Civil Engineering Reference
In-Depth Information
centrifugal force effects)
V
out
=
V
LL+I
(
0.903
+
0.110
)
=
1.013
V
LL+I
,
V
in
=
1.097
V
LL+I
,
M
out
=
M
LL+I
(
0.916
+
0.110
)
=
1.026
M
LL+I
,
M
in
=
1.084
M
LL+I
.
4.3.2.4
Lateral Forces from Freight Equipment
In addition to the centrifugal lateral forces due to track curvature, lateral forces caused
by track irregularities and the wheel-rail interface geometry must be considered in
the design of steel railway bridges. The differential equation of horizontal (lateral)
vibration, neglecting equivalent lateral motion viscous damping, is
∂
4
z(x
,
t)
∂x
4
m
∂
2
z(x
,
t)
∂t
2
EI
y
+
=
h
L
(x
,
t)
,
(4.31)
where
z(x
,
t)
is the superstructure lateral deflection at distance
x
and time
t
,
I
y
is the
lateral moment of inertia (with respect to the vertical axis),
h
L
is given by
N
=
1
δ
+
s
i
−
h
L
(x
,
t)
(x
Vt)H
L
i
(t)
,
i
=
s
i
is the distance from load
H
i
(t)
to the first load
H
1
(t)
, and
H
L
i
(t)
is the applied
random horizontal lateral force (due to track irregularities and wheel-rail interface
motion).
Assuming later
a
l, vertical, and torsional vibrations are uncoupled, the solution of
Equation 4.31 for
z(L/
2,
t)
is (see Equation 4.13)
sin
π
ω
y1
t
,
2
H
L
(t)
Vt
L
−
V
ω
y1
L
sin
π
z(L/
2,
t)
=
(4.32)
2
V/L)
2
mL
[ω
y1
−
(
π
]
2
/L
2
EI
y
/m
.
Therefore, as even simplified dynamic methods are often inappropriate for routine
or ordinary design, it is desirable to determine lateral forces from tests conducted on
in-service bridges.
Recent tests concerning the dynamic lateral forces on in-service bridges (Otter
et al., 2005) have confirmed that the AREMA (2008) design recommendation of a
single moving lateral force of 25% of the heaviest axle of Cooper's E80 load is an
appropriate representation of these effects.
The magnitude of lateral forces is of particular importance regarding the design
of span lateral and cross bracing.
∗
Therefore, in addition to the recommendation of
where
ω
y1
= π
∗
Lateral loads from freight rail equipment are considered applied directly to bracing members (see
Chapter 5) without producing lateral bending of supporting member flanges or chords.
