PRACTICAL STRAIN GAGE MEASUREMENTS
APPENDICES AND
BIBLIOGRAPHY
AVERAGE PROPERTIES OF SELECTED ENGINEERING MATERIALS
EXACT VALUES MAY VARY WIDELY
MATERIAL
ABS (unfilled)
Aluminum (2024-T4)
Aluminum (7075-T6)
Red Brass, soft
Iron-Gray Cast
Polycarbonate
Steel-1018
Steel-4130/4340
Steel-304 SS
Steel-410 SS
Titanium alloy
APPENDIX A: TABLES
WIRE RESISTANCE
SOLID COPPER WIRE
AWG
Ω/FOOT (25°C) DIAMETER (IN)
18
20
22
24
26
28
30
32
0.0065
0.0104
0.0165
0.0262
0.0416
0.0662
0.105
0.167
0.040
0.032
0.0253
0.0201
0.0159
0.0126
0.010
0.008
ELASTIC
STRENGTH (*)
TENSION (psi)
4500-7500
48000
72000
15000
—
8000-9500
32000
45000
35000
40000
135000
(*) Elastic strength can be represented by proportional limit, yield point,
or yield strength at 0.2 percent offset.
APPENDIX B: BRIDGE CIRCUITS
Equations compute strain from unbalanced bridge voltages:
Vr = [(VOUT /VIN)strained – (VOUT /VIN)unstrained]:
sign is correct for VIN and VOUT as shown
GF = Gage Factor
MODULUS OF
ELASTICITY, E
psi X 106
0.2-0.4
10.6
10.4
15
13-14
0.3-0.38
30
30
28
29
14
POISSON'S
RATIO, —
0.32
0.32
0.33
—
0. 285
0.285
0.28-0.29
0.25
0.27-0.29
0.34
= Strain: Multiply by 10
= Poisson’s ratio:
6
for microstrain:
tensile is (+) and compressive is (–)
Quarter-Bridge Configurations
Rl
Rl
R1
+
–
V
IN
–
VOUT
Rl
+
R2
+
OR
–
V
IN
–
Rl
R3
Half-Bridge Configurations
R1
Rg (
)
VOUT
Rl
+
Rg (Dummy)
R2
=
–4Vr
GF(1 + 2Vr )
•
(
1+
Rl
)
Rl
Rg
(AXIAL)
(BENDING)
Rl
Rl
R1
+
– V
+
OUT
V
IN
–
R2
=
GF[(1 +
) -2Vr( – 1)]
R1
Rg ( + )
Rl
+
–
V
•
IN
–
Rg ( – )
Rl
–4Vr
Rg (
)
(
1+
Rl
VOUT
Rl
+
R2
)
Rg
=
Rl
–2Vr
GF
•
(
1+
© Agilent
Rl
Rg ( + )
Rg (– )
)
Rg
Technologies, Inc. 1999. Reproduced with
Permission, Courtesy of Agilent Technologies, Inc.
E-103
PRACTICAL STRAIN GAGE MEASUREMENTS
Full-Bridge Configurations
–
V
–
VOUT
+
(AXIAL)
+
–
+
IN
(BENDING)
+
IN
–
–
VOUT
GF
+
+
+ –Vr
=
–
V
IN
–
– +
–2Vr
=
– V
+
OUT
V
–
+
– +
– +
GF( + 1)
–2Vr
=
GF[( + 1) – Vr ( – 1)]
APPENDIX C: EQUATIONS
BIAXIAL STRESS STATE EQUATIONS
x =
y =
X
–
E
y
–
E
y
z =
E
x
E
E
x =
E
X
–
1-
y
–
E
(
x +
2
y =
y )
E
2
1-
(
x +
x)
z = 0
ROSETTE EQUATIONS
Rectangular Rosette:
3
1
p,q =
E
2
45°
2
2
[ [ 1
1
+
+
3
3
(
1 – 3)
±
1
±
1+
1–
2
+ (2
2 – 1 – 3 ) 2
(
1 – 3)
2
]
+ (2
2 – 1 – 3 ) 2
]
STRAIN GAGES
p,q =
p,q = 1 TAN -1 2
2 – 1 – 3
45°
1
2
1
–
3
Delta Rosette:
2
3
60°
60°
1
p,q =
1
p,q =
E
3
[
[
1
1
+ 2 + 3 ±
+ 2 + 3
1–
p,q = 1 TAN -1 3 (
2
2
±
2[(
1 – 2)
1
1+
2
+ (
2 – 3 ) 2 + (
3 – 1) 2]
2[(
1 – 2)
2
]
+ (
2 – 3 ) 2 + (
3 – 1) 2]
E
]
3 )
2
1 – 2 – 3
© Agilent
Technologies, Inc. 1999. Reproduced with
Permission, Courtesy of Agilent Technologies, Inc.
WHERE:
p,q =
p,q =
3
Principal strains
Principal stresses
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 manufacturer’s literature.
E-104