398 11 Matrix Stiffness Method
Stiffness matrix for structure in whole in local coordinates is
kQ.55/D
2 6 6 6 6 6 4
0:667 0:333 0 0 0
0:333 0:667 0 0 0
00210
00120
0 0 001:5
3 7 7 7 7 7 5
EI 0
Matrix proceduresIntermediate matrix complex
kAQ TDEI 0
2 6 6 6 6 6 4
0:667 0:333 0 0 0
0:333 0:667 0 0 0
00210
00120
0 0 001:5
3 7 7 7 7 7 5
2 6 6 6 6 6 4
00
10
10
01
01
3 7 7 7 7 7 5
DEI 0
2 6 6 6 6 6 4
0:333 0
0:667 0
21
12
01:5
3 7 7 7 7 7 5
Stiffness matrix for structure in whole in global coordinates and inverse stiffness
matrix are
KDAkAQ
T
D
01100
00011
EI 0
2 6 6 6 6 6 4
0:333 0
0:667 0
21
12
01:5
3 7 7 7 7 7 5
DEI 0
2:667 1
13:5
;
K^1 D
1
EI 0
0:42 0:12
0:12 0:32
Vector of joint displacements
ZEDK^1 PED^1
EI 0
0:42 0:12
0:12 0:32
EI 0
0:02667
0:015
D
0:0094
0:0016
Vector of unknown bending moments of the second state is
ES 2 DkAQ TZDEI 0
2 6 6 6 6 6 4
0:333 0
0:667 0
21
12
01:5
3 7 7 7 7 7 5
0:0094
0:0016
DEI 0
2 6 6 6 6 6 6 6 6
0:00313
0:00627
0:0204
0:0126
0:0024
3 7 7 7 7 7 7 7 7