FRP Lamella V3 Manual Eng

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    FRP Lamella

    user manualfor design software

    version 3

    flexural and shearstrengtheningusing FRP materials

    Peter Onken Wiebke vom BergDirk Matzdorff

    bow ingenieure gmbhbraunschweig hamburg

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    FRP Lamella

    design program

    for flexural and shear strengthening with FRP materials

    according to Eurocode 2

    User Manual

    version 3.4

    Peter Onken, Wiebke vom Berg, Dirk Matzdorff

    bow ingenieure gmbh braunschweig / hamburg germany

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    Contents

    Part I Design concept

    1. Introduction 5

    2. Notation 6 3. Design program features 9

    4. Basic assumptions 10

    5. Safety concept 12

    6. Degree of strengthening 13 6.1 Definition according to Eurocode 2 13 6.2 Failure of the FRP system 13

    7. Material behaviour 14

    7.1 Concrete 14

    7.2 Reinforcing steel 14

    7.3 Prestressing steel 14 7.4 FRP material 15

    8. Design aspects for FRP systems 16 8.1 Externally bonded FRP laminates 16 8.2 Externally bonded carbon sheets 17

    8.3 Near surface mounted CFRP laminates 17

    9. Imposed actions 18

    10. Design procedure 19 10.1 Capacity of the unstrengthened cross-section 19 10.2 Required cross-sectional area of FRP 19 10.3 Conditions of equilibrium 20

    10.4 Control of strain profiles 21 10.5 Control of stresses 21

    11. Bond check of the FRP system 22

    11.1 Anchorage of externally bonded CFRP laminates 22

    11.2 Anchorage of externally bonded carbon sheets 23

    11.3 Calculation of the envelope line / verification of the anchorage 24 11.4 Anchorage of near surface mounted CFRP laminates 27 11.5 Surface tensile strength of concrete 29

    12. Anchorage of bottom reinforcement at end support 30

    13. Detailing provisions 31

    14. Shear design 32 14.1 Shear capacity according to Eurocode 2 32

    14.2 Design of the additional shear reinforcement 35 14.3 Anchorage of external stirrups 37

    15. Further checkings 38 16. Fire protection 38

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    Part II Use of the program

    17. Program user interface 39 17.1 Start of the program 39

    17.2 Settings 39 17.3 Basic information about the FRP Lamella user interface 39 17.4 Data input 40

    17.5 Output of results 41

    18. Input and output windows 42

    18.1 Input window project 42

    18.2 Input window code 43 18.3 Input window geometry 44 18.4 Output window cross-section 45

    18.5

    Input window concrete 46

    18.6 Input window steel 47

    18.7 Input window main flexural reinforcement 48

    18.8 rebar tables for the selection of reinforcement cross-sectional area 49

    18.9 Input window flexural reinforcement at support 50 18.10 Input window loads in unstrengthened state 51 18.11 Input window loads in strengthened state 53 18.12 Input window FRP system 55

    18.13 Input window FRP cross-section 56

    18.14 Output window design 58 18.15 Output window strains in ultimate limit state 60 18.16 Output window strains / stresses in service state 61

    18.17 Input window FRP end anchorage 62 18.18 Output window FRP end anchorage 64 18.19 Input window anchorage of flexural reinforcement at support 65

    18.20 Output window anchorage of flexural reinforcement at support 66 18.21 Input window shear reinforcement and loads 67

    18.22 Input window shear strengthening 68

    18.23 Output window shear strengthening 69 18.24 Output window shear strengthening anchorage of additional external stirrups 70

    19. Program menu and tool bar 72

    19.1 Menu bar items 72 19.2 Tool bar symbols 74

    20. Installation instructions 75

    Appendix 1 example T-beam according to Eurocode 2Appendix 2 example two-span slab according to Eurocode 2

    Appendix 3 example prestressed concrete beam according to Eurocode 2Appendix 4 bow engineers experts for strengthening design

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    1. Introduction

    FRP Lamella is a design program for the strengthening of reinforced and prestressed or post-tensioned concrete structural members subjected to uniaxial flexure and axial forces using FRP

    materials (FRP Fibre Reinforced P olymer). This program can be used for the predesign ofstrengthening measures as well as for complete calculations within the scope of structural analysis.The program provides the user with the required FRP cross-sectional area for the strengthened stateand is performing the necessary verifications of the bond strength and the shear capacity of theconcrete member based on the assumptions of the German Guidelines for the strengthening ofconcrete members using CFRP laminates [2], [3] and carbon sheets [4], (cf. [11]). The design conceptaccording to Eurocode 2 is explained in [10].

    The program FRP Lamella is used in almost 15 other countries, adapted to the relevant regulations,guidelines and national standards. Meanwhile different versions corresponding to the followinginternational codes are available:

    Eurocode 2

    DIN 1045 (7/88) (German DIN-Norm)

    British Standard 8110

    BAEL 91 (Normes Franaises)

    ACI (American Concrete Institute)

    KCI (Korean Concrete Institute)

    Fig. 1 Opening window of the FRP Lamella software

    NoteThe software FRP Lamella is based on the material parameters of S&P FRP systems. If other

    types of reinforcing fibres or adhesive systems will be used, the results provided by thesoftware will no longer be valid. Under these circumstances the system supplier S&P willrefuse any liability for the application of S&P products.

    5

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    2. Notation

    As a rule, in this manual the standard notations derived from Eurocode 2 are used. They may differfrom notations of other national design codes and guidelines. The following list gives an overview of

    the notations used in this manual and in the software.

    Notation ProgramGeometrywidth of the component bweb width b0overall height h, h0effective flange width of upper flange b 1thickness of upper flange h 1effective flange width of lower flange b2thickness of lower flange h 2span ltotal cross-sectional area A cdistance of the centroid from top edge of the member z cgmoment of inertia of concrete cross-section I ysection modulus above the gravity axis W topsection modulus below the gravity axis W bottomReinforcementcross-sectional area of longitudinal rebars A spre-strain of the longitudinal reinforcement due to prestressing p0cross-sectional area of internal stirrup rebars a sw

    distance from centroid of rebars to top edge of the member z sdiameter of rebars d sanchorage length of rebars from the support front l s,Aconcrete cover of the stirrups c wSteelcharacteristic yield strength of reinforcing steel f ykmodulus of elasticity of reinforcing steel Esstrain limit of reinforcing steel sucharacteristic tensile strength of prestressing steel f pkmodulus of elasticity of prestressing steel E pstrain limit of prestressing steel pureduction coefficient for the tensile strength of prestressing steel ppartial safety factor for steel sConcretecharacteristic compressive strength of concrete (EC 2) f ckstrain limit of concrete custrain at the axis of the parabolic curve of the stress-strain line of concrete c1reduction factor for the compressive strength of concrete (long term effects) design shear strength of concrete Rdaverage modulus of elasticity of concrete E cmaverage axial tensile strength of concrete f ctm

    partial safety factor for concrete c

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    FRP materialmodulus of elasticity of FRP material E f failure strain of FRP material fu

    strain limit of FRP material f,limitcharacteristic tensile strength of FRP material f fkpartial safety factor for FRP material f reduction factor for the strain limit of FRP material knumber of FRP plies one on top of each other n f number of FRP strips one next to each other m f spacing of FRP strips s f cross-sectional area of FRP strengthening A f distance from centroid of FRP strip to top edge of the member z f distance of FRP strips to the lateral edge of the member a r thickness of FRP reinforcement t f width of FRP reinforcement b f Designcharacteristic bending moment at time of strengthening M Sk0characteristic axial force at time of strengthening N Sk0characteristic prestressing force N pstatically determinated prestressing moment M p0statically indeterminated part of prestressing moment M pdesign bending moment of strengthened state M Sdf design axial force of strengthened state N Sdf characteristic bending moment of strengthened state M Skf characteristic axial force of strengthened state N Skf average partial safety factor for bending moments caused by loads M,maverage partial safety factor for axial forces caused by loads N,mdesign moment of resistance of unstrengthened cross-section M Rd0characteristic moment of resistance of unstrengthened cross-section M Rk0design moment of resistance of strengthened cross-section M Rdf strengthening ratio remaining global safety in case of loss of FRP strengthening strain of extreme compression fibre of concrete cdistance from neutral axis to extreme compression fibre x

    maximum strain of reinforcing steel smaximum strain of prestressing steel pmaximum strain of FRP reinforcement f stress of extreme compression fibre of concrete cmaximum stress of reinforcing steel smaximum stress of prestressing steel pmaximum stress of FRP reinforcement f Anchoragesubstrate strength of concrete (median of the population) f csmdesign value of the substrate strength of concrete f csdcharacteristic compressive strength of adhesive f Kc,kcharacteristic tensile strength of adhesive f Kt,k

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    characteristic shear strength of adhesive K,kdistance from calculated axis of support to edge of support a idistance from end of the FRP strip to edge of support f

    horizontal displacement of the envelope line of tensile force a Ldesign moment of strengthened state in point E M Sdf,Edesign axial force of strengthened state in point E N Sdf,Edistance from point E to theoretical axis of support x Etensile force of FRP reinforcement in point E F fd,Edesign value of the maximum bond force F bd,maxrequired bond length of maximum bond force l bd,maxrecommended bond length l bdesign value of shear force at support V Sdf,Adesign value of axial force at support N Sdf,Atotal required anchorage force at support F A,reqanchorage force covered by internal reinforcement F s,Adesign bond strength of internal rebars f bdforce covered by FRP anchorage F f,Aanchorage length of FRP reinforcement from the support front l f,AShearcross-sectional area of internal stirrups a swdesign shear force of strengthened state in relevant section X V Sdf,Xdesign axial force of strengthened state in relevant section X N Sdf,Xdesign bending moment of strengthened state in relevant section X M Sdf,Xstrain limit of additional shear reinforcement limitcharacteristic modulus of elasticity of FRP Sheet E fkcharacteristic tensile strength of FRP Sheet f fkreduction factor for modulus of elasticity due to manual lamination Emodulus of elasticity of steel plates for shear strengthening E scharacteristic yield strength of steel plates for shear strengthening f ykpartial safety factor for shear strengthening steel plates sdistance from resultant of concrete stress to extreme compression fibre a ceffective depth of internal steel rebars d seffective depth of FRP reinforcement d f average effective depth d m

    average lever arm of internal forces z mshear force limit of the strengthened cross-section V maxdesign shear resistance provided by concrete V Rd1design shear resistance of the concrete cross-section without web crushing V Rd2design shear resistance of concrete cross-section with internal stirrups V Rd3cross-sectional area of additional shear reinforcement a wthickness of additional external stirrups t wwidth of additional external stirrups bwcross-sectional area of one additional external stirrup A wspacing of additional external stirrups s wstress of the internal shear reinforcement swstress of the additional shear strengthening fw

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    3. Design program features

    FRP Lamella is developed as a pure design program for the strengthening of reinforced andprestressed or post-tensioned concrete elements, i.e. the program does not perform any structural

    analysis. As a consequence the user has to determine the internal forces in advance with a calculationby hand or by using structural analysis software for instance. The updated version 3.x now alsoconsiders prestressed or post-tensioned elements or concrete structures subjected to axial forces.

    The program supports 4 types of cross-section: slabs as well as rectangular beams, T-beams anddouble-T-beams . These options cover almost all reinforced or pre-stressed concrete componentssubjected to bending which will appear in practice.

    There are 3 different FRP-systems for flexural strengthening: externally bonded CFRP laminates , nearsurface mounted (slot-in) CFRP laminates and externally bonded carbon sheets (unidirectional fabric).The program includes the complete range of S&P products for flexural and shear strengthening.

    The required cross-sectional area of FRP strengthening is determined by variation of the strain profilewithin the limits defined in the regulations. The implementation of non-linear stress-strain relations forconcrete as well as for reinforcing and prestressing steel and the iterative solution procedure lead toprecise results. Compared with hand calculations the program provides particularly economic amountsof FRP strengthening. Additionally the strain and stress distributions can be controlled. The verificationof the bond strength is based on the German Guideline for the strengthening of concrete componentsusing CFRP laminates [2], [3] and carbon sheets [4]. The verification of anchorage lengths of theinternal rebars as well as the design of the shear strengthening follows the concept of Eurocode 2.

    For structures to be strengthened the geometry, internal reinforcement, steel grades, concrete

    compressive strength and bending moments can be derived from existing as-built documents. If notavailable this information has to be established by on-site testing.

    In addition the program offers useful tools for the definition of the relevant national concrete strength,the reinforcing and prestressing steel grades and the selection of the existing rebar cross-sections.

    The serviceability of the strengthened state cannot be proved by the program. If necessary, the user isresponsible to check the deflections and crack widths of the strengthened structure.

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    4. Basic assumptions

    According to the regulations it can be assumed for the design at ULS (ultimate limit state) thatexternally bonded FRP reinforcement can be calculated like an additional layer of reinforcement within

    the provided strain limits. The calculations are based on the well-known assumptions of concretedesign:

    For bending a linear strain distribution is assumed (Bernoulli hypothesis).

    For reinforced concrete elements it is assumed that concrete has no tensile strength. Alltensile forces necessary for the equilibrium of the internal forces are covered by internalreinforcement and FRP strengthening.

    For prestressed or post-tensioned concrete elements the tensile strength of the concretemay be considered in the uncracked state.

    There is no slip between FRP strengthening and concrete. All cross-section fibres with thesame distance to the neutral axis are subjected to the same strain.

    The determination of the required FRP cross-sectional area and the resisting moments before andafter strengthening result from calculation of the equilibrium of internal forces.

    References

    [1] Allgemeine bauaufsichtliche Zulassung fr die Verstrkung von Stahlbetonbauteilen durchschubfest aufgeklebte S&P Kohlenfaserlamellen (Z-36.12-62); Deutschland.

    [2] Richtlinie fr das Verstrken von Betonbauteilen durch Ankleben von unidirektionalen kohlen-stoffaserverstrkten Kunststofflamellen (CFK-Lamellen), Anlage 2 der Zulassung [1], Deutsches Institut fr Bautechnik, Berlin.

    [3] Richtlinie fr das Verstrken von Betonbauteilen durch Einkleben von unidirektionalen kohlen-stofffaserverstrkten Kunststofflamellen in Schlitze im Beton, Deutsches Institut frBautechnik, Berlin.

    [4] Richtlinie fr das Verstrken von Betonbauteilen durch Auflaminieren von unidirektionalen

    Kohlenstofffaserlaminaten (CFK-Laminate), Deutsches Institut fr Bautechnik, Berlin.[5] CEB-FIP Model Code 1990; EPF Lausanne 1991.

    [6] Eurocode 2: Planung von Stahlbeton- und Spannbetontragwerken; Teil 1: Grundlagen und Anwendungsregeln fr den Hochbau; Juni 1992.

    [7] Rostsy, F.S.; Holzenkmpfer, P. und Hankers, C.: Geklebte Bewehrung fr die Verstrkungvon Betonbauteilen. Beton-Kalender 1996, T.II, Berlin: Ernst & Sohn 1996.

    [8] Holzenkmpfer, P.: Ingenieurmodelle des Verbunds geklebter Bewehrung fr Betonbauteile.Dissertation TU Braunschweig, 1994.

    [9] Onken, P.; vom Berg, W.; Matzdorff, D.; Nolte, T.: Bemessungsprogramm fr CFK-Lamellen.Beton- und Stahlbetonbau 95, 9/2000, S. 551 552.

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    [10] Onken, P.; vom Berg, W.: Biegezugverstrkung mit CFK-Lamellen Neues Bemessungs-modell nach EC 2 und DIN 1045-1. Beton- und Stahlbetonbau 96, 2/2001, S. 61 70.

    [11] Rostsy, F. S.: Expert Opinion No. 98/0322; S&P Reinforcement, Eisenstadt, sterreich.

    [12] Blaschko, M. A.: Zum Tragverhalten von Betonbauteilen mit in Schlitze eingeklebten CFK-

    Lamellen, Dissertation an der TU Mnchen, 2001.[13] Design guidance for strengthening concrete structures using fibre composite materials,

    Technical Report No. 55, The Concrete Society, Berkshire, UK, 2000.

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    5. Safety concept

    The ultimate limit state design is based on the following condition (cf. EC 2, section 2.3.2):

    Sdf Rdf (1)S df corresponds to the design value of internal forces or moments due to loads and R df to the designresistance, for instance the moment capacity of the cross-section at strengthened state. The index f defines the state after strengthening (with FRP). Both, Sdf and R df , are d esign values and associatedwith the partial safety factors for actions and materials properties as shown in table 1.

    Loads Resistancedead loads live loads concrete reinforcing steelCode

    G Q C S

    Eurocode 2 1.35 1.5 1.5 1.15

    DIN 1045-1 (Germany-new) 1.35 1.5 1.5 1.15

    DIN 1045 (7/88) (Germany-old) 1.75 2.1 1.0

    BS 8110 (UK) 1.4 1.6 1.5 1.15

    BAEL 91 (France) 1.35 1.5 1.5 1.15

    SIA 160 / 262 (Switzerland) 1.3 1.5 1.2

    ACI 318 (USA) 1.4 1.7 1 / 0.9

    KCI (Korea) 1.4 1.7 1 / 0.85

    Tab. 1 Partial safety factors according to different design codes

    For actions additionally the combination values for the probability of occurrence of several variableloads have to be considered. Additional partial safety factors for the FRP systems are missing intable 1 since different safety concepts are used according to the FRP system and the nationalguideline. In many cases, e.g. for externally bonded FRP laminates, the design strain is limited insteadof introducing a partial safety factor for the tensile strength of the material. For further information seechapter 8.

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    6. Degree of strengthening

    6.1 Definition according to Eurocode 2

    In the German Guidelines for the strengthening of concrete members with external bonded FRPlaminates [2], [3] and unidirectional carbon sheets [4] it is recommended, that the flexural capacity ofthe strengthened element should not exceed twice the flexural capacity of the unstrengthenedelement. This is expressed by the flexural strengthening ratio.

    A limitation of the strengthening ratio is only mentioned in the German guidelines [2] [4]. There existsno such limitation in other regulations or guidelines. One reason for the limitation of the strengtheningratio is the scant knowledge about the behaviour of highly strengthened structures. Other reasonswere the insufficient design methods for strengthening with externally bonded FRP reinforcement inthe past. Hand calculations do not allow the verification of strains and stresses at service state. On theother hand the design software FRP Lamella provides the strain distributions and stresses at

    strengthened state in all parts of the section. By this means yielding of internal reinforcement can beavoided, strain limits can be controlled. Therefore the limitation of the strengthening ratio based on theGerman guidelines [2] [4] may not be applied very strictly but it is highly recommended not toincrease the strengthening ratio far beyond the point which is twice the capacity of the unstrengthenedelement. The bond behaviour of externally bonded FRP strips will be influenced unfavourably by theincreased formation of cracks in highly stressed concrete elements.

    Since there is no experience with highly strengthened structures, the limitation of the strengtheningratio is also recommended for other national guideline or standards:

    2M

    M

    0Rd

    f Sd

    EC,B = . (2)

    M Sdf describes the imposed bending moment at strengthened state, M Rd0 corresponds to the designmoment of resistance of the unstrengthened cross-section. For M Sdf , the combination principles ofactions according to EC 2 have to be considered.

    When the strengthening ratio exceeds the limit of 2, the design and detailing should be carried out withspecial care. For near surface mounted laminates there exist no requirements for the limitation of thestrengthening ratio.

    6.2 Failure of the FRP system

    In other national regulations (e.g. ACI) there is a demand of minimum safety ( > 1,0) after loss of theFRP strengthening under service (unfactored) loads. In this case the following equation is valid:

    1MM

    Skf

    0RkEC >= (3)

    The subscript k in the equation indicates characteristic values.

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    7. Material behaviour

    7.1 Concrete

    For the determination of the concrete compressive stress a parabolic-rectangular stress-strainrelationship can be assumed, as provided by Eurocode 2, shown in figure 2a. The parabolic curveends at a strain value c1 = 0.2 % and the maximum compressive strain is limited to cu = 0.35 %(cf. [5]). However, the program also offers the possibility to modify the shape of the parabolic-rectangular stress-strain by adjusting the strain parameters ( c1 , cu ). The design value of the concretecompressive strength f cd is determined by dividing the characteristic strength f ck by the appropriatepartial safety factor in table 1. The reduction factor takes into account the reduced compressivestrength under long-term loading.

    c

    ckcd

    f f

    = ( = 0.85; C according to table 1) (4)

    example: C 20/25 mm/N33.115.1

    2085.0f cd ==

    The design shear strength can be determined from the characteristic concrete compressive strengthusing the following equation:

    c

    3/2ck

    c

    05.0,ctkRd

    f 0525.0

    f 25.0

    =

    = (5)

    The average modulus of elasticity and the axial tensile strength of concrete are calculated from the

    concrete compressive strength. According to Eurocode 2 the following equations are used:

    ( ) 3/1ckcm 8f 9500E += (6)

    ( ) 3/2ckctm f 3.0f = (7)

    7.2 Reinforcing steel

    For the steel reinforcement, an idealised bilinear stress-strain relationship is considered with a design

    yield strength f yd as shown in fig. 2b. The appropriate parameters of strength and strains depend onthe selected steel grade. For the design at strengthened state the strain of reinforcing steel is limitedto su = 1 % according to Eurocode 2, section 4.2.2. The design value of the yield strength f yd isdetermined by dividing the characteristic strength f yk by the appropriate partial safety factor in table 1.

    7.3 Prestressing steel

    For prestressing steel the same bilinear line with a horizontal branch is applied (fig. 2b). The designvalue of the tensile strength f pd is determined by dividing the characteristic strength f pk by theappropriate partial safety factor in table 1. For the design of the member cross-section, the tensilestrength is reduced to 90 % according to Eurocode 2. Therefore the reduction factor p is introduced infig. 2b.

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    7.4 FRP material

    The tensile stress-strain behaviour of FRP can be idealised by means of a linear response, defined infig. 2c. The modulus of elasticity depends on the selected FRP system. It is quoted from the relevantnational approval or guideline. At present, the characteristic values of the German General Approval

    [1]are applied, as far as national approvals or guidelines are not available:

    modulus of elasticity:

    CFRP laminate 150/2000 E f = 164'000 [N/mm]CFRP laminate 200/2000 E f = 205'000 [N/mm]C-Sheet 240 E f = 240'000 [N/mm]C-Sheet 640 E f = 640'000 [N/mm]

    tensile strength:

    CFRP laminate 150/2000 f fk = 2'500 [N/mm]CFRP laminate 200/2000 f fk = 2'500 [N/mm]C-Sheet 240 f fk = 3'800 [N/mm]C-Sheet 640 f fk = 2'650 [N/mm]

    ultimate strain:

    CFRP laminate 150/2000 fu = 1.40 [%]CFRP laminate 200/2000 fu = 1.30 [%]C-Sheet 240 fu = 1.55 [%]C-Sheet 640 fu = 0.40 [%]

    For externally bonded FRP the ultimate tensile strength or the strain at failure are not significant forthe design of strengthened structures, because other mechanisms like bond failure are prematurelyresponsible for the failure. Therefore, to determine the design moment of resistance for thestrengthened state, the design strain of the external bonded FRP system will be limited toapproximately 50 % of the ultimate elongation at failure ( fu).

    concrete reinforcing / prestressing steel FRP material

    f

    f E fk

    Efd

    fu f,lim

    f fu

    f fd

    E s

    py su sy

    s

    s

    p f pk

    f ykf yk s

    p f pk s

    E cm

    c

    ccu c1

    f ck

    f ck c

    Fig. 2 Stress-strain diagrams for concrete, reinforcing and prestressing steel as well as FRP Material

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    8. Design aspects for FRP systems

    8.1 Externally bonded FRP laminates

    Externally bonded FRP laminates cannot be stressed up to their tensile strength. Before externallybonded FRP reinforcement will reach the tensile strength, the strengthened system is failing, e.g. dueto rupture of the anchorage or bond failure at shear or flexural cracks. For this reason, based on theGerman Guideline for the strengthening of concrete components using externally bonded CFRPlaminates [2], the strain of externally bonded systems is limited. This design principle is meanwhileadopted by many other national guidelines.

    The strain limits for CFRP laminates are defined in the national approvals and guidelines. Normally,the design strain is limited to about 50 % of the average ultimate strain in direction of the fibres. Below,the design strain limits for flexural strengthening are given according to the German General Approval[1]:

    The lowest strain value f,limit of the two following conditions is decisive:

    Depending on the type of laminate and modulus of elasticity in fibre direction:

    S&P CFRP laminate 150/2000 f,limit = 0.75 [% ]S&P CFRP laminate 200/2000 f,limit = 0.65 [% ]

    Furthermore, the following condition is valid for reinforced concrete components:

    s

    sykitlim,f E

    f 5= (8)

    f syk/Es yield strain of the reinforcing steel(always refers to the outer layer of the internal reinforcement)

    Given that the strains can hardly be controlled by hand calculation, the last condition indirectly helps toprevent yielding of the internal reinforcement at service state. However, the program offers thepossibility to check the strains at service state. Anyway, this condition is only relevant for internalreinforcement with low steel strength.

    Considering the low limits of the design strain there is no need for any additional partial safety factor( > 1.0) for externally bonded CFRP systems.

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    8.2 Externally bonded carbon sheets

    For externally bonded Carbon sheets the same principles as for externally bonded CFRP laminatesare valid. The design strain at ultimate limit state is limited:

    C-Sheet 240 f,limit = 0.75 [%]Following the German Guideline for the strengthening of concrete components using unidirectionalCarbon sheets [4], the number of layers should not exceed 5 layers.

    8.3 Near surface mounted CFRP laminates

    CFRP laminates can also be glued into slots which will be cut into the concrete surface. Compared toexternally bonded FRP strips, near surface mounted laminates have a higher anchoring capacity,therefore they can almost be stressed up to their tensile strength. The bond behaviour of near surfacemounted CFRP laminates is comparable to embedded steel rebars. A sufficient bond length prevents

    bond failure and debonding problems will not occur. The design of near surface mounted laminates isbased on recent investigations in Germany [12].

    The design value of the tensile strength f fd and the ultimate strain fd are determined by dividing thecharacteristic values by the following partial safety factors f for FRP laminates:

    f fd = f fk / f (9)

    fd = fu / f (10)

    The characteristic values of the tensile strength and the ultimate strain are quoted from chapter 7.4. According to the German Guideline for the strengthening of concrete elements using unidirectionalCFRP laminates glued into slots [3] the following partial safety factors are valid:

    f = 1.2 for fundamental combinations

    f = 1.0 for accidental combinations

    Additionally it has to be proved, that the maximum strain in the laminate does not exceed f,max atultimate limit state:

    f,max k fd (11)

    As a contribution to the reduced ductility of CFRP strengthened elements the reduction factor k isassumed to 0.8.

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    9. Imposed actions

    Similar to the design of new elements, the imposed actions of the reinforced concrete element to bestrengthened must be known. The easiest way is to analyse the available as-built documents of the

    structure. If these documents are not available, geometry, idealised model of the structure and loadsmust be established by investigations on site. The bending moment, normal and shear force diagramshave to be determined considering the different type of loads and their combinations.

    It is necessary to determine the imposed bending moment of the structure during application of theFRP strengthening system for the evaluation of the initial state of strain. Normally this will be themoment due to dead load of the structure and eventually to the prestressing force. In any case thebending moment of the initial state results from service loads (load safety factor = 1.0).

    Furthermore, the characteristic and design bending moment due to expected future loads arerequired. The procedure of the determination of the moment curves is shown in figure 3.

    The design value of the bending moment M Sdf due to expected future loads must include the partialsafety factors (table 1) and the additional combination values which consider the probability ofoccurrence of several variable loads. For prestressed or post-tensioned elements the staticallyindeterminate part of the prestressing moment M p has to be considered for the determination of M Sdf .The statically determinate part of the prestressing moment M p0 , which is defined by the prestressingforce and the distance to centre of gravity of the concrete section, is considered by the designprogram.

    Q

    Q

    G

    G

    G

    MSd0,g+q

    MSk0,g

    MSdf,g+q

    Fig. 3 Load cases before, during and after

    strengthening with FRP system

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    10. Design procedure

    10.1 Capacity of the unstrengthened cross-section

    To check the strengthening ratio

    the bending capacity of the unstrengthened cross-section has to becalculated first. The design resistance of the unstrengthened cross-section M Rd0 is determinedconsidering the existing geometry, reinforcement, prestressing steel, concrete quality as well as thepartial safety factors for material properties listed in table 1. If as-built documents are not available thisinformation has to be established by investigations on site. Samples may be taken to check theconcrete compressive strength.

    10.2 Required cross-sectional area of FRP

    In the next step the program determines the strain distribution of the initial strain state. At this point theFRP material is still unstressed. The required cross-sectional area of FRP A f,req is calculated for the

    additional demand at strengthened state by superposition of the strain profiles. A strain state isestablished, which leads to an equilibrium of the internal and external forces of the cross-section.Figure 4 shows the superposition of the strains and the internal forces acting on a reinforced and aprestressed or post-tensioned concrete cross-section respectively. Normally prestressed or post-tensioned concrete cross-sections are uncracked in unstrengthened state, unless the prestressingforces are very low. Commonly under additional loads at strengthened state the prestressed or post-tensioned cross-section turns over into a cracked stage.

    =+

    =+Stahl-beton

    Spann-beton

    x

    x

    s s0 s= +

    c c0 c= +

    c c0 c= + c

    s s0

    c c0

    c,o

    c,u f

    f f

    f

    p p0 p= + p p0 Fp

    FsF f

    FsF f

    Fc

    ac

    d s d f

    dp d s d f

    a cFc

    Fig. 4 Superposition of the strain profiles and internal forces

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    10.3 Conditions of equilibrium

    The unknown values like the capacity of the unstrengthened cross-section M Rd0 , the imposed initialstrain state 0 , the required cross-sectional area of the FRP material A f,req and the resisting moment ofthe strengthened state M Rdf are derived from the conditions of equilibrium H = 0 and M = 0

    considering the mechanical behaviour of each material.

    Internal forces

    steel Fs = Es As s ss

    yk Af

    (12)

    FRP Ff = Ef Af f f f,limit (13)

    concrete c

    ckRc

    f xbF

    = ( R: parabolic form parameter) (14)

    H = 0Fc Fs Fp Ff = 0 (15)

    M = 0

    Fc ac Fs ds Fp dp Ff df = 0 (16)

    The solution for the equilibrium conditions in equations 15 and 16 is found by variation of the strainprofile. The strains are assumed to have linear distribution (Hypothesis of Bernoulli).The conditions forequilibrium are checked while running through the possible strain profiles within the defined limits:

    unstrengthened cross-section:

    0 < s su MRd0 is determined iteratively

    0 < c cu

    initial strain state:

    MSk0 is known S0 and C0 are determined iteratively

    design:

    MSdf is known

    0 < s su0 < c cu Af,req is determined iteratively

    0 < f f,limit

    strengthened cross-section:

    Af,prov is known

    0 < s su

    0 < c cu MRdf , and are determined iteratively

    0 < f f,limit

    The system of equations always leads to an unique solution.

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    10.4 Control of strain profiles

    Strains in ultimate limit state

    The program provides the user with the calculated strain profiles. The determined strain values can be

    compared with the strain limits of concrete and FRP (Fig. 5). Normally the design will be controlled byhighly stressed FRP material, i.e. the strain limit of CFRP. In cases where the design is limited byfailure of the compression zone the user should check if strengthening with FRP is still reasonable

    The design can be checked by hand calculation using the provided strain profiles and the equilibriumconditions in equations 15 and 16.

    cu

    f,lim 0 f,lim

    0 cu

    Lamellendehnungausgenutzt

    Betondehnungausgenutzt

    design controlled byconcrete strain limit

    design controlled bylaminate strain limit

    Fig. 5 Strain distribution in ultimate limit state

    Strains in service state

    The strain distribution in service state allows to control yielding of internal reinforcement under serviceloads. In addition stresses at service state are determined for concrete, reinforcing and prestressingsteel as well as the selected FRP cross-section.

    10.5 Control of stresses

    If the design and detailing is not in compliance with the rules given in Eurocode 2 to limit concrete andsteel stresses in service state, a verification of the stresses is necessary. In that case the followingstress limits for the rare combination of loads have to be respected.

    concrete c,limit = 0.6 f ck (17)

    reinforcing steel s,limit = 0.8 f yk (18)

    prestressing steel p,limit = 0.75 f pk (19)

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    11. Bond check of the FRP system

    11.1 Anchorage of externally bonded CFRP laminates

    The bonding characteristics of externally bonded CFRP laminates is totally different compared toembedded steel rebars. While steel rebars can be stressed up to the yielding point by increasing thebond length, the bond force of FRP laminates is limited. An increase in bond length above the lengthl bd does not result in an increase in resisting tensile stresses (see fig. 6). Based on tests a designmodel for the maximum bond failure force has been established in [8] for externally bonded steelplates on concrete structures.

    Fbd,max

    lbd,maxlb

    Fb

    bond force

    bond length

    Fig. 6 Relationship between bond length and bond force

    This model can also be applied to CFRP laminates in a modified form. It has become a substantialpart of the German guideline [2] and is generally accepted as being the most up-to-date andstraightforward to apply.

    The maximum bond failure force F bd,max (corresponds to T k,max in the German guideline [2]) can bedetermined using the design value of the surface tensile strength f ctd of the concrete:

    [N] f tnEkkbm5.0F csdf f f Tbf f max,db = (20)

    [N/mm] f f withc

    csmcsd

    = (21)

    The subscript d in equation 20 indicates a d esign value considering the partial safety factor forconcrete. Subscript f describes the properties of the FRP material while b corresponds to b ond.

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    The associated bond length l bd,max can be derived from the following equation (cf. [10]):

    [mm] f

    tnE58.0lcsd

    f f f max,bd = (22)

    where:

    mf number of laminates next to each other [ - ]bf laminate width [mm]nf number of laminates on top of each other [ - ]tf laminate thickness [mm]Ef modulus of elasticity of FRP laminates [N/mm]f csm surface tensile strength of the concrete [N/mm],

    valid for: 1.5 N/mm f ctm 3.0 N/mm. c partial safety factor for concrete [-]kT temperature reduction factor [-],

    taking into account temperature variations between -20C and +30C,0.9 for exterior components, 1.0 for interior components.

    kb width factor according to the German guideline [2]

    400/b1b/b206.1k

    f

    f b +

    = [-]

    b beam width or laminate spacing for slabs [mm]

    The factor 0.5 in equation 20 refers to the material characteristics of the adhesive bond. This

    explanation is also valid for equation 22. Additional information is given in the German guideline [2] orin the publications of Rostsy [7], [11] and Onken [10] respectively.

    The bond force F bd related to a bond length l b lbd,max can be calculated by the following equation:

    =

    max,bd

    b

    max,bd

    bmax,bdbd l

    l2l

    lFF (23)

    11.2 Anchorage of externally bonded carbon sheets

    The bond failure behaviour of FRP sheets is based on the same mechanical principles as CFRPlaminates. In the equation stated above the thickness of the laminate t f is replaced by the theoreticalfibre thickness of the selected sheet. The factor l f gives the number of layer glued one on top of eachother. The width factor k b is set to 1 for the calculation of the bond failure force of carbon sheets.

    Compared to CFRP laminates the surface of sheets is relatively large, so the bond behaviour is muchbetter than for CFRP laminates.

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    11.3 Calculation of the envelope line / verification of the anchorage

    The verification of the anchorage is carried out for ultimate limit state, considering the partial safetyfactors listed in table 1. For the application of externally bonded FRP systems the envelope line of thetensile forces has to be covered over the total length of the reinforced concrete element. Therefore the

    CFRP laminate or sheet should be extended to the support line as close as possible. It has to beproved that the design tensile force of the FRP material F fd,E does not exceed the bond failure forceF bd,max that can be transmitted by the associated length l bd,max (see fig. 6). The tensile force of the FRPsystem is determined from the moment line in the same way as the force of the internal tensionrebars.

    A distinction has to be made between solid slabs and beams. Since CFRP laminates applied on slabscannot be clasped by strap binders, the bond failure force has to be reduced. According to theGerman guidelines [2], [4]a reduction factor of 1.2 is introduced for slabs.

    beams: (24)df bd FF

    solid slabs: df bd F2.1

    F (25)

    Verification at an end support

    To avoid the determination of the whole envelope line for the tensile forces the bond check can becarried out for a certain point E according to the German guidelines [2], [4]. For the end support ofbeams or slabs it is assumed that the first crack due to the imposed moment will appear at the point E,which corresponds to the associated bond length l bd,max of the maximum bond failure force F bd,max . Themaximum distance from the end of the CFRP laminates or sheets to the edge of support should notexceed 50 mm for sagging moments (cf. [11]).

    x E

    ME

    E

    A s1 A f

    a Llbd a L

    f a i

    M(x)

    Fig. 7 Verification of the FRP end anchorage at the end support

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    25

    For reinforced concrete elements the definite point E for the calculation of the existing tensile forcein the FRP strengthening can be simply determined by adding up the following lengths (see fig. 7):

    xE = a i + f + lbd,max + aL (26)

    xE distance from point E to the theoretical support axisa i distance from the support axis to the support frontf distance from the end of FRP strengthening to the support front ( 50 mm)lbd,max bond length related to F bd,max according to equations 20 and 22aL horizontal displacement of the envelope line

    According to Eurocode 2 the following values are valid for the horizontal displacement of the envelopeline:

    beams: a L = 0.5 zm (cot cot ) (27)simplified for vertical stirrups and compression struts at 45:

    (cot cot ) = 1

    T-beams: a L = 0.5 zm (cot cot ) + x (28)with x = distance of reinforcement placed in the flange outside the web

    slabs: a L = dm (29)

    The distance x E is calculated by the program. The user must determine the corresponding bendingmoment M Sdf,E from the moment line of the structure. The tensile force F fd,E of the FRP material atpoint E is calculated from the entered design value of the bending moment by iteration of theequilibrium.

    From the entered design value of the bending moment at point E the program calculates the tensileforce of the FRP material F fd,E by iteration of the equilibrium.

    As prestressed or post-tensioned concrete members are usually uncracked near the support linethe bond check has to be modified. Externally bonded FRP systems always have to be anchoredbeyond the last flexural crack. The design program determines the cracking moment of theprestressed or post-tensioned cross-section considering the tensile strength of the concrete. The userthen has to enter the value x E which means the distance of the cracking moment from the support line,measured from the moment curve of the structure. Considering the selected FRP cross-section theprogram is calculating the tensile force F fd,E in the section at the point where the first crack will occur.

    This force is compared to the maximum bond force F bd,max of the selected FRP system.

    Following possibilities are recommended, if the anchorage verification according to equations 24 and25 may fail:

    increase the cross-sectional are of FRP,

    reduce the distance f between the end of FRP strengthening and the front of support,

    verify substrate strength (pull-off-test) and increase if possible,

    extend the FRP reinforcement beyond the support (e.g. slot-in end)

    increase the contact pressure of FRP reinforcement using additional anchorage devicesThe design program gives adequate advice.

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    Verification at an intermediate support for moment of span

    Since the position of the moment zero point varies with different load combinations the FRP systemshould be anchored at least 1 m beyond the zero-crossing of the horizontal displaced envelope line ofthe tensile forces. However, at least the bond length l bd,max related to the maximum bond force should

    be applied. According to the German guidelines [2], [4] the maximum distance from the end of FRPstrengthening to the front of support should not exceed 50 mm for sagging moments (cf. [11]).

    Ea

    L

    a i

    xE

    lb

    f

    M(x)

    As1 Af

    Fig. 8 anchoring verification for CFRP laminates and sheets at intermediate support

    At the intermediate support the point E refers to the zero point of the bending moment line. From thedistance x E , the program determines the distance f between the end of the CFRP laminates or sheetsand the front line of the support (see fig. 8).

    f max = xE a i aL lbd,max (30)

    Recommendation: f = xE a i aL lb with lb = 1 m

    xE distance from the theoretical support line to the moment zero pointaL horizontal displacement of the envelope linelb bond lengthf distance from the end of FRP strengthening to the support front

    If the existing length at the intermediate support is not sufficient to anchor the external bonded FRPsystem with the minimum bond length l bd,max , the program will calculate a negative value for f . In thiscase the bond forces have to be proved equivalent to the bond check at the end support or the FRPsystem must be extended beyond the support line.

    For prestressed or post-tensioned elements the verification of the anchorage at intermediate supportcan be performed by the same approach as for the end support.

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    Verification at an intermediate support for the moment at support

    The verification of the anchorage for the FRP top strengthening can be carried out in a similar way asfor the FRP bottom strengthening at the intermediate support. In the German guidelines [2], [4] it isrecommended to anchor the FRP system at least 1 m beyond the zero-crossing of the displaced

    envelope line. The program determines the distance from the intermediate support front line to the endof the FRP strengthening material (see fig. 9).

    a L

    As1

    Af lba LxE

    f a i

    E

    M(x)

    Fig. 9 Verification of the anchorage of FRP top strengthening at intermediate support

    f min = xE a i + aL + lbd,max (31)

    Recommendation :

    f = xE a i + aL + lb with lb = 1 m

    xE distance from point E to the theoretical support lineaL horizontal displacement of the envelope linelb bond lengthf distance from the end of FRP strengthening to the support front line

    11.4 Anchorage of near surface mounted CFRP laminates

    As already mentioned, compared to externally bonded strips, near surface mounted laminates have ahigher anchoring capacity. Therefore they can almost be stressed up to their tensile strength withincreasing bond length. Based on the investigations in [12] a design model was established for theanchoring of near surface mounted FRP laminates in the surrounding concrete cover. According to[12] the bond force F bd of the laminate depends on the bond length l b. It can be described by thefollowing equations:

    ( ) ]mm[115lfor l0015.04.0labmF bbb4 r d,Kf f bd = (32)

    ( ) ]mm[115lfor 115l70atanh065.02.26abmF bbr 4 r d,Kf f bd >

    += (33)

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    where:

    mf number of slotsbf width of the FRP laminate [mm]a r distance of the laminate axis to the edge of the member [mm],

    (valid for ar 150 mm)K,d design bond strength of the epoxy adhesive [N/mm]

    The characteristic bond strength K,k of the epoxy adhesive is determined with the following equation:

    ( ) k,Ktk,Kck,Ktk,Kc2 k,Ktk,Ktk,K f f f f f 2f 2

    ++= (34)

    For the determination of the design bond strength K,d according to the German Guideline for thestrengthening of concrete components using unidirectional CFRP laminates glued into slots in theconcrete [3] the following partial safety factors are valid:

    K,d = K,k / b (35)

    b = 1.3 for fundamental combinations

    b = 1.05 for accidental combinations

    The envelope line of the tensile forces is carried out at ultimate limit state under consideration of thehorizontal displacement in the same way as for externally bonded FRP systems. The envelope linehas to be covered by the envelope line of the resisting tensile force considering the internal steelreinforcement and the near surface mounted FRP laminates. Unlike externally bonded FRP systemsnear surface mounted laminates can be anchored from the point where they are theoretically nolonger required to cover the entire tensile force.

    The required bond length for near surface mounted FRP laminates results from transformation ofequations 32 and 33:

    [ ] ]mm[115lfor mmab0015.0

    F000009.0

    16.0003.0

    4.0l bd4r k,Kf

    E,fdbd

    = (36)

    ( ) ( ) [ ] ]mm[115lfor mm115

    tanh065.0

    2.26

    abtanh065.0

    Fl bd

    70a4

    r k,Kf 70a

    E,fdbd

    r r >+

    = (37)

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    11.5 Surface tensile strength of concrete

    A proper execution of strengthening with externally bonded FRP systems on site will always lead to afailure in the concrete covering layer (bond failure) and not to a failure in the adhesive substance. Anessential parameter for the adhesive bond of FRP systems is the surface tensile strength f csm of the

    existing concrete cover. The testing of the surface tensile strength has to be carried out according tothe relevant national regulation. Due to the German guidelines [2], [4], at least five tests should beperformed on each concrete element.

    For the calculation of the bond failure force the surface tensile strength can be applied according tothe German guidelines [2], [4] as the median value of the population. This value can be derived fromtest results under consideration of the student distribution with a statistical safety of 95%.

    arithmetic mediann

    ixxm

    = (38)

    standard deviation )xx(1n

    1smi

    = (39)

    median of the population (40)skxf mcsm =

    xi strength of test in number of testsk reduction factor

    Depending on the number of tests, the reduction factor k can be taken from the following table (seeGerman DIN 1048 )

    n 5 6 7 8 9 10 15 20 25 30 35

    k 0.953 0.823 0.734 0.67 0.62 0.58 0.455 0.387 0.342 0.31 0.286

    Tab. 2 Reduction factor k for the calculation of the median of the population (German DIN 1048)

    Example

    Test Nr. x i [N/mm] (xi xm)1 2.0 1.10252 2.2 0.7225

    05.363.18xm ==

    3 3.5 0.20254 4.0 0.90255 3.1 0.0025

    792.0135.316 1s ==

    6 3.5 0.2025Total 18.3 3.135

    ]mm/N[40.2792.0823.005.3f csm ==

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    12. Anchorage of bottom reinforcement at end support

    On account of the truss model used for the shear design the bottom reinforcement has to be properlyanchored at end and intermediate supports. The required conditions are stated in Eurocode 2. It is

    necessary toa) retain not less than 25% (or 50% for slabs) of the required steel section present in the

    span

    b) cover the tension force, which is derived from the truss analogy considering the shearand normal force at the support

    A,Sdf m

    L A,Sdf sR Nd

    aVF +

    = (41)

    The maximum value of both conditions is valid for the anchorage of the bottom reinforcement.

    Normally the first condition is only valid for the new design of structural concrete elements, not forstrengthening. Applied to existing concrete elements to be strengthened 25% (or 50%) of the tensionalforce due to the maximum moment of span has to be anchored at the supports. For strengthenedsystems the combined maximum tensile force of the internal steel reinforcement and the external FRPsystem has to be considered.

    As long as the existing bottom reinforcement is not curtailed, the internal rebars extended beyond thesupport line are normally sufficiently anchored an strengthened state. The program calculates therequired anchorage force at the support from the two conditions mentioned above and determines thepart of the tensile force covered by the internal rebars. It is calculated from the circumference of the

    bar and the bond strength f bd:

    bds

    s A,s A,s f d

    A4lF

    = (42)

    If the internal reinforcement is not sufficient for the anchorage an strengthened state, a part of the FRPstrengthening has to be extended beyond the support front line. The software determines the tensileforce to be anchored and the required bond length.

    In practice the anchorage of FRP systems beyond the support line is very difficult and questionable.Under slabs supported by masonry walls, externally bonded CFRP laminates can be extended to theadjacent span by removing one brick of the wall.

    At concrete walls and beams the only adequate solution is to slot-in the end of the laminate and injectthe slot with epoxy paste. If the slot is sufficiently thin (d 10 mm), a verification of the anchorageaccording to chapter 11.4 is possible.

    In contrast to externally bonded FRP systems, an additional anchorage of near surface mountedlaminates beyond the support front line can hardly be realised in practice.

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    13. Detailing provisions

    For externally bonded FRP strengthening the spacing of the strips is limited. According to the German guidelines [2] [4]different limits are valid for the FRP systems.

    Externally bonded laminates and sheets

    edge distance: a r,min = cw (43)

    axial spacing: s f,max = 0.2 l (bearing distance) (44)sf,max = 5 h (slabs) (45)sf,max = 0.4 l (cantilevering length)

    Near surface mounted laminates

    edge distance: a r,min = 2 bf (46)a r,min = dk (47)

    axial spacing: s f,min = dk (48)sf,min = bf (bei a s > 2 ds) (49)

    slot: ts,max = cw h (50)bs,min = tf + 1 [mm] (51)bs,max = tf + 3 [mm] (52)

    where:

    cw concrete cover of internal stirrupsdk maximum diameter of aggregates in concreteas axial spacing of internal longitudinal rebarsds diameter of internal longitudinal rebarsts, depth of the slotbs width of the slot h allowance for tolerances of the concrete cover

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    14. Shear design

    14.1 Shear capacity according to Eurocode 2

    In most cases of flexural strengthening with FRP systems, it is necessary to check the shear capacityof the concrete structure as well. Especially beams they also require shear strengthening. On theother hand for concrete solid slabs it may be proven that shear reinforcement is dispensable forexpected future loads. If not, other strengthening methods have to be considered.

    According to Eurocode 2 the imposed shear force V Sd can either be transferred by the concrete aloneor in combination with shear reinforcement. The shear resistance is described by the design valuesV Rd1 to V Rd3 . For the calculation of the shear reinforcement the standard method is applied consideringvertical stirrups and an inclination of the compression struts of 45. The relevant equations accordingto Eurocode 2 can be taken from the following flowchart (fig. 11).

    VRd1 shear resistance without shear reinforcement shear force is transferred by concretealone,

    VRd2 maximum shear resistance the capacity of the inclined compression struts isdecisive for the shear resistance,

    VRd3 shear resistance with shear reinforcement the shear force transmission results fromconcrete and shear reinforcement.

    The lower design value V Rd1 is the relevant value for slabs which are usually constructed without anyshear reinforcement. Presenting the uppermost limit, V Rd2 must not be exceeded by the imposed shear

    force.Following the conditions given in the German guidelines [2] [4] and according to Eurocode 2, adistinction has to be made between four different cases with regard to the shear force capacity of astrengthened concrete structure (see [10]):

    1. In case that the existing shear force V Sdf of the structure at strengthened state is lower than theshear resistance V Rd1 of the concrete alone, no shear strengthening is necessary. This casegenerally applies to slabs.

    1RdSdf VV (53)

    V Sdf and V Rd1 are determined considering the partial safety factors in Table 1.2. If the shear force at strengthened state can be completely covered by the existing internal stirrups,

    minimum shear strengthening is necessary to complete the mechanical truss model

    VV 3RdSdf (54)

    The additional shear reinforcement has to clasp the flexural strengthening and is designed for theshear force difference V depending on the strengthening ratio.

    Sdf V1V

    = (55)

    In this case, anchorage of the shear strengthening in the compression zone can be omitted (seeFig. 11).

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    The fact that additional shear reinforcement in the form of external bonded stirrups is necessarydespite sufficient internal shear reinforcement is justified by the concrete beam design trussanalogy. The additional tension chord of the external flexural strengthening must be connected tothe tension struts of the internal stirrups for completion of the truss model (fig. 10, see [10]).

    Fig. 10 Connection of the FRP flexural strengthening to the internal truss structure

    As1 Af

    internal stirrups

    compression chord

    tension chords

    concrete compression strut

    s w

    shear s trengthening

    3. If the shear force demand at strengthened state exceeds the shear capacity of the existing cross-section, the shear strengthening has to be designed for the remaining amount of shear force.

    VV 3RdSdf > (56)

    VVV 3RdSdf = or Sdf V1V

    = (57)

    The higher value V of both conditions in equation 57 is valid for the design. Since the additionalshear reinforcement is necessary to cover the total shear force of the cross-section, the external

    stirrups have to be anchored in the compression zone (see fig. 11).4. The maximum shear resistance V Rd2 provides the upper limit of the shear force also for

    strengthened state. However, the German guidelines [2] [4] do not permit shear strengthening ofhigh stressed beams. Therefore in the program it is recommended to limit the maximum shearcapacity in the design concept of Eurocode 2 as well. Reducing the maximum shear capacity to50 % (Vmax = 0.5 VRd2) corresponds approximately to the limitation given in the German guidelines [2] [4]

    VV maxSdf (58)

    V5.0V 2RdSdf (59)

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    x

    VSdf < VRd3 VSdf > VRd3

    x

    Fig. 11 Anchorage of the additional shear reinforcement depending on the imposed shear force

    Fig. 12 Flowchart for the shear check of strengthened beams according to Eurocode 2

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    Even if additional external stirrups are not required to cover the imposed shear force (case 1), it isrecommended for beams to clasp the FRP flexural strengthening system at least with 2 externalstirrups at the end of the beam. For strengthening the moment of span these external stirrups shouldbe anchored in the compression zone. For moments of support an additional anchorage of the flexuralstrengthening with external stirrups can be omitted.

    14.2 Design of the additional shear reinforcement

    As additional shear reinforcement, steel plates as well as high modulus carbon sheets (unidirectionalfabrics) can be used. The sheets have a modulus of elasticity of about 640'000 N/mm (C-Sheet 640),they are easier to handle than steel plates and therefore the application is more economical despitethe price of the material.

    The required cross-section of the additional shear reinforcement in form of steel plates or sheets has

    to be determined for the remaining shear force difference V (eq. 55 and 57).

    The internal steel stirrups and the external stirrups made of steel plates or carbon sheets areconsidered as parallel connected elastic or elastic-plastic elements. The strain conformity of theseelements must be ensured also at strengthened state. Therefore the same strain limit of limit = 0.2 %according to [7]will be taken as a basis for the design.

    The stress of the internal stirrups to determine the shear capacity V Rd3 must be limited according toequation 60:

    ydsitlimsw f E = (60)

    The required cross-sectional area of the additional external shear reinforcement results from thefollowing equation:

    fwf req,w z

    Va

    = (61)

    where:

    V shear force difference covered by the additional external shear reinforcementzf internal lever arm between the concrete compressive force and the flexural strengthening

    is iteratively determined by the program fw stress of the additional external shear reinforcement (at limit= 0.2 %)

    Steel plates:

    ydsitlimfw f E = (62)

    Carbon sheets:

    fditlimfw E= (63)

    Since the carbon sheets are rather weak during handling and are applied by hand lamination atbuilding site conditions, it is doubtful that the high modulus of elasticity of about 640'000 N/mm will be

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    achieved in practice. Therefore the modulus of elasticity in equation 63 should be reduced for carbonsheets as shown in figure 13. For this a reduction factor of E = 1.2 is recommended in [10]:

    f

    fu

    f

    E f k E f d

    lim

    Efd = Efk / E (64)

    Fig. 13 Reduction of the modulus of elasticity of carbon sheets (design value)

    Spacing of external stirrups

    Steel plates:

    The maximum spacing of the plates s w,max results from the truss analogy and is approximately equal tothe effective depth of the FRP flexural strengthening (see fig. 10) which corresponds to the overallheight of the beam.

    sw,max = h (65)

    Carbon sheets:

    When strengthening with carbon sheets C-Sheets 640, a maximum strip spacing of 80 % of the overallheight of the beam is recommended.

    sw,max = 0.8 h (66)

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    14.3 Anchorage of external stirrups

    If only minimum external stirrups are required without anchorage in the compression zone, (case 2:Vsdf VRd3), it has to be proved, that the adhesive bond of the external stirrups provides a sufficientanchorage. For this check the bond behaviour as stated in chapter 11 can be applied, where the

    material properties of steel plates or carbon sheets have to be considered.

    As the form an the location of shear cracks can not be predicted, according to the German guideline [2] it has to be proved, that the tensile force of the additional external stirrups does not exceed 50 % ofthe bond force F bd as given in equation 23:

    Fwd 0.5 Fbd (67)

    The external stirrups always have to be bonded over the whole height of the web. But only half of theexisting bond length l bw at the side of the web can be considered for l b in equation 23 (see fig. 14):

    lb 0.5 lbw (68)

    hlbw

    s wbws ws w

    s w,max = 0,5 h l b = 0,5 l bw

    h1

    lb

    FRP LamelleFRP laminate

    Laschenbgelexternal stirru Schubrishear crack

    Fig. 14 Adhesive bond anchorage of minimum external stirrups

    The tensile force of the external stirrups is determined according to Eurocode 2 using the followingequations:

    zV5.0f wdwd = per meter for one side of the web (69)

    zsV

    5.0F wwdwd

    = each leg of a stirrup (70)

    For external stirrups that are only anchored by adhesive bond, differing from equations 65 and 66 thefollowing is valid:

    sw,max = 0.5 h (71)

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    15. Further checkings

    In addition to the calculations which can be carried out with the program FRP Lamella , the structuralengineer should also check cracks and deformations of the strengthened structure if necessary.

    According to the most national regulations or guidelines, the control of crack widths at strengthenedstate is not required. Nevertheless, in a special case where it may be necessary, you should makesure that durability and serviceability of the strengthened concrete structure are ensured. Please notethat strengthening with FRP products has no significant influence on the deformations of astrengthened concrete structure. In case of deflection problems, preference should be given to otherstrengthening methods like for instance sprayed concrete.

    16. Fire protection

    If fire protection is required, the program enables the user to check the remaining safety for serviceloads under the condition that the external bonded FRP system and the external stirrups willcompletely fail. Please note that epoxy resins may loose their load bearing capacity when thetemperature approaches 80 C. If necessary it has to be proved in special cases by an approval or anexpert opinion that the FRP system and the external stirrups are sufficiently protected against fire,using additional protective measures as for instance fire protection plates.

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    17. Program user interface

    17.1 Start of the program

    The program is developed for the following Windows operating systems: Win 9x, 2000, NT.

    After successful installation of FRP Lamella you start the program by either clicking the FRP Lamella icon on the Desktop or choosing the option FRP Lamella in the Windows start menu of your computer.First the disclaimer will appear. You have to accept to start the FRP Lamella program window.

    To exit the program FRP Lamella and close the window, click the cross in the title bar at the upperright corner of the program window. Instead you can either choose the option exit of the file menu.

    17.2 Settings

    To ensure optimum display performance of the FRP Lamella program on your screen a minimumscreen resolution of 800 x 600 pixel is assumed.

    The display font size is also essential for a proper display of the program window. In the Windowsmenu Start point to Settings , click Control Panel , and then double click Display . On the Settings tab,click Advanced , then you will find the Font Size list on the General tab. Small fonts (standard) shouldbe selected, otherwise several items might not be completely displayed.

    17.3 Basic information about the FRP Lamella user interface

    You will find general information about Windows user interfaces in your Windows manual or in theonline help function of your Windows operating system.

    Title bar The uppermost line of the FRP Lamella program window shows informationabout program, data file and path.

    Menu bar The items File, Calculation, Extras and Info on the menu bar lead to differentsubmenus. You will find a detailed list of all menu items in chapter 19.1.

    Tool bar The most frequently required functions can easily be called from the toolbar byclicking one of the symbols. You will find a detailed list of all tool bar symbolsin chapter 19.2.

    Tree view The tree views in the left part of the program window enable you to call thedifferent input and output windows directly. Click the + symbol in front of aheading to display the subordinated items. A click on the symbol hides thesubordinated items again.

    Quick info Positioning the mouse pointer on one of the input or output fields anexplanation (tooltiptext) will appear after a few seconds. Proceed in the sameway to get explanations for the functions of the tool bar.

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    17.4 Data input

    The required data is entered on several input windows shown in the upper part of the program userinterface. The titles of the different windows are listed in the opposite tree view. They are classifiedaccording to the topics general information, cross-section, loads, strengthening and proofs. Everyinput window shows a graphic to illustrate the essential data.

    To show the different input windows click the related title in the tree view . If one heading includesseveral subordinated windows, the first window will be displayed automatically. Input windows thatare not accessible yet are displayed in light grey.

    Use the button on the right below the picture box of each input window to display the nextwindow. It is recommended to follow the sequence of the windows to make sure that no window isleft out. The button on the left below the picture box leads to the previous input window.

    Enter the required data in the provided text boxes of each window. If necessary overwrite theentry 0 . Text boxes with a grey font are locked and cannot be modified. Disabled text boxeshaving a dark background are not considered in the calculations.

    The key button in the toolbar enables you to unlock input fields having a grey font and modify thepreselected values.

    For some items you can choose from a list of different values.

    After you have entered all required data you can start the calculation either by clicking thecalculation button below the graphic of the input window FRP cross-section or by clicking the

    calculator symbol in the toolbar.

    Start the proofs of anchorage and shear capacity by clicking the proof button below the graphicof the corresponding input window. A click on the tick symbol in the toolbar will carry out allproofs successively. This function is useful after reopening an existing input data file.

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    17.5 Output of results

    The results are displayed in additional windows located in the lower part of the program user interface.The titles of the different windows are listed in the opposite tree view. They are classified according tothe topics general information, strengthening and proofs.

    To show the different output windows click the related title in the tree view . If one headingincludes several subordinated windows, the first window will be displayed automatically. Outputwindows that are not accessible yet are displayed in light grey

    The result values are displayed in text fields having a light grey or coloured background. Thesevalues cannot be modified.

    Pay attention to the output fields highlighted in blue or red colour. They will show you if the proofconditions are met and if special details of construction have to be followed.

    The output windows of strains in ultimate limit state and strains in service state additionally show agraphical representation of the strain distribution (s. chap. 18.15 and 18.16) . You can changethe scale by clicking the picture.

    After the calculation of certain proofs you have to design a sufficient strengthening. The requiredinput data is entered in the white text boxes of the output window (s. chap. 18.20 and 18.23) .

    The performed calculations can be printed on any printer installed under Windows operating systems.You can modify the content of the heading line in the menu Extras >> company letterhead . It ispossible to print each page individually.

    pages 1 4 design of flexural strengthening

    page 5 proof of FRP end anchoragepage 6 proof of anchorage of flexural reinforcement at supportpage 7 design of shear strengthening

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    18. Input and output windows

    18.1 Input window project

    When you start the program the first window project opens. It offers the possibility to enter somegeneral project and structural element data. This information appears on each page of the printout andwill help you administrating your projects.

    Enter the project number and the project name .

    For each structural element you can enter a number and an appropriate description .

    tipUse the button on the right below the picture box to display the next window.

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    18.2 Input window code

    In this window you can choose the underlying code and guideline for the design. Additionally youdetermine the material properties as well as the unit measurement for the input and output.

    Choose the code according to which standard you want to perform the design of thestrengthening measure simply by clicking the related option button (not every version offers thepossibility to choose the code).

    Afterwards choose the guideline on which the design of FRP strengthening shall base.

    Select a country for the available steel and concrete grades based on the national standard thatwill appear on the steel and concrete window, respectively. The appropriate national flag appearsnext to the selection box.

    You have the choice from different units of measurement: the unit of lengths and forces as well asthe unit of strains.

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    18.3 Input window geometry

    FRP Lamella offers the possibility to strengthen the most frequent types of cross-section: slabs,rectangular beams, T-beams and I-beams. According to your choice FRP Lamella will present anappropriate illustrating graphic.

    Click the geometry list and choose the type of cross-section.

    Enter the dimensions of the cross-section in the corresponding data fields.note

    After entering all data the graphic turns into a true to scale graphic to allow a visual control of thevalues.

    Please indicate whether you want to strengthen an exterior or interior structural member. According to the German guidelines [2], [3] for external concrete members the program willconsider a temperature reduction factor k T for the bond strength of externally bonded FRP stripsdue to temperature variations from 20 C to 30 C (s. chap. 11.1, 11.2) .

    For slabs please indicate the span or the cantilever length. This input data field will be displayedwhen you select a slab. The length is required to calculate the maximum spacing of FRP strips.(s. chap. 18.13) .

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    18.4 Output window cross-section

    After entering the size of the structural member the cross-section values are calculated and shown inthe lower part of the user interface.

    The upper field shows the gross cross-sectional area A g of the structural member.

    The gravity axis z cg of the cross-section is related to the top of the member.

    Furthermore the moment of inertia I y of the cross-section is given.

    The section modulus W top and W bottom apply to the top and the button of the cross-section.

    noteThe cross-section values are related to the gross cross-section of the member.

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    18.5 Input window concrete

    The window concrete indicates the material properties of the concrete. You can select the concreteclasses according to the chosen code.

    Select the existing concrete class of the member from the list. The appropriate characteristiccompressive strength f ck will be displayed in the next field. If the required concrete class is notavailable in the list, select the option other , this enables you to define the characteristic strength(s. chap. 7.1) .

    The concrete maximum strain cu is limited to 0.35 [%] according to Eurocode 2.

    The strain at the axis of the parabolic curve c1 is assumed to be 0.2 [%] according toEurocode 2 (Model Code).

    The reduction factor is a coefficient taking into account long term effects on the compressivestrength. It is generally assumed to be = 0.85.

    The basic value of the design shear strength Rd is calculated from the characteristic cylindercompressive strength (s. chap. 7.1) .

    The average modulus of elasticity of concrete E cm is necessary for the calculation of theuncracked state of the structural member.

    The characteristic tensile strength of the concrete f ctm defines the transition between theuncracked and the cracked state of the cross-section.

    The partial safety factor c for concrete is preselected as c = 1.5 according to Eurocode 2.(s. chap. [1])

    noteYou can modify the proposed values by using the key button in the tool bar.

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    18.8 rebar tables for the selection of reinforcement cross-sectional area

    The cross-sectional area of reinforcement can be copied from a table which offers a wide selection ofrebar diameters. The cross-sectional area is depending on the number of rebars in a beam or thespacing of rebars in a slab. To open the rebar table just click the number button in the input windowsmain reinforcement and reinforcement at support , respectively.

    Choose a cross-sectional area by clicking a white field in the table. The background of a selectedfield turns into blue. For beams, a multiple choice is possible. The sum of the cross-sectionalarea A s of the selected rebars is displayed below the table.

    You cancel the selection by clicking the blue field again.

    You can copy the selection to the reinforcement window by clicking the copy button. The rebartable will be closed.

    Close the table without copying the value by clicking the cancel button.

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    18.9 Input window flexural reinforcement at support

    Details about the existing rebars at support can be entered in the window flexural reinforcement atsupport . Additional information is needed for the proof of anchorage at support.

    Enter the cross-sectional area A s for every layer of reinforcement. The value is automaticallycopied from the previous input window main reinforcement .

    tipClick the number button at the beginning of each line and an additional window shows a table ofrebars diameters. You can select the number and the cross-section for groups of rebars and copythe total sum of the cross-sectional area of reinforcement to the input window (s. chap. 18.8) .

    The position of the reinforcement is given by the depth z s measured from the top edge of thestructural member to the axis of the rebars. The default values are copied from the previous inputwindow main flexural reinforcement .

    For prestressed steel layers the prestress p0 at the region of support is needed. The defaultvalues are copied from the previous input window main flexural reinforcement .

    Enter the diameter d s

    of the rebars.

    For determination of the anchorage force the anchorage length l s,A from the support front isneeded.

    Choose the coefficient for effectiveness of anchorage a . According to Eurocode 2 the value is1.0 for straight bars. For hooks, bends, loops and welded transverse bars in the anchorage zonethe value can be reduced to 0.7.

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    To define the transition between the uncracked and the cracked state of the cross-section, decideif the bending tension zone of the cross-section is already cracked under service loads.Reinforced concrete members are usually always cracked, for prestressing members it dependson the degree of prestress and the history of loading. As a rule the cross-section is uncracked formaximum prestress (no tensile forces in service state).

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    18.11 Input window loads in strengthened state

    The window loads in strengthened state defines the future actions. You have to enter the bendingmoments which are imposed to the concrete member after strengthening with FRP (s. chap. 9) . Thegraphic schematically presents the strengthened state as a bridge girder, which is loaded by deadload of the structure and an additional high live load.

    Choose the design for a positive (moment of span) or negative moment (moment at support).

    noteThis choice is linked with the type of moment in the window loads in strengthened state . It is notpossible to choose different types of moments in both windows.

    If the member is subjected to an external axial force, e.g. the dead load of an inclined beam, youhave to choose between compressive and tensile force .

    Enter the design bending moment M Sdf for the expected loads considering the partial safetyfactors for permanent and variable loads as well as the combination value . For staticallyindeterminated systems you may have to add the secondary moment from prestressing M p ' . (s.chap. 18.10) .

    Proceed in the same way for the design axial force N Sdf . Take also into consideration thedifferent partial safety factors and the combination value .

    You can either enter the exact values of imposed actions in service state or choose the optionapproximate . In this case the characteristic values of the bending moment and axial force arecalculated from the given design values as follows:

    m,M

    Sdf Skf

    MM

    = m,N

    Sdf Skf

    NN

    =

    note

    The use of the option approximate is especially recommended if the design actions aredetermined by a complicated structural analysis (e.g. finite elements). Using the average safetyfactors you can avoid another analysis applying characteristic loads without partial safety factors.

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    18.13 Input window FRP cross-section

    On the window FRP cross-section you are asked to choose the number and arrangement of the FRPproducts. Observe the minimum and maximum spacing respectively. You can choose up to threelayers with different cross-sectional areas as well as different effective depths.

    Before selecting the FRP cross-section, start the iteration either by clicking the calculation button on the bottom right of the window or by clicking the calculator symbol in the toolbar. Therequired FRP cross-sectional area will be calculated and displayed in the output window design below.

    noteTo carry out the design calculation, in this window only the depth z f1 of the FRP layer 1 from thetop edge of the concrete member has to be given. As the design iteration can only determine thecross-sectional area of one FRP layer (one unknown), FRP layers 2 and 3 are initially locked, butthey are enabled after the design calculation.

    For each layer choose an FRP cross-section . The available selection depends on the chosenFRP product in the window FRP System. For sheets the theoretical fibre thickness t f is given

    and you can choose the width b f of the sheet. The delivery width of the sheet is preselected. Enter the number of FRP plies n f lying on top of each other. One single ply is preselected. The

    maximum is two plies of laminates or five plies of sheets.

    For beams enter the number m f of FRP strips lying next to each other. The spacing s f of the stripsis calculated.

    For slabs of a standard width (1 [m] or 12 [in]), enter the spacing s f of the strips. The number m f of FRP strips lying next to each other is calculated. The limit spacing s f,max or s f,min respectively, iscalculated according to the German guideline s [2] [4]with following conditions(s. chap. 13) :

    s f,max = 0,2- times span

    s f,max = 5- times slab thicknesss f,max = 0,4- times cantilevering lengths f,min = maximum size of aggregate 32 mm (near surface mounted laminates)

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    For each layer the cross-sectional area A f is calculated. The total sum of FRP strips in one layeris calculated from the number of plies l f multiplied by the number of strips n f .

    For each layer determine the depth z f of the FRP reinforcement from the top edge of the concretemember. To guarantee the position of the bonded FRP system in the tension zone, keep the limitz f,min and z f,max respectively. The depth of the tension zone corresponds approximately to a fifth ofthe member height.

    The lateral distance a r of FRP strips to the edge of the member is only required for thecalculation of the bond force of near surface mounted laminates (s. chap. 11.4) .For all types of FRP keep the minimum distance a r,min (s. chap. 13) .

    tipThe program checks if the arrangement of FRP strips fits to the tension face of the member, takinginto consideration the lateral distance to the edge. A message will appear if the strengtheningdoes not fit.

    note After the determination of the required FRP cross-section the outstanding information can be given toensure the sufficient moment capacity of the strengthened member (s. chap. 18.14) . All 3 FRP layersare taken into account for the determination of the resisting moment in strengthened state.

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