International Journal of Fatigue 25 (2003) 359–369
www.elsevier.com/locate/ijfatigue
Comparison of different calculation methods for structural stresses
at welded joints
O. Doerk, W. Fricke ∗, C. Weissenborn
Technical University Hamburg-Harburg, Laemmersieth 90, Hamburg 22305, Germany
Received 24 May 2002; received in revised form 29 October 2002; accepted 18 November 2002
Abstract
Different methods and procedures exist for the computation of the structural hot-spot stress at welded joints. These are either
based on the extrapolation of stresses at certain reference points on the plate surface (or edge) close to the weld toe—as known
from experimental investigations—or on the linearization of stresses in the through-thickness direction. Procedures for the application
of both methods to finite element analysis have recently been proposed in the literature. In the present paper, the different methods
are reviewed and applied to four different details in order to compare the methods with each other and to illustrate the differences.
Conclusions are drawn with respect to their accuracy and sensitivity to finite element meshing.
 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Welded joint; Structural stress; Hot-spot stress; Finite element method; Stress analysis
1. Introduction
The crack initiation and early propagation at weld toes
is governed by the local stress distribution around the
weld. Its analysis and assessment with respect to fatigue
has already a rather long history. According to [18], first
investigations were performed in the 1960’s by several
researchers, including Peterson, Manson and Haibach, to
relate the fatigue strength to a local stress or strain measured at a certain point close to the weld toe, for example
at a distance of 2 mm [7]. Although the characteristic
fatigue strength related to this local stress shows fairly
small scatter it has been shown e.g. in [1] that it is still
affected by the local notch at the weld toe and, therefore,
not independent from local notch geometry. Investigations of relatively thick tubular joints have shown that
the local notch effect of the weld toe affects the stress
in the region up to 0.3⫺0.4·t (t ⫽ plate thickness) away
from the weld toe. This resulted in the 1970’s in the
development of the well-known hot-spot stress approach
with the definition of reference points for stress evalu-
Corresponding author. Tel.: +49-40-428-32-3148; fax: +49-40428-32-3337.
E-mail address: w.fricke@tu-harburg.de (W. Fricke).
∗
ation and extrapolation at certain distances away from
the weld, which depend on the plate or shell thickness.
This development, which was reviewed a. o. by van
Wingerde et al. [19], was particularly successful for the
fatigue strength assessment of tubular joints due to their
complex joint geometry and high local bending of the
tubular walls.
First attempts to apply the approach to welded joints
at plates were already seen in the early 1980’s. Remarkable investigations were performed in Japan to analyse
the stress concentration due to the local structural
geometry of ship hull details, which were summarized
a. o. by Matoba et al. [11]. The design stress was
obtained from finite element analyses by linearization of
the stress through the plate thickness. Radaj [17] summarized these and other investigations and defined the
structural stress at the hot spot (weld toe) as the surface
stress which can be calculated at the hot spot in accordance with structural theories used in engineering. He
demonstrated that the structural stress can be analysed
either by surface extrapolation or by linearization, e.g.
through the wall thickness, in order to exclude the local
non-linear stress peak caused by the weld toe.
In the early 1990’s, Petershagen et al. [16] derived a
generalized hot-spot stress approach for plate structures
using Radaj’s effective notch stress approach [17] and
0142-1123/03/$ - see front matter  2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0142-1123(02)00167-6
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O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
Nomenclature
b
B
F
l
M
SCF
t
width of doubling plate
width of parent plate
force
element length
bending moment
stress concentration factor
plate thickness
applied it to complex welded structures [4]. Detailed recommendations concerning stress determination for
fatigue analysis of welded components were given by
Niemi [12].
However, several applications showed that the stress
results are still affected by the finite element meshing
and element properties. Additional recommendations for
finite element modelling and hot-spot stress evaluation
were given by Huther et al. [9] and by Fricke [6], the
latter based on extensive round-robin stress analyses of
several details. Special considerations have been shown
to be necessary for in-plane notches such as welded edge
gussets, where plate thickness is no more a relevant parameter for the definition of the reference points for stress
evaluation. Niemi and Tanskanen [13] as well as Fricke
and Bogdan [5] proposed alternative procedures for the
hot-spot stress analysis in such cases, using absolute distances for the reference points. A comprehensive IIWguidance for the structural hot-spot stress approach is
currently under preparation [14].
Dong [2] utilized the structural stress definition by
Radaj [17] and evaluated the structural stress directly at
the weld toe position from finite element results by using
principles of elementary structural mechanics. Mesh
insensitivity is claimed and demonstrated by several
examples, however, mainly on 2D basic joints [2], [3].
In this paper, the different methods for structural
stress evaluation are explained in more detail and compared with each other. Afterwards, their application is
illustrated by several 2D and 3D examples, showing the
similarities of the methods and answering the question,
how far mesh-insensitivity can be reached.
It should be emphasized that the structural stress
approach is restricted to the fatigue strength assessment
of weld toes, where cracks start from the surface of the
structure. Cracks starting from the root of not fully penetrated welds are not covered and require a different
assessment procedure.
w
x, y, z
d
s
sm
sb
t
attachment width
coordinates
distance
normal stress
membrane stress
bending stress
shear stress
2. Evaluation of structural stresses from finite
element models
2.1. Finite element modelling of welded structures
As mentioned in the introduction, different types of
weld toes can be identified, see Fig. 1, which require
different stress evaluation techniques:
a) weld toe on the plate surface at the end of an attachment
b) weld toe at the plate edge at the end of an attachment
c) weld toe along the weld of an attachment (the more
highly stressed of both weld toes)
Types a) and c) are in principle similar, however, the
influence of modelling is particularly large at the ends
of welded attachments, i.e. at type a) and b), where the
local stress singularity is more pronounced due to the
additional stress concentration at the V-shaped corner.
In order to limit the computational effort, relatively
simple models and coarse meshes are preferred in practice. Basically, two types of finite element modelling are
usual, which are illustrated in Fig. 2 by the example
shown above:
Fig. 1.
Types of weld toes.
O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
Fig. 2. Typical finite element models and stress evaluation paths.
1. using plate or shell elements which are arranged in
the middle plane of the plates. The weld is frequently
omitted, except in cases with plate offsets (e.g.
doubler plates) or welds close to each other, where
interaction effects occur. In such cases the weld can
be modelled by vertical or inclined plate elements or
by rigid links (constrained equations). The plate or
shell elements should generally contain improved inplane behaviour to model steep stress gradients.
2. using solid elements allowing the weld to be easily
modelled with prismatic elements. If isoparametric
20-node elements are applied, one element is sufficient in thickness direction due to the quadratic displacement function and linear stress distribution. In
connection with reduced integration, the linear part of
the stresses can directly be evaluated.
361
For type a) and c) weld toes, the IIW recommendations [8,14] propose a linear extrapolation over two
reference points, which are located 0.4·t and 1.0·t away
from the hot spot, where t is the thickness of the adjacent
plate (Fig. 3.1). The stresses are typically evaluated at
nodal points, so that the length of the first element is
0.4·t and the second 0.6·t. In case of a coarser mesh with
higher order elements, having lengths equal to t, the
stresses in the surface centres of solid elements or at
mid-side nodes of shell elements may be evaluated and
extrapolated over 0.5·t and 1.5·t (see Figs. 2 and 3.2),
as proposed by some ship classification societies.
At type a) weld toes, however, the width of the solid
element or the two shell elements in front of the hot spot
should not exceed either two times the plate thickness t
or the attachment width w (=attachment thickness plus
two weld leg lengths).
The situation is different for type b) weld toes, i.e. at
plate edges. As plate thickness is not relevant for the
element size nor the location of the reference points,
fixed reference points are proposed. Following the proposal by Niemi and Tanskanen [13] to apply quadratic
extrapolation over three points, 4 mm, 8 mm and 12 mm
away from the hot spot, element lengths of 4 mm or
even better 2 mm are required to obtain stresses at nodal
points not affected by the stress singularity (Fig. 3.3).
The alternative proposal by Fricke and Bogdan [5]
implies a linear extrapolation of stresses obtained from
the mid-side points of higher-order elements (e.g. isoparametric 8-node shell elements) with 10 mm length and
depth, which means that the stresses are extrapolated
over points 5 mm and 15 mm away from the hot spot
(Fig. 3.4).
2.2. Structural stress evaluation by surface stress
extrapolation
The ‘classical’ way of evaluating the structural stress
at the hot spot is the linear or quadratic extrapolation
over two or three reference points in a similar way as
done experimentally with strain gauges. Fig. 2 shows
typical stress evaluation paths. In case of shell models
without weld representation it is recommended to
extrapolate the stress to the structural intersection point
as modelled in order to avoid stress under-estimation due
to the decreased stiffness of the model [6].
Fig. 3.
Extrapolation of surface stresses to the hot spot acc. to [14].
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O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
2.3. Structural stress evaluation according to Dong [2]
The structural stress evaluation method proposed by
Dong [2] generally focusses on the linearization through
the wall thickness directly at the hot spot, however,
depends on the type of modelling.
For solid models, where the element stresses might be
disturbed by the singularity at the weld toe, the element
stresses are evaluated at a certain distance d away from
the weld toe, e.g. equal to the element length, see Fig.
4. Assuming equilibrium between the axial and shear
stresses acting here (Section B-B) and in the section
directly at the weld toe (Section A-A), the linear part of
the latter can directly be derived (stresses acting on the
other sides of the element are neglected). Using trapezoidal integration for n ⫹ 1 equally spaced nodes over
the plate thickness yields two equations for sm and sb:
冕
t
1
1
[s ⫹ 2·sxx,1 ⫹ …
sm ⫽ sxx(z)·dz ⫽
t
2·n xx,0
0
⫹ 2·sxx,n⫺1 ⫹ sxx,n]
冕
t
冕
t
t2
t2
t2
[s
sm ⫹ sb ⫽ sxx(z)·dz⫺d· txz(z)·dz ⫽
2
6
6·n2 xx,0
0
For a shell model, the structural stress can be evaluated directly at the hot spot because the linear stress distribution is already assumed in the elements, see Fig. 5.
In order to avoid inaccuracies due to stress distribution
assumed in the element formulation, the structural stress
is calculated directly from the nodal forces and moments
at the element edge in question.
A multi-linear stress distribution is assumed for several elements along the weld which is derived from an
equation system for the stress values at the element corners.
By using these stresses, mesh insensitivity is claimed
by Dong [2] even for hot spots with high stress singularity, i.e. types a) and b) in Fig. 1.
0
⫹ 6·sxx,1·z2 ⫹ 12·sxx,2 ⫹ … ⫹ (n⫺1)·6·sxx,n⫺1
t
⫹ (3n⫺1)·sxx,n]⫺d [txz,0 ⫹ 2·txz,1 ⫹ … ⫹ 2·txz,n⫺1
2·n
⫹ txz,n]
Fig. 4 shows the stress linearization through the whole
plate thickness t, resulting in the structural stress as
defined by Radaj [17]. Alternatively, the linear stress can
be derived for part of the thickness t1, which allows the
structural stress to be derived for a crack having propa-
Fig. 4.
gated only through a part of the thickness. In this case,
the stresses acting at the lower boundary of the area, i.e.
in the depth t1, have to be included in the a.m. equations,
because the lower boundary is no more a free surface.
In thick section joints and some other joint configuration, such as fillet welds that are symmetric with respect
to geometry and loading, there is a non-monotonic
trough-thickness stress distribution. In these cases the
linearization is also performed to a finite depth t1, which
is equal to t/2 in case of symmetry.
Structural stress evaluation for solid models (acc. to [2]).
3. Examples
In the following, four examples with different types
of weld toes are described, where the methods mentioned above are applied to derive the structural hot-spot
stress, i.e.
앫 surface stress extrapolation acc. to IIW [8,14], i.e. linearly over 0.4 t /1.0 t for type a) and c) joints and
quadratically over 4 mm /8 mm /12 mm for type b)
joints in connection with element lengths of at least
0.4 t or 4 mm, respectively (Figs. 3.1 and 3.3)
앫 surface stress extrapolation over 0.5 t /1.5 t (5 mm
and 15 mm for type b) joints) in connection with relatively coarse meshes, having elements with quadratic
Fig. 5.
Structural stress evaluation for shell models (acc. to [2]).
O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
shape function and lengths of 1.0t or 10 mm, respectively (Figs. 3.2 and 3.4)
앫 structural stress evaluation acc. to Dong [2], using
meshes with different element sizes. All calculations
were performed by the authors on the basis of the
references given.
The element type and weld representation have not
been varied within each comparison.
3.1. Plate lap fillet weld
The first example concerns a 2D example, the plate
lap fillet joint described in [2]. Fig. 6a illustrates the onesided lap joint, which is subjected to an axial force F.
The weld toe belongs to type c) according to Fig. 1.
Due to the eccentricity of the lap joint and the boundary conditions at the ends, a constant bending moment
without any shear force is acting in the plate in front of
the weld. Therefore, a constant structural stress is acting
which is determined by the stiffness of the actual structure.
363
The application of the structural stress approach
according to Dong [2] yields almost the same structural
SCF for several mesh densities, as shown in Fig. 6d. As
no shear stress is acting in the plate, the stress evaluation
can simply be reduced to a linearization through the
thickness at any section in the right part, yielding a structural stress SCF of approximately 1.19.
The same value is achieved by extrapolating the surface stresses, see Fig. 7. As expected, the mesh density
plays almost no role also in the case of surface stress
extrapolation. The constant structural stress distribution
would even allow any location of the reference points,
as long as they are beyond 0.4 t.
Fig. 7. Plate fillet lap joint and results obtained for surface stress
extrapolation.
Fig. 6.
Plate fillet lap joint and results obtained by Dong [2].
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O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
3.2. One-sided doubling plate
The second example is the one-sided doubling plate
shown in Fig. 8, where the critical weld toe on the plate
surface belongs to type c) in Fig. 1. The model was
investigated in a Japanese research project [20]. The
example is similar to the first one, however, the round
doubling plate causes a non-uniform stress distribution
in the transverse direction.
The example was also investigated in the round-robin
analysis described by Fricke [6], where different techniques of modelling the one-sided doubling plate by
shell elements were applied. In the present analysis, the
doubling plate was modelled by solid elements, allowing
the weld to be realistically considered. Fig. 9 shows three
different finite element models. In all cases, 20-node
solid elements with reduced integration order were used.
One element was arranged over the plate thickness,
while the element lengths in front of the weld toe ranged
from approx. 0.4–2 t.
The computed stress distribution in front of the weld
toe is plotted in Fig. 10. In contrast to the previous study
[6], no stress magnification due to weld distortion was
considered. For this reason, the measurement results
from Yagi et al. [20] have not been included in Fig. 10,
because these were obviously affected by this.
Although the resulting stresses are fairly close
together, a slight influence of the element size can be
observed. The extrapolation of the surface stresses to the
hot spot, performed for the associated models and indicated by arrows in Fig. 10, yields hot-spot stress ratios
of 1.25 (over 0.4 t /1.0 t) and 1.26 (over 0.5 t /1.5 t).
The round-robin study [6] showed a higher scatter (±6%)
due to the application of different element types and
particularly due to simplified weld modelling in case of
shell models, where plate connections and rigid links
were used.
A scatter of approximately 10% is contained in the
results based on the approach by Dong [2], which are
plotted on the left side of Fig. 10. The structural stress
in this example is obviously not insensitive to the mesh
density. The aforementioned scatter due to different
element types and simplified modelling may additionally occur.
Fig. 8. One-sided doubling plate investigated by Yagi et al. [17].
Fig. 9. Different finite element meshes for modelling the one-sided
doubling plate (1/2-model).
Fig. 10. Surface stress and structural stress ratio for one-sided doubling plate.
O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
In order to clarify the reasons for this mesh-sensitivity, the geometry of the one-sided doubling plate has
been varied. For the sake of simplification, a rectangular
doubling plate with constant length (60 mm), but varying
width b has been chosen. The thickness of the doubling
plate is 10 mm. The dimensions of the parent plate are
B ⫽ 240 mm and t ⫽ 15 mm.
Fig. 11 shows three models with different ratios b/B,
ranging from 1/12 (shallow longitudinal stiffener) to 1/1
(2D case). The element length in front of the doubling
plate was again varied from 0.4 t to 2.0 t.
Fig. 12 shows the structural stress evaluated at the
centre line according to Dong [2]. It can clearly be seen
that the difference between the results becomes larger if
365
Fig. 12. Structural stress according to Dong [2] evaluated from different meshes of rectangular doubling plates.
the concentration becomes more localized. The reason
is seen in the neglect of vertical shear stresses acting on
the transverse element sides in the equilibrium equation
described in section 2.3.
3.3. Bracket toe
The third example concerns a bracket toe, which was
investigated within the European Research Project
FatHTS [15]. Fig. 13 shows the test model with a diagonally acting hydraulic cylinder, which produces a combination of axial force, shear force and bending moment
in two horizontal and vertical I-beams.
The critical position is the bracket toe, which exists
four times in each test model. The plate thickness of the
flange is 20 mm, while the bracket is 12 mm thick. Full
penetration welding was applied with a leg length of the
fillet weld reinforcement of 8.5 mm.
During the investigation, strain measurements and
finite element calculations were performed. Fig. 14
shows two different finite element models of the critical
area based on above described recommendations, where
the element length in front of the bracket corresponds
to the flange thickness. Fig. 15 compares the computed
Fig. 11. Finite element models of rectangular doubling plates having
different width.
Fig. 13. Bracket investigated by Paetzold et al. [15].
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O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
Fig. 14. Shell and solid finite element models of the bracket with
longitudinal stress distribution.
Fig. 15. Stress distribution in front of the bracket from measurements
and f.e. models (Fig. 14).
longitudinal stress in front of the hot spot with measured
values for a cylinder force of 100 kN. Apart from the
measured stress close to the hot spot, which is affected
by the local notch, the agreement is very good.
Only the shell model is considered for the present
comparison of the different methods. 8-noded quadratic
shell elements have been chosen to represent the I-beam,
the bracket and the flange. The weld was not modelled
as frequently done in practice. In total six meshes have
been created with element sizes in front of the bracket
toe ranging from 0.4 t × t / 2 to 2 t × 2 t. Half the attachment width (w / 2 ⫽ 14.5 mm) was partly taken for the
element width as recommended by Niemi [14] and
Fricke [6].
The resulting stress distribution is shown in Fig. 16.
The stress singularity influences the results close to the
hot spot. However, the structural hot-spot stress derived
from surface extrapolation is almost the same for both
alternative methods mentioned above. A slight stress
under-estimation can be observed when comparing the
results with Fig. 15—an effect which has frequently
been found in connection with shell models. The restriction of the element width to w/2 has only a small effect
on the results in this example.
The results obtained by application of Dong’s method
are generally higher and show a very large scatter. This
is obviously due to the stress singularity, as the local
stress becomes infinite if the element size approaches
zero. The method [2] as applied to this model is highly
mesh-dependent and not able to yield a reasonable structural stress for simplified models. The surface stress
extrapolation method has, of course, also problems in
such cases, however they seem to be less severe.
The mesh density effect is normally related only to
the elements in front of the hot spot. However, Fig. 17
shows that also the modelling of other areas—in this
case the bracket—may strongly affect the results. A
coarse modelling of the bracket toe would increase the
local stress by approximately 10% and, thus, closing the
gap between shell and solid models. This means that we
Fig. 16. Stress distribution in front of the bracket toe and structural
hot-spot stresses for various shell models.
O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
Fig. 17. Stress distribution in front of the bracket toe for two different
meshes of the bracket.
have to accept an additional scatter in the finite element
results due to the meshing around the critical area.
3.4. Fillet weld around plate edge
The last example is a flat bar welded to an I-beam,
where the critical hot spot is located at the plate edge,
see upper part of Fig. 18, i.e. it belongs to type b)
367
according to Fig. 1. The model was investigated experimentally by Kim et al. [10]. It was also included in the
round-robin study [6].
Again, shell modelling with 8-noded elements was
chosen for the present finite element analysis. The weld
was modelled in a simplified way as illustrated in Fig.
18. In this way, the correct weld toe position was kept.
The area in front of the weld toe was modelled in three
different ways by choosing element lengths ᐉ=2 mm,
ᐉ=5 mm and ᐉ=10 mm, respectively.
Fig. 19 shows the computed stress distribution at the
plate edge of the flat bar close to the weld. The force F
was chosen such that a unit nominal stress is acting at
the welded toe. As expected for in-plane notches, the
stress distribution is affected by the stress singularity,
showing increased stresses in the elements adjacent to
the notch. The stress extrapolation yields a stress value
of 1.77 MPa for the fine mesh (quadratic extrapolation)
and 1.68 MPa for the coarse mesh (linear extrapolation),
which means a slight difference between the two
methods. The difference is higher than expected from
the former investigation [5], where only 2D structures
with 135° and 90° corners have been analysed.
Dong’s method was applied for an assumed crack
depth of 10 mm, defining the end of the fatigue life for
this specimen. The structural stress computed for the
three meshes in accordance with 2.3 shows only little
scatter, however, the stress is higher that that obtained
from surface extrapolation.
It should be mentioned here that the calculated structural stress is higher than the measured one and that the
corresponding fatigue life prediction has shown to be
very conservative for this example [6].
4. Conclusions
From the application of different structural stress
evaluation methods to four examples of welded plate
Fig. 18. Flat bar welded to an I-beam and modelling of the critical
area around the weld toe.
Fig. 19. Stress distribution in front of the fillet weld and structural
hot-spot stresses for various models.
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O. Doerk et al. / International Journal of Fatigue 25 (2003) 359–369
structures, the following conclusions are drawn and recommendations are given:
1. The two alternative methods for surface stress extrapolation (as shown on the right and left side of Fig.
3) yield almost the same results. The first procedure
with reference points 0.4 t / 1.0 t away from the weld
toe (or 4/8/12 mm at plate edges) requires a finer
mesh with element lengths of at least 0.4 t (or 4 mm,
respectively), if higher-order elements are used. However, finer mesh densities are also allowed. The
second procedure with reference points 0.5t /1.5 t
away from the weld toe (or 5/15 mm at plate edges),
which is preferred by several ship classification
societies, requires fixed sizes of higher-order elements
to achieve consistent results.
2. The procedure proposed by Dong [2] for the evaluation of the structural stress directly at the weld toe
shows mesh-insensitivity for 2D problems. However,
in the case of 3D stress concentration, some scatter is
observed in the results evaluated from different mesh
densities. This seems to be due to the neglect of
stresses in the equilibrium equations acting at the
transverse element sides. The scatter increases if the
notch is very localized, as exemplified by the toe of
a bracket oriented in stress direction, which is in practice often very simply modelled by using shell
elements. In case of in-plane notches, i.e. at plate
edges, the structural stress depends on the assumption
of a crack depth, which defines the range of stress linearization.
3. Additional scatter of the stress results is expected due
to the usage of different element types offered by
finite element programs and due to different techniques of modelling the weld, particularly if shell
elements are applied. This scatter is typically between
±5% and ±10% [6]. In addition, the investigations
have shown that also the meshing outside the stress
evaluation area in front of the weld toe can further
affect the results, so that mesh-insensitivity remains
generally questionable. The analyst should always be
aware of the limitations set by the finite element
model as well as by the evaluation method of the
structural hot-spot stress.
4. The definition of the structural stress is principally
the same in all methods, except for cases with nonmonotonic trough-thickness stress distributions (see
section 2.3). Therefore, the fatigue assessment by SN curves should also be comparable. Niemi [14] recommends for welds at steel FAT 100 for normal cases
and FAT 90 for cases with full-load carrying fillet
welds (example 4) and side attachments longer than
100 mm. The FAT number corresponds to the characteristic fatigue strength reference value of the design
S-N curve at 2 million cycles. The fatigue lives evalu-
ated with the structural stress by Dong [2] seem not
to be in contradiction to this.
Although the examples chosen cover a variety of different types of weld toes and practical situations, they
are still relatively simple. Several questions remain open,
e. g. the applicability of the methods to complex, biaxial stress states or to very thick structural members,
e. g. bulbs of profiles, where it is difficult to select an
appropriate thickness for the definition of stress extrapolation points or for the depth for stress linearization. All
the aforementioned aspects should be considered when
assessing the reliability of the different methods. In
addition the practicability is very important for the
industrial application.
Furthermore it should be noted that the fatigue prediction may strongly be affected by other influence factors
such as positive (compressive) residual stresses or large
variations in the local weld profile, which should be
taken into account when assessing the methods. In this
sense, the structural hot-spot stress approach remains to
be a relatively coarse, however, very practical approach.
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