Determine ultimate bearing capacity of connection shown below in tension. M20 bolts of grade C and property class 5.6 are used. Also, find thickness of cover plate. `f_y=250\ MPa` and `f_u=410\ MPa`.

Solution:

For M20 bolts of class 5.6,

`d=20 mm`

`d_0=20+2=22\ mm`

`f_(ub)=500 MPa`

`f_(yb)=300 MPa`

Also, Given,

 `f_y=250 MPa` and `f_u=410\ MPa`

The Design shearing strength of bolts is,

`V_(dsb)=V_(nsb)/gamma_(mb)`

`=(f_(ub)/(root()(3) gamma_(mb)))(n_n*A_(nb)+n_s*A_(sb))`

Here,

`n_n=1`

`n_s=1`

Now, `A_s=(pi d^2)/4=(pi*20^2)/4=314.15\ mm^2`

And, `A_n=0.78**314.15=245.044\ mm^2`

Thus,

`V_(dsb)=500/(root()(3)**1.25)**(245.044+314.15)`

`=129140\ N`

`=129.140\ KN`

Again, the design bearing shear strength of a single bolt is,

`V_(d....

Solution:

For M20 bolts of class 5.6,

`d=20 mm`

`d_0=20+2=22\ mm`

`f_(ub)=500 MPa`

`f_(yb)=300 MPa`

Also, Given,

 `f_y=250 MPa` and `f_u=410\ MPa`

The Design shearing strength of bolts is,

`V_(dsb)=V_(nsb)/gamma_(mb)`

`=(f_(ub)/(root()(3) gamma_(mb)))(n_n*A_(nb)+n_s*A_(sb))`

Here,

`n_n=1`

`n_s=1`

Now, `A_s=(pi d^2)/4=(pi*20^2)/4=314.15\ mm^2`

And, `A_n=0.78**314.15=245.044\ mm^2`

Thus,

`V_(dsb)=500/(root()(3)**1.25)**(245.044+314.15)`

`=129140\ N`

`=129.140\ KN`

Again, the design bearing shear strength of a single bolt is,

`V_(dpb)=(2.5 K_b d tf_u)/gamma_(mb)`

Where, `K_b` is the smaller value of `e/(3d_0)`, `p/(3d_0)-0.25`, `f_(ub)/f_u`, and `1`

Let `e=40 mm > 1.5d_0` and `p=60 mm >2.5 d`.

Here, `e/(3d_0)=40/(3**22)=0.6060`

`p/(3d_0)-0.25=60/(3**22)-0.25=0.6590`

`f_(ub)/f_u=500/410=1.219`

Thus, `K_b=0.6060`

Hence, the design bearing shear strength of a single bolt is,

`V_(dpb)=(2.5**0.6060**20**20**410)/1.25`

`=198768 N`

`=198.768\ KN`

Thus, the design strength of a single bolt is `129.140\ KN`

The design strength of the connection of 6 bolts is `6**129.140=774.84\ KN`

Now, the design strength of plates governed by rupture is given by,

`T_(dn)=(0.9 f_u A_n)/gamma_(m1)`

`=(0.9**410**(250-1**22)**20)/1.25`

`=1346112\ N`

`=1346.112\ KN`