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Laporan Projek Tahun Akhir ADTEC Shah Alam
Tugas ini dibuat untuk memenuhi Tugas UAS Mata Kuliah Fisika Material dan Divais NanoDeskripsi lengkap
Summary This experiment was conducted to analyze stress and strain in a thin walled cylinder using a thin cylinder device (SM1007). It shows the strain on a thin cylinder wall as it is being stressed by internal pressure. It then compares the laboratory results to the results calculated.
Introduction Cylinders are used in many engineering applications and they are all subjected to fluid pressure, when a cylinder is experiencing internal pressure there are three types of stresses which are acting on the cylinder wall, hoop stress, longitudinal stress, and radial pressure (this is negligible because it is insignificant when dealing with thin cylinders). Analyzation of the distribution of stress in a thin cylinder is important in pressure vessels because of its ability to detect if a structure will be able to withstand the forces both internally and externally expected of it, this can be used to detect structural failure. This experiment demonstrates the stress in a thin cylinder.
Background A cylinder is considered thin when its w all thickness is smaller than 10% of its internal radius. Being so thin its bending stresses can be ignored leaving only two types of stress, longitudinal and hoop stress. Finding the stresses in a cylinder ex periencing internal pressure is arduous. Solving it requires considering equilibrium forces, displacement compatibility, stress and strain relationship, and the boundary considerations. For thin cylinders, however, a satisfactory solution can be found by some simplifying calculations.
Experimental Procedure The experiment was carried out using a SM1007 thin cylinder. Two experiments are car ried out the first being the open ends experiments and t he other being the closed ends experiment. Open Ends When the thin cylinder is switched on it is allowed to reach a stable tem perature by letting it run for about 5 minutes, this gives more accurate readings. The pressure control is then opened and the hand wheel is screwed in t o set the open ends condition. The pressure control is then shut and the and the strain gauge and pressure readings are reset. The readings are then taken starting at 0MN.m-2 in increments of 0. 5MN.m-2 until 3MN.m -2. Open the pressure control to reset the pressure back to 0MN.m-2. Closed Ends The cylinder is switched on and is allowed to r each a stable temperature by letting it run for about 5 minutes, this gives more accurate readings. The pressure control is opened and the hand wheel is then unscrewed to set up the closed ends condition. Check that the frame is not taking any load by turning the pressure control valve and pumping until the pressure gauge reaches 3MN.m-2 then push and pull the cylinder gently along its axis, if the cylinder moves then it is not taking any load. If it does not, then the hand wheel must be wound out and redone. The pressure control is then shut and the strain gauge and pressure readings are r eset. The readings are then taken starting at 0MN.m-2 in increments of 0. 5MN.m-2 until 3MN.m -2. Open the pressure control to reset the pressure back to 0MN.m-2.
Results Open Ends Condition. Pressure
Strain (Gauges) 1
2
3
4
5
6
0
1
-1
1
2
2
4
0.5
112
-35
2
39
73
113
1
210
-67
4
73
139
211
1.5
311
-97
4
104
202
306
2
409
-130
3
137
266
405
2.5
505
-162
5
170
331
501
3
605
-194
3
203
395
596
Direct hoop stress (σH) = /2 Where; p = Internal Pressure d = Internal diameter of the cylinder t = Wall thickness of the cylinder Using the formula above direct hoop stress is then calculated.
Pressure 0
Direct Hoop Stress 0
0.5
6.6
1
13.3
1.5
20
2
26.6
2.5
33.3
3
40
Strain Gauge 1 700 600 500 n i a r t S
400 300 200 100 0 0
0.5
1
1.5
2
2.5
3
3.5
2
2.5
3
3.5
Pressure
Figure 1: Graph of Strain (1) against Pressure
Strain Gauge 2 (Longitudinal Strain) 0 0
0.5
1
1.5
-50
-100 n i a r t S
-150
-200
-250
Figure 2: Graph of Strain (2) against Pressure
Pressure
Strain Gauge 3 6 5 4 n i a r t S
3 2 1 0 0
0.5
1
1.5
2
2.5
3
3.5
3
3.5
Pressure
Figure 3:Graph of Strain (3) against Pressure
Strain Gauge 4 250
200
150 n i a r t S
100
50
0 0
0.5
1
1.5
Pressure
Figure 4:Graph of Strain (4) aga inst Pressure
2
2.5
Strain Gauge 5 450 400 350 300 n i a r t S
250 200 150 100 50 0 0
0.5
1
1.5
2
2.5
3
3.5
Pressure
Figure 5:Graph of Strain (5) against Pressure
Strain Gauge 6 700 600 500 n i a r t S
400 300 200 100 0 0
0.5
1
1.5
Pressure
Figure 6:Graph of Strain (6) against Pressure
2
2.5
3
Hoop Stress and Strain Relationship 40 y = 0.0673x - 0.6587
35 30 25 s s e r t S
20 15 10 5 0 -5
0
100
200
300
400
500
600
700
Strain
Steel is three times harder than aluminum and its Young’s Modulus is 210 GN.m-2. If the cylinder had been made of steel the strain values would be lower for the same stre ss.
Longitudinal and Hoop Strain Relationship 0 0
100
200
300
400
500
-50 n i a r t S l a n i
d u t i g n o L
-100
-150
-200
-250
y = -0.3262x + 1.5468
Hoop Strain
600
700
Gradient of the graph = 0.3262 Given Poisson’s Ratio = 0.33 Percent error = 1.165%
Theoretical Principal Strain Poisson’s Ratio = 0.33 Young’s Modulus = 69GN.m-2
Discussion In the open ends experiment there is no direct longitudinal strain but gauge 2 measures longitudinal strain because the hoop stress causes an indirect longitudinal strain. The longitudinal strain is negative meaning that is was caused by a compressive stress. In the graph showing the relationship between longitudinal and hoop strain, the gradient for the line is almost exactly the Poisson’s ratio thereby showing that the longitudinal strain was caused by a compressive stress. Also from the analysis of the Mohr’s circle in the open ends experiment we can see the circle almost predicts the direct strain exactly. This is the same in the closed ends experiment as it is shown that the Mohr’s circle predi cts the direct strain almost exactly.
Conclusion From the report above we observe the strain in a thin cylinder both experimentally and theoretically, using the apparatus and through calculations using the Mohr’s circle. The report show and explains internal pressure and complex stresses in a thin cylinder using the experiment and the c alculations.
