300 lecture presentation chp 8

8/10/2019 300 Lecture Presentation Chp 8

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MEASURING STRAIN

When a force is applied to a structure, the componentsof 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.


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Strain has units of inches per inch or millimeters per millimeter and

hence is dimensionless. In most structures the values of strain areusually 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 Eis a property of the material called the modulus of

elasticity (also called Young's modulus).

Figure 8.1


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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 belogarithmically differentiated

to obtain

dD/D, is known as the transverse strain ,. Solid mechanics provides the

following relationship between the axial and the transverse strain:


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Here,is a property of the material known as Poisson's ratio 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 todefine the strain gage

factor, S:


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[This backing can, in

turn, be glued to thestructure]


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Using Ohm's law again, the voltage drop across


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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.


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where 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 velocity-

measuring 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.


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http://en.wikipedia.org/wiki/Doppler_effect
http://en.wikipedia.org/wiki/Doppler_effecthttp://en.wikipedia.org/wiki/Doppler_effect

300 lecture presentation chp 8

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