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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
Platform for dynamic tests: preliminary studies, design and construction
1. Introduction
The study of induced vibrations in slabs has been intensified in
recent years. There are several causes that led to this reality
and, among the most important may be mentioned the increas-
ing use of more resistant materials that lead to more slender
and flexible slabs and the use of structures for activities that
were not initially foreseen in the original project . These factors
have contributed with increasing frequency to the appearance of
vibration problems in structures and, mainly, in the slabs. Flex-
ible structures are generally more susceptible to the effects of
dynamic loads. A major factor is the low natural frequency pre-
sented by this type of structure, which responds, in an amplified
way, to dynamic loads that present a frequency close to the one
in the structure. Among the dynamic loads of low performance
frequency that are common in slabs, can be mentioned the
loads generated by human activities, such as, walking, dancing,
jumping, etc.
Therefore, may be mentioned several reports of structures that
presented problems related to dynamic loads response, generated
by movements of people, including the Maracanã (RJ), Nilson-
Nelson (DF), Mangueirão (PA) stadiums, the Universal Church of
the Kingdom of God (RJ) and the Millennium Footbridge (London,
England). (Faisca, [1]).
The Millennium Footbridge, located in London, was interdicted less
than an hour after its opening, due to the presentation of strong
lateral vibrations. The walkways suspended of the Hyatt Regency
hotel in Kansas City / USA presented excessive vibrations during
a dance championship, which culminated in the collapse of the
structure and caused the death of 114 people and injuried another
200. (Ramroth, [2]).
Thornton et al, [3] apud Ritchey and Kenneth, [4], studied two
buildings cases, a one used as a high school, and the other as a
college, both with large spans and spaces, and containing rooms
for physical activities conduction, in which were perceived exces-
sive vibrations, causing discomfort to users.
Webster and Vaicaitis, [5], apud Ritchey and Kenneth, [4] investi-
gated the strong vibrations present in a system of mixed slabs, of
a building in the city of New York, produced by people who used to
dance near a restaurant, causing fear to occupants of the restau-
rant during dinner. These vibrations produced accelerations in the
slab of up to 7m/s² and, displacements of 3.3 mm.
Battista and Varela [6] found problems with excessive vibrations
in floors of residential buildings, even though they met the criteria
standards for structural design.
In cases like those mentioned structures becomes necessary a
thorough study of the vibrations induced by the activities that peo-
ple develop, because these oscillations can cause problems of dis-
comfort and injury to health, and, in extreme cases, can endanger
the safety of the structure. It is also important to mention that the
characterization of this type of loads is not yet consensus among
researchers in the field and should be studied, besides other as-
pects, the effect of the crowd, the lateral vibrations, etc.
Moreover, for the development of a reliable theoretical model for the
analysis, design and verification of buildings slabs under the action
of dynamic loads induced by people, it is important that this model
is validated through theoretical and experimental correlations of the
structure dynamic responses. Hence the importance of being able
to perform experimental tests on slabs subjected to dynamic loads.
Based on the foregoing, it is numerically studied the dynamic
behavior of some configurations of slabs subjected to loads
induced by man, with a view to build a platform for dynamic
tests. The structures are modeled using a finite element pack-
age (ANSYS 2007, [7]) that allows the realization of modal and
transient analyzes, providing as results images, animations,
displacements records, nodal velocities and accelerations, as
well as, displacement amplitude versus frequency and request-
ed moments graphics, used for dimensioning the structure.
With these elements is done the slab scaling, which will be used
as test platform to simulate different situations of human loads,
thereby, allowing both, numerical characterization of loads in-
duced by people moving, as wel as the evaluation of the struc-
tural response.
1.1 Considerations about induced load
The vibrations caused by human activities may occur either ver-
tically or horizontally (lateral and longitudinal), motivated by the
vertical and horizontal components of the force exerted by peo-
ple (Bachman, [8]). This force can, generally, be considered as
periodic (CEB, [9]) and, can be represented by a static portion
representative of the person´s weight of the person and, by a
Fourier series, in which, the first harmonic has a frequency vary-
ing between 1, 8 and 3.5 Hz according to the activity performed
(step frequency). In the other hand, the following harmonics
are characterized by multiple frequencies of that first one.
According to Bachmann and Ammann [10], a person jumping
produces a vertical force which can be written as:
(1)
Where:
K
p
= F
p,max
/G:Dinamic impact factor.
F
p,Max
: Dynamic load peak.
G: Person´s weight (generally considered G=800N)
t
p
: Contact duration.
T
p
= 1/f
s
: Loading period.
The loading, and consequently the vibrations, in the lateral di-
rection are caused by the person’s body movement in this direc-
tion. Generally, the functions of horizontal lateral and horizon-
tal longitudinal loadings, resulting from the action of walking,
running, dancing, etc. can also be modeled in the same way,
by choosing the appropriate Fourier coefficients. These lateral
vibrations need special attention because they were responsi-
ble, for example, for the problems that occurred at the opening
of the Millennium Footbridge in London. According to Dallard
et al, [11], people are less stable laterally than vertically and
therefore, more sensitive to lateral motion, which leads them to
modify the movement characteristics when experiencing lateral
vibrations, trying to “tune” their movements with the structure
and causing, thereby, an increase of the vibration´s amplitude.
This problem is known as lock-in effect.