610
Appendix A: The Stiffness Matrix
Fig. A.5 Space frame
member
where
l 1 = cos θ and m 1 = sin θ
It can be shown that the stiffness matrix in global coordinate system is given by
[K ] e = [T ]
T
[k] e [T ]
(A.4)
For the truss member
[K ] e =
E A
L
⎡
⎢
⎢
⎣
l
2
1
Symmetrical
l 1 m 1 m
2
1
−l
2
1 −l 1 m 1
l
2
1
−l 1 m 1 −m
2
1
l 1 m 1
m
2
1
⎤
⎥
⎥
⎦
(A.5)
A typical frame member is shown in Fig. A.5. The member of the frame has three
degrees of freedom at each end-two translations and one rotation. X
, Y
, Z
is the
local axis system and X, Y, Z is the global axis system. The relationship between
them is given by
Appendix A: The Stiffness Matrix
Fig. A.5 Space frame
member
where
l 1 = cos θ and m 1 = sin θ
It can be shown that the stiffness matrix in global coordinate system is given by
[K ] e = [T ]
T
[k] e [T ]
(A.4)
For the truss member
[K ] e =
E A
L
⎡
⎢
⎢
⎣
l
2
1
Symmetrical
l 1 m 1 m
2
1
−l
2
1 −l 1 m 1
l
2
1
−l 1 m 1 −m
2
1
l 1 m 1
m
2
1
⎤
⎥
⎥
⎦
(A.5)
A typical frame member is shown in Fig. A.5. The member of the frame has three
degrees of freedom at each end-two translations and one rotation. X
, Y
, Z
is the
local axis system and X, Y, Z is the global axis system. The relationship between
them is given by