-25
-
APPENDIX G - CALCULATION OF AXIAL LOADS AND BENDING STRAINS FROM
THREE STRAIN GAGES, AT 60 DEGREES, ON A CIRCULAR PIPE
Average Axial Strain
A
=
(
ε
1
+
ε
2
+
ε
3
)
/3
Maximum Bending Strain around the YY Axis,
(X)
=
+/- [ (
ε
2
-
ε
3
)
/1.732 ]
Maximum Bending Strain around the XX Axis,
(Y)
=
+/- [
(
(
ε
1
+
ε
2
+
ε
3
)
/3) -
ε
1
]
The maximum strain,
P, = +/- [Xcos
θ
+ Ysin
θ
] +A
and
tan
θ
= Y/X
Example:
Let
ε
1
= 20,
ε
2
= 192 and
ε
3
= 88
(all tensile strains)
Average Axial Strain, A
= (20 +192 + 88)/3 = +100 microstrain tension
X
= +/- (104/1.732) = +/- 60
Y
= +/- (300/3 - 20) = +/- 80
Tan
θ
= 80/60 = 1.333 and
θ
= 53
degrees from the X axis
P
=+/- [60 x 0.60 +80 x 0.8] + 100 = +200 microstrain. tensile. (and +0 microstrain
minimum)
P
Θ
θ
ε
1
Y
Y
X
X
P
ε
3
ε
2
