Seastead Leg Side-Load Capacity — ½″ Marine Aluminum Foil Legs

First permanent bending (yield)

≈120,000 lbf

per leg · ≈14,000 lb/ft over the 8.5 ft wetted span

Collapse / fracture (“break”)

≈210,000–290,000 lbf

per leg · ≈25,000–34,000 lb/ft

Wave height to reach yield

≈80–150 ft

individual wave height, period 6–12 s

Wave height to break a leg

≈110–230 ft

beyond any reliably recorded ocean wave

Bottom line: the ½″-wall legs are enormously strong in side bending. A single leg begins to take a permanent set at roughly 120,000 lbf of side load spread evenly over its wetted length, and it will not tear apart until roughly 210,000–290,000 lbf. Wave drag on an 8.5 ft chord cannot build that kind of force until individual wave heights reach roughly 80–150 ft (damage) to 110–230 ft (fracture) depending on period — taller than any wave ever reliably instrumented at sea.

Design implication: side-load fracture of the legs is not your governing failure mode. Long before a leg snaps, you would lose the root welds / frame corners, see local plate buckling if internal framing is too widely spaced, suffer breaking-wave slam damage to the plating, or simply capsize or fail the mooring hardware. Engineer those instead (§5–6).

1. What was analyzed — assumptions

Structure modeled: one leg as a vertical cantilever, fixed at the underside of the triangle frame near a corner, free at the bottom tip. Side load applied as a uniform (evenly distributed) lateral pressure over the wetted span, since that is where water acts.
Material: marine aluminum 5083‑H116 plate: yield 33 ksi (228 MPa), ultimate 46 ksi (317 MPa), E = 10.3×10⁶ psi. At the root weld the heat-affected zone knocks yield down to ≈24 ksi (165 MPa) — this governs first yield.
Loading: quasi-static. Dynamic amplification, slamming, and platform motions are treated separately as corrections (§4–5).
Results are per leg. Each leg fails independently at the same load, so even if all three legs are loaded simultaneously, the per-leg numbers stand.

Geometry reconciliation (please confirm): your description gives the leg as 21.5 ft long but also states submergence as “0.5 × 14.5 ft.” Your 27,500 lbf buoyancy figure is almost exactly consistent with ≈8.5 ft submerged (3 legs × 17.3 ft² foil area × 8.5 ft × 64 lb/ft³ ≈ 28,000 lbf). The baseline below therefore assumes a 21.5 ft leg with its top ~7 ft built into the frame, 14.5 ft exposed, 8.5 ft submerged. Variants for other readings are tabulated in §3 — the conclusions do not change materially.

Consistency checks on your numbers: buoyancy ≈ 28,000 lbf vs. your 27,500 lbf ✓. Waterplane area 3 × 17.3 ft² ≈ 52 ft² → 1 ft of water-level change ≈ 3,300 lbf ≈ 1/8 of displacement — close to your stated 1/7 ✓.

2. Leg cross-section properties (½″ wall, NACA 0035, 8.5 ft chord)

For thin-walled bending about the fore-aft (chord-parallel) axis — the axis a sideways load bends about:

I = 2 t ∫ y² ds → numerical integration of the NACA 0035 profile

Property	Value	Notes
Chord c	102 in (8.5 ft)	fore-aft
Max half-thickness y_max	17.85 in	35% of chord
Skin thickness t	0.5 in	marine aluminum
Wall cross-section area A	≈105 in²	perimeter ≈210 in × 0.5 in
Moment of inertia I (side-load axis)	≈18,600 in⁴	strong axis
Elastic section modulus S = I/y_max	≈1,040 in³
Plastic modulus Z	≈1,310 in³	shape factor ≈1.25
Gyration radius r	≈13.3 in	L/r ≈ 19 → column buckling a non-issue
Shell weight	≈122 lb/ft → ≈2,600 lb/leg	before stiffeners, ladder, plates

Foil section used for the property integrals (drawing to scale from the NACA thickness equation; wall thickness exaggerated for visibility).

Footnote: a head-sea (fore-aft) load bends about the weak axis, I ≈ 341,000 in⁴ — about 18× stronger — so forward/backward drag is even less of a concern than side load.

3. How much evenly distributed side force breaks a leg

Treating the leg as a cantilever with the load resultant acting ≈17.25 ft below the root (uniform load over the 8.5 ft wetted span of a 21.5 ft leg):

M_root = F × 17.25 ft = F × 207 in σ = M·c / I

Limit state	Stress basis	Root moment (lb·in)	Total side force F (lbf)	Uniform w over wetted 8.5 ft (lb/ft)
First yield — weld HAZ (permanent bending begins)	24,000 psi × S	25.0 × 10⁶	≈121,000	≈14,200
First yield — base metal	33,000 psi × S	34.4 × 10⁶	≈166,000	≈19,600
Full plastic hinge (base metal)	33,000 psi × Z	43.1 × 10⁼	≈208,000	≈24,500
Fracture / collapse estimate	0.85 × 46,000 psi × Z	51.1 × 10⁼	≈247,000	≈29,000
Absolute upper bound	46,000 psi × Z	60.1 × 10⁼	≈290,000	≈34,200

Answer: evenly distributed side load of about 14,000 lb/ft (120 kips total) starts to permanently bend a leg; about 25,000–34,000 lb/ft (210–290 kips total) breaks it.

Variants (other readings of your geometry)

Geometry variant	Yield (welded)	Plastic hinge	Fracture est.
A — Baseline: 21.5 ft leg, 8.5 ft wetted (used above)	121 kip	208 kip	247 kip
B — Same leg but load spread over the full 21.5 ft (incl. part in air)	194 kip	334 kip	396 kip
C — Leg is really 14.5 ft total, 7.25 ft wetted	192 kip	330 kip	392 kip

All variants land in the same place: hundreds of thousands of pounds of evenly distributed side force per leg.

Secondary checks (all pass comfortably)

Root shear: τ ≈ 0.035×F → only ≈8.7 ksi at the 247-kip fracture load vs. ≈14 ksi allowable. Not governing.
Column buckling of the leg: L/r ≈ 19 — far too stocky to buckle axially.
Heel-induced lateral load: at a 20° heel the leeward leg’s buoyancy (≈12,900 lbf) contributes only ≈4,400 lbf of sideways component — under 4% of yield load.
3-kt current: ≈2,200 lbf total per leg. Negligible.

Local plate buckling — the one real caveat in the skin itself. The compression skin can buckle between internal frames before the material yields. Flat-panel estimate σ_cr = 37.2×10⁶(t/b)² psi:

Transverse frame spacing b	12 in	16 in	20 in	24 in
Buckling stress	65 ksi ✓	36 ksi ✓	23 ksi ⚠	16 ksi ✗

Keep transverse frames ≤16 in on center (12 in is better) in the lower half of each leg, or add longitudinal stringers. Curvature of the foil helps you everywhere except mid-chord, which behaves like a flat panel.

4. What wave height produces that much force?

Model the side load as drag from wave orbital velocities on the submerged foil, treated broadside (projected width = the 8.5 ft chord, C_d ≈ 1.2 for a broadside foil of this aspect ratio). Deep-water Airy wave: particle velocity u(z) = (πH/T)·e^−kz:

F = ½ ρ C_d c (πH/T)² · (1 − e^−2kh)/(2k) λ = gT²/2π, k = 2π/λ

With ρ = 1.99 slug/ft³, c = 8.5 ft, h = 8.5 ft: F ≈ K_T·H² (lbf, H in ft):

Wave period T	Wavelength	K_T (lbf per ft²)	H at yield (121 kip)	H at plastic (208 kip)	H at fracture (247 kip)
6 s (steep, short)	184 ft	17.9	≈82 ft	≈108 ft	≈118 ft
8 s	328 ft	11.4	≈103 ft	≈135 ft	≈148 ft
10 s	512 ft	7.7	≈125 ft	≈165 ft	≈180 ft
12 s (long swell)	738 ft	5.5	≈148 ft	≈194 ft	≈212 ft

H is the individual trough-to-crest height of a regular wave. For irregular seas, compare against H_max ≈ 1.8–2.0 × significant wave height. Allowing a 1.5× dynamic amplification (platform surge/roll adding to orbital velocity) lowers these thresholds by only ≈20% — e.g., fracture at T = 8 s drops from 148 ft to ≈121 ft.

Context — how big is that?

Sea state	Typical individual max wave
Caribbean trade-wind seas	4–10 ft
Winter North Atlantic gale	30–50 ft
Hurricane core	50–90 ft
Largest waves ever reliably instrumented (rogue records)	≈85–95 ft
Needed to yield the legs	≈80–150 ft
Needed to break a leg	≈110–230 ft

Worked examples (reassurance)

30-ft wave, 10-s period: F ≈ 6,900 lbf → root bending stress ≈ 1.4 ksi — about 6% of welded yield, 3% of ultimate. Also low enough that weld fatigue is a non-issue.
60-ft wave, 10-s period: F ≈ 27,700 lbf → ≈5.5 ksi. Still under 25% of welded yield.
80-ft wave, 8-s period (near record territory): F ≈ 72,700 lbf → ≈14.4 ksi — approaching welded yield for the first time.

5. What would actually fail first (ranked)

The root joint and frame corner — not the leg. The numbers above assume the frame can react a 25–51×10⁼ lb·in moment at each corner. A nominal 10-in-deep frame wall cannot come close; the corner must be heavily reinforced with gussets and doubler plates, or it becomes the structural fuse. This is the item to engineer hardest.
Local skin buckling if frame spacing exceeds ~16–20 in (§3 table).
Breaking-wave slam. A 16-in unstiffened panel begins to yield locally at ≈80 psi impact pressure (a 12-in bay tolerates ≈145 psi). Violent breaking crests can briefly reach that order — expect possible local denting near the waterline in extreme breakers, but not global failure.
Capsize / mooring hardware. Stability limits and the helical tension-leg screws, shackles, and lines will be overwhelmed in seas far smaller than those needed to hurt the legs.
Appurtenances: walkway brackets, railings, doors, thruster mounts, and the trailing-edge conduit — design these to shed or sacrifice before the primary structure.
Weld fatigue: at realistic sea states root stresses stay ≲1.5 ksi, comfortably below aluminum welded-joint fatigue limits.

6. Recommendations

Detail each leg-to-frame corner to develop at least the leg’s plastic moment (43×10⁼ lb·in) — full-penetration welds, 5356 filler, AWS D3.5 practice, corner gussets and doubler plates — or consciously design a sacrificial fuse and document it.
Transverse frames ≤16 in o.c. in the lower half of each leg; consider ⅝-in plating over the bottom 8–10 ft for slam resistance.
Verify as-welded properties with test coupons; the 24-ksi HAZ yield drives the first-yield number.
Run an FE model of the frame corner: the leg calculation is only as good as the assumed rigid root.
Set operational sea-state limits by stability, mooring, and crew comfort — they will bind decades before leg strength does.
If container weight gets tight, a ⅜-in wall still delivers ≈75% of these capacities (≈90,000 lbf at yield) — still far beyond any wave demand.

Appendix — formulas and constants used

Section: I = 2t∫y²ds ≈ 18,600 in⁴; S = I/y_max ≈ 1,040 in³; Z ≈ 1,310 in³; A = perimeter×t ≈ 105 in².
Cantilever: M = F·arm (arm = 207 in baseline); σ = Mc/I; first yield at σ = F_ty; plastic hinge at M = F_tyZ; fracture estimated at 0.85·F_tuZ.
Plate buckling: σ_cr = kπ²E/[12(1−ν²)]·(t/b)², k = 4, E = 10.3×10⁶ psi, ν = 0.33.
Wave drag: F = ½ρC_dc(πH/T)²(1−e^−2kh)/(2k); ρ = 1.99 slug/ft³, C_d = 1.2, c = 8.5 ft, h = 8.5 ft; λ = gT²/2π.
Material: 5083-H116 — F_ty = 33 ksi, F_tu = 46 ksi, welded HAZ F_ty ≈ 24 ksi, weight density 168 lb/ft³.
1 kip = 1,000 lbf. Key SI: 121 kip ≈ 538 kN; 247 kip ≈ 1,099 kN; 33 ksi ≈ 228 MPa; 46 ksi ≈ 317 MPa.