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## Thursday, December 7, 2017

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 4.5.3.1(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.

Solved Example
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.

Analysis Results
NA,Ed = 250 KN (compression)
NB,Ed = 250 KN (compression)
NC,Ed = 17.5 KN (compression)
NB,Ed = 17.5 KN (compression)

Geometric Data
Gusset plate thickness      tg = 10mm
Web thickness                  tw = 8mm
Angle between gusset and web      Î±a = 90°
Number of fillet welds      na = 1
Length of weld                  L= 400mm
Effective throat thickness a = ?

Material Data
Yield strength fy = 275 N/mm2
Ultimate tensile strength fu = 430 N/mm2

Partial factor (resistance of weld) Î³M2 = 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

Î±i = 35°
Ng,Ed =  2(250 cos 35) = 409.576 KN
Vg,Ed =  2(250 sin 35) = 286.788 KN

Assuming a uniform distribution of load in the section, the normal stress is given by;

Ag is the cross-sectional area and it is given by Ag = tg. Lw = 10mm × 400mm = 4000 mm2

Ïƒg,max = (409.576 × 1000) / (4000) = -102.394 N/mm2

The mean shear stress is given by;
Ï„g,max = (286.788 × 1000) / (4000) = 71.697 N/mm2

By directional Method;
Assuming a uniform distribution in the throat section of the weld;

Ïƒ = the normal stress to the throat plane
Ï„ = the shear stress (in the plane of throat) perpendicular to the axis of the weld
Ï„// = 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 Ïƒ = [(102.394 × 1.0) / 1.0] / (sin 45°) = 72.403 N/mm2
Ï„ = [(102.394 × 1.0) / 1.0] / (cos 45°) = 72.403 N/mm2

a Ï„// = [(71.697 × 1.0) / 1.0] = 71.697 N/mm2

The design resistance of the fillet weld will be sufficient if the following conditions are both fulfilled:

Ïƒw = [72.4032 + 3(72.4032 + 71.6972]0.5 = 190.762 N/mm2
Î²w = 0.85 (Table 4.1 EN 1993-1-8:2005)

Therefore;
f/ Î²w.Î³M2 = 410 / (0.85 × 1.25) = 385.882 N/mm2

190.762 N/mm2 < 385.882 N/mm2    OK

Also verify;
0.9f/ Î³M2 = 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 = Ï„g,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

Note:
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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