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Sample Problem : Principal Stress Calculation with Strain Gage Rosette Measurements

On the foot of a machine, strain measurement has
been done with 45° strain gage rosette as shown in the figure. Measurement results
recorded from the strain gages are
ε_{1}=65 μin/in, ε_{2}= 700 μin/in
and
ε_{3}= 150 μin/in. (Use E=205 GPa
and
v=0.29)

Using the measurement results of strain gage rosette, calculate:

a) Strain components
ε_{x},ε_{y},γ_{xy}.

b) The principal stresses (in XY plane) at the measurement point.

##### Solution:

## Step 1 : Write down input parameters which are defined in sample example

INPUT PROPERTIES SUMMARY |

Parameter |
Symbol |
Value |
Unit |

Measured strain-1 |
ε_{1} |
65 |
μin/in |

Measured strain-2 |
ε_{2} |
700 |
μin/in |

Measured strain-1 |
ε_{3} |
150 |
μin/in |

Strain gage rosette angles |
θ |
0-45-90 |
deg |

Elastic Modulus |
E |
205 |
GPa |

Poisson's Ratio |
v |
0.29 |
--- |

## Step 2 : Go to "Strain Measurement with Strain Rosette" page to calculate
strain components ε_{x},ε_{y},γ_{xy} by using the values summarized in step 1.

Strain components are calculated as
ε_{x}=65, ε_{y}=150,γ_{xy}=1185. This is the answer of clause a) of the problem.

## Step 3 : Since the measurement has been recorded from the free surface of the
machine, it can be assumed that the situation is plane stress state. For
the calculation of principal stresses, go to "Calculation of Plane Stress
State With Strain Gage Rosette Results" page to calculate principal stresses.

Principal stresses are calculated as 125.4 MPa and -63.4 MPa . This is the answer of clause
b) of the problem.

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Summary

The problem is fully solved with calculators which are summarized as
follows.