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  post #1  
04-07-2009, 10:18 PM
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Measuring stress and strain

The simplest device for measuring strain is a ruler. The vernier is a device for increasing the accuracy of the ruler about ten times. The simple pointer that marks the position of the object moving along the line of the ruler is extended with a series of marks that are nine tenths as far apart as the marks on the ruler. The picture below illustrates the process.

The exact position of the arrow between the millimetre marks is given by the number of the mark on the vernier scale that coincides with any mark on the millimetre scale. The measurement in this case is 3.7 mm.

The vernier principle has many uses in conservation research and surveillance. The sketch shows an experiment to measure the biaxial stress-strain performance of canvas. This construction was tested in a five day course at the Copenhagen Conservation School. Given the appalling instability and variability of canvas the results are just as useful as those made with elaborate mechanical and electronic apparatus.
Lamination of one material to another is a frequent operation in conservation, particularly of textiles, paintings and paper. Distressingly often one can see at a glance that the material chosen to reinforce an object is more extensible than the object and is therefore simply adding weight, providing no support but giving the illusion that the object can be handled more robustly.
It is quite feasible to set up a simple apparatus in the conservation workshop to study, quantitatively, the likely mechanical result of a suggested treatment. Conservators are very diligent in studying the performance of various varnishes, adhesives and other chemical treatments but are strangely reluctant to tackle mechanical aspects of conservation treatment.
Verniers can be made by photographing a scale at two magnifications, one nine tenths of the other, onto polyester base high contrast film. Nowadays an office copier with zoom will give almost as good results on transparency film.

In real life things seldom move smoothly past each other but tend to warp and twist at the same time. Parallax error can entirely wreck the precision of the vernier. The problem can be eased by fixing two millimetre scales exactly over one another. The vernier part slides between them so that the eye can detect the alignment of all three lines.
There are many variations on the theme of measurement by lines coming into coincidence. Moire patterns, resulting from the periodic coincidence of two sets of parallel lines superimposed with a small angle between them, allow the measurement of tiny rotations, for example. One could imagine a fine net of lines printed over a whole canvas, with a matching pattern on an inextensible plastic overlay. But one would not want to spoil the fun of people doing the same sort of thing with holographic laser interferometry.

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  post #2  
04-07-2009, 10:19 PM
Senior Member
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The electrical resistance strain gauge

Measuring stress and strain, part 2

The electrical resistance strain gauge

Automatic strain measurement is usually done with an electrical resistance strain gauge (or gage). It looks like this:

A thin plastic base supports thin ribbons of metal, joined in a zig-zag to form one long electrically conductive strip. The entire device is typically 10 mm long, with 16 or more parallel metal bands. When the plastic is stretched the wires become longer, and thinner. The electrical resistance therefore increases. The % increase is about twice the % extension, because if the wire is stretched to twice its original length the electrons have to struggle twice as far through a conductor of half the original cross section. There are other influences on this "gauge factor" so the manufacturer kindly prints the exact multiplication factor on the wrapper.
All we need now is an ohm meter and some epoxy glue to fasten the plastic securely to the material whose stretch is to be investigated. There are, however, some small, and some major details that will vastly improve the accuracy of measurement and impress referees.
The most major detail of all is that strain gauges can hardly be strained at all! Different materials have different limits but about 1% extension is the limit for reliable performance.

If you have been using a vernier to check the shrinkage of the planks on your hen-house you cannot just substitute an electrical strain gauge. The movement at the gauge has to be reduced somehow, and made uniform over the length of the sensitive strips on the gauge.

This is done by glueing the gauge
somewhere on a flexible beam which has one end fastened securely to one plank and whose outer end is somehow following the movement of the next plank.
The length and thickness of the beam are chosen so that the expected movement between the planks will cause an extension, or compression of the gauge which is less than about 1%.

The principle of the bending beam can be adapted to all kinds of situations. Here, for example, is a device that I made to measure the expansion of the facade of a building whose artificial stone facing was connected by steel pins across a gap to a massive brick wall. The stainless steel strip changes its radius of curvature as the facade moves up and down by about 1,5 mm during the day.
The support for the gauge is usually stainless steel or an aluminium alloy. It is often difficult for ordinary people to get the specialised alloys. The aluminium extrusions found in hobby and do-it-yourself stores are OK. Suitable stainless steel beams can be found as flexible spatulas in kitchen equipment shops and as palette and painting knives in art shops. Two part epoxy glues are suitable adhesives, acrylic and rubber based glues creep too much.
Strain gauges can be adapted to all sorts of measurements and are often the cheapest and simplest technique for automating collection of non-mechanical data. A standard RH sensor, for example, uses a strain gauge to sense the change in length of a ribbon of moisture sensitive plastic. Strain gauges, once has got the hang of using them, are extraordinarily useful experimental devices. They are also cheap, once one has acquired the specialised resistance measuring box which is necessary because of the relatively small change of resistance that must be measured accurately. The manufacturers of strain gauges give good advice on the geometry of beams, the details of gluing without bubbles and wiring to reduce the effect of temperature on the measurement (metals change resistance with temperature as well as with extension). I .
There are other strain measuring and detecting devices. Building conservators use brittle plates that are designed to break all at once, or plastic foils with a sequence of conductive strips that break in sequence. These are put across cracks in Cathedral vaults to reinforce the urgency of appeals for repair funds.
Brittle paint is fun to use and has been repeatedly reinvented by modern artists. Paint that alters the plane of polarisation of light as it is stretched gives impressive colour displays that show the points of high strain in complex machine parts.
  post #3  
04-07-2009, 10:21 PM
Senior Member
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slight bending

Stress is measured by detecting, with a strain gauge, the slight bending of a stiff bar attached to the piece under test, while the resulting strain is measured by the bending of a flexible beam, that exerts negligible force on the piece under test. A slight correction to the strain is necessary, because the stress sensor does move the top of the test piece slightly.
The measurement of the force, stress, on the piece under test, is made by a device that is deformed as little as possible by the applied force, while the measurement of extension, strain, requires a device that follows the movement of the test piece without affecting its behaviour. The basic technology, however, is the same for both measurements.
The stress measuring device is often called a load cell and is seldom made as shown in the sketch, because more complicated geometries reduce the deformation, improve the linearity of the signal from the strain gauge and compensate better for loads that are not perfectly aligned and therefore twist the beam.
All my illustrations have shown just one strain gauge. Strain gauges are usually used in pairs or in sets of four, glued on both sides of the beam. This increases the signal and also compensates for a variety of interferences such as strain caused by temperature change.
For many laboratory experiments a simple beam arrangement with a pair of strain gauges glued opposite each other near the clamp is entirely adequate. The details of wiring and measurement can be obtained from the two companies named in the previous section.


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