7/27/2019 Mechanics eBook_ Strain Gages and Strain Rosette

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Ch 8. Strain Analysis Multimedia Engineering Mechanics

PlaneStrain

Mohr's Circlefor Strain

StrainGages

Mechanics Strain Gages and Strain Rosette Case Intro Theory Case Solution Example Chapter 1. Stress/Strain2. Torsion3. Beam Shr/Moment4. Beam Stresses5. Beam Deflections6. Beam-Advanced7. Stress Analysis8. Strain Analysis9. Columns Appendix

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Author(s):

Kurt Gramoll

Kurt Gramoll

MECHANICS - THEORY

Strain Gage Basics

Basic Linear Strain Gage

It is not possible (currently) to measure stress directlyin a structure. However, it is possible to measurestrain since it is based on displacement. There are anumber of techniques to measure strain but the twomore common are extensometers (monitors thedistance between two points) and strain gages.

Strain gages are constructed from a single wire that iswound back and forth. The gage is attached to thesurface of an object with wires in the direction wherethe strain is to be measured.

The electrical resistance in the wires change whenthey are elongated. Thus, the voltage change in thewires can be collaborated to the change in strain.Most strain gage measurement devices automaticallycollaborate the voltage change to the strain, so thedevice output is the actual strain.

Strain Rosette

Strain Gage Rosette at Arbitrary Angles

Since a single gage can only measure the strain in onlya single direction, two gages are needed to determinestrain in the x and y. However, there is no gage that

is capable of measuring shear strain.There is a clever solution to finding shear strain. Threegages are attached to the object in any three differentangles. Recall, any rotated normal strain is a functionof the coordinate strains, x, y and xy, which areunknown in this case. Thus, if three different gages areall rotated, that will give three equations, with threeunknowns, x, y and xy. These equations are,

Any three gages used together at one location on astressed object is called a strain rosette.

Strain Rosette - 45 o

hanics eBook: Strain Gages and Strain Rosette http: //www.ecourses .ou.edu/cgi-bin/ebook.cgi?doc=&topic=me&chap_...

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7/27/2019 Mechanics eBook_ Strain Gages and Strain Rosette

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Strain Gage Rosette at 45 o

To increase the accuracy of a strain rosette, largeangles are used. A common rosette of three gages iswhere the gages are separated by 45 o, or a = 0

o , or

b = 45o , or c = 90

o . The three equations can then besimplify to

Solving for x, y and xy gives,

Strain Rosette - 60 o

Strain Gage Rosette at 60 o

Similarly, if the angles between the gages are 60 o , or

a = 0 o, or b = 60 o , or c = 120 o., the unknownstrains, for x, y and xy will be,

hanics eBook: Strain Gages and Strain Rosette http: //www.ecourses .ou.edu/cgi-bin/ebook.cgi?doc=&topic=me&chap_...

2 19/03/2013 18:52