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some extent subjective that they’re not
confident on previous methods.

For this reason Arup developed a
It means method based on first principles, using the
best data available on footfall forces, and
Where, , is the deflection under unit load, which is flexibility. well-established response-calculation
The inverse of is stiffness. This proportionality is useful for the methods of general applicability to the
approximate evaluation of the effects of minor design changes, prediction of the dynamic response of
because quite significant flexibility (or stiffness) changes can structures. With this basis Arup believed
often be accomplished with only minor changes in the structural that their method would be applicable
system. In absence of significant changes in the mass; the change to the majority of structures, simple
in the stiffness controls the change in the natural frequency, or complex, of conventional or novel
enabling one to estimate how much the flexibility or stiffness of structural form, and constructed of any
a given floor design needs to be changed to meet a given velocity material.
criterion.
• Measured footfall force
[6]
Arup used research data of Kerr ,
Example 5
who measured 880 single footfall force
VC-A (50 m/s=2000 in/s) floor to VC-C (12.5 m/s=500 in/s) time histories from over 40 individuals
Solution: walking on an instrumented force plate
set into a floor at a range of walking
speeds; and other footfall force–time
history data from other published sources
That is, the floor stiffness needs to be increased by a factor of 2.5 [7–10] are also adopted. The continuous
records were then analyzed to obtain
Improved methodologies for the prediction of parameters suitable for predicting the
footfall-induced vibration response of low-frequency and high-
Michael Willford and Caroline Field, both are colleague of Arup frequency floors. For low-frequency
Consulting Engineering, published a paper on SEMICONDUCTOR floors, the harmonic components of
FABTECH 28th Edition, Dec. 2005 , which introduced improved the force functions were derived to
[4]
methodologies for the prediction of footfall-induced vibration. permit the response of the floor to many
They developed new and claimed more accurate ‘performance- successive footfalls to be calculated by
based’ prediction procedures incorporating recent, comprehensive, ‘steady-state’ resonance calculations.
experimental research into footfall forces, and taking advantage For higher-frequency floors, identifying
of the capabilities of modern design-office computer software. the peak velocity of a floor due to each
They said the new methods are not limited by the approximations separate footfall of the continuous record
and inaccuracies inherent in the old empirical approaches, and was concerned.
extensive calibration against field measurements has shown them
to be far more reliable than other methods currently in use. • Harmonic components of footfall
force
• Background Figure 11 shows the dynamic load
Recall the Gordon and AISC equation, both of them can be factors (DLFs – defined as harmonic force
expressed as a general form: , where C is amplitude/weight of person) for the first
three harmonics of footfall forces derived
an semi-empirical coefficient, since the natural frequency
from all the measured data. The mean
, it implies that less mass will be helpful to increase trend is indicated by a line through the
natural frequency and then reduce the velocity response; but individual data points. It can be seen
Arup has found mass to be beneficial. Arup also considered the that the first harmonic force increases
semi-empirical coefficient to be crude corrections and and to strongly with footfall rate, and

NEW FAB TECHNOLOGY JOURNAL APRIL 2012 51