Internal vs External Pressure
Why internal and external pressure produce fundamentally different structural responses — membrane tension versus compression and instability — and the implications for analysis method selection.
Technical provenance
Applicable standards / specifications
- ASME BPVC Section VIII Division 1 (2025) — Rules for Construction of Pressure Vessels
- ASME BPVC Section VIII Division 2 (2025) — Alternative Rules for Construction of Pressure Vessels
- EN 13445 — Unfired pressure vessels — Relevant European pressure-vessel code family where specified by the project.
References
- ASME Boiler and Pressure Vessel Code — 2025 edition — Primary code family reference for pressure-vessel design where ASME BPVC is the governing basis.
- Moss, D. R. & Basic, M. — Pressure Vessel Design Manual — Background engineering reference for pressure-vessel load paths, stresses and design checks.
Internal pressure — membrane tension
Internal pressure produces tensile membrane stresses in the vessel wall. In a cylinder, the hoop stress is tensile and the longitudinal stress is tensile. In a sphere, the membrane stress is biaxial tension. The failure mode under internal pressure is typically yielding, plastic collapse or burst — strength-governed failures where the material must carry the pressure-induced membrane forces. The structural response is generally stable: increasing pressure produces proportional stress until yielding begins.
External pressure — compression and instability
External pressure produces compressive membrane stresses in the vessel wall. In a cylinder, the hoop stress is compressive. The governing failure mode is typically buckling or collapse — a stability-governed failure where the shell loses stiffness and deforms inward at a stress well below the material yield strength. The structural response is fundamentally unstable: once the critical pressure is reached, the shell collapses with little additional load. This is why external pressure design cannot use the same approach as internal pressure design.
Different analysis approaches
For internal pressure, the design check is typically a stress check: the membrane stress must be below the material allowable. For external pressure, the design check is a stability check: the applied pressure must be below the critical buckling pressure with an adequate margin. The critical buckling pressure depends on geometry, imperfections, boundary conditions and material stiffness — not just the material yield strength. Linear eigenvalue analysis provides an upper bound; nonlinear analysis with imperfections provides a realistic prediction.
Pressure on both sides
When pressure acts on both sides of the wall, the structural response is governed by the pressure differential. A vessel with 5.0 MPa internal pressure and 3.0 MPa external pressure has the same membrane stress as a vessel with 2.0 MPa internal pressure and atmospheric external pressure — the differential is 2.0 MPa in both cases. However, the absolute pressure levels affect the radial stress boundary conditions and may influence seal behaviour and fluid properties.
Vacuum conditions
A vacuum vessel is a special case of external pressure where the internal pressure is reduced below the external atmospheric pressure. A full vacuum with atmospheric external pressure produces a differential pressure of approximately 0.1 MPa. While this seems small, it is sufficient to collapse thin-walled vessels that have not been designed for external pressure. Vacuum collapse is a common failure mode in vessels that are designed for internal pressure only and then subjected to vacuum conditions during operation or cleaning.
Subsea and hydrostatic loading
Subsea vessels and equipment experience external hydrostatic pressure that increases with depth. At 1000 m depth, the external pressure is approximately 10 MPa. The structural design is governed by external pressure buckling, material yield under compression, and potential implosion. The analysis must account for the external pressure, the vessel geometry, the material properties at the operating temperature, and the imperfection sensitivity of the shell.
A vessel designed for internal pressure is not automatically safe under external pressure. The failure modes are different: internal pressure causes yielding or burst; external pressure causes buckling or collapse. Always assess external pressure separately using stability-based methods.
Different physics, not just different signs
Internal and external pressure are not merely the same load with opposite sign. Internal pressure tends to stabilise a shell while generating tensile membrane stress. External pressure generates compressive membrane stress and can trigger buckling, where geometric imperfections, ovality and boundary conditions dominate the response. Reversing the pressure sign in a linear static model does not provide an adequate assessment of external-pressure collapse.
Internal pressure behaviour
For a regular closed vessel, internal pressure produces membrane tension that can often be predicted accurately from equilibrium. Local bending then appears near closures, nozzles, thickness transitions and supports. Yielding or fatigue may govern depending on the pressure level and cycle history. Because the global membrane state is stable, local stress assessment is often the main numerical challenge.
External pressure behaviour
Under external pressure or internal vacuum, the membrane state is compressive and the shell can lose stability. Critical pressure depends strongly on radius-to-thickness ratio, length, stiffener spacing, end restraint and initial imperfections. Linear eigenvalue buckling can identify likely modes, but realistic collapse capacity may require an imperfection-sensitive geometrically nonlinear analysis.
Pressure reversal and cyclic service
Some systems alternate between positive internal pressure and vacuum. The structure then experiences a reversal from tensile to compressive membrane action and may have different governing locations in each half-cycle. The fatigue range can include this reversal, while the vacuum condition must also be checked independently for stability.
Absolute pressure and cavitation are separate issues
Structural differential pressure is not the only reason absolute pressure matters. Low absolute pressure may also affect fluid behaviour, boiling or cavitation, which can generate dynamic loads not represented by the static differential alone. Those fluid phenomena should be treated as separate load-definition questions rather than hidden inside the structural sign convention.
Choose the analysis route from the failure mode
Use membrane and local stress methods for internal-pressure strength; use stability methods for external pressure; use fatigue methods for repeated reversals; and use transient analysis when pressure changes occur quickly enough to excite structural or fluid dynamics. Selecting the method from the physics is more reliable than selecting it from the load label.
Verification point: Use membrane and local stress methods for internal-pressure strength; use stability methods for external pressure; use fatigue methods for repeated reversals; and use transient analysis when pressure changes occur quickly enough to excite structural or fluid dynamics. Selecting the method from the physics is more reliable than selecting it from the load label.
Illustrative design consequence
Consider a thin cylindrical chamber designed comfortably for several bar of internal pressure. Its tensile membrane stress may remain well below yield, yet the same shell can be vulnerable to a fraction of that pressure applied externally because collapse is governed by slender-shell stability rather than material strength. This contrast is why vacuum cases should be identified during load-definition work rather than discovered after a strength model has been completed.