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Annoying Floor Vibrations

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Fellow Engineers,

        I have been retained by an architect for the renovation of a
multi million dollar house.  Part of the work required the removal of a
number of adjustable columns in the basement of the residence and
replacing them with longer spanning beams in order to provide larger
clear open spaces.  One of the new beams has vibration characteristics
which the owner finds annoying.  The particulars are described in the
following paragraphs.  For those who are not interested in this problem,
please excuse the fact that this may be rather lengthy.

        The annoying beam was originally three 2x10 supported on posts.
It was upgraded by applying two C10x25, one on either side, with a
simple span of 23 feet and supported by new steel columns and footings
on either end.

        The loading consists of 2x10 floor joists at 16" centres
spanning 12 feet on one side and 14" on the other with specified live
load of 40 psf.  In addition, there is an open hearth fire place (a
masonry fire pit supported on the floor with a metal hood and chimney
suspended from the roof) of unknown weight (conservatively estimated at
7,000 pounds) located  near the third point of the 23' steel beam.

        Although renovation work is ongoing the owner has been living in
the house for most of the summer.  As I understand it he has only
recently become annoyed by the vibrations which must have been occurring
for a few months.  In reviewing the problem I also would find the
vibrations somewhat undesirable.  I guess I would describe them as "not
really bad but some improvement is desirable".  The vibrations can be
noticed by a person standing anywhere in the beam's tributary loading
area when another person is walking or jumping anywhere else in the
beam's tributary area, even from opposite sides of the steel beam; so
the problem appears not to be the with floor joists but rather to be
with the steel beam.

        The steel beam which I designed has a live load deflection of
L/445 and a natural frequency of approximately 5 Hz based on dead load
only.  The supported floor joists (14' span) have a natural frequency of
about 12 hz based on the joists acting alone, and about 17 Hz if the
plywood sheathing is assumed glued to the joists to create full T-beam
action.  Nails may secure the plywood sufficiently to increase the
natural frequency of the joist system but the magnitude of the increase
is questionable.

        I have consulted two references: Commentary A, from the
Structural Commentaries to the National Building Code of Canada, 1995
(Alberta Building Code references 1995 edition); and CSA S16.1 M94,
Appendix G.  These references have suggested remedies including
increasing the stiffness (which I can do by increasing the the beams),
and increasing damping (which I don't know how to do, except by adding
cover plates which are loosely bolted to the beams to allow slipping;
and I'm not too confident with this).  They specifically recommend
AGAINST adding mass to the system.

        I would appreciate anything anyone can suggest to help me solve
this problem.


H. Daryl Richardson

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