Civil Engineering Reference
In-Depth Information
beam is equal to minus the area of the shear force diagram between those sections.
Again, using the cantilever beam of Fig. 3.12 as an example, we see that the change in
bending moment from A to B is
wL
2
/2 and that the area of the shear force diagram
between A and B is
wL
2
/2.
−
Finally, from Eqs (3.1) and (3.4)
d
2
M
d
x
2
d
S
d
x
=−
=−
w
(
x
)
(3.8)
The relationships established above may be used to construct shear force and bending
moment diagrams for some beams more readily than when the methods illustrated in
Exs 3.4-3.9 are employed. In addition they may be used to provide simpler solutions
in some beam problems.
E
XAMPLE
3.10
Construct shear force and bending moment diagrams for the beam
shown in Fig. 3.19(a).
2kN
5kN
4 kN/m
A
B
C
D
E
R
A
4.5 kN
R
E
6.5 kN
1m
1m
1m
1m
(a)
6.5 kN
Shear force
2.5 kN
ve
A
B
C
E
D
ve
2.5 kN
4.5 kN
(b)
A
B
C
D
E
Bending
moment
F
IGURE
3.19
Shear
force and bending
moment diagrams
for the beam of
Ex. 3.10
ve
4.5 kN m
4.5 kN m
7kNm
(c)
