Connection Design Joints resistance according to EC.3

Connection Design

Joints resistance according to EC.3 – 1 – 8

Edit by Dott. Ing. Simone Caffè

FIN PLATE CONNECTION

Shear resistance per shear plane §Table 3.4:

,

2 v s ub v Rd

M

F  A f



 





_v

 0.6 for classes 8.8



_v

 0.5 for classes 10.9 A

s

area of the bolts

f

ub

ultimate tensile strength



_M2

 1.25 safety factor

Shear bolt resistance §3.6.1:

,

,1 2 2

max max

1

v Rd

Rd Ed

x x

b b b

V F V

e x e y

n J J

 

     

 

   

   

e

x

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

n number of bolts.

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

,



V Ed

y Ed b

V V

n

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

 

 

 



^max

,

Ed x T

y Ed

b

V e x

V J

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

 

 

 



^max

,

Ed x T

x Ed

b

V e y

V J

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

     

        

   

2 2

max max

,

1

_{x x}

b Ed v Rd

b b b

e x e y

R V F

n J J

Bolts polar moment calculated in the centroid of the bolts:

 

 

²



²

b i i

i

J x y

Axial resistance for the bolts in shear §3.6.1:

Shear bearing resistance of beam web §Table 3.4:

,2 2 2

max max

, , , ,

1

Rd

1

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 Ed

N  n F   N

Bearing resistance in “y” direction:

, ,

2

y y bw u

y b Rd

M

k d t f

F 



   



Without notch Single notch Double notch

1 1

min ; 1

3 1 4

y pd

  ^  ^

  

 

1 1 1

min ; ; 1

3 0 3 0 4

e p

y d d

  ^    ^

1,min 1 1

min ; ; 1

3 0 3 0 4

e p

y d d



 

 

 

 

 

 

 

2 2

min 2.8 1.7 ; 1.4 1.7 ; 2.5

0 0

e p

ky d d

 

 

      

 

 



y

bearing coefficient in the direction of load transfer.

k

y

bearing coefficient perpendicular to the direction of load transfer.

e

1

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).

e

2

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).

p

1

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

p

2

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

d diameter of the fastener.

d

0

diameter of the hole.

t

bw

thickness of the beam web.

f

u

ultimate tensile strength Bearing resistance in “x” direction:

, ,

2

x x bw u

x b Rd

M

k d t f

F 



   



Without notch Single notch Double notch

2 2 1

min ; ; 1

3 0 3 0 4

e p

x d d

  ^    ^

min 1.4 1 1.7 ; 2.5 0

kx dp

 

 

 

  

 

 

1 1

min 2.8 1.7 ; 1.4 1.7 ; 2.5

0 0

e p

kx d d

 

 

      

 

 

1,min 1

min 2.8 1.7 ; 1.4 1.7 ; 2.5

0 0

e p

kx d d

 

 

 

    

 

 

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 J

V F F

Shear bearing resistance of fin plate §Table 3.4:

,3 2 2

max max

, , , ,

1

Rd

1

Ed

x x

b b b

y b Rd x b Rd

V V

e x e y

n J J

F F

 

 

    

   

    

   

   

   

Bearing resistance in “y” direction:

, ,

2 y

y p u

y b Rd

M

k d t f

F 



   



Bearing coefficient in the direction of load transfer:

  ^{ }       ^{ }   

1 1

0 0

min ; 1 ; 1

3 3 4

y

e p

d d

Bearing coefficient perpendicular to the direction of load transfer:

 

 

      

 

 

2 2

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5

y

e p

k d d

e

1

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).

e

2

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).

p

1

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

p

2

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

d diameter of the fastener.

d

0

diameter of the hole.

t

p

thickness of the fin plate.

Bearing resistance in “x” direction:

, ,

2

x x p u

x b Rd

M

k d t f

F 



   



Bearing coefficient in the direction of load transfer:

  ^{ }       ^{ }   

2 2

0 0

min ; 1 ; 1

3 3 4

x

e p

d d

Bearing coefficient perpendicular to the direction of load transfer:

 

 

      

 

 

1 1

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5

x

e p

k d d

Axial bearing resistance of beam web §Table 3.4:

,2 , ,

Rd b x b Rd Ed

N  n F   N

Axial bearing resistance of fin plate §Table 3.4:

,3 x b Rd, ,

Rd b Ed

N  n F   N

Beam web in shear (gross section):



  

,4

 3

0

v y

Rd Ed

M

V A f V

Without notch Single notch Double notch

 

^0.9

 

 ²   ^bw ^2b 

 

v b b bf bf

A A b t t r t A_v 0.9

 

A_b  2 b_bt_bf 



d_ntt_bf



t_bw

 

A_v 0.9

  

h d_b _ntd_nb



t_bw

 

A

b

cross – sectional area of the beam.

h

b

height of the beam.

b

b

flange width of the beam.

t

bf

thickness of the beam flange.

t

bw

thickness of the beam web.

d

nt

depth of the top notch.

d

nb

depth of the bottom notch.

Beam web in shear (net section):

, ,5

3

2 v net u

Rd Ed

M

A f

V V



  



Shear net area: A

_{v net,}

 A

_v

 n

_{b v,}

 t

_bw

 d

₀

,

n

b v

number of bolts in a single vertical line.

f

u

ultimate tensile strength.

Fin plate in shear (gross section):

,6

1.27 3

0

p p y

Rd Ed

M

h t f

V V



   

 

h

p

height of the fin plate.

t

p

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.

Fin plate in shear (net section):



, 0



,7

3

2

p b v p u

Rd Ed

M

h n d t f

V V



   

 



h

p

height of the fin plate.

t

p

thickness 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 h f W f

V V

e  e 

  

  

    

  

 

,

W

el p

elastic fin plate modulus.

Beam web in bending:

, ,9

0 el b y

Rd Ed

n M

W f

V V

e 

  



Without notch Single notch Double notch

,

Wel b

W_{el b, ,min}

of the “T” shape

²

, 6

bw nt nb

el b

t h d d W     

e

n

eccentricity between the shear force and the notch end.

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 f

V V

 

  

  



,

A

nt p

net area subjected to tension:

   

0

, 2

, 2 , 2 , 0

2

1 0.5

nt p p

nt p b h b h p

A e d t

A e n p n d t

  

  

  

 

             



for a single vertical line of bolts

for more than one vertical line of bolts

,

A

nv p

net area subjected to shear:

 

, 1 ,

0.5

0

nv p p b v p

A    h  e  n   d    t

,

n

b h

number of bolts in a single horizontal line.

,

n

b v

number of bolts in a single vertical line.

Beam web in shear (Block tearing):

, , ,11

2 0

0.5

3

nv b y nt b u

Rd Ed

M M

A f A f

V V

 

  

  



,

A

nt p

net area subjected to tension:

   

0

, 2

, 2 , 2 , 0

2

1 0.5

nt b bw

nt b b h b h bw

A e d t

A e n p n d t

  

  

  

 

             



for a single vertical line of bolts

for more than one vertical line of bolts

,

A

nv b

net area subjected to shear:

Without notch Single notch Double notch

   

1 , 1 , 0

, _{b v} 1 _{b v} 0.5

nv b bw

A en   p n  dt A_{nv b}, e1



n_{b v},   1

 

p1 n_{b v}, 0.5



d0t_bw A_{nv b}, e1,min



n_{b v},   1

 

p1 n_{b v}, 0.5



d0t_bw

Fin plate in tension (Block tearing):

 

_,

, ,4

2 0

0.5

3

nt p u nv p y

Rd Ed

M M

A f A f

N N

 

  

  





_{nt p,}

A net area subjected to tension:



nt p^,



b v,

1 

1



b v,

1 

0 p

A    n   p  n   d    t



_{nv p,}

A net area subjected to shear:



    

, 2 0

, 2 , 2 , 0

2 2

2 1 0.5

nv p p

nv p b h b h p

A e d t

A e n p n d t

      

  

  

            

  



for a single vertical line of bolts

for more than one vertical line of bolts

,

n

b h

number of bolts in a single horizontal line.

,

n

b v

number of bolts in a single vertical line.

Beam web in tension (Block tearing):



_,



_,

,5

2 0

0.5

3

nt b u nv b y

Rd Ed

M M

A f A f

N N

 

  

  





_{nt b,}

A net area subjected to tension:



nt b^,



b v,

1 

1



b v,

1 

0 bw

A    n   p  n   d    t



_{nv b,}

A net area subjected to shear:



    

, 2 0

, 2 , 2 , 0

2 2

2 1 0.5

nv b bw

nv b b h b h bw

A e d t

A e n p n d t

  

   

  

 

              



for a single vertical line of bolts

for more than one vertical line of bolts

,

n

b h

number of bolts in a single horizontal line.

,

n

b v

number of bolts in a single vertical line.

Fin plate in tension (net section):



, 0



,6

2

0.9

_{p b v p u}

Rd Ed

M

h n d t f

N N



    

 

Beam web in tension (net section):



, 0



,7

2

0.9

_{p b v bw u}

Rd Ed

M

h n d t f

N N



    

 

h

p

height of the fin plate (conservatively).

Joint resistance:

, pl Rd

V design plastic resistance of the beam

If V

_Ed

 0.5  V

_{pl Rd,}

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 V

_Ed

 0.5  V

_{pl Rd,}

then

   

 

   

2

§6.2.10

2 2

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

, ,4 ,11

, ,4

EC.3 ,

,7

min ; ; min ; ; 1.00

min ; ;

mi

2 1

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

Shear resistance per shear plane §Table 3.4:

,

2 v s ub v Rd

M

F  A f



 





_v

 0.6 for classes 8.8



_v

 0.5 for classes 10.9 A

s

Area of the bolts

f

ub

Ultimate tensile strength



_M2

 1.25 Safety factor

Shear bolt resistance §3.6.1:

,

,1 2 2

max max

1

v Rd

Rd Ed

x x

b b b

V n F V

e x e y

n J J

  

     

 

   

   

e

x

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

n

b

number of bolts.

2

n  number of shear plane.

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

,

V Ed

y Ed

b

V V

 n n



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

max ,

Ed x T

y Ed

b

V e x

V n J

 

 

 

 

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

max ,

Ed x T

x Ed

b

V e y

V n J

 

 

 

 

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

2 2

max max

,

Ed

1

x x

b v Rd

b b b

V e x e y

R F

n n J J

     

        

   

Bolts polar moment calculated in the centroid of the bolts:

 

 

²



²

b i i

i

J x y

Axial resistance for the bolts in shear §3.6.1:

Shear bearing resistance of beam web §Table 3.4:

,2 2 2

max max

, , , ,

1

Rd

1

Ed

x x

b b b

y b Rd x b Rd

V V

e x e y

n J J

F F

 

 

    

   

    

   

   

   

Bearing resistance in “y” direction:

, ,

2

y y bw u

y b Rd

M

k d t f

F 



   



,1 ,

Rd b v Rd Ed

N   n n F   N

Bearing coefficients

1 1

min ; 1

3 1 4 p

y d

  ^  ^

  

 

2 2

min 2.8 1.7 ; 1.4 1.7 ; 2.5

0 0

e p

ky d d

 

 

      

 

 



y

bearing coefficient in the direction of load transfer.

k

y

bearing coefficient perpendicular to the direction of load transfer.

e

1

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).

e

2

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).

p

1

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

p

2

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

d diameter of the fastener.

d

0

diameter of the hole.

t

bw

thickness of the beam web.

f

u

ultimate tensile strength Bearing resistance in “x” direction:

, ,

2

x x bw u

x b Rd

M

k d t f

F 



   



Bearing coefficients

2 2 1

min ; ; 1

3 0 3 0 4

e p

x d d

  ^    ^

min 1.4 1 1.7 ; 2.5 0

kx dp

 

 

 

  

 

 

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 n

n n n J n J

V F F

         

  

              

   

      

   

   

   

Shear bearing resistance of cover plates §Table 3.4:

,3 2 2

max max

, , , ,

1

Rd

1

Ed

x x

b b b

y b Rd x b Rd

V V

e x e y

n J J

F F

 

 

    

   

    

   

   

   

Bearing resistance in “y” direction:

 

, ,

2

2

y y p u

y b Rd

M

k d t f

F 



    



Bearing coefficient in the direction of load transfer:

  ^{ }       ^{ }   

1 1

0 0

min ; 1 ; 1

3 3 4

y

e p

d d

Bearing coefficient perpendicular to the direction of load transfer:

 

 

      

 

 

2 2

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5

y

e p

k d d

e

1

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).

e

2

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).

p

1

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

p

2

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

d diameter of the fastener.

d

0

diameter of the hole.

t

p

thickness of a single plate.

Bearing resistance in “x” direction:

 

, ,

2

2

x

x p u

x b Rd

M

k d t f

F 



    



Bearing coefficient in the direction of load transfer:

  ^{ }       ^{ }   

2 2

0 0

min ; 1 ; 1

3 3 4

x

e p

d d

Bearing coefficient perpendicular to the direction of load transfer:

 

 

      

 

 

1 1

0 0

min 2.8 1.7 ; 1.4 1.7 ; 2.5

x

e p

k d d

Axial bearing resistance of beam web §Table 3.4:

,2 , ,

Rd b x b Rd Ed

N  n F   N

Axial bearing resistance of cover plates §Table 3.4:

,3 x b Rd, ,

Rd b Ed

N  n F   N

Beam web in shear (gross section) :

,4

0

0.9 3

v y

Rd Ed

M

V A f V



 

 



 

2 2

v b b bf bw b bf

A  A   b t   t   r  t

A

b

cross – sectional area of the beam.

h

b

height of the beam.

b

b

flange width of the beam.

t

bf

thickness of the beam flange.

t

bw

thickness of the beam web.

Beam web in shear (net section):

, ,5

3

2 v net u

Rd Ed

M

A f

V V



  



Shear net area: A

_{v net,}

 A

_v

 n

_{b v,}

 t

_bw

 d

₀

,

n

b v

number of bolts in a single vertical line.

f

u

ultimate tensile strength Cover plates in shear (gross section):

 

,6

0

2 1.27 3

p p y

Rd Ed

M

h t f

V V



  

 

 

h

p

height of the double plate.

t

p

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):



, 0

  

,7

2

2 3

p b v p u

Rd Ed

M

h n d t f

V V



    

 



h

p

height of the double plate.

t

p

thickness of a single 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 f

V V

 

  

  



,

A

nt p

net area subjected to tension:

 

     

, 2 0

, 2 , 2 , 0

2 2

1 0.5 2

nt p p

nt p b h b h p

A e d t

A e n p n d t

  

   

  

 

              



for a single vertical line of bolts

for more than one vertical line of bolts

,

A

nv p

net area subjected to shear:

   

, 1 ,

0.5

0

2

nv p p b v p

A    h  e  n   d     t

,

n

b h

number of bolts in a single horizontal line.

,

n

b v

number of bolts in a single vertical line.

Beam web in shear (Block tearing):

, , ,9

2 0

0.5

3

nv b y nt b u

Rd Ed

M M

A f A f

V V

 

  

  



,

A

nt p

net area subjected to tension:

   

, 2 0

, 2 , 2 , 0

2

1 0.5

nt b bw

nt b b h b h bw

A e d t

A e n p n d t

     

  

 

             



for a single vertical line of bolts

for more than one vertical line of bolts

,

A

nv b

net area subjected to shear:

   

, 1 ,

1

1 ,

0.5

0

nv b b v b v bw

A    e  n   p  n   d    t

Cover plates in tension (Block tearing):

 

_,

, ,4

2 0

0.5

3

nt p u nv p y

Rd Ed

M M

A f A f

N N

 

  

  





_{nt p,}

A net area subjected to tension:



nt p^,



b v,

1 

1



b v,

1 

0

 2

p



A    n   p  n   d     t



_{nv p,}

A net area subjected to shear:

  

      

, 2 0

, 2 , 2 , 0

2 2

2

2 1 0.5 2

nv p p

nv p b h b h p

A e d t

A e n p n d t

       

  

  

             

  



for a single vertical line of bolts

for more than one vertical line of bolts

,

n

b h

number of bolts in a single horizontal line.

,

n

b v

number of bolts in a single vertical line.

Beam web in tension (Block tearing):

 

_,

, ,5

2 0

0.5

3

nt b u nv b y

Rd Ed

M M

A f A f

N N

 

  

  





_{nt b,}

A net area subjected to tension:



nt b^,



b v,

1 

1



b v,

1 

0 bw

A    n   p  n   d    t



_{nv b,}

A net area subjected to shear:



    

, 2 0

, 2 , 2 , 0

2 2

2 1 0.5

nv b bw

nv b b h b h bw

A e d t

A e n p n d t

  

   

  

 

              



for a single vertical line of bolts

for more than one vertical line of bolts

,

n

b h

number of bolts in a single horizontal line.

,

n

b v

number of bolts in a single vertical line.

Cover plates in tension (net section):



, 0

  

,6

2

0.9

_{p b v}

2

_{p u}

Rd Ed

M

h n d t f

N N



     

 

Beam web in tension (net section):



, 0



,7

2

0.9

_{p b v bw u}

Rd Ed

M

h n d t f

N N



    

 

h

p

height of double plate (conservatively).

Joint resistance:

, pl Rd

V design plastic resistance of the beam

If V

_Ed

 0.5  V

_{pl Rd,}

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 V

_Ed

 0.5  V

_{pl Rd,}

then

   

 

   

2 2

,1 ,2 ,3 ,1 ,2

2

§6.2.10 EC.3

,3

, ,4 ,9

, ,7

,

,4

min ; ; min ; ; 1.00

min ; ;

min ; ; 1

2 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



 

 

 

 

   

 

  

   

   

 

   

   

   





 





 





SPLICE CONNECTION – Bracing

Shear resistance per shear plane §Table 3.4:

, ,

2

0.75 1 15 1.00

200

v fb ub v fb Rd

M

j fb

fb

F A f

L d

d

 





 

  

 

  

    

 



_{, ,}

2

v wb ub

v wb Rd

M

A f

F 



 



v

0.6

  for classes 8.8



_v

 0.5 for classes 10.9

A

fb

area of the flange bolts A

wb

area of the web bolts f

ub

ultimate tensile strength



_M2

 1.25 safety factor

Bolt resistance of the beam flange:

, ,1 , ,

f Rd fsp fb v fb Rd

N  n  n F 

n

fsp

number of flange shear plane 1 for a single cover plate 2 for double cover plate

fsp fsp

n n

 

 



n

fb

number of flange bolts

Bearing resistance of the beam flange:

, ,2 , ,

f Rd fb b bf Rd

N  n F 

Bearing resistance in “x” direction:

, ,

2

bf bf fb bf u b bf Rd

M

k d t f

F 



   



Bearing coefficient in the direction of load transfer:

1, 1,

0, 0,

min ; 1 ; 1

3 3 4

bf bf

bf

fb fb

e p

d d

  ^{ }       ^{ }   

Bearing coefficient perpendicular to the direction of load transfer:

2, 2,

0, 0,

min 2.8

^bf

1.7 ; 1.4

^bf

1.7 ; 2.5

bf

fb fb

e p

k d d

 

 

      

 

 

d

fb

diameter of the flange bolt.

d

0,fb

hole diameter of the flange bolt.

t

bf

thickness of the beam flange.

Bearing resistance of the flange cover plates:

, ,3 , ,

f Rd fb b fcp Rd

N  n F 

Bearing resistance in “x” direction:

 

, ,

2

fcp fcp fb fsp fcp u

b fcp Rd

M

k d n t f

F 



    



Bearing coefficient in the direction of load transfer:

1, 1,

0, 0,

1, 1,

min ; 1 ; 1

3 3 4

fcp fcp

fcp

fb fb

fcp bf

e p

d d

p p

       

      

  

 



Bearing coefficient perpendicular to the direction of load transfer:

 

2, ,min 2,

0, 0,

2, 2,

2, ,min 2, 2,

min 2.8 1.7 ; 1.4 1.7 ; 2.5

min ; e

fcp fcp

fcp

fb fb

fcp bf

fcp fcp fcp

e p

k d d

p p

e e

         

  

 

  

 

 

 

 

t

fcp

thickness of a single flange cover plate.

Beam flange in tension (gross section):

 

, ,4

0 bf bf y f Rd

M

b t f

N 

 



b

bf

flange width of the beam.

t

bf

thickness of the beam flange.

Beam flange in tension (net section):



0,



, ,5

2

0.9

_bf

2

_{fb bf u}

f Rd

M

b d t f

N 

    



Flange cover plates in tension (gross section):

 

, ,6

0 fcp fcp y f Rd

M

b t f

N 

 

 for a single top flange cover plate

 

, ,6 , ,6

0

2

fcp fcp y f Rd f Rd

M

b t f

N N



  

  for double flange cover plate

b

fcp

top flange cover plate width.

b

fcp

bottom flange cover plate width.

Flange cover plates in tension (net section):



0,



, ,7

2

0.9

_fcp

2

_{fb fcp u}

f Rd

M

b d t f

N 

    

 for a single top flange cover plate



^0,



, ,7 , ,7

2

0.9 2

fcp

2

fb fcp u f Rd f Rd

M

b d t f

N N



     

  for double flange cover plate

b

fcp

top flange cover plate width.

b

fcp

bottom flange cover plate width.

Beam flange in tension (Block tearing):

 

_,

, , ,8

2

3

0

nv bf

nt bf u y

f Rd

M M

A f

A f

N  

 

 



Net area subjected to tension:



_,

2, 0,

2

nt bf bf fb bf

A     e  d    t

Net area subjected to shear:



nv bf^,

2

1,bf



b h,

1 

1,bf



b h,

0.5 

0,fb bf

A     e  n   p  n   d    t

,

n

b h

number of bolts in a single horizontal line.

Flange cover plates in tension (Block tearing):

 

_,

, , ,9

2

3

0

nv fcp

nt fcp u y

f Rd

M M

A f

A f

N  

 

 

 for a single top flange cover plate

, ,

, ,9 , ,9

2

3

0

nv fcp

nt fcp u y

f Rd f Rd

M M

A f

A f

N N

 

 

  

 for double flange cover plate



_{nt fcp,}

A net area subjected to tension:

Net area subjected to tension:



_,

2, 0,

nt fcp fcp fb fcp

A    p  d    t

,

2

2, 0,

nt fcp fcp fb fcp

A     e  d    t

Net area subjected to shear:



nv fcp^, nv fcp^,

2

1,fcp



b h,

1 

1,fcp



b h,

0.5 

0,fb fcp

A  A     e  n   p  n   d    t

Joint flange resistance:

 

, ,

min

, ,1

;...;

, ,9

j f Rd f Rd f Rd

N  N N

Shear bolt resistance of the beam web:

, ,1

2

, ,

w Rd wb v wb Rd

N   n  F

n

wsp

number of web shear plane

wb

2

n  number of web bolts

Bearing resistance of the beam web:

, ,2 , ,

w Rd wb b wb Rd

N  n  F

Bearing resistance in “x” direction:

, ,

2

bw bw wb bw u

b bw Rd

M

k d t f

F 



   



Bearing coefficient in the direction of load transfer:

1, 1,

0, 0,

min ; 1 ; 1

3 3 4

bw bw

bw

wb wb

e p

d d

  ^{ }       ^{ }   

Bearing coefficient perpendicular to the direction of load transfer:

2, 0,

min 1.4

^bw

1.7 ; 2.5

bw

wb

k p

d

 

 

    

 

 

t

bw

thickness of the beam web.

d

wb

diameter of the web bolts.

d

0,wb

hole diameter of the web bolts.

Bearing resistance of the web cover plates:

, ,3 , ,

w Rd wb b wcp Rd

N  n  F

Bearing resistance in “x” direction:

 

, ,

2

wcp wcp wb

2

wcp u

b wcp Rd

M

k d t f

F 



    



Bearing coefficient in the direction of load transfer:

1, 1,

0, 0,

min ; 1 ; 1

3 3 4

wcp wcp

wcp

wb wb

e p

d d

  ^{ }       ^{ }   

Bearing coefficient perpendicular to the direction of load transfer:

2, 2,

0, 0,

min 2.8

^wcp

1.7 ; 1.4

^wcp

1.7 ; 2.5

wcp

wb wb

e p

k d d

 

 

      

 

 

t

wcp

thickness of a single web cover plate.

Cover plates in tension (gross section):

 

, ,4

0

wcp

2

wcp y

w Rd

M

h t f

N 

  



Cover plates in tension (net section):



, 0,

  

, ,5

2

0.9

_{wcp b v wb}

2

_{wcp u}

w Rd

M

h n d t f

N 

     



Beam web in tension (net section):

, ,6

0 wcp bw y w Rd

M

h t f

N 

 



h

wcp

height of the web cover plate (conservatively).

Beam web in tension (net section):



, 0,



, ,7

2

0.9

_{wcp b v wb bw u}

w Rd

M

h n d t f

N 

    



h

wcp

height of the web cover plate (conservatively).

Cover plates in tension (Block tearing):



_,



_,

, ,8

2

3

0

nv wcp

nt wcp u y

w Rd

M M

A f

A f

N  

 

 





_{nt wcp,}

A net area subjected to tension:



nt wcp^,



b v,

1 

2,wcp



b v,

1 

0,wb

 2

wcp



A    n   p  n   d     t



_{nv wcp,}

A net area subjected to shear:



nv wcp^,

2

^1,wcp



b h,

1 

1,wcp



b h,

0.5 

0,wb

 2

wcp



A     e  n   p  n   d     t

,

n

b h

number of bolts in a single horizontal line.

,

n

b v

number of bolts in a single vertical line.

Beam web in tension (Block tearing):



_,



_,

, ,9

2

3

0

nv bw

nt bw u y

w Rd

M M

A f

A f

N  

 

 





_{nt bw,}

A net area subjected to tension:



nt bw^,



b v,

1 

2,bw



b v,

1 

0,wb bw

A    n   p  n   d    t



_{nv bw,}

A net area subjected to shear:



nv bw^,

2

1,bw



b h,

1 

1,bw



b h,

0.5 

0,wb bw

A     e  n   p  n   d    t

,

n

b h

number of bolts in a single horizontal line.

,

n

b v

number of bolts in a single vertical line.

Joint web resistance:

 

, ,

min

, ,1

;...;

, ,9

j w Rd w Rd w Rd

N  N N

Joint resistance:

,

2

, , , ,

j Rd j f Rd j w Rd

N   N  N

SPLICE CONNECTION – N+M+V

Shear resistance per shear plane §Table 3.4:

, ,

2

0.75 1 15 1.00

200

v fb ub v fb Rd

M

j fb

fb

F A f

L d

d

 





 

  

 

  

    

 



_{, ,}

2

v wb ub

v wb Rd

M

A f

F 



 



v

0.6

  for classes 8.8



_v

 0.5 for classes 10.9

A

fb

area of the flange bolts A

wb

area of the web bolts f

ub

ultimate tensile strength



_M2

 1.25 safety factor

Bolt resistance of the beam flange:

,1 , ,

Rd fsp fb v fb Rd

F  n  n F 

n

fsp

number of flange shear plane 1 for a single cover plate 2 for double cover plate

fsp fsp

n n

 

 



n

fb

number of flange bolts