ME 320 Harvard University Combined Stress Pop Can Experiments Lab Report See Instruction, I will send you the lecture while the mister upload it and also t
ME 320 Harvard University Combined Stress Pop Can Experiments Lab Report See Instruction, I will send you the lecture while the mister upload it and also the example if I got one. Combined Strain experiment
Date
27-Jul-20
group
gage factor
unload voltage (V)
unload strain
2.070
Delta Rosette
0 deg
60 deg
1
2
-4.34160E-03
-0.0014514
0
0
120 deg
3
-0.0035962
0
2.095
2.100
2.095
Rectangular Rosette
0 deg
45 deg
90 deg
1
2
3
-0.0041220
-0.0028902
-0.0026624
0
0
0
torsion load (lbs) =
voltages (V)
Vr
Strain
20
-4.34780E-03
-0.0000012
0.0000023
-0.0041192
-0.0001020
0.0001971
-0.0041786
-0.0000110
0.0000211
principle strain +
principle strain acute angle (rad)
acute angle (deg)
0.000229157
-0.000229706
-0.779709428
-44.67405945
pressure (psi) =
voltages (V)
Vr
strain
2000
-4.57300E-03
-0.0000451
0.0000872
principle strain +
principle strain acute angle (rad)
acute angle (deg)
0.00031718
8.71886E-05
0.006056906
0.347035173
combined load
voltages (V)
Vr
strain
-4.57580E-03
-0.0000457
0.0000883
principle strain +
principle strain acute angle (rad)
acute angle (deg)
2.070
0.0004589
-0.0000563
0.5581708
31.9808310
-0.0009198
0.0001037
-0.0002003
2.070
-0.0022804
0.0001189
-0.0002264
-0.0025956
0.0000130
-0.0000249
-0.0033760
-0.0000947
0.0001805
-0.0034854
-0.0001605
0.0003065
-0.0027634
0.0000247
-0.0000471
-0.0034158
-0.0001469
0.0002806
0.000223806
-0.0002276
-0.73442375
-42.0793811
-0.0021372
-0.0001337
0.0002585
-0.0042884
-0.0001350
0.0002609
-0.0043142
-0.0000375
0.0000716
0.000306808
7.12484E-05
0.036389394
2.084958689
-0.0016038
-0.0000297
0.0000574
-0.0048120
-0.0002371
0.0004583
-0.0043682
-0.0000480
0.0000917
0.0004377
-0.0000655
0.5929928
33.9759842
A
C
B
A
B
C
shear
Excitation
Voltage
(Volts)
5.1285
5.1285
-0.0001
-0.0002
-0.0003
5.1285
5.1285
Mohr’s strain circle (combined) delta rosette
Mohr’s strain circle (torsion) delta rose
0.0002
0.0002
0.0001
0.0001
shear
0.0003
shear
0.0003
0
0
-0.0001
-0.0001
-0.0002
-0.0002
-0.0003
-0.0001
0.0001
0.0003
0.0005
-0.0003
-0.0003
-0.0001
normal
Mohr’s strain circle (combined) rectangular rosette
0.0003
0.0003
0.0002
0.0002
0.0001
0.0001
shear
shear
Mohr’s strain circle (torsion) rectangular ros
0
0
-0.0001
-0.0001
-0.0002
-0.0002
-0.0003
-0.0001
0
0.0001
0.0002
normal
0.0003
0.0004
0.0005
-0.0003
-0.0003
-0.0001
Mohr’s strain circle (pressure) delta rosette
ohr’s strain circle (torsion) delta rosette
0.0002
0.00015
0.0001
shear
0.00005
0
-0.00005
-0.0001
-0.00015
-0.0002
-0.0001
0.0001
0
0.0003
0.0001
normal
0.0002
0.0003
normal
Mohr’s strain circle (pressure) rectangular rosette
strain circle (torsion) rectangular rosette
0.0002
0.00015
0.0001
shear
0.00005
0
-0.00005
-0.0001
-0.00015
-0.0002
-0.0001
normal
0.0001
0.0003
0
0.0001
0.0002
normal
0.0003
delta rosette
0.0004
ctangular rosette
0.0004
Data tables used to gen
max strain
min strain
angle
radius
center
angle(radians)
0.00
0.39
0.79
1.18
1.57
1.96
2.36
2.75
3.14
3.53
3.93
4.32
4.71
5.11
5.50
5.89
6.28
line a data
line b data
line c data
line A data
line B data
line C data
Data tables used to generate mohr’s circles
delta rossette
torsion
max strain
2.29157E-04
min strain
-2.29706E-04
angle
-7.79709E-01
radius
0.000229432
center
-2.74191E-07
x
angle(radians)
X for plotting
0.00
2.29157E-04
0.39
2.11693E-04
0.79
1.61958E-04
1.18
8.75255E-05
1.57
-2.74191E-07
1.96
-8.80738E-05
2.36
-1.62507E-04
2.75
-2.12241E-04
3.14
-2.29706E-04
3.53
-2.12241E-04
3.93
-1.62507E-04
4.32
-8.80738E-05
4.71
-2.74191E-07
5.11
8.75255E-05
5.50
1.61958E-04
5.89
2.11693E-04
6.28
2.29157E-04
y
Y for plotting
0.00000E+00
8.77996E-05
1.62233E-04
2.11967E-04
2.29432E-04
2.11967E-04
1.62233E-04
8.77996E-05
2.81088E-20
-8.77996E-05
-1.62233E-04
-2.11967E-04
-2.29432E-04
-2.11967E-04
-1.62233E-04
-8.77996E-05
-5.62175E-20
rectangular rosette
torsion
2.23806E-04
-2.27602E-04
-7.34424E-01
0.000225704
-1.89814E-06
x
y
X for plotting
Y for plotting
2.23806E-04 0.00000E+00
2.06625E-04
8.63732E-05
1.57699E-04
1.59597E-04
8.44751E-05
2.08523E-04
-1.89814E-06
2.25704E-04
-8.82713E-05
2.08523E-04
-1.61495E-04
1.59597E-04
-2.10421E-04
8.63732E-05
-2.27602E-04
2.76521E-20
-2.10421E-04 -8.63732E-05
-1.61495E-04 -1.59597E-04
-8.82713E-05 -2.08523E-04
-1.89814E-06 -2.25704E-04
8.44751E-05 -2.08523E-04
1.57699E-04 -1.59597E-04
2.06625E-04 -8.63732E-05
2.23806E-04 -5.53042E-20
line a data
2.33610E-06 2.75318E-04
2.33610E-06 -2.75318E-04
2.10723E-05
2.10723E-05
2.70845E-04
-2.70845E-04
line b data
-2.00260E-04 2.75318E-04
-2.00260E-04 -2.75318E-04
-2.26430E-04
-2.26430E-04
2.70845E-04
-2.70845E-04
line c data
1.97101E-04 2.75318E-04
1.97101E-04 -2.75318E-04
-2.48686E-05
-2.48686E-05
2.70845E-04
-2.70845E-04
line A data
-2.74191E-07 0.00000E+00
-2.88449E-06 -0.00022942
-1.89814E-06
2.10723E-05
0.00000E+00
2.24532E-04
line B data
-2.74191E-07 0.00000E+00
1.99712E-04 0.000112448
-1.89814E-06
-2.26430E-04
0.00000E+00
2.29704E-05
line C data
-2.74191E-07 0.00000E+00
-1.97650E-04 0.000116969
-1.89814E-06
-2.48686E-05
0.00000E+00
-2.24532E-04
delta rossette
y
Y for plotting
0.00000E+00
4.40070E-05
8.13143E-05
1.06242E-04
1.14996E-04
1.06242E-04
8.13143E-05
4.40070E-05
1.40887E-20
-4.40070E-05
-8.13143E-05
-1.06242E-04
-1.14996E-04
-1.06242E-04
-8.13143E-05
-4.40070E-05
-2.81774E-20
rectangular rosette
pressure
3.06808E-04
7.12484E-05
3.63894E-02
0.00011778
1.89028E-04
x
y
X for plotting Y for plotting
3.06808E-04 0.00000E+00
2.97842E-04 4.50723E-05
2.72311E-04 8.32828E-05
2.34100E-04 1.08814E-04
1.89028E-04 1.17780E-04
1.43956E-04 1.08814E-04
1.05745E-04 8.32828E-05
8.02139E-05 4.50723E-05
7.12484E-05 1.44298E-20
8.02139E-05 -4.50723E-05
1.05745E-04 -8.32828E-05
1.43956E-04 -1.08814E-04
1.89028E-04 -1.17780E-04
2.34100E-04 -1.08814E-04
2.72311E-04 -8.32828E-05
2.97842E-04 -4.50723E-05
3.06808E-04 -2.88595E-20
combined
4.58934E-04
-5.62694E-05
5.58171E-01
0.000257602
2.01332E-04
x
X for plotting
4.58934E-04
4.39325E-04
3.83484E-04
2.99912E-04
2.01332E-04
1.02752E-04
1.91804E-05
-3.66606E-05
-5.62694E-05
-3.66606E-05
1.91804E-05
1.02752E-04
2.01332E-04
2.99912E-04
3.83484E-04
4.39325E-04
4.58934E-04
8.71971E-05 1.37995E-04
8.71971E-05 -1.37995E-04
7.15602E-05 1.41336E-04
7.15602E-05 -1.41336E-04
8.82523E-05
8.82523E-05
2.58472E-04 1.37995E-04
2.58472E-04 -1.37995E-04
1.80464E-04 1.41336E-04
1.80464E-04 -1.41336E-04
5.74262E-05
5.74262E-05
2.60884E-04 1.37995E-04
2.60884E-04 -1.37995E-04
3.06496E-04 1.41336E-04
3.06496E-04 -1.41336E-04
4.58319E-04
4.58319E-04
2.02184E-04 0.00000E+00
8.71971E-05 1.39300E-06
1.89028E-04 0.00000E+00
7.15602E-05 8.56430E-06
2.01332E-04
8.82523E-05
2.02184E-04 0.00000E+00
2.58472E-04 -1.00278E-04
1.89028E-04 0.00000E+00
1.80464E-04 -1.17468E-04
2.01332E-04
5.74262E-05
2.02184E-04 0.00000E+00
2.60884E-04 1.00278E-04
1.89028E-04 0.00000E+00
3.06496E-04 -8.56430E-06
2.01332E-04
4.58319E-04
pressure
3.17180E-04
8.71886E-05
6.05691E-03
0.000114996
2.02184E-04
x
X for plotting
3.17180E-04
3.08427E-04
2.83499E-04
2.46191E-04
2.02184E-04
1.58177E-04
1.20870E-04
9.59422E-05
8.71886E-05
9.59422E-05
1.20870E-04
1.58177E-04
2.02184E-04
2.46191E-04
2.83499E-04
3.08427E-04
3.17180E-04
delta rossette
y
Y for plotting
0.00000E+00
9.85799E-05
1.82152E-04
2.37993E-04
2.57602E-04
2.37993E-04
1.82152E-04
9.85799E-05
3.15600E-20
-9.85799E-05
-1.82152E-04
-2.37993E-04
-2.57602E-04
-2.37993E-04
-1.82152E-04
-9.85799E-05
-6.31201E-20
rectangular rosette
combined
4.37728E-04
-6.54925E-05
5.92993E-01
0.00025161
1.86118E-04
x
y
X for plotting Y for plotting
4.37728E-04 0.00000E+00
4.18576E-04 9.62872E-05
3.64033E-04 1.77915E-04
2.82405E-04 2.32458E-04
1.86118E-04 2.51610E-04
8.98308E-05 2.32458E-04
8.20250E-06 1.77915E-04
-4.63398E-05 9.62872E-05
-6.54925E-05 3.08260E-20
-4.63398E-05 -9.62872E-05
8.20250E-06 -1.77915E-04
8.98308E-05 -2.32458E-04
1.86118E-04 -2.51610E-04
2.82405E-04 -2.32458E-04
3.64033E-04 -1.77915E-04
4.18576E-04 -9.62872E-05
4.37728E-04 -6.16520E-20
3.09122E-04
-3.09122E-04
9.16675E-05 3.01933E-04
9.16675E-05 -3.01933E-04
3.09122E-04
-3.09122E-04
-4.70921E-05 3.01933E-04
-4.70921E-05 -3.01933E-04
3.09122E-04
-3.09122E-04
2.80568E-04 3.01933E-04
2.80568E-04 -3.01933E-04
0.00000E+00
2.31455E-04
1.86118E-04 0.00000E+00
9.16675E-05 2.33210E-04
0.00000E+00
-2.13658E-04
1.86118E-04 0.00000E+00
-4.70921E-05 -9.44505E-05
0.00000E+00
-1.77974E-05
1.86118E-04 0.00000E+00
2.80568E-04 -2.33210E-04
ME220 Mechanics of Materials Laboratory
TEST TITLE: Combined Stress & Pop Can Experiments
NAME:
(refer to lab manual pp. 74-90)
1. Summary (1/12) (The summary should be succinct (limited to one page), but contain
the following four pieces of information, namely, the purpose of the experiment;
experimental methods; results; and conclusion.)
2. Results (5/12)
1. Tabulate the test results as follows
Torque only (a)
( in-lb)
(experiment)
Pressure only (b)
(psi)
(experiment)
Sum of
(a) and (b)
Combined Torque and
Pressure
(experiment)
gage 1
gage 2
gage 3
gage 4
gage 5
gage 6
4. Tabulate the principal strains measured from delta and rectangular strain gage
rosettes as follows (for the combined loading only).
?1
?2
Delta rosette
Rectangular rosette
5. For each strain gage rosette, calculate the corresponding ? 1 , ? 2 , and ?max using the
measured ?1 and ? 2 . The Youngs modulus (E) and Poissons ratio for steel are 30×106
psi and 0.25 respectively.
6. Calculate the theoretical ? 1 , ? 2 , and ?max using the thick and thin-walled pressure
vessel equations as described below.
2
stress due to P
Stress due to T
Thick-walled tube
? a = pri2 / (ro2 ? ri2 )
? = Tro / J
(outer surface)
? c = 2? a
Thin-walled tube
? a = Prm / (2t )
(outer surface)
? c = 2? a
(
? = T / 2?rm2t
Principal stresses: ? 1, 2 = (? a + ? c ) / 2 ± {[(? a ? ? c ) / 2] + ? 2
2
}
1/ 2
Maximum shear stress: ? max = {[? a ? ? c ) / 2] + ? 2 }
2
1/ 2
[
(
Where:
ro = outer radius
ri = inner radius
rm = mean radius [= (ro + ri ) / 2]
t = wall thickness
J = polar moment of inertia of the tube = (? / 2) ro4 ? ri4
P = pressure
T = torque
? a = axial stress
? c = circumferential stress
? = shear stress
3
)]
)
7. Tabulate the results from steps 5 and 6 as follows.
?1
?2
? max
Experiment (delta)
Experiment (rectan.)
Thick-wall calc.
Thin-wall calc.
3. Discussion (2/12)
1. Comment on the superposition principle applied in the current experiment.
2. Compare analytical and experimental results.
3. Discuss any sources of error in the analytical calculations.
4. Discuss any sources of error in the experimental method.
4. Conclusion (1/12)
(Continue to next page)
4
THIN-WALLED PRESSURE VESSEL EXPERIMENT
Lab Report
1. Summary (0.5/12)
2. Results (1/12)
The results of the pop can experiment are as follows:
Diameter before opening: 2.6005 inches
Strain value: ?840 ×10?6 in/in
Wall Thickness: 0.0038 inches
Calculate the pressure based on the measured strain
(E and ? for aluminum are 10×106 psi and 0.33 respectively)
3. Discussion (1/12)
1. Do some research to see if you could find some information on the range of pressure
inside the beverage can and comment on your results.
2. A circular shaft with radius r is subjected to a torque T. The modulus of elasticity and
Poisson’s ratio of the shaft are E and ? respectively. Show how a single strain gage
mounted in the 450 direction with respect to the longitudinal axis can be employed
to determine the applied torque. In other words, write T in terms of E, ? , r, and ?,
where ? is the reading of the strain gage.
4. Conclusion (0.5/12)
5
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