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TABLE 5.5
Outline of the Force and Displacement Methods
Unknowns
Force Method
Displacement Method
Global coordinates
Forces
X
Displacements
Y
T
i
)
−
1
v
i
v
i
f
i
p
i
T
i
)
−
1
p
i
p
i
f
i
v
i
v
i
=
(
→
=
p
i
=
(
→
=
v
1
v
2
.
f
1
p
1
p
2
.
p
1
p
2
.
k
1
v
1
v
2
.
f
2
k
2
=
=
=
=
For a network structure
(I)
v
=
fp
(I)
p
=
kv
.
.
.
.
.
.
Primary system, e.g.
Statistically determinate
Kinematically determinate
Equilibrium:
p
a
+
p
a
+
p
a
=
Compatibility:
v
a
=
v
a
=
v
a
=
P
a
V
a
=
(
+
)
=
=
(
+
)
=
In general
(II)
p
b
0
b
1
X
P
b P
(II)
v
a
0
a
1
Y
V
a V
=
a
∗
v
(
a
∗
a
=
)
=
b
∗
p
(
b
∗
b
=
)
Conditions to be satisfied
Compatibility:
V
I
Equilibrium:
P
I
b
T
v
[
b
0
+
(
T
]
v
a
T
p
[
a
0
+
(
T
]
p
(III)
V
=
=
b
1
X
)
(III)
P
=
=
a
1
Y
)
b
1
v
a
1
p
0
=
0
=
b
1
fp
b
1
f
a
1
kv
a
1
k
0
=
=
(
b
0
+
b
1
X
)
P
0
=
=
(
a
0
+
a
1
Y
)
V
b
1
fb
0
+
b
1
fb
1
X
=
0
→
X
→
b
a
1
ka
0
+
a
1
ka
1
Y
=
0
→
Y
→
a
Results
(II)
p
=
b P
(III)
v
=
aV
(I)
v
=
fp
=
fbP
(I)
p
=
kv
=
kaV
b
T
v
[
b
0
+
(
T
]
fbP
b
0
fbP
a
T
p
[
a
0
+
(
T
]
kaV
a
0
kaV
(III)
V
=
=
b
1
X
)
=
(II)
P
=
=
a
1
Y
)
=
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