Civil Engineering Reference
In-Depth Information
140
m
0
0
0
0
0
⎡
⎤
x
⎢
⎥
0
156
m
0
0
0
22
m L
⎢
y
y
⎥
⎢
⎥
0
0
156
m
0
22
m L
0
−
L
z
z
⎢
⎥
(9.34)
m
=
11
0
0
0
140
m
0
0
⎢
⎥
420
θ
⎢
⎥
2
0
0
22
mL
0
4
mL
0
−
⎢
⎥
z
z
⎢
⎥
2
0
22
mL
0
0
0
4
mL
⎣
⎦
y
y
70
m
0
0
0
0
0
⎡
⎤
x
⎢
⎥
0 4
m
0
0
0
−
3
m L
⎢
⎥
y
y
⎢
⎥
0
0
54
m
0
13
m L
0
L
z
z
⎢
⎥
(9.35)
m
=
12
0
0
0
70
m
0
0
420
⎢
⎥
θ
⎢
⎥
2
0
0
13
mL
0
3
mL
0
−
−
⎢
⎥
z
z
⎢
⎥
2
0 3
mL
0
0
0
3
mL
−
⎣
y
y
⎦
140
m
0
0
0
0
0
⎡
⎤
x
⎢
⎥
0
156
m
0
0
0
−
22
m L
⎢
⎥
y
y
⎢
⎥
0
0
156
m
0
22
m L
0
L
z
z
⎢
⎥
(9.36)
m
=
22
0
0
0
140
m
0
0
420
⎢
⎥
θ
⎢
⎥
2
0
0
22
mL
0
4
mL
0
⎢
⎥
z
z
⎢
⎥
2
0
22
mL
0
0
0
4
mL
−
⎣
⎦
y
y
The element property matrices given above may be found in many text books, see e.g.
Hughes [25] and Cook et.al. [29]. They have been included here mainly for the sake of
completeness. It should be noted that the development of damping properties at element
level is not necessarily a rational choice. Alternatively, damping properties may be
introduced at a structural global level (i.e. associated directly with the global degrees of
freedom), e.g. in the form of Rayleigh damping or simply a diagonal type of modal
damping matrix.
9.3 The wind load
All the necessary equations for the determination of the mean (static) as well as the
fluctuation (dynamic) wind load at element level has previously been developed in
Chapter 5. It is now simply a matter of implementing this theory into the framework of a
finite element approach, i.e. to expand Eqs. 5.8 - 5.14 and 5.24 - 5.25 into the twelve
degrees of freedom force and displacement system adopted for a finite element
approach.
