Civil Engineering Reference
In-Depth Information
©
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.