visoki stomanobetonni komini

5/27/2018 visoki stomanobetonni komini

1/66

.

2011.


2/66

, ,

, ,

,

.

113 , 48 24 .

18 , 18 18

. 145

, 4 141 .

.................................. ...................

.................

. 427.


3/66

.

02.15.04

: . -.

: . -.

. -.

2011.


4/66

.

.

. -. ,

. - . .


5/66

3

-

.

.

. ,

.

,

.

,

.

.

.

.

. -

.

.

.

, .

.

.

.


6/66

4

1

1.1.

,

. ,

( ,

.), .

1.2.

20--

. ,

. , 1876.

, 1907. 1910.

.

1900., 1916.

165.

.

.

.

Bancroft (1885)

[13] Christie (1899) [36].

. 1934. (ACI).

ACI307-08 [6][7] EN13084

[49][50]. CICIND [40][41].

1.3.

,

.1.1.


7/66

5

.1.1.[86]

1.4.

. -

,

,

(GLC) ,

. ,

:- ;

- ;

- .

.

, , ,

, .

,

1:50 1:100, .

.

1.5.

1.5.1.

,

. , ,

, .

.


8/66

6

1.5.1.1.

,

.

,

. , ,

,

.

1.5.1.2.

,

.

.

. -

Vickery [131][132][133][134][135][137], Basu [15][16], Kareem [71][72][73][74][75] Holmes [64].

EN1991-1-4 [52], .

,

.

,

, ,

. ,

, .

.

, ,

. ,

,

. , , :

- , ;

- , , ;

- ,

.

:

- , ,

;

- ,

.


9/66

7

, ,

.

, .

, .

, .

, ,

. .

.

.

,

.

.1.2.

. .

, , ,

(.1.2).

, .

.

.

,

, .

, Reynolds

Strouhal, , , . -

Scruton Vickery. -,

, , Vickery

Basu,

(CICIND, ACI307). ,

25%-30% [10].


10/66

8

. , ,

Raynolds, ,

[138].

,

.

1.5.1.3.

1.5.1.3.1.

,

, .

.

, , ,

.

,

.

. , EN1998-6 [56] .5.4

,

.

1.5.1.3.2.

EN1998-1 [55] .4.3.3 :

- (modal response spectrum

analysis);

- (non-linear pushover analysis);

- (non-linear time history analysis).

EN1998-6 [56] .4.3.1

, EN1998-1 [55] .3.2.2. ,

-

. EN1998-1 [55] .3.2.2.2. (6)

,

, EN1998-1 [55] Annex A.

,

, ,

EN1998-1 [55] .3.2.2.5. EN1998-6 [56] .3.3(2)


11/66

9

51,=q .

, EN1998-6 [56] .5.2

52,=q .

:

- D ;

- D ;

- D , .

D .

.

1.5.1.4.

1.5.1.4.1.

. .

.

. ,

. , ,

. , , ,

.

EN1991-5 [53]

:

- (.1.3);

- (.1.3).

(.1.3.b,d)

.

.1.3. N1991-5 [53]

.


12/66

10

,

..

1.5.1.4.2.

.

, . ,

- ,

(.1.4). TM

.1.4.

CICIND [41] .4

(.1.5):

- 0

t

IETM

IcmT

T

.=

(1.1)

- 1

ctI

T fWM = (1.2)

,

.

- 2

,

mI ,

t

ITEM

m

cmTT

=

(1.3)


13/66

11

Icm

IIcm

T

mcm

T

IE

M

IE

M

IE

M 150,= (1.4)

, ,

.

..

, ,

CICIND [41] .6.

, .

.1.5. CICIND [41]

1.5.2.

1.5.2.1.

,

,

.

,

, . ,

, ,

() .

,

.

1.5.2.2.

,

, .

, ,


14/66

12

.

, ,

20t

R .

, .

.

.

, -

. :

- ;

- ;

- ;- ;

Isada [66],

.

,

, :

- () Euler-Bernouli,

/;

- () Timoshenko,

, .

- ,

Timoshenko, ,

[43][78][83].

.

, -.

. -,

. , ,

, .

, .

(.1.6):

- ;

- ;


15/66

13

.

.

.

- - .

,

.

-

,

, .

.1.6.

, .

.

, [90]:- Raylegh-Ritz , -,

;

- , -Galerkin.

.

.

1.5.2.3. ,

1.5.2.3.1. -

.


16/66

14

,

.

.

:

- ,

;

-

.

,

.

.

-, -

, ,

.

.

.

1.5.2.3.2.

,

. ,

( 300).

,

-.

1.5.3.

1.5.3.1. .

:

- , ;

- ,

.

:

- ;

- .

:- ,

;


17/66

15

- .

1.5.3.2. .

,

,

. ,

. .

EN1992-1 .3.1.7 [54] (.1.7)

:

cdccc f225011000 = 20 cc (1.5)

cdc f= 22 cucc (1.6)

EN1992-1 .3.1.7 [54] (.1.8)

:

sss E = sys 0 (1.8)

yds f= ukssy (1.9)

.1.7.[54]

.1.8.[54]


18/66

16

CICIND .6.1.2, .6.2.6 [40] 2c sy

0,2%.

:

00302 ,=cu ; (1.11)

003502 ,=cu ; (1.12)

040,=uk ; (1.13)

010,=uk . (1.14)

1.5.3.3.

EN1990 .6.4.2

[51] :

dd RE (1.15)

:

dE ;

dR .

,

CICIND .8.2 [40].

2cu ,

100(.1.5.1.4.1). (1.11).

,

(.1.5.1.4.2).

1.5.3.4.

:

- ;

- .

kw EN13084-2 Annex B [50]

s

crseffs

cm

scrsk

Ef

d

w,,

,

,

,, ,

,

40

53

890

670

880

= (1.16)

. ,

.

1.6.

-

.

.

.


19/66

17

, .

,

.

,

.

.

.

.

. -

.

EN1992-1

.

, .

,

.

.

.

.

:

.

:

1.

;

2.

;3.

;

4.

;

5.

;

6.

.


20/66

18

2

2.1.

, -

,

,

.

, , :

1.

.

( ) ,

.

2. .

3.

(, ) t

, .

4. ,

,

,

.

-

. ,

, -

.

-

.

2.2.

,

. :

- ;

- ;

- ;

- .

.

.

, .


21/66

19

,

.

, ,

.

,

.

-

,

.

().

. -, ,

, ,

, .

.

.

,

.

. ,

.

, .

,

.

,

, ,

.

2.3.

2.3.1.

,

.

)(xEI )(xm ,

L . v

t, .. ),( txvv= .


22/66

20

),( txq .

,

(.2.1).

.

dAlambert (, ),

(.2.2).

)(xN )(xc , [43]:

),(),(

)(),(

)(),(

)(),(

)( txqt

txvxm

t

txvxc

x

txvxN

xx

txvxEI

x=

+

+

2

2

2

2

2

2

(2.1)

(2.1),

:

02

2

2

2

2

2

=

+

+

t

txvxm

t

txvxc

x

txvxN

xx

txvxEI

x

),()(

),()(

),()(

),()( (2.2)

.2.1. [43]

:

00 =),( tv (2.3)

00

=

x

tv ),( (2.4)

02

2

=

x

tHv ),( (2.5)

03

3

=

x

tHv ),( (2.6)

(2.4) :


23/66

21

2

2 00

0

x

tvEI

x

tvKf

=

),()(

),( (2.7)

fK .

,

fsf IkK = (2.8)

sk , fI

.

(2.4) (2.7) =fK .

(2.2) [43].

:

022

2

2

2

2

2

=

)()(

)()()()(

)()( xfxm

dx

xdf

dx

xdN

dx

xfdxN

dx

xfdxEI

dx

d (2.14)

(2.14)

(2.3)-(2.7),

0000 == )(),( ftv (2.15)

0

2

2

02

2

00

00

==

=

=

xx

ffdx

fdEI

dx

dfK

x

tvEI

x

tvK )(

),()(

),( (2.16)

002

2

2

2

=

=

=Lxdx

fd

x

tHv ),( (2.17)

003

3

3

3

=

=

=Lxdx

fd

x

tHv ),( (2.18)

)(tZ :

022

2

=++ )()(

)(

)()(tZ

dt

tdZ

xm

xc

dt

tZd (2.19)

(2.19) :

constxm

xc=

)(

)( (2.20)

)(xc )(xm ,

,

, , .

, - ,

. ,

- )(xc .

)(tZ ,

[21][38][43][77].


24/66

22

2.3.2.

.

D t

[ ] [ ]{ } )()()()()()()( xtxDxtxDxtxDxA =+= 224 (2.30)

[ ] [ ]{ }864

344 )()(

)()()()()(xtxD

xtxDxtxDxI

+= (2.31)

:

)()()()( xtxDxAxm == (2.32)

.

0D , 0t , 0A , 0I 0m , , ,

, 1D 1t

.

L

x= (2.44)

:

( )( ) = 110AA )( (2.45)

( ) ( ) = 11 30II )( (2.46)

( )( ) = 110mm )( (2.47)

( ) ( )( )

++= 11

2

11

3

1 230LgmN )( (2.48)

( )( )

= 110Lgm

d

dN )( (2.49)

00

10

DD

DDD == - (2.50)

00

10

t

t

t

tt =

= - (2.51)

(2.45)-(2.49) (2.14)

0202

2

02

2

2

2

=+

)()(

)()(

)()(

)()(

fq

d

dfqn

d

fdrn

d

fdp

d

d (2.55)

:

( ) ( ) = 11 3)(p (2.56)

( )( ) = 11)(q (2.57)


25/66

23

( ) ( )( ) ++= 112

11

3

1 23)(r (2.58)

0

30

0EI

Lgmn = - (2.59)

0

40

EI

Lm

=

(2.60)

00 =)(f (2.62)

0

2

2

0

0 ==

=

d

fdEI

d

dfKf (2.63)

01

2

2

=

=d

fd

(2.64)

0

1

3

3

=

=d

fd (2.65)

2.3.3. DTM

(2.55) .

. a

(2.14) [67][88][89][90][117].

(DTM) [144][78],

Taylor-Maclaurin.

,

.

DTM , Taylor-Maclaurin

.

, , .

, ,

-

.

2.3.3.1. DTM

DTM )(xf

=

=0

0k

kxxkFxf ))(()( (2.66)


26/66

24

0

1

xx

k

k

dx

xfd

kkF

=

=

)(

!)( (2.67)

)(kF

)(xf . )(xf

=

=N

k

kxxkFxf

0

0 ))(()( (2.68)

N,

+=

1

0

Nk

kxxkF ))(( (2.69)

.

(2.44) (2.68)

(2.61) 00=x

=

=N

k

kkFf

0

)()( (2.70)

0

1

=

=

k

k

d

fd

kkF

)(

!)( (2.71)

)(kP , )(kQ )(kR )(p , )(q )(r .

DTM, (2.55)

,

011

221

221221

3321112

44321

0

2

0

0

0

0

0

0

0

=++

++++

++++++++

++++++++

++++++

==

=

=

=

=

k

i

k

i

k

i

k

i

k

i

k

i

iFikQiFiikQn

iFiiikRn

iFiiikPikik

iFiiiikPik

iFiiiiikP

)()()())((

)())()((

)())()(())((

)())()()(()(

)())()()()((

(2.84)

)(kP , )(kQ )(kR (2.67).

.2.2.

)(kP , )(kQ )(kR

k

0 1 2 3 4 5..N

)(kP 1 3 ( ) +3 ( ) 32 + 3 0


27/66

25

)(kQ 1 0 0 0

)(kR 1 -12

+

3

0 0

2.3.3.2.

(2.62)-(2.65)

0000 == )()( Ff (2.94)

0221 0

0

2

2

0

0

=

=

==

)()( FkFd

fdEI

d

dfKf

(2.95)

010

21

2

2

==

==

N

k

kFkkd

fd)()(

(2.96)

021031

3

3

==

==

N

k

kFkkkd

fd )())((

(2.97)

fLK

EIk 00 = (2.98)

, .

00 =k .

2.3.4.

)(0F Taylor-Maclaurin (2.94).

(2.94)-(2.97) , )()..( NFF 1 .

)( 3N (2.84) )..( 40 = Nk .

)( 1N ,

2 .

. 2 ,

(2.60),

40

0

Lm

EIjj = (2.101)

, .

.


28/66

26

2.3.5.

j , (2.101),

)()..( NFF1 .

,

. constNF =)( .

)()..( 11 NFF )(NF -

. (2.68).

2.3.6.

,

, (FEM)

. :

- 1: mL 200= , mD 0140 ,= ,

mt 600 ,= , mD 060 ,= , mt 200 ,= ,

25/30;

- 2: mL 400= , mD 0250 ,= ,

mt 010 ,= , mD 090 ,= , mt 200 ,= ,

25/30.

1 2 .2.3.

.2.3. DTM FEM

DTM FEM

1 2.264 2.284 0.9%

2 8.571 8.612 0.5%

3 20.520 20.536 0.1%

4 38.256 38.127 -0.3%

5 61.851 61.384 -0.8%

1

6 91.326 89.214 -2.4%

1 1.145 1.157 1.0%

2 3.892 3.930 1.0%

3 8.930 9.006 0.8%

4 16.367 16.485 0.7%

5 26.244 26.395 0.6%

2

6 38.582 38.740 0.4%

,

. DTM,

,

, .

.

, DTM


29/66

27

.

.

DTM 3,

,

.

2.4.

2.4.1.

N Taylor-Maclaurin.

,

. -

. 0== .

.2.4.

N

15 20 25 30 35 40

3.516015 3.516015 3.516015 3.516015 3.516015 3.516015 3.516015

22.03449 21.99346 22.03424 22.03449 22.03449 22.03449 22.03449

61.69721 - - 61.80604 61.69679 61.69721 61.69721

. ,

.

20 .

-

30 Taylor-Maclaurin. ,

)( iF 4 )( 14 +iF )..(4

0 Ni= .

.

.

2.4.2..

. mN ,

.

.

EN1998-1 [55] .4.3.3.3.1(3)

0,90.

, j -

= 1

0

2

21

0

dfm

dfm

MM

j

j

j

)().(

)().(

(2.109)


30/66

28

, 3 4

.

0,90

6 7 . ,

.

EN1998-1 [55] .4.3.3.3.1(3) - 5% .

.

[88] , ,

3 -

.

2.4.3..

, ,

,

. II , P .

, ,

.

, , ,

.

(2.55)

0n , (2.59), (2.31)

2

00

30

0

8

==

D

L

E

Lg

EI

Lgmn

(2.110)

0D

L

.,

. -, -

-. -

,

.

,

.

,

.


31/66

29

. ,

250,

-.

25100

=D

L . -

0n - .

(2.110) 0n 0,202,00.

(2.101).

1 ,

, .2.6. 00 =n

, . -

.

.2.6. 1 0n

0n 0.0 0.5 1.0 1.5 2.0

0.0 3.516 3.402 3.285 3.163 3.036

0.4 4.097 4.014 3.930 3.844 3.7560.0

0.8 5.399 5.374 5.350 5.328 5.307

0.0 3.737 3.650 3.562 3.472 3.380

0.4 4.319 4.281 4.246 4.212 4.1810.4

0.8 5.627 5.693 5.767 5.850 5.942

0.0 4.314 4.384 4.469 4.573 4.697

0.4 4.907 5.131 5.391 5.689 6.0270.8

0.8 6.233 6.821 7.447 8.099 8.709

.

:

-

;

- ;

- ;

- -

.

2.4.4.

.

0k

(2.98),


32/66

30

fsf I

I

Lk

E

LK

EIk 000 == (2.111)

.

, .

,

.

-,

.

.

. -

. ,

. ,

, .

.

fI

I0 .

0,050,15.

--,

500 ,=k 020 ,=k

mL 150= .

,

-. .2.8. .2.9.

.

.2.8. 0k 00 =n

0k

0.0 0.5 1.0 1.5 2.0

1 4.319 2.729 2.149 1.829 1.619

2 20.049 15.314 14.580 14.287 14.129

3 51.337 42.745 41.926 41.620 41.462

4 98.004 85.561 84.713 84.412 84.264

5 160.209 143.919 143.042 142.773 142.544

0.4 0.4

6 232.834 216.310 215.723 215.312 215.333


33/66

31

.2.9. 0k 500 ,=n

0k

0.0 0.5 1.0 1.5 2.0

1 4.281 2.629 1.996 1.631 1.380

2 19.873 15.111 14.370 14.073 13.9133 51.113 42.503 41.679 41.373 41.213

4 97.760 85.299 84.447 84.149 83.998

5 159.936 143.621 142.788 142.448 142.271

0.4 0.4

6 232.683 216.230 215.354 215.157 215.089

:

- ( 500 ,=n )

;

- ;

- -

, 3

. ,

10% .

2.4.5. .

, ,

1 .

0n 0k 01 = ,

. .

0= .

.2.10. 0k ,

0n 0.0 0.5 1.0 1.5 2.0

0.0 3.80 1.79 1.13 0.79

0.4 5.30 2.57 1.66 1.210.0

0.8 8.55 4.27 2.84 2.13

0.0 5.29 2.56 1.65 1.20

0.4 7.28 3.62 2.41 1.800.4

0.8 11.34 5.80 3.96 3.05

0.0 8.83 4.55 3.14 2.45

0.4 11.76 6.23 4.40 3.500.8

0.8 17.08 9.15 6.49 5.15


34/66

32

,

010 ,


35/66

33

, 500 ,n . -

.

,

0k . ,

300%.

, .

10 n .

15% .

7%.

,

1n .

, 10


36/66

34

.

, .

(3.1)

[ ] [ ] ),(),(,),(

),(,),( txtxxEIx

txvtxxEItxM =

=

2

2

(3.3)

[ ]),(, txxI . (2.1)

[ ] ),(),(

)(),(

)(),(

)(),(

),(, txqt

txvxm

t

txvxc

x

txvxN

xx

txvtxxEI

x=

+

+

2

2

2

2

2

2

(3.4)

(3.4) .

2

2

x

txvtx

=

),(),(

, , [ ]),(, txxI ),( txq

),( tx . , (3.4) .

. ,

, 2.

--:

1. [ ]),(, txxI

[ ] )()(),(, xIxtxxI red =

(3.5) )(x ,

, )(xIred

,

)()()( xIxxIred = (3.6)

)(x )(xI

(2.31) )(xIred .

2.

.

.

3. , x , t,

. )(xred .

4. )(xred

. (3.4)

.

-,

(3.4)


37/66

35

( )

),(),(

)(),(

)(),(

)(

),()()(

txqt

txvxm

t

txvxc

x

txvxN

x

x

txvxIxxE

xred

=

+

+

2

2

2

2

2

2

(3.7)

),( txv , )(xred )(x .

(2.1). ,

)(xI , (2.1), (3.7)

)()()( xIxxred .

(3.7) , 2.

(2.14)

022

2

2

2

2

2

=

)()(

)()()()(

)()()()( xfxm

dx

xdf

dx

xdN

dx

xfdxN

dx

xfdxIxxE

dx

dred (3.9)

(3.9) (2.55)

0202

2

02

2

2

2

=+

)()(

)()(

)()(

)()(

fq

d

dfqn

d

fdrn

d

fdp

d

d (3.10)

:

)()()()( pp red= (3.11)

(3.10) DTM

)(xred

)(x .

3.2.

:

- ,

;

-

.

, -

.

.

.

EN1992-1 [55] .7.4.3

effM

( ) crueff += 1 (3.12)

cr u

, eff () .

eff


38/66

36

2

1

=

eff

cr

M

M (3.13)

effcm

effeff

E

MI

= (3.14)

[22][23][28][97][99][102].

. Branson [28],

u

eff

crcr

eff

creff I

M

MI

M

MI

+

=

33

1 (3.15)

Bischoff [22], EN1992-1-1 Error! Reference source not

found.,

ueff

cr

creff

cr

eff IM

M

IM

M

I

11

11

22

+

= (3.16)

[24][60], Branson

, Bischoff

, .

.3.2. -

.

, -

.3.2.

, .

.3.1 )(xred )(x .


39/66

37

.

3.3.

.

.

,

.

, .

3.3.1..

3.3.1.1. .

, . , , ,

, .

-,

.

:

- Bernoulli ;

- ;

-

;

- ;

- ,

;

- EN1992-1-1 3.1.7. [54]

(.1.5.3.2) ;

- ;

- .3.3.1.2.

3.3.1.2. .

ctmf EN13084-2 .5 [50]

:

32 /.... cmvcctm fccccf = (3.17)

:

012200

6040 ,,, += cc - ; (3.18)

450,=c - ; (3.19)


40/66

38

tcv 20850 ,, = - ; (3.20)

.,

..,

601

660

+

+= t

cc - ; (3.21)

t

tct

4001

2462

+

+=

,

,- ; (3.22)

8+= ckcm ff - ; (3.23)

Nt

M= - . (3.24)

t.

(3.21) ,

c tc .

, 1 . ,

, tc

c

001950 ., . , tcc = .

:

( ) 324001

246220850450

/

,

,,,, cmctm f

t

ttf

+

+= (3.25)

, EN13084-2 Error! Reference source not found., -

EN1992-1-1 [54] mt 400, ..

ctmE ,

, Cho [37],

ckctm fE 3000= (3.26)

3.3.1.3.

,

.3.5.


41/66

39

.3.5.

-:

:

2

12 +=m (3.27)

R2

12

= (3.28)

:

ck

ykxsx

f

f = (3.29)

cosRm = (3.32)

:

( ) ( ) RRm coscoscos == (3.33)

:

- 0

( ) ( ) ( ) ( ) ckctmctmc fRREE coscoscoscos === 3000 (3.34)

-

( ) ( ) ( )[ ] ckc RfR coscoscoscos = 25011000 (3.35)

:

( ) ( ) ( ) ( ) yky

ykss RfR

fE

coscoscoscos === 500 (3.36)

:

( ) ( )

( )( )[ ]

+++

++=

coscossincos

sincossincos

1000

sx

ckck

R

ftfRN

312250

226

2

2 (3.43)


42/66

40

( ) ( )

( )[ ]

+++

++

=

sx

ckck

R

ftfRM

2

3

233

1000

226

cossinsincos

sincossin

500 (3.44)

:

ck

pRtf

Nn

2= (3.45)

ck

ptfR

Mm

22= (3.46)

pn pm

,

( ) ( )

( )( )[ ]

+++

++

=

coscossincos

sincossincos

5

sx

ckp

R

fRn

312250

226

00

2

(3.47)

( ) ( )

( )[ ]

+++

++

=

sx

ckp

R

fRm

223

3

1000

226

5

cossinsincos

sincossin

02 (3.48)

(3.47) (3.48)

R .

crM

ck

ctm

ctm

ctmct

f

f

E

f

30001 === (3.49)

Rcr crpm ,

(3.47) (3.48)

.

, .3.6.

:

0,)()( pp KRRK = (3.50)

0,pK ,

( )RKK pR

p 0

0

= lim, (3.51)

-

RKRRRKm ppp 0,)()( == (3.52)


43/66

41

.3.6. -

,

,

. 1=)( R .

cr

crcr

E

MI

= (3.53)

(3.46) (3.52) (3.53)

II

E

fKI

E

f

R

mI ckp

ck

cr

crpcr 0022

=== ,,

(3.54)

I, (2.31).

0

:

E

fK ckp 00 2 ,= (3.55)

Rcr , crpm , 0,pK 25/30 ,

, .

3.3.1.4. .

uI

(.3.7).


44/66

42

.3.7.

.3.7 :

( ) 21

ysy

R

R=

+

cos

coscos (3.56)

( ) 21

ycy

R

R=

++cos

coscos (3.57)

:

RR

R

R

yyymsy

+=

+=

+= cos

coscos (3.58)

cos

coscos =

=

=

RR

R

R

yymycy (3.59)

:

- cy

( ) ( ) ( )[ ] ckc RfR coscoscoscos = 25011000 (3.1)

- cy

( ) ckc f= (3.2)

:

- sy0

( ) yks f= (3.3)- cysy

( ) ( ) ( ) ( ) yky

ykss RfR

fE

coscoscoscos === 500 (3.4)

- cy

( ) yks f= (3.5)

(3.45) (3.46) :


45/66

43

( )( )

( ) ( )[ ]

+++

+

++

++

=

cysysycysxsycysx

cycycy

cy

cycycy

p

R

R

R

n

sinsincos

sincoscossin

cossincos

sinsincos

500

4

321125000

1000

12

22 (3.71)

( ) ( )( )

( )( )

( )

+

+

+++

+

+

+

++

++

=

cycysysy

cysysycy

sx

sycysx

cycycy

cy

cycy

cycycy

cy

cy

p

R

R

R

m

cossincossin

sinsincos

sinsin

coscoscossin

sinsincos

sinsincos

cossinsincos

cossinsin

2

250

3

3

23

3

250000

2500

1222

(3.72)

Ru upm ,

2cu y .

,

- .

.

:

u

uu

E

MI

= (3.73)

(3.54)

IIE

fKI u

ckupu == ,2 (3.74)

R

mK

u

upup

,, = (3.75)

E

fK ckupu ,2= (3.76)

Ru , upm , upK , ,

.

25/30

, Ru .3.1 .3.8.

.3.1. Ru

pn

sv 0.0 0.1 0.2 0.3 0.4 0.5


46/66

44

0.10 0.00115 0.00135 0.00154 0.00176 0.00205 0.00246

0.20 0.00123 0.00140 0.00159 0.00179 0.00204 0.00245

0.30 0.00129 0.00145 0.00162 0.00181 0.00204 0.00239

0.40 0.00134 0.00149 0.00165 0.00183 0.00203 0.00234

0.50 0.00139 0.00153 0.00168 0.00184 0.00203 0.00230

0.60 0.00143 0.00156 0.00170 0.00185 0.00203 0.00227

0.70 0.00146 0.00159 0.00172 0.00186 0.00202 0.00225

0.80 0.00150 0.00161 0.00174 0.00187 0.00202 0.002230.90 0.00152 0.00164 0.00176 0.00188 0.00202 0.00221

1.00 0.00155 0.00166 0.00177 0.00189 0.00202 0.00219

0.0010

0.0015

0.0020

0.0025

0 0.1 0.2 0.3 0.4 0.5

np

uR

0.10

0.20

0.30

0.40

0.500.60

0.70

0.80

0.90

1.00

.3.8. Ru

.3.8 , Ru

.

380,=pn . ,

. 380,>pn ,

.

3.3.2..

.

crI .

,

.

. ,

, .

sv


47/66

45

.

(3.14)

(3.16). , u ,

uI ,

effM .

(3.14) ,

.

.

, effM

eff u .

( )

=

=

u

cr

u

cruu

cr

eff

M

M

13

3 (3.77)

-

.

(3.16)

, (3.14).

, (3.16), :

( )crueff III

11

11 += (3.78)

=

2

1

eff

cru

M

M (3.79)

22

2

cru

uu

MM

M

= (3.80)

:

cr

uu

I

I= - (3.81)

cr

effeff

I

I= - (3.82)

cr

effeff

= - (3.83)


48/66

46

cr

uu

= - (3.84)

uu

cr

uu

M

M == - (3.85)

effeffcr

eff

eff M

M

== - (3.86)

(3.80)

12

2

=

u

uu

(3.87)

(3.78)

111

+=

ueff

(3.88)

2

21

eff

effu

= (3.89)

eff

creff

effeff

EI

M

= (3.90)

crI uI

(3.54) (3.74).

.3.12.

- -

.3.14.

.3.12.

1

u

1 u


49/66

47

.3.14.-

3.4.

, eff

,

eff ,

eff . EN1998-6 .5.2 (1) [56]

52,=q 5101 ,, =q .

eff

e

M

Mq= (3.91)

eM ,

(.3.15)

effcre EIM = (3.92)

.3.15.-

(3.14) (3.92) (3.91)

effeff

cr

effeff

effcr

I

I

EI

EIq

1=== (3.93)

1

u

1 u


50/66

48

queff

1=, (3.94)

ueff, (3.88).

( )

( ) ( )( )

( ) ( ) uuuuu

uueffuueffu

uueffuueff

q

11

1

11

1

=

=

,,

,, (3.95)

ueff, (3.86)

ueffueff q ,, = (3.96)

3.5.

.

, .

.

,

.

. ,

,

.

, , ..

2

ueffcrred

III

,+= (3.97)

(3.82) (3.94)

red

q

q

I

I ueff

cr

redred

2

1

2

1 +=

+==

, (3.98)

( )( ) ( )

( )( )( )( ) ( ) uuu

uu

ureduredu

uredured

qq

q

111

11

11

1

+

+=

= (3.99)

red

,

)(xred .

)(xsx

. ,

.


51/66

49

3.6.

(SRSS), ,

.

, -2sec, 2 [3]

,

. , , -

,

. , , .

EN1998-1 [55]

, -. , -

, (3.46)

(.3.16). ,

, -.

, .

,

.

0

1

mef f

.3.16.

(3.10)

, .

,

crredm


52/66

50

, .

,

.

(3.10) :

1. 0n 0k

(2.59) (2.98);2. (.2.9).

fI ;

3. (3.10) 1=red

;

4. )(xsx

;

5. crpm ,

pn

(3.47) (3.48).

(3.71) (3.72)

upm , ;

6.

0,pK upK , (3.54) (3.75), u u

(3.87) (3.81);

7. red

0

)(xred )(x . ,

1=red ;

8. (3.10)

)(xred )(x ;

9. 4

.

3.7.

:

-

,

;

- )(xred

)(x ;

- .

:


53/66

51

- ,

,

;

-

,

;

(3.7)

.

, .

4

4.1.

,

.

.

, .

,

.1.5.1.4.2,

, .

,

. -

, . -

.

.

.

4.2. .

4.2.1. .

CICIND [40] (8.10)


54/66

52

)()(

,)( xDC

xwkxM

D

mtWh 090= (4.1)

EN 1991-1-4 [52] (2.160)

)()(

,)( xDC

xqxM

D

pWh 090= (4.2)

:

pq EN1991-1-4 . 4.5[52].

DC CICIND [40] (7.5).

, 70,=DC .

)()(,)( xDxqxM pWh 1290= (4.4)

4.2.2..

:

- ,

;

- , ,

.

,

, 1

ckpD

DD

g

fxnxRixt

xNi

xtxR

xRxNixRxQxN )()(

)(

)(

)()(

)()()().()( ====

222 (4.5)

)(xnp (2.154).

1, ,

ckpe fxnxtxR

xNxN )(

)()(

)()(

==

22 (4.1)

Poisson . EN1992-1-1 [54] .3.1.3(4)

, 200,= .

,

.

. ,

.

(4.5) (4.6) , 200,RL

D .

%1=L

D %2=

L

D mR 20=

mR 10= . mR 10>


55/66

53

( mH 300> ) - .

mR 10> ,

, .

.

4.3.

4.3.1.

.

cr

1 crM

.

. ,

.

,

.

.

.

, ,

, .

u

1 , uI uM .

:

- ;

- ;

- ;

- ;

- ;

- .1.5.3.2 ;

-

;

- ctmf EN13084-2 [50] .5 (. 3.3.1.2);

- .3.3.1.2.

4.3.2..

crM

ct ,

(.4.2), ..


56/66

54

ck

ctm

ctm

ctmct

f

f

E

f

30001 === (4.7)

.4.2.

, ..

2

tAA vss

== ' (4.9)

ck

yksvsvf

f = (4.10)

t

xx = (4.11)

( )xt = 11 (4.14)

:

( ) ( )zxtzz == 11 (4.15)

t

zz= (4.16)

:

-

( )axs taa === 11)( (4.17)

t

aa = (4.18)

-

( )axsc tatat ')'()'( === 1 (4.19)

t

aa

'' = (4.20)

:

- ( xtz 0 )

( ) ( ) ckzxctmc ftzEz == 13000)( (4.21)

- ( tzt )


57/66

55

( ) [ ]( ) ( )[ ] ckzxzx

ckc

tft

fzzz

=

==

1250111000

25011000 )()( (4.22)

:

( ) ykaxsyksss ftfE === 1500500 (4.23)

:

( ) ykaxscykscssc ftfE ' === 500500 (4.24)

:

( ) ( )

+++

= t

fftN xsvaaxx

ck

xck

322

22

3

1000212

16250 ' (4.35)

( ) ( ) ( )

( )( ) ( )( )[ ]

++

+

+

+

=

svaaxaax

xxxx

ck

xx

ck

tfftM

'' 21211

23

500

3

212

2112

125

322

3 (4.36)

(.3.3.1.3)

ck

pvtf

Nn 2= (4.37)

ck

pv

ft

Mm

2= (4.38)

(4.35) (4.36) (4.37) (4.38)

( ) ( )

++

+

= svaaxxx

ck

xpv t

ftn

'21

3

50012

16250

22

(4.39)

( ) ( ) ( )

( )( ) ( )( )[ ]

++

+

+

+

=

svaaxaax

xxxx

ck

xx

pv

tftm

'' 21211

23

500

3

212

2112

125

322

(4.40)

'aa= (4.39) (4.40)

( ) ( )

+

+

= svxxx

ck

xpv t

ftn

21

3

50012

16250

22

(4.41)

( ) ( ) ( )

( )

+

+

+

+

=

sva

xxxx

ck

xx

pv

t

ftm

2

322

21

23

500

3

212

2112

125 (4.42)

.4.2.2, crpvm ,

0=crpvn , (4.7).


58/66

56

ct (4.7)

-.4.1.

.4.1.

t[m]

0.2 0.4 0.6 0.8 1.0 1.2 1.4

25/30 2.056E-04 1.706E-04 1.532E-04 1.407E-04 1.302E-04 1.206E-04 1.117E-04

30/37 2.062E-04 1.710E-04 1.537E-04 1.411E-04 1.305E-04 1.210E-04 1.121E-04

35/45 2.073E-04 1.720E-04 1.545E-04 1.418E-04 1.312E-04 1.216E-04 1.127E-04

crx,

.

crI

(3.53), (4.38)

I

E

f

t

m

E

ft

t

mI

cm

ck

cr

crpv

cm

ck

cr

crpvcr

,,12

3

== (4.2)

12

3tI= . (4.3)

,

-

, -

. .

4.3.3..

effI

(3.14).

uI

.

pvm

, .. 02 =N .

'aa= (4.41) (4.42)

( )

+

+= svxxxpv ttn 21

3

50012250

2 (4.45)

( ) ( )

++

= svaxxxxpv ttm

232212

3

500

3

212125 (4.46)

upvm , ,

, CICIND [41] .6

.

0020,== ys (4.47)


59/66

57

(4.17)

axax

sut

=

=

1

0020

1

, (4.48)

(4.48) (4.45) , 0=pvn ,

ux,

:

( ) ( ) 012

1

2

31

3

2 23 =+

svaxsvaxsvax (4.49)

ux, ,

, .

64600850

,,

, = svux (4.4)

2 3 -

, 10 -

.

uI (4.43)

IE

f

t

mI

cm

ck

u

uuvu

,12= (4.51)

, 80%.

20% 50%.

4.3.4. .

, ,

( ) ( )zTz tt = (4.52)

, .

, ,

t

T

t

ttT

==

(4.53)

,

TeffcmT IEM = (4.54)


60/66

58

creff II = (4.43). , ,

, (4.53) cr :

t

crcr

tT

= (4.55)

maa 0450,'==

25/30 .4.9.

(4.39) (4.40)

. uT ,

.

.4.1.

t[m]

sv 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.20 7.35 12.21 16.46 20.16 23.32 25.94 28.04

0.40 7.43 12.34 16.63 20.37 23.57 26.22 28.33

0.60 7.50 12.45 16.78 20.55 23.77 26.45 28.58

0.80 7.55 12.54 16.90 20.70 23.95 26.64 28.79

1.00 7.60 12.62 17.01 20.83 24.09 26.81 28.97

crTu >>

.

(3.88), Teff = .

.3.3.2 :

( ) ( ) 01222 =+ ueffeffueffeffuu (4.56)

( )( )

( ) effuu

uuueffueffu

eff

+

+++=

2

1422

(4.57)

-

- .4.12 .4.13.


61/66

59

.4.12.-

.4.13.-

4.4. .

.

(.4.2.2) , (4.4).

(4.39) (4.40)

02 =N . (4.42).

, -,

(3.88),

effcmeff

IE

M= (4.58)

.

,

.

.3.3.2 (.3.10

.3.11) . .

:

cr u

crM

uM

1

u

1 u


62/66

60

-

;

- ,

.

- , T

T (4.53) - -

.

wT .

wu TTT =max (4.5)

.

4.5.

-

, .4.13.

25/30

.4.15 .4.21.

4.6.

.

, 15 -

. ,

8,0312,40

-.

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6 7 8 9 10 11 12 13

0.2

0.4

0.6

0.8

1.0

.4.1. mt 200,=

sv


63/66

61

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.2

0.4

0.6

0.8

1.0

.4.2. mt 001,=

, ,

2,705,30-.

mt 401200 ,, = .

,

.

sv


64/66

62

, :

- -

;-

,

.

.

.

-

.

.

:

-

10


65/66

63

1.

.

2.

EN1991-1-4.3. .

4. .

5.

.

1.

;

2. ,

;

3.

,

;4.

;

5.

.

6.

;

7.

.

1. , . ,

,

, , 2008

2. , .

, ,

, 2010


66/66

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