Chapter-2 General arrangement:
Principal Stress and Strain
S K Mondal’s
The orientation of strain gauges is given in the figure. To relate strain we have to use the following formula.
T
x y 2
x y 2
cos 2T
J xy 2
sin 2T
We get
a
b c
x y 2 x y 2 x y 2
x y 2 x y 2 x y 2
cos 2D
J xy 2
sin 2D
cos 2 D E
J xy 2
cos 2 D E G
sin 2 D E
J xy 2
sin 2 D E G
From this three equations and three unknown we may solve x , y , and J xy
x Two standard arrangement of the of the strain rosette are as follows: (i)
45° strain rosette or Rectangular strain rosette. In the general arrangement above, put
D
0o ; E
45o and G
45o
Putting the value we get
x a x x x J xy 2 2 c y
x b x (ii)
45
o
60° strain rosette or Delta strain rosette In the general arrangement above, put
D
0o ; E
60o and G
60o
Putting the value we get x a y x
b
x
c
60o
x 3 y
3 J xy 4 4 x 3 y 3 J xy 4 4
or
Solving above three equation we get
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