Connection Design: Joints resistance according to EC.3 – 1 – 8

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Connection Design Joints resistance according to EC.3 – 1 – 8

Edit by Dott. Ing. Simone Caffè

Connection Design

FIN PLATE CONNECTION

Shear resistance per shear plane §Table 3.4:

Fv,Rd 

 v  As  fub  M2

 v  0.6  v  0.5

for classes 8.8

As

area of the bolts

fub

ultimate tensile strength

 M2  1.25

safety factor

for classes 10.9

Shear bolt resistance §3.6.1:

VRd,1 

ex

Fv,Rd 2

 1 ex  xmax   ex  ymax       Jb  nb   Jb 

2

 VEd

eccentricity between the centroid of the bolts and the supporting beam web or supporting column flange.

nb

number of bolts.

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2

Connection Design

Shear force in “y” direction per shear plane due to external shear:

VyV,Ed 

VEd nb

Shear force in “y” direction per shear plane due to torsion:

V  e   x VyT,Ed   Ed x  max Jb Shear force in “x” direction per shear plane due to torsion:

V  e   y VxT,Ed   Ed x  max Jb Total shear force per shear plane due to shear and torsion: 2

2

 1 ex  xmax   ex  ymax  Rb  VEd        Fv,Rd n J J b b  b    Bolts polar moment calculated in the centroid of the bolts:



Jb   xi2  yi2 i



Axial resistance for the bolts in shear §3.6.1:

NRd,1  nb  Fv,Rd  NEd

Shear bearing resistance of beam web §Table 3.4:

VRd,2 

1  1 ex  xmax n  Jb  b Fy ,b,Rd   

2

  ex  ymax   Jb     Fx,b,Rd    

     

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2

 VEd

3

Connection Design

Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d  tbw  fu  M2 Without notch

Single notch

Double notch

 p   1   y  min  1  ; 1 3  d 4    1 

 p 1   e   y min 1 ; 1  ; 1 3  d 3  d 4   0 0  

e  p  1   y  min  1,min ; 1  ; 1 3d  0 

3d 4 0

 

  e p   k min2.8 2 1.7 ; 1.4 2 1.7 ; 2.5 y d d   0 0  

y

bearing coefficient in the direction of load transfer.

ky

bearing coefficient perpendicular to the direction of load transfer.

e1

end distance from the center of fastener hole, to the adjacent end of any part measured in the direction of load transfer (Figure 3.1 – EC3-1-8 : 2005).

e2

edge distance from the center of fastener hole, to the adjacent edge of any part measured at right angles to direction of load transfer (Figure 3.1 – EC3-18 : 2005).

p1

spacing between centers of fasteners in a line in the direction of load transfer (Figure 3.1 – EC3-1-8 : 2005).

p2

spacing measured perpendicular to load transfer direction between adjacent line of fasteners (Figure 3.1 – EC3-1-8 : 2005).

d

diameter of the fastener.

d0

diameter of the hole.

tbw

thickness of the beam web.

fu

ultimate tensile strength

Bearing resistance in “x” direction:

Fx,b,Rd 

 x  kx  d  tbw  fu  M2 Without notch

Single notch

Double notch

 p 1   e   x min 2 ; 2  ; 1 3d 3d 4   0 0  

  p   k x  min 1.4 1 1.7 ; 2.5 d   0  

  e p   k min2.8 1 1.7 ; 1.4 1 1.7 ; 2.5  x d d   0 0  

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  e p   k x  min 2.8 1,min 1.7 ; 1.4 1 1.7 ; 2.5  d d   0 0  

4

Connection Design

Bearing check:

  1 ex  xmax   nb Jb   VEd   Fy ,b,Rd  

2

    ex  ymax    Jb       F x ,b,Rd    

2

   1   

Shear bearing resistance of fin plate §Table 3.4:

VRd,3 

1  1 ex  xmax n  Jb  b  F y ,b,Rd  

2

  ex  ymax   Jb     F x ,b,Rd    

     

2

 VEd

Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d  tp  fu  M2

Bearing coefficient in the direction of load transfer:

 p1 1   e1  ;  ; 1  3  d0 3  d0 4   

 y  min 

Bearing coefficient perpendicular to the direction of load transfer:

  p e2   ky  min 2.8   1.7 ; 1.4  2  1.7 ; 2.5 d0 d0    

e1

end distance from the center of fastener hole, to the adjacent end of any part measured in the direction of load transfer (Figure 3.1 – EC3-1-8 : 2005).

e2

e distance from the center of fastener hole, to the adjacent edge of any part measured at right angles to direction of load transfer (Figure 3.1 – EC3-18 : 2005).

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5

Connection Design

p1

spacing between centers of fasteners in a line in the direction of load transfer (Figure 3.1 – EC3-1-8 : 2005).

p2

spacing measured perpendicular to load transfer direction between adjacent line of fasteners (Figure 3.1 – EC3-1-8 : 2005).

d

diameter of the fastener.

d0

diameter of the hole.

tp

thickness of the fin plate.

Bearing resistance in “x” direction:

F x ,b,Rd 

 x  k x  d  tp  fu  M2

Bearing coefficient in the direction of load transfer:

 e2  p2 1   ;  ; 1  3  d0 3  d0 4   

 x  min 

Bearing coefficient perpendicular to the direction of load transfer:

  p e1   k x  min 2.8   1.7 ; 1.4  1  1.7 ; 2.5 d0 d0     Axial bearing resistance of beam web §Table 3.4:

NRd,2  nb  Fx,b,Rd  NEd Axial bearing resistance of fin plate §Table 3.4:

NRd,3  nb  F x,b,Rd  NEd

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6

Connection Design

Beam web in shear (gross section):

VRd,4 

Av  fy 3   M0

 VEd

Without notch

Av  0.9 

Ab hb bb tbf tbw dnt dnb

Single notch

 Ab  2  bb  tbf  tbw 2rb   tbf 

Av  0.9 

 Ab  2  bb  tbf  dnt tbf   tbw 

Double notch

Av  0.9 

 hb dnt dnb   tbw 

cross – sectional area of the beam. height of the beam. flange width of the beam. thickness of the beam flange. thickness of the beam web. depth of the top notch. depth of the bottom notch.

Beam web in shear (net section):

VRd,5 

Av,net  fu 3   M2

 VEd Av,net  Av  nb,v  tbw  d0

Shear net area:

nb,v

number of bolts in a single vertical line.

fu

ultimate tensile strength.

Fin plate in shear (gross section):

VRd,6 

hp  tp  fy 1.27  3   M0

 VEd

hp

height of the fin plate.

tp

thickness of the fin plate.

The coefficient 1.27 takes in to account the redaction of shear resistance, due to the presence of bending moment. © Edit by Simone Caffè: This material is copyright - all rights reserved

7

Connection Design

Fin plate in shear (net section):

VRd,7 

h

p



 nb,v  d0  tp  fu 3   M2

 VEd

hp

height of the fin plate.

tp

thickness of the fin plate.

Fin plate in bending:

VRd,8

 tp  hp2     fy Wel ,p  fy  6     VEd ex   M0 ex   M0

Wel ,p

elastic fin plate modulus.

Beam web in bending:

VRd,9 

en

Wel ,b  fy en   M0

 VEd

Without notch

Single notch

Wel ,b

Wel ,b ,min of the “T” shape

Double notch

Wel ,b 

eccentricity between the shear force and the notch end.

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tbw  hdnt dnb  6

2

8

Connection Design

Fin plate in shear (Block tearing):

VRd,10  Ant ,p

0.5  Ant ,p  fu

 M2



Anv,p  fy 3   M0

 VEd

net area subjected to tension:

 d0    Ant ,p  e2    tp 2    A  e  n  1  p  n  0.5  d   t  0 p  nt ,p  2  b,h  2  b,h Anv,p

for a single vertical line of bolts

for more than one vertical line of bolts

net area subjected to shear:

Anv,p  hp  e1   nb,v  0.5  d0   tp   nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

Beam web in shear (Block tearing):

VRd,11  Ant ,p

0.5  Ant ,b  fu

 M2



Anv,b  fy 3   M0

 VEd

net area subjected to tension:

 d0    Ant ,b  e2    tbw 2    A  e  n  1  p  n  0.5  d   t  0  bw  nt ,b  2  b,h  2  b,h Anv,b

for a single vertical line of bolts

for more than one vertical line of bolts

net area subjected to shear: Without notch

Single notch

Double notch

Anv ,b  e1 nb ,v 1p1 nb ,v 0.5d0   t bw

Anv ,b  e1 nb ,v 1p1 nb ,v 0.5d0   t bw

Anv ,b  e1,min  nb ,v 1p1 nb ,v 0.5d0   tbw

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9

Connection Design

Fin plate in tension (Block tearing):

NRd,4 

 nt ,p  f 0.5  A u

 M2

 nt ,p A



 nv,p  f A y 3   M0

 NEd

net area subjected to tension:

 nt,p   n  1  p   n  1  d   t A 1 b,v 0 p  b,v

 nv,p A

net area subjected to shear:

 d0   A nv ,p  2   e2     tp  2    A  nv,p  2  e2   n  1  p   n  0.5   d   t b ,h 2 b ,h 0 p    nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

for a single vertical line of bolts

for more than one vertical line of bolts

Beam web in tension (Block tearing):

NRd,5 

 nt ,b  f 0.5  A u

 M2

 nt ,b A



 nv,b  f A y 3   M0

 NEd

net area subjected to tension:

 nt,b   n  1  p   n  1  d   t A 1 b,v 0  bw  b,v

 nv,b A

net area subjected to shear:

 d0    Anv,b  2  e2    tbw 2   A   2  e2   nb,h  1  p2   nb,h  0.5   d0   tbw  nv,b

nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

Fin plate in tension (net section):

NRd,6 





0.9  hp  nb,v  d0  tp  fu

 M2

 NEd

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for a single vertical line of bolts

for more than one vertical line of bolts

10

Connection Design

Beam web in tension (net section):

NRd,7 

hp





0.9  hp  nb,v  d0  tbw  fu

 M2

 NEd

height of the fin plate (conservatively).

Joint resistance:

Vpl,Rd

design plastic resistance of the beam

If VEd  0.5  Vpl ,Rd

If VEd  0.5  Vpl ,Rd

 Vj ,Rd  minVRd,1;; VRd,11  VEd  Nj ,Rd  minNRd,1;; NRd,7   NEd

then 

then

2 2     NEd VEd     1.00   min  N ; N ; N    min  V ; V ; V       Rd ,1 Rd ,2 Rd ,3  Rd ,1 Rd ,2 Rd ,3     V  minV ; ; V   V  j ,Rd Rd ,4 Rd ,11 Ed  Nj ,Rd  minNRd,4 ; ; NRd,7   1    NEd  2   2  VEd   1 §6.2.10 EC.3      Vpl ,Rd 

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11

Connection Design

WEB COVER PLATE CONNECTION

Shear resistance per shear plane §Table 3.4:

Fv,Rd 

 v  As  fub  M2

 v  0.6  v  0.5

for classes 8.8

As

Area of the bolts

fub

Ultimate tensile strength

 M2  1.25

Safety factor

for classes 10.9

Shear bolt resistance §3.6.1:

VRd,1 

n  Fv,Rd 2

 1 ex  xmax   ex  ymax       Jb  nb   Jb 

2

 VEd

ex

eccentricity between the centroid of the bolts and the beam end.

nb n2

number of bolts. number of shear plane.

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12

Connection Design

Shear force in “y” direction per shear plane due to external shear:

VyV,Ed 

VEd n  nb

Shear force in “y” direction per shear plane due to torsion:

V  e   x VyT,Ed   Ed x  max n  Jb Shear force in “x” direction per shear plane due to torsion:

V  e   y VxT,Ed   Ed x  max n  Jb Total shear force per shear plane due to shear and torsion: 2

2

 1 ex  xmax   ex  ymax  V Rb  Ed        Fv,Rd n Jb  nb   Jb  Bolts polar moment calculated in the centroid of the bolts:



Jb   xi2  yi2 i



Axial resistance for the bolts in shear §3.6.1:

NRd,1  n  nb  Fv,Rd  NEd Shear bearing resistance of beam web §Table 3.4:

VRd,2 

1  1 ex  xmax n  Jb  b Fy ,b,Rd   

2

  ex  ymax   Jb     Fx,b,Rd    

     

Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d  tbw  fu  M2

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2

 VEd

13

Connection Design

Bearing coefficients 



  3d1 4

 

 p 1   y  min  1  ; 1   e p   k min2.8 2 1.7 ; 1.4 2 1.7 ; 2.5 y d d   0 0  

y

bearing coefficient in the direction of load transfer.

ky

bearing coefficient perpendicular to the direction of load transfer.

e1

end distance from the center of fastener hole, to the adjacent end of any part measured in the direction of load transfer (Figure 3.1 – EC3-1-8 : 2005).

e2

edge distance from the center of fastener hole, to the adjacent edge of any part measured at right angles to direction of load transfer (Figure 3.1 – EC3-18 : 2005).

p1

spacing between centers of fasteners in a line in the direction of load transfer (Figure 3.1 – EC3-1-8 : 2005).

p2

spacing measured perpendicular to load transfer direction between adjacent line of fasteners (Figure 3.1 – EC3-1-8 : 2005).

d

diameter of the fastener.

d0

diameter of the hole.

tbw

thickness of the beam web.

fu

ultimate tensile strength

Bearing resistance in “x” direction:

Fx,b,Rd 

 x  kx  d  tbw  fu  M2 Bearing coefficients  p 1   e2  ; 2  ; 1 3  d 3  d 4   0 0  

 x min

  p   k x  min 1.4 1 1.7 ; 2.5 d   0  

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14

Connection Design

Bearing check:

  1 e x  x max  n  n  nb n  Jb VEd     Fy ,b,Rd  

2

    ex  ymax    n       n  Jb   Fx ,b,Rd    

2

   1   

Shear bearing resistance of cover plates §Table 3.4:

VRd,3 

1  1 ex  xmax n  Jb  b  F y ,b,Rd  

2

  ex  ymax   Jb     F x ,b,Rd    

     

2

 VEd

Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d   2  tp   fu  M2

Bearing coefficient in the direction of load transfer:

 p1 1   e1  ;  ; 1  3  d0 3  d0 4   

 y  min 

Bearing coefficient perpendicular to the direction of load transfer:

  p e2   ky  min 2.8   1.7 ; 1.4  2  1.7 ; 2.5 d0 d0    

e1

end distance from the center of fastener hole, to the adjacent end of any part measured in the direction of load transfer (Figure 3.1 – EC3-1-8 : 2005).

e2

edge distance from the center of fastener hole, to the adjacent edge of any part measured at right angles to direction of load transfer (Figure 3.1 – EC3-18 : 2005).

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15

Connection Design

p1

spacing between centers of fasteners in a line in the direction of load transfer (Figure 3.1 – EC3-1-8 : 2005).

p2

spacing measured perpendicular to load transfer direction between adjacent line of fasteners (Figure 3.1 – EC3-1-8 : 2005).

d

diameter of the fastener.

d0

diameter of the hole.

tp

thickness of a single plate.

Bearing resistance in “x” direction:

F x,b,Rd 

 x  k x  d   2  tp   fu  M2

Bearing coefficient in the direction of load transfer:

 p2 1   e2  ;  ; 1  3  d0 3  d0 4   

 x  min 

Bearing coefficient perpendicular to the direction of load transfer:

  p e1   k x  min 2.8   1.7 ; 1.4  1  1.7 ; 2.5 d0 d0     Axial bearing resistance of beam web §Table 3.4:

NRd,2  nb  Fx,b,Rd  NEd Axial bearing resistance of cover plates §Table 3.4:

NRd,3  nb  F x,b,Rd  NEd Beam web in shear (gross section) :

VRd,4 

0.9  Av  fy 3   M0

 VEd

Av  Ab  2  bb  tbf   tbw  2  rb   tbf

© Edit by Simone Caffè: This material is copyright - all rights reserved

16

Connection Design

Ab hb bb tbf tbw

cross – sectional area of the beam. height of the beam. flange width of the beam. thickness of the beam flange. thickness of the beam web.

Beam web in shear (net section):

VRd,5 

Av,net  fu 3   M2

 VEd Av,net  Av  nb,v  tbw  d0

Shear net area:

nb,v

number of bolts in a single vertical line.

fu

ultimate tensile strength

Cover plates in shear (gross section):

VRd,6 





hp  2  tp  fy

 VEd

1.27  3   M0

hp

height of the double plate.

tp

thickness of a single plate.

The coefficient 1.27 takes in to account the redaction of shear resistance, due to the presence of bending moment. Cover plates in shear (net section):

VRd,7 

h

p





 nb,v  d0  2  tp  fu 3   M2

 VEd

hp

height of the double plate.

tp

thickness of a single plate.

Cover plates in shear (Block tearing):

VRd,8 

0.5  Ant ,p  fu

 M2



Anv,p  fy 3   M0

 VEd

© Edit by Simone Caffè: This material is copyright - all rights reserved

17

Connection Design

Ant ,p

net area subjected to tension:

 d0    Ant ,p  e2    2  tp 2    A  e  n  1  p  n  0.5  d   2  t  0 p  nt ,p  2  b,h  2  b,h







Anv,p

for a single vertical line of bolts



for more than one vertical line of bolts

net area subjected to shear:



Anv,p  hp  e1   nb,v  0.5  d0   2  tp  



nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

Beam web in shear (Block tearing):

VRd,9  Ant ,p

0.5  Ant ,b  fu

 M2



Anv,b  fy 3   M0

 VEd

net area subjected to tension:

 d0    Ant ,b  e2    tbw 2    A  e  n  1  p  n  0.5  d   t  0  bw  nt ,b  2  b,h  2  b,h

Anv,b

net area subjected to shear:

Anv,b  e1   nb,v  1  p1   nb,v  0.5  d0   tbw Cover plates in tension (Block tearing):

NRd,4   nt ,p A

 nt ,p  f 0.5  A u

 M2



 nv,p  f A y 3   M0

 NEd

net area subjected to tension:



 nt,p   n  1  p   n  1  d   2  t A 1 b,v 0 p  b,v

 nv,p A



net area subjected to shear:

© Edit by Simone Caffè: This material is copyright - all rights reserved

for a single vertical line of bolts

for more than one vertical line of bolts

18

Connection Design

 d0     Anv,p  2  e2  2   2  tp  A  nv,p  2  e2   n  1  p   n  0.5   d   2  t b ,h 2 b ,h 0 p   







for a single vertical line of bolts



nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

for more than one vertical line of bolts

Beam web in tension (Block tearing):

NRd,5 

 nt ,b  f 0.5  A u

 M2

 nt ,b A



 nv,b  f A y 3   M0

 NEd

net area subjected to tension:

 nt,b   n  1  p   n  1  d   t A 1 b,v 0  bw  b,v

 nv,b A

net area subjected to shear:

 d0    Anv,b  2  e2    tbw 2   A   2  e2   nb,h  1  p2   nb,h  0.5   d0   tbw  nv,b nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

Cover plates in tension (net section):

NRd,6 







0.9  hp  nb,v  d0  2  tp  fu

 M2

 NEd

Beam web in tension (net section):

NRd,7 

hp





0.9  hp  nb,v  d0  tbw  fu

 M2

 NEd

height of double plate (conservatively).

© Edit by Simone Caffè: This material is copyright - all rights reserved

for a single vertical line of bolts

for more than one vertical line of bolts

19

Connection Design

Joint resistance:

Vpl,Rd

design plastic resistance of the beam

If VEd  0.5  Vpl ,Rd

If VEd  0.5  Vpl ,Rd

 Vj ,Rd  minVRd,1;; VRd,9   VEd  Nj ,Rd  minNRd,1;; NRd,7   NEd

then 

then

2 2     NEd VEd     1.00   min  N ; N ; N    min  V ; V ; V      Rd ,1 Rd ,2 Rd ,3  Rd ,1 Rd ,2 Rd ,3    V  minV ; ; V   V  j ,Rd Rd ,4 Rd ,9 Ed  Nj ,Rd  minNRd,4 ; ; NRd,7   1    NEd  2   2  VEd   1 §6.2.10 EC.3      Vpl ,Rd 

© Edit by Simone Caffè: This material is copyright - all rights reserved

20

Connection Design

SPLICE CONNECTION – Bracing

Shear resistance per shear plane §Table 3.4:

 v  Afb  fub  Fv,fb,Rd     M2   0.75    1 L j  15  dfb  1.00  200  dfb 

 v  0.6  v  0.5

for classes 8.8

Afb

area of the flange bolts

Awb fub

area of the web bolts

 M2  1.25

safety factor

Fv,wb,Rd 

 v  Awb  fub  M2

for classes 10.9

ultimate tensile strength

Bolt resistance of the beam flange:

Nf ,Rd,1  nfsp  nfb  Fv,fb,Rd nfsp

number of flange shear plane

nfb

number of flange bolts

© Edit by Simone Caffè: This material is copyright - all rights reserved

 nfsp  1 for a single cover plate   nfsp  2 for double cover plate

21

Connection Design

Bearing resistance of the beam flange:

Nf ,Rd,2  nfb  Fb,bf ,Rd

Bearing resistance in “x” direction:

Fb,bf ,Rd 

 bf  kbf  dfb  tbf  fu  M2

Bearing coefficient in the direction of load transfer:

 p1,bf 1   e1,bf  ;  ; 1  3  d0,fb 3  d0,fb 4   

 bf  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e p   kbf  min 2.8  2,bf  1.7 ; 1.4  2,bf  1.7 ; 2.5 d0,fb d0,fb    

dfb

diameter of the flange bolt.

d0,fb

hole diameter of the flange bolt.

tbf

thickness of the beam flange.

© Edit by Simone Caffè: This material is copyright - all rights reserved

22

Connection Design

Bearing resistance of the flange cover plates:

Nf ,Rd,3  nfb  Fb,fcp,Rd

Bearing resistance in “x” direction:

Fb,fcp,Rd 

 fcp  kfcp  dfb   nfsp  tfcp   fu  M2

Bearing coefficient in the direction of load transfer:

 p1,fcp 1   e1,fcp ;  ; 1  fcp  min   3  d0,fb 3  d0,fb 4     p1,fcp  p1,bf Bearing coefficient perpendicular to the direction of load transfer:

   e2,fcp,min p  1.7 ; 1.4  2,fcp  1.7 ; 2.5  kfcp  min 2.8  d0,fb d0,fb      p2,fcp  p2,bf  e2,fcp,min  min e2,fcp ; e2,fcp  



tfcp



thickness of a single flange cover plate.

Beam flange in tension (gross section):

Nf ,Rd,4 

 bbf  tbf   fy  M0

bbf

flange width of the beam.

tbf

thickness of the beam flange.

© Edit by Simone Caffè: This material is copyright - all rights reserved

23

Connection Design

Beam flange in tension (net section):

Nf ,Rd,5 

0.9   bbf  2  d0,fb   tbf  fu

 M2

Flange cover plates in tension (gross section):

Nf ,Rd,6 

b



 tfcp  fy

fcp

for a single top flange cover plate

 M0

Nf ,Rd,6  Nf ,Rd,6 





2  bfcp  tfcp  fy

for double flange cover plate

 M0

bfcp

top flange cover plate width.

bfcp

bottom flange cover plate width.

Flange cover plates in tension (net section):

Nf ,Rd,7 





0.9  bfcp  2  d0,fb  tfcp  fu

for a single top flange cover plate

 M2

Nf ,Rd,7  Nf ,Rd,7 





0.9  2  bfcp  2  d0,fb  tfcp  fu

 M2

bfcp

top flange cover plate width.

bfcp

bottom flange cover plate width.

© Edit by Simone Caffè: This material is copyright - all rights reserved

for double flange cover plate

24

Connection Design

Beam flange in tension (Block tearing):

Nf ,Rd,8 

 nt ,bf  f A u

 nv,bf  f A y



 M2

3   M0

Net area subjected to tension:

 nt,bf  2  e  d   t A 2,bf 0,fb  bf  Net area subjected to shear:

 nv,bf  2  e   n  1  p   n  0.5  d   t A b,h 1,bf b,h 0,fb  bf  1,bf

nb,h

number of bolts in a single horizontal line.

Flange cover plates in tension (Block tearing):

Nf ,Rd,9 

 nt ,fcp  f A u

 M2

Nf ,Rd,9  Nf ,Rd,9 

 nt ,fcp A



 nv,fcp  f A y

for a single top flange cover plate

3   M0

Ant ,fcp  fu

 M2



Anv,fcp  fy 3   M0

net area subjected to tension:

© Edit by Simone Caffè: This material is copyright - all rights reserved

for double flange cover plate

25

Connection Design

Net area subjected to tension:

 nt,fcp   p A  2,fcp  d0,fb   tfcp

Ant ,fcp  2  e2,fcp  d0,fb   tfcp   Net area subjected to shear:

 nv,fcp  Anv,fcp  2  e   n  1  p  A b,h 1,fcp   nb,h  0.5   d0,fb   tfcp  1,fcp

Joint flange resistance:

Nj ,f ,Rd  minNf ,Rd,1;...; Nf ,Rd,9 

© Edit by Simone Caffè: This material is copyright - all rights reserved

26

Connection Design

Shear bolt resistance of the beam web:

Nw,Rd,1  2  nwb  Fv,wb,Rd

nwsp

number of web shear plane

nwb  2

number of web bolts

Bearing resistance of the beam web:

Nw,Rd,2  nwb  Fb,wb,Rd

Bearing resistance in “x” direction:

Fb,bw,Rd 

 bw  kbw  dwb  tbw  fu  M2

Bearing coefficient in the direction of load transfer:

 e1,bw  p1,bw 1   ;  ; 1  3  d0,wb 3  d0,wb 4   

 bw  min 

Bearing coefficient perpendicular to the direction of load transfer:

  p   kbw  min 1.4  2,bw  1.7 ; 2.5 d0,wb     tbw

thickness of the beam web.

dwb

diameter of the web bolts.

d0,wb

hole diameter of the web bolts.

© Edit by Simone Caffè: This material is copyright - all rights reserved

27

Connection Design

Bearing resistance of the web cover plates:

Nw,Rd,3  nwb  Fb,wcp,Rd

Bearing resistance in “x” direction:

Fb,wcp,Rd 

 wcp  kwcp  dwb   2  twcp   fu  M2

Bearing coefficient in the direction of load transfer:

 p1,wcp 1   e1,wcp  ;  ; 1  3  d0,wb 3  d0,wb 4   

 wcp  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e p   kwcp  min 2.8  2,wcp  1.7 ; 1.4  2,wcp  1.7 ; 2.5 d0,wb d0,wb    

twcp

thickness of a single web cover plate.

Cover plates in tension (gross section):

Nw,Rd,4 





hwcp  2  twcp  fy

 M0

Cover plates in tension (net section):

Nw,Rd,5 







0.9  hwcp  nb,v  d0,wb  2  twcp  fu

 M2

© Edit by Simone Caffè: This material is copyright - all rights reserved

28

Connection Design

Beam web in tension (net section):

Nw,Rd,6 

hwcp

hwcp  tbw  fy

 M0 height of the web cover plate (conservatively).

Beam web in tension (net section):

Nw,Rd,7 

hwcp





0.9  hwcp  nb,v  d0,wb  tbw  fu

 M2 height of the web cover plate (conservatively).

Cover plates in tension (Block tearing):

Nw,Rd,8 

 nt ,wcp A

 nt ,wcp  f A u

 M2



 nv,wcp  f A y 3   M0

net area subjected to tension:



 nt,wcp   n  1  p  A 2,wcp   nb,v  1  d0,wb   2  twcp  b,v

 nv,wcp A



net area subjected to shear:



 nv,wcp  2  e1,wcp   n  1  p  A b,h 1,wcp   nb,h  0.5   d0,wb   2  twcp  nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

© Edit by Simone Caffè: This material is copyright - all rights reserved



29

Connection Design

Beam web in tension (Block tearing):

Nw,Rd,9 

 nt ,bw A

 nt ,bw  f A u

 M2



 nv,bw  f A y 3   M0

net area subjected to tension:

 nt,bw   n  1  p  A 2,bw   nb,v  1  d0,wb   tbw  b,v

 nv,bw A

net area subjected to shear:

 nv,bw  2  e   n  1  p   n  0.5  d   t A b,h 1,bw b,h 0,wb  bw  1,bw

nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

Joint web resistance:

Nj ,w,Rd  minNw,Rd,1;...; Nw,Rd,9 

Joint resistance:

Nj ,Rd  2  Nj ,f ,Rd  Nj ,w,Rd

© Edit by Simone Caffè: This material is copyright - all rights reserved

30

Connection Design

SPLICE CONNECTION – N+M+V

Shear resistance per shear plane §Table 3.4:

 v  Afb  fub  Fv,fb,Rd     M2   0.75    1 L j  15  dfb  1.00  200  dfb 

 v  0.6  v  0.5

for classes 8.8

Afb

area of the flange bolts

Awb fub

area of the web bolts

 M2  1.25

safety factor

Fv,wb,Rd 

 v  Awb  fub  M2

for classes 10.9

ultimate tensile strength

Bolt resistance of the beam flange:

FRd,1  nfsp  nfb  Fv,fb,Rd nfsp

number of flange shear plane

nfb

number of flange bolts

© Edit by Simone Caffè: This material is copyright - all rights reserved

 nfsp  1 for a single cover plate   nfsp  2 for double cover plate

31

Connection Design

Bearing resistance of the beam flange:

FRd,2  nfb  Fb,bf ,Rd

Bearing resistance in “x” direction:

Fb,bf ,Rd 

 bf  kbf  dfb  tbf  fu  M2

Bearing coefficient in the direction of load transfer:

 e1,bf  p1,bf 1   ;  ; 1    3  d0,fb 3  d0,fb 4 

 bf  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e p   kbf  min 2.8  2,bf  1.7 ; 1.4  2,bf  1.7 ; 2.5 d0,fb d0,fb    

dfb

diameter of the flange bolt.

d0,fb

hole diameter of the flange bolt.

tbf

thickness of the beam flange.

© Edit by Simone Caffè: This material is copyright - all rights reserved

32

Connection Design

Bearing resistance of the flange cover plates:

FRd,3  nfb  Fb,fcp,Rd

Bearing resistance in “x” direction:

Fb,fcp,Rd 

 fcp  kfcp  dfb   nfsp  tfcp   fu  M2

Bearing coefficient in the direction of load transfer:

 p1,fcp 1   e1,fcp ;  ; 1  fcp  min   3  d0,fb 3  d0,fb 4     p1,fcp  p1,bf Bearing coefficient perpendicular to the direction of load transfer:

   e2,fcp,min p  1.7 ; 1.4  2,fcp  1.7 ; 2.5  kfcp  min 2.8  d0,fb d0,fb      p2,fcp  p2,bf  e2,fcp,min  min e2,fcp ; e2,fcp  



tfcp



thickness of a single flange cover plate.

Beam flange in tension (gross section):

FRd,4 

 bbf  tbf   fy  M0

bbf

flange width of the beam.

tbf

thickness of the beam flange.

© Edit by Simone Caffè: This material is copyright - all rights reserved

33

Connection Design

Beam flange in tension (net section):

FRd,5 

0.9   bbf  2  d0,fb   tbf  fu

 M2

Flange cover plates in tension (gross section):

FRd,6 

b



 tfcp  fy

fcp

for a single top flange cover plate

 M0

FRd,6  FRd,6 





2  bfcp  tfcp  fy

for double flange cover plate

 M0

bfcp

top flange cover plate width.

bfcp

bottom flange cover plate width.

Flange cover plates in tension (net section):

FRd,7 





0.9  bfcp  2  d0,fb  tfcp  fu

FRd,7  FRd,7 

for a single top flange cover plate

 M2





0.9  2  bfcp  2  d0,fb  tfcp  fu

 M2

bfcp

top flange cover plate width.

bfcp

bottom flange cover plate width.

© Edit by Simone Caffè: This material is copyright - all rights reserved

for double flange cover plate

34

Connection Design

Beam flange in tension (Block tearing):

FRd,8 

Ant ,bf  fu

 M2

Ant ,bf



Anv,bf  fy 3   M0

net area subjected to tension:

Ant,bf  2  e2,bf  d0,fb   tbf

Anv,bf

net area subjected to shear:

Anv,bf  2  e1,bf   nb,h  1  p1,bf   nb,h  0.5  d0,fb   tbf nb,h

number of bolts in a single horizontal line.

Flange cover plates in tension (Block tearing):

FRd,9 

Ant ,fcp  fu

 M2

FRd,9  FRd,9 



Anv,fcp  fy

Ant ,fcp  fu

 M2

for a single top flange cover plate

3   M0 

Anv,fcp  fy 3   M0

© Edit by Simone Caffè: This material is copyright - all rights reserved

for double flange cover plate

35

Connection Design

Ant ,fcp

net area subjected to tension:

Ant,fcp   p2,fcp  d0,fb   tfcp

Ant ,fcp  2  e2,fcp  d0,fb   tfcp   Anv,fcp

net area subjected to shear:

Anv,fcp  Anv,fcp  2  e1,fcp   nb,h  1  p1,fcp   nb,h  0.5  d0,fb   tfcp

Joint flange resistance:

Fj ,f ,Rd  minF1,Rd ;...; F9,Rd  Joint flange check:

Fbf ,Ed 

MEd b t  bf bf  NEd  Fj ,f ,Rd hb  tbf Ab

© Edit by Simone Caffè: This material is copyright - all rights reserved

36

Connection Design

Shear bolt resistance of the beam web:

2  Fv,wb,Rd

VRd,1 

2

 1    e x e y 1  x max     x max   Jb Jb  nwb   nwb  tan 

2

ex

eccentricity between the centroid of the bolts and the beam end.

nwb nwsp  2

number of web bolts. number of web shear plane.

Shear force in “y” direction per shear plane due to external shear:

VyV,Ed 

VEd nwsp  nwb

Shear force in “y” direction per shear plane due to torsion:

V  e   x VyT,Ed   Ed x  max nwsp  Jb Shear force in “x” direction per shear plane due to external in web axial force:

 N Nw,Ed VEd w , Ed Vx ,Ed   nwsp  nwb nwsp  nwb  tan   Ab  2  bbf  tbf   NEd Nw,Ed  A b       arctan  VEd    Nw,Ed  Shear force in “x” direction per shear plane due to torsion:

V  e   y VxT,Ed   Ed x  max nwsp  Jb Total shear force per shear plane due to shear, axial force and torsion:

 R  VEd   b n wsp   2  Jb   xi i 



2

2

 1    e x e y 1  x max     x max   Fv,Rd  Jb Jb  nwb   nwb  tan   yi2



© Edit by Simone Caffè: This material is copyright - all rights reserved

37

Connection Design

Shear bearing resistance of beam web §Table 3.4:

VRd,2 

1 ex  xmax  1 n  Jb  wb Fy ,b,bw,Rd   

2

ex  ymax   1   n  tan  Jb    wb Fx ,b,bw,Rd      

     

2

Bearing resistance in “x” direction:

Fx,b,bw,Rd 

 x,bw  kx,bw  dwb  tbw  fu  M2

Bearing coefficient in the direction of load transfer:

 p2,bw 1   e2,bw  ;  ; 1  3  d0,wb 3  d0,wb 4   

 x,bw  min 

Bearing coefficient perpendicular to the direction of load transfer:

  p   kx,bw  min 1.4  1,bw  1.7 ; 2.5 d0,wb     Bearing resistance in “y” direction:

Fy ,b,bw,Rd 

 y ,bw  ky ,bw  dwb  tbw  fu  M2

Bearing coefficient in the direction of load transfer:

 1   p1,bw   ; 1    3  d0,wb 4 

 y ,bw  min 

© Edit by Simone Caffè: This material is copyright - all rights reserved

38

Connection Design

Bearing coefficient perpendicular to the direction of load transfer:

  e p   ky ,bw  min 2.8  2,bw  1.7 ; 1.4  2,bw  1.7 ; 2.5 d0,wb d0,wb    

tbw

thickness of the beam web.

dwb

diameter of the web bolts.

d0,wb

hole diameter of the web bolts.

Shear bearing resistance of the web cover plates §Table 3.4:

VRd,3 

1 ex  xmax  1 n  Jb  wb  Fy ,b,wcp,Rd  

2

ex  ymax   1   n  tan  Jb    wb Fx ,b,wcp,Rd      

     

2

Bearing resistance in “x” direction:

Fx,b,wcp,Rd 

 x,wcp  kx,wcp  dwb   2  twcp   fu  M2

Bearing coefficient in the direction of load transfer:

 p2,wcp 1   e2,wcp  ;  ; 1  3  d0,wb 3  d0,wb 4   

 x,wcp  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e p   kx,wcp  min 2.8  1,wcp  1.7 ; 1.4  1,wcp  1.7 ; 2.5 d0,wb d0,wb     © Edit by Simone Caffè: This material is copyright - all rights reserved

39

Connection Design

Bearing resistance in “y” direction:

Fy ,b,wcp,Rd 

 y ,wcp  ky ,wcp  dwb   2  twcp   fu  M2

Bearing coefficient in the direction of load transfer:

 e1,wcp  p1,wcp 1   ;  ; 1    3  d0,wb 3  d0,wb 4 

 y ,wcp  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e p   ky ,wcp  min 2.8  2,wcp  1.7 ; 1.4  2,wcp  1.7 ; 2.5 d0,wb d0,wb    

twcp

thickness of a single web cover plate.

dwb

diameter of the web bolts.

d0,wb

hole diameter of the web bolts.

Cover plates in shear and tension (gross section): If VEd  0.5  Vpl ,Rd then:

Vw,Rd,4 

Nw,Rd,1 





hwcp  2  twcp  fy 1.27  3   M0





hwcp  2  twcp  fy

 M0

 VEd

 Nw,Ed 

Ab  2  bbf  tbf  NEd Ab

If VEd  0.5  Vpl ,Rd then:

Vw,Rd,4 





hwcp  2  twcp  fy 1.27  3   M0



 VEd



2 hwcp  2  twcp  fy   2  VEd   A  2  bbf  tbf Nw,Rd,1   1   1   Nw,Ed  b  NEd     Vpl ,Rd  M0 A b   

© Edit by Simone Caffè: This material is copyright - all rights reserved

40

Connection Design

Cover plates in shear and tension (net section): If VEd  0.5  Vpl ,Rd then:

Vw,Rd,5 

Nw,Rd,2 

h

wcp





 nb,v  d0  2  twcp  fu 3   M2





 VEd



0.9  hwcp  nb,v  d0  2  twcp  fu

 M2

 Nw,Ed

If VEd  0.5  Vpl ,Rd then:

Vw,Rd,5 

Nw,Rd,2

h

wcp





 nb,v  d0  2  twcp  fu 3   M2





 VEd



2 0.9  hwcp  nb,v  d0  2  twcp  fu   2  VEd     1   1   Nw,Ed     Vpl ,Rd  M2   

Beam web in shear and tension (net section): If VEd  0.5  Vpl ,Rd then:

Vw,Rd,6 

Nw,Rd,3 

hwcp  tbw  fy 1.27  3   M0 hwcp  tbw  fy

 M0

 VEd

 Nw,Ed

If VEd  0.5  Vpl ,Rd then:

Vw,Rd,6 

Nw,Rd,3

hwcp  tbw  fy 1.27  3   M0

 VEd

2 hwcp  tbw  fy   2  VEd     1   1   Nw,Ed     Vpl ,Rd  M0   

© Edit by Simone Caffè: This material is copyright - all rights reserved

41

Connection Design

Beam web in shear and tension (net section): If VEd  0.5  Vpl ,Rd then:

Vw,Rd,7 

Nw,Rd,4 

h



 nb,v  d0  tbw  fu

wcp

3   M2



 VEd



0.9  hwcp  nb,v  d0  tbw  fu

 M2

 Nw,Ed

If VEd  0.5  Vpl ,Rd then:

Vw,Rd,7 

Nw,Rd,4

h



 nb,v  d0  tbw  fu

wcp

3   M2



 VEd



2 0.9  hwcp  nb,v  d0  tbw  fu   2  VEd     1   1   Nw,Ed     Vpl ,Rd  M2   

Cover plates in shear and tension (block tearing):

If VEd  0.5  Vpl ,Rd then:

Vw,Rd,8 

Nw,Rd,5 

0.5  Ant ,wcp  fu

 M2  nt ,wcp  f A u

 M2





Anv,wcp  fy 3   M0

 nv,wcp  f A y 3   M0

 VEd

 Nw,Ed

© Edit by Simone Caffè: This material is copyright - all rights reserved

42

Connection Design

If VEd  0.5  Vpl ,Rd then:

Vw,Rd,8 

Nw,Rd,5

Ant ,wcp

0.5  Ant ,wcp  fu

 M2



Anv,wcp  fy 3   M0

 VEd

2   nv,wcp  f    2  V  nt ,wcp  f A A  y u Ed    1   Nw,Ed   1    3   M0    Vpl ,Rd   M2   

net area subjected to tension:



Ant,wcp  e2,wcp   nb,h  1  p2,wcp   nb,h  0.5  d0,wb   2  twcp Anv,wcp

net area subjected to shear:



Anv,wcp  hwcp  e1,wcp   nb,v  0.5  d0,wb   2  twcp  nt ,wcp A



net area subjected to tension:



 nt,wcp   n  1  p  A 1,wcp   nb,v  1  d0,wb   2  twcp  b,v

 nv,wcp A





net area subjected to shear:



 nv,wcp  2  e2,wcp   n  1  p  A b,h 2,wcp   nb,h  0.5   d0,wb   2  twcp  nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

Beam web in shear and tension (block tearing):

© Edit by Simone Caffè: This material is copyright - all rights reserved



43

Connection Design

If VEd  0.5  Vpl ,Rd then:

Vw,Rd,9 

Nw,Rd,6 

0.5  Ant ,bw  fu

 M2  nt ,bw  f A u

 M2





Anv,bw  fy 3   M0

 nv,bw  f A y 3   M0

 VEd

 Nw,Ed

If VEd  0.5  Vpl ,Rd then:

Vw,Rd,9 

Nw,Rd,6

Ant ,bw

0.5  Ant ,bw  fu

 M2



Anv,bw  fy 3   M0

 VEd

2  nv,bw  f    2  V  nt ,bw  f A A   y u Ed    1   Nw,Ed   1       V 3    M2   M0     pl ,Rd

net area subjected to tension:

Ant,bw  e2,bw   nb,h  1  p2,bw   nb,h  0.5  d0,wb   tbw Anv,bw

net area subjected to shear:

Anv,bw  e1,bw   nb,v  1  p1,bw   nb,v  0.5  d0,wb   tbw  nt ,bw A

net area subjected to tension:

 nt,bw   n  1  p   n  1  d   t A 1,bw b,v 0,wb  bw  b,v

 nv,bw A

net area subjected to shear:

 nv,bw  2  e  A  2,bw   nb,h  1  p2,bw   nb,h  0.5  d0,wb   tbw nb,h

number of bolts in a single horizontal line.

nb,v

number of bolts in a single vertical line.

© Edit by Simone Caffè: This material is copyright - all rights reserved

44

Connection Design

ANGLES CONNECTION – Type A

Shear resistance per shear plane §Table 3.4:

Fv,Rd 

 v  As  fub  M2

 v  0.6  v  0.5

for classes 8.8

As

area of the bolts

fub

ultimate tensile strength

 M2  1.25

safety factor

for classes 10.9

Shear bolt resistance §3.6.1:

NRd,1 

n  Fv,Rd 2

 1   ey  xmax       nb   Jb 

2

ey

eccentricity between the centroid of the bolts and the angle centroid.

nb

number of bolts.

n

number of shear plane: 

n  1 n  2

for a single angle for double angles

Shear force in “x” direction per shear plane due to external axial force:

VxN,Ed 

NEd n  nb

© Edit by Simone Caffè: This material is copyright - all rights reserved

45

Connection Design

Shear force in “y” direction per shear plane due to torsion:

 NEd  ey   xmax VyT,Ed   n  Jb Total shear force per shear plane due to axial force and torsion: 2

2

  1  e x N Rb  Ed      y max   Fv,Rd n  nb   Jb  Bolts polar moment calculated in the centroid of the bolts:

 

Jb   xi2 i

Bearing angle resistance:

NRd,2 

1 2

 1   ey  xmax  n   Jb  b    Fx ,b,Rd   Fy ,b,Rd      

     

2

Bearing resistance in “x” direction:

Fx,b,Rd 

 x  kx  d   n  ta   fu  M2

Bearing coefficient in the direction of load transfer:

 e1 p1 1  ;  ; 1  3  d0 3  d0 4 

 x  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e kx  min 2.8  2  1.7 ; 2.5 d0   ta

thickness of a single angle

n

number of shear plane: 

n  1 n  2

© Edit by Simone Caffè: This material is copyright - all rights reserved

for a single angle for double angles

46

Connection Design

Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d   n  ta   fu  M2

Bearing coefficient in the direction of load transfer:

 e2  ; 1  3  d0 

 y  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e p ky  min 2.8  1  1.7 ; 1.4  1  1.7 ; 2.5 d0 d0   ta

thickness of a single angle

n

number of shear plane: 

n  1 n  2

for a single angle for double angles

Bearing plate resistance:

NRd,3 

1 2

 1   ey  xmax  n   Jb  b    F x ,b,Rd   F y ,b,Rd      

     

2

Bearing resistance in “x” direction:

F x ,b,Rd 

 x  k x  d  tp  fu  M2

Bearing coefficient in the direction of load transfer:

 p1 1   e1  ;  ; 1   3  d0 3  d0 4  

 x  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e2,min   k x  min 2.8   1.7 ; 2.5 d0     © Edit by Simone Caffè: This material is copyright - all rights reserved

47

Connection Design

tp

thickness of the plate

Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d  tp  fu  M2

Bearing coefficient in the direction of load transfer:

 e2,min    ; 1  3  d0   

 y  min 

Bearing coefficient perpendicular to the direction of load transfer:

  p e1   ky  min 2.8   1.7 ; 1.4  1  1.7 ; 2.5 d0 d0    

tp

thickness of the plate

Single angle in tension (net section): Angle with one single bolt:

 ,4  NRd

2   e2  0.5  d0   ta  fu

 M2

Angle with two bolts:

 ,4  NRd

2   Aa  d0  ta   fu  M2

 2  0.4     2  0.7

p1  2.5  d0 p1  5.0  d0

Angle with three or more bolts:

 ,4  NRd

Aa

3   Aa  d0  ta   fu  M2

 3  0.5     3  0.7

area of a single angle

© Edit by Simone Caffè: This material is copyright - all rights reserved

p1  2.5  d0 p1  5.0  d0

48

Connection Design

Double angle in tension (net section):

NRd,4 

0.9  2   Aa  d0  ta    fu

 M2

Angle in tension (gross section):

NRd,5 

n  Aa  fy

 M0

n  1 n  n  2

for a single angle for double angles

Plate in tension (net section):

hp  2  p1   nb  1  tan  30 

NRd,6 

0.9  2  p1   nb  1  tan  30   d0   tp  fu

 M2

Plate in tension (gross section):

hp  2  p1   nb  1  tan  30 

2  p1   nb  1  tan  30   tp   fy NRd,7  

 M0

© Edit by Simone Caffè: This material is copyright - all rights reserved

49

Connection Design

Angle in shear and tension (block tearing):

NRd,8 

 nt A

 nt  f 0.5  A u

 M2



 nv  f A y 3   M0

net area subjected to tension:

 nt  n  e  d0   t A  2 2 a  

 nv A

net area subjected to shear:

 nv  n  e   n  1  p   n  0.5  d   t A b 1 b 0 a  1 Joint flange resistance:

Nj ,Rd  minNRd,1;...; NRd,8 

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50

Connection Design

ANGLES CONNECTION – Type B

Shear resistance per shear plane §Table 3.4:

Fv,Rd 

 v  As  fub  M2

 v  0.6  v  0.5

for classes 8.8

As

area of the bolts

fub

ultimate tensile strength

 M2  1.25

safety factor

for classes 10.9

Shear bolt resistance §3.6.1:

NRd,1 

na  Fv,Rd 2

 1   ey  xmax      nb,a   Jb,a

  

2

ey

eccentricity between the centroid of the bolts and the angle centroid.

nb,a

number of bolts “in a single angle”.

na

number of angles.

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51

Connection Design

Bearing angle resistance:

NRd,2 

na 2

 1   ey  xmax  n   Jb  b,a     Fx ,b,Rd   Fy ,b,Rd      

     

2

Bearing resistance in “x” direction:

Fx,b,Rd 

 x  kx  d  ta  fu  M2

Bearing coefficient in the direction of load transfer:

 e1 p1 1  ;  ; 1  3  d0 3  d0 4 

 x  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e kx  min 2.8  2  1.7 ; 2.5 d0   ta

thickness of a single angle

Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d  ta  fu  M2

Bearing coefficient in the direction of load transfer:

 e2  ; 1  3  d0 

 y  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e p ky  min 2.8  1  1.7 ; 1.4  1  1.7 ; 2.5 d0 d0   ta

thickness of a single angle

© Edit by Simone Caffè: This material is copyright - all rights reserved

52

Connection Design

Bearing plate resistance:

NRd,3 

na 2

 1   ey  xmax  n   Jb  b,a     F x ,b,Rd   F y ,b,Rd      

     

2

Bearing resistance in “x” direction:

F x ,b,Rd 

 x  k x  d  tp  fu  M2

Bearing coefficient in the direction of load transfer:

 e1  p1 1   ;  ; 1   3  d0 3  d0 4  

 x  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e2,min   k x  min 2.8   1.7 ; 2.5 d0    

tp

thickness of the plate

Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d  tp  fu  M2

Bearing coefficient in the direction of load transfer:

 e2,min    ; 1   3  d0  

 y  min 

Bearing coefficient perpendicular to the direction of load transfer:

  p e1   ky  min 2.8   1.7 ; 1.4  1  1.7 ; 2.5 d0 d0    

© Edit by Simone Caffè: This material is copyright - all rights reserved

53

Connection Design

Single angle in tension (net section): Angle with one single bolt:

 ,4  NRd

2   e2  0.5  d0   ta  fu

 M2

Angle with two bolts:

 ,4  NRd

 2  0.4     2  0.7

2   Aa  d0  ta   fu  M2

p1  2.5  d0 p1  5.0  d0

Angle with three or more bolts:

 ,4  NRd

  3  0.5    3  0.7

3   Aa  d0  ta   fu  M2

Aa

p1  2.5  d0 p1  5.0  d0

area of a single angle

Double angle in tension (net section):

NRd,4 

0.9  2   Aa  d0  ta    fu

 M2

Angle in tension (gross section):

NRd,5 

na  Aa  fy

 M0

Plate in tension (net section):

hp  2  p1   nb  1  tan  30 

NRd,6  na 

0.9  2  p1   nb  1  tan  30   d0   tp  fu

 M2

© Edit by Simone Caffè: This material is copyright - all rights reserved

54

Connection Design

Plate in tension (gross section):

hp  2  p1   nb  1  tan  30 

2  p1   nb  1  tan  30   tp   fy NRd,7  na  

 M0

Angle in shear and tension (block tearing):

 nv  f   nt  f  0.5  A A y u NRd,8  na      M2 3   M0  

 nt A

net area subjected to tension:

 nt  e  d0   t A  2 2 a  

 nv A

net area subjected to shear:

 nv  e   n  1  p   n  0.5  d   t A b 1 b 0 a  1 Joint flange resistance:

Nj ,Rd  minNRd,1;...; NRd,8 

© Edit by Simone Caffè: This material is copyright - all rights reserved

55

Connection Design

END PLATE CONNECTION

Shear resistance per shear plane §Table 3.4:

Fv,Rd 

 v  As  fub  M2

 v  0.6  v  0.5

for classes 8.8

As

area of the bolts

fub

ultimate tensile strength

 M2  1.25

safety factor

for classes 10.9

Tension resistance §Table 3.4:

Ft ,Rd 

0.9  As  fub

 M2

As

area of the bolts

fub

ultimate tensile strength

 M2  1.25

safety factor

Shear bolt resistance:

VRd,1  nb  Fv,Rd Tension bolt resistance:

NRd,1  nb  Ft,Rd © Edit by Simone Caffè: This material is copyright - all rights reserved

56

Connection Design

Bolt in shear and tension check:

VEd NEd   1.00 VRd,1 1.4  NRd,1

End plate in bearing:

VRd,2  nb  Fy ,b,Rd Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d  tp  fu  M2

Bearing coefficient in the direction of load transfer:

 e1 p1 1  ;  ; 1  3  d0 3  d0 4 

 y  min 

Bearing coefficient perpendicular to the direction of load transfer:

  e ky  min 2.8  2  1.7 ; 2.5 d0  

Supporting member in bearing:

VRd,3  nb  Fy ,b,Rd Bearing resistance in “y” direction:

Fy ,b,Rd 

 y  ky  d  tcf ,s  fu  M2

for column flange

tcf ,s : column flange thickness

Fy ,b,Rd 

 y  ky  d  tcw,s  fu  M2

for column web

tcw,s : column web thickness

Fy ,b,Rd 

 y  ky  d  tbw,s  fu  M2

for beam web

tbf ,s : supporting beam web thickness

Bearing coefficient in the direction of load transfer:

 p1 1   ; 1  3  d0 4 

 y  min 

© Edit by Simone Caffè: This material is copyright - all rights reserved

57

Connection Design

Bearing coefficient perpendicular to the direction of load transfer:

  e ky  min 2.8  2,c  1.7 ; 2.5 d0  

for column flange

  p ky  min 1.4  3  1.7 ; 2.5 d0  

for column web and beam web

End plate in shear (gross section):

VRd,4  2 

h

p



 tp  fy

1.27  3   M0

End plate in shear (net section):

VRd,5  2 

h

p



 d0  nb,v  tp  fu 3   M2

© Edit by Simone Caffè: This material is copyright - all rights reserved

58

Connection Design

End plate in shear (block shear):

 0.5  Ant  fu A f  VRd,6  2    nv y   M2 3   M0   Ant

net area subjected to tension:

d   Ant  e2  0   tp 2 

Anv

net area subjected to shear:

Anv  e1   nb,v  1  p1   nb,v  0.5  d0   tp End plate in bending (in plane):

VRd,7

 t  h2  2   p p   fy  6    s   M0

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59

Connection Design

Bending moment (in plane): Bending resistance:

MEd  0.5  VEd  s

MRd 

tp  hp2 6



fy

 M0

Supported beam in shear:

VRd,8  tbw

0.9  twb  hp  fy 3   M0 thickness of the supported beam

End plate in bending (out of plane):

NRd,2  min FT ,1,Rd ; FT ,2,Rd 

Geometry definition:

m

p3  tbw  2  0.8  ag  2 2

ag : throat thickness of the web fillet weld

n  mine2 ; e2,c ; 1.25  m Effective lengths for the end – plate:

Leff ,1  2    m  p1   2   nb,v  2   p1

 2   2  m  0.625  e2  0.5  p1    nb,v  2   p1 Leff ,2  min   2    m  p1   2   nb,v  2   p1 © Edit by Simone Caffè: This material is copyright - all rights reserved

60

Connection Design

Plastic moment for the end – plate:

Mpl ,1,Rd 

Mpl ,2,Rd 

0.25  Leff ,1  tp2  fy

 M0 0.25  Leff ,2  tp2  fy

 M0

Design resistance of a T – stub flange:

FT ,1,Rd  FT ,2,Rd 

4  Mpl,1,Rd m 2  Mpl ,2,Rd  n  NRd,1 m n

Beam web in tension:

NRd,3 

hp

tbw  hp  fy

 M0 height of the plate (conservatively).

Joint resistance:

Vpl,Rd

design plastic resistance of the beam

If VEd  0.5  Vpl ,Rd

If VEd  0.5  Vpl ,Rd

 Vj ,Rd  minVRd,1;; VRd,8   VEd  Nj ,Rd  minNRd,1;; NRd,3   NEd

then 

then

  Vj ,Rd  minVRd,1; ; VRd,8   VEd  Nj ,Rd  minNRd,1; ; NRd,3   1    NEd  2  2  VEd    1 §6.2.10 EC.3     Vpl ,Rd   End

© Edit by Simone Caffè: This material is copyright - all rights reserved

61

Connection Design

© Edit by Simone Caffè: This material is copyright - all rights reserved

62