Specifications

Appendix B
Strain Gage Equations and Material Tables
Rosette and Biaxial Stress State Equations
Rosette Equations 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.
ε
p,q
=
1
2


ε
1
+ ε
3
± √ (ε
1
− ε
3
)
2
+ (2ε
2
− ε
1
− ε
3
)
2


σ
p,q
=
E
2



ε
1
+ ε
3
1−ν
±
1
1+ν
√(ε
1
− ε
3
)
2
+ (2ε
2
− ε
1
− ε
3
)
2



θ
p,q
=
1
2
TAN
−1
2ε
2
− ε
1
− ε
3
ε
1
− ε
3
ε
p,q
=
1
3


ε
1
+ ε
2
+ ε
3
± √ 2 [(ε
1
− ε
2
)
2
+ (ε
2
− ε
3
)
2
+ (ε
3
− ε
1
)
2
] 

σ
p,q
=
E
3



ε
1
+ ε
2
+ ε
3
1 − ν
±
1
1
+ ν
√ 2[(ε
1
− ε
2
)
2
+ (ε
2
− ε
3
)
2
+ (ε
3
− ε
1
)
2
]



θ
p,q
=
1
2
TAN
−1
√3(ε
2
− ε
3)
2ε
1
− ε
2
− ε
3
where: ε
p,q
= Principal strains, σ
p,q
= Principal stresses, and θ
p,q
= the acute angle from the
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.
Biaxial Stress State
Equations
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.
ε
x
=
σ
x
E
− ν
σ
y
E
ε
z
= − ν
σ
x
E
− ν
σ
y
E
σ
y
=
E
1 − ν
2
(ε
y
+ ν ε
x
)
ε
y
=
σ
y
E
− ν
σ
x
E
σ
x
=
E
1 − ν
2
( ε
x
+ ν ε
y
) σ
z
= 0
Appendix B Strain Gage Equations and Material Tables 105
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