Strain and stress calculations from strain gage leg data

When you use the Analyze Strain Gage command, the software calculates the durability functions using the equations NOTE described here from the strain gage leg data:

• εa is the true strain from leg a.

• εb is the true strain from leg b.

• εc is the true strain from leg c.

You can correct the measured leg strains for parasitic effects of resistance changes. These changes are transverse to the gage axis. To correct for these changes, use the options in the Transverse Correction group of the Durability Strain Gage Rosette Analyzer dialog box.

Maximum and absolute maximum principal strains

Depending on the strain gage rosette type, the principal strains are given by:

• Delta rosette (0 – 60 – 120)

• Rectangular rosette (0 – 45 – 90)

For both rosette types, the maximum principal strain is given by: εmaxP = max (ε1, ε2).

For both rosette types, the absolute maximum principal strain is given by: εabsMaxP = max (|ε1|, |ε2|).

Maximum and absolute maximum principal angles

Depending on the strain gage rosette type, the maximum principal angle is given by:

• Delta rosette (0 – 60 – 120)

• Rectangular rosette (0 – 45 – 90)

The quadrant in which the maximum principal angle is located is determined using the signs of the tangent and sinusiod of the angle θNOTE.

For both rosette types, the absolute maximum principal angle is given by:

Maximum and absolute maximum principal stresses

Depending on the strain gage rosette type, the principal stresses are given by:

• Delta rosette (0 – 60 – 120)

• Rectangular rosette (0 – 45 – 90)

For both rosette types, the maximum principal stress is given by: σmaxP = max (σ1, σ2).

For both rosette types, the absolute maximum principal stress is given by: σabsMaxP = max (|σ1|, |σ2|).

Maximum and absolute maximum shear strains and stresses

For both rosette types, the maximum and absolute maximum shear strains and stresses are the same.

• The maximum shear strain is given by: γmax = ε1 – ε2.

• The absolute maximum shear strain is given by: γabsMax = |γmax|.

• The maximum shear stress is given by: τmax = 0.5(σ1 – σ2).

• The absolute maximum shear stress is given by: τabsMax = |τmax|.

Von Mises and signed Von Mises Stresses

For both rosette types, the Von Mises stress is given by:

The signed Von Mises stress has the same magnitude as the Von Mises stress, but is assigned the sign of the absolute maximum principal stress:

Effective strain and stress

For both rosette types, the effective strains are obtained by resolving the time history of strains at the gage location in the effective primary loading direction that is determined from the stress axis search. The effective stress history is the time history of the stress component in the effective primary loading direction that is obtained by transformation of the stress tensor along the angle determined by the axis search.

Learn more

Analyzing strain gage rosette data

Look up more details

Introduction to durability analysis

Understanding the strength evaluation

Strength calculations for orthotropic failure criteria

Fatigue evaluation on element free faces

Fatigue life criteria

Biaxial fatigue evaluation on element free faces

Using a notch factor for modeling the local plastic behavior

Understanding cyclic stress-strain behavior

Understanding the fatigue safety evaluation

Cumulative damage

Random fatigue methods

Strain gage transverse corrections for rosette legs

Scientific literature references for durability

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Strain and stress calculations from strain gage leg data, Simcenter 3D 2021.1 Series

© 2020 Siemens

Murray, W.W. and Miller, W.R., “The Bonded Electrical Resistance Strain Gage”, Chapters 8 and 9, Oxford University Press, 1992.

Murray, W.W. and Miller, W.R., “The Bonded Electrical Resistance Strain Gage”, Chapters 8 and 9, Oxford University Press, 1992.

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