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Tubo rettangolare Materiale
a b t L A Jmin E
[mm] [mm] [mm] [mm] [Mpa]
120 150 2.0 6136.44 944.00 260909.6! 210000
"n#tabilit$ globale %olonna &%r ' 143.61 ()
(
&annello a*L 210.9 M&a 4.000
&annello b*L 134.9! M&a 4.000
&%r' 12!.41 ()
+ ,16.20
[mm2] [mm4]
-%r'
-%r'
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e/ione a
a b t L A
[aim] [mm] [mm] [mm] [mm]
0.30 0 150 2.0 5224.3!9 612.00 13092.00
"n#tabilit$ globale %olonna &%r ' 30.5 ()
&annello a*L 50.42 M&a
&annello b*L 134.9! M&a
&%r' 30.5 ()
+ 0.00
[mm2] [mm3]
-%r'
-%r'
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Materiale Tubo uaro, Momen
g Jmin E a b
[mm] [Mpa] [aim] [mm] [mm]
21.39 406319.2! 210000 0.30 150 150.00
( &annello 2,4
0.425 &annello 3,4
4.000
M %riti%o i bu%(lin e
[mm4]
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o Materiale
t L A J el E
[mm] [mm] [Mpa] [aim]
1.5 4000 91.00 32!5093.25 4366!.91 210000 0.3
(
4!2.33 M&a 23.9
!9.05 M&a 4.0
!9.05
a#ti%o M%r ' 3.45 ()7m
[mm2] [mm4] [mm3]
-%r'
-%r'
-%r.min
'
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Tubo quadro- Formula di Von Karman Materiale
a b t L A E
[mm] [mm] [mm] [mm] [Mpa]
150 150.00 1.5 4000 91.00 210000
( 8
[Mpa] [aim] [aim] [mm]
&annello !9.05 4.0 0.50 14!.0
pigolo
e#i#ten/a in a##en/a i bu%(ling
e#i#ten/a in pre#en/a i bu%(ling
iu/ione re#i#ten/a a %au#a el bu%(ling
[mm2]
-%r
ap
)'
)b.
'
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7/25/2019 Buckling 005
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Tubo quadro- Formula di Winter
a b t
[aim] [Mpa] [aim] [mm] [mm] [mm]
0.3 235 9.00 150 150.00 1.5
Ae Atot e:
[mm] [mm;] [mm;] [Mpa]
5.26 12!.9 &annello !9.05
2.25 520.55 pigolo
209.39 () e#i#ten/a in a##en/a i bu%(ling
122.33 () e#i#ten/a in pre#en/a i bu%(ling
-41.58% iu/ione re#i#ten/a a %au#a el bu
ap
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7/25/2019 Buckling 005
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Materiale Tubo qua
L A E a
[mm] [Mpa] [aim] [Mpa] [aim] [mm]
4000 91.00 210000 0.3 235 9.00 150
( 8 Ae Atot e:
[aim] [aim] [mm] [mm] [mm;] [mm;]
4.0 0.496 14!.0 !2.90 109.34 &annello
2.25 446.3 pigolo
209.39 () e#i#ten/a
104.90 () e#i#ten/a
(ling -49.90% iu/ione
ap
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ro- Formula di Winter Modi!ata Materiale
b t L A E
[mm] [mm] [mm] [Mpa] [aim] [Mpa]
150.00 1.5 4000 91.00 210000 0.3 235
( 8 Ae
[Mpa] [aim] [aim] [mm] [mm] [mm;]
!9.05 4.0 0.506 14!.0 !4.3 111.5!
2.25
in a##en/a i bu%(ling 209.39 ()
in pre#en/a i bu%(ling 10".99 ()
re#i#ten/a a %au#a el bu%(ling -48.90%
[mm2]
-%r
ap
ae
)'
)b.
'
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0.22
0.055
+
0.!4165!39
41!.!!! 0.!506991 0.!3991
1.0001!04 ,0.0001!04
115.
!335.2
63.3262=
36.6!13 2666666.!
136.6!14 53!916.1!
320452. !45956.419
3.4
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Tubo quadro- Formula #$3-1-5
a b t L A
[aim] [mm] [mm] [mm] [mm]
9.00 150.00 150.00 1.5 4000 91.00
Atot e: (
[mm;] [Mpa] [aim] [aim]
&annello !9.05 4.0 1.!24
455.2 pigolo
e#i#ten/a in a##en/a i bu%(ling
e#i#ten/a in pre#en/a i bu%(ling
iu/ione re#i#ten/a a %au#a el bu%(ling
app
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Tubo rettanolare &ura 'e((ione- Formula #$3-1-5
a b t L A
[mm] [mm] [mm] [mm]
100.00 200.00 2.0 4000 114.00
? (
[Mpa] [aim] [aim]
&annello #up 329.51 1.0 4.0
&annelle @ert ,1.0
pigolo
e#i#ten/a in a##en/a i bu%(ling
e#i#ten/a in pre#en/a i bu%(lingiu/ione re#i#ten/a a %au#a el bu%(ling
30!029! !02036
513!0.2 11063.6
12.0!2
[mm3]
-%r
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Materiale Tubo )tta
E r
[Mpa] [aim] [Mpa] [aim] [aim] [mm]
210000 0.3 235 1.00 9.00 150
? 8 Ae Atot.e:
[aim] [aim] [mm;] [mm;] [mm;]
1.0 0.506 220.5 111.5! &annello
2.25 455.2!634 pigolo
Bon C. inter inter Mo E3,1,5
209.39 209.39 209.39 209.39 e#i#ten/a
122.33 104.90 106.99 10".99 e#i#ten/a
,41.5D ,49.90D ,4.90D -48.90% iu/ione
b
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Materiale
e E
[Mpa] [aim] [Mpa] [aim] [aim] [aim]
64303.!9 210000 0.3 235 1.00 4.00 9.00
8
[aim] [aim] [mm]
0.44 0.!6 .063
Bon C. inter inter Mo E3,1,5
0.00 0.00 0.00 2*8.24
0.00 0.00 0.00 0.000.00D 0.00D 0.00D -100.00%
a
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onale- Materiali
n lati t b A E
[] [mm] [mm] [mm] [aim] [Mpa]
1.5 114.1 113.56 !5.!1 13!0.20 210000
( ? 8
[Mpa] [aim] [aim] [aim] [aim]
132.46 4.0 1.332 1.0 0.62!
E3,1,5
in a##en/a i bu%(ling 322.00 ()
in pre#en/a i bu%(ling 202.4* ()
re#i#ten/a a %au#a el bu%(ling -3*.12%
b1
b1p
)'
)b.
'
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[aim] [Mpa] [aim]
0.3 235 1.00
Ae Atot.e:
[mm;] [mm;] [mm;]
1!0.34 106.!6
0.932 61.5!0!
b17t
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p#i (
1.0 4.000
0.9 4.202
0. 4.4160.! 4.654
0.6 4.92
0.5 5.250
0.4 5.632
0.3 6.06
0.2 6.624
0.1 !.25
0.0 .000
,0.1 .62
,0.2 9.56
,0.3 10.994
,0.4 12.2
,0.5 13.!50
,0.6 15.392
,0.! 1!.226
,0. 19.264
,0.9 21.51
,1.0 24.000
p#i (
1.0 4.000 4.00 4.000 11.300 0
0.9 4.205 4.00 4.205 10.0!1 0.0059
0. 4.432 4.00 4.432 9.03! 0.04!4
0.! 4.66 4.00 4.66 .199 0.16146
0.6 4.9!0 4.00 4.9!0 !.55! 0.32!2
0.5 5.290 4.00 5.290 !.110 0.!4!5
0.4 5.655 4.00 5.655 6.59 1.2916
0.3 6.0!4 4.00 6.0!4 6.03 2.05114
0.2 6.560 4.00 6.560 6.943 3.061!6
0.1 !.130 4.00 !.130 !.2!9 4.35942
0.0 !.10 4.00 !.10 !.10 5.9
,0.1 .53! 4.00 .632 .53! !.9593
0.0.51.01.5
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,0.2 9.459 4.00 9.64! 9.459 10.33344
,0.3 10.5!! 4.00 10.933 10.5!! 13.1306
,0.4 11.91 4.00 12.615 11.91 16.40912
,0.5 13.400 4.00 14.909 13.400 20.125
,0.6 15.105 4.00 1.222 15.105 24.4940
,0.! 1!.005 4.00 23.429 1!.005 29.3!9!4
,0. 19.101 4.00 32.00 19.101 34.!536,0.9 21.393 4.00 54.66! 21.393 41.0162
,1.0 23.0 4.00 164.000 23.0 4!.40.00.51.01.5
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,1.5,1.0,0.5
0.0
5.0
10.0
15.0
20.0
25.0
30.0
15.0
20.0
25.0
30.0
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,1.5,1.0,0.5
0.0
5.0
10.0
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a b
1 2 3 4
a
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4.5 !.2600 4.6944 4.055!
4.6 !.4!90 4.!!64 4.0!6
4.! !.!036 4.619 4.1049
4. !.9336 4.9506 4.1344
4.9 .1691 5.0426 4.16!0
5 .4100 5.13! 4.2025
5.1 .6563 5.2360 4.2405.2 .90!9 5.33!3 4.21!
5.3 9.1649 5.4415 4.3252
5.4 9.42!2 5.546 4.3!12
5.5 9.694! 5.656 4.4196
5.6 9.96!6 5.!!14 4.4!02
5.! 10.2456 5.!0 4.5231
5. 10.529 6.0053 4.5!1
5.9 10.1!4 6.1263 4.6353
6 11.1111 6.2500 4.6944
6.1 11.4100 6.3!63 4.!556
6.2 11.!141 6.5052 4.1!
6.3 12.0233 6.636 4.3!
6.4 12.33!! 6.!!0 4.9506
6.5 12.65!2 6.90!5 5.0193
6.6 12.91 !.0466 5.09
6.! 13.3116 !.13 5.1621
6. 13.6465 !.3324 5.2360
6.9 13.965 !.4!90 5.311!
! !.621 5.390
!.1 !.!!96 5.460
!.2 !.9336 5.546
!.3 .0900 5.6309
!.4 .24 5.!14!
!.5 .4100 5.001
!.6 .5!36 5.!0
!.! .!396 5.9!55
!. .90!9 6.0655
!.9 9.0!! 6.15!0
9.251! 6.2500
.1 9.42!2 6.3445
.2 9.6050 6.4405
.3 9.!51 6.53!9
.4 9.96!6 6.636
.5 10.1523 6.!3!1
.6 10.3395 6.3
.! 10.529 6.9420
. 10.!20! !.0466
.9 10.914! !.1526
9 11.1111 !.2600
9.1 11.309 !.36
9.2 11.510 !.4!90
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9.3 11.!141 !.5906
9.4 11.9196 !.!036
9.5 12.12!5 !.1!9
9.6 12.33!! !.9336
9.! 12.5501 .050!
9. 12.!64 .1691
9.9 12.91 .2910 13.2011 .4100
7/25/2019 Buckling 005
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1
1.4142 0
1.4142 4.5000
0 1 2 3 4 5 6 ! 9 10 11
0
1
2
3
4
5
6
!
9
0
1
23
4
5
6
!
9
0
1
2
3
4
56
!
9
m'1
m'2
m'3
m'4
a+b
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a b
1 2 3 4
a
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4.5
4.6
4.!
4.
4.9
5
5.15.2
5.3
5.4
5.5
5.6
5.!
5.
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.!
6.
6.9
!
!.1
!.2
!.3
!.4
!.5
!.6
!.!
!.
!.9
.1
.2
.3
.4
.5
.6
.!
.
.9
9
9.1
9.2
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9.3
9.4
9.5
9.6
9.!
9.
9.910
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1
1.4142 0
1.4142 EFG
0 1 2 3 40
2
4
6
10
12
14
16
1
20
22
24
26
2
30
32
34
36
m'1
m'2
m'3
m'4
a+b
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