Civil Engineering Reference
In-Depth Information
The bending moment,
M
C
, at any location, C, due to moving concentrated and
uniform loads as shown in
Figure 5.4
is
M
C
=
R
A
L
2
−
x
P
i
x
i
,
−
(5.11)
Σ
where
P
i
x
i
is the sum of moments due to loads to the left of C. The left reaction,
R
A
,is
P
i
z
i
+
(wl
w
/
2
)
R
A
=
.
(5.12)
L
Substitution of Equation 5.12 into Equation 5.11 yields
P
i
z
i
+
L
2
−
wl
w
/
2
x
P
i
x
i
.
M
C
=
−
(5.13)
L
From Figure 5.4, the sum of the moments of concentrated loads about B is
P
i
z
i
=
P
i
l
P
.
P
T
(x
P
)
+
(5.14)
Substitution of Equation 5.14 into Equations 5.12 and 5.13 yields
+
P
i
l
P
+
wl
w
/
2
L
P
T
(x
P
)
R
A
=
(5.15)
and
P
T
(x
P
)
L
2
−
+
P
i
l
P
+
wl
w
/
2
L
x
P
i
x
i
.
M
C
=
−
(5.16)
Equations 5.15 and 5.16 illustrate that to determine the end shear force and bending
moment at any location in the simple span due to moving concentrated and uniform
loads (such as the Cooper's E80 load), the following is required:
• The sum of the bending moments of all concentrated loads in front of, and
P
T
(x
P
)
.
• The sum of all concentrated loads on the span,
Σ
P
i
.
• The negative bending moment or the sum of the moments about C of all
concentrated loads in front of C,
Σ
P
i
x
i
.
Since the Cooper's load pattern is constant, it is possible to develop charts and
tables to readily determine the bending moment for various simple span lengths using
Equation 5.16.
Table 5.1
is developed for the wheel load (1/2 of axle load) of
the Cooper's E80 live load. The legend to Table 5.1 outlines the methods used to
