Advanced Methods of Structural Analysis

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