On the foot of a machine, strain measurement has
been done with 45° strain gauge rosette (rectangular rosette) as shown in the figure. Measurement results
recorded from the strain gauges 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 gauge rosette, calculate:

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

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

**Step 1 :** Write down input parameters which are given.

INPUT PROPERTIES SUMMARY | ||

Parameter | 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 gauge rosette angles (θ) | 0-45-90 | deg |

Elastic Modulus (E) | 205 | GPa |

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

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

RESULTS | ||

Parameter | Value | Unit |

Normal strain in x-direction (ε_{x}) |
65 | μm/m (μin/in) |

Normal strain in y-direction (ε_{y}) |
150 | |

Shear strain in xy-direction (γ_{xy}) |
1185 |

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 Gauge Rosette Results" page to calculate principal stresses by using the values summarized in step 1.

RESULTS | ||

Parameter | Value | Unit |

STRAINS ON REFERENCE AXIS (X-Y) | ||

Normal strain in x-direction (ε_{x}) |
65 | μm/m (μin/in) |

Normal strain in y-direction (ε_{y}) |
150 | |

Shear strain in xy-direction (γ_{xy}) |
1185 | |

PLANE STRESSES | ||

Normal stress in x-direction (σ_{x}) |
24.3 | MPa |

Normal stress in y-direction (σ_{y}) |
37.8 | |

Shear stress in xy plane (τ_{xy}) |
94.2 | |

PRINCIPAL STRESSES | ||

Maximum principal stress (σ_{max}) |
125.4 | MPa |

Minimum principal stress (σ_{min}) |
-63.4 | |

Maximum shear stress (τ_{max}) |
94.4 | |

Average principal stress (σ_{avg}) |
31 | |

Von Mises stress (σ_{mises}) |
166.4 |

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

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

Calculator | Usage |

Calculation of Plane Stress State With Strain Gauge Rosette Results | To calculate principal stresses for plane stress state with the usage of strain gauge rosette measurement. |

Strain Calculation with Strain Rosette Measurement | To calculate normal and shear strain by using the measurement results of strain gauge rosette. |

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