Joints - The Behaviour and Design of Steel Structures to EC3 - page 430

The maximum bending force per unit weld length can be determined from
equation 9.50b as

F Ty , Ed = ( − 0.05 Q × 10 6 ) × ( 268.7 / 2 )
2 × 268.7 3 / 12

= 2.078 Q N / mm.

Using equation 9.30, the resultant of these is
F w , Ed = √ [ ( 1.861 Q ) 2 + ( 2.078 Q ) 2 ]= 2.789 Q N / mm.

For S355 Grade steel, β w = 0.9 EC3-1-8T4.1

f vw , d = 510 / √ 3

0.9 × 1.25 = 261.7N / mm 2

EC3-1-8 4.5.3.3

F w , Rd = 261.7 × 6 / √ 2 = 1110N / mm.

EC3-1-8 4.5.3.3

Hence 2.789 Q ≤ 1110,
so that Q w ≤ 398.1 < 443.0 ( ≥ Q p )
Using the directional method of EC3-1-8 with equations 9.32-9.34,

σ ⊥ = ( − 0.05 Q × 10 6 ) × ( 268.7 / 2 ) sin45 o

=− 0.346 Q N / mm 2

2 × (268.7 3 / 12 ) × ( 6 / √ 2 )

τ ⊥ = ( − 0.05 Q × 10 6 ) × ( 268.7 / 2 ) cos45 o
2 × (268.7 3 / 12 ) × ( 6 /

=− 0.346 Q N / mm 2 √

2 )

Q × 10 3
2 × 268.7 × ( 6 /

= 0.439N / mm 2 τ || = √

2 )

The strength condition is

510
0.9 × 1.25
EC3-1-8 4.5.3.2(6)

{ ( − 0.346 Q ) 2 + 3 ×[ ( − 0.346 Q ) 2 + ( 0.439 Q ) 2 ]} 0.5 ≤

so that

Q w ≤ 441.0 < 443.0 ( ≥ Q p )

and

0.346 Q ≤ 0.9 × 510 / 1.25

so that

Q w ≤ 1060 > 441.0.

Thus the connection capacity is governed by the shear and bending resistance
of the welds.