Civil Engineering Reference
In-Depth Information
Example 4.20
Global joint stiffness
Determine the global joint deformations, support reactions, and local
member forces for the rigidly connected frame structure loaded as shown
in Figure 4.35.
The area of each member,
A
x
, is 10 in
2
, the moment of inertia,
I
z
, is
1000 in
4
, and the modulus of elasticity,
E
, is 10,000 ksi. Note the structure
is in the XY coordinate system and the numbering system is similar to
Example 4.19.
Y
3 k/ft
18k
2
2
3
16'-0"
1
3
X
1
4
24'-0"
Figure 4.35.
Example 4.20 Global joint stiffness.
The member stiffness for each member is first found from
Equation 4.34 (step 1).
=
[]
[
]
[]
T
KRKR
g
m
=
[]
[
]
[]
T
K
a
K
a
g
m
Using the local member stiffness for the XY system from Section 4.11
which has translation in
x
and
y
direction and rotation about the
z
direc-
tion, the rotation transformation of members will be about the
z
-axis or
a
.
cos sin
sincos
α
−
α
00 00
00 00
α
α
0
0 10 00
[]
=
T
0
0
0
cos sin
sinco
α
−
α
0
0
0
0
α
s
α 0
0
0 00 01
