LAB 1: STRESS AND STRAIN
Name: Sereana. K. Cabemaiwai
Student Id: S11202884
Lab Session: Thursday 1 – 4pm
1. OBJECTIVES:
The aim of this procedure was to find the relationship between normal stress and
normal strain in 2-D tensile loading and to compare the experimental and theoretical
values of stress and strain of steel, copper, aluminum and brass specimens.
2. EQUIPMENTS USED:




Strain Gauge Trainer
1kg loads
VDAS Software
Metal Specimens
3. INTRODUCTION
A stress-strain profile for a specimen used in engineering and materials science is
used to display the relationship between stress and strain. “In continuum
mechanics, stress is a physical quantity that expresses the internal forces that
neighboring particles of a continuous material exert on each other, while strain is the
measure of the deformation of the material”. [1]
A tensile test on a metal specimen is commonly used to determine the material's
stress-strain diagram.
Stress is the intensity of the internal force on a specific plane passing through a
point which can be found by:
∆𝐹
∆𝐴
Where F, is the force applied and A is the area upon which the force acts upon.
𝜎 = 𝑙𝑖𝑚∆𝐴→0
Strain is defined as the amount of distortion sustained by the material in the
direction of applied force divided by the body's starting dimensions. Strain within the
specimen is calculated by:
𝐿𝐷𝑒𝑓𝑜𝑟𝑚𝑒𝑑 − 𝐿𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙
𝜀=
𝐿𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙
∆𝐿
=
𝐿
1|MM211 Lab Report
That is, the change in the specimen’s length over its original length.
“Clearly, stress and strain are related. Stress and strain are related by a constitutive
law, and we can determine their relationship experimentally by measuring how much
stress is required to stretch a material. This measurement can be done using a tensile
test” [2]
4. PROCEDURE





The steel specimen was first measured with the use of Vernier Calipers. The
measurements were then noted in a table.
A strain gauge trainer was then used mount the specimen.
The strain display was connected to the red and yellow gauge of the tension
system.
For a maximum of one minute, the equipment was left untouched to allow for
stabilization until the display read zero.
With the use of the VDAS software the results were tabulated into an excel file.
5. RESULT ANALYSIS:
Table 1: Steel Specimen
Gauge Factor: 2.12
Specimen Dimension: Width =10, Thickness= 2
Specimen Cross-Specimen: 20mm
Young’s Modulus: 207GPa
Load (Kg)
Force (N)
Displayed
Tensile Strain
(𝜇𝜖)
0
0
0
1
9.81
1
2
19.62
3
3
29.43
6
4
39.24
9
5
49.05
11
6
58.86
14
7
68.67
16
8
78.48
19
9
85.29
23
2|MM211 Lab Report
Calculated
Tensile Stress
(𝑁. 𝑚2 )
0
0.49
0.98
1.47
1.96
2.45
2.94
3.43
3.92
4.41
Calculated Tensile
Strain
0
2.37
4.74
7.11
9.48
11.85
14.22
16.59
18.96
21.33
Table 2: Copper Specimen
Gauge Factor: 2.12
Specimen Dimension: Width= 10, Thickness= 2
Specimen Cross-Specimen: 20mm
Young’s Modulus: 130GPa
Load (Kg)
Force (N)
Displayed
Tensile Strain
(𝜇𝜖)
0
0
0
1
9.81
4
2
19.62
7
3
29.43
12
4
39.24
16
5
49.05
20
6
58.86
24
7
68.67
28
8
78.48
32
9
85.29
36
Calculated
Tensile Stress
(𝑁. 𝑚2 )
0
0.49
0.98
1.47
1.96
2.45
2.94
3.43
3.92
4.41
Calculated Tensile
Strain
Calculated
Tensile Stress
(𝑁. 𝑚2 )
0
0.49
0.98
1.47
1.96
2.45
2.94
3.43
3.92
4.41
Calculated Tensile
Strain
0
3.77
7.55
11.22
15.09
18.86
22.63
26.41
30.18
33.96
Table 3: Aluminum Specimen
Gauge Factor: 2.12
Specimen Dimension: Width= 10, Thickness= 2
Specimen Cross-Specimen: 20mm
Young’s Modulus:
Load (Kg)
Force (N)
Displayed
Tensile Strain
(𝜇𝜖)
0
0
0
1
9.81
6
2
19.62
13
3
29.43
20
4
39.24
27
5
49.05
34
6
58.86
33
7
68.67
40
8
78.48
47
9
85.29
53
3|MM211 Lab Report
0
7.12
14.24
21.36
28.48
35.60
42.71
49.83
57.21
64.04
Table 4: Brass
Gauge Factor: 2.12
Specimen Dimension: Width= 10, Thickness= 2
Specimen Cross-Specimen: 20mm
Young’s Modulus: 105.0 GPa
Load (Kg)
Force (N)
Displayed
Tensile Strain
(𝜇𝜖)
0
0
0
1
9.81
4
2
19.62
9
3
29.43
14
4
39.24
19
5
49.05
23
6
58.86
28
7
68.67
33
8
78.48
37
9
85.29
46
Calculated
Tensile Stress
(𝑁. 𝑚2 )
0
0.49
0.98
1.47
1.96
2.45
2.94
3.43
3.92
4.1
Result Analysis:
1. To find the cross sectional area and the force for each load:
Dimensions: (For all four specimens).
Width= 10mm, Thickness= 2
Area:
𝐴=𝐿∗𝑊
=10 * 2
= 20mm
Sample Force Calculations:

For 1kg,
F = Mg
= (1)*(8.9)
=9.8N
For 3kg:
F = M*g
= (3)*(9.81)
= 29.4N
4|MM211 Lab Report
For 2kg:
F = Mg
= (2)*(9.8)
= 19.6N
Calculated Tensile
Strain
0
4.67
9.34
14.01
18.67
23.36
28.03
32.70
37.37
42.04
2. Finding the Theoretical Stress of the specimens:
Steel: (For a 1kg load)
𝜎=
𝐹 9.81
=
= 𝟎. 𝟒𝟗 (𝑵. 𝒎−𝟐 )
𝐴
20
Copper: (For a 2kg load)
𝐹
19.62
𝐴
20
𝜎= =
= 𝟎. 𝟗𝟖𝟏(𝑵. 𝒎−𝟐 )
Aluminum: (For a 3kg load)
𝜎=
𝐹 29.43
=
= 𝟏. 𝟒𝟕𝟏(𝑵. 𝒎−𝟐 )
𝐴
20
Brass: (For a 4kg load)
𝜎=
𝐹 39.43
=
= 𝟏. 𝟗𝟔𝟐(𝑵. 𝒎−𝟐 )
𝐴
20
3. Sample Calculations for Theoretical Strain:
Steel Specimen: (For 1kg load)
𝜀=
𝜎 0.4905 × 106
=
= 𝟐. 𝟑𝟕(𝝁𝜺)
𝐸
207 × 109
Copper Specimen: (For a 2kg load)
𝜎 0.981 × 106
𝜀= =
= 𝟕. 𝟓𝟓(𝝁𝜺)
𝐸
130 × 109
Aluminum Specimen: (For a 3kg load)
𝜎 1.4715 × 106
𝜀= =
= 𝟐𝟏. 𝟑𝟔(𝝁𝜺)
𝐸
68.9 × 109
5|MM211 Lab Report
Brass Specimen: (For a 4kg load)
𝜎 1.962 × 106
𝜀= =
= 𝟏𝟖. 𝟔𝟕(𝝁𝜺)
𝐸 105.0 × 109
Visual Representation of Results:
Theoretical Vs Displayed Strain
Stress Vs Strain
Stress vs Strain (Steel)
25
25
20
20
Stress/ Strain
Tensile Strain
Theoretical Vs Displyed Strain (Steel)
15
10
5
0
15
10
5
0
0
2
4
6
8
10
0
2
4
Load (Kg)
Calculated strain
Displayed Strain
Stress
Graph 1: Steel Specimen
8
10
Strain
Graph 5: Stress vs Strain for Steel Specimen
Theoretical vs Displayed Strain
(Copper)
Stress vs Strain(Copper)
40
Stress/ Strain
40
Tensile Srain
6
Load
30
20
30
20
10
10
0
0
0
2
4
6
8
10
0
2
4
Load
Calculated Strain
Displayed Strain
Graph 2: Copper Specimen
6|MM211 Lab Report
6
8
Load
Stress
Strain
Graph 6: Stress vs Strain for Copper Specimen
10
Stress vs Strain (Aluminum)
80
80
Stress/ Strain
Tensile Strain
Theoretical vs Displayed Strain
(Aluminum)
60
40
20
0
60
40
20
0
0
2
4
6
8
10
0
2
4
Load
Calculated Strain
Displayed Strain
Stress
Graph 3: Aluminum Specimen
8
10
Strain
Graph 7: Stress vs Strain for Aluminum Specimen
Theoretical Vs Displayed Strain (Brass)
Stress vs Strain (Brass)
50
Stress/ Strain
50
Tensile Strain
6
Load
40
30
20
10
40
30
20
10
0
0
0
2
4
6
8
10
0
2
4
Displayed Strain
Graph 4: Brass Specimen
Stress
Strain
Graph 2: Stress vs Strain for Brass Specimen
6. DISCUSSION
As portrayed in Graphs 1-4, it can be seen that the theoretical strain and the displayed strain
provide by the VDAS software is of small differences proving that most of the experimental
calculations were correct.
7|MM211 Lab Report
8
Load
Load
Calculated Strain
6
10
7. REFRENCES
[1] "Stress (Mechanics)," Wikipedia, 2 April 2022. [Online]. Available:
https://en.wikipedia.org/wiki/Stress_(mechanics). [Accessed 11 April 2022].
[2] "Mechanics of Slender Structures," Boston University, [Online]. Available:
https://www.bu.edu/moss/mechanics-of-materials-strain/. [Accessed 12 April 2022].
8|MM211 Lab Report