GT AE 3145 - Strain Transformation and Rosette Gage Theory (7 pages)

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Strain Transformation and Rosette Gage Theory



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Strain Transformation and Rosette Gage Theory

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Pages:
7
School:
Georgia Institute of Technology
Course:
Ae 3145 - Structures Laboratory

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Strain Transformation and Rosette Gage Theory It is often desired to measure the full state of strain on the surface of a part that is to measure not only the two extensional strains x and y but also the shear strain xy with respect to some given xy axis system It should be clear from the previous discussion of the electrical resistance strain gage that a single gage is capable only of measuring the extensional strain in the direction that the gage is oriented Assuming that the x and y axes are specified it would be possible to mount two gages in the x and y directions respectively to measure the associated extensional strains in these directions However there is no direct way to measure the shear strain xy Nor is it possible to directly measure the principal strains since the principal directions are not generally known The solution to this problem lies in recognizing that the 2D state of strain at a point on a surface is defined by three independent quantities which can be taken as either a x y and xy or b 1 2 and where case a refers to strain components with respect to an arbitrary xy axis system and case b refers to the principal strains and their directions Either case fully defines the state of 2D strain on the surface and can be used to compute strains with respect to any other coordinate system This situation implies that it should be possible to determine these 3 independent quantities if it is possible to make three independent measurements of strain at a point on the surface The most obvious approach is to place three strain gages together in a rosette with each gage oriented in a different direction and with all of them located as close together as possible to approximate a measurement at a point As will be shown below if the three strains and the gage directions are known it is possible to solve for the principal strains and their directions or equivalently the state of strain with respect to an arbitrary xy coordinate system The relations needed are



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