Investigating the Load Contribution Percentage Applied to an
Infinitely Long Plate with a Welded Faying Pad Attached
by
Christopher R. Hadnot
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
August, 2012
© Copyright 2012
by
Christopher R. Hadnot
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
ACKNOWLEDGMENT ................................................................................................. vii
ABSTRACT ................................................................................................................... viii
1. Introduction.................................................................................................................... 1
2. Background .................................................................................................................... 3
3. Theory/Methodology ..................................................................................................... 5
3.1 Finite Element (FE) Modeling ............................................................................... 5
3.2 Applied Load ......................................................................................................... 7
3.3 Nominal Force Determination ............................................................................... 7
3.4 Finite Element Model Characteristics ................................................................... 9
3.5 Boundary Conditions ........................................................................................... 11
4. Results and Discussion ................................................................................................ 12
5 Conclusion .................................................................................................................... 16
6. References.................................................................................................................... 17
Appendix A..................................................................................................................... A1
iii
LIST OF TABLES
Table 1: 0.125-inch Fillet Weld Results .......................................................................... 13
Table 2: 0.25-inch Fillet Weld Results ............................................................................ 13
Table 3: 0.5-inch Fillet Weld Results ............................................................................. 14
iv
LIST OF FIGURES
Figure 1: Example of a Faying Pad and Flange Plate Configuration ................................ 1
Figure 2: Faying Pad attached to an I-beam Flange .......................................................... 6
Figure 3: Shape of Each Faying Pad/Flange Plate Arrangement ..................................... 6
Figure 4: Final Shape of Each Faying Pad/Flange Plate Arrangement used in the
Analysis ....................................................................................................................... 6
Figure 5: Applied Forces Location .................................................................................... 7
Figure 6: 0.125-inch Fillet Weld with 1-inch Faying Pad – Undeformed Shape ........... 10
Figure 7: Boundary Conditions’ Locations ..................................................................... 11
Figure 8: 0.125-inch Fillet Weld with 1-inch Faying Pad – Deformed Shape ................ 12
Figure 9: All Fillet Weld Results .................................................................................... 14
Figure A.1: 0.125-inch Fillet Weld with 1-inch Faying Pad – Undeformed Shape ....... A2
Figure A.2: 0.125-inch Fillet Weld with 1-inch Faying Pad – Deformed Shape ........... A2
Figure A.3: 0.125-inch Fillet Weld with 3.125-inch Faying Pad – Undeformed Shape A3
Figure A.4: 0.125-inch Fillet Weld with 3.125-inch Faying Pad – Deformed Shape .... A3
Figure A.5: 0.125-inch Fillet Weld with 6.25-inch Faying Pad – Undeformed Shape .. A4
Figure A.6: 0.125-inch Fillet Weld with 6.25-inch Faying Pad – Deformed Shape ..... A4
Figure A.7: 0.125-inch Fillet Weld with 12.5-inch Faying Pad – Undeformed Shape .. A5
Figure A.8: 0.125-inch Fillet Weld with 12.5-inch Faying Pad – Deformed Shape ...... A5
Figure A.9: 0.25-inch Fillet Weld with 1-inch Faying Pad – Undeformed Shape ........ A6
Figure A.10: 0.25-inch Fillet Weld with 1-inch Faying Pad – Deformed Shape ........... A6
Figure A.11: 0.25-inch Fillet Weld with 3.125-inch Faying Pad – Undeformed Shape A7
Figure A.12: 0.25-inch Fillet Weld with 3.125-inch Faying Pad – Deformed Shape ... A7
Figure A.13: 0.25-inch Fillet Weld with 6.25-inch Faying Pad – Undeformed Shape .. A8
Figure A.14: 0.25-inch Fillet Weld with 6.25-inch Faying Pad – Deformed Shape ...... A8
Figure A.15: 0.25-inch Fillet Weld with 12.5-inch Faying Pad – Undeformed Shape . A9
Figure A.16: 0.25-inch Fillet Weld with 12.5-inch Faying Pad – Deformed Shape ...... A9
v
Figure A.17: 0.5-inch Fillet Weld with 1-inch Faying Pad – Undeformed Shape ....... A10
Figure A.18: 0.5-inch Fillet Weld with 1-inch Faying Pad – Deformed Shape .......... A10
Figure A.19: 0.5-inch Fillet Weld with 3.125-inch Faying Pad – Undeformed Shape A11
Figure A.20: 0.5-inch Fillet Weld with 3.125-inch Faying Pad – Deformed Shape .... A11
Figure A.21: 0.5-inch Fillet Weld with 6.25-inch Faying Pad – Undeformed Shape . A12
Figure A.22: 0.5-inch Fillet Weld with 6.25-inch Faying Pad – Deformed Shape ...... A12
Figure A.23: 0.5-inch Fillet Weld with 12.5-inch Faying Pad – Undeformed Shape .. A13
Figure A.24: 0.5-inch Fillet Weld with 12.5-inch Faying Pad – Deformed Shape ...... A13
vi
ACKNOWLEDGMENT
To God be the glory, great things He has done.
Isaiah 40:28-31: Do you not know? Have you not heard? The Lord is the
everlasting God, the Creator of the ends of the earth. He will not grow tired or weary,
and His understanding no one can fathom. He gives strength to the weary and increases
the power of the weak. Even youths grow tired and weary, and young men stumble and
fall; but those who hope in the Lord will renew their strength. They will soar on wings
like eagles; they will run and not grow weary, they will walk and not be faint.
Thank you to Katrina, my best friend and wife, for her unfailing love and her
continued encouragement and support throughout this project and life in general. I’m
very blessed with you in my life. I love you.
Special thank you to one of my best friends Doug Fortin for helping me with the
technical aspects of this project since its inception, for helping me understand welding
and its many factors in practice, and your continued guidance in all things related to
welding.
Lastly, thanks to all of my friends and family for your continued support,
prayers, and encouragement during the course of this project.
vii
ABSTRACT
This study focuses on resulting interpolated nodal stresses in finite element (FE)
shell models involving a cover plate (or faying pad) attached to an infinitely long flange
plate to determine the percentage of the applied total load going into the faying pad.
In some cases, it may be advantageous to use two plates, a flange (or an infinitely
long bottom) plate and a faying pad, to make up the flange. This will permit 1) the use of
the thinner plates with lower section moduli to take advantage of its higher allowable
stresses, and 2) from a fatigue strength perspective, since any abrupt change in beam
section will reduce the beam’s fatigue strength, a gradually tapered width at the end of a
faying pad (hence, a fillet weld) has been proven historically favorable.
Thus, this study specifically investigates each faying pad/plate arrangement as
it’s loaded with a varied fillet weld size (0.125-inch, 0.25-inch, and 0.5-inch fillet weld)
how the applied load contribution gets translated through the fillet weld into the faying
pad. The results show that between 7% and 14% of the total applied load contribution
translates into the faying pad.
Errors in interpolated stresses range from 0% to -1.69%, depending on the weld
joint configuration. The key conclusion of this paper is that for a given weld size, weld
geometry, and faying pad size, interpolated stresses show that a maximum of 14% of the
total load applied gets translated into the faying pad.
viii
1. Introduction
Reference [1] defines a cover plate (or faying pad) as the mating surface of a
member that is in contact with or in close proximity to another member to which is to be
joined. And in some cases, it may be advantageous to use two plates, a flange (or
bottom) plate and a faying pad, to make up the flange. Many methods have been
suggested for termination of faying pads. But because there are so many configurations
of faying pads, it is impossible to effectively recommend one specific faying pad end.
However, the simplest manner to do so is to instill the use of a large transverse fillet
weld across the end of a faying pad as it rests on a flange plate. Tensile forces, which are
assumed to be uniformly distributed across the width of the cover plate, should be
transferred simply and directly into the corresponding flange (bottom plate) of an I-beam
or T-stiffener for example without causing any stress concentration. And additionally,
any abrupt change in beam section will reduce the beam’s fatigue strength. Thus, it
favors the use of a gradually tapered width at the end of a faying pad, as shown in Figure
1 below. And over the years, the load carrying fillet weld joint has become a very
common structural configuration because it allows the engineer to attach thinner plates
to one another via the fillet weld, thereby having a lower section moduli, resulting in
higher allowable stresses.
Figure 1: Example of a Faying Pad and Flange Plate Configuration
The subject of this paper is thus limited to the analysis of a faying pad welded to an
infinitely long plate with a partial penetration fillet weld joint. This is of particular
importance to the fatigue analysis of cyclically loaded engineered structures that employ
FE analysis during design, and welding during fabrication or construction. Examples of
such structures include ship hulls, holding tanks, pressure vessels, decks, girders,
bridges, buildings, offshore structures, etc. The fatigue strength of the welded joints in a
structure will typically govern the fatigue life of the structure because welded joints
exhibit poorer fatigue performance than that of the parent base metals being joined.
Stresses also tend to be high at such intersections, making them prime fatigue failure
sites.
2
2. Background
Welding is a crucial manufacturing process and is one of the main joining methods
used in industries to assemble various products including ships, automobiles, trains,
bridges, and other important items. For instance, the assembly process in shipbuilding
essentially involves the intense joining of large plates. Typically, these plates are allwelded, thin-plate structures. Fatigue cracks in steel ships often occur at welded joints
where stress concentrations due to the joint geometry are relatively high and the fatigue
strength of the weld is reduced in comparison to that of the base metal. This becomes
more critical in ships built of High Strength Steels (HSS) because the fatigue strength of
steel in the as-welded condition does not increase in proportion to the yield or tensile
strength.
Designing against fatigue failure is an important consideration in structural analysis.
According to the Reference [2] article (p.5) titled "Fracture and Structure," the majority
of structural failures are due to brittle fracture (as opposed to other failure modes, such
as ductile fracture, plastic collapse, buckling, etc.). The above referenced article lists
several examples of crack-producing processes that can lead to brittle fracture, such as
machining, quenching, fatigue, hydrogen embrittlement, liquid-metal embrittlement, and
stress corrosion. The article then goes on to state, "Of these, the single most prevalent
initiator of brittle fractures is the fatigue crack, which conservatively accounts for at
least 50% of all brittle fractures in manufactured products by one account."
The presence of welds in or to a structural member can substantially reduce the
fatigue strength of the member. Fatigue curves for weldments typically exhibit
significantly lower intercepts, slopes, and fatigue limits than fatigue curves for parent
base materials. The Reference [2] article (p.5) titled "Fatigue and Fracture Control of
Weldments" points out that "An examination of structural and component failures
documented in open literature over the past 50 years or so clearly indicates that failures
predominately start at connections, and in particular, welded joints."
Two main phenomena cause welds to exhibit poorer fatigue performance than the
parent base material being joined:

Stress concentration due to weld profile and joint geometry

Tensile residual stresses due to weld shrinkage and distortion
3
Each of these phenomena reduces fatigue strength for reasons described in the
following paragraphs.
As is known from the theory of elasticity, stresses concentrate near changes in the
geometry of a load-carrying component. The re-entrant angle found at the weld toe of a
partial penetration weld joint is a classic example of an abrupt change that will lead to
stress concentration at the toe. This raises stresses at the weld, thereby reducing fatigue
life for cyclically loaded members. The stress concentration can also cause a local plastic
zone, further decreasing fatigue performance.
Per Reference [2], typically high residual stresses are already in the weld and plate(s)
when they are fabricated together, and can approach yield magnitude. They are caused
by thermal expansion and contraction during welding, and are typically tensile
transverse to the weld toe. Using higher-strength parent alloys and weld filler materials
will increase the magnitude of residual stresses since these materials can sustain more
damaging weld shrinkage before locally yielding. As a result, the mean stress for any
cyclic loading pattern is always tensile. Compressive loading generally cannot improve
fatigue performance of as welded joints, since the compressive loading cycle is
superimposed onto the tensile residual stress field. Stress levels will fluctuate down from
yield magnitude during compressive cycles. Applied tensile stresses would cause local
yielding during the first cycle(s), and then result in stress levels fluctuating up to yield
magnitude during subsequent cycles.
Per Reference [2], the weld toe is often the primary location for fatigue cracking in
welded joints. This is due to the factors discussed above. Fatigue cracks can also
originate from ripples in the weld bead or at weld terminations, but only when the
loading applied is longitudinal to the weld. Cracking from the toe or root occurs when
the applied loading is transverse to the weld. However, cracking from the root is only a
factor for partial penetration welds with sufficiently small weld throats. Per Reference
[3], if the throat thickness is increased, failure is more likely to occur at the weld toe.
Therefore, it can be suggested that the severity of the weld root stress concentration
decreases as the throat thickness increases. With increasing throat thickness, the stress
concentration factor at the weld root decreases and the fatigue failure occurs at the weld
toe.
4
3. Theory/Methodology
Based on the discussion in the above sections, a finite element analysis will need to
be conducted in order to accurately predict the percentage of the total load applied to the
faying pad. This analysis will include a model of a transversely loaded, 100% efficient,
single fillet-welded, T-joint.
3.1 Finite Element (FE) Modeling
Electric Boat Corporation's in-house FE softwares Altair HyperMesh and Abaqus
are used for all FE analyses. HyperMesh is the preprocessing software and Abaqus is the
processing and post-processing software. Shell elements are used for all FE analyses
Element size width was 10 elements per inch in both the flange plate and the faying
pad. This was to coincide with the load applied as described in Section 3.2 below. The
fillet weld’s mesh was composed of mix of tri and quad shell elements so as to line up
with the mesh already dictated in the two plates.
Plain strain was used in each analysis conducted. For the plane strain analyses, the
plane strain condition is simulated by strategically fixing boundaries in order to ensure
that Poisson’s Ratio is zero (see Section 3.5 below for further explanation).
As shown in Appendix A of this paper, a 2-dimensional model was built to
represent the faying pad and flange plate arrangement. In addition, only a slice was taken
out of a faying pad and cover plate attachment, only to conservatively examine the
effects in a small section, as shown in Figures 2 and 4 below. Figure 1 above and Figure
3 below show a simple depiction of the faying pad welded to a flange. Figure 2 shows
the original location and the practical applications of this project. Figures 3 and 4 take a
small location from Figure 2 to show the simplified geometry used for the analytical
purposes of this project. Any natural load transfer from the web to the flange, or vice
versa, in an I-beam or a T-stiffener was assumed to be zero. This project solely focused
on the effects of the load transfer between the flange and the faying pad.
5
Looking Down
Faying Pad
Figure 2: Faying Pad attached to an I-beam Flange
Figure 3: Shape of Each Faying Pad/Flange Plate Arrangement
Figure 4: Final Shape of Each Faying Pad/Flange Plate Arrangement used in the
Analysis
6
3.2 Applied Load
Only one load case will be utilized for all of the analyses conducted in this paper. It
was assumed that the flange plate (whether for an I-beam or a T-stiffener) would endure
a maximum deflection of 0.1 inches in the x-direction due to the applied compressive
axial loading. This was calculated using the following formula (Reference [4]):
𝛿=
𝑃𝐿
𝐴𝐸
[3.2.1]
L = Flange Plate = 25 inches (for all analyses)
E = Modulus of Elasticity for steel (see Section 3.4 below) = 30,000,000 psi
𝑃
= 12,000𝑝𝑠𝑖
𝐴
[3.2.2]
A = 1in2 (see Section 3.3 below) >> P = 12,000 lbs.
This 12,000 pound compressive axial load was equally divided into each element of
the bottom (flange) plate in Abaqus, resulting in an applied force of 1090.91 lbs./node at
the extreme column of nodes on the flange plate only for each model (see Figure 5
below). Section 3.3 below further explains the force determination for each model.
F
Figure 5: Applied Forces Location
3.3 Nominal Force Determination
References [1] and [2] do not provide specific details regarding the method of
nominal force range calculation or measurement during fatigue testing. Reference [2]
simply states that the test specimen is cycled at “known stress ranges.” Reference [5]
provides more detail on nominal stress determination stating that “In general, nominal
7
stresses are those calculated using simple formulae found in elementary text books,” and
proceeds to give the equation of stress at a position on a beam under combined axial and
bending stress:
𝑆=
𝐹 𝑀𝑐
+
𝐴
𝐼
[3.3.1]
Assumption: Mx is assumed to be zero. Even though it may be non-zero due to
eccentricity inducing some bending, the force applied is an axial load only; very little to
no bending is produced.
𝑆=
𝐹
𝐴
[3.3.2]
Rearranging Eq. 3.3.2 results in the following:
𝑆𝐴 = 𝐹
[3.3.3]
From Section 3.2 above, A = 1in2, and thus S = F for all nodes in all locations. “S”
is defined as x-directional stresses. X-directional stresses, or tensile-compressive stresses
in the X-direction, are similar to principal stresses, in that shear stresses in way of this
area are considered zero, which simplify the analysis. Directional stresses instead allow
the presentation of stress in a uniform manner so one can better assess the stress path in a
given direction. Directional stresses do redefine the element orientation, but instead
realign the element’s in-plane stress vector such that it is aligned to the global X (as is
the case in this project), global Y, or global Z. By collecting directional stresses, a force
per linear-inch in the X-direction about the X-axis can be found.
Rather than calculate the directional stresses with hand calculations, it was desired
to build a finite element model of Figure 4 above in the HyperMesh/Abaqus FE
Software, and using the characteristics discussed in Section 3.4 below, apply the 12,000
pound compressive axial load to the bottom plate in order to generate directional stresses
>> Sxx= Tensile–Compressive (normal) stress in the X-direction. These stresses were
then used as described below:
8
Calculation of Forces
1
𝐹𝑥 = ∫ 𝑆𝑥𝑥 𝑑𝑌
0
[3.3.4]
That is to say, the stress at a "point,” or node for this analysis, (Sxx) is taken and then
multiplied by an infinitesimal vertical length (dY) to convert it to a force per linear inch.
Y= Spatial dimension in the thickness direction (vertical). Y = 0 at the lower corner of
the flange plate and Y = 1 at the upper corner of the flange plate (same for the faying
pad). Hence, the thickness of the flange plate and the faying pad are always 1-inch each.
Simpson’s Rule
Simpson’s Rule was used to numerically integrate Eq. 3.3.4 in order to find the
forces applied to both the faying pad and the bottom plate. Simpson’s Rule better
approximates deflected plates than the Trapezoidal Rule.
𝑏
∫𝑎 𝑓(𝑥)𝑑𝑥 ≈ 𝑆𝑛 =
∆𝑥
3
[𝑓(𝑥0 ) + 4𝑓(𝑥1 ) + 2𝑓(𝑥2 ) + 4𝑓(𝑥3 ) + ⋯ + 2𝑓(𝑥𝑛−2 ) +
4𝑓(𝑥𝑛−1 ) + 𝑓(𝑥𝑛 )] >>> Where n is even (n = 10 for all analyses) and Δx = (b-a)/n = (10)/10 = 0.1
[3.3.5]
Since stress values are taken at nodes, and since the exact function is Sxx = f(Y),
Simpson's Rule numerical integration is used to approximate the force per linear inch in
the plate using the following method:
1. Find and plot the nodal "Sxx" stress values.
2. Find "Fx". Note this is conducted for each plate separately: the faying pad and
the flange plate.
3. Use Eq. 3.3.4
4. Numerically integrate using Simpson's Rule.
5. Fx of faying pad + Fx of flange plate = Fx applied to the model
3.4 Finite Element Model Characteristics
Per Reference [6], though the AWS Bridge Specifications limit the thickness of
cover plates (faying pads) to 1.5 times the thickness of the flange to which it is attached.
In some areas of industry, faying pads are outside of this specification; thus, all cases of
9
faying pads/flanges will not be included in this investigation. Rather, the bottom plate
and the faying pad will be restricted to 1.0-inch thick each so as to simplify the analysis.
Figure 6 below represents the undeformed model of a 0.125-inch Fillet Weld with 1inch Faying Pad. Each model was meshed with an element representing a length of 0.1
inches: 10 elements run across the y-direction (vertical) of each bottom plate and faying
pad and 250 elements run across x-direction (horizontal) of each bottom plate. The
element size was refined several times, to both smaller and larger values, and the final
element size of 0.1 was found to be the most suitable for the problem at hand. This mesh
follows suit with each faying pad size for each model. For all other model
representations, see Appendix A of this paper.
Figure 6: 0.125-inch Fillet Weld with 1-inch Faying Pad – Undeformed Shape
12 models will be developed to establish the framework for this analysis. The faying
pad will be varied in length in the following intermediate cases:

For the purposes of this project, the faying pad lengths represent the majority of
lengths used in the shipbuilding industry only:
o 12.5 inches
o 6.25 inches
10
o 3.125 inches
o 1-inch
In addition to varying the faying pad’s length, three fillet weld sizes will be used for
each model: 0.125 inches, 0.25 inches, and 0.5 inches. This is also indicative of the
majority of weld joint sizes used in the shipbuilding industry.
Lastly, the materials of the plates and the weld metal will both be high strength steel
(DH-36 steel, ASTM A131), where the yield strength is 50ksi (Reference [7]); this is to
simplify the analyses. Fully elastic behavior is assumed, and plasticity is not modeled.
3.5 Boundary Conditions
Figure 7: Boundary Conditions’ Locations
X-direction >> Horizontal
Y-direction >> Vertical
Z-direction >> In and Out of the page
From Figure 7 above, all nodes along the edge wall (flange plate and faying pad –
yellow oval) were fixed in this way: Dx = 0 and Ry = 0. Since 2D models were
developed in the x and y directions only for this project, any deflections in the zdirection were automatically assumed zero and thus Dz = 0, which mimicked the plane
strain condition. The bottom corner node of the flange plate (flange plate – black circle)
was fixed in this way to allow the model to deflect freely and accurately while
undergoing the plane strain condition: Dy = 0 and Dz = 0.
11
4. Results and Discussion
Tables 1 through 3 and Figures 8 and 9 below show the results of all of the analyses
conducted. By following the method shown in Section 3.3, the maximum portion of the
total applied load was found for each faying pad/flange plate/weld size configuration. In
addition, the error percentage was calculated for each configuration to show the FEA
results and how much they differed from the original closed-form solution that
calculated the preliminary applied load of 12,000 lbs. to the model.
Figure 8: 0.125-inch Fillet Weld with 1-inch Faying Pad – Deformed Shape
Each model shows the plates with a very similar type of deflected shape. The reason
being is because, as stated previously in Section 3.5, the bottom corner node is essential
to this type of deflected shape. What the node does is, although it’s fixed in the Dx, Dy,
Dz, and Ry directions, it allows the model to “pivot” around a certain location and
thereby show an accurate deflection. The Dy boundary condition would be the exact
location of a web plate (if it were modeled), which in real life, the flange’s deflected
shape would look similar to Figure 8, and all other models in this paper. This deflected
shape is in bending, analogous to column buckling. Locally this shows a buckling-type
12
deflection, but in the overall picture (see Figure 2), this load would only produce a
bending deflection in the flange.
After summing the resulting forces going into faying pad using Simpson’s Rule, the
load percentages, shown in Tables 1 through 3 below, were calculated by dividing the
sum of the forces going into the faying pad by the total load applied, multiplied by 100%
to get the final number.
As Section 3.3 discussed, Fx of faying pad + Fx of flange plate = Fx applied to the
model. Simpson’s Rule solves for each force described here for each model. This
resulting applied force (Fx – described in the previous paragraph) is compared to the
actual force applied to the model (12,000 lbs) from the start to see how they differ.
These differences, or error percentage values, are shown below in Tables 1 – 3. They are
calculated by taking this Fx and dividing it by 12,000 lbs, multiplying it by 100%.
Faying Pad
Length
1
3.125
6.25
12.5
Weld Size: 0.125"
Load
Percentage
7.22
9.62
10.46
10.96
Error
Percentage
0.54
0.72
0.79
0.74
Table 1: 0.125-inch Fillet Weld Results
Faying Pad
Length
1
3.125
6.25
12.5
Weld Size: 0.25"
Load
Percentage
10.6
12.63
13.3
13.7
Error
Percentage
-1.26
-1.51
-1.61
-1.69
Table 2: 0.25-inch Fillet Weld Results
13
Faying Pad
Length
1
3.125
6.25
12.5
Weld Size: 0.5"
Load
Percentage
10.68
11.67
11.99
12.18
Error
Percentage
-0.000092
-0.000079
-0.000089
-0.00019
Table 3: 0.5-inch Fillet Weld Results
Figure 9: All Fillet Weld Results
See Appendix A for deflected shapes of all analyses. Very low errors percentages
were produced out of all of analyses conducted. This shows that interpolating the final
Sxx stresses using the Simpson’s Rule method was a very accurate method to match the
final load contribution total to the originally calculated applied load.
However, it is interesting to note that the load percentage contributed by plates with
a 0.25-inch fillet weld size was the same or higher than the load contribution by plates
with a 0.5-inch fillet weld size. It was expected that the load contributions for the 0.5inch fillet weld size would be higher overall than the 0.25-inch fillet. This could be
attributed to several reasons:
14
1. Shell element representations of real fillet weld joints typically only connect the
mid-surface of the abutting T-member to the passing continuous member. Solid
elements should therefore be considered as an alternative.
2. In some cases, interpolated stresses may be artificially low because the stiffness
of the weld metal and the distributed support it provides to the continuous plate
is not modeled.
3. This analysis only looked at slice of a faying pad/flange plate attachment; it
would be prudent for the future student to investigate analyzing more of the
weld, the faying pad, and the flange plate in the FE model so as to accurately
represent its behavior.
4. The type of mesh used needs to be reanalyzed to further validate the results
presented. The models associated with the 0.25-inch fillet weld may have been
more mesh sensitive since its results were higher than the expected load
contributions for the 0.5-inch fillet weld size. Because of this, the meshing of all
three models may potentially need to be re-evaluated in the future so as to give
more accurate results.
15
5. Conclusion
The fatigue analysis of welded structures typically requires determination of
nominal principal stresses at the weld toes of weldments. When a faying pad is filletwelded to a flange plate, if its weld isn’t large enough to accommodate a large enough
path needed for stress to flow thru, failure is more like to occur at the root rather than the
toe. Thus, it is important to increase the weld throat thickness as is shown in this study.
Larger weld throat thickness signifies more load path between the two plates and a more
accurate and potentially higher fatigue life of the weld joint.
16
6. References
1. AWS D1.1, Structural Welding Code – Steel. American Welding Society. March 11,
2010.
2. ASM Handbook Volume 19, Fatigue & Fracture, Fourth Printing, ASM
International, 2005
3. Lahti K , Hanninen H, Niemi E. Nominal Stress Range Fatigue of Stainless Steel
Fillet Welds – The Effect of Weld Size. J Constructional Steel Research 2000;
54:161–172
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17
Appendix A
Appendix A shows the undeformed plots and the deformed plots of each cover
plate/flange plate/weld fillet configuration analyzed for this project. The deformed
pictures plot the x-directional stresses.
A1
Figure A.1: 0.125-inch Fillet Weld with 1-inch Faying Pad – Undeformed Shape
Figure A.2: 0.125-inch Fillet Weld with 1-inch Faying Pad – Deformed Shape
A2
Figure A.3: 0.125-inch Fillet Weld with 3.125-inch Faying Pad – Undeformed Shape
Figure A.4: 0.125-inch Fillet Weld with 3.125-inch Faying Pad – Deformed Shape
A3
Figure A.5: 0.125-inch Fillet Weld with 6.25-inch Faying Pad – Undeformed Shape
Figure A.6: 0.125-inch Fillet Weld with 6.25-inch Faying Pad – Deformed Shape
A4
Figure A.7: 0.125-inch Fillet Weld with 12.5-inch Faying Pad – Undeformed Shape
Figure A.8: 0.125-inch Fillet Weld with 12.5-inch Faying Pad – Deformed Shape
A5
Figure A.9: 0.25-inch Fillet Weld with 1-inch Faying Pad – Undeformed Shape
Figure A.10: 0.25-inch Fillet Weld with 1-inch Faying Pad – Deformed Shape
A6
Figure A.11: 0.25-inch Fillet Weld with 3.125-inch Faying Pad – Undeformed Shape
Figure A.12: 0.25-inch Fillet Weld with 3.125-inch Faying Pad – Deformed Shape
A7
Figure A.13: 0.25-inch Fillet Weld with 6.25-inch Faying Pad – Undeformed Shape
Figure A.14: 0.25-inch Fillet Weld with 6.25-inch Faying Pad – Deformed Shape
A8
Figure A.15: 0.25-inch Fillet Weld with 12.5-inch Faying Pad – Undeformed Shape
Figure A.16: 0.25-inch Fillet Weld with 12.5-inch Faying Pad – Deformed Shape
A9
Figure A.17: 0.5-inch Fillet Weld with 1-inch Faying Pad – Undeformed Shape
Figure A.18: 0.5-inch Fillet Weld with 1-inch Faying Pad – Deformed Shape
A10
Figure A.19: 0.5-inch Fillet Weld with 3.125-inch Faying Pad – Undeformed Shape
Figure A.20: 0.5-inch Fillet Weld with 3.125-inch Faying Pad – Deformed Shape
A11
Figure A.21: 0.5-inch Fillet Weld with 6.25-inch Faying Pad – Undeformed Shape
Figure A.22: 0.5-inch Fillet Weld with 6.25-inch Faying Pad – Deformed Shape
A12
Figure A.23: 0.5-inch Fillet Weld with 12.5-inch Faying Pad – Undeformed Shape
Figure A.24: 0.5-inch Fillet Weld with 12.5-inch Faying Pad – Deformed Shape
A13