Civil Engineering Reference
In-Depth Information
the multi-parametric nature and the complexity of the problem have not
yet permitted the development of specifi c design provisions to be included
in modern seismic codes, hence the effect of asynchronous excitation is only
partially or indirectly considered. More specifi cally, most modern codes in
the US and Japan deal with the problem solely on the basis of seating length
provisions. AASHTO prescribes a minimum bearing support length
N
s
for
the expansion ends of all girders which is a function of the length of the
deck
L
(in meters), the height
H
of the column or pier (in m), and the skew
angle
of the support (in degrees), based on the following dual relationship
and the Seismic Performance Categories (SPCs, in particular A, B, C and
D, as defi ned in AASHTO):
α
(
)
(
)
⋅
2
⎧
⎩
203
+
1 67
.
LH
+
6 66
.
1
+
0 000125
.
α
for
:
SPC
AandB
(
)
=
N
in mm
[22.4]
s
(
)
(
)
⋅
2
305
+
2
50
LH
+
10 0
1
+
0 000125
α
for
SPC
CandD
A similar expression is provided by MCEER/ATC-49 (MCEER/ATC,
2003) wherein the minimum seating length
N
s
is prescribed as a function of
the distance between joints
L
, the tallest pier height
H
between the joints,
the width of the superstructure
B
and the skew angle
α
:
⎡
⎤
2
B
L
11
+
.25
FS
a
+
⎛
⎝
⎞
⎠
(
)
=
v
1
N
s
in mm
0 10
.
+
0 0017
.
L
+
0 007
.
H
+
0 05
.
H
⋅
1
2
⋅
⎢
⎢
⎥
⎥
cos
⎣
⎦
[22.5]
where the ratio
B/L
should not exceed 3/8,
F
v
is the site coeffi cient for the
long-period branch of the design response spectrum, and
S
1
the one-second
period spectral acceleration.
Moreover, it is recommended that if geotechnical conditions at abut-
ments and intermediate piers result in different soil classifi cations, then
response spectra should be determined separately for each abutment and
pier, having a different site classifi cation and then the design response
spectra can be taken as the envelope of the individual spectra.
An effort to relate the expected relative displacements of the deck d
a
of a multiply excited bridge system to the overall length
L
, has also been
made through a statistically derived amplifi cation factor
R
D
(Sextos
et al.
,
2003b):
(
()
−
)
δ
=
R
δ
=
08
.ln
L
28
.
δ
[22.6]
a
D
s
s
where d
s
is the relative displacement that would result from 'standard' syn-
chronous motion analysis and
L
is the overall bridge length (in m). A model
to compute the differential displacements of points on the ground and on
the top of a SDOF linear elastic system has also been proposed while
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