Civil Engineering Reference
In-Depth Information
The first column contains the entire set of global displacements in numerical
order. Each succeeding column represents an element and contains the number of
the element displacement corresponding to the global displacement in each row.
A zero entry indicates no connection, therefore no stiffness contribution. The
individual terms in the global stiffness matrix are then obtained by allocating the
element stiffness terms per the table as follows:
K
11
=
k
(1)
11
+
0
k
(1)
12
K
12
=
+
0
K
13
=
0
+
0
K
14
=
0
+
0
k
(1)
13
K
15
=
+
0
k
(1)
14
K
16
=
+
0
k
(1)
22
K
22
=
+
0
K
23
=
0
+
0
K
24
=
0
+
0
k
(1)
23
K
25
=
+
0
k
(1)
24
K
26
=
+
0
k
(2)
11
K
33
=
0
+
k
(2)
12
K
34
=
0
+
k
(2)
13
K
35
=
0
+
k
(2)
14
K
36
=
0
+
k
(2)
22
K
44
=
0
+
k
(2)
23
K
45
=
0
+
k
(2)
24
K
46
=
0
+
k
(1)
33
k
(2)
33
K
55
=
+
k
(1)
34
k
(2)
34
K
56
=
+
k
(2)
44
where the known symmetry of the stiffness matrix has been implicitly used to
avoid repetition. It is readily shown that the resulting global stiffness matrix is
identical in every respect to that obtained in Section 3.2 via the equilibrium
equations. This is the direct stiffness method; the global stiffness matrix is
“assembled” by direct addition of the individual element stiffness terms per the
nodal displacement correspondence table that defines element connectivity.
k
(1)
44
K
66
=
+
