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It is always best to locate gauges in pairs, one on each side of the neutral axis
corresponding to the section of the I-beam to which the gauge is attached. This,
along with locating the gauges on the web making them easy to protect from
accidental damage, is why the configuration shown above is preferable.
Note: This configuration is not recommended for tunnel arches.
Strain gauges mounted on the central web can measure axial strain as well as
bending moments around both XX and YY axis. In this configuration, four strain
gauges (1, 2, 3, and 4 in the previous figure) are welded back to back in pairs on
the central web. The gauges are at a height (d) above the center of the web (Axis
YY) and at a distance (c). The width of the I-beam flange is represented by 2b
and the depth of the web by 2a.
The axial stress is given by averaging the strain reading from all four strain
gauges and multiplying by the modulus, as shown in the equation below.
(ε
+ε
+ε
+ε
)
1
2
3
4
σ
=
axial
4
EQUATION 1: Axial Stress Calculation
The stress due to bending is calculated by looking at the difference between
pairs of gauges mounted on opposite sides of the neutral axis. Thus, the
maximum stress due to bending around Axis YY is given by:
(ε
+ε
) - (ε
+ε
)
1
3
2
4
σ
=
yy
2
EQUATION 2: Stress Due to Bending on Axis YY
The maximum stress due to bending about Axis XX is given by:
(ε
+ε
) - (ε
+ε
)
1
2
3
4
σ
=
xx
2
EQUATION 3: Stress Due to Bending on Axis XX
σ
= σ
+ σ
+ σ
maximum
axial
xx
yy
EQUATION 4: Maximum Stress
In all of the above calculations, pay strict regard to the sign of the strain. A
positive change is tensile and a negative change is compressive.
Note that the total strain, at any point in the cross section, is the algebraic sum
of the bending strains and the axial strain. The strains in the outer corners of
the flange can be much higher than the strains measured on the web,
and that failure of the section can be initiated at these points, hence the
importance of analyzing the bending moments.
The above consideration would seem to lead to the conclusion (from the point of
view of obtaining the best measurement of the maximum strains) that the ideal
location for the strain gauges would be on the outer corners of the flanges, as
shown in the figure below. However, this configuration makes it difficult to
protect the gauges and cables from accidental damage. In addition, a serious
problem can arise from the fact that each of the four gauges can be
subjected to localized bending forces, which affect only one gauge, but
not the others. For example, it is not uncommon for welding to take place at
points close to a strain gauge; this often produces large strain changes in the
gauge. It is also not uncommon for local blocking (e.g., tunnel arch supports)
and the addition of struts, to cause strain changes on a single nearby gauge.
MODEL 4100/4150 SERIES VIBRATING WIRE STRAIN GAUGES | GAUGE LOCATION | 17
x E
b
x
x E
d
a
x
x E
c
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