Civil Engineering Reference
In-Depth Information
P
n
P
n
-1
P
3
P
2
P
1
P
... ...
C
n
-1
C
2
C
1
Vehicle with fixed axle spacings
Simplified denotation
(a)
(b)
P
n
P
n
-1
P
3
P
2
P
1
P
n
P
n
-1
P
3
P
2
P
1
P
n
P
n
-1
P
3
P
2
P
1
... ...
... ...
... ...
... ...
C
n
-1
C
2
C
1
≥
m
C
n
-1
C
2
C
1
≥
m
C
n
-1
C
2
C
1
Procession of identical vehicles with a minimum spacing
(c)
P
P
P
... ...
≥
a
≥
a
Simplified denotation of procession of identical vehicles
(d)
P
P
P
P
w
P
P
P
... ...
... ...
≥
a
≥
a
≥
a
2
≥
a
1
≥
a
≥
a
Simplified denotation of procession containing overweighted vehicles
(e)
Figure 3.15
(a-e) Typical vehicle loads and vehicle processions.
and trailing spacing between other vehicles. When determining the extreme
positions of such a procession, these spacing are variables in addition to the
location of the first vehicle. As each vehicle can be treated as constant, this
type of procession can be simplified as shown in Figure 3.15d. Further, a
procession may contain one and only one overweight vehicle with different
leading and trailing spacing to other regular vehicles. Similarly, it can be
simplified as shown in Figure 3.15e.
Figure 3.16a shows an example of the influence line. The goal of search-
ing extreme live loads is to find the number and positions of vehicles on
the influence line that makes the influence value maximal or minimal.
Considering the minimum can be reached by the same procedures as the
maximum after reversing influence value signs, the following procedures
are illustrated for reaching maximum values only.
An extreme value function
e
( )
is introduced in the dynamic planning
method (Shi et al. 1987). The value of
e
( )
is the extreme influence value of a
particular vehicle or vehicle procession in the loading range from 0 to
x
. As
a longer range will not produce less influence value than a shorter range,
e
( )
is a monotonically increasing function as shown in Figure 3.16b. Taking a
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