Mohr's Circle Calculator - Principal Stresses and Stress Transformation

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Normal stress acting perpendicular to the vertical face of the element. Tensile is positive, compressive is negative.
MPa
Normal stress acting perpendicular to the horizontal face of the element. Tensile is positive, compressive is negative.
MPa
In-plane shear stress. Positive if it acts upward on the right face (standard mechanics of materials convention).
MPa
Counter-clockwise angle from the x-axis for the rotated element stress calculation. Range: -90 to 90 degrees.
deg
Maximum principal stress (σ1)Combined tension/compression
94.03MPa

Largest normal stress; acts on the plane where shear stress is zero

Minimum principal stress (σ2)-34.03MPa
Maximum in-plane shear stress (τmax)64.03MPa
Mean (hydrostatic) stress (σavg)30MPa
von Mises stress (σVM)114.89MPa
Principal plane angle (θp)19.33deg
Max shear plane angle (θs)-25.67deg
Rotated normal stress (σx')89.64MPa
Rotated normal stress (σy')-29.64MPa
Rotated shear stress (τx'y')-23.3MPa
Max principal (σ1)94.03
Min principal (σ2)-34.03
Max shear (τmax)64.03
von Mises (σVM)114.89

Principal stresses are 94.0 MPa and -34.0 MPa.

  • The Mohr's circle has center at 30.00 MPa and radius 64.03 MPa.
  • Principal stresses are 94.03 MPa and -34.03 MPa, acting on planes rotated 19.3 deg from the x-axis.
  • Maximum in-plane shear stress is 64.03 MPa (occurring 45 deg from the principal planes).
  • The von Mises stress is 114.89 MPa. Compare this to the material yield strength to assess risk of yielding.

Next stepTension and compression coexist: check both principal directions for failure criteria, especially for brittle materials.

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