Page 146 - Handbook of Materials Failure Analysis

142 CHAPTER 6 Failure analysis of concrete sleepers/bearers

l g

M r ¼ q r :
8
For sleepers with bearing plates fitted (Figure 6.15c), then the maximum bending
moment at the rail seat for this condition is given by:

l g j
M r ¼ q r ;
8
where j is the length of sleeper bearing plate.

4.2.2 Maximum sleeper bending moment at the center of the sleeper
Maximum bending at the center of the sleeper generally occurs when it is said to be
centerbound (or when load is greater in the center). The two common solutions for
this problem are the Battelle Solution and the Raymond Solution. Battelle assumes
that the sleeper is resisted by a single-point load at the center of the sleeper, and can
be calculated from:
g
M c ¼ q r ;
2
where M c is the maximum sleeper bending at sleeper center.
This solution is believed to be extremely unlikely to occur in real-world situa-
tions, but can still be considered an upper-bound solution for the maximum sleeper
bending moment at the center of the sleeper.
Raymond assumes a uniform bearing pressure over the total length of the sleeper,
based upon experimental work carried out by Talbot [20]. Therefore, the maximum
bending moment can be calculated from:

g l 2g l
M c ¼ q r ¼ q r :
2 4 4

4.2.3 Flexural requirements of sleepers
As noted earlier, the type of flexural limit imposed upon sleepers varies according to
the sleeper type. For prestressed concrete sleepers, the design bending moment
capacity of the sleeper is what must be considered. There are various methods of
analysis, as outlined below.

4.2.3.1 The AREA design method
The AREA method assumes that, due to a gradual redistribution over time, the
sleepers will settle on the ballast to a uniform contact distribution over the entire
length of the sleeper [20]. This produces positive flexure at the rail seat and negative
flexure at the center of the sleeper. Based on its own method of determining the rail
seat load, the maximum positive bending moment at the rail seat is given by:
2
ð
Wl gÞ
M r ¼ ;
8