# lab thick cylinder

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 obtained was positive which indicate that angle was measured in the anticlockwise direction from the minimum principal strain axis. The calculated value 35.01º varied only slightly from the theoretical (30º); possessing a mere 5.01o percentage difference. This small deviation can be attributed to sources of error in the experiment Using the derived principal strains at the chosen pressure of 25Mpa, it was also possible to calculate the principal stresses on the outer surface of the pressure vessel, assuming that the material used in the experiment was homogeneous and isotopic. Along its circumference, the vessel experienced a principal stress, of 55.019MPa and along its length, an axial stress of 35.798MPa. The think cylinder theory was then used to calculate principal stress to compare to that of the experimental values. These values were calculated to be , and , 32.146.it is expected that the vessel experienced greater circumferential caused by the oil which exerts a force perpendicular to the vessel’s inner walls. These experimental values were then compared to those derived from the thick cylinder theory, and showed only moderate deviations. The percentage difference between that of the experiment and theoretical circumferential and longitudinal stresses were calculated to understand the level of fluctuation in the values. These said values deviated by 14.41% and 17.59% respectively. The deviations were acceptable given the factors which affected the apparatus during the experiment. Errors in the experiment produced small deviations between experimental and theoretical values. Notably the vessel did not meet the ideal conditions necessary when using equations 5 and 6 to derive principal stresses; homogeneous and isotropic vessel material. Faulty seals may have caused the axial stress to have a greater percentage error; since the experiment requires closed ends integral with the cylinder. Wear might have also had an effect on the vessel sealing; pockets of air...

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

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