Hilti Calculation Examples

4 Examples Example 1

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Example 2

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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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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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