MohrMethode

MohrMethode, or Mohr’s circle method, is a graphical and analytical technique for transforming and analyzing stresses in materials. Named after the German engineer Christian Otto Mohr, it provides a compact representation of the stress state and enables the determination of principal stresses, their orientations, and the stresses on any material plane.

In two-dimensional stress analysis, given the in-plane normal stresses σx, σy and the shear stress τxy, a Mohr circle can be drawn. The circle’s center is at ((σx+σy)/2, 0) and its radius is sqrt(((σx−σy)/2)^2 + τxy^2). Principal stresses are σ1,2 = (σx+σy)/2 ± radius, and the principal orientation θp satisfies tan(2θp) = 2τxy/(σx−σy). For a plane inclined by an angle φ, the normal and shear stresses are σn = (σx+σy)/2 + ((σx−σy)/2) cos(2φ) + τxy sin(2φ) and τn = −((σx−σy)/2) sin(2φ) + τxy cos(2φ).

For three-dimensional states, several Mohr circles can be used to visualize principal stresses and their orientations, though practical analysis often relies on algebraic methods. The method is widely used for teaching stress transformation, evaluating failure criteria (such as Tresca and von Mises), and performing quick visual checks of how stresses vary with orientation.

Limitations include its primarily instructional nature and its applicability to linear elastic, homogeneous states. Complex loading, material anisotropy, or nonuniform stress distributions may require numerical or more advanced analytical approaches.