Stressturn user guide

Getting started: your first stress state in two minutes

Default and gallery parameters are synthetic demonstration inputs, not sourced material properties. Replace all strengths, elastic constants and density with independently verified values for your material.

Interference must be nonnegative: clearance fits are refused. Arbitrary rosettes use QR and refuse ill-conditioned gauge directions (condition of R in the infinity norm above 1e6); spread the gauges. Cohesionless materials (c = 0) are outside the current Mohr–Coulomb contract. Computed exports require authorization; report UI migration is pending.

Stressturn transforms stress and strain: give it a stress state, strain-gauge readings, a pressurised cylinder or a spinning disc, and it returns principal values and directions, Mohr circles, safety factors under six failure criteria and the stress distributions. Everything runs in your browser; your study is stored only in this browser (autosave) and in files you save.

• Open the tool. The Stress state tab starts with a worked plane-stress element.
• Type the six components (σx, σy, σz, τxy, τyz, τzx). Results update as you type; there is no Run button.
• Drag around the Mohr circle, or focus it and press the arrow keys, to rotate the element. Press P to snap to the principal axes and S to the maximum-shear plane.
• Enter the strengths of your material in Material strengths. Each failure criterion lists the safety factor it gives and which data it still needs.
• Use Examples for ready-made engineering problems, Export for files and a printable report.

Sign conventions and units

• Tension is positive, compression negative. Pressures in the cylinder and disc tabs are entered positive when they compress the wall.
• τxy is positive when it acts in the +y direction on the face whose outward normal is +x.
• Angles are counter-clockwise from the +x axis. The element angle θ turns the axes by θ.
• The Mohr circle plots shear downward, so turning the element by θ turns the diameter by 2θ in the same screen direction.
• Strain tensors use tensor shear (γ/2) in the Mohr plot; the engineering shear strain γ is shown separately.
• Units: Stressturn does not convert units. Stress, strength, modulus and pressure must share one unit; the label next to them is only a label. Cylinder and fit lengths are in mm. The rotating-disc tab works in mm, kg/m³, rpm and MPa.

The four analyses

Stress state, principal values and Mohr circles

The six components form a symmetric tensor. Stressturn finds its three principal values σ1 ≥ σ2 ≥ σ3 and unit directions with a Jacobi eigen-decomposition, which uses orthogonal rotations only and returns orthonormal vectors even when two principal values coincide. The sign of each vector is fixed so its largest component is positive.

• The three Mohr circles join the pairs (σ1, σ3), (σ1, σ2) and (σ2, σ3). The largest circle gives the absolute maximum shear (σ1 − σ3)/2.
• The solid circle is the x–y plane circle. Its points X and Y are the original faces, X′ and Y′ the rotated faces at your angle.
• Invariants: I1 is the trace, I2 the sum of the principal 2×2 minors, I3 the determinant. They do not change when you rotate the element.
• Octahedral normal stress is I1/3 and octahedral shear is √(2·J2/3), where J2 is the second invariant of the deviatoric stress. The von Mises stress is √(3·J2).
• The Lode angle runs from 0° (tension-like state) through 30° (pure shear) to 60° (compression-like state).

Failure criteria and safety factors

Every safety factor is the proportional-loading factor: the number by which all stresses can be multiplied together before the criterion is reached. That definition is the same for every row, so the rows are directly comparable. A value below 1 means the state is outside the failure surface. The criteria use the three 3-D principal stresses, so a plane state still has σ3 = 0 as one of them.

Strengths are entered as positive numbers. Nothing is guessed: a criterion whose data are missing says what it needs. The Mohr–Coulomb line and the Coulomb–Mohr line coincide for matching strengths (sin φ = (Suc − Sut)/(Suc + Sut), c = √(Sut·Suc)/2), and the Guide’s verification cases check that.

Plane-stress failure envelope

When σz, τyz and τzx are zero, the Stress state tab draws the σ3 = 0 section of the chosen criterion in the (σ1, σ2) plane with your state marked. Points outside a curve have failed by that criterion.

Stress concentration (Kt)

Stressturn contains no concentration-factor charts or tables. You enter Kt (and, optionally, a notch sensitivity q) from a source you are entitled to use. The tool returns the peak stress Kt·σnom, the fatigue-type factor Kf = 1 + q(Kt − 1) when q is given, and the static safety factors of the peak against yield and ultimate strength.

Strain-gauge rosettes

A gauge at angle a from the x axis reads εa = εx cos²a + εy sin²a + γxy sin a cos a. Rectangular and delta rosettes use the exact closed forms; an arbitrary rosette solves the 3×3 system, or a least-squares fit when you add a fourth or further gauge, and then reports the rms residual so you can spot a bad gauge.

• Principal strains are the centre ± radius of the strain Mohr circle; θp is the angle from x to ε1.
• Plane stress: σz = 0 and εz = −ν(εx + εy)/(1 − ν). Plane strain: εz = 0 and σz = ν(σx + σy). Pick the one that matches the part; a free surface is normally plane stress.
• Readings are in microstrain. Transverse sensitivity, gauge-factor and lead-wire corrections are not applied.

Thick-walled cylinders and interference fits

The Lamé solution gives σr = A − B/r² and σθ = A + B/r², with A and B fixed by the internal and external pressures. The axial stress depends on the ends: open ends carry none, closed ends carry the end-cap load, and fixed ends hold the axial strain at zero.

• The chart shows σr, σθ, σz and von Mises through the wall; focus it and press ← and → to move the cursor. The table lists the bore and outer values.
• The yield check scales all pressures together to first yield (Tresca and von Mises).
• Interference fit: enter the diametral interference δ, both materials and radii. The interface pressure follows from δ/2 = p·(hub flexibility + shaft flexibility) with both members in plane stress. Holding force and torque use the friction coefficient you enter.
• Enter the effective interference after any smoothing of surface roughness; the tool does not model roughness, thermal assembly or fretting.

Rotating discs

Uniform-thickness discs of constant density in plane stress. The spin loading is combined with the Lamé solution for the bore and rim pressures. Use a negative rim pressure for a blade pull. First-yield speed is the speed at which Tresca or von Mises first reaches Sy including any edge loads.

• Solid disc: σr = σθ at the centre, the largest stress there.
• Annular disc: the hoop stress is largest at the bore.
• There is no thermal, thickness-variation or plasticity model. First-yield speed is not a burst speed.

Files and exports

• Save / Open write and read a JSON study file (format: "stressturn", version: 1). The format is a plain, documented object of numbers and text.
• Export offers the study file, a CSV of the stress-state results, a CSV of every radial profile (on the cylinder, fit and disc tabs), the Mohr circle as SVG or PNG, and a full report you can print or save as PDF from the browser’s print dialog.
• Every export ends with “Made with Stressturn · simulations4all.com” and the professional-use notice. Study files carry a copyright and terms field.
• Autosave keeps the current study in this browser only. Clearing site data removes it.

Keyboard shortcuts

Limitations: what this tool does not do

• Linear-elastic, small-strain, isotropic material only. No plasticity, creep, anisotropy or composite laminates.
• No fatigue life, fracture mechanics, buckling or dynamic effects. Kt is a multiplier you supply.
• No thermal stresses, no residual stress, no varying thickness or density in the disc.
• Interference fits assume free ends, plane stress and uniform contact.
• Failure criteria are screening checks for a single stress state. Brittle criteria use the strengths you enter; the tool ships no material database.
• Radial profiles are limited to 5001 points; study files to 2 MB.

Compared with other tools

Stressturn is a focused stress-transformation tool, not a finite-element package. Hand-calculation worksheets and spreadsheets can do any of these formulas but leave unit, sign and formula errors to you; general-purpose finite-element programs solve far more general geometry but need a model. Stressturn covers the closed-form cases an engineer meets daily, shows its checks, and runs without installation. For anything beyond the list above, use a tool built for it.

How we verify this tool

The Verify view runs 143 reference cases in your browser and shows, for each, what is checked, the independent reference, the computed value, the difference, the tolerance and PASS or FAIL. The same cases are run by the project’s automated tests.

• Eigenvalues, eigenvectors and invariants are compared with arbitrary-precision mpmath (40 digits) and a second numerical library.
• Cylinders, interference fits and discs are compared with a different formulation (the displacement equation with the boundary conditions solved as a linear system), also in mpmath.
• Rosettes are generated forward with the gauge equation and recovered; Hooke’s law is inverted through the Lamé constants.
• Closed forms, conserved invariants under rotation, force balances and limits (thin ring, thin wall, matching Mohr–Coulomb and Coulomb–Mohr lines) are checked, and hand derivations are written out beside each value.
• Published textbook examples are listed as pending source, with no numbers recorded, until a legitimate copy is supplied. They are never counted as passes.

Troubleshooting

Professional-use notice

Results are for education and preliminary design. They must be checked by a qualified professional, and they are not a substitute for code-compliant design or licensed engineering judgement.