Civil Engineering Reference
In-Depth Information
Table 17.6
Section properties for the bridge model
Element properties
CIP box superstructure
Bent cap beam
Bent column
Area in ft
2
(m
2
)
72.74 (6.76)
27.00 (2.51)
12.57 (1.17)
I
x
-Torsion in ft
4
(m
4
)
a
1177 (10.16)
100,000
a
25.13 (0.22)
I
y
in ft
4
(m
4
)
b
401 (3.46)
100,000
b
9.00 (0.08)
I
z
in
ft
4
(m
4
)
c
9697 (83.69)
100,000
c
9.00 (0.08)
a
This value has been increased for force distribution to bent columns. Actual value is
I
x
=
139 ft
4
(1.20 m
4
).
b
This value has been increased for force distribution to bent columns. Actual value is
I
y
=
90 ft
4
(0.78 m
4
).
c
This value has been increased for force distribution to bent columns. Actual value is
I
z
=
63 ft
4
(0.54 m
4
).
L
=
0 08
.
L
+
0 15
.
f d
≥
0 3
.
f d
(17.26)
p
ye bl
ye bl
where:
d
bl
is the diameter of the longitudinal reinforcement (ft)
f
ye
is the effective yield strength of steel reinforcement (ksi)
L
is the distance from the critical section of the plastic hinge to the
point of contraflexure (ft)
In this example,
L
is the clear height of the column since the column base is
pinned. The second element is the actual column element. The third element
represents the varying section between the column section and the column
head, which is modeled by the fourth element. The moments of inertia for
the column and the plastic hinge elements are based on a cracked section
calculated using the moment-curvature and moment-rotation curves.
NL-THA was performed to the three bridges to compare its results with the
SPA and MPA results. Three actual acceleration histories were implemented
in this example; which were adjusted to match the design response spectrum
for each analysis case. Those actual acceleration time histories are as follows:
• El Centro 1940
• Northridge 1994, Century City LACC North
• Santa Monica 1994, City Hall Grounds
Maximum seismic demand displacement of monitoring point is predicted
using the SPA, MPA (without inelastic behavior correction for demand dis-
placement), and the modified MPA (using modified control point displace-
ment
u
cn
) and then compared with the average demand displacement of the
same node obtained from the NL-THA using three different ground accel-
eration histories closely matching the demand spectrum.
Results of the modal analysis, modal periods and frequencies, modal
participation factors, and modal participating mass ratios are shown in
Table
17.7a
-
c, respectively.
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