Civil Engineering Reference
In-Depth Information
from which
W
2
S
BC
=+
and we see that
S
BC
is constant at all sections of the beam between B and C so that
the complete shear force diagram has the form shown in Fig. 3.13(d). Note that the
change
in shear force from that at a section immediately to the left of B to that at a
section immediately to the right of B is
+
W
. We shall consider the implications of this
later in the chapter.
It would also appear from Fig. 3.13(d) that there are two different values of shear
force at the same section B of the beam. This results from the assumption that
W
is
concentrated at a point which, practically, is impossible since there would then be an
infinite bearing pressure on the surface of the beam. In practice, the load
W
and the
support reactions would be distributed over a small length of beam (Fig. 3.14(a)) so
that the actual shear force distribution would be that shown in Fig. 3.14(b).
The distribution of the bendingmoment inAB is now found by considering themoment
equilibrium about X
1
of the length AX
1
of the beam in Fig. 3.13(b). Thus
W
2
x
M
AB
−
=
0
or
W
2
x
M
AB
=
(i)
Therefore
M
AB
varies linearly from zero at A (
x
=
0) to
+
WL
/4 at B (
x
=
L
/2).
W
W
W
2
2
(a)
W
W
2
2
ve
ve
W
W
2
2
F
IGURE
3.14
Shear force diagram in a
practical situation
(b)
