Civil Engineering Reference
In-Depth Information
The change in bending moment,
Δ
M
BC
, in panel BC is
P
T
a
P
L
+
P
BC
d
s
p
Δ
M
BC
=
L
−
Δ
x
T
.
(5.10)
−
P
L
+
P
BC
(d/s
p
)
=
When
P
T
(a/L)
0, maximum bending moment occurs in
panel BC.
The relative changes in bending moment given by Equation 5.10 can be examined
to determine the location of the concentrated loads for maximum bending moment at
any panel in the span. The maximum bending moment will occur at the panel point
nearest the center of the span.
5.2.1.1.5 Maximum Bending Moment with Cooper's E80 Load
The criteria for maximum shear force and bending moment in a simply supported span
illustrate that loads must be stepped across the span and their effects investigated at
the location of interest. In particular, the load position for maximum bending moment
is of interest to engineers.
For live load configurations, such as Cooper's E80, that are expressed as a series
of concentrated loads (with or without uniform load segments), the wheel load under
whichthemaximumbendingmomentoccursmaynotbereadilyknownbyinspection,
particularlyonlongerspans.Insuchcases,thedevelopmentofamomenttableorchart
is of benefit for determining the maximum bending moments at any location along the
span. For example, to determine the maximum moment at location C in Figure 5.4,
the load configuration would have to be moved in many successive increments across
thespan.Theconstructionofamomenttable,fortheparticularliveloadconfiguration,
makes such an iterative analysis unnecessary.
P
T
©
Direction of
movement
x
P
P
i
w
A
B
C
x
i
x
l
w
s
l
P
z
i
L
/2
L
/2
FIGURE 5.4
Bending moment at location C for a series of concentrated moving loads.
