Civil Engineering Reference
In-Depth Information
Midspan section
Diaphragm
Figure 2.32
Finite element model of a box girder bridge.
Hh
=
V
1
a
=
M
1
(
d
/
R
)
V
1
[(
D
/3) −
a
] +
V
2
b
=
M
2
(
d
/
R
)
V
2
[(
D
/3) −
b
] +
V
3
c
=
M
3
(
d
/
R
)
V
3
[(
D
/3) −
c
] =
M
4
(
d
/
R
)
Adding the equations:
Inside
girder
L
Outside
girder
a
b
c
H
M
1
+
M
2
+
M
3
+
M
4
RD
/3
d
and
V
1
= V
2
+
V
3
=
H
Substituting
V
+
V
1
+
V
3
V
2
−
V
1
=
V
/3:
V
1
V
2
V
3
10
3
Σ
M
RD
/3
d
Σ
M
(10/9)(
RD
/3
d
)
V
=
V
1
V
/3
V
/3
V
V
=
or
V
=
D
/6
D
/6
3
D
/6
3
D
/6
Using
K
=
RD
/
d
as for a two-girder system
Σ
M
(10/9)
K
D
V
=
Figure 2.33
V-Load method for curved I-girder bridges.
Load on conj. bm. = (±
M
−
R
t
)
+
A
B
V
−
−
p
V
+
dV
T
(a)
M
—diagram of developed
girder
M
M
+
dM
t
(c) Conjugate beam
y
x
R
α
z
d
α
R
T
+
dT
+
−
−
(b)
t
—diagram of developed
girder
(d)
V
—diagram of conjugate
beam =
T
T—diagram of
developed girder
Figure 2.34
M/R method for curved box girder bridges.
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