Principal Stress Calculator

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Stress unit for all inputs and outputs. The formulas are dimensionless; pick whichever unit your problem uses.
Normal stress on the X face (positive = tension, negative = compression).
MPa
Normal stress on the Y face (positive = tension, negative = compression).
MPa
Shear stress on the XY plane. Sign convention: positive when the stress on the +X face points in the +Y direction.
MPa
Angle to rotate the element (degrees). Outputs for the rotated element appear as extra fields. Leave at 0 for the standard principal-stress result only.
deg
Maximum principal stress (sigma1)Combined tension-compression
94.031MPa

Largest normal stress; shear stress is zero on this plane.

Minimum principal stress (sigma2)-34.031MPa
Max in-plane shear stress (tau_max)64.031MPa
Average normal stress (sigma_avg)30MPa
Von Mises stress114.891MPa
Principal angle (theta_p)19.33deg
Max-shear angle (theta_s)64.33deg
Rotated normal stress X80MPa
Rotated normal stress Y-20MPa
Rotated shear stress40MPa
sigma1 (max principal)94.031
sigma2 (min principal)-34.031
tau_max (in-plane shear)64.031
Von Mises114.891

Principal stresses: 94.03 MPa (max) and -34.03 MPa (min).

  • sigma1 = 94.03 MPa and sigma2 = -34.03 MPa. These are the extreme normal stresses at this point; shear stress vanishes on the planes they act on.
  • The maximum in-plane shear stress is 64.03 MPa, acting on planes rotated 45 degrees from the principal planes. This is the radius of Mohr's circle.
  • Von Mises equivalent stress is 114.89 MPa. Compare this to your material's tensile yield strength to check for yielding under this loading.
  • The principal plane is rotated 19.3 degrees counter-clockwise from the X axis.

Next stepTo check whether the material will yield, divide the Von Mises stress by the material yield strength. A ratio above 1.0 predicts yielding under von Mises (distortion-energy) theory.

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