Bolted Legs Without Cables — Structural Feasibility Study

Trimaran-wing seastead · 44 ft equilateral frame · NACA 0035 legs · joint stress analysis, frame sizing, and cable vs. no-cable trade study

Rev A — Preliminary / Scoping Level Units: kip = 1,000 lbf Material basis: Duplex 2205 (σ_y = 65 ksi) Displacement: 27,500 lb

1 · Executive Verdict

Can the legs be simply bolted on?

YES

The 8.5-ft-chord foil legs have enormous bending stiffness. Even the worst credible storm and accidental loads stress the leg shell to under ~11 ksi against a 65 ksi yield — a margin of 6× or more.

Governing element

The corner nodes

The leg shell is never the weak link. The design effort belongs in the corner node castings/fabrications and the slip-critical bolted flange. Both are conventional, well-understood steelwork.

Cables required?

NO — optional

Cables would add stiffness and redundancy but are not needed for strength. They add ~$2–12k capex, ongoing tensioning/inspection, and possible strum noise. Go cable-free; weld in retrofit lugs as insurance.

Bottom line A fully bolted, cable-free structure works for this mission profile (Caribbean, protected waters, tension-leg parking). The feared "long lever" effect is real as a moment, but the foil's giant section modulus crushes the resulting stress. Size the corner nodes for ~150 kip-ft working / 250 kip-ft ultimate, use 20–24 slip-critical 1″ duplex bolts per leg, and add sacrificial fuse bolts for collision survivability.

2 · Basis of Analysis & Assumptions

You specified the geometry precisely; the environmental criteria were not specified, so the following design environment was assumed. If your survival criterion is harsher (e.g., open-ocean hurricane), the loads scale roughly with the square of velocity and must be rerun — see §11.

Parameter	Value used	Source
Displacement Δ	27,500 lb (854 slugs)	Your rating
Seawater density γ	64 pcf	Standard
Leg foil	NACA 0035, chord 8.5 ft, max thickness 2.98 ft, span 21.5 ft, height 14.5 ft (7.25 ft draft)	Your spec
Foil section area	≈ 17.2 ft² (0.68 × t × c)	Computed
Leg shell skin	3/16 in duplex, internal frames @ 12–18 in	Assumed (see §5)
Operating environment	15 kt wind, 3-ft seas, 5 kt cruise	Assumed
Survival environment (parked on tethers)	70 kt gusting wind, H_s = 15 ft, T ≈ 9–11 s	Assumed
Tension-leg pull-down	3 ft → +9.9 kip buoyancy, ≈ 3.3 kip static tension per tether	Your spec
Allowable stresses	30 ksi extreme (≈ 0.46 σ_y); weld details checked for fatigue separately	Practice
Bolts	Duplex A4-90, 1″ dia., slip-critical (Class B faying, μ ≈ 0.45–0.5)	Assumed

Honesty note This is a scoping-level hand analysis intended to answer "is it crazy?" — it is not a substitute for finite-element analysis, classification review, and a strain-gauged prototype load test. All conclusions below have comfortable margins, which is exactly why they are robust to the assumptions.

3 · Mass & Buoyancy Check

3.1 Does the geometry close?

Item	Value	Note
Submerged volume per leg (17.2 ft² × 7.25 ft)	125 ft³	≈ 7,980 lb per leg
Three legs, bare foil	23,940 lb	—
+ heave plates, conduit, thruster pods, appendages	+3,560 lb	Scales to your 27,500 lb rating ✓
Waterplane area (3 foils)	≈ 52 ft²	3,300 lb per ft of level change
Buoyancy change per 1 ft of water level	12% of Δ	You quoted 1/7 (14%) — you're in the right range; heave-plate edges close the gap
Static buoyancy share per leg	9.2 kip	27,500 ÷ 3

3.2 Preliminary mass budget — a caution flag

Building up the full weight from component estimates, the design comes out heavy against the 27,500 lb rating. This is independent of the cable question, but you should see it:

Group	Est. weight (lb)
Legs (3 × ~2,300: shell, frames, 4 airtight bulkheads, flange, ladder, conduit)	6,900
Frame, walls, floor, ceiling, corner nodes	9,800
Walkway, railing, ladders (aluminum)	1,400
Heave plates, thruster mounts, conduit	1,100
6 rim-driven thrusters	700
Batteries (25% of Δ, LFP ≈ 340 kWh)	6,875
Solar array + racks + charge controllers	900
Wiring, plumbing, electronics	1,100
Interior fitout (berths, galley, head)	1,600
Dinghy + HARMO outboard	700
Safety gear, misc.	500
Total estimate	≈ 31,600
Your rating	27,500
Gap	≈ −4,100

Lightweighting paths to close the ~4,100 lb gap

Interior fitout in aluminum/composite modules rather than steel-framed: save 600–900 lb
Leg skin 1/8 in with 8-in frame spacing (hydrostatics still fine at 7.25 ft draft): save ~900 lb
Wall studs and secondary framing downsized one gauge; walkway grating already aluminum: save 500–700 lb
Battery pack at 20% of Δ instead of 25% (still ~270 kWh): save 1,375 lb
Trim solar rack and wiring (structural cable routes in the trailing-edge conduit only): save 300 lb

Executed together, these bring the estimate to ≈ 27,000–28,500 lb. Tight but closable.

4 · Load Cases on a Leg

All demands below are per leg, at the top joint (the flange plane at +7.25 ft, i.e., the underside of the floor). "Shear" is horizontal force; "M" is bending moment at the joint; "Axial" is vertical force (compression positive).

Figure 1 — Leg as a cantilever off the frame corner. The lever arm is real, but so is the section modulus.

Load case	Axial (kip)	Shear (kip)	Moment M_joint (kip-ft)	Notes
LC1 — Transit: 5 kt, 15 kt wind, 3-ft seas	9.2 ± 1.5	0.6	≈ 2	Thrust ≈ 0.1 kip/leg at 12.5 ft below joint; tiny
LC2 — Parked on tethers: 25 kt, 6-ft seas	12.4 ± 3	1.2	≈ 6	Incl. 3.3 kip static tether tension
LC3 — Survival: 70 kt gusts, H_s 15 ft, on tethers	+19 / −10	4.1	60 (design)	Wind 9.4 kip on house ÷ 3 legs; wave dynamics; tether snap to ~10 kip; uplift case in troughs
LC4 — Accidental: collision/grounding, 40 kip at 3 ft below WL	—	40	≈ 410	Fuse bolts recommended (§6.4)
LC5 — Heave-plate slam (survival sea)	—	12 (impulsive)	≈ 66 into shell	Spread by internal ring girder; fatigue-governed

Derivations: storm wind q = 0.00256 V² ≈ 24.6 psf × ~380 ft² of house/walkway area = 9.4 kip at ≈ +11 ft → heel moment 103 kip-ft, reacted as vertical couples at the legs (only ±2.9 kip of buoyancy shift — trivial) and horizontal shear of 3.1 kip per leg. Wave horizontal load per leg (Morison, H_s 15 ft, T = 10 s, beam-sea projected width ≈ 1.8 ft avg) ≈ 0.9–1.0 kip with centroid ≈ 10.9 ft below the joint. Spanning buoyancy imbalance between legs in a 15-ft sea is bounded quasi-statically at ~500 kip-ft of hull-girder moment but the platform largely follows waves of this period; §7 uses a design value of 200–250 kip-ft.

5 · Leg Cantilever Capacity — Why the "Long Lever" Fear Doesn't Materialize

A lever multiplies force into moment. Whether that moment is dangerous depends on the section modulus resisting it. Your legs are not slender tubes — they are 8.5-ft-chord airfoils. Even a thin skin on that shape is a monster beam.

5.1 Section properties (3/16 in duplex skin, thin-ring theory)

Property	Athwartship bending (weak axis)	Fore-aft bending (strong axis)
Shell cross-sectional area	0.30 ft² (43.8 in²)
Moment of inertia I	0.39 ft⁴	≈ 1.7 ft⁴
Section modulus Z	455 in³	≈ 690 in³

5.2 Bending stress check: σ = M / Z

Case	M (kip-ft)	σ (psi)	Utilization vs 30 ksi
LC3 survival design moment	60	1,580	5%
Hull-girder-scale hypothetical (250 kip-ft)	250	6,600	22%
LC4 collision, no fuse	410	10,800	36%

Punchline The leg shell never gets remotely close to yield — not in the survival storm, not even hit by a boat. Axial stress (battery + tether loads) is ~280 psi; shear ~460 psi; global Euler buckling capacity is orders of magnitude above the load; local panel buckling is controlled by ordinary 12–18 in internal framing. The leg is not the problem. The joint detailing and the frame are the design work — and both are conventional.

Hydrostatic check: 3.2 psi at 7.25 ft draft requires frame spacing ≈ 12 in at 3/16 in skin, or ≈ 8 in at 1/8 in — normal shipyard practice, already reflected in the mass budget.

6 · The Bolted Joint — Demand vs. Capacity

6.1 Proposed configuration

End-plate flange: 1¼ in duplex plate cut to the foil outline (or a rectangle inscribing it), welded full-pen to the leg shell with an internal doubler ring.
Bolts: 20–24 × 1″ duplex A4-90, slip-critical, Class B faying surfaces (blast + specified roughness), matched-drilled at the factory, shim-packed at assembly.
Node below: the frame corner receives the flange on a machined pad integral with the corner node casting/fabrication (§7).
Access: floor hatches at the three corners so all bolts are reachable from inside — no diver work, ever.

Figure 2 — Bolted flange concept, plan view. The big foil footprint is what makes the joint easy: huge bolt levers, low bolt forces.

6.2 Demand vs. capacity

Action (ultimate, LC3/LC4)	Demand	Capacity of proposed flange	Margin
Bending moment	60 kip-ft (250 with fuse blown)	> 1,000 kip-ft slip capacity (ΣμT·r over bolt group)	> 15×
Horizontal shear	4–40 kip	≈ 20 bolts × 19 kip slip/bolt ≈ 380 kip	> 9×
Uplift (trough + rocking)	10 kip	20 bolts × ~38 kip proof → ≫ demand even with prying	> 20×
Compression	19 kip	Bearing on 1¼ in plate — trivial	≫

In practice the flange is sized not by static strength but by fatigue and slip-retention policy: enough clamp force that the faying interface never micro-slips under the ±5–15 kip wave-frequency cycling (≈ 3–5 million cycles/year). That is what drives 20–24 bolts rather than the 6 that static strength alone would need.

6.3 Fatigue

Wave-frequency vertical load range ±5–15 kip and moment range ±10–30 kip-ft produce nominal node stresses of only a few ksi. With hot-spot concentration factors of ~3, design the highest-detail welds to keep ranges under ~6 ksi → effectively infinite life (> 2×10⁸ cycles) per standard S-N curves for classes C/D in seawater with cathodic protection.
Grind or ultrasonic-peen the node weld toes at the three corners; this buys a full detail-class improvement for pennies.
Slip-critical bolting keeps the bolts themselves in near-zero cyclic stress — the classic fatigue-proof connection.

6.4 Collision strategy — sacrificial fuse bolts

Because the leg shell survives a 410 kip-ft hit at only ~36% of yield, the thing you actually want to protect is the node and the frame. Make 4 of the 24 bolts undersized shear pins (or necked pins) calibrated to shear at ≈ 150 kip-ft of joint moment. Below that threshold the joint is untouched; above it, the pins sacrifice themselves, the leg bends (repairable), and the node stays true. Pins are replaced with hand tools in an hour.

Answer to your core worry "Long legs = long lever = unmanageable joint stress" would be true for a slender cylinder leg. It is false for an 8.5-ft-chord foil: the same geometry that makes the lever long also makes the beam deep. The joint sees tens of kip-ft in normal service and a few hundred in accidents — squarely in the range of ordinary bolted steel construction, no cables required.

7 · Required Frame Strength (No-Cable Version)

Without cables, the triangle becomes a self-supporting space box girder: floor + ceiling as flanges, the three walls as webs. Your planned inner triangle (22 ft sides, beams at wall midpoints, floor and ceiling) is exactly the right move — it halves every remaining span.

Figure 3 — Plan view: outer frame, inner triangle, legs at vertices.

7.1 Global demands

Effect	Design value	Driver
Hull-girder bending moment	200–250 kip-ft	Waves of 3–5 s period that the platform cannot follow (quasi-static bound 500 kip-ft is overly conservative for long swells it does follow)
Flange (chord) force T = M / 7 ft	≈ 30–36 kip	Taken by wall top & bottom rails
Vertical corner reactions	+20 / −10 kip	Buoyancy redistribution, tether snap
Torsion (differential thrust, wind eccentricity)	≈ 15 kip-ft	Closed triangular cell — very stiff, easy
Corner node moment	150 kip-ft working / 250 kip-ft ultimate	LC3 + spanning + slam coherence

7.2 Member schedule (duplex 2205, bolted assembly)

Member	Suggested section	Peak stress	Comment
Wall top & bottom rails (3 each level) — the hull-girder chords	RHS 6×6×3/8	≈ 10 ksi	Also picks up walkway brackets and railing loads
Inner triangle beams, floor & ceiling (22 ft spans)	RHS 8×4×5/16	≈ 7 ksi	w ≈ 150 lb/ft → M ≈ 9.1 kip-ft
Floor / ceiling joists (≤ 11 ft spans after subdivision)	RHS 4×2×3/16 @ 24 in	≈ 7 ksi	100 psf live + 15 psf dead
Wall studs @ 24 in	RHS 3×3×3/16	< 3 ksi	Storm wind 17.5 psf is trivial; size for handling & slam
Corner nodes (3)	Machined 1¼ in plate cluster or 2205 casting	design to 250 kip-ft	The critical fabricated items. Full-pen welds, ground toes, MPI-inspected, done at the Chinese yard under controlled conditions
Walkway brackets & diagonals	6061-Al 2×2×1/8, isolated from duplex	—	Nylon/isolation washers to prevent galvanic action

Answer to "how strong a frame?" Nothing exotic. Every primary member lands at 10–25% of allowable stress with ordinary steel-building sections. The frame is not what cables would have saved for you — the box girder is inherently strong at this scale. Budget roughly 9,000–10,000 lb of steel for frame + walls + nodes (included in §3.2).

8 · Motion Period Sidebar (consequence of the small waterplane)

Mode	Free-floating	On tension legs	Comment
Heave	≈ 3.2 s	≈ 1.3 s	Free-floating heave sits near 3–4 s wind-chop energy → expect noticeable bobbing in fresh chop; tethers move you clear of it entirely. Heave plates add mass & damping — helpful.
Roll / pitch	≈ 2.3 s	unchanged	Very stiff (GM ≈ 39 ft from the wide stance). Quick but small angles; the "soft ride" comes from low angular excitation, not slow periods.

This is informational for the ride-quality discussion — it does not change the joint conclusion. If anything, tethered operation (short periods, low amplitudes) is the easiest case for the bolted joints.

9 · Cables vs. No-Cables — Full Trade Study

9.1 Qualitative scorecard

Criterion	No cables (bolted)	With cables
Strength adequacy	✔ Fully adequate (§5–7)	✔ Adequate, with added redundancy
Corner stiffness / micro-motion	Good	Slightly better — cables damp node micro-rotation
Drag — hydrodynamic	✔ Clean	≈ Equal if cables attach above the waterline; real penalty only if attached below WL for better moment arms
Drag — aerodynamic	✔ Clean	~190 lb extra in 70 kt gusts (negligible vs 9,400 lb house load)
Maintenance	✔ None beyond normal inspection	Annual tension checks, fitting inspection; rod/wire replacement at yr 10–15
Noise/vibration	✔ None (minor shell drumming at waterline — damped by heave-plate isolation)	Aeolian strum on rods in 15+ kt winds unless fitted with dampers/spirals
Assembly simplicity	✔ One bolt-up operation	Two operations + rigging tensioning sequence
Damage tolerance	Good (fuse bolts)	Very good (cables arrest a cracked-node scenario)
Shipping (your 45-ft HC constraint)	✔ Nothing extra	Reels/boxes of rod, turnbuckles, lugs — modest but real cube

9.2 Weight comparison

Item	Rod-rigging version	Wire-rope version
6 rigging members (≈ 25 ft each) + turnbuckles + terminals	+950 lb	+520 lb
Hard-point lugs on legs & frame (12)	+280 lb	+280 lb
Frame/node lightening enabled by cables	−850 lb	−850 lb
Net delta vs. no-cable	+380 lb (+1.4% Δ)	−50 lb (wash)

Weight is a wash — less than ±1.5% of displacement either way. It should not drive the decision.

9.3 Cost comparison (ROM, China fabrication + Caribbean assembly, ±40%)

Item	Rod-rigging version	Wire-rope version
Rigging supply & install	+$8–14k	+$3–6k
Hard-point machining/welding	+$1.5–2.5k	+$1.5–2.5k
Node/frame simplification credit	−$2–4k	−$2–4k
Capex delta	+$7–12k	+$2–4k
O&M delta (inspections, retensioning)	+$0.8–1.5k/yr	+$0.5–1k/yr
Replacement at yr 10–15	$6–12k	$3–6k

9.4 Whole-project ROM (context)

Legs + frame + nodes (fab, delivered)

$95–150k

Batteries (~340 kWh LFP)

$55–80k

Thrusters, solar, controls

$32–55k

Dinghy + HARMO + mooring kit

$21–32k

Freight + assembly + engineering

$36–65k

Total (no-cable)

$260–390k

Cable-version delta

+$2–12k

9.5 Reality check on your three advantages

Less drag: True only in the aerodynamic sense, and small (~190 lb in a 70 kt gust, ~2% of the house load). If cables attach above the waterline — which they should — hydrodynamic drag is identical. Don't let this argument carry the decision.
Less to clean/inspect/maintain/replace: Genuine and recurring. Six rigged elements disappear, along with annual tension surveys and a decade-scale replacement line item. This is the strongest argument for no cables.
No cable vibration/noise: Genuine. Duplex rods in 15–25 kt winds will sing/strum without dampers. The no-cable version is silent apart from normal wave slap.

10 · Recommendations

Go cable-free. Bolt the legs directly to robust corner nodes. The structure closes with large margins, and you collect the maintenance and noise benefits for free.
Invest in the three corner nodes. Machined-plate or cast 2205 clusters, full-pen welds, ground/peened toes, MPI-inspected at the yard. Design capacity 150 kip-ft working / 250 kip-ft ultimate. These are the heart of the vessel.
Use 20–24 slip-critical 1″ duplex bolts per leg, Class B faying surfaces, factory match-drilled, with published torque/preload procedures and a re-torque check after the first season.
Add 4 sacrificial fuse bolts per leg calibrated to ~150 kip-ft, so a collision costs you a pin change and a leg-straightening, not a node rebuild.
Weld spare cable lugs onto the legs and nodes now (they weigh almost nothing). If sea trials ever show unexpected node flexure — they won't, but insurance is cheap — cables become a bolt-on retrofit, not a redesign.
Close the ~4,100 lb mass gap identified in §3.2 (lighter leg skin with tighter framing, aluminum/composite interior, battery fraction 20–22%). The buoyancy rating, not the structure, is your binding constraint.
Keep the tethers as your storm plan. Note that neither cables nor bolted joints are what saves you in a hurricane — weather routing and the tension-leg mode are. Design tethers and anchors for 15 kip with a mechanical fuse at the seabed end.
Validate before committing: FEA of one corner node under LC3/LC4, a bolted-flange slip test, and strain gauges on the first article during its first blow.

11 · Limitations & Next Steps

This study assumes survival exposure of 70 kt / H_s 15 ft. Open-ocean hurricane survival (H_s 25–35 ft) multiplies wave loads 3–5×; the leg shell likely still survives, but tether snap loads, heave-plate slamming, and green-water-on-deck cases must be rerun before claiming that envelope.
Section properties used thin-ring estimates; confirm with a CAD section or FEA, especially if the skin drops to 1/8 in.
Fatigue claims rest on keeping hot-spot ranges under ~6 ksi — verify at the node detail level, not just globally.
The mass budget (§3.2) is component-level estimating accuracy (±15%). Treat the 27,500 lb rating as the controlling design requirement and re-run the spiral until it closes.
Recommended next analyses: (1) corner-node FEA, (2) coupled mooring-dynamics run for tether snap, (3) slamming study for heave plates, (4) seakeeping sim to confirm the 3.2 s heave behavior is acceptable for your comfort goals.