Find principal stresses, maximum shear stress and principal angle for plane stress.
Find principal stresses, maximum shear stress and principal angle for plane stress.
Major principal stress σ₁ (MPa)
How to use this tool
Normal stresses on the x and y faces, in megapascals; tensile is positive.
Shear stress on the same element, in megapascals.
These are the maximum and minimum normal stresses, acting on planes with zero shear.
The rotation to the principal planes, measured from the x-axis.
Formula & worked example
σx = 100, σy = 50, τxy = 30 MPa: average 75 MPa, radius 39.051 MPa, σ₁ = 114.051 MPa, σ₂ = 35.949 MPa, τ_max = 39.051 MPa, θp = 25.097°.
Limitations — read this before you rely on it
This is plane stress (a thin element with zero out-of-plane stress). Full three-dimensional stress states need the third principal stress, and failure prediction additionally requires a material criterion such as von Mises or Tresca.
Frequently asked questions
The extreme normal stresses at a point, acting on planes where shear stress vanishes.
On Mohr’s circle the radius is exactly the largest shear stress, reached on planes at 45° to the principal planes.
Tensile normal stress is positive and compressive negative; shear sign follows the standard element convention.
Then σx and σy are already the principal stresses and the principal angle is zero.
Compare the principal stresses against a yield criterion for your material; this tool reports stresses only, not a pass or fail.