Civil Engineering Reference
In-Depth Information
0
.
6327
−
0
.
1003
−
0
.
2585
−
0
.
1003
k
(4)
=
−
0
.
1003
0
.
6327
−
0
.
1003
−
0
.
2585
−
0
.
2585
−
0
.
1003
0
.
6906
−
0
.
0713
−
0
.
1003
−
0
.
2585
−
0
.
0713
0
.
6906
Utilizing the direct assembly-superposition method with the element-to-global node
assignment relations, the global conductance matrix is
0
.
6906
−
0
.
1003
0
−
0
.
0713
−
0
.
2585
0
0
0
0
−
0
.
1003
1
.
2654
−
0
.
1003
−
0
.
2585
−
0
.
2006
−
0
.
2585
0
0
0
0
−
0
.
1003
0
.
6906
0
−
0
.
2585
−
0
.
0713
0
0
0
−
0
.
0713
−
0
.
2585
0
1
.
3812
−
0
.
2006
0
−
0
.
0713
−
0
.
2585
0
[
K
]
=
−
0
.
2585
−
0
.
2006
−
0
.
2585
−
0
.
2006
2
.
5308
−
0
.
2006
−
0
.
2585
−
0
.
2006
−
0
.
2585
0
−
0
.
2585
−
0
.
0713
0
−
0
.
2006
1
.
3812
0
−
0
.
2585
−
0
.
0713
0
0
0
−
0
.
0713
−
0
.
2585
0
0
.
7484
−
0
.
2585
0
0
0
0
−
0
.
2585
−
0
.
2006
−
0
.
2585
−
0
.
2585
1
.
3812
−
0
.
0713
0
0
0
0
−
0
.
2585
−
0
.
0713
0
−
0
.
0713
0
.
7484
The nodal temperature vector is
180
180
180
T
4
T
5
T
6
T
7
T
8
T
9
{
T
}=
and we have explicitly incorporated the prescribed temperature boundary conditions.
Assembling the global force vector, noting that no internal heat is generated, we
obtain
17
.
7084
+
F
1
35
.
4168
+
F
2
17
.
7084
+
F
3
35
.
4168
47
.
2224
35
.
4168
23
.
6112
35
.
4168
23
.
6112
{
F
}=
Btu/hr
where we use
F
1
,
F
2
, and
F
3
as general notation to indicate that these are unknown
“reaction” forces. In fact, as will be shown, these terms are the heat flux components at
nodes 1, 2, and 3.
