Civil Engineering Reference
In-Depth Information
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P T
Direction of
movement
P L
P n
C
x L
A
B
b n
x T
a
L /2
L /2
FIGURE 5.2 Concentrated moving loads applied directly to the superstructure.
where P T is the total load on the span and P L is the load to left of location C.
Equation 5.1 indicates that V C will be a maximum at a location where P T ( x T / L )is
a maximum and P L a minimum. If P L =
0 the absolute maximum shear in the span
occurs at the end of the span and is
P T x T
V A =
L .
(5.2)
For any span length, L , the maximum end shear, V A , will be largest when the product
P T x T is greatest. Therefore, for a series of concentrated loads (such as the Cooper's
E loading), the maximum end shear, V A , must be determined with the heaviest loads
included in P T and these heavy loads should be close to the end of the beam (to
maximize the distance, x T ) .
This information assists in determination of the absolute maximum value of end
shear force, which can be determined by a stepping the load configuration across the
span (by each successive load spacing) until P T x T causes a decrease in V A . With the
exception of end shear in spans between L =
23 and 27.3 ft, this occurs when the
second axle of the Cooper's design load configuration is placed at the end of the
beam (locationA in Figure 5.2). For spans between L
=
23 and 27.3 ft, the maximum
shear occurs with the fifth axle at the end of the span.
The maximum shear force at other locations, C, may be determined in a simi-
lar manner by considering a constant P T moving from x T to x T +
b n (where b n is
successive load spacing). In that case, the change in shear force,
Δ
V C , at location C is
b n
L
Δ
V C =
P T
P L .
(5.3)
The relative changes in shear given by Equation 5.3 can be examined to determine the
location of the concentrated loads for maximum shear at any location, C, in the span.
The first driving wheel of the configuration.
 
 
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