| Item | Value used | Comment |
|---|---|---|
| Living area (plan) | 40 ft × 16 ft | Above water platform |
| Leg/float orientation | 45° down/out from each corner | Matches your “bottom rectangle” size well |
| Leg length (along axis) | 24 ft | Top at platform corner, bottom outward/down |
| Horizontal projection | 24·cos(45°) ≈ 17.0 ft | So bottom footprint grows by ~34 ft in each direction |
| Bottom rectangle (given) | ~74 ft × 50 ft | Consistent with ~17 ft offsets from a 40×16 platform |
| Leg “width” | 4 ft diameter assumed | You said “4 foot wide”; I modeled as a 4 ft OD cylinder |
| Submergence | Half the leg length submerged | So 12 ft submerged (along axis); waterline at mid-length |
| Seawater density | 64 lb/ft³ | Typical engineering value |
| Total displacement/weight target | ~36,000 lb | As provided |
| Leg shell thickness | 0.25 in side shell; 0.5 in dished ends | As provided (duplex stainless) |
| Internal overpressure | 10 psi | “Modest pressure” per your note |
For a thin cylinder, hoop stress ≈ σ = p·r/t.
With p=10 psi, r=24 in, t=0.25 in ⇒ σ ≈ 10·24/0.25 = 960 psi.
This is small compared to typical duplex stainless yield strengths (often 60–80 ksi range),
so pressure is not likely the governing structural issue (connections/fatigue usually are).
A = πr² = π·(2 ft)² = 12.57 ft²L_sub = 12 ftV = A·L_sub ≈ 12.57·12 = 150.8 ft³B = ρ·V ≈ 64·150.8 = 9,650 lbSo four legs give ~38,600 lb buoyancy at “half submerged”, which is consistent with your ~36,000 lb estimate. That’s a good sign the geometry is self-consistent.
The key difference is where the buoyancy load gets “closed out” structurally:
Model: treat buoyancy on the submerged half as a single upward resultant acting at the centroid of the submerged portion. For a uniform cylinder with submerged segment from 12 ft to 24 ft (measured from the top joint along the leg), the centroid is at 18 ft from the top joint along the leg axis.
s = 18 ftx = s·cos45° ≈ 18·0.707 = 12.7 ftB ≈ 9,650 lbFor an upward force with horizontal offset x, the bending moment about the corner joint is approximately:
M_joint ≈ B · x ≈ 9,650 lb · 12.7 ft = 122,600 ft·lb
So per leg, you should expect on the order of 123 kip-ft of moment at the joint in a static “half submerged” condition.
In inch-units: 122,600 ft·lb × 12 = 1.47×10^6 in·lb.
In real seas, loads are commonly multiplied by dynamic factors due to: heave acceleration, wave drift forces, slam, and cyclic fatigue. A crude concept-stage multiplier might be 3× to 5× on the moment for survival cases.
| Case | Moment per leg at corner joint |
|---|---|
| Static (calm water) | ~123 kip-ft |
| Moderate dynamic factor (3×) | ~370 kip-ft |
| High dynamic factor (5×) | ~615 kip-ft |
Those higher numbers are not “predictions”; they’re a reminder that your connection must be designed for sea states, not for dockside equilibrium.
A moment of ~123 kip-ft (and potentially several times that dynamically) must be carried as a force couple through the platform frame and the leg attachment. The force couple magnitude is roughly:
F_couple ≈ M / h
where h is the effective vertical separation between the “tension side” and “compression side”
of the frame/joint (think: top and bottom chords of a deep box frame, or a tall gusseted bracket).
If you only have a shallow frame, the required forces become very large.
| Assumed effective couple depth, h | Force couple per leg (static) F ≈ 123 kip-ft / h | Force couple per leg (3× dynamic) |
|---|---|---|
| 1 ft | ~123,000 lb | ~370,000 lb |
| 2 ft | ~61,500 lb | ~185,000 lb |
| 4 ft | ~30,800 lb | ~92,000 lb |
This is the key conceptual point: to make a cable-free corner work in bolts, you typically need a deep, 3D corner node (a box node / deep bracket / deep truss) so the moment can be reacted with manageable forces. Shallow “flat plate” connections tend to explode bolt forces.
If a flange-type bolted joint resists moment by bolt tension at some radius r,
a rough estimate is T_total ≈ M / r.
Example: if you only get a 12 in (1 ft) effective tension radius,
then T_total ≈ 123 kip-ft / 1 ft ≈ 123,000 lb of total bolt tension on the tension side
(then multiply by dynamic factor).
That implies many large bolts, very thick flanges, and careful fatigue detailing.
A simple way to see the advantage: if the leg is treated as a beam with supports at top and bottom, and the buoyancy resultant acts at 18 ft from the top along a 24 ft leg, then vertical reactions are:
R_top ≈ B · (distance from load to bottom)/L = B · (24-18)/24 = 0.25BR_bot ≈ 0.75BNumerically:
R_top ≈ 0.25·9,650 ≈ 2,410 lbR_bot ≈ 7,240 lbIn that idealized “pinned at both ends” model, the moment at the top support is near zero. In practice, you’ll still have some moment due to connection stiffness and distributed loads, but this illustrates the big structural advantage: cables move you from a cantilever problem to a braced problem.
If the legs are intended to act primarily as 45° struts supporting the platform, the axial force in a leg to provide ~9,000–10,000 lb vertical component is on the order of:
N_leg ≈ B / sin45° ≈ 9,650 / 0.707 ≈ 13,650 lb
The horizontal component is similar magnitude:
H ≈ N_leg·cos45° ≈ 9,650 lb
That horizontal “spreading” is what the cable network counters. If two cables share that at a corner node, you might see several thousand pounds to ~10,000 lb class tensions per cable in benign conditions, then higher under dynamics. This is generally a more efficient and buildable load path than trying to bolt-resist hundreds of kip-ft moments at the platform corners.
If (in the cable-free concept) the leg behaves cantilever-like, the maximum bending stress occurs near the top joint. Using a 4 ft OD, 0.25 in wall tube approximation:
I ≈ (π/64)(Do^4 − Di^4) ≈ 10,700 in^4 (approx.)S = I/c ≈ 10,700 / 24 ≈ 446 in^3M ≈ 1.47×10^6 in·lbσ ≈ M/S ≈ 1.47e6 / 446 ≈ 3,300 psiEven at 5× dynamic, that’s ~16–17 ksi, which may still be below duplex yield. So the leg tube may be OK in strength; however, the corner joint, frame, local shell-to-node load introduction, and fatigue are much more likely to govern.
At 0.5–1 mph, the water drag from your large inclined floats will typically dominate. Cables add drag, but it may be relatively small compared to the floats (unless you use many/large lines or have lots of marine growth).
Very rough example at 1 mph (0.45 m/s): dynamic pressure q ≈ 104 Pa (~2.2 psf). A 1-inch cable has projected area ~diameter × length. Even 250 ft of cable total only gives a couple m² of projected area, so the drag can be only tens of pounds in clean condition. Marine growth can change that substantially.
For a 4 ft OD cylinder, 24 ft long, 0.25 in wall: surface area ≈ circumference×length ≈ (π·4 ft)·24 ≈ 302 ft². Metal volume ≈ area×thickness ≈ 302×(0.25 in = 0.0208 ft) ≈ 6.3 ft³. At ~490 lb/ft³ ⇒ ~3,100 lb per leg shell, plus ends (order 500 lb) ⇒ ~3,600 lb per leg. Four legs ⇒ ~14,000–15,000 lb of duplex stainless in the legs alone (ballpark).
| Aspect | With cables / braced bottom nodes | No cables (moment-resisting corner joints) |
|---|---|---|
| Primary structural demand on platform frame | Mostly axial + shear; lower corner moments | High corner moments (hundreds of kip-ft class under dynamics) |
| Added hardware weight | Low: cables + turnbuckles + lugs (often < 1,000 lb total) | Potentially high: deep corner nodes, thick flanges, many large bolts, gussets (can be several thousand to 10,000+ lb depending on design) |
| Fabrication risk | Moderate: cable lugs + alignment + corrosion/fatigue detailing | High: precision of large bolted moment joints, thick duplex plates, welding distortion control, fatigue hotspots |
| Maintenance | Inspect/replace cables; manage marine growth | Inspect complex joints for cracking/crevice corrosion; harder-to-repair heavy nodes |
| Cost tendency | Usually lower material cost, simpler load path | Usually higher due to heavy duplex structure + complex machining/fit-up |
| Hydrodynamic drag | Slightly higher (cables add some drag; growth increases it) | Slightly lower, but floats likely dominate drag anyway |
Bottom line on weight/cost: Cables are typically the lightest/cheapest way to close out the horizontal spreading and to avoid making the platform corners into huge moment connections. A cable-free version can work, but it usually forces you into a much heavier 3D frame/node architecture, which tends to raise both fabrication complexity and cost.
Yes, but conceptually it should look less like “legs bolted to a flat frame” and more like one of these:
If your main motivation is “no cable vibration” and “less maintenance,” consider a hybrid: a small number of rigid struts/tie-rods (or a submerged rigid ring) sized for fatigue, instead of many tension cables. That can preserve the braced load path without requiring giant moment joints at the platform.
If you provide these, I can produce a cleaner set of load cases and sizing estimates (still preliminary):