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TABLE 5.6
Force and Displacement Methods for Applied Forces
P
and Displacements
V
FORCE METHOD
DISPLACEMENT METHOD
P
x
Unknowns
V
y
b
1
(
a
1
(
Compatibility
v
−
v
)
=
0
Equilibrium
p
−
p
)
=
0
or
b
1
v
or
a
1
p
Conditions
:
=
V
Condition
s:
=
P
b
1
f
a
1
k
(
b
0
P
+
b
1
P
x
)
=
V
This leads to
(
a
0
V
+
a
1
V
y
)
=
P
F
−
1
[
V
b
1
f
K
−
1
[
P
a
1
k
P
x
=
−
(
b
0
P
)
]
(1)
V
y
=
−
(
a
0
V
)
]
=
+
b
1
F
−
1
(
−
b
1
fb
0
)
+
b
1
F
−
1
V
=
+
a
1
K
−
1
(
−
a
1
ka
0
)
+
a
1
K
−
1
P
p
[
b
0
]
P
from which
v
[
a
0
]
V
v
=
fp
Since
p
=
kv
then
b
0
v
b
0
fbP
b
0
fb
1
F
−
1
V
a
0
p
a
0
kaV
a
0
ka
1
K
−
1
P
V
p
=
=
+
(
)
(2)
P
v
=
=
+
(
)
The unknowns can be obtained from (1) and (2):
.
.
V
p
··
V
b
0
···
b
1
b
0
fb
0
P
a
0
···
a
1
a
0
ka
0
b
0
fb
1
······ ··· ······
b
1
fb
0
P
···
P
x
a
0
ka
1
······ ··· ······
a
1
ka
0
V
···
V
y
v
··
P
=
=
v
=
p
=
.
.
b
1
a
1
ka
1
fb
1
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