Geology Reference
In-Depth Information
Table 1. Response descriptors for inelastic buildings under earthquake ground motion
Response parameter
Definition
Maximum ductility
x t
x y
Number of times velocity changes sign
( ) |
µ max
=
max |
0 t
≤ ≤
t f
Number of yield reversals
x
x
p i
,
x
= ≤ ≤
max |
|
p i
,
0
t
t
Maximum normalized plastic deformation range
f
y
1
|
x
x
|
N
p i
,
1
µ ac
=
+
.
Normalized cumulative ductility
i
=
y
x t
x
( ) |
f
µ res
= |
Residual (permanent) ductility
y
t f
1
E I
=
E I
( )
t dt
f y x y
0
Normalized earthquake input energy
t f
1
E H
=
E H t dt
( )
f y x y
Normalized total hysteretic energy dissipated
0
E
E
r
=
H
E
Ratio of total hysteretic energy to input energy
I
1
dE t
dt
( )
P
=
max
I
I
,max
f x
0
≤ ≤
t
t
f
Maximum rate of normalized input energy
y
y
1
dE t
dt
( )
P
=
max
D
D
,max
f x
0
≤ ≤
t
t
f
y
y
Maximum rate of normalized damping energy
1
dE t
dt
( )
P
=
max
H
H
,max
f x
0
≤ ≤
t
t
f
y
y
Maximum rate of normalized hysteretic energy
2.2 Damage Measures for
Inelastic Structures
during the ground shaking. This measure does not
incorporate information on how the earthquake
input energy is imparted on the structure nor how
this energy is dissipated. Earthquake damage oc-
curs due to the maximum deformation or ductil-
ity and the hysteretic energy dissipated by the
structure. Therefore, the definition of structural
damage in terms of the ductility is inadequate.
The last three measures indicate the rate of the
earthquake input energy to the structure (i.e., how
fast the input energy E I is imparted by the earth-
The literature on damage measures for structures
under earthquake loads is vast (e.g., Cosenza et
al, 1993, Ghobarah et al, 1999). Damage indices
are quantified in terms of a single or a combina-
tion of structural response parameters. Table 1
summarizes several damage measures that are
based on a single response parameter (Powell &
Allahabadi 1988, Cosenza et al, 1993). The first
measure represents the ultimate ductility produced
 
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