Civil Engineering Reference
In-Depth Information
These rotation transformations will be used later to relate the local mem-
ber stiffness to the global member stiffness.
4.3
tRAnSMiSSiOn MAtRiX
In addition to knowing the local components of global forces, the effect a
force applied to one end of a member has on the other end is important. It
is often necessary to state the
effect
at one point in a structural system due
to a
cause
known to exist at some other point in the system. This is where
the transmission transformation is used. In Figure 4.5, the cause of a force
at point 2 is transmitted to the effect at point 1. This is achieved by using
an equivalent static force at 1. In the study of rigid body equilibrium, this
is stated as SF
1
= SF
2
.
The six orthogonal forces at a point are shown in Figure 4.6. These
are the forces and moments in each direction X, Y, and Z. The moments
are represented with double arrowheads.
The static equivalent force system is found where the moment arm
distances (
x
2
−
x
1
), (
y
2
−
y
1
), and (
z
2
−
z
1
) are measured from the
effect
point,
1, to the
cause
point, 2.
Z
Y
2 . (x
2
,y
2
,z
2
)
1 . (x
1
,y
1
,z
1
)
X
Figure 4.5.
Transformation locations.
M
Z
M
Y
P
Z
P
Y
1
P
X
M
X
Figure 4.6.
Orthogonal forces.
