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# Re: Analysis of a dome

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Analysis of a dome
• From: Daryl Richardson <h.d.richardson(--nospam--at)shaw.ca>
• Date: Fri, 17 Jan 2003 15:35:46 -0700

John,

If you want something rough and dirty try the following.

Consider a spherical dome of radius, R, and thickness, T, such that a segment of this sphere is contained within your "wall".  Now the compressive stress, f, for a spherical dome subject to UNIFORM PRESSURE, P, is obtained from the well known formula

f = (PR)/(2T).

This comes from (P pi R squared) divided by (2 pi R T) for pressure in cylinders.

The results will depend on how uniform the pressure is.  If you can't make it work with this approach you can't make it work, period.  If you can make it work using this approach you may still need to consider the effects of non uniform pressure before you "bet the rent".  You will require a fairly high "containment force" if your dome radius is significantly larger than tunnel radius; but the tunnel wall may provide this.

Your basic idea seems reasonable and practical but it does lack ductility.  If you're in seismic zone 3 or 4 and have a thin dome you may want to think about this.

Regards,

H. Daryl Richardson

John Yao wrote:

Hello,

I am in the process of designing a headwall at the end of a tunnel.  The wall will have no reinforcement.  Although cracking will occur at the tensile face, the wall will be thick enough so that it acts as a dome.

I need to do some calculations to show that the wall will work, however I don't want to use FEM software.  Are there any quick method of doing this calculations?

I thought of taking sections and using a truss with 3 hinges, but that may be too simple.

Thanks,
John Yao

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