Civil Engineering Reference
In-Depth Information
Maximum stress in the CWR
:
k
d
EA
=
10
−4
in.
−1
λ
d
=
7.30
×
k
t
EA
=
10
−4
in.
−1
λ
t
=
3.65
×
l
d
L
=
1.97.
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
(
1.97
−
1
+
0.14
)
] =−
12,688 psi for both rails.
Force in each rail
=
12.688
(
13
)/
1000
=
165 kips compression; there is risk
of rail buckling.
Rail separation
:
k
d
=
200 lb/in. (rapid strain rate)
k
t
=
50 lb/in. (rapid strain rate)
k
d
EA
r
=
10
−4
in.
−1
,
λ
d
=
5.16
×
k
t
EA
r
=
10
−4
in.
1
.
λ
t
=
2.58
×
Substitution into Equation 4.44 yields
10
−4
10
−4
1
1
Δ
x
s
=−
4.55
×
10
−4
+
=
2.65 in., OK.
5.16
×
2.58
×
Relative displacement
:
Substitution into Equation 4.48 with
n
=
1 yields
e
−λ
L
)
,
Δ
x
=
0.24
(
1
+ λ
L
−
Δ
x
=
0.24
(
1
+
1.97
−
0.14
)
=
0.68 in., which may be excessive requiring a
longitudinally stiffer deck.
Fixed bearing force at the abutment
:
Substitution into Equation 4.47 yields
t
α
0
Δ
C
1
)
T
X
F
=
N
3
(
0
)
−
N
2
(
0
)
=−
EA
r
αΔ
t
(C
2
−
=−
131, 250
(C
2
−
C
1
)
,
2
αΔ
e
−λ
L
C
1
=
=
0.14,
C
1
)
e
−λ
L
C
2
=
(
λ
d
L
+
=
0.30,
X
F
=
131,250
(
0.30
−
0.14
)
=
20,386 lb for both bearings.
