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Re: Granite Artwork - need anchorage advice

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An estimate of expected life may require non-corrosive materials.

I would be concerned of orthogonal motions causing concentrated stresses at
corners. Spawling of a corner could lead to a violent drop of elevation.

A round base hidden in a key-way might be best. The shaft could also begin
to cantilever resistance after allowing some movement.

A low friction base with a dish curvature will cause the mass to act as
though it were swinging from a pendulum. The pendulum height is the radius
of the dish. I once studied hinged legs that all tilt inward and inline with
lines that intersect above the object. Do not use this method. That acts as
a pendulum also, but it does not work in the orthogonal directions.
Orthogonal directions cause a binding in the geometry of the legs. I believe
this will be part of the reference -The Behavior of Inverted Pendulum
Structures During Earthquakes-, published 1956 by EERI.

Structural analysis programs i.e. Sframe has non-linear linkages that can
model a rocking motion. Be careful, single mass and element models sometimes
don't work in programs designed for large matrixes.

I have some references for rocking solid masses. I was first introduced to
solid massed as in a nuclear reactor shell. A good spring and mass matrix
can be found in work by Novak, as I recall he was in Canada. Later his work
was translated into simpler terms in one of the first seismic ATC documents
from the 80's. It models soil springs and demonstrates the used of damping

ATC-3: The report, Tentative Provisions for the Development of Seismic
Regulations for Buildings (ATC-3-06). The second printing of this report,
which includes proposed amendments, is available through the ATC office.
(Published 1978, amended 1982, 505 pages plus proposed amendments)

Rocking between solid objects is different from the soil springs, but the
above is a good first attempt to understand a possible range of behavior.

I worked with Bernard Gabrielsen of San Jose State. He developed rocking
models of tall thick wall segments supporting a concrete roof. The blocks
were stacked and post tensioned through the core to the base. It was for an
existing large structure at Lawrence Livermore Laboratories. Leaving a
message at the University will eventually get to him. He might be happy to

Dr. James N. Brune shares an interest in rocking solid masses. He can be
found at the Geology Department at the Reno University of Nevada. He has
been awarded several large grants to search for and study precarious rocks.
If they stand for thousands of years, then that area may not have had high
seismic activities. I believe there is an interest in finding areas of the
Southern California to secure facilities that need to survive for a long
time. He has contracted several studies for the rocking phenomena. The
following are some of the papers.

Resulting analysis work by his consultants left Dr. Brune with equations too
complicated to verify. Their best results have been to attach accelerometers
to balanced rocks and gently push on them to not cause damage, and observe
the measured motions. A model of your monument might tell the best story.

 -Estimates of the Ground Accelerations at Pont Reyes Station during the
1906 San Francisco earthquake.- By Abdorasool Anooshehpoor, Thomas H.
Heaton, Baoping Shi, and James Brune, Bulletin of the Seismological Society
of America, 89, 4, pp. 845-853, August 1999. This has a rocking block
diagram and equations.

Precarious Rocks along the Mojave Section of the San Andreas Fault,
California: Constraints on Ground Motion form Great Earthquakes, James N.
Brune, Seismological Research Letters Vol. 70, No.1 Jan/Feb 1999, This has a
long list of references.

Precarious Rock Evidence for Low Ground Shaking on the Foot-Wall of Major
Normal Faults, James N. Brune Seismological Laboratory, University of
Nevada, Reno, To be published Or may have in Bulletin of the Seismological
Society of America.

David Merrick, SE

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