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Re: Foundations for a 3-pinned arch stadium

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> From: "Kevin Below" <kbofoz(--nospam--at)>

> For an indoor sports stadium with 200-ft span, I have seen several examples
> using huge curved glu-lam beam sections about 6 ft high, at about 30 ft
> spacing.  These beams are assembled on-site into a 3-pinned arch
> configuration (a pin at each support, and a pin at mid-span.)
> The horizontal reaction at the base pins is enormous, and exceeds the
> vertical reaction.  For example, 470 kips horizontal, and 405 kips
> vertical.  The horizontal reaction is provided mostly by passive soil
> reaction on the perimeter wall.
> Is this good enough ?  Any thoughts on that ?

The foundation of a long-span arch structure with a high span/ht ratio (high
horizontal reactions relative to vertical reactions) requires more than
ordinary consideration. Small movements can have significant structural
consequences. Consider the difference between brittle failure and
elastic/plastic failure as a comparison.

For most structures, those with a span/ht aspect ratio closer to 1,
foundation movement (failure) is likely to be more closely associated with
service condition issues (e.g. cracking drywall), than collapse.

> Is the passive reaction going to allow movement before it mobilizes ?
> Enough to be noticeable ?

Yes. Do a simple diagram and you can calculate the mid-point deflection of a
3 pinned rigid body for 1" foundation displacement (a common structural
accommodation spec).

> What about seismic effects on the soil behind the wall ?  Will it cause the
> soil to move under the pressure from the arches ?

> What about a tie-rod (it would need to be big) under the sports surface,
> tying the 2 sides together ?

If you even start to think about a tie-rod, ask the arch designer what base
movement tolerance has been considered ("zero" is not a real world response
but may be the actual boundary conditions of the analysis). Then do this
A = P*L/(E*delta)
As you note, this will need to be big. If the arch has not been assessed for
base movement, it will be REALLY big.

Consider also:
Tie-rod will generally permit/cause foundation to return to dead load
equilibrium location after occasional load (snow, wind). You may want to
Independent pier, especially relying on passive earth resistance, just keeps
moving away over time.

Check out these 2 articles:

Civil Engineering vol 73, no. 12, Dec 2003, Flying High. Eugene Kettering
building at the US Air Force Museum in Dayton Ohio. This describes and has
foundation details for the post-tensioned buttress with bearing mat
supporting the 300' wide x 88' high arches.

Civil Engineering vol 74, no. 2, Feb 2004, Air Show. Smithsonian National
Air and Space Museum at Washington Dulles International Airport, Chantilly,
Virginia. The article is very light on foundation information (bedrock
within 3m (10ft) of surface) for the arch which is 72 m wide x 31 m tall
(236' x 102').

Okay, so they're exceptional because they hang aircraft from the rafters but
the concepts are the same.

These 2 museums are on my structural tourism list. I might even look at the

Paul Ransom, P.Eng.

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