Page 49 - Vol.06

1/3 Length
Area Used
for Dancing
The dynamic forces for rhythmic activities
tend to be large and resonant vibration is
generally too great to be reduced practically
by increasing the damping and or mass. This 1/2 Length
means that for design purposes, the natural
frequency of the structural system, must
be made greater than the forcing frequency, 1.4 m
ƒ, of the highest harmonic that can cause Joist Spacing
large resonant vibration. Equation (3) can 1.25 m
be inverted to provide the following design
criterion (Allen 1990a):

22.5 m
Figure 8
Note: = forcing frequency=
where is the step frequency and
is a constant (1.3 for dancing, 1.7 for lively Forcing Weight of Dynamic Dynamic
Load
rticipants*
concert or sports event, 2.0 for aerobics) Activity Frequency W P Coefficient a i W P
f, Hz a i
The parameters of equation (4) are shown kPa kPa
as Table 3. Dancing: First harmonic 1.5-3 0.6 0.5 0.3
The minimum required fundamental Lively concert or Sports
Event
natural frequencies of different rhythmic First Hamonic 1.5-3 1.5 0.25 0.4
events are shown as Table 4. Secon Hamonic 3-5 1.5 0.05 0.075
Jumping exercises:
First Hamonic 2-2.75 0.2 1.5 0.3
Example 3 Secon Hamonic 4-5.5 0.2 0.6 0.12
The effective weight of the floor is 3.6 Third Hamonic 6-8.25 0.2 0.1 0.02
*Based on maximum density of participants on the occupied area of the floor for
kPa, including 0.6 kPa for people dancing
commonly encountered conditions. For special events the density of participants can
and dining. The effective composite moment be greater.
of inertia is 1,100 x106 mm4.
Table 3. Estimated Loading During Rhythmic Events

Effective Weight of Minimum Required
Forcing Total Weight Wt
Activity Acceleration Limit Construction Participants Wp Fundaamental Natural
(1)
Frequency f, Hz (3)
kPa kPa Frequency f n , Hz
Dancing and Dining a 0 /g=0.02
Heavey floor 5 kPa 3 0.6 5.6 6.4
Light floor 2.5 kPa 3 0.6 3.1 8.1
Lively concert or Sports Event a 0 /g=0.05
Heavey floor 5 kPa 5 1.5 4.6 5.9 (2)
Light floor 2.5 kPa 5 1.5 5 6.4 (2)
Aerobics only a 0 /g=0.06
Heavey floor 5 kPa 8.25 0.2 5.2 8.8 (2)
Light floor 2.5 kPa 8.25 0.2 2.7 9.2
Jumping Exerxises Shared with Weight Lifting a 0 /g=0.02
Heavey floor 5 kPa 8.25 0.12 5.12 9.2 (2)
Light floor 2.5 kPa 5.5 0.12 2.62 10.6 (2)
Notes to Table 4:
(1) Equation (4) is supplied to all harmonics listed in Table 3 and the governing forcing frequency is shown.
(2) May be reduced if, according to Equation (3), damping times mass is sufficient to reduce second and third harmonic resonance to an acceptable level.
(3) From Equation (5).
Table 4. Application of Design Criterion, Equation (5), for Rhythmic Events

NEW FAB TECHNOLOGY JOURNAL APRIL 2012 49