Civil Engineering Reference
In-Depth Information
where
m
A
=
A/g
; where
A
is the axle load,
g
is the acceleration due to gravity,
V
is
the speed of the train, and
R
is the radius of the curve. This can be expressed as
0.0000117
AV
2
D
,
CF
A
=
(4.30)
where CF
A
is the centrifugal force at each axle, kips;
A
is the axle load, kips;
V
is the
speed of the train, mph;
R
5730
/D
, ft;
D
is the degree of the curve (see Chapter 3).
Duetotherail-wheelinterface,theentirecentrifugalforcewillbetransmittedatthe
outer or high rail and, therefore, centrifugal effects are not considered for longitudinal
members inside the curve. The calculation of centrifugal force on a curved railway
bridge is shown in Example 4.10.
=
Example 4.10
A ballasted steel through plate girder railway bridge is to be designed with
a6
◦
curvature track across its 70 ft span. The railroad has specified a 5 in
superelevation based on a 40 mph operating speed. Both the tie depth and
rail height of the track are 7 in. The girders are spaced at 16 ft and the plane
at the top of the rails elevation is 2 ft-8 in above the deck surface at the track
centerline. Determine the effects of the curvature on the design live load
shear and bending moment for each girder.
Geometrical effects (see Example 3.1 in Chapter 3)
:
V
out
=
0.903
V
LL+I
,
V
in
=
1.097
V
LL+I
,
M
out
=
0.916
M
LL+I
,
M
in
=
1.084
M
LL+I
.
Centrifugal effects
:
0.0000117
V
2
D
0.0000117
(
40
)
2
(
6
)
=
CF
A
/A
=
=
0.112,
(M
CF
/M
LL
)
=
(V
CF
/V
LL
)
=±
0.150. (See
Figure 4.16)
(Note that the girder design forces due to centrifugal effects are independent
of impact.)
0.112
[
(
8
+
2.67
)/ (
16
/
2
)
]=±
Combined geometrical and centrifugal effects
:
Since centrifugal forces are not affected by impact (rocking and dynamic ver-
ticaleffects),thecentrifugaleffectonthegirderdesignforces,whichincludes
impact, must be reduced as follows:
(
8
M
CF
(
out
)
M
LL+I
V
CF
(
out
)
V
LL+I
0.112
(
1
2.67
)
(
16
/
2
)
+
0.150
=
=±
=±
0.371
)
=±
0.110.
+
(
1
+
I)
Therefore, the following is determined for the shear,
V
LL+I
, and bend-
ing moment,
M
LL+I
, live load forces (combining impact, geometric and
