Depending on the application and the anchor type one of the following two concepts can be applied: Partial safety factor concept.

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1 Anchor design Safety concept Depending on the application and the anchor type one of the following two concepts can be applied: For anchors for use in concrete having an European Technical Approval (ETA) the partial safety factor concept according to the European Technical Approval Guidelines ETAG 001 or ETAG 020 shall be applied. It has to be shown, that the value of design actions does not exceed the value of the design : S d R d. For the characteristic given in the respective ETA, reduction factors due to e.g. freeze/thaw, service temperature, durability, creep behaviour and other environmental or application conditions are already considered. In addition to the design, in this manual recommended loads are given, using an overall partial safety factor for action γ = 1,4. Partial safety factor concept design action characteristic value of action partial safety factors for action action S d R d 5% fractile environmental conditions (temperature, durability) partial safety factor for material (anchor, base material) mean ultimate characteristic (ETA) design recommended load Global safety factor concept 5% fractile mean ultimate characteristic (basic value) For the global safety factor concept it has to be shown, that the characteristic value of action does not exceed the recommend load value. The characteristic given in the tables is the 5% fractile value obtained from test results under standard test conditions. With a global safety factor all environmental and application conditions for action and are considered, leading to a recommended load. characteristic value of action action global safety factor recommended load / 2012

2 Design methods Metal anchors for use in concrete according ETAG 001 The design methods for metal anchors for use in concrete are described in detail in Annex C of the European Technical Approval guideline ETAG 001 and for bonded anchors with variable embedment depth in EOTA Technical Report TR 029. Additional design rules for redundant fastenings are given in Part 6 of ETAG 001. The design method given in this Anchor Fastening Technology Manual is based on these guidelines. The calculations according to this manual are simplified and lead to conservative results, i.e. the results are on the save side. Tables with basic load values and influecing factors and the calculation method are given for each anchor in the respective section. Anchors for use in other base materials and for special applications If no special calculation method is given, the basic load values given in this manual are valid, as long as the application conditions (e.g. base material, geometrie, environmental conditions) are observed. Redundant fastenings with plastic anchors Design rules for redundant fastings with plastic anchors for use in concrete and masonry for non-structural applications are given in Annex C of ETAG 020. The additional design rules for redundant fastenings are considered in this manual. Resistance to fire When to fire has to be considered, the load values given in the section to fire should be observed. The values are valid for a single anchor. Hilti design software PROFIS Anchor For a more complex and accurate design according to international and national guidelines and for applications beyond the guidelines, e.g. group of anchors with more than four anchors close to the edge or more than eight anchors far away from the edge, the Hilti design software PROFIS Anchor yields customised fastening solutions. The results can be different from the calculations according to this manual. The following methods can be used for design using PROFIS Anchor: - ETAG - CEN/TS - ACI CSA (Canadian standard) - Solution for Fastening (Hilti internal design method) 09 /

3 Simplified version of the design method A according ETAG 001, Annex C or EOTA Technical Report TR 029. Design according data given in the relevant European Technical Approval (ETA) Influence of concrete strength Influence of edge distance Influence of spacing Valid for a group of two anchors. (The method may also be applied for anchor groups with more than two anchors or more than one edge. The influencing factors must then be considered for each edge distance and spacing. The calculated design loads are then on the save side: They will be lower than the exact values according ETAG 001, Annex C. To avoid this, it is recommended to use the anchor design software PROFIS anchor) The design method is based on the following simplification: No different loads are acting on individual anchors (no eccentricity) The differences to the design method given in the guideline are shown in the following. Annex C of ETAG 001 and EOTA TR 029 compared to simplified design Design tensile The design tensile is the lower value of - Design steel - Design pull-out (Design combined pull-out and concrete cone for bonded anchors) - Design concrete cone - Design splitting N Rd,s N Rd,p N Rd,c N Rd,sp Design steel N Rd,s Annex C of ETAG 001 / EOTA TR 029 N Rd,s = N Rk,s / γ Ms * N Rk,s : characteristic steel * γ Ms : partial safety factor for steel failure ** N Rd,s ** Value given in the respective tables in this manual Design pull-out N Rd,p for anchors designed according Annex C of ETAG 001 Annex C of ETAG 001 N Rd,p = (N Rk,p / γ Mp ) ψ c * N Rk,p : characteristic pull-out * γ Mp : partial safety factor for pull-out failure * ψ c : influence of concrete strength N Rd,p = N 0 Rd,p f B ** N 0 Rd,p: Basic design pull-out ** f B : influence of concrete strength ** Values given in the respective tables in this manual / 2012

4 Design combined pull-out and concrete cone N Rd,p for bonded anchors designed according EOTA TR 029 EOTA TR 029 N Rd,p where 1 1 edge edges group strength = (N 0 Rk,p / γ Mp ) (A p,n / A 0 p,n) ψ s,np ψ g,np ψ ec,np ψ re,np ψ c N 0 Rk,p = π d h ef τ Rk ψ g,np = ψ 0 g,np (s / s cr,np ) 0,5 (ψ 0 g,np 1) ψ 0 g,np = n 0,5 (n 0,5 1) {(d τ Rk )/[k (h ef f ck,cube ) 0,5 ] } 1,5 s cr,np = 20 d (τ Rk,ucr / 7,5) 0,5 3 h ef * γ Mp : partial safety factor for combined pull-out and concrete cone failure + A 0 p,n: influence area of an individual anchor with large spacing and distance at the concrete surface (idealised) + A p,n : actual influence area of the anchorage at the concrete surface, limited by overlapping areas of adjoining anchors and by edges of the concrete member + ψ s,np : influence of the disturbance of the distribution of stresses due to + ψ ec,np : influence of excentricity + ψ re,np : influence of dense reinforcement * ψ c : influence of concrete strength * d: anchor diameter * h ef : (variable) embedment depth * τ Rk : characteristic bond s: anchor spacing s cr,np : critical anchor spacing n: number of anchors in a anchor k: = 2,3 in cracked cocrete = 3,2 in non-cracked cocrete f ck,cube : concrete compressive * τ Rk,ucr : characteristic bond for non-cracked concrete + Values have to be calculated according data given in the relavant ETA (details of calculation see TR 029. The basis of the calculations may depend on the critical anchor spacing). N Rd,p = N 0 Rd,p f B,p f 1,N f 2,N f 3,N f h,p f re,n ** N 0 Rd,p: Basic design combined pull-out and concrete cone ** f B,p : influence of concrete strength ** f 1,N, f 2,N : influence of edge distance ** f 3,N : influence of anchor spacing ** f h,p : influence of (variable) embedment depth ** f re,n : influence of dense reinforcement ** Values given in the respective tables in this manual For the simplified design method the factor ψ g,np (see TR 029) is assumed to be 1 and the critical anchor spacing is assumed to be s cr,np = 3 h ef, both leading to conservative results = beeing on the save side. 09 /

5 Design concrete cone N Rd,c Annex C of ETAG 001 / EOTA TR 029 N Rd,c = (N 0 Rk,c / γ Mc ) (A c,n / A 0 c,n) ψ s,n ψ re,n ψ ec,n where N 0 Rk,c = k 1 f 0,5 1,5 ck,cube h ef * γ Mc : partial safety factor for concrete cone failure + A 0 c,n: area of concrete cone of an individual anchor with large spacing and edge distance at the concrete surface (idealised) + A c,n : actual area of concrete cone of the anchorage at the concrete surface, limited by overlapping concrete cones of adjoining anchors and by edges of the concrete member edges + ψ s,n : influence of the disturbance of the distribution of stresses due to + ψ re,n : influence of dense reinforcement + ψ ec,n : influence of excentricity k 1 : = 7,2 for anchorages in cracked concrete = 10,1 for anchorages in non-cracked concrete f ck,cube : concrete compressive strength * h ef : effective anchorage depth + Values have to be calculated according data given in the relavant ETA (details of calculation see Annex C of ETAG 001 or EOTA TR 029) N Rd,c = N 0 Rd,c f B f 1,N f 2,N f 3,N f h,n f re,n ** N 0 Rd,c: Basic design concrete cone ** f B : influence of concrete strength ** f 1,N, f 2,N : influence of edge distance ** f 3,N : influence of anchor spacing ** f h,n : influence of embedment depth ** f re,n : influence of dense reinforcement ** Values given in the respective tables in this manual / 2012

6 Design concrete splitting N Rd,sp Annex C of ETAG 001 / EOTA TR 029 N Rd,sp = (N 0 Rk,c / γ Mc ) (A c,n / A 0 c,n) ψ s,n ψ re,n ψ ec,n ψ h,sp where N 0 Rk,c = k 1 f ck,cube 0,5 h ef 1,5 * γ Mc : partial safety factor for concrete cone failure ++ A 0 c,n: area of concrete cone of an individual anchor with large spacing and edge distance at the concrete surface (idealised) ++ A c,n : actual area of concrete cone of the anchorage at the concrete surface, limited by overlapping concrete cones of adjoining anchors and by edges of the concrete member edges depth + ψ s,n : influence of the disturbance of the distribution of stresses due to + ψ re,n : influence of dense reinforcement + ψ ec,n : influence of excentricity k 1 : = 7,2 for anchorages in cracked concrete = 10,1 for anchorages in non-cracked concrete + ψ h,sp : influence of the actual member f ck,cube : concrete compressive strength * h ef : embedment depth + Values have to be calculated according data given in the relavant ETA (details of calculation see Annex C of ETAG 001 or EOTA TR 029) ++ Values of A 0 c,n and A c,n for splitting failure may be different from those for concrete cone failure, due to different values for the critical edge distance and critical anchor spacing N Rd,sp = N 0 Rd,c f B f 1,sp f 2,sp f 3,sp f h,n f re,n ** N 0 Rd,c: Basic design concrete cone ** f B : influence of concrete strength ** f 1,sp, f 2,sp : influence of edge distance ** f 3,sp : influence of anchor spacing ** f h,n: influence of base material thickness (concrete member depth) ** f re,n : influence of dense reinforcement ** Values given in the respective tables in this manual 09 /

7 Design shear The design shear is the lower value of - Design steel - Design concrete pryout - Design concrete edge V Rd,s V Rd,cp V Rd,c Design steel V Rd,s (without lever arm) Annex C of ETAG 001 / EOTA TR 029 V Rd,s = V Rk,s / γ Ms * V Rk,s : characteristic steel * γ Ms : partial safety factor for steel failure For steel failure with lever arm see Annex C of ETAG 001 or EOTA TR 029 ** V Rd,s ** Value given in the respective tables in this manual Steel failure with lever arm is not considered for the simplified design method Design concrete pryout V Rd,cp for anchors designed according Annex C of ETAG 001 Annex C of ETAG 001 V Rd,cp for = (V Rk,cp / γ Mp/Mc ) = k N Rd,c N Rd,c = N Rk,c / γ Mc N Rk,c : characteristic tension concrete cone failure (see design concrete cone failure) * γ Mc : partial safety factor for concrete cone failure (see design concrete cone failure) * k: influence of embedment depth V Rd,cp = k N Rd,c *** N Rd,c : characteristic tension for concrete cone failure (see design concrete cone failure) ** k: influence of embedment depth ** Value given in the respective tables in this manual / 2012

8 Design concrete pryout V Rd,cp for bonded anchors designed according EOTA TR 029 EOTA TR 029 V Rd,cp for cone failure (see design combined pullout for and = (V Rk,cp / γ Mp/Mc ) = k lower value of N Rd,p and N Rd,c N Rd,p = N Rk,p / γ Mp N Rd,c = N Rk,c / γ Mc N Rd,p : characteristic tension N Rk,c : combined pull-out and concrete and concrete cone failure) characteristic tension concrete cone failure (see design concrete cone failure) * γ Mp : partial safety factor for combined pull-out and concrete cone failure (see design combined pull-out concrete cone failure) * γ Mc : partial safety factor for concrete cone failure (see design concrete cone failure) * k: influence of embedment depth V Rd,cp = k lower value of N Rd,p and N Rd,c N Rd,p : characteristic tension for combined pull-out and concrete cone failure (see design combined pull-out and concrete cone failure) N Rk,c : characteristic tension for concrete cone failure (see design concrete cone failure) ** k: influence of embedment depth ** Values given in the respective tables in this manual 09 /

9 Design concrete edge V Rd,c Annex C of ETAG 001 / EOTA TR 029 V Rd,c = (V 0 Rk,c / γ Mc ) (A c,v / A 0 c,v) ψ s,v ψ h,v ψ α,v ψ ec,v ψ re,v where V 0 Rk,c = k 1 d α h β ef f 0,5 1,5 ck,cube c 1 α = 0,1 (h ef / c 1 ) 0,5 β = 0,1 (d / c 1 ) 0,2 * γ Mc : partial safety factor for concrete edge failure + A 0 c,v: area of concrete cone of an individual anchor at the lateral concrete surface not affected by edges (idealised) + A c,v : actual area of concrete cone of anchorage at the lateral concrete surface, limited by overlapping concrete cones of adjoining anchors, by edges of the concrete member and by member thickness further + ψ s,v : influence of the disturbance of the distribution of stresses due to edges + ψ h,v : takes account of the fact that the shear does not decrease proportially to the memebr thickness as assumed by the idealised ratio A c,v / A 0 c,v ++ ψ α,v : Influence of angle between load applied and the direction perpendicular to the free edge ++ ψ ec,v : influence of excentricity ++ ψ re,v : influence of reinforcement k 1 : = 1,7 for anchorages in cracked concrete = 2,4 for anchorages in non-cracked concrete * d: anchor diameter f ck,cube : concrete compressive strength c 1 : edge distance + Values have to be calculated according data given in the relavant ETA (details of calculation see Annex C of ETAG 001 or EOTA TR 029) ++ Details see Annex C of ETAG 001 or EOTA TR 029 V Rd,c = V 0 Rd,c f B f ß f h f 4 f hef f c ** V 0 Rd,c: Basic design concrete edge ** f B : influence of concrete strength ** f ß : Influence of angle between load applied and the direction perpendicular to the free edge ** f h: Influence of base material thickness ** f 4 : Influence of anchor spacing and edge distance ** f hef: influence of embedment depth ** f c : influence of edge distance ** Values given in the respective tables in this manual The factors f hef and f c replace the function d α h ef β, leading to conservative results = beeing on the save side. Special case: more than 2 anchors close to an edge For a group of anchors f 4 can be calculated according to the following equation, if all anchors are equally loaded. This can be achieved by filling the annular gaps with a high performance injection mortar (e.g. Hilti HIT-RE 500- SD or Hilti HIT-HY 150 MAX. Where s 1, s 2, s n-1 3 c And c 2,1, c 2,2 1,5 c / 2012

10 Combined tension and shear loading The following equations must be satisfied ß N 1 ß V 1 ß N + ß V 1,2 or ß N α + ß V α 1 With ß N = N Sd / N Rd and ß V = V Sd / V Rd N Sd (V Sd ) = tension (shear) design action N Rd (V Rd ) = tension (shear) design Annex C of ETAG 001 α = 2,0 if N Rd and V Rd are governed by steel failure α = 1,5 for all other failure modes Failure mode is not considered for the simplified method α = 1,5 for all failure modes (leading to conservative results = beeing on the save side) 09 /

11 Design example Design example Adhesive anchoring system with variable embedment depth in non-cracked concrete Anchoring conditions concrete Non-cracked concrete C50/60 service temperature range of base material temperature range II number of anchors Group of two anchors close to the edge base material thickness h 100 mm anchor spacing s 150 mm edge distance c 100 mm shear load direction perpendicular to free edge β 0 TENSION design action (fixing point) N Sd 15,0 kn SHEAR design action (fixing point) 15,0 kn TENSION design action per anchor SHEAR design action per anchor effective anchorage depth V Sd N Sd (1) (1) V Sd h ef 7,5 kn 7,5 kn 70 mm anchor external diameter typical anchorage depth minimum edge distance minimum spacing Hilti HIT-RE 500-SD with HIT-V 5.8, size M12 d 12 mm h ef,typ s min c min 110 mm 60 mm 60 mm The parameters are given in the anchor-section in the tables setting details and setting parameters 5.8, size M12) Critical spacings and edge distances critical spacing for concrete cone failure s cr,n and critical spacing for combined pull-out and concrete cone failure s cr,np h ef = 70 mm s cr,n = s cr,np = 3 h ef = 210 mm critical edge distance for concrete cone failure c cr,n and critical edge distance for combined pull-out and concrete cone failure c cr,np h ef = 70 mm c cr,n = c cr,np = 1,5 h ef = 105 mm critical edge distance for splitting failure for h 1,3 h ef for 1,3 h ef < h < 2 h ef for h 2 h ef c cr,sp = c cr,sp = 2,26 h ef 4,6 h ef - 1,8 h c cr,sp = 1,0 h ef h = 100 mm h ef = 70 mm h/h ef = 1,43 c cr,sp = 142 mm critical spacing for splitting failure c cr,sp = 142 mm General remarks s cr,sp = 2 c cr,sp = 284 mm According EOTA Technical Report TR 029, concrete cone, combined concrete cone and pull-out, splitting, pryout and concrete edge design must be verified for the anchor group. Steel design must be verified for the most unfavourable anchor of the anchor group. According to the simplified design method given in this Fastening Technology Manual all anchors of a group are loaded equally, the design values given in the tables are valid for one anchor / 2012

12 Design example Tension loading Design steel N Rd,s = 28,0 kn See basic design tensile Design combined pull-out and concrete cone basic N 0 Rd,p 29,9 kn concrete Non-cracked concrete C50/60 f B,p 1,09 h ef = 70 mm h ef,typ = 110 mm f h,p = h ef /h ef,typ = 0,64 c = 100 mm c cr,n = 105 mm c/c cr,n = 0,95 f 1,N 0,99 f 2,N 0,97 s = 150 mm s cr,n = 210 mm s/s cr,n = 0,71 f 3,N 0,86 h ef = 70 mm f re,n 1,00 N Rd,p = N 0 Rd,p f B,p f 1,N f 2,N f 3,N f h,p f re,n = 17,1 kn Design concrete cone basic N 0 Rd,c 32,4 kn concrete Non-cracked concrete C50/60 f B 1,55 h ef = 70 mm h ef,typ = 110 mm f h,n = (h ef /h ef,typ ) 1,5 = 0,51 c = 100 mm c cr,n = 105 mm c/c cr,n = 0,95 f 1,N 0,99 f 2,N 0,97 s = 150 mm s cr,n = 210 mm s/s cr,n = 0,71 f 3,N 0,86 h ef = 70 mm f re,n N Rd,c = N 0 Rd,c f B f h,n f 1,N f 2,N f 3,N f re,n = 1,00 21,1 kn Design splitting basic N 0 Rd,c 32,4 kn concrete Non-cracked concrete C50/60 f B 1,55 h ef = 70 mm h ef,typ = 110 mm f h,n = (h ef /h ef,typ ) 1,5 = 0,51 c = 100 mm c cr,sp = 142 mm c/c cr,sp = 0,70 f 1,sp 0,91 f 2,sp 0,85 s = 150 mm s cr,sp = 284 mm s/s cr,sp = 0,53 f 3,sp 0,76 h ef = 70 mm f re,n 1,00 N Rd,sp = N 0 Rd,c f B f h,n f 1,sp f 2,sp f 3,sp f re,n = 15,0 kn See basic design tensile See basic design tensile and influencing factors Influencing factors may be interpolated. See basic design tensile and influencing factors Influencing factors may be interpolated. Tension design : lowest value N Rd = 15,0 kn 09 /

13 Design example Shear loading Design steel V Rd,s = 16,8 kn See basic design shear Concrete pryout design lower value of N Rd,p and N Rd,c V 0 = 17,1 kn h ef = 70 mm k 2 V Rd,cp = k V 0 = 34,3 kn Concrete edge design basic V 0 Rd,c 11,6 kn concrete Non-cracked concrete C50/60 f B 1,55 shear load direction perpendicular to free edge 0 f β 1,00 h = 100 mm c = 100 mm h/c = 1,00 f h 0,82 c = 100 mm h ef = 70 mm c/h ef = 1,43 f 4 s = 150 mm h ef = 70 mm s/h ef = 2,14 1,28 h ef = 70 mm d = 12 mm h ef /d = 5,83 f hef 0,97 c = 100 mm d = 12 mm c/d = 8,33 f c 0,67 V Rd,c = V 0 Rd,c f B f ß f h f 4 f hef f c = 12,3 kn See basic design shear and influencing factors See basic design shear and influencing factors Influencing factors may be interpolated. Shear design : lowest value V Rd = 12,3 kn Combined tension and shear loading The following equation must be satisfied for combined tension and shear loads: (Eq. 1) (β N ) 1,5 + (β V ) 1,5 1 β N (β V ) ratio between design action and design for tension (shear) loading According to ETAG 001, Annex C, the following simplified equation may be applied: (Eq. 2) β N + β V 1,2 and β N 1, β V 1 Example (load values are valid for one anchor) N Sd (1) = V Sd (1) = N Rd = V Rd = 7,5 kn 7,5 kn 15,0 kn 12,3 kn β N = N (1) Sd /N Rd = 0,500 1 β V = V (1) Sd /V Rd = 0,612 1 β N + β V = 1,112 1,2 (β N ) 1,5 + (β V ) 1,5 = 0, ,2 1 0,8 0,6 0,4 0,2 0 βn (Eq. 1) (Eq. 2) 0 0,2 0,4 0,6 0,8 1 1,2 β V / 2012

14 Design example 09 /

1 Input data. Profis Anchor Company: Specifier: Address: Phone I Fax: Page: Project: Sub-Project I Pos. No.

1 Input data. Profis Anchor Company: Specifier: Address: Phone I Fax: Page: Project: Sub-Project I Pos. No. 1 Specifier's comments: Check of Existing Base plate (B6)- According to max. forces on Node No. 11979, LC 1.4(D.L.+WX) 1 Input data Anchor type and diameter: HIT-HY 200 + HIT-V-F (8.8) M27 Seismic/Filling