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k
i
=
/
L
)
i
, where
E
is the modulusofelasticity,
A
represents the cross-
sectional area and
L
is the length of the member; (2) there aretwocom-
ponents of displacement ateach joint.For the statically indeterminate truss
shown the displacementformulationyields the symmetricequations
Ku
(
E A
=
p
,
where
⎡
⎣
⎤
⎦
.
.
−
.
.
.
27
58
7
004
7
004
0
0000
0
0000
7
.
004
29
.
57
−
5
.
253
0
.
0000
−
24
.
32
K
=
−
7
.
004
−
5
.
253
29
.
57
0
.
0000
0
.
0000
MN/m
0
.
0000
0
.
0000
0
.
0000
27
.
58
−
7
.
004
0
.
0000
−
24
.
32
0
.
0000
−
7
.
004
29
.
57
0000
45
T
kN
p
=
−
Determine the displacements
u
i
of the joints.
15.
P
6
P
6
P
5
P
3
P
4
P
P
4
P
45
o
3
45
o
5
P
2
P
P
P
1
2
1
18 kN
12 kN
In the
force formulation
of a truss, the unknowns are the member forces
P
i
.For
the staticallydeterminate truss shown, the equilibrium equations of the joints
are:
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
/
√
2
−
11
−
1
0
0
0
P
1
P
2
P
3
P
4
P
5
P
6
0
18
0
12
0
0
/
√
21
0
0
001
/
√
2
0
0
−
1
00
−
1
/
√
2
0
=
00
001
/
√
2
1
00
001
√
2 0
00
0
−
1
−
1
/
where the units of
P
i
arekN. (a) Solve the equations as theyare with a computer
program. (b) Rearrange the rows and columnssoastoobtain a lower triangular
coefficient matrix, and then solve the equations by back substitutionusing a
calculator.
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