Bolted pinned plate

Calculation design shear resistance V_Rd for connection element

The design shear resistance V_Rd is given by

The bolt holes are not taken into account when

When Av.net is less than this limit, an effective shear area of A_v= (f_u/f_y) A_v.net may be assumed, else A_v=A.

with

fy	the yield strength of the element
γM0	the partial safety factor
A	h t n
W	n t h² / 6
N	the present normal force
a	x1
σN	the normal stress generated by normal force N
n	the number of plates
Av.net	the reduced shear area

Calculation design shear resistance V_Rd for beam

The design shear resistance V_Rd is given by :

The bolt holes are not taken into account when

When Av.net is less than this limit, an effective shear area of A_v1=(f_u/f_y) A_v.net may be assumed, else A_v1=A_v.

with

fy	the yield strength of the beam
γM0	the partial safety factor
n	the number of bolt in a section
Av	the shear area of the beam
Av.net	the reduced shear area of the beam element
fu	the ultimate tensile strength of the element

Calculation design shear resistance V_Rd for bolts in beam

The extreme bolt of the plate is submitted to the following forces (see Ref.[12] IW E1 and Ref. [13] p162-207):

Vertical forces :

Horizontal forces :

The resulting forces acting on this bolt is conditioning by F_v,Rd (See 11.3.1) and F_{b,RD,Plate and Beam}:

Considering that in the limit state V_Rd is acting, we get the following equation for V_Rd. The final V_Rd is taken as the minimum (in absolute value) of the roots of this equation:

with

a	the position (x direction) of bolt center with regard to underside of the plate
b	the position (y direction) of the bolt center with regard to underside of the plate
d	the maximum vertical distance between bolts and bolt center
c	the maximum horizontal distance between bolts and bolt center
e1	the end distance
p	the pitch
Ip	: the polar moment of inertia of the bolts with regard to the bolt center
n	the number of bolts
R	the shear force
N	the normal force
M	the moment: R a

Calculation design block shear resistance for beam element V_Rd

The design value of effective resistance to block shear is determined by using the following expression given by EN 1993-1-8 Article 3.10.2 (2):

with:

A_nt - the net area subjected to tension calculated as:

for a single vertical line of bolts:

for two vertical lines of bolts:

A_nv - the net area subjected to shear calculated as:

t_w - thickness of the beam web

e₂ - horizontal distance from the side bolt to the edge of beam

d₀ - borehole diameter

p₂ - horizontal space between the bolts

h_b - height of the beam

e₁ - vertical distance from the bottom of the beam to the bolt

n₁ - number of bolt-rows

Calculation design block shear resistance V_Rd in connection element (beam side)

The design value of effective resistance to block shear is determined by using the following expression given by EN 1993-1-8 Article 3.10.2 (2):

with:

A_nt - the net area subjected to tension calculated as:

for a single vertical line of bolts:

for two vertical lines of bolts:

A_nv - the net area subjected to shear calculated as:

t_p - thickness of the element

e₂ - horizontal distance from the side bolt to the element edge

d₀ - borehole diameter

p₂ - horizontal space between the bolts

h_p - height of the element

e₁ - vertical distance from the bottom of the element to the bolt

n₁ - number of bolt-rows

Calculation design compression/tension resistance N_Rd for connection element

The design compression N_Rd is given by  (see Ref.[2], 5.4.4.(1))

The design tension N_Rd is given by  (see Ref.[2], 5.4.3.(1))

with

fy	the yield strength of the element
fu	the ultimate tensile strength of the element
γM0	the partial safety factor
A	the area of the element (n h t)
Anet	the reduced area of the element
n	the number of plates

Calculation design compression/tension resistance N_Rd for beam

The design compression resistance N_Rd is given by  (see Ref.[2], 5.4.4.(1))

The design tension N_Rd is given by  (see Ref.[2], 5.4.3.(1))

with

fy	the yield strength of the beam
fu	the ultimate tensile strength of the beam
γM0	the partial safety factor
A	the area of the beam
Anet	the reduced area of the beam

Calculation design compression resistance N_Rd for column web

See chapter '"Calculation design compression resistance NRd for column web"'