Joints - The Behaviour and Design of Steel Structures to EC3 - page 419

loads are limited by

F w , Ed ≤ F w , Rd (9.29)

where F w , Ed is the resultant of all of the forces transmitted by the weld per unit
length given by

F Ty , Ed + F Tz , Ed + F L , Ed F w , Ed = (9.30)

and

F w , Rd = f vw , d a (9.31a)

is the design weld resistance per unit length, in which

√

f vw , d = f u /

3
β w γ M 2

(9.31b)

is the design shear strength of the weld, f u is the ultimate tensile strength of the
plate which is less than that of the weld, β w is a correlation factor for the steel
type between 0.8 and 1.0 given in Table 4.1 of EC3-1-8, and γ M 2 = 1.25 is the
connector resistance partial safety factor.
EC3-1-8alsoprovidesalessconservativedirectionalmethodwhichisbasedon
equations 9.23 to 9.25, and which makes some allowance for the dependence of
the weld strength on the direction of loading by assuming that the normal stress
paralleltotheaxisoftheweldthroatdoesnotinfluencethedesignresistance.For
this method, the normal stress perpendicular to the throat σ ⊥ is determined from
equation 9.23 as

σ ⊥ a = F Ty , Ed sin α + F Tz , Ed cos α , (9.32)

the shear stress perpendicular to the throat τ ⊥ from equation 9.24 as

τ ⊥ a = F Ty , Ed cos α − F Tz , Ed sin α , (9.33)

and the shear stress parallel to the throat τ || from equation 9.24 as

τ || a = F L , Ed . (9.34)

The stresses in equations 9.32 to 9.34 are then required to satisfy

f u
β w γ M 2

σ ⊥ + 3 τ ⊥ + τ ||

≤ (9.35)

and

σ ⊥ ≤ 0.9 f u /γ M 2

(9.36)

where γ M 2 = 1.25 and β w is the correlation factor used in equation 9.31b.