Civil Engineering Reference
In-Depth Information
Comparing the situation in Fig. 6.4.b and c to the general definition
of external load
components in Fig. 6.4.a, it is then seen that the contribution from
p
Q
to the load
vector is
T
T
[
]
R
RRRR RR
⎡
0
QQ Q
θ
0
0
⎤
=
=
−
(6.6)
p
1
2
3
4
5
6
⎣
y
z
⎦
m
p
m
p
m
if
m
is horizontal, and
T
T
[
]
RRRR RR
⎡
QQ
000
Q
θ
⎤
R
=
=
−
−
(6.7)
⎣
⎦
p
1
2
3
4
5
6
z
y
p
m
m
p
m
if
m
is vertical. Thus,
⎛ ⎞
2
V
L
ρ
m
R θ Q
=⋅
=
⋅
⋅
θ b
⋅
(6.8)
⎜
⎜
⎝ ⎠
p
mp
mq
m
m
2
2
m
p
where
00 0
10 0
01 0
00 1
00 0
00 0
010
10 0
00 0
00 0
00 0
00 1
⎡
⎤
⎡
−
⎤
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
θ
=
if
m
is horizontal, and
θ
=
if
m
is vertical.
⎢
⎥
⎢
⎥
m
m
−
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
−
⎥
⎣
⎦
⎣
⎦
The six by one load vector
R
in node
p
is then given by the sum of the contributions
from all adjoining elements, i.e.
T
[
]
∑
R
=
RRRRRR
=
R
(6.9)
p
1
2
3
4
5
6
p
p
m
m
T
and the total
6
N
by one load vector is given by:
⎡
""
.
⎤
⋅
RR R R
=
⎣
⎦
1
p
N
