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
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