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Solution to Exercise 2.9

20 一月, 2016 - 09:21

First, we need to enter the data sets. Because it is rather a large table, using Variable Editor is more convenient. See the figures below:

media/image13.png
Figure 2.12 Load in Newtons 
 
media/image14.png
Figure 2.13 Extension length in mm. 
 

Next, we will calculate the cross-sectional area.

Area=pi/4*(0.0127^2)
Area =
    1.2668e-004

Now, we can find the Stress values with the following, note that we are obtaining results in MPa:

      Sigma=(Load_N./Area)*10^(-6)
Sigma =
           0
     38.6022
     77.1964
    115.8065
    154.4086
    193.0108
    218.0351
    232.0076
    257.9792
    268.0047
    272.9780
    278.0302
    281.9773
    320.0269
    381.9955
    465.9888
    519.9844
    548.0085
    549.9820
    537.9830
    480.0403

For strain calculation, we will first find the change in length:

Delta_L=Length_mm-50.800

Delta_L =

         0
    0.0102
    0.0203
    0.0305
    0.0406
    0.0508
    0.0610
    0.0711
    0.1016
    0.1270
    0.1524
    0.1778
    0.2032
    1.0160
    2.5400
    5.0800
    7.6200
   10.1600
   10.6680
   12.7000
   15.2400

Now we can determine Strain with the following:

Epsilon=Delta_L./50.800

Epsilon =

         0
    0.0002
    0.0004
    0.0006
    0.0008
    0.0010
    0.0012
    0.0014
    0.0020
    0.0025
    0.0030
    0.0035
    0.0040
    0.0200
    0.0500
    0.1000
    0.1500
    0.2000
    0.2100
    0.2500
    0.3000

The final results can be tabulated as foolows:

[Sigma Epsilon]

ans =

          0            0
    38.6022       0.0002
    77.1964       0.0004
    115.8065      0.0006
    154.4086      0.0008
    193.0108      0.0010
    218.0351      0.0012
    232.0076      0.0014
    257.9792      0.0020
    268.0047      0.0025
    272.9780      0.0030
    278.0302      0.0035
    281.9773      0.0040
    320.0269      0.0200
    381.9955      0.0500
    465.9888      0.1000
    519.9844      0.1500
    548.0085      0.2000
    549.9820      0.2100
    537.9830      0.2500
    480.0403      0.3000