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Lecture 11.2.3: Welded Connections -

Applications of Fillet

Weld Calculation

OBJECTIVE/SCOPE

To use the design methods given in Eurocode 3 for fillet welds.

PREREQUISITES

Lectures 1B.5: Introduction to Design of Buildings

Lecture 2.1: Characteristics of Iron-Carbon Alloys

Lecture 2.3: Engineering Properties of Steels

Lecture 3.2: Erection

Lecture 3.5: Fabrication/Erection of Buildings

Lecture 3.6: Inspection/Quality Assurance

Lecture 11.1.2: Introduction to Connection Design

RELATED LECTURES:

Lecture 2.4: Steel Grades and Qualities

Lecture 2.6: Weldability of Structural Steels

Lecture 3.3: Principles of Welding

Lecture 3.4: Welding Processes

Lecture 11.4: Analysis of Connections

Lectures 11.2.1 & 11.2.2: Other lectures on Welded Connections

SUMMARY

This lecture illustrates the design of fillet welds subject to loads of different directions. A comparison is made between the mean stress method and the alternative method in Eurocode 3 [1].

A cross-section area of plate [mm²]

a throat thickness of weld [mm]

b width of flange [mm]

b_eff effective breadth [mm]

F external load [N]

f_y, f_yp nominal yield stress of parent metal [MPa]

f_u nominal ultimate tensile stress of parent metal [MPa]

f_vw design shear strength of weld metal [MPa]

l, l₂ length of fillet welds [mm]

r radius of fillet in rolled sections [mm]

t, t_p thickness of plate [mm]

t_f thickness of flange [mm]

t_w thickness of web [mm]

b_w reduction factor

g_Mw partial safety factor for welds

g_M2 partial safety factor for parent material

s₁ normal stress perpendicular to the throat area of the weld [MPa]

t₁ shear stress in the plane of the throat area transverse to the weld axis [MPa]

t₂ shear stress in the plane of the throat area parallel to the weld axis [MPa]

1. INTRODUCTION

Lecture 11.2.2 sets out the two methods proposed in Eurocode 3 [1] for designing fillet welds, the mean stress method and the alternative method.

The mean stress method (Eurocode 3 - Clause 6.6.5.3) is a simplification of the alternative method. The welds, must satisfy

F/al £ f_vw = f_u/[Ö3.b_wg_Mw]                     (1)

where

F is the external force (independent of orientation) transmitted by the fillet welds

a is the throat thickness

l is the length of the weld

f_vw is the design shear strength of the weld.

The alternative method (Eurocode 3, Annex M) requires a calculation of the different stress components in the weld to determine an equivalent stress. The following conditions must be satisfied:

Ö[s₁² + 3(t₁² + t₂²)]  £  f_u/[b_wg_Mw]                         (2)

and s₁ £ f_u/g_Mw                                                    (3)

where

s₁, t₁, and t₂ are the tensile and shear stress components (see Figure 1) applied to the throat area of the weld

f_u is the nominal ultimate tensile strength of the weaker part joined

g_Mw is the partial safety factor for welds = 1,25

b_w is the correlation factor for which the values are:

b_w = 0,8 for S235 steel, (f_u = 360MPa)

b_w = 0,85 for S275 steel, (f_u = 430MPa)

b_w = 0,90 for S355 steel, (f_u = 510MPa)

A comparison of designs produced by the two methods follows.

2. SIDE FILLET WELDS

Side fillet welds transfer an axial force F applied in a direction parallel to the weld length. Consider a lap joint with two side fillet welds (Figure 2). Each weld transmits the force .

2.1 Application of the Mean Stress Method

Condition (1) gives F/(2al) £  f_u/[Ö3.b_wg_Mw]

Hence, the throat thickness must satisfy

a ³ (Ö3/2)F/(f_ul).b_wg_Mw                        (4)

2.2 Application of the Alternative Method

With this axial force, only the stress component t₂ is considered:

t₂ =

s₁ = t₁ = 0

Condition (2) gives

Ö(3t₂²)  = Ö3F/(2al)  £  f_u/(b_wg_Mw)

and the minimum throat thickness is:

a ³ (Ö3/2)F_y/(f_ul).b_wg_Mw 

Condition (3) need not be considered here (s₁ = 0). For side welds, the two methods lead to the same result for the throat area of the welds.

2.3 Connection Strength Equal to Member Strength

The connection can be designed by comparison to be as strong as the connected member. For this purpose it is not necessary to determine the magnitude of the force acting on the connection.

In the case of two side fillet welds transferring an axial force, the following condition for equal strength can be set:

 2alf_u/(Ö3.b_wg_Mw)  ³ A f_y

or

a ³ Ö3Af_y/(2lf_u).b_wg_Mw                              (5)

where

A is the cross-section area of the connected member

f_y is the nominal yield strength of the member

3. END FILLET WELDS

End fillet welds transfer an axial force applied in a direction perpendicular to the weld length. Consider a tee joint with two end fillet welds (Figure 3). Each weld transmits the force .

3.1 Application of the Mean Stress Method

Condition (1) gives

F/(2al) £ f_u/(Ö3.b_wg_Mw)

and a ³ Ö3F/(2lf_u).b_wg_Mw                   (6)

3.2 Application of the Alternative Method

Only the stress components s₁ and t₁ are determined in the throat area of the weld.

s₁ = t₁ =

t₂ = 0

Using condition (2)

Ö[s₁² + 3t₁²]  £  f_u/[b_wg_Mw]

then

The minimum throat thickness for each weld is:

a ³ (Ö2/2)(F/f_ul)[b_wg_Mw]                          (7)

Condition (3) s₁ = F/(2Ö2al)  £  f_u/g_Mw

gives a ³ F_x/(2Ö2f_ul).g_Mw                (7')

Comparison of (7) and (7') shows that the throat thickness given by (7) governs the choice of weld dimensions.

For end welds, the alternative method is more advantageous than the mean stress method. The reduction of the throat thickness is = 0,82.

From (7) and (4) the equivalent strength for an end fillet weld f_ew and a side fillet weld f_sw according to the alternative method can easily be deduced. These values as well as condition (8) for different steel grades are given in Table 1.

	S235	S275	S355
few [N/mm2] (end fillets) equal strength with two welds	255 a ³ 0,46 t	286 a ³ 0,48 t	321 a ³ 0,55 t
fsw [N/mm2] (side fillets)	208	234	262

Table 1 Equivalent strength for end and side fillet welds for different steel grades

3.3 Connection Strength Equal to Member Strength

In the case of two end fillet welds transferring a force perpendicular to the weld length, the following condition for equal strength applies (the alternative method):

2alf_u /(Ö2b_wg_Mw) ³ t l f_y

or

a ³  (Ö2/2)(tf_y/f_u).b_w g_Mw                 (8)

where

t is the thickness of the connected member.

4. OBLIQUE LOADING

The two loading conditions described in chapters 2 and 3 occur frequently. A fillet weld may also be subject to oblique loading. Figure 4 shows some cases of oblique loaded welds.

Using the mean stress method, the design of oblique loaded welds is very simple. With the alternative method the design is made as follows:

1. The load is resolved into components parallel and transverse to the longitudinal axis of the weld and normal and transverse to the plane of its throat, see Figure 1.
2. The stress components s₁, t₁, and t₂ due to each load component are calculated.
3. Stress components of each kind are introduced into the basic formula (2).

Figure 5 shows the relation between the calculated required throat thickness according to the alternative and the mean stress method for a tee-joint subject to an oblique load.

5. LOAD-DEFORMATION BEHAVIOUR

The load-deformation behaviour of fillet welds is illustrated in Figure 6. It is clear that an end fillet weld is considerably stronger than a side fillet weld. The difference is actually larger than one would expect from the calculation methods described here. One reason is that the failure plane for an end fillet weld differs from the theoretical throat plane, resulting in a larger failure area of the weld. The failure plane for a side fillet weld, however, is closer to the throat plane.

Figure 6 also shows that the ductility of an axially loaded weld is much larger than a weld loaded in the transverse direction.

6. WELD TO UNSTIFFENED FLANGES

If a plate is welded to an unstiffened flange of an I- or a box section, loading will tend to deform the flange or the box side unequally along the breadth. The result is that the parts of the weld near the web will be more heavily loaded than the other parts, see Figure 7. Therefore a reduced effective breadth shall be taken into account both for the parent material and for the welds.

For an I-section the effective breadth b_eff should be taken as:

b_eff = t_w + 2r + 7 t_f (9)

but

b_eff = t_w + 2r + 7 (10)

where

the geometrical parameters t_w, r, t_f and t_p are shown in Figure 7.

f_y is the design yield strength of the member

f_yp is the design yield strength of the plate.

If b_eff < 0,7 b the joint should be stiffened.

For a box section the effective breadth b_eff should be taken as:

b_eff = 2t_w + 5t_f (11)

but

b_eff £ 2t_w + 5 (12)

7. BASE METAL CHECKING

Whatever weld design method is used it is also necessary to ascertain that the base metal of the connected parts has sufficient resistance. To check the base metal three possible failures have to be considered, see Figure 8:

• Tensile failure in member 1 (path 1-1)
• Tensile failure in member 2 (path 2-2)
• Failure in member 2, along the line 3-3, with tensile failure (path b-c) and shearing rupture (paths a-b and c-d). In this case, the total resistance can be taken as the sum of the ultimate strength of each individual path.

{2l₁/Ö3 + l₂}t₂f_u2 /g_M2  ³  f_u2                      (13)   

where

t₂ is the thickness of member 2

f_u2 is the ultimate deign strength of member 2

g_M2 is the partial safety factor against ultimate = 1,25.

Note that tensile failure in the members need not be checked again in the design of the connection. The previous design of the members satisfies the strength requirements.

8. CONCLUDING SUMMARY

• Eurocode 3 proposes two methods for the design of fillet welds. The alternative method in Annex M is the more economical but involves more calculations. The calculation steps are:

i) determination of the load components acting on the throat section of the fillet welds,

ii) calculation of the corresponding stress components,

iii) checking with the basic formula.

• End fillet welds are much stronger than side fillet welds but their ductility is less.
• Both the basic and the alternative methods may be used for welds loaded obliquely.
• For attachments to unstiffened flanges of members, concentration of load transfer in the stiffer regions may be allowed for by using an effective breadth of weld.
• The possibility of tensile failure in the base metal of the connected parts should always be checked.

9. REFERENCES

[1] Eurocode 3: "Design of Steel Structures": ENV 1993-1-1: Part 1: General rules and rules for buildings, CEN, 1992.

10. ADDITIONAL READING

[1] Blodgett, O.W., "Design of welded structures", James F Lincoln Arc Welding Foundation, Cleveland, Ohio, USA, 1972.

[2] Owens, G.W. and Cheal, B.D., Structural Steelwork Connections, 1st Ed., 1989.

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