Civil Engineering Reference
In-Depth Information
• Acceptable relative displacement between rail/deck and deck/span to pre-
clude damage to deck and/or fasteners. Occurs due to excessive longi-
tudinal movements (lower longitudinal stiffness) at either rail-to-deck or
deck-to-superstructure.
• Avoidance of bearing component damage.
4.4.3.1
Safe Rail Separation Criteria
If the steel bridge is modeled as a series of spans with a distributed longitudinal
force due to thermal expansion of rails transferred through an elastic deck system,
the magnitude of the axial force in the CWR,
N(x)
,is
EA
r
d
x(x)
d
x
− αΔ
t
c
,
N(x)
=
(4.41)
where EA
r
is the axial stiffness of the CWR;
A
r
is the cross-sectional area of the CWR
(about 13 in.
2
on typical heavy freight railroads);
α
is the coefficient of thermal expan-
sion of the CWR and is
10
−
6
/
◦
F;
Δ
t
c
is the cold weather rail temperature
change (with respect to neutral temperature).
Assuming zero displacement far from the rail break,
x(
∼
6.5
×
∞
)
=
0, and zero force at
the rail break,
N(
0
)
=
0, Equations 4.39 and 4.40 yield
=
−αΔ
t
c
e
−λ
x
,
x(x)
(4.42)
λ
e
−λ
x
)
,
N(x)
=−
EA
r
αΔ
t
c
(
1
−
(4.43)
λ =
√
k
1
/
EA
r
,
k
1
is the longitudinal stiffness associated with a high strain rate
event such as a rail breaking. It is generally about 1/2 of normal strain rate event (such
as rail thermal expansion and contraction) stiffness.
∗
The separation of the CWR at fracture (assumed to occur over the expansion
bearings) is
where
t
c
1
,
1
λ
t
Δ
x
s
=−αΔ
λ
d
+
(4.44)
λ
d
=
√
k
d
/
EA,
where
k
t
EA
,
λ
t
=
k
d
is the equivalent high strain rate event horizontal spring constant for the bridge
deck, and
k
t
is the equivalent high strain rate event horizontal spring constant for
the track ap
proach.
Figure 4.21
outlines the relationship of Equation 4.44, where
F
k
=
+
√
(k
d
/k
t
)
.
1
∗
From Association of American Railrods, Transportation Technology Center, Inc. (AAR/TTCI) testing
related to draft report of “Thermal Forces on Open Deck Steel Bridges,” January, 2009.
