Thick Cylinder Lab Report
Thick Cylinder Lab Report
Thick Cylinder Lab Report
I confirm that this assignment is my own work, is not copied from any other person's work,
and has not previously submitted for assessment either at University of Johannesburg or
elsewhere.
i
ii
1. Aim
The objective of this experiment is to determine and compare the Hoop and Radial strain in
thick cylinders.
2. Assumptions
• The longitudinal stress is assumed to be zero.
3. Apparatus
• Strain gauges
• Strain gauges terminals
• Thick cylinder
• Bridge-box
• Hydraulic hand pump
• Air relief valve
• Pressure gauge
• Return valve
4. Procedure
• The thick cylinder unit was connected to the bridge-box and the bridge-box to the strain
indicator box.
• The power supply was turned on for about 10 minutes to allow strain gauges to warm
up.
• The strain readings (Gauges 1 to 10) were recorded at zero pressure. The strain readings
were to read “0.000”. If they are not close to zero, the corresponding knob was adjusted
on the bridge-box to bring the reading near to zero.
• The oil return valve was then closed and operated the manual oil pump to increase the
pressure in the thick cylinder to 60 kg/cm2.
• The strain readings of Gauges 1 to 10 were recorded, at this single pressure of 60
kg/cm2.
1
5. Results
Test Pressure …60……kg/cm2
6. Results analysis
Calculations performed below, used data from the specifications provided (Tlali, 2019).
6.1 Specifications:
Cylinder
Length 300 mm
Outer radius, 𝑅𝑜 75 mm
Inner radius, 𝑅𝑖 20 mm
𝑅𝑜
𝐾= 3.75
𝑅𝑖
Young’s modulus (𝐸) 71.7 GPa
Poisson’s ratio (𝜈) 0.33
Strain gauge
6.2 Calculations
Effective strain gauge reading calculation:
2
𝑒4 = −0.132 − 0.008 = −𝟎. 𝟏𝟒𝟎 𝒎𝑽
𝑒5 = 0.691 − 0.578 = 𝟎. 𝟏𝟏𝟑 𝒎𝑽
𝑒6 = −0.240 − (−0.229) = −𝟎. 𝟎𝟏𝟏 𝒎𝑽
𝑒7 = −0.261 − (−0.314) = 𝟎. 𝟎𝟓𝟑 𝒎𝑽
𝑒8 = −0.261 − (−0.277) = 𝟎. 𝟎𝟏𝟔 𝒎𝑽
𝑒9 = −0.142 − (−0.217) = 𝟎. 𝟎𝟕𝟓 𝒎𝑽
𝑒10 = −0.556 − (−0.572) = 𝟎. 𝟎𝟏𝟔 𝒎𝑽
𝑒2 × 4
𝑠𝑡𝑟𝑎𝑖𝑛2 =
𝐵𝑉 × 𝐺𝐹
−0.1×4
=
6245×2.1
= −𝟑𝟎. 𝟓 × 𝟏𝟎−𝟔
𝑒3 × 4
𝑠𝑡𝑟𝑎𝑖𝑛3 =
𝐵𝑉 × 𝐺𝐹
0.199×4
=
6245×2.1
= 𝟔𝟎. 𝟕 × 𝟏𝟎−𝟔
𝑒4 × 4 −0.140 × 4
𝑠𝑡𝑟𝑎𝑖𝑛4 = = = −𝟒𝟐. 𝟕 × 𝟏𝟎−𝟔
𝐵𝑉 × 𝐺𝐹 6245 × 2.1
𝑒5 × 4 0.113 × 4
𝑠𝑡𝑟𝑎𝑖𝑛5 = = = −𝟑𝟒. 𝟒𝟕 × 𝟏𝟎−𝟔
𝐵𝑉 × 𝐺𝐹 6245 × 2.1
𝑒6 × 4 −0.011 × 4
𝑠𝑡𝑟𝑎𝑖𝑛6 = = = −𝟑𝟑. 𝟓𝟓 × 𝟏𝟎−𝟔
𝐵𝑉 × 𝐺𝐹 6245 × 2.1
3
𝑒7 × 4 0.053 × 4
𝑠𝑡𝑟𝑎𝑖𝑛7 = = = 𝟏𝟔. 𝟏𝟕 × 𝟏𝟎−𝟔
𝐵𝑉 × 𝐺𝐹 6245 × 2.1
𝑒8 × 4 0.016 × 4
𝑠𝑡𝑟𝑎𝑖𝑛8 = = = 𝟒. 𝟖𝟖 × 𝟏𝟎−𝟔
𝐵𝑉 × 𝐺𝐹 6245 × 2.1
𝑒9 × 4 0.075 × 4
𝑠𝑡𝑟𝑎𝑖𝑛9 = = = 𝟐𝟖. 𝟖𝟖 × 𝟏𝟎−𝟔
𝐵𝑉 × 𝐺𝐹 6245 × 2.1
𝑒10 × 4 0.016 × 4
𝑠𝑡𝑟𝑎𝑖𝑛10 = = = 𝟒. 𝟖𝟖 × 𝟏𝟎−𝟔
𝐵𝑉 × 𝐺𝐹 6245 × 2.1
𝑝 𝑅𝑜 2 𝑅𝑜 2
𝜀𝐻 = 2 [(1 + 2 ) − 𝜈(1 − 2 )]
(𝐾 − 1)𝐸 𝑟 𝑟
60×105 752 752
= (3.752 −1)(71.1×109 ) [(1 + ) − 0.33 (1 − )]
𝑟2 𝑟2
5625 5625
= 6.4603 × 10−6 [(1 + 2
) − 0.33 (1 − 2 )]
𝑟 𝑟
5625 5625
r = 35 mm: 𝜀𝐻1 = 6.4603 × 10−6 [(1 + ) − 0.33 (1 − )] = 𝟒𝟑. 𝟕𝟖 × 𝟏𝟎−𝟔 𝒎/𝒎
352 352
5625 5625
r = 43 mm: 𝜀𝐻3 = 6.4603 × 10−6 [(1 + ) − 0.33 (1 − )] = 𝟑𝟎. 𝟒𝟔 × 𝟏𝟎−𝟔 𝒎/𝒎
432 432
5625 5625
r = 51 mm: 𝜀𝐻5 = 6.4603 × 10−6 [(1 + ) − 0.33 (1 − )] = 𝟐𝟐. 𝟗𝟏 × 𝟏𝟎−𝟔 𝒎/𝒎
512 512
5625 5625
r = 59 mm: 𝜀𝐻7 = 6.4603 × 10−6 [(1 + ) − 0.33 (1 − )] = 𝟏𝟖. 𝟐𝟏 × 𝟏𝟎−𝟔 𝒎/𝒎
592 592
4
5625 5625
r = 67 mm: 𝜀𝐻9 = 6.4603 × 10−6 [(1 + ) − 0.33 (1 − )] = 𝟏𝟓. 𝟎𝟗 × 𝟏𝟎−𝟔 𝒎/𝒎
672 672
𝑝 𝑅𝑜 2 𝑅𝑜 2
𝜀𝑅 = 2 [(1 − 2 ) − 𝜈(1 + 2 )]
(𝐾 − 1)𝐸 𝑟 𝑟
60×105 752 752
= (3.752 −1)(71.1×109 ) [(1 − ) − 0.33 (1 + )]
𝑟2 𝑟2
5625 5625
= 6.4603 × 10−6 [(1 − 2
) − 0.33 (1 + 2 )]
𝑟 𝑟
5625 5625
r = 35 mm: 𝜀𝑅2 = 6.4603 × 10−6 [(1 − ) − 0.33 (1 + )] = −𝟑𝟓. 𝟏𝟑 × 𝟏𝟎−𝟔 𝒎/𝒎
352 352
5625 5625
r = 43 mm: 𝜀𝑅4 = 6.4603 × 10−6 [(1 − 432
) − 0.33 (1 + 432
)] = −𝟐𝟏. 𝟖𝟏 × 𝟏𝟎−𝟔 𝒎/𝒎
5625 5625
r = 51 mm: 𝜀𝑅6 = 6.4603 × 10−6 [(1 − ) − 0.33 (1 + )] = −𝟏𝟒. 𝟐𝟓 × 𝟏𝟎−𝟔 𝒎/𝒎
512 512
5625 5625
r = 59 mm: 𝜀𝑅8 = 6.4603 × 10−6 [(1 − ) − 0.33 (1 + )] = −𝟗𝟓. 𝟓𝟔 × 𝟏𝟎−𝟔 𝒎/𝒎
592 592
5625 5625
r = 67 mm:𝜀𝑅10 = 6.4603 × 10−6 [(1 − ) − 0.33 (1 + )] = −𝟔𝟒. 𝟑𝟖 × 𝟏𝟎−𝟔 𝒎/𝒎
672 672
60
Hoop Strain (〖10〗^(−6)
50
40
30
20
10
0
35 43 51 59 67
cylinder radius (mm)
5
Experimental and Observed Radial Strain against
Cylinder radius
20
0
35 43 51 59 67
Radial Strain (10^-6)
-20
-40
-60
-80
-100
-120
Cylinder radius (mm)
The experimental and observed hoop strain values obtained are comparable. The hoop strain
in the cylinder decreases as the cylinder radius increases (Uomustansiriyah.edu.iq, 2019).
There is a small deviation between the experimental strain and the observed strain graph due
to inaccurate measurement of the readings, calculation errors and formula errors and lastly the
unstable material of the apparatus also contributes to the difference between the observed and
experimental strain graphs.
The radial strain in the cylinder increases with an increase in the cylinder radius
(Uomustansiriyah.edu.iq,2019). This is observed in the experimental and observed radial strain
graph although there is a small deviation between the two graphs due to the above-mentioned
defects.
6
7. Conclusion
The aim of this experiment was to determine and compare the Hoop and Radial strain of the
thick cylinder. The aim was satisfied as it has been observed that the hoop strain in a thick
cylinder decreases with an increase in thick cylinder radius. It was also observed that the radial
strain increases with an increase in thick cylinder radius. However, the results were not accurate
enough and satisfying due to inaccurate measurement of the readings in the lab, unstable
material of the apparatus used, and calculation and formula errors were also accountable in the
errors.
It is recommended that in the future the experiment should be done at least three times and
average values be used to perform calculations for more accurate results. It is also
recommended that calculations should be done using software’s which are more accurate rather
than manually. This experiment taught me the variations of radial and hoop strains in the thick
cylinder in relation to the thick cylinder radius. It also taught me that the hoop strain is a
maximum at an inner radius and minimum at the outer radius, and also that the radial strain is
a negative pressure at the inner radius and a positive pressure at the outer radius.
7
9. References
[1] Tlali, W.M. (2019). Experiment 3: The Thick Cylinder. Laboratory guide. University of
Johannesburg
[2] Uomustansiriyah.edu.iq. (2019). [online] Available at:
https://uomustansiriyah.edu.iq/media/lectures/5/5_2016_04_18!11_51_13_AM.pdf
[Accessed 12 Sep. 2019].
10. Appendix
8
9