Railroad Eng., Track Analysis

1. Chapter 15 – Track Analysis
CE 533

2.  Basic Requirements
 Track must support the loadings
and guide the train’s path
 Track Quality Determines
 Permissible wheel loadings
 Safe speed of the train
 Overall safety of operations
 Dependability of operations
 FRA Class 1,2,3,4,5,6,7,8,9

3. Track Cross-Section
 Railroad track is designed to be
economical and easy to maintain
Rail
Crosstie
Ballast
Subgrade
Subballast

4. Track Functions
 Guide vehicles
 Provide a high vehicle ride quality
 Withstand and distribute loadings
 Static (36 tons/axle) or
(36,000 lbs./wheel)
 Plus Dynamic (Impact)

8. Major Rail-Related Agencies/Groups
 AREMA – American Railway Engineering and
Maintenance-of-Way Association
 Technical society, individual professional members,
primarily publishes Recommended Practices and other
technical literature
 AAR – Association of American Railroads
 Composed primarily of Railroad Companies that represent
the industry in many ways, mainly large Class I railroads
 ASLRRA – American Short Line and Regional
Railroad Association
 Similar to AAR for Short Line and Regional RR Companies
 FRA – Federal Railroad Administration
 Part of USDOT, mainly promulgates and enforces railway
safety regulations
 STB – Surface Transportation Board
 Part of USDOT, mainly an economic regulatory agency

9. AREMA
 AREMA develops engineering standards and
recommended practices for railroad track,
structures, and facilities
 Manual for Railway Engineering
 Practical Guide to Railway Engineering
 AREMA also holds conferences and conducts
training seminars
 www.arema.org

10. www.arema.org

11. The FRA
 Establishes minimum track safety
standards (TSS) applicable to railroad
companies
 Require railroads to have program to find and
address track defects
 Inspects to ensure that the each railroad’s
program is effective
 FRA does not enforce TSS on industrial
track
 FRA can halt operations on unsafe
industry track
 www.fra.dot.gov

13. FRA Classes of Track
Part 213 -- Subparts A to F for Class 1-5, Subpart G for Class 6-9

16. Class 1 Track
10 mph or less
Class 4 Track
60 mph freight
80 mph passenger
Class 2 Track
25 mph freight
30 mph passenger

17. Static Wheel Loads
(Wheel Load)(# of wheels) = Gross Weight of Car
Axle Load Gross Weight of Cars
Axle load
(tons) Gross weight of cars (lbs) Type
10 80,000 Light rail transit
15 120,000 Heavy rail transit
25 200,000 Passenger Cars
25 200,000 Common European freight limit
27.5 220,000 U.K. and Select European limit
33 263,000
North American free interchange
limit
36 286,000
Current Heavy Axle load weight
for North American Class 1
39 315,000 Very limited use; research phase
Heavy Tonnage
Freight

18. Wheel/Rail Contact “Patch”
The contact “patch” is
about the size of a dime
=0.50 in2

19. Track
 Track is a dynamic
system of interacting
components that
distributes the loads
and provides a smooth,
stable running surface
for rail vehicles.
 System must provide
vertical, lateral and
longitudinal stability 132 lb
rail
Dense-Graded Agg.
9”wide x 7”thick x 9’ long
Ballast

20. Track Design and Construction
Desirable Attributes:
 Balance Stiffness and Resiliency
 Resistance to Permanent Deformation
 Stability
 Adjustability

22.  A profitable RR must have good track.
 Track is apparently a simple structure, has
changed little
 Loadings (pressures) must be reduced
through the rail, ties, ballast and subballast to
within the bearing capacity of the underlying
subgrade.

23. Methods used to design track and cross-
section
 Trial and Error
 Empirical – based on trial and error
 Empirical/Rational – measure
loadings and material properties
 Rational – stress/strain analysis
and measurements
• Trackbed is NOT the permanent way – varies greatly, must be
maintained continuously

24. layer 4 bedrock
layer 3 subgrade
layer 2 sublayer
layer 1 ballast
Beam Element
Spring
Symmetry
Line
Tie
Rail
all-granular ballast trackbed
subgrade
wood tie
subballast
ballast

25.  Requirements
 It acts as an elastic, load-distributing structure, thus
the load distribution depends on the STIFFNESS and
FLEXIBILITY of the track.
 Assume a 100-ton car: wheel load = 33,000 lbf on
rail. Area of contact is assumed to be 0.5 sq in., thus
contact stress is 66,000 psi static (dynamic more)
 Average subgrade will support 20 psi (1.4 ton/sq ft).
Thus, the rail, ties, ballast, etc. must reduce 66,000
psi to 20 psi or problems will occur.

26. Trackbed is subjected to a variety of loads
and stresses
 Dead loads
 Live loads
 Dynamic loads
 Centrifugal loads
 Lateral loads – hunting and nosing of wheels
 Thermal loads – continuously welded rail (CWR)
 Longitudinal loads – wave action

27. •263,000 lb/8
=33,000 lb/wheel
•286,000 lb/8
=36,000 lb/wheel
•315,000 lb/8
=39,000 lb/wheel
•Axle (ton)=
(wheel load(lb) X 2)/2000

28.  Each component distributes the load.
 STIFFNESS (resistance to deflection)
 RESILIENCY (elasticity)
 RESISTANCE TO PERMANENT DEFORMATION
 Chap 26, pages 593-597, track geometry terms
 Gage
 Line
 Surface
 STABILITY
 ADJUSTABILITY
 GOAL – safe and cost effective

29.  Gage (or gauge) – transverse distance
between the rails measured 5/8 inch from
top-of-rail

30.  Line – adherence of
the centerline of the
track to the
established alignment
and to corresponding
presence or lack of
irregularities or
departures

31.  Surface – adherence
to established grade
and uniformity of
cross-level in the
plane across the
heads of the two rails
and adherence to the
established
superelevation on
curves

32. TRACK ANALYSIS
 Must determine allowable loads and deformations
 Must determine actual loads and deformations
 Compare and Adjust (component materials and thicknesses)
 Much early work performed by A.N. Talbot
 Many early researches idealized systems – Winkler,
Westergaard, Boussinesq, etc.
 Talbot treated track as a continuous and elastically supported
beam
 Computer systems (layered analysis) have been developed
recently
 Geotechnical and Pavement Design Technologies are applied

33.  TALBOT’S FORMULAS
 Load from a group of wheels is distributed over
adjacent ties in decreasing magnitude –
proportional part depends on track stiffness.
 The differential equation for an elastic beam is:
0
4
4










y
dx
y
d
EI 
y
p 



34.  Tie Loads
 Generally assume approx. 40% of axle load is
carried on one tie (for 20” tie spacing, lt). See
Chart.
 Generally assume 2/3 of bottom of tie is in bearing
against the ballast (middle 1/3 is not tamped
because of center binding)

37.  Dynamic Loads
s
s
v P
P
P 


100
33



w
D
V

Dynamic Static
Impact

41.  TRACK STIFFNESS
 Up and down movement (pumping) of track under
repetitively applied and released loads is a prime
source of track deterioration.
 Design of track should keep deflection to a
minimum.
 Differential movement causes wear of track
components.
 Modulus is defined: load per unit length of rail
required to depress that rail by one unit. (lb/in./in.)

42.  TRACK STIFFNESS continued…
 Some of deflection is due to rail and ties 0.06 in.
 Ballast deflection (compression) 0.15 in.
 Rest is due to subgrade (variable) 0.05 – 0.15 in.

44. Figure 5 Figure 6

47.  Need high quality material under ballast

49.  Calculation:
 3
1
3
4
64EI
Y
P
o










Note: Increasing rail size has little effect on μ

50.  Distribution of Pressures
 For ballast pressure
 Talbot developed empirical
formula for subgrade
pressure
40
.
0
3
2
2









bL
P
P
dyn
a
<65 psi
25
.
1
8
.
16
h
P
P a
c  <20 psi
See eq. 15.33 & fig. 15.13

53.  If well compacted, good quality subgrade, then Pc
will become uniform at h=lt; thus h should be ≥ lt
(Fig. 15.14)
 Maybe h should be > lt if poor subgrade ,or quality
of subgrade should be improved

56. Example Calculation—Talbot Design
Calculate Pa and Pc for the following:
 100 ton car loaded, 33-inch diameter wheel
 50 mph speed
 9-inch wide by 8 ½-feet long wood ties at 20
inches c-c tie spacing use h=20 inches and
h=10 inches. Pv
Pa
Pc

57. 100 ton car=200,000 lb+63,000 lb=263,000/8=P
=33,000 lb wheel load
=P+θP=33,000+(0.50)33,000
=49,500 lb/wheel dynamic

58. < 65psi ok

59.  When h=20 inches:
 When h=10 inches:

60. Example Calculation—Track Modulus
(Kerr Method)
 Wheel Load (P)=33,000 lbf on 140-lb rail on
wood ties
 p = -μy
 Calculate “k” or “μ” for Track Deflection
(y)=9/64 inch, also y=18/64 inch

61. P=(33,000 lb/wheel)/(2,000 lb/ton)
=16.5 tons/wheel
Wm=9/64 in. or 0.1406 in.
Wm/P=0.1406/16.5=0.00852
Table 1: μ=3200 lb/in./in.
Figure 5: μ=3200 lb/in./in.
(About Optimum for wood tie track)

62. Wm=18/64 in. or 0.2812 in.
Wm/P=0.2812/16.5=0.01704
Table 1: μ=1450 lb/in./in.
Figure 5: μ=1450 lb/in./in.
(Not stiff enough for wood tie
track)

66. Kentrack
 Layer-Elastic
 Finite Element
 Design Method
(Later)