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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