Civil Engineering Reference
In-Depth Information
9.9.1
Structural damping
An extensive database of free vibration measurements from tall buildings in Japan has
been collected (Tamura
et al.,
2000). This database includes data on frequency as well as
damping. More than 200 buildings were studied, although there is a shortage of values at
larger heights—the tallest (steel encased) reinforced concrete building was about 170m in
height and the highest steel-framed building was 280 m.
For reinforced concrete buildings, the Japanese study proposed the following
empirical formula for the critical damping ratio in the first mode of vibration, for
buildings less than 100 m in height and for low-amplitude vibrations (drift ratio,
(x
t
/h)
less than 2×10
−5
):
(9.27)
where
n
1
is the first mode natural frequency and
x
t
the amplitude of vibration at the top of
the building
(z=h)
.
The corresponding relationship for steel-framed buildings is:
(9.28)
The range of application for Equation (9.28) is stated to be:
h
<200 m and
(x
t
/h)
< 2×10
−5
.
Equations (9.27) and (9.28) may be applied to tall buildings for serviceability limit
states criteria (i.e. for the assessment of acceleration limits). Much higher values are
applicable for the high amplitudes appropriate to strength (ultimate) limit states, but
unfortunately little, or no, measured data are available.
9.9.2
Visco-elastic dampers
Visco-elastic dampers incorporate visco-elastic material which dissipates energy as heat
through shear stresses in the material. A typical damper, as shown in Figure 9.14, consists
of two visco-elastic layers bonded between three parallel plates (Mahmoodi, 1969). The
force versus displacement characteristic of such a damper forms a hysteresis loop as
shown in Figure 9.15. The enclosed area of the loop is a measure of the energy dissipated
per cycle and, for a given damper, is dependent on the operating temperature (Mahmoodi
and Keel, 1986) and heat transfer to the adjacent structure.
