Joints - The Behaviour and Design of Steel Structures to EC3 - page 418

s 2

a

s 1

La
w

2 V Tz

L

2 V Ty La

w

2 V Ty

2 V L

Throat

2 V L

V Ty

2 V Tz

V L

V Tz

(a) Connection (b) Part weld

Figure 9.21 Fillet welded joint.

weld is reached when
√ σ w + 3 τ w = f uw

(9.25)

in which f uw is the ultimate tensile strength of the weld, which is assumed to be
greaterthanthatoftheplate.Thisequationissimilartoequation1.1usedinSection
1.3.1 to express the distortion energy theory for yield under combined stresses.
Substituting equations 9.23 and 9.24 into equation 9.25 and rearranging leads to

− 2 V Ty sin α + V Tz cos α 2 = ( f uw La ) 2 .

V Ty + V Tz + V L 3 (9.26)

This is often simplified conservatively to

V R

La = f u √ 3

(9.27)

in which V R is the vector resultant

V Ty + V Tz + V L V R = (9.28)

of the applied forces V Ty , V Tz , and V L .
In the simple design method of EC3-1-8 [1] based on equations 9.27 and 9.28,
thedesignweldforces F Ty , Ed , F Tz , Ed ,and F L , Ed perunitlengthduetothefactored