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4
Examples
Examples
Example Example 1 1 314314 Example Example 2 2 3183184
4
60°
c1 c2
F
N=9,0 kN
V=15,6 kN F=18,0 kN
Single-anchor fastening close to two edges of a column
Given: Hilti HVA adhesive anchor with HVU capsule and HAS-R M20 rodgrade of concrete: C20/25
inclined working load: F = 18.0 kN
thickness of concrete member: h = 300 mm
edge distance: c1 = 100 mm, c2= 150 mm
Calculation:
1.
Tension
Valid design tensile load:
Rd,c Rd,s
Rd min N ;NN
1.1 Design tensile load to resist pull-out and concrete failure, NRd,c:
4
Initial value of design tensile load, N0Rd,c
kN 62,9 NRd,0 c
Influence of concrete strength
0 , 1 100 25 f 1 f B ck,cube
; for f ck,cube
25N/mm2Influence of anchorage depth
; 0 , 1 h h f nom act
T
for hact
hnom;
hnom
hact
2,0
hnom
Influence of anchor spacing
; 0 , 1 h 4 s 5 , 0 f nom N ,
A
because of single-anchor fasteningInfluence of edge distance
70 , 0 mm 170 mm 100 72 , 0 28 , 0 h c 72 , 0 28 , 0 f nom 1 N , 1 R
92 , 0 mm 170 mm 150 72 , 0 28 , 0 h c 72 , 0 28 , 0 f nom 2 N , 2 R
Design tensile load to resist pull-out of concrete cone kN 40,5 0,92 0,7 1,0 1,0 1,0 kN 62,9 c Rd, N
Design tensile load to resist steel failure, NRd,s
kN 3 , 84 NRd,s
Final design tensile resistance:
N ;N
40,5 kN min2.
Shear
Valid design shear load:
Rd,c Rd,s
Rd min V ;VV
2.1 Design shear load to resist concrete edge failure, VRd,c:
Concrete design resistance, V Rd,c for a single anchor in a multiple-anchor fastening:
V , AR V , V , B 0 c , Rd c , Rd V f f f V
Initial value of design shear load at a concrete edge with minimum edge distance kN
12,4 VRd,0 c
Influence of concrete strength
; 0 , 1 25 f
f B,V
ck,cube
for f ck,cube
25N/mm2Influence of loading direction
o o V , o o V , o o V , 180 90 ; 0 , 2 f 90 55 ; sin 5 , 0 cos 1 f 55 0 ; 0 , 1 f
; 0 , 2 f ,V
for
90oInfluence of edge distance
28 , 1 mm 85 mm 100 mm 85 mm 100 c c c c f min min V , AR
; kN 31,7 2,0 1,28 1,0 kN 12,4 VRd,c
2.2 Design shear load to resist steel failure, VRd,s:
V
4
3.
Combined Load:
The design resistance for a combined load is given by:
kN
30,7
31,7kN
sin60
kN
40,5
cos60
V
sin
N
cos
(
F
3 2 1,5 o 1,5 o 3 2 1,5 Rd 1,5 Rd Rd
Design action load:
F Sd F
F
assuming a partial safety factor for the working load,
F, of 1.4kN 2 , 25 4 , 1 kN 0 , 18 FSd
Proof:
30,7 kN F kN 25,2 FSd
Rd
This application is safe if designed according to the Hilti FTM.
N
F ( )
V Rdc
s
1 hs
2s
2 V1
2
3
4
5
6
N FSix-anchor fastening close to one edge
Given: Hilti HDA-T M16 design anchoranchoring in non-cracked concrete
grade of concrete: C30/37
inclined working load: F = 80,0 kN
angle of inclination:
= 20°thickness of concrete member: h = 400 mm
edge distance: c = 160 mm,
spacing: s1 = 190 mm, s2= 300 mm
Calculation:
1.
Tension
Valid design tensile load:
Rd,c Rd,s
Rd min N ;NN
1.1 Design tensile load to resist pull-out and concrete failure, NRd,c:
4
kN 63,0 0,76 0,67 1,22 kN 101,4 NRd,2,6c
kN 47,9 0,76 0,76 0,67 1,22 kN 101,4 NRd,4 c
kN 42,8 0,68 0,76 0,67 1,22 kN 101,4 N1,5Rd,c
kN 32,6 0,68 0,76 0,76 0,67 1,22 kN 101,4 N3Rd,c
Design tensile load to resist concrete cone pull-out for a multiple-anchor fastening kN 292,1 kN 32,6 kN 47,9 2 kN) 42,8 kN (63,0 NRd,groupc
1.2 Design tensile load to resist steel failure, NRd,s kN
0 , 84 NRd,s
Design tensile load to resist steel failure for a multiple-anchor fastening kN 0 , 504 6 kN 0 , 84 NgroupRd,s
1.3 Final design tensile resistance:
N ;N
292,1 kN minNRdgroup
Rd,groupc Rd,groups
Initial value of design tensile load, N0Rd,c
kN 101,4 N0Rd,c
Influence of concrete strength
22 , 1 mm / N 25 mm / N 37 25 f f 2 2 cube , ck B
Influence of anchor spacing
67 , 0 mm 190 6 mm 190 5 , 0 h 6 s 5 , 0 f ef 1 1 N , A
76 , 0 mm 190 6 mm 300 5 , 0 h 6 s 5 , 0 f ef 2 2 N , A
Influence of edge distance
68 , 0 mm 190 mm 160 49 , 0 27 , 0 h c 49 . 0 27 , 0 f ef N , R
2.
Shear
Valid design shear load:
Rd,c Rd,s
Rd min V ;VV
2.1 Design shear load to resist concrete edge failure, VRd,c:
Concrete design resistance, VRd,c for a single anchor in a multiple-anchor fastening:
V , V , AR B 0 c , Rd c , Rd V f f f V
Initial value of design shear load at a concrete edge with minimum edge distance kN
26,1 VRd,0 c
Influence of concrete strength
22 , 1 mm / N 25 mm / N 37 25 f f 2 2 cube , ck B
Influence of shear loading direction
o V
, 1; 0
f
Influence of anchor spacing and edge distance
83 , 0 mm 150 mm 160 mm 150 3 3 mm 300 2 mm 160 3 c c c n 3 s ... s s c 3 f min min 1 n 2 1 V , AR
kN 26,4 1,0 0,83 1,22 kN 26,1 VRd,c
Design shear load to resist concrete edge failure for a multiple-anchor fastening kN 79,2 3 kN 26,4 VRd,groupc
4
2.2 Design shear load to resist steel failure, VRd,s : kN
3 , 93 VRd,s
Design shear load to resist steel failure for a multiple-anchor fastening kN 0 , 560 6 kN 3 , 93 VRdgroup,s
2.3 Final design shear resistance:
V ;V
66,0kN minVRdgroup
Rdgroup,c Rdgroup,s
3.
Combined Load:
The design resistance for a combined load is given by:
kN
166,3
kN
79,2
sin20
kN
292,1
cos20
V
sin
N
cos
(
F
3 2 1,5 o 1,5 o 3 2 1,5 Rd 1,5 Rd Rd
Design action: F Sd F F
assuming a partial safety factor for the working load,
F, of 1.4kN 0 , 112 4 , 1 kN 0 , 80 FSd
Proof:
166,3kN F kN 112,0 FSd
Rd
This application is safe if designed according to the Hilti FTM.
N
