Advanced Methods of Structural Analysis

412 11 Matrix Stiffness Method

Thus, the static matrix becomes

A.56/D

2 6 6 6 6 6 6 6 4

0  10 0:707 0 0

0000:70710

1000:70700

00 0:707 0  10

0 0 0:707 0 0 1

3 7 7 7 7 7 7 7 5

The stiffnesses of each member in local coordinates are

k 1 D

EA

l 1

D

EA

d

Œ1I k 2 Dk 5 Dk 6 Dk 1 D

EA

d

Œ1I

k 3 Dk 4 D

EA

d

p

2

Œ1D

EA

d

Œ0:707 :

So stiffness matrix of all structure in local coordinates is

kQDEA

d

2 6 6 6 6 6 6 6 4

10 0 0 00

01 0 0 00

0 0 0:707 0 0 0

0000:70700

00 0 0 10

00 0 0 01

3 7 7 7 7 7 7 7 5

Stiffness matrix of all structure in global coordinates is

KDAkAQ

T

D

EA

d

2 6 6 6 6 4

1:3534 0:3534 0:3534 0 0

0:3534 1:3534 0:3534  10

0:3534 0:3534 1:3534 0 0

0  1 0 1:3534 0:3534

000 0:3534 1:3534

3 7 7 7 7 5

Inverse matrix may be calculated by computer using a standard program. This
matrix is

K^1 D

d

EA

2 6 6 6 6 6 4

0:8965 0:5 0:1035 0:3965 0:1035

0:5 2:4149 0:5 1:9149 0:5

0:1035 0:5 0:89655 0:3965 0:1035

0:3965 1:9149 0:3965 2:313 0:6035

0:1035 0:5 0:1035 0:6035 0:8965

3 7 7 7 7 7 5