Three stress analysis methodologies were used to analyze stresses in a mild steel specimen with an eccentric hole under tension: theoretical analysis using equations, computational analysis using FEA software, and experimental analysis using strain gauges. Each method agreed the maximum stress occurred in the hole area, with the second highest in the net area and lowest in the gross area. Theoretical and experimental results differed by an average of 10%, theoretical and computational by 5.1%, and computational and experimental by 4.8%. Retesting revealed a bending moment induced by the testing machine, requiring averaging of results. Overall the different methodologies correlated well.

1. Stress Analysis Methodology
Comparison
1 ABSTRACT
Three stress analysis methodologies were conducted in order to obtain stress values in different
locations of a mild steel specimen containing an eccentric hole under in-plane uniaxial tension from
a 10kN applied load. These were; a theoretical analysis, using assumptions and analytical equations,
experimental analysis, using strain gauges and a tensile testing machine and finally a computational
analysis, using Finite Element Software called Abaqus. The stresses for the gross area, net area and
hole area were computed. Each methodology agreed on the stress distribution, with the maximum
present in the hole area, the second highest in the net area and the least in the gross area. Large
percentage differences existed in the gross area between theoretical and experimental, and
computational and experimental, 23.04% and 21.99% respectively. Retesting of the mild steel
specimen, rotating the specimen 180° between loadings, revealed the inducement of a bending
moment from the tensile testing machine. Averaging all the experimental results obtained and
comparing the results from each methodology, all results are seen to correlate well. Theory and
experimental differ within an average of 10%, theory and computational differing within an average
of 5.1% and computational and experimental with 4.8%.
2 NOMENCLATURE
A Cross Sectional Area m
E Young’s modulus Pa
E0 Bridge voltage V
F Applied force N/m2
H Width of the element m
M Bending moment N/m
Ks Gauge factor %
Ktg Gross section stress concentration factor -
Ktn Net area stress concentration -
R1-4 Resistance components of the Wheatstone bridge Ω
a Radius m
c Distance from hole centre to the closest edge of the specimen m
d Diameter m
e0 Wheatstone Bridge output voltage V
h Element thickness m
l Length m
n Misalignment error µε
β Angle of mounting angular error °
ε Strain με
εp Maximum principal strains με
εq Minimum principal strains με

2. ε(φ±β) Strain along gage axis with angular mounting error με
ν Poisson's Ratio -
σ Stress N/m2
σmax Maximum stress N/m2
σn Net stress N/m2
σnet A-B Average stress line A-B N/m2
Δl Change in length m
ΔR Change in resistance Ω
φ Angle between intended measurement axis and the principal axis °
3 INTRODUCTION
The analysis of stress and strain in a given structural material is often partaken as a method to
validate a design and to ensure structural integrity. Strain can be defined as the amount of
deformation an object undergoes in response to an applied force. This deformation induces stresses
in the material body, analytically expressed as the ratio of the applied force to the cross sectional
area of the material body. Stresses may be induced in a structural material from various factors,
such as manufacturing or fabrication processes, in-service repair or modification, and installation or
assembly procedures. Significant stress(es) and/or cyclic stress(es) may induce damage,
detrimentally leading to failure in a material. As a result the analysis of this parameter is of essential
importance in engineering.
Many methods of stress analysis exist, some of which include;
 Theoretical analysis- uses assumptions and analytical equations to arrive at stress values,
 Computational analysis- uses computer-aided design to model the component of interest
and appropriate mathematical models, solved using various methods i.e. finite element
method, to obtain stress values,
 Digital image correlation- uses a full-field image analysis method, based on grey value digital
images that can determine the contour and the displacement of an object under load and in
turn stress (DIC, 2015).
 Strain Gauges- bonded to the material surface, computing strain values through the variance
of electrical resistance proportional to displacement of its gage length as a result of strain in
the area of application,
The choice of stress analysis methods is dependent on various factors, such as geometry complexity,
ease of access to the points of interest, accuracy required, time, and so forth. Each method provides
its own advantages. DIC provides a fast and contactless full field stress analysis, which can prove
beneficial in pinpointing problem areas. Computational analysis methods, although timely, can
compute accurate stress values and many other parameters throughout the entire structure under
analysis. This method is, however, subjective to the skillset of the engineer conducting the analysis.
Theoretical calculations prove a quick and efficient tool in obtaining approximate stress values at
certain points in a structures material. Strain gauges, when applied accurately, prove an accurate
and reliable tool in computing the stress in a material. Identifying the areas of significant stresses
and applying strain gauges, the stress can be obtained with minimal error. The coupling of methods
is often conducted, for example the use of DIC or computational analysis to identify areas of
significant stress and employing strain gauges in these locations to obtain accurate stress values.

3. In this report a mild steel bar with an eccentric transverse hole is under analysis. The specimen was
subject to in-plane uniaxial tension from the application of a 10kN load. The eccentric hole acts as a
stress concentrator, due to the discontinuity in the material i.e. reduction in cross-sectional area,
leading to a non-uniform stress pattern through the material. This non-uniformity will allow the
comparison of different stress analysis methods. The methods conducted were theoretical analysis,
computational analysis and experimental analysis i.e. strain gauges. The theoretical used
assumptions and known equations to compute the stress at various points in the specimen. Abaqus,
a finite element method software, was used to conduct the computational analysis. Finally a test
specimen, containing three strain gauges, was subjected to a uniaxial load within the elastic region.
The data was processed using a data acquisition logger and results were obtained. The details of
each analysis will be outlined further in the report. Each analysis generated results for comparison
and discussion.
3.1 OBJECTIVES
The objectives of the work involved in this paper are as follows;
 Obtain stress values through the use of assumptions and theoretical equations
 Computationally model the specimen and conduct a stress analysis
 Apply strain gauges to a mild steel specimen to compute stress values under experimental
uniaxial in-plane tension
 Compare all results obtained
3.2 SPECIMEN SPECIFICATIONS
The specimen under analysis was a mild steel bar containing an eccentrically positioned transverse
hole, illustrated in figure 1. Note the specimen has a thickness, t = 6mm, and material properties
displayed in table 1.
Figure 1: Mild steel specimen and dimensions
Young’s Modulus, E 200GPa
Poisons ratio, ν 0.33
Table 1: Properties of specimen

4. 3.3 THEORY
3.3.1 Theoretical Analysis
Firstly, in order to conduct the theoretical analysis, certain assumptions were made about the
material. The material was assumed to be;
 Linear
o Obeys Hooke’s law.
 Homogeneous
o Material properties are the same at every point and are invariant upon translation.
 Isotropic
o Material properties are invariant of rotation of axes at a point.
 Elastic
o Deformations due to the applied load are completely and instantaneously reversible
upon load removal.
Under these assumptions, well known and well defined equations may be used to analysis different
properties of the stressed specimen.
Stress can be calculated at a given point of constant section i.e. in the absence of stress
concentrators, using the following equation:
𝜎 =
𝐹
𝐴
(Rees, 2000) [1]
Where:
𝜎 = Stress
F = Force Applied
A = Cross-Sectional Area
Strain can be calculated at a given point, in the absence of stress concentrators, in the geometry
using the following equation:
𝜀 =
∆𝑙
𝑙
(Rees, 2000) [2]
Where,
ε = Strain
∆l = Change in Length
l = Original Length
The Young’s Modulus can be evaluated using the following equation:
𝐸 =
𝜎
𝜀
(Rees, 2000) [3]
Where,

5. E = The Young’s Modulus
σ = Stress
ε = Strain
When the mild steel bar undergoes in-plane uniaxial tension, the eccentrically placed transverse
hole reduces the cross-sectional area in the middle of the specimen and results in localized high
stresses denoted stress concentration. This stress concentration is measured by the stress
concentration factor, which is defined as the ratio of the peak stress in the material body to a
reference stress. The stress concentration factor Ktg has a reference stress based on the gross cross
sectional area, and Ktn has the reference stress based on the net cross-sectional area. For a two
dimensional element with a single hole, the formulas for these stress concentration factors are:
𝐾𝑡𝑔 =
𝜎 𝑚𝑎𝑥
𝜎
(Walter & Pilkey, 2008) [4]
Where Ktg is the stress concentration factor based on the gross stress, σmax is the maximum stress at
the edge of the hole, σ is the stress on gross section far from the hole and,
𝐾𝑡𝑛 =
𝜎 𝑚𝑎𝑥
𝜎 𝑛
(Walter & Pilkey, 2008) [5]
Where Ktn is the stress concentration factor based on net (nominal) stress, σn is the net stress σ/(1-
d/H), with d the hole diameter and H the width of element.
These stress concentration factors have been solved analytically by many investigators and are
available schematically for given criterion. The chart used in order to obtain the stress concentration
factors is presented in figure 2. The average stress present from the line A-B, the minimum net
section, schematically present on the RHS of figure 2, can be calculated from the nominal stress as;
𝜎 𝑛𝑒𝑡 𝐴−𝐵 =
𝜎𝑐ℎ√1−(
𝑎
𝑐
)2
ℎ(𝑐−𝑎)[1−(
𝑒
𝑐
)(√1−(
𝑎
𝑐
)
2
)]
(Walter & Pilkey, 2008) [6]
Where 𝜎 is the gross area stress, c is the distance from the centre of the eccentric hole to the closest
edge of the specimen, h is the thickness of the specimen, a is the radius of the hole and e is the
distance of the centre of the hole to the furthest edge of the specimen.

6. Figure 2: Stress concentration factors for the tension of a finite-width element having an eccentrically loaded circular hole
(based on mathematical analysis of Sjostrom 1950 (Walter & Pilkey, 2008))
3.3.2 Experimental analysis
3.3.2.1 Strain gauge theory
It is not possible to measure stress directly from experimentation; however it is possible to measure
strain through changes in length resulting from an applied load, i.e. equation 2. However the
displacement of a simple metal specimen, loaded within the elastic limit, is often small and hard to
measure. In order to accurately measure this displacement the application of strain gauges is
necessary. Various types of strain gauges exist for a given application, which predominantly function
as transducers, varying electrical resistance in proportion to the amount of strain in a given
component. The most widely used strain gauge is the bonded metallic strain gauge. This type of
gauge consists of a fine wire, fabricated from metallic foil, arranged in a grid pattern. The grid
arrangement maximises the amount of foil subject to strain, thus increasing accuracy. The grid is
bonded to a thin backing, referred to as a carrier, which is directly attached to the specimen. The
strain induced in the specimen lengthens the grid length, increasing electrical resistance linearly.
Due to the fact that strain is significantly small in value, a Wheatstone is required to accurately
convert the resistance change of the displaced gauge length into a voltage change. The output
voltage e0 of a Wheatstone bridge may be determined from the following equation:
𝑒0 =
𝑅1 𝑅3−𝑅2 𝑅4
(𝑅1+𝑅2)(𝑅3+𝑅4)
. 𝐸0 (KYOWA, 2015) [7]
Where R1-4 are resistance components of the Wheatstone bridge in figure 3, and E0 is the Bridge
voltage.

7. Letting R1=ΔR, the change in strain gauge resistance, and taking the initial condition that
R1=R2=R3=R4, the above equation becomes;
𝑒0 =
𝑅2+𝑅∆𝑅−𝑅2
(2𝑅+∆𝑅)2𝑅
. 𝐸 (KYOWA, 2015) [8]
As R may be considered extremely larger than ΔR, the equation reduces to;
𝑒0 =
1
4
.
∆𝑅
𝑅
. 𝐸 =
1
4
. 𝐾𝑠. 𝜀. 𝐸 (KYOWA, 2015) [9]
Where Ks is the gauge factor, i.e. the coefficient expressing strain gauge sensitivity. Thus what is
obtained is an output voltage that is proportional to the change in resistance.
Figure 3: Wheatstone bridge configuration (KYOWA, 2015)
3.3.2.2 Strain gauge misalignment theory
In bonding strain gauges, angular errors with respect to the intended axis of strain can occur. This
misalignment will incur inaccurate results and must be factored for. The error induced as a result of
angular misalignment may be calculated from equation;
𝑛 =
𝜀 𝑝−𝜀 𝑞
2
[𝑐𝑜𝑠2(𝜙 ± 𝛽) − 𝑐𝑜𝑠2𝜙] (VPG, 2015) [10]
Where n is the error (με), εp and εq are the maximum and minimum principal strains respectively, 𝜙
is the angle between intended measurement axis and the principal axis, and 𝛽 is the angle of
mounting angular error ie. angle of strain gauge to intended axis. The actual strain may then be
found from the following equation;
𝑛 = 𝜀(𝜙±𝛽) − 𝜀 𝜙 (VPG, 2015) [11]
Where 𝜀(𝜙±𝛽) is the strain along gage axis with angular mounting error of ±𝛽, 𝜀 𝜙 is the strain along
the axis of intended measurement at the angle 𝜙 from the principal axis.

8. Figure 4: Polar strain distribution corresponding to uniaxial stress, illustrating the error in indicated strain when a gauge is
misaligned by ±𝛽 from the intended angle 𝜙 (VPG, 2015)
4 METHODOLOGY
4.1 EXPERIMENTAL ANALYSIS
4.1.1 Strain gauge application
Three 120Ω Kyowa gauges were used in the experimental analysis. Two gauges were 5mm strain
gauges with a gauge factor of 2.1±1.0% and the other was a 2mm with a gauge factor of 2.13±1.0%.
Gauge 6 was placed in the gross section i.e. area of maximum section, gauge 7 was positioned in the
net area i.e. area of minimum section and gauge 10 was positioned on the inside of the hole where
the highest stress is to be expected.
Figure 5: Mild steel test specimen with applied strain gauges 6,7 & 10
Gauge 6
Gauge 7
Gauge 10

9. The strain gauges were applied in the following manner;
 The area of application on the specimen was prepared by initially sanding the area, to
minimise imperfections, and secondly wiped with acetone, to clean the area.
 Conditioner A and Neutraliser where applied with a medical gaze to further clean the
surface.
 Guidelines were implemented on the test specimen to ensure application accuracy. Note
these lines were not applied to the application area, however in close proximity.
 A strain gauge was positioned on a glass slide with a tweezers and attached to Mylar tape to
minimise handling.
 The Mylar tape containing the Strain gauge was
o Positioned to the clean surface, ensuring alignment with the guidelines.
o Pulled at a shallow angle to allow the application of glue under the strain gauge.
o Depressed with a finger and allowing sufficient time for the glue to dry.
o The tape was then removed
 A terminal was positioned on the specimen and soldered to the lead wires of the strain
gauge.
 An appropriate plug, for connection to the data acquisition system, was then soldered to the
terminal.
 To ensure no electrical shorting, as a result of the soldering process, an ohmmeter was used
to read the resistance through the unstrained gauge.
4.1.2 Experimental Apparatus & Procedure
The experimental analysis was conducted using a Tinius Olsen H25KS Tensile Testing Machine,
illustrated in figure 6.
Figure 6: Tensile Testing Machine
With the strain gauges connected to the data acquisition system, the test specimen was;
o Secured in the tensile testing machine via the two 8mm diameter grip holes.
o The specimen was then loaded from 0 to 10kN at a displacement rate of 1mm/min.

10. The data acquisition system converts the change in resistance into strain, which it logs and saves for
extraction. The Tenius Olsen computer control system logs and saves the load-displacement
behaviour for extraction.
4.2 COMPUTATIONAL ANALYSIS
4.2.1 Abaqus, Finite Element Modelling
Abaqus/CAE 6.14-3 (Finite Element Analysis Software) was used to computationally compute the
strains within the specimen. The specimen was modelled in the following manner:
1. The specimen was modelled using the computer-aided design feature in Abaqus. Availing of
symmetry, a quarter of the specimen was modelled. The part was created using the material
properties in table 1.
2. The part was partitioned appropriately in order to generate an accurate mesh.
Figure 7: modelled and partitioned specimen
3. Boundary conditions were created, constraining the bottom surface in y and z-direction and
the right hand surface in the x and z-direction. A reaction point was created offset from the
part.
Figure 8: Boundary conditions and reaction points
4. The reaction point was then constrained to the inside of the quartered modelled grip hole
i.e. displaces proportionally to the reaction point. This will allow for the load to be applied.
Figure 9: Grip hole constrained to reaction point

11. 5. A quadrilateral mesh was applied with a seed size of 0.1, containing 9463 nodes and 9179
elements. 9164 of the elements were linear quadrilateral (CPS4R) and 15 were linear
triangular (CPS3).
Figure 10: Meshed Model
6. A load of -5000N was applied to the reaction point in the x-direction. The load was halved to
factor in the symmetrical modelling of the specimen.
5 RESULTS
5.1 THEORETICAL ANALYSIS
Three theoretical calculations were made: (1) stress in gross area, (2) stress at the area of minimum
section and (3) stress at the edge of the eccentric hole.
1. Gross area
a. Calculating the CSA as width x height yields 2.28x10-4
m2
b. Knowing the applied load, 10kN, and through use of equation 1, the stress is
calculated to be 43.86MN/m
2. Net area
a. Through use of the gross section stress, and geometric dimensions of the test
specimen, the averaged stress from the edge of the hole to the side of the specimen
(presented schematically as line A-B in figure 1) was calculated using equation 6. The
minimum area stress was calculated to be 63.4MN/m
3. Hole area
a. Using the chart in figure one the stress concentration, Ktg, was calculated to be 3.6.
b. With knowledge of the gross area stress, and rearranging equation 4 the maximum
stress was calculated to be 157.9MN/m
From these stresses, rearranging equation 3, the corresponding strains may be calculated, and are
presented in table 3, section 5.4.

12. 5.2 EXPERIMENTAL ANALYSIS
Figure 11: Load versus displacement of mild steel bar under uniaxial tension
Figure 11 displays the extension of the mild steel load cell under uniaxial in-plane tension. The
specimen experiences a maximum displacement of 1.01mm @ 10kN. The spcimen displaced
proportionally with the induced load. This linear fashion, and the absence of yielding or plastic
deformation, verifies that the specimen was loaded within the elastic region, confirming that the
specimen is elastic and obeys Hooke’s laws, and further confirming the appropriate use of
theoretical equations.
Figure 12: Stress versus strain of load cell under uniaxial in-plane tension
Figure 12 presents the experimental results obtained from the strain gauges, adjusted for angular
misalignment. As expected, strain gauge 10 experienced the highest stress, 129.8 MN/m, as localised
stresses are most dominant at the perimeter of the hole nearest the edge of the load cell. Strain
gauge 7 experienced the second highest stress, 62.83 MN/m, as it was positioned in the area of
0
0.2
0.4
0.6
0.8
1
1.2
0 2000 4000 6000 8000 10000 12000
Displacement(mm)
Load (N)
0.E+00
2.E+07
4.E+07
6.E+07
8.E+07
1.E+08
1.E+08
1.E+08
0.E+00 1.E-04 2.E-04 3.E-04 4.E-04 5.E-04 6.E-04 7.E-04
Stress(N/m)
Strain
Strain gauge 6
Strain gauge 7
Straing gauge 10

13. minimum section. Strain gauge 6 experienced the lowest stress, 34.8 MN/m, as it is positioned in the
gross area.
5.3 COMPUTATIONAL ANALYSIS
Computation
Figure 13: Computational Strain Scalar Scene In the x direction
Figure 13 displays the strain results from the computational analysis. The intensity of the colour on
the specimen indicates the severity of the local strain and can be estimated from the legend on the
left hand side. Note that this strain is in the x-direction, normal to the applied load. The colour
contour verifies the stress trend obtained from the theoretical and experimental analysis.
Figure 14: Strain gauge placement approximations
Approximate probes were implemented to obtain strain values comparable to the theoretical and
experimental results. These values are located in table 2, section 5.4.

14. 5.4 RESULTS COMPARISON
Theoretical Strain
(µε)
Experimental Strain
(µε)
Computational Strain
(µε)
Gross area 219.3 174 217
Hole area 789.5 650 710
Net area 317 314 305
Table 2: Strain as obtained from the methods employed
Theory &
Experimental
Theory &
Computational
Computational &
Experimental
Gross area 23.04% 1.05% 21.99%
Hole area 19.38% 10.6% 8.82%
Net area 0.95% 3.85% 2.91%
Table 3: Percentage difference between results obtained
6 DISCUSSION
Figure 12 illustrates the stress and strain experienced by the strain gauges, as the 10kN was applied.
It is evident that strain gauge 10 experienced the highest strain, with strain gauge 7 second and
strain gauge 6 the lowest. This is expected due to the stress concentration induced by the eccentric
hole. The decrease in section induces localised stress concentrations as a resulting from the fact that
stress is inversely proportional to CSA.
The computed strain scalar scene, displayed in figure 13, allows for the visual interpretation of the
induced stresses within the specimen material. Evidently, a stress gradient formulates from the
discontinuity in geometry and the maximum stress is seen to be located at the perimeter of the hole,
nearest the specimen edge. Along the line, represented by line A-B in figure X, as the distance from
the centre of the hole increases, the stress distribution recovers to a uniform distribution. In a line
parallel to the specimen edge, running through the centre of the hole, the stress present is lower in
magnitude than the gross stress. As the distance from the centre of the hole progresses, the stress
eventually reaches uniform distribution. The computational analysis proves a useful tool in
computing a full view of the stress distribution.
Comparing all the data for strain in the gross, net and hole area, it is clear that they all agree upon
the stress distribution. However percentage differences are present. The computational and
experimental analyses correlate well. However, a 21.99% difference is present in the gross area.
Additionally, a 23.04% difference also exists between the theoretical and experimental results in the
gross area, while the theory and computational analysis differ by 1.05%. Note that in the three
cases, the strain gauge results are lower in magnitude. The experimental difference might loan itself
to the positioning of strain gauge 6 (see figure 5). Strain gauge 6 was positioned in the gross area,
although its proximity was significantly close to the hole and in turn lowered localised stress area.
This location may have affected the strain gauge reading; however comparison of the computational
scalar scene depicts that the strain gauge was sufficiently distant from the low stress gradient.
Further investigation into the reasoning revealed that the tensile testing machine was inducing some
form of bending moment on the specimen that in turn affected the strain gauge readings. Retesting
of the specimen was conducted by Daniel Powers, Meng Mechanical Engineer University of Limerick
Postgraduate, revealing a 40% difference in strain readings in the gross area when the specimen

15. initially tested and then rotated 180 degrees in the tensile testing machine, these results are shown
in appendix A, table 3. Analysing the results generated, strain gauge 6 readings indicate that the
specimen experienced a compressive force and tensile force on either surface, analogous to figure
15, indicating the presence of a bending moment. This can be concluded as the strain was 40%
higher when the specimen was orientated at 180 degrees, as opposed to 0 degrees. Therefore, in
order to obtain strain values comparable to the other methods, the averaged values from all the
tests conducted will be used. The averaged values can be found at the bottom of table 3, and the
revised percentage difference table for all the methods is present in Appendix B, table 4.
Figure 15: Induced bending moment on specimen during tensile test
Studying table 4, it is evident that the averaged strain values better agree with the computed
theoretical and computational results. Computational and experimental results complement one
another, with a maximum percentage difference of 8.15% in the gross area, which may be a factor of
the induced bending moment. Likewise, theoretical and experimental agree, with a maximum
percentage difference of 11.44% in the hole area. Note, the strain gauge results in the hole area are
lower in magnitude and this factor may loan itself to the fact that the strain gauge averages the
strain over the 2mm gauge length. The stress is a maximum at a specific point, therefore averaging
the strain over the 2mm length, and not specifically the point of maximum stress, would decrease its
value. Finally, computational and theoretical results correlate, with a maximum difference of 10.60%
in the hole area. The difference could be a function of the computational modelling i.e.
partition/seed/mesh choice or the idealisation of the theoretical calculations i.e. assumptions.
All in all, theory and experimental differ within an average of 10%, theory and computational
differing within an average of 5.1% and computational and experimental 4.8%. It is clear that each
method is affective in computing the distributed stress, and the choice of method, outside of
scholarly applications, comes down to factors discussed in the introduction.
M
TensionCompression
Surface of strain gauge
applicationM

16. 7 CONCLUSION
From the report it may be concluded that:
 The mild steel specimen behaved as expected during the experimentation, with the linearity
of the load-displacement plot confirming that the specimen was loaded within the elastic
limit, further validating the use of the theoretical formulae.
 High percentage discrepancies between the experimental and theory, and the experimental
and computational stresses in the gross area revealed that the tensile testing machine was
not applying in-plane tension.
 Averaging the strain gauges results and comparing all the stress obtaining methodologies, it
was seen that they all agreed on the stress trend, with the highest stress in the hole area,
the next highest at the net area and the least in the gross area.
 Computational analysis displayed a full view of the stress gradient present, revealing the
presence of a stress region lower in magnitude than the stress in the gross area of the
specimen. This area is at an angle of π/2 radians from the maximum stress.
 Averaging the percentage differences between the methodologies, theory and experimental
differ within an average of 10%, theory and computational differing within an average of
5.1% and computational and experimental with 4.8%.
From the conduction of the report, theoretical calculations proved the quickest method in
computing stress values in the specific points of interest. Strain gauges were also non time
consuming and proved useful tool, as they revealed problems with the tensile testing machine
through discrepancies in readings when the specimen was rotated 180 degrees between testing.
Computation analysis, although more time dominant, gave a full material view of the distributed
stress gradient resulting from the hole. To finally conclude, each methodology in obtaining stress
prove effective, all correlating well, and the choice of methodology is a function of various
parameters discussed briefly in the introduction, such as geometry complexity, ease of access, time,
and so forth.
8 REFERENCES
1. Digital Image Correlation (DIC) Measurement Principles. 2015. Digital Image Correlation
(DIC) Measurement Principles. [ONLINE] Available at:
http://www.dantecdynamics.com/measurement-principles-of-dic. [Accessed 16 October
2015].
2. David W A Rees, 2000. Mechanics of Solids and Structures. 1st Edition. World Scientific
Publishing Company.
3. Walter D. Pilkey, 2008. Peterson's Stress Concentration Factors. 3 Edition. Wiley.
4. Principle of Strain Measuement | KYOWA. 2015. Principle of Strain Measuement | KYOWA.
[ONLINE] Available at: http://www.kyowa-
ei.com/eng/technical/strain_gages/measurement.html. [Accessed 1 November 2015].
5. VPG - Micro-Measurements - Strain Gage Knowledge Base - Technical Notes. 2015. VPG -
Micro-Measurements - Strain Gage Knowledge Base - Technical Notes. [ONLINE] Available
at: http://www.vishaypg.com/micro-measurements/stress-analysis-strain-gages/technotes-
list/. [Accessed 22 October 2015].

17. 9 APPENDIX
9.1 APPENDIX A
Retesting of Mild Steel Specimen
Strain gauge 6
(µε)
[Gross area]
Strain gauge 7
(µε)
[Net area]
Strain gauge 10
(µε)
[Hole area]
235 298 631
206 271 634
Rotated test
151 249 607
137 228 605
Percentage difference between initial and rotated test
43.52% 17.91% 3.87%
40.23% 17.23% 4.68%
Averaged Strain Values
200 289 704
Figure 16: Retest of specimen, two tests computing strain reading and two tests of the specimen rotated 180°. Retesting
conducted by Daniel Powers, University of Limerick Postgraduate. Note the averaged strains are an average of all
experimental data obtained for the report.
9.2 APPENDIX B
Theory &
Experimental
Theory &
Computational
Computational &
Experimental
Gross area 9.20% 1.05% 8.15%
Hole area 11.44% 10.60% 0.85%
Net area 9.24% 3.85% 5.38%
Table 4: Revised percentage differences using averaged strain gauge data