Civil Engineering Reference
In-Depth Information
10 kN
10 kN
A
B
A
B
X
1
1m
C
E
D
E
D
C
R
2
1m
1m
(a)
(b)
A
B
A
B
1
1
C
C
F
IGURE
16.19
Statically
indeterminate truss
of Ex. 16.9
E
D
E
D
1
(c)
(d)
2. Unlike the truss in Ex. 16.18, we could not remove
any
member since, if BC or
CD were removed, the outer half of the truss would become a mechanism while the
portion ABDE would remain statically indeterminate. Therefore we select AD and
the support at C as the releases, giving the statically determinate truss shown in Fig.
16.19(b); we shall designate the force in themember ADas
X
1
and the vertical reaction
atCas
R
2
.
In this case we shall have two compatibility conditions, one for the diagonal AD and
one for the support at C. We therefore need to investigate three loading cases: one
in which the actual loads are applied to the released statically determinate truss in
Fig. 16.19(b), a second in which unit loads are applied to the cut member AD (Fig.
16.19(c)) and a third in which a unit load is applied at C in the direction of
R
2
(Fig.
16.19(d)). By comparison with the previous example, the compatibility conditions are
AD
+
a
11
X
1
+
a
12
R
2
=
0
(i)
v
C
+
a
21
X
1
+
a
22
R
2
=
0
(ii)
in which
AD
and
v
C
are, respectively, the change in length of the diagonal AD and
the vertical displacement of C due to the actual loads acting on the released truss,
while
a
11
,
a
12
, etc., are flexibility coefficients, which we have previously defined (see
