Agilent Technologies HP E1355A, Руководство пользователя

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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
ε
1,
ε
2, and
ε
3
is contained in Chapter 3.
ε
p,q
=
1
2
ε
1
+ ε
3
± √ (ε
1
− ε
3
) 2 + (
2
ε
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
+ (
2
ε
2
− ε
1
− ε
3
)
2



θ
p,q
=
1
2
TAN
−
1
2
ε
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
)
2
ε
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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