Lecture Presentation Chp-8

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MEASURING STRAIN
When a force is applied to a structure, the components
of the structure change slightly in their dimensions and
are said to be strained. Devices to measure these small
changes in dimensions are called strain gages.
Figure 8.1
Strain has units of inches per inch or millimeters per millimeter and
hence is dimensionless. In most structures the values of strain are
usually very small; for example, a low-strength steel will yield (take a
permanent deformation) at a strain of only about 0.0014. As a result
it is common to talk about strain in units of micro-strain .
Micro-strain is the actual strain multiplied by 106. Thus, a strain of
1400 strain is an actual strain of 0.0014.
Hooke's law,
is the normal stress and E is a property of the material called the modulus of
elasticity (also called Young's modulus).
For a wire to function as a strain gage, we must determine the
relationship between the strain and the change in resistance. The
resistance of a wire such as that
shown in Figure 8.1- is given by
This equation can be logarithmically differentiated to obtain
This equation can also be
logarithmically differentiated
to obtain
dD/D, is known as the transverse strain ε,. Solid mechanics provides the
following relationship between the axial and the transverse strain:
Here, ν is a property of the material known as Poisson's ratio ν the
minus sign indicates that as the wire becomes longer, the transverse
dimension decreases.
The relationship between the change in resistance of the wire, strain,
and the change in resistivity of the wire. At this point, it is useful to
define the strain gage
factor, S:
[This backing can, in
turn, be glued to the
structure]
Using Ohm's law again, the voltage drop across
Creating a common denominator, this becomes
This analysis is what is known as a quarter-bridge circuit. This
means that there is a single strain gage and three fixed resistors.
This arrangement is common when many strain gages are
applied to a structure.
where λ is the wavelength of the incident radio waves. For most engineering applications,
the radar beam places essentially no load on the measured system. Doppler radar velocitymeasuring devices are readily available commercially. They are used by police to measure
vehicle velocities, and they are often used to measure velocities in sports. Doppler velocity
measurements can also be made using laser-generated light beams. Devices that use the
Doppler effect with laser light, called laser-Doppler velocimeters,
are commonly used to measure fluid velocities and are described in Chapter 10.
http://en.wikipedia.org/wiki/Doppler_effect
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