Civil Engineering Reference
In-Depth Information
The distance
x
is measured from the cause location to the effect
location.
(
)
=−
(
)
=−
x
=−
xx xx
c
L
e
i
j
This can be substituted into Equation 4.4 and the unneeded distances and
forces are removed to get a 3×3 matrix involving only
P
x
,
P
y
, and
M
z
.
100 000
010 000
001 000
000100
00 010
0
P
P
P
P
M
M
M
x
2
x
1
P
P
M
M
M
y
2
y
1
z
2
z
1
=
x
2
x
1
L
y
2
y
1
−
L
0 001
z
2
z
1
100
010
0
P
P
M
P
P
M
xi
xj
=
yi
yj
−
L
1
zi
zj
The axial force in the member,
P
x
, is a direct transmission, whereas the
shear,
P
y
, and bending,
M
z
, forces are linked. The transmission for just the
shear and bending will be used later in the chapter and can be written as
follows:
10
1
P
M
=
P
M
yj
yi
(4.5)
−
L
zj
zi
A similar transmission matrix can be derived for shear and bending in the
XZ system.
10
1
P
M
=
P
M
zi
zj
(4.6)
L
yi
yj
4.4 AREA MOMEnt MEtHOD
Area moment and the next five sections are review topics on structural
analysis. These topics will be used to derive many of the equations and
