0.3 Strain gages and force measurement  (Page 3/4)

A theoretical estimate of the strain can be obtained by drawing on topics from CEEn 203. The stress on thesurface 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 thetheoretically obtained strain compare to the value determined from measurements? If they are different, what are some possiblereasons?

Part 4: experiments with half and full bridges

Repeat parts 2 and 3 for the half bridge and the full bridge configurations.

Part 5: measurement of an unknown load

Based upon the calibration determined in step 2, use your beam to determine the weight of an arbitrary object.You may use the quarter bridge, the half bridge, or full bridge configuration for this test. Measure the actual weight using aprecision scale. How does the weight determined with your beam compare to the object's true weight? How certain is yourmeasurement? What are some possible sources of uncertainty?

Part 6: sensitivity to extraneous loads and temperature variations

Strain gages are often used as transducers to measure force in a structure or mechanical device. A perfect sensoris sensitive only to changes in the variable of interest and is completely insensitive to changes in extraneous parameters. (Such asensor is impossible to create.) In practice, every effort should be made to minimize sensitivity to extraneous variables. In thecase of the cantilever-beam scale, the objective is to measure the weight of objects or alternatively, to measure forces in thevertical plane. As such, a good design will be much less sensitive to loads in other directions (axial, lateral, torsional, etc.).Also a good design will not be sensitive to strains induced by other means, such as thermal expansion.

Your TA will supervise in the following two demonstrations.

6.1 lateral sensitivity

Use the instrumented beam of square cross section provided by your TA.

1. Clamp the beam in a cantilever fashion so that it will measure vertically applied loads.

2. Using your hand, gently apply lateral and axial loads to the beam. Do your best to not apply vertical bendingloads to the beam.

3. Compare the sensitivity of the quarter bridge to that of either the half bridge or full bridge to theseextraneous loads. Which configuration seems to work the best overall? Explain why this is so. Which extraneous loads are"rejected" by which configurations? Explain why. (Note: The steps of this paragraph are more easily said than done. The point is thatthe quarter bridge is more sensitive to off-axis loads than either the half bridge or full bridge. If you have difficultydemonstrating this, don't stress out.)