Civil Engineering Reference
In-Depth Information
Example 4.17
The double track open deck steel multibeam railway bridge shown in
Figure
E4.1
comprises two 45 ft simple spans (
Figure E4.10).
The CWR with elastic
rail fastenings is used on the friction-bolt fastened timber deck. Determine
the maximum stress in the CWR, relative displacement between the rail and
superstructure, rail separation, and longitudinal bearing force at the pier. The
following are characteristics of the bridge:
100
◦
F
Δ
T
c
= Δ
t
c
=−
50
◦
F
Δ
t
h
=
40
◦
F
Δ
T
h
=
10
−4
(bridge)
α
0
Δ
T
c
=−
5.00
×
10
−4
(CWR)
αΔ
t
c
=−
6.50
×
10
−4
(bridge)
α
0
Δ
T
h
=
2.00
×
10
−4
(CWR)
αΔ
t
h
=
3.25
×
10
6
(
26
)
=
10
8
lb (for two typical CWRs)
EA
r
=
29
×
7.5
×
k
d
=
400 lb/in. (normal strain rate)
k
t
=
100 lb/in. (normal strain rate)
Maximum stress in the CWR
:
k
d
EA
r
=
10
−4
in.
−1
,
λ
d
=
7.30
×
k
t
EA
r
=
10
−4
in.
−1
,
λ
t
=
3.65
×
l
d
L
=
0.39.
Substitution into Equation 4.45 with
n
=
2 yields
9425
1
0.31
e
−λ
d
L
e
−λ
d
L
,
σ
cwr
=−
+
λ
d
L
−
1
+
λ
d
L
+
σ
cwr
=−
9425 [1
+
0.31
(
0.39
−
1
+
(
0.39
+
0.67
)
0.67
)
]
=−
9758 psi for two rails.
Force in each rail
=
9758
(
13
)/
1000
=
127 kips compression, OK.
Rail separation
:
k
d
=
200 lb/in. (rapid strain rate)
k
t
=
50 lb/in. (rapid strain rate)
k
d
10
−4
in.
−1
,
λ
d
=
EA
r
=
5.16
×
k
t
EA
r
=
10
−4
in.
−1
.
λ
t
=
2.58
×
