Page 135 - Marine Structural Design

Chapter 6 Offshore Structural Analysis 111

{TI = (6.16)

Having the stiffness matrix [E] defined in local axes for each beam element, the stiffness
matrix [K] in global axes for the beam element, may be derived using the transformation
matrix [TI,

(6.17)

EA
-
I
0 - 12EI
i3
12EI
0 0 - Symmetric
13
GJ
0 0 0 -
I
6EZ
0 0 -- 0 - 4EI
i2 1
8EZ 4EI
0 - 0 0 0 -
I2 1
-- EA 0 0 0 0 0 - EA
1 1
12EI 6EI 12e1
0 -- 0 0 0 -- -
c3 l2 13
0 0 -- 12EI 0 - 6EI 0 0
1' l2
0 0 0 .- GJo 0 0 0 0 - GJ
I 1
0 0 _- 6EI 0 - 2EI 0 0 - 6e1 - 4e1
0
I2 I 12 1
6EZ 2EZ 4e1
0 - 0 0 0 - 0 0 0 -
lZ I 1
For a member having circular cross-section, I,J,and A are defined in terms of the external
diameter De and the internal diameter Di as,