Civil Engineering Reference
In-Depth Information
the nodes. For example, the moments at the nodes in this example for each of the elements
are given as follows:
Element 1
M
1
=
31
.
78
M
2
=
22
.
14
Element 2
M
1
=−
22
.
14
M
2
=
26
.
06
Element 3
M
1
=−
+
=−
29
.
06
3
.
00
26
.
06
M
2
=
0
.
33
−
3
.
00
=−
2
.
67
Element 4
M
1
=
1
.
87
+
0
.
80
=
2
.
67
M
2
=
0
.
53
−
0
.
53
=
0
.
00
Internal equilibrium is maintained, for example
M
2
of element 1 is equal and opposite
to
M
1
of element 2, and so on. A bending moment diagram for the beam based on these
values is given in Figure 4.16.
0
1
2
3
4
5
6
7
8
9
10
x
(m)
Figure 4.16
Bending moment diagram from first Program 4.3 example
A second example of the use of Program 4.3 is illustrated in Figure 4.17 and represents
a laterally loaded pile which is to be modelled as a “beam on an elastic foundation”, with
