04 Acciaio Connection Design

Connection Design Joints resistance according to EC.3 1 8

Edit by Dott. Ing. Simone Caff

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

2 Connection Design

FIN PLATE CONNECTION

Shear resistance per shear plane Table 3.4:

,

2

v s ubv Rd

M

A fF

0.6v

for classes 8.8

0.5v

for classes 10.9

sA area of the bolts

ubf ultimate tensile strength

2

1.25M

safety factor

Shear bolt resistance 3.6.1:

,

,12 2

max max1

v Rd

Rd Ed

x x

b b b

FV V

e x e y

n J J

xe eccentricity between the centroid of the bolts and the supporting beam

web or supporting column flange.

bn number of bolts.


3 Connection Design

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

,

V Edy Ed

b

VV

n

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

max

,

Ed xT

y Ed

b

V e xV

J

Shear force in x direction per shear plane due to torsion:

max

,

Ed xT

x Ed

b

V e yV

J

Total shear force per shear plane due to shear and torsion:

2 2

max max,

1 x xb Ed v Rd

b b b

e x e yR V F

n J J

Bolts polar moment calculated in the centroid of the bolts:

2 2b i ii

J x y

Axial resistance for the bolts in shear 3.6.1:

Shear bearing resistance of beam web Table 3.4:

,22 2

max max

, , , ,

1

1Rd Ed

x x

b b b

y b Rd x b Rd

V V

e x e y

n J J

F F

,1 ,Rd b v Rd EdN n F N


4 Connection Design

Bearing resistance in y direction:

, ,

2

y y bw u

y b Rd

M

k d t fF

Without notch Single notch Double notch

11min ; 13 41

py d

11 1min ; ; 13 3 4

0 0

e p

y d d

11,min 1min ; ; 13 3 4

0 0

e p

y d d

2 2min 2.8 1.7 ; 1.4 1.7 ; 2.5

0 0

e pky d d

y bearing coefficient in the direction of load transfer.

yk bearing coefficient perpendicular to the direction of load transfer.

1e 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).

2e 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 EC3-1-8 : 2005).

1p spacing between centers of fasteners in a line in the direction of load transfer

(Figure 3.1 EC3-1-8 : 2005).

2p spacing measured perpendicular to load transfer direction between

adjacent line of fasteners (Figure 3.1 EC3-1-8 : 2005).

d diameter of the fastener.

0d diameter of the hole.

bwt thickness of the beam web.

uf ultimate tensile strength

Bearing resistance in x direction:

, ,

2

x x bw ux b Rd

M

k d t fF

Without notch Single notch Double notch

12 2min ; ; 13 3 4

0 0

e p

x d d

1min 1.4 1.7 ; 2.5

0

pk

x d

1 1min 2.8 1.7 ; 1.4 1.7 ; 2.50 0

e pkx d d

1,min 1min 2.8 1.7 ; 1.4 1.7 ; 2.50 0

e pk

x d d


5 Connection Design

Bearing check:

2 2

max max

, , , ,

1

1

x x

b b b

Ed

y b Rd x b Rd

e x e y

n J JV

F F

Shear bearing resistance of fin plate Table 3.4:

,32 2

max max

, , , ,

1

1Rd Ed

x x

b b b

y b Rd x b Rd

V V

e x e y

n J J

F F


, ,

2

yy p uy b Rd

M

k d t fF

Bearing coefficient in the direction of load transfer:

1 1

0 0

1min ; ; 1

3 3 4y

pe

d d

Bearing coefficient perpendicular to the direction of load transfer:

2 2

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5ype

kd d

1e 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).

2e 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 EC3-1-8 : 2005).


6 Connection Design


(Figure 3.1 EC3-1-8 : 2005).





pt thickness of the fin plate.


, ,

2

xx p ux b Rd

M

k d t fF


2 2

0 0

1min ; ; 1

3 3 4x

pe

d d


1 1

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5xpe

kd d

Axial bearing resistance of beam web Table 3.4:

,2 , ,Rd b x b Rd EdN n F N

Axial bearing resistance of fin plate Table 3.4:

, ,,3 x b RdRd b EdN n F N


7 Connection Design

Beam web in shear (gross section):

,4

03

v y

Rd Ed

M

A fV V

Without notch

Single notch

Double notch

0.9 2 2bw bv b b bf bfA A b t t r t 0.9 2 nt bfv b b bf bwA A b t d t t 0.9 b nt nbv bwA h d d t

bA cross sectional area of the beam.

bh height of the beam.

bb flange width of the beam.

bft thickness of the beam flange.


ntd depth of the top notch.

nbd depth of the bottom notch.

Beam web in shear (net section):

,

,5

23

v net u

Rd Ed

M

A fV V

Shear net area: , , 0v net v b v bw

A A n t d

,b vn number of bolts in a single vertical line.

uf ultimate tensile strength.

Fin plate in shear (gross section):

,6

01.27 3

p p y

Rd Ed

M

h t fV V

ph height of the fin plate.


The coefficient 1.27 takes in to account the redaction of shear resistance, due to the

presence of bending moment.


8 Connection Design

Fin plate in shear (net section):

, 0,7

23

p b v p u

Rd Ed

M

h n d t fV V

ph height of the fin plate.


Fin plate in bending:

2

,

,8

0 0

6

p p

y

el p y

Rd Ed

x M x M

t hf

W fV V

e e

,el pW elastic fin plate modulus.

Beam web in bending:

,

,9

0

el b y

Rd Ed

n M

W fV V

e

Without notch

Single notch

Double notch

,el bW , ,minel b

W of the T shape 2

, 6

bw nt nb

el b

t h d dW

ne eccentricity between the shear force and the notch end.


9 Connection Design

Fin plate in shear (Block tearing):

, ,

,10

2 0

0.5

3

nt p u nv p y

Rd Ed

M M

A f A fV V

,nt pA net area subjected to tension:

0, 2

, 2 , 2 , 0

2

1 0.5

nt p p

nt p b h b h p

dA e t

A e n p n d t

for a single vertical line of bolts

for more than one vertical line of bolts

,nv pA net area subjected to shear:

1, , 00.5nv p p b v pA h e n d t

,b hn number of bolts in a single horizontal line.


Beam web in shear (Block tearing):

,,

,11

2 0

0.5

3

nv b ynt b u

Rd Ed

M M

A fA fV V


0, 2

, 2 , 2 , 0

2

1 0.5

nt b bw

nt b b h b h bw

dA e t

A e n p n d t



,nv bA net area subjected to shear:

Without notch

Single notch

Double notch

1 , 1 , 0, 1 0.5b v b vnv b bwA e n p n d t 1 , 1 , 0, 1 0.5b v b vnv b bwA e n p n d t

1,min , 1 , 0, 1 0.5b v b vnv b bwA e n p n d t


10 Connection Design

Fin plate in tension (Block tearing):

,,

,4

2 0

0.5

3

nv pnt p yuRd Ed

M M

A fA fN N


, , 1 , 01 1nt p b v b v pA n p n d t


0, 2

, 2 , 2 , 0

22

2 1 0.5

nv p p

nv p b h b h p

dA e t

A e n p n d t





Beam web in tension (Block tearing):

,,

,5

2 0

0.5

3

nv bnt b yuRd Ed

M M

A fA fN N

,nt bA net area subjected to tension:

, , 1 , 01 1nt b b v b v bwA n p n d t


0, 2

, 2 , 2 , 0

22

2 1 0.5

nv b bw

nv b b h b h bw

dA e t

A e n p n d t





Fin plate in tension (net section):

, 0,6

2

0.9p b v p u

Rd Ed

M

h n d t fN N



Beam web in tension (net section):

, 0,7

2

0.9p b v bw u

Rd Ed

M

h n d t fN N

ph height of the fin plate (conservatively).

Joint resistance:

,pl RdV design plastic resistance of the beam

If ,

0.5Ed pl Rd

V V then

, ,1 ,11

, ,1 ,7

min ; ;

min ; ;

j Rd Rd Rd Ed

j Rd Rd Rd Ed

V V V V

N N N N

If ,

0.5Ed pl Rd

V V then

2

6.2.10

2 2

,1 ,2 ,3 ,1 ,2 ,3

, ,4 ,11

, ,4

EC.3

,

,7

1.00min ; ; min ; ;

min ; ;

mi

21

n ; ; 1

Ed Ed

Rd Rd Rd Rd Rd Rd

j Rd Rd R

Ed

d Ed

j Rd

pl

d

d

R

R

Rd Ed

V

V

N V

N N N V V V

V V V V

N N N N



WEB COVER PLATE CONNECTION


,

2

v s ubv Rd

M

A fF

0.6v

for classes 8.8

0.5v

for classes 10.9

sA Area of the bolts

ubf Ultimate tensile strength

2

1.25M

Safety factor


,

,12 2

max max1

v Rd

Rd Ed

x x

b b b

n FV V

e x e y

n J J

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

bn number of bolts.

2n number of shear plane.




,

V Edy Ed

b

VV

n n


max

,

Ed xT

y Ed

b

V e xV

n J


max

,

Ed xT

x Ed

b

V e yV

n J

Total shear force per shear plane due to shear and torsion:

2 2

max max,

1Ed x xb v Rd

b b b

V e x e yR F

n n J J


2 2b i ii

J x y

Axial resistance for the bolts in shear 3.6.1:


,22 2

max max

, , , ,

1

1Rd Ed

x x

b b b

y b Rd x b Rd

V V

e x e y

n J J

F F


, ,

2

y y bw u

y b Rd

M

k d t fF

,1 ,Rd b v Rd EdN n n F N



Bearing coefficients

11min ; 13 41

py d

2 2min 2.8 1.7 ; 1.4 1.7 ; 2.5

0 0

e pky d d

y bearing coefficient in the direction of load transfer.

yk bearing coefficient perpendicular to the direction of load transfer.

1e 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).

2e 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 EC3-1-8 : 2005).


(Figure 3.1 EC3-1-8 : 2005).








, ,

2

x x bw ux b Rd

M

k d t fF

Bearing coefficients

12 2min ; ; 13 3 4

0 0

e p

x d d

1min 1.4 1.7 ; 2.5

0

pk

x d



Bearing check:

2 2

max max

, , , ,

1

1

x x

b b b

Ed

y b Rd x b Rd

e x e yn n

n n n J n JV

F F

Shear bearing resistance of cover plates Table 3.4:

,32 2

max max

, , , ,

1

1Rd Ed

x x

b b b

y b Rd x b Rd

V V

e x e y

n J J

F F


, ,

2

2yy p uy b Rd

M

k d t fF


1 1

0 0

1min ; ; 1

3 3 4y

pe

d d


2 2

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5ype

kd d

1e 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).

2e 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 EC3-1-8 : 2005).




(Figure 3.1 EC3-1-8 : 2005).





pt thickness of a single plate.


, ,

2

2xx p ux b Rd

M

k d t fF


2 2

0 0

1min ; ; 1

3 3 4x

pe

d d


1 1

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5xpe

kd d

Axial bearing resistance of beam web Table 3.4:

,2 , ,Rd b x b Rd EdN n F N

Axial bearing resistance of cover plates Table 3.4:

, ,,3 x b RdRd b EdN n F N

Beam web in shear (gross section) :

,4

0

0.9

3

v y

Rd Ed

M

A fV V

2 2v b b bf bw b bfA A b t t r t



bA cross sectional area of the beam.

bh height of the beam.

bb flange width of the beam.



Beam web in shear (net section):

,

,5

23

v net u

Rd Ed

M

A fV V

Shear net area: , , 0v net v b v bw

A A n t d



Cover plates in shear (gross section):

,6

0

2

1.27 3

p p y

Rd Ed

M

h t fV V

ph height of the double 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):

, 0,7

2

2

3

p b v p u

Rd Ed

M

h n d t fV V

ph height of the double plate.


Cover plates in shear (Block tearing):

, ,

,8

2 0

0.5

3

nt p u nv p y

Rd Ed

M M

A f A fV V




0, 2

, 2 , 2 , 0

22

1 0.5 2

nt p p

nt p b h b h p

dA e t

A e n p n d t




1, , 00.5 2nv p p b v pA h e n d t



Beam web in shear (Block tearing):

,,

,9

2 0

0.5

3

nv b ynt b u

Rd Ed

M M

A fA fV V


0, 2

, 2 , 2 , 0

2

1 0.5

nt b bw

nt b b h b h bw

dA e t

A e n p n d t




, 1 , 1 , 01 0.5nv b b v b v bwA e n p n d t

Cover plates in tension (Block tearing):

,,

,4

2 0

0.5

3

nv pnt p yuRd Ed

M M

A fA fN N


, , 1 , 01 1 2nt p b v b v pA n p n d t




0, 2

, 2 , 2 , 0

2 22

2 1 0.5 2

nv p p

nv p b h b h p

dA e t

A e n p n d t






,,

,5

2 0

0.5

3

nv bnt b yuRd Ed

M M

A fA fN N

,nt bA net area subjected to tension:

, , 1 , 01 1nt b b v b v bwA n p n d t


0, 2

, 2 , 2 , 0

22

2 1 0.5

nv b bw

nv b b h b h bw

dA e t

A e n p n d t





Cover plates in tension (net section):

, 0,6

2

0.9 2p b v p u

Rd Ed

M

h n d t fN N


, 0,7

2

0.9p b v bw u

Rd Ed

M

h n d t fN N

ph height of double plate (conservatively).



Joint resistance:


If ,

0.5Ed pl Rd

V V then

, ,1 ,9

, ,1 ,7

min ; ;

min ; ;

j Rd Rd Rd Ed

j Rd Rd Rd Ed

V V V V

N N N N

If ,

0.5Ed pl Rd

V V then

2 2

,1 ,2 ,3 ,1 ,2

2

6.2.10 EC.3

,3

, ,4 ,9

, ,7

,

,4

1.00min ; ; min ; ;

min ; ;

min ; ; 1

21

Ed Ed

Rd Rd Rd Rd Rd Rd

j Rd Rd R

Ed

d Ed

j Rd

pl

d

d

R

R

Rd Ed

V

V

N V

N N N V V V

V V V V

N N N N



SPLICE CONNECTION Bracing


, ,

2

150.75 1 1.00

200

v fb ubv fb Rd

M

j fb

fb

A fF

L d

d

, ,

2

v wb ubv wb Rd

M

A fF

0.6v

for classes 8.8

0.5v

for classes 10.9

fbA area of the flange bolts

wbA area of the web bolts


2

1.25M

safety factor

Bolt resistance of the beam flange:

, ,1 , ,f Rd fsp fb v fb RdN n n F

fspn number of flange shear plane

1 for a single cover plate

2 for double cover plate

fsp

fsp

n

n

fbn number of flange bolts



Bearing resistance of the beam flange:

, ,2 , ,f Rd fb b bf RdN n F


, ,

2

bf bf fb bf ub bf Rd

M

k d t fF


1, 1,

0, 0,

1min ; ; 1

3 3 4

bf bf

bf

fb fb

e p

d d


2, 2,

0, 0,

min 2.8 1.7 ; 1.4 1.7 ; 2.5bf bfbf

fb fb

e pk

d d

fbd diameter of the flange bolt.

0,fbd hole diameter of the flange bolt.




Bearing resistance of the flange cover plates:

, ,3 , ,f Rd fb b fcp RdN n F


, ,

2

fcp fcp fb fsp fcp u

b fcp Rd

M

k d n t fF


1, 1,

0, 0,

1, 1,

1min ; ; 1

3 3 4

fcp fcp

fcp

fb fb

fcp bf

e p

d d

p p


2, ,min 2,

0, 0,

2, 2,

2,2, ,min 2,

min 2.8 1.7 ; 1.4 1.7 ; 2.5

min ; e

fcp fcp

fcp

fb fb

fcp bf

fcpfcp fcp

e pk

d d

p p

e e

fcpt thickness of a single flange cover plate.

Beam flange in tension (gross section):

, ,4

0

bf bf y

f Rd

M

b t fN

bfb flange width of the beam.




Beam flange in tension (net section):

0,, ,5

2

0.9 2bf fb bf u

f Rd

M

b d t fN

Flange cover plates in tension (gross section):

, ,6

0

fcp fcp y

f Rd

M

b t fN

for a single top flange cover plate

, ,6 , ,6

0

2 fcp fcp yf Rd f Rd

M

b t fN N

for double flange cover plate

fcpb top flange cover plate width.

fcpb bottom flange cover plate width.

Flange cover plates in tension (net section):

0,, ,7

2

0.9 2fcp fb fcp u

f Rd

M

b d t fN


0,, ,7 , ,7

2

0.9 2 2fcp fb fcp uf Rd f Rd

M

b d t fN N






Beam flange in tension (Block tearing):

,,

, ,8

2 03

nv bfnt bf yuf Rd

M M

A fA fN

Net area subjected to tension:

, 2, 0,2nt bf bf fb bfA e d t

Net area subjected to shear:

, 1, , 1, , 0,2 1 0.5nv bf bf b h bf b h fb bfA e n p n d t


Flange cover plates in tension (Block tearing):

,,

, ,9

2 03

nv fcpnt fcp yuf Rd

M M

A fA fN


,,, ,9 , ,9

2 03

nv fcpnt fcp yuf Rd f Rd

M M

A fA fN N


,nt fcpA net area subjected to tension:



Net area subjected to tension:

, 2, 0,nt fcp fcp fb fcpA p d t

, 2, 0,2nt fcp fcp fb fcpA e d t

Net area subjected to shear:

, , 1, , 1, , 0,2 1 0.5nv fcp nv fcp fcp b h fcp b h fb fcpA A e n p n d t

Joint flange resistance:

, , , ,1 , ,9min ;...;j f Rd f Rd f RdN N N



Shear bolt resistance of the beam web:

, ,1 , ,2

w Rd wb v wb RdN n F

wspn number of web shear plane

2wb

n number of web bolts

Bearing resistance of the beam web:

, ,2 , ,w Rd wb b wb RdN n F


, ,

2

bw bw wb bw ub bw Rd

M

k d t fF


1, 1,

0, 0,

1min ; ; 1

3 3 4

bw bw

bw

wb wb

e p

d d


2,

0,

min 1.4 1.7 ; 2.5bwbw

wb

pk

d


wbd diameter of the web bolts.

0,wbd hole diameter of the web bolts.



Bearing resistance of the web cover plates:

, ,3 , ,w Rd wb b wcp RdN n F


, ,

2

2wcp wcp wb wcp u

b wcp Rd

M

k d t fF


1, 1,

0, 0,

1min ; ; 1

3 3 4

wcp wcp

wcp

wb wb

e p

d d


2, 2,

0, 0,

min 2.8 1.7 ; 1.4 1.7 ; 2.5wcp wcp

wcp

wb wb

e pk

d d

wcpt thickness of a single web cover plate.

Cover plates in tension (gross section):

, ,4

0

2wcp wcp y

w Rd

M

h t fN

Cover plates in tension (net section):

, 0,, ,5

2

0.9 2wcp b v wb wcp u

w Rd

M

h n d t fN




, ,6

0

wcp bw y

w Rd

M

h t fN

wcph height of the web cover plate (conservatively).


, 0,, ,7

2

0.9wcp b v wb bw u

w Rd

M

h n d t fN

wcph height of the web cover plate (conservatively).

Cover plates in tension (Block tearing):

,,

, ,8

2 03

nv wcpnt wcp yuw Rd

M M

A fA fN

,nt wcpA net area subjected to tension:

, , 2, , 0,1 1 2nt wcp b v wcp b v wb wcpA n p n d t

,nv wcpA net area subjected to shear:

, 1, , 1, , 0,2 1 0.5 2nv wcp wcp b h wcp b h wb wcpA e n p n d t






,,

, ,9

2 03

nv bwnt bw yuw Rd

M M

A fA fN

,nt bwA net area subjected to tension:

, , 2, , 0,1 1nt bw b v bw b v wb bwA n p n d t

,nv bwA net area subjected to shear:

, 1, , 1, , 0,2 1 0.5nv bw bw b h bw b h wb bwA e n p n d t



Joint web resistance:

, , , ,1 , ,9min ;...;j w Rd w Rd w RdN N N

Joint resistance:

, , , , ,2

j Rd j f Rd j w RdN N N



SPLICE CONNECTION N+M+V


, ,

2

150.75 1 1.00

200

v fb ubv fb Rd

M

j fb

fb

A fF

L d

d

, ,

2

v wb ubv wb Rd

M

A fF

0.6v

for classes 8.8

0.5v

for classes 10.9

fbA area of the flange bolts

wbA area of the web bolts


2

1.25M

safety factor

Bolt resistance of the beam flange:

,1 , ,Rd fsp fb v fb RdF n n F

fspn number of flange shear plane

1 for a single cover plate

2 for double cover plate

fsp

fsp

n

n

fbn number of flange bolts



Bearing resistance of the beam flange:

,2 , ,Rd fb b bf RdF n F


, ,

2

bf bf fb bf ub bf Rd

M

k d t fF


1, 1,

0, 0,

1min ; ; 1

3 3 4

bf bf

bf

fb fb

e p

d d


2, 2,

0, 0,

min 2.8 1.7 ; 1.4 1.7 ; 2.5bf bfbf

fb fb

e pk

d d

fbd diameter of the flange bolt.

0,fbd hole diameter of the flange bolt.




Bearing resistance of the flange cover plates:

,3 , ,Rd fb b fcp RdF n F


, ,

2

fcp fcp fb fsp fcp u

b fcp Rd

M

k d n t fF


1, 1,

0, 0,

1, 1,

1min ; ; 1

3 3 4

fcp fcp

fcp

fb fb

fcp bf

e p

d d

p p


2, ,min 2,

0, 0,

2, 2,

2,2, ,min 2,

min 2.8 1.7 ; 1.4 1.7 ; 2.5

min ; e

fcp fcp

fcp

fb fb

fcp bf

fcpfcp fcp

e pk

d d

p p

e e

fcpt thickness of a single flange cover plate.

Beam flange in tension (gross section):

,4

0

bf bf y

Rd

M

b t fF

bfb flange width of the beam.




Beam flange in tension (net section):

0,,5

2

0.9 2bf fb bf u

Rd

M

b d t fF

Flange cover plates in tension (gross section):

,6

0

fcp fcp y

Rd

M

b t fF


,6 ,6

0

2 fcp fcp yRd Rd

M

b t fF F




Flange cover plates in tension (net section):

0,,7

2

0.9 2fcp fb fcp u

Rd

M

b d t fF


0,,7 ,7

2

0.9 2 2fcp fb fcp uRd Rd

M

b d t fF F






Beam flange in tension (Block tearing):

,,

,8

2 03

nv bf ynt bf u

Rd

M M

A fA fF

,nt bfA net area subjected to tension:

, 2, 0,2

nt bf bf fb bfA e d t

,nv bfA net area subjected to shear:

, 1, , 1, , 0,2 1 0.5nv bf bf b h bf b h fb bfA e n p n d t


Flange cover plates in tension (Block tearing):

, ,

,9

2 03

nt fcp u nv fcp y

Rd

M M

A f A fF


,,,9 ,9

2 03

nv fcpnt fcp yuRd Rd

M M

A fA fF F




,nt fcpA net area subjected to tension:

, 2, 0,nt fcp fcp fb fcpA p d t

, 2, 0,2nt fcp fcp fb fcpA e d t

,nv fcpA net area subjected to shear:

,, 1, , 1, , 0,2 1 0.5nv fcpnv fcp fcp b h fcp b h fb fcpA A e n p n d t


, , 1, 9,min ;...;j f Rd Rd RdF F F

Joint flange check:

, , ,Ed bf bf

bf Ed Ed j f Rd

b bf b

M b tF N F

h t A



Shear bolt resistance of the beam web:

, ,

,12 2

max max

2

1 1

tan

v wb Rd

Rd

x x

wb b wb b

FV

e x e y

n J n J

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

wbn number of web bolts.

2wsp

n number of web shear plane.


,

V Edy Ed

wsp wb

VV

n n


max

,

Ed xT

y Ed

wsp b

V e xV

n J

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

, ,

,

,

,

tan

2

arctan

w EdN w Ed Edx Ed

wsp wb wsp wb

b bf bfw Ed Ed

b

Ed

w Ed

N VV

n n n n

A b tN N

A

V

N


max

,

Ed xT

x Ed

wsp b

V e yV

n J

Total shear force per shear plane due to shear, axial force and torsion:

2 2

max max,

2 2

1 1

tanEd x x

b v Rd

wsp wb b wb b

b i ii

V e x e yR F

n n J n J

J x y




,22 2

max max

, , , , , ,

1

1 1

tan

Rd

x x

wb b wb b

y b bw Rd x b bw Rd

V

e x e y

n J n J

F F


, ,

, , ,

2

x bw x bw wb bw u

x b bw Rd

M

k d t fF


2, 2,

,

0, 0,

1min ; ; 1

3 3 4

bw bw

x bw

wb wb

e p

d d


1,

,

0,

min 1.4 1.7 ; 2.5bwx bw

wb

pk

d


, ,

, , ,

2

y bw y bw wb bw u

y b bw Rd

M

k d t fF


1,

,

0,

1min ; 1

3 4

bw

y bw

wb

p

d




2, 2,

,

0, 0,

min 2.8 1.7 ; 1.4 1.7 ; 2.5bw bwy bw

wb wb

e pk

d d




Shear bearing resistance of the web cover plates Table 3.4:

,32 2

max max

, , , , , ,

1

1 1

tan

Rd

x x

wb b wb b

y b wcp Rd x b wcp Rd

V

e x e y

n J n J

F F


, ,, , ,

2

2x wcp x wcp wb wcp u

x b wcp Rd

M

k d t fF


2, 2,

,

0, 0,

1min ; ; 1

3 3 4

wcp wcp

x wcp

wb wb

e p

d d


1, 1,

,

0, 0,

min 2.8 1.7 ; 1.4 1.7 ; 2.5wcp wcp

x wcp

wb wb

e pk

d d




, ,, , ,

2

2y wcp y wcp wb wcp u

y b wcp Rd

M

k d t fF


1, 1,

,

0, 0,

1min ; ; 1

3 3 4

wcp wcp

y wcp

wb wb

e p

d d


2, 2,

,

0, 0,

min 2.8 1.7 ; 1.4 1.7 ; 2.5wcp wcp

y wcp

wb wb

e pk

d d

wcpt thickness of a single web cover plate.



Cover plates in shear and tension (gross section):

If ,

0.5Ed pl Rd

V V then:

, ,4

0

2

1.27 3

wcp wcp y

w Rd Ed

M

h t fV V

, ,1 ,

0

22b bf bf

Ed

b

wcp wcp y

w Rd w Ed

M

A b tN

A

h t fN N

If ,

0.5Ed pl Rd

V V then:

, ,4

0

2

1.27 3

wcp wcp y

w Rd Ed

M

h t fV V

2

, ,1 ,

0 ,

22 21 1 b bf bf

Ed

b

wcp wcp y Edw Rd w Ed

M pl Rd

A b tN

A

h t f VN N

V



Cover plates in shear and tension (net section):

If ,

0.5Ed pl Rd

V V then:

, 0, ,5

2

2

3

wcp b v wcp u

w Rd Ed

M

h n d t fV V

, 0, ,2 ,

2

0.9 2wcp b v wcp u

w Rd w Ed

M

h n d t fN N

If ,

0.5Ed pl Rd

V V then:

, 0, ,5

2

2

3

wcp b v wcp u

w Rd Ed

M

h n d t fV V

2

, 0

, ,2 ,

2 ,

0.9 2 21 1

wcp b v wcp u Edw Rd w Ed

M pl Rd

h n d t f VN N

V

Beam web in shear and tension (net section):

If ,

0.5Ed pl Rd

V V then:

, ,6

01.27 3

wcp bw y

w Rd Ed

M

h t fV V

, ,3 ,

0

wcp bw y

w Rd w Ed

M

h t fN N

If ,

0.5Ed pl Rd

V V then:

, ,6

01.27 3

wcp bw y

w Rd Ed

M

h t fV V

2

, ,3 ,

0 ,

21 1

wcp bw y Edw Rd w Ed

M pl Rd

h t f VN N

V



Beam web in shear and tension (net section):

If ,

0.5Ed pl Rd

V V then:

, 0, ,7

23

wcp b v bw u

w Rd Ed

M

h n d t fV V

, 0, ,4 ,

2

0.9wcp b v bw u

w Rd w Ed

M

h n d t fN N

If ,

0.5Ed pl Rd

V V then:

, 0, ,7

23

wcp b v bw u

w Rd Ed

M

h n d t fV V

2

, 0

, ,4 ,

2 ,

0.9 21 1

wcp b v bw u Edw Rd w Ed

M pl Rd

h n d t f VN N

V

Cover plates in shear and tension (block tearing):

If ,

0.5Ed pl Rd

V V then:

, ,

, ,8

2 0

0.5

3

nt wcp u nv wcp y

w Rd Ed

M M

A f A fV V

,,

, ,5 ,

2 03

nv wcpnt wcp yuw Rd w Ed

M M

A fA fN N



If ,

0.5Ed pl Rd

V V then:

, ,

, ,8

2 0

0.5

3

nt wcp u nv wcp y

w Rd Ed

M M

A f A fV V

2,,

, ,5 ,

2 ,0

21 1

3

nv wcpnt wcp yu Edw Rd w Ed

M pl RdM

A fA f VN N

V


, 2, , 2, , 0,1 0.5 2nt wcp wcp b h wcp b h wb wcpA e n p n d t


, 1, , 0,0.5 2nv wcp wcp wcp b v wb wcpA h e n d t


, , 1, , 0,1 1 2nt wcp b v wcp b v wb wcpA n p n d t


, 2, , 2, , 0,2 1 0.5 2nv wcp wcp b h wcp b h wb wcpA e n p n d t



Beam web in shear and tension (block tearing):



If ,

0.5Ed pl Rd

V V then:

,,

, ,9

2 0

0.5

3

nv bw ynt bw u

w Rd Ed

M M

A fA fV V

,,

, ,6 ,

2 03

nv bwnt bw yuw Rd w Ed

M M

A fA fN N

If ,

0.5Ed pl Rd

V V then:

,,

, ,9

2 0

0.5

3

nv bw ynt bw u

w Rd Ed

M M

A fA fV V

2,,

, ,6 ,

2 ,0

21 1

3

nv bwnt bw yu Edw Rd w Ed

M pl RdM

A fA f VN N

V


, 2, , 2, , 0,1 0.5nt bw bw b h bw b h wb bwA e n p n d t


, 1, , 1, , 0,1 0.5nv bw bw b v bw b v wb bwA e n p n d t


, , 1, , 0,1 1nt bw b v bw b v wb bwA n p n d t


, 2, , 2, , 0,2 1 0.5nv bw bw b h bw b h wb bwA e n p n d t





ANGLES CONNECTION Type A


,

2

v s ubv Rd

M

A fF

0.6v

for classes 8.8

0.5v

for classes 10.9



2

1.25M

safety factor


,

,122

max1

v Rd

Rd

y

b b

n FN

e x

n J

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

bn number of bolts.

n number of shear plane: 1 for a single angle

2 for double angles

n

n

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

,

N Edx Ed

b

NV

n n




max

,

Ed yT

y Ed

b

N e xV

n J

Total shear force per shear plane due to axial force and torsion:

22

max

,

1 yEdb v Rd

b b

e xNR F

n n J


2b ii

J x

Bearing angle resistance:

,222

max

, , , ,

1

1Rd

y

b b

x b Rd y b Rd

N

e x

n J

F F


, ,

2

x x a u

x b Rd

M

k d n t fF


1 1

0 0

1min ; ; 1

3 3 4x

e p

d d


2

0

min 2.8 1.7 ; 2.5x

ek

d

at thickness of a single angle


2 for double angles

n

n




, ,

2

y y a u

y b Rd

M

k d n t fF


2

0

min ; 13

y

e

d


1 1

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5y

e pk

d d



2 for double angles

n

n

Bearing plate resistance:

,322

max

, , , ,

1

1Rd

y

b b

x b Rd y b Rd

N

e x

n J

F F


, ,

2

xx p ux b Rd

M

k d t fF


1 1

0 0

1min ; ; 1

3 3 4x

pe

d d


2,min

0

min 2.8 1.7 ; 2.5xe

kd



pt thickness of the plate


, ,

2

yy p uy b Rd

M

k d t fF


2,min

0

min ; 13

ye

d


1 1

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5ype

kd d


Single angle in tension (net section):

Angle with one single bolt:

2 0,4

2

2 0.5a u

Rd

M

e d t fN

Angle with two bolts:

2 0

,4

2

a a u

Rd

M

A d t fN

2 1 0

1 02

0.4 2.5

5.00.7

p d

p d

Angle with three or more bolts:

3 0

,4

2

a a u

Rd

M

A d t fN

3 1 0

1 03

0.5 2.5

5.00.7

p d

p d

aA area of a single angle



Double angle in tension (net section):

0,4

2

0.9 2a a u

Rd

M

A d t fN

Angle in tension (gross section):

,5

0

a y

Rd

M

n A fN

n 1 for a single angle

2 for double angles

n

n

Plate in tension (net section):

12 1 tan 30p bh p n

1 0,6

2

0.9 2 1 tan 30b p u

Rd

M

p n d t fN

Plate in tension (gross section):

12 1 tan 30p bh p n

1,7

0

2 1 tan 30b p y

Rd

M

p n t fN



Angle in shear and tension (block tearing):

,8

2 0

0.5

3

nvnt yuRd

M M

A fA fN

ntA net area subjected to tension:

02

2nt a

dA n e t

nvA net area subjected to shear: 1 1 01 0.5nv b b aA n e n p n d t


, ,1 ,8min ;...;j Rd Rd RdN N N



ANGLES CONNECTION Type B


,

2

v s ubv Rd

M

A fF

0.6v

for classes 8.8

0.5v

for classes 10.9



2

1.25M

safety factor


,

,12 2

max

, ,

1

a v Rd

Rd

y

b a b a

n FN

e x

n J

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

,b an number of bolts in a single angle.

an number of angles.



Bearing angle resistance:

,222

max

,

, , , ,

1

aRd

y

b a b

x b Rd y b Rd

nN

e x

n J

F F


, ,

2

x x a ux b Rd

M

k d t fF


1 1

0 0

1min ; ; 1

3 3 4x

e p

d d


2

0

min 2.8 1.7 ; 2.5x

ek

d



, ,

2

y y a u

y b Rd

M

k d t fF


2

0

min ; 13

y

e

d


1 1

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5y

e pk

d d




Bearing plate resistance:

,322

max

,

, , , ,

1

aRd

y

b a b

x b Rd y b Rd

nN

e x

n J

F F


, ,

2

xx p ux b Rd

M

k d t fF


1 1

0 0

1min ; ; 1

3 3 4x

pe

d d


2,min

0

min 2.8 1.7 ; 2.5xe

kd



, ,

2

yy p uy b Rd

M

k d t fF


2,min

0

min ; 13

ye

d


1 1

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5ype

kd d



Single angle in tension (net section):

Angle with one single bolt:

2 0,4

2

2 0.5a u

Rd

M

e d t fN

Angle with two bolts:

2 0

,4

2

a a u

Rd

M

A d t fN

2 1 0

1 02

0.4 2.5

5.00.7

p d

p d

Angle with three or more bolts:

3 0

,4

2

a a u

Rd

M

A d t fN

3 1 0

1 03

0.5 2.5

5.00.7

p d

p d

aA area of a single angle

Double angle in tension (net section):

0,4

2

0.9 2a a u

Rd

M

A d t fN

Angle in tension (gross section):

,5

0

a a y

Rd

M

n A fN

Plate in tension (net section):

12 1 tan 30p bh p n

1 0,6

2

0.9 2 1 tan 30b p u

Rd a

M

p n d t fN n



Plate in tension (gross section):

12 1 tan 30p bh p n

1,7

0

2 1 tan 30b p y

Rd a

M

p n t fN n

Angle in shear and tension (block tearing):

,8

2 0

0.5

3

nvnt yuRd a

M M

A fA fN n


02

2nt a

dA e t

nvA net area subjected to shear: 1 1 01 0.5nv b b aA e n p n d t


, ,1 ,8min ;...;j Rd Rd RdN N N



END PLATE CONNECTION


,

2

v s ubv Rd

M

A fF

0.6v

for classes 8.8

0.5v

for classes 10.9



2

1.25M

safety factor

Tension resistance Table 3.4:

,

2

0.9s ub

t Rd

M

A fF



2

1.25M

safety factor

Shear bolt resistance:

,1 ,Rd b v RdV n F

Tension bolt resistance:

,1 ,Rd b t RdN n F



Bolt in shear and tension check:

,1 ,1

1.001.4

Ed Ed

Rd Rd

V N

V N

End plate in bearing:

,2 , ,Rd b y b RdV n F


, ,

2

y y p u

y b Rd

M

k d t fF


1 1

0 0

1min ; ; 1

3 3 4y

e p

d d


2

0

min 2.8 1.7 ; 2.5y

ek

d

Supporting member in bearing:

, ,,3 y b RdRd bV n F


,, ,

2

yy cf s uy b Rd

M

k d t fF

for column flange

,cf st : column flange thickness

,, ,

2

yy cw s uy b Rd

M

k d t fF

for column web

,cw st : column web thickness

,, ,

2

yy bw s uy b Rd

M

k d t fF

for beam web

,bf st : supporting beam web thickness


1

0

1min ; 1

3 4y

p

d




2,

0

min 2.8 1.7 ; 2.5cye

kd

for column flange

3

0

min 1.4 1.7 ; 2.5yp

kd

for column web and beam web

End plate in shear (gross section):

,4

0

21.27 3

p p y

Rd

M

h t fV

End plate in shear (net section):

0 ,,5

2

23

p b v p u

Rd

M

h d n t fV



End plate in shear (block shear):

,6

2 0

0.52

3

nv ynt uRd

M M

A fA fV


02

2nt p

dA e t

nvA net area subjected to shear:

1 , 1 , 01 0.5nv b v b v pA e n p n d t

End plate in bending (in plane):

2

,7

0

26

p p

y

Rd

M

t hf

Vs



Bending moment (in plane): 0.5Ed Ed

M V s

Bending resistance:

2

06

p p y

Rd

M

t h fM

Supported beam in shear:

,8

0

0.9

3

wb p y

Rd

M

t h fV

bwt thickness of the supported beam

End plate in bending (out of plane):

,2 ,1, ,2,min ;

Rd T Rd T RdN F F

Geometry definition:

32 0.8 2

2

bw gp t a

m

g

a : throat thickness of the web fillet weld

2 2,min ; ; 1.25 mcn e e

Effective lengths for the end plate:

,1 1 , 12 2 2eff b vL m p n p

2 1 , 1

,2

1 , 1

2 2 0.625 0.5 2min

2 2 2

b v

eff

b v

m e p n pL

m p n p



Plastic moment for the end plate:

2

,1

,1,

0

0.25eff p y

pl Rd

M

L t fM

2

,2

,2,

0

0.25eff p y

pl Rd

M

L t fM

Design resistance of a T stub flange:

,1,

,1,

4pl Rd

T Rd

MF

m

,2, ,1

,2,

2pl Rd Rd

T Rd

M n NF

m n

Beam web in tension:

,3

0

bw p y

Rd

M

t h fN

ph height of the plate (conservatively).

Joint resistance:


If ,

0.5Ed pl Rd

V V then

, ,1 ,8

, ,1 ,3

min ; ;

min ; ;

j Rd Rd Rd Ed

j Rd Rd Rd Ed

V V V V

N N N N

If ,

0.5Ed pl Rd

V V then

, ,1 ,8

, ,1

2

6.2.10 EC.3

,3

,

min ; ;

min ; ; 1

21

j Rd Rd Rd Ed

j Rd Rd Rd Ed

Ed

pl Rd

V V V V

N N N N

V

V

End

Documents

04 Acciaio Connection Design