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Pressurized cabin of a transport fuselage: 14 CFR 25.365 design pressures, skin loads and the frame share by Flügge's shell-ring interaction
| Tool | Pressurization Loads |
| Source | Flügge, W. (1952). Stress Problems in Pressurized Cabins. NACA Technical Note 2612, National Advisory Committee for Aeronautics, Washington, DC. Equations (1), (10) to (14) and (18a) to (18b); Federal Aviation Administration (2016). 14 CFR Part 25, Sections 25.303, 25.365 and 25.841; U.S. Standard Atmosphere, 1976, Table IV. |
| Level | Professional |
Problem
A circular cabin of 74 in radius with 0.040 in skin and 0.30 in² frames at 20 in flies at 41,000 ft with the cabin at 8,000 ft; the relief valves are set to 8.6 lb/in². Find the operating differential by the standard atmosphere, the limit and ultimate design pressures of 14 CFR 25.365, the skin hoop and longitudinal stresses, the frame hoop load by the interaction between shell and rings of NACA TN 2612, the hemispherical bulkhead stress, the loads a 34 × 72 in door throws onto its edge frames, and the margins against F_tu 60 ksi / F_ty 40 ksi.
Inputs to Enter
- Cabin altitude 8,000 ft, flight altitude 41,000 ft, relief-valve setting 8.6 lb/in², factor of safety 1.5, no external suction
- Circular section r = 74 in, skin 0.040 in, E 10.5 Msi, ν 0.33; frames 0.30 in² at 20 in, no stringer data; hemispherical bulkhead R_b = 74 in, 0.040 in
- Door 34 × 72 in with 0.60 in² edge frames; F_tu 60 ksi, F_ty 40 ksi; 60,000 design flights
Answers
- Standard atmosphere: 752.71 mb at 8,000 ft and 179.43 mb at 41,000 ft (Table IV), differential Δp = 10.917 − 2.602 = 8.315 lb/in²
- 25.365(d) factor 1.33 (to 45,000 ft): limit pressure 1.33 × 8.6 = 11.44 lb/in², ultimate 1.5 × 1.33 × 8.6 = 17.16 lb/in² (the pressure part of the combined case (a) is 12.9 lb/in²)
- Skin at ultimate: N_θ = p r = 1,270 lb/in, σ_θ = 31.74 ksi, σ_x = 15.87 ksi; operating hoop stress 15.38 ksi, one cycle per flight at R = 0
- Frame (TN 2612 eq. 14): β = 0.7432 /in, βl/2 = 7.43, T = 14.19 lb/in, N_R = 2 T r = 2,100 lb (8.3 % of p r l = 25,400 lb; rigid-ring bound 2,854 lb), σ_R = 7.00 ksi; skin hoop at the frame 12.24 ksi, bending at the frame 35.8 ksi, hoop overshoot 2.7 % between frames
- Hemisphere N = p R/2 = 634.8 lb/in, 15.87 ksi, no radial kick; door: stop load 291.7 lb/in per edge, intercepted hoop 21,580 lb to each edge frame, edge frame 39.47 ksi
- Margins: skin +0.89 (ULT) and +0.89 (LIM yield), frame +7.57, bulkhead +2.78, edge frame +0.52
Notes
The tool's default inputs are this cabin; press Submit. TN 2612 gives the method, not this example; the numbers are the tool's own, checked against an independent numpy solution of the bay equation (test_pressurization_loads.php, 241 checks). The same model with the stringers of the NACA TN 993 Lockheed test section gives a frame stress of 5,404 psi against that report's 5,490 psi.