lab thick cylinder
Results
Table showing strains form grids 1 – 3 at different pressures
Pressure
Ɛ1,Grid #1(μƐ)
Ɛ2, Grid #2 (μƐ)
Ɛ3, Grid #3 (μƐ)
(Bar)
Up
Down
Avg
Up
Down
Avg
Up
Down
Avg
0
0
0
0
0
29
14.5
0
-12
-6
68.95
31.5
32.5
32
79.5
95
87.25
38.5
46
42.25
137.89
65
65.5
65.25
154
166
160
97.5
103.5
100.5
206.84
98.5
97.5
98
224
231.5
227.75
154.5
161.5
158
275.79
133.5
131.5
132.5
297.5
299.5
298.5
219.5
220
219.75
344.74
166.5
166.5
166.5
366.5
366.5
366.5
277.5
277.5
277.5
Graph showing pressure vs. strain for grids 1 - 3
Calculations
Discussion
The lab was completed as instructed and the results obtained were used to plot a graph of pressure against strain for each of the tree grids. The line produced by the ratio plotted was linear in nature which yields that pressure is proportional to strain. This was a gave a direct relation to Hooke’s law which states that , for relatively small deformations of an object, the magnitude of the deformation is directly proportional to the deforming force provided that its yield strength is not exceeded. Under these conditions the object returns to its original size and shape upon removal of the deforming force. It is therefore expected that the cylinder underwent no permanent deformation during this experiment.
Strain rosette measurements were taken from the graph a s pressure of 25Mpa to calculate the angle from the principal axis. At 25mPa grid one (1) gave value of , grid two (2) and grid three (3) These values were then used to calculated then used to derive the principal strains using equation 3. Principal strain was calculated to be and .Using these principal strains the angle from the strain rosette measurement was calculated to be 35.01°, the angle represent the acute angle from the principal axis to the reference grid of the rosette. The value
Table showing strains form grids 1 – 3 at different pressures
Pressure
Ɛ1,Grid #1(μƐ)
Ɛ2, Grid #2 (μƐ)
Ɛ3, Grid #3 (μƐ)
(Bar)
Up
Down
Avg
Up
Down
Avg
Up
Down
Avg
0
0
0
0
0
29
14.5
0
-12
-6
68.95
31.5
32.5
32
79.5
95
87.25
38.5
46
42.25
137.89
65
65.5
65.25
154
166
160
97.5
103.5
100.5
206.84
98.5
97.5
98
224
231.5
227.75
154.5
161.5
158
275.79
133.5
131.5
132.5
297.5
299.5
298.5
219.5
220
219.75
344.74
166.5
166.5
166.5
366.5
366.5
366.5
277.5
277.5
277.5
Graph showing pressure vs. strain for grids 1 - 3
Calculations
Discussion
The lab was completed as instructed and the results obtained were used to plot a graph of pressure against strain for each of the tree grids. The line produced by the ratio plotted was linear in nature which yields that pressure is proportional to strain. This was a gave a direct relation to Hooke’s law which states that , for relatively small deformations of an object, the magnitude of the deformation is directly proportional to the deforming force provided that its yield strength is not exceeded. Under these conditions the object returns to its original size and shape upon removal of the deforming force. It is therefore expected that the cylinder underwent no permanent deformation during this experiment.
Strain rosette measurements were taken from the graph a s pressure of 25Mpa to calculate the angle from the principal axis. At 25mPa grid one (1) gave value of , grid two (2) and grid three (3) These values were then used to calculated then used to derive the principal strains using equation 3. Principal strain was calculated to be and .Using these principal strains the angle from the strain rosette measurement was calculated to be 35.01°, the angle represent the acute angle from the principal axis to the reference grid of the rosette. The value
References: Ayob, A. B., Tamin, M. N. & M. Kabashi Elbasheer, ‘Pressure Limits of Thick-Walled Cylinders’, Proceedings of the International MutiConference of Engineers and Computer Scientists 2009 Vol. II, IMECS: 2009, March 18, Hong Kong. J. M. Kihiu, S. M. Mutuli & G. O. Rading, n. d.,Stress characterization of autofrettaged thick-walled cylinders, pp. 370, International Journal of Mechanical Engineering Education, 31/4, Department of Mechanical Engineering, University of Nairobi. P. P., Benham, R. J., Crawford & C. G., Armstrong, 1996, ‘Chapter 14 – Applications of the Equilibrium and Strain-Displacement Relationships’, in Mechanics of Engineering Materials, 2ndedn., Pearson Longman, China