Page 525 - Aircraft Stuctures for Engineering Student

506 Matrix methods of structural analysis

u1 v1 u2 v2 u3 v3
1 0 -1 0 0 0 '
0 1 0 0 0 -1 2.41 =o
1
1
-1 0 I+----- 1 1 -
2Jz 24 2Jz 2Jz 211 = 0
1 1 1 1 u2
0 0 -- - - --
2.\/2 2Jz 2Jz 2J2 v2
1 1 1 1 u3 = 0
0 0 -- - - --
24 2J2 2Jz 2Jz v3 = 0
1 1 1 1
0 -1 - -- -- 1 +-
2a 2Jz 24 2Jz.
If we now delete rows and columns in the stiffness matrix corresponding to zero
displacements, we obtain the unknown nodal displacements u2 and v2 in terms of
the applied loads Fx,2(= 0) and Fv,2(=- W). Thus
1 1
1+- --
24 2Jz
-- -
2Jz 2J2
Inverting Eq. (v) gives

(vi)
from which

(vii)

(viii)

The reactions at nodes 1 and 3 are now obtained by substituting for u2 and v2 from
Eq. (vi) into Eq. (iv). Thus

0 O l

--1 -1-
0 0
- 0 I } : 1: {
-
- 0 -1 -