calculation of the secondary bending moment effect …
TRANSCRIPT
CALCULATION OF THE SECONDARY BENDING MOMENT EFFECT IN THE
SINGLE-SIDED FILLET-WELDED JOINTS.
Lappeenranta–Lahti University of Technology LUT
Master’s Programme in Mechanical Engineering, Master’s Thesis.
2021
Vladislav Bobylev
Examiner(s): Prof. Timo Björk
D.Sc. (Tech) Antti Ahola
ABSTRACT
Lappeenranta–Lahti University of Technology LUT
LUT School of Energy Systems
Mechanical Engineering
Vladislav Bobylev
Calculation of the secondary bending moment effect in the single-sided welded joints.
Master’s thesis
2021
50 pages, 31 figures, 7 tables and 7 appendices
Examiner(s): Prof. Timo Björk
D.Sc. (Tech.) Antti Ahola
Keywords: secondary bending moment, eccentricity, single-sided welds.
In this study, the effect of the secondary bending moment in the single-sided welds is
investigated. The research was based on comparison analysis of analytical and experimental
results. The current EN 1993-1-8. 2005 code does not provide explicit guidance for design
calculation of the single-sided welds; therefore, the main focus is made on the alternative
design verification guide described in Teräsnormikortti № 24/2018.
The analytical results strength capacities were calculated according to EN 1993-1-8:2005
and Teräsnormikortti № 24/2018. Experimental tests consist of the tensile tests of single-
sided welded plate connections made of S355 and S700 with total amount of 8 specimens.
Four weld geometries with different eccentricity values are designed for laboratory tests.
Explicit analysis of laboratory tests is conducted by means of Finite element analysis in
FEMAP software.
Comparison of strength capacities obtained by directional method provided in EN 1993-1-
8: 2005 and actual capacities, indicated that EN 1993-1-8:2005 was not capable of making
safe predictions for welds with relatively high eccentricity. On the contrary, results obtained
with Teräsnormikortti № 24/2018 verified the ability of modified calculation model
toproduce safe prediction for single-sided fillet welds. Although, Teräsnormikortti strength
predictions for welds with relatively small eccentricity (0,5 mm) correlated well with test
results, in case of specimens possessing larger eccentricity (>2 mm), obtained prediction
were overconservative. Further, finite element analysis facilitated identification of results
variation cause, which was clamping conditions of the test specimens which prevented
development of maximum bending moment amplitude. According to the results, it can be
concluded that design calculation of single-sided welded joints considering eccentricity is
challenging due to major dependence on local structure rigidity.
ACKNOWLEDGEMENTS
I would like to express my gratitude to Prof. Timo Björk and D.Sc. (Tech.) Antti Ahola for
for their assistance and guidance at every stage of the research. Their immense knowledge
and novel thinking have encouraged me to strive for progressing in this project. I also have
to thank employees of the Laboratory of Steel Structures for planning and conducting
experimental part of the thesis. I would like to extend my sincere thanks to my groupmates
Ahmed Yusuf and Riku Turkia for giving me valuable tips and motivation throughout this
work.
Additionally, I would like to express my deepest gratitude to my both families for
tremendous understanding and invaluable support which were indispensable for me all
through my studies.
Vladislav Bobylev
In Lappeenranta, 1st of December 2021
SYMBOLS AND ABBREVIATIONS
a Critical throat thickness [mm]
b Plate width [mm]
e Eccentricity [mm]
E Young’s modulus [MPa]
F Load [kN]
fu nominal tensile strength [MPa]
fy Yield strength [MPa]
Hv Vickers Hardness value [-]
I Current [A]
k Stress distribution factor [-]
M Moment [kNmm]
U Voltage [V]
z1 Butt weld penetration depth [mm]
z2 Fillet weld leg length [mm]
α Angle [degree]
βw Correlation factor for tensile strength of base material and weld material [-]
γM2 partial material safety factor [-]
ν Poisson’s ratio [-]
σ Stress [MPa]
σ|| Normal stress parallel to the throat [MPa]
σ⊥ Normal stress perpendicular to the throat [MPa]
σb Bending stress [MPa]
σm Membrane stress [MPa]
σx Normal stress [MPa]
τ|| Shear stress parallel to the axis of the weld [MPa]
τ⊥ Shear stress perpendicular to the axis of the weld [MPa]
DOB Degree of bending
EC3 Eurocode 3
FEA Finite element analysis
FW Fillet weld
HAZ Heat affected zone
SBW Single side bevel weld
6
Table of contents
Abstract
Acknowledgements
Symbols and abbreviations
1. Introduction ........................................................................................................................ 8
1.1 Background of the study ......................................................................................... 8
1.2 Objectives ................................................................................................................ 9
1.3 Structure and limitations of the study ................................................................... 10
2. Theory .............................................................................................................................. 11
2.1 Eurocode 3 ............................................................................................................ 13
2.2 Calculation model for single sided filled welds .................................................... 15
3. Research Methods ............................................................................................................ 19
3.1 Experimental tests ................................................................................................. 19
3.2 Test specimens ...................................................................................................... 20
3.4 Test set-up and instrumentation ............................................................................ 23
3.5 Finite Element Analysis ........................................................................................ 24
4. Results .............................................................................................................................. 27
4.1 Tested weld geometries ......................................................................................... 27
4.2 Comparison of analytical and test results. ............................................................. 31
4.3 FEA results ............................................................................................................ 34
5 Discussion ..................................................................................................................... 44
5.1 Further research ..................................................................................................... 46
6 Summary ....................................................................................................................... 48
References ............................................................................................................................ 49
Appendices
Appendix 1. Welding Parameters of Test Specimens.
7
Appendix 2. Test Welds’ Geometries.
Appendix 3. Welds’ Failure Planes.
Appendix 4. Hardness Measurements Points and Values, Evaluation of tensile strength
along potential failure lines according to Equation 12.
Appendix 5. Fracture surfaces of test specimens.
Appendix 6. Force displacement curves FE versus test data.
Appendix 7. Verification of the weld according to Teräsnormikortti №24/2018.
8
1. Introduction
The history of arc welding as we know it nowadays counts more than 100 years. For many
decades engineers invested many efforts in research targeted on development of numerical
models for prediction of welded structures’ behavior in various service conditions. As a
result of many researcher projects, engineering community got universal technical standards
which allowed to unify requirements to the design of welded connections. For decades, set
of technical standards such as EC3 have being fulfilled needs of major industrial
applications. However, recent increase of high strength and ultra-high strength steels
utilization in combination with trends in modern design require revision and amendment of
current design rules. Lack of standard design instructions created the need for research
projects in field of metal structures. One of the current topics for research pointed out by
Björk et al. (2018) is development of design rules for welds subjected to bending moment.
1.1 Background of the study
In many applications, where fillet weld joints are under tensile loading, due to asymmetric
geometry of weld or structural misalignments, a secondary or primary bending moment
occur. Figure 1 represents joints where bending moment occurs at the root of weld. Such
joints can be represented by single-sided butt welds, single-sided fillet welds, beveled groove
single-sided weld where eccentricity appears due to position of weld legs or defects of
insufficient penetration of weld root. (Bjork et al., 2018, p.10.) In practice, single-sided weld
joints are used in connections between hollow sections and manufacturing of welded box
sections.
The EC3 standard does not provide clear instructions for considering of tensile stresses
occurring in welds due to bending. However, it has been already indicated by Tuominen et
al. (2017) that tensile stresses in the root side of the weld due to bending and tension loads
is the combination which decreases capacity of the joint. Furthermore, Teräsrakenneyhdistys
(Finnish Constructional Steelwork Association) issued supplementary design guidance
9
Teräsnormikortti № 24/2018 to EC3 which contained updated regulation for considering of
design resistance of single sided welds. Even though Teräsnormikortti № 24/2018 has been
already adopted for use, there is still demand for verification of guidance by experimental
results.
Figure 1. Bending moment occurring in joints due to: a) weld eccentricity, b) external
bending, c) chord flange deformation (Tuominen et al. 2017, p. 1).
1.2 Objectives
The core objective of this research is to determine the effect of asymmetric geometry and
loading on the static strength of load-carrying single-sided welded joints. The magnitude of
effect is predicted by computational analysis based on Teräsnormikortti №24/2018 and FE
models. Obtained results are compared with data from experimental tests. Tests are
conducted to examine influence of weld geometry variables e.g., throat thickness,
eccentricity of critical weld throat in relation to load direction. Eventually, this study is
designed in conformity with following research questions:
• How does eccentricity of weld influence the static strength of load-carrying one-
sided fillet weld joints?
• Are the numerically obtained capacities by use of Teräsnormikortti №24/2018
reliable?
• When weld eccentricity is essential to consideration for strength capacity
calculation?
10
1.3 Structure and limitations of the study
The research is based on comparison analysis between laboratory tests of single-sided welds
and their capacities obtained by utilization of Teräsnormikortti №24/2018 and FE models.
The examined weld geometries are prepared in Laboratory of Steel Structures where they
are subsequently tested for evaluation of static strength. Software used for building and
analyzing of FE models is Femap with NX Nastran.
Only load-carrying joints are selected for being studied in this research. For simplification
of modelling and compliance to selected range of variable geometry parameters, welds are
assumed to possess ideal geometry which means that welds have equal leg lengths and flank
angle is 45 °. In order to reach planned weld geometry without over penetration in laboratory
tests, infusible tungsten strip is used at the weld root.
11
2. Theory
Metal structures in service often designed to withstand complex loadings in tension,
compression, bending, etc., so that at any given point material might be subjected to
combined stresses acting in several directions. If magnitude of these stresses reaches a
critical value, the material starts to yield or fracture. In order to predict behavior of material
under combined loading and determine the safe limits, it is necessary to apply failure
criterion. In other words, it is needed to correlate material’s strength properties with stresses
occurring in structure. (Dowling 2013, p. 275.)
Failure criteria can be divided according to predicted failure mechanism: yielding or
brittle/cleavage fracture. Since, the focus of this research made on structural steels which
dominantly have ductile behavior, it is worth to further extend yield criteria. Moreover,
design of fillet according to EC3 is also based on von Mises yield criterion.
𝜎ℎ =
𝜎1 + 𝜎2 + 𝜎3
3
(1)
𝜏ℎ =
1
3√(𝜎1 − 𝜎2)2 + (𝜎2 − 𝜎3)2 + (𝜎3 − 𝜎1)2 (2)
The von Mises yield criterion predicts a failure to occur when shear stress reaches critical
value on octahedral plane which is plane oriented with principal axes making angles α=β=γ
as represented on Figure 2 (a). Thus, the octahedral normal stress σh and octahedral shear
stress τh can be expressed in terms of principal stresses by Equation 1 and 2.
In general, eight octahedral planes have similar stresses σh and τh. Together these planes
form an octahedron, as shown on Figure 2 (b). Since the opposite face of the octahedron are
parallel, the octahedral stresses are acting in four different directions.
12
Figure 2. Octahedral planes relatively to the principal axes (a), and the octahedron formed
by the similar planes (Dowling 2013, p. 261).
𝜏ℎ =
√2
3𝜎 1 (3)
Applying Equation 2 to uniaxial loading case as illustrated by Figure 3, so that σ2= σ3=0 and
substituting σ1 by yield strength of material obtained from tensile test σo, resulting in
Equation 3.
As can be observed from Figure 2 and Figure 3, the plane on which the uniaxial stress acts
is situated at the angle α = 57° relatively to octahedral plane.
Figure 3. The plane of octahedral shear in uniaxial tension test. (Dowling 2013, p. 289).
13
𝜎 o =
1
√2√(𝜎1 − 𝜎2)2 + (𝜎2 − 𝜎3)2 + (𝜎3 − 𝜎1)2 (4)
Combination of Equation 2 and 3 is resulting in general form of von Mises yield criterion
Equation 4 expressed in terms of yielding strength obtained from uniaxial tensile test. The
von Mises yield criterion served as the basis for evaluation of fillet welds resistance
described in Eurocode 3.
2.1 Eurocode 3
The EC3 provides two methods for evaluation of design resistance of fillet welds. The one
used in this work is called Directional method which resolves the force carried by a unit
length of weld into four components which presented in Figure 4:
• σ⊥ is the normal stress perpendicular to the weld throat.
• σ|| is the normal stress parallel to the weld axis which is not considered in resistance
verification
• τ⊥ is the shear stress (in the plane of the throat) perpendicular to the axis of the weld
• τ|| is the shear stress (in the plane of the throat) parallel to the axis of the weld
(SFS-EN 1993-1-8 2005, p. 43.)
Figure 4. Stresses in the throat section of fillet weld. (SFS-EN 1993-1-8 2005, p. 43).
14
The directional method’s weld resistance verification model is based on the modified
octahedral shear stress yield criterion, where only perpendicular normal stress and shear are
considered in the critical plane due to transverse loading. The critical plane location is
assumed to be 45 degrees in the case of symmetric fillet welds under transverse axial loading.
However, as it was shown by Björk et al. (2018), 45 degrees as not correct either theoretically
or in practice, but overall influence on ultimate capacity was not remarkable. Modified for
fillet weld geometry, EC3 calculation model looks as follows:
[𝜎⊥
2 + 3(𝜏⊥2 + 𝜏||
2)]0,5 ≤𝑓𝑢
𝛽𝑤 ∙ 𝛾𝑀2
(5)
and 𝜎⊥ ≤
0.9𝑓𝑢
𝛾𝑀2 (6)
where:
• fu is the nominal tensile strength of the weaker part of the joint so that in case of
welded connections between steels with different strength value, for calculation the
lowest strength property should be determined.
• γM2 is a partial material safety factor.
• βw is the appropriate correlation factor which represents strength relation between
base and filler materials. Proper value should be selected from the standard according
to steel grade used. (SFS-EN 1993-1-8 2005, p. 43,44.)
The EC3 includes the paragraph 4.12 giving recommendations for cases where eccentrically
loaded single fillet or single-sided partial penetration butt welds could not be avoided in
design. The standard pointed out two cases where local eccentricity should be considered.
Firstly, welded joints where bending moment conducted about the longitudinal axis of the
weld causes tension at the root as presented in Figure 5 (a). Secondly, when tensile force
directed perpendicularly to the longitudinal axis of the weld induces bending moment,
resulting in tension force at the root of the weld, as could be observed from Figure 5 (b).
(SFS-EN 1993-1-8 2005, p. 48.)
15
Figure 5. Single fillet welds and single-sided partial penetration butt welds. (SFS-EN 1993-
1-8 2005, p. 48).
2.2 Calculation model for single sided filled welds
As it was firstly indicated by Tuominen et al. (2017), EC3 instructions referred to single
fillet or single-sided partial penetration butt welds do not provide explicit guide for
numerical evaluation of welds design resistance. Conducted research was focused on
investigation of secondary moment effect on the static strength of the welds. Analytical
calculation model was based on extended von Mises yield criterion as follows:
√(𝜎𝑚 + 𝜎𝑏)2 + 3𝜏2 =𝑓𝑢
𝛽𝑤𝛾𝑀2 (7)
where all stress components are calculated for the critical plane of the weld as can be
observed from Figure 6. The stress induced due to presence of bending moment and
secondary bending moment occurring due to weld eccentricity is:
𝜎𝑏 =𝑘(𝑀 ± 𝐹𝑒)
𝑎2𝑏 (8)
where k = 6 is used for elastic and k = 4 for fully plastic stress distribution; M is the constant
primary or secondary bending moment affecting the adjacent member; F is tension force
applied axially in weld; e is eccentricity measured as the perpendicular from the force action
line to the center line of assumed critical weld throat; a is the throat thickness of the critical
weld plane; and b is the effective length of the weld. (Tuominen et al. 2017, p. 2.)
16
The membrane and shear stress components depend on the angle α between axes of acting
force F and the normal to the critical plane.
𝜎𝑚 =
𝐹 cos 𝛼
𝑎𝑏
(9)
𝜏 =
𝐹 sin 𝛼
𝑎𝑏 (10)
Test results obtained in the research confirmed the ability of analytical model to predict a
load-carrying capacity of one-sided welds. Therefore, this model was adopted as a main tool
for stress analysis in this thesis.
Figure 6. Eccentricity of weld and load components (Tuominen et al. 2017, p. 2).
Teräsnormikortti №24/2018 is currently available guidance for calculation of design
resistance for one-sided welds. The core of the recommendation is based on the directional
method presented in EN 1993-1-8: 2005 since the method considers in details stress
components applied to weld. The first step in the calculation of design resistance is
identifying of the critical weld throat and its orientation in the joint. There are three
highlighted weld geometries in the guidance, those are partial penetration butt weld, single
fillet weld and partial penetration butt weld with reinforcing fillet weld. For each of these,
the critical throat parameters are defined in Table 1. (Teräsnormikortti №24/2018, p. 2-5.)
17
Table 1. Identification of critical weld throat width and orientation (Teräsnormikortti
№24/2018, p. 5).
Weld Geometry Critical weld throat angle (β) Critical throat width (a)
Fillet Weld with leg length z2 45 degs 𝑎 =𝑧2
√2
Partial Penetration butt weld with
penetration depth z1
0 degs 𝑎 = 𝑧1
Partial penetration butt welds with penetration z1 with reinforcing fillet weld with leg length z2
If z2 > z1 45 degs 𝑎 = 𝑧1√2 +(𝑧2 − 𝑧1)
√2
If z2 = z1 45 degs 𝑎 = 𝑧1√2
If z2 < z1 𝛽 = atan𝑧2
𝑧1
𝑎 = √𝑧22 + 𝑧1
2
The analytical model for calculation of stress components which are membrane, bending and
shear stresses, is identical to presented by Tuominen et al. 2017. The explicit part of the
guidance suggests verifying the resistance of weld against two cases of stress states
developed in critical weld throat plane line 1-1 and across the fusion line perpendicular to
applied load, line 2-2 as shown in Figure 7.
Figure 7. Weld Dimension Labels (Modified Teräsnormikortti №24/2018, p. 6).
18
Eventually, evaluation of weld’s resistance is going according following procedure:
• Firstly, identification of critical weld throat and its position relatively to loading
according to Table 1.
• Secondly, expressing Fw critical loading magnitude from equation 7 by substuting
stress components with equations 8, 9 and 10 which will consequently lead to
equation 11.
𝐹𝑤 =𝑎2𝑏𝑓𝑢
√(𝑎 cos 𝛼 + 𝑘𝑒)2 + 3𝑎2 sin2 𝛼 (11)
It should be note that βw correlation factor and γM2 are both assumed to be 1, since the goal
is to obtain the magnitude of load at failure. The value fu is based on the filler material
ultimate strength, normally calculation is based on the base material as βw is used for
consideration of potential strength difference contributing to the result safety.
In addition, it is worth noticing that Teräsnormikortti does not consider the case where failure
occurs along vertical or inclined fusion line depending on fillet weld penetration as shown
in Figure 7 by orange dash line. Failure along this line happens mainly by shear, which
magnitude reaches maximum in comparison with other presumable failure paths as
illustrated in Figure 8. In case of joints made of high strength steels which are more prone
to fail around fusion lines as was described by Björk et al. (2018), shear mode failure along
the inclined fusion line is more probabilistic than along path 2-2.
Figure 8. Stress components on the single-sided fillet weld’s legs with linear elastic
bending moment distribution.
19
3. Research Methods
This thesis project employs both analytical and experimental approaches. The core of the
research is comparison of welded joints’ strength performance obtained by analytical
calculation with laboratory test results.
3.1 Experimental tests
Experimental part of the research is required for verification and calibration of analytical
computation model. Specimens’ preparation and subsequent tests were conducted in the
Laboratory of Steel Structures at LUT University.
Since the main variable parameter considered in this research is geometry of weld, therefore
the goal of laboratory tests was covering the range of single-sided welds’ geometries. The
summary of dimensions for laboratory specimens are presented in test matrix, Table 2.
Table 2. Established test matrix for laboratory tests specimens.
ID Steel
Grade
t*
[mm]
z1
[mm]
z2
[mm]
e
[mm]
SBW_S355_7 S355 8 7 - 0,5
SBW&FW_S355_4&4 S355 8 4 4 2
SBW&FW_S355_2&6 S355 8 2 6 4
FW_S355_8 S355 8 - 8 6
SBW_S700_7 S700 8 7 0,5
SBW&FW_S700_4&4 S700 8 4 4 2
SBW&FW_S700_2&6 S700 8 2 6 4
FW_S700_8 S700 8 - 8 6 * plate thickness t
20
3.2 Test specimens
Four specimens of the test set were made of SSAB DOMEX 355MC D with minimum yield
strength of 355 MPa and ultimate tensile strength of 430-550 MPa. The rest of the set were
made of STRENX 700 MC PLUS with nominal yield strength of 700 MPa and ultimate
tensile strength of 750-950 MPa. The chemical composition and mechanical properties of
both filler and base materials are available from Table 3.
Table 3. Nominal Mechanical properties and chemical compositions of the base and filler
materials (SSAB, 2019; Böhler, 2019, p. 243; Elga, 2019, p. 80).
Mechanical Properties
Material
Yield
Strength
fy [MPa]
Ultimate Strength
fu [MPa]
Elongation A5
[%]
Charpy V-Notch
CVN [J]
CE
(IIW)
SSAB 355MC 355 430-550 23 27 0.39
Elgamatic 100 470 550 26 50 0.32
STRENX 700 700 750-950 13 40 0.51
Union NiMoCr 720 780 16 47 0.60
Chemical composition [weight-%]
Material C Si Mn P S Altot Nb V Ti Ni Cr Mo
SSAB 355MC 0.10 0.03 1.50 0.025 0.010 0.015 0.09 0.2 0.15 - - -
Elgamatic 100 0.08 0.82 1.45 - - - - - - - - -
STRENX 700 0.12 0.25 2.10 0.020 0.010 0.015 0.09 0.2 0.15 - - -
Union NiMoCr 0.08 0.6 1.70 - - - - - - 1.50 0.2 0.5
The dimensions of test specimens are presented in Figure 9. The identical test specimens
were used for both tested steel grades S355 and S700. The thickness of plates was 8 mm for
both materials. Prior to welding, test plates were bevelled according to desired weld
geometries, in total, three bevel types were utilized as could be found from Figure 10.
Furthermore, in order to control weld root penetration, infusible tungsten strip was placed in
the weld zone.
21
Figure 9. Dimensions of tensile test specimen.
Figure 10. Type of bevels used in preparation of test welds and placement of tungsten strip
for root penetration control.
Preassembly process consisted of possession of tungsten strip at the weld root and tack
welding of plates. Alignment of vertical plates was ensured by utilization of custom-made
support Figure 11. Start and end welds’ sections were moved outside actual specimen as
could be seen in Figure 11. After welding these sections were sawed and machined to avoid
possible imperfections. Cut sections, further, were used for hardness measurements and
inspection of weld geometry.
Tungsten
22
Figure 11. Tack welded specimen and positioning of plates with tungsten strip in custom
made support prior tack welding.
Welding of specimens was conducted by robotized GMAW process. Robot welding was
selected in order to minimize the variation in throat thickness and penetration along welds’
length. Welding sequence and passes are designated in Figure 12. Welding parameters for
each pass are given in Appendix I.
Figure 12. Welding sequence. Welding position is PB (horizontal vertical).
3.3 Measurements
Start and end sections of welds were cut and polished so that leg length of fillet weld and
penetration depth of butt weld could be evaluated. Examples of polished sections are shown
in Figure 13. All polished section figures are seen in Appendix II. Examination of welds
revealed deviation of weld dimensions from planned ones. Actual parameters were used for
23
analytical evaluation of weld load capacities in Equation 11. Employment of robotic welding
provides substantial ground for assuming constant weld dimensions throughout total length.
Even though, precision of tungsten strip positioning is problematic, utilization of tungsten
strips proved its effectiveness in controlling of root penetration. Therefore, obtained welds
possessed sufficient ability for root opening under tensile loading.
Figure 13. Polished sections of FW_S700_8 and SBW_FW_S700_4_4 specimens.
3.4 Test set-up and instrumentation
All specimens were tested under uniaxial tensile loading at the room temperature till failure.
The test rig used in the experiment had maximum loading capacity equal to 1200 kN.
Schematic representation of the test setup introduced in Figure 14. The speed of applied
displacement by rigs was equal to 0.01 m/s. Strain values was recorded from extensometer
and initial measuring length was 80 mm.
Figure 14. Schematic tensile test setup.
24
3.5 Finite Element Analysis
The finite element method (FEM) is a computational tool which can be used for solving
complex engineering problems. In general, FEM is based on principal of substitution the
complicated problem by simpler one. Since the actual problem is replaced by simplified
model, it is possible to obtain an approximated solution rather than exact one. In the finite
element method, the solution region is divided into small, interconnected subregions which
are called finite elements. In whole structure, an approximate response solution is assumed
for each element, then, based on overall equilibrium, these local solutions are summarized
into overall system behavior. In combination with high-speed digital computers, FEM found
wide application in field of structural mechanics. (Rao 2005, p. 3.) Nowadays, there are
many software packages that employ FEM for solving various engineering problems. The
one of them is Simcenter Femap 12.0 which was used in this research.
A finite element model consists of many points, called nodes, which form a geometry of the
tested part. Nodes create a grid known as finite element mesh which divides a material into
finite elements. Each element contains material properties and defines a reaction of model
to various loading conditions. The density of mesh may vary throughout the model,
depending on anticipated stress level fluctuation in certain regions. Thus, areas experiencing
significant gradients changes usually requires high mesh density while areas of minor stress
changes can be modeled by larger elements without compromising results. Points of interest
might be represented by stress-concentration points such as weld root or determined from
failure paths of previously tested specimens.
For this research, each specimen was represented by simplified model. For simplification of
analysis and obtaining proper meshing, welds were represented by idealized triangular
shapes. In order to optimize the time required for obtaining FEA solution, each model
constituted a half symmetry. The nonlinear static analysis mode was selected for this
research since it was desired to observe the joint behavior after initial yield of material.
25
Bi-linear Elasto-Plastic material models were defined for plate and weld materials. Table 4
presents the true stress-strain material models used in FE models. Poisson’s ratio ν was
similar for all materials and was equal to 0.3. The Young’s modulus, E for S700 was obtained
from research conducted by Shakil et al. (2020) and its value was 216 GPa. For the rest of
materials, the conventional value of 210 GPa for E was used. Isotropic hardening was
employed for analysis since this model sufficiently reflected material behavior in case of
monotonic loading since it sufficiently reflected material behavior in case of monotonic
loading and more preferable for saving computational time.
Table 4. Bi-linear material models used in FEA.
Material
Plastic Strain 1st
point
[mm/mm]
Stress 1st point
[MPa]
Plastic Strain 2nd
point
[mm/mm]
Stress 2nd point
[MPa]
SSAB 355MC 0 415 0.33 481
Elgamatic 100 0 470 0.26 550
STRENX 700 0 725 0.16 850
Union NiMoCr 0 720 0.16 780
Tensile specimens were modeled by solid elements in FEMAP. Since the focus of interest
was weld joint, so more refined mesh was selected for weld representation. The element size
in the weld area varied from 0.6 to 1 mm. Element size was gradually increased with
accordance to distance from the weld.
Figure 15. Meshing of the fillet weld model.
26
Nodal set of constraints were applied to FE models in order to reproduce the conditions of
laboratory tests. The set of constraints was assumed to be completely rigid which might
cause some challenges in comparison with test results. A symmetry constraint was applied
to the bottom of middle plate in order to compensate another half of the specimen. The
second constraint set was used for reproduction of the clamping condition of specimen in
the test rig. Importance of clamping constraint was considerable because it had major effect
on test specimen deformation and development of the secondary bending moment. In Figure
16, constraint setup can be seen. In the analysis, loading was applied in form of nodal
displacement.
Figure 16. Applied constraints and loading used in FEA.
27
4. Results
The target of this study was to determine the effect of secondary bending moment on strength
capacity of single-sided fillet welds. Desired outcome of tests was obtaining weld failure.
Welded specimens with different degree of bending (DOB) were manufactured and tested
under similar loading conditions.
𝐷𝑂𝐵 =𝜎𝑏
|𝜎𝑚| + |𝜎𝑏| (12)
Equation 12 defines DOB value where σm is the membrane stress and σb is the bending
moment in the weld critical throat thickness. DOB for tested weld geometries is presented
in Table 5. Critical throat thickness was identified according to Teräsnormikortti №24/2018
and actual weld geometries illustrated in Appendix II. Locations of failure planes for all
specimen beside specimen SBW_S355_7 are available from Appendix III. Unfortunately,
the specimen SBW_S355_7 failed from base material.
Table 5. Test Matrix with DOB at assumed critical throat and actual failure location.
Test Specimen
DOB
Assumed critical
throat angle
α [deg]
Eccentricity
e[mm]
Location of
failure*
SBW_S355_7 0.34 18.7 1.10 BMF
SBW&FW_S355_4&4 0.68 45 2.32 FLF&WF
SBW&FW_S355_2&6 0.79 45 4.13 FLF
FW_S355_8 0.86 45 6.05 WF
SBW_S700_7 0.28 13.4 0.86 FLF
SBW&FW_S700_4&4 0.67 45 2.10 FLF
SBW&FW_S700_2&6 0.78 45 3.73 FLW
FW_S700_8 0.85 45 6.23 WF
*BMF=base material, FLF=fusion line failure, WF=weld failure
4.1 Tested weld geometries
The first tested weld geometry was fillet weld without root penetration insured by tungsten
strip. Two specimens FW_S355_8 and FW_S700_8 were prepared. These welds were in
28
particular interest since they possessed the maximum eccentricity and the major effect of
secondary bending moment was expected during tensile test. Both specimens failed from the
weld. The failure plane of the S355 specimen inclined at an angle 48° which is in conformity
with failure path predicted by Eurocode 3 and maximum shear stress e.g., the Tresca
criterion. The failure ligament of S700 specimen was located at an angle 30° which is typical
for transversely loaded fillet welds as was noticed by Björk et al. (2017).
Following specimens were designed with an idea, while keeping perpendicular weld leg
length equal, to increase weld penetration. Thus, it was planned to gradually decrease an
effect of eccentricity on weld’s strength. Next geometry for specimens
SBW_FW_S355&S700_2&6 was designed so that partial penetration butt weld was
expected to have 2 mm penetration and reinforcing fillet weld to have leg length of 6 mm.
Failure location of S355 is parallel fusion line. Further examination of failure plane surface
Figure 17 revealed porosity of a filler material at the weld root. This weld defect caused the
crack development along the fusion line. The specimen made of S700 failed along the
parallel fusion line even though assumed magnitude of the secondary bending moment in
this plane is less than in the weld metal and perpendicular fusion line. However, proneness
of high strength steel joints to fail around fusion was previously described by Björk et al.
(2018). The research revealed that due to the softening and other metallurgical effects, the
areas around fusion lines might become the weakest zone in a joint (Björk, Ahola &
Tuominen, 2018, p. 8). Furthermore, more supporting evidences can be derived from
hardness measurement results along the fusion lines presented in Appendix IV.
𝑓𝑢 𝑎𝑣𝑔 = −93,8 + 3,295𝐻𝑣 (13)
Dependence of hardness and strength can be described by Equation 13 (Pavlina & Van Tyne,
2008). Equation 13 was used for evaluation of metal strength along fusion lines and weld
metal. Results obtained from specimen SBW_FW_S700_2&6 (Appendix IV) displayed that
parallel fusion line was the weakest from examined potential failure paths.
29
Figure 17. Fracture surface of SBW_FW_S355_2_6.
Subsequent couple of specimens SBW_FW_S355&S700_4&4 was beveled in a way to
reach 4 mm penetration for butt weld and reinforced by fillet weld with leg length 4 mm.
Obtained weld geometries slightly deviated from the plan, especially in the butt weld
penetration, but nevertheless, the eccentricity parameter kept decreasing. The failure path of
S355 specimen had two directions as could be seen from Appendix III. The failure crack
started to propagate from the weld root along the perpendicular fusion line. Then the crack
reached the fillet part of the weld, it changed it direction towards a plane making 46° angle
with load action line. The cause for such failure crack propagation became lack of fusion at
the weld root as can be seen from Figure 18. Thus, once the failure crack had overcome
plane weakened by lack of fusion, the crack continued to propagate along maximum shear
criterion plane.
Figure 18. Fracture surface of SBW_FW_S355_4_4.
30
The specimen S700 failed from perpendicular fusion line. Force-displacement curve Figure
19 obtained from the movement of test cylinder, revealed the lack of deformation capacity.
As it was written by Guo et al. (2016), welding of high strength steels is very challenging
due to their high hardenability and tendency to form the martensite below the fusion
boundary. Such area of HSS joint has low toughness value which might lead to brittle
fracture or lack of deformation capacity of the joint under loading. This is also supported by
relatively high carbon equivalent CE of STRENX 700 and Union NiMoCr from table 3.
Photos of fracture surfaces are available in Appendix V.
Figure 19. Load-displacement curve for SBW_FW_S700_4_4.
Design of the last two specimens SBW_S355&S700_7 was made in conformity with goal to
investigate the effect of 1 mm under-penetration in single sided butt weld loaded in tension.
Under-penetration was successfully achieved; however, the welds’ size was excessive due
to fillet portion. There was an option to grind the excessive fillet weld, but modification of
welds’ geometry might cause other uncertainties such as creation of additional stress risers.
Therefore, it was decided to test specimens in as welded condition. The S355 joint performed
well in the test because the weld strength exceeded the base material strength so failure
occurred outside the weld area. The result with S700 joint was different since the weld failed
in the perpendicular failure line. This type of failure might result from softening of the
adjacent heat affected zone in similar manner with specimen SBW_FW_S700_2&6.
31
4.2 Comparison of analytical and test results.
In the first column of Table 6, theoretical capacities of joints were calculated according to
design guide presented in Teräsnormikortti №24/2018 equation 11. Measured test welds’ leg
lengths z1 and z2 were used for evaluation and are seen in Table 7. The second column
represents capacities calculated with use of equation 11 according to actual location and
length of failure path as presented in Appendix III. Even though, current Eurocode 3 doesn’t
have clear guide for design of single-sided fillet welds, it was interesting to utilize directional
method Equation 5 for comparison. Therefore, the third column contains capacity values
evaluated in respect to critical throat thicknesses which are marked by yellow lines in the
Appendix II. Actual welds’ strength capacities obtained from tensile tests are shown in the
last column.
Table 6. Comparison of analytical and tested weld capacities.
ID
Fw
(Teräsnormikortti)
k = 4
[kN]
*
Fa
(Actual
failure
path)
k = 4
[kN]
**
FEC
(Eurocode
3)
[kN]
***
Ft
(Test)
[kN]
SBW_S355_7 195,57 1,18 193,37 1,21 249,77 0,94 233,87
SBW&FW_S355_4&4 83,10 2,13 83,10 2,13 170,89 1,03 176,8
SBW&FW_S355_2&6 54,32 3,08 57,79 2,89 129,55 1,29 167,12
FW_S355_8 38,02 3,00 45,11 2,53 135,19 0,84 114,04
SBW_S700_7 329,67 1,15 334,85 1,13 441,86 0,86 378,64
SBW&FW_S700_4&4 123,67 1,75 141,10 1,53 247,01 0,87 215,85
SBW&FW_S700_2&6 85,02 2,66 125,91 1,79 203,73 1,11 225,74
FW_S700_8 66,79 2,65 73,47 2,4 351,01 0,5 176,69
*Ft / Fw ** Ft / Fa ***Ft / FEC
Main calculation variables used for calculation capacities Fw and Fa are presented in the
Table 7. It was problematic to calculate the Fa for specimen SBW&FW_S355_4&4 since
actual failure path didn’t follow single direction, therefore Fw and Fa are the same. The
ultimate tensile strength fu for materials was taken from Table 2. Ultimate strength used for
S355 was 550 MPa and 850 MPa for S700. Selection of reduced value for S700 is explained
by determination of various weld defects associated with welding HSS.
32
Table 7. Calculation Parameters used for analytical model.
ID
z1 [mm] z2 [mm] a [mm] α [deg] e [mm]
SBW_S355_7 FW
7,26 2,45 9,20 18,65 1,10
FA 9,71 0,00 1,60
FEC 8,26 18,00 -
SBW&FW_S355_4&4 FW
3,91 4,99 6,29 45,00 2,32
FA 6,29 45,00 2,32
FEC 6,80 37,00 -
SBW&FW_S355_2&6 FW
2,00 6,52 6,02 45,00 4,13
FA 7,20 0,00 5,60
FEC 5,60 46,00 -
FW_S355_8 FW
0,00 8,20 5,80 45,00 6,05
FA 6,57 42,00 6,44
FEC 5,64 42,00 -
SBW_S700_7 FW
7,57 1,80 9,12 13,38 0,86
FA 8,05 0,00 0,46
FEC 9,12 13,38 -
SBW&FW_S700_4&4 FW
4,00 4,40 5,94 45,00 2,10
FA 8,30 0,00 4,15
FEC 6,36 37,00 -
SBW&FW_S700_2&6 FW
2,33 5,90 5,82 45,00 3,73
FA 6,84 64,00 3,17
FEC 5,55 43,00 -
FW_S700_8 FW
0,00 8,92 6,31 45,00 6,23
FA 7,10 60,00 5,78
FEC 7,94 24,00 -
The results in Table 6 show that traditional calculation guidance provided in EC3 does not
provide safe strength capacities for pure fillet welds where the effect of the secondary
moment is maximum. However, for other S355 geometries EC3 produces safe predictions.
The specimen SBW_S355_7 should not imply any uncertainties, since the Ft for this
specimen is obtained from base material failure. Predicted nominal strengths for S700 can
be compared with test results for all geometries beside S700_4&4 specimen since the full
joint strength was not developed due to weld defect. Strength prediction with sufficient
safety margins was obtained only for S700_2&6.
Nominal strength predictions by Teräsnormikortti can be best analyzed on the example of
S355 set of specimens due to absence of severe weld defects. Representation of results
comparison is illustrated in Figure 20. The results obtained for S355 joints proved the
33
functionality of the concept about capacity reduction. Calculated values obtained for welds
with minimal eccentricity SBW_7 corresponds to actual values and provides safer results
than EC3. However, with increasing eccentricity parameter, deviation of calculated results
is significantly progressing. While test results possess linear regression behavior, calculated
capacities regression is more exponential. So that, if generally compared to EC3,
Teräsnormikortti provides more conservative results. Example of Teräsnormikortti design
check calculation can be found from Appendix VII.
Teräsnormikortti:
𝐹𝑤 =𝑎2𝑏𝑓𝑢
√(𝑎 cos 𝛼 + 𝑘𝑒)2 + 3𝑎2 sin2 𝛼
EC3:
𝐹𝑤 =𝑎𝑏𝑓𝑢
√cos2 𝛼 + 3 sin2 𝛼
Figure 20. Comparison of actual strengths and design strengths per Teräsnormikortti
№24/2018 and EC3 for S355 joints.
Comparison of calculated and theoretical capacities for S700 joints (Figure 21) is revealing
the same pattern as for S355. However, the certain assumption should be made for specimen
S700_4&4, since flawless joint was expected to develop equal or surpassing strength as
specimen S700_2&6. It can be also noticed that EC capacity prediction for pure fillet is
absolutely unconservative.
233,87 176,8 167,12
114,04
198,57
83,1054,32
38,02
0
50
100
150
200
250
300
1,60 2,32 5,60 6,44
Str
ength
(kN
)
eccentricity (mm)
Test Results
TeräsnormikorttiResults
EC3
34
Teräsnormikortti:
𝐹𝑤 =𝑎2𝑏𝑓𝑢
√(𝑎 cos 𝛼 + 𝑘𝑒)2 + 3𝑎2 sin2 𝛼
EC3:
𝐹𝑤 =𝑎𝑏𝑓𝑢
√cos2 𝛼 + 3 sin2 𝛼
Figure 21. Comparison of actual strengths and design strengths per Teräsnormikortti
№24/2018 and EC3 for S700 joints.
In summary, Teräsnormikortti strength capacity predictions are considerably lower than
experimentally obtained weld strengths. Deviation from the actual failure loads is
progressing with the eccentricity factor and consequently with growth of secondary bending
moment. It seems that the influence of the secondary moment on strength capacity reduction
was over estimated for tested specimens. The variation of calculated strengths from actual
failure loads is not similar for both materials. Thus, test results obtained with S700
specimens are closer to predictions by Teräsnormikortti. Therefore, it might be concluded
that the secondary bending moment is more critical is HSS joints than in conventional
structural steels e.g., S355.
4.3 FEA results
Welding analysis is an important field of research, since welding is the main metal joining
process employed in modern fabrication. Computer modelling is one of the modern,
effective tools used in design and research. In particular, FEA is the most important tool
used in simulation of welding process and determination of welded joints strength capacities
(Lindgren, 2001. p.144). However, FEA of welds is associated with many different
phenomena, consideration of which is a challenging task. The major obstacle is material
properties and their distribution within welded joint. (Lindgren, 2001. pp.144-145.)
Moreover, welded joints might have various imperfections such as porosity, lack of fusion,
cracks, HAZ softening etc. Consideration of all possible variables in FEA does not seem
378,64
215,85
225,74176,69
329,67
123,6785,02 66,79
0
100
200
300
400
500
0,86 2,10 3,73 6,23
Str
ength
(kN
)
eccentricity (mm)
Test Results
TeräsnormikorttiResults
EC3
35
possible and in many cases is not even necessary, hence, simplified models are utilized.
However, it is worth mentioning, that every FE model requires a validation by actual test
results.
Approach selected for creation of FE models for this research was going along with an
intention to build simplified representation of test specimens which would perform in a way
close to actual testing data. Each model consisted of two material properties: base plate and
filler wire. Material behavior function was defined by two linear functions representing
elastic and plastic regions. Validation of FEA conformity with test results was executed by
comparison of force-displacement curves.
Figure 22. Freebody location in FE models.
During laboratory tests, displacement was measured from movement of the force cylinder.
Displacement and loading of FE models was obtained from Freebody selection located close
to the end of the model presented on Figure 22. Displacement was taken from summation
node of the Freebody. Loading values were derived by means of Force Balance Interface
Load Summary tool from the same location.
An example of force displacement curve is presented in Figure 23. Results obtained by FEA
for S355 specimens showed sufficient correspondence with test results in both plastic and
elastic regions which allowed to assume that overall behavior of FE models and test
36
specimens had been comparable. Thus, it was possible to receive reasonable FEA data from
weld area. FEA for S700 fillet weld specimen indicated a good correspondence with test
results, however for partial penetration welds the behavior of the weld distinguished from
the test data as could be seen from Appendix VI.
Figure 23. Load Displacement curve (FW_S355_8).
As it was mentioned previously, Teräsnormikortti weld strength capacity predictions for
fillet welds significantly distinguished from test capacities. The reason of such deviation
might be misestimation of the secondary bending moment effect. Calculation of stress
induced by secondary bending moment in given in Equation 8. Beside weld length b and
throat thickness a, magnitude of the secondary bending moment depends of the eccentricity
parameter e, which is assumed to stay constant. However, e could change throughout loading
due to deformation of the test specimens. It can be seen on the example of FW_S355_8.
Figure 24 presents deformation of the joint during FEA. Blue lines show profile of the model
before loading. The specimen deformed in a way that the weld moved towards the load
application line, thus, decreasing the eccentricity parameter and consequently the bending
moment. In order to compare prediction of the secondary bending moment magnitude by
Teräsnormikortti and FE, case of the perpendicular fusion line of the specimen S355_8 was
selected.
0
20
40
60
80
100
120
140
0 1 2 3 4
Load
[kN
]
Displacement [mm]
Test Data
FE-data
37
Figure 24. Deformation of FE model (FW_S355_8).
The secondary bending moment FE data was obtained by utilization of Freebody tool.
Location of selected elements and nodes representing perpendicular fusion line can be
observed from Figure 25. According to Teräsnormikortti, the secondary bending moment is
calculated as a product of tensile load F and eccentricity e. For perpendicular fusion line of
specimen S355_8, eccentricity is equal to 8 mm. Summary of two data sets is presented in
Figure 26.
Figure 25. Freebody representing perpendicular fusion line FW_S355_8.
38
My
Figure 26. Comparison of FEA and Teräsnormikortti tensile loading versus bending
moment occurring in the perpendicular fusion line (FW_S355_8).
According to FEA data, the secondary bending moment growth is linearly depended from
the load up to yielding point, after which increase in load doesn’t affect significant gain in
the moment magnitude. In contrast, Teräsnormikortti prediction of the secondary bending
moment is a continuously rising function throughout loading history and dependent just on
the tensile load magnitude. Thus, the moment’s values obtained by the design code are
higher than FE results due to omitting variation of eccentricity and formation of plastic
hinges.
The closest matching between predicted and actual strengths was obtained in case of
specimens SBW_7, which was initially planned as butt welds with 1 mm of under
penetration, however during welding some fillet portion of welds was formed. The fillet part
of the welds was neglected in FE models. Stress contour for SBW_S355_7 is presented in
Figure 27.
0
100
200
300
400
500
600
700
800
900
1000
0 50 100 150
My
[kN
mm
]
Fx [kN]
FE
Teräsnormikortti
39
Figure 27. Deformation of FE model (SBW_S355_7).
The same procedure was conducted for derivation of the bending moment values as for pure
fillet weld. The resultant curves could be seen in Figure 27. The comparison of the maximum
secondary bending moment magnitudes predicted by design code and obtained from FE
revealed, as expected, smaller difference than in case of the fillet weld joint.
Figure 28. Comparison of FEA and Teräsnormikortti tensile loading versus bending
moment occurring in the perpendicular fusion line (SBW_S355_7).
Further, closer matching of Teräsnormikortti load capacity prediction with test results of
S700 welds, can be explained by lower ductility of S700. Therefore, S700 test specimens
experience relatively smaller deformation. Consequently, diminishing of the secondary
bending moment effect had less influence on S700 specimens than on ones made from S355
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250
My
[kN
mm
]
Fx [kN]
FE
Teräsnormikortti
40
steel. So, inherently, high strength steels welded joints are more vulnerable to the secondary
moment impact.
In order to further investigate the influence of deformation pattern of weld capacity, it was
decided to modify the FEA conditions for S355 fillet weld. As it could be seen from Figure
24, overall deformation of the specimen consisted of middle plate translation to the negative
z-direction and bending of the web. New set of nodal constraints was implemented with
purpose to restrict any translation of the vertical plate in z direction. The final view of the
model presented in Figure 29.
Figure 29. Deformation of FE model with additional TZ constraints (FW_S355_8).
Maximum stress level obtained from constraint model was slightly higher than during
simulation of laboratory test conditions. However, due to locking of bending moment
deformations in the middle plate and web, overall joint performance possessed better
strength capacity as could be seen from Figure 30. Applied additional constraints set
simulate the stress-strain conditions similar to that occurring in fillet welds to hollow
structural sections which had been earlier investigated by Packer et al. (2016). Actual
strength capacities obtained by Packer et al. (2016) were on average 2.04 higher than EC3
predictions, which proved validity of the directional method for design of hollow section
joints.
41
Figure 30. Force displacement curves obtained for specimen FW_S355_8.
In order to further research the effect of constraining web deformation on the welded joint
performance, it was decided to investigate stress distribution along the perpendicular fusion
line in case of FE model representing laboratory test conditions and FE model with
constrained deformation of the web. For the comparison, geometry of FW_S355_8 specimen
was utilized. Stress distribution values were obtained from the nodes in the middle section
of the weld model in form of non-linear solid normal stress σx.
𝜎𝑚 =1
𝑙∫ 𝜎(𝑥)𝑑𝑥
𝑙
0
(14)
𝜎𝑏 =6
𝑙2∫(𝜎(𝑥) − 𝜎𝑚) ∙ (
𝑙
2− 𝑥) 𝑑𝑥
𝑙
0
(15)
Membrane stress was calculated according to equation 14, where l is the length of the
perpendicular fusion line. Bending stress was obtained from Equation 15.
Summary for stress distributions is presented in Figure 31. Visual representation of stresses
allows to see how significant is the effect of web deformation freedom on the magnitude of
the bending stress. Furthermore, interesting detail can be noticed from contour von Mises
0
20
40
60
80
100
120
140
160
180
0 1 2 3 4
Load
Fx
[kN
]
Displacement Tx [mm]
Test Data
FE-data
FE (TZ deformationconstraints)
42
solid stress view of welds Figure 31. Thus, in case of freely deformed web, the critical stress
plane is located in the weld metal, while it constrained model this plane coincides with
parallel fusion line.
a)
b)
c)
d)
Figure 31. FE stress distribution along perpendicular fusion line and von Mises stress
contour view for model with laboratory tests conditions a, c and for model with
constrained web condition b, d.
-1000
-500
0
500
1000
1500
0 2 4 6 8 10
Stre
ss M
agn
itu
de
(MP
a)
Distance from weld root (mm)
Total normal stress
Membrane stress
Bending stress
Non-Linear Stress Peak
-400
-200
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10
Stre
ss M
agn
itu
de
(MP
a)
Distance from weld root (mm)
43
All in all, employment of FEA in this research allowed to shed light on the reasons behind
variation between analytical and test results. It helped to clarify the secondary bending
moment mechanism and its distribution. Furthermore, the last example of constrained model
successfully demonstrated the importance of the secondary bending moment consideration
in different boundary conditions.
44
5 Discussion
In this thesis, computational and experimental results were used to investigate the ability of
Teräsnormikortti №24/2018 to predict the strength capacities for single-sided welds. The
main challenge in design calculations was consideration of the secondary bending moment
which appeared in a joint under tensile loading. According to design code, influence of the
additional bending moment was linearly dependent from weld eccentricity which consisted
in the distance between load application line and location of weld’s critical failure plane.
The core of design calculation guide was based on directional method provided in EC3,
therefore, as a reference values, theoretical capacity strength predictions included results
obtained by EC3.
The experimental part of this research involves laboratory tests of welded joints made from
S355 and S700 steel grades. Design of specimens was prepared with intention to obtain
welds with different degree of bending (DOB) values. It was mainly achieved by
manipulation of eccentricity parameter and weld root penetration control executed by
utilization of infusible tungsten strip. Obtained welds’ dimensions varied from original
design, however the consistency of DOB was attained.
Finite element analysis (FEA) was also employed in this research. The main reason for
utilization of FEA was investigation of the bending moment magnitude and deformation
pattern of the test specimens. FE 3D models were created and analyzed in Femap NX Nastran
software. Material models for base plates and filler wires were defined by simplified bi-
linear models. Validation of FEA results based on force displacement curves revealed good
conformity with test results.
Comparison of numerically obtained capacities by EC3 and test results, revealed good
conformity with test results attained from S355 single sided bevel welds, however
predictions made for pure fillet weld exceeded actual strength. As for S700 specimens,
45
comparison analysis was associated with uncertainty related with softening of material
around fusion lines which might prevent welds to develop the full-strength capacity. From
tested welds, the safe predictions were obtained only for one weld’s geometry.
Application of Teräsnormikortti design guide allowed to make safe capacity predictions for
all tested geometries. However, while safe and close conformity results were obtained for
specimens with minimum DOB, capacity predictions for geometries with higher DOB
appeared to be over conservative. The deviation of predicted capacities from test results was
progressing with growth of eccentricity parameter. Therefore, it could be concluded that
prediction for the secondary bending moment effect was overestimated in case of tested
specimens.
FEA results revealed the redistribution of the secondary bending moment omitted in design
code provided by Teräsnormikortti. FEA indicated that the secondary bending moment
effect was partially compensated by deformation of specimen. Thus, the maximum predicted
magnitude of the bending moment was never achieved in test conditions. Furthermore, the
constrained model case demonstrated the influence of the boundary conditions on the single-
sided welds’ capacity.
Utilization of S700 steel for experimental part of this research once again confirmed
challenges arisen in design and manufacturing of welded structures made from HSS.
Namely, weakening of the areas around fusion lines due to softening and other metallurgical
effects as described by Björk et al. (2018). Moreover, comparison of numerical and test
results, revealed greater emphasis effect of the secondary bending moment on the reduction
of strength capacity.
It also can be added that Teräsnormikortti design guide is missing consideration of critical
plane along parallel fusion line. Where combination of shear stress and metallurgical effects
gives probability of failure along this path more than transverse fusion line or weld throat.
46
5.1 Further research
The experimental part of this research included laboratory tests of welded joints made from
two steel grades S355 and S700. For each material, four different weld geometries were
prepared. Results obtained from S355 specimens allowed to observe actual dependence of
strength capacity from weld eccentricity. However, as for S700, this dependence could not
be unambiguously derived due to weld defects (S700_4&4). Therefore, in order to make
amendments to existing design code for better conformity with actual welds’ performance,
it is necessary to increase number of test specimens representing welds with different DOB.
FEA could be further improved with implementation of actual stress-strain material models
obtained from test of tensile coupons made from base and filler materials. Furthermore,
variation of material strength properties in the weld area, in some cases, might have a major
influence on failure location and overall joint performance, e.g., S700_4&4. In order to
determine strength variation effect in FEA, it is necessary to use several material properties
for modelling welds as could be seen from example in Figure 32.
Figure 32. Modelling of welded joint with distinguished HAZ (Mohammed, 2015, p.38).
47
One of the observations made during FEA was effect of clamping on the joint’s strength.
Explicitly, the clamping was dictating the ability of the specimen to deform to the direction
perpendicular to load action line. Thus, the development of the secondary bending moment
was restricted by deformation limit. In order, to achieve maximum deformation, the flexible
pin joint can be utilized between the weld section of the specimen and clamping.
48
6 Summary
The research was conducted to investigate the effect of the secondary bending moment
occurring in the single-sided welded joints under tensile loading. The numerical evaluation
of strength capacities was done according to design guidance given in Teräsnormikortti
№24/2018 and EC3. The analytical results were compared to actual strength capacities
obtained from the laboratory tests. In total, two steel grades were used for test specimen
manufacturing, those were S355 and S700. Additional analysis was performed by means of
finite element method which was facilitated by utilization of Femap NX Nastran.
Correlation between Teräsnormikortti and test results obtained for S355 specimens varied
from 1,18 to 3. The deviation growth was progressing with increase of weld’s eccentricity.
The similar correlation pattern was also obtained for S700 with 1.15 to 2.65. Overall, for
used test setup conditions, Teräsnormikortti provided overconservative results where
eccentricity was expected to have significant growth of the secondary bending moment.
Analytical overevaluation of the secondary bending moment effect had two causes. The first
one was stress redistribution due to deformation of specimens. It was supported by higher
criticality of the secondary bending moment in S700 specimens due to lower ductility of
HSS. The second cause was clamping of specimens in the test rigs in a way which prevented
specimens webs from achieving maximum deformation values. This was demonstrated by
FEA.
Even with overconservative strength capacity predictions, Teräsnormikortti affirmed its
actuality by providing safe predictions for single-sided welds’ strength capacity. It was
affirmed that conventional EC3 design code had not been valid for design of plate structures
connected by single-sided welds with considerable under penetration values. Thus,
Teräsnormikortti is a valid, existing design guide for single-sided welds.
49
References
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strength steel. Weld World 62:5. Pp. 985–995. https://doi.org/10.1007/s40194-018-0624-4
Böhler. 2013. Filler Metals Bestseller for Joining Applications [web document]. [Reffered:
20.10.2019]. Available: https://www.selfasoldadura.com/Catalogo/Item/36_Item/Filler-
Metals-Bestseller-for-Joining-Applications-EN.pdf
Dowling, N. 2013. Mechanical behavior of materials. 4th ed. Boston: Pearson. 951p.
Elga.2019. Welding Consumables for the Professionals [web document]. [Referred:
20.10.2019]. Available:
http://www.itwwelding.com/media/Pdf/Literature_download/Elga_Svetskatalog_2017.pdf
SFS-EN 1993-1-8 2005. Eurocode 3: Design of Steel Structures. Part 1-8: Design of joints.
Brussels: European Committee for Standardization. 133p.
Guo, W, Li, L, Crowther, D, Dong, S, Francis, JA & Thompson, A 2016. Laser welding of
high strength steels (S960 and S700) with medium thickness. Journal of Laser Applications,
28:2. Pp. 022425-1–022425-10. https://doi.org/10.2351/1.4944100.
Lars-Erik Lindgren (2001) FINITE ELEMENT MODELING AND SIMULATION OF
WELDING PART 1: INCREASED COMPLEXITY, Journal of Thermal Stresses, 24:2. Pp.
141-192. https://doi.org/10.1080/01495730150500442
Mohammed, R. 2015. Finite Element Analysis of Fillet Welded Joint. Bachelor Thesis.
University of Southern Queensland. Faculty of Health Engineering and Sciences. 86p.
Packer, J. A., Sun, M. & Tousignant, K. 2016. Experimental evaluation of design procedures
for fillet welds to hollow structural sections. Journal of Structural Engineering, American
Society of Civil Engineers 142:5. Pp. 04016007-1 – 04016007-12.
https://doi.org/10.1061/(ASCE)ST.1943-541X.0001467
50
Saani Shakil, Wei Lu, Jari Puttonen. 2020. Experimental studies on mechanical properties
of S700 MC steel at elevated temperatures. Fire Safety Journal 116:12. Pp. 103157-1–
103157-13. https://doi.org/10.1016/j.firesaf.2020.103157.
Singiresu S. Rao. 2005. The Finite Element Method in Engineering (Fourth Edition),
Butterworth-Heinemann. 663p.
SSAB. 2019. SSAB Domex 355MC [SSAB webpage]. [Reffered: 20.10.2019]. Available:
https://www.ssab.com/products/brands/ssab-domex/products/ssab-domex-355mc
SSAB. 2019. Strenx 700MC Plus [SSAB webpage]. [Referred: 20.10.2019]. Available:
https://www.ssab.com/products/brands/strenx/products/strenx-700-mc-plus
Teräsnormikortti №24/2018. Design Resistance of One-sided Welds to EN 1993-1-8:2005.
Teräsrakenneyhdistys ry. 14p.
Tuominen, Niko & Björk, Timo & Ahola, Antti. 2017. Effect of bending moment on capacity
of fillet weld. Conference: 16th International Symposium on Tubular Structures (ISTS 2017)
At: Melbourne, Australia. Tubular Structures XVI Pp. 675-683
1
Appendix 1: Welding Parameters of Test Specimens
Current Voltage Travel
Speed
Wire feed
speed
Lead
angle
Specimen Pass I U Vtravel Vwire
[-] [A] [V] [mm/s] [m/min] [degs]
SBW_S355_7 1 203 24,5 9 10 5
2 203 24,4 9 10 5
3 199 25,0 8 10 10
4 196 25,2 7 10 10
SBW_S700_7 1 203 24,1 10 10 5
2 203 24,1 10 10 5
3 199 24,9 6 10 10
4 207 25,0 6 10 10
SBW_FW_S355_2&6 1 219 26,1 10 11 5
2 217 26,0 10 11 5
3 212 26,7 10 9 10
4 212 26,6 10 9 10
SBW_FW_S700_2&6 1 223 25,6 10 11 5
2 227 26,0 10 11 5
3 186 24,5 10 9 10
4 190 24,5 10 9 10
SBW_FW_S355_4&4 1 190 23,6 13 9 5
2 189 23,4 13 9 5
3 189 24,1 8 9 10
4 189 23,9 8 9 10
SBW_FW_S700_4&4 1 188 23,0 13 9 5
2 189 22,9 13 9 5
3 191 24,1 8 9 10
4 189 24,1 8 9 10
1
Appendix 2: Test Welds’ Geometries
FW_S355_8 FW_S700_8
SBW_FW_S355_2&6 SBW_FW_S700_2&6
SBW_FW_S355_4&4 SBW_FW_S700_4&4
SBW_S355_7 SBW_S700_7
1
Appendix 3: Welds’ Failure Planes
FW_S355_8 FW_S700_8
SBW_FW_S355_2&6 SBW_FW_S700_2&6
SBW_FW_S355_4&4 SBW_FW_S700_4&4
SBW_S355_7 (Base material Failure) SBW_S700_7
1
Appendix 4: Hardness Measurements Points and Values, Evaluation of tensile strength
along potential failure lines according to Equation 12.
FW_S355_8 FW_S700_8
Line 1
(HV 5)
Line 2
(HV 5)
Line 3
(HV 5)
Line 1
(HV 5)
Line 2
(HV 5)
Line 3
(HV 5)
173 172 219 221 237 320
165 170 225 233 248 308
177 167 221 243 250 308
176 167 218 242 251 305
181 178 225 252 247 306
179 181 218 254 277 303
180 187 225 248 299 297
177 192 222 252 304 297
176 198 246 306 296
173 211 249 306 297
178 221 250 305 303
173 222 254 306 299
176 218 250 297 275
181 222 243 305 246
181
fu [MPa]
FL1=493 FL2=504 FM=636 FL1=722 FL2=769 FM=912
2
SBW_FW_S355_2&6 SBW_FW_S700_2&6
Line 1
(HV 5)
Line 2
(HV 5)
Line 3
(HV 5)
Line 1
(HV 5)
Line 2
(HV 5)
Line 3
(HV 5)
181 186 247 248 276 365
187 189 268 258 365 377
181 192 267 258 381 363
181 200 258 257 360 334
180 221 264 257 290 365
187 231 257 257 296 393
187 228 235 258 287 390
180 240 229 254 284 385
181 242 243 264 294
185 237 252 261 311
187 233 243 311
181 217 248 310
178 209 273
224 270
213 264
198 254
244
fu [MPa]
FL1=508 FL2=618 FM=736 FL1=745 FL2=889 FM=1130
3
SBW_FW_S355_4&4 SBW_FW_S700_4&4
Line 1
(HV 5)
Line 2
(HV 5)
Line 3
(HV 5)
Line 1
(HV 5)
Line 2
(HV 5)
Line 3
(HV 5)
175 180 263 281 261 380
179 194 251 308 262 380
192 214 258 303 258 390
190 214 259 284 273 387
198 213 246 262 262 372
206 215 248 247 261 377
197 218 233 250 258 367
186 221 246 284 257 380
194 227 252 356 259 356
196 221 259 349 247 363
191 222 347 282 344
188 225 353 322 353
195 206 358 296
196 310
320
277
257
fu [MPa]
FL1=538 FL2=608 FM=735 FL1=915 FL2=810 FM=1128
4
SBW_S700_7
Line 1
(HV 5)
Line 2
(HV 5)
Line 3
(HV 5)
303 299 380
289 316 390
322 312 385
360 308 385
351 289 380
344 292 377
322 301 372
322 277 377
353 270 363
351 326 353
303 303 322
294 284 342
294 282 344
296 289 353
351 353 375
353 380
379
382
fu [MPa]
FL1=979 FL2=939 FM=1114
1
Appendix 5: Fracture surfaces of test specimens.
FW_S355_8
FW_S700_8
SBW_FW_S355_2&6
SBW_FW_S700_2&6
SBW_FW_S355_4&4
SBW_FW_S700_4&4
2
SBW_S355_7
SBW_S700_7
1
Appendix 6: Force displacement curves FE versus test data.
0
50
100
150
0 1 2 3 4
Load
[kN
]
Displacement [mm]
FW_S355_8
Test Data
FE-data
0
50
100
150
200
0 1 2 3 4
Load
[kN
]
Displacement [mm]
FW_S700_8
Test Data
FE-data
0
50
100
150
200
0 2 4 6 8
Load
[kN
]
Displacement [mm]
SBW&FW_S355_2&6
Test Data
FE-data
0
50
100
150
200
250
0 1 2 3
Load
[kN
]
Displacement [mm]
SBW&FW_S700_2&6
Test Data
FE-data
2
0
50
100
150
200
0 2 4 6
Load
[kN
]
Displacement [mm]
SBW&FW_S355_4&4
Test Data
FE-data
0
50
100
150
200
250
0 0,5 1 1,5
Load
[kN
]
Displacement [mm]
SBW&FW_S700_4&4
Test Data
FE-data
0
50
100
150
200
250
0 20 40 60
Load
[kN
]
Displacement [mm]
SBW_S355_7
Test Data
FE-data
0
100
200
300
400
0 2 4 6 8
Load
[kN
]
Displacement [mm]
SBW_S700_7
Test Data
FE-data
1
Appendix 7: Verification of the weld according to Teräsnormikortti №24/2018
Figure 33 Parameters used in example design calculation (Teräsnormikortti №24/2018, p.
10).
Weld geometry and material properties in this example were selected from fillet weld used
in experimental part of this thesis.
Material properties: S355, EN 10025-2; fy = 355 N/mm2; fu = 510 MPa; t = 8 mm.
Weld properties: Fillet weld z= z2 = 8,2 mm.
External applied load at the centerline of the plate: 1000 N/mm
Line 1-1
Line length (weld throat):
L1-1=z
√2=5,79 mm
Eccentricity of applied load:
e1-1=t+z
2√2√2-
t
2=
t
2+
z
4=4,05 mm
Additional bending moment:
M1=Ne1-1=4052 Nmm/mm
Stress from applied axial load, N
σ⊥,1=N
√2L1-1
=122,1 MPa
2
τ⊥,1=N
√2L1-1
=122,1 MPa
τ∣,1=0 MPa
Maximum perpendicular stress from total applied moment to Line 1-1 (elastic
distribution):
σ⊥,2=6∙M1
(L1-1)2 =725 MPa
Total maximum perpendicular stress applied to weld along line 1-1:
σ⊥=σ⊥,1+σ⊥,2=847,1 MPa
Design check 1, Line 1-1:
βw=0,9, γM2=1,25
σw=√σ⊥2 + 3(τ⊥
2 + τ∥2) ≤
𝑓𝑢
βwγM2
σw=873,1>453,3 MPa. Utilization ratio=1,93 => NOT OK
Design check 2, Line 1-1:
σ⊥≤0,9fu
γM2
σ⊥=847,1>367,2 MPa. Utilization ratio=2,3 => NOT OK
Maximum loading obtained from laboratory test for calculated fillet weld geometry was
114 kN or 1900 N/mm. (Specimen FW_S355_8)