Mohr's Circle — validation & limitations

What it calculates

• Principal stresses (σ1, σ2) and principal angle θp via Mohr's circle — exact closed-form
• Von Mises (distortion-energy) and Tresca (max-shear-stress) safety factors against Sy — the headline verdict reports whichever GOVERNS (the lower of the two)
• 3D triaxial stress state with absolute max shear and triaxiality ratio (σm / σVM)
• Strain rosette back-calculation: 0-45-90 and 0-60-120 gauge layouts → principal stresses
• Multiaxial fatigue screening: Goodman, Gerber, Soderberg and Sines (1955) criteria (endurance limit uncorrected unless you enter one)
• Failure-envelope charts (Von Mises ellipse, Tresca hexagon, brittle-fracture Sut limit)
• Fails closed on invalid input: a blank strength, an out-of-range Poisson ratio or an unrecognised rosette layout is refused with a named message rather than answered

Validation evidence — independent reference cases (1)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• Distortion-energy and maximum-shear safety factors, plane stress

  Agrees

  Source: Budynas & Nisbett, Shigley's Mechanical Engineering Design, 9th ed., Example 5-1; Eqs. 3-13, 5-3, 5-13/5-15, 5-19 (hand recomputation)

  Inputs: Sy 100 kpsi; (sx, sy, txy) = (70,70,0), (60,40,-15), (0,40,45), (-40,-60,15)

  Quantity	Reference value	Tolerance
  distortion-energy factor, cases a-d	1.428571 / 1.696378 / 1.141460 / 1.696378	1e-5 relative
  maximum-shear factor, cases a-d	1.428571 / 1.469988 / 1.015346 / 1.469988	1e-5 relative
  principal stresses, case c	69.244 / -29.244	1e-5 relative

  tests/golden/REF-mohr-criteria.golden.test.ts

Limitations

Not checked by this tool

• Stress concentrations at notches, holes and fillets — Enter the peak (notch) stresses, or use /fatigue with Kt
• Pressure-vessel stress categorisation and linearisation (Pm, PL, Pb, Q) — Not a code design check; use ASME VIII Div. 2 Part 5 or /pressure for vessels
• Residual stresses — Not included; add known residual stresses to the applied stresses
• Out-of-plane shear in a triaxial state — sigma_z is taken as a principal stress; for a full 3-D tensor use a general eigenvalue solution
• Buckling of thin or slender parts under compressive stress — Yield only; check stability with /buckling