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In-Depth Information
Beam Begins at
Beam Ends at
Beam No.
System Node No.
System Node No.
1
a
b
2
b
c
3
c
d
The entries of the incidence table permit the element stiffness matrix for any beam element
to be assigned subscripts corresponding to the global node numbers.
The next step is to compute the element stiffness matrix referred to global coordinates.
Element 1:
Use
2 3
m 2 , and EA
=
=
3
.
464 m ,EI
=
4
.
712 MN
·
=
640 MN.
From Eq. (5.94),
.
.
184
76
0
0
184
76
0
0
0
1
.
3604
2
.
3561
0
1
.
3604
2
.
3561
0
2
.
3561
5
.
4411
0
2
.
3561
2
.
7206
k 1
=
(1)
184
.
76
0
0
184
.
76
0
0
0
1
.
3604
2
.
3561
0
1
.
3604
2
.
3561
0
2
.
3561
2
.
7206
0
2
.
3561
5
.
4411
The next step is to transform the stiffness matrix from a local to the global coordinate
system. From the incidence table, bar 1 begins at a and ends at b . For a global coordinate
system XZ placed at a ,
is a positive 60
α
(Figs. 5.10 and 5.20b). With cos
α =
0
.
5 and
sin
α =
0
.
866,
.
0
.
5
0
.
866
0
0
.
866
0
.
50
0
0
0
1
T 1
·······································
=
(2)
.
0
.
5
0
.
866
0
.
.
0
0
866
0
50
0
0
1
The stiffness matrix referred to global coordinates is then formed as [Eq. (5.93)]
k aa .
k ab
··· · ···
k ba .
k 1 T 1
k 1
T 1 T
=
=
k bb
.
47
.
210
79
.
412
2
.
0404
47
.
210
79
.
412
2
.
0404
.
79
.
412
138
.
90
1
.
1781
79
.
412
138
.
90
1
.
1781
.
2
.
0404
1
.
1781
5
.
4411
2
.
0404
1
.
1781
2
.
7206
=
(3)
······
······
······ ·
······
······
······
.
47
.
210
79
.
412
2
.
0404
47
.
210
79
.
412
2
.
0404
.
79
.
412
138
.
90
1
.
1781
79
.
412
138
.
90
1
.
1781
.
2
.
0404
1
.
1781
2
.
7206
2
.
0404
1
.
1781
5
.
4411
where the subscripts of the submatrices have been taken from the incidence table.
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