E

V

( )

.

2003

i

7. A.....................................................................................1

7.1 . .............................................. 1 7.2 ................................................................................... 4

7.2.1 ......................................................... 4 7.2.2 . ................................................ 8

7.3 .................. 8 7.3.1 .. ........... 9

8. (PUSH-OVER ANALYSIS) ................................................................................................... 18

8.1 ............................................... 18 8.1.1 . ..................................................................... 18 8.1.2 ........................................................... 21 8.1.3 - .......................................................... 21

8.2 .. ......................................................... 23 8.2.1 .. ............................... 24

8.2.2 - . ........................................................................... 25

ii

9. ............................................ 35 9.1 .............. 36

9.1.1 - ................................ 37 9.1.2 ........................... 40 9.1.3 ............................................ 44

9.2 ............. 53 9.2.1 ............... 53 9.2.2 ................... 56 9.2.3 .. ................ 61

1

7

7.1

(mode superposition method), (direct integration method). / . , , . . 1. . , , ( 2000), , . , , .

1 N. Lagaros, Y. Tsompanakis, M. Papadrakakis, Optimum design of structures with inelastic behavior under seismic loading, V. European Conference on Structural Dynamics, Munich, 2002.

2

- , . : ( q=1). H Pd

d eP P / q= , eP q . , , . q . . q , , , . , , . q

d 0

e e u

y u y

P P Pq q qP P P

= = = (7.1)

d 0

e e u u

u u y y

P U P Uq , qP U P U

= = = = (7.2 ,) yP uP , yU , eU uU yP , eP uP , .

3

7.1 - -

. () , () 1T 0.6> s u eU U (. 7.1), : 0q q= (7.3)

1(0.1s T 0.6 s)< < (. 7.1). (. 7.1) :

uu es

UU U ,U2 1

= = (7.4 ,)

0 d 0

q q 2 1 q q= < (7.5) sU uP .

4

() , q. 7.2

: (i) () , (ii) , . , . , .

7.2.1 () , .

[M]{U(t)} [C]{U(t)} [K]{U(t)} {P(t)}+ + = (7.6)

[M]{X(t)} [C]{X(t)} [K]{X(t)} {P(t)}+ + = (7.7)

5

{U(t)} [ ]{X(t)}= (7.8)

T T[M] [ ] [M][ ], [C] [ ] [C][ ]= = (7.9 ,)

{ }T T[K] [ ] [K][ ], {P(t)} [ ] P(t)= = (7.10,) [], [C], [K] (N) , , , , {P(t)} . [] :

2i i i[K]{ } [ ]{ } , i 1, N = = (7.11)

}]}...{}{[{][ N21 = (7.13)

21

22 2

2N

[ ]

=

%

(7.15) [ ]Tj i{ } M { } 0 , =

[ ]Tj i{ } K { } 0 = j i , , (7.9) (7.10) :

1122

N N

kmkm

m k

[K][M]

== %% ,

(7.12,)

[ ]T 2j j j j j jm { } M { } , k m= = (7.15,) (7.7)

6

2 Tj j j jj

{P(t)}x (t) x (t) { } , j 1, Nm

+ = = (7.16) { } [ ]T 1 2 NX(t) x (t) x (t) ... x (t)= (7.17) , Duhamel. {U(t)} [ ]{X(t)}= (7.18) () , (7.16), }U{ max,i . . (Square Root of the Sum of the Squares-SRSS):

12 2 2 2max 1,max 2,max N,max{U } [{U } {U } ... {U } ]= + + + (7.19)

. () : 1: m N

7

Tj j jm { } [M]{ } , j 1, m= = A (7.22) 3: jL Tj jL { } [M]{r}= (7.23) {r} . 4:

j

jj m

L= (7.24) 5:

j

2jeff

j m

Lm = (7.25)

6: m N<

8

7.2 7: S )T(a j

j jT (. 7.2).

8:

j

jj,max j j2j

Sa(T ){U } { }= (7.27)

9:

SRSS 2 2 1/ 2max i,max 2,max ,max{U } [{U } {U } {U } ]= + + + A (7.28) }U{ max .

7.2.2 () ( )1=A 1 totm m= . . .

9

7.3 , . . 2. . () (static push-over) . () (incremental dynamic analysis) . . . , /. . , , . - (, , , ). , ,

2 M. Papadrakakis, N. Lagaros, V. Plevris, Optimum design of space frames under seismic loading, International Journal of Structural Stability and Dynamics, 2001

10

. , , (displacement-based seismic design method) (capacity spectrum method) . ATC-40 FEMA 273. . 7.2.1 , - P-U, , . P-U Sa-Sd.

7.3 () , () ( P-U) : 1:

().

11

, , 5 8 . P-U (capacity curve) , P=Vb U (. 7.3). , , . 2: () -

. ( n ndf (number of degrees of freedom) ) (capacity spectrum) . , . . . 2.1 { }1 ,

1 1 .

2.2 m -

1 totm = a m (7.29)

totm 1 . Freeman (1998)

12

( ) ( )2 21 i 1i i i 1ii i = (m ) m (m ) , i = 1, n (7.30)

i 1im , i , . 2.3

2

Sa = P/mSd = U/a

(7.31, 7.32)

2a .

22 i 1i i 1ii ia = (m ) (m ) (7.33) 2.4 (Sa,Sd ) 2.5

y y k = m Sa Sd

T = 2 m k (7.34, 7.35)

y y y y 2Sa = m , Sd = U a (. 7.4,).

7.4 ()

()

13

3: . (Acceleration Displacement Response Spectrum-ADRS), (demand spectrum), , . . Priestley (1995) eff el u = + c (7.36) el ( el = 5% ), u u = 2( -1) () (7.37) u y = U U . uU yU (. 7.4). c (7.36) . c 0.60 , c 0.40 . (7.37) . , , ( )eff = 7 2 + 0.7 (7.38)

14

7.5 ()

() 4:

ADRS. (7.38) , ADRS, . (. 7.5). Sa, Sd :

elSa = Sa (7.39)

elSd = Sd (7.40)

ADRS (Sa,Sd) (Sa,T)

2

2

TSd = Sa4

(7.41)

15

7.6 E ADRS Sa,Sd (. 7.5). 5: . : (. 7.6). 5.1 1T

eff el = :

( )eff el i 1 el= Sd T , (7.42)

5.2 , eqT , eff

i y = Sd Sd (7.43)

eq 1T = (7.44) ( )u eff el u = 2 -1 = + c (7.45 ,)

16

( )eff = 7 2 + (7.46) 5.3 iSd ( eqT , eff ).

iSd ADRS ( )eff . eqT eqT .

5.4 (performance point).

5.3 eqT ADRS ( )eff . d dE(Sa ,Sd ) . . E , , .

- eff . eqT , . , , (. 7.7):

17

7.7 E 1. eff

(7.45) (7.46) u u 2Sd U /= ( ) .

2. ADRS( eff,u ) (7.39), (7.40), .

3. ADRS( eff,u ).

4. , ( 7.43) eff (7.45) , ADRS . . ,

dSd . dSd dSa ,

18

d 2 dU Sd= (7.47) b 1 tot dV m Sa= (7.48) 1, 2 (7.30) (7.33).

19

8 (PUSH-OVER ANALYSIS)

. () (static push-over analysis) . () (incremental dynamic analysis) . .

8.1 H () , : (i) , (ii) , (iii) , (iv) - .

8.2.1 o . . ,

[ ]{ } [ ]{ }1 1 1K = M (8.1)

1 minT = 2/ (8.2)

1min = (8.3)

20

( )1 min},{ { }1 min . . . , .

8.1

b 1 kk

V = Sa w /g (8.4) kw k ( )n1k = , n 1 1Sa = Sa(T ) (. 7.2). . k

21

k

k k 1bk

k 1k

wQ = V , k = 1,nw (8.5)

{ } 1 2 k n1 1 1 1 1 = (8.6) k=1,2,,n (. 8.1).

8.2 () , () (. 8.2) nk

k1 h/h= (8.7)

kh k . Qk

k k k bk k

k

w hQ = Vw h (8.8)

22

kw 8.2. (8.8) (8.5) , , -- . , .

8.2.1

. .

8.2.1 -

, , . . . ( 90%) (. 7.2.1). , , .

23

. - A : 1: mA

[ ]{ } [ ]{ }K = (8.9)

1 2 mT , T ,..., TA (8.10)

{ } { } { }1 2 m , ,..., A (8.10) 2:

Tj j jm { } [M]{ } , j 1,= = Am (8.11)

Tj jL { } [M]{r}= (8.12)

j

2jeff

j m

Lm = (8.13)

3: A

effj totj 1

m m=

A (8.14) 4: Sa(j), j 1,= A

k b, j j k

kV = Sa w /g , j 1,= A , k =1,n (8.15)

24

k

k jkj b, jk

k jk

wQ V

w= (8.16)

( ) 1/ 22k kjQ Q = j (8.17) 8.1.2 A m

( ) 1/22k km j,mj

Q = Q , j = 1, A k =1,n (8.18)

Qkm 1 4 m . 8.2 , . . .

8.3

25

8.2.1 , (. 5 ) , . (. 8.3): 1 1:

[ ]{ } [ ]{ }0 1 1 1 1,1 1,1K = , { } (8.19)

. 1: Y

b,1 1,1 k

kV = Sa w /g (8.20)

k

k 1,1k1 b,1k

i 1,1k

wQ V , k = 1, n

= w (8.21) { }T 1 2 n1 1 1 1Q Q Q Q = (8.22) 1:

{ } { }11 Qq = R (8.23)

R .

1: 1 [ ] { } { } i, j i, j0 1 1 1 1 1K U q = min ,= (8.24)

j i .

{ } { }1 1 1P q= (8.25)

26

2, 3, , m -1 m 1: [ ]{ } [ ]{ }m-1 m m m 1,m 1, mK = M T , { } (8.26) 1:

b,m 1,m k

kV = Sa w /g (8.27)

k

k 1,mkm b, mk

i 1,mk

wQ V , k = 1, n

w= (8.28)

{ }T 1 2 nm m m mQ Q , Q , ,Q = (8.29)

{ } { }mm Qq R= (8.30) 1:

m

[ ] { } { } ( ) ( )

{ } { } { }i, j i, j i, j i, j i, j

m m m m p 3 m 3m 1 mi, j

m m m m 1 m m

U q M M M

min P P Q

= = + = = +K

(8.31) 1m m= + m . 8.2.2 - . - .

27

. - -. 9.

8.4 -

8.5

m

28

. - (. 8.4 8.5): 1: 1:

[ ]{ } [ ]{ }

{ }0 1 1 1 1,1 1,1

b,1 1

K , { }

V Q

= (8.32)

1:

{ }11 Q{q } R= (8.33) 2: - 2: }q{ 1

1

{ } { } { }

{ } { } { }(0) (1) (1)0 1 1 1

(1) (1) (1)1 1 1

K U q U

U U F

=

(8.34)

{ }(1)1F 1 (. 8.5 m ). ......

A

{ } { } { } { }

{ } { } { }( 1) ( ) ( 1) ( )0 1 1 1 1

( ) ( ) ( )1 1 1

K U q F U

U U F

=

A A A A

A A A (8.35)

......

29

j : { }(j)1 1 1 1{q } F {q } (8.36) 1 ( )2 61 10 ~ 10 =

2: { }1 1 1 1m{q } (m ) q

1 { } { } { } { }

{ } { } { }(0) (1) (0) (1)m-1 m 1 m m

(1) (1) (1)m m m

K U = q - F U

U U F

(8.37)

......

A

{ } { } { } { }

{ } { } { }(0) ( ) ( -1) ( )m-1 m 1 m m

( ) ( ) ( )m m m

K U q F U

U U F

=

A A A

A A A (8.38)

......

j: { }

{ }(j)

1 m1

1

m{q }- F

m q (8.39)

.

8.6 . () 1, () m

30

8.7 , - (. 8.6), (. 8.7, 8.8 8.9):

8.8

i

31

1: 1:

0 1 1 1 1,1 1,1b,1 1

[K ]{ } [M]{ } T { }V {Q } =

(8.40) 1:

{ } { }11 Qq R= (8.41) 2: -

}q{ 1

1:

{ } { } { }

{ } { } { }(0) (1) (1)0 1 1 1

(1) (1) (1)1 1 1

K U = q U

U U F

(8.42)

......

A :

{ } { } { } { }

{ } { } { }( 1) ( ) ( 1) ( )0 1 1 1 1

( ) ( ) ( )1 1 1

K U q F U

U U F

=

A A A A

A A A (8.43)

......

j: ( j)

1 11

1

{q } {F }{q } (8.44)

32

8.9

m+1 3: 1 1i{q } (i 1){q } (.

8.9)

1:

{ } { } { } { }

{ } { } { }(0) (1) (0) (1)i-1 i 1 i i

(1) (1) (1)i i i

K U = i q - F U

U U F

(8.45)

...... A :

{ } { } { } { }

{ } { } { }( 1) ( ) ( 1) ( )i 1 1 1 1 i

( ) ( ) ( )i i

K U q F U

U U F

=

A A A A

A A Ai

i (8.46)

...... j : { }(j)1 1 1 1i{q } F {iq } (8.47)

33

4: (. 8.7 8.9)

: T

1 11 T

1 1

{q } {U }k ={U } {U }

(8.48)

: T

1 ii T

i i

{q } { U }k{ U } { U }

= (8.49)

K : i 21

k < k

(8.50)

2 ( )2 0.5 ~ 0.1 = . E 5 i m= . 3 1ii += .

5: 1:

(. 8.9)

[ ]{ } [ ]{ }{ }

{ }

m m+1 m+1 m+1

1,m+1 1,m 1

b,m+1 m+1

K M

T ,

V Q+

=

(8.51)

1:

m+12{Q }{q }

R= (8.52)

6: -

}q{ 2 (. 8.9)

1: { } { } { }

{ } { } { }(0) (1) (1)m m+1 2 m+1

(1) (1) (1)m+1 m+1 m+1

K U = q U

U U F

(8.53)

......

34

A :

{ } { } { } { }( 1) ( ) ( -1) ( )m m+1 1 2 m+1 m+1K U mq + q F U = A A A A { } { } { }( ) ( ) ( )m+1 m+1 m+1U U F A A A (8.54) ......

j: ( j)

1 2 m 11

1 2

{mq q } {F }

{mq q }++ + (8.55)

7: ( ) ( )}q){1i(}q{m}q{i}q{m 2121 ++ (. 8.7)

1:

{ } { }(0) (1) (0)m+i-1 m+i 1 2 m+1K U = m{q }+ i{q }- F (8.56) { } { } { } { }(1) (1) (1) (1)m+i m+1 m+i m+iU U U F ......

A :

{ } { }( -1) ( ) ( -1)m+i-1 m+i 1 2 m+1K U = m{q }+ i{q }- F A A A (8.57) { } { } { } { }( ) ( ) ( ) ( )m+i m+i m+i m+iU U U F A A A A ...... j:

{ }{ }

(j)1 2 m+i

11 2

mq + iq -{F }

mq + iq (8.58)

35

8: .

m+1:

T

2 mm T

m m

{q } {U }k ={U } {U }

(8.59)

:

T

2 m+im+i T

m+i m+i

{q } {U }k ={U } {U }

(8.60)

: 2m

imk

k + (8.61)

5 m=n. 7 i=i+1.

- . P-U (8.38) (8.56) / : (i) ( ), (ii) , (iii) (8.38) (8.56). . - - - (8.17) (816) j=1. , - - (8.18).

36

37

9.

H : (i) (concentrated plasticity), (. 5, ). (plastic node). (ii) (distributed plasticity) . P-U. . - , , , . , . , , . , . .

9.1

38

9.1 , 9.1. (. 9.2).

9.2

0),,,,,,(f y312312332211 = 5, ,

1 2 3 1 2 3 yf (F ,F ,F ,M ,M ,M , ) 0.= , . 9.3

}{d , , :

}{d}{d}{d plel += (9.1)

39

9.3 - (. 9.3)

T pl

d dE Hd d = = = (9.2,)

TT

el pl d dd = E (d + d ) = E +E H

(9.3)

T

E H EE = = E 1-

E + H E + H (9.4)

TE E

9.12 9.13. 9.1.1 -

,

40

. , - - . . Newton-Raphson (9.4) :

9.4 Newton-Raphson . Newton-Raphson m+1 B 1: m-1[K ]

m-1. B 2: 2: (. 9.1.3)

(0)m-1 m-1K = [K ] (9.5)

41

2:

{ } { } { }(0) (1) (0)m-1 m m mK U = P - F (9.6) { } { }(1) (0) (1)m m mU = U + U (9.7) { } { }(1) (0) (1)m m mU = U + U (9.8) 2: { }(1)mF

(. 9.1.2). .

...... B 3: A 3: ( -1)m-1K A 3:

{ } { } { }( -1) ( ) ( -1)m-1 m m mK U = P - F A A A (9.9) { } { }( ) ( -1) ( )m m mU = U + U A A A (9.10)

{ } { }( ) (0) ( )m m mU = U + U A A (9.11) 3: { }( )mF A ......

j : { }

{ }( j)

m m

m

{P } F

P

(9.12)

2 610 10 . mj = :

{ } { } { }(0) (j)m+1 m+1 mU = U = U (9.13)

42

{ } { } { }(0) ( j)mm 1 m 1F F F+ += = (9.14)

}{}P{}P{ m1m +=+ (9.15)

{ } . m=m+1 1. 1= +A A 3.

Newton-Raphson { }(j)mF (j-1)mK j m . 9.1.2 . - (beam-column) 1 2 . : . j m: 1:

{ } { } { }(j-1) (j) (j-1)m-1 m m mK U = P - F (9.16)

2: { }(i)D i .

{ } { } { }(j) (j) (i)m mU U D , (9.17) m j.

43

3: 11A i 1,2 A (.

9.5).

9.5 4:

(elastic prediction) A (. 9.6)

11 11elp = E (9.18)

( ) ( ) ( )11 11(j) (j)(0)elp elp11 mm m = + (9.19)

i 1,2.

44

9.6 j: () , () , () 5: A ,

m, j, i , 1 2. 5: :

( ) ( ) ( )11 11 11(j) (j)(j)elp elpy mm m < = (9.20) 5: (. 9.6):

( ) ( )11 11(j)elp y ym-1m > < (9.21) ( )(j) (j)11 y T 11 m ym = + E [( ) - ] (9.22)

45

5: (. 9):

( )11 11(j)elp (0)y m ym > ( ) > (9.23) ( )(j) ( j) (0)11 11 m 1 T 11 m 11 mm ( ) E [( ) ( ) ] = + (9.24) 5: : ( ) ( )( j)(0) elp11 y 11 11 m 1m m ( ) > < (9.25) ( ) ( j) elp ( j)11 m 11 m( ) = (9.26)

. 1 2 - j m A . , j m

{ } T(j) (j) (j) (j)1 2 3F = F F M , j 1,2 = (9.27) (. 9.5): 1 11F = t b , = 1, n A A A

AA (9.28)

3 11 3 3M = b t y M = M A A A A A AA

(9.29)

n . (. 9.7) ( )1 1 2 22 3 3 2F M M L F= + = (9.30)

46

9.7

9.1.3 - (beam-column approach) (. , . , , 2002 , . , , 2000). - .

9.8 -

- . () - 9.8

=

66655655

44kk

FF0FF000F

]F[ (9.31)

47

ijF - (. - , . , , 1996):

L L5 1 5 14 1 4 1

44 550 0

M (x )M (x )N (x )N (x )F dx , F dxEA EI

= = (9.32 ,)

L

5 1 6 156 65

0

M (x )M (x )F F dxEI

= = (9.33) 4(x1), 5(x1), 6(x1) - , 2 , . , [Fkk]

2

A 0 0 -A 0 0B C + BL 0 -B -C - BL

D + 2CL + BL 0 -C -D - CL[K] =D A 0 0

B CD

(9.34)

44F1A = , 66 56 55B F H C F H , D F H= = = (9.35)

255 66 56H = F F - F 44 55 66 56F ,F ,F ,F .

48

. F44 k - 1P4 = , 9.9.

L

4 4 10

P = N (x ) d (9.36)

4 1 11 1 2 21 1A A A

d dN (x ) (x )d E(x ) dA E(x )ddx dx = = = (9.37)

9.9 (9.37) (9.32) 44F ,

L

4 1 4 1 10

442

A

N (x )N (x )dxF

E(x )dA=

(9.38)

49

)x(E 2 2x .

9.10

(9.10). (9.38)

L

4 1 4 1 10

N (x )N (x )dx L= (9.39) , (9.38)

( )12 2 2A

E(x )dA E b x x += A A A AA

(9.40)

12 2x x t+ =A A A A (. 9.11) AA E,b

E A ,

50

. , , 9.11, - , 1, 2, 7, 8 , 3, 4, 5, 6 .

9.11

. - - 566655 F,F,F k (. 9.10 9.12). 66F 1P6 =

L

6 6 10

P M (x )d = (9.41)

6 1 11 1 2 2 11 1 2A A

M (x ) (x )x d E(x ) (x )x dA= = (9.42)

51

9.12

9.13

x3

(. 9.13)

2 211 11

(x ) x(x ) ddx = = + (9.43)

. (9.43) (9.42)

52

26 1 2 2 2 21 A A

dM (x ) E(x )x dA E(x )x ddx

= (9.44) d (9.44) (9.41) =66F

L

6 1 6 1 10

662

2 2 2 2A A

M (x )M (x ) dxF

E(x )x dA E(x )x dA=

(9.45)

L , 6P 1= (. 9.10):

L

6 1 6 1 10

M (x )M (x ) dx L= (9.46) (. 9.11)

( )L 32 3 12 2 2 20

E(x )x dA 1/ 3 E b (x ) x + = A A A AA (9.47)

( )L 22 12 2 2 20

E(x )x dA 1/ 2 E b (x ) x + = A A A AA (9.48)

9.12:

4 1 11 1 2 11 1A A

N (x ) (x ) dA E(x ) (x ) d 0= = = (9.49) (9.43) (9.49)

0dA)x)(x(E1 2A

2 =+ (9.50)

53

( ) ( )( )

2 212 2 2 2

A1

2 22A

E(x )x dA 1/ 3 E b x x

1/ 2 E b x xE(x ) dA

+

+

= =

A A A A

AA A A A

A

(9.51)

F55 . ...

L

5 5 10

P M (x ) d = (9.52) . 55 5F (P 1)= =

( ) ( )L 5 1 5 1 1 3

055

2 22 2 2 2 2 2 2 2

A A A A

M x M x dxL / 3F

E(x )x dA E(x )x dA E(x )x dA E(x )x dA= =

(9.53) F56 ,F65

( ) ( )L 5 1 6 1 1 20

56 652 2

2 2 2 2 2 2 2 2A A A A

M x M x dxL / 2F F

E(x )x dA E(x )x dA E(x )x dA E(x )x dA= = =

(9.54) + = yy 0= :

3 3

55 2 1 22 2 2

2 2A

L / 3 L / 3F1/ 3 E b (x ) (x )

E(x )x dA+= =

A A A AA (9.55)

54

66 2 1 22 2 2

2 2A

L LF1/ 3 E b (x ) (x )

E(x )x dA+= =

A A A AA (9.56)

2 2

56 2 1 22 2 2

2 2A

L / 2 L / 2F1/ 3 E b (x ) (x )

E(x )x dA+= =

A A A AA (9.57)

ijk (9.34) (9.35),

( )144 2 21A 1/ F E b x xL += = A A A AA (9.58)

4 42

55 66 56 2 22 1 22

2 22 2A

L /12 L /12F F F1 E b (x ) (x )E(x )x dA 2

+ = = =

A A A A

A

(9.59)

( ) ( )3 32 166 2 2 2 23 3A

F 12 12 1B E(x )x dA E b x xH L L 3

+ = = = A A A AA (9.60) 2 3 1 356 2 2 2 22 2

A

F 6 6 1C E(x )x dA E b (x ) (x )H L L 3

+ = = = A A A AA

(9.61)

2 3 1 355 2 2 2 2A

F 4 4 1D E(x )x dA E b (x ) (x )H L L 3

+ = = = A A A AA

(9.62)

[k] (9.34) .

55

9.2 9.2.1

9.14 () 1, ()

1 2

. (. 9.14). 1 3 3r = , 1 , (. 4.3 , . , , 1996):

[ ]22 23 25 26

1 1

32 1 33 1 35 36

52 53 55 56

62 63 65 66

k 0 k k k0 c -c 0 0

k -c k + c k kk =k 0 k k kk 0 k k k

2 3 3 5 623356

(9.63)

c1 1 ijk . (9.63) .

56

[ ]{ } { }k = P , 2 5 6 0 = = = 3 1 = ,

3 11

3 1 33

cr = =c + k

(9.64)

. , (9.14)

22 23 25 26

1 1

32 1 33 1 35 36

52 53 55 56

2 2

62 63 65 2 66 2

k 0 k k 0 k0 c c 0 0 0

k c k c k 0 kk

k 0 k k 0 k0 0 0 0 c c

k 0 k k c k c

+= +

2 3 3 5 6 6233566

(9.65)

[ ]{ } { }k P = ( 3 6 ), 2 5 6 0 = = = 1 3 3r = 2 5 3 0 = = =

2 6 6r = :

3 11

3 1 33

6 22

6 2 66

crc k

crc k

= = += = +

(9.66,)

3 3 , 6 (9.63) (9.65), .

57

1, 1c cc ce ee eck k k k k

= :

[ ]22 25 26 23

1 132 1 35 36

52 55 56 53 33 1

62 65 66 63

0 22 23 32 1 23 0 25 23 35 0 26 23 36

1 32 1 33 1 35 1 36

0 52 53 32 1 0 55 53 35 0 560

k 0 k k k0 c 0 0 c 1k k c k k

k 0 k k k k ck 0 k k k

k k k k c k k k k k k k k kc k c k c k c k1

k k k k c k k k k k kk

= = +

= 53 36

0 62 63 32 1 0 65 63 35 0 66 63 36

k kk k k k c k k k k k k k k

(9.67)

0 3 1k k c= + . 1 2 3 6 (9.65) :

22 25 23 261

33 1 36 32 1 351 1

63 66 2 62 65 252 55 53 56

2 2

k 0 k 0 k kk c k k c k 00 c 0 0 c 0

kk k c k 0 k ck 0 k 0 k k

0 0 0 c 0 c

+ = +

1

33 1 36 66 2 36

63 66 2 63 33 166 2 33 36 63 1 66 1 2

k c k k c k a b1k k c k k c c d(k c )k k k c k c c

+ + = =+ ++ + +

(4x4) :

58

22 23 26 32 23 26 62 23 26 12

1 32 1 62 2 2

52 53 56 32 53 56 62 53 56 1

2 32 2 62 1 2

25 23 26 35 23 26 65 23 26 2

1 35

k

k (k a k c)k (k b k d)k (k a k c)c

c ak c bk c c a=

k (k a k c)k (k b k d)k (k a k c)cc ck c dk c cc

k (k a k c)k (k b k d)k (k b k d)cc ak

+ + + + + + + +

+ + ++ 1 65 1 2

55 53 56 35 53 56 65 53 56 22

2 35 2 65 2 2

c bk c bck (k a k c)k (k b k d)k (k b k d)c

c ck c dk c c d

+ + + +

(9.68) r

jr 1= , j(c )= , , r 0= , ( jc o= ). , , . 1 2, .. 9.2.2 r p ( ) ( ). ( yM ) pM . 9.15.

59

9.15

. y . p y , u . M

( ) ( ) ( )( )( ) 12 22y p y p y p pM M M M = + (9.69) 0 = p = . . (9.15) ( 0) = (dM d ) = .

60

. , p dM 0= dM d 0 = . (9.70)

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

2p p

T 12 222

p p p p p

M MydMk

dM My M My

= = (9.70)

. . 1 2c , c dM d (9.64) (9.66) p

133

kp =k + k

1

1

(9.71)

266

kp =k + k

2

2

(9.72)

c1 1Tk c1, c2 1 2T Tk ,k (9.67), (9.68) k .

. . 1:

.

61

( )p 1, 0= = .

2:

.

: dM / d . 3: j 1, 2= i

. , , M My,> (9.69) , ( ) = :

( )( )

12 2

p p 2

M My1

M My

= (9.73)

4: (9.73) (9.70)

- dM / d 1 2p , p ( 9.71, 9.72).

% = ( )j ,100 1 p j 1,2 = (9.74)

.

5: ,

(9.67, 9.68), .

6:

2.

62

. , My M Mp

mMy M N 1.0Mp Mp Np

+ (9.75) . m (.. 2=m ) yNp A= .

1mMyNy Np

Mp = (9.76)

M 0= (9.75).

9.16

63

(9.16) 1m = ( ) . p 1 p 0 . M N , , Oy M y My s = Op M p Mp s = , . 1>s M N . M y M p (9.69) (9.70) - , . . My Mp . 9.2.3 (Federal Emergency Management Agency-FEMA) , , . ( 1=p ). (9.67), (9.68), ( )p 1< , . .

r1

y

UU

= (9.77)

64

( ) ( )2 k k 1 k k 1 yU U U U = (9.78)

Ur , Uy , kU k ( )k k 1 yU U k k -1 ( ) . Ur . : (i) IO (Immediate Occupancy), (ii) DC(Damage Control), (iii) LS (Life Safety), (iv) SC (Structural Collapse). 1

9.17 .

. 9.17 W : 14x257, 33x118, 24x68. 1T 1.01s= . y

p 0.045 rad = , u . (9.75) 1=m .

65

1 Sa 0.0008g= .

ab

SV Wg

= () W , , k

k vk bQ C V= ()

s

k kk r

i ii

w hC , i 1 3w h

= = ()

kh k s . 1 = 2s . 9.18 . 9.18 .

IO DC LSU 0.7%h, U 2.5%h U 5%h= = = .

1:

(kN)

(kN)

(Cvk)

(kN)

1 4688 11.556 0.068 0.786 2 4688 0.271 3.132

11405071 0.661 7.639

66

2:

(cm)

1

(k)

yU 4.39= 1.00 1710.33 0.1184g IO IOU 8.32= 1.89 3154.09 0.2183g DC DCU 29.72= 6.77 5041.37 0.3489g LS LSU 59.44= 13.55 5326.28 0.3687g SS

scU = 5339.09 0.3695g

3:

3 2 DC 15 15 LS 3 27

9.18

67

9.19