughness degree o at least 0.3 mm; such level o roughness can be meas-

86 ured by suitable instruments (e.g., a laser proilometer or an optical proile-measuring device). (2) Poor concrete suraces that do not need remedial work beore FRP application, should be treated with a consolidating agent beore primer application takes place. (3) Cleaning o the concrete surace shall remove any dust, laitance, oil, surace lubricants, oreign particles, or any other bond-inhibiting material. (4) All inside and outside corners and sharp edges shall be rounded or chamered to a minimum radius o 20 mm Recommendations or the installation (1) FRP strengthening o RC members is highly dependant upon environmental temperature and humidity as well as the characteristics o the concrete substrate. In addition to the above mentioned measure, and regardless o the strengthening type, urther speciic precautions to ensure quality o FRP installation are highlighted in the next sections Humidity and temperature conditions in the environment and substrate (1) It is suggested not to install FRP material when the environment is very moist; a high degree o humidity may delay the curing o resin and aect the overall perormance o the strengthening system especially or wet lay-up applications. (2) FRP strengthening systems shall not be applied to substrates having a surace humidity level greater than 10 %; such conditions could delay the penetration o the primer in the concrete pores and generate air bubbles that could compromise bond between concrete and FRP system. Substrate humidity may be evaluated with a hygrometer or mortar or simply by employing absorbent paper. (3) FRP material shall not be applied i both environment and surace temperature is too low, because curing o the resins as well as iber s impregnation could be compromised. It is also recommended not to install FRP material when concrete surace is heavily exposed to sunlight. It is suggested not to apply any FRP material i temperatures all outside the range o 10 to 35 C. In low temperature environments where the construction site schedule does not allow FRP installation to be delayed, it is suggested to artiicially heat the locations where FRP reinorcement is to be applied. (4) I curing o FRP reinorcement takes place under rainy conditions, heavy insulation, large thermal gradients, or in the presence o dust, protective measures can be employed to ensure proper curing Construction details (1) Anchorage length o at least 200 mm shall be provided or the end portion o FRP systems used or strengthening RC members. Alternatively, mechanical connectors may be used. (2) Proper ibers alignment shall be provided or in-situ wet lay-up application; waving o FRP reinorcement shall also be avoided during installation. (3) When carbon ibers reinorcement is to be used or strengthening RC members where there is potential or direct contact between carbon and existing steel reinorcement, layers o insulating material shall be installed to prevent the occurrence o galvanic corrosion. 76

87 (4) When semi-destructive tests are planned, it is suggested to provide additional strengthening areas ( witness areas ) in properly selected parts o the structure having dimensions o at least x200 mm, with a minimum extension o 0.1 m nor less than 0.5 % o the overall area to be strengthened. Witness areas shall be realized at the same time o the main FRP installation, using the same materials and procedures in areas where removal o FRP strengthening system does not imply alteration o the ailure mechanisms. In addition, witness areas shall be exposed to the same environmental conditions o the main FRP system and shall be uniormly distributed on the strengthened structure Protection o the FRP system (1) For outdoor FRP applications it is recommended to protect the FRP system rom direct sunlight, which may produce chemical-physical alterations in the epoxy matrix. This can be achieved by using protective acrylic paint provided that cleaning o the composite surace with a sponge soaked in soap is perormed. (2) Alternatively, a better protection can be achieved by applying plastering or mortar layer (preerably concrete-based) to the installed strengthening system. The plaster, whose thickness is recommended by the FRP manuacturers/suppliers, is to be laid on the strengthening system ater treating the surace by means o epoxy resin applications with subsequent quartz dusting green-ongreen. The inal layer is particularly suitable to receive any kind o plastering. (3) For ire protection, two dierent solutions may be adopted: the use o intumescent panels or the application o protective plasters. In both cases, manuacturers/suppliers shall indicate the degree o ire protection as a unction o the panel/plaster thickness. The panels -generally based on calcium silicates -are applied directly on the FRP system provided that ibers will not be cut during their installation. Protective plasters represent the most widely adopted solution or ire protection; they shall be applied to the FRP system as indicated beore. Protective coatings o adequate thickness and consistency capable o keeping the composite temperature below 80 C or 90 minutes are available Quality control during installation (1) Quality control during FRP installation should include at least one cycle o semi-destructive tests or the mechanical characterization o the installation itsel, and at least one non destructive mapping to ensure its uniormity Semi-destructive tests (1) Both pull-o tests and shear tearing tests may be carried out. Semi-destructive tests shall be carried out on witnesses and, where possible, in non-critical strengthened areas at the rate o one 2 test or every 5 m o application, and in any case, not less than 2 per each type o test. (2) Pull-o test. The test is used or assessment o the properties o restored concrete substrate; it is carried out by using a 20 mm thick circular steel plates with a diameter o at least 3 times the characteristic size o the concrete aggregate nor less than 40 mm, adhered to the surace o the FRP with an epoxy adhesive. Ater the steel plate is irmly attached to the FRP, it is isolated rom the surrounding FRP with a core drill rotating at a speed o at least 2500 rpm; particular care shall be taken to avoid heating o the FRP system while a 1-2 mm incision o the concrete substrate is achieved. FRP application may be considered acceptable i at least 80 % o the tests (both tests in case o only two tests) return a pull-o stress not less than MPa provided that ailure occurs in the concrete substrate. 77

88 (3) Shear tearing test. The test is particularly signiicant to assess the quality o bond between FRP and concrete substrate. It may be carried out only when it is possible to pull a portion o the FRP system in its plane located close to an edge detached rom the concrete substrate. FRP application may be considered acceptable i at least 80 % o the tests (both in the case o two tests) return a peak tearing orce not less than 24 kn Non destructive tests (1) Non destructive tests may be used to characterize the uniormity o FRP application starting rom adequate two-dimensional survey o the strengthened surace with a dierent spatial resolution as a unction o the strengthening area (see Table 4-1). (2) Stimulated Acoustic testing. Similar to impact-echo testing, such tests rely on the dierent oscillatory behavior o the composite layer depending on the bond between FRP layers and concrete substrate. In its most basic version, such a test may be carried out by a technician hammering the composite surace and listening to the sound rom the impact. More objective results may be obtained with automated systems. (3) High-requency ultrasonic testing. They should be carried out using relection methods with requencies no less than 1.5 MHz and probes with a diameter no greater than 25 mm, adopting the technique based on the irst peak amplitude variation to localize deects. Table 4-1 Minimum resolution or deects thickness to be identiied with non destructive tests. Shear stress transer at interace Example Non destructive test Surace mapping grid Minimum resolution or deects thickness absent wrappings, with the exception o the overlapping area in single-layer application Optional 250 mm 3.0 mm weak central area o very extensive plane reinorcement Optional 250 mm 3.0 mm moderate central area o longitudinal lexural strengthening Suggested 100 mm 0.5 mm critical anchorage areas, overlapping areas between layers, stirrups or shear strengthening, interace areas with connectors, areas with large roughness or cracks in the substrate Required 50 mm 0.1 mm (4) Thermographic tests. They are eective only or FRP systems with low thermal conductivity and can not be applied to carbon or metallic FRP strengthening systems unless special precautions are taken. The heat developed during the test shall be smaller than the glass transition temperature o the FRP system. (5) Acoustic emission tests. The technique is based on the acoustic emission (AE) method and allows the assessment o a damage inside a structural member subjected to loading by listening to and recording the sound generated by either ormation o cracks or delamination phenomena that propagates as elastic waves. Such a test is particularly suitable or detecting deects in the application o FRP composites on RC structures as well as the occurrence o delamination rom the concrete substrate Personnel qualiication (1) Personnel in charge o the tests shall have one o the three qualiication levels speciied in Table 4-2, according to UNI EN 473 and UNI EN

89 Level 1 Level 2 Level 3 Table 4-2 Qualiication levels to perorm semi and non-destructive tests. Proper knowledge o tests equipment; perorming tests; recording and classiying test results according to written criteria; writing a report on test results. Choosing the way o perorming the test; deining the application limits o the test or which the level 2 technician is certiied; understanding test speciications and translating them into practical test instructions suitable to the in-situ working conditions; adjusting and calibrating test equipments; perorming and controlling the test; interpreting and evaluating test results according to the speciications to comply with; preparing written test instructions or level 1 personnel; perorming and supervising all level 1 unctions; training personnel o level 1; organizing test results and writing the inal report. Be in charge o a laboratory acility; establishing and validating test techniques and procedures; interpreting speciications and procedures; having the skill to evaluate and understand test results according to existing speciications; having a suicient practical knowledge o materials, production methods and installation technology o the system to be tested to be able to choose appropriate methods, establish techniques and collaborate in the deinition o acceptance criteria when they are not pre-established; be knowledgeable in dierent application ields; being able to lead personnel o level 1 and Monitoring o the strengthening system (1) Due to the poor availability o data regarding long term behavior o FRP systems used or strengthening RC structures, it is recommended to perorm appropriate monitoring o the installed FRP system by means o semi and non-destructive tests periodically conducted on the strengthened structure. The aim o such a monitoring process is to keep the ollowing parameters under control: Temperature o the installed FRP system. Environmental humidity. Measure o displacements and deormations o the strengthened structure. Potential damage o ibers. Extensions o deects and delaminations in the installed FRP system. 4.9 NUMERICAL EXAMPLES Some numerical examples concerning FRP strengthening o RC structures are reported in Appendix E. 79

90 5 STRENGTHENING OF MASONRY STRUCTURES 5.1 INTRODUCTION Scope (1)P This chapter speciies design recommendations or masonry structural members strengthened with FRP. (2)P The primary objective o FRP strengthening is to increase the capacity o each member as well as the overall capacity o the masonry structure; whenever possible, enhancement o structural displacement at ailure is also recommended Strengthening o historical and monumental buildings (1)P Strengthening o historical and monumental buildings shall be justiied only when inevitable; the adopted strengthening technique shall be in compliance with the theory o restoration (see Section 3.1 item (3)) FRP strengthening design criteria (1) Strengthening methodologies addressed in this document consist o the application o FRP materials in the orm o laminates, sheets, grids, and bars, installed on the members by adhesion or by means o mechanical anchorage devices. FRP reinorcement may be applied to the external suraces o the masonry structure as well as in slots or grooves cut in the masonry itsel. (2) FRP strengthening can be employed or the ollowing reasons: Flexural and shear strengthening to carry tensile stresses within the structural member or between adjoining members. Connection between members (vault and wall ties, connections between orthogonal walls, etc.). Floor stiening to act as a sti diaphragm. Crack width limitation. Columns coninement to increase the material strength. (3)P Design o FRP reinorcement shall ensure that the selected FRP system is always in tension. In act, compression FRP is unable to increase the perormance o the strengthened masonry member due to its small area compared to that o compressed masonry. Moreover, FRP in compression may be subjected to debonding due to local instability. (4) For masonry structures strengthened with FRP and subjected to cyclic loads (e.g.,seismic, thermal variations), bond between masonry and FRP may degrade remarkably during the structure s lietime. In such a case, it could be necessary to properly anchor the FRP system to the masonry by either inserting FRP reinorcement in suitable grooves to prevent local instability or applying mechanical anchoring devices. (5) For proper anchoring, FRP shall be extended up to the compressed masonry areas. (6)P FRP strengthening shall be applied to structural members having suitable mechanical properties. I the masonry is damaged, not uniorm, or cracked, it shall irst be repaired with appropriate techniques to ensure a proper sharing o loads between support and FRP. The selection o the ap- 80

91 propriate strengthening material (carbon, glass, or aramid FRP) shall also take into account physical and chemical properties o the masonry. (7)P FRP reinorcement that completely encases the strengthened member may prevent migration o moisture. Such FRP systems shall not be applied continuously on extended areas o the wall surace to ensure migration o moisture Strengthening Rationale (1) For the appropriateness o a FRP system or a particular application, the engineer should evaluate the existing structure to establish its existing load-carrying capacity, identiy deiciencies and their causes, and determine the condition o the masonry substrate. The overall evaluation should include a thorough ield inspection, review o existing design or as-built documents, as well as a structural analysis. The load-carrying capacity o the existing structure should be based on the inormation collected in the ield investigation as well as the review o the existing documents and determined by analytical or any other suitable methods. FRP strengthening may be aimed at the ollowing: Increasing the capacity o panels, arches, or vault. Wrapping o columns to enhance their compressive strength and ductility. Reducing thrust orces in thrusting structures. Transorming non structural members into structural members by increasing their stiness and strength. Strengthening and stiening horizontal non-thrusting structures. Wrapping buildings at loors and roo locations. 5.2 SAFETY EVALUATION Structural modelling (1)P Design o FRP reinorcement shall be based on a structural scheme representing the behavior o the building or the expected uture use. (2)P Internal orces acting on the masonry shall be determined using the methods o structural analysis. In particular, the structure can be modeled as either linear elastic or through proven non linear models capable o simulating the inelastic behavior and the negligible tensile strength o the masonry. (3) Simpliied schemes can also be used to describe the behavior o the structure. For example, provided that tensile stresses are directly taken by the FRP system, the stress level may be determined by adopting a simpliied distribution o stresses that satisies the equilibrium conditions but not necessarily the compatibility o strain. The use o simpliied stress distributions should be very careully chosen because a statically satisactory stress level could have already caused the structure to collapse due to the brittle nature o the FRP-masonry system. In case o structures with regular or repetitive parts, partial structural schemes may be identiied that allow or a rapid evaluation o the overall behavior o the strengthened structure. Likewise, simpliied models may be adopted or veriications o local ailure mechanisms, provided that their use is correctly motivated Veriication criteria (1)P Possible ailure modes o masonry walls strengthened with FRP systems can be summarized as ollows: Excessive cracking due to tensile stresses in the wall. Crushing o masonry. 81

92 Shear-slip o masonry. FRP rupture. FRP debonding. Failure mode o FRP strengthened masonry structures usually involves a combination o the above mentioned mechanisms Saety veriications (1) Masonry can be considered an anisotropic material exhibiting a non-linear behavior. The stress-strain relationship may vary quite signiicantly depending whether the structure is built using artiicial or natural blocks as well as the type o mortar employed. (2) Masonry exhibits a brittle behavior when subjected to tensile loading; the corresponding tensile strength is negligible compared to its compressive strength. For design purposes, it is accepted to neglect tensile strength o masonry. (3)P Laboratory tests show that the stress-strain diagram o masonry blocks subjected to compressive loads can be described as ollows: Basically linear or low strain values. Non-linear as the load increases up to the ultimate value. Non-linear sotening ater the load at ultimate has been reached. (4) The masonry behavior or compressive load also depends on the availability o transverse coninement. By increasing the transverse coninement, strength and ductility o the material is improved. (5)P Masonry shear strength depends on the applied axial load because it usually relies upon cohesion and riction o the material. (6)P The characteristic values or strength are as ollows: mk or vertical compression. h mk or horizontal compression. or shear. vk Such values shall be determined in compliance with the current building code. A reerence value or h mk is 50 % o mk. (7) Design values or mechanical properties o masonry are computed by dividing the characteristics values by the partial actor o the material γ m = γ M as well as by the partial actor or resistance model, γ Rd, according to the current building code and the present document. (8)P For most engineering applications, the behavior o masonry under uniaxial loads may be simpliied as ollows: tensile stress: neglected. compression: linear behavior with slope equal to the secant modulus o elasticity up to both design strength o md and design strain o ε m ; design strength equal to mk or strain between ε m ε ε mu ; and zero strength or strain larger than ε mu. 82

93 (9)P Unless experimental data is available, the masonry ultimate design strain, ε mu, may be assumed equal to 0.35 %. (10) Alternatively, appropriate stress-strain diagrams embracing the behavior described in (3)P may be used, provided that their perormance is validated on the basis o experimental investigations. (11)P FRP materials are characterized by an anisotropic behavior, as described in detail in Section 6.2. When stressed in the iber direction, FRP exhibits a linear elastic behavior up to ailure, whose characteristic value is k. The maximum design strain allowed to the FRP system shall be expressed as ollows: ε ε = min η, ε k d a dd γ (5.1) where ε k represents the FRP characteristic strain at ailure, and ε dd is the maximum FRP strain once FRP debonding takes place (see next section). Unless more accurate data is available, ε dd shall be taken rom item (7) o Section The values to be assigned to the conversion actor, η, and the partial actor, γ = γ, are indicated in Table 3-4 and Table 3-2, respectively. a m (12)P Design recommendations are based on limit-states-design principles. For ultimate limit states analysis, two possible approaches may be recognized depending upon the type o structural analysis perormed. I non linear models are used, the member s load carrying capacity shall be larger than the actored applied load. The latter is computed according to the current building code. Care shall be taken to ensure that the proposed solution is not aected by the particular discretization adopted or the computation. I linear elastic models or simpliied schemes adopting a balanced distribution o stresses that satisy equilibrium conditions but not necessarily compatibility o strain are used, the resulting stress on each structural member shall be veriied. In particular, or bidimensional members (slabs, shells), the unit stress shall be considered (e.g., those evaluated per unit length o the member). Assuming that a plane section beore loading remains plane ater loading, the design criteria is met when actored shear orces and bending moments due to the applied loads are smaller than the corresponding design actored shear and lexural capacities. The latter shall be evaluated as a unction o the applied axial orce, considering the non linear behavior o the material represented by the simpliied stress-strain diagram introduced in item (8)P. (13)P Other limit states shall be veriied according to the current building code requirements. 5.3 EVALUATION OF DEBONDING STRENGTH (1)P Bond between masonry and FRP is o great relevance because debonding yields to undesirable, brittle ailure modes. When designing according to the capacity design criterion, FRP debonding shall always ollow the post-elastic behavior o compressed masonry. I special anchorage devices or the FRP system are used, ailure by FRP debonding is accepted, provided that the variation o the resisting scheme is accounted or. (2) Due to the wide variety o existing masonry structures (e.g., artiicial clay, concrete masonry blocks, squared or non-squared stones, etc.), debonding may occur at the interace between dierent materials. Moreover, in masonry structures with irregular aces, a layer o mortar may be used to 83

94 create a suitable surace or FRP application. The same strengthening system may then be linked to dierent materials characterized by dierent interace properties. (3) I the tensile strength o the adhesive used to install FRP reinorcement is larger than that o the substrate, debonding between FRP and masonry takes place at the masonry ace-level General considerations and ailure modes (1)P Debonding between FRP reinorcement applied in isolated strips along straight lines and masonry may occur according to the ollowing ailure modes: plate end debonding or intermediate crack debonding. In masonry structures strengthened with FRP and loaded such to provide tensile stresses in FRP reinorcement both at laminate ends as well as close to the locations o existing cracks, the FRP-masonry interace undergoes high stresses localized within 50 to 200 mm rom the discontinuity section. 2) Combined stresses reduce the bond strength. In particular, when FRP strengthening is applied to curved suraces or when high lexural stiness FRP reinorcement is used, signiicant tensile stresses perpendicular to the masonry-frp interace (peeling stresses) arise, thus reducing the orce that may be transerred. In case o FRP laminates applied with ibers inclined with respect to the orthogonal direction o the crack, stresses around cracks generated by relative movements produce a stress concentration at the masonry-frp interace. (3) Shear debonding takes place close to FRP reinorcement ends (anchorage sections) and may be ollowed by removal o a signiicant portion o brick (rip-o ailure), speciically when shear stresses at the FRP end are combined with normal tensile stresses. Such ailure mode appears with ormation o cracks due to spreading o anchorage stresses that may be accompanied by tensile stresses in the masonry responsible or its racture (Figure 5-1). t End o laminate F max Figure 5-1 Failure due to rip-o o the anchorage brick Bond strength at ultimate limit state (1)P Experimental bond tests show that the ultimate value o the orce transerred rom FRP reinorcement to the support prior to FRP debonding depends on the length, l b, o the bonded area. This value grows with l b up to a maximum corresponding to a length l e ; urther increase o the bonded area does not increase the orce that it is possible to transer. The length l e is called optimal bond length and corresponds to the minimal bond length able to carry the maximum anchorage orce. (2) The optimal bond length, l e, may be estimated as ollows: 84

95 l e = E t 2 mtm [lengths in mm] (5.2) where: - E is the Young modulus o elasticity o FRP reinorcement - t represents FRP thickness - mtm is the masonry average tensile strength; and unless speciic data is available, it may be assumed equal to 0.10 mk (in particular, because bond between FRP and masonry is generally granted, the value o mtm to be considered in Equation (5.2) is the average tensile strength o the masonry). (3) I debonding involves the irst masonry layers, the characteristic value, Γ Fk, o the speciic racture energy o the FRP strengthened masonry shall be given as ollows: Γ = c [orces in N and lengths in mm] (5.3) Fk 1 mk mtm where c 1 is an experimentally determined coeicient. Unless speciic data is available, the value o c 1 may be assumed equal to (4) When debonding involves the irst masonry layers and the bond length is longer or equal to the optimal bond length, the design bond strength, dd, shall be expressed as ollows: dd 1 2 E Γ = γ γ t,d M Fk (5.4) where γ, d is the partial actor as per Table 3-2 (Section 3.4.1), and γ M is the partial actor o the masonry. (5) The maximum design strain, ε dd, beore FRP debonding takes place is given by the ratio between the design bond strength, dd, and the FRP Young modulus o elasticity, E. (6) For bond lengths, l b, smaller than l e, the design bond strength shall be reduced as ollows: dd,rid l b b = dd 2 le le l (5.5) (7) I debonding mechanism between FRP and masonry takes place by rupture o a portion o the masonry unit, it shall be assumed that each masonry unit can not concur or more than 80 % o its length to the determination o the above mentioned lengths l b and l e. (8) When special anchorage devices (FRP transverse bars, FRP end wrapping) are used, the maximum bond orce shall be evaluated with experimental investigations Bond strength with stresses perpendicular to the surace o bond (1) Experimental data carried out on FRP strengthened masonry structures should be used or 85

96 the determination o the bond strength in case o stresses perpendicular to the bonding surace. (2) Unless a more detailed analysis is carried out, bond strength o low curvature FRP strengthened masonry structures should be evaluated by reducing the value o the orce transerred rom the FRP system to the support depending upon the magnitude o the stress perpendicular to the bonding surace. (3) The design value o the bond strength with stresses perpendicular to the surace o bond can be expressed as ollows: σ Sd pd = dd 1 (5.6) mtd where dd is the design value o the bond strength given in Equation (5.4), mtd is the design value o the tensile strength o the masonry, and σ Sd represents the magnitude o the stress perpendicular to the bonding surace. I the bond length, l b, is smaller than the optimal length, l e, the value dd, rid shall be used in Equation (5.6). (4) The magnitude o the stress perpendicular to the bonding surace, σ Sd, or FRP strengthening o curved proile having bending radius r and subjected to a constant tensile stress σ, can be calculated as ollows: σ 1 = σ t (5.7) r Sd 5.4 SAFETY REQUIREMENTS (1) Principles as stated in Section 5.2 are hereater reerred to practical applications Strengthening o masonry panels (1) Masonry panels may be strengthened with FRP to increase their load carrying capacities or their ductilities or in-plane or out-o-plane loads. In the ollowing, simple requirements to control the degree o saety o the strengthened masonry panel are suggested. Such requirements are not exhaustive and should be integrated with urther analysis suitable to the complexity o the case studied Strengthening or out-o-plane loads (1) Out-o-plane collapse o masonry panels is one o the most requent mechanism o local crisis or masonry structural members. Such mechanism is primarily due to seismic actions and secondary to horizontal orces originated by the presence o arches and vaults. Out-o-plane collapse can appear as any o the ollowing: Simple overturning. Vertical lexure ailure. Horizontal lexure ailure Simple overturning (1) The kinematic motion is represented by an overturning about a hinge at the bottom o the masonry panel. Due to the small tensile strength o the masonry, the hinge is usually located on the outer surace o the panel. Collapse by overturning may happen in the presence o walls not con- 86

97 nected to the orthogonal walls nor restrained at their top. Collapse by overturning may depend on several actors, such as boundary conditions, slenderness o the wall, and geometry o masonry member. A possible retroitting technique may consist in the use o FRP applied to the top portion o the masonry panel and properly anchored into the orthogonal walls. The optimal solution rom a perormance point o view, would be embracing the entire perimeter o the building with the selected FRP system. Particular care shall be taken in the rounding o masonry corners to avoid stress concentration in the FRP. As an example, a masonry panel subjected to the ollowing loads (design values) is considered: P d panel sel weight. N d axial orce acting on top o the panel. Q d horizontal load due to seismic eects. F d orce exerted on the masonry panel by the FRP system. N d F d Q d h P d h * t Figure 5-2 Collapse mechanism by simple overturning. Assuming that loors and walls perpendicular to the panel being studied provide negligible restraint to the panel itsel (Figure 5-2), tensile orce in the FRP reinorcement can be calculated via moment equilibrium as ollows: 1 Fd = Q * d h Nd t Pd t 2 h ( ) (5.8) * where h is the distance between FRP and the bottom portion o the masonry panel. To prevent simple overturning o the masonry panel, the two ollowing conditions shall be met: FRP tensile strength It shall be veriied that F d 2 F (5.9) Rd where FRd = A d, A represents the FRP reinorcement area, and d is the design tensile strength o the FRP. 87

98 Rip-o o FRP rom orthogonal walls It shall be veriied that F d 2 F (5.10) pd where Fpd = A pd represents the maximum anchorage orce o the FRP applied to one o the two orthogonal walls. Usually, rip-o is more demanding than tensile strength on FRP. In the case o a ully wrapped structure with an appropriate overlapping length, the second condition becomes unnecessary. Additional requirements include determination o stresses due to combined axial load and bending moment as well as determination o shear orce on panel horizontal sections according to Section Vertical lexural ailure (1) For masonry panels restrained at both top and bottom regions and subjected to horizontal loading, ailure may occur due to lexure with ormation o three hinges: one at the bottom o the panel, one at the panel top and the last at a certain height o the panel itsel. Failure occurs when the orce corresponding to the applied axial load and bending moment alls outside to the masonry cross section. Flexural collapse may occur in very high masonry panels and/or panels restrained ar apart rom orthogonal walls. In case o seismic loads, masonry panels loaded rom opposite side by loors located at dierent heights are particularly sensitive to lexural collapse mechanisms. Such masonry panels may be strengthened with FRP having ibers running in the vertical direction. As an example, a unit width strip o masonry panel strengthened with FRP and subject to the ollowing external loading (design values) is considered: () s P d weight o the upper side o the panel. () i P d weight o the lower side o the panel. () s Q d seismic orce related to the upper side o the panel. () i Q d seismic orce related to the lower side o the panel. N d axial orce acting on the panel. Q d load due to a urther horizontal loading condition. By orce equilibrium, the horizontal reaction in C may be calculated as ollows (Figure 5-3): H C,d (i) (s) (s) (i) hi (2 Qd + Qd ) + Qd (2 h hs) t ( Nd + Pd + Pd ) = 2 h (5.11) The masonry panel at cross-section B where the FRP is applied to prevent ormation o the hinge is subjected to axial orce and bending moment equal to the ollowing: N = N + P (s) Sd d d (s) hs MSd = HC,d hs Qd. 2, (5.12) 88

99 h s C (s) Q d (s) P d H C,d h (i) Q d B Q d h i (i) P d A t Figure 5-3 Collapse mechanism by vertical lexure. The masonry panel lexural capacity is veriied when the ollowing relationship is met: M Sd M (5.13) Rd The lexural capacity o the strengthened masonry panel, M Rd, may be determined as a unction o the mechanical characteristics o masonry and FRP, the thickness t o the masonry panel, and the value o the applied axial orce (the partial actor or resistance models, γ Rd, can be taken rom Table 3-3 o Section 3.4.2; or this particular case it shall be assumed equal to 1.00). The compressive stress-strain relationship or masonry can be assumed to be rectangular with a uniorm compressive stress o 0.85 md distributed over an equivalent compression zone bounded by the edges o the cross section and a straight line located parallel to the neutral axis, x, at a distance o x. The maximum masonry and FRP strain shall be taken as indicated in Section FRP vertical reinorcements shall be placed at a center-to-center distance, p, such that: p 3 t+ b (5.14) where b is the FRP width. Larger center-to-center spacing can be used only i adequately justiied Horizontal lexural ailure (1) For masonry panels restrained at the bottom as well as irmly connected with transversal walls, the resistance to horizontal orces is ensured by arching eect o the top strip as illustrated in Figure 5-4(a). The value o the maximum uniormly distributed horizontal load, q, that can be carried out can be expressed as ollows: 2 2 t h q= 2 md (5.15) L h where L is the panel width, and md represents the design compressive strength o the masonry in the horizontal direction. I the applied load is larger than the value o q given by Equation (5.15), the panel would collapse due to crushing o the masonry. In such a case, the application o a FRP strengthening system could be beneicial. For masonry panels restrained at the bottom, but not 89

100 irmly connected with transversal walls, the masonry panel may collapse as illustrated in Figure 5-4(b). With reerence to the unit strip located on top o the panel, ailure occurs when the orce corresponding to the applied axial load and bending moment alls outside to the masonry cross section. (a) (b) Figure 5-4 Collapse by horizontal lexure. The use o FRP prevents such mechanisms rom ailure providing lexural capacity to the mentioned unit strip can be considered a masonry beam strengthened with FRP. The applied bending moment, M sd, is due to earthquake loads, wind pressure, and other possible horizontal loads due to the presence o other structural members. Flexural saety o the masonry panel is satisied when Equation (5.13) is met. The moment M rd may be determined as a unction o the mechanical characteristics o masonry and FRP and the thickness t o the masonry panel. Unless a more detailed analysis is available, the horizontal orce due to the presence o transversal walls may be considered equal to zero when evaluating M. rd An additional shear check shall be carried out on the connection joints between masonry panel and transversal walls by taking into account the two-dimensional eect o the entire panel. Veriication o the magnitude o tensile loads on transversal walls close to the main masonry panel shall also be perormed Strengthening or in-plane loads (1) The ollowing checks shall be carried out or masonry panels subjected to in-plane loads: In-plane combined bending and axial load. Shear orce In-plane combined bending and axial load (1) FRP materials can eectively enhance the in-plane capacity with regard to combined bending and axial load o masonry panels when installed on both sides o the panel where tension loads are expected. Such FRP reinorcements shall be adequately anchored to the end portions o the masonry panel. (2) Assuming that sections perpendicular to the axis o bending which are plane beore bending remain plane ater bending, the compressive stress-strain relationship or masonry can be assumed to be rectangular with a uniorm compressive stress o 0.85 md distributed over an equivalent compression zone bounded by the edges o the cross section and a straight line located parallel to the neutral axis, x, at a distance o x. The maximum masonry and FRP strain shall be taken as indicated in Section Shear orce 90

101 (1P) The shear capacity o masonry panels strengthened with FRP applied on both sides o the panel can be seen as the combination o two resisting mechanisms: (1) shear orces due to riction in presence o compression loads, and (2) or elements capable o resisting tensile stress a truss mechanism becomes active, and shear orces are carried out by equilibrium. (2) Usually, shear strengthening with FRP o masonry panels is obtained by applying external reinorcement to carry tensile loads due to lexure and shear orce such to allow the ormation o the mentioned truss mechanism. When FRP reinorcement is not applied to carry lexural loads, shear strengthening with FRP can be carried out by installing external reinorcement along the panel diagonals. (3) When ormation o truss mechanism is ensured, the design shear capacity, V Rd, o the FRP strengthened masonry panel is computed as the sum o the masonry contribution, V Rd, m, and the FRP contribution, strut o the truss: V Rd,, up to the maximum value V Rd, max inducing ailure o the compressed { } V = min V + V, V (5.16) Rd Rd,m Rd, Rd,max I shear strengthening is placed parallel to the mortar joints, the above deined contributions may be evaluated as ollows: 1 VRd,m = d t γ Rd vd (5.17) V Rd, d A γ p w d = (5.18) Rd where: - γ Rd is the partial actor to be assumed equal to 1.20 (Table 3-3, Section 3.4.2). - d is the distance between the compression side o the masonry and the centroid o FRP lexural strengthening. - t is the masonry panel thickness. - vd is the design shear strength o the masonry, equal to vk γ M. - A w is the area o FRP shear strengthening in the direction parallel to the shear orce. - p is the center-to-center spacing o FRP reinorcement measured orthogonally to the direction o the shear orce. - d is the design strength o FRP reinorcement, deined as the lesser between FRP tensile ailure strength and debonding strength. The value o the partial actor or masonry, γ M, shall be set according to the current building code; the partial actor or resistance model, γ Rd, shall be obtained rom Table 3-3 o 3.4.2; or shear it is set equal to I the angle o riction, φ, o mortar joints is smaller than 45, the value o provided by Equation (5.18) shall be reduced by a multiplicative actor o cot ( 90 φ). 91 V Rd, (4) The design shear capacity, max Rd, V, o the masonry panel corresponding to ailure o the compressed strut o the truss can be calculated as ollows:

102 V = 0.3 t d (5.19) Rd,max h md where h md is the design compressive strength o the masonry parallel to the mortar joints. (5) In case o FRP lexural strengthening o masonry panels, shear capacity enhancement due to the increased compressive strength o the masonry can be calculated by computing the value o the parameter vk related to the average compressive strength (including the one due to lexure) acting on the masonry panel. (6) I shear strengthening is not placed parallel to the mortar joints, Equations (5.17) and (5.18) valid or FRP strengthening placed parallel to the mortar joints, should be careully evaluated with suitable models Lintel and tie areas (1)P The areas connecting dierent wall bays within a masonry panel are named tie areas. Their unction is twoold: (1) restrain the adjoining wall to assume deormed shapes compatible with the applied horizontal load, and (2) support the masonry wall located above openings. The ormer mechanism generates shear and lexural stresses within the tie area itsel and plays a signiicant role in case o seismic loads; the latter is played by lintels located above any opening that are primary subjected to vertical loads. (2)P Due to the presence o vertical loads, two eects in the areas above openings are displayed: (1) the portion o masonry wall above the opening can not withstand its own weight and shall be supported by lintel unctioning as a beam; and (2) when the wall bays surrounding the openings are slender so as not to withstand the horizontal load due to the presence o the opening itsel, the lintel shall be such to provide adequate strength to carry the tensile stresses to ensure the overall equilibrium o the wall. (3) P In the next two sections, three methods or designing both lintels and tie areas subjected to seismic loads are presented (see Figure 5-5). q d h N ql 8h 2 d Sd = * * h M Sd Figure 5-5 Lintels design subjected to combined bending and axial loads Design o lintels (1) Lintels may be realized using structural elements having both axial and lexural capacity; alternatively, lintels having only axial capacity can be employed. In the ormer case, lintels are capable o unctioning as a beam and carry tensile stresses to ensure the overall equilibrium o the wall; in the latter, support to the wall above the opening shall be ensured by ormation o a reinorced 92 L

103 masonry member located just above the opening where tensile stresses are carried out by the applied FRP strengthening system. In this case, equilibrium condition is probably reached with remarkable displacements showed by the masonry wall above the strengthened member. Such FRP strengthening system shall be applied on the bottom portion o the lintel; unless appropriate explanation is given, the selected FRP system shall not be installed on the sides o the masonry wall. (2) To ensure proper unctioning o lintels, FRP reinorcement shall be properly anchored into the adjacent masonry walls. (3) The portion o the FRP strengthened lintel shall have a lexural capacity, M Rd the applied moment,. The latter can be calculated as ollows: M Sd, larger than M Sd γ = G gtl (5.20) where g is the masonry weight per cubic meter, t is the thickness o the masonry, L is the net span o the opening, and γ G is the partial actor or sel weight at ultimate limit state. FRP shall also be capable to withstand the ollowing orce: N q L 8 h 2 d Sd = * (5.21) where q d is the design vertical load at ultimate limit state acting on the lintel (sum o actored dead and live loads), and h * is the internal lever arm, to be assumed not larger than the span L o the opening nor the height h o the tie area Design o tie areas (1) FRP strengthened tie areas shall be veriied or bending moment, shear, and axial loads acting at the connection with vertical masonry walls. Flexural and shear capacity shall be calculated according to the rules given or the masonry wall panels by tacking into account the compressive h strength o the masonry md parallel to the mortar joints. (2) FRP strengthening o tie areas may be carried out by installing reinorcement with ibers running in the horizontal direction located at the level o the loor; alternatively, external FRP reinorcement may be located at the top or bottom region o tie areas itsel. FRP reinorcement may be continuous or discontinuous and applied to either the internal or external ace o the masonry wall. When FRP reinorcement is applied to the external ace o the masonry wall, it also may unction as external wrapping o the building. (3) To ensure a satisying behavior with respect to the applied shear orce, FRP reinorcement with ibers running in the diagonal direction could also be applied to tie areas. FRP reinorcement should be installed symmetrically on both internal and external sides o the strengthened masonry wall. 93

104 5.5 STRENGTHENING OF STRUCTURAL MEMBERS WITH SINGLE OR DOUBLE CURVATURE (1)P Structural members with single or double curvature generally lose their unctionality due to the ormation o hinges that promote the mechanisms o collapse. Hinges orm in such masonry structures due to the negligible tensile strength o the masonry. (2)P Such hinges are located in regions o limited contact area, externally to the mid plane o the structure. As irst approximation, they can be located either at the intrados or extrados o the masonry panel. A masonry hinge can carry axial and shear orces. As a result, the hinged section can only carry an axial orce having an eccentricity equal to hal o the structure thickness. (3)P FRP reinorcement delays both opening o cracks and ormation o hinges within the masonry panel located on the opposite side with respect to the one where the FRP system is installed. Thereore, a properly anchored FRP reinorcement applied to the extrados (intrados) prevent the ormation o hinges on the opposite side o the intrados (extrados). FRP reinorcement is not recommended when collapse is controlled by either crushing o the masonry or shear ailure. (4)P FRP reinorcement used as external strengthening o masonry structures is such to prevent the ormation o certain hinges Arches (1)P Two structural schemes can be taken into consideration: Arch scheme, or arches resting on ixed and/or hinged supports. Arch-pier scheme, also known as rame scheme, or arches resting on piers. (2)P Both schemes generally tend to collapse due to the ormation o at least our hinges. In particular, a possible mechanism may be due to the ormation o three (real) hinges and a double pendulum (pseudo-hinge) leading to a shear ailure o a portion o the arch with respect to the other Arch scheme (1)P To prevent the mechanism characterized by the ormation o our hinges, FRP reinorcement may be bonded either to the extrados or the intrados o the masonry arch. Experimental evidence shows that application o FRP reinorcement on the side surace o the arch does not provide signiicant improvement o the structural behavior. In such a case, a premature debonding o the FRP reinorcement rom the masonry ace takes place. Such debonding is localized in the arch compressed region and it is due to local FRP instability, ollowed by a ast degradation o the bond between masonry and FRP. (2) FRP strengthening is preerably carried out by applying FRP reinorcement on the extrados o the masonry arch to prevent the ormation o hinges on the intrados. Alternatively, FRP reinorcement may be applied on the arch intrados to prevent the ormation o hinges on the extrados. As a inal remark, FRP reinorcement may also be applied to both extrados and intrados o the masonry arch to prevent the ormation o irst and second type-hinge. However, this application is not common. (3) Unless the ormation o hinges is prevented in the region o the masonry arch close to supports, when computing internal orces o the strengthened arch the ormation o hinges at supports shall always be considered. (4) Partial FRP strengthening carried out on a portion o the extrados or intrados does not pre- 94

105 vent the possibility o ormation o hinges responsible or the activation o a kinematic mechanism o the structure. However, when FRP strengthening is properly designed and realized, it may enhance the structure s ultimate capacity. It shall be preerable to do the ollowing: Carry out complete FRP strengthening on the extrados or intrados o the arch. Choose FRP abric over laminate, because they better it the geometry o the masonry arch. Apply FRP strengthening on the arch extrados; in this case the arch curvature is such to display compressive stress orthogonal to the FRP reinorcement. On the other hand, when FRP is installed on the intrados, the curvature is such to display tensile stress orthogonal to the FRP reinorcement that enhance debonding between FRP and masonry. (5) When computing internal orces o the FRP strengthened masonry arch, the ormation o hinges located on the opposite side with respect to the side o FRP installation shall be taken into account. A more realistic approach should consider that the hinge will orm at a certain distance to the side located at the opposite ace o FRP reinorcement. Such a distance depends on the masonry compressive strength; it increases as the masonry compressive strength decreases. (6)P When masonry tensile stresses can be neglected, the ollowing checks shall be perormed or FRP strengthened arches: Overall stability o the structure. Combined bending and axial orce, when ailure occurs by either crushing o the masonry and/or FRP rupture. Shear. FRP debonding. (7) Combined bending and axial orce as well as shear check shall be in compliance with the procedure indicated or masonry panels. Check or FRP debonding shall be perormed at a distance l b rom the end o FRP reinorcement; the moment corresponding to such section shall be evaluated using the FRP design strength according tosection item (3) Arch-pier scheme (1) For arch-pier structures, application o FRP reinorcement to the arch intrados or extrados may not be suicient to prevent relative displacements o the pier-arch connections. In such a case, it is preerable to either act on the piers or set a tie rod between the pier-arch connections. (2)P Checks to be carried out are the same as those considered or the arch scheme Single curvature vaults: barrel vaults (1)P In most situations, the study o barrel vaults is similar to that o a unit depth arch. Consequently, barrel vaults may be strengthened with FRP applied both on the extrados and intrados. To satisy saety requirements, FRP strengthening shall be applied along the entire longitudinal length o the vault. For this reason, FRP reinorcement shall be placed at a center-to-center distance, p, calculated as ollows: p 3 t+ b (5.22) where t is the vault thickness and b is the FRP width. A greater distance is allowed only i properly substantiated. 95

106 (2) Longitudinal FRP strengthening has only the secondary importance o bridging the ideal arches orming the barrel vault. Such mechanism is particularly important in cases o horizontal loading. (3) Typically, it is suggested to install in the longitudinal direction at least 10 % o the FRP reinorcement applied in the transversal direction. It shall be increased to 25 % or FRP strengthening in seismic area. (4) I vaults are used in cellular buildings with small-size rooms, FRP strengthening should be perormed on the building walls rather than the vault Double curvature vaults: domes (1)P Domes exhibit membrane-type and lexural-type stresses Membrane-type stresses (1) In a dome subjected to vertical loads, normal tensile stresses directed along the dome parallels are displayed. The typical cracking pattern with cracks located along the meridians is primarily due to the negligible tensile strength o the masonry. The mentioned crack pattern modiies the equilibrium condition o the dome enhancing the horizontal orces where the dome connects with the supporting structure. The use o FRP reinorcement applied in a circle around the lower portion o the dome s perimeter may help in preventing the opening o cracks as well as reducing the magnitude o the horizontal orce acting on the supporting structure. (2)P The degree o saety o a masonry dome shall be perormed by checking the ollowing: Tensile stress in FRP reinorcement. FRP debonding according to Section Flexural-type stresses (1) Flexural-type stress is typically localized where the dome meets the supporting structure or at the edge o skylight, when available. In particular, lexural-type stress may cause collapse o portions o the dome delimitated by meridian cracks. I the load carrying capacity o such portions is controlled by ailure o the region connecting the dome to the supporting structure, the dome may be strengthened by applying FRP reinorcement in a circle around the lower portion o the dome perimeter. I the dome supporting structure does not show any displacement, the above mentioned FRP circular strengthening is inactive. In such a case, FRP reinorcement shall be applied along the dome meridians. (2) P The degree o saety o a masonry dome shall be perormed by checking the ollowing: Combined bending and axial orce. Shear. FRP debonding. For combined bending and axial loads as well as shear check, internal orces shall be evaluated on a unit dome element according to Sections and Possible strength reductions or the loading carrying capacity o the strengthened dome shall be considered due to the complexity o the internal orces associated to the analysis o dome structures. Precautions shall be taken in case o combined bending and axial load when the tensile zone in one direction corresponds to a compression zone in the opposite direction. In such a case, unless a more rigorous analysis is perormed, the ratio o the absolute value o the design applied moment to the nominal moment calculated under the applied axial load shall not be larger than 1. On the contrary, unless a more rigorous analysis is 96

107 perormed, the speciic lexural capacity in each plane can be assumed equal to the one resulting rom a monoaxial loading condition. Planar shear design can be perormed according to the irst o the two cases previously mentioned. It is to be noted that lexural and shear capacity shall be calculated with reerence to the design compressive strength o the masonry by taking into account dierences due to loading perpendicular or parallel to the masonry texture (Section item (6)P). Othogonal shear design can not take into account the presence o FRP reinorcement and shall be perormed as in the case o unreinorced masonry considering the complexity o the existing internal orces. Checks or FRP debonding shall consider tensile stresses acting perpendicular to the FRP reinorcement according to Section (3) To ensure proper behavior o the FRP system applied in a circle around the lower portion o the dome perimeter, FRP reinorcement shall be accurately anchored to the dome supporting structure eventually by means o mechanical anchorage Double curvature vaults on a square plane (1) FRP strengthening o double curvature vaults resting on a square plane shall primarily be perormed on the masonry walls o the room that support the vault itsel. For vertically loaded structures, integrity and stiness o the supporting masonry walls ensure that the vault is primarily subjected to compression stresses. I this is not the case, FRP strengthening may be perormed within the corner region o the vaults where tensile stress is expected to exist in a direction orthogonal to the room diagonals. 5.6 CONFINEMENT OF MASONRY COLUMNS (1)P FRP coninement o masonry columns subjected to axial loads increases both ultimate capacity and strain. It also may enhance the column perormance under service limit state. (2)P FRP reinorcement is typically installed by wrapping o the member; such wrapping exerts a beneicial eect on the lateral strain o the column by providing a tri-axial coninement. FRP strengthening may be employed either in case o rehabilitation o deteriorated structures or or their seismic upgrade. (3) Coninement with composites may be perormed by using FRP sheets or bars. FRP sheets are applied as external reinorcement along the perimeter o the member to be strengthened in orm o continuous or discontinuous wrap. Instead, FRP bars are inserted in spread holes drilled through the member that requires upgrade. (4) FRP bars are inserted in holes drilled along two directions orthogonal to the member transversal cross section. Each set o two bars inserted in one o the two directions represents a layer o bars (Figure 5-6). Such reinorcement can eectively contrast the transversal strain o the masonry. To ensure continuity between FRP bars and surrounding masonry, each hole is illed with epoxy paste or, alternatively, FRP bar ends are mechanically astened to the masonry. (5)P When FRP sheets and bars are used in the same application or strengthening masonry columns, it is recommended that such FRP materials exhibit similar mechanical characteristics. (6) Coninement with FRP o masonry structures shall be perormed using design mechanical parameters in compliance with the current building code. 97

108 Layer o bars Figure 5-6 Lateral view o a column with FRP bars arranged along two orthogonal directions Design o axially loaded conined members (1)P Design o FRP conined masonry columns is based upon the appropriateness o the FRP system as a unction o the member geometry. (2)P It is recommended to install FRP reinorcement with ibers running in the orthogonal direction with respect to the vertical axis o the strengthened member. Eectiveness o spiral FRP reinorcement shall be adequately proven. (3)P The axial capacity o FRP strengthened member, N Rmc, d, shall exceed the design axial orce due to applied loads calculated according to the current building code, N Sd, as ollows: N Rmc,d N (5.23) Sd (4)P N Rmc, d is given as ollows: 1 N = A A (5.24) Rmc,d m mcd m md γ Rd where the partial actor, γ Rd, shall be set equal to 1.10 (Table 3-3, Section 3.4.2), A m represents the cross sectional area o the FRP conined member, md represents the design compressive strength o unconined masonry, and mcd is the design compressive strength o FRP conined member. (5) The design compressive strength, mcd, or members conined with FRP subjected to a lateral conining pressure, 1, can be written as ollows: = + k' (5.25) mcd md l,e where k is a non-dimensional coeicient, and l,e represents the eective conining pressure. (6) Unless a more detailed analysis is perormed, k may be calculated as ollows: 98

109 g 1000 m k ' = (5.26) where g is the masonry mass-density expressed as 3 kg m. m (7) The eective conining pressure, 1, e, is a unction o cross section shape and the FRP system. Deining V m as the volume o the masonry member to be strengthened, and V c, e as the portion o the eectively conined volume, the ollowing coeicient o eiciency can be written: k e V c,e = (5.27) V m The eective conining pressure may be deined as a unction o the coeicient o eiciency. In turn, this may be expressed as the product o a horizontal and vertical coeicient o eiciency, k H and k V, respectively: l,e = ke l = kh kv l (5.28) (8) When spiral FRP sheets are used, the eectiveness o FRP coninement is penalized by ibers inclinations. Indicating with α the FRP iber inclination with respect to the horizontal plane o the member cross section, the ollowing coeicient can be deined: k α = tg α (5.29) Such coeicient shall multiply the lateral conining pressure, 1, reported in Equation (5.28). FRP strengthening perormed with FRP bars inserted in holes shall not be aected by such coeicient. (9) To restrict axial deormation and prevent damage at serviceability limit state, the increased axial capacity due to FRP coninement shall not be larger than 50 % o the design compressive strength, md, o the unconined member Coninement o circular columns (1) The geometric ratio o FRP conined members when both FRP sheets and bars are employed can be deined as ollows: 4 t b ρ = D p ρ n A b b, b = D pb (5.30) where: - t is the FRP thickness. - b is the FRP strip width. - D is the masonry cross-section diameter. - p is the center-to-center spacing o FRP strips. 99

110 - n b is the number o bars installed in the generic layer o bars (or circular cross section it is assumed that all layers are realized with the same number o bars). - A b is the cross sectional area o each FRP bar. - p b is the center-to-center distance between two subsequent layers o bars along the same direction. In case o continuous FRP wrapping, the ratio ρ becomes equal to 4 t D. (2) Via equilibrium, the conining pressure, 1, can be calculated as ollows: 1 l = ( ρ E + 2 ρb Eb ) εd,rid (5.31) 2 where E and E b are the Young modulus o elasticity o FRP sheets and bars, respectively, and ε d,rid represents the reduced design value o the FRP strain measured at column collapse. (3)P In case o combined use o FRP sheets and bars, the reduced design strain or FRP reinorcement can be written as ollows: (r) (r) (b) (b) { } ε = min η ε γ ; η ε γ (5.32) d,rid a k a k where a r b k ε k represent ultimate strain o FRP sheets and bars, respectively; and ( r γ ) and ( b γ ) are the partial actors o FRP sheets and bars, respectively (Table 3-2; or FRP bars, not included in the table, a value o ( b γ ) = 1.50 is recommended). η is the environmental conversion actor (Table 3-4); ε ( ) and ( ) (4) For circular cross section strengthened with FRP sheets, the horizontal coeicient o eiciency, k H, can be assumed equal to 1. For continuous vertical FRP wrapping, the coeicient o vertical eiciency, k V, is assumed equal to 1. For spiral FRP wrapping, the eectiveness o FRP strengthening shall appropriately be reduced by means o the k α coeicient (Eq. (5.29)). (5) When discontinuous FRP reinorcement having a strip width b and center-to-center spacing p is used, the coeicient o vertical eiciency, k V, can be assumed as ollows (Figure 5-7): ' p k V 1 = 2 D 2 (5.33) where p is the net distance between FRP strips. (6) Coninement with FRP bars inserted in holes drilled through the member are less eective than external wrapping with FRP sheets. Such applications shall thereore be careully analyzed. When FRP bars are used or strengthening masonry columns, staggering o bars along the vertical direction is necessary; moreover, the center-to-center distance between dierent layers o bars shall 100

111 not exceed D 5. (7) Similar to discontinuous wrapping with FRP sheets, the reduction o coninement eectiveness o masonry columns strengthened with FRP bars is to be attributed to the stress diusion phenomenon, which may be described by a parabolic relationship with a starting slope o 45 located at the termination point o the FRP reinorcement. Unless a more detailed analysis is available, the coeicient o eiciency deined by Equation (5.27) can be evaluated rom Equation (5.33) with p replaced by the center-to-center spacing between FRP bars, p b. Unconined area Figure 5-7 Front view o circular masonry member conined with discontinuous FRP strips Coninement o prismatic columns (1)P FRP coninement o non-circular cross sections shows only a slight increase in the load carrying capacity. Such applications shall thereore be careully analyzed. (2)P Prior to FRP wrapping o the masonry member, a minimum 20 mm radius (rounding radius) when the sheet is wrapped around outside corners shall be provided. (3) The conining pressure, 1, o a rectangular member having dimension bxd can be calculated as ollows: 1 l = min { ρ, x E+ 2 ρb, x Eb ; ρ, y E+ 2 ρb, y Eb} εd, rid (5.34) 2 where the non-dimensional parameters 5-8): ρ, x, ρ, y, ρ b, x, and ρ b, y are deined as ollows (Figure ρ,x 4 t b = d p 4 t b ρ = b p,,y, ρ bx, nb, x A = p d b b, ρ by, nb, y A = p b b b (5.35) and n b, x and n b, y represent the number o bars in the x and y direction, respectively. Only or the case o continuous FRP wrapping, the conining pressure can be calculated according to Equation (5.31), assuming ρ = 4 t max{ b, d} and ρ b = 0. (4) Figure 5-8 shows a rectangular cross section conined with a continuous FRP reinorcement. 101

112 Due to the arch-eect displayed in the igure, the conined section is only a portion o the total area o the masonry column. The extension o the conined area depends on the adopted rounding radius. Unconined area Figure 5-8 Coninement o rectangular sections externally wrapped with FRP. (5) The horizontal coeicient o eiciency is given by the ratio between the conined area and the total area o the masonry column, A m, as ollows: k H '2 '2 b + d = 1 3 A m (5.36) where b and d are dimensions indicated in Figure 5-8. (6) Unless experimental testing is available, FRP coninement o rectangular member with aspect ratio ( bd ) larger than 2 or when max { b, d} > 900mm shall be neglected. (7)P The combined use o external FRP wrapping and internal FRP bars inserted in holes drilled through the member cross section may increase the area eectively conined or square, rectangular, or more complex cross sections (Figure 5-9). Figure 5-9 Coninement o masonry members with FRP sheets and bars. (8) When discontinuous FRP reinorcement has a strip width b and center-to-center spacing p is used, the coeicient o vertical eiciency, k V, can assumed as ollows (Figure 5-7): ' p kv = 1 2min{, bd } 2 (5.37) For spiral FRP wrapping, the eectiveness o FRP strengthening shall appropriately be reduced by means o the k α coeicient (Eq. (5.29)). (9) When FRP bars are used or strengthening masonry columns, staggering o bars along the 102

113 vertical direction is necessary. With reerence to Figure 5-10, it can be assumed that the area o the eectively conined masonry is reduced with respect to the total member area due to the arch eect between dierent layers o FRP reinorcement. (10) The reduction o the eectively conined area between layers o dierent FRP reinorcement is due to the stress diusion phenomenon described by a parabolic relationship with a starting slope o 45 (Figure 5-10). c y p b d c x p b b Figure 5-10 Plan and lateral view o coninement with FRP bars. (11) Unless a more appropriate determination o the portion o the eective conined volume is made, the coeicient o eiciency, k e, according to Equation (5.27) can be assumed as ollows: 1 nbx 1 d nby 1 b 3 p b ke = kh kv = nbx b nby d nbx n by 2 min { b, d} 2 (5.38) In case o square cross sections, the coeicient o eiciency reduces to the ollowing: 1 4 nb 1 pb ke = kh kv = nb 2 b 2 (5.39) where b is the member width and n bx = nby = nb. (11) FRP bars inserted in holes drilled through the strengthened masonry member shall be anchored or a length at least equal to 10 times the FRP bar diameter. When such length is greater than 1/5 o the FRP bar length, the anchorage orce should be adequately spread at the two bar ends. (12) Horizontal and vertical FRP bar spacing shall not be greater than hal o the width o the strengthened member; similarly, the distance between the member edge and the FRP bar closer to the edge itsel shall not be larger than 1/4 o the member width. 5.7 DESIGN FOR SEISMIC APPLICATIONS Design objectives (1)P FRP strengthening o masonry structures subjected to seismic loads can be perormed when the unstrengthened member does not satisy one or more limit states according to the current build- 103

114 ing code. (2)P This part o the document recognizes the provisions o the current building code as well as the indications provided in the most updated literature related to seismic constructions; particular importance is given to the ollowing: Evaluation o seismic saety. Saety requirements (veriication o limit states). Levels o seismic protection (magnitude o the associated seismic action). Methods o analysis. Veriication criteria (distinction between ductile and brittle members). Materials characteristics to be used or design Selection criteria or FRP strengthening (1)P Type and size o selected FRP systems shall take into account the ollowing: Masonry structure unable to withstand vertical and horizontal loads shall be strengthened or replaced. Walls ending on masonry T-junctions or masonry edges shall be appropriately connected. Unsatisactory connections between loors/roo and vertical walls shall be made eective. Horizontal orces generated rom roos, arches, and vaults shall be taken by appropriate structural members. Floors eectively connected to vertical walls shall be properly stiened in their plane to be able to transer horizontal orces to the vertical walls located in the earthquake direction. They also shall provide restraint to the movement o vertical walls located in the earthquake orthogonal direction. Weak members or which strengthening is not appropriate shall be eliminated. In case o strongly irregular buildings (in term o resistance and/or stiness), FRP strengthening is usually unable to provide relie to the structure. It may be used or ew structural members to grant a minimum regularity to the structure. FRP strengthened members where local ductility is enhanced are always recommended. Local FRP strengthening shall never reduce the overall ductility o the structure. (2)P FRP retroitting is typically aimed at the ollowing: Total or partial strengthening, replacing, or rebuilding o structural members. Modiying the overall structural behavior by means o connection o dierent structural members. (3)P Design o FRP reinorcement shall include the ollowing: Rational choice o the retroitting technique. Choice o the appropriate technique and/or material. Preliminary dimensioning o FRP reinorcement. Structural analysis, taking into account the FRP strengthened structure. Saety checks o the strengthened structure perormed on strengthened and newly added members (or existing, repaired, or strengthened members saety checks shall be carried out according to this Guideline; or newly added members, saety checks shall be in compliance with the current building code). (4)P FRP strengthening in a seismic area shall be aimed at the ollowing: Increase lexural and shear capacity o masonry panels ensuring transer o tensile stresses within single members or between adjacent members. Eliminate horizontal orces applied orthogonally to the masonry walls. Connect members resisting horizontal loads to achieve a box-like behavior o the structure. 104

115 In-plane loors stiening to achieve a sti diaphragm behavior. Limiting crack width to improve energy dissipation. Conining columns to increase material strength and ductility. (5)P The FRP-based retroitting strategy shall ollow the principle o increasing the capacity o under-designed members, with the aim o achieving at the same time a greater structural regularity and elimination o possible local collapse o masonry walls or structural components. (6) Seismic eiciency o the designed retroitting technique may be measured by the increase o horizontal displacement o the strengthened member close to collapse. (7)P To avoid seismic vulnerability o masonry structures, care shall be taken to ensure that the FRP system will not decrease the overall ductility o the structure. Particular care shall be taken to remedial work aiming at joining vertical columns to avoid ormation o hinges in arches and vaults. It is preerable to increase hinges ductility o both masonry columns and vaults. Similarly, or bracing walls o ordinary buildings, FRP reinorcement shall be placed such to increase the overall structural ductility and to make sure that the collapse o tie areas will anticipate the rupture o columns. 5.8 INSTALLATION, MONITORING, AND QUALITY CONTROL (1)P Several aspects inluence the eectiveness o FRP material used as externally bonded systems or strengthening o masonry members. In addition to those discussed in previous chapters, surace preparation and FRP installation will be dealt with in this section. The relative importance o each o these aspects depends on whether reerence is made to applications deined as bondcritical (lexure or shear) or contact-critical (coninement). For example, some tests on the quality o the substrate can be omitted or contact-critical applications (e.g., coninement by wrapping) or when the FRP system is properly anchored provided that its eectiveness is tested by an independent laboratory. (2)P Once FRP strengthening has been carried out, over time monitoring by non destructive or semi-destructive tests as listed in the ollowing sections shall be perormed to ensure the eectiveness o the proposed strengthening solution. (3)P This document describes the tests that can be carried out or quality control as well as over time monitoring o the selected FRP system. The type and number o tests to be perormed shall be linked to the importance o the application by taking into account the ollowing: For strategic buildings when their unctionality during seismic events is o undamental importance or civil protection or when their roles become relevant due to the consequences o a possible collapse. Historical and cultural value. Whether FRP application concerns primary structural members (e.g., vaults, domes, columns, arches, walls) or secondary elements. The extent o FRP application compared to the size o the structure. (4)P The numerical values indicated in the ollowing are to be understood as suggested values Quality control and substrate preparation (1)P Quality control o the support implies determination o the masonry conditions, removal, and reconstruction o any deteriorated or loose masonry block, cleaning, and removal o a portion o masonry subjected to moisture, vegetation plants, or similar. (2)P When special devices are used to properly anchor the selected FRP system, testing o such devices shall be conducted in compliance with available standardization documents. Anchoring de- 105

116 vices shall be installed according to the manuacturer/supplier speciications regarding both material used as well as surace preparation, environmental conditions, and sequence o each phase. The investigation shall also evaluate the eect o such parameters on the inal result Evaluation o substrate deterioration (1) Prior to FRP application, tests on the homogeneity o the portion o the structure to be strengthened shall be perormed to ensure proper quality o the masonry support. 2 (2) Mechanical characterization tests on masonry shall be at least 1 every 100 m o area to be strengthened, with a minimum o 2 tests or each homogeneous area. Tests shall be perormed according to at least o one o the ollowing categories: Compression test on a masonry specimen. Shear test on a masonry specimen. Flat jack test. Shear test by jack. Dilatometer test. Ultrasonic test. (3) When homogeneity tests are perormed on the entire area to be strengthened with the exception o critical areas, they shall be distributed according to a square mesh spaced 1 m apart or areas 2 smaller than 5 m, and proportionally increased or larger areas. Tests shall be perormed as ollows: Hand hammering o the interested area. X-ray analysis. Ultrasound speed in near-surace mode. Recording speed o sonic pulse (with instrumented hammer and accelerometers). Penetrometry. Thermography. Tomography Removal and reconstruction o deective masonry support (1) Masonry substrate may have undergone physical-chemical, physical-mechanical or impactcaused deterioration. Deteriorated masonry shall be removed rom all damaged areas (2) Removal o deective masonry allows examining characteristics o both natural or artiicial masonry as well as mortar. When exoliation, pulverization, cracking, or chemical attack processes are in place, it is necessary to remove all deective areas and protect them with appropriate inhibitors. (3) Once all deteriorated masonry has been removed, and suitable measures have been taken to prevent urther deterioration o the existing substrate as well as all other phenomena causing masonry degradation (e.g., water leakage, vegetation), masonry restoration using masonry-compatible materials shall be perormed. Roughness o masonry between 10 and 20 mm shall be leveled with compatible epoxy paste; speciic illing material shall be used or unevenness larger than 20 mm. Crack widths wider than 0.5 mm shall be closed using epoxy injection methods beore FRP strengthening can take place. (4) To improve the bond between masonry support and FRP, sandblasting o the portion o masonry surace to be strengthened shall be perormed. Sandblasting shall provide a roughness degree 106

117 o at least 0.3 mm; such level o roughness can be measured by suitable instruments, such as a laser proilometer or an optical proile-measuring device. (5) Poor quality masonry suraces that do not require remedial work beore FRP application should be treated with a reinorcing agent prior to primer installation. (6) Cleaning o the surace to be strengthened shall remove any dust, laitance, oil, surace lubricants, oreign particles, or any other bond-inhibiting material. (7) All inside and outside corners and sharp edges that require FRP strengthening shall be rounded or chamered to a minimum radius o 20 mm Recommendations or the installation (1) FRP strengthening o masonry structures is highly dependant upon environmental temperature and humidity as well as the characteristics o the substrate. In addition to the above mentioned measure, and regardless o the strengthening type, urther speciic measures to ensure quality o FRP installation are highlighted in the next sections Humidity and temperature conditions in the environment and substrate (1) It is suggested not to install FRP material when the environment is very moist; a high degree o humidity may delay curing o the resin and aect the overall perormance o the FRP system especially or wet lay-up applications. (2) FRP systems shall not be applied to substrates having a surace humidity level greater than 10 %; such conditions could delay penetration o the primer in the concrete pores and generate air bubbles that could compromise bond between concrete and FRP system. Substrate humidity may be evaluated with a hygrometer or mortar or simply by employing absorbent paper. (3) FRP material shall not be applied i both environment and surace temperature is too low, because curing o the resins as well as ibers impregnation could be compromised. It is also recommended not to install FRP material when the masonry surace is heavily exposed to sunlight. It is suggested not to apply any FRP material i temperatures all outside the range o 10 to 35 C. In low temperature environments where the construction site schedule does not allow FRP installation to be delayed, it is suggested to artiicially heat the locations where FRP reinorcement is to be applied. (4) I curing o FRP reinorcement takes place under rainy conditions, heavy insulation, large thermal gradients, or in presence o dust, protective measures can be employed to ensure proper curing Construction details (1) Anchorage lengths o at least 300 mm shall be provided or the end portion o FRP systems used or strengthening masonry members. Alternatively, mechanical connectors may be used. (2) Proper ibers alignment shall be provided or in-situ wet lay-up application; waving o FRP reinorcement shall also be avoided during installation. (3) When semi-destructive tests are planned, it is suggested to provide additional strengthening areas ( witness areas ) in properly selected portions o the structure having dimensions o at least x300 mm, with a minimum extension o 0.15 m nor less than 0.5 % o the overall area to be 107

118 strengthened. Witness areas shall be realized at the same time o the main FRP installation, using the same materials and procedures in areas where removal o FRP strengthening system does not imply alteration o the ailure mechanisms. In addition, witness areas shall be exposed to the same environmental conditions o the main selected FRP system and shall be uniormly distributed on the strengthened structure Protection o FRP systems (1) For outdoor FRP applications it is recommended to protect the FRP system rom direct sunlight, which may produce chemical-physical alterations in the epoxy matrix. This can be achieved by using protective acrylic paint provided that cleaning o the composite surace with a sponge soaked in soap is perormed. (2) Alternatively, a better protection can be achieved by applying plastering or mortar layer (preerably concrete-based) to the installed strengthening system. The plaster, whose thickness is recommended by the FRP manuacturers/suppliers, is to be laid on the strengthening system ater treating the surace by means o epoxy resin applications with subsequent quartz dusting green-ongreen. The inal layer is particularly suitable to receive any kind o plastering. (3) For ire protection, two dierent solutions may be adopted: use o intumescent panels, or application o protective plasters. In both cases, manuacturers/suppliers shall indicate the degree o ire protection as a unction o the panel/plaster thickness. The panels -generally based on calcium silicates- are applied directly on the FRP strengthening system, provided that ibers will not be cut during their installation. Protective plasters represent the most widely adopted solution or ire protection; they shall be applied to the FRP system as indicated beore. Protective coatings o adequate thickness and consistency capable o keeping the composite temperature below 80 C or 90 minutes are available Quality control during installation (1) Quality control during FRP installation should include at least one cycle o semi-destructive tests or the mechanical characterization o the installation itsel, and at least one non destructive mapping to ensure its uniormity Semi-destructive tests (1) Both pull-o tests and shear tearing tests may be carried out. Semi-destructive tests shall be carried out on witnesses and, where possible, in non-critical strengthened areas at the rate o one 2 test or every 5 m o application, and, in any case, not less than 2 per each type o test. (2) Pull-o test. The test is used or assessment o the properties o the restored substrate; it is carried out by using a 20 mm thick circular steel plates with a diameter o at least 40 mm. Ater the steel plate is irmly attached to the FRP, such steel plate is isolated rom the surrounding FRP with a core drill rotating at a speed o at least 2500 rpm; particular care shall be taken to avoid heating o the FRP system while a 1-2 mm incision o the masonry substrate is achieved. FRP application may be considered acceptable i at least 80 % o the tests (both in case o only two tests) return a pull-o stress not less than 10 % o the compressive strength o the support provided that ailure occurs in the substrate itsel. (3) Shear tearing test. The test is particularly signiicant to assess the quality o bond between FRP and masonry substrate. It may be carried out only when it is possible to pull a portion o the FRP system in its plane located close to an edge detached rom the masonry substrate. FRP applica- 108

119 tion may be considered acceptable i at least 80 % o the tests (both in the case o two tests) return a peak tearing orce not less than 5 % o the compressive strength o the support Non destructive tests (1) Non destructive tests may be used to characterize the uniormity o FRP application starting rom adequate two-dimensional survey o the strengthened surace with a dierent spatial resolution as a unction o the strengthening area (see Table 5-1). Table 5-1 Minimum resolution or deects thickness to be identiied with non destructive tests. Shear stress transer at interace Example Non destructive test Surace mapping grid Minimum resolution or deects thickness absent wrappings, with the exception o the overlapping area in single-layer application optional 250 mm 3 mm weak central area o very extensive reinorcement optional 250 mm 3 mm moderate central area o longitudinal lexural strengthening suggested 100 mm 0.5 mm critical anchorage areas, overlapping areas between layers, stirrups or shear strengthening, interace areas with connectors, areas with large roughness or cracks in the substrate required 50 mm 0.1 mm (2) Stimulated Acoustic testing. Similar to impact-echo testing, such tests rely on the dierent oscillatory behavior o the composite layer depending on the bond between FRP layers and substrate. In its most basic version, such a test may be carried out by a technician hammering the composite surace and listening to the sound rom the impact. More objective results may be obtained with automated systems. (3) High-requency ultrasonic testing. They should be carried out using relection methods with requencies no less than 1.5 MHz and probes with a diameter no greater than 25 mm, adopting the technique based on the irst peak amplitude variation to localize deects. (4) Thermographic tests. They are eective only or FRP systems with low thermal conductivity and can not be applied to carbon or metallic FRP strengthening systems unless special precautions are taken. The heat developed during the test shall be smaller than the glass transition temperature o the FRP system. (5) Acoustic emission tests. The technique is based on the acoustic emission (AE) method and allows the assessment o a damage inside a structural member subjected to loading by listening to and recording the sound generated by either ormation o cracks or delamination phenomena that propagates as elastic waves. Such a test is particularly suitable or detecting deects in the application o FRP composites masonry structures as well as the occurrence o delamination rom the substrate Personnel qualiication (1) Personnel in charge o the tests shall have one o the three qualiication levels speciied in Table 5-2, according to UNI EN 473 and UNI EN

120 Level 1 Level 2 Level 3 Table 5-2 Qualiication levels to perorm semi and non-destructive tests. Proper knowledge o tests equipment; perorming tests; recording and classiying test results according to written criteria; writing a report on test results. Choosing the way o perorming the test; deining the application limits o the test or which the level 2 technician is certiied; understanding test speciications and translating them into practical test instructions suitable to the in-situ working conditions; adjusting and calibrating test equipments; perorming and controlling the test; interpreting and evaluating test results according to the speciications to comply with; preparing written test instructions or level 1 personnel; perorming and supervising all level 1 unctions; training personnel o level 1; organizing test results and writing the inal report. Be in charge o a laboratory acility; establishing and validating test techniques and procedures; interpreting speciications and procedures; having the skill to evaluate and understand test results according to existing speciications; having a suicient practical knowledge o materials, production methods and installation technology o the system to be tested to be able to choose appropriate methods, establish techniques and collaborate in the deinition o acceptance criteria when they are not pre-established; be knowledgeable in dierent application ields; being able to lead personnel o level 1 and Monitoring o the strengthening system (1) Due to the poor availability o data regarding long term behavior o FRP systems used or strengthening masonry structures, it is recommended to perorm appropriate monitoring o the installed FRP system by means o semi and non-destructive tests periodically conducted on the strengthened structure. The aim o such a monitoring process is to keep the ollowing parameters under control: Temperature o the installed FRP system. Environmental humidity. Measure o displacements and deormations o the strengthened structure. Potential damage o ibers. Extensions o deects and delaminations in the installed FRP system. 110

121 6 APPENDIX A (MANUFACTURING TECHNIQUES AND STRESS-STRAIN RELATIONSHIP OF ORTHOTROPIC LINEAR ELASTIC MATERIALS) 6.1 MANUFACTURING TECHNIQUES Pultrusion Pultrusion is a technology mainly used or production o iber-reinorced laminates. Such products are widely utilised in civil engineering ield. This technology is based on a continuous manuacturing process, consisting o three main phases: Forming. Impregnation. Hardening. In the most common version designed or thermosetting resin, the components (resin and ibers) are separately ed into a machine that catches and pulls the ibers through the dierent production stages. A widespread version o the process includes impregnation with resin bath, as shown in Figure 6-1. Figure 6-1 Pultrusion process with resin bath impregnation. The ibers are taken directly rom the rovings and conveyed to a resin bath where impregnation takes place. Bundles o impregnated ibers enter the heating die where the material is ormed and crosslinked under high pressure. During this phase, gaps between ibers are eliminated to ensure proper continuity in the transverse direction. Heating is generally supplied by electrical resistances and the temperature is controlled by means o thermocouples. The duration o the heating stage is regulated by production speed. Upon exiting rom the die, the matrix is cured and the composite it is pulled at a constant speed. At the end o the process the material is cut to length. Fabric layers may be added to ensure strength o FRP in directions other than the longitudinal. Weaving, winding, and twisting may be carried out directly on the production line with special equipment. FRP pultruded material is light, corrosion-resistant, with constant cross section and thicknesses up to ew centimeters. Typically pultruded products include laminates, bars, structural shapes (C, double T, etc.), panels and plates. They are used as internal and external reinorcement or existing and new structures, structural components or transportation, supports or lighting and billposters, risers 111

122 or oil industry, etc Lamination Lamination is used nearly exclusively to produce innovative and high perormance composites. It is a discontinuous process that allows producing laminates o maximum thickness up to ew centimeters by totally controlling iber orientation and the complexity o the structure. Compared to pultrusion, it allows a nearly complete reedom as to iber orientation and curvature o produced material is concern. The main limitation regards the speed o production, which is roughly 0.5 kg/h or simple components. The ollowing undamental phases can be identiied in the lamination process: a) Material preparation. b) Lamination (cut o material, stacking o plies and compaction). c) Vacuum bag preparation. d) Material curing (at room temperature, oven, or autoclave). e) Inspection (visual, by ultrasound and X-rays). ) Finishing (cutting o edges with cutters or high pressure water jet). Lamination may be carried out with dry ibers impregnated during ield installation, or preimpregnated ibers running in either one or multiple directions. The next phase in the lamination process requires preparation o vacuum bag (phase c) as it is shown in Figure 6-2. The vacuum allows or a ast removal o solvents and entrapped air in the laminates prior to complete curing o the resin. Figure 6-2 Lamination system. The main advantage o this technology is the extreme versatility that allows producing o complex components using inexpensive molds. Main applications reer to the aeronautical and aerospace ields, car racing, sailing, and transportation. FRP strengthening o columns or RC beams by means o dry or pre-impregnated ibers represents one ield o application where lamination can eectively be used in the construction ield. 6.2 MECHANICAL BEHAVIOR OF COMPOSITES Fiber-reinorced composites are heterogeneous (e.g., made o dierent materials) and anisotropic (e.g., exhibiting dierent properties when tested in dierent directions) materials. Because the application related to iber-reinorced composites or civil engineering is ar greater than the material micro-structure (see Table 2-2), the heterogeneity may be neglected, and the actual material may be considered to behave homogeneously. I the stress and strain at a generic location o iberreinorced composite may be represented by the components o the tensor o stress σ (Figure 6-3) 112

123 and strainε, the mechanical behavior o a homogeneous, elastic, and anisotropic solid may be deined by 21 independent elastic constants as ollows: Figure 6-3 Representation o stresses or an ininitesimal element. σ 1 C11 C12 C13 C14 C15 C16 ε1 σ 2 C12 C22 C23 C24 C25 C 26 ε 2 σ 3 C13 C23 C33 C34 C35 C 36 ε 3 σ = [ C] ε = τ 23 C14 C24 C34 C44 C45 C46 γ 23 τ 31 C15 C25 C35 C45 C55 C 56 γ 31 τ 12 C16 C26 C36 C46 C56 C66 γ 12 (6.1) where [ C ] is the stiness matrix. The complete characterization o the stiness matrix would require the evaluation o the 21 constants by means o combinations o tensile and shear tests. The number o tests to be perormed can signiicantly be reduced i the material has some degree o symmetry, a circumstance that occurs in a majority o iber-composite materials having engineering interest. Many unidirectional composites may be considered transversely isotropic, as it is shown in Figure 6-4, where the 2-3 plane perpendicular to ibers is the isotropy plane. In this case, the independent elastic constants reduce rom 21 to 5 and the stiness matrix becomes: C11 C12 C C12 C22 C C 12 C23 C C = 1 (6.2) ( C22 C23 ) C C66 [ ] 113

124 Figure 6-4 Unidirectional composite with a transverse isotropy plane. It is oten convenient to reer to the so-called engineering constants: E (Young modulus o elasticity), ν (Poisson ratio), and G (shear modulus) or which well-established procedures or their experimental evaluation exist. Such constants have generally dierent values in dierent directions. The Young modulus o elasticity in the iber direction, E 1, may be expected to be greater compared to the transverse direction, E 2, which in turn can be dierent rom that in the third direction, E 3. The same consideration is applied to the modules G 12, G 13, G 23 (directions 1, 2, and 3 are deined according to Figure 6-4). The deormability matrix [ S ], deined as the matrix inverse o the stiness matrix [ ] can be expressed as a unction o the engineering constants as ollows: C (Eq. (6.2)), [ S] 1 ν12 ν E1 E1 E 1 ν12 1 ν E1 E2 E 2 ν12 ν E1 E2 E2 = 2 ( 1+ ν 23 ) E G G12 (6.3) The independent engineering constants are as ollows: E 1, E 2, ν 12, ν 23, G 12 For unidirectional thin laminate subjected to plane stresses, the deormability matrix becomes: 114

125 1 ε E1 1 = ν ε 2 E γ ν E 1 E σ 1 0 σ 2 1 τ 12 G12 (6.4) The mechanical behavior o unidirectional laminates can thereore be characterized by our independent elastic constants. For their determination, uniaxial tensile tests are typically carried out with ibers inclined with an angle θ with respect to the direction o the applied load. By setting θ = 0 (e.g., ibers parallel to the load direction), E 1 and ν 12 may be obtained, while with θ = 90 (ibers perpendicular to the direction o load), E 2 may be determined. G 12 can be determined depending upon the choice o the angle θ as a unction o the selected strengthening geometry. Approximate values o the mentioned elastic constants can also be determined with simple micromechanical models based on properties o each components (ibers and matrix) and their volumetric raction. For unidirectional laminate, longitudinal properties may be evaluated by using a relationships known as the rule o mixtures. It derives rom the application o a simple micromechanical model where ibers and matrix work in parallel. The model provides good results or the value E 1 o the Young modulus o the elasticity in the ibers direction and the Poisson ratio ν 12 : E = V E + (1 V ) E, 1 ib ib ib m ν = V ν + (1 V ) ν, 12 ib ib ib m (6.5) where V ib is the iber volumetric raction (ratio between the volume o ibers and the overall volume o composite); E ib and E m are the Young modulus o elasticity o ibers and matrix, respectively; and ν ib and ν m are the corresponding Poisson ratios. Instead o the volumetric raction, the weight raction o ibers and matrix, P ib and P m, respectively, are more oten known. I ρ ib and ρ m represent the density o ibers and matrix, respectively, the ollowing relationships apply: V P ib ib = P ib ib ib m m + P = 1. m P ρ ρib + P ρ, (6.6) As an example, the computation o the volumetric raction o ibers in a glass-iber reinorced composite having weight raction equal to 60 %, is presented. The characteristics o each o the components are reported in Table 6-1. Table 6-1 Weight raction Density [g/cm 3 ] Fiber Matrix By applying Eq. (6.6), a volumetric raction o glass ibers equal to 42 % is obtained. Considering 115

126 the values o both ibers ( E ib = 80 GPa, ν ib = 0. 3) and matrix ( E m = 3 GPa, ν m = ) mechanical properties, the ollowing values o the elastic constants can be obtained. E 1 = 35.2 GPa ν 12 = 0.32 For more details on micro-mechanical modes the reader should reer to specialized literature Eect o loading acting on directions other than that o material symmetry Once the elastic constants o the material are known, the behavior o iber-reinorced material is completely determined or any loading direction irrespectively o the axes o symmetry o the material. For example, Figure 6-5 relates to a laminate with continuous unidirectional ibers; the equivalent elastic constants E x, Ey, Gxy and ν xy, reerred to the reerence axes x and y o the load system may be determined as a unction o the angle θ and the elastic constants o the material E, E, G ν , 12 G xy In Figure 6-6 and Figure 6-7, the values o both Young modulus o elasticity, E x, and shear modulus,, are plotted as a unction o the angle, θ, between ibers and applied load, or dierent values o the modulus E 1. Figure 6-5 Deinition o the reerence systems x, y and 1,

127 Figure 6-6 Young modulus o elasticity E x as a unction o θ or iber-reinorced composites or several values o the Young modulus o elasticity E 1 ( E 2 = 5 GPa ; G 12 = 3 GPa ; ν 12 = 0. 35). The signiicant variations o the modules E x and G xy with the angle θ are apparent. In case o abrics, ibers are distributed along two or more directions (multi-axial abrics). I one were to neglect the crimping due to weaving o ibers and assuming the abric made out o two separated unidirectional layer o ibers running at 0 and 90 direction, the modulus o elasticity, E x, can be evaluated with simpliy methods neglecting the slip between layers. For the particular case on abric having the same percentage o ibers in the two considered directions (balanced abric), Figure 6-8 plots the relationship between E and θ. x Figure 6-7 Shear modulus G xy as a unction o θ or iber-reinorced composites or several values o the Young modulus o elasticity E 1 ( E 2 = 5 GPa ; G 12 = 3 GPa ; ν 12 = 0. 35). 117

128 Figure 6-8 Modulus o elasticity, E x, as a unction o θ or balanced abric depending upon the modulus o elasticity, E 1 ( E 2 = E 1 ; G 12 = 3 GPa; ν 12 = 0.35) Failure criteria The micro-mechanic collapse mechanism o iber-reinorced materials is a complex phenomenon that depends on a multitude o parameters that include type o loading, and iber and resin type. For such a reason, ailure criteria or composites usually reer to the macro-mechanical level assuming that the composite itsel can be regarded as a homogeneous material exhibiting a linear elastic behaviour up to collapse. In the case o laminates subjected to a planar stresses, one o the simplest ailure criteria is that o the maximum stress. I σ 1u, t ( σ1u,c ) and σ 2u, t ( σ 2u,c ) represent the tensile (compressive) ailure stress in the symmetry directions, and τ 12u is the corresponding shear stress at ailure, this criterion can be represented as ollows: σ1u,t per σ1 > 0, σ1 σ1u,c per σ1 < 0, σ2u,t per σ2 > 0, σ 2 σ2u,c per σ2 < 0, τ τ u (6.7) The criterion does not depend on the sign o the shear stress nor does it consider the interactions between dierent ailure modes. Dierent ailure modes can occur irrespectively one rom another. The maximum stress that the laminate can withstand is given by the lowest among the ollowing values (Figure 6-5): σ σ σ 1u xu 2 2u xu 2 xu σ <, cos θ σ <, sin θ τ12u <. sinθ cosθ (6.8) 118

129 Figure 6-9 shows the variation o σ xu as a unction o θ. Figure 6-9 Criterion o maximum stress: Tensile ailure stress as a unction o θ or unidirectional laminates ( σ 1u =1600 MPa, σ 2u = 40 MPa, τ 12u = 70 MPa ). The criterion o the maximum stress is usually in good agreement with experimental data only or tensile test with θ smaller than 15 and larger than 45. Otherwise, the measured values or compression are quite higher. Another widely used criterion to estimate the ailure o a laminate is due to Tsai-Hill, which may be expressed as ollows: σ 1 σ 2 σ1 σ 2 τ σ1u σ2u σ1u τ12u (6.9) The stress at ailure as unction o θ can be written as ollows (Figure 6-5): 4 4 cos θ sin θ σxu = + cos θ sin θ σ1u τ12u σ1u σ2u 1 2 (6.10) and it is plotted in Figure

130 Figure 6-10 Tsai-Hill criterion: tensile ailure stress as a unction o θ or unidirectional laminates ( σ 1u =1600 MPa, σ 2u = 40 MPa, τ 12u = 70 MPa ). As it is previously shown, the great variability o elastic and strength properties o iber-reinorced materials depends upon the direction o the ibers compared to the direction o applied load. 6.3 MECHANICAL CHARACTERIZATION TESTS FOR FIBER-REINFORCED MATERIALS The mechanical characterization o composite materials is generally more complex than or any other materials due to their signiicant anisotropy. This has led to either modiication o existing test methods related to isotropic material as well as the deinition o new tests suitable or anisotropic material. The great variety o existing test methods or the characterization o physical and mechanical properties o iber-reinorced composites makes their detailed description too long to be addressed in this document. For inormation the reader is reerred to speciic tests as well as international standards such as the International Organization or Standardization (ISO) and the American Society or Testing and Materials (ASTM) which have been reerenced in the technical data sheet o chapter 2 o this document. Speciic test methods are also available in a number o guidelines, design recommendations and technical documents, including: - ACI 440.3R 04 Guide Test Methods or Fiber-reinorced Polymers or Reinorcing or Strengthening Concrete Structures ; - JSCE (1995) Test methods or continuous iber reinorcing materials ; - JSCE (2000) Test methods or continuous iber sheets ; - ISO (TC71/SC6N) Non-conventional strengthening o concrete - Test methods-part 1: Fiber strengthened polymer (FRP)bars and grids ; - ISO (TC71/SC6N) Non-conventional strengthening o concrete - Test methods-part 2: Fiber strengthened polymer (FRP) sheets. The phase o specimen preparation is o undamental importance because the quality o the samples has a great impact on the mechanical properties. The specimen subjected to testing shall be identical as much as possible to that realized during the in-situ installation in compliance to Section 2.4. The technique adopted or specimen preparation changes depending upon the preparation site (ield site or laboratory), the nature o materials (iber and resin type), and the adopted strengthening system 120

131 (unidirectional or multi-directional dry abrics, pre-impregnated abrics, pultruded laminates). Specimen laboratory preparation allows or a better control o sampling; conversely, on-site preparation is more signiicant or the speciic application. There are many important issues related to specimen preparation. Some o the most relevant irregularities may be caused by the ollowing actors: Misalignments o ibers during lamination. Presence o undesired contaminating agents (entrapped during the lamination process). High residual raction o gaps (poor debulking). Misalignments during the inal cut o the laminate (imperect parallelism between the cut line and the main direction o the specimen). Figure 6-11 describes each phase starting rom specimen preparation to the perormance o the inal experimental test. Figure 6-11 Phases o specimen preparation. In the ollowing, recommendations are given or specimens preparation. Such recommendations are o a general nature and do not take into account a number o speciic actors related to type o material and type o application. Reerence shall be made to speciic guidelines such as ISO 1268(E) and ASTM D5687/D5687M-95. Surace parallelism and regularity: or specimen preparation, an aluminium-type plate unction as support is usually used to lay out the composite material. Ater the lamination phase is concluded, a second aluminium plate to ensure uniormity o thickness is placed on top the specimen. Both aluminium plate suraces in contact with the specimen shall be treated with a detaching layer, either in spray or ilm orm (typically PTFE), to allow easy removal o the sample ater the hardening phase. Plies orientation: layers are to be laid ollowing pre-deined lamination sequence. Removal o gaps within the laminate: it is carried out using vacuum or simply through a spatula or a roller. This operation can be carried out both at high or room temperature. Sample contamination: during lamination, samples shall be protected rom dust and any other possible contaminating agents. 121

132 Laminate hardening: the pressure and temperature to be applied or hardening o samples shall be clearly speciied by the system manuacturer. Hardening o samples may also be improved by vacuum. Surace protection: the laminate may be coated with a protective ilm to prevent surace contamination. Using protective ilms may be useul or multiple layer o reinorcement. Cutting o samples: it may be carried out with several cutting tools (diamond blades, water jet, etc.). The choice shall be made according to the material properties and the sample dimensions (thickness). When urther surace inishing is needed, abrasive paper or suitable tools can be adopted. Conditioning: when required, conditioning shall be carried out prior to testing, according to the available literature guideline. Depending upon the selected test method, tabs may be required or proper anchoring to avoid localized damage o the specimen. Tabs shall have a larger deormability compared to the specimen and a suitable length to ensure transer o loading rom the testing apparatus to the sample. Depending upon the mechanical property to be determined, dierent readings shall be taken while perorming the test. The most common measurements are reerred to the applied load, displacements, strain (by means o Linear Variable Dierential Transducers, LVDTs, or strain gages) as a unction o time. When needed, temperature and relative humidity can also be recorded. 122

133 7 APPENDIX B (DEBONDING) 7.1 FAILURE DUE TO DEBONDING The main ailure modes o FRP-strengthened structural members due to debonding are summarized as ollows: Mode 1 (plate end debonding) (Figure 7-1). The end portions o the FRP system are subjected to high interacial shear stresses or a length o approximately mm. RC beam direction o delamination laminate delamination at laminate end Figure 7-1 Plate end debonding. When strengthening is carried out with FRP laminates, tensile stress perpendicular to the interace between FRP and support (normal stress) may arise due to the signiicant stiness o FRP laminate (Figure 7-2(a)). Such a normal stress may reduce the value o interacial shear stress as shown in Figure 7-2(b). Failure mode by end debonding is characterized by brittle behavior. FRP cut-o section Interacial shear stress Normal stress Distance along FRP (a) Figure 7-2 (a) Interacial shear and normal stress along the length o a bonded FRP laminate (linear-elastic analysis); (b) Strength domain represented by interacial shear and normal stresses. Mode 2 (Debonding by lexural cracks in the beam) (Figure 7-3). Flexural cracking generates discontinuity within the support that enhances interacial shear stress responsible or FRP debonding. Cracking may be oriented perpendicular to the beam axis when lexural (b) 123

134 loads are predominant; inclined when there is a combination o lexure and shear. Figure Debonding starting rom vertical cracks in concrete. Mode 3 (Debonding by diagonal shear cracks) (Figure 7-4). For members where shear stresses are predominant compared to lexural stresses, a relative displacement between the edges o the crack is displayed. Such displacement increases normal stress perpendicular to the FRP laminate responsible or FRP debonding. Such a debonding mechanism is active irrespectively o the presence o stirrups. Collapse due to debonding by diagonal shear cracks is peculiar o our-point-bending laboratory tests; it is not common or ield application where the applied load is distributed over the beam s length. For heavily strengthened beams with low transverse reinorcement, debonding usually generates at the end plate section due to peeling. Figure 7-4 Debonding by diagonal shear crack. Mode 4 (Debonding by irregularities and roughness o the concrete surace). Localized debonding due to surace irregularities o the concrete substrate may propagate and cause ull debonding o the FRP system. This ailure mode can be avoided i the concrete surace is treated in such a way to avoid excessive roughness. 7.2 BOND BETWEEN FRP AND CONCRETE In the ollowing, additional recommendations related to bond between FRP and concrete support are given. Reerence is made to Figure 7-5; symbols are those introduced in Section

135 l b l e F max t b Figure 7-5 Maximum orce allowed to FRP reinorcement Speciic racture energy When the stiness o the concrete support is much greater compared to the stiness o the FRP system, the ollowing relationship applies: b F = b 2 E t Γ (7.1) max F between the maximum orce, F max, allowed to the FRP reinorcement considered o ininite length and the racture energy, Γ, assuming: F = b τ ( x) dx, ΓF = τb() s ds (7.2) max b 0 where t, b, E represent FRP thickness, width, and Young modulus o elasticity in the direction o the applied orce, respectively. The racture energy depends on the strength properties o both concrete and adhesive, as well as on the characteristics o the concrete surace. For properly installed FRP systems, ailure by debonding takes place on the concrete support and the speciic racture energy may be written in a similar ashion to that used or ailure mode 1 o the concrete: Γ F G b ck ctm 0 = k k [orce in N, length in mm] (7.3) where the coeicient k G shall be experimentally adjusted. The value o such coeicient has been computed over a large population o experimental results available in the literature. The statistical analysis o the results has provided an average value equal to 0.064, a standard deviation equal to 0.023, and a 5th percentile o the statistical distribution equal to When the latter value is used in Eq. (7.3), the characteristic value, Γ Fk, o the speciic racture energy is obtained. On the basis o this consideration, this Guideline suggest adopting the value o 0.03 or k G Bond-slip law Bond between FRP and concrete is typically expressed with a relationship between interacial shear stress and the corresponding slip ( τ b s relationship). Both FRP and concrete mechanical characteristics as well as geometry o the FRP system and concrete support shall be considered in the analysis. 125

136 The τ b s relationship is typically non linear with a descending branch; or design purposes, it may be treated as a bi-linear relationship as shown in Figure 7-6. The irst ascending branch is deined by taking into account the deormability o adhesive layer and concrete support or an appropriate depth. Unless a more detailed analysis is perormed, the average mechanical parameters deining the τ s relationship, can be evaluated as ollows: b τ b [N/mm 2 ] b arctg K s [mm] Figure 7-6 Bi-linear τ s relationship ( 20 MPa, k 1). b ck = - Maximum bond strength, b : The maximum experimental average bond strength can be expressed as ollows: b = kb ck ctm [orce in N, length in mm] (7.4) where ck and ctm represent the concrete characteristic compressive strength and the average concrete tensile strength, respectively; and the geometrical actor kb can be written as ollows: b = k b b 2 = b b [length in mm] (7.5) where b and b represent beam and FRP width, respectively. Equation (7.5) is valid when b b 0.33 (when b b < the value corresponding to b b = shall be adopted or k b ). - Slope, K 1, o the ascending branch: K 1 c1 = t G + t G a a c c (7.6) where G a, G c represent shear modules o adhesive and concrete, respectively; t a is the nominal thickness o the adhesive; and t c is the eective depth o concrete (suggested values or t c and c 1 are mm and , respectively). 126

137 - Interace slip corresponding to ull debonding, s : s = 0.2 mm (7.7) This value o s ensures the speciic racture energy, Γ, (represented by the area subtended the τ b s relationship) is equal to the value reported in Equation (7.3). At SLS, the τ b s relationship reduces to the ascending branch only and K 1 is given by Equation (7.6) or c 1 = SIMPLIFIED METHOD FOR DEBONDING DUE TO FLEXURAL CRACKS (MODE 2) AT ULTIMATE LIMIT STATE As an alternative to the general method reported at item 1(P) o Section 4.1.4, this simpliied method is based on the deinition o the maximum design strain, ε dd, or FRP reinorcement to be evaluated with Equation (4.7), hereater reported or the sake o completeness: ε 1 = k = k 2 Γ dd Fk dd cr cr E γd, γ E c t (7.8) This relationship is similar to that proposed or maximum stress or strain in FRP reinorcement when mode 1 FRP debonding controls. However, or a constant applied orce, the maximum interacial shear stresses are signiicantly smaller compared to that achieved close to the end o the FRP itsel due to the reduced distance between cracks. This implies that the value o maximum FRP strain related to ailure mode 2 is greater than that pertaining to ailure mode 1. These considerations have suggested adopting a magniying coeicient k cr > 1 or Equation (4.7). The calibration o k cr has been carried out on reinorced concrete beams strengthened with FRP laminates or abrics ailed by FRP intermediate debonding (mode 2). The statistical analysis o the results has provided an average value equal to 4.289, a standard deviation o 0.743, and a 5 th percentile value equal to Given the limited scattering exhibited by the application o Equation (4.6) and considering the lower brittleness o FRP intermediate debonding compared to FRP end debonding, it is suggested to use Equation (4.6) or the evaluation o the design strain, assuming k equal to 3.0 that corresponds to the 5 th percentile o the statistical distribution. cr 127

138 8 APPENDIX C (STRENGTHENING FOR COMBINED BENDING AND AXIAL LOAD OF REINFORCED CONCRETE MEMBERS) 8.1 FLEXURAL CAPACITY OF FRP STRENGTHENEND MEMBERS SUBJECTED TO COMBINED BENDING AND AXIAL LOAD FRP strengthened members subjected to combined bending and axial load shall be designed as ollows: M M ( N ) (8.1) Sd Rd Sd where M sd is the design applied moment and M rd represents the lexural capacity o the strengthened member considering the design axial orce N sd. A possible design procedure is hereater described. The mechanical ratio μ s and μ related to tension steel reinorcement and FRP system, respectively, can be calculated as ollows: μ = s A s1 ccd ccd yd bd b t d μ = bd (8.2) (8.3) where A s1 and yd represent area and design yield strength o existing steel reinorcement, respectively; is equal to the design concrete compressive strength,, suitably reduced i it is necessary; b and d are width and eective depth o the FRP strengthened member, respectively; b and cd cd t are FRP width and thickness, respectively; and d is FRP ultimate design strength calculated according to Section , item (2)P. Material design strengths or non-seismic applications shall be in compliance with Section 3.3.3, item (7); or seismic applications, such values shall be obtained rom in-situ experimental tests. For seismic applications, unless a more detailed analysis regarding structural details and material properties is available, mechanical properties o existing materials shall be divided by an appropriate coeicient greater than 1. The ollowing non-dimensional equations relecting applied loads are introduced: n m Sd = = ccd N Sd bd M Sd Sd 2 ccd bd (8.4) (8.5) When FRP width and mechanical properties are known, a trial and error procedure can be initiated to evaluate the thickness o FRP reinorcement as ollows. 128

139 Step 1 η is computed as ollows: η = n + μ (1 u) + μ (8.6) Sd s Step 2 The ollowing parameters η i (i = 0, 1, 2, 3) are deined: 2 r η0 = μs u, η 1 = 3 r + 1, r η2 = 1.75 r +, η 1 3 = μ (1 r) (8.7) where: - u is the ratio o steel existing compression, A s2, and tension, A s1 area. r = 2 /1000ε. - d Step 3 From Table 8-1, ailure mode (Figure 4-5, ) and the corresponding value o the parameter m η can be determined as a unction o η when compared with the limits presented in Step 2. ( mr)( ) Step 4 Table 8-1 Failure mode η W ( η) (mr) 1a η0 η η1 1b η1 η η2 2 η2 η η3 W 1 η (1 η ) η ( η) = η + ( η η ) (1a) η1 η0 W (1b)( η) = { η1 η2 + [ 1 ( η1 + η2) ] η} The non-dimensional lexural capacity, m Rd ( n Sd ), o the strengthened member is evaluated as ollows: Step 5 The ollowing relationship shall be met: (0.75 η3) η2 (1 η2) W (2)( η) = η2 (1 η2) + ( η η2) 2 η3 η2 1 mrd( nsd ) = W (mr) ( η) + [ μs (1 + u) + μ ] (8.8) 2 m ( n ) m (8.9) Rd Sd Sd I this is not the case, the thickness, t, o the strengthening system is increased as well as its me- 129

140 chanical ratio, μ, and the iterative procedure is repeated rom Step

141 9 APPENDIX D (CONFINED CONCRETE) 9.1 CONSTITUTIVE LAW OF CONFINED CONCRETE Modeling the mechanical behavior o FRP-conined concrete members calls or the preliminary deinition o a suitable constitutive law σ ( ε ) related to the mechanical behavior o members subjected to uni-axial compression (σ and ε are considered positive in compression). In this context, as an alternative method to the parabolic-rectangular model proposed in 4.5.3, a non-linear relationship can be adopted similar to that shown in Figure 9-1, where a parabolic branch is ollowed by a linear ascending branch. At the intersection point between the two branches, the σ ε shall be assumed continuous. irst derivative o the unction ( ) Figure 9-1 Stress-strain model o FRP-conined concrete. The mathematical expression o such relationship can be written as ollows: - (parabolic branch) c - (linear branch) = 1+ b ε cd c cd 2 = a ε ε or 0 ε 1 (9.1) or 1 ε ε ε ccu c0 (9.2) where: - ε is a non-dimensional coeicient deined as ollows: ε ε c ε = (9.3) c0 - cd and ε c0 are the design strength o unconined concrete and the concrete strain at peak (typically assumed equal to 0.2%), respectively. - ε ccu is the design ultimate strain o conined concrete corresponding to the design strength ccd (chapter 4). 131

142 - the coeicients a and b are taken as ollows: a =1+ γ, b = γ 1 (9.4) where (see Figure 9-1): γ + E cd t c0 = (9.5) E cd ε ccd cd t = (9.6) ε ccu 132

143 10 APPENDIX E (EXAMPLES OF FRP STRENGTHENING DESIGN) In this Appendix, numerical examples o non-seismic FRP strengthening o RC members are provided. It is assumed that FRP strengthening is necessary due to increase o applied loads. Design is only perormed at ultimate limit state. Serviceability limit state design is not carried out because similar to traditional RC members theory GEOMETRICAL, MECHANICAL, AND LOADING DATA The building considered or design is shown in Figure Structural elements are deined as ollows: Main rectangular beams with cross-section o 30 cm x 50 cm (concrete cover d 1 =d 2 =3 cm). Secondary rectangular beams with cross-section o 30 cm x 40 cm (concrete cover d 1 =d 2 =3 cm). Rectangular columns with cross-section o 20 cm x 30 cm (concrete cover d 1 =d 2 =3 cm). Material mechanical properties are as ollows: Concrete: R ck = 20 N/mm 2. Steel: FeB32k ( yk =31.5 N/mm 2 ). Figure 10-1 Building geometry (dimensions in m). Loading conditions are deined as ollows: Live load at level 1: a 1 = 2.00 kn 2 m. Live load at level 2: a 2 = 0.50 kn 2 m. Snow (zone III, height a s < 200 m ): b = 0.75 kn 2 m. Dead load due to looring (or each level): g = 6.00 kn 2 m. Factored loads acting at ULS can be evaluated as ollows: Level 1: q 1 = kn/m. Level 2: q 2 = kn/m. 133

144 Figure 10-2 shows existing steel bar arrangement or beams and columns. Figure 10-2 Steel bars location or beams and columns INCREASE OF APPLIED LOADS New loads are deined as ollows: Level 1: a 1 = 6.00 kn/m 2. Level 2: a 2 = 4.00 kn/m 2. New actored loads acting at ULS can be evaluated as ollows: Level 1: q 1 = kn/m. Level 2: q 2 = kn/m DESIGN OF FLEXURAL REINFORCEMENT Design material properties are determined as ollows: Concrete ( = N/mm 2, γ c =1.60, cd =10.38 N/mm 2, ctm = 1.95 N/mm2, ctd ctm c ck. = 0.7 γ = 0.85 N/mm 2 ) 134

145 Steel ( yk = N/mm 2, γ s = 1.15, yd = N/mm 2 ) The ollowing relationship shall be met: M Sd M Rd (10.1) As indicated in Table 10-1, Equation (10.7) is not met at mid-span o both levels or 5.5 m long beams. Level 1 2 Span [m] Section Table 10-1 M Sd [kn m] A s1 [cm 2 ] A s2 [cm 2 ] M Rd [kn m] Eq. (10.7) satisied 4.0 let support Yes 4.0 mid-span Yes 4.0 right support Yes 5.5 let support Yes 5.5 mid-span No 5.5 right support Yes 4.0 let support Yes 4.0 mid-span Yes 4.0 right support Yes 5.5 let support Yes 5.5 mid-span No 5.5 right support Yes FRP lexural strengthening is perormed by installing carbon iber reinorcement using the wet-layup method with the ollowing geometrical and mechanical characteristics (0:α E =α =0.9): CFRP thickness: t,1 = mm. CFRP width: b = mm. CFRP Young modulus o elasticity in ibers direction (beam axis): α E E = N/mm 2 = N/mm 2. CFRP characteristic strength: α k = N/mm 2 = 2700 N/mm 2. For Type A application, the partial actors γ and γ,d are 1.10 and 1.20, respectively (Table 3-2, Section 3.4.1). The environmental conversion actor, η a, is set equal to 0.95 (Table 3-4, Section 3.5.1). A trial and error procedure is initiated or the determination o the number o CFRP plies, n, needed to satisy Equation (10.7). Thereore, assuming n =1, the maximum CFRP design strain, ε d, can be calculated as ollows (Equation (4.19): ε k εd = min ηa, εdd = εdd = (10.2) γ where: k ε k = = 0.01 (10.3) E 135

146 dd,2 ε dd = = (10.4) E CFRP design strength, dd,2, when ailure mode 2 (debonding) controls and when k cr rom Equation (4.6) is set equal to 3.0, can be calculated as ollows (Equations (4.3), (4.2), and (4.6)): k b b 2 = b b (10.5) Γ = 003. k = 0.17 N/mm 2 (10.6) Fk b ck ctm dd,2 k = γ γ,d cr Fk c 2 E Γ n t,1 =1469 N/mm 2 (10.7) CFRP lexural ailure mechanism may be o two types, depending whether CFRP maximum tensile strain, ε d, or concrete maximum compressive strain, ε cu, is reached (Figure 10-3). ε yd ε c0 1a 1b εcu ε cu ε' s ε ' s x = ξd d' 2 μ 1-2 μ = μ 1-2 d 2 ε s > s> ε yd yd ε yd d'' d 1 ε d ε 0 ε d ε 0 Figure 10-3 Failure regions o RC members strengthened with FRP. To identiy the ailure mode or this particular case, the CFRP mechanical ratio, μ, is computed: b ( n t ) μ = b d,1 dd,2 cd (10.8) and compared with the balanced mechanical ratio, μ 1-2, deined as ollows: μ 1 2 h 08. εcu = d μs ε + ε + ε cu d 0 ( 1 u) (10.9) 136

147 In Equation (10.8) is equal to the design concrete compressive strength,, suitably reduced i cd cd it is necessary; in Equation (10.9), μ s is deined in Equation (8.2), u represents the ratio between steel compression, A s2, and tension, A s1, area; ε 0 is the initial strain o the tension side o concrete, evaluated as: M gk ε 0 = 0.9 d E A s s2 (10.10) where M gk is the moment due to dead loads at SLS. I μ μ1 2, ailure takes place in region 1; i μ > μ1 2, ailure takes place in region 2 (Figure 10-3). Once the ailure mode is known, the position, x, o the neutral axis can be identiied rom Equation (4.20). The lexural capacity, M Rd, can be calculated rom Equation (4.21), assuming that the partial actor, γ Rd, is set equal to 1.00 (Table 3-3, Section 3.4.2). The calculated lexural capacity, M Rd, or a single layer CFRP reinorcement (Table 10-2) is greater than the applied moment, M Sd. Level Span [m] Section M Sd [kn m] Table 10-2 n ε d μ.1 μ.1-2 Region x [m] M Rd [kn m] l e [m] mid-span mid-span I Equation (10.1) is not satisied, the number, n, o CFRP plies shall be progressively increased, iterating the design procedure. CFRP strengthening shall be installed along the beam axis until Equation (10.1) is not met. Proper anchorage length shall be provided to CFRP reinorcement according to Section Table 10-2 also summarizes the value o the optimal bond length, l e, calculated according to Equation (4.1): l e E t E n t 2 2 = = ctm,1 ctm (10.11) 10.4 DESIGN OF SHEAR REINFORCEMENT The ollowing relationship shall be met: V Sd V Rd (10.12) where V Sd is the design applied shear orce, and V Rd represent the shear capacity to be calculated as ollows: { } V = min V + V, V (10.13) Rd Rd,ct Rd,s Rd,max where V Rd,ct and V Rd,s represent concrete and steel existing contribution to the shear capacity, re- 137

148 spectively; and V Rd,max is the maximum shear capacity representing the resistance o the concrete compressed strut. According to the current building code, the above mentioned quantities may be expressed as ollows: VRd,max = 0.3 cd b d (10.14) V = 0.6 b d δ (10.15) Rd,ct ctd Asw VRd,s = ywd 0.9 d (10.16) s where: - δ = 1 when axial orce is negligible, δ = 0 or tension axial orce, δ = 1+ M 0 MSd or compression axial orce (M 0 is the decompression moment reerred to the extreme iber o the cross section evaluated along the beam axis where M Sd acts); - A sw, s, and ywd represent area, spacing, and steel stirrups yield strength, respectively. According to the current building code, steel contribution to the shear capacity shall be as ollows: V Sd VRd,s (10.17) 2 Table 10-3 summarizes the as-built shear capacity. As it can be seen, all members require shear strengthening. Level 1 2 Span [m] Section V Sd [kn] Table 10-3 V Rd,max [kn] A sw [cm 2 ] s [cm] V Rd,s [kn] V Rd,ct [kn] V Rd [kn] Eq. (10.18) satisied 4.0 let support NO 4.0 right support NO 5.5 let support NO 5.5 right support NO 4.0 let support NO 4.0 right support NO 5.5 let support NO 5.5 right support NO FRP shear strengthening is perormed by installing U-wrap carbon iber reinorcement having the ollowing geometrical and mechanical characteristics (mode 1, Section :α E =α =0.9): CFRP thickness: t,1 = mm. CFRP width: w = mm. CFRP Young modulus o elasticity: α E E = N/mm 2 = N/mm 2. CFRP characteristic strength: α k = N/mm 2 = 2700 N/mm 2. For Type-A application, the partial actors γ and γ,d are 1.10 and 1.20, respectively (Table 3-2, Section 3.4.1). The ollowing iber orientations with respect the axis o the beam are considered: Level 1: β =

149 Level 2: β = 90. The design shear capacity o the strengthened member may be evaluated rom Equation (4.24): { } V = min V + V + V, V (10.18) Rd Rd,ct Rd,s Rd, Rd,max where: - V Rd,ct is the concrete contribution to the shear capacity: ( ρ ) V = 0.25 r 1 50 b d δ (10.19) Rd,ct ctd l w where ctd is the design tensile strength o the concrete, and δ = 1. - VRd,s is the steel contribution to the shear capacity taken rom Equation (10.16). - VRd, is the CFRP contribution to the shear capacity taken rom Equation (4.26) as ollows: 1 w V = 0.9 d 2 t ( cotθ + cot β) (10.20) p Rd, ed γ Rd with γ Rd set equal to 1.2 (Table 3-3, Section 3.4.2), and θ =45. - V Rd,max is the maximum shear capacity representing the resistance o the concrete compressed strut taken rom Equation (10.14). For CFRP U-wrap reinorcement, the eective design strength, ed, can be evaluated rom Equation (4.30) as ollows: ed 1 = dd l sin β e 1 3 min 0.9, { dh} w (10.21) where: - h w is the beam depth. - l e is the eective bond length rom Equation (10.11). - dd is the bond strength or mode 1 rom Equation (4.4): dd 1 2 E Γ = γ γ n t,d c,1 Fk (10.22) Assuming the CFRP strip width, w, equal to 150 mm, both center-to-center spacing, p, and number o CFRP plies, n, can be determined with a trial and error procedure until Equation (10.12) is satisied. Table 10-4 and Table 10-5 as well as Table 10-6 and Table 10-7 summarize the perormed shear design o CFRP U-wrapped strengthened member or both level 1 and 2, respectively. 139

150 Span [m] CNR-DT 200/2004 Table 10-4 Section n p [mm] Γ Fk [N/mm 2 ] dd [N/mm 2 ] l e [mm] ed [N/mm 2 ] 4.0 let support right support let support right support Span [m] Table 10-5 Span [m] Section V Rd,ct [kn] V Rd,s [kn] V Rd,max [kn] V Rd [kn] V Sd [kn] 4.0 let support right support let support right support Table 10-6 Section n p [mm] Γ Fk [N/mm 2 ] dd [N/mm 2 ] l e [mm] ed [N/mm 2 ] 4.0 let support right support let support right support Span [m] Section Table 10-7 V Rd,ct [kn] V Rd,s [kn] V Rd,max [kn] V Rd [kn] V Sd [kn] 4.0 let support right support let support right support V Rd, [kn] V Rd, [kn] 10.5 CONFINEMENT OF COLUMNS SUBJECTED TO COMBINED BENDING AND SLIGHTLY ECCENTRIC AXIAL FORCE A P-M diagram according to the current building code is built based on the speciied material mechanical properties. As summarized in Table 10-8, there are two cases or each level where columns require strengthening. 140

151 Table 10-8 Level Column Section N Sd [kn] 1 2 M Sd [kn m] n sd m sd μ s Strengthening required let side bottom NO let side top NO central bottom YES central top YES right side bottom NO right side top NO let side bottom NO let side top NO central bottom NO central top NO right side bottom YES right side top YES Because the central column o level 1 is subjected to a slightly eccentric axial orce, FRP coninement is perormed to ensure that the ollowing equation is met: N Sd N Rcc,d (10.23) A continuous CFRP wrapping o the column is carried out assuming the ollowing parameters (Section : α E =α =0.9): CFRP thickness: t,1 = mm. CFRP Young modulus o elasticity: E = N/mm 2 = N/mm 2. CFRP characteristic strength: k = N/mm 2 = 2700 N/mm 2. For Type-A application, the partial actors γ and γ,d are set equal to 1.10 (Table 3-2, Section 3.4.1) and 1.20 (Table 3-3, Section 3.4.2), respectively. The environmental conversion actor, η a, is set equal to 0.95 (Table 3-4, Section 3.5.1). A trial and error procedure is initiated or the determination o the number o CFRP plies, n, needed to satisy Equation (10.29). Thereore, assuming n =1, the design axial capacity, N Rcc,d can be written as ollows (Equation (4.40)): 1 N = A + A (10.24) Rcc, d c ccd s yd γrd where: - γ Rd is the partial actor or the resistance model, equal to 1.10 (Table 3-3, Section 3.4.2). - A c is the concrete cross section area. - ccd is the design strength o conined concrete. - A s is the area o steel existing reinorcement. - yd is the design strength o steel existing reinorcement, calculated according to the current building code. The design strength, ccd, or conined concrete may be evaluated according to Equation (4.41): ccd cd l,e = + cd 2/ 3 (10.25) 141

152 where cd is the design strength o unconined concrete according to the current building code, and l,e is the eective coninement pressure, depending upon member cross section shape and type o FRP application. The latter is given by Equation (4.42) as ollows: 1 = k = k ρ E ε 2 l,e e l e d,rid (10.26) where: - k e ( 1) is the coeicient o eiciency deined by Equation (4.44): k = k k k e H V α (10.27) - ρ is the CFRP geometric ratio; or rectangular cross section conined with continuous FRP reinorcement it may be written as ollows: 2 t ( b+ d) ρ = bd (10.28) where b and d are dimensions o the column cross-section. - E represents CFRP Young modulus o elasticity in the ibers direction. - ε d,rid is the CFRP reduced design strain, taken rom Equation (4.47): ε = min{ η ε / γ ; 0.004} = (10.29) d,rid a k The coeicient o vertical eiciency, k V, as well as the k α coeicient can be set equal to 1 when continuous wrapping with iber running perpendicular to the member axis is perormed. The coeicient o horizontal eiciency, k H, or rectangular cross sections can be written as ollows (Equation (4.51)): k H 2 g 2 b' + d' = 1 (10.30) 3 A where b and d are the dimensions shown in Figure 4-12 o Section , and A g is the member cross sectional area. The calculated axial capacity, N Rcc,d, o the CFRP conined column is summarized in Table Table 10-9 Section n K H k e ρ 1,e [N/mm 2 ] ccd [N/mm 2 ] N Rcc,d [kn] bottom top Beore CFRP wrapping takes place, cross section edges shall be rounded to 20 mm according to Equation (4.49). 142

153 10.6 CONFINEMENT AND FLEXURAL STRENGTHENING OF COLUMNS SUBJECTED TO COMBINED BENDING AND AXIAL FORCE WITH LARGE ECCENTRICITY In this paragraph, design o CFRP strengthening or level 2 o the right side column subjected to combined bending and axial orce is perormed. Flexural CFRP reinorcement is carried out assuming the ollowing geometrical and mechanical parameters (mode 1, Section : α E =α =0.9): CFRP thickness: t,1 = mm. CFRP Young modulus o elasticity: α E E = N/mm 2 = N/mm 2. CFRP characteristic strength: α k = N/mm 2 = 2700 N/mm 2. In addition, in the regions o the column close to the beams, the same CFRP material is applied as column wrapping as suggested in Appendix C. For Type A application, the partial actors γ is set equal to 1.10 (Table 3-2, Section 3.4.1). The environmental conversion actor, η a, is set equal to 0.95 (Table 3-4, Section 3.5.1). Due to coninement, the concrete design compressive strength can be written as ollows:. 2/ 3 l,e ccd = cd cd =15.43 N/mm 2 (10.31) A trial and error procedure is initiated according to Appendix C by calculating the non-dimensional coeicients: n m Sd = = ccd N Sd bd M Sd Sd 2 ccd bd (10.32) (10.33) where b and d are the dimensions o the column cross-section; is equal to the design concrete cd compressive strength,, suitably reduced i it is necessary. cd Design is satisied when the number, n, o CFRP plies is equal to 3 (Table 10-10, Table 10-11). Table Section n Sd m Sd μ s u n u Γ k [N/mm 2 ] ε d d [N/mm 2 ] bottom top Table Section η 0 η 1 η 2 η 3 η Failure mode W m Sd Checked bottom YES top YES μ 143

154 11 ACKNOWLEDGEMENTS This document has been translated verbatim rom Italian with the support o the Center o Excellence on Structural Composites or Innovative Construction (SCIC). The translation has been carried out by the members o the Task Group with the supervision o Renato Parretti, whose contribution is grateully acknowledged. The members o the Task Group thank all the practitioners, industries, and academia who have worked in order to achieve the general consensus on the present document. 144