Page 148 - Handbook of Materials Failure Analysis

144 CHAPTER 6 Failure analysis of concrete sleepers/bearers

Q b
Λ ¼ ;
2
where Λ is the lever arm; Q is the sleeper end distance; and b is the half length of rail
loading at sleeper neutral axis.
The theoretical bending moment is calculated with:

q r
M r ¼ Λ;
2
where M r is the rail seat bending moment.
To account for the theoretical and experimental moments measured, the lever arm
is factorized:
Λ m ¼ ϕ Λ;

where Λ m is the factorized lever arm and ϕ¼dynamic impact factor of the sleeper
bending moment at the rail seat.
The empirical coefficient ϕ is found to be 1.6, and combining all these equa-
tions provides the maximum sleeper bending moment at the rail seat:
Λ
M r ¼ ε c 1 φ P:
2
Similarly, the bending moment at the center can be determined to be:
ð
EI centreÞ
M c ¼ M r ζ ;
EI railseatÞ
ð
where M c is the bending moment at sleeper center; ζ is the scale factor relating bend-
ing stress at rail seat to sleeper center; and EI is the sleeper stiffness.

4.2.3.3 Australian design code
The Australian design code is in many ways similar to the AREA method, but is more
rigorous [20]. The positive moment, with load distributed as shown in Figure 6.17a,
at the rail seat is given by:
q r l gÞ
ð
M r + ¼ ;
8
where M r+ is the maximum positive bending moment at rail seat; q r is the design seat
load; l is the sleeper length; g is the distance between rail centers.
The maximum negative bending moment is given by either 67% of the maximum
positive moment, or 14 kN m, whichever is greater.
For the center of the sleeper, the maximum positive moment, with load distrib-
uted as shown in Figure 6.17b, is given by:
M c+ ¼ 0:05q r l gÞ, for standard gauge;
ð

M c+ ¼ 0:10q r l gð Þ, fornarrow gauge;
where M c+ is the maximum positive bending moment at the sleeper center.