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32 | CALCULATIONS | GEOKON
APPENDIX F.
CALCULATIONS FROM THREE STRAIN
GAUGES, AT 60 DEGREES, ON A CIRCULAR PIPE
FIGURE 30: Three Strain Gauges Mounted on a Circular Pipe Diagram
A = (ε
+ ε
+ ε
) / 3
1
2
3
EQUATION 15: Average Axial Strain
(Y) = ±[((ε
+ ε
+ ε
) / 3) – ε
]
1
2
3
1
EQUATION 16: Maximum Bending Strain Around the YY Axis
(X) = ±[(ε
– ε
) / 1.732]
2
3
EQUATION 17: Maximum Bending Strain Around the XX Axis
P = ±[Xcosθ + Ysinθ] + A and tanθ = Y/X
EQUATION 18: Maximum Strain
Example:
Let ε
= 20, ε
= 192 and ε
1
2
3
Average Axial Strain, A = (20 + 192 + 88) / 3 = 100 microstrains, tension
X = ±(104 / 1.732) = ±60
Y = ±(300 / 3 – 20) = ±80
θ
θ
tan
= 80 / 60 = 1.333 and
P = ±[60 x 0.6 + 80 x 0.8] + 100 = 200 microstrains, tensile, 0 microstrain
minimum
= 88 (all tensile strains)
= 53 degrees from the X axis
30:
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