Civil Engineering Reference
In-Depth Information
Example 5.3
Member stiffness
Determine the global joint deformations, support reactions, and local
member forces for the pin-connected bracing structure loaded as shown
in Figure 5.5.
The area of each member,
A
x
, is 20 in
2
, the moment of inertia,
I
z
, is
1,000 in
4
, and the modulus of elasticity, E, is 10,000 ksi. Note the structure
is in the X-Y coordinated system and the numbering system is shown.
1.5 k/ft
Hinge
4
2
4
1
1
8 ft
3
2
Y
X
5
5
3
8 ft
12 ft
12 ft
Figure 5.5.
Example 5.3 Member stiffness.
The member stiffness for each member is first found from Equation 4.34
(step 1). Member 2 will have a released stiffness matrix and will be cre-
ated last. Selecting member 2 instead of member 1 will result in not having
to use modified fixed-end forces and moments.
=
[]
[
]
[]
T
KRKR
g
m
=
[]
[
]
[]
T
K
a
K
a
g
m
Using the local member stiffness for the X-Y system from Section 4.11,
which has translation in the
x
and
y
directions and rotation about the
z
direc-
tion, the rotation transformation of members will be about the
z
-axis or
a
.
cos sin
sin os
αα
αα
-
0 0 0 0
00 00
0
0 10 00
[]
=
T
0
0
0
cos sin
sin o
αα
α
-
0
0
0
0
s
α 0
0
0 00 01
AE
AE
