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P
Zb
1
L
b
a
4
X
2
Z
5
L
L
3
P
Xc
c
d
FIGURE 5.19
Five-bar truss (Chapter 3, Example 3.5 and
Example 5.4).
P
Zc
one technique for accomplishing this is to use an incidence table. For the truss of Fig. 5.19,
Bar Begins at
Bar Ends at
Bar No.
System Node No.
System Node No.
1
a
b
2
b
c
3
c
d
4
a
c
5
d
b
The element stiffness matrices for each bar can now be assigned subscripts corresponding
to the global node numbers in the incidence table. Equation (5.85) gives the element stiff-
ness matrix referred to global coordinates. For each bar, in addition to the assignment of
subscripts corresponding to the global node numbers, values for
,
A
,
E
, and the angle
α
(see Fig. 5.10) are needed to utilize Eq. (5.85). We find
0
◦
90
◦
180
◦
Bar 1 :
α
=
Bar 2 :
α
=
Bar 3 :
α
=
k
aa
k
bb
k
cc
k
cd
k
ab
k
bc
k
1
k
2
k
3
=
(
1
a
)
=
(
1
b
)
=
(
1
c
)
k
ba
k
bb
k
cb
k
cc
k
dc
k
dd
(1)
45
◦
45
◦
Bar 4 :
α
=
Bar 5 :
α
=−
k
aa
k
dd
k
ac
k
db
k
4
=
(
1
d
)
k
5
=
(
1
e
)
k
ca
k
cc
k
bd
k
bb
The global stiffness matrix is assembled by summation of the submatrices with
k
i
jk
K
jk
=
(2)
i
where the summation is taken over all bars. For example,
k
aa
+
k
aa
,
k
bb
+
k
bb
+
k
bb
K
aa
=
K
bb
=
(3)
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