Civil Engineering Reference
In-Depth Information
E
XAMPLE
20.4
A load of length 2m and intensity 2 kN/m crosses the simply sup-
ported beam AB shown in Fig. 20.9(a). Calculate the maximum positive and negative
values of shear force and the maximum value of bending moment at the quarter
span point.
A
K
B
2.5 m
10 m
(a)
0.25
ve
k
a
b
ve
S
K
IL
0.75
(b)
k
1
b
1
a
1
F
IGURE
20.9
Maximum shear
force and bending
moment at the
quarter span point
in the beam of
Ex. 20.4
ve
M
K
IL
1.875
(c)
The shear force and bending moment influence lines for the quarter span point K are
constructed in the same way as before and are shown in Fig. 20.9(b) and (c).
Maximum shear force at K
The maximum positive shear force at K occurs with the head of the load at K. In this
position the ordinate under the tail of the load is 0
.
05. Hence
1
2
(0
.
05
S
K
(max
+
ve)
=
2
×
+
0
.
25)
×
2
=
0
.
6kN
The maximum negative shear force at K occurs with the tail of the load at K. With the
load in this position the ordinate under the head of the load is
−
0
.
55. Thus
1
2
(0
.
75
S
K
(max
−
ve)
=−
2
×
+
0
.
55)
×
2
=−
2
.
6kN
Maximum bending moment at K
We position the load so that K divides the load in the same ratio that it divides
the span. Therefore 0
.
5m of the load is to the left of K and 1
.
5m to the right of K.
