Civil Engineering Reference
In-Depth Information
shows directly the surface of the beamnear which themajor steel reinforcement should
be provided. Also, drawing the bendingmoment diagramon the tension side of a beam
can give an indication of the deflected shape as illustrated in Exs 3.4-3.7. This is not
always the case, however, as we shall see in Exs 3.8 and 3.9.
In this case the beamwill bend as shown in Fig. 3.11(e), so that the upper surface of the
beam is in tension and the lower one in compression; the bending moment diagram
is therefore drawn on the upper surface as shown in Fig. 3.11(d). Note that negative
(hogging) bending moments applied in a vertical plane will always result in the upper
surface of a beam being in tension.
E
XAMPLE
3.5
Cantilever beam carrying a uniformly distributed load of intensity
w
.
Again it is unnecessary to calculate the reactions at the built-in end of the cantilever;
their values are, however, shown inFig. 3.12(a). Note that for the purpose of calculating
themoment reaction the uniformly distributed loadmay be replaced by a concentrated
load (
=
wL
) acting at a distance
L
/2 from A.
There is no loading discontinuity between A and B so that we may consider the shear
force and bending moment at any section X between A and B. As before, we insert
A
w
X
B
w
wL
2
2
M
AB
X
B
S
AB
x
wL
L
x
L
(a)
(b)
Shear force
A
B
ve
wL
(c)
wL
2
2
F
IGURE
3.12
Shear
force and bending
moment diagrams
for the beam of
Ex. 3.5
ve
Bending moment
A
B
(d)
