Tensile Test Lab 1
Tensile Test Lab 1
Tensile Test Lab 1
Group 1
Mykenson Pierre
Hanser Castro
Adam Wechsler
3903289
3256769
1152905
EMA3702L
Lab 1. Tensile Test
Table of Content
List of Figures.........................................................................................2
List of table............................................................................................3
Nomenclature.........................................................................................4
Abstract..................................................................................................5
Introduction............................................................................................6
Data and Results....................................................................................8
Discussion............................................................................................11
Conclusion............................................................................................13
Recommendation.................................................................................14
References...........................................................................................15
Appendices...........................................................................................16
Appendix A...........................................................................................17
Appendix B...........................................................................................18
Appendix C...........................................................................................19
Appendix D...........................................................................................20
Appendix E...........................................................................................28
List of Figures
Figure
Figure
Figure
Figure
Figure
Figure
Figure
List of tables
Table
Table
Table
Table
1
2
3
4
Nomenclature
Symbol
L
F
L
E
A
Description
gauge length elongation
axial tensile load
length of the specimen
Young's modulus of
elasticity
cross-sectional area of the
specimen
engineering stress
the engineering strain
Units
in
lbs.
in
psi
in2
psi
n/a
Abstract
The purpose of this experiment is to understand the principle of uniaxial tensile
testing and gain experience using tensile test machine to obtain necessary tensile
properties.
On the experiment we will analyze load-extension and stress-strain relationships
and represent them in graphical form. Also we will evaluate ultimate tensile stress,
percent elongation, fracture strain and Youngs Modulus of elasticity of materials such as
aluminum and carbon steel when subjected to uniaxial tensile load.
Introduction
The mechanical properties of materials are found by performing delicate
experiments on the part to see how it reacts under physical forces. In real life there are
innumerable number of factors in which load are applied on materials, some of the most
frequent examples include tensile, compressive and shear. These properties are extremely
important in mechanical design selection.
During tensile test experiment a plot of stress () versus strain () is created by the
software, we reproduce the same graph on Excel spreadsheet. The value of stress on this
experiment is calculated by dividing the amount of force (F) which is applied by the
machine on the cross section area (A) which is measure at the beginning of the
experiment.
Stress is mathematically express in equation 1. The stress strain value can be
found from equation 2 where L is the instantaneous length of the specimen and L0 is the
initial length of the specimen
F
A
L L0
L0
(Eq. 1)
(Eq. 2)
Figure 1. Various
Theoretically the stress-strain curve can be constructed by assuming that the volume of
the specimen remain the same throughout the experiment, even without measuring the
cross sectional area (2).
Figure 2. Aluminum,
Figure 3.
Force vs Extension
Stress vs Strain
Yield Strength Line
40000
Stress
Yield Strength
Proportional Limit
20000
Elastic Limit
Ultimate Point
0
-0.04 -0.02
Fracture Point
-20000
-40000
Strain
Figure 4 Aluminum: Stress vs Strain
X-Sect Area:
Length:
E:
0.019663
3.000000
1,889,751.708820
yield strength:
proportional limit:
0.026487
0.012663
elastic limit:
0.016433
ultimate point:
0.075988
fracture point:
0.102300
46275.123
62
44451.04
45363.081
81
48850.924
33
37214.813
75
Stress
Stress vs
Strain
Yield Strength
Line
Yield Strength
Proportional
Limit
Elastic Limit
Ultimate
Point
Fracture Point
Strain
0.029413
3.000000
2,091,175.786312
yield strength:
0.032545
proportional limit:
0.011712
elastic limit:
0.017901
ultimate point:
0.028258
fracture point:
0.093777
63874.827
37
38365.894
49
51120.360
93
64041.784
61
29703.936
52
Discussion
10
12
Conclusion
The primary goal on this lab was to analyze the derivation of
experimental formulas that are used in materials engineering. By
examining the reaction of the specimens under uniaxial tension, we
can collect relevant information on their structural and mechanical
properties. This lab helped us as engineers explore and understand the
behavior of materials under axial stretch loading.
13
Recommendation
Roark's Formulas for Stress and Strain is a book that includes an extended coverage of
joints and shearing stress. It also covers material behavior and stress strain
measurements.
Stress, Strain, and Structural Dynamics by Bingen Yang is a book that focus
on the analysis of Stress, Strain, and Structural Dynamics, this is an
extremely useful reference to statics and dynamics of solids and
structures, including mechanics of materials, structural mechanics,
elasticity, rigid-body dynamics, vibrations, and structural dynamics.
14
References
1) Beer, Ferdinand P. Mechanics of Materials. 6th ed. New York:
McGraw-Hill, 2011. Print.
2) Roark, Raymond J., and Warren C. Young. Roark's Formulas for
Stress and Strain. 7th ed. New York: McGraw-Hill, 2002. Print.
3) Yang, Bingen. Stress, Strain, and Structural Dynamics: An
Interactive Handbook of Formulas, Solutions, and MATLAB Toolboxes.
Amsterdam: Elsevier, 2007. Print.
15
Appendices
Appendix A: Apparatus
Appendix B: Procedure
Appendix C: Calibration Data
Appendix D: Experimental Data
Appendix E: Sample Calculations
16
Appendix A
Apparatus
The United Model SSTM testing machine is a computer
inclusive, electromechanical, test system designed to
accommodate a variety of testing instruments and
accessories to test various types of material including
ceramics, plastics, polymers, metals and composites
17
Appendix B
Procedure
The first step was to measure the specimen, then we insert the values of width, thickness
and area into the software and reproduce figures 2 and 3. Sample data is collected from
the software in for of Excel table after the figures are obtained,
Aluminum Specimen Dimensions:
Thickness 0.053 in
Width: 0.371 in
Initial Length (L): 3.0 in
Final Length (L2): 3.216 in
A = t*w = (0.053)(0.371) = 0.019663 in2
= F/A
Strain calculation:
L = 3.000
Strain = (L2-L)/L
Carbon Steel Specimen Dimensions:
Thickness 0.067 in
Width: 0.430 in
Initial Length (L): 3.0 in
Final Length (L2): 3.305 in
Strain calculation:
L = 3.000
Strain = (L2-L)/L
18
Appendix C
Calibration Data
We did not use calibration on this experiment.
FORCE
STRESS
EXT
STRAIN
del-del-L
yield str
Append
ix D
Experimenta
l Data
19
ultimate point
POSITION
0.025933
39.03631
1985.267
-0.01961
-0.00654
-16130.8
18116.01781
1985.267166
0.030299
48.21369
2452.001
-0.01524
-0.00508
0.004366
-13380.5
15832.50745
2452.000799
0.030299
48.20651
2451.635
-0.04554
-0.01518
-0.0303
-32466.3
34917.90385
2452.000799
0.031573
59.38021
3019.896
-0.04427
-0.01476
0.001274
-31663.8
34683.67487
3019.895788
0.03327
67.68148
3442.073
-0.04257
-0.01419
0.001697
-30594.7
34036.76273
3442.07295
0.034121
72.12654
3668.135
-0.04172
-0.01391
0.000851
-30058.8
33726.92156
3668.135134
0.03495
76.74393
3902.961
-0.04089
-0.01363
0.000829
-29536.5
33439.44771
3902.961247
0.035809
81.47623
4143.632
-0.04003
-0.01334
0.000859
-28995.1
33138.77283
4143.631532
0.036686
86.23006
4385.397
-0.03915
-0.01305
0.000877
-28442.9
32828.31395
4385.396774
0.037541
91.07005
4631.544
-0.0383
-0.01277
0.000855
-27904.3
32535.83827
4631.544174
0.038383
95.96032
4880.248
-0.03746
-0.01249
0.000842
-27373.8
32254.08308
4880.248157
0.039208
100.9655
5134.796
-0.03663
-0.01221
0.000825
-26854.3
31989.051
5134.796312
0.040041
106.0712
5394.456
-0.0358
-0.01193
0.000833
-26329.2
31723.68676
5394.456467
0.040879
111.3851
5664.705
-0.03496
-0.01165
0.000838
-25801.5
31466.19152
5664.705351
0.041734
117.1227
5956.502
-0.03411
-0.01137
0.000855
-25262.9
31219.37001
5956.50224
0.042589
122.7239
6241.362
-0.03325
-0.01108
0.000855
-24724.2
30965.60194
6241.361941
0.043427
128.9067
6555.8
-0.03241
-0.0108
0.000838
-24196.5
30752.30041
6555.799853
0.044282
135.0751
6869.506
-0.03156
-0.01052
0.000855
-23657.9
30527.38384
6869.50637
0.045137
141.6672
7204.761
-0.0307
-0.01023
0.000855
-23119.2
30324.00786
7204.760505
0.045992
148.0009
7526.873
-0.02985
-0.00995
0.000855
-22580.6
30107.50295
7526.87282
0.046843
154.3488
7849.708
-0.029
-0.00967
0.000851
-22044.7
29894.43557
7849.707606
0.04769
160.1438
8144.423
-0.02815
-0.00938
0.000846
-21511.5
29655.97135
8144.423477
0.048536
165.8383
8434.029
-0.0273
-0.0091
0.000846
-20978.4
29412.38925
8434.028511
0.049374
171.6118
8727.651
-0.02647
-0.00882
0.000838
-20450.6
29178.26641
8727.650976
0.050233
177.4427
9024.193
-0.02561
-0.00854
0.000859
-19909.3
28933.47012
9024.192811
0.051101
183.2593
9320.007
-0.02474
-0.00825
0.000868
-19362.5
28682.49706
9320.006744
0.051965
189.4205
9633.347
-0.02387
-0.00796
0.000864
-18818.4
28451.77122
9633.346982
0.052807
195.3807
9936.465
-0.02303
-0.00768
0.000842
-18288
28224.42983
9936.464771
0.053641
201.4629
10245.79
-0.0222
-0.0074
0.000833
-17762.9
28008.72864
10245.7868
0.054483
207.5667
10556.21
-0.02136
-0.00712
0.000842
-17232.5
27788.68838
10556.20689
0.055325
213.7638
10871.37
-0.02051
-0.00684
0.000842
-16702
27573.38877
10871.37232
0.05618
220.1763
11197.49
-0.01966
-0.00655
0.000855
-16163.4
27360.88612
11197.49276
0.057061
226.6248
11525.44
-0.01878
-0.00626
0.000881
-15608.5
27133.89801
11525.44381
0.057916
233.1306
11856.31
-0.01792
-0.00597
0.000855
-15069.8
26926.13405
11856.3088
0.058762
239.6365
12187.18
-0.01708
-0.00569
0.000846
-14536.6
26723.82321
12187.17923
0.059626
246.3434
12528.27
-0.01621
-0.0054
0.000864
-13992.6
26520.84923
12528.27132
0.060472
253.5027
12892.37
-0.01537
-0.00512
0.000846
-13459.4
26351.76873
12892.3715
0.061319
260.6908
13257.94
-0.01452
-0.00484
0.000846
-12926.2
26184.15257
13257.93602
0.062165
268.3025
13645.04
-0.01367
-0.00456
0.000846
-12393
26038.07292
13645.04349
0.06302
276.2948
14051.51
-0.01282
-0.00427
0.000855
-11854.4
25905.92011
14051.5079
0.063871
284.4809
14467.83
-0.01197
-0.00399
0.000851
-11318.5
25786.33832
14467.8277
0.064713
292.624
14881.96
-0.01113
-0.00371
0.000842
-10788
25670.00509
14881.96068
0.065555
300.6952
15292.44
-0.01028
-0.00343
0.000842
-10257.6
25550.01586
15292.43709
0.066406
309.0896
15719.35
-0.00943
-0.00314
0.000851
-9721.68
25441.02882
15719.35105
0.067231
317.8645
16165.62
-0.00861
-0.00287
0.000825
-9202.1
25367.71327
16165.61572
0.068043
326.4097
16600.2
-0.0078
-0.0026
0.000812
-8690.68
25290.87715
16600.19827
0.068881
335.2564
17050.11
-0.00696
-0.00232
0.000838
-8162.94
25213.05168
17050.11487
0.06971
344.1821
17504.05
-0.00613
-0.00204
0.000829
-7640.63
25144.68292
17504.04813
0.070556
353.5099
17978.43
-0.00528
-0.00176
0.000846
-7107.45
25085.88418
17978.43095
20
0.071416
363.4481
18483.86
-0.00442
-0.00147
0.000859
-6566.11
25049.96349
18483.85748
0.072271
373.695
19004.98
-0.00357
-0.00119
0.000855
-6027.49
25032.46963
19004.98435
0.073143
384.5954
19559.34
-0.0027
-0.0009
0.000872
-5477.98
25037.32561
19559.34486
0.073977
394.9644
20086.68
-0.00186
-0.00062
0.000833
-4952.96
25039.64097
20086.67985
0.074819
405.915
20643.6
-0.00102
-0.00034
0.000842
-4422.5
25066.09211
20643.595
0.075656
416.3845
21176.04
-0.00018
-6.1E-05
0.000838
-3894.76
25070.79636
21176.04084
0.076499
427.8018
21756.69
0.000659
0.00022
0.000842
-3364.29
25120.98127
21756.68964
0.077388
438.9821
22325.29
0.001549
0.000516
0.00089
-2803.9
25129.18937
22325.28537
0.078248
450.3922
22905.57
0.002408
0.000803
0.000859
-2262.57
25168.1351
22905.56944
0.079107
461.4002
23465.4
0.003268
0.001089
0.000859
-1721.22
25186.6204
23465.40241
0.079949
472.1425
24011.72
0.00411
0.00137
0.000842
-1190.76
25202.48095
24011.72184
0.080804
482.9278
24560.23
0.004965
0.001655
0.000855
-652.133
25212.36273
24560.22964
0.081646
493.8065
25113.49
0.005807
0.001936
0.000842
-121.674
25235.16086
25113.48665
0.082475
504.52
25658.34
0.006636
0.002212
0.000829
400.6281
25257.71442
25658.34252
0.083343
516.5116
26268.2
0.007504
0.002501
0.000868
947.4151
25320.7839
26268.19899
0.084194
527.9863
26851.77
0.008355
0.002785
0.000851
1483.318
25368.45027
26851.76871
0.085045
539.7481
27449.94
0.009206
0.003069
0.000851
2019.217
25430.71974
27449.93683
0.0859
551.5602
28050.66
0.010061
0.003354
0.000855
2557.842
25492.82077
28050.6627
0.086742
562.9271
28628.75
0.010903
0.003634
0.000842
3088.308
25540.44309
28628.75065
0.087576
574.2508
29204.64
0.011736
0.003912
0.000833
3613.325
25591.3129
29204.63782
0.088413
585.6248
29783.09
0.012574
0.004191
0.000838
4141.07
25642.0162
29783.08584
0.089286
597.0275
30362.99
0.013446
0.004482
0.000872
4690.578
25672.41465
30362.99277
0.090162
608.1573
30929.02
0.014323
0.004774
0.000877
5242.801
25686.21727
30929.01834
0.091009
619.8616
31524.26
0.015169
0.005056
0.000846
5775.982
25748.28069
31524.26244
0.091855
630.7114
32076.05
0.016016
0.005339
0.000846
6309.162
25766.89036
32076.05278
0.092693
641.4463
32622
0.016854
0.005618
0.000838
6836.908
25785.08734
32621.99507
0.093527
652.1523
33166.47
0.017687
0.005896
0.000833
7361.925
25804.54406
33166.46914
0.094364
662.7292
33704.38
0.018525
0.006175
0.000838
7889.669
25814.70891
33704.37812
0.095198
673.9379
34274.42
0.019358
0.006453
0.000833
8414.687
25859.73378
34274.42035
0.09604
684.5722
34815.25
0.020201
0.006734
0.000842
8945.159
25870.08849
34815.24714
0.096878
695.185
35354.98
0.021038
0.007013
0.000838
9472.897
25882.08439
35354.98131
0.097685
705.9197
35900.91
0.021846
0.007282
0.000808
9981.594
25919.32079
35900.91429
0.098532
716.9274
36460.73
0.022692
0.007564
0.000846
10514.78
25945.95421
36460.73484
0.099395
727.4395
36995.35
0.023556
0.007852
0.000864
11058.84
25936.50764
36995.34731
0.100255
738.0881
37536.9
0.024415
0.008138
0.000859
11600.18
25936.7168
37536.90046
0.101097
747.9827
38040.11
0.025258
0.008419
0.000842
12130.65
25909.46236
38040.11224
0.101926
757.9491
38546.97
0.026087
0.008696
0.000829
12652.95
25894.01911
38546.9713
0.102751
767.2908
39022.06
0.026912
0.008971
0.000825
13172.53
25849.5267
39022.06029
0.10361
777.6233
39547.54
0.027771
0.009257
0.000859
13713.87
25833.66889
39547.54061
0.104483
787.5035
40050.02
0.028643
0.009548
0.000872
14263.38
25786.63711
40050.01673
0.105338
797.3191
40549.21
0.029498
0.009833
0.000855
14802
25747.20605
40549.20876
0.10618
807.0198
41042.56
0.03034
0.010113
0.000842
15332.46
25710.09278
41042.55584
0.107018
816.067
41502.67
0.031178
0.010393
0.000838
15860.21
25642.46365
41502.67083
0.107851
825.028
41958.4
0.032012
0.010671
0.000833
16385.23
25573.16821
41958.39979
0.108693
833.6588
42397.34
0.032854
0.010951
0.000842
16915.69
25481.64502
42397.33578
0.109561
841.9377
42818.37
0.033722
0.011241
0.000868
17462.48
25355.896
42818.37375
0.110446
849.8576
43221.16
0.034607
0.011536
0.000885
18020.14
25201.01305
43221.15674
0.111297
856.9446
43581.58
0.035458
0.011819
0.000851
18556.04
25025.53391
43581.5786
0.112152
863.7156
43925.93
0.036313
0.012104
0.000855
19094.66
24831.26766
43925.93074
0.112999
869.0004
44194.7
0.037159
0.012386
0.000846
19627.85
24566.85306
44194.70209
21
0.113828
874.0408
44451.04
0.037989
0.012663
0.000829
20150.14
24300.89427
44451.03857
0.115521
881.1637
44813.29
0.039681
0.013227
0.001693
21216.51
23596.77486
44813.28873
0.117244
885.2206
45019.61
0.041405
0.013802
0.001723
22301.92
22717.68553
45019.60947
0.11895
887.5685
45139.02
0.04311
0.01437
0.001706
23376.45
21762.56847
45139.0165
0.121437
889.6437
45244.55
0.045598
0.015199
0.002487
24943.35
20301.19962
45244.55458
0.123955
891.1587
45321.6
0.048116
0.016039
0.002518
26529.3
18792.29884
45321.60359
0.12652
892.925
45411.43
0.050681
0.016894
0.002565
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85834.98
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22
0.219835
944.709
48045.01
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86925.81
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48045.0076
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93351.21
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94423.02
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48326.18588
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48404.33373
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952.5714
48444.87
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100867.4
-52422.58299
48444.86656
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952.5785
48445.23
0.167847
0.055949
0.001719
101950.2
-53504.92734
48445.22663
0.246178
953.196
48476.63
0.170339
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0.002492
103519.8
-55043.15256
48476.63042
0.248722
953.9858
48516.8
0.172882
0.057627
0.002544
105122
-56605.24249
48516.79697
0.251222
954.4597
48540.9
0.175383
0.058461
0.0025
106697.1
-58156.2408
48540.9
0.253731
955.429
48590.2
0.177892
0.059297
0.002509
108277.6
-59687.41563
48590.1956
0.256275
955.8384
48611.01
0.180435
0.060145
0.002544
109879.9
-61268.85317
48611.01454
0.258015
955.8599
48612.11
0.182176
0.060725
0.00174
110976.2
-62364.06289
48612.11027
0.260537
956.6928
48654.47
0.184698
0.061566
0.002522
112564.8
-63910.36032
48654.46829
0.263085
957.102
48675.28
0.187246
0.062415
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114169.9
-65494.57619
48675.27792
0.264821
957.5831
48699.75
0.188982
0.062994
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115263.5
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48699.74724
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957.5759
48699.38
0.190683
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116335.2
-67635.81628
48699.74724
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957.978
48719.83
0.193236
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117942.9
-69223.10492
48719.83051
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958.3156
48737
0.194946
0.064982
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119020.1
-70283.14968
48736.99907
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958.811
48762.19
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120619.7
-71857.51029
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958.8828
48765.85
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121699.7
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48765.84512
0.276762
959.0264
48773.15
0.200923
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122785.1
-74011.9524
48773.14897
0.279249
959.0264
48773.15
0.20341
0.067803
0.002487
124352
-75578.8124
48773.14897
0.281776
959.6582
48805.28
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125943.4
-77138.10672
48805.27911
0.284306
959.7947
48812.22
0.208467
0.069489
0.002531
127537.5
-78725.29382
48812.21979
0.28679
959.7085
48807.84
0.21095
0.070317
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129101.7
-80293.82405
48812.21979
0.289337
959.8808
48816.6
0.213498
0.071166
0.002548
130706.6
-81890.03047
48816.59962
0.291056
960.1896
48832.3
0.215217
0.071739
0.001719
131789.3
-82957.03144
48832.30307
0.293578
960.527
48849.46
0.217739
0.07258
0.002522
133378
-84528.58395
48849.46232
0.295297
960.5342
48849.83
0.219458
0.073153
0.001719
134460.7
-85610.85638
48849.8286
0.29702
960.2398
48834.86
0.221181
0.073727
0.001723
135546.1
-86711.235
48849.8286
0.298739
960.1896
48832.3
0.2229
0.0743
0.001719
136628.8
-87796.49406
48849.8286
0.301265
960.2327
48834.5
0.225426
0.075142
0.002526
138220.2
-89385.72395
48849.8286
0.303805
960.5557
48850.92
0.227965
0.075988
0.002539
139819.8
-90968.84104
48850.92433
0.306314
960.2542
48835.59
0.230474
0.076825
0.002509
141400.2
-92564.63614
48850.92433
0.308853
959.9885
48822.08
0.233014
0.077671
0.002539
142999.8
-94177.70129
48850.92433
0.310563
960.0316
48824.27
0.234724
0.078241
0.00171
144077.1
-95252.79823
48850.92433
0.312282
960.2183
48833.77
0.236443
0.078814
0.001719
145159.7
-96325.94162
48850.92433
0.314804
960.0531
48825.36
0.238965
0.079655
0.002522
146748.4
-97923.05608
48850.92433
0.316527
960.01
48823.17
0.240688
0.080229
0.001723
147833.8
-99010.58957
48850.92433
0.318246
959.7013
48807.47
0.242406
0.080802
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148916.5
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48850.92433
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959.3638
48790.31
0.244946
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150516
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48850.92433
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151601.4
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48850.92433
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48778.98
0.249208
0.083069
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153201
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48850.92433
23
0.3276
958.6889
48755.98
0.25176
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154808.7
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0.253488
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157485.5
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159052.4
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160140.5
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161704.7
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955.9819
48618.31
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163279.8
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48590.93
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164351.6
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48850.92433
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955.0054
48568.65
0.268637
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165439.7
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48850.92433
0.347003
953.914
48513.15
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167031.1
-118517.9834
48850.92433
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952.6216
48447.42
0.272878
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168111
-119663.6285
48850.92433
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951.2646
48378.41
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169201.9
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170796
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172354.8
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942.3179
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173429.3
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937.8447
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174503.8
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175551.1
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926.4927
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0.286382
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176617.5
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48850.92433
0.363923
918.9176
46733.34
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177689.3
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48850.92433
0.36565
910.3802
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0.289811
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178777.4
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48850.92433
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905.4689
46049.38
0.290675
0.096892
0.000864
179321.5
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48850.92433
0.367343
900.3925
45791.21
0.291504
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179843.8
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48850.92433
0.368181
895.3735
45535.95
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180371.5
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48850.92433
0.369032
889.579
45241.26
0.293192
0.097731
0.000851
180907.4
-135666.1702
48850.92433
0.3699
883.7486
44944.75
0.29406
0.09802
0.000868
181454.2
-136509.4679
48850.92433
0.370785
877.7746
44640.93
0.294946
0.098315
0.000885
182011.9
-137370.9391
48850.92433
0.371653
871.097
44301.33
0.295814
0.098605
0.000868
182558.7
-138257.3806
48850.92433
0.3725
864.8932
43985.82
0.29666
0.098887
0.000846
183091.9
-139106.0586
48850.92433
0.373337
857.641
43617
0.297498
0.099166
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183619.6
-140002.6109
48850.92433
0.374154
850.6188
43259.87
0.298314
0.099438
0.000816
184133.8
-140873.8942
48850.92433
0.374996
842.8568
42865.12
0.299156
0.099719
0.000842
184664.2
-141799.0936
48850.92433
0.375868
834.1686
42423.26
0.300029
0.10001
0.000872
185213.7
-142790.4174
48850.92433
0.37674
825.107
41962.42
0.300901
0.1003
0.000872
185763.2
-143800.8038
48850.92433
0.377621
814.8823
41442.42
0.301782
0.100594
0.000881
186318.2
-144875.7665
48850.92433
0.378468
804.5138
40915.11
0.302628
0.100876
0.000846
186851.3
-145936.2313
48850.92433
0.379319
793.2622
40342.89
0.303479
0.10116
0.000851
187387.3
-147044.3841
48850.92433
0.380165
781.235
39731.22
0.304326
0.101442
0.000846
187920.4
-148189.2237
48850.92433
0.381016
767.7072
39043.24
0.305176
0.101725
0.000851
188456.3
-149413.0611
48850.92433
0.381884
751.9319
38240.95
0.306044
0.102015
0.000868
189003.1
-150762.1847
48850.92433
0.382739
731.7549
37214.81
0.306899
0.1023
0.000855
189541.7
-152326.9038
48850.92433
POSIT
FORCE
STRESS
EXT
STRAIN
0.025933
38.68444
1315.216
-0.01884
-0.00628
0.030299
57.04637
1939.495
-0.01454
-0.00485
0.030299
56.95302
1936.321
-0.03553
-0.01184
0.031573
62.62604
2129.196
-0.03512
0.03327
70.44618
2395.07
-0.03427
del-del-L
yield str
stress - yieldline
ultimate point
-17312.8
18627.99078
1315
0.004297
-14317.5
16257.04359
1939
-0.02099
-28947.5
30883.79173
1939
-0.01171
0.00041
-28661.5
30790.69721
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21760.79544
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20325.12304
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20091.05683
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19828.27676
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19174.5807
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18985.5232
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18831.29521
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12511.25
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18695.04922
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381.6082
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18570.92693
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18451.93231
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452.4459
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267.2159
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857.2328
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0.008085
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1453.264
17561.91887
1901
25
0.076499
575.1268
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2043.276
17510.21299
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623.3082
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22269.9
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687.7388
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1955
591.4985
20110.1
0.00976
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2621.244
17488.85949
201
607.3747
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3199.22
17450.65247
2064
21191.59
0.011414
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0.000825
3774.182
17417.4075
2119
21730.14
0.012235
0.004078
0.000821
4346.139
17383.99686
2173
0.013068
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0.000833
4927.11
17342.78684
2226
22824.55
0.013911
0.004637
0.000842
5514.124
17310.43075
2282
23382.14
0.014748
0.004916
0.000838
6098.112
17284.0237
2338
705.2878
23978.78
0.015603
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0.000855
6694.147
17284.63075
2397
0.084194
722.9517
24579.33
0.016467
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0.000864
7296.203
17283.12338
2457
0.085045
740.5222
25176.7
0.017314
0.005771
0.000846
7886.215
17290.48338
2517
0.0859
759.2056
25811.91
0.018169
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8482.242
17329.66553
2581
0.086742
776.2877
26392.67
0.019011
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9069.256
17323.41846
2639
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794.5475
27013.48
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17369.26338
2701
0.088413
812.1249
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17376.85787
2761
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2821
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2883
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12028.35
17419.50339
2944
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884.5456
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12624.39
17448.90114
3007
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901.9291
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13217.41
17446.89208
3066
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17494.67594
3128
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938.735
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17545.30482
3191
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17590.00682
325
0.09604
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3322
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3387
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1015.326
34519.63
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17762.14287
3451
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1034.483
35170.95
0.030887
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17347.5
17823.44322
3517
0.099395
1052.943
35798.56
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17928.48
17870.07785
3579
0.100255
1072.207
36453.51
0.032558
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18512.48
17941.03253
3645
0.101097
1090.373
37071.13
0.033422
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0.000864
19114.53
17956.59565
3707
0.101926
1109.809
37731.92
0.034277
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0.000855
19710.56
18021.35532
377
0.102751
1128.456
38365.89
0.035136
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0.000859
20309.61
18056.28407
3836
0.10361
1147.856
39025.46
0.035974
0.011991
0.000838
20893.6
18131.86313
3902
0.104483
1166.833
39670.66
0.036812
0.012271
0.000838
21477.6
18193.06065
396
0.105338
1185.48
40304.63
0.037637
0.012546
0.000825
22052.56
18252.07007
4030
0.10618
1204.148
40939.31
0.038444
0.012815
0.000808
22615.48
18323.82924
4093
0.107018
1183.326
40231.4
0.038898
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22931.55
17299.84111
4093
0.107851
1318.46
44825.76
0.042875
0.014292
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25704.02
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4482
0.108693
1514.612
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0.017014
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31396.44
20098.20805
5149
0.109561
1688.718
57414
0.059432
0.019811
0.008391
37245.4
20168.6002
5741
0.110446
1821.969
61944.34
0.067823
0.022608
0.008391
43094.35
18849.99174
6194
0.111297
1875.578
63766.97
0.076218
0.025406
0.008395
48946.33
14820.64749
6376
0.112152
1883.661
64041.78
0.084773
0.028258
0.008555
54909.67
9132.114984
6404
0.112999
1881.314
63961.99
0.093419
0.03114
0.008646
60936.23
3025.755178
6404
0.113828
1876.051
63783.06
0.102073
0.034024
0.008654
66968.86
-3185.801649
6404
0.115521
1869.669
63566.07
0.110629
0.036876
0.008555
72932.2
-9366.121292
6404
0.117244
1862.446
63320.51
0.119067
0.039689
0.008438
78814.26
-15493.74949
6404
0.11895
1854.528
63051.3
0.127479
0.042493
0.008413
84678.26
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6404
0.121437
1845.539
62745.69
0.135896
0.045299
0.008417
90545.27
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6404
0.123955
1835.265
62396.39
0.14446
0.048153
0.008564
96514.67
-34118.27583
6404
26
0.12652
1823.67
62002.18
0.153127
0.051042
0.008667
102556.3
-40554.09741
6404
0.129068
0.131625
1810.826
61565.5
0.161777
1797.588
61115.43
0.170289
0.053926
0.00865
108585.8
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6404
0.056763
0.008512
114519.1
-53403.63045
0.133352
1783.695
60643.08
6404
0.178732
0.059577
0.008443
120404.2
-59761.10412
0.135861
1768.949
6404
60141.74
0.187174
0.062391
0.008443
126289.2
-66147.50264
0.137593
6404
1753.068
59601.81
0.195626
0.065209
0.008451
132180.4
-72578.55587
6404
0.139299
1734.896
58983.99
0.204181
0.06806
0.008555
138143.7
-79159.71067
6404
0.14179
1714.657
58295.89
0.212835
0.070945
0.008654
144176.2
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6404
0.143505
1691.245
57499.91
0.221494
0.073831
0.008659
150211.9
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6404
0.145215
1664.494
56590.42
0.230032
0.076677
0.008538
156163.1
-99572.72886
6404
0.147715
1633.112
55523.48
0.238474
0.079491
0.008443
162048.3
-106524.7999
6404
0.150229
1594.629
54215.11
0.246909
0.082303
0.008434
167927.3
-113712.2313
6404
0.151939
1545.42
52542.07
0.255334
0.085111
0.008425
173800.4
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6404
0.153658
1478.412
50263.9
0.263906
0.087969
0.008572
179775.7
-129511.8445
6404
0.155364
1375.712
46772.24
0.272578
0.090859
0.008672
185820.3
-139048.0968
6404
0.157894
873.6819
29703.94
0.281332
0.093777
0.008754
191922.2
-162218.2587
6404
27
Appendix E
Sample Calculations
Modulus of elasticity and proportional limit calculations:
The modulus of elasticity E is equal to the slope of the linear section of the stress-strain
curve, with the y-axis representing stress and the x-axis representing strain. The first and
last points of the linear section were determined by identifying where l experienced
significant changes. A linear regression was performed on the points in the linear
selection, and E is equal to its slope, which is approximately 1.89 x 106 psi. The stress of
the last point of the linear section is the proportional limit.
Yield strength calculation:
The yield strength is equal to the stress at which a line parallel to the linear section and
intersecting the point representing a stress of 0 and strain of 0.002 (0.2 %) intersects the
stress-strain curve. The formula of this line was determined by initially using the pointslope form for a line with slope E and point (0.002, 0)
y 0 = 1.89 x 106(x 0.002)
which simplifies to
y = 1.89 x 106x + 1.89 x 106*0.002
All strain values in the data set were entered into this formula, generating the yield
strength line. It was then determined between which two points in the original data set
the yield strength line intersected. Linear interpolation was then used to approximate the
yield strength of 46275 psi.
Elastic limit calculation:
The elastic limit of 45363 psi was approximated by finding the average of the yield
strength and the proportional limit.
Ultimate strength calculation:
The ultimate strength of 48851 psi is the highest stress in the data set.
Fracture point calculation:
The fracture point of 37215 psi is the final stress in the data set.
28
29