E1C11 09/14/2010
13:14:3 Page 481
The simplified form of Equation 11.25 is suitable for all but those measurements demanding the
greatest accuracy possible, and remains valid for values of dR=R ( 1. The bridge constant concept
is illustrated in Example 11.5.
Example 11.5
Determine the bridge constant for two strain gauges mounted on a structural member, as shown in
Figure 11.12. The member is subject to uniaxial tension, which produces an axial strain e a and a
lateral strain e L ¼ Ày p e a . Assume that all the resistances in Figure 11.12 are initially equal, so that
the bridge is initially balanced. Let (GF) 1 ¼ (GF) 2 .
KNOWN Strain gauge installation shown in Figure 11.12
FIND The bridge constant for this installation
ASSUMPTION The change in the strain gauge resistances are small compared to the initial
resistance (see explanation as follows).
SOLUTION The gauges are mounted so that gauge 1 is aligned with the axial tension and gauge 2
is mounted transversely on the member. The changes in resistance for the gauges may be expressed
dR 1
R 1
¼ e a GF
ð Þ 1
ð11:26Þ
and
dR 2
R 2
¼ Ày p e a GF
ð Þ 2 ¼ Ày p
dR 1
R 1
ð11:27Þ
With only one gauge active, Equation 11.14 would be applicable, and yields
dE 0
E i
¼
dR 1 =R 1
4 þ 2 dR 1 =R 1
ð
Þ
%
dR 1 =R 1
4
ð11:14Þ
But with both gauges installed and active, as shown in Figure 11.12, the output of the bridge is
determined from an analysis of the bridge response, which results in
dE 0
E i
¼
dR 1 =R 1
ð
Þ 1 þ y p
À
Á
4 þ 2 dR 1 =R 1
ð
Þ 1 þ y p
À
Á
2
1
R 4
R 3
1
2
E i
E o
Figure 11.12 Bridge circuit with two arms active; strain gauge installation for increased sensitivity.
11.5 Practical Considerations for Strain Measurement 481
13:14:3 Page 481
The simplified form of Equation 11.25 is suitable for all but those measurements demanding the
greatest accuracy possible, and remains valid for values of dR=R ( 1. The bridge constant concept
is illustrated in Example 11.5.
Example 11.5
Determine the bridge constant for two strain gauges mounted on a structural member, as shown in
Figure 11.12. The member is subject to uniaxial tension, which produces an axial strain e a and a
lateral strain e L ¼ Ày p e a . Assume that all the resistances in Figure 11.12 are initially equal, so that
the bridge is initially balanced. Let (GF) 1 ¼ (GF) 2 .
KNOWN Strain gauge installation shown in Figure 11.12
FIND The bridge constant for this installation
ASSUMPTION The change in the strain gauge resistances are small compared to the initial
resistance (see explanation as follows).
SOLUTION The gauges are mounted so that gauge 1 is aligned with the axial tension and gauge 2
is mounted transversely on the member. The changes in resistance for the gauges may be expressed
dR 1
R 1
¼ e a GF
ð Þ 1
ð11:26Þ
and
dR 2
R 2
¼ Ày p e a GF
ð Þ 2 ¼ Ày p
dR 1
R 1
ð11:27Þ
With only one gauge active, Equation 11.14 would be applicable, and yields
dE 0
E i
¼
dR 1 =R 1
4 þ 2 dR 1 =R 1
ð
Þ
%
dR 1 =R 1
4
ð11:14Þ
But with both gauges installed and active, as shown in Figure 11.12, the output of the bridge is
determined from an analysis of the bridge response, which results in
dE 0
E i
¼
dR 1 =R 1
ð
Þ 1 þ y p
À
Á
4 þ 2 dR 1 =R 1
ð
Þ 1 þ y p
À
Á
2
1
R 4
R 3
1
2
E i
E o
Figure 11.12 Bridge circuit with two arms active; strain gauge installation for increased sensitivity.
11.5 Practical Considerations for Strain Measurement 481