Case Studies



Gymnasium Floor

Problem Definition:
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.


Solution Approach:



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”.




We set the auditorium vibration criterion limits to be less than or equal to the human threshold of perception (about 8000 micro-inches/sec).




We followed steps below in order to determine the basketball event forcing function:


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).


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.


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.)


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).




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.




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.



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