Composite Tube and Cylinder Analysis

Membrane stresses, torsional stiffness, and buckling with NASA SP-8007 knock-down factors for thin-walled composite cylinders.

A thin-walled composite cylinder is a tube or shell whose wall is a laminate, carrying pressure, axial load, torsion, or bending through membrane stresses in the wall. The cylinder tool analyses such a cylinder for stresses, torsional properties, and buckling under five load cases, using thin-wall membrane theory¹ with the laminate's effective moduli from CLT engineering constants.

Cylinders are where composites earn their keep: a filament wound or wrapped tube puts fibres exactly where the load runs, hoop plies against pressure, ±45° plies against torsion, axial plies against bending. The same geometry is also where buckling theory is at its least forgiving, which is why this tool never reports a classical buckling value without an empirical knock-down.

When to use this tool

Use the cylinder tool for drive shafts, masts and booms, pressure piping, tanks, launch and rocket body tubes, and any filament wound or roll-wrapped tube. It sizes the wall for membrane stress, gives the torsional stiffness a shaft design needs, and answers the question that dominates thin shells in compression: at what load does the wall buckle, after real-world imperfections are accounted for.

The membrane stresses can be taken straight to the First Ply Failure tool as applied loads for a strength check, since the cylinder tool itself works with stiffness data only. For non-circular sections or thick walls, this model does not apply; the tool flags a radius-to-thickness ratio below 10, where thin-shell assumptions become questionable.

As with all the structural tools, the intent is preliminary sizing and trade studies. Pressure equipment that falls under a design code (ASME, EN 13121, DNV) still needs the code's own analysis route and factors; this tool gets the wall thickness and layup into the right neighbourhood before that work starts, and shows which physics will govern once it does.

Inputs

• Mean radius (r) and length (L) of the cylinder. The laminate provides the wall thickness (h).
• Load case: Internal pressure, External pressure, Axial compression, Torsion, or Bending (3-point).
• Load magnitude: pressure (MPa), axial force (N), torque (N·mm), or transverse load (N), depending on the load case.

What each load case computes

Key formulas

• σ_θ - Hoop stress: Circumferential membrane stress (MPa) from pressure p, positive for internal pressure, negative for external. Twice the axial value, which is why hoop plies dominate pressure vessel layups.
• σ_z - Axial stress: Longitudinal membrane stress (MPa) in a closed pressurised cylinder, half the hoop value.
• GJ - Torsional stiffness: Resistance to twist (N·mm²), using the laminate's in-plane shear modulus G_xy. The twist rate follows as dφ/dz = T/GJ (rad/mm) for applied torque T. Adding ±45° plies is what raises G_xy, and with it GJ.
• N_cr - Classical axial buckling: Classical (Donnell) axial buckling line load (N/mm), using the laminate's effective membrane modulus E_x. Dividing by the wall thickness h gives the classical buckling stress - a bifurcation value real shells never reach, hence the knock-down below.
• γ - NASA SP-8007 knock-down: Empirical reduction factor for geometric imperfections². The design buckling stress is γ times the classical one. Typical values run 0.3 to 0.7: thinner shells (larger r/h) are punished harder.

Matching the layup to the load case

The load case table above is also a layup guide, because each case reads a different laminate property. Pressure loading produces a 2:1 hoop-to-axial stress ratio, which is why classical netting analysis puts filament winding angles near ±55° for pipes and why hoop-dominated layups rule pressure vessels. Torsion reads only G_xy, so a shaft that twists too much needs ±45° plies, not more axial ones. Axial compression and bending read E_x twice: once in the stress the load produces and once in the buckling capacity, so 0°-dominated layups win there on both counts.

Because the tool recomputes the effective constants from the laminate every time, this trade-off is directly explorable: change the winding angle in the laminate builder, and watch the hoop margin, the twist rate, and the buckling value move against each other. A layup that is optimal for one load case is usually mediocre for the others, and seeing all the numbers from one laminate is what makes the compromise explicit.

One caveat applies across all cases: the analysis works with smeared laminate properties and membrane theory, so it does not resolve ply-by-ply stresses around the circumference or capture layup asymmetry effects (B ≠ 0) such as a wound tube's tendency to twist under pressure. For ply-level detail, feed the membrane stresses into the ply stress and failure tools.

Why the knock-down factor is not optional

Classical cylinder buckling theory overestimates capacity by 2 to 5 times. A cylindrical shell in axial compression is the most imperfection-sensitive structure in common use: a wall out-of-roundness of a fraction of the thickness is enough to trigger buckling far below the classical load, and no practical manufacturing process avoids imperfections at that scale. The NASA SP-8007 factor² is the standard empirical lower bound built from decades of test data, and the tool applies it to the axial compression and bending load cases.

External pressure buckling is less imperfection-sensitive than axial compression, so the SP-8007 axial factor would be overly conservative there; the tool uses a fixed γ = 0.75 instead⁴. In the results, the classical bifurcation value, the knock-down factor, and the design value are shown separately, so the design number is traceable rather than a black box.

The cylinder tool under external pressure. The classical bifurcation value and the knock-down factor are shown separately, so the design value is traceable rather than a black box.

Author: Rick Schrijver

References

1. Barbero, E.J. (2018). Introduction to Composite Materials Design, 3rd ed. CRC Press. Chapter 8. (Thin-walled composite cylinders and shells) doi:10.1201/9781315296494
2. NASA. (1968). Buckling of Thin-Walled Circular Cylinders. NASA Space Vehicle Design Criteria (Structure), NASA SP-8007. ntrs.nasa.gov
3. Jones, R.M. (1999). Mechanics of Composite Materials, 2nd ed. Taylor & Francis. Chapter 8. ISBN: 978-1560327127. (Laminated shells)
4. Bushnell, D. (1981). Buckling of shells - pitfall for designers. AIAA Journal, 19(9), 1183-1226. (Imperfection sensitivity by load case; basis for the external pressure factor) doi:10.2514/3.60058

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