Static Equilibrium of Structures - Programming the Finite Element Method - page 134

x'

g(8)

g(12)

g(11)

2

g(7)

g(9) g(10)

y

g(2)

1

g(5)

g(6)

z x

g(1)

g(3)

g(4)

Figure 4.23 Node and freedom numbering for 3D beam-rod elements

g is the rotation
about the local x' axis

y'

Parallel to
xz-plane

g

g

z'

View as seen from the
positive x' direction

Figure 4.24 Transformation angle for “non-vertical” elements

x',y

g is the angle between z and z'
measured towards x

x

z'

g

y'

z

Figure 4.25 Transformation angle for “vertical” elements