Civil Engineering Reference
In-Depth Information
Table 5.10
Example 5.3 Member stiffness
0
0
0
−833
0
0
0
0
0
0
0.0750
0
−51.4
−51.4
0
0
0
0
1042
0
0
0
0
16.9
15
31.9
−9
−2.4521
0
0
0
0
−1042
83333
0
0
0
0
0.0000
2132.9 600 2732.9
0
0
0
0
0
0
−1389
0
0
0
0.0617
51.4
0
51.4
0
0
0
0
0
0
0
2894
2894
16.1
0
16.1
−40
−2.2562
−0.0026
−0.0370
−2.2525
−0.0045
−
0.0212
be added back to get the final reactions. The reaction forces are in kips and
inches (k-in).
[]
=
−
[
]
[]
T
−
PK PM FEPM R
∆
&
g
g
g
m
[]
=
PK
∆
g
g
The final step is finding the member forces for each of the members using
Equation 4.35 (step 6). The member force will be in kips and inches.
The local member stiffness matrix and the rotation matrix were shown
in step 1 and are omitted here. The sign convention for the X-Y system
applies when interpreting the final end forces and moments.
[
]
=
[
]
[]
+
[
]
PM KR FEPM
&
∆
m
m
g
m
[
]
=
[
]
[]
PM K
&
a
∆
m
m
g
For member 1, the deformations at joints 2 and 1 are used. Since this
member had a load, the fixed-end forces and moments must be added to
the results. Table 5.11 contains the final member end forces in the local
system along with global deformations used to find those end forces.
For member 2, the deformations at joints 1 and 3 are used. Table 5.12
contains the final member end forces in the local system along with global
deformations used to find those end forces.
For member 3, the deformations at joints 3 and 2 are used. Table 5.13
contains the final member end forces in the local system along with global
deformations used to find those end forces.
