Abstract
The objective to determine the buckling stress for range of slenderness ratios and the
experimental critical buckling stress and the theoretical critical buckling stress of three different
metals were compared. There are two parts to the experiment, where Experiment 1 consisted of
three metal struts of different material (copper, brass, and aluminum) of length 60 cm, while
Experiment 2 consisted of three steel struts of different length (50 cm, 65 cm and 70 cm). Both
experiments were conducted by taking the readings of the deflection as the force is increased in
increments of 200 N. For Experiment 1, the experimental critical buckling stress and the theoretical
critical buckling stress of three different metals were compared and showed negligible difference
in values for all conditions except for steel strut of length 65cm with percentage error of 14.73 %.
For Experiment 2, As the slenderness ratio is increased from 433 - 606, the critical buckling stress
decreases. The large percentage error could be due to method of readings taken in this experiment.
The large percentage error can be solved by taking the readings as the force applied is increased
in increments of 50 N or to take the force readings as the deflection is increased in increments of
0.5 mm.
1.0 Introduction
When a strut is subjected to vertical forces this can cause the strut to fail in two ways. One
is if the compressive strain is too excess this can cause the strut to be plasticized and flattened. The
other kind is when admissible compressive strain is applied it causes sudden shift to one side and
buckle. Buckling is the deformation of a material under a pressure of a load. If a force is laterally
applied to a strut which is long and slender buckling will be the principal mode of failure instead
of failure by direct compression. This is due to when the compressive forces reach a certain level
this causes the strut to undergo bending action in which the lateral deflection becomes large with
little increase in the force this can be seen in Figure 1.0. Failures that occur due to buckling happen
very suddenly with very little warning which makes it catastrophic mode of failure.
Figure 1.0 : Schematic Diagram of Buckling test.
The lateral deflection of the strut will be in a direction which is perpendicular to that axis of the
cross section about which the moment of inertia is the smallest. In a complex shape such as the
H-column the bend will be in the direction perpendicular to its major axis while in square shape
the bend will be in a direction that is perpendicular to its two major axes and for a tubular shape
it bends in any direction.
The objective of this experiment was to investigate how different struts deform when
subjected to compressive forces, as well as design an experiment to determine the buckling stress
for a range of slenderness ratios and to compare the experiment results with the theoretical stress
of three different metals. In order to carry out the experiment the WP 120 test stand was used. The
metal struts were attached to the WP 120 test stand at the part where the v notch of the bar aligns
with the v notch of the specimen holder. Compressive force was then applied using the load cross
bar. There were two parts to the experiment in the first one 60 cm struts made of copper, brass and
aluminum were used. In the second part different lengths of 50 cm, 65 cm and 70 cm steel struts
were used. The data obtained from the experiment is then used to calculate
Moment of inertia, I:
In a strut the moment of inertia is an important factor for the ability for the column to resist
bending.
𝑏ℎ3
I = 12
(1)
where, b is the base (m), and h is the height (m).
Radius of gyration, k:
The radius of gyration is used to compare how different structural shapes react when a compressive
force is applied to it. It is also used in predicting buckling in a compression beam. It can be
calculated using the following equation (2):
𝐼
k = √𝐴
(2)
where, I is the moment of inertia (kg m−2) and A is the cross-sectional area (m2 ).
Slenderness ratio:
Slenderness ratio is the ratio of the length of a column to the least radius of gyration. It is used to
categorize columns into either short, slender or long columns. It is calculated using equation (3).
𝐿
λ=𝑘
(3)
where, l is the length of the metal bar (m) and k is the radius of gyration (mm).
Critical buckling load, 𝑃𝑒 :
Critical buckling load represents the load at which the material will start to deform. It can be
calculated with equation (4).
𝑃𝑒 =
𝜋 2 𝐸𝐼
𝐿2
(4)
where,
E = Modulus of elasticity (Pa)
l = Moment of inertia (kg m−2 )
L = Length of the metal bar (m)
Euler’s formula, σ 𝑒 :
𝑃
σ 𝑒 = 𝐴𝑒
(5)
where,
σ 𝑒 = Euler failure stress (Pa)
𝑃𝑒 = Euler’s load (N)
𝐴 = Cross sectional area (m2 )
Rankine’s formula, σ 𝑟 :
σ𝑦
𝑎 = 𝐸𝜋2
σ𝑦
σ 𝑟 = 1+𝑎λ2
where,
𝜎𝑦 = Yield compressive stress (Pa)
(6)
(7)
𝐸 = Modulus of elasticity (Pa)
𝑎 = Rankine’s constant
𝜆 = Slenderness ratio
Perry-Robertsons formula, σ 𝑝 :
1
1
2
σ 𝑝 = [2 ( 1 + 𝑛)(𝜎𝑒 + 𝜎𝑦 )] − √4 ( 1 + 𝑛)(𝜎𝑒 + 𝜎𝑦 ) − 𝜎𝑒 𝜎𝑦
(8)
where,
𝑛 = Curvature factor
σ 𝑒 = Euler’s failure stress
𝜎𝑦 = Yield compressive stress (Pa)
Johnsons Parabolic formula, σ𝑗 :
σ𝑦 2
σ𝑗 = σ𝑦 − 4𝐸𝜋2 (λ2 )
where,
𝜎𝑦 = Yield compressive stress (Pa)
𝐸 = Modulus of elasticity (Pa)
(9)
2.0 Experimental Design
This section includes the experimental set up of the Buckling Apparatus, the methodology,
procedures and variables involved in Experiment 1 and Experiment 2.
2.1 Experimental Setup
WP 120 test stand was used to carry this experiment out and a measuring gauge was attached to
the lateral guiding column of the WP test stand using the Measuring gauge holder. Measuring tape
was used to measure the midpoint of the rod specimen. Aluminum, Copper, and Brass rods of 60
cm length were used, and steel rods of 50 cm, 60 cm and 70 cm were used.
Figure 2.1 Experimental Setup of Bucking Apparatus.
2.2 Methodology
There are two parts to this experiment, Experiment 1 requires analyzing of three of the
same length metal bars of 60 cm but with brass, copper and aluminum, and Experiment 2 requires
analyzing of three of the same material metal struts which is steel but with varying lengths of 50
cm, 65 cm, and 70 cm.
The materials needed for this experiment includes, measuring tape, bubble level tool,
deflection gauge, three steel metal struts of length 50 cm, 65 cm, 70 cm and three metal struts of
60 cm made of copper, aluminum, and brass. The rods are as shown in Figure 2.2.
The experiment was conducted by first loosening the load cross-bar by rotating the left and right
clamping screws and aligning it to fit the metal struts vertically into the buckling apparatus and
verifying or making sure the metal strut is centered in the apparatus and placed vertically by using
the bubble level tool. The copper strut was placed into the specimen holder by aligning the v notch
with the v notch of the specimen holder. Loading cross-bar was then lowered and pre-tightened
with a low non-measurable force. Force was then applied to the metal strut to determine the
direction of the deflection. The deflection gauge was then placed at the center and aligned
perpendicularly to the strut at the direction of deflection. The deflection gauge was then adjusted
to touch the metal strut as well as tared to zero for an accurate reading. The deflection readings
were taken down for each interval of 200 N force applied until the metal strut’s deflection exceeds
10mm. Figure 2.1 shows the experimental set up of the buckling apparatus to conduct the
experiment. The experiment was repeated for brass, aluminum of 65 cm and steel struts of 50, 65
and 75 cm.
The force of deformation can be determined by first drawing a line across the points which
the material is still undergoing elastic deformation and then taking the next point that is not within
the best fit line of the material that is undergoing elastic deformation.
Figure 2.2 Steel, copper, aluminum, and brass metal rod beside a measuring tape.
2.3 Variables
Experiment 1
Independent variable – Material of rod specimen, Compression force applied
Dependent variable – Deflection of rod
Constant Variable – Rod length and width
Experiment 2
Independent variable – Length of rod specimen, compression of force Applied
Dependent variable -Deflection of rod
Constant Variable – Material of rod
3.0 Results
Table 3.1 represents the calculated Force for deformation, slenderness ratio, compressive yield
strength, critical buckling load and critical buckling stresses for aluminum, copper, and brass metal
bars of length 60 cm.
Table 3.1 Calculated data for aluminum, copper, and brass strut with length 60 cm.
Type of
material
Aluminium
Copper
Brass
Force for
Elastic
Slenderness
deformation,
Modulus,
ratio, λ
F (N)
E (GPa)
800
1400
1200
346.410
346.410
346.410
69.500
125.000
104.000
Compressive
yield strength,
σ𝑦 (MPa)
Critical
buckling
load, 𝑃𝐸 (N)
Critical
buckling stress,
σe (MPa)
120.000
130.000
220.000
857.422
1542.126
1283.049
5.716
10.281
8.554
Table 3.2 Represents the calculated Buckling stresses using the Euler’s Formula, Rankine’s
Formula, Perry Robertson’s formula and Johnson’s Parabolic Formula for different Slenderness
Ratios.
Table 3.2 Calculated Buckling Stresses for different slenderness ratio of aluminum, copper,
and brass struts of length 60 cm.
Buckling stress (MPa)
Type of
material
Force for
deformation,
F (N)
Slenderness
ratio, λ
Aluminium
Copper
Brass
800
1400
1200
346.410
346.410
346.410
Euler's,
σe
Rankine's,
σr
PerryRobertson's, σp
Johnson's
Parabolic, σj
5.716
10.281
8.554
5.434
9.470
8.092
5.716
10.280
8.553
-88.432
-114.618
-480.563
Figure 3.1 shows the trends of deflection due to the forces applied on Aluminum, Brass, and
Copper metal rods.
Deflection due to Force Applied on Aluminum, Brass and
Copper
Force Applied on the Strut (N)
1600
1400
1200
1000
800
Aluminum
600
Brass
400
Copper
200
0
-2
0
2
4
6
8
10
Deflection (mm)
Figure 3.1 Graph of Force Applied on Aluminum, Brass and Copper against deflection.
Table 3.3 represents the calculated Force for deformation, slenderness ratio, compressive yield
strength, critical buckling load and critical buckling stresses for steel metal bars of length 50 cm,
65 cm, and 70 cm.
Table 3.3 Calculated experimental data for metal strut of 50 cm, 65 cm, and 70 cm.
Length of
strut (m)
Force for
deformation,
F (N)
0.50
0.65
0.70
900
600
500
Slenderness
ratio, λ
Elastic
Modulus, E
(GPa)
Compressive
yield strength,
σ𝑦 (MPa)
Critical
buckling
load, 𝑃𝐸 (N)
433.010
562.920
606.220
210.000
210.000
210.000
250.000
250.000
250.000
884.317
523.264
451.182
Critical
buckling
stress, σe
(MPa)
11.050
7.670
5.630
Table 3.4 represents the measured Force for deformation and calculated slenderness ratio,
compressive yield strength and the theoretical buckling stresses for steel metal bars of length 70
cm, 65 cm, 50 cm.
Table 3.4 Calculated theoretical buckling stress for metal struts of length 0.50 cm, 0.65 cm,
and 0.70 cm.
Buckling stress (MPa)
Length of
strut (m)
Force for
Deformation,
F (N)
Slenderness
ratio, λ
0.50
0.65
0.70
900
600
500
433.010
562.920
606.220
Euler's,
σe
Rankine's,
σr
PerryRobertson's, σp
11.053
6.540
5.639
10.661
6.401
5.536
11.053
6.541
5.640
Johnson's
Parabolic,
σj
-1163.504
-2138.880
-2520.521
Figure 3.2 shows the deflection trends of the Steel rods of length 50 cm, 65 cm, and 70cm.
Force Applied on Steel with 70 cm, 65 cm, and 50 cm
Force Applied on the Struts (N)
1000
900
800
700
600
500
Steel 70cm
400
Steel 65 cm
300
Steel 50 cm
200
100
0
0
2
4
6
8
10
Deflection (mm)
Figure 3.2 Force Applied on Steel against deflection with 70 cm, 65 cm, and 50 cm.
Figure 3.3 shows the graphical analysis of the critical bucking stress against slenderness ratio of
aluminum, copper, and brass struts with length 60 cm.
Critical buckling stress against Slenderness Ratio
Critical buckling stress (MPa)
12.000
10.281
10.000
8.554
8.000
5.716
6.000
4.000
2.000
0.000
Aluminium
Copper
Brass
Slenderness ratio
Figure 3.3 Comparison of slenderness ratio against experimental critical buckling stress of
aluminum, copper, and brass struts with length 60 cm.
Figure 3.4 represents the graphical analysis of critical buckling stress against elastic modulus for
steel of length 65 and, aluminum, copper, and brass struts with length 60 cm respectively.
Critical buckling stress against Elastic Modulus
Critical buckling stress (MPa)
16
14.7168
14
12
10.281
10
8.554
8
5.716
6
4
2
0
210
70
125
104
Elastic modulus (GPa)
Figure 3.4 Comparison of elastic modulus against experimental critical buckling stress of
steel of length 65 and, aluminum, copper, and brass struts with length 60 cm respectively.
Figure 3.5 shows a graphical analysis of critical buckling stress against slenderness ratio for the
steel struts with lengths 50 cm. 65 cm, and 70 cm.
Critical buckling stress against Slenderness Ratio
Critical buckling stress (MPa)
12
11.05
10
7.67
8
5.63
6
4
2
0
433.01
562.92
606.22
Slenderness ratio
Figure 3.5 Comparison of slenderness ratio against the experimental critical buckling stress
of steel struts with lengths 50 cm. 65 cm, and 70 cm.
The critical buckling stress calculated with the Euler’s formula, Rankine’s formula, and PerryRobertson’s formula can be seen in Figure 3.6.
Critical Buckling Stress (Mpa)
Critical Buckling Stress against Length of Steel Struts
12
11.053
11.0532
10.6611
10
8
6.540
6.4012 6.5405
6
5.639 5.5357 5.6395
4
2
0
0.50
0.65
0.70
Length of Steel Struts (m)
Euler's formula
Rankine's formula
Perry- Robertson's formula
Figure 3.6 Theoretical experimental critical buckling ratio against the experimental critical
buckling stress of steel struts with lengths 50 cm. 65 cm, and 70 cm.
Critical Buckling Stress against Type of Material
Critical Buckling Stress (MPa)
16
14.717 14.716
14.029
14
10.281 10.280
9.470
12
10
8
8.554 8.553
8.092
5.716
5.716
5.434
6
4
2
0
Steel
Aluminium
Copper
Euler's formula
Rankine's formula
Brass
Perry- Robertson's formula
Figure 3.7 Theoretical experimental critical buckling ratio against the experimental critical
buckling stress of steel strut with length 65 cm and copper, aluminum, and brass struts
with lengths 60 cm.
Theoretical calculations for steel strut when length is 0.5 m, height 0.004 m and base 0.002 m
Calculating Moment of inertia, I with equation (1):
𝐼=
=
𝑏ℎ3
12
(0.02𝑚)(0.0004𝑚)3
12
= 1.067 X 10-10 m4
Calculating Radius of gyration, k with equation (2):
𝐼
k = √𝐴
1.067 𝑋 10−10
= √ 0.02 𝑋 0.0004
= 1.15 x 10 − 3 m
Calculating Slenderness ratio with equation (3):
𝐿
λ=𝑘
=
0.5
1.115 𝑋 10−3
= 433.01
Calculating Critical buckling load with equation (4):
𝑃𝑒 =
=
𝜋 2 𝐸𝐼
𝐿2
𝜋 2 (210 𝑋 109 )(1.067 𝑋 10−4 )
(0.5)2
= 884.3166 N
Calculating Critical bucking stress with equation (5):
𝑃
σ𝑒 = 𝐴𝑒
884.3166
= (0.02)(0.006)
= 7.676 MPa
Calculating Buckling Stress with Euler’s formula using equation (5):
σ𝑒 =
=
𝑃𝑒
𝐴
884.3166
(0.02)(0.006)
= 7.676 MPa
Calculating Buckling Stress with Rankine’s formula using equation (7) and (8):
σ𝑦
Rankine’s constant,
a = 𝐸𝜋2
=
250 𝑋106
(250𝑋109 )𝜋 2
= 1.013 × 10−3 Pa
σ𝑦
σ𝑟 = 1+𝑎λ2
(250𝑋106 )
= 1+1.013𝑋10−3 (433.012)
= 7.4848 MPa
Calculating Perry-Robertsons formula using equation (8):
1
1
2
𝜎𝑝 = [ ( 1 + 𝑛)(𝜎𝑒 + 𝜎𝑦 )] − √ ( 1 + 𝑛)(𝜎𝑒 + 𝜎𝑦 ) − 𝜎𝑒 𝜎𝑦
2
4
1
= [2 ( 1 + 0.003)(7.676 𝑋106 + 250 𝑋106 )] −
1
√ ( 1 + 0.003)(7.676 𝑋106 + 250 𝑋106 ) − ((7.676 𝑋106 )(250 𝑋106 ))
4
=7.6759 MPa
Calculating Johnsons Parabolic formula using equation (9):
σ𝑗 = σ𝑦 −
σ2𝑦
(λ2 )
4𝐸𝜋 2
(250𝑋106 )2
= (250𝑋106 ) − 4(210𝑥109)𝜋2 (433.012 )
= -1163.504 MPa
4.0 Discussions
Table 3.1 and Table 3.3 shows that the values of experimental force of deformation of
Aluminum, Copper and Brass closely follows the theoretical critical buckling load with some
minor errors which will be explained later in the Error Analysis section.
It can be seen in Figure 3.1 that the Aluminum strut fails with the least amount of force of
about 800N followed by brass with 1200N and then copper with 1400N. Since the materials are
different but have the same length, this means that when slenderness ratio is kept constant and the
modulus of elasticity is different, the modulus of elasticity of the material will affects how much
force is required to deform the metal strut. As the modulus of elasticity increases the force required
to deform the metal strut increases as well.
Table 3.2 and Table 3.4 shows that the Critical Buckling Stress calculated using the
Rankine's Formula, Euler's formula and Perry Robertson's Formula has a slight but negligible
difference in value and can be considered the same for the three formulas. However, this is not the
case for Johnson's Parabolic Formula. This is because the Johnson's Parabolic Formula has a
condition where it can only be used when the yield compressive stress is more than the critical
buckling stress and the critical buckling stress is less than half the yield compressive stress.
Therefore, in this experiment the critical buckling stress is less than half the yield compressive
stress that is why the results for Johnson’s Parabolic formula will be neglected, and the results
used is the ones calculated using the Euler’s Formula.
It observed in Figure 3.2 for a steel strut of 50 cm, 65 cm, and 70 cm the force needed to
deform the steel strut is affected by the length and base, this can be calculated using the slenderness
ratio. As the slenderness ratio is increased the less force is required to deform the steel strut. With
less effective length of the steel strut, more force is required to deform the steel strut which can be
seen in the Figure 3.2 that for steel 50cm, 65cm and 70cm, the force of deformation is
approximately 900N, 500N and 400N respectively.
Figure 3.3 shows that with slenderness ratio being the same for all materials, the critical
stress is affected by the elastic of modulus. As the modulus of elasticity is increased, the critical
buckling stress required to put the metal strut to failure is higher as well. This can be proven as
copper, brass and aluminum has an elastic modulus of rigidity of 125 GPa, 104 GPa, and 70 GPa
respectively.
However, Figure 3.5 shows that the critical stress is also affected by the slenderness ratio.
This is so because in experiment 2 with the same material, elastic modulus of the steel strut but
different slenderness ratio value, the critical stress is affected by the slenderness ratio. It can be
seen that as the slenderness ratio increases from 433.01 to 606.22, the critical buckling stress
decreases from 11.05MPa to 5.63MPa.
5.0 Error Analysis
Table 5.1 and 5.2 shows tabulation of the different percentage error for steel strut of 0.50 m, 0.65
m, and 0.70 m.
Table 5.1 Comparison between the force for deformation and theoretical critical buckling
load and its percentage error for steel strut of 0.50 m, 0.65 m, and 0.70 m.
Length of
material (m)
Force for
deformation, F (N)
0.50
0.65
0.70
900
600
500
Theoretical
Critical buckling
load, 𝑷𝑬 (N)
884.317
523.264
451.182
Percentage
Error %
1.77
14.66
10.82
Table 5.2 Comparison between the experimental critical buckling stress and Euler’s
buckling stress, and its percentage error for steel strut of 0.50 m, 0.65 m, and 0.70 m.
Length of
material (m)
0.5
0.65
0.7
Critical buckling
stress (MPa)
11.05
7.67
5.63
Euler's buckling
stress (MPa)
11.053
6.540
5.639
Percentage
Error %
0.03
14.73
0.17
Table 5.3 and 5.4 shows the different tabulation of the percentage error for Aluminum, Copper,
and Brass strut of 0.60 m.
Table 5.3 Comparison between the Force for deformation and theoretical critical buckling
load and its percentage error for Aluminum, Copper, and Brass strut of 0.60 m.
Type of
material
Force for
deformation, F (N)
Aluminium
Copper
Brass
800
1400
1200
Theoretical
Critical buckling
load, 𝑷𝑬 (N)
857.422
1542.126
1283.049
Percentage
Error %
6.70
9.22
6.47
It can be seen in Table 5.1 that the percentage error of 14.66% and 10.82% for 0.65 m and
0.70 m is random and inconsistent which means that the large error is more likely to be caused by
random error rather than systematic error. The same can be said for Table 5.2 and 5.3. Due to the
force interval readings increment taken was too large with 200N increment, therefore less readings
were taken, and this affected the graph plot and the ability to accurately locate the point of
deformation. In addition to that, since the force of deformation readings taken were only until the
point before the deflection meter exceeds 10mm, the line drawn was not as conclusive as well as
incomplete. Hence, this increased the percentage error of both experiments 1 and 2. Therefore,
more readings should be taken for example with intervals of 50N to draw out a conclusive line.
Other than that, some of the possible systematic error that may have cause a difference in
the readings taken can be due to the placement of the deflection meter. It was not possible to place
the deflection meter accurately perpendicular and centered to the metal strut. This was because the
metal rod holding the deflection meter was long and would come in contact with the metal strut
when the deflection meter is adjusted to be pointing perpendicularly and center of the metal strut.
Hence, due to the metal strut restricting the metal rod holding the deflection meter, the deflection
meter was not able to be placed accurately at the center of the metal strut. One of the ways this can
be improved is by using a shorter metal rod or shortening the long metal rod with an angle grinder
to hold the deflection meter so that the metal rod with deflection meter will not be restricted by the
metal strut and can be rotated and adjusted for the deflection meter to point at the center of the
metal strut. Lastly, the metal struts used in this experiment has undergone slight plastic
deformation as it was not perfectly vertical when measured with a bubble level, indicating the
metal struts is already permanently deformed.
6.0 Conclusion
In conclusion, the objective to determine the buckling stress for varying slenderness ratios
were achieved, as well as the Force for deformation measured and the theoretical stress (Critical
buckling load) of three different metals were compared. As slenderness ratio increase then less
force is required to deform the metal strut and the critical buckling load required to put the metal
strut to failure reduce. When slenderness ratio is constant, but elastic modulus of elasticity is
increased, the more force is required to deform the metal strut and the critical buckling load
required to put the metal strut to failure will increase. Furthermore, The Euler's, Rankine's and
Perry Robertson's Formula gives a value of buckling stress that is similar and of negligible
difference. Other than that, the percentage errors can be reduced by using a shorter metal rod to
hold the deflection meter so that the metal rod with will not be interfered by the metal strut and
can be adjusted for the deflection meter to point at the center and perpendicular to the metal strut.
The random errors causing the large percentage errors can be solved by taking the readings as the
force applied is increased in increments of 50N. The other alternative is to take the force readings
as the deflection is increased in increments of 0.5mm.
References
[1] Rosato, D., & Rosato, D. (2007, September 2). Product design. Plastics Engineered Product
Design. Retrieved May 26, 2022, from
https://www.sciencedirect.com/science/article/pii/B9781856174169500053
[2] Moment of inertia. (2019, July 25). Retrieved from https://byjus.com/jee/moment-of-inertia/
[3] Just a moment... (n.d.). Retrieved from
https://www.sciencedirect.com/topics/engineering/radius-of-gyration
Appendix
Appendix A. Raw Data measured for deflection of the 60cm aluminum bar as force is
varied from 100 N to 1400 N with 100N interval.
No.
1
2
3
4
5
6
7
8
9
6
7
8
Force Applied on the Bar/N
100
200
300
400
500
600
700
800
900
1000
1200
1400
deflection reading
0
3.7
16
28
51
73
139
205
340
N/A
N/A
N/A
Deflection of the bar/mm
0
0.037
0.16
0.28
0.51
0.73
1.39
2.05
3.4
N/A
N/A
N/A
Appendix B. Raw Data measured for deflection of the 60 cm brass bar as force is varied
from 100 N to 1400 N with 200N interval.
No.
1
2
3
4
5
6
7
8
Force Applied on the Bar/N
100
200
400
600
800
1000
1200
1400
deflection reading
0
1.8
5
9
15.5
27
59.5
949
Deflection of the bar/mm
0
0.018
0.05
0.09
0.155
0.27
0.595
9.49
Appendix C. Raw Data measured for deflection of the 60 cm copper bar as force is varied
from 100 N to 1400 N with 200N interval.
No.
1
2
3
4
5
6
7
8
Force Applied on the Bar/N
100
200
400
600
800
1000
1200
1400
deflection reading
0
0.5
5
12.2
21
35.5
59
109.5
Deflection of the bar/mm
0
0.005
0.05
0.122
0.21
0.355
0.59
1.095
Appendix D. Raw Data measured for deflection of the 70 cm steel bar as force is varied
from 100 N to 800 N with 200N interval.
No.
1
2
3
4
5
6
7
8
Force Applied on the Bar/N
100
200
300
400
500
600
700
800
deflection reading
0
49
96.5
171
350
927
N/A
N/A
Deflection of the bar/mm
0
0.49
0.965
1.71
3.5
9.27
N/A
N/A
Appendix E. Raw Data measured for deflection of the 65 cm steel bar as force is varied
from 100 N to 800 N with 200N interval.
No.
1
2
3
4
5
6
7
8
Force Applied on the Bar/N
100
200
300
400
500
600
700
800
deflection reading
0
54.5
100
117
217
472.5
N/A
N/A
Deflection of the bar/mm
0
0.545
1
1.17
2.17
4.725
N/A
N/A
Appendix F. Raw Data measured for deflection of the 50 cm steel bar as force is varied
from 100 N to 900 N with 200N interval.
No.
1
2
3
4
5
6
7
8
9
Force Applied on the Bar/N
100
200
300
400
500
600
700
800
900
deflection reading
0
2
6
11
12.5
31
48.5
61
126
Deflection of the bar/mm
0
0.02
0.06
0.11
0.125
0.31
0.485
0.61
1.26