Geoscience Reference
In-Depth Information
∆
d
and
define expected displacement shape of structure
Select design displacement
Derive displacement
∆
sys
and effective mass Msys
for the equivalent SDOF system
m
e
F
Σ
m
i
∆
i
2
Σ
m
i
∆
i
Σ
m
i
∆
i
1.
2.
D
sys
=
h
e
M
sys
=
∆
sys
From the ductility
µ
=
∆
d
/
∆
y
estimate equivalent damping
ξ
(of SDOF system)
ξ
=
ξ
(
µ
, structural type
)
30
F
u
F
y
Elasto - Plastic
Streel Frame
Concrete Frame
3.
r k
i
20
ξ
(%)
k
i
k
eff
10
Unbonded
Prestressing
0
∆
y
∆
d
123456
µ
After defining DRS (
T
,
ξ
) = DRS (
T
, 5%)
η
(
T
,
ξ
), find:
effective period
T
e
0.5
0.4
0.3
0.2
0.1
0
5%
4.
Stiffness
10%
15%
2
M
sys
T
eff
2
4π
20%
k
eff
=
∆
d
30%
T
e
01234
5
Period (seconds)
Compute base shear, design storey forces (and design structural members)
5.
m
i
∆
i
V
b
=
k
eff
∆
sys
F
i
=
V
b
m
i
∆
i
Σ
Fig. 2.1. Outline ofmain steps of theDirect Displacement Based Design (DDBD)
method (courtesy ofProf. Rui Pinho)
ofdata,theamplificationofspectralresponseondifferentgroundprofiles,andthespecial
analysis devoted to alluvium filled valleys and basins. Finally, the type of hazard maps
produced is illustrated both in terms of uniform hazard (UH) spectra and of a simplified
bilinear
DRS
model.
2. Empirical prediction of displacement spectral response (
DRS
)
over a broad period range
The experience gained from a previous study on
DRS
at long periods (Faccioli et al.,
2004) indicated at an early stage that crucial for the entire work was a tool for mak-
ing reliable empirical predictions of horizontal and vertical, arbitrarily damped
DRS
,at
periods from
<
1sto
>
10s. Existing attenuation relations for spectral ordinates typically
