Civil Engineering Reference
In-Depth Information
Z
3
4
5
7
5
1
2
2
X
4
6
1
3
Figure 4.34.
Example 4.19 Global joint stiffness.
if it is desired to find the rotation of the member ends, but this can easily
be found from the final deformed position of the structure.
A numbering system must be assigned to the joint and members for
easy bookkeeping. Figure 4.34 shows a numbering system for the five
joints and the seven members of the structure. The member numbers are
circled for clarity.
The member stiffness for each member is first found from Equation 4.34
(step 1).
=
[]
[
]
[]
T
KRKR
g
m
=
[]
[
]
[]
T
K
b
K
b
g
m
Expand the general local member stiffness to include just the
x
and
z
forces and motions. Also note that rotation transformation of members
will be about the
y
-axis or
b
.
AE
L
AE
L
0
−
0
cos sin
sin os
b
b
0
0
−
b
b
0
0
0000
=
K
g
0
0
cos sin
sin os
b
b
AE
L
AE
L
−
0
0
0
0
−
b
b
0000
cos
b
sin
b
0
0
−
sin os
b
b
0
0
×
0
0
cos sin
sin os
b
b
0
0
−
b
b
To simplify the process, we can multiply the expanded global stiffness
equation and factor out the axial stiffness term.
