Civil Engineering Reference
In-Depth Information
Table 4.12
Typical values of inter-storey drifts for the seismic performance assessment of framed structures.
Performance level
Damage type
Seismic hazard
Inter - storey drift (
d
/
h
)
Limit State
Level
Type
Prob. event (in %)
Values (in %)
Serviceability
Non - structural
Frequent
50% in 50 years
0.2 <
d
/
h
< 0.5
Damage control
Moderate structural
Occasional
10% in 50 years
0.5 <
d
/
h
< 1.5
Collapse prevention
Severe structural
Rare
2% in 50 years
1.5 <
d
/
h
< 3.0
500
500
1st beam yielding
1st column yielding
1st column crushing
Global yield
2.5% ID ratio
10% strength drop
400
400
V
max
300
300
0.75V
max
200
200
100
100
Δ
y
0
0
0
50
100
150
200
0
50
100
150
200
Top Lateral Displacement (mm)
Top Lateral Displacement (mm)
Figure 4.41
Limit states of the three-storey RC irregular frame (positive x-direction) in Figure 4.2: response curve
and evaluation of global yielding
engineering LSs and PLs mentioned above. Some LSs, for example, crushing, plastifi cation and buck-
ling, may belong to either ' damage control ' or 'collapse prevention' depending on their severity within
the structural system; the classifi cation in Table 4.11 is, therefore, indicative rather than defi nitive.
For practical applications, structural assessment should be based on values of measurable physical
parameters that can be associated with engineering limit states and damage states. Comprehensive
reviews of typical response parameters for seismic structural assessment, i.e. damage parameters and
indices, and their values for different LSs, were given by Williams and Sexsmith (1995), Kappos (1997)
and Ghobarah
et al
. (1999) . Since earthquake -induced damage of building and bridge structures is
generally related to inelastic deformations, deformation-based damage indices are more appropriate
than force-based ones. Modern displacement-based seismic design guidelines provide values that rely
primarily on inter-storey drifts
d
/
h
to assess the performance of structural systems. For bridge systems,
maximum values of the lateral drift of the piers are generally recommended. Guiding values for the
assessment of PLs at different seismic hazard levels are provided in Table 4.12 for buildings. For ductile
multi-storey MRFs, the values of
d
/
h
may also be used as an indicator of the fl exural rotational capacity
θ
of members (beams and columns) and connections, i.e.
θ
≈
d
/
h
(Krawinkler
et al
., 2003 ). These values
are, however, not universally accepted.
An example of evaluation of LSs for an RC building is shown in Figure 4.41, depicting the response
curve along positive
x
-direction of the sample frame in Figure 4.2 .
The response curve in Figure 4.41 is obtained by conventional pushover analysis using a force pattern
proportional to the fi rst mode of vibration, as presented in Section 4.6.2.2. The assessment is performed
in terms of both local and global LSs. The local LSs include member yielding and column crushing,
while the global LSs are the onset of global yield, inter-storey drift ID equal to 2.5% and 10% strength
drop. For the structural response curve in Figure 4.41, member yielding is conservatively defi ned as
reaching the yield strain in longitudinal reinforcing steel, i.e.
ε
y
= 0.002. Column crushing is defi ned
