The document discusses the analysis and design of pre-stressed concrete sleepers used in railways. It covers the general functions of sleepers in providing support and transferring loads to the ballast bed. The most common types of pre-stressed sleepers are then described, including twin-block, longitudinal, and mono-block sleepers. Finally, the key design considerations for sleepers are outlined, such as loads from static and dynamic wheel forces, distribution of loads to the rail seat and ballast, and moments and stresses experienced by the sleeper.

1. ANALYSIS AND DESIGN OF
PRE-STRESSED CONCRETE SLEEPERS
BY
YUSUF M. HASHIM,
HASSANABBAMUSA
M.TECH. STRUCTURAL ENGINEERING, SHARDA UNIVERSITY
AT

3. the ballast and the subgrade. Prestressed concrete sleepers
are supplied ready for laying straight from the factory,
meaning that all the reinforcing has been built into the
sleeper and prestressed in accordance with the standards.
They were first of all used in France round about in 1914
but are common since 1950 and later developed and used
by the British and German federal railways after the Second
World War.

4. GENERAL FUNCTIONS AND
REQUIREMENTS OF SLEEPERS
• To provide support and fixing possibilities for the rail
foot and fastenings.
• To sustain rail forces and transfer them as uniformly as
possible to the ballast bed.
• To preserve track gauge and rail inclination.
• To provide adequate electrical insulation between both
rails.
• To be resistant to mechanical influences and weathering
over a long time period.

5. TYPES OF PRESTRESSED SLEEPERS
The most commonly used Pre-stressed sleepers which have
been adopted by the railways of various countries are:
1. Twin-block sleepers: These are connected by a coupling
rod or pipe filled with concrete and containing high-tensile
bars for compressing the concrete in the blocks as
illustrated in fig. 1
2. Longitudinal sleepers located continuously under the rails
and connected by flexible tie bars for gauge retention as
illustrated in fig 2

6. 3. Mono-block sleepers: These are Beam-type single-piece
prestressed concrete sleepers, and have roughly the same
dimensions as timber sleepers.
The advantages of the twin-block sleeper over the mono-block
sleeper are: well-defined bearing surfaces and also high lateral
resistance in the ballast bed. The advantages of beam-type
sleepers are their lower cost and high flexural stiffness. They also
provide greater measure of rigidity to the track if the rails are
tightly fastened to the sleepers, preventing rotations at the seating
and buckling of the rails.

7. DESIGN CONSIDERATIONS OF SLEEPERS
The principal function of rail road tie is to distribute the wheel
loads carried by the rails to the ballast. Although the sleeper
is a simple determinate structural element, it is not possible
to precisely evaluate the loads to which a concrete sleeper is
subjected to during its service life, due to the various
uncertainties and complexities inherent in the variables
involved, together with the inadequate knowledge of the
dynamics of the track structure.

8. The various factors influencing the design of sleepers are;
1. The static and dynamic loads imposed on rail seats which
depend upon;
• The type of track (straight or curved)
• It’s construction and standard of maintenance
• The axle load and their spacing
• The running characteristics, speed and standard of
maintenance of vehicles.

9. 2. The ballast reaction on the sleeper, which is influenced
by;
• The shape of the sleeper.
• It’s flexibility and spacing.
• The unit weight of the rail.
• The standard on maintenance of the track.
• The characteristics of the ballast.
END OF FIRST PRESENTER

10. The “permissible stress” method is currently most commonly used to
design sleepers. However, the permissible stress principle does not
consider the ultimate strength of materials, probabilities of actual loads,
and the risks associated with failure, all of which could lead to the
conclusion of cost-ineffectiveness and over design of current pre-stressed
concrete sleepers.
Recently, the limit states design method, which appeared in the last
century and has been already proposed as a better method for the design of
pre-stressed concrete sleepers. The limit states design has significant
advantages compared to the permissible stress design, such as the
utilisation of the full strength of the member, and a rational analysis of the
probabilities related to sleeper strength and applied loads.
First Concept
DESIGN OF PRE-STRESSED CONCRETE SLEEPERS
 introduction

11.  Codes of practice for design of pc sleepers
 Indian standard (IS: 12269 – 1987) with amendment No.6 of June 2000,
Specification for 53-S grade cement for manufacture of concrete sleepers.
 Indian Railway Standard Specification for Pre-tensioned Pre-stressed
Concrete Sleepers, For Broad Gauge And Metre Gauge , Serial No. T-39-
85 (Fourth Revision – Aug’ 2011).
 Australian Standard (AS 1085.14-2003), Railway track material Pre-
stressed concrete sleepers
 design of pc sleepers
(A) - GENERAL CONDITION
1. TYPE AND SPACING
The sleepers shall be pre-stressed concrete sleepers intended for track
designs using centre-to-centre spacings of sleepers of 500 mm to 750 mm.
The sleepers are designed as fully prestressed sections where the limiting
stresses are based on the fatigue resistance of the concrete.

12. 2. SHAPE AND DIMENSIONS
The depth and width of the sleeper may vary throughout its length. The
minimum length of the sleeper shall be determined by the bond development
requirements of the pre-stressing tendons, and the base width shall then be
determined by the allowable bearing pressure.
3. CLEAR TENDON COVER
Minimum clear concrete cover to tendons at the soffit of the sleeper shall
be 35 mm. Elsewhere, the minimum clear concrete cover to tendons
generally shall be 25 mm with the exception that the tendon may be exposed
at the end faces.
(B) - DESIGN FORCES
1. VERTICAL WHEEL LOAD
The design static wheel load shall be specified by the purchaser. NOTE: For
information about dynamic effects on wheel loads and sleepers, See Appendix
2. QUASISTATIC LOAD
The Quasistatic load is the sum of the static load and the effect of the static
load at speed. It includes the effects of the geometrical roughness of the track
on vehicle response and the effect of unbalanced superelevation.

13. The dynamic load is the load due to high frequency effects of the wheel/rail
load interaction and track component response. A minimum allowance of 150
percent of static wheel load shall be used.
3. DYNAMIC LOAD
The combined quasistatic and dynamic design load is the sum of the static
load, the allowance for the effects of the static load at speed and the allowance
for dynamic effects and shall be not less than 2.5 times the static wheel load.
Therefore, the combined quasistatic and dynamic design load factor (j) shall be
not less than 2.5.
4. COMBINED VERTICAL DESIGN LOAD FACTOR (J)
FIGURE 4.1 AXLE LOAD DISTRIBUTION FACTOR (DF)

14. The proportion of vertical load taken by a single sleeper resulting from
a single wheel may be determined from the following equation provided the
values used in the equation can be determined:
where
Qx = the load carried by any sleeper, per rail, in kilonewtons, for a single wheel at
distance x
x = distance from the sleeper to the wheel load, in metres
zx = rail deflection at distance x from a point load
s = sleeper spacing, in metres
Q = static wheel load, in kilonewtons
λ = (k/4EI)0.25
k = track modulus, in megapascals
E = Young's modulus for the rail steel, in megapascals
I = second moment of area for the rail section, in metres

15. RAIL SEAT LOAD
The value of the rail seat load (R) shall be based on the impact and load
distribution factors determined in accordance with Clauses 4.2.1 and 4.2.2 and
shall be calculated as follows:
R = jQ DF/100 .
BALLAST AND BALLAST PRESSURE
The maximum ballast pressure shall be determined from loading conditions similar
to those for the maximum positive bending moment at the rail seat (see Clause
4.3.2.1 and Table 4.1). This maximum ballast pressure )( ab p is based on a
uniform pressure distribution beneath each rail seat and is calculated using the
appropriate equation from Table 4.1.
Table 4.1 maximum ballast pressure

16. LATERAL LOADS
In order to prevent gauge-widening under traffic, fastenings shall restrain
the rail from lateral movement when a lateral load is applied at the rail head
in addition to vertical wheel load as specified in Clause 4.2.1.1. AS 1085.19
provides requirements for resilient fastenings (see Section 5).
LONGITUDINAL LOADS
The rail shall be restrained to avoid excessive longitudinal movement. A minimum
longitudinal restraint force of 10 kN per rail seat shall be allowed. Maximum movement of
the rail relative to the rail seat under such a load shall not exceed the values given in
AS 1085.19 (see Section 5).

18. RAIL SEAT NEGATIVE DESIGN BENDING MOMENT
The rail seat negative design bending moment (MR−) shall be not less than 67 percent of
the rail seat positive design bending moment or 14 kNm, whichever is greater.

19. MOMENTS AT CENTRE
CENTRE POSITIVE DESIGN BENDING MOMENT
The maximum positive bending moment of the sleeper shall be based on a
pressure distribution beneath each rail seat, similar to that shown in Figure 4.2(a).
The length of the ballast pressure distribution beneath each rail seat and the centre
positive design bending moment (MC+) shall be calculated from the appropriate
equation given in Table 4.3.

20. CENTRE NEGATIVE DESIGN BENDING MOMENT
The maximum negative bending moment shall be taken to occur at the centre of
the sleeper, under partially or totally centrebound conditions producing tensile stress
at the top and compressive stress at the underside of the sleeper.
The value of the centre negative design bending moment (MC−) for track gauge of
1600 mm and greater is based on a ballast pressure distribution as shown in Figure
4.2(b) and is calculated as follows:
The value of the maximum centre negative bending moment (MC−) for track gauge of
1435 mm is based on a uniform distribution of ballast pressure on the sleeper soffit
and is calculated as follows:

23. LOSS OF PRESTRESS
The loss of pre-stress shall be determined by the methods specified in AS
3600. For preliminary design, a value of 25 percent may be assumed.
NOTE: A lower value of total loss may be considered if it can be proven by
testing (see Paragraph E7, Appendix E).
DEVELOPMENT LENGTH AND END ZONE
The development lengths of tendons shall comply with AS 3600. Bursting
and spalling forces shall be assessed and reinforcement provided if needed.

24. Thank you
!
ANY QUESTIONS TO BE CLARIFIED
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