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English Pages 62
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.
© Edit by Simone Caffè: This material is copyright - all rights reserved
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 3d 0
3d 4 0
e p k min2.8 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 3d 3d 4 0 0
p k x min 1.4 1 1.7 ; 2.5 d 0
e p k min2.8 1 1.7 ; 1.4 1 1.7 ; 2.5 x d d 0 0
© Edit by Simone Caffè: This material is copyright - all rights reserved
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 2rb 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 hdnt 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 1p1 nb ,v 0.5d0 t bw
Anv ,b e1 nb ,v 1p1 nb ,v 0.5d0 t bw
Anv ,b e1,min nb ,v 1p1 nb ,v 0.5d0 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
© 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
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 minVRd,1;; VRd,11 VEd Nj ,Rd minNRd,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 minV ; ; V V j ,Rd Rd ,4 Rd ,11 Ed Nj ,Rd minNRd,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 n2
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
3d1 4
p 1 y min 1 ; 1 e p k min2.8 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
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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
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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 minVRd,1;; VRd,9 VEd Nj ,Rd minNRd,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 minV ; ; V V j ,Rd Rd ,4 Rd ,9 Ed Nj ,Rd minNRd,4 ; ; NRd,7 1 NEd 2 2 VEd 1 §6.2.10 EC.3 Vpl ,Rd
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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.
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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 minNf ,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 minNw,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 minF1,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 minNRd,1;...; NRd,8
© Edit by Simone Caffè: This material is copyright - all rights reserved
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.
© Edit by Simone Caffè: This material is copyright - all rights reserved
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 minNRd,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
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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
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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 mine2 ; 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 minVRd,1;; VRd,8 VEd Nj ,Rd minNRd,1;; NRd,3 NEd
then
then
Vj ,Rd minVRd,1; ; VRd,8 VEd Nj ,Rd minNRd,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