Page 134 - Marine Structural Design

110 Part I Structural Design Principles

a P o o 00
-Pao o 00
0 01 0 00 (6.13)
[TI =
0 ooil po
o 00-PRO
0 00 0 01
with A = cosa, p = sin a.
Similarly, we have for the nodal displacement components:

@I= [TW
@> = [TIT @I
where (i7) and (u) are defined by

Based on the element stifiess equation in the local axes,
@I= rm@) (6.14)

we may easily obtain, the element stiffness equation in the global axes,
[KI = [TIT[m [TI (6.15)

Figure 6.4 Nodal Forces for 3D Beam Element in Local Axes

If we write force and corresponding displacement vectors as