English Version. Eurocode 2: Design of concrete structures - Part 4: Design of fastenings for use in concrete

Transcription

1 EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM DRAFT pren September 213 ICS ; Will supersede CEN/TS :29, CEN/TS :29, CEN/TS :29, CEN/TS :29, CEN/TS :29 English Version Eurocode 2: Design of concrete structures - Part 4: Design of fastenings for use in concrete Eurocode 2 - Calcul des structures en béton - Partie 4: Conception et calcul des éléments de fixation pour béton Eurocode 2 - Bemessung und Konstruktion von Stahlbetonund Spannbetontragwerken - Teil 4: Bemessung der Verankerung von Befestigungen in Beton This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee CEN/TC 25. If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to provide supporting documentation. Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without notice and shall not be referred to as a European Standard. EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1 Brussels 213 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. pren :213: E

2 Contents Foreword Scope General Type of fasteners and fastening groups Fastener dimensions and materials Fastener loading Concrete strength Concrete member loading Normative references Definitions and symbols Definitions Notations Indices Superscripts Actions and resistances Concrete and steel Units Basis of design General Required verifications Design format Verification by the partial factor method Partial factors for actions Partial factors for resistance Project specification and installation of fasteners Determination of concrete condition Durability Derivation of forces acting on fasteners - analysis General Headed fasteners and post-installed fasteners Tension loads Shear loads Anchor channels General Tension loads Shear loads Forces assigned to supplementary reinforcement General Tension loads Shear loads Verification of ultimate limit state General Headed and post-installed fasteners Tension load Shear load Combined tension and shear load Fasteners for multiple use for non-structural applications Anchor channels Tension load Shear load Combined tension and shear loads Page 2

3 8 Verification of ultimate limit state for fatigue loading General Derivation of forces acting on fasteners - analysis Resistance Verification for seismic loading General Requirements Derivation of forces acting on fasteners Resistance Verification for impact loading Verification for fire resistance Verification of serviceability limit state...81 Annex A (normative) Additional rules for verification of concrete elements due to loads applied by fastenings...82 A.1 General...82 A.2 Verification of the shear resistance of the concrete member...82 Annex B (informative) Durability...84 B.1 General...84 B.2 Fasteners in dry, internal conditions...84 B.3 Fasteners in external atmospheric or in permanently damp internal exposure...84 B.4 Fasteners in high corrosion exposure by chloride and sulphur dioxide...84 Annex C (normative) Design of fastenings under seismic actions...85 C.1 General...85 C.2 Performance categories...85 C.3 Design criteria...86 C.3.1 General...86 C.4 Derivation of forces acting on fasteners analysis...88 C.4.1 General...88 C.4.2 Addition to EN :24, C.4.3 Addition to EN :24, C.4.4 Additions and alterations to EN :24, C.4.5 Additions and alterations to EN :24, C.5 Resistance...9 C.6 Anchor displacements...92 Annex D (informative) Exposure to fire design method...93 D.1 General...93 D.2 Partial factors...93 D.3 Resistance under fire exposure...93 D.3.1 General...93 D.3.2 Tension load...93 D.3.3 Shear load...95 D.3.4 Combined tension and shear load...96 Annex E (normative) Characteristics for the design of fastenings to be supplied by European Technical Products Specification

4 Foreword This document (pren :213) has been prepared by Technical Committee CEN/TC 25 Structural Eurocodes, the secretariat of which is held by BSI. This document is currently submitted to the CEN Enquiry. This document will supersede CEN/TS :29, CEN/TS :29, CEN/TS :29, CEN/TS :29, CEN/TS :29. The numerical values for partial factors and other reliability parameters are recommended values. The recommended values apply when: a) the fasteners comply with the requirements of 1.2 (2), and b) the installation complies with the requirements of 4.5. National Annex for EN This EN gives values with notes indicating where national choices may have to be made. When this EN is made available at national level it may be followed by a National Annex containing all Nationally Determined Parameters to be used for the design of fastenings according to this EN for use in the relevant country. National choice of the partial factors and reliability parameters is allowed in design according to this EN in the following sections: 4.4.1(2), Note; (1), Note 1; (1), Note; (1), Note; 4.6(2), Note 2; Annex B (informative); C.2(2), Table C.1; D.2(1), Note. 4

5 1 Scope 1.1 General (1) This EN provides a design method for fastenings (connection of structural elements and non-structural elements to structural components), which are used to transmit actions to the concrete. Inserts embedded in precast concrete elements during production, under Factory Production Control (FPC) conditions and with the due reinforcement, intended for use only during transient situations for lifting and handling, are covered by the CEN/TR Design and Use of Inserts for Lifting and Handling Precast Concrete Elements, by CEN/TC 229. (2) This EN is intended for safety related applications in which the failure of fastenings will result in collapse or partial collapse of the structure, cause risk to human life or lead to significant economic loss. In this context it also covers non-structural elements. (3) The support of the fixture may be either statically determinate or statically indeterminate. Each support may consist of one fastener or a group of fasteners. (4) This EN is valid for applications which fall within the scope of the series EN In applications where special considerations apply, e.g. nuclear power plants or civil defence structures, modifications may be necessary. The transmission of the fastener loads to the supports of the concrete member shall be shown for the ultimate limit state and the serviceability limit state according to EN (5) This EN does not cover the design of the fixture. The design of the fixture shall be carried out to comply with the appropriate Standards. (6) This document relies on characteristic resistances and distances which are stated in a European Technical Product Specification (see Annex E). At least the characteristics of Annex E, Table E.1 should be given in a European Technical Product Specification providing a basis for the design methods of this EN. 1.2 Type of fasteners and fastening groups (1) This EN uses the fastener design theory 1) (Figure 1.1) and applies to: a) cast-in fasteners such as headed fasteners, anchor channels with rigid connection between anchor and channel; b) post-installed mechanical fasteners such as expansion anchors, undercut anchors and concrete screws; c) post-installed bonded anchors, bonded expansion anchors and bonded undercut anchors. NOTE Connections with post-installed ribbed reinforcing bars should be covered by a European Technical Product Specification and comply with the requirements of EN (2) For other types of fasteners modifications of the design provisions may be necessary. (3) This EN applies to fasteners with established suitability for the specified application in concrete covered by provisions, which refer to this EN and provide data required by this EN. The suitability of the fastener is stated in the relevant European Technical Product Specification. 1) In fastener design theory the concrete tensile capacity is directly used to transfer loads into the concrete component. 5

6 Figure 1.1 Fastener design theory, example (4) This EN applies to single fasteners and groups of fasteners. In a fastening group the loads are applied to the individual fasteners of the group by means of a common fixture. In this EN it is assumed that in a fastener group only fasteners of the same type and size are used. The configurations of fastenings with cast-in place headed fasteners and post-installed fasteners covered by this EN are shown in Figure 1.2. For anchor channels the number of fasteners is not limited. 6

7 Key 1 Fastener 2 Steel plate a) Fastenings without hole clearance for all edge distances and for all load directions, and fastenings with hole clearance according to Table 6.1 situated far from edges (c max{1h ef, 6d nom }) for all load directions and fastenings with hole clearance according to Table 6.1 situated near to an edge (c< max{1h ef, 6d nom }) loaded in tension only b) Fastenings without and with hole clearance according to Table 6.1 situated near to an edge (c <max{1h ef, 6d nom }) for all load directions Figure 1.2 Configuration of headed and post-installed fastenings covered by this EN NOTE Configuration with three fasteners is not recommended close to an edge (c i < 1mm) as there are no safe design models for shear loads. 1.3 Fastener dimensions and materials (1) This EN applies to fasteners with a minimum diameter or a minimum thread size of 6 mm (M6) or a corresponding cross section. In general, the effective embedment depth should be: h ef 4 mm. The actual value for a particular fastener shall be taken from the relevant European Technical Product Specification. In case of post-installed chemical fasteners the effective embedment depth is limited to h ef 2d nom. In case of fasteners for multiple use for non-structural applications as addressed in 7.3 the minimum thread size is 5 mm (M5) and the effective embedment depth shall be at least 3 mm, which in special cases (internal exposure conditions only) can be reduced to 25 mm. (2) This EN covers metal fasteners made of either carbon steel (ISO 898, EN 125, EN 18), stainless steel (EN 188, ISO 356) or malleable cast iron (ISO 5922). The surface of the steel may be coated or uncoated. This EN is valid for fasteners with a nominal steel tensile strength f uk 1 N/mm². This strength limit does not apply to concrete screws. The binding material of bonded fasteners may be made primarily of resin, cement or a combination of the two. In addition inorganic fillers may be used. 7

8 1.4 Fastener loading (1) Loading on the fastenings may be static, quasi-static, fatigue, impact and seismic. The suitability of the fastener to resist fatigue, impact and seismic loadings is specifically stated in the relevant European Technical Product Specification. Anchor channels subjected to fatigue loading or seismic loading are not covered by this EN. NOTE Design rules for anchor channels subjected to fatigue loading or seismic loading may be found in the CEN/TR "Anchor channels" which is under preparation. (2) The loading on the fastener resulting from the actions on the fixture (e.g. tension, shear, bending or torsion moments or any combination thereof) will generally be axial tension and/or shear. When the shear force is applied with a lever arm a bending moment on the fastener will arise. Any axial compression on the fixture should be transmitted to the concrete either without acting on the fastener or via fasteners suitable for resisting compression. (3) In case of anchor channels shear in the direction of the longitudinal axis of the channel is not covered by this EN. NOTE Design rules for anchor channels with loads acting in the direction of the longitudinal axis of the anchor channel may be found in the CEN/TR "Anchor channels" which is under preparation. 1.5 Concrete strength (1) This EN is valid for fasteners installed in members using normal weight concrete with strength classes in the range C12/15 to C9/15 all in accordance with EN However in the design of fastenings the strength class is limited to C6/75 even if the structure uses a higher strength class. The range of concrete strength classes in which particular fasteners may be used is given in the relevant European Technical Product Specification and may be more restrictive than stated above. 1.6 Concrete member loading (1) In general fasteners are prequalified for applications in concrete members under static loading. If the concrete member is subjected to fatigue or seismic loading, prequalification of the fastener specific to this type of loading and a corresponding European Technical Product Specification are required. 8

9 2 Normative references This European Standard incorporates by dated or undated reference, provisions from other publications. These normative references are cited at the appropriate places in the text and the publications are listed hereafter. For dated references, subsequent amendments to or revisions of any of these publications apply to this European Standard only when incorporated in it by amendment or revision. For undated references the latest edition of the publication referred to applies. EN 26-1, Concrete Part 1: Specification, performance, production and conformity EN 199, Eurocode Basis of structural design EN , Eurocode 1: Actions on structures EN :24, Eurocode 2: Design of concrete structures Part 1-1: General rules and rules for buildings EN :25, Eurocode 3: Design of steel structures Part 1-1: General rules and rules for buildings EN :25, Eurocode 3: Design of steel structures Part 1-8: Design of joints EN :24, Eurocode 8: Design of structures for earthquake resistance Part 1: General rules, seismic actions and rules for buildings EN 125-1, Hot rolled products of structural steels - Part 1: General technical delivery conditions EN 18, Steel for the reinforcement of concrete - Weldable reinforcing steel - General EN 188-2, Stainless steels Part 2: Technical delivery conditions for sheet/plate and strip of corrosion resisting steels for general purposes EN 188-3, Stainless steels Part 3: Technical delivery conditions for semi-finished products, bars, rods, wire, sections and bright products of corrosion resisting steels for general purposes ISO 898-1, Mechanical properties of fasteners made of carbon steel and alloy steel Part 1: Bolts, screws and studs with specified property classes Coarse thread and fine pitch thread ISO 898-2, Mechanical properties of fasteners made of carbon steel and alloy steel Part 2: Nuts with specified property classes Coarse thread and fine pitch thread ISO 356-1, Mechanical properties of corrosion-resistant stainless-steel fasteners Part 1: Bolts, screws and studs ISO 356-2, Mechanical properties of corrosion-resistant stainless steel fasteners Part 2: Nuts ISO 5922, Malleable cast iron 9

10 3 Definitions and symbols 3.1 Definitions anchor element made of steel or malleable iron either cast into concrete or post-installed into a hardened concrete member and used to transmit applied loads (see Figures 3.1 to 3.3). In this EN 'anchor' and 'fastener' are used synonymously. In the case of anchor channels, one or more steel anchors is/are rigidly connected to the back of the channel and embedded in concrete anchor channel steel profile with rigidly connected anchors (also called channel bar, see Figure 3.2) installed prior to concreting anchor channel loading: Axial tension load applied perpendicular to the surface of the base material anchor channel loading: Combined axial and shear loading applied simultaneously (oblique loading) anchor channel loading: Flexure bending effect induced by a tension load anchor channel loading: Shear load acting parallel to the concrete surface and transversely with respect to the longitudinal axis of the channel anchor group number of fasteners with identical characteristics acting together to support a common attachment, where the spacing of the anchors does not exceed the characteristic spacing anchor loading: Axial load applied perpendicular to the surface of the base material and parallel to the fastener longitudinal axis anchor loading: Bending bending effect induced by a shear load applied with a lever arm with respect to the surface of the concrete member anchor loading: Combined axial and shear loading applied simultaneously (oblique loading) anchor loading: Shear shear induced by a load applied perpendicular to the longitudinal axis of the fastener anchor spacing distance between the centre lines of the fasteners 1

11 attached element structural or non-structural component that is connected to the attachment attachment assembly that transmits loads to the fastener. In this EN 'attachment' and 'fixture' are used synonymously base material material in which the fastener is installed blow-out failure spalling of the concrete on the side face of the concrete element at the level of the embedded head with no major breakout at the top concrete surface. This is usually associated with fasteners with small side cover and deep embedment bonded anchor Fastener placed into a hole in hardened concrete, which derives its resistance from a bonding compound placed between the wall of the hole in the concrete and the embedded portion of the fastening (see Figure 3.3g)) bonded expansion anchor bonded anchor designed such that the anchor bolt can move relative to the hardened bonding compound resulting in follow-up expansion (see Figure 3.3h)) cast-in fastener headed bolt, headed stud, hooked bolt or anchor channel installed before placing the concrete, see headed anchor channel bolt screw or bolt which connects the element to be fixed to the anchor channel (Figure 3.2) characteristic resistance 5 % fractile of the resistance (value with a 95 % probability of being exceeded, with a confidence level of 9 %) characteristic spacing spacing required to ensure the characteristic resistance of a single fastener concrete breakout failure Failure that corresponds to a wedge or cone of concrete surrounding the fastener or group of fasteners separating from the base material concrete pry-out failure failure that corresponds to the formation of a concrete spall opposite to the loading direction under shear loading 11

12 concrete related failure modes failure modes under tension loading: Pull-out failure, combined pull-out and concrete failure (bonded fasteners), concrete cone failure, blow-out failure, splitting failure, anchorage failure of supplementary reinforcement. Failure modes under shear loading: Concrete pry-out failure, concrete edge failure concrete screw threaded anchor screwed into a predrilled hole where threads create a mechanical interlock with the concrete (see Figure 3.3f)) deformation-controlled expansion anchor post-installed fastener that derives its tensile resistance by expansion against the side of the drilled hole through movement of an internal plug in the sleeve (see Figures 3.3c)) or through movement of the sleeve over an expansion element (plug). Once set, no further expansion can occur displacement movement of the loaded end of the fastener relative to the concrete member into which it is installed in the direction of the applied load. In the case of anchor channels, movement of a channel bolt (Fig. 3.2) or the anchor channel relative to the concrete element. In tension tests, displacement is measured parallel to the anchor axis. In shear tests, displacement is measured perpendicular to the anchor axis ductile steel element element with sufficient ductility. The ductility conditions are given in the relevant sections edge distance distance from the edge of the concrete member to the centre of the fastener effective embedment depth the definition of the effective embedment depth for the different types of fasteners is given in Figures 3.1 to european Technical Product Specification harmonized European Product Standard (hen) or European Technical Approval or European Technical Assessment fastener see anchor fastening assembly of fixture and fasteners used to transmit loads to concrete 12

13 Key a) without anchor plate b) with a large anchor plate in any direction, b 1 >,5 h n or t >,2 h n c) with a small anchor plate in each direction, b 1 h n and t,2 h n Figure 3.1 Definition of effective embedment depth h ef for headed fasteners Key 1 anchor 2 connection between anchor and channel 3 channel lip 4 channel bolt Figure 3.2 Definitions for anchor channels 13

14 Key a) torque controlled fastener, sleeve type b) torque controlled fastener, wedge type c) deformation controlled fastener d) undercut fastener, type 1 e) undercut fastener, type 2 f) concrete screw g) bonded fastener h) bonded expansion anchor Figure 3.3 Definition of effective embedment depth h ef for post-installed fasteners, examples Fixture See attachment Headed anchor steel fastener installed before placing concrete (see Figure 3.1). It derives its tensile resistance from mechanical interlock at the anchor head. The definitions given in Figure 3.1b) and 3.1c) should be verified for directions 1 and 2 according to Figure istallation safety factor partial factor that accounts for the sensitivity of a fastener to installation inaccuracies on its performance mechanical interlock load transfer to a concrete member via interlocking surfaces minimum edge distance Minimum allowable edge distance to allow adequate placing and compaction of concrete (cast-in place fasteners) and to avoid damage to the concrete during installation (post-installed fasteners), given in the European Technical Product Specification minimum member thickness minimum member thickness, in which a fastener can be installed, given in the European Technical Product Specification minimum spacing Minimum fastener spacing to allow adequate placing and compaction of concrete (cast-in fasteners) and to avoid damage to the concrete during installation (post-installed fasteners), measured centreline to centreline, given in the European Technical Product Specification 14

15 post-installed fastener fastener installed in hardened concrete (see Figure 3.3) pull-out failure failure mode in which the fastener pulls out of the concrete without development of the full concrete resistance or a failure mode in which the fastener body pulls through the expansion sleeve without development of the full concrete resistance. In case of bonded anchors this failure occurs at the interface between the bonding material and the base material or between the bonding material and the anchor element (bond failure). This failure may also contain a concrete cone at the top end and is therefore denoted as combined pull-out and concrete failure splitting failure concrete failure mode in which the concrete fractures along a plane passing through the axis of the fastener or fasteners steel failure of fastener Failure mode characterised by fracture of the steel fastener parts supplementary reinforcement reinforcement tying a potential concrete breakout body to the concrete member torque-controlled expansion anchor post-installed expansion anchor that derives its tensile resistance from the expansion of one or more sleeves or other components against the sides of the drilled hole through the application of torque, which pulls the cone(s) into the expansion sleeve(s) during installation. After setting, tensile loading can cause additional expansion (follow-up expansion), see Figures 3.3a) and 3.3b) undercut anchor post-installed fastener that develops its tensile resistance from the mechanical interlock provided by undercutting of the concrete at the embedded end of the fastener. The undercutting is achieved with a special drill before installing the fastener or alternatively by the fastener itself during its installation, see Figures 3.3d) and 3.3e) 3.2 Notations Indices E L M N R V a b action effects load material normal force resistance, restraint shear force acceleration bond 15

16 c ca cb cp d el eq fat concrete connection blow-out concrete pry-out design value elastic seismic (earthquake) fatigue fi fix flex k l max min nom p pl re s sp u y fire fixture bending characteristic value local maximum minimum nominal pull-out plastic reinforcement steel splitting ultimate yield Superscripts g h exponent in the interaction equations load on or resistance of a group of fasteners highest loaded (most stressed) fastener in a group basic value 16

17 3.2.3 Actions and resistances ratio of the design ground acceleration on type A ground a g to the acceleration of gravity g eq gap v a z A a A' i C C Ed E R g F H N N Ed S V M reduction factor to take into account the influence of large cracks and scatter of load displacement curves reduction factor to take into account inertia effects due to fastener displacement in case of tension loading or an annular gap between fastener and fixture in case of shear loading, given in the relevant European Technical Product Specification ratio of the vertical design ground acceleration on type A ground a vg to the acceleration of gravity g partial factor importance factor of the non-structural element height of the non-structural element above the level of application of the seismic action seismic amplification factor (Equation (C.2)) ordinate of a triangle with the height 1 at the position of the load N Ed or V Ed and the base length 2 l i at the position of the anchors i of an anchor channel nominal value, e.g. limiting displacement resultant design compression force beneath the fixture effect of action resistance acceleration of gravity force in general building height, measured from the foundation or from the top of a rigid basement axial force (positive = tension force, negative = compression force) resultant design tension force of the tensioned anchors soil factor shear force moment M 1 bending moment on fixture around axis in direction 1 M 2 bending moment on fixture around axis in direction 2 S a S Va horizontal seismic coefficient applicable to non-structural elements vertical seismic coefficient applicable to non-structural elements 17

18 T T a T 1 W a F a FRk ( N Rk ; VRk ) FRd ( N Rd ; VRd ) torsional moment on fixture fundamental period of vibration of the non-structural element fundamental period of vibration of the building in the relevant direction weight of the non-structural element horizontal seismic force, acting at the centre of mass of the non-structural element in the most unfavourable direction characteristic value of resistance of a single fastener or a group (axial force, shear force) design value of resistance of a single fastener or a group (axial force, shear force) Rk characteristic bond resistance of a post-installed chemical fastener, depending on the concrete strength class, in non-cracked ( Rk, ucr ) or cracked concrete ( Rk, cr ) F Ek (N Ek ; V Ek ;M Ek ; T Ek ) characteristic value of actions acting on the fixture (axial load, shear load, bending moment, torsion moment) F Ed (N Ed ; V Ed ; M Ed ; T Ed ) design value of actions acting on the fixture (axial load, shear load, bending moment, torsion moment), in the case of anchor channels design value of actions acting on the channel bolt a a a FEd ( N Ed ; VEd ) F a a a Ed, i ( N Ed, i ; VEd, i N h h Ed ( V Ed ) N g g Ed ( V Ed) N Ed,re a N Ed,re Concrete and steel ) design value of action on one anchor of the anchor channel design value of action on anchor i of the anchor channel design value of tensile load (shear load) acting on the most stressed fastener of a group design value of the resultant tensile (shear) loads of the fasteners in a group effective in taking up tension (shear) loads design value of tension load acting on the supplementary reinforcement design value of tension load acting on the supplementary reinforcement of one anchor of the anchor channel f bd f ck f yk f uk A s A s,re design bond strength of supplementary reinforcement characteristic compressive cylinder strength (15 mm 3 mm) characteristic steel yield strength or steel proof strength (nominal value) characteristic steel ultimate tensile strength (nominal value) stressed cross section cross section of one leg of the supplementary reinforcement I y moment of inertia of the channel [mm 4 ] relative to the y-axis of the channel (Figure 3.2) 18

19 W el elastic section modulus calculated from the stressed cross section Fasteners and fastenings, reinforcement Notation and symbols frequently used in this EN are given below and are illustrated in Figures 3.1 to 3.4, 6.3, 6.6, 6.7, 7.1 and Further notation and symbols are given in the text. a 1 (a 2 ) spacing between outer fasteners in adjoining fastenings in direction 1 (direction 2) (Figure 3.4) a 3 b distance between concrete surface and point of assumed restraint of a fastener loaded by a shear force with lever arm (Figure 6.6) width of concrete member b ch width of the channel, (Figure 3.2) b fix c width of fixture edge distance from the axis of a fastener or the axis of an anchor channel c 1 edge distance in direction 1 (Figures 3.4 and 7.11) c 2 edge distance in direction 2 (Figures 3.4 and 7.11), where direction 2 is perpendicular to direction 1 c cr c min d d f characteristic edge distance for ensuring the transmission of the characteristic resistance of a single fastener minimum allowable edge distance diameter of fastener bolt or thread diameter, diameter of the stud or shank of headed studs diameter of clearance hole in the fixture d h diameter of anchor head (headed anchor, Figure 3.1) d nom d s d outside diameter of a fastener diameter of reinforcing bar nominal diameter of drilled hole e 1 distance between shear load and concrete surface (Figure 6.6) e N e s e V eccentricity of resultant tension force of tensioned fasteners in respect to the centre of gravity of the tensioned fasteners (Figure 6.3) distance between the axis of the shear load and the axis of the supplementary reinforcement for shear (Figure 6.7) eccentricity of resultant tension force of sheared fasteners in respect to the centre of gravity of the sheared fasteners (Figure 7.14) h thickness of concrete member in which the fastener is installed (Figure 3.4) h ch height of the channel (Figure 3.2) h ef effective embedment depth (Figures 3.1 to 3.3) h min minimum allowed thickness of concrete member 19

20 l a l b,min l i lever arm of the shear force acting on a fastener minimum anchorage length of supplementary reinforcement influence length of an external load N Ed or V Ed along an anchor channel l 1 anchorage length of the reinforcing bar in the assumed failure cone (Figure 7.1) n n re s number of fasteners in a group number of legs of the supplementary reinforcement effective for one fastener centre to centre spacing of fasteners in a group (Figure 3.4) or anchors of an anchor channel (Figure 6.6) or spacing of reinforcing bars s 1 (s 2 ) spacing of fasteners in a group in direction 1 (direction 2), (Figure 3.4) s cr s min t t fix t grout z characteristic spacing for ensuring the transmission of the characteristic resistance of a single fastener minimum allowable spacing time Units thickness of the fixture thickness of grout layer internal lever arm calculated according to the theory of elasticity In this EN SI-units are used. Unless stated otherwise in the equations, the following units are used: Dimensions are given in mm, cross sections in mm 2, section modulus in mm 3, moment of inertia in mm 4, forces and loads in N and stresses, strengths and moduli of elasticity in N/mm². 2

21 Key 1 indices 1 and 2: For shear loads the indices depend on the edge for which the verification of concrete edge failure is performed (index 1: direction perpendicular to the edge for which verification is made; index 2: perpendicular to direction 1) a) fastenings subjected to tension load b) fastenings subjected to shear load in the case of fastening near an edge Figure 3.4 Definitions related to concrete member dimensions, fastener spacing and edge distance 4 Basis of design 4.1 General (1) With appropriate degrees of reliability fasteners shall sustain all actions and influences likely to occur during execution and use (ultimate limit state). They shall not deform to an inadmissible degree (serviceability limit state) and remain fit for the use for which they are required (durability). They shall not be damaged by accidental events to an extent disproportional to the original cause. (2) Fastenings shall be designed according to the same principles and requirements valid for structures given in EN 199 including load combinations. NOTE A design using the partial factors given in this EN and the partial factors given in the EN 199 Annexes is considered to lead to a structure associated with reliability class RC2, i.e. a ß-value of 3,8 for a 5 year reference period. For further information, see EN 199:22, Annexes B and C. (3) The design working life of the fasteners shall not be less than that of the fixture. The safety factors for resistance and durability in this EN are based on a nominal working life of at least 5 years for the fastening. (4) Values of actions shall be obtained from the relevant parts of EN 1991 and EN 1998 in the case of seismic actions (see also Annex C of this EN). (5) If the fastening is subjected to impact, fatigue or seismic actions, only fasteners suitable for this application shall be used (see relevant European Technical Product Specification). (6) The design of the concrete member to which the fixture transfers loads should comply with the requirements of Annex A for safe transmission of loads to the supports of the member. 21

22 (7) For the design and execution of fastenings the same quality requirements are valid as for the design and execution of structures and the attachment: The design of the fastening shall be performed by qualified personnel; the fastenings shall be installed according to project specifications. (8) The execution shall comply with the requirements stated in Required verifications (1) For the fasteners the following limit states shall be verified: ultimate limit state, including effects of impact, fatigue and seismic loading, where appropriate; serviceability limit state. Furthermore the durability of the fastening for the intended use shall be demonstrated. Information is given in Informative Annex B. (2) In the ultimate limit state, verifications are required for all appropriate load directions and all relevant failure modes. (3) In the serviceability limit state, it shall be shown that the displacements occurring under the relevant actions are not larger than the admissible displacement. (4) The material of the fastener and the corrosion protection shall be selected taking into account the environmental conditions at the place of installation, and whether the fasteners are inspectable, maintainable and replaceable. (5) Where applicable the fastening shall have an adequate fire resistance. For the purpose of this EN it is assumed that the fire resistance of the fixture is adequate. Annex D describes the principles, requirements and rules for the design of fastenings exposed to fire. 4.3 Design format (1) At the ultimate limit state it shall be shown that. Ed R d and at the serviceability limit state it shall be shown that Ed C d (2) The forces in the fasteners shall be derived using appropriate combinations of actions on the fixture as recommended in EN 199. When indirect action Q ind arises from the restraint to the deformation of the fastened member (fixture, attachment), the design action shall be taken as ind Q ind. Forces resulting from restraint to deformation, intrinsic (e.g. shrinkage) or extrinsic (e.g. temperature variations) of the attached member shall be taken into account in the design of fasteners, where applicable. (3) In general actions in the fixture may be calculated ignoring the displacement of the fasteners. However the effect of displacement of the fasteners should be considered when a statically indeterminate stiff element is fastened. (4) In the ultimate limit state the value of the design resistance is obtained from the characteristic resistance of the fastener or the group of fasteners as follows: (4.1) (4.2) R d Rk / M (4.3) 22

23 (5) In the serviceability limit state the value E d, which is the design value of fastener displacement, shall be evaluated from the information given in the relevant European Technical Product Specification. For C d see Clause Verification by the partial factor method Partial factors for actions (1) Partial factors shall be in accordance with in EN 199. (2) For the verification of indirect and fatigue actions (ultimate limit state) the values of the partial factors ind and F,fat shall be used. NOTE The values of ind and F,fat for use in a Country may be found in its National Annex. The recommended values are ind = 1,2 for concrete failure and ind = 1, for other modes of failure, and in case of fatigue loading F,fat =1, Partial factors for resistance Ultimate limit state (static, impact and seismic loading) (1) Partial factors for fastenings under static, impact and seismic loading shall be applied to characteristic resistances. NOTE 1 The value of a partial factor for use in a country may be found in its National Annex, when the partial factor is not product dependent. The recommended values are given in Table 4.1. They take into account that the characteristic resistance is based on f uk, except f yk should be used for bending of the channel of anchor channels and steel failure of supplementary reinforcement. The value of the partial factor for installation inst of post-installed fasteners has its origin in the prequalification of the product and is product dependent. Therefore it should not be reduced. NOTE 2 Installation aspects may affect different failure modes to a different extent. Verification taking into account installation safety of a fastening may be found in the CEN/TR "Installation". (2) The recommended values for the partial factors for fastenings under impact or seismic loading should be identical to the corresponding values for static loading. For accidential loads the partial factors according to Table 4.1 are recommended Ultimate limit state (fatigue loading) (1) Partial factors for fastenings under fatigue loading Ms,fat, Mc,fat, Msp,fat and Mp,fat shall be applied to characteristic resistances. NOTE The values of the partial factors for fastenings under fatigue loading for use in a Country may be found in its National Annex. It is recommended to take the partial factor for material as Ms,fat =1,35 (steel failure), Mc,fat = Msp,fat = Mp,fat =1,5 inst (concrete cone failure, splitting failure and pull-out failure) Serviceability limit state (1) The partial factor for resistance is M and shall be applied to characteristic resistances. NOTE The value of the partial factor for serviceability limit state for use in a Country may be found in its National Annex. For the partial factor M the value M = 1, is recommended. 23

24 4.5 Project specification and installation of fasteners (1) The resistance and reliability of fastenings are significantly influenced by the manner in which the fasteners are installed. The partial factors given in 4.4 are valid only when the following conditions and the assumptions given in (4) are fulfilled: a) The manufacturer's installation instructions and all necessary information for correct installation shall be available at the time the installation takes place. The installation instructions for the fastener, which are normally given in the European Technical Product Specification, shall be followed. b) Gross errors shall be avoided by the use of qualified personnel and adequate supervision. Failure modes Table 4.1 Recommended values of partial factors Partial factor Steel failure - fasteners Tension =1,2 f uk /f yk 1,4 Shear with and without a lever arm Ms =1, f uk /f yk 1,25 when f uk 8 N/mm 2 and f yk /f uk,8 = 1,5 when f uk > 8 N/mm 2 or f yk /f uk >,8 Steel failure anchor channels Tension in anchors =1,2 f and channel bolts uk /f yk 1,4 Shear with and without Ms = 1, f uk /f yk 1,25 when f uk 8 N/mm 2 and f yk /f uk,8 a lever arm in channel bolts = 1,5 when f uk > 8 N/mm 2 or f yk /f uk >,8 Connection between anchor and channel in tension and shear Ms,ca = 1,8 Local failure of anchor channel by bending of lips in tension and Ms,l = 1,8 shear Bending of channel Ms,flex = 1,15 Steel failure supplementary reinforcement Tension Ms,re = 1,15 Concrete failure -tension Cone break-out failure, Mc = c inst edge break-out failure, blow-out failure and c = 1,5 generally, but see EN 1998 for seismic repair and pry-out failure strengthening of existing structures the requirements of 4.5 inst 1, for post-installed fasteners, see relevant European = 1, for headed fasteners and anchor channels satisfying Technical Product Specification Splitting failure Msp = Mc Pull-out failure Pull-out and combined pull-out and concrete failure Mp = Mc (2) The project specification shall typically include the following: a) Strength class of the concrete used in the design and indication as to whether the concrete is assumed to be cracked or not cracked. If non-cracked concrete is assumed, verification is required (see 4.6). b) Environmental exposure assumed in design (EN 26-1). 24

25 c) A note indicating that the number, manufacturer, type and geometry of the fasteners shall not be changed unless verified and approved by the responsible designer. d) Construction drawings, which shall include location of the fasteners in the structure, including tolerances; number and type of fasteners (including embedment depth); spacing and edge distance of the fastenings including tolerances (normally these should be specified with positive tolerances only); thickness of fixture and diameter of the clearance holes (if applicable); position of the attachment on the fixture including tolerances; maximum thickness of an eventual intervening layer e.g. grout or insulation between the fixture and surface of the concrete; (special) installation instructions (if applicable) that shall not contradict the manufacturer's installation instructions. e) Reference to the manufacturer's installation instructions. f) A note that the fasteners shall be installed ensuring the specified embedment depth. (3) If the conditions in this clauses are complied with, no proof testing of the fasteners is necessary. (4) The following assumptions regarding welding design of headed fasteners and in respect to installation of the relevant type of fastener have been made in this EN. The installation instructions should reflect the assumptions stated below. a) Post-installed fasteners: i) Concrete has been compacted adequately in the area of the fastening. This should be checked prior and during installation via visual check. ii) Requirements for drilling operation and bore hole are fulfilled when: Holes are drilled perpendicular to the surface of the concrete unless specifically required otherwise by the manufacturer s installation instructions. Drilling is carried out by method specified by the manufacturer. Hard metal hammer-drill bits which comply with ISO or National Standards are used. The diameter of the segments for diamond core drilling complies with the prescribed diameter. Reinforcement in close proximity to the hole position is not damaged during drilling. In prestressed concrete structures it is ensured that the distance between the drilling hole and the prestressed reinforcement is at least 5mm; for determination of the position of the prestressed reinforcement in the structure a suitable device e.g. a reinforcement detector shall be used. Holes are cleaned according to the manufacturer s installation instructions which are typically given in the European Technical Product Specifications. 25

26 Aborted drill holes are filled with high strength non-shrinkage mortar. iii) Inspection and approval of the correct installation of the fasteners is carried out by appropriately qualified personnel. NOTE Many drill bits exhibit a mark indicating that they are in accordance with ISO or National Standards. If the drill bits do not bear a conformity mark, evidence of suitability should be provided. b) Headed fasteners: i) Design of welding is in accordance with EN ii) The fastener is fixed in a way that no movement of the fastener will occur during placing of reinforcement or during pouring and compacting of the concrete. iii) iv) Requirements for adequate compaction particularly under the head of the stud or fastener and under the fixture as well as provisions for vent openings in fixtures larger than 4 mm 4 mm are fulfilled. Requirement for inspection and approval of the correct installation of the fasteners, which is carried out by appropriately qualified personnel are observed. v) The following conditions are observed if the fasteners are vibrated (not just punched) into the wet concrete immediately after pouring: vi) The size of the fixture does not exceed 2 mm 2 mm and the number of fastenings is limited to 4 fasteners, so that it can be placed simultaneously during vibrating by the available personnel. The installation is done according to a quality system. The fastenings are not moved after vibrating has been finished. The concrete under the head of the headed stud or anchor as well as under the base plate is properly compacted. The welding procedure for studs is done in accordance with the provisions given in the relevant European Technical Product Specification. vii) Inspection and approval of the correct installation of the fasteners is carried out by appropriately qualified personnel. c) Anchor channels i) The anchor channel is fixed in a way that no movement of the anchor channel will occur during placing of reinforcement or during pouring and compacting of the concrete. ii) iii) iv) Requirements for adequate compaction particularly under the head of the anchor and under the channel are fulfilled. Requirements for inspection and approval of the correct installation of the anchor channels by appropriately qualified personnel are observed. Placing anchor channels by only pushing them into the wet concrete is not allowed. v) Anchor channels might be vibrated into the wet concrete immediately after pouring observing the following conditions: 26

27 The size and number of fastenings is limited to anchor channels with a length of < 1m if placed by one person, so that it can be placed simultaneously during vibrating by the available personnel. Longer channels should be placed by at least two persons. The installation is carried out according to a quality system. The anchor channels are not moved after vibrating has been finished. The concrete in the region of the anchor and the anchor channel is properly compacted. 4.6 Determination of concrete condition (1) In the region of the fastening the concrete may be cracked or non-cracked. The condition of the concrete for the service life of the fastener shall be determined by the designer. NOTE In general, it is conservative to assume that the concrete is cracked over its service life. (2) Non-cracked concrete may be assumed if it is proven that under service conditions the fastener with its entire embedment depth is located in non-cracked concrete. This will be satisfied if Equation (4.12) is observed (compressive stresses are negative): L R adm L R adm stresses in the concrete induced by external loads including fastener loads (4.12) stresses in the concrete due to restraint of intrinsic imposed deformations (e.g. shrinkage of concrete) or extrinsic imposed deformations (e.g. due to displacement of support or temperature variations). If no detailed analysis is conducted, then R = 3 N/mm² should be assumed. admissible tensile stress for the definition of non-cracked concrete. NOTE 1 The stresses L and R should be calculated assuming that the concrete is non-cracked. For concrete members which transmit loads in two directions (e.g. slabs, walls and shells) Equation (4.12) should be fulfilled for both directions. NOTE 2 The value of adm may be found in a Country's National Annex. The recommended value is adm =. (3) For seismic design situations the concrete shall always be assumed to be cracked in the region of the fastening (see Clause 9) unless it is demonstrated that the concrete remains uncracked during the seismic event. 5 Durability Fasteners and fixtures shall be chosen to have adequate durability taking into account the environmental conditions for the structure. EN applies. NOTE Information is given in informative Annex B. 6 Derivation of forces acting on fasteners - analysis 6.1 General (1) The actions acting on a fixture shall be transferred to the fasteners as statically equivalent tension and shear forces. 27

28 (2) When a bending moment and/or a compression force act on a fixture, which is in contact with concrete or mortar, a friction force will develop. If a shear force is also acting on a fixture, this friction will reduce the shear force on the fastener. However, in this EN friction forces are neglected in the design of the fastenings. (3) Eccentricities and prying effects shall be explicitly considered in the design of the fastening (Figure 6.1). Prying forces C arise with deformation of the fixture and displacement of the fasteners. (4) In general, elastic analysis may be used for establishing the loads on individual fasteners both at ultimate and serviceability limit states. NOTE For ultimate limit states plastic analysis for headed and post-installed fasteners may be used, if the conditions of CEN/TR "Plastic design" are observed. Key 1 eccentricity a) eccentricity b) prying action Figure 6.1 Example for eccentricity and prying action 6.2 Headed fasteners and post-installed fasteners Tension loads (1) The design value of tension loads acting on each fastener due to the design values of normal forces and bending moments acting on a rigid fixture may be calculated assuming a linear distribution of strains across the fixture and a linear relationship between strains and stresses. If the fixture bears on the concrete with or without a grout layer, the compression forces are transmitted to the concrete by the fixture. The load distribution to the fasteners may be calculated analogous to the elastic analysis of reinforced concrete using the following assumptions (Figure 6.2): a) The fixture is sufficiently rigid (flatness of transversal cross sections after deformation) such that linear strain distribution will be valid. b) The axial stiffness of all fasteners is equal. The stiffness should be determined on the basis of the elastic steel strains in the fastener. c) The modulus of elasticity of the concrete is taken from EN As a simplification, the modulus of elasticity of concrete may be assumed as E c = 3 N/mm². If no specific information is available in the relevant European Technical Product Specification the modulus of elasticity of steel of the fastener may, as a simplification, be assumed as E s = 21 N/mm 2. 28

29 d) In the zone of compression under the fixture the fasteners do not take forces. (2) For fastener groups with different levels of tension forces N Ed,i acting on the individual fasteners of a group, g the eccentricity EN of the tension force N Ed of the group with respect to the centre of gravity of the tensile fasteners influences the concrete cone resistance of the group. Therefore this eccentricity shall be calculated (Figures 6.2 and 6.3). If the tensioned fasteners do not form a rectangular pattern (see Figure 6.3c)) for reasons of simplicity the group of tensioned fasteners may be shaped into a rectangular group to calculate the centre of gravity. It may be assumed as point 'A' in Figure 6.3c). This simplification will lead to a larger eccentricity and a reduced concrete resistance. (3) The assumption of a linear distribution of strains is valid only if the fixture is sufficient rigid. The base plate shall remain elastic under design actions and its deformation shall remain negligible in comparison with the axial displacement of the fasteners. If this requirement is not fulfilled the deformation behaviour of the fixture has to be taken into account adequately to determine the design value of tension loads acting on each fastener. C =,5 b fx xs c E c Figure 6.2 Fastening with a rigid fixture bearing on the concrete loaded by a bending moment and a normal force 29

30 6.2.2 Shear loads Distribution of loads The load distribution depends on the effectiveness of fasteners to resist shear loads which is e.g. influenced by the hole clearance. If the diameter of the hole in the fixture is not larger than the value d f given in Table 6.1 the following cases are distinguished: All fasteners are considered to be effective if the fastening is located far from an edge (c max(1h ef, 6d nom )) for verification of steel failure and pry out failure if the fastening is loaded by a shear load parallel to the edge or by a torsion moment (see Figures 6.4 and 6.5). Only fasteners closest to the edge are assumed to be effective for the verification of concrete edge failure if the fastening is located close to the edge and loaded perpendicular to the edge (Figure 6.5b). A fastener is not considered to resist shear loads if the hole is slotted in the direction of the shear force. 1 external diameter d a b or d nom 2 diameter d f of clearance hole in the fixture a b if bolt bears against the fixture. if sleeve bears against the fixture. [mm] [mm] Table 6.1 Hole clearance NOTE Applications where bolts are welded to the fixture or screwed into the fixture, or in the cases where any gap between the fastener and the fixture is filled with mortar of sufficient compressive strength or eliminated by other suitable means may be considered to have no hole clearance. 3

31 Key 1 compressed area 2 neutral axis 3 geometric centre of gravity of tensile fasteners 4 point of resultant tensile force of tensile fasteners 5 point 'A' a) eccentricity in one direction, all fasteners are loaded by a tension force b) eccentricity in one direction, only a part of the fasteners of the group are loaded by a tension force c) eccentricity in two directions, only a part of the fasteners of the group are loaded by a tension force Figure 6.3 Examples of fastenings subjected to an eccentric tensile force N Ed 31

32 Key with a,5 2 2 T s1 s2 2 2 V ed anchor I p I p = radial moment of inertia (here: I p = s 1 ² + s 2 ²) Figure 6.4 Determination of shear loads when all fasteners are effective in verification, example of torsion moment acting on a quadruple fastening a) group with two fasteners loaded parallel to the edge; b) group with four fasteners loaded perpendicular to the edge c) quadruple fastening loaded by an inclined shear load Figure 6.5 Determination of shear loads when only the fasteners closest to the edge are effective (concrete edge failure), examples NOTE In case of fastener groups where only the fasteners closest to the edge are effective the component of the load acting perpendicular to the edge is taken up by the fasteners closest to the edge, while the components of the load acting parallel to the edge due to reasons of equilibrium are equally distributed to all fasteners of the group (Figure 6.5c)). Shear loads acting away from the edge do not significantly influence the concrete edge resistance. Therefore for the proof of concrete edge failure these components may be neglected in the calculation of the shear forces on the fasteners close to the edge. 32

33 Shear loads with and without lever arm (1) Shear loads acting on fastenings may be assumed to act without a lever arm if all of the following conditions are satisfied: a) The fixture is in metal and in contact with the fastener over a length of at least,5t fix. b) The diameter d f of the hole is not greater than the value given in line 2 of Table 6.1. c) The fixture is fixed either directly to the concrete without an intermediate layer; or using a levelling mortar not exceeding,5d in thickness as intermediate layer on a rough concrete surface and the strength of the mortar is at least that of the base concrete but not less than 3 N/mm². When the above conditions are not satisfied, shear force on fastenings should be assumed to act with lever arm. If only condition c) is not satisfied (2) may be applied. (2) In the case of monotonic loading reduced shear capacity in accordance with may be used instead of design with lever arm provided the shear force is applied without tension force on the base plate; and the fastener spacing in the direction of the shear force exceeds 1d (if inclined shear forces are acting this condition shall be fulfilled for both directions); and the thickness of the mortar bed is less than or equal to 4mm; and mortar bed is applied on a rough concrete surface (see EN :24,6.2.5); and the strength of the mortar bed is at least that of the base concrete but not less than 3 N/mm². (3) If the shear load acts with a lever arm Equation (6.1) applies. with l a a3 e 1 e 1 distance between shear load and concrete surface (Figure 6.6) (6.1) a 3 =,5 d nom = if a washer and a nut are directly clamped to the concrete surface or if a levelling grout layer with a compressive strength 3 N/mm² and a thickness t Grout > d/2, is present. The design moment acting on the fastening is calculated according to Equation (6.2) la MEd VEd M (6.2) 33

34 Figure 6.6 Definition of the lever arm The value M depends on the degree of restraint of the fastening at the side of the fixture of the application in question and shall be determined according to good engineering practice. No restraint ( M = 1,) shall be assumed if the fixture can rotate freely. Full restraint ( M = 2,) may be assumed only if the fixture cannot rotate and the fixture is clamped to the fastening by a nut and washer. 6.3 Anchor channels General (1) The distribution of tension loads acting on the channel to the anchors of the anchor channel may be calculated treating the channel as a beam on elastic support (anchors) with a partial restraint of the channel ends as statical system. The resulting anchor forces depend significantly on the assumed anchor stiffness and degree of restraint. For shear loads the load distribution is also influenced by the pressure distribution in the contact zone between channel and concrete. (2) As a simplification for anchor channels with two anchors the loads on the anchors may be calculated assuming a simply supported beam with a span length equal to the anchor spacing. (3) For anchor channels with more than two anchors as an alternative in the following the triangular load distribution method to calculate the distribution of tension and shear loads to the anchors is introduced. (4) In the case of shear loads, this EN covers only shear loads acting on the channel perpendicular to its longitudinal axis. NOTE channels". Shear loads acting parallel to the longitudinal axis of the anchor channel are covered in CEN/TR "Anchor Tension loads (1) The tension in each anchor caused by a tension load acting on the channel is calculated according to Equation (6.3), which assumes a linear load distribution over the influence length l i and takes into account the condition of equilibrium. The influence length l i shall be calculated according to Equation (6.5). An example for the calculation of the forces acting on the anchors is given in Figure

35 ' NEd, a i k Ai NEd (6.3) with ' Ai ordinate at the position of the anchor i of a triangle with the unit height at the position of load N and the base length 2l i 1 k n A' i 1,5,5 li 13 I y s s [mm] (6.4) (6.5) n number of anchors on the channel within the influence length l i to either side of the applied load N Ed (Figure 6.7) (2) If several tension loads are acting on the channel a linear superimposition of the anchor forces for all loads shall be assumed. (3) If the exact position of the load on the channel is not known, the most unfavourable loading position shall be assumed for each failure mode (e.g. load acting over an anchor for the case of failure of an anchor by steel rupture or pull-out and load acting between anchors in the case of bending failure of the channel). (4) The bending moment in the channel due to tension loads acting on the channel may be calculated assuming a simply supported single span beam with a span length equal to the anchor spacing. 35

36 NOTE The assumption of a simply supported beam to calculate the moments is a simplification which neglects the influence of partial end restraints, continuous beam action for channels with more than two anchors and catenary action after yielding of the channel. The characteristic values of the moments of the resistance given in the European Technical Product Specification take these effects into account. They may be larger than the plastic moment, calculated with the dimensions of the channel and nominal yield strength of the steel. ' li es a ' A2 NEd,2 A2kN l i ' li e a ' A3 NEd,3 A3 kn l i ' li se a ' A4 NEd,4 A4 kn l i N a Ed Ed Ed Ed a,1 N,5 Figure 6.7 Example for the calculation of anchor forces according to the triangular load distribution method for an anchor channel with five anchors Shear loads (1) The provisions given in shall be used to determine whether a shear load acts with or without a lever arm on the channel bolt. (2) The shear forces of each anchor due to a shear load acting on the channel perpendicular to its longitudinal axis may be calculated in the same manner as described in NOTE Shear loads applied perpendicular to anchor channels are transferred mainly as compression at the interface between channel and concrete. A small proportion of the applied load is transferred to the anchors as a result of bending the channel. In addition for reasons of equilibrium the anchors are stressed by tension forces. In the approach presented above it is assumed that shear forces are transferred by bending of the channel to the anchors and by the anchors into the concrete. This simplified approach has been chosen to allow for simple interaction between tension and shear forces acting on the channel. Ed 36

37 6.4 Forces assigned to supplementary reinforcement General The design tension forces N Ed, re acting in the supplementary reinforcement shall be established using an appropriate strut and tie model Tension loads The design tension forces N Ed, re in the supplementary reinforcement shall be calculated using the design load on the fastener or in case of anchor channels on the anchor Shear loads The design tension force N Ed, re in the supplementary reinforcement caused by the design shear force V Ed acting on a fixture is given by Equation (6.6). es NEd, re 1 Ved z with (see Figure 6.8): e s z = distance between reinforcement and shear force acting on a fixture,85 d (Figure 6.8)), where 2 hef d min 2 c1 with d =(h - h ch -,5d s ) in case of anchor channels (Figure 6.8b)) If the supplementary reinforcement is not arranged in the direction of the shear force then this must be taken into account in the calculation of the design tension force of the reinforcement. In the case of different shear forces on the fasteners of a fixture or on the anchors of an anchor channel, Equation (6.6) shall be solved for the shear load V h Ed of the most loaded fastener or anchor resulting in h N. Ed,re (6.6) Figure 6.8 Surface reinforcement to take up shear forces detailing of reinforcement 37

38 7 Verification of ultimate limit state 7.1 General (1) It shall be demonstrated that Equation (4.1) is fulfilled for all loading directions (tension, shear, combined tension and shear) as well as all failure modes (see Table 7.1). (2) This section applies when forces on the fasteners have been calculated using elastic analysis. (3) Both minimum edge distance and spacing should only be specified with positive tolerances. If this requirement cannot be met, then the influence of negative tolerances on the design resistance shall be taken into account in the design. (4) The spacing between outer fasteners of adjoining groups or the distance between single fasteners or single fasteners and outer fasteners of adjoining groups shall be a s cr,n. (5) Aborted drill holes filled with high strength non-shrinkage mortar do not have may be neglected in the design. NOTE For fastenings with post-installed fasteners and edge distances c < 5 mm the concrete might be predamaged due to hammer drilling, especially in case of concrete with aggregate of maximum size > 2 mm. In this case it may be prudent to reduce the characteristic concrete cone and concrete edge resistance. 7.2 Headed and post-installed fasteners Tension load Required verifications The verifications of Table 7.1 apply Detailing of supplementary reinforcement When the design relies on supplementary reinforcement, concrete cone failure according to Table 7.1 and need not to be verified but the supplementary reinforcement shall be designed to resist the total load. The supplementary reinforcement to take up tension loads shall comply with the following requirements (see also Figure 7.1): a) In general, the same diameter of the reinforcement shall be provided for all fasteners of a group. The reinforcement shall consist of ribbed reinforcing bars (f yk 6 N/mm 2 ) with a diameter d s not larger than 16 mm and shall be detailed as stirrups or loops with a mandrel diameter according to EN b) The supplementary reinforcement should be placed symmetrically as close to the fasteners as practicable to minimize the effect of eccentricity associated with the angle of the failure cone. Preferably, the supplementary reinforcement should enclose the surface reinforcement. Only these reinforcement bars with a distance,75 h ef from the fastener shall be assumed as effective. 38

39 Figure 7.1 Example for a multiple fastening with supplementary reinforcement to take up tension loads and corresponding strut and tie model 1 2 Table 7.1 Required verifications for headed and post-installed fasteners in tension Steel failure of fastener Pull-out failure of fastener a Single fastener NEd NRd, s NEd NRd, p NRk, s Ms NRk, p Mp Fastener group most loaded fastener fastener group h NEd NRd, s h NEd NRd, p NRk, s Ms NRk, p Mp 3 Combined pull-out N Ed N Rd,p =N Rk,p / Mp g and concrete failure b NEd N Rd,p = N Rk,p / Mp 4 Concrete cone failure 5 Splitting failure NEd NRd, c NEd NRd, sp NRk, c Mc NRk, sp Msp N 6 Blow-out failure c Rk, cb NEd NRd, cb Mc 7 8 a b c Steel failure of reinforcement NEd,re NRd, re NRk, re Ms, re h NEd, re NRd, re NRk, re Ms, re Anchorage failure of NEd, re N h Rd, a N N reinforcement Ed, re Rd, a Not required for post-installed chemical fasteners Not required for headed and post-installed mechanical fasteners Not required for post-installed fasteners and in case of headed fasteners where c >,5 h ef g NEd NRd, c g NEd NRd, sp NRk, c Mc NRk, sp Msp g NRk, cb NEd NRd, cb Mc c) The minimum anchorage length of supplementary reinforcement in the concrete failure cone is minl 1 =4d s (anchorage with bends, hooks or loops) or minl 1 =1d s (anchorage with straight bars with or without welded transverse bars). d) The supplementary reinforcement shall be anchored outside the assumed failure cone with an anchorage length l bd according to EN In reinforced elements the tension in the anchored rebar shall be transferred to the reinforcement in the element by adequate lapping. Otherwise concrete cone failure corresponding to the end of the supplementary reinforcement should be verified using Equation (7.14). 39

40 e) Reinforcement should be provided as shown in Figure 7.1 designed to resist the forces arising from the assumed strut and tie model, taking into account the splitting forces according to Steel failure of fastener The characteristic resistance of a fastener in case of steel failure N Rk,s is given in the relevant European Technical Product Specification. The strength calculation is based on f uk Pull-out failure of fastener The characteristic resistance in case of pull-out failure N Rk,p of post-installed mechanical and headed fasteners is given in the relevant European Technical Product Specification. NOTE For headed fasteners the characteristic resistance N Rk,p is limited by the concrete pressure under the head of the fastener according to Equation (7.1): with N Rk, p = k 1 A h f ck (7.1) A h k 1 = load bearing area of the head of the fastener 2 2 = d h d 4 = 7,5 for fasteners in cracked concrete = 1,5 for fasteners in non-cracked concrete Combined pull-out and concrete failure in case of post-installed chemical fasteners The characteristic resistance of a fastener, a group of fasteners and the tensioned fasteners of a group of fasteners in case of combined pull-out and concrete failure may be obtained by Equation (7.3). A p, N N Rk, p N Rk, p g, Np s, Np re, N ec, Np Ap, N The different factors of Equation (7.3) are given below. (1) The characteristic resistance of a single bonded fastener N Rk, p fasteners or edges of the concrete member is: (7.2) (7.3) not influenced by adjacent bonded N Rk,p Rk d hef (7.4) with Rk = Rk,Cr for cracked concrete = Rk,ucr for non-cracked concrete Rk, Cr and Rk,ucr are given in the relevant European Technical Product Specification. 4

41 (2) The geometric effect of axial spacing and edge distance on the characteristic resistance is taken into account by the value A p,n / A p,n, where A p,n Ap,N = s cr,np s cr,np, reference bond influence area of an individual fastener actual bond influence area, limited by overlapping areas of adjacent fasteners (s <s cr,np ) as well as by edges of the concrete member (c <c cr,np ). s cr,np = 7,3 d Rk 3hef (7.5) NOTE Rk = value Rk,ucr for non-cracked concrete C2/25 c cr,np = s cr,np /2 (7.6) A and p,n A are calculated similar to the reference projected area p,n A and the actual projected area c,n A in case of concrete cone failure (Figures 7.3 and 7.4). However, then the values s c,n cr,n and c cr,n are replaced by the values s cr,np and c cr,np, respectively. The value s cr,np calculated according Equation (7.5) is valid for cracked and noncracked concrete. (3) The factor g, Np with takes account of a group effect for closely spaced fasteners. 1 1 [ ] s,5 g, Np g, Np ( ) g, Np scr,np Rk 1,5 g, Np n ( n 1) ( ) 1 [ ] k8 Rk, c d k 8 hef fck Rk, c = 7,7 for cracked concrete = 11, for non-cracked concrete In case of unequal spacing the mean value of the spacing should be used in Equation (7.7). (4) The factor s,np takes account of the disturbance of the distribution of stresses in the concrete due to the proximity of an edge of the concrete member. For fastenings with several edge distances (e.g. fastening in a corner of the concrete member or in a narrow member), the smallest edge distance c shall be inserted in Equation 7.1). c s, Np,7,3 1 [-] (7.1) ccr,np (5) The shell spalling factor re, N applies when h ef < 1 mm and accounts for the effect of dense reinforcement between which the fastener is installed: hef re,n,5 1 [-] (7.11) 2 (7.7) (7.8) (7.9) The factor re, N may be taken as 1, in the following cases: 41

42 a) Reinforcement (any diameter) is present at a spacing 15 mm, or b) reinforcement with a diameter of 1 mm or less is present at a spacing 1 mm. (6) The factor ec, Np takes account of a group effect when different tension loads are acting on the individual fasteners of a group. 1 ec, Np en / s [-] (7.12) cr,np Where there is an eccentricity in two directions, ec, Np shall be determined separately for each direction and the product of both factors shall be inserted in Equation (7.3). (7) For the case of fasteners in a narrow member, i.e. in an application with three or more edge distances less than c cr,np from the fastener (Figure 7.4), the calculation according to Equation (7.3) leads to conservative results. More precise results are obtained if h ef is substituted by h ' ef, which is determined according to Equations (7.19) and (7.2) with replacing c cr,n by c cr,np and s cr,n by s cr,np. The value h ' ' ef is inserted in Equations (7.4), (7.5) and (7.9). The values to determine A p,n and A p, N as well as in Equations (7.7), (7.1) and (7.12) Concrete cone failure scr,np and c ' cr, Np =,5 s ' cr,np are used (1) The characteristic resistance of a fastener, a group of fasteners and the tensioned fasteners of a group of fasteners in case of concrete cone failure may be obtained by Equation (7.13). Ac, N N Rk, c N Rk, c s, N re, N ec, N M, N [N] (7.13) A c, N The different factors of Equation (7.13) are given below. (2) The characteristic resistance of a single fastener placed in concrete and not influenced by adjacent fasteners or edges of the concrete member is obtained by: with 1,5 N Rk, c k9 fck hef [N] (7.14) k 9 = k cr,n for cracked concrete = k ucr,n for non-cracked concrete k cr,n and k ucr,n are given in the corresponding European Technical Product Specification. NOTE According to current experience the values for k cr,n and k ucr,n are k cr,n = 7,7 and k ucr,n = 11, for post-installed fasteners and the values k cr,n = 8,9 and k ucr,n = 12,7 apply for cast-in headed fasteners. In case of anchor channels k cr,n and k ucr,n depend on the shape of the anchor channel. (3) The geometric effect of axial spacing and edge distance on the characteristic resistance is taken into account by the value A c, N /A, where c, N c, = s s cr,n cr,n (7.15) = reference projected area, see Figure

43 A c,n = actual projected area, limited by overlapping concrete cones of adjacent fasteners (s <s cr,n ) as well as by edges of the concrete member (c <c cr,n ). An example for the calculation of A c,n is given in Figure 7.3. s cr,n and c cr,n are given in the corresponding European Technical Product Specification. NOTE For headed and post-installed fasteners according to current experience s cr,n = 2 c cr,n = 3 h ef. A c, N scr,n scr,n Key 1 Concrete cone Figure 7.2 Idealized concrete cone and area A c, N of concrete cone of an individual fastener A c, N = (c 1 + s 1 +,5 s cr, N ) (c 2 + s 2 +,5 s cr, N ) if: c 1 ; c 2 c cr, N s 1 ; s 2 s cr, N When the fastening is close to one edge only the value of c 1 (or c 2) parallel to the edge should be replaced by,5 s cr,n and the expression for A c,n should be modified accordingly Figure 7.3 Example of the actual area A c, N of the idealised concrete cone for a group of four fasteners (4) The factor s, N takes account of the disturbance of the distribution of stresses in the concrete due to the proximity of an edge of the concrete member. For fastenings with several edge distances (e.g. fastening in a corner of the concrete member or in a narrow member), the smallest edge distance c should be inserted in Equation (7.16). c s,n,7,3 1 ccr,n (7.16) 43

44 (5) For the shell spalling factor re, N the corresponding provisions in apply. (6) The factor ec, N takes account of a group effect when different tension loads are acting on the individual fasteners of a group. 1 ec, N e / N s [-] (7.17) cr, N Where there is an eccentricity in two directions, ec, N shall be determined separately for each direction and the product of both factors should be inserted in Equation (7.13). (7) The factor M, N takes into account the effect of a compression force between fixture and concrete. M, N = 1, fastenings close to an edge (c < 1,5 h ef ), fastenings with c h ef loaded by a bending moment and a tension force with C Ed /N Ed <,8 or fastenings with z/h ef = 2,67 z/h ef (7.18) all other fastenings loaded by a bending moment and a normal force In case of bending in two directions z shall be determined for the resultant direction. (8) For the case of fasteners in an application with three or more edge distances less than c cr, N from the fasteners (see Figure 7.4) the calculation according to Equation (7.13) leads to conservative results. More precise results are obtained if in the case of single fasteners the value h ef is substituted by ' cmax hef hef ccr, N or in the case of groups h ef with ' c max { max s h ; max ef hef hef } ccr, N scr, N is substituted by the larger value of c max = maximum distance from centre of a fastener to the edge of concrete member c cr,n s max = maximum centre to centre spacing of fasteners s cr,n ; s 2,max ( s cr,n ) for applications with three edges (7.19) (7.2) Key a) (c 1 ; c 2,1 ; c 2,2 ) c cr,n b) (c 1,1 ; c 1,2 ; c 2,1 ; c 2,2 ) c cr,n Figure 7.4 Examples for fastenings in concrete members where ' h ef, ' scr,n and ' ccr,n may be used 44

45 The value ' h ef is inserted in Equation (7.14). In Equations (7.15), (7.16), (7.17) and for the determination of A according to Figure 7.3 the values c, N ' scr,n and c ' cr,n, defined as ' ' ' hef scr, N 2ccr, N scr, N hef are inserted for s cr,n and c cr,n, respectively. (7.21) NOTE An example for the calculation of ' hef is illustrated in Figure 7.5. c 1 c 2 c 3 c 4 s h ef hef = 11 mm = 1 mm = 12 mm = c max = 8 mm = 21 mm = 2 mm max 12 /1,5;21 / 3 8mm Figure 7.5 Illustration of the calculation of Splitting failure ' hef for a double fastening influenced by 4 edges (1) Splitting failure during installation (e.g. when applying the installation torque on a fastener) is avoided by complying with minimum values for edge distances c min, spacing s min, member thickness h min and requirements for reinforcement as given in the relevant European Technical Product Specification. NOTE Although the headed fasteners are not torqued, minimum values for edge distance and spacing should be observed to facilitate adequate placing and compaction of concrete. 45

46 (2) Splitting failure due to loading shall be taken into account according the following rules. The characteristic values of edge distance and spacing in the case of splitting under load, c cr,sp and s cr,sp, are given in the relevant European Technical Product Specification. No verification is required if at least one of the following conditions is fulfilled: a) The edge distance in all directions is c >1, c cr,sp for single fasteners and c >1,2 c cr,sp, for fastener groups and the member depth is h>h min in both cases. b) The characteristic resistance for concrete cone failure and pull-out failure is calculated for cracked concrete and reinforcement resists the splitting forces and limits the crack width to w k,3 mm. NOTE The required cross-section A s of the splitting reinforcement may be determined as follows: As k12 Ed fyk/ Ms, re [mm²] (7.22) with k 12 = 2, deformation-controlled expansion fasteners = 1,5 torque-controlled expansion fasteners = 1, undercut fasteners =,5 bonded fasteners, headed fasteners, anchor channels Ed = sum of the design tensile force of the fasteners in tension under the design value of the actions [N] f yk = nominal yield strength of the reinforcing steel 6 N/mm² If the conditions a) and b) are not fulfilled, then the characteristic resistance of a fastener or a group of fasteners in case of splitting failure shall be calculated according to Equation (7.23). with: N Rk, sp N N Rk,sp Rk, sp A A c, N c, N s, N re, N ec, N h, sp given in the relevant European Technical Product Specification (7.23) s, N, re,n, ec,n according to , however the values c cr,n and s cr,n shall be replaced by c cr,sp and s cr,sp, respectively, which are based on a member thickness h min. h,sp takes into account the influence of the actual member thickness h on the splitting resistance. For fasteners according to current experience it is given by Equation (7.24). 2 / 3 2 / 3 h hef 1,5 c1 h, sp max {1; } 2 hmin hmin (7.24) If in the relevant European Technical Product Specification c cr,sp for more than one member thickness h is given, then the member thickness valid for the used c cr,sp shall be inserted in Equation (7.24). NOTE If N Rk,sp conservatively calculated as is not available in the relevant European Technical Product Specification this value may be N = min { N, Rk,sp Rk, p mechanical and cast-in fasteners or replaced by N Rk, p N }, with Rk,c N according to in case of post-installed Rk, p according to in case of chemical fasteners. 46

47 Blow-out failure Verification of blow-out failure is required in case of headed fasteners and for post-installed mechanical undercut fasteners acting as headed fasteners if the edge distance in one direction is c,5 h ef. The characteristic resistance in case of blow-out failure is: Ac, Nb N Rk, cb N Rk, cb s, Nb g, Nb ec, Nb [N] (7.25) A c, Nb The different factors of Equation (7.25) are given below. NOTE For groups of fasteners perpendicular to the edge, which are loaded uniformly, verification is only required for the fasteners closest to the edge. (1) The characteristic resistance of a single fastener, not influenced by adjacent fasteners or free structural component edges is obtained by: where N Rk, cb k4 c1 Ah fck [N] (7.26) k 4 = 8,7 for cracked concrete A h = 12,2 for non-cracked concrete as defined in Equation (7.2) or given in the relevant European Technical Product Specification. (2) The geometric effect of axial spacing and edge distance on the characteristic resistance is taken into account by the value A c, Nb /Ac, Nb where A c, Nb = reference projected area for an individual fastener with an edge distance c, see Figure = (4 c 1 )² (7.27) A c, Nb = actual projected area, limited by overlapping concrete break-out bodies of adjacent fasteners (s < 4 c 1 ) as well as by proximity of edges of the concrete member (c 2 < 2 c 1 ) or the member thickness. Examples for the calculation of A c,nb are given in Figure 7.7. Figure 7.6 Idealized concrete break-out body and area Ac, Nb blow-out failure of an individual fastener in case of 47

48 A c, Nb 4 c1 ( c2 s 2 c1) c2 2 c1 s 4 c1 A c, Nb f 2 c s 4 c (2 c Figure 7.7 Examples of actual areas A c, Nb of the idealized concrete break-out bodies for different arrangements of headed fasteners in case of blow-out failures (3) The factor s, Nb takes account of the disturbance of the distribution of stresses in the concrete due to the proximity of a corner of the concrete member. For fastenings with several edge distances (e.g. fastening in a narrow concrete member), the smallest edge distance, c 2, shall be inserted in Equation (7.28). c,7,3 2 s, Nb 1 2c1 (4) The factor g, Nb accounts for the group effect of a number of fasteners n in a row parallel to the edge. s n (1 n) 1 g, Nb 1 4 c1 with f ) (4 c 1 s) (7.28) (7.29) s 1 4c 1 (5) The factor ec, Nb takes account of a group effect, when different loads are acting on the individual fasteners of a group. 1 ec, Nb 1 2 en/(4 c1) (7.3) 48

49 Supplementary reinforcement (1) The characteristic resistance of the supplementary reinforcement N Rk,re of one fastener is N Rk, re = n re A s,re f yk,re (7.31) with f yk 6 N/mm² (2) The design resistance N Rd,a of the supplementary reinforcement provided for one fastener associated with anchorage failure in the concrete cone is: with l1 ds fbd NRd, a (7.32) l 1 f bd n re l b,min =4 d s (anchorage with bends, hooks or loops) 1 d s (anchorage with straight bars with or without welded transverse bars) = design bond strength according to EN , taking into account the concrete cover of the supplementary reinforcement = influencing factor, according to EN =,7 for hooked bars = 1, for straight bars Shear load Required verifications The verifications of Table 7.2 apply. 49

50 Table 7.2 Required verifications for headed and post-installed fasteners in shear Single fastener most loaded fastener Fastener groups fastener group 1 Steel failure of fastener without lever arm 2 Steel failure of fastener with lever arm 3 Concrete edge failure 4 Concrete pry-out failure 5 Steel failure of supplementary reinforcement 6 Anchorage failure of supplementary reinforcement a exception see VRk, s,m VEd VRd, s Ms VRk, s VEd VRd, s Ms VRk, c VEd VRd, c Mc VRk, cp VEd VRd, cp Mc NRk, re VEd, re VRd, re Ms, re V Ed, re N Rd, a Detailing of supplementary reinforcement h VRk, s,m VEd VRd, s Ms V h Rk, s V V Ed Rd, s Ms h NRk, re V Ed, re VRd, re Ms, re h VEd, re NRd, a g VRk, c V V Ed Rd, c Mc g VRk, cp V V Ed Rd, cp a Mc When the design relies on supplementary reinforcement, concrete edge failure according to Table 7.2 and need not to be verified but the supplementary reinforcement shall be designed to resist the total load. The supplementary reinforcement may be in the form of a surface reinforcement (Figure 7.8) or in the shape of stirrups or loops. The supplementary reinforcement shall be anchored outside the assumed failure body with an anchorage length l b,net according to EN In reinforced elements the tension in the anchored rebar shall be transferred to the reinforcement in the element by adequate lapping. Otherwise concrete edge failure corresponding to the end of the supplementary reinforcement should be verified using Equation (7.39). In general, for all fasteners of a group the same diameter of reinforcement shall be provided. It shall consist of ribbed bars with f yk 6 N/mm² and a diameter not larger than 16 mm. The mandrel diameter, d b, shall comply with EN If the shear force is taken up by a surface reinforcement according to Figure 7.8, the following additional requirements shall be met: a) c 1 from the fastener shall be assumed as effective. b) The anchorage length l 1 (see Figure 7.8) in the concrete breakout body is at least min l 1 = 1 d s, straight bars with or without welded transverse bars = 4 d s bars with a hook, bend or loop c) Reinforcement along the edge of the member shall be provided and be designed for the forces according to an appropriate strut and tie model (see Figure 7.8). As a simplification an angle of the compression struts of 45 may be assumed. 5

51 Figure 7.8 Surface reinforcement to take up shear forces with simplified strut and tie model to design edge reinforcement If the shear forces are taken up by a supplementary reinforcement detailed in the shape of stirrups or loops, the reinforcement shall enclose and contact the shaft of the fastener and be positioned as closely as possible to the fixture Steel failure of fastener Shear load without lever arm For headed fasteners welded or not welded to a steel fixture and post-installed fasteners the characteristic resistance of a single fastener in case of steel failure V Rk,s is given in the relevant European Technical Product Specification. For a single fastener without sleeve in the sheared section (threaded rod) and without significant reduction in cross-section along its total length V Rk,s shall not be larger than: with V Rk,s = k 5 A s f uk (7.33) k 5 =,6 f uk 5 N/mm² =,5 5 N/mm²< f uk 1 N/mm² NOTE According to current experience for fasteners with a ratio h ef/d < 5 and a concrete compressive strength class < C2/25 the characteristic resistance V Rk,s should be multiplied by a factor of,8. In general, in presence of a grout layer with a thickness t grout d/2 the characteristic resistance of the fastener V Rk, s, m is: V Rk,s,m = k 51 V Rk,s (7.34) In case of groups with fasteners with a maximum hole clearance d f as given in Table 6.1 and made of nonductile steel, this characteristic shear resistance shall be multiplied with the factor k 51. The factor k 51 is given in the relevant European Technical Product Specification. For single fasteners k 51 = 1. NOTE According to current experience the factor k 51 for ductile steel is k 51 = 1, for non-ductile steel is k 51 =,8. Steel with rather low ductility (rupture elongation A 5 %) may be treated as non-ductile. 51

52 In case of a fastening with two or more fasteners located in uncracked concrete and arranged in the direction of the shear load and a grout layer with a thickness t grout 4mm the characteristic resistance of one fastener V Rk, s, m is: V Rk,s,m = ( 1,1 t grout ) k51 V Rk, s NOTE In the absence of better information for cracked concrete V Rk,s,m = ( 1,15 t grout ) k51 V Rk, s assumed. (7.35) may be Shear load with lever arm The characteristic resistance in case of steel failure V Rk,s shall be obtained from Equation (7.36). VRk, s M M Rk, s [N] (7.36) l with M, l see M Rk, s = M 1 N / N ) N Rd,s Rk, s ( Ed Rd, s = N Rk, s / Ms (7.37) The characteristic resistance under tension load in case of steel failure N Rk,s, the partial factor Ms and the characteristic bending resistance of a single fastener M Rk, s are given in the relevant European Technical Product Specification where applicable Concrete pry-out failure Fastenings may fail due to a concrete pry-out failure at the side opposite to load direction. The corresponding characteristic resistance V Rk,cp shall be calculated from Equation (7.38). with V Rk, cp = k 3 N Rk,c (7.38) k 3 factor to be taken from the relevant European Technical Product Specification, valid for applications without supplementary reinforcement. In case of supplementary reinforcement (Figure 7.8) the factor k 3 should be multiplied with,75. N Rk,c according to determined for a single fastener or all fasteners in a group loaded in shear For anchor groups with shear forces (or components thereof) on the individual anchors in opposing directions (e.g. anchorages loaded predominantly by a torsion moment), the most unfavourable anchor should be verified. When calculating the area A c,n it should conservatively be assumed that there is a virtual edge (c =,5s) in the direction of the neighbouring anchor(s) (see Figure 7.9) Concrete edge failure (1) The following verifications are valid for shear loads acting on fastenings without lever arm. (2) The following conditions shall be observed: For single fasteners and groups with not more than 4 fasteners with or without hole clearance and with an edge distance in all directions c > max(1 h ef ;6d), a check of the characteristic concrete edge failure resistance may be omitted. 52

53 NOTE For fastenings with more than one edge (see Figure 7.1), the resistances for all edges shall be calculated. The smallest value should be used in the verification. The minimum spacing for a group of fasteners should be s min 4d. group of four anchors away from edges group of two anchors located in a corner Figure 7.9 Calculation of area A c,n for pryout failure for group anchorages with shear load (or components thereof) on anchors acting in opposing directions 53

54 V E1 = V Ed cos V E2 = V Ed sin Key 1 loaded fastener 2 unloaded fastener a) applied action b) verification for the left edge c) verification for the bottom edge 1 2 Figure 7.1 Verification for a quadruple fastening with hole clearance at a corner, example (3) The characteristic resistance V Rk,c of a fastener or a fastener group loaded towards the edge is: Ac, V VRk, c VRk, c s, V h, V ec, V, V re, V Ac, V [N] (7.39) The different factors of Equation (7.39) are given below. (4) The initial value of the characteristic resistance of a fastener loaded perpendicular to the edge corresponds to: V Rk, c k 5 d nom lf f ck c 1,5 1 [N] (7.4) with k 5 = 1,7 for cracked concrete = 2,4 for non-cracked concrete,5 l,1 f c1 [-] (7.41) 54

55 ,2 dnom,1 [-] (7.42) c1 l f = h ef in case of a uniform diameter of the shank of the headed fastener and a uniform diameter of the post-installed fastener 12 d nom in case of d nom 8 d nom, 3mm) in case of d nom >24mm d nom 6 mm The values d nom and l f are given in the relevant European Technical Product Specification. (5) The geometrical effect of spacing as well as of further edge distances and the effect of thickness of the concrete member on the characteristic resistance is taken into account by the ratio A c, V /A, where: c, V A c, V = reference projected area, see Figure 7.11 Ac, V = 4,5 2 c 1 (7.43) area of the idealized concrete break-out body, limited by the overlapping concrete cones of adjacent fasteners (s < 3 c 1 ) as well as by edges parallel to the assumed loading direction (c 2 < 1,5 c 1 ) and by member thickness (h < 1,5 c 1 ). Examples for calculation of A c,v are given in Figure Figure 7.11 Idealized concrete break-out body and area A for a single fastener c, V 55

56 A c, V = 1,5 c 1 (1,5 c 1 + c 2 ) h 1,5 c 1 c 2 1,5 c 1 A c, V = (2 1,5 c 1 + s 2 ) h h < 1,5 c 1 s 2 3 c 1 a) Single anchor at a corner b) Group of anchors at an edge in a thin concrete member Figure 7.12 Examples of actual projected areas A c,v of the idealized concrete break-out bodies for different fastener arrangements under shear loading NOTE The resistance for a fastening under torsion consisting of two fasteners where the fasteners are loaded in shear in opposite directions calculated in accordance with Equation (7.4) may be unconservative for concrete edge failure due to overlapping of the concrete breakout bodies. If the ratio between the concrete edge breakout resistance (verified edge) to the concrete breakout resistance of the second fastener (pry-out or edge failure) is larger than,7 and s 2 s crit, Equation (7.4) should be multiplied by a factor of,8. Herein, s crit is defined as follows: s crit = 1,5h ef + 1,5c 1, if the second fastener is governed by pry-out failure; s crit = 1,5h ef, if the second fastener is governed by concrete edge failure with respect to a second edge (perpendicular to the verified edge). (6) The factor s, V takes account of the disturbance of the distribution of stresses in the concrete due to further edges of the concrete member on the shear resistance. For fastenings with two edges parallel to the direction of loading (e.g. in a narrow concrete member) the smaller edge distance shall be used for c 2 in Equation (7.44). c,7,3 2 s, V 1 1,5 c1 (7.44) (7) The factor h, V takes account of the fact that the concrete edge resistance does not decrease proportionally to the member thickness as assumed by the ratio A c, V /A (Figure 7.12b)). c, V, 5 15, c1 h, V 1 h (7.45) (8) The factor ec, V takes into account a group effect when different shear loads are acting on the individual fasteners of a group (see Figure 7.13). ec,v ev /(3 c1) (7.46) e V eccentricity of the resulting shear load acting on the fasteners relative to the centre of gravity of the fasteners loaded in shear 56

57 Figure 7.13 Resolving unequal shear components into an eccentric shear load resultant, example (9) The factor,v takes into account the angle V between the applied load V Ed and the direction perpendicular to the free edge under consideration for the calculation of the concrete edge resistance (see Figure 7.1). 1 (,5 sin ), V 2 2 (cos ) V V 1 (7.47) V = angle between design shear load V Ed and a line perpendicular to the verified edge, V, see Figure 7.1 NOTE In case of a single fastener with c 2 < 1,5 c 1 and the shear load directed towards a corner the factor,5 in Equation (7.47) should be replaced by 1,. This modification accounts for the possibility that in this special case the corner may break off instead of a breakout body developing at one of the edges. (1) The factor re, V takes account of the effect of the reinforcement located on the edge. re, V = 1, re, V = 1,4 fastening in non-cracked as well as cracked concrete without edge reinforcement or stirrups fastening in cracked concrete with edge reinforcement (Figure 7.8) and closely spaced stirrups or wire mesh with a spacing a < 1 mm and a 2 c 1 A factor re, V > 1 for applications in cracked concrete shall only be applied, if the embedment depth h ef of the fastener is h ef 2,5 times the concrete cover of the edge reinforcement. (11) For fastenings in a narrow, thin member with c 2,max < 1,5 c 1 and h < 1,5 c 1 (see Figure 7.14) the calculation according to Equation (7.39) leads to conservative results. More precise results are achieved if c 1 in case of single fasteners is ' c1 max { c2, max /1,5; h /1,5} (7.48) with c 2,max = larger of the two edge distances parallel to the direction of loading or in case of groups c 1 is 57

58 ' c1 max {c2, max /1,5; h /1,5; s2, max /3} (7.49) with s 2,max = maximum spacing in direction 2 between fasteners within a group The value of c, V ' c1 instead of c 1 is used in Equations (7.4) to (7.46) as well as in the determination of the areas A and A c,v according to Figures 7.11 and Supplementary reinforcement (1) The characteristic resistance of one fastener in case of steel failure of the supplementary reinforcement may be calculated according to Equation (7.5). with N Rk, re = k 6 n re A s,re f yk (7.5) k 6 f yk = efficiency factor = 1, surface reinforcement according to Figure 7.1 =,5 supplementary reinforcement in the shape of stirrups or loops enclosing the fastener 6 N/mm² NOTE The factor k 6 =,5 for supplementary reinforcement in the shape of stirrups or loops takes account of unavoidable tolerances in workmanship. max (c 2,1 and c 2,2 ) < 1,5 c 1 and h < 1,5 c 1 s = 1 mm, c 1 = 2 mm, h = 12 mm < 1,5 2 mm, c 2,1 = 15 mm 1,5 2 mm, c 2,2 = 1 mm < 1,5 2 mm, ' c 1 = max {15/1,5 ; 12/1,5 ; 1/3} = 1 mm Figure 7.14 Fasteners in thin, narrow members where the value ' c1 may be used 58

59 (2) For applications with supplementary reinforcement in the shape of stirrups or loops enclosing the fastener no proof of the anchorage capacity of the supplementary reinforcement is necessary. For applications according to Figure 7.8 the design resistance N Rd,,a of the supplementary reinforcement of one fastener in case of an anchorage failure in the concrete edge break-out body is given by Equation (7.51). with l d f N 1 s bd Rd, a (7.51) n re l 1 l b,min =4 d s (anchorage with bends, hooks or loops) 1 d s (anchorage with straight bars with or without welded transverse bars) f bd = design bond strength according to EN , taking into account the concrete cover of the supplementary reinforcement = influencing factor, according to EN =,7 for hooked bars = 1, for straight bars Combined tension and shear load Fastenings without supplementary reinforcement The required verifications are given in Table 7.3. Verifications for steel and concrete failure modes are carried out separately. Both verifications shall be fulfilled. 1 Table 7.3 Required verifications for headed and post-installed fasteners without supplementary reinforcement in combined tension and shear load Steel failure of fastener with: N N Ed Rd, s 2 V V Verification Ed Rd, s N Ed /N Rd,s 1 and V Ed /V Rd,s (7.53) If N Ed and V Ed are associated with different fasteners in the group the interaction shall be verified for all fasteners. 2 Failure modes 1,5 1,5 other than steel N Ed VEd 1 or N N N Rd, i Ed Rd, i V V V Ed Rd, i Rd, i with: N Ed /N Rd,i V Ed /V Rd,i 1,2 (7.54) (7.55) The largest value of N Ed /N Rd,i and V Ed /V Rd,i for the different failure modes shall be taken. 59

60 Fastenings with supplementary reinforcement For fastenings with a supplementary reinforcement for tension and shear loads applies. For fastenings with a supplementary reinforcement to take up tension or shear loads only, Equation (7.52) shall be used with the largest value of N Ed /N Rd,i and V Ed /V Rd,i for the different failure modes other than fastener steel failure. N N Ed Rd, i k7 V V Ed Rd, i k7 1 (7.52) with: N Rd,i minimum value of N Rd,c, N Rd,p, N Rd,cb V Rd,i k 7 minimum value of V Rd,c, V Rd,cp given in the relevant European Technical Product Specification N Ed /N Rd,i V Ed /V Rd,i NOTE If no value for k 7 is given in the relevant European Technical Product Specification, k 7 = 2/3 may be assumed according to current experience. 7.3 Fasteners for multiple use for non-structural applications By multiple fastener use it is assumed that in the case of excessive slip or failure of one fastener the load can be transmitted to adjacent fasteners without violating the requirements on the fixture in the serviceability and ultimate limit state. The definition of multiple use for fasteners is given in the National Regulations. Details on the design for fasteners for multiple use are given in CEN/TR "Redundant fasteners". 7.4 Anchor channels Tension load Required verifications The verifications of Table 7.4 apply Detailing of supplementary reinforcement When the design relies on supplementary reinforcement, concrete cone failure according to Equation (7.56) needs not to be verified but the supplementary reinforcement shall be designed to resist the total load. The reinforcement shall be anchored adequately on both sides of the potential failure planes applies. For anchor channels located parallel to the edge of a concrete member or in a narrow concrete member, the plane of the supplementary reinforcement shall be located perpendicular to the longitudinal axis of the channel (see Figure 7.15) Steel failure The characteristic resistances N Rk,s,a (failure of anchor), N Rk,s,c (failure of the connection between anchor and channel), N Rk,s,l (local failure by flexure of the channel lips), N Rk,s (failure of the channel bolt) and M Rk,s,flex (failure by flexure of the channel) are given in the relevant European Technical Product Specification. 6

61 Pull-out failure The characteristic resistance N Rk,p for pull-out failure of the anchor is given in the relevant European Technical Product Specification. NOTE The characteristic resistance N Rk,p should be limited by the concrete pressure under the head of the anchor according to

62 Table 7.4 Required verifications for anchor channels in tension Failure mode Channel Most unfavourable anchor or channel bolt 1 2 a anchor N Ed N Rd,s,a N Rk,s,a / Ms connection a N between anchor and channel Ed N Rd,s,c N Rk,s,c / Ms, ca Steel 3 failure local flexure of channel lip N Ed N Rd,s,l N Rk,s,l / Ms, l 4 channel bolt N Ed N Rd,s N Rk,s / Ms b 5 flexure of channel M Ed M Rd,s,flex M Rk,s,flex / Ms,flex 62

63 Table 7.4 (continued) Failure mode Channel Most unfavourable anchor or channel bolt a 6 Pull-out failure N Ed N Rd,p N Rk,p / Mp a 7 Concrete cone failure N Ed N Rd,c N Rk,c / Mc a 8 Splitting failure N Ed N Rd,sp N Rk,sp / Msp 9 Blow-out failure a a N N N / Ed Rd,cb Rk,cb Mc c c c 1 11 Steel failure of a N N N / supplementary reinforcement Ed,re Rd,re Rk,re Ms, re Anchorage failure of supplementary a N reinforcement Ed, re N Rd, a a not required for anchors with c >,5 hef b most loaded anchor or channel bolt c the load on the anchor in conjunction with the edge distance and spacing should be considered in determining the most unfavourable anchor pren :213 (E) 63

64 Key 1 supplementary reinforcement 2 surface reinforcement Concrete cone failure Figure 7.15 Arrangement of supplementary reinforcement (1) The characteristic resistance of one anchor of a channel bar in case of concrete cone failure may be calculated according to Equation (7.56). N Rk, c N Rk,c ch,s,n ch,e,n ch,c,n The different factors in Equation (7.56) are given in the following: re,n (7.56) (2) For the determination of the basic characteristic resistance of one anchor not influenced by adjacent anchors, edges or corners of the concrete member located in cracked or non-cracked concrete Equation (7.14) applies. (3) The influence of neighbouring anchors on the concrete cone resistance is taken into account by the factor ch,s, N according to Equation (7.57). ch,s, N 1 n ch 1 1 (7.57) with (see Figure 7.16): s i 1 s 1,5 N N i1 cr, N i s i distance between the anchor under consideration and the neighbouring anchors s cr,n s cr, N = 2 (2,8 1,3 h ef /18) h ef 3 h ef (7.58) N i tension force of an influencing anchor 64

65 N n ch tension force of the anchor under consideration number of anchors within a distance s cr,n to both sides of the anchor under consideration Key 1 anchor under consideration Figure 7.16 Example of an anchor channel with different anchor tension forces (4) The influence of an edge of the concrete member on the characteristic resistance is taken into account by the factor ch,e, N according to Equation (7.59). with c 1 ch, e,n c cr,n c ( c 1 cr,n ),5 1 edge distance of the anchor channel (see Figure 7.17a)) =,5s cr,n (7.59) With anchor channels located in a narrow concrete member with different edge distances c 1,1 and c 1,2 (see Figure 7.17b)) the minimum value of c 1,1 and c 1,2 shall be inserted for c 1 in Equation (7.59). 65

66 Figure 7.17 Channel bar at an edge or in a narrow member (5) The influence of a corner of the concrete member on the characteristic resistance is taken into account by the factor ch,c, N according to Equation (7.6). with ch, c, N c c 2 cr, N,5 1 c 2 corner distance of the anchor under consideration (see Figure 7.18). (7.6) If an anchor is influenced by two corners, then the factor ch,c, N has to be calculated for the values c 2,1 and c 2,2 and the product of the factors ch,c, N shall be inserted in Equation (7.56). 66

67 Key a) Resistance of anchor 1 is calculated b) Resistance of anchor 2 is calculated c) Resistance of anchor 2 is calculated d) Resistance of anchor 1 is calculated Figure 7.18 Definition of the corner distance of an anchor channel in the corner of a concrete member (6) The shell spalling factor re, N takes account of the effect of a dense reinforcement for embedment depths h ef 1 mm applies. (7) For the case of anchor channels with h ef > 18 mm in a narrow member with influence of neighbouring anchors and influence of an edge and 2 corners (Figures 7.18c) and 7.18d)) located with edge distance less than c cr,n from the anchor under consideration the calculation according to Equation (7.56) leads to conservative results. More precise results are obtained if the value h ef is substituted by the larger value of: with cmax s h 18 mm and max ef hef hef hef 18 mm ccr,n scr,n c max s max (7.61) maximum distance from centre of an anchor to the edge of the concrete member c cr,n. In the example given in Figure (7.18c)) c max is the maximum value of c 1, c 2,1 and c 2,2 maximum centre to centre spacing of anchors s cr,n the value h is inserted in Equation (7.14) as well as in Equation (7.58). ' ef Splitting failure (1) In case of splitting failure due to installation of the channel bolt the relevant provision of applies. (2) In case of splitting failure due to loading the relevant provision of applies whereas an anchor channel corresponds to a fastener group. In case of verification of the splitting failure Equation (7.23) is replaced by Equation (7.62). N Rk, sp N Rk ch,s,n ch,e,n ch,c,n re,n h,sp (7.62) 67

68 with N Rk min( N Rk, p, N Rk, c N Rk, p according to Rk, c ch,s,n, ch,e,n, ) N, according to , re, N ch,c,n according to , h, sp according to However, the values c cr,n and s crn shall be replaced by c cr,sp and s cr,sp in Equations (7.57) to (7.61). The values c cr,sp and s cr,sp are valid for the member thickness h min Blow-out failure Verification of blow-out failure is not required with anchors when the distance between the anchorage area and the side surface of the structural component exceeds c=,5 h ef. If verification is required, the characteristic resistance of one anchor in case of blow-out is: N Rk, cb N Rk, cb ch,s,nb ch,g,nb ch,c,nb ch,h,nb The different factors in Equation (7.63) are given in the following. [N] (7.63) NOTE For anchor channels located perpendicular to the edge, which are loaded uniformly, verification is only required for the anchors closest to the edge. (1) The characteristic resistance of a single anchor N is calculated according to Rk,cb (2) The influence of neighbouring anchors on the blow-out resistance is taken into account by the factor ch,s, Nb, which may be calculated analogous to Equation (7.57), however, with s cr, Nb =4c 1 instead of s cr,n. (3) The influence of a corner of the concrete member on the characteristic resistance is taken into account by the factor ch,c, Nb according to Equation (7.64): with ch, c, Nb c c 2 cr, Nb, 5 1 c 2 corner distance of the anchor, for which the resistance is calculated (Figure 7.18) c cr, Nb = s cr, Nb /2 (7.64) If an anchor is influenced by two corners ( c 2 2c 1 ) example see Figure 7.18c) then the factor ch,c,nb Equation (7.63). shall be calculated for the values of c 2,1 and c 2,2 and the product of the factors shall be inserted in (4) The effect of the bearing area is taken into account by the factor ch,g, Nb according to Equation (7.29). (5) The effect of the thickness of the concrete member in case of a distance f c 1 between the anchor head and the upper or lower surface of the concrete member is taken into account by the factor ch,h, Nb according to Equation (7.65). hef f 2c1 f ch, h,nb 4c1 4c1 1 (7.65) 68

69 with f distance between the anchor head and the lower surface of the concrete member (Figure 7.19). Figure 7.19 Channel bar at the edge of a thin concrete member Supplementary reinforcement (1) In case of steel failure of the supplementary reinforcement the relevant provision of applies. (2) In case of anchorage failure of the supplementary reinforcement in the concrete cone the relevant provision of applies Shear load Required verifications The following verifications apply: Table 7.5, lines 1 to 7 for anchor channels without supplementary reinforcement Table 7.5, lines 1 to 6 and 8, 9 for anchor channels with supplementary reinforcement Detailing of supplementary reinforcement applies. 69

70 Table 7.5 Verifications for anchor channels loaded in shear 1 Failure mode Channel Most unfavourable anchor or channel bolt Steel failure shear force without lever arm channel bolt V Ed V Rd, s V Rk, s / Ms anchor V Ed V Rd, s, a V Rk, s, a / Ms Connection between anchor and channel V Ed V Rd, s, c V Rk, s, c / Ms local flexure of V Ed V channel lip Rd, s l V Rk s l / Ms, l a 5 shear force with lever arm channel bolt V V / Ms V Ed Rd, s Rk, s 7,,,

71 a b 6 Failure mode Channel Table 7.5 (continued) Most unfavourable anchor or channel bolt 7 V a Ed Rd, cp Rk, cp Pry-out failure V V / Mc V a Ed Rd, c Rk, c Concrete edge failure V V / Mc 8 Steel failure of supplementary h V reinforcement Ed, re V Rd, re N Rk, re / Ms, re 9 Anchorage failure of supplementary reinforcement V h Ed, re N Rd, a verification for most loaded channel bolt. the load on the anchor in conjunction with the edge distance and spacing should be considered in determining the most unfavourable anchor. a b b pren :213 (E) 71

72 Steel failure Shear force without lever arm The characteristic resistances V Rk, s (failure of channel bolt), V Rk, s, a (failure of anchor), V Rk, s, c (failure of connection anchor/channel) and V Rk, s, l (failure due to local flexure of channel lips) are given in the relevant European Technical Product Specification Shear force with lever arm The characteristic resistance of a channel bolt in case of steel failure, V Rk,s, shall obtained from Equation (7.66). with M MRk,s VRk,s [N] (7.66) l a M The value M depends on the degree of restraint of the anchor channel at the side of the fixture of the application in question and shall be determined according to good engineering practice. No restraint ( M 1, ) shall be assumed if the fixture can rotate freely. Full restraint ( M 2, ) may be assumed only if the fixture cannot rotate. M Rk,s = M Rk, s (1 N Ed /N Rd, s ) N Rd,s = N Rk, s / Ms M Rk, s characteristic bending resistance of the channel bolt, given in the relevant European Technical Product Specification Concrete pry-out failure (7.67) The characteristic resistance of the most unfavourable anchor for concrete pry-out failure shall be calculated according to Equation (7.68). with VRk, cp k3 N Rk,c k 3 factor to be taken from the relevant European Technical Product Specification valid for applications without supplementary reinforcement; in case of supplementary shear reinforcement the factor k 3 shall be multiplied with,75; (7.68) N Rk, c according to , determined for the anchors loaded in shear Concrete edge failure For anchor channels with an edge distance in all directions c > max{1 h ef ; 6 d} with d = diameter of the channel bolt, a check of the characteristic concrete edge failure resistance may be omitted. (1) The characteristic resistance of one anchor loaded perpendicular to the edge corresponds to V Rk, c V Rk,c ch,s,v ch,c,v ch,h,v ch,9,v re,v [N] (7.69) The different factors of Equation (7.69) are given below. 72

73 (2) The basic characteristic resistance of an anchor channel with one anchor loaded perpendicular to the edge not influenced by neighbouring anchors, member thickness or corner effects is: V Rk, c k 1 f ck c 1,5 1 (7.7) with k 1 = 2,5 for cracked concrete = 3,5 for non-cracked concrete (3) The influence of neighbouring anchors on the concrete edge resistance is taken into account by the factor ch,s, V according to Equation (7.71): ch,s,v 1 n 1 s 1 s 1 (7.71) with (see Figure 7.2): s i V i V n 1,5 V i V i1 cr,v i distance between the anchor under consideration and the neighbouring anchors s cr,v s cr, V = 4 c b ch shear force of an influencing anchor shear force of the anchor under consideration number of anchors within a distance s cr,v to both sides of the anchor under consideration (7.72) Figure 7.2 Example of an anchor channel with different anchor shear forces (4) The influence of a corner on the characteristic edge resistance is taken into account by the factor ch, c, V. 73

74 ch, c,v c c 2 cr,v,5 1 (7.73) with c cr, V =,5 s cr, V (7.74) If an anchor is influenced by two corners (Figure 7.21b)), then the factor ch,c, V according Equation (7.73) shall be calculated for each corner and the product shall be inserted in Equation (7.69). Figure 7.21 Example of an anchor channel with anchors influenced by one (a) or two (b) corners, anchor 2 is under consideration (5) The influence of a member thickness h < h cr, V is taken into account by the factor ch,h, V. with ch, h, V h h cr, V, 5 1 (7.75) h cr, v = 2 c h ch (see Figure 7.22) (7.76) Figure 7.22 Example of an anchor channel influenced by the member thickness (6) The factor ch, 9, V takes into account the influence of shear loads acting parallel to the edge (Figure 7.23). This applies only to the anchor closest to the edge. ch, 9,V 2,5 (7.77) 74

75 Figure 7.23 Anchor channel loaded parallel to the edge (7) The factor re, V accounting for the type of reinforcement on the edge is calculated according to In case of presence of edge reinforcement for applications in cracked concrete a factor used, if the height of the channel is h 4 ch mm (see Figure 6.8b)). re, V > 1 shall only be (8) For an anchor channel in a narrow, thin member (see Figure 7.24) with c 2, max c cr, v (c cr, V according to Equation (7.74)) and h < h cr, V (h cr, V according to Equation (7.76)), the calculation according to Equation (7.69) leads to conservative results. More precise results are achieved if the edge distance c 1 in Equation (7.69) is ' limited to c 1: with ' c1 max(( c2, max bch) / 2 ; ( h 2hch) / 2) c 2,max = max (c 2,1 ; c 2,2 ), largest of the two edge distances parallel to the direction of load The value ' c1 is inserted in Equations (7.7), (7.72), and (7.76). (7.78) Figure 7.24 Illustration of an anchor channel influenced by two corners and member thickness (in this example c 2,2 is decisive for the determination of c' 1 ) Supplementary reinforcement (1) In case of steel failure of the supplementary reinforcement the relevant provision of applies. (2) In case of anchorage failure of the supplementary reinforcement in the concrete cone the relevant provision of applies. 75

76 7.4.3 Combined tension and shear loads Anchor channels without supplementary reinforcement The required verifications are given in Table 7.6. Verifications for steel failure of channel bolt, other steel failure modes and failure modes other than steel are carried out separately. All three verifications shall be fulfilled Anchor channels with supplementary reinforcement For anchor channels with supplementary reinforcement to take up tension and shear loads applies. In the case of anchor channels at the edge with supplementary reinforcement to take up shear loads, Equation (7.83) shall be used. N + V 1 (7.83) with: N NEd / NRd 1 and V VEd / VRd Table 7.6 Required verifications for anchor channels without supplementary reinforcement in combined tension and shear load Steel failure Failure modes other than steel channel bolt other steel failures N N Ed Rd, s 2 V V Verification Ed Rd, s 2 1 with: N Ed /N Rd,s 1 and V Ed /V Rd,s 1 N N Ed Rd, s, i 1 V V Ed Rd, s, i with: for V Rd,s,i N Rd,s,i 1 = 2, 1 1 (7.79) (7.8) for V Rd,s,i > N Rd,s,i 1 = given in the European Technical Product Specification a corresponding values of N Rd,s,a, N Rd,s,c, N Rd,s,l and V Rd,s,a, V Rd,s,c, V Rd,s,l shall be used for each failure mode N Ed /N Rd,si 1 and V Ed /V Rd,si 1 N N N N Ed Rd, i 1,5 V V Ed Rd, i Ed Ed Or 1, 2 Rd, i V V Rd, i 1,5 1 (7.81) (7.82) with: N Rd,i minimum value of N Rd,c, N Rd,sp, N Rd,p, N Rd,cb V Rd,i minimum value of V Rd,c, V Rd,cp N Ed /N Rd,i V Ed /V Rd,i The largest value of N ed /N Rd,i and V Ed /V Rd,i for the different failure modes shall be taken. a 1 = 1 may be conservatively used in absence of other information. 76

77 8 Verification of ultimate limit state for fatigue loading 8.1 General (1) This EN covers applications with post-installed fasteners and headed fasteners under pulsating tension or shear load and alternating shear load and combinations thereof. NOTE For anchor channels relevant information is given in CEN/TR "Anchor channels". (2) Fatigue verification shall be carried out when fasteners are subjected to regular load cycles (e.g. fastening of cranes, reciprocating machinery, guide rails of elevators). (3) Fasteners used to resist fatigue loading shall be prequalified by a European Technical Product Specification for this application. (4) Annular gaps are not allowed and loosening of the nut or screw shall be avoided. Therefore a permanent prestressing force on the fastener shall be present during the service life of the fastener. (5) The verification of the resistance under fatigue loading consists of both, the verification under static and fatigue loading. Under static loading the fasteners shall be designed based on the design methods given in Clause 7. The verifications under fatigue loading are given in Derivation of forces acting on fasteners - analysis 6.1 and 6.2 apply. 8.3 Resistance The required verifications for tension and shear load are summarised in Tables 8.1 and 8.2. For combined tension and shear loading the following equations shall be satisfied: F, fat N Ek N, fat FN N Rk /M F, fat VEk V, fat FV VRk /M (, 1 1 N, fat ) ( V fat ) 1 (8.1) (8.2) (8.3) with FN, FV Ek V Ek N Rk,V Rk = required in the case of steel failure in tension and shear or pull-out failure in tension, taken from a European Technical Product Specification = taken from a European Technical Product Specification = Ek,max - Ek,min, peak to peak amplitude of the fatigue tensile action = V Ek,max - V Ek,min, peak to peak amplitude of the fatigue shear action = minimum values of resistance of the governing failure mode In Equations (8.1) to (8.3) the largest value of N,fat and V,fat for the different failure modes shall be taken. The maximum number of cycles is stated in the relevant European Technical Product Specification. 77

78 1 Steel failure 2 Pull-out failure Concrete cone failure Concrete splitting failure Table 8.1 Required verifications tension loading F, fat Single fastener F, fat F, fat F, fat N N N N Ek Ek Ek Ek N Rk, s Ms, N, fat N Rk, p Mp, fat N N Rk, c Mc, fat Rk, sp Mc, fat Fastener group most loaded fastener fastener group h FN N Rk, s F, fat N Ek Ms, N, fat F, fat N h Ek FN N Mp, fat Rk, p F, fat F, fat N N g Ek g Ek N N Rk, c Mc, fat Rk, sp Mc, fat Concrete NRk, cb g NRk, cb blow-out F, fat NEk F, fat NEk failure Mc, fat Mc, fat F,fat, Mc,fat, Mp,fat, according to 4.4 Ms,N,fat = Ms,fat according to FN Rk,s = fatigue resistance, tension, steel, see European Technical Product Specification Rk,c =,6 N Rk,c, fatigue resistance, tension, concrete Rk,p = fatigue resistance, tension, pull-out, see European Technical Product Specification Rk,sp =,6 Rk,sp, fatigue resistance, tension, concrete splitting =,6 Rk,cb, fatigue resistance, tension, concrete blow-out Rk,cb 3 Concrete pry-out failure 4 Concrete edge failure Table 8.2 Required verifications shear loading Single fastener Fastener group most loaded fastener fastener group Steel failure VRk, s h FV VRk, s F, fat VEk without lever arm F, fat V Ek Ms, V, fat Ms, V, fat Steel failure VRk, s h FV VRk, s F, fat VEk with lever arm F, fat V Ek Ms, V, fat Ms, V, fat VRk, cp g VRk, cp F, fat VEk F, fat VEk Mc, fat Mc, fat VRk, c g VRk, cp F, fat VEk F, fat V Ek Mc, fat Mc, fat F,fat, Mc,fat according to 4.4 FV For groups with 2 fasteners under shear load perpendicular to the axis of the fasteners when the fixture is able to rotate FV = 1. Ms,V, fat = Ms,fat according to V Rk,s = fatigue resistance, shear, steel, see European Technical Product Specification V Rk,c =,6 V Rk,c, fatigue resistance, shear, concrete edge failure =,6 V Rk,cp, fatigue resistance, shear, concrete pry-out failure V Rk,cp 78

79 9 Verification for seismic loading 9.1 General (1) This Clause provides requirements for the design of post-installed fasteners and cast-in headed fasteners used to transmit seismic actions by means of tension, shear, or a combination of tension and shear load between connected structural elements or between non-structural attachments and structural elements. NOTE For anchor channels relevant information is given in CEN/TR "Anchor channels". (2) In cases of very low seismicity according to EN it shall be permitted to design as for permanent and transient situations (Clauses 4 to 7, 12). (3) For the seismic design situation where the seismic tension component of the design force at the ultimate limit state applied to a single fastener or a group of fasteners is equal to or less than 2 per cent of the total design tensile force, the tension component acting on a single fastener or a group of fasteners may be verified as for persistent and transient tension loads. (4) For the seismic design situation where the seismic shear component of the design force at the ultimate limit state applied to a single fastener or a group of fasteners is equal to or less than 2 per cent of the total design shear force, the shear component acting on a single fastener or a group of fasteners may be verified as for persistent and transient shear loads. (5) If either condition (3) or (4) is not met the interaction between tension and shear forces shall be verified according to Normative Annex C. (6) Fastenings in stand-off installation or with a grout layer as well as fasteners qualified for multiple use only (see clause 7.3) are not covered. (7) Detailed information on the design of fasteners under seismic actions is given in Normative Annex C. 9.2 Requirements (1) Fasteners used to resist seismic actions shall meet all applicable requirements for non-seismic applications. (2) Only fasteners qualified for cracked concrete and seismic applications shall be used (see relevant European Technical Product Specification). (3) In the design of fastenings one of the following options a1), a2) or b) shall be satisfied: a) Design without requirements on the ductility of the fasteners. It shall be assumed that fasteners are non-dissipative elements and they are not able to dissipate energy by means of ductile hysteretic behaviour and that they do not contribute to the overall ductile behaviour of the structure: a1) Capacity design: The fastener or group of fasteners is designed for the maximum tension and/or shear load that can be transmitted to the fastening based on either the development of a ductile yield mechanism in the fixture or the attached element taking into account strain hardening and material over-strength or the capacity of a non-yielding attached element. a2) Elastic design: The fastening is designed for the maximum load obtained from the design load combinations that include seismic actions E E,d corresponding to the ultimate limit state (EN ) assuming elastic behaviour of the fastening and the structure. Furthermore uncertainties in the model to derive seismic actions on the fastening shall be taken into account. b) Design with requirements on the ductility of the fasteners: The fastener or group of fasteners is designed for the design actions including the seismic actions E E,d corresponding to the ultimate limit state (EN ). The tension steel capacity of the fastening shall be smaller than the tension capacity governed by concrete related failure modes. Sufficient 79

80 elongation capacity of the fasteners is required. The fastening shall not be accounted for energy dissipation in the global structural analysis or in the analysis of a non-structural element unless proper justification is provided by a non-linear time history (dynamic) analysis (acc. to EN ) and the hysteretic behaviour of the fastener is provided by a European Technical Product Specification. This approach is applicable only for the tension component of the load acting on the fastener. NOTE Option b) may not be suitable for the fastening of primary seismic members (EN ) due to the possible large non-recoverable displacements of the fastener that may be expected. It is recommended to use option b) for the fastening of secondary seismic members. Furthermore, unless shear loads acting on the fastening are resisted by additional means, additional fasteners should be provided and designed in accordance with option a1) or a2). (4) The concrete in the region of the fastening shall be assumed to be cracked when determining design resistances unless it is demonstrated that the concrete remains uncracked during the seismic event. (5) The provisions in this section do not apply to the design of fastenings in critical regions of concrete elements where concrete spalling or yielding of the reinforcement might occur during seismic events as e.g. in plastic hinge zones. (6) Displacement of the fastening shall be accounted for in the design. This requirement need not to be applied to anchoring of non-structural elements of minor importance. The displacement shall be limited when a rigid connection in the analysis is assumed or when the operability of the attached element during and after an earthquake shall be ensured. NOTE Fastener displacements for seismic applications at both damage limitation state and ultimate limit state are provided in the relevant European Technical Product Specification for fasteners with seismic performance category C2 as defined in Annex C. (7) In general, an annular gap between a fastener and its fixture should be avoided in seismic design situations. With fastenings of non-structural elements in minor non-critical applications an annular gap (d f d f,1 ) is allowed. The effect of the annular gap on the behaviour of fastenings shall be taken into account (see Annex C). (8) Loosening of the nut or screw shall be prevented by appropriate measures. 9.3 Derivation of forces acting on fasteners (1) The design value of the effect of seismic actions E Ed acting on the fixture shall be determined according to EN :24 and its additional parts. Additional provisions are given in Annex C. (2) Distribution of forces to the individual fasteners of a group shall be in accordance with Clause 6 if the base plate remains elastic in the seismic design situation. 9.4 Resistance (1) The seismic characteristic resistance R k,eq of a fastening shall be determined in accordance with Annex C taking into account the seismic reduction factors gap and eq. The basic characteristic seismic resistances for steel, pull-out and combined pull-out and concrete failure under tension load and steel failure under shear load are given in the relevant European Technical Product Specification. For all other failure modes R k,eq shall be determined based on the characteristic resistance obtained for the persistent and transient design situation according to Clause 7 as described in Annex C. (2) The partial factors for resistance M,eq shall be determined according to Verification for impact loading For the verification of impact loading Clause 7 applies. Fasteners used to resist impact loading shall be prequalified by a European Technical Product Specification for this application. 8

81 11 Verification for fire resistance Informative Annex D of this document provides a design method for cast-in-place headed anchors and anchor channels, expansion anchors, undercut anchors and concrete screws exposed to fire. 12 Verification of serviceability limit state (1) For the required verifications see 4.2 and 4.3. (2) The admissible displacement C d should be evaluated by the designer taking into account the type of application in question (e.g. the structural element to be fastened). It may be assumed that the displacements C d are a linear function of the applied load. In the case of combined tension and shear load, the displacements for the shear and tension components of the resultant load should be added vectorially. The characteristic displacement of the fastener under given tension and shear loads shall be taken from the relevant European Technical Product Specification. 81

82 Annex A (normative) Additional rules for verification of concrete elements due to loads applied by fastenings A.1 General Compliance with the design methods given in this document will result in satisfactory transmission of the loads on the fixture to the concrete member. Safe transmission of the fastener loads by the concrete member to its supports shall be demonstrated for the ultimate limit state and the serviceability limit state according to EN taking into account the additional provisions given in A.2 and A.3. Loads may be assumed to be transferred to the whole of composite construction comprising precast elements with added structural topping only if a) adequate shear reinforcement is provided at the interface between the precast element and the in-situ topping, in cases where the fasteners are attached only to the precast element; or b) fasteners are embedded in the topping for a depth of h ef. In other cases only ceilings or similar construction (with unit loading not exceeding 1 kn/m²) may be fastened to the precast elements. A.2 Verification of the shear resistance of the concrete member A.2.1 No special additional verification for local transmission of loads is required, if one of the following conditions is met a) The shear force V Ed at the support caused by the design actions including the fastener loads is V Ed,8 V Rd,c for a member without shear reinforcement (A.1),8 min(v Rd,s, V Rd,max ) for a member with shear reinforcement with V Rd,c, V Rd,s V Rd,max = shear resistance according to EN b) Under the characteristic actions, the resultant tension force N Ek of the tensioned fasteners is N Ek < 3 kn and the spacing a between the outermost fasteners of adjacent groups or between the outer fasteners of a group and individual fasteners satisfies Equation (A.3) (A.2) a > 2 N Ek [mm] (A.3) with N EK [kn] c) The fastener loads are taken up by additional hanger reinforcement, which encloses the tension reinforcement and is anchored at the opposite side of the concrete member. Its distance from an individual fastener or the outermost fasteners of a group shall be smaller than h ef. 82

83 d) The embedment depth of the fastener is h ef,8 h. A.2.2 value If no condition of A.2.1 is fulfilled, the shear forces V Ed,a caused by fastener loads shall not exceed the V Ed,a,4 V Rd,c for a member without shear reinforcement (A.4) =,4 min (V Rd,s, V Rd,max ) for a member with shear reinforcement (A.5) When calculating V Ed,a the fastener loads shall be assumed as point loads with a width of load application t 1 = a h ef and t 2 = a h ef, with a 1 (a 2 ) equal to the spacing between the outer fasteners of a group in direction 1 (2) (see Figure 3.4). The active width over which the shear force is transmitted shall be calculated according to the theory of elasticity. A.2.3 If under the characteristic actions the resultant tension force N Ek of the tensioned fasteners is N Ek > 6 kn, then the conditions in A.2.1c) or A.2.1d) shall be complied with. 83

84 Annex B (informative) Durability B.1 General In the absence of better information in National Regulations or in the relevant European Technical Product Specification the provisions of this Annex may be used. These provisions are based on an assumed intended working life of the fastener of 5 years. Electrolytic corrosion must be prevented between dissimilar metals by suitable separation or by the choice of compatible materials. B.2 Fasteners in dry, internal conditions These conditions are similar to exposure class XC1 according to EN for dry environment. In general, no special corrosion protection is necessary for steel parts as coatings provided for preventing corrosion during storage prior to use, to ensure proper functioning is considered sufficient. Malleable cast iron parts in general do not require any protection. B.3 Fasteners in external atmospheric or in permanently damp internal exposure These conditions are similar to exposure classes XC2, XC3 and XC4 according to EN Normally stainless steel fasteners of appropriate grade should be used. The grade of stainless steel suitable for the various service environments (marine, industrial, etc.) should be in accordance with existing national rules. In general, austenitic steels with at least 17 % to 18 % chromium and 12 % to 13 % nickel and addition of molybdenum e.g. material 1.441, 1.444, , and according to EN 188-2, EN or equivalent may be used. B.4 Fasteners in high corrosion exposure by chloride and sulphur dioxide These conditions are similar to exposure classes XD and XS according to EN Examples for these conditions are permanent, alternating immersion in seawater or the splash zone of seawater, chloride atmosphere of indoor swimming pools or atmosphere with extreme chemical pollution (e.g. in desulphurisation plants or road tunnels, where de-icing materials are used), where special considerations to corrosion resistance shall be given. The metal parts of the fastener (bolt, screw, nut and washer) should be made of a stainless steel suitable for the high corrosion exposure and shall be in accordance with national rules. In general stainless steel with about 2 % chromium, 2 % nickel and 6 % molybdenum e.g. materials , and according to EN 188-2, EN or equivalent should be used under high corrosion exposure. 84

85 Annex C (normative) Design of fastenings under seismic actions C.1 General (1) This Annex provides detailed requirements for fastenings used to transmit seismic actions in addition to Clause 9 and EN (2) The following types of connections are distinguished: Type 'A' Connection between structural elements of primary and/or secondary seismic members. Type 'B' Attachment of non-structural elements. C.2 Performance categories (1) The seismic performance of fasteners subjected to seismic loading is categorized by performance categories C1 and C2. Performance category C1 provides fastener capacities only in terms of resistances at ultimate limit state, while performance category C2 provides fastener capacities in terms of both resistances at ultimate limit state and displacements at damage limitation state and ultimate limit state. The requirements for category C2 are more stringent compared to those for category C1. The performance category of a fastener is given in the corresponding European Technical Product Specification. (2) Table C.1 relates the seismic performance categories C1 and C2 to the seismicity level and building importance class. The level of seismicity is defined as a function of the product a g S, where a g is the design ground acceleration on Type A ground and S the soil factor both in accordance with EN NOTE The recommended seismic performance categories are given in Table C.1. The value of a g or that of the product a g S used in a Country to define threshold values for the seismicity classes may be found in its National Annex. Furthermore the assignment of the seismic performance categories C1 and C2 to the seismicity level and building importance classes in a Country may also be found in its National Annex. Table C.1 Recommended seismic performance categories for fasteners Seismicity level a Importance Class acc. to EN :24, Class a g S c I II III IV 2 Very low b a g S g No additional requirement 3 Low b,5 g < a g S g C1 C1 d or C2 e C2 4 > low a g S >,1 g C1 C2 a The values defining the seismicity levels are subject to a National Annex. The recommended values are given here. b Definition according to EN :24, c a g = design ground acceleration on type A ground (EN :24, 3.2.1), S = soil factor (see e.g. EN :24, 3.2.2). d C1 for fixing non-structural elements to structures e C2 for fixing structural elements to structures 85

86 C.3 Design criteria C.3.1 General (1) For the design of fasteners according to 9.2 (3), option a1), for both Type A and Type B connections, the fastening is designed for the maximum load that can be transmitted to the fastening based either on the development of a ductile yield mechanism in the attached steel component (see Figure C.1a)) or in the steel base plate (see Figure C.1b)) taking into account material overstrength effects, or on the capacity of a nonyielding attached component or structural element (see Figure C.1c)). NOTE The assumption of a plastic hinge in the fixture (Figure C.1b)) requires to take into account specific aspects including e.g. the redistribution of loads to the individual fasteners of a group, the redistribution of the loads in the structure and the low cycle fatigue behaviour of the fixture. Key a) yielding in attached element; b) yielding in baseplate; c) capacity of attached element Figure C.1 Seismic design by protection of the fastening (2) For the design of fasteners according to 9.2 (3), option a2) the action effects for Type 'A' connections shall be derived according to EN with a behaviour factor q = 1,. For Type 'B' connections the action effects shall be derived with q a = 1, for the attached element. If action effects are derived in accordance with the simplified approach given in C.4.4 with q a = 1, they shall be multiplied by a amplification factor equal to 1,5. If the action effects are derived from a more precise model this further amplification may be omitted. (3) For the design of fasteners according to 9.2(3), option b) the following additional conditions shall be observed: a) The fastener shall have a European Technical Product Specification that includes a qualification for Performance Category C2. b) To ensure steel failure of the fastening condition (b1) shall be satisfied for fastenings with one fastener in tension and condition (b2) for groups with two and more tensioned fasteners. In addition for groups with two and more tensioned mechanical fasteners condition (b3) applies. NOTE In case of fastenings with supplementary reinforcement in the verification the resistance for concrete cone failure should be replaced by the resistance of the supplementary reinforcement. b1) Fastenings with one fastener in tension: Rk,conc, eq Rk, s,eq, 7 inst (C.1) with 86

87 Rk,s,eq Rk,conc,eq inst minimum characteristic seismic resistance for steel failure calculated according to Equation (C.8) minimum characteristic seismic resistance for all non-steel failure modes (pull-out, concrete cone, blowout and splitting failure) calculated according to Equation (C.8) partial factor for installation safety according to the relevant European Technical Product Specification b2) For fastener groups with two and more tensioned fasteners Equation (C.2) shall be satisfied for the fasteners loaded in tension: Rk, s, eq h E Rk,conc,eq Rk, conc, eq,7 (C.2) g E inst minimum characteristic seismic resistance for combined concrete and pull-out (only bonded fasteners), concrete cone, blowout and splitting failure calculated according to Equation (C.8) b3) For a group of mechanical fasteners with two and more tensioned fasteners the highest loaded fastener shall be verified for pull-out failure according to Equation (C.1) where Rk,conc, eq is the seismic pull-out resistance of one fastener. c) Fasteners that transmit tensile loads shall be ductile and shall have a stretch length of at least 8d unless otherwise determined by analysis. Illustrations of stretch lengths are shown in Figures C.2a and C.2b. Key a) illustration of stretch length anchor chair; b) illustration of stretch length sleeve or debonded length; c) fastening displacements and rotations 1 stretch length Figure C.2 Seismic design by yielding of a ductile fastener 1) A fastener is considered as ductile if the nominal steel ultimate strength of the load transferring section does not exceed f uk 8 MPa, the ratio of nominal yield strength to nominal ultimate strength does not exceed f yk / f uk,8, and the rupture elongation (measured over a length equal to 5d) is at least 12 percent. 87

88 2) The steel strength N uk of fasteners that incorporate a reduced section (e.g. thread) over a length smaller than 8 d (d = fastener diameter of reduced section) shall be greater than 1,3-times the yield strength N yk of the unreduced section. C.4 Derivation of forces acting on fasteners analysis C.4.1 General (1) The design value of the effect of seismic actions E E,d acting on the fixture shall be determined according to EN and 9.2(3). Provisions in addition to EN including vertical seismic actions acting on nonstructural elements are provided in this Clause. (2) The maximum value of each action effect (tension and shear component of forces for a fastener) shall be considered to act simultaneously if no other more accurate model is used for the estimation of the probable simultaneous value of each action effect. C.4.2 Addition to EN :24, (1) For the design of the fasteners in Type 'A' connections the vertical component of the seismic action shall be taken into account according to EN : (2) to (4) if the vertical design ground acceleration a vg is greater than 2,5 m/s 2. C.4.3 Addition to EN :24, (1) In the design of fastenings for non-structural elements subjected to seismic actions, any beneficial effects of friction due to gravity loads should be ignored. C.4.4 Additions and alterations to EN :24, (1) The horizontal effects of the seismic action of non-structural elements are determined according to Equation (4.24) of EN :24. However, the behaviour factor q a may be taken from Table C.2. NOTE Table C.2 includes information in addition to the values q a given in EN1998-1:24, Table 4.4. (2) Equation (4.25) of EN :24 may be rearranged as: with S a z S 1 Aa,5 S h (C.3) A a 3 T 1 (1 T a 1 ) 2 (C.4) The seismic amplification factor A a may be calculated according to Equation (C.4) or taken from Table C.2 if one of the fundamental vibration periods is not known. NOTE When calculating the forces acting on non-structural elements according to Equation (4.25) of EN , it can often be difficult to establish with confidence the fundamental vibration period T a of the non-structural element. Table C.2 provides a pragmatic approach and may not be conservative in all cases. 88

89 Table C.1 Values of q a and A a for non-structural elements Type of non-structural element q a A a 1 Cantilevering parapets or ornamentations 3, 2 Signs and billboards 3, 3 Chimneys, masts and tanks on legs acting as unbraced cantilevers along more than one half of their total height 4 Hazardous material storage, hazardous fluid piping 3, 1, 3, 5 Exterior and interior walls 1,5 6 Partitions and facades 1,5 7 Chimneys, masts and tanks on legs acting as unbraced cantilevers along less than one half of their total height, or braced or guyed to the structure at or above their centre of mass 8 Elevators 1,5 9 Computer access floors, electrical and communication equipment 3, 2, 1 Conveyors 3, 11 Anchorage elements for permanent cabinets and book stacks supported by the floor 1,5 12 Anchorage elements for false (suspended) ceilings and light fixtures 1,5 13 High pressure piping, fire suppression piping 3, 14 Fluid piping for non-hazardous materials 3, 15 Computer, communication and storage racks 3, (3) The vertical effects of the seismic action should be determined by applying to the non-structural element a vertical force F va acting at the centre of mass of the non-structural element which is defined as follows: with F Va = (S Va W a a )/q a (C.5) 1,5 SVa V Aa (C.6) q a, A a may be assumed to be equal to the values valid for horizontal forces NOTE The vertical effects of the seismic action F Va for non-structural elements may be neglected for the fastener when the ratio of the vertical component of the design ground acceleration a Vg to the acceleration of gravity g is less than,25 and the gravity loads are transferred through direct bearing of the fixture on the structure (see fastening 2 in Figure C.3). 89

90 Key 1 include F Va 2 neglect F Va if a vg /g,25 3 gravity force 4 partion wall 5 floor Figure C.3 Vertical effects of the seismic action C.4.5 Additions and alterations to EN :24, Upper values for the behaviour factor q a for non-structural elements may be selected from Table C.2. C.5 Resistance (1) The seismic design resistance of a fastening is given by: with Rd,eq Rk,eq M,eq (C.7) M,eq in accordance with (2) The characteristic seismic design resistance R k,eq of a fastening shall be determined as follows: R k, eq gap eq R k, eq (C.8) with eq reduction factor to take into account the influence of large cracks and scatter of load displacement curves, see Table C.3 Rk,eq basic characteristic seismic resistance for a given failure mode. 9

91 For steel and pull-out failure under tension load and steel failure under shear load R k,eq N Rk,s,eq, N Rk,p,eq, V Rk,s,eq ) shall be taken from the relevant European Technical Product Specification. For combined pull-out and concrete failure in case of post-installed chemical fasteners R (i.e. N Rk,p ) shall be determined based on the characteristic bond resistance ( Rk,eq ) k,eq given in the relevant European Technical Product Specification. For all other failure modes R shall be determined as for the persistent and transient,eq k design situation according to Clause 7 (i.e. N Rk,c, N Rk,sp, N Rk,cp, N Rk,re, V Rk,c and V Rk,cp ). (i.e. gap reduction factor to take into account inertia effects due to an annular gap between fastener and fixture in case of shear loading, given in the relevant European Product Technical Specification NOTE The forces on the fasteners are amplified in presence an annular gap under shear loading due to a hammer effect on the fastener. For reasons of simplicity this effect is considered only in the resistance of the fastening. In absence of information in the European Technical Product Specification the following values gap may be used. These values are based on a limited number of tests. Shear loading: Loading tension shear gap = 1,, no hole clearance between fastener and fixture (general case, see 9.2 (8)) =,5, connections with hole clearance according to Table 6.1 Table C.2 Reduction factor eq Failure mode Single fastener Fastener group Steel failure 1, 1, Pull-out failure 1,,85 Combined pull-out and concrete failure 1,,85 Concrete cone failure Headed fastener and undercut anchors with k 9 -factor same as headed fastener 1,,85 all other fasteners,85,75 Splitting failure 1,,85 Blow-out failure 1,,85 Steel failure of reinforcement 1, 1, Anchorage failure of reinforcement,85,75 Steel failure 1,,85 Concrete edge failure 1,,85 Concrete pry-out failure Headed fastener and undercut anchors with k 9 -factor same 1,,85 as headed fastener all other fasteners,85,75 Steel failure of reinforcement 1, 1, Anchorage failure of reinforcement,85,75 (3) The interaction between tension and shear forces shall be determined according to Equation (C.9). 91

92 k11 k11 N Ed VEd 1 N Rd, i VRd, i (C.9) with k 11 = 2/3 for fastenings with a supplementary reinforcement to take up tension or shear loads only =1 in all other cases N Ed /N Rd,i V Ed /V Rd,i NOTE More precise values for k 11 may be taken from the relevant European Technical Product Specification. In Equation (C.9) the largest ratios N Ed / N Rd, eq and V Ed /V Rd, eq for the different failure modes shall be inserted, where N Ed and V Ed are the design actions on the fasteners including seismic effects. C.6 Anchor displacements (1) The anchor displacement under tensile and shear load at damage limitation state (DLS) shall be limited to a value N,req(DLS) and V,req(DLS) to meet requirements regarding e.g. functionality and assumed support conditions. These values shall be selected based on the requirements of the specific application. When assuming a rigid support in the analysis the designer shall establish the limiting displacement compatible to the requirement for the structural behaviour. NOTE In a number of cases, the acceptable displacement associated to a rigid support condition is considered to be in the range of 3 mm. (2) If deformations (displacements or rotations) are relevant for the design of the connection (such as, for example, on secondary seismic members or façade elements) it shall be demonstrated that these deformations can be accommodated by the fasteners. The rotation of the connection p (Figure C.2c) is defined by Equation (C.1) with p = N,eq / s max N,eq = displacement of the anchor under seismic loading; s max = distance between the outermost row of anchors and the opposite edge of the baseplate. (C.1) (3) If the fastener displacements N,eq(DLS) under tension loading and/or V,eq(DLS) under shear loading provided in the relevant European Technical Product Specification are higher than the corresponding required values N,req(DLS) and/or V,req(DLS), the design resistance may be reduced according to Equation (C.11). NRd,eq,reduced NRd,eq V Rd,eq,reduced V Rd,eq N,req(DLS) N,eq (DLS) V,req(DLS) V,eq (DLS) (C.11a) (C.11b) (4) If fastenings and attached elements shall be operational after an earthquake the relevant displacements have to be taken into account. 92

93 Annex D (informative) Exposure to fire design method D.1 General (1) The design method is valid for cast-in-place headed anchors, anchor channels and post-installed fasteners. (2) The characteristic resistances under fire exposure should be taken from the relevant European Technical Product Specification. In the absence of such data conservative values are given in D.3. However, for anchor channels only concrete and pull-out failure modes shall be verified with the given approach, while the verification for steel failure shall be based on the values given in the relevant European Technical Product Specification. In case of bonded fasteners under tension the verification for combined bond and concrete failure the value Rk,fi shall be taken from the relevant European Technical Product Specification. (3) The fire resistance is classified according to EN using the Standard ISO time-temperature curve (STC). (4) The design method covers fasteners with a fire exposure from one side only. For fire exposure from more than one side, the design method may be used only, if the edge distance of the fastener is c 3 mm and c 2h ef. (5) In general, the design under fire exposure is carried out according to the normal design method for ambient temperature given in this EN. However, partial factors and characteristic resistances under fire exposure are used instead of the corresponding values under ambient temperature. D.2 Partial factors (1) Partial factors for actions F,fi and for materials M,fi might be defined in a National Annex to this Specification. NOTE Values for F,fi and M,fi may be found in a country's National Annex to this EN. The recommended values are F,fi = 1, and M,fi =1,. D.3 Resistance under fire exposure D.3.1 General (1) If characteristic resistances under fire exposure are not available in a European Technical Product Specification the conservative values given below may be used. D.3.2 Tension load D Steel failure (1) The characteristic tension strength Rk,s,fi of a fastener in the case of steel failure under fire exposure given in the following Tables D.1 and D.2 is also valid for the unprotected steel part of the fastener outside the concrete and may be used in the design. The characteristic resistance N Rk,s,fi is obtained as: 93

94 N Rk,s,fi = Rk,s,fi A s (D.1) Table D.1 Characteristic tension strength of a carbon steel fastener under fire exposure anchor bolt/thread diameter [mm] anchorage depth h ef [mm] characteristic tension strength Rk,s,fi of an unprotected fastener made of carbon steel according to EN 125 in case of fire exposure in the time up to: 3 min (R 15 to R3) 6 min (R45 and R6) Rk,s,fi [N/mm²] 9 min (R9) 12 min ( R12) Ø Ø Ø Ø 12 and greater Table D.2 Characteristic tension strength of a stainless steel fastener under fire exposure anchor bolt/thread diameter [mm] anchorage depth h ef [mm] characteristic tension strength Rk,s,fi of an unprotected fastener made of stainless steel of at least according to ISO 356 in case of fire exposure in the time up to: 3 min (R 15 to R3) 6 min (R45 and R6) Rk,s,fi [N/mm²] 9 min (R9) 12 min ( R12) Ø Ø Ø Ø 12 and greater D Pull-out/pull-through failure (1) The characteristic resistance of fasteners installed in concrete classes C2/25 to C5/6 may be obtained from Equation (D.2) and (D.3). N Rk,p,fi(9) =,25 N Rk,p for fire exposure up to 9 minutes (D.2) N Rk,p,fi(12) =,2 N Rk,p for fire exposure between 9 and 12 minutes (D.3) N Rk,p = characteristic resistance given in the relevant European Technical Product Specification in cracked concrete C2/25 under ambient temperature 94

95 D Concrete cone failure (1) The characteristic resistance of a single fastener N Rk, c, fi not influenced by adjacent fasteners or edges of the concrete member installed in concrete classes C2/25 to C5/6 may be obtained using Equations (D.4) and (D.5). The influence of the different effects of geometry, shell spalling, eccentricity, position and further influencing parameters is taken from the relevant product specific part of this EN. However, the characteristic spacing and edge distance for fasteners under fire exposure near the edge shall be taken as s cr, N, fi 2 ccr, N, fi 4 hef. N = Rk,c,fi( 9 ) hef N Rk,c N Rk,c for fire exposure up to 9 minutes (D.4) 2 N Rk,c,fi( 12 ) =,8 h ef D N Rk,c hef N Rk,c N Rk,c for fire exposure between 9 and 12 minutes (D.5) 2 = effective embedment depth in mm = characteristic resistance of a single fastener in cracked concrete C2/25 under ambient temperature according to Splitting failure (1) The assessment of splitting failure due to loading under fire exposure is not required because the splitting forces are assumed to be taken up by the reinforcement. D.3.3 Shear load D Steel failure (1) For the characteristic shear strength Rk,s,fi of a fastener in the case of shear load without lever arm and steel failure under fire exposure the values given in Tables D.1 and D.2 for the characteristic tension strength may be used ( Rk,s,fi = Rk,s,fi ). These values apply also for the unprotected steel part of the fastener outside the concrete and may be used in the design. The characteristic resistance V Rk,s,fi is obtained as follows: V Rk,s,fi = Rk,s,fi A s = Rk,s,fi A s NOTE Limited numbers of tests have indicated, that the ratio of shear strength to tensile strength increases under fire conditions above that for ambient temperature design. This is a discrepancy to the behaviour in the cold state where the ratio is,6. (2) The characteristic resistance of a fastener in case of shear load with lever arm may be calculated according to However, the characteristic bending resistance of a single fastener under fire exposure is limited to the characteristic tension strength according to D The characteristic bending resistance M Rk, s, fi may be taken from Equation (D.7). (D.6) M Rk, s, fi 1,2 Wel Rk, s, fi (D.7) NOTE D This approach is based on assumptions. Concrete pry-out failure (1) The characteristic resistance in case of fasteners installed in concrete classes C2/25 to C5/6 may be obtained using Equations (D.8) and (D.9). V Rk,cp,fi(9) = k 3 N Rk,c,fi(9) for fire exposure up to 9 min (D.8) 95

96 V Rk,cp,fi(12) = k 3 N Rk,c,fi(12) for fire exposure between 9 min and 12 min (D.9) k 3 = factor to be taken from the relevant European Technical Product Specification (ambient temperature) N Rk,c,fi(9), N Rk,c,fi(12) = calculated according to D D Concrete edge failure (1) The characteristic resistance of a single fastener installed in concrete classes C2/25 to C5/6 may be obtained using Equation (D.1) and (D.11). The influence of the different effects of geometry, thickness, load direction, eccentricity and so on is taken from V Rk,c,fi(9) =,25 V Rk, c for fire exposure up to 9 min (D.1) V Rk,c,fi(12) V Rk, c =,2 VRk,c for fire exposure between 9 min and 12 min (D.11) = initial value of the characteristic resistance of a single fastener in cracked concrete C2/25 under ambient temperature according to D.3.4 Combined tension and shear load (1) The interaction conditions according to for headed and post-installed fasteners and for anchor channels may be taken with the characteristic resistances under fire exposure for the different loading directions for combined tension and shear loads. 96

97 Annex E (normative) Characteristics for the design of fastenings to be supplied by European Technical Products Specification (1) The characteristic values used for the design of fastenings shall be provided in corresponding European Technical Product Specifications. The characteristics of Tables E.1 shall be given for fastenings under static and impact loading. For the design of fastenings under fatigue loading the characteristics of Table E.2 and for fastenings under seismic actions the characteristics of Table E.3 are required in addition. Table E.1 Characteristics used for the design of fastenings under static and impact loading to be taken from a European Technical Product Specification type of fastener characteristic post-installed cast-in mechanical chemical headed fastener anchor channel N Rk,s, V Rk,s x x x x N Rk,s,a, N Rk,s, c, N Rk,s, l, V Rk,s,a, V Rk,s, c, V Rk,s, l, M Rk, s,flex M Rk,s x x x x N Rk,p x x x N Rk,sp x x x Rk,cr, Rk, ucr c cr,n, s cr,n x x x x c cr,sp, s cr,sp x x x x c min, s min, h min x x x x s i x k cr,v, k ucr,v x k cr,n, k ucr,n, k 2, k 3 x x x k 2, k 3, k 7 x x d nom, h ef, l f, A s x x x d h x A h, b ch, d, h ef, h ch, A s, I y, 1 x fastener displacement under given tension and shear loads x x x x limitations on concrete strength classes of base material x x x x M x x x x x x 97

98 Table E.2 Additional characteristics used for the design of fastenings under fatigue loading to be taken from a European Technical Product Specification characteristic type of fastener post-installed cast-in mechanical chemical headed fastener anchor channel F,N, F,V x x x x x x Maximum number of load cycles x x x N Rk,s, N Rk,p, V Rk,s x x x Table E.3 Additional characteristics used for the design of fastenings under seismic loading to be taken from a European Technical Product Specification characteristic type of fastener post-installed cast-in mechanical chemical headed fastener anchor channel gap x x x eq x x x N Rk,s,eq, N Rk,p,eq, V Rk,s,eq x x Performance category x x x Rk, eq, N Rk,s,eq, V Rk,s,eq Rupture elongation x x x N,eq (DLS), V,eq (DLS) x x x x 98