t Fr the seismic severity of a site, because it 1 K Fr = lends itself naturally to: 2π...

M
c severity comparison,
time-history
spectrum
c elaboration of severity envelopes for several sites,
fig. 7: application of seismic excitation (time-history, see fig. 6) to 1st single DOF, induces c simple severity increases,
accelerations. The maximum value (γmax ) is by definition one point on the response spectrum of the seismic system.
c approximate estimates of seismic
effects on equipment (damage
potential).
Remark:
M1
The response spectrum must not be
Mi
confused with the FOURIER series
Mn
expansion of a periodic phenomenon,
λ
K1
or the FOURIER transform of an
λ
Ki
λ
Kn
aperiodic phenomenon, which are not
used in seismic studies.
defining the seismic
severity of a site
γ
Safe Shutdown Earthquake (SSE) -
Maximum Historical Earthquake
Likelihood (MHEL)
Defining the seismic severity of a site generally requires the site’s geological data and seismic history.
In France for example, data from the
response spectrum
exceptionally well documented seismic
history (100 years) enables the seismic risk of a site to be established.
Fr
Fr
1
Fri
Frj
Frn
This allows the Maximum Historical
fig.8: construction of seismic response spectrum (various K/M with λ constant).
Earthquake Likelihood to be defined
Cahier Technique Merlin Gerin n° 180 / p.8
which is likely to provoke the maximum Acceleration / velocity /
effect on a given site. For the
displacement conversion
λ
dimensioning of works or equipment it
Response spectra are often
is the SSE which is taken into account: represented in an acceleration/
the SSE is equivalent to the MHEL plus
frequency system of coordinates but
λ
one degree on the MSK scale (modified
1 > λ2 > λ3
are sometimes represented in the
Mercalli scale).
velocity/frequency system of
Basic response spectrum
coordinates. For low damping of
Macro seismic data which correspond
equipment studied (i10%), the
to the above definitions are not
response spectra measured in terms of
sufficient for the engineer who has to
velocity and the relative displacement
design a building or an equipment. He
Fr
can both be deduced from acceleration
will also require the representative
spectra by applying the following
λ :
λ :
λ :
1
2
3
response spectrum of the site
equations to each frequency:
fig. 9: family of response spectra obtained concerned, which is established by
γ
γ
for different dampings during the same
V max max
=
;
D max max
=
.
using instrumental seismic data.
2
earthquake.
π f
(2 π f)2
A seismotheque has been created
(readings taken in regions of
considerable seismic activity), which
γ (g)
corresponds to a scale of magnitudes,
seismic focus depths and epicentral
distances for very diverse geological
6
+ 27
contexts. This seismotheque allows the
5
form of the response spectrum, or basic 4
response spectrum as it is called, to be
+ 7
established, for a given region, with its 3
amplitude depending on the chosen
0
SSE.
This response spectrum defines
2
seismic severity at ground level. The
seismic severity for the storey where
the equipment will be installed still has to be evaluated.
1
Dimensioning spectrum
0.8
Seismic withstand specifications are
widely presented in the form of a family 0.6
of response spectra for each storey.
0.5
These are calculated by taking the
building’s transfer impedance into
0.4
account. An example is given in
figure 10.
0.3
reading the response
0.2
spectrum applicable to a
piece of equipment
Fr (Hz)
The benefit of the response spectrum is 0.1
that it visualises the extreme
1
2
3
5
10
20
30
50
acceleration effects (or displacement
fig. 10: dimensioning spectrum, according to floor levels (in metres) for an industrial site. This is effects) provoked by excitation on a
a spectrum for a damping of 2 %.
single DOF system.
Cahier Technique Merlin Gerin n° 180 / p.9
In fact, everything occurs as if sinusoidal quantities were involved,
velocity (cm/s)
with
1000
V = γ (t) dt et d
∫
= γ (t)dt
∫ ∫
With log/log coordinates the response
500
spectrum can be read along
acceleration, velocity or displacement
200
axes, (see fig. 11).
100
acceleration (g)
Maximum floor acceleration and
200
damping (%)
50
displacement
2
Since the energy from the seismic
20
100
excitation is limited to a frequency
5
100
10
of 35 Hz, the points on the spectrum
10
50
situated above this frequency
5
20
50
represent the behaviour of a «rigid»
20
2
oscillator (very high K/M), which
10
remains dimensionally stable under
1
seismic excitation.
5
20
0.5
The relative displacement of the mass
2
in relation to the support is therefore 0.2
zero and its acceleration is equivalent 10
1
to the support’s acceleration
0.1
(see fig. 12 a).
0.5
5
0.05
The high frequency asymptotic curve
on the response spectrum
0.2
0.02
(Fr u 35 Hz) corresponds therefore to
0.1
0.01
the maximum floor acceleration (see
2
displacement (cm)
right-hand part of figure 13).
0.05
0.005
Remark:
0.02
0.002
For the right hand part of the spectrum 1
0.01
(which corresponds to the
0.001
«infinite»relative frequency), experts
frequency (Hz)
0.5
0.005
use the abbreviation ZPA (Zero Period
0.1