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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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