How this calculation works
Three strain gauges at zero, forty-five and ninety degrees contain enough information to recover a small in-plane strain state. This calculator converts those normal-strain readings into principal strains, engineering shear strain and a principal-axis direction.
γxy = 2ε45 − ε0 − ε90; ε1,2 = (ε0+ε90)/2 ± √[((ε0−ε90)/2)²+(γxy/2)²]A worked example
With readings 100, 100 and zero microstrain, engineering shear is 100 microstrain. The average normal strain is fifty and the Mohr radius is 70.7107 microstrain. Principal strains are 120.7107 and −20.7107, with the first principal axis at 22.5 degrees.
Good to know
Small coplanar strains only. The calculation does not compensate temperature, gauge misalignment, transverse sensitivity or instrument calibration. No elastic modulus or Poisson ratio is entered, so it does not convert these strains into material stresses.
Reference: Jönköping University — Mohr circle and strain transformation (opens in a new tab) ↗
What this model answers
Three strain gauges at zero, forty-five and ninety degrees contain enough information to recover a small in-plane strain state.
This calculator converts those normal-strain readings into principal strains, engineering shear strain and a principal-axis direction.
The Plane stress principal stresses and Mohr circle calculator transforms a supplied stress state. This page stops at strain because material stiffness and lateral coupling have not been entered.
Keep the input conventions consistent
Enter all three readings in microstrain using the same angular datum.
The gauges must form a rectangular rosette, with directions progressing consistently counterclockwise. A sixty-degree delta rosette has a different transformation and cannot use these labels unchanged.
Read the result carefully
Engineering shear strain is twice the corresponding tensor shear component.
The principal-strain radius therefore uses gamma divided by two. Forgetting that factor changes both the extreme strains and the direction even when the three gauge readings are correct.
The three readings must correspond to the stated zero, forty-five and ninety-degree gauge directions with consistent strain units. The recovered engineering shear strain is not the same quantity as tensor shear strain. A mistaken factor of two can distort transformed directions even when the two normal readings look plausible.
Work through the numbers
With readings 100, 100 and zero microstrain, engineering shear is 100 microstrain.
The average normal strain is fifty and the Mohr radius is 70.7107 microstrain. Principal strains are 120.7107 and −20.7107, with the first principal axis at 22.5 degrees.
Where the calculation stops
Small coplanar strains only.
The calculation does not compensate temperature, gauge misalignment, transverse sensitivity or instrument calibration. No elastic modulus or Poisson ratio is entered, so it does not convert these strains into material stresses.
A few questions, answered
Why not multiply engineering shear directly into the circle radius?
The strain circle uses half of engineering shear, corresponding to the tensor shear component.
What should I change in the comparison?
Set the diagonal reading to the mean of the other gauges and inspect the zero-shear state.