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Stability of inverted catenary arches

Sir, I have to submit a paper tommorrow on the types of arches. I am permitted to use the web. I heard that the most stable arch is the inverted catenary arch. But even after surfing for hours I didn’t get the physics hlvehind it. Please explain how can I prove it is the most stable curve. Please do help as soon as possible.

Posted Muralikrishnan A

Answer:

In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The curve has a U-like shape, superficially similar in appearance to a parabola, but it is not a parabola: it is a (scaled, rotated) graph of the hyperbolic cosine. The curve appears in the design of certain types of arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings.

The catenary is also called the alysoid, chainette or, particularly in the material sciences, funicular

 

Please visit

https://en.wikipedia.org/wiki/Catenary#Inverted_catenary_arch

for some details

More links to refer:

http://mathworld.wolfram.com/Catenary.html

 

http://xahlee.info/SpecialPlaneCurves_dir/Catenary_dir/catenary.html

 

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