In modern construction, the commonest methods of connecting steel members are by bolting and welding. Eurocode 3 identifies different types of welding such as;
- fillet welding
- butt welding
- plug welding,
- and flare groove welds.
Fillet welds are generally used for connecting parts where the fusion faces form an angle of between 60° and 120°. Although there are other special cases and generalities stated in the code regarding fillet weld (kindly refer).
According to clause 220.127.116.11(1) of EN 1993-1-8, design resistance of a fillet weld should be determined using either the directional method or the simplified method.
The directional method is based on the comparison between the design tensile strength and the applied stress in the most severely loaded part of the weld throat. The applied stress, being determined from a Von Mises formulation, accounts for the influence on the weld strength of the inclination of the resultant force per unit length to the weld axis and plane.
The simplified method is based on the design shear strength of the weld to which is compared directly to an applied weld throat shear stress obtained by dividing the resultant force per unit of length of the weld throat size. The simplified method is always safe compared to the directional method, but both methods have been demonstrated here.
For the welded connection (K-Joint) given as shown below, establish the minimum throat thickness of fillet weld for the gusset plate. The basic assumption is that gusset plate transfers axial forces acting in its plane and in the direction of the member axes.
NA,Ed = 250 KN (compression)
NB,Ed = 250 KN (compression)
NC,Ed = 17.5 KN (compression)
NB,Ed = 17.5 KN (compression)
Gusset plate thickness tg = 10mm
Web thickness tw = 8mm
Angle between gusset and web αa = 90°
Number of fillet welds na = 1
Length of weld Lw = 400mm
Effective throat thickness a = ?
Steel grade = S275
Yield strength fy = 275 N/mm2
Ultimate tensile strength fu = 430 N/mm2
Partial factor (resistance of weld) γM2 = 1.25 (recommended)
Design forces in the gusset plate at the chord web face
The effects of the small eccentricity from the chord axis will be neglected.
The gusset plate section is verified for the following forces:
Ng,Ed is the axial force at an eccentricity of ez = 0 to the centreline of the gusset plate
Vg,Ed is the shear force
αi = 35°
σg,max = (409.576 × 1000) / (4000) = -102.394 N/mm2
The mean shear stress is given by;
τg,max = (286.788 × 1000) / (4000) = 71.697 N/mm2
By directional Method;
Assuming a uniform distribution in the throat section of the weld;
σ⊥ = the normal stress to the throat plane
τ⊥ = the shear stress (in the plane of throat) perpendicular to the axis of the weld
τ// = the shear stress (in the plane of throat) parallel to the axis of the weld
On the throat section of the weld, the force per unit length are:
Where eg is the average eccentricity. In our own case, we will be taking the eccentricity as unity.
a σ⊥ = [(102.394 × 1.0) / 1.0] / (sin 45°) = 72.403 N/mm2
a τ⊥ = [(102.394 × 1.0) / 1.0] / (cos 45°) = 72.403 N/mm2
The design resistance of the fillet weld will be sufficient if the following conditions are both fulfilled:
σw = [72.4032 + 3(72.4032 + 71.6972]0.5 = 190.762 N/mm2
βw = 0.85 (Table 4.1 EN 1993-1-8:2005)
fu / βw.γM2 = 410 / (0.85 × 1.25) = 385.882 N/mm2
190.762 N/mm2 < 385.882 N/mm2 OK
0.9fu / γM2 = 0.9 × 410 / (1.25) = 295.2 N/mm2
72.403 N/mm2 < 295.2 N/mm2 OK
From these conditions, a minimum value for the effective throat thickness can be derived;
a1,min = 190.762 / 385.882 = 0.494 mm
a2,min = 72.403 / 295.2 = 0.245 mm
amin = max[a1,min , a2,min ] = 0.494 mm
But according to clause 4.5.2(2), the effective throat thickness of a fillet weld should not be less than 3mm, therefore, adopt 4mm effective throat thickness.
By Simplified Method
The design resistance of a fillet weld may be assumed to be adequate if, at every point along its length, the resultant of all the forces per unit length transmitted by the weld satisfies the following criterion (see Eurocode 3, Part 1-8):
Fw,Ed ≤ Fw,Rd
Where Fw,Ed is the design value of the weld force per unit length and Fw,Rd is the design weld resistance per unit length. The design strength resistance per unit length (Fw,Rd) is given by;
Fw,Rd = Fvw,d a
Where Fvw,d is the design shear strength of the weld and a is the throat thickness of the weld.
Fw,Ed = τg,max = (286.788 × 1000) / (400) = 716.97 N/mm (shear force per unit length of weld)
fvw,d = (430 / √3) / (0.8 × 1.25) = 233.657 N/mm2
Assuming a weld throat thickness of 4 mm
Fw,Rd = Fvw,d a = 233.657 × 4 = 934.628 N/mm
Fw,Ed (716.97 N/mm) < Fw,Rd (934.628 N/mm) Ok
According to clause 4.5.1(2) of EN 1993-1-8:2005, a fillet weld with an effective length less than 30 mm or less than 6 times its throat thickness, whichever is larger, should not be designed to carry load.
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