PI Fatigue HDA

Detailed design method - Hilti CC

Nrec,p/c/s
(The Hilti CC-Method is a simplified Version of ETAG Annex C)
s
TENSION c

h
The tensile design resistance of a single
anchor is the minimum of:
∆NRd,p : concrete pull out resistance
(only in cracked concrete)
∆NRd,c : concrete cone resistance
∆NRd,s : steel resistance

NRd,p : Concrete pull-out resistance (only in cracked concrete)

∆NRd, p = ∆NRd
o
, p ⋅ fB

∆ N0Rd,p1) : Concrete pull-out design resistance

• concrete compressive strength f ck,cube(150) = 25 N/mm2
Anchor size HDA-T/HDA-P M10 M12 M16

∆N0Rd,p [kN] in cracked concrete 9.9 13.8 29.6

The initial value of the tensile design load against pull out is calculated from ∆N°Rd,p=∆N°Rk,p/γMc, where the partial safety factor
1)

for concrete is γMc=1.62, with ∆N°Rk,p =64%NRk,p. The load values are corresponding to a constant load. The displacement is
smaller than d95% ≤ 3 mm after 1000 crack cycles (w = 0.3 mm).

∆ NRd,c : Concrete cone resistance

∆NRd ,c = ∆NRd
o
,c ⋅ fB ⋅ f A,N ⋅ fR ,N

∆ N0Rd,c: Concrete cone design resistance

•
2
concrete compressive strength f ck,cube(150) = 25 N/mm

Anchor size HDA-T/HDA-P M10 M12 M16

∆ N Rd,c
0 1)
[kN] in cracked concrete w = 0.3mm 16.4 22.9 42.9
The value of the tensile design load against concrete coin failure is calculated from ∆N°Rd,c=∆N°Rk,c/γMp, where the partial safety
1)

factor for concrete is γMc=1.62, with ∆N°Rk,c=64%N°Rd,c

fB : Influence of concrete strength

Concrete strength Cylinder compressive Cube compressive
designation strength strength
(ENV 206) fck,cyl [N/mm²] fck,cube [N/mm²]
fB fck,cube
C20/25 20 25 1 fB =
C25/30 25 30 1.1 25
C30/37 30 37 1.22
C35/45 35 45 1.34 Limits:
C40/50 40 50 1.41
25 N/mm2 ≤ f ck,cube ≤ 60 N/mm2
C45/55 45 55 1.48
C50/60 50 60 1.55
Concrete cylinder: Concrete cube:
height 30cm, 15cm side length 15cm
diameter
Concrete test specimen geometry

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 PI Fatigue HDA
f A,N : Influence of anchor spacing, fR ,N : Influence of edge distance,
Anchor spacing HDA-T/HDA-P anchor size Edge distance HDA-T/HDA-P anchor size
s [mm] M10 M12 M16 c [mm] M10 M12 M16
100 0.67 80 0.66
125 0.71 0.67 100 0.76 0.66
150 0.75 0.70 120 0.86 0.74
190 0.82 0.75 0.67 140 0.96 0.82
200 0.83 0.77 0.68 150 1.00 0.87 0.66
250 0.92 0.83 0.72 160 0.90 0.68
300 1.00 0.90 0.76 180 0.98 0.73
350 0.97 0.81 187 1.00 0.75
375 1.00 0.83 200 0.79
400 0.85 220 0.84
450 0.89 240 0.89
500 0.94 260 0.94
550 0.98 280 0.99
570 1.00 285 1.00

s c
f A,N = 0.5 + fR,N = 0.27 + 0.49 ⋅
6 ⋅ h ef h ef

Limits: smin ≤ s ≤ s cr,N Limits: c min ≤ c ≤ c cr,N Note: If more than 3 edges are
smaller than ccr,N consult
smin = h ef c min = 0.8 ⋅ h ef your Hilti Technical
s cr,N = 3 ⋅ h ef c cr,N = 1.5 ⋅ h ef Advisory Service

∆ NRd,s : Steel tensile design resistance

Anchor size HDA-T/HDA-P M10 M12 M16

∆ NRd,s
1)
[kN] 6.7 11.8 22.9

∆ NRd : System tensile design resistance

∆ NRd = minimum of ∆ NRd,p , ∆ NRd,c and ∆ NRd,s

Combined load: see page 24

21
PI Fatigue HDA
Detailed design method – Hilti CC
(The Hilti CC-Method is a simplified Version of ETAG Annex C)

c2 > V rec,c/s
1.5
c
s
c c2 >
SHEAR 1 .5
c
h>1
.5 c
The design shear resistance of a single
anchor is the minimum of:
∆VRd,c : concrete edge resistance
∆VRd,s : steel resistance Note: If the conditions regarding h and c2 are not met,
consult your Hilti technical advisory service.

∆ VRd,c : Concrete edge design resistance

The weakest concrete edge resistance must be calculated. All nearby edges must be checked, (not only the
edge in the direction of shear). Shear direction is accounted for by the factor fβ,V.

∆VRd ,c = ∆VRd
o
,c ⋅ fB ⋅ f β ,V ⋅ f AR ,V

∆ V0Rd,c : Concrete edge design resistance

• concrete compressive strength f ck,cube(150) = 25 N/mm2

• at minimum edge distance c min
Anchor size HDA-T/HDA-P M10 M12 M16
∆ V Rd,c
0 1)
[kN] in cracked concrete w = 0.3 mm 3.1 4.6 9.5
∆ V Rd,c1)
0
[kN] in uncracked concrete 4.3 6.5 13.3
cmin [mm] cracked and non-cracked concrete 80 100 150
The design value of the ultimate state in shear is calculated from the characteristic anchor shear resistance, ∆V°Rk,c, divided by
1)

∆V°Rd,c= ∆V°Rk,c/γMc,V, where the partial safety factor, γMc,V, is 1.62 and ∆VRk,c=55%VRk,c

fB : Influence of concrete strength

Concrete strength Cylinder compressive Cube compressive
designation strength strength
(ENV 206) fck,cyl [N/mm²] fck,cube [N/mm²]
fB
C20/25 20 25 1
C25/30 25 30 1.1
C30/37 30 37 1.22
C35/45 35 45 1.34
C40/50 40 50 1.41
C45/55 45 55 1.48
C50/60 50 60 1.55
Concrete cylinder: Concrete cube:
height 30cm, 15cm side length 15cm
diameter
Concrete test specimen geometry

f ck,cube
Limits: 25 N/mm2 ≤ f ck,cube ≤ 60 N/mm2 fB =
25

22
 PI Fatigue HDA
fβ ,V : Influence of shear load direction

Formulae: V ... applied shear force

Angle β [°] fβ ,V
0 to 55 1 fβ,V = 1 for 0° ≤ β ≤ 55° β
60 1.1
1
70 1.2 fβ,V = for 55° < β ≤ 90°
cos β + 0.5 sin β
80 1.5
f β,V = 2 for 90° < β ≤ 180°
90 to 180 2

fAR,V : Influence of spacing and edge

Formula for single anchor influenced
only by edge
c 2,1
c c
f AR,V = s n-1
c min c min
results s3
tabulated s2
Formula for anchor pair valid for s < 3c s1
below
c 2 ,2
3c + s c c
f AR,V =
6c min c min
h >1,5 c
General formula for n anchors (edge plus n-1 spacing)
only valid where s1 to sn-1 are all < 3c It is important that the base plate is designed and installed such
that the applied shear is distributed onto all anchors, as assumed in
3c + s 1 + s 2 + ... + s n−1 c these calculations
f AR,V = ⋅
3nc min c min
If c2,1 or c2,2 or h are less than 1.5c reductions apply, please contact
the Hilti Technical Advisory Service

fAR,V c/cmin
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
Single anchor with
edge influence 1.00 1.31 1.66 2.02 2.41 2.83 3.26 3.72 4.19 4.69 5.20 5.72 6.27 6.83 7.41 8.00
s/cmin 1.0 0.67 0.84 1.03 1.22 1.43 1.65 1.88 2.12 2.36 2.62 2.89 3.16 3.44 3.73 4.03 4.33
1.5 0.75 0.93 1.12 1.33 1.54 1.77 2.00 2.25 2.50 2.76 3.03 3.31 3.60 3.89 4.19 4.50
2.0 0.83 1.02 1.22 1.43 1.65 1.89 2.13 2.38 2.63 2.90 3.18 3.46 3.75 4.05 4.35 4.67
2.5 0.92 1.11 1.32 1.54 1.77 2.00 2.25 2.50 2.77 3.04 3.32 3.61 3.90 4.21 4.52 4.83
3.0 1.00 1.20 1.42 1.64 1.88 2.12 2.37 2.63 2.90 3.18 3.46 3.76 4.06 4.36 4.68 5.00
3.5 1.30 1.52 1.75 1.99 2.24 2.50 2.76 3.04 3.32 3.61 3.91 4.21 4.52 4.84 5.17
4.0 1.62 1.86 2.10 2.36 2.62 2.89 3.17 3.46 3.75 4.05 4.36 4.68 5.00 5.33
4.5 1.96 2.21 2.47 2.74 3.02 3.31 3.60 3.90 4.20 4.52 4.84 5.17 5.50
5.0 2.33 2.59 2.87 3.15 3.44 3.74 4.04 4.35 4.67 5.00 5.33 5.67
5.5 2.71 2.99 3.28 3.57 3.88 4.19 4.50 4.82 5.15 5.49 5.83
6.0 2.83 3.11 3.41 3.71 4.02 4.33 4.65 4.98 5.31 5.65 6.00
6.5 3.24 3.54 3.84 4.16 4.47 4.80 5.13 5.47 5.82 6.17
7.0 3.67 3.98 4.29 4.62 4.95 5.29 5.63 5.98 6.33
7.5 4.11 4.43 4.76 5.10 5.44 5.79 6.14 6.50
8.0 These results are for a pair of 4.57 4.91 5.25 5.59 5.95 6.30 6.67
8.5 anchors. 5.05 5.40 5.75 6.10 6.47 6.83
9.0 5.20 5.55 5.90 6.26 6.63 7.00
9.5 For more than 2 anchors, use 5.69 6.05 6.42 6.79 7.17
10.0 the general formulae for n 6.21 6.58 6.95 7.33
10.5 anchors at the top of the page. 6.74 7.12 7.50
11.0 7.28 7.67
11.5 7.83
12.0 8.00

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PI Fatigue HDA

∆ VRd,s : Steel design shear resistance

Anchor size M10 M12 M16

HDA-T 6.3 11.3 17.3

∆ VRd,s [kN]
HDA-P 2.0 4.4 6.1

The shear design resistance is calculated from ∆VRd,s= ∆VRk,s/γMs,V. The partial safety factor γMs,V for HDA-T is equal to 1.5 and 1.25 for HDA-
1)

P.

∆ VRd : System design shear resistance

VRd : System design shear resistance
∆ VRd = minimum of VRd,c and VRd,s

COMBINED LOADS
γ ⋅ ∆N γ ⋅ ∆V h h

steel: F ,N
+ ≤ 1.0Sd F ,V Sd
highest loaded single anchor
∆N ∆V
Rk , s Rk , s

γ MsN
γ MsV

∆N g
∆V g

concrete: Sd
+ Sd
≤ 1.0 anchor group
 ∆N g
  ∆V g

 Rk ,c
  Rk ,c

 γ Mc   γ Mc 

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 PI Fatigue HVZ
4.2 Productinformation HVZ

Basic load data (for a single anchor): HAS-TZ

steel failure in cracked and uncracked concrete
Characteristic resistance Rk [kN]: concrete C20/25 (according DIBt)
Anchor size M10x75 M12x95 M16x105 M16x125 M20x170
Tensile ∆NRk,s 10.5 19.8 21.1 27.6 27.6
Shear ∆VRk,s 3.9 6.9 12.4 12.4 12.4
Design resistance Rd [kN]: concrete f ck,cube =25 N/mm2
Anchor size M10x75 M12x95 M16x105 M16x125 M20x170
Tensile ∆NRd,s 8.1 14.7 15.6 15.6 15.6
Shear ∆VRd,s 3.6 6.3 11.3 11.3 11.3
Group factors: Tension: γ F,N / Shear: γ F,V γ F,N=γγF.V=1.0 for single anchor
γ F,N= 1.45 γ F.V=1.3 for more than one anchor
TENSION
The tensile design resistance of a single anchor N rec,c/s
is the minimum of,
∆NRd,p: concrete pull-out resistance c
s

∆NRd,c : concrete cone resistance

h

∆NRd,s : steel resistance

∆ NRd,p: Concrete pull-out resistance

∆NRd, p = ∆NRd
o
, p ⋅ fB

∆ N0Rd,p1) : Concrete pull-out design resistance

2
concrete compressive strength f ck,cube(150) = 25 N/mm

Anchor size HVZ M10x75 M12x95 M16x105 M16x125 M20x170

∆N0Rd,p [kN] in cracked concrete 5.3 10.8 12.5 15.5 29.4

∆N0Rd,p [kN] in uncracked concrete 6.6 12.5 15.5 18.6 35.6

The initial value of the tensile design load against pull out is calculated from ∆N°Rd,p=∆N°Rk,p/γMp, where the partial safety factor
1)

for concrete is γMp=2.27 (M10) resp. 1.94 (M12, M16, M20), with ∆N°Rk,p =60%NRk,p. The load values are corresponding to a constant
load. The displacement is smaller than d95% ≤ 3 mm after 1000 crack cycles (w = 0.3 mm).

∆ NRd,c: Concrete cone resistance

∆N Rd , c
= ∆N 0
Rd ,c
⋅f B.N
⋅f A, N
⋅f R ,N

∆ N Rd,c :Concrete cone/pull-out design resistance

0

concrete compressive resistance: fck,cube(150)=25N/mm2

Anchor Size M10x75 M12x95 M16x105 M16x125 M20x170
∆ N0Rd,c1) [kN] in non-cracked concrete 12.1 17.3 20.1 26.1 41.4
∆ N Rd,c [kN]
0 1)
in cracked concrete 8.7 12.3 14.3 18.6 29.6
hef [mm] Actual anchorage depth 75 95 105 125 170

25
 PI Fatigue HVZ
The tensile design resistance is calculated from the tensile characteristic resistance ∆N by ∆N ∆N
1) o o o
Rk,c=60%NRk,c Rd,c= Rk,c/γMc,N, where the
partial safety factor γMc,N is equal to 1.62.

25
PI Fatigue HVZ

fB,N :Influence of concrete strength

Designation of
Cylinder Cube compressive
grade of concrete
compressive strength, fck,cube
(ENV 206) fB,N
strength, [N/mm²]
fck,cyl [N/mm²]
M10 M12 M16 M20
C20/25 20 25 1 1
C25/30 25 30 1.03 1.07
C30/37 30 37 1.06 1.17
C35/45 35 45 1.10 1.29
C40/50 40 50 1.13 1.36
C45/55 45 55 1.15 1.43
C50/60 50 60 1.18 1.51
Concrete cylinder: Concrete cube:
height 30cm, 15cm side length 15cm
diameter
Concrete test specimen geometry

K = 197.5 for M10 and M12

K = 68.75 for M16 and M20

f − 25 
fB,N = 1 +  ck,cube  Limits: 25 N/mm² ≤ f ck,cube ≤ 60 N/mm²
 K 

fA,N: Influence of spacing

Spacing, Anchor size
s [mm] M10 M12 M16 M16L M20
60 0.63
65 0.64
70 0.66
75 0.67 0.63
80 0.68 0.64
85 0.69 0.65 0.63 0.61
90 0.70 0.66 0.64 0.62
100 0.72 0.68 0.66 0.63
120 0.77 0.71 0.69 0.66
135 0.80 0.74 0.71 0.68 0.63
140 0.81 0.75 0.72 0.69 0.64
160 0.86 0.78 0.75 0.71 0.66
180 0.90 0.82 0.79 0.74 0.68
200 0.94 0.85 0.82 0.77 0.70
220 1.00 0.89 0.85 0.79 0.72
240 0.92 0.88 0.82 0.74
270 0.97 0.93 0.86 0.76
300 1.00 0.98 0.90 0.79
330 1.00 0.94 0.82
360 0.98 0.85
390 1.00 0.88
420 0.91
450 0.94
480 0.97
510 1.00

s
f A,N = 0.5 + Limits: smin ≤ s ≤ scr,N
6h ef

Anchor size M10 M12 M16 M16L M20

smin [mm] 60 75 85 135
scr,N [mm] 225 285 315 375 510

26
 PI Fatigue HVZ
fR,N: Influence of edge distance
Edge Anchor size
distance,
M10 M12 M16 M16L M20
c [mm]
60 0.65
65 0.68
70 0.72
75 0.75 0.64
80 0.78 0.67
85 0.82 0.70 0.65 0.59
90 0.85 0.72 0.68 0.61
95 0.88 0.75 0.70 0.63
100 0.92 0.78 0.73 0.65
105 0.95 0.80 0.75 0.67
110 0.98 0.83 0.77 0.69
115 1.00 0.86 0.80 0.71
125 0.91 0.85 0.75
135 0.96 0.89 0.79 0.65
145 1.00 0.94 0.83 0.68
155 1.00 0.87 0.71
165 0.91 0.74
175 0.95 0.76
185 1.00 0.79
205 0.85
230 0.93
255 1.00

c
fR,N = 0.25 + 0.50 Limits: cmin ≤ c ≤ ccr,N
h ef

Anchor size M10 M12 M16 M16L M20

cmin [mm] 60 75 85 135
ccr,N [mm] 113 143 158 188 255

Note: If more than 3 edge distances are smaller than ccr,N, please contact your Hilti sales
representative.

∆ NRd,s : Steel tensile design resistance

Anchor size M10x75 M12x95 M16x105 M16x125 M20x170

∆ NRd,s [kN] HAS-TZ steel grade 8.8
1)
8.1 14.7 15.6 15.6 15.6

The partial safety factor, γMs,N =1.35.

1)

27
PI Fatigue HVZ
SHEAR
The design shear resistance of a single anchor is the minimum of,
∆VRd,c : concrete edge resistance
∆VRd,s : steel resistance

c2 > V rec,c/s
1 .5
c
s
c c2 >
1 .5
c
h>
1 .5
c

Note: If the conditions shown for h and c2 cannot be observed, please contact your Hilti sales representative.

∆ VRd,c : Concrete edge design resistance

The weakest concrete edge resistance must be calculated. All nearby edges must be checked, (not only the
edge in the direction of shear). Shear direction is accounted by the factor fβ,V.

∆V Rd , c
= ∆V 0
Rd , c
⋅f B ,V
⋅f β ,V
⋅f AR ,V

∆ V0Rd,c : Concrete edge design resistance

• concrete compressive strength f ck,cube(150) = 25 N/mm2
• at minimum edge distance c min

Anchor size M10x75 M12x95 M16x105 M16x125 M20x170

∆ V Rd,c1)
0
[kN] in non-cracked concrete 2.6 4.0 5.3 5.5 12.6
∆ V Rd,c
0 1)
[kN] in cracked concrete 1.8 2.8 3.8 3.9 9.0
cmin [mm] Min. edge distance 60 75 85 135
The design value of the ultimate state in shear is calculated from the characteristic anchor shear resistance, ∆V°Rk,c=60% V°Rk,c divided by
1)

γMc,V, where the partial safety factor, γMc,V, is 1.62.

fB,V : Influence of concrete strength

Concrete strength Cylinder compressive Cube compressive
designation strength strength
(ENV 206) fck,cyl [N/mm²] fck,cube [N/mm²]
fB,V
C20/25 20 25 1
C25/30 25 30 1.1
C30/37 30 37 1.22 fck,cube
C35/45 35 45 1.34 fB,V =
C40/50 40 50 1.41 25
Limits: 25 N/mm ≤ f ck,cube ≤ 60 N/mm
2 2
C45/55 45 55 1.48
C50/60 50 60 1.55
Concrete cylinder: Concrete cube:
height 30cm, 15cm side length 15cm
diameter
Concrete test specimen geometry

28
 PI Fatigue HVZ

fβ ,V : Influence of shear load direction

Angle β [°] fβ ,V Formulae:

V ... applied shear force
0 to 55 1 fβ,V = 1 for 0° ≤ β ≤ 55°
60 1.1 β
1
70 1.2 fβ,V = for 55° < β ≤ 90°
cos β + 0.5 sin β
80 1.5
f β,V = 2 for 90° < β ≤ 180°
90 to 180 2

fAR,V : Influence of spacing and edge

Formula for single anchor influenced
only by edge c2,1
c c s n-1
f AR,V =
c min c min results s3
s2
tabulated s1
Formula for anchor pair valid for s < 3c
below c 2,2 c
3c + s c
f AR,V =
6c min c min
h >1,5 c

General formula for n anchors (edge plus n-1 spacing)

only valid where s1 to sn-1 are all < 3c
Note: It is assumed that only the row of anchors closest to
3c + s 1 + s 2 + ... + s n−1 c the free concrete edge carries the centric shear load
f AR,V = ⋅
3nc min c min

29