Civil Engineering Reference
In-Depth Information
100
200
dx
EI
dx
E
dx
1
10000
100 0
100
−
200 100
−
=
∫
∫
∫
S
1
=
=
+
=
+
0 00015
.
100
200
E
200
y
0
100
100
200
dx
EI
xdx
E
xdx
E
1
100 0
2 100
2
−
2
200 100
2 200
2
−
2
∫
∫
∫
S
=
x
=
+
=
+
2
(
)
(
)
100
200
10000
y
0
100
=
0 0125
.
100
200
2
2
3
3
3
3
dx
EI
xdx
E
xdx
E
1
10000
100 0
3 100
−
200 100
3 200
−
=
∫
x
2
∫
∫
S
+
+
=
+
=
15
.
3
(
)
(
)
100
200
y
0
100
=−=
(
−
(
)
=
2
DSSS
2
0 00015 15 0 0125
.
.
.
0 00006875
.
13 2
100
200
dx
EA
dx
E
dx
E
1
10000
100 0
10
−
200 100
20
−
=
∫
∫
∫
f
=
=
+
=
+
0 0015
.
10
20
x
0
100
1
1
0 0015
K
== =
666 67
.
f
.
Since the
j-
end of the member is fixed, there is no need to build the entire
member stiffness matrix. The
j-
end motions will be eliminated and only
the
i-
i-end of the member stiffness needs to be developed.
1
0
0
f
666 67
.
0
0
S
D
S
D
i
[]
=
K
0
1
−
2
=
0
2 18
.18
−
181 81
.
0
−
181 81
.
21818
S
D
S
D
0
−
2
3
The fixed-end forces and moments must be derived and applied to the
system.
100
200
dx
EI
xdx
E
3
xdx
E
3
1
10000
100 0
4 100
4
−
4
200 100
4 200
4
−
4
∫
∫
∫
S
4
=
x
3
+
=
+
=
212 5
.
(
)
(
)
100
200
y
0
100
0
0
w
D
=
[]
−
[
]
=−
−
(
)
PPFEPM
g
FEP
FEM
iy
=
−
SS SS
SSS
−
iz
14 23
2
(
)
2
−−
3
24
0
0 00015 212500125 15
0
4 7727
147 73
005
2000006875
.
(
)
−
()
P
=
−
.
.
.
.
=−
.
(
)
g
.
.
2
(()
−
(
)
−
15
.
0 0125 212 5
.
.
