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Lecture 11.2.2: Welded Connections -

Basis for Weld Calculation

OBJECTIVE/SCOPE:

To present the general methods for conducting calculations to determine the strength of butt and 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

Lecture 11.2.1: Generalities on Welded Connections

RELATED LECTURES:

Lecture 2.4: Steel Grades and Qualities

Lecture 2.6: The Weldability of Structural Steels

Lecture 3.3: Principles of Welding

Lecture 3.4: Welding Processes

Lectures 11.4: Analysis of Connections

SUMMARY:

The bases for the calculation of weld strength are set out. A large part of the lecture deals with the actual stress distribution and the deformability of fillet and butt welds. Some experimental results are presented to show the relevance of the design formulae.

a throat thickness of weld [mm]

F external force [N]

F_s^ normal force perpendicular to the plane of the throat area of the weld [N]

F_t^ shear force in the plane of the throat area transverse to the weld axis [N]

F_t// shear force in the plane of the throat area parallel to the weld axis [N]

f_u nominal ultimate tensile stress of parent metal [MPa]

f_vw design shear strength of weld [MPa]

L_j length of lap joint [mm]

L_w length of weld (in long joint) [m]

l length of weld [mm]

b_w correlation factor

b_LW reduction factor for long weld

g_MW partial safety factor for welds

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

s₂ normal stress parallel to the axis of the weld [MPa]

s_eq equivalent stress [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

The purpose of this lecture is to present the basis for weld strength calculation according to Eurocode 3 [1], to discuss the assumptions on which the methods are based and to examine the general methods used to determine stresses in welds. In practice, weld calculations are principally concerned with fillet welds since these account for approximately 80% of all structural welds. For this reason the lecture concentrates on fillet welds and gives less attention to other weld types (butt, slot, plug).

For weld design, three fundamental assumptions are made [2]:

• The welds are homogeneous and isotropic elements.
• The parts connected by the welds are rigid and their deformations are negligible.
• Only nominal stresses due to external loads are considered. Effects of residual stresses, stress concentrations and shape of the welds are neglected in static design.

These assumptions lead to a uniform stress distribution in the weld, whereas variation of stress and strain are observed along the weld. In fact, stress concentrations and residual stresses can reach the yield stress locally. However, the ductility of the material leads to a redistribution of stresses along the weld length, producing an appreciable reduction of stress magnitude. The redistribution also occurs when the weld is subject to the action of external loads. According to the theory of plasticity, the final stress distribution will be optimum when the yield stress is reached over the full length of the weld.

Eurocode 3 [1] specifies that the filler metal shall have mechanical properties (yield strength, ultimate tensile strength, elongation at failure and minimum Charpy V-notch energy value) equal to, or better than, the corresponding properties of the parent material. Therefore, for weld calculation and design, the strength of the parent material is normally taken as the reference strength.

Although fillet welds are the more important case, butt welds are treated first since the design requirements are simpler.

2. BUTT WELD CALCULATION

Providing the welding process has been correctly carried out, the butt weld filler metal may be considered as parent metal. Hence, to determine the resistance of the joint, the calculation is based on the throat area, i.e. the penetration area. Depending on the penetration, two kinds of butt welds are defined: full and partial penetration welds.

2.1 Full Penetration Butt Welds

For a full penetration butt weld, calculation is not necessary because the filler metal strength is at least as high as the parent metal strength of the weaker part joined and the throat thickness of the weld is equal to the thickness of the plate, see Figure 1. Thus the butt weld may effectively be regarded simply as replacing the parent material.

2.2 Partial Penetration Butt Welds

For a partial penetration butt weld, the throat thickness considered in the design is the depth of preparation, slightly reduced. According to Eurocode 3 [1], the throat thickness must be taken as the depth of the butt preparation minus 2mm, where the preparation is the depth of the bevel, see Figure 2. However, if appropriate procedure trials have been made, the throat thickness can be taken as equal to the preparation.

A partial penetration tee-butt joint with superimposed fillet welds may be considered as a full penetration butt weld, if the total throat thickness is greater than the material thickness and the gap dimension meets certain conditions (Figure 3).

2.3 Stress Distribution in Butt Welds

As already pointed out, in weld calculation a uniform stress distribution along the weld length is assumed. In the ultimate state a plastic redistribution of stresses makes this assumption more or less true. In the elastic stage, which is of interest in fatigue design, the stresses are not uniformly distributed, especially not when the filler metal yield point is much higher than that of the parent metal. For example, consider a bar loaded by an axial tensile force as shown in Figure 4. The bar will elongate and, due to the Poisson's ratio effect, its initial width will decrease. This lateral contraction is uniform if the bar is homogeneous. But near the weld line, which has a different yield point, the lateral contraction is less than in the parent metal. This effect causes a varying stress distribution along the weld (Figure 4), in which the tensile stress at the centre is greater than the average stress.

It is good engineering practice to avoid high stress concentrations occurring at sharp re-entrant corners in joints connecting different cross-sections. Avoiding stress concentrations is especially important if the connection will be subject to fatigue loads. To reduce the stress concentration, a gradual transition from one section to the other is recommended (Figure 5). These aspects are also discussed in the lecture on fatigue design and in Lecture 3.5 and Lecture 3.6 concerning fabrication and erection of steel structures.

3. FILLET WELD CALCULATION

3.1 Assumptions

The assumptions adopted for fillet weld calculations according to Eurocode 3 [1] concern mechanical and geometric characteristics. As already pointed out, the mechanical properties of the filler metal shall be compatible with the parent material properties. The throat area of a fillet weld considered in the calculation is shown in Figure 6. This throat area is the product of the throat thickness and the effective length of the weld. Generally, the effective length of a fillet weld is equal to the overall length of the full size fillet, including end returns, if the fillet weld is continuous. For long welds and intermittent welds, the effective length may be reduced.

Fillet welds required to carry loads are normally produced with a throat thickness of at least 4mm. Welds with effective lengths shorter than 40mm or 6 times the throat thickness, whichever is larger, should be ignored for transmission of forces.

3.2 Basic Method

The basic method for the design of fillet welds is described here. It is given in Eurocode 3, Annex M [1] as an alternative design method.

The load acting on the fillet weld is resolved into load components parallel and transverse to the longitudinal axis of the weld and normal and transverse to the plan of its throat (see Figure 6). The corresponding stresses are calculated:

s₁ =  F_s^/al is the normal stress perpendicular to the plane of the throat area.

t₁ =  F_t^/al is the shear stress in the plane of the throat area, transverse to the weld axis.

t₂ =  F_t///al is the shear stress in the plane of the throat area, parallel to the weld axis.

s₂ is the normal stress parallel to the weld axis.

The normal stress s₂ is not considered because the cross-section of the weld is very small and has negligible strength in comparison with the strength of the throat area subjected to the shear stress component t₂.

Application of the von Mises criterion to these stress components gives the equivalent stress s_eq in the throat area of the weld:

s_eq = Ö[s₁² + 3(t₁² + t₂²)]                          (1)

Eurocode 3, Annex M [1] specifies that the fillet weld will be adequate if both the following conditions are satisfied:

s_eq £ f_u/(b_wg_Mw)                         (2)

and s₁ £ f_u/g_Mw

where

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

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

The value of the correlation factor b_w should be taken as follows:

For intermediate values of f_u the value of b_w may be determined by linear interpolation.

3.3 Mean Stress Method

Eurocode 3 gives, in the main text, a simplified design formula which does not require determination of the stress components in the weld. The formula is based on the mean stress method which considers the weld strength as being equal to the shear strength, independent of the direction of the force acting on it. Since the weld is weakest in pure shear the mean stress method always gives results on the safe side.

The fillet welds must satisfy:

F/a1 £  f_vw = f_u/[Ö3.b_wg_Mw](3)

where

F is the external force acting on the weld.

f_vw is the design shear strength of the weld.

3.4 Long welds

Figure 7 indicates the stress distribution for long welds in a lap joint. The distribution is analogous to that observed in long riveted or bolted joints (see Lectures 11.3). Large stresses occur at the ends of the connection. In the ultimate state, just before failure, the plastic deformation near the ends contributes to a more uniform shear stress in the welds. However, if the connection is long the stress redistribution will not be fully uniform.

Eurocode 3 specifies that the design resistance for a long weld in a lap joint shall be multiplied by a reduction factor b_lw to allow for the effects of non-uniform stress distribution. If the lap joint is longer than 150a

b_LW = 1,2 - £ 1

where

L_j is the overall length of the lap in the direction of the force transfer.

For fillet welds longer than 1,7 metres connecting transverse stiffeners in plated members

b_LW = 1,1 -

but 0,6 £ b_LW £ 1,0

where

L_w is the length of the weld (in metres)

4. SLOT AND PLUG WELD CALCULATION

The strength of slot and plug welds is calculated with the mean stress method as for fillet welds. In the calculation, the effective area of the slot or plug weld is taken as the area of the slot or hole.

5. CONCLUDING SUMMARY

• The basis for calculating the strength of welds is given.
• It is noted that residual stresses and stress concentrations are neglected since there is a considerable stress redistribution in the ultimate state. For long welds in lap joints, however, a non-uniform stress distribution is taken into consideration.
• Generally, butt welds require no calculations for design. Calculation is only required in the case of partial penetration welds.
• Following Eurocode 3, a mean stress method as well as an alternative method (Annex M) are given for fillet weld design. The mean stress method does not require calculation of individual stress comments in the welds but generally leads to more conservative results.

6. REFERENCES

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

[2] Bresler, B., Lim, T. Y., Scalzi, J. B., Design of steel structures, 2nd Edition, 1968.

6. ADDITIONAL READING

1. Owens, G. W. and Cheal, B. D., Structural Steelwork Connections, 1st Edition, 1989.
2. Bludgett, O.W., 'Design of welded structures', James F Lincoln Arc Welding Foundation, Cleveland, Ohio, USA, 1972.

Informative and well illustrated reference manual covering all aspects of welded design and construction.

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