Cylindrical Shells (`shells`)

Cylindrical Shells

Thin-shell hoop, axial and bending stress screening

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Indicative closed-form or numerical model

Assumptions

Linear elastic material behavior unless noted otherwise.
User is responsible for load combinations and load factors per the selected design code.
Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

Check	IND	US	EU	ISO
Hoop stress	implemented	—	—	—
von Mises stress	implemented	—	—	—
Stress safety factor	implemented	—	—	—

Purpose

Screen thin cylindrical shells under internal pressure, axial force and bending moment using membrane theory plus von Mises combined stress.

Physics & theory

For a thin cylinder of mean radius $r$ and wall thickness $t$ , hoop stress from internal pressure is $σ_{h} = p r / t$ . Closed ends add axial membrane stress $σ_{a} = p r / (2 t)$ . External axial load and bending add further normal stress. von Mises equivalent stress combines hoop, axial and bending components for yield screening.

Governing equations

σ_{h} = \frac{p r}{t}, σ_{a, membrane} = \frac{p r}{2 t} (closed ends)

σ_{v m} = σ_{x}^{2} - σ_{x} σ_{y} + σ_{y}^{2}

Numerical method

Closed-form membrane and simplified beam bending deflection estimate via solveShellEngine.

Inputs

Parameter	Description
`radius`, `thickness`, `length`	Shell geometry
`internalPressure`, `axialForce`, `bendingMoment`	Loads
`endCondition`	Open or closed ends
`allowableStress`	Design allowable

Outputs

Hoop, axial, bending and von Mises stress; safety factor; indicative deflection; status message.

Design codes & checks

Indicative: Membrane + von Mises screening
US/EU: ASME BPVC / EN 13445 context (screening only)

Assumptions & limitations

Thin-shell theory ( $t / r < 0.1$ ); no nozzle, knuckle or buckling under external pressure.
User supplies load combinations and factors.

References

Roark, R. J., & Young, W. C. Formulas for Stress and Strain, Ch. 7.
ASME BPVC Section VIII — pressure vessel design context.

Maintainer note: Thin cylindrical shell membrane + bending screening.

Cylindrical Shells

Assumptions

Limitations

Engineering checks

Cylindrical Shells (shells)

Cylindrical Shells (`shells`)