exampl1, Budownictwo, IV semestr, Metody Obliczeniowe
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8
<
dx
2
+ u = g 8x2(a,b)
du
u(x)2C
2
,
:
dx
(a) = c
u(b) = d
v
i
Z
b
Z
b
(u
00
+ u)v dx =
gv dx
a
a
Z
b
Z
b
Z
b
−
u
0
v
0
dx + u
0
v|
a
+
uv dx =
gv dx
a
a
a
Z
b
Z
b
Z
b
−
u
0
v
0
dx + u
0
(b)v(b)−u
0
(a)v(a) +
uv dx =
gv dx
a
a
a
v(b) = 0
otrzymujemy
Z
b
Z
b
Z
b
u
0
(a) = c
i
−
u
0
v
0
dx +
uv dx =
gv dx + cv(a)
a
a
a
Z
b
Z
b
u(x)
,
b
u(b) = d
i
−
u
0
v
0
dx +
uv dx =
gv dx + cv(a) 8v, v(b) = 0
a
a
a
Z
Z
Z
ij
=−
i
j
dx +
i
j
dx, f
el
i
=
g
i
dx + c
i
(a)
el
el
el
d
2
u
Z
K
el
u
4
u
3
u
2
u
6
u
1
u
5
s=sin
c=cos
o
K
e
=
EA
L
0
@
c
2
cs−c
2
−cs
cs s
2
−cs−s
2
−c
2
−cs c
2
cs
1
A
P
e
=
qL
2
0
@
c
s
c
s
1
A
−cs−s
2
cs s
2
K
1
= 100
0
@
72 96−72 −96
96 128−96−128
−72 −96 72 96
−96−128 96 128
1
A
P
1
=
0
@
0
0
0
0
1
A
K
2
= 100
0
@
0 0 0 0
0 250 0−250
0 0 0 0
0−250 0 250
1
A
P
2
=
0
@
0
−40
0
−40
1
A
K = 100
0
@
72 96−72 −96 0 0
96 128−96−128 0 0
−72 −96 72 96 0 0
−96−128 96 378 0−250
0
1
A
P =
0
@
0
0
0
−40
0
−40
1
A
0
0
0 0
0
0
0
0−250 0 250
Ku = P + W
0
1
0
1
0
1
0
1
72 96−72 −96 0 0
96 128−96−128 0 0
−72 −96 72 96 0 0
−96−128 96 378 0−250
0
u
1
= 0
u
2
= 0
u
3
u
4
u
5
= 0
u
6
= 0
0
0
0
−40
0
−40
0
0
10
0
0
0
100
@
A
@
A
=
@
A
+
@
A
0
0
0 0
0
0
0
0−250 0 250
u =
0 0 0.00423−0.00213 0 0
T
[m]
W = Ku−P
0
72 96−72 −96 0 0
96 128−96−128 0 0
−72 −96 72 96 0 0
−96−128 96 378 0−250
0
1
0
1
0
0
0
0
−40
0
−40
1
0
−10
−13.333
10
0
0
93.333
1
100
@
A
@
A
−
@
A
=
@
A
0
0
0 0
0
0
0
0−250 0 250
K
el
u
el
−P
el
= Q
el
100
0
@
72 96−72 −96
96 128−96−128
−72 −96 72 96
−96−128 96 128
1
A
0
@
1
A
−
0
@
1
A
=
0
@
−10
−13.333
10
13.333
1
A
100
0
@
0 0 0 0
0 250 0−250
0 0 0 0
0−250 0 250
1
A
0
@
1
A
−
0
@
1
A
=
0
@
0
−13.333
0
93.333
1
A
13.333
13.333
0
10
10
93.333
13.333
0
N
1
= 16.667kN
N
2
=−13.333−20L
2
[kN]
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