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Strain Gage Equations and Material Tables
Rosette and Biaxial Stress State Equations
Rosette Equations
Biaxial Stress State
Equations
σ
x
E − ν
ε
=
x
σ
y
ε
=
E − ν
y
Appendix B
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The following equations are used to calculate the strain measured with a
three element rectangular or delta rosette. Rosette measurements are
covered in Chapter 4, and an example which measures strains ε1, ε2, and ε3
is contained in Chapter 3.
1
ε
=
2 ε
+ ε
± √
p,q
1
3
ε
+ ε
E
1
3
σ
=
1−ν ±
p,q
2
1
2ε
−1
θ
=
2 TAN
p,q
1
3 ε
ε
=
+ ε
+ ε
p,q
1
2
ε
+ ε
E
1
2
σ
=
1 − ν
p,q
3
√
1
−1
θ
=
2 TAN
p,q
2ε
where: ε
= Principal strains, σ
p,q
axis of gage 1 to the nearest principal axis. When positive, the direction is the same as that of
the gage numbering and when negative, opposite. NOTE: Corrections may be necessary for
transverse sensitivity; refer to gage manufacturers literature.
The following equations relate stress to strain for a biaxial stress state.
Stress-strain relationships are described in detail in Hewlett-Packard's
Application Note 290-1 Practical Strain Gage Measurements.
σ
y
ε
= − ν
z
E
σ
E
x
σ
=
x
E
1 − ν
Strain Gage Equations and Material Tables
(ε
− ε
)
2
+ (2ε
− ε
− ε
1
3
2
1
1
)
1+ν √
(ε
− ε
2
+ (2ε
− ε
1
3
2
− ε
− ε
1
2
3
ε
− ε
1
3
− ε
)
2
+ (ε
± √
2 [(ε
− ε
3
1
2
2
+ ε
1
3
±
1 + ν √
2[ (ε
− ε
1
2
− ε
3(ε
2
3)
− ε
− ε
1
2
3
= Principal stresses, and θ
p,q
σ
σ
x
y
E − ν
σ
E
( ε
+ ν ε
)
x
y
2
Appendix B
)
2
3
− ε
)
2
1
3
2
+ (ε
− ε
2
)
)
]
3
3
1
)
2
+ (ε
− ε
)
2
+ (ε
− ε
)
2
2
3
3
1
= the acute angle from the
p,q
E
=
(ε
+ ν ε
)
y
y
x
1 − ν
2
σ
= 0
z
]
105
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