Fuselage Skin-Stringer Panel (vehicle-design/structures-integration/fuselage-skin-stringer)
Use when the task is sizing the pressurized fuselage skin-stringer
panel at the conceptual level: skin thickness from the hoop stress
with the 1.5 factor of safety, stringer spacing from the flat panel
buckling allowable, frame pitch from the stringer column buckling
length, and stringer area from the effective skin width.
Domain quick reference
- Thin-cylinder membrane stresses from the cabin differential
pressure p and radius r on a skin of thickness t:
hoop stress sigma_h = p * r / t and longitudinal stress
sigma_l = p * r / (2 * t). The hoop stress governs the pressure
skin.
- FAR-25.303 context: the factor of safety between limit and
ultimate loads is 1.5, so the pressure skin thickness is
t = p * r * 1.5 / sigma_allowable, floored by the minimum gauge
(typical transport minimum gauge about 1.0 to 1.2 mm).
- Flat panel buckling between stringers (compression):
sigma_cr = k * pi^2 * E * (t / b)^2 / (12 * (1 - nu^2)), with k
about 4.0 for a long plate with simply supported edges. Solving
for the spacing gives b = t * pi * sqrt(k * E / (12 * (1 - nu^2) *
sigma_cr)).
- Stringer column buckling between frames (Euler):
sigma_cr = pi^2 * E * I / (A * L^2), so the frame pitch is
L = pi * sqrt(E * I / (A * sigma_cr)).
- Effective skin width in compression:
b_eff = 1.9 * t * sqrt(E / sigma_allowable). The stringer area
follows from the strip load P on one stringer bay:
A = P / sigma_allowable - b_eff * t; the skin alone carries the
strip when this goes to zero or below.
- Units: pressure in Pa, stress in Pa, radius and thickness in m,
area in m^2, inertia in m^4, load in N, spacing and pitch in m.
Workflow
- Collect the cabin differential pressure, the fuselage radius, the
skin material allowable stress, the factor of safety (default
1.5), and the minimum gauge.
- Compute the hoop and longitudinal membrane stresses with
hoop_stress and longitudinal_stress.
- Derive the skin thickness with skin_thickness; the hoop stress
term governs under pressure and the minimum gauge floors the
result.
- Bound the stringer spacing with stringer_spacing from the skin
thickness, the modulus, and the panel buckling allowable.
- Set the frame pitch with frame_pitch from the stringer area and
inertia, the modulus, and the column buckling allowable.
- Size the stringer area with effective_skin_width and
stringer_area from the compression strip load.
- Check the sized panel: the hoop stress of the chosen skin must
stay below the allowable scaled by the factor of safety.
Pitfalls
- Using the longitudinal stress instead of the hoop stress for the
skin thickness: the hoop stress p * r / t is twice the
longitudinal stress and governs the pressure skin.
- Sizing at limit load without the 1.5 factor of safety: FAR-25.303
requires the structure to carry ultimate load, so scale the
pressure stress by 1.5 before comparing with the allowable.
- Forgetting the minimum gauge: manufacturing and corrosion practice
floor the skin well above the pure stress thickness on small
fuselages.
- Setting the frame pitch from the skin panel buckling length: the
frames stop the stringer column, not the skin panel, so the pitch
follows from the stringer Euler load, not the plate formula.
- Double counting the skin in the stringer area: the stringer only
carries the strip load beyond the effective skin width b_eff * t,
so subtract that term or the stringer comes out oversized.
- Mixing units: keep Pa, m, m^2, m^4, and N consistent; pressure in
bar instead of Pa shifts every result by six orders.
Behavior contract (gate 3)
The hoop and longitudinal stress, skin thickness, stringer spacing,
frame pitch, effective skin width, and stringer area logic is
exercised by the gate 3 contract test:
scripts/test_fuselage_skin_stringer.py against
scripts/fuselage_skin_stringer_logic.py (stdlib unittest, offline).
Run:
python3 scripts/test_fuselage_skin_stringer.py
Compliance
- Standards referenced, not reproduced: FAR-25 is US government work
(public domain) and CS-25 is a free EASA download; the membrane
stress, panel buckling, and column buckling formulas are common
aircraft structural analysis methodology, summary-only per
standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.
1---2name: fuselage-skin-stringer3description: Use when you must size a pressurized fuselage skin-stringer panel at the conceptual level: compute the hoop and longitudinal membrane stresses from the cabin differential pressure and the fuselage radius, derive the skin thickness from the governing hoop stress with the 1.5 factor of safety and the minimum gauge, bound the stringer spacing from the flat panel buckling allowable, set the frame pitch from the stringer column buckling length between frames, and size the stringer area from the compression strip load with the effective skin width. Produces the skin thickness, stringer spacing, frame pitch, and stringer area that gate the fuselage structure integration. Trigger: fuselage skin stringer, pressurized fuselage, hoop stress, stringer spacing, frame pitch, panel buckling.4license: Apache-2.05---67# Fuselage Skin-Stringer Panel (vehicle-design/structures-integration/fuselage-skin-stringer)89Use when the task is sizing the pressurized fuselage skin-stringer10panel at the conceptual level: skin thickness from the hoop stress11with the 1.5 factor of safety, stringer spacing from the flat panel12buckling allowable, frame pitch from the stringer column buckling13length, and stringer area from the effective skin width.1415## Domain quick reference1617- Thin-cylinder membrane stresses from the cabin differential18 pressure p and radius r on a skin of thickness t:19 hoop stress sigma_h = p * r / t and longitudinal stress20 sigma_l = p * r / (2 * t). The hoop stress governs the pressure21 skin.22- FAR-25.303 context: the factor of safety between limit and23 ultimate loads is 1.5, so the pressure skin thickness is24 t = p * r * 1.5 / sigma_allowable, floored by the minimum gauge25 (typical transport minimum gauge about 1.0 to 1.2 mm).26- Flat panel buckling between stringers (compression):27 sigma_cr = k * pi^2 * E * (t / b)^2 / (12 * (1 - nu^2)), with k28 about 4.0 for a long plate with simply supported edges. Solving29 for the spacing gives b = t * pi * sqrt(k * E / (12 * (1 - nu^2) *30 sigma_cr)).31- Stringer column buckling between frames (Euler):32 sigma_cr = pi^2 * E * I / (A * L^2), so the frame pitch is33 L = pi * sqrt(E * I / (A * sigma_cr)).34- Effective skin width in compression:35 b_eff = 1.9 * t * sqrt(E / sigma_allowable). The stringer area36 follows from the strip load P on one stringer bay:37 A = P / sigma_allowable - b_eff * t; the skin alone carries the38 strip when this goes to zero or below.39- Units: pressure in Pa, stress in Pa, radius and thickness in m,40 area in m^2, inertia in m^4, load in N, spacing and pitch in m.4142## Workflow43441. Collect the cabin differential pressure, the fuselage radius, the45 skin material allowable stress, the factor of safety (default46 1.5), and the minimum gauge.472. Compute the hoop and longitudinal membrane stresses with48 hoop_stress and longitudinal_stress.493. Derive the skin thickness with skin_thickness; the hoop stress50 term governs under pressure and the minimum gauge floors the51 result.524. Bound the stringer spacing with stringer_spacing from the skin53 thickness, the modulus, and the panel buckling allowable.545. Set the frame pitch with frame_pitch from the stringer area and55 inertia, the modulus, and the column buckling allowable.566. Size the stringer area with effective_skin_width and57 stringer_area from the compression strip load.587. Check the sized panel: the hoop stress of the chosen skin must59 stay below the allowable scaled by the factor of safety.6061## Pitfalls6263- Using the longitudinal stress instead of the hoop stress for the64 skin thickness: the hoop stress p * r / t is twice the65 longitudinal stress and governs the pressure skin.66- Sizing at limit load without the 1.5 factor of safety: FAR-25.30367 requires the structure to carry ultimate load, so scale the68 pressure stress by 1.5 before comparing with the allowable.69- Forgetting the minimum gauge: manufacturing and corrosion practice70 floor the skin well above the pure stress thickness on small71 fuselages.72- Setting the frame pitch from the skin panel buckling length: the73 frames stop the stringer column, not the skin panel, so the pitch74 follows from the stringer Euler load, not the plate formula.75- Double counting the skin in the stringer area: the stringer only76 carries the strip load beyond the effective skin width b_eff * t,77 so subtract that term or the stringer comes out oversized.78- Mixing units: keep Pa, m, m^2, m^4, and N consistent; pressure in79 bar instead of Pa shifts every result by six orders.8081## Behavior contract (gate 3)8283The hoop and longitudinal stress, skin thickness, stringer spacing,84frame pitch, effective skin width, and stringer area logic is85exercised by the gate 3 contract test:86scripts/test_fuselage_skin_stringer.py against87scripts/fuselage_skin_stringer_logic.py (stdlib unittest, offline).88Run:89python3 scripts/test_fuselage_skin_stringer.py9091## Compliance9293- Standards referenced, not reproduced: FAR-25 is US government work94 (public domain) and CS-25 is a free EASA download; the membrane95 stress, panel buckling, and column buckling formulas are common96 aircraft structural analysis methodology, summary-only per97 standards-map.yaml.98- compliance: STANDARDS-REF, gated: false.
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