Civil Engineering Reference
In-Depth Information
Example 5.2
Determine the bending moment per rail at location C under axles
NP
3, 4,
and 13 of the Cooper's E80 load on a 60 ft long through plate girder span with
a floor system comprising floorbeams and 20 ft long stringers (
Figure E5.2).
With
NP
=
=
3 (Cooper's load configuration wheel number 3)
From Table 5.1:
x
1
=
(S
1
)
3
=
13 ft
since
x
1
≤
L/
2
≤
30 ft; N1
=
1
support B is
(
2
L/
3
+
x
1
)
=
40
+
13
=
53 ft from N1
since(
S
1
)
9
=
48 ft,
NL
=
9,and
xL
=
53
−
48
=
5 ftfrom
NL
=
9tosupportB
NE
is the last wheel on the span and is equal to
NL
=
9
M
B
L
M
(
NL
−
1
)
,N1
+
P
N1,NE
(xL)
60
M
8,1
+
P
1,9
(xL)
60
R
B
=
=
=
6992
+
284
(
5
)
60
=
=
140.20 kips,
R
B
L
3
R
B
L
3
M
(
NP−1
)
,N1
=
M
2,1
M
C
=
−
−
=
140.2
(
20
)
−
460
=
2344 ft-kips.
The superstructure with transverse floorbeams has a 100
[
1
−
(
2344
/
2391
)
]=
2.0% decrease in bending moment with
NP
=
3 at the location
of maximum moment.
With
NP
=
4 (Cooper's load configuration wheel number 4)
From
Table 5.1:
x
1
=
(S
1
)
4
=
18 ft
since
x
1
≤
L/
2
≤
30 ft; N1
=
1
support B is
(
2
L/
3
+
x
1
)
=
40
+
18
=
58 ft from N1
©
N1
NP
NL
C
x
1
B
A
xL
L
/3
L
/2
L
/2
FIGURE E5.2
