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The stress analysis with strain gauge is used to determine the stress in a single component.
In the stress analysis with strain gauges usually bridge circuits are used with only one active measurement grid.
In a uniaxial stress condition, it is sufficient to detect the strain with a single measuring grid. The direction of the mechanical stress is required in this case, as known. The strain gauge is used to determine the amount. To calculate the mechanical power from the measured strain of the elastic modulus of the material as well as the k-factor of the strain gauge must be known.
If it is a biaxial stress state in which the magnitude and direction of the principal stresses are unknown, the stretching must be measured in three directions become. For this strain rosettes are used with three active measuring grids. To calculate the mechanical power from the measured strain of the elastic modulus of the material, the Poisson's ratio of the material as well as the k-factor of the strain gauge must be known.
The uniaxial stress state occurs for example in tension and compression members as in Fig. 1
In uniaxial bending there is also uniaxial stress state.
The maximum tensile / compressive stresses are created at tension rod / compression rod in the direction of the force.
In all other directions tensions are smaller and follow the equation 1
φ:. Angle between the direction (here the line of action of force) and viewing direction (measuring direction)
σ 1: First main direction
Despite the uniaxial stress state can be found but a biaxial strain state, due to the lateral expansion of the material.
When biaxial stress state the maximum stresses occur in two mutually perpendicular directions.
These directions are called principal stress directions, indicated with 1 and 2.
In general, the principal stress directions are unknown in the stress analysis.
In this case, a stress analysis is performed with rosettes.
The strain gage rosette is the expansion in three directions "a", "b" and "c" gemesen.
The grids "b" and "c" are respectively oriented relative to the measuring grid "a" through 45 ° or 90 ° counterclockwise.
Alternatively, measuring grids 0, 60 ° and 120 ° are used. The equations listed here can then not be used.
Because of the ambiguity of the tangent function must be determined on the basis of the case analysis,
in which the quadrants I to IV is the solution for this angle φ:
|y ≥ 0||y > 0||y ≤ 0||y < 0|
|x > 0||x ≤ 0||x < 0||x ≥ 0|
|Hauptrichtung||φ = 1/2 · (0° + |ψ|)||φ = 1/2 · (180° - |ψ|)||φ = 1/2 · (180° + |ψ|)||φ = 1/2 · (360° - |ψ|)|
Table 1: determining the angle φ from the auxiliary angle ψ using a case distinction.
Note: the sum of ψ is used.
Links in Forum: Links-stress analysis
The "E-MechLAB" of the Institute of Applied Mechanics of the Technical University of Berlin presents the basics in a clear way:
types of voltages: normal and shear stresses
principal stress, reference stress, Mohr's stress circle: principal stresses, equivalent stresses
in the TechNotes Vishay be shown the basics of strain gauge rosettes. The Grid "a", "b", "c" are here, however, with "1", "2", "3" indicated: