[Ferro List] subterranean - catenary strongest shape & tensile vs compressive forces

[Lloyd Turner]

Gents -

Earlier this winter my son and I had some fun with this catenary  
phenomenon.  I made a catenary shaped airform made of light weight  
Tyvek fabric (5 mils thick) and shipped it to him in Anchorage.  He  
and a friend anchored it down to a 20 foot diameter circular base,  
inflated it with a small centrifugal fan, then sprayed it with several  
passes of water mist.  After just misting on the first coat the  
structure was self supporting and the fan was turned off.  At this  
point the dome was no more than a  frozen wet rag in a 20 foot high  
catenary dome shape.  It was amazingly strong.  By using a garden hose  
on this already rigid structure the ice thickness was built up to  
about an inch.  It lasted for weeks until the first rainstorm and 43  
degree (F) temperature.

Lloyd -

On Apr 4, 2008, at 2:25 AM, chuck east wrote:
> Keith
>
> Thanks for the in-depth explanation however I'll need a bit of time  
> to gain
> the knowledge to fully appreciate what you probably see as a surface
> explanation.  As to the self-supporting 'free standing' form you  
> reference,
> I'm assuming that St Louis' Gateway Arch is such a structure, but to  
> try to
> explain my confused use of catenary, I had seen (on the same  
> Wikipedia page)
> a 'trussed arch' bridge by Eiffel which purportedly uses an inverted
> catenary arch and it seems fully capable of supporting 'x' amount of  
> weight
> in addition to its own.  I'm sure that the base is well 'anchored'  
> to resist
> spread but my impression (= lack of knowledge) is that outward  
> forces at the
> base of an arch can be controlled by the angle of the arch at the  
> base and
> in the instance of subterranean structures the exterior earth forces  
> and, if
> need be, the use of a tensile ring (if that's the right word wherein  
> rebar
> might be used).
>
> I had also, in an earlier fc discussion re using LFC for my 'flipped  
> boat'
> subterranean home, wondered aloud if the pressures on a ship, which  
> can bob
> up and down in relation to the ocean's forces, were similar enough  
> to the
> earth pressures on a subterranean home which has no or little  
> 'bobbing' room
> ... this was/is directly concerned with the use of rebar.
>
> So that's a sampling of the 'inclinations' that had led me to the  
> idea that
> 'possibly' an LFC structure might, with ample bulkheads, work nicely  
> and
> safely in a subterranean home.
>
> I'm three years away from building and will use this prep period to  
> explore
> ideas, build some small test models (to destroy) and eventually a  
> small but
> inhabitable model of the final structure.  Of course I would be  
> thrilled if
> our home doesn't collapse ... and I would love it if, in the  
> process, we can
> find ways to minimize our carbon footprint and extend new ways to  
> others for
> eco-friendly homes.
>
> Thanks, again
> Chuck
>
> -----Original Message-----
> From: list-bounces at ferrocement.net [mailto:list-bounces at ferrocement.net 
> ] On
> Behalf Of Keith B
> Sent: Thursday, April 03, 2008 3:22 PM
> To: Ferrocement Discussion List
> Subject: Re: [Ferro List] subterranean - catenary strongest shape &  
> tensile
> vs compressive forces
>
> Chuck,
>
> The Catenary Arch/Curve is interesting, but of limited use and subject
> to some misconceptions.  It's what you get if a long member with  
> tensile
> but no bending strength is restrained at its ends and allowed to sag
> under gravity to its naturally stable position.  String or cable can
> closely approximate it, but conceptually, it's best to think of a  
> length
> of chain, since it's clearer that neither compressive nor bending
> strength can be involved.
>
> As tension is increased, the curve flattens.  Decrease in tension
> produces a deeper sag, but it's important to note that the force  
> vector
> at the ends can NEVER become parallel with that of gravity.  There is
> always some inwards component.  It follows that, for the
> reverse/inverted case of the Catenary Arch, the compressive force  
> vector
> at the foot ALWAYS has some outward component.  Whether that can be
> dealt with by an angled block and a simple foundation or needs a  
> tension
> ring or beam depends on the design.  For comparable height and width,
> the difference in that respect between Catenary and circular or
> spherical is minor to negligible.
>
> More important is the possible misconception that the Catenary Arch is
> per se intrinsically self stable.  That's only true in one rarely met
> case.  By definition, that's where the member is freestanding with no
> other forces acting but gravity on the element alone and resisted  
> solely
> by the element's compressive strength.  (Like the chain, it's fine for
> the arch to be made of discontinuous parts, so the element as a whole
> has zero tensile strength but has the compressive strength of the  
> parts.)
>
> It's fine if you want to live under that, but if you want to also
> support lateral thrust from being partially or fully buried, or if you
> wish to vertically load it with weights not in proportion to the
> projected mass distribution in the arch itself, or, for that matter,  
> to
> support floors, resist wind or seismic forces, then the Catenary is
> probably not the optimal curve and what you use MUST meet the general
> stability requirements for arches.  The last requires contribution  
> from
> section thickness and may rule out a thin FC skin, for that reason.
>
> kb
>
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