Civil Engineering Reference
In-Depth Information
WL
WL
8
8
ve
ve
ve
F
IGURE
13.27
Complete bending
moment diagram for
fixed beam of
Ex. 13.19
WL
8
L
/4
L
/2
L
/4
and the resultant bending moment diagram has principal values as shown in Fig.
13.27. Note that the maximum positive bending moment is equal in magnitude to the
maximum negative bending moment and that points of contraflexure (i.e. where the
bending moment changes sign) occur at the quarter-span points.
Having determined the support reactions, the deflected shape of the beam may be
found by any of the methods described in the previous part of this chapter.
E
XAMPLE
13.20
Determine the fixed-end moments and the fixed-end reactions
for the beam shown in Fig. 13.28(a).
W
A
C
B
M
A
M
B
EI
R
B
R
A
a
b
L
(a)
M
A
M
B
ve
ve
Wa
b
A
B
L
F
IGURE
13.28
Fixed beam of
Ex. 13.20
ve
(b)
The resultant bending moment diagram is shown in Fig. 13.28(b) where the line AB
represents the datum from which values of bending moment are measured. Again the
net area of the resultant bending moment diagram is zero since the change in slope
between the ends of the beam is zero. Hence
1
2
(
M
A
+
1
2
L
Wab
M
B
)
L
=
L
which gives
Wab
L
M
A
+
M
B
=
(i)
