Civil Engineering Reference
In-Depth Information
Example 4.19
In order to reduce the relative displacements at the rail-to-deck-to-
superstructure system in Example 4.18, a fastening system on the bridge
with greater horizontal elastic spring stiffness is proposed. Determine the
maximum stress in the CWR, relative displacement between the rail and
superstructure and rail separation.
k
d
=
850 lb/in. (normal strain rate)
k
t
=
100 lb/in. (normal strain rate)
Relative displacement
:
k
d
EA
=
10
−3
in.
−1
,
λ
d
=
1.06
×
l
d
L
=
2.87.
Substitution into Equation 4.48 with
n
=
1 yields
e
−λ
L
)
,
Δ
x
=
0.16
(
1
+ λ
L
−
Δ
x
=
0.16
(
1
+
2.87
−
0.056
)
=
0.63 in.; relative displacement remains quite
large.
Maximum stress in the CWR
:
Substitution into Equation 4.45 with
n
=
1 yields
9425
1
e
−λ
d
L
)
σ
cwr
=−
+
0.31
(
λ
d
L
−
1
+
σ
cwr
=−
9425 [1
+
0.31
(
2.87
−
1
+
0.056
)
]
=−
15,052 psi for both rails.
Force in each rail
=
15,052
(
13
)/
1000
=
196 kips compression; the rail may
buckle.
Rail separation
:
k
d
=
425 lb/in. (rapid strain rate)
k
t
=
50 lb/in. (rapid strain rate)
k
d
EA
r
=
10
−4
in.
−1
,
λ
d
=
7.53
×
k
t
EA
r
=
10
−4
in.
−1
.
λ
t
=
2.58
×
Substitution into Equation 4.44 yields
10
−4
1
1
Δ
x
s
=−
4.55
×
10
−4
+
=
2.37 in., OK.
10
−4
7.53
×
2.58
×
