Mechanics of the spar design
May 16, 2008 at 12:01 pm #477
I just had a long and very interesting discussion with my brother who is a (currently unemployed) mechanical engineer and has hands-on experience with mechanical stressing of composites (helicopter rotor blades). He has taken a good look at the spar design of seasteads, and his conclusion is that we will need a specifically tailored material and/or a very experienced engineer for the structure if we go this way. Concrete can bear 20-40 MPa in compression, has an elastic module of 27000 MPa (it’s average) but an elastic limit of 2.1-2.7 MPa only: it means it can accept deformations of roughly 0.01% of its size only before breaking, in traction or flexion (which is why it is mixed with steel and other things, and preconstrained, when used in land applications). On a floating spar design, the length of the pillar makes flexion stresses too great, so unless we have an engineer very “fluent” with ferrocement and use the same very advanced tricks used in bridge design (which may require much more upkeep than we’re willing to do, like monitoring stresses and retightening the steel rebar regularly) a long spar design will likely break around the middle or around the water surface. The cylinder shape itself is sound, but the length of it on a single spar design is very problematic. Even if we use a different material above the water (steel beams should be the most practical choice) and hence divide the length of the pillar, the junction will face the same problems.
So his suggestion was to drop the single pillar design and instead use multiple, shorter cylinder feet for the submerged structure, and anything suitable above water (more ferrocement, steel beams, wood ?). He also made a suggestion of using hollow concrete spheres as a stackable, raw floatation material in other designs. They could be made in a very wide range of diameters while still being significantly buoyant and capable of resisting 1MPa (the hydrostatic pressure found at ~300 feet depth) ; the bigger the more buoyant but the more susceptible to flexion stress. Different sizes could be mixed.
Of course we may also use a specific sort of concrete mixed with fiberglass or other things, which would withstand the stresses. He suggested we consult the catalogs of concrete producers for something with better suited mechanical characteristics. But that still implies calling upon an experienced engineer for determining the masses and thicknesses required.May 16, 2008 at 1:42 pm #2014
Wouldn’t some (a good portion) of the overall buoyancy being below the center of gravity make a difference? Part of the Spar design’s appeal as I understand it, is that by placing a good portion of displacement below the wave line, we make it less susceptible to wave action. But it also would seem to decrease some of the tensile force being applied to the spar body, essentially holding it up from the bottom. You’d have several force vectors:
- The ballast is pulling the spar down from the point where it attaches under the lower displacement hull. This gravitic force tests the tensile strength of the material holding the ballast and attaching it to the lower displacement hull.
- The depth pressure gradient forces the hull inward (crushing- no real benefit)) and upward (floating, and increasing the buoyant force the further down you go), somewhat supporting the ballast and partially mitigating the pull from gravity between ballast, lower displacement hull, and safety hull. The ballast is at the lowest point for stability, and thus subject to the greatest buoyancy force. So the portion subject to the greatest test of tensile strength, is also subject to the greatest supporting force. The supporting force gradient decreases in the opposite direction from the gravitic force in a constant curve, so there’s not any one point that is most subject to tensile failure, unless the integrity of the shape is interrupted or flawed somehow (hatches, maybe).
- You have the safety hull at or about the waterline that forces the spar to be vertical. The connection between the safety hull and the body of the spar below it is subjected to the sum of the force vectors applied below it, i.e. weight and buoyancy, which partially cancel each other out. It’s also subject to sheering forces as waves beat on it.
- It’s important to note that even some of the weight of the ballast is canceled out by buoyancy. We typically think of buoyancy as “floating” but it’s not just that. It’s a lessening of apparent weight. Whatever we use for ballast will appear lighter in the amount of an equivalent volume of water at that depth.
- Then you have the living platform above the wave, with a compressive force pushing downwards and shearing force from the wind.
Tipping the spar from horizontal to vertical still would appear to have some serious shearing force problems.
May 16, 2008 at 2:04 pm #2016
- I welcome comments if I have missed or mis-stated something. Still wrapping my head around the problem and I’m not viscerally certain yet that the vertical spar is the best design.
You’re missing the forces of flexion imposed on the long cylinder. If there is a little wind and current in different directions, maybe some oscillation from the waves too, then a too long cylinder will break. Think also of the maneuvering we might impose on the structure. Maybe even a change of current direction would, out of the inertia of the structure, suffice to break the pillar – buoyancy does not compensate inertia.May 16, 2008 at 2:49 pm #2017
You’re absolutely right- that’s what I was getting at with shearing forces. I’m assuming that a lot of the flexion/shearing forces can be designed for with ferreo-cement- steel-rebar-reinforcement. That’s how tall building taking the shearing forces of high winds.
- But you could be right that changes in current direction, trying to tow or push the spar might cause it to flex too much along its length, depending on how long it is.
- And oscillation from wind, waves, and current may well cause it to act more like a bridge span than a tower.
Cross-section, thickness of the cylindar walls, internal cross-bracing, and type of concrete and internal reinforcment of the concrete would all be factors to consider.
- As I recall from pictures of oil platforms, the legs seem to be mostly open struts with a huge concret ballast that in some cases can be raised or lowered. I still don’t see a reason why the entire spar length has to be a hollow concrete tube. The bottom section could be a metal framework that merely supports a ballast.
- As long as the majority of the positive buoyancy is below the wave line, with a safety hull and more positive buoyancy at or near the water line, it should achieve the goal of vertical stability in normal wave conditions, The ballast could be a huge chunk of concrete on a massive cable or chain and hang below the rest of the structure. It could even hang far below and rest on the sea floor if shallow enough, and be winched up to diving depth for service or movement, and as long as it still hangs down, provides the correct orientation.
So what would be the easiest and cheapest answer? How about external (or internal) vertical ribs integral to the concrete tube? Metal superstructure like the support arch of a bridge?May 16, 2008 at 9:40 pm #2026
Thanks for the research, Jesrad. It is true that concrete is very bad at taking flexion, and this may be a problem for us. We will know more when we commission an engineering study. Possible solutions are:
- Use multiple spars
- Use a large-diameter spar
- Make the spar out of steel, either as a tube, or an open truss system (like a jack-up rig)
I certainly expect that large platforms will use multiple spars, but I think it is possible that a single spar can be made to work for a small platform.May 17, 2008 at 1:40 pm #2034
There is no reason a single spar design couldn’t be made to work, but the real point here is that it’ll certainly require expert knowledge, take more time and end up being more costly than expected.
I thought about it some more, and realised the weight of the ballast itself is working against us instead of helping: a seastead will tilt in the wind, even by fractions of degrees, which will inevitably cause serious shear on the spar with every wind velocity change (whether in direction or strength). As for using a larger diameter spar, I doubt it would help: the flexion from wind will be proportional to the frontal surface, so it will grow linearly with diameter against a rigidity growing linearly with diameter (at fixed thickness), too – I think it would only help against axial torsion stress where the wall being further from the axis means the stress decreases linearly with diameter. More thickness in the wall would rise rigidity, but also greatly increase weight for the same buoyancy. Constructing the spar from steel would just move the problem to the junction: the steel will simply transmit the stress to the ferrocement, where it will cause problems. In the FLIP ship the whole structure is steel, which solves the problem, but we cannot really afford it for cost and longevity reasons.
Basically, we’d have to get out of the beam mechanics domain, which means having a length no higher than five times the diameter. It also means many of the expected advantages of a spar design (low wave coupling, elevation against rogue waves) would no longer apply. Here’s a numerical application for a 5 meters diameter, 50 meters long simple spar with 0.25 m thick walls: with these dimensions it would be 187 cubic meters of ferrocement or 430 metric tonnes, meaning 21.9 meters of its 50 meters of length would be submerged. In order to move the center of mass down 5 meters, an additional ballast of 86 tonnes will be required at the bottom, bringing the mass to 516 tonnes and the submerged heighth to 26.3 meters, so the waterline would be a bit higher than half the spar. Assuming no drag from water (steady currents), a Cd (coefficient of drag) of 0.75, an aerodynamic center for the emerged structure at 11.8 meters above water, with a frontal surface in the air of 118.5 square meters, a velocity difference between current and wind would induce a drag of Cd*118.5*0.5*sq(windspeed relative to current)*airdensity. At standard pressure with a 20 knots relative wind (10.3 m/sec) it gives 5763 N, applied 18.2 meters from the center of mass, or a torque of 104886 Nm. This force pushes sideways on the cylinder where it has a section of 3.73 square meters of ferrocement to resist it: that should be 154.4 KPa, if I didn’t mess up, so even simple concrete should resist it. However there’s also the torque tearing on the cylinder, flexing it, but I don’t know how to finish this kind of calculation and say if it could resist, as I never learned tensor calculus…
But keep in mind that this is a purely static shear force at equilibrium we got here, it’s really the minimal stress the structure can be expected to face all the time at sea. This force will grow with the square of windspeed relative to sea current, and linearly with the length of the spar. I’m afraid the most violent gusts of wind might be capable of cutting the emerged part of the spar from its submerged part, or at least causing wide cracks, if the concrete is not reinforced around the middle with a pretensed rebar lattice.
Further calculation indicates such basic wind will give the seastead a tilt of about 0.07 degrees. This tilt will basically double the torque exercised on the spar (actually, a bit more than double), at static equilibrium. If the wind suddendly changes direction hard enough, we end up with over four times the stress on the cylinder. That’s really not good.
So, my conclusion is… that the overall shape of the seastead should be boxy, and not elongated at all. Especially not vertically elongated.May 17, 2008 at 4:03 pm #2037May 17, 2008 at 6:32 pm #2039
The Brent Spar was built out of steel, not ferrocement. My objections are valid only for brittle materials like concrete.May 17, 2008 at 10:07 pm #2040
I’ve been trying to find info on the design of the Brent Spar but all google wants to give me is all the bitching about disposal of it. I did note one place that said at least part of it was made of steel, so point taken.May 17, 2008 at 10:54 pm #2041
I found some discussion on Spar design, and corresponded with the gentleman
- Mike says:
“OK. In reviewing my calculations and I found that I forgot to convert one length from feet to inches so the hull weight is low by a factor of 12, so it takes 120,000 lbs of steel. This sounds like a lot of steel, but at $0.25/pound this is only $30,000 in material cost.”
Mike, if you read this, please let us know where you are getting your cost quotes from, and if that is a scrap price or a price for sheet steel in the correct guage, etc. I’m not doubting you, but as a matter of practicality, I want to question all assumptions (particularly of cost).
See his design hereMay 18, 2008 at 4:39 am #2050
First let me say that I am a Mechanical Engineer with 28 years experience in Aerospace Engineering and I have a personal interest in marine systems. I also believe that I am the originator of Spar Buoy House concept see http://www.boatdesign.net/forums/showthread.php?t=815&highlight=spar+house. I came up with this idea over 30 years ago and I spent thousands of hours think about it, designing it and optimizing the configuration. It was one of those ideas that refused to go away until it was done.
The above discussion is interesting, although some of the terminology is inconsistent with engineering convention and therefore slightly confusing. Such as confusing bending with flexure, …
The intent of the Spar Buoy House was to design a home that could be anchored in international waters to avoid government restrictions and survive up to 6 sigma sea conditions. To survive 6 sigma storms in most areas requires that living area be several meters above the waterline and to make it livable it needs to resist the vertical and lateral forces of the waves and wind. In the open Ocean the currents will be minimal, but it is open to wind and waves. There are many approaches that can meet these requirements, however the need to be so far above the waterline required a large and very broad structure to make it stable. The vertical column “Spar” design is an efficient and elegant design solution and I believe it will provide the lowest cost solution. I analyzed bending due to 150 mph winds, shear due to wave action, buckling due to the vertical weight and hydrostatic pressure. The worst case loading is buckling. The weight could be reduced by using 1/4″ steel plate and welding horizontal ribs on about 2 foot centers, but by the time I estimated the weight of the ribs the weight reduction was only about 20% and the cost for the additional labor would be higher. My final design was a 1/2″ thick steel tube which provided a factor of safety of about 10:1.
I would stay away from Ferro cement because you will need a complex network of steel reinforcing which will require a lot of labor to cut, bend and wire into place. The main advantage of Ferro cement is for producing complex shapes. The Spar Buoy is a simple shape to make from steel.
I gave up on trying to get a carrage return in the post.May 18, 2008 at 8:07 am #2051
I found that to use the proper tags and get carriage returns to work, you have to switch to plain text editor and manually put in your tags. Do it before you start, or all your carriage returns, “< " or even quotation marks come out all messed up.May 18, 2008 at 8:29 am #2055
Thanks for the link, Portager. Just a few questions on your spar buoy home design: You assume no inertia from drifting, but don’t the currents in some places get significant speeds ? You say that buckling is the main concern when building a spar out of steel, which seems was the reason TSI had chosen ferrocement instead, and I remember one point my brother rised was that, around the water line the compression would be awful from the buoyancy below and the structure’s weight above – if I understand that right we can expect double the Archimedes’ force at that place, right ?
My main concern is dynamic changes of the loads: wind changes combined with ballast trying to rebalance the structure from tilting, which may put enormous bending efforts on the spar ; current direction change with a significant speed, as well ; and above all vertical tear from rapid changes in waterline. I’d really like your opinion on this: it seems that the oscillation period of the structure when in waves would have to be higher than the highest wave period observed (wouldn’t that be something like 7 seconds ?), in order to damp vertical oscillations instead of resonating in them, but that means waves with enough amplitudes would cause enormous transient loads, both in excessive buoyancy (doubled at the water line, I think, because of the whole structure’s inertia) while the spar accelerates up, and in excessive tear while the spar accelerates down.
(Sorry if the terms I used were unusual, the discussion I got them from was in French, and I’m not a mechanical engineer so some accuracy was lost in translation.)May 18, 2008 at 9:13 am #2056
Well, the Troll-A platform was made of ferrocement, and it floated to its destination. But it had several “spars” and 1 meter thick walls on those, plus it was not built to float all the time and in all weather.
There truly is a large gap in engineering proof-of-concepts as far as ferrocement spar goes I’m afraid this means the conception stage for early seasteads will be more costly than previously thought, with the end result of rising the cost to entry for every other seasteaders group…May 18, 2008 at 10:07 am #2057
OK, I’m not entirely sold on anything here yet. Not even a particular material. I think the design is still very notional, so I’m going to throw out more ideas.
- For ferrocement, what about external buttresses? Essentially, there’s a cylindar that contains your displacement. On the outsie of the cylinder, 3 or 4 extrusions of ferrocement provide reinforcement against lateral stresses and shear forces due to current (including deliberate propulsion) , wind, and wave action.
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