Engineering source
The selected geometry and loads are reduced to the local plane-stress tensor used by the common Mohr-circle engine.
Rosette reconstruction
Gauge orientation, measured strain and fit residuals.
Strain Mohr circle
Vertical coordinate is γ/2; positive engineering shear is drawn downward.
Effective-stress Mohr–Coulomb
total-stress circleeffective-stress circlefailure envelopeclosest envelope point
Increasing pore pressure translates the effective circle left by u without changing its radius.
3D stress state
drag plane normal
n = —t = —σn = —|τ| = —
Isometric stress cube with principal directions, selected plane, unit normal n and traction vector t = σn.
Principal Mohr circles
σ1–σ3σ1–σ2σ2–σ3selected plane
The red point is (σn, |τ|). An arbitrary 3D plane generally lies inside the admissible Mohr region, not on a circle boundary.
Physical element
drag handle
Drag the circular handle to rotate the material plane. Arrow directions and values are the transformed stresses on x′–y′ faces.
Mohr circle
drag X′
Mohr circlecurrent planeprincipal axes
Positive shear is plotted downward. A physical rotation θ moves X′ by 2θ around the circle.
Failure assessment
The principal-stress point does not move when only the coordinate plane is rotated: failure measures are rotational invariants.
| # | Angle α | Measured ε | Δε (µε) | |
|---|
Three gauges are solved exactly. Four to eight gauges use ordinary least squares and report residuals.
Sign convention
Equations
Equations
3D equations