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We were asked to provide our second opinion on the vibration
design of a multi-function community center. The roof of an
auditorium will be used as gym floor for basketball, indoor
soccer and volleyball. The problem was further exaggerated
by having to span the full width of the auditorium in order
to avoid interior columns in an auditorium space, and the
depth of the truss was limited due to building height restrictions.
So a very significant vibration and noise generating event
located directly above a very sensitive and quiet space. All
columns will be supported by deep end bearing piles.
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1. |
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The very first step is to quantify the forcing
function associated with a “game” event. We understood
that a combination of different types of forcing functions
are applied to a structure when a game is played: jogging
force, impact force from bouncing a basketball, and most importantly
the simultaneous jumping of multiple players for, say, a rebound.
An upper bound forcing function must be obtained to represent
all of these components of a “game”. |
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2. |
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We set the auditorium vibration criterion
limits to be less than or equal to the human threshold of
perception (about 8000 micro-inches/sec). |
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3. |
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We followed steps below in order to determine
the basketball event forcing function: |
| a. |
Identify an elevated facility which
is used for basketball playing; here, we used the practice
facility of a San Francisco Bay Area professional basketball
team. Apply impact force (using an instrumented
hammer) to the structure at several locations to determine
the mobility of the structure (mobility is defined as
the velocity response of the structure vs. frequency
due to unit load). |
| b. |
Obtain actual vibration responses (at
the same locations where mobility spectra were obtained
in item “a”) during one of the professional
team's scrimmage matches. |
| c. |
Actual responses (from “b”) divided
by mobility (step “a”) yields the forcing
functions of the basketball game itself -- independent
of the structure. These data are therefore applicable
on any structure for which we can calculate mobility,
so we can apply these spectra to the structure under
design. (We should note that the tests carried
out are not trivial as some difficulties exist in obtaining
accurate data from these types of testing. For
instance, limitations are encountered in trying to obtain
accurate measurements in the low frequency region.
This is due to the difficulty one encounters in applying
enough hammer energy in the low frequency region to
overcome the background amplitudes.) |
| d. |
We obtained the basketball “playing”
forcing function from tests run in the NBA team’s
practice facility. The forcing function was most significant
in low frequencies below about 12 Hz (about 220 lbf
broadband), as we had predicted. The higher frequency
force amplitude (particularly above 30 Hz) was insignificant
(again matching our intuitions). |
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The forcing function obtained in Step 2 above
was applied to our project floor using direct frequency response
analysis option of the FEA program. Response of the auditorium
floor was calculated and found to be rather high. |
5. |
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We looked at several modifications to the structure, including
the proposed isolation of the gym column/structure from the
rest of the building (without isolating the foundations).
We finally settled at the most economical solution of using
same columns (no isolation breaks) but larger sizes for both
gym and auditorium floors. We also sized up the pile columns
from one to four. By doing so, we had enough combined stiffness
in our columns/foundations which resulted in amplitude meeting
the criterion limits. |
