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Title:

Stability Theory of Structures

Description:

... COLLAPSE OF EXPOSITION HALL, Bucharest, 1963 local buckling snap - through : ( ) : ... – PowerPoint PPT presentation

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Transcript and Presenter's Notes

Title: Stability Theory of Structures


1
(No Transcript)
2
????? ??????? ???? ??
Stability Theory of Structures
???? ?????
3
??? ??? ????? (????? ?????)
4

??? ??? ????? (????? ?????)
?- ????? ? ????? ???? ??????? ???? ??
Heavy and Thick Structures
?? ??? ???? ?? ???????? ??? ?? ????
?
Light and Thin Structures
??? ??? ?? ???
  • ??????? ?? ????? ?? ?????? ????
  • ????? ??????? ???? ???? ??
  • ???? ?? ????? ??? ?????? ? ???? ???? ??
  • ?????? ??? ??? ????? ? ????? ?????? ????
  • ?????? ??? ???????? ????
  • ?????? ????? ??? ????? ????
  • ????? ????? ????

5
??? ??? ????? (????? ?????)
??? ???? ?? ????? ??? ?? ?? ?? ????? ????
Light and Thin
  • ?? ???? ????? ?????? ???? ??????
  • ?????? ???? ? ???? ?? ???? ??? ???????
  • ???? ?? ???? ?????? ? ?????? ?? ????? ? ?????
    ???? ??.

(Specialized Design Capacity)
??? ?? ???? ??? ???? ? ?????? ?? ????? ? ?????
???? ??? ?????? ?? ????? ??????? ???? ?? ?? ????.
6
??? ??? ????? (????? ?????)
????? ????? ????? ?? ???? ???? ?? ?? ??? ?? ?????

??? - ?? ???? ????? ???? ???? (Very Squat Tube-
Short Thick Tube)
(?? ????? ??? ???? ????? ??? ??? ? ??? ??? ???
?????? ??????? ????? ???? ????)
  • ????? ??? ????? ????? ?? ????? ?? ?? ????????
    ????? ????? ?????? ?? ?? ????? (Limit
    Proportionality) ?? ???? a ????? ???? .
  • ???? ????? ??????? ??? ??????? ?? ????
    ??????????? ??? P ?? ???? a ??????? ?? ?????
    ???????? ????? ???. ???????? ?? ????? ??? (Linear
    Analysis) ???? ????? ???? ????? ??? .
  • ??? ???????? ???? ?? ??? ??? ????
    (Bulging)????? ???.

7
??? ??? ????? (????? ?????)
? - ???? ???? ???? ???? (Longer Thick Tube)
( ?? ????? ??? ???? ????? ??? ? ??? ??? ??? ?????
????? ?????? ??????? ???? ????)
  • ???????? ?? ??? ???? ????? (Bowing Sideway)
    ????? ???.
  • ???? ?????????? ?? ???? b ?? ????? ???? ?? ?????
    ?? ???? c ??????.
  • ???? ????? ??????? ???? ???? ?????????? ??
    ???? b ??????? ?? ????? ???????? ????? ???.
    ???????? ?? ????? ??? ?? ????? ?????? ????? ? ??
    ?? ????? ?????? ??????? Nonlinear Analysis)
    (Elastic???????? ?? ??? ?????? ????? ?????? ?? ??
    ?? ????.

8
????? ??????? ???? ??
( ?? ????? ??? ???? ????? ??? ? ??? ??? ???
????? ????? ?????? ??????? ???? ????)
????? ??? ?? ??? ????? (Buckling)????? ??? .
(???? ??? ?? ?????? ????? ?? ????? ???????? ???)
Buckling is used to denote the dynamic process in
which a structure moves from an unstable to
another possibly distant stable state
9
??? ??? ????? (????? ?????)
???? ????? ??????? ??? ??????? ?? ???? ??????
???? ???? ????? ?? a ??????? ?? ????? ????????
????? ???. ??? ?? ????? ???? ??????? ????? ???
???? ?? ?????. ???????? ?? ?? ????? ??????
????? ?? ???? ?????? ??? ????? ? ????? ?????
???? ??? ???? ????? ???? ???? ???? ??? ( ??
????? ?? ??? ????? ?????????? ?? ????? ???? ???
Arc-Length Method ) ? ?? ????? ??? ??
????? ??? ?????? ?? ????? ???????? ????.
10
??? ??? ????? (????? ?????)
???? ???? ??? ????? ????????? ?? ??? ????? ?? ???

??? - ????? ?? ???? ?? ?? ???
11
??? ??? ????? (????? ?????)
12
??? ??? ????? (????? ?????)
? - ?????? ????? ?? ?? ?? ???? ??? ??
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
??? ??? ????? (????? ?????)
? ????? ?? ?????
? - ????? ?? ??? ??? ?????
17
??? ??? ????? (????? ?????)
? ????? ??????? Ronan Point
18
??? ??? ????? (????? ?????)
? - ????? ???? ????????? ?? ?????? (Exposition
Hall in Bucharest)
19
??? ??? ????? (????? ?????)
COLLAPSE OF EXPOSITION HALL, Bucharest, 1963
Before collapse
After collapse
20
??? ??? ????? (????? ?????)
21
??? ??? ????? (????? ?????)
? - ????? ??? ??? ??? (Sun Kink)
22
Dynamic Buckling of Bridge
??? ??? ????? (????? ?????)
23
??? ??? ????? (????? ?????)
??? ????? ?? ????? ??? ????? ??? ???? ???????
????.
???? ??? ????? ?? ??? ???? ????? ?? ????? ??????
???? (Load- Carrying Capacity) ??? ?? ?????? ??
???? ?? ????? ????? ??? ???? ?? ?? ??? ????? ???.
24
?? ???? ??? ????? ????? ????????? ????? ?
????????? ???? ??
25
??? ??? ????? (????? ?????)
?- ??????? ??????? ?? ????? ?????????
26
??? ??? ????? (????? ?????)
Tompson ? ???????? ?? ????? ??? 1960? ?????
1970? ????? ?????? ??????? ?? ?? ??????? ??
?????? ????? ????? ???? ????? ??? ????? ??
????? ???? ??? ?? ??? ?????.
27
??? ??? ????? (????? ?????)
Croll and Walker ? ?? ????? 1970? ??? ??? ????
???? ??????? ????? ? ?????????? ?? ???? ?? ?????
????? ?? ???? ????? ?????? ??????? ????? ??? ????
Tompson ????????? ?? ??? ?????.
28
?- ?????? ??????? ? ????????? ?? ???? ??
??? ??? ????? (????? ?????)
??????? ? ????????? ????? ???? ????? ?? ????? ??
????? ??? ?????? ???? ? ????? ?? ???? ?? ?????
????? .
???? ?? ????? ?? ?? ???? ?? ????? ??????
(Stable) ?????? ?? ??? ??? ??????? ????? ? ????
(Relatively Small Changes) ?? ?????????? ?????
????? ? ?? ?? ????? ????? ??? ???? ???????
????? ? ???? ?? ???? ????? ?? ????? ???.
(Proportional Changes)
29
??? ??? ????? (????? ?????)
???? ?? ????? ?? ?? ???? ?? ????? ????????
(Unstable) ?????? ?? ??? ?????????? ????? ? ????
?? ?????????? ????? ????? ? ?? ?? ????? ?????
??? ???? ??????? ????? ????? (Lrage Change) ??
???? ????? ?? ????? ???. (Non-Proportional
Changes)
???? ????? ?? ???? ?? ? ???? ????? ????? ???? ??
(Equilibrium State)
???? ????? ?? ????? ???? ?? ???? ?????
?????? ????(Configuration) ? ????? ????? ?? ??
????? ????? ? ??????? ?? ???? ?? ????? ?? ??? ??
???.
????? ????? ???? ?? (?????? ????? ? ??????? ????)
?????????? ??????????
????? ????? ????? ???????? ?????? ? ??????????
30
??? ??? ????? (????? ?????)
???? ????? ?? ????? ???? ?? ?????? ??????
?? ???? ??? ?????? ??? ???? (Small
Perturbation Small Disturbance) ?? ?? ?????
?? ?? ??????? ???? ?? ???????? ?? ?????? ??? ????
?? ?????????? ????? ????? ???? ?? ?? ????
??????? ?? ????? ????? ???? ?? ? ?? ?? ????? ????
?? ???? ?? ???? ???? ?????? ??? ???? ?? ????
????? ????? ????? ???.
???? ????? ?? ????? ???? ?? ???????? ?????? ??
???? ??? ?????? ??? ???? ?? ?? ????? ?? ??
??????? ???? ?? ???????? ?? ?????? ??? ????
?? ?????????? ????? ????? ???? ?? ?? ???? ???????
?? ????? ????? ???? ?? ? ?? ?? ????? ???? ??
???? ?? ???? ???? ?????? ??? ???? ?? ???? ?????
????? ????? ???? ?? ???? ?? ?? ?? ????? ?? ??
?????? (Upseting) ??? ???.
31
??? ??? ????? (????? ?????)
?- ????? ??????? ????? ??? ??????? ? ?????????
32
??? ??? ????? (????? ?????)
5- ??? ??? ????? ??????? ???? ?? ( ? ????????
???? ?? ??? ??? ?? )
???) ??? ????? ??????? (Static Equilibrum Method)
33
??? ??? ????? (????? ?????)
???? ??? ???? ???? ????? ?????? ????? ??????? ??
???? ??? ????? ??? ????? ???? ????? ?? ???????
????? ?????? ?? ???? ?? ??? ????? ???? ???? ???
???
34
??? ??? ????? (????? ?????)
???? ????? ??????? ??? ????? ?????? ???? ??
?????? ????? ????? ???? ( ???? ) ?? ?????
????? ???? ? ????? ???? ?????? ???? ?? ???? ?????
???? ????
?? ??? ???? ???? ?????? ????? ??? ??
35
??? ??? ????? (????? ?????)
?? ????? ??? ??? ???? ?? ???? ??? ?? ?? ???
???? ?????? (Critical States)
36
??? ??? ????? (????? ?????)
???????? ????? ??????? ??? ?? ??? ????? ????? ???
??
??? ??????? ???????? ??? ????? ?? ??? ?? ??????
??? ?? ?? ????????? ???? ?? ??? ???? ?????? ??
???? ????? ?? ???? ???? ????? ?? ???? ????? ?????
??? ???????? ?????? ????? ?? ?? ???? ????? ??????
?? ?????.
??? ??????? ???????? ??? ????? ?? ??? ?? ??????
??? ?? ?? ????? ???? ???? ?? ??? ???? ?????? ??
???? ????? ?? ???? ???? ????? ?? ???? ?????
????? ??? ??? ??? ? ????? ???? ?? ??? ????
?????? ????? ?? ?? ???? ????? ???????? ?? ?????.
37
??? ??? ????? (????? ?????)
? - ??? ?????
??? ????? ?? ???? ?? ??? ????? ?????? ???
1- ????? ????? (Stationary Value)????? ?????
??????? ???? ???? ?? ?? ????? ?? ??? ????? ?????
??? ???? ? ???? ???? ????? ?? ???? ???
2- ?????? ???? ????? ????? ??????? ???(Total
Potential Energy Functional ) ???? ?? ?? ?????
???? ( ?? ??? ????? ????)? ??? ???? ? ???? ????
??????? ?? ???? ????? ???. ?? ????? ????? ????
??? ????? ????? ??????? ??? ?? ????? ???? ?? ??
????? ???? ( ?? ??? ????? ????)? ??????? ??
????????? ????? ????? ?? ????? ?? ???? ?? ???.
38
??? ??? ????? (????? ?????)
39
??? ??? ????? (????? ?????)
???? ????? ?????? ??? ?????? ??? ???? ?? ??????
?? ??? ?? ?????
????? ????? ??????? ??? ?? ???? ??? ?? ????
40
??? ??? ????? (????? ?????)
  • ??? ??? ????? ???? ???? ?? ????? ?? ????? ?? ???
    ????? ????? ??? ? ??? ??? ???? ??? ????? ?????
    ??????? ??? ???? ?? ?? ????? ???? ????? ???
    ???? (???????? ????? ??????? ???)

??? ?????? ???? ?????? ?? ??? ?? ?? ??????? ??
??? ????? ?? ??? ???? ???.
  • ??? ??? ????? ???? ????? ??????? ????? ?? ?????
    ?? ??????? ?? ??????? ???? ??? ????? ?????
    ??????? ???? ?? ?? ????? ???? ????? ???? ???

41
??? ??? ????? (????? ?????)
42
??? ??? ????? (????? ?????)
???? ????? ??????? ??? ???? ??????? ???? ??????
?? ????? ?????? ????? ?? ???? ??????? ???? ????
43
??? ??? ????? (????? ?????)
????? ??????? ??? ?? ??? ?????
  • ??? ????? ????? ?? ?????? ???? ?? ???? ????? ??
    ?????? ?????? ????? ??????? ??? ????? ???? ????
    ?? ???? ?????? ?????? ???.
  • ??? ????? ????? ?? ?????? ???? ?? ???? ????? ??
    ?????? ???? ????? ??????? ??? (???? ??? ?????)
    ????? ???? ???? ?? ???? ?????? ???????? ???.

44
??? ??? ????? (????? ?????)
? - ??? ????? ????????
45
??? ??? ????? (????? ?????)
?? ?? ?? ?????
???? ?? ????? ? ???? ?????? ???? ?? ???? ???
?? ????
46
??? ??? ????? (????? ?????)
??? ????? ????? ?? ?? ???? ??? ?? ??? ?????? (
?? ???? t 0)
?? ??? ???? ???? ??? ??? ?? ?????? ????
47
??? ??? ????? (????? ?????)
??? ?? ?? ??? ???? t ??? ????? ?????????
??? ?? ?????? ????
?????? ?? ???? ?? ????? ???? ?????? ?????? ??
????? 2 a ??? ? 2 a ??? ?????? ?? (1-p) ???
  • ?? ???? p 0? ???? ????? ?? ?? ?????? ?????? ??
    ????? ?? ?????? ????? ???? ?? ????.(a2gtgt0)
  • ?? ?????? p (???? ?????? W1)? ?????? ????? ????
    ?? ???? ?? ??? ? ?? ????? ?? p 1 ?? ?????? ???
    ?? ???.(a20)
  • ?? ???? p gt1? ???? ????? ?? ???? ?? ??? ?? ?? ??
    ?????? ???? ?? ?????? ????? ????? ? ???? ?? ???
    ?????? ???? ?? ???.(a2lt0)

48
??? ??? ????? (????? ?????)
????? ??????? ??? ?? ??? ????? ???????? ????? ???
??
  • ??? ???? ?????? ??? ????? ???? ???????? ???? ???
    ?? ???? ?????? ????? (real)? ???? ?????? ?? ???
    ???? ???? ????? ?? ???? ????? ?????? ???.
  • ??? ????? ?? ?????? ?????? ???? ??? ?? ????
    ?????? ?????? (Imaginary) ????? ?? ??? ???? ????
    ????? ?? ???? ????? ???????? ??? .
  • ??? ????? ?? ?????? ?????? ???? ??? ?? ????
    ?????? ???(zero) ????? ?? ??? ???? ???? ????? ??
    ???? ?????? ??? .
  • ????? ???? ?? ???? ???? ???? ? ????? ?? ??
    ?????? ????(?k/m1/2)

49
??? ??? ????? (????? ?????)
?? ?????? ?????? ??? ???????? ???? ?? ??? ????? ?
??? ????? ???????? ?? ???? ???? ????? ?? ??? ????
?? ?? ???? ????? ??? ????? ???? ????? ??? ?? ??
??? ??????? ???? ?? ??? .
50
??? ??? ????? (????? ?????)
  • ???? ???? p 1 ? a20? ??? ?? ?????? ???? ???
    ??? ???? ????? ????? ????? ??? ? ?? ??? ????
    ?????? ?? ????? ????? ??? ??? ????? ??? (??????
    ????).
  • ( ??????? ??? ?????? ????? ?????)
  • ???? ???? p lt1 ? a2gt0? ??? ?? ?????? ???? ???
    ??? ???? ????? ????? ????? ??? ? ?? ??? ????
    ?????? ?? ????? ????? ??? ??? ????? ??? (??????
    ?????).
  • ( ??????? ??? ?????? ????? ?????)
  • ???? ???? p 1 ? a20? ??? ?? ?????? ????? ???
    ????? ???? ????? ????? (?????? ???).
  • ( ??????? ??? ?? ?????? ? ?? ???????)
  • ???? ???? p gt1 ? a2lt0? ??? ?? ???? ??????? ??
    ???? ????? ????? ??? ?? ??? ???? ????? ??????
    ???? ????? ???? (?????? ??????).
  • ( ??????? ??? ??????? ?????)
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