Shear bolt connection EC3

Check the shear connection for the IPE450-S275 for the design shear V_Ed=500KN. Bolts M20-8.8, plate thickness t=20mm.

Solution

e 1=60mm > 1.2*do=1.2*22=26.4mm

e 2=50mm > 1.2*do=1.2*22=26.4mm

e 1, e 2< 4*t+40=120mm

ρ1>2.2*do=2.2*22=48.4mm

ρ2>2.4*do=2.4*22=52.8mm

ρ1 and ρ2< min(14t,200)=200mm

F_V,Rd=a_v*A_S*f_ub/γ_Μ2=(2*0.6*245mm² *800 N/ mm² )/1.25=188.2KN

α=min(e1/ 3*do, ρ1/ 3*do-1/4, f_ub/f_u,1)=

= min(60/ 3*22, 100/ 3*22-1/4, 800/430,1)=0.9

k₁ = min(2.8*e₂/do-1.7,1.4 *ρ2/ do-1.7,2.5)=

=min(4.664,4.663,2.5)=2.5

F_b,Rd=k₁* α *d*t* f_u/γ_Μb =(2.5*0.9*20mm* 20mm*430 N/ mm²)/1.25=309.6KN

Every bold gets vertical force 500/3=166.6KN and the torsional moment is 500KN*50mm=2500KN*cm and it is assigned at the farthest bolts as horizontal force 2500KN*cm/20cm=125KN.

At the farthest bolts the maximum force is