Calculator for Finding Principal Strains
engineering fundamentals Principal Strain Calculator
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Calculator Introduction

Given the strain components ex, ey, and exy, this calculator computes the principal strains e1 and e2, the principal angle qp, the maximum shear strain exy max and its angle qs. It also illustrates an approximate Mohr's cirlce for the given strain state.

  Normal Strain ex:    
  Normal Strain ey:    
  Shear Strain exy:    
  Maximum Normal Stain e1:  1.65  
  Minimum Normal Strain e2:  -0.547  
  Principal Angle qp:  32.9  deg
  Maximum Shear Strain exymax:  1.10  
  Maximum Shear Angle qs1:  77.9  deg
  and qs2:  -12.1  deg

Note: The strain measure exy is used in this calculation. Please adjust accordingly when using the engineering shear strain .


The Mohr's circle associated with the above strain state is similar to the following figure. However, the exact loaction of the center eAvg, the radius of the Mohr's circle R, and the principal angle qp may be different from what are shwon in the figure.

Equations behind the Calculator
The formulas used in this calculator are,

Principal Angle

Principal Strains

Maximum Shear Strain

Maximum Shear Angle

Further information can be found in the plane strain, Mohr's Circle, and the Mohr's Circle usage pages.

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