Civil Engineering Reference
In-Depth Information
ΣΣ
ΣΣ
ΣΣ
Σ
FFPP
FFPP
FFPP
MM
= ∴=
= ∴=
= ∴=
=
x
1
x
2
x
1
x
2
y
1
y
2
y
1
y
2
z
1
z
2
z
1
z
2
(
)
+
(
)
MMPz z Pyy
MMMMPz z
Σ
∴=−
−
−
x
1
x
2
x
1
x
2
y
2
2
1 22 1
z
(
)
−
(
)
Σ
= ∴=+ −
Σ
Px x
−
y
1
y
2
y
1
y
2 22
x
1
z
2
2
1
(
)
+
(
)
Σ
MMMMPyyPxx
= ∴=− −
Σ
−
z
1
z
2
z
1
z
2 22 1
x
y
2
2
1
We can simplify the moment arm distances as
x
,
y
, and
z
. The concept of
transmitting
cause
to
effect
may be denoted in matrix form as [
T
]:
100 000
010 000
001 000
0
P
P
P
M
M
M
P
P
P
M
M
M
x
2
x
1
y
2
y
1
z
2
z
1
=
(4.4)
−
zy
1 00
x
2
x
1
z
0
−
0 10
0001
x
y
2
y
1
−
yx
z
2
z
1
Example 4.4
Transmission matrix
Determine the transmission matrix for the coplanar XY system from the
origin end,
i
, to other end,
j.
The cause end is
i
as shown in Figure 4.7 and the effect end is
j
at the
right end a distance
L
away.
Y
i = cause
j = effect
X
L
Z
Figure 4.7.
Transformation effects.
