Gurdur

When building an arch that will not have to support a load more than a rather small fraction of the arch's own weight, which would then be stronger and more stable (including shear and torsion) --- a catenary arch or a parabolic arch ?

abe smith

Let your OEdificial needs express themselves in TENTS ("tabernacles"); we are all sojourners here in this World-Wildernesse; take up your tent-pegs & keep moving-on. Your wishful spires & vaunting towers are not goina reach up to gawd in the empyrean; and Time will tear them down.

Gurdur

The yurt is a type of tent, and is structurally based on the domed arch.

Gurdur

Oh well, no takers for helping me with my question, I see.

I found out anyway elsewhere that (according to that source) a catenary arch is stronger than a parabolic arch except when carrying a long horizontal load, as in the case of a suspension bridge.
However, the source was unclear where the load is not horizontal but only comprises a small fraction of the arch's own weight.

Anyone ?

hyzer

Gurdur: what are you designing? Is this a mental game? Model for school? Actually want to design a bridge?

Bridge designers typically want to know the required horizontal span, and the required vertical clearance and then pick the shape of the arch (if the solution even is an arch) to suit. Most will solve the problem with a circular arc since it renders the math easier to perform (it is only when us architects get into the picture and ask the structural engineer to design the span as a parabola or a catenary ‘cause we like the shape better

The question you pose would be tough for a structural engineer to answer since the safety factors would render the differences between the amount of materials needed for an arch with a true catenary shape vs one with a parabolic shape moot (given that the parabola and the catenary are drawn through the same three points, i.e., the span and rise are the same).

However, the flatter the arch the greater the horizontal force outward at each end that must be resisted. Since a parabola will be flatter than a catenary (again, through the same three points), the parabola solution will require larger buttresses (all materials being equal), but the difference will be minute.

-hyzer, registered practicing architect

Gurdur

Hey !
Many, many thanks indeed !
I was beginning to despair; I had also posted my question on a "Bridge-Building Forum" bulletin board, but the board looks awfully unattended, and no-one has answered.

To your question:
My answer may seem a bit odd to you, and absurdly perfectionist.
That's OK; I am an absurd person, with the occasional outburst of perfectionism.


The structure in question that I wish to make soon is a garden pergola, formed out of three (relatively narrow and high) arches which bend in at the top towards each other, joined at top by a keystone, thus forming three more super-arches, so to speak, in a dome.

Material is brick and mortar, and because of a couple of factors, hidden M12 galvanized mild steel rodding running through the middle of the bricks the course of the arches.

The only real load is the weight of the arches (old fired housebricks not being terribly light), and the joining keystone (granite, but in essence in comparison negligable), and the eventual weight of vegetation (climbing roses, wine-grape vines and clematis).

Now at this stage you're going to scream at me and say,
"WHY THE FUCK ARE YOU BEING SO DUMB AND WORRYING ABOUT THIS, BECAUSE UNTIL YOU GET AT LEAST THE EQUIVALENT OF A THREE-TON TRUCK BOUNCING ON TOP OF YOUR ARCH IT WON'T MAKE ANY FUCKING DIFFERENCE IF IT'S A PARABOLA OR A CATENARY, YOU DUMB FUCK !!!"

And I would reply, "True, but sometimes I'm a perfectionist for the hell of it, and also the pergola dome will be helping to anchor a ¾-circular arch that is only secured at one end (the other end floating in mid-air, thusly being simply a weirdly-shaped beam), also of brick and (M16) rodding, and hey what if the climate changes so much we actually get real tornados here, or for all I know thousands of invading triffids or mutant ice-bears or millions of my bloody neighbours' children climbing the arches on a dare when I'm not there......"

but mainly, I just wanna be absurdly perfectionist about this.


I'll let you know span and height later, but it's roughly a span of 3 metres and a height of around just over 4 metres. Or something like that. Maybe 2½ by 3. I'll measure it properly soon.

To an architect, does a parabola or does a catenary look nicer ?

Many thanks,
Gurdur

enigma555

Unless this thing you're designing is really big, the steel should be able to support it just fine either way.

So, you answered yourself when you said that it won't make any F'ing difference.

The catenary is the shape which a rope will naturally assume if left hanging from two points under its own weight.

The catenary will also have more force directed straight downward at the bases, but that means that more strain energy will be held in the steel (instead of the ground pushing back).

Again, unless you're building a massive structure, we're talking about next to no difference in structural stability, so the question you should be asking yourself is: "Which do I think looks better?"

Gurdur

Well, yes, I'm asking that too, but since I'm so idiotically anal given an aesthetic/intellectual puzzle, I'm also asking which is more stable etc.
I really don't mind that the difference is physically negligable, I just would like to KNOW the theoretical 0.00000001 difference.

pmurray

And it's formula is the hyperbolic cosine:

cosh(x) = e^x + e^-x

Tenpudo

This description stand out to any other Robert Jordan fans here?