WYZNACZENIE SIŁY SPRĘŻAJĄCEJ METODĄ GRAFICZNĄ.
DŹWIIGAR 1.
Y
x
A = ,
0 70 ⋅ 5
,
1 9 + ,
0 21⋅ 1
,
2 4 = 5
,
1 62 m 2
b ≤
h
3
,
0
m 1
dź
b
= 54 cm
m 1
b
= 90 cm
m 2
b
= 70 cm
dź
h
= 180 cm
dź
b
≤
h
3
,
0
= 3
,
0 ⋅180 = 54 cm = 5
,
0 4 m
m 1
dź
K = 2 ,
5 6 MPa
0
K ' = − 1
,
2 0 MPa
0
K = 23 1
, MPa
1
K ' = 0 MPa
1
K = 23 1
, MPa
2
K ' = 0 MPa
2
- geometria przekroju
,
0 70 ⋅ 5
,
1 9 ⋅ ( 5
,
0 4 + 3
,
0 5)
1
,
2 4
+ ,
0 21⋅ 1
,
2 4 ⋅
2
xsc =
= 9
,
0 42
,
1 25
5
,
1 9
,
0 21
,
0 70 ⋅ 5
,
1 9 ⋅
+ ,
0 21⋅ 1
,
2 4 ⋅ 5
,
1 9 +
2
2
ysc =
= ,
1 054
,
1 25
,
0 7 ⋅ 5
,
1 93
5
,
1 9
1
,
2 4 ⋅ ,
0 213
2
,
0 21
I =
+ ( ,
0 7 ⋅ 5
,
1 9) ⋅ ,
1
( 054 −
) +
+ ( 1
,
2 4 ⋅ ,
0 2 )
1 ⋅ ( ,
0 746 −
)2 = 5
,
0 15 m 4
x
12
2
12
2
I
5
,
0 15
W
x
=
=
= ,
0 4886 m 3
V
,
1 054
I
5
,
0 15
W
x
' =
=
= ,
0 6903 m 3
V '
,
0 746
W '
,
0 6903
r =
=
= ,
0 442 m
A
5
,
1 62
W
,
0 4886
r' =
=
= 3
,
0 13 m
A
5
,
1 62
e = V − 1
,
0 5 = ,
1 054 − 1
,
0 5 = 9
,
0 04 m
- wyznaczenie Y0, Y1, Y2, Y0’, Y1’, Y2’
1
1
−5
Y =
=
= 1
,
3 3 ⋅10
0
M
585 ,
5 63
q
3
η ⋅
+ K
8
,
0 5 ⋅
+ 2 ,
5 6 ⋅10
0
W
,
0 4886
1
1
−5
Y =
=
= ,
2 62 ⋅10
1
M q + ∆ q
7363 1
, 3
3
+ K
+ 231
, ⋅10
1
W
,
0 4886
−1
−1
−5
Y =
=
= 181
, 2 ⋅10
2
M q + ∆ q + M k + M
1213 ,
6 28
w
3
− K
− 231
, ⋅10
2
W '
,
0 6903
−1
−1
'
−5
Yo =
=
= −111,2 ⋅10
M
585 ,
5 63
q
'
3
η ⋅
+ K
8
,
0 5 ⋅
+ 1
,
2 ⋅10
0
W '
,
0 6903
−1
−1
'
−5
Y =
=
= − 3
,
9 8 ⋅10
1
M q + ∆ q
7363 1
, 3
'
+ K
− 0
1
W '
,
0 6903
1
1
'
−5
Y =
=
= ,
4 03 ⋅10
2
M
q + ∆ q + M k + M
1213 ,
6 28
w
'
+ K
+ 0
2
W
,
0 4886
Na podstawie otrzymanych wartości, sporządzono wykres i wyznaczono punkt ζ: ς = 1 ,
4 40 ⋅10 5
− m 2 / kN
A
5
,
1 62
N =
=
= 10847,22 kN
ς 1 ,
4 40 ⋅10−5
Sprawdzenie czy naprężenia dopuszczalne nie zostały przekroczone:
- stan „0”
włókna górne
N
N ⋅ e
η
M q
'
3
2
− η
+
≥ K = − 1,
2 ⋅10 kN / m 0
A
W '
W '
10847,22
10847,22 ⋅ 9,
0 04
8
,
0 5
8
,
0 5
585 ,
5 63
3
'
3
2
−
+
= − ,
0 0594 ⋅10 > K = − 1
,
2 ⋅10 kN / m 0
5
,
1 62
,
0 6903
,
0 6903
włókna dolne
N
N ⋅ e
η
M q
3
2
+ η
−
≤ K = 2 ,
5 6 ⋅10 kN / m 0
A
W
W
10847,22
10847,22 ⋅ 9,
0 04
8
,
0 5
8
,
0 5
585 ,
5 63
3
3
2
+
−
=1 ,
9 796 ⋅10 < K = 2 , 5 6 ⋅10 kN / m 0
5
,
1 62
,
0 4886
,
0 4886
- stan „1”
włókna górne
N
N ⋅ e
M q+ q
∆
'
2
−
+
≥ K = 0 kN / m 1
A
W '
W '
10847,22
10847,22 ⋅ 9
,
0 04
7363 1
, 3
3
'
2
−
+
= ,
3 4 ⋅10 > K = 0 kN / m 1
5
,
1 62
,
0 6903
,
0 6903
włókna dolne
N
N ⋅ e
M q+ q
∆
3
2
+
−
≤ K = 231,⋅10 kN / m 1
A
W
W
10847,22
10847,22 ⋅ 9
,
0 04
7363 1
, 3
3
3
2
+
−
= 11 9
, 43 ⋅10 < K = 23 1
, ⋅10 kN / m 1
5
,
1 62
,
0 4886
,
0 4886
- stan „2”
włókna górne
N
N ⋅ e
M +∆ + M + M
q
q
k
w
3
2
−
+
≤ K = 231
, ⋅10 kN / m 2
A
W '
W '
1084 ,
7 22
10847,22 ⋅ 9
,
0 04
1213 ,
6 28
3
3
2
−
+
= 10 3
, 2 ⋅10 < K = 23 1
, ⋅10 kN / m 2
5
,
1 62
,
0 6903
,
0 6903
włókna dolne
N
N ⋅ e
M +∆ + M + M
q
q
k
w
'
2
+
−
≤ K = 0 kN / m 2
A
W
W
10847,22
10847,22 ⋅ 9
,
0 04
1213 ,
6 28
3
'
2
+
−
= 1
,
2 74 ⋅10 > K = 0 kN / m 2
5
,
1 62
,
0 4886
,
0 4886
Wyznaczenie uogólnionych promieni:
K
η
0 ⋅ A ⋅
3
2 ,
5 6 ⋅10 ⋅ 5
,
1 62 ⋅ 8
,
0 5
r'
⋅
−
1 = 3
,
0 13 ⋅
−
1 = ,
0 668 m
N
10847,22
r
min
uo =
'
K
η
0 ⋅ A ⋅
3
− 1,
2 ⋅10 ⋅ 5
,
1 62 ⋅
8
,
0 5
r ⋅ 1 −
= ,
0 442 ⋅
1 −
=
5
,
0 56 m
N
1084 ,
7 22
K 1 ⋅ A
3
23 1
, ⋅10 ⋅ 5
,
1 62
r'
⋅
−1 = 3
,
0 13 ⋅
−
1 = ,
0 728 m
N
10847,22
r
min
u 1 =
'
K 1 ⋅ A
0 ⋅ 5
,
1 62
r ⋅ 1 −
= ,
0 442 ⋅ 1 −
=
,
0 442 m
N
10847,22
K 2 ⋅ A
3
23 1
, ⋅10 ⋅ 5
,
1 62
r'
⋅
−
1 = 3
,
0 13 ⋅
−1 = ,0728 m
N
10847,22
r
min
u 2 =
'
K 2 ⋅ A
0 ⋅ 5
,
1 62
r ⋅ 1 −
= ,
0 442 ⋅ 1 −
=
,
0 442 m
N
10847,22
'
K ⋅ A ⋅η
3
0
− 1,
2 ⋅10 ⋅ 5
,
1 62 ⋅
8
,
0 5
r ⋅' 1 −
= 3
,
0 13 ⋅
1 −
= 3
,
0 93 m
'
N
10847,22
r
min
uo =
K
η
0 ⋅ A ⋅
3
23 1
, ⋅10 ⋅ 5
,
1 62 ⋅ 8
,
0 5
r ⋅
−1 = ,
0 442 ⋅
−
1 = 9
,
0 43 m
N
10847,22
'
K ⋅ A
3
1
0 ⋅10 ⋅
5
,
1 62
r ⋅' 1 −
= 3
,
0 13 ⋅
1 −
= 3
,
0 13 m
N
10847,22
r
min
u 1 =
K 1 ⋅ A
3
23 1
, ⋅10 ⋅ 5
,
1 62
r ⋅
−
1 = ,
0 442 ⋅
−1 = ,1028 m
N
10847,22
'
K ⋅ A
3
2
0 ⋅10 ⋅
5
,
1 62
r ⋅' 1 −
= 3
,
0 13 ⋅
1 −
= 3
,
0 13 m
N
10847,22
r
min
u 2 =
K 2 ⋅ A
3
23 1
, ⋅10 ⋅ 5
,
1 62
r ⋅
−
1 = ,
0 442 ⋅
−
1 = ,
1 028 m
N
10847,22
Rzędne obwiedni granicznej: Lp.
0
1
2
3
4
5
M
− r '
0
+
1
uo
N
-0,556
-0,391
-0,262
-0,171
-0,116
-0,097
η
'
M
2
− r
1
+
-0,442
-0,198
-0,008
0,128
0,210
0,237
u 1
N
'
M
3
− r
2
+
-0,442
-0,047
0,272
0,499
0,634
0,677
u 2
N
M
r
0
+
uo
4
N
0,393
0,558
0,687
0,778
0,833
0,852
η
M
5
r
1
+
0,313
0,557
0,747
0,883
0,965
0,992
u 1
N
M
6
r
2
+
0,313
0,708
1,027
1,254
1,389
1,432
u 2
N
DŹWIIGAR 2.
Y
x
A = ,
0 21⋅ 5
,
2 0 + ,
0 70 ⋅ 5
,
1 9 = ,
1 638 m 2
b
= 90 cm
m 2
b
= 70 cm
dź
h
= 180 cm
dź
K = 2 ,
5 6 MPa
0
K ' = − 1
,
2 0 MPa
0
K = 23 1
, MPa
1
K ' = 0 MPa
1
K = 23 M
1
,
Pa
2
K ' = 0 MPa
2
- geometria przekroju
,
0 7 ⋅ 5
,
1 9 ⋅ ( 9
,
0 0 + 3
,
0 5)
5
,
2 0
+ ,
0 21⋅ 5
,
2 0 ⋅ 2
xsc =
= ,
1 25
,
1 638
5
,
1 92
,
0 21
,
0 7 ⋅ 5
,
1 9 ⋅
+ ,
0 21⋅ 5
,
2 0 ⋅ 5
,
1 9 +
2
2
ysc =
= ,1083
,
1 638
,
0 7 ⋅ 5
,
1 93
5
,
1 9
5
,
2 ⋅ ,
0 213
2
,
0 21
I =
+ ( ,
0 7 ⋅ 5
,
1 9) ⋅ ,
1
( 083 −
) +
+ ( 5
,
2 ⋅ ,
0 2 )
1 ⋅ ( ,
0 717 −
)2 = 5
,
0 25 m 4
x
12
2
12
2
I
5
,
0 25
W
x
=
=
= ,
0 4848 m 3
V
,
1 083
I
5
,
0 25
W
x
' =
=
= ,
0 7322 m 3
V '
,
0 717
W '
,
0 7322
r =
=
= ,
0 447 m
A
,
1 638
W
,
0 4848
r' =
=
= ,
0 296 m
A
,
1 638
e = V − 1
,
0 5 = ,
1 083 − 1
,
0 5 = 9
,
0 33 m
- wyznaczenie Y0, Y1, Y2, Y0’, Y1’, Y2’
1
1
−5
Y =
=
= 1,
3 2 ⋅10
0
M
5847,75
q
3
η ⋅
+ K
8
,
0 5 ⋅
+ 2 ,
5 6 ⋅10
0
W
,
0 4848
1
1
−5
Y =
=
= ,
2 62 ⋅10
1
M q + ∆ q
733 ,
1 62
3
+ K
+ 231,⋅10
1
W
,
0 4848
−1
−1
−5
Y =
=
= 1 ,
2 64 ⋅10
2
M q + ∆ q + M k + M
1112 ,
2 42
w
3
− K
− 231,⋅10
2
W '
,
0 7322
−1
−1
'
−5
Yo =
=
= 1
− ,
1 66 ⋅10
M
5847,75
q
'
3
η ⋅
+ K
8
,
0 5 ⋅
+ 1
,
2 ⋅10
0
W '
,
0 7322
−1
1
'
−5
Y =
=
= − 9
,
9 9 ⋅10
1
M q + ∆ q
733 ,
1 62
'
+ K
− 0
1
W '
,
0 7322
1
1
'
−5
Y =
=
= 3
,
4 6 ⋅10
2
M
q + ∆ q + M k + M
1112 ,
2 42
w
'
+ K
+ 0
2
W
,
0 4848
Na podstawie otrzymanych wartości, sporządzono wykres i wyznaczono punkt ζ: ς = 16 8
, 3 ⋅10 5
− m 2 / kN
A
,
1 638
N =
=
= 973 ,
2 62 kN
ς 16 8
, 3 ⋅10−5
Sprawdzenie czy naprężenia dopuszczalne nie zostały przekroczone:
- stan „0”
włókna górne
N
N ⋅ e
η
M q
'
3
2
− η
+
≥ K = − 1
,
2 0 ⋅10 kN / m 0
A
W '
W '
973 ,
2 62
973 ,
2 62 ⋅ 9,
0 33
8
,
0 5
8
,
0 5
5847,75
'
3
2
−
+
= 38 ,
6 61 > K = − 1
,
2 0 ⋅10 kN / m 0
,
1 638
,
0 7322
,
0 7322
włókna dolne
N
N ⋅ e
η
M q
3
2
+ η
−
≤ K = 2 ,
5 6 ⋅10 kN / m 0
A
W
W
973 ,
2 62
973 ,
2 62 ⋅ 9,
0 33
8
,
0 5
8
,
0 5
5847,75
3
3
2
+
−
= 16 9
, 6 ⋅10 < K = 2 , 5 6 ⋅10 kN / m 0
,
1 638
,
0 4848
,
0 4848
- stan „1”
włókna górne
N
N ⋅ e
M q+ q
∆
'
2
−
+
≥ K = 0 kN / m 1
A
W '
W '
973 ,
2 62
973 ,
2 62 ⋅ 9
,
0 33
733 ,
1 62
3
'
2
−
+
= 5
,
3 5 ⋅10 > K = 0 kN / m 1
,
1 638
,
0 7322
,
0 7322
włókna dolne
N
N ⋅ e
M q+ q
∆
3
2
+
−
≤ K = 231
, ⋅10 kN / m 1
A
W
W
973 ,
2 62
973 ,
2 62 ⋅ 9
,
0 33
733 ,
1 62
3
3
2
+
−
= 5
,
9 5 ⋅10 < K = 23 1
, ⋅10 kN / m 1
,
1 638
,
0 4848
,
0 4848
- stan „2”
włókna górne
N
N ⋅ e
M +∆ + M + M
q
q
k
w
3
2
−
+
≤ K = 231
, ⋅10 kN / m 2
A
W '
W '
973 ,
2 62
973 ,
2 62 ⋅ 9
,
0 33
1112 ,
2 42
3
3
2
−
+
= ,
8 73 ⋅10 < K = 23 1
, ⋅10 kN / m 2
,
1 638
,
0 7322
,
0 73221
włókna dolne
N
N ⋅ e
M +∆ + M + M
q
q
k
w
'
2
+
−
≤ K = 0 kN / m 2
A
W
W
973 ,
2 62
973 ,
2 62 ⋅ 9
,
0 33
1112 ,
2 42
3
'
2
+
−
= ,173⋅10 > K = 0 kN / m 2
,
1 638
,
0 4848
,
0 4848
Wyznaczenie uogólnionych promieni:
K
η
0 ⋅ A ⋅
3
2 ,
5 6 ⋅10 ⋅ ,
1 638 ⋅ 8
,
0 5
r'
⋅
−1 = ,
0 296 ⋅
−1 = ,0788 m
N
973 ,
2 62
r
min
uo =
'
K
η
0 ⋅ A ⋅
3
− 1
,
2 0 ⋅10 ⋅ ,
1 638 ⋅ 8
,
0 5
r ⋅ 1 −
= ,
0 447 ⋅
1 −
=
5
,
0 81 m
N
973 ,
2 62
K 1 ⋅ A
3
23 1
, ⋅10 ⋅ ,
1 638
r'
⋅
−1 = ,
0 296 ⋅
−1 = 8,
0 55 m
N
973 ,
2 62
r
min
u 1 =
'
K 1 ⋅ A
0 ⋅ ,
1 638
r ⋅ 1−
= ,
0 447 ⋅ 1 −
=
,
0 447 m
N
973 ,
2 623
K 2 ⋅ A
3
23 1
, ⋅10 ⋅ ,
1 638
r'
⋅
−1 = ,
0 296 ⋅
−1 = 8,
0 55 m
N
973 ,
2 62
r
min
u 2 =
'
K 2 ⋅ A
0 ⋅ ,
1 638
r ⋅ 1−
= ,
0 447 ⋅ 1 −
=
,
0 447 m
N
973 ,
2 62
'
K ⋅ A ⋅η
3
0
− 1
,
2 0 ⋅10 ⋅ ,
1 638 ⋅
8
,
0 5
r ⋅' 1 −
= ,
0 296 ⋅
1 −
= 3
,
0 85 m
'
N
973 ,
2 62
r
min
uo =
K
η
0 ⋅ A ⋅
3
2 ,
5 6 ⋅10 ⋅ ,
1 638 ⋅ 8
,
0 5
r ⋅
−1 = ,
0 447 ⋅
−1 = 1,
1 90 m
N
973 ,
2 62
'
K ⋅ A
3
1
0 ⋅10 ⋅
,
1 638
r ⋅' 1 −
= ,
0 296 ⋅
1 −
= ,
0 296 m
N
973 ,
2 62
r
min
u 1 =
K 1 ⋅ A
3
23 1
, ⋅10 ⋅ ,
1 638
r ⋅
−1 = ,
0 447 ⋅
−1 = ,1291 m
N
973 ,
2 62
'
K ⋅ A
3
0
2
⋅10 ⋅
,
1 638
r ⋅' 1 −
= ,
0 296 ⋅
1 −
= ,
0 296 m
N
973 ,
2 62
r
min
u 2 =
K 2 ⋅ A
3
23 1
, ⋅10 ⋅ ,
1 638
r ⋅
−1 = ,
0 447 ⋅
−1 = ,1291 m
N
973 ,
2 62
Rzędne obwiedni granicznej: Lp.
0
1
2
3
4
5
M
− r '
0
+
1
uo
N
-0,385
-0,201
-0,058
0,044
0,105
0,126
η
'
M
2
− r
1
+
-0,296
-0,025
0,186
0,337
0,427
0,457
u 1
N
'
M
3
− r
2
+
-0,296
0,109
0,434
0,665
0,803
0,847
u 2
N
M
r
0
+
uo
4
N
0,581
0,765
0,908
1,010
1,071
1,092
η
M
5
r
1
+
0,447
0,718
0,929
1,080
1,170
1,200
u 1
N
M
6
r
2
+
0,447
0,852
1,177
1,408
1,546
1,590
u 2
N
Y
x
A = ,
0 21⋅ 5
,
2 0 + ,
0 70 ⋅ 5
,
1 9 = ,
1 638 m 2
b
= 90 cm
m 2
b
= 70 cm
dź
h
= 180 cm
dź
K = 2 ,
5 6 MPa
0
K ' = − 1
,
2 0 MPa
0
K = 23 1
, MPa
1
K ' = 0 MPa
1
K = 23 M
1
,
Pa
2
K ' = 0 MPa
2
- geometria przekroju
,
0 7 ⋅ 5
,
1 9 ⋅ ( 9
,
0 0 + 3
,
0 5)
5
,
2 0
+ ,
0 21⋅ 5
,
2 0 ⋅ 2
xsc =
= ,
1 25
,
1 638
5
,
1 92
,
0 21
,
0 7 ⋅ 5
,
1 9 ⋅
+ ,
0 21⋅ 5
,
2 0 ⋅ 5
,
1 9 +
2
2
ysc =
= ,1083
,
1 638
,
0 7 ⋅ 5
,
1 93
5
,
1 9
5
,
2 ⋅ ,
0 213
2
,
0 21
I =
+ ( ,
0 7 ⋅ 5
,
1 9) ⋅ ,
1
( 083 −
) +
+ ( 5
,
2 ⋅ ,
0 2 )
1 ⋅ ( ,
0 717 −
)2 = 5
,
0 25 m 4
x
12
2
12
2
I
5
,
0 25
W
x
=
=
= ,
0 4848 m 3
V
,
1 083
I
5
,
0 25
W
x
' =
=
= ,
0 7322 m 3
V '
,
0 717
W '
,
0 7322
r =
=
= ,
0 447 m
A
,
1 638
W
,
0 4848
r' =
=
= ,
0 296 m
A
,
1 638
e = V − 1
,
0 5 = ,
1 083 − 1
,
0 5 = 9
,
0 33 m
- wyznaczenie Y0, Y1, Y2, Y0’, Y1’, Y2’
1
1
−5
Y =
=
= 1
,
3 2 ⋅10
0
M
585 ,
5 63
q
3
η ⋅
+ K
8
,
0 5 ⋅
+ 2 ,
5 6 ⋅10
0
W
,
0 4848
1
1
−5
Y =
=
= ,
2 61⋅10
1
M q + ∆ q
7363 1
, 3
3
+ K
+ 231
, ⋅10
1
W
,
0 4848
−1
−1
−5
Y =
=
= 1 ,102 ⋅10
2
M q + ∆ q + M k + M
10272 8
, 3
w
3
− K
− 231
, ⋅10
2
W '
,
0 7322
−1
−1
'
−5
Yo =
=
= −1 ,
1 65 ⋅10
M
585 ,
5 635
q
'
3
η ⋅
+ K
8
,
0 5 ⋅
+ 1
,
2 ⋅10
0
W '
,
0 7322
−1
1
'
−5
Y =
=
= − 9
,
9 4 ⋅10
1
M q + ∆ q
7363 1
, 3
'
+ K
− 0
1
W '
,
0 7322
1
1
'
−5
Y =
=
= ,
4 72 ⋅10
2
M
q + ∆ q + M k + M
10272 8
, 3
w
'
+ K
+ 0
2
W
,
0 4848
Na podstawie otrzymanych wartości, sporządzono wykres i wyznaczono punkt ζ: ς = 17 5
, 0 ⋅10 5
− m 2 / kN
A
,
1 638
N =
=
= 936 ,
0 00 kN
ς 17 5
, 0 ⋅10−5
Sprawdzenie czy naprężenia dopuszczalne nie zostały przekroczone:
- stan „0”
włókna górne
N
N ⋅ e
η
M q
'
3
2
− η
+
≥ K = − 1,
2 0 ⋅10 kN / m 0
A
W '
W '
9360
9360 ⋅ 9,
0 33
8
,
0 5
8
,
0 5
585 ,
5 63
'
3
2
−
+
= 688 3
, 5 > K = − 1
,
2 0 ⋅10 kN / m 0
,
1 638
,
0 7322
,
0 7322
włókna dolne
N
N ⋅ e
η
M q
3
2
+ η
−
≤ K = 2 ,
5 6 ⋅10 kN / m 0
A
W
W
9360
9360 ⋅ 9,
0 33
8
,
0 5
8
,
0 5
585 ,
5 63
3
3
2
+
−
= 15 8
, 4 ⋅10 < K = 2 , 5 6 ⋅10 kN / m 0
,
1 638
,
0 4848
,
0 4848
- stan „1”
włókna górne
N
N ⋅ e
M q+∆ q
'
2
−
+
≥ K = 0 kN / m 1
A
W '
W '
9360
9360 ⋅ 9
,
0 33
7363 1
, 3
3
'
2
−
+
= 8
,
3 4 ⋅10 > K = 0 kN / m 1
,
1 638
,
0 7322
,
0 7322
włókna dolne
N
N ⋅ e
M q+ q
∆
3
2
+
−
≤ K = 231
, ⋅10 kN / m 1
A
W
W
9360
9360 ⋅ 9
,
0 33
7363 1
, 3
3
3
2
+
−
= 5
,
8 4 ⋅10 < K = 23 1
, ⋅10 kN / m 1
,
1 638
,
0 4848
,
0 4848
- stan „2”
włókna górne
N
N ⋅ e
M +∆ + M + M
q
q
k
w
3
2
−
+
≤ K = 231
, ⋅10 kN / m 2
A
W '
W '
97360
9360 ⋅ 9
,
0 33
10272 8
, 3
3
3
2
−
+
= 7 8
, 2 ⋅10 < K = 23 1
, ⋅10 kN / m 2
,
1 638
,
0 7322
,
0 73221
włókna dolne
N
N ⋅ e
M +∆ + M + M
q
q
k
w
'
2
+
−
≤ K = 0 kN / m 2
A
W
W
9360
9360 ⋅ 9
,
0 33
10272 8
, 3
3
'
2
+
−
= 5
,
2 4 ⋅10 > K = 0 kN / m 2
,
1 638
,
0 4848
,
0 4848
Wyznaczenie uogólnionych promieni:
K
η
0 ⋅ A ⋅
3
2 ,
5 6 ⋅10 ⋅ ,
1 638 ⋅ 8
,
0 5
r'
⋅
−1 = ,
0 296 ⋅
−1 = 8,
0 31 m
N
9360
r
min
uo =
'
K
η
0 ⋅ A ⋅
3
− 1
,
2 0 ⋅10 ⋅ ,
1 638 ⋅ 8
,
0 5
r ⋅ 1 −
= ,
0 447 ⋅
1 −
=
5
,
0 87 m
N
9360
K 1 ⋅ A
3
23 1
, ⋅10 ⋅ ,
1 638
r'
⋅
−1 = ,
0 296 ⋅
−1 = 9,
0 00 m
N
9360
r
min
u 1 =
'
K 1 ⋅ A
0 ⋅ ,
1 638
r ⋅ 1−
= ,
0 447 ⋅ 1 −
=
,
0 447 m
N
9360
K 2 ⋅ A
3
23 1
, ⋅10 ⋅ ,
1 638
r'
⋅
−1 = ,
0 296 ⋅
−1 = 9,
0 00 m
N
9360
r
min
u 2 =
'
K 2 ⋅ A
0 ⋅ ,
1 638
r ⋅ 1−
= ,
0 447 ⋅ 1 −
=
,
0 447 m
N
9360
'
K ⋅ A ⋅η
3
0
− 1
,
2 0 ⋅10 ⋅ ,
1 638 ⋅
8
,
0 5
r ⋅' 1 −
= ,
0 296 ⋅
1 −
= 3
,
0 88 m
'
N
9360
r
min
uo =
K
η
0 ⋅ A ⋅
3
2 ,
5 6 ⋅10 ⋅ ,
1 638 ⋅ 8
,
0 5
r ⋅
−1 = ,
0 447 ⋅
−1 = 5,
1 56 m
N
9360
'
K ⋅ A
3
1
0 ⋅10 ⋅
,
1 638
r ⋅' 1 −
= ,
0 296 ⋅
1 −
= ,
0 296 m
N
9360
r
min
u 1 =
K 1 ⋅ A
3
23 1
, ⋅10 ⋅ ,
1 638
r ⋅
−1 = ,
0 447 ⋅
−1 = 3,
1 60 m
N
9360
'
K ⋅ A
3
0
2
⋅10 ⋅
,
1 638
r ⋅' 1 −
= ,
0 296 ⋅
1 −
= ,
0 296 m
N
9360
r
min
u 2 =
K 2 ⋅ A
3
23 1
, ⋅10 ⋅ ,
1 638
r ⋅
−1 = ,
0 447 ⋅
−1 = 3,
1 60 m
N
9360
Rzędne obwiedni granicznej: Lp.
0
1
2
3
4
5
M
− r '
0
+
1
uo
N
-0,388
-0,197
-0,048
0,059
0,122
0,144
η
'
M
2
− r
1
+
-0,296
-0,013
0,207
0,365
0,459
0,491
u 1
N
'
M
3
− r
2
+
-0,296
0,095
0,405
0,627
0,759
0,802
u 2
N
M
r
0
+
uo
4
N
0,587
0,778
0,927
1,034
1,097
1,119
η
M
5
r
1
+
0,447
0,730
0,950
1,108
1,202
1,234
u 1
N
M
6
r
2
+
0,447
0,838
1,148
1,370
1,502
1,545
u 2
N