Civil Engineering Reference
In-Depth Information
Moving direction
Front axle
e
(
l
)
P
P
P
P
e
x
0
(a)
Extreme function of a forward-moving procession
l
Backward-moving direction
re
P
P
P
P
Front axle
re
(
l
)
x
0
Extreme function of a backward-moving procession
l
(b)
Figure 3.17
Extreme functions of (a) forward- and (b) backward-moving processions.
function. To determine extreme values due to leading vehicles, a similar
extreme function
re
( )
is introduced. As shown in Figure 3.17b,
re
( )
defines the extreme value within the range
[ , ]
x l
for a procession moving
backward from
l
to
0
.
Having the extreme function for reverse-moving procession established,
searching the location and maximum value of a procession that contains
an overweight vehicle is equivalent to finding the maximum value of the
following equation:
( )
=
(
)
+
( )
+
(
)
L x
e x a
−
o x
re x a
+
1
(3.66)
2
where
o
( )
is the influence value of the overweight vehicle at position
x
.
Simply moving the overweight vehicle from 0 to
l
will give the maximum
value by Equation 3.66. The influence values of following and leading nor-
mal vehicles can simply be obtained from forward and backward extreme
functions, respectively. However, it should be noted that the finding of fol-
lowing vehicles' positions on
e
( )
is from
x
−
2
to 0, and the leading vehi-
cles' positions on
e
( )
is from
x
+
1
to
l
.
When implementing this method, the following issues should be taken
into consideration: (1) the length of the original influence line has to be
extended at both ends to ensure the last axle is moving out of range;
(2) the extreme positions and values obtained are based on moving vehicles
from 0 to
l
(this value should be compared with that of moving vehicles
from
l
to 0 which can be simply obtained by reversing the influence line);
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