Welded connections - Basis for weld calculation


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


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]

Fσ┴      normal force perpendicular to the plane of the throat area of the weld [N]

Fτ┴       shear force in the plane of the throat area transverse to the weld axis [N]

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

fu          nominal ultimate tensile strength of parent metal [MPa]

fvw        design shear strength of weld [MPa]

Lj           length of lap joint [mm]

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

l            length of weld [mm]

βw        correlation factor

βLW      reduction factor for long weld

γMW     partial safety factor for welds

σ1         normal stress perpendicular to the plane of the throat area of the weld [MPa]

σ2        normal stress parallel to the axis of the weld [MPa]

σeq      equivalent stress [MPa]

τ1         shear stress in the plane of the throat area transverse to the weld axis [MPa]

τ2        shear stress in the plane of the throat area parallel to the weld axis [MPa]


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, this lecture concentrates on fillet welds and butt welds and gives less attention to other weld types (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 more relevant, butt welds are examined first since the design requirements are simpler.

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