Civil Engineering Reference
In-Depth Information
CWR stress criteria (
n
= 2 spans)
-5000
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
-15,000
F
= (
α
0
Δ
T)/(
α
Δ
t)
-25,000
-35,000
-45,000
CWR stress
F
= 0.75
-55,000
CWR stress
F
= 1.00
-65,000
-75,000
L
L = L
(k/EA)
1/2
FIGURE 4.23
Typical relationships between stress in the CWR, length of span, deck and
track stiffness, and rail size for two expansion/contraction ratios.
e
−λ
L
,
C
n
=
C
n
−
1
)
e
−λ
L
for
n
where
C
1
=
(
λ
L
+
≥
2,
α
0
is the coefficient of thermal
expansion of the bridge,
Δ
t
h
is the hot weather rail temperature change with respect to
neutral temperature,
T
h
is the hot
weather
bridge temperature change with respect
to construction temperature,
Δ
λ =
√
k
2
/
EA
r
, and
k
2
is the equivalent normal strain
rate event horizontal spring constant for the rail-to-deck-to-superstructure system.
Figure 4.23 outlines the relationship of Equation 4.45 for a two-span bridge with two
expansion ratios.
The forces in the fixed bearings may also be determined from Equation 4.45 by
considering
F
abt
=
N
3
(
0
)
−
N
2
(
0
)
,
(4.46)
F
pier
=
N
4
(
0
)
−
N
3
(
0
)
.
(4.47)
Figure 4.24
outlines the relationship of Equation 4.46 for a two-span bridge with two
expansion ratios.
4.4.3.3
Acceptable Relative Displacement between Rail-to-Deck
and Deck-to-Span
Assuming a multiple span bridge with
n
spans of equal length,
L
, and alternating fixed
and expansion bearings on substructures, Equation 4.40 with the boundary conditions
outlined in
Section 4.4.3.2
may be solved to yield
=
α
0
Δ
T
Δ
x
=
x
2
(n
+
1
)
(L)
−
x
n
+
1
(L)
(
1
+ λ
L
−
C
n
)
(4.48)
2
λ
where
T
is the bridge temperature change with respect to construction temperature,
λ =
√
k/
EA
r
, and
k
2
is the equivalent horizontal spring constant for the rail-to-deck-
to-superstructure system.
Δ
