In this step, we will compare a theoretically
based estimate of strain for a given load to that which was
measured earlier. First we will determine the strain corresponding
to the voltage measurements of step 2.

1. Measure the excitation voltage for bridge
circuit, Vi.

The circuit analyses from step one showed that
the bridge output Vo is related to the excitation voltage by the
following relationship

where K equals 1/4 for a quarter bridge, 1/2
for a half bridge, and 1 for a full bridge. The voltage measured in
LabVIEW is related to the bridge output by

where Kamp is the gain of the signal
conditioning board. Because the bridge resistances are not balanced
exactly and the weight of the beam itself produces some strain, you
will observe a nonzero output voltage when there is no load
applied.

2. Measure the output voltage with no load.
Call this voltage Voffset.

3. To determine the strain induced by the
applied loads, measure the changes in the display voltages relative
to this offset voltage (Vdisplay–Voffset).

For a strain gage, the gage factor is defined
as

where epsilon is the strain experienced by the gage.
The gages used in this lab have a gage factor of 2.12±0.8%.

4. Derive an expression for the strain in the
beam using equations (2) through (4). Your empirical strain
estimate should be in the range of 0 to 2000 microstrains.

A theoretical estimate of the strain can be
obtained by drawing on topics from CEEn 203. The stress on the
surface of a beam in bending is given by

where M is the applied moment at the location
of interest, y is the distance from the neutral axis (in this case,
the half height of the beam cross section), I is the area moment of
inertia of the cross section with respect to the neutral axis.
Recall that for a rectangular cross section,

Recall also that stress and strain are related
by Young’s modulus:

For aluminum, E = 10.4x10^6 psi.

5. Using equations (5) through (7), estimate
the strain where the gages are bonded to the beam. How does the
theoretically obtained strain compare to the value determined from
measurements? If they are different, what are some possible
reasons?

Comments:"This course is the lab portion of ME 363, an instrumentation class in the Mechanical Engineering Department at Brigham Young University. This course covers the use of oscilloscopes, function […]"