# γ γ τ σ γ β τ τ σ γ σ ≤ γ β τ =τ τ σ τ σ γ β σ σ γ β σ ```WORKED EXAMPLES 3.1
Welded Connection of Tie
Check the resistance of the connection of the flat section, shown in Fig. 1WE3-1, loaded in tension by
the factored force FSd = 330 kN. The steel is Grade S460N. The material partial safety factors are
γ M 0 = 1,0 and γ Mw = 1,25 .
10
6
3
3
330 kN
80
3
170
Figure 1WE3-1
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The structural welds should be (i) longer than 40 mm, and (ii) longer than 6 aw = 6 ∗ 3 = 18 mm. Both
of these are satisfied. The full length of the weld can be taken into account in the strength calculation,
because 150 aw = 50 ∗ 3 = 450 mm &gt; 170 mm .
Longitudinal welds
In the longitudinal welds is σ ⊥ = τ ⊥ = 0 . Based on the fillet welds
resistance
f
fu
σ ⊥2 + 3(τ ⊥2 + τ //2 ) ≤
and σ ⊥ ≤ u
β w γ Mw
aw
τII
τ_I
γ Mw
1,4 a w
is the shear strain
Figure 2WE3-1
τII
fu
τ II .Rd =
σ_I
3 β w γ Mw
.
FSd
τII
The design resistance is
550
∗3 ∗ 2 ∗ 170 = 259 ,1 ∗ 10 3 N .
3∗ 1,0 ∗ 1,25
FII .w.Rd = τ II .Rd awII 2 LwII =
awII
LwII
Figure 3WE3-1
Front weld
The equation for the resistance may be at the front weld
( τ II .Rd = 0 and σ ⊥ = τ ⊥ =
σw
2
2
) rewritten:
σ
Lw
aw
2
fu
 σw 
σ 
.

 + 3 w  ≤
β w γ Mw
 2
 2
fu
β w γ Mw 2
τ
Figure 4WE3-1
The front weld design strain is
σ w.Rd =
σw
.
1
FSd
The design resistance of the front weld is
550
F⊥.w .Rd = σ w.Rd aw⊥ Lw⊥ =
∗ 3 ∗ 80 = 74 ,7 ∗ 10 3 N
1,0 ∗ 1,25 ∗ 2
Connection resistance
The connection resistance is
Fw.Rd = FII .w.Rd + F⊥.w.Rd = 259 ,1 + 74 ,7 = 333,8 kN &gt; FSd = 330 kN .
The connection resistance is satisfactory.
P 6 - 300 x 800
80 x 10 - 1 500
3
3
3
170
Steel S460N J2
Scale: 1 : 10
Figure 5WE3-1 Design drawing of the connection
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Note:
1) The weld resistance may conservatively be checked independent of the loading direction as
follows:
Fw.Rd =
f u aw Lw
550 ∗ 3 ∗ ( 2 ∗ 170 + 80 )
=
= 320 ,0 ∗ 10 3 N &lt; FSd = 330 kN .
β w γ Mw 3
1,0 ∗ 1,25 ∗ 3
The welds are not satisfactory uder this model.
2) The tension resistance of a member is
N u .Rd =
A fy
γ M0
=
80 ∗ 10 ∗ 460
= 368 ,0 ∗ 10 3 N &gt; 330 kN .
1,0
The tension resistance is satisfactory.
2
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