Civil Engineering Reference
In-Depth Information
The number of nodes is six, each having 3 degrees of freedom, a total of 18. The
number of constraints is three so that the kinematic indeterminacy of the frame is
given by
n
k
=
18
−
3
=
15
E
XAMPLE
16.4
Determine the degree of statical and kinematic indeterminacy in
the space frame shown in Fig. 16.13(a).
F
IGURE
16.13
Space frame
of Ex. 16.4
(a)
(b)
In the completely stiff structure shown in Fig. 16.13(b),
M
=
19,
N
=
13 and
r
=
0.
Therefore from Eq. (16.2)
n
s
=
6(19
−
13
+
1)
−
0
=
42
There are 13 nodes each having 6 degrees of freedom, a total of 78. There are six
constraints at each of the four supports, a total of 24. Thus
n
k
=
78
−
24
=
54
We shall now consider different types of statically indeterminate structure and the
methods that may be used to analyse them; the methods are based on the work and
energy methods described in Chapter 15.
16.4 S
TATICALLY
I
NDETERMINATE
B
EAMS
Beams are statically indeterminate generally because of their support systems. In
this category are propped cantilevers, fixed beams and continuous beams. A propped
cantilever and some fixedbeams were analysed inSection 13.6 using either the principle
of superposition or moment-area methods. We shall now apply the methods described
in Chapter 15 to some examples of statically indeterminate beams.
