Civil Engineering Reference
In-Depth Information
P
n
C
A
B
a
b
L
/2
L
/2
FIGURE 5.24
Determination of equivalent uniform loads for simple span shear and bending
at location C.
Equivalent uniform loads for Cooper's and other locomotive and train live loads
have been presented often in the early railway bridge design literature (Waddell, 1916;
Ketchum, 1924).
5.2.1.3.5 Shear Force and Bending Moment at any Location in Simply
Supported Spans [with Concentrated Moving Loads Applied
Directly to the Superstructure (Figure 5.24)]
The use of uniform loads can be generalized for shear, bending, and floorbeam reac-
tion at any location, C, on a simple span. The area under the shear influence line
in Figure 5.24 is
b
2
/
2
L
and the area under the bending moment influence line in
Figure 5.24 is
ab/
2. Therefore, the equivalent uniform load for Cooper's live load
shear and bending moments, respectively, are
V
LL
2
L
,
w
ev
=
(5.28)
b
2
M
LL
2
ab
.
w
em
=
(5.29)
Theequivalentuniformload,
w
ev
or
w
em
,canbecalculatedforvariousspanlengths,
L
b
, at location C (with
a < b
) and plotted to provide curves for use by design
engineers. The curves will be of the general form shown in
Figure 5.25.
Curves such
asthesewerepreparedbythebridgeengineerDavidB.Steinman
∗
in1915.Thecurves
=
a
+
∗
David B. Steinman also designed long-span suspension bridges and further developed J. Melan's
“deflection theory” for suspension bridge design (Steinman, 1953; Petroski, 1995).
