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

[Keith B]

Hi Lance,

If the dam is in compression (which it is), since there's nothing for it 
to push on on the downstream side, all the force must be directed within 
that thin shell.  That, in fact, is a condition required for a plain 
compression arch to be stable.  It's not so much that it's so thin which 
makes it such elegant engineering, it's the precision with which such a 
small amount of concrete has been positioned to the only position where 
it could work... 

As with a vertical arch, the direction of the force at the support is 
that of the arch itself at that point.   For a load bearing vertical 
arch, regardless of  geometry and load distribution, all you have to 
know to calculate the lateral thrust at the foundation is the mass 
involved and the angle of  the arch at the bottom.  All the weight must 
be balanced by an equal vertical force, so, for a symmetrical 
arrangement, it's trivial to solve the force distribution graphically.  
Draw the bottom of the arch.  Draw a tangent to the curve at its bottom 
end and a vertical line through the point of intersection.  Choose a 
suitable scale to express half the mass involved (two support points = 
half mass each) and mark the the vertical line to that length from the 
intersection.  Then draw a horizontal line from the marked point to 
intersect the tangent line.  The length of that line gives the lateral 
force in the scale chosen, and the length of the tangent marked off the 
force in the arch.  Do this once, and you immediately see what's going 
on and can estimate the forces whenever you look at an arch in the future.

kb

Lance Collins wrote:
> I have the impression that the catenary idea somehow had the force on 
> the arch being resolved vertically and avoided the problem of 
> horizontal support.  Not so, of course.
>
> Recently I overlooked the Gordon dam in Tasmania.  I was most 
> impressed by the thinness of the concrete wall and how it engaged the 
> rock walls on each side of the gorge.  It seemed to me that the shape 
> of the arch had the water pressure on the wall become a force along 
> the line of the wall pushing into the rock sides.
>
> Lance
>
>   
>