4 Examples Example 1
314
Example 2
318
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Issue 2005
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Example 1
Single-anchor fastening close to two edges of a column Given:
Hilti HVA adhesive anchor with HVU capsule and HAS-R M20 rod grade of concrete: C20/25 inclined working load: F = 18.0 kN thickness of concrete member: h = 300 mm edge distance: c1 = 100 mm, c 2 = 150 mm
N=9,0 kN 60°
c1
c2
V=15,6 kN
F=18,0 kN
F
Calculation: 1.
Tension Valid design tensile load: NRd
1.1
min NRd,c ; NRd,s
Design tensile load to resist pull-out and concrete failure, NRd,c : Concrete design resistance, NRd,c for a single anchor in a multiple-anchor fastening: NRd,c
314
o NRd ,c f B,N f T f A,N f R,N
Issue 2005
Example 1
0 Initial value of design tensile load, NRd ,c 0 NRd, c
62,9 kN
Influence of concrete strength f B
25 f 1,0 ; 1 ck,cube 100
for f ck,cube
25 N / mm 2
Influence of anchorage depth f T
hact
hnom
1,0;
for h act
h nom ; h nom h act 2,0 h nom
Influence of anchor spacing
0,5
f A,N
s 4 hnom
1,0;
because of single-anchor fastening
Influence of edge distance f R1,N
0,28 0,72
f R2,N
0,28 0,72
c1 hnom c2 hnom
0,28 0,72
100mm
0,28 0,72
150mm
170mm
170mm
0,70
0,92
4
Design tensile load to resist pull-out of concrete cone N Rd, c
62,9kN 1,0 1,0 1,0 0,7 0,92 40,5 kN
Design tensile load to resist steel failure, NRd,s NRd,s
84,3 kN
Final design tensile resistance: NRd
min NRd,s; NRd,c 40,5 kN
Issue 2005
315
Example 1
2.
Shear Valid design shear load: VRd
2.1
min VRd,c ; VRd,s
Design shear load to resist concrete edge failure, VRd,c : Concrete design resistance, VRd,c for a single anchor in a multiple-anchor fastening: VRd,c
0 VRd , c f B, V f , V f AR, V
Initial value of design shear load at a concrete edge with minimum edge distance 0 VRd, c
12,4 kN
Influence of concrete strength
f B, V
f ck,cube
25
1,0;
for f ck,cube
25 N / mm 2
Influence of loading direction 0o
f ,V
1,0;
f ,V
f ,V
2,0;
f ,V
2,0;
1 cos 0,5 sin
;
55 o
55 o
90 o
90 o
180 o
V
for 90 o
Influence of edge distance
2.2
85mm
1,28 ;
the smallest edge distance, c, must be inserted.
Design shear load to resist steel failure, VRd,s :
60,6 kN
Final design shear resistance: VRd
316
85mm
100mm
12,4 kN 1,0 1,28 2,0 31,7 kN
c min
100mm
VRd,c
c min
c
VRd,s 2.3
c
f AR,V
min VRd,s ; VRd,c 31,7kN Issue 2005
Example 1
3.
Combined Load: The design resistance for a combined load is given by:
cos 1,5 sin FRd ( V NRd Rd cos60 o 40,5 kN 30,7 kN
1,5
2
1,5 3
sin60 o 31,7kN
FRd ()
N
V 1,5
2 3
Design action load: FSd
F F
assuming a partial safety factor for the working load, FSd
F, of 1.4
18,0 kN 1,4 25,2 kN
Proof: FSd
25,2 kN FRd 30,7 kN
This application is safe if designed according to the Hilti FTM.
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Issue 2005
317
Example 2
Six-anchor fastening close to one edge Given:
Hilti HDA-T M16 design anchor anchoring in non-cracked concrete grade of concrete: inclined working load: angle of inclination: thickness of concrete member: edge distance: spacing:
C30/37 F = 80,0 kN = 20° h = 400 mm c = 160 mm, s1 = 190 mm, s 2 = 300 mm
N F
c
s1 6 5 2
2
3
s
h
4
s 2
1
V
Calculation: 1.
Tension Valid design tensile load: NRd
1.1
min NRd,c ; NRd,s
Design tensile load to resist pull-out and concrete failure, NRd,c : Concrete design resistance, NRd,c for a single anchor in a multiple-anchor fastening: NRd,c
318
o NRd , c f B f A,N f R,N
Issue 2005
Example 2
0 Initial value of design tensile load, NRd ,c 0 NRd, c
101,4 kN
Influence of concrete strength
f B
f ck,cube
25
37 N / mm 2 25 N / mm 2
1,22
Influence of anchor spacing s1
f A,N1
0,5
f A,N2
0,5
6 h ef
0,5
s2 6 h ef
190 mm 6 190 mm
0,5
0,67
300 mm 6 190 mm
0,76
Influence of edge distance f R,N
0,27 0.49
c h ef
0,27 0,49
160 mm 190 mm
0,68
2,6 NRd, c
101,4 kN 1,22 0,67 0,76 63,0 kN
4 NRd, c
101,4 kN 1,22 0,67 0,76 0,76 47,9 kN
N1,5 Rd,c
101,4 kN 1,22 0,67 0,76 0,68 42,8 kN
3 NRd, c
101,4 kN 1,22 0,67 0,76 0,76 0,68 32,6 kN
4
Design tensile load to resist concrete cone pull-out for a multiple-anchor fastening group
NRd,c
1.2
(63,0 kN 42,8 kN) 2 47,9 kN 32,6 kN 292,1 kN
Design tensile load to resist steel failure, NRd,s NRd,s
84,0 kN
Design tensile load to resist steel failure for a multiple-anchor fastening group NRd ,s
1.3
84,0 kN 6 504,0 kN
Final design tensile resistance: group
NRd
Issue 2005
group group ; NRd,s 292,1 kN min NRd, c
319
Example 2
2.
Shear Valid design shear load: VRd
2.1
min VRd,c ; VRd,s
Design shear load to resist concrete edge failure, VRd,c : Concrete design resistance, VRd,c for a single anchor in a multiple-anchor fastening: VRd,c
0 VRd , c f B f AR, V f , V
Initial value of design shear load at a concrete edge with minimum edge distance 0 VRd, c
26,1 kN
Influence of concrete strength
f B
f ck,cube
25
37 N / mm2 25 N / mm 2
1,22
Influence of shear loading direction f ,V
1; 0 o
Influence of anchor spacing and edge distance f AR,V
3 c s1 s2
... sn 1
3 n c min
c c min
3 160 mm 2 300 mm 3 3 150 mm
160 mm 150 mm
0,83 VRd,c
26,1 kN 1,22 0,83 1,0 26,4 kN
Design shear load to resist concrete edge failure for a multiple-anchor fastening group
VRd,c
320
26,4 kN 3 79,2 kN
Issue 2005
Example 2
2.2
Design shear load to resist steel failure, VRd,s : VRd,s
93,3 kN
Design shear load to resist steel failure for a multiple-anchor fastening group VRd ,s
2.3
Final design shear resistance: group VRd
3.
93,3 kN 6 560,0 kN
group group min VRd ,c ; VRd,s 66,0 kN
Combined Load: The design resistance for a combined load is given by:
cos 1,5 sin FRd ( N V Rd Rd cos20 o 292,1 kN 166,3 kN
1,5
N
2
1,5 3
sin20 o 79,2 kN
FRd ()
V
1,5
2 3
4
Design action: FSd
F F
assuming a partial safety factor for the working load, FSd
F, of 1.4
80,0 kN 1,4 112,0 kN
Proof: FSd
112,0 kN FRd 166,3 kN
This application is safe if designed according to the Hilti FTM.
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