Civil Engineering Reference
In-Depth Information
Rail separation criteria
0
0
0.5
1
1.5
2
2.5
3
-0.001
-0.002
-0.003
Fk = 0.50
-0.004
-0.005
Fk = 1.00
-0.006
-0.007
Fk = 1.50
-0.008
-0.009
Fk = 2.00
-0.01
L
L = L(k/EA)
1/2
FIGURE 4.21
Typical relationships between rail separation, length of span, deck and track
stiffness, and rail size for four stiffness ratios.
4.4.3.2
Safe Stress in the CWR to Preclude Buckling
Assuming a multiple span bridge with
n
spans of equal length,
L
, and alternating fixed
and expansion bearings on substructures, Equation 4.39 with the boundary conditions
• Zero displacement of the CWR away from the bridge [e.g.,
x
5
(
∞
)
=
0]
•
C
ompatibility of displacements in the rail over bearings [e.g.,
x
2
(L
2
)
=
x
3
(
0
)
]
• Zero displacement at fixed bearings [e.g.,
x
7
(
0
)
=
0
]
• Rail force compatibility over bearings [e.g.,
N
2
(L
2
)
=
N
3
(
0
)
]
• Zero forces at expansion bearings [e.g.,
N
6
(L
6
)
=
0]
may be solved to yield
t
h
1
C
n
)
,
N
n
+
1
(L)
A
r
+
α
0
Δ
T
h
σ
cwr
=
=−
E
αΔ
(
λ
L
−
1
+
(4.45)
2
αΔ
t
h
CWR
Deck
4
5
1
2
3
k
6
7
8
Span
L
6
=
L
FIGURE 4.22
Three-span bridge model.
