Civil Engineering Reference
In-Depth Information
Calculation of the maximum dynamic live load bending moments for
strength and fatigue design is as follows:
• The maximum bending moment impact for strength design
= ( 0.167
+
1809.2 ft-kips.
• The mean bending moment range impact for fatigue design
0.362 )( 3420.0 ) =
=
633.2 ft-kips.
• The maximum dynamic live load bending moment for strength design
[
0.35 ( 0.167
+
0.362 ) ] ( 3420.0 ) =
=
5229.2 ft-kips.
• The mean dynamic live load bending moment range for fatigue design
3420.0
+
1809.2
=
=
3420.0
+
633.2
=
4053.2 ft-kips.
4.3.2.2
Longitudinal Forces due to Traction and Braking
Longitudinalforces,duetotrainbraking(actingatthecenterofgravityoftheliveload)
and locomotive tractive effort (acting at the freight equipment drawbars or couplers),
are considerable for modern railway freight equipment. Longitudinal forces from
railway live loads exhibit the following characteristics (Otter et al., 2000):
• Tractive effort and dynamic braking forces are greatest when accelerat-
ing/decelerating at low train speeds.
• Span length does not affect the relative magnitude of braking forces, due to
the distributed nature of emergency train braking systems.
• Traction forces from locomotives may affect a smaller length of the bridge.
• Participation of the rails is relatively small (particularly when the bridge and
approaches are loaded) due to the relatively stiff elastic fastenings used in
modern bridge deck construction.
• The ability of the approach embankments to resist longitudinal forces is
reduced when the bridge and approaches are loaded.
• Grade-related traction is relatively insignificant for modern high adhesion
locomotives.
The locomotive and car wheels may be modeled as accelerating or decelerating
rolling masses that do not slide (complete adhesion ) as they traverse the bridge
superstructure.Theforcescreatedbythevertical,horizontal,androtationaltranslation
of the rolling mass are shown in Figures 4.10a-c. The longitudinal traction forces
applied to the superstructure may be determined by superposition of the vertical,
horizontal, and rotational effects of the rolling mass for linear elastic structures.
Neglecting axle bearing and wheel rim friction, the force equilibrium relating
to the vertical effects of rolling motion, considering complete adhesion (no sliding),
provides (Figure 4.10a)
d 2 y(t)
d t 2
W
m F
R V (t)
=
0.
(4.19)
Rolling is the superposition of translation and rotation (Beer and Johnston, 1976).
Nonuniform speed (acceleration for starting and deceleration for braking) and adhesion must exist
between the wheel and rail interface to start and stop trains.
Axle bearing and wheel rim friction are very small in comparison to rolling friction.
 
 
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