Civil Engineering Reference
In-Depth Information
B
D
F
IGURE
4.6
Construction of a Warren
truss
A
C
E
Now consider the construction of a simple pin-jointed truss. Initially we start with a
single triangular unit ABC as shown in Fig. 4.6. A further triangle BCD is created by
adding the
two
members BD and CD and the
single
joint D. The third triangle CDE
is then formed by the addition of the
two
members CE and DE and the
single
joint
E and so on for as many triangular units as required. Thus, after the initial triangle
is formed, each additional triangle requires
two
members and a
single
joint. In other
words the number of additional members is equal to twice the number of additional
joints. This relationship may be expressed qualitatively as follows.
Suppose that
m
is the total number of members in a truss and
j
the total number of
joints. Then, noting that initially there are three members and three joints, the above
relationship may be written
m
−
3
=
2(
j
−
3)
so that
m
=
2
j
−
3
(4.1)
If Eq. (4.1) is satisfied, the truss is constructed from a series of statically determi-
nate triangles and the truss itself is statically determinate. Furthermore, if
m
<
2
j
−
3
the structure is unstable (see Fig. 4.3(b)) or if
m
>
2
j
3, the structure is statically
indeterminate. Note that Eq. (4.1) applies only to the internal forces in a truss; the
support system must also be statically determinate to enable the analysis to be carried
out using simple statics.
−
E
XAMPLE
4.1
Test the statical determinacy of the pin-jointed trusses shown in
Fig. 4.7.
In Fig. 4.7(a) the truss has five members and four joints so that
m
=
5 and
j
=
4. Then
2
j
−
3
=
5
=
m
and Eq. (4.1) is satisfied. The truss in Fig. 4.7(b) has an additional member so that
m
=
6 and
j
=
4. Therefore
m
>
2
j
−
3
and the truss is statically indeterminate.
