PHNG PHP PH PHN NG NHIU DNG DAO NG V TNH TON NH CAO TNG CHU NG T

THEO TCXDVN 375 : 2006

TS. NGUYN I MINH Vin Khoa hc Cng ngh Xy dng

Tm tt: Trong tiu chun TCXDVN 375:2006, phng php ph phn ng nhiu dng dao ng khng c hng dn chi tit nh i vi phng php tnh lc ngang tng ng. V vy, bi bo ny trnh by c s tnh ton ng t i vi nh cao tng theo phng php ph phn ng nhiu dng dao ng. Hy vng bi bo c th gip ngi c nm c bn cht phng php ny trong tnh ton thit k khng chn. Mt khc, do s thun tin v tnh d kim sot ca phng php phn tch tnh lc ngang tng ng, trong thc hnh thit k, phng php ny c th vn c p dng khi tnh ton nh cao tng chu ng t. Do vy, bi bo cng trnh by cc tnh ton so snh gia phng php phn tch tnh lc ngang tng ng v phng php ph phn ng nhiu dng dao ng i vi nh cao tng. T , xut cc ci tin c th vn dng c phng php phn tch tnh lc ngang tng ng trong tnh ton nh cao tng chu ng t nhm tit kim thi gian, cng sc ca ngi thit k v c bit l d kim sot quy trnh tnh ton v cc kt qu u ra.

T kha: ng t, nh cao tng, phng php phn tch tnh lc ngang tng ng, phng php ph phn ng nhiu dng dao ng, TCXDVN 375:2006. 1. M u

Tnh ton kt cu chu tc ng ngang do gi/bo hay ng t c xem l mt trong nhng khu quan trng trong thit k nh cao tng. Trong thc hnh thit k, tnh ton ng t i vi nh cao tng theo tiu chun TCXDVN 375:2006 Thit k cng trnh chu ng t [1], tiu chun chu u BS EN 1998-1:2004 (Eurocode 8) [2] v tiu chun M UBC:1997 [3], c th c thc hin theo phng php phn tch tnh lc ngang tng ng. Quy trnh n gin xc nh ti trng ng t tc dng ln cng trnh theo TCXDVN 375:2006 bng phng php phn tch tnh lc ngang tng ng c trnh by trong [4, 5]. Tuy nhin, TCXDVN 375:2006 v EN 1998-1:2004 quy nh phng php ny ch p dng cho nh cao tng c chu k dao ng ring c bn T1 nh hn 2s (i vi t nn loi B, C, D, E theo phn loi t nn theo ng t) hay nh hn 1.6 s (i vi t nn loi A), tng ng vi nh cao t 20 tng tr xung. Tiu chun UBC:1997 cng quy nh phng php phn tch tnh lc ngang tng ng p dng cho cc nh cao tng cao di 240 ft (73.15 m, qung 20 tng).

Tiu chun TCXDVN 375:2006 v tiu chun EN 1998-1:2004 u khng nh phng php ph phn ng nhiu dng dao ng (hay cn gi l phng php ng tuyn tnh) c th p dng cho tt c cc loi kt cu khi thit k khng chn. Nh vy, vi nh cao t 20 tng tr ln, theo quy nh ca TCXDVN 375:2006, khi tnh ton ng t phi p dng phng php ph phn ng nhiu dng dao ng. Cc tiu chun M UBC:1997 v tiu chun Nga SNiP II-7-81* [6] cng p dng phng php ny khi thit k khng chn i vi cc kt cu cao tng. Tiu chun SNiP quy nh i vi cng trnh c chu k dao ng ring c bn T1 > 0.4 s (tng ng t 5 tng tr ln), phi xt n t nht 3 dng dao ng khi tnh ton ng t. Khc vi tiu chun M, l tiu chun coi phng php phn tch tnh lc ngang tng ng l phng php tham chiu (reference method) trong thit k khng chn, tiu chun Eurocode 8 xem phng php ph phn ng nhiu dng dao ng l phng php tham chiu [7]. V vy, phng php ny c khuyn ngh p dng cho mi loi kt cu. Ngoi ra, trong tnh ton kt cu chu tc ng ng t, EN 1998-1:2004 cn khuyn khch p dng phng php ph phn ng nhiu dng dao ng c xt n nh hng ca cc dng dao

ng bc cao khng gian theo c 3 phng: ngang nh, dc nh v xon theo phng chiu cao nh.

Mc d l phng php tham chiu, nhng phng php ph phn ng nhiu dng dao ng khng c hng dn chi tit trong TCXDVN 375:2006 v EN 1998-1:2004. Trong ti liu [5], tuy trnh by quy trnh tnh ton theo phng php ny nhng cha nu r c s xc nh cc khi lng hu hiu (hoc trng lng hu hiu) trong cng thc tnh cc lc ct y ca cc dng dao ng ring bc cao ca kt cu cng nh c s thit lp phng trnh phn phi lc ng t ln cc cao trnh tng cc dng dao ng ring ny. C th TCXDVN 375:2006 coi ngi s dng rt quen thuc vi phng php ph phn ng nhiu dng dao ng. V vy, bi bo ny trnh by c s v cch tnh ton theo phng php ph phn ng nhiu dng dao ng p dng trong TCXDVN 375:2006, vi hy vng bi bo s gip cho ngi c nm c bn cht ca phng php ny trong thit k khng chn.

Do s thun tin v tnh d kim sot ca phng php phn tch tnh lc ngang tng ng, trong thc hnh thit k, khng ch nc ta m cn chu u [8], phng php ny vn thng c p dng trong tnh ton ng t i vi nh cao tng nm ngoi phm vi p dng ca phng php. V vy, bi bo s trnh by cc tnh ton so snh gia phng php phn tch tnh lc ngang tng ng v phng php ph phn ng nhiu dng dao ng i vi kt cu cao tng chu ng t. Trn c s , xut cc ci tin vn dng cho phng php phn tch tnh lc ngang tng ng c th p dng c trong thit k khng chn i vi nh cao hn 20 tng. Nh vy, vic p dng phng php tnh lc ngang tng ng c ci tin s thun tin, d kim sot u ra, tit kim thi gian v cng sc ca ngi thit k so vi tnh ton theo phng php ph phn ng nhiu dng dao ng. 2. H mt bc t do v phng php ph phn ng

Thc ra, phng php ph phn ng nhiu dng dao ng c trnh by rt chi tit v c ging dy trong cc trng i hc M v phng Ty [9, 10]. Vit Nam, phng php ny cng c gii thiu trong cc ti liu [11, 12]. Tuy nhin, vic gn kt gia c s l thuyt ca phng php ny vi tiu chun khng chn hin hnh (TCXDVN 375:2006) cha cp c th. Phng php ph phn ng nhiu dng dao ng p dng khi tnh ton ng lc i vi h nhiu bc t do, khng ch i vi tc ng ng t m cn i vi tc ng gi. V vy, trc khi trnh by phng php ny i vi h nhiu bc t do, cn thit phi xem xt phng php ph phn ng trong tnh ton ng t i vi h 1 bc t do.

Hnh 1. Dao ng ca h 1 bc t do di tc dng

ca gia tc nn )(0 tu Xt h 1 bc t do chu tc dng ca chuyn ng t nn cho hnh 1. Theo nguyn l

dAlembert, phng trnh dao ng ca h mt bc t do theo phng x (hay u) c vit nh sau [9]: 0)()()()( 0 tuktuctutum (1a) hay 0umukucum (1b) hoc 0

22 uuuu (1c) vi iu iu kin u l: 0)0( u v 0)0( u .

Trong : m khi lng tp trung, t bin thi gian; u,u v u dch chuyn, vn tc v gia tc tng ng theo phng ngang u ti im tp

trung khi lng m; 0u - gia tc t nn (gin gia tc nn ag(t));

c h s cn nht, k cng kt cu;

Tn s ring (tn s vng) mk

(ch thch: quan h gia vi chu k dao ng ring

T v tn s dao ng ring f ca h l:

2T

v f

T 1 );

- h s cn nht khng th nguyn, xc nh nh sau:

mc

2 .

Nghim ca phng trnh (1c) l tch phn Duhamel, c biu din di dng:

dteutut

dt

d 0

)(0 )(sin)(

1)( (2)

Trong 21 d l tn s ring c xt n nh hng ca cn dao ng. Do gi tr thng nh (vo khong 5% khi tnh ton ng t) nn d .

Lc ng t tc dng ln khi lng m s l: )(tumFb (3)

Trong 22

)(tdudtu , u(t) xc nh theo cng thc (2).

Khi tnh ton thit k, cn thit phi quan tm n lc ng t ln nht tc dng ln khi lng m do hm gia tc nn )(0 tu gy ra. Vi hm )(0 tu cho trc, gi tr gia tc ln nht (nh gia tc hay ph) maxu tng ng vi tn s ring (hoc chu k dao ng ring T ) c xc nh cn c vo gi tr max ca tch phn Duhamel. Tp hp cc gi tr

maxu tng ng vi cc chu k dao ng ring T chnh l ng cong ph phn ng gia tc Sa() (hay Sa(T)) i vi gia tc nn 0u cho trc. Minh ha v ph phn ng gia tc Sa cho hnh 2 [7, 9, 13, 14]. .

Hnh 2. th minh ha v ph phn ng gia tc ca kt cu [14]

T cng thc (2), c th xc nh c ph phn ng dch chuyn, ph phn ng vn tc

v ph phn ng gia tc (t y gi l ph gia tc), xp x nh sau:

2max a

dSSu ;

ad

SSu max

; ad SSu 2

max (4)

Nh vy lc ng t tc dng ln kt cu s l:

max

umFb gSWdteu

gW a

tt )()(sin)(1

max0

)(0

(5)

Trong : g gia tc trng trng, W trng lng kt cu, Sa() - ph gia tc.

Hnh 3. Ph dng 1 (Eurocode 8) [2] Hnh 4. Ph dng UBC:1997 [3]

Ph gia tc xc nh theo (5) l ph n hi. Trong cc tiu chun khng chn, ph gia tc

s dng trong thit k thng l cc ng cong trn c chun ha, thun tin cho ngi s dng, m bo an ton cng trnh, c xt n s lm vic ngoi min n hi (tnh do ca kt cu), cc c tnh a chn ca quc gia hay khu vc (nh gia tc nn, chu k tri ca gin gia tc, thi gian ko di ca ng t, ngun pht sinh ng t...) v loi t nn theo iu kin ng t. Ngi thit k, cn c vo chu k dao ng ring c bn ca cng trnh, c th xc nh c gi tr ca ph gia tc tng ng. T , xc nh c lc ng t tc dng ln cng trnh. Ph ng t n hi (cha chia cho h s ng x q theo Eurocode 8 hay cha chia cho h s vt cng R theo UBC:1997) c th hin trong cc hnh 3 v hnh 4. 3. H nhiu bc t do v phng php ph phn ng nhiu dng dao ng

Xt dao ng ca h n bc t do cho hnh 5. Theo nguyn l dAlembert, h phng trnh dao ng ca h nhiu bc t do di tc dng ca gia tc nn )(0 tu theo phng x (hay u) c biu din nh sau [9]:

Hnh 5. H n bc t do

00 ukucuuM (6a) hay 0uMukucuM (6b)

Trong : nT uuu ...21u , n

T uuu ...21u , nT uuu ...21u ,

000 ... uuuT 0u ;

)(00 tuu - l gia tc t nn ( trnh by mc 2 i vi h 1 bc t do),

ui , iu , iu chuyn v, vn tc, gia tc ti im tp trung khi lng tng th i, tdud

tu ii )( ,

2

2

)(tdudtu ii ,

[M] ma trn khi lng, [c] ma trn cn vn tc, [k] ma trn cng, xc nh nh sau:

nm

mm

0000...00000000

2

1

M ;

nnnn

n

n

ccc

cccccc

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

...

...

21

22221

11211

c ;

nnnn

n

n

kkk

kkkkkk

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

...

...

21

22221

11211

k

mi tp trung khi lng ti tng th i, i = 1, 2, ..., n. Gii h phng trnh vi phn (6b) kh do cc phng trnh ph thuc ln nhau khng phi

l cc phng trnh vi phn c lp nh bi ton dao ng ca h 1 bc t do. Tuy nhin, bin h phng trnh vi phn (6b) thnh h n phng trnh vi phn c lp,

dng php bin i modal (php bin i dng dao ng), vc-t bin {u} s thay th bng vc-t cc bin mi {Y}, c th l:

Yu (7) trong :

nnnn

n

n

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

...

...

21

22221

11211

- ma trn dng dao ng ring ca h,

nY

YY

...2

1

Y - bin mi.

Th (7) vo (6b), h phng trnh (6b) tr thnh:

0uMYkYcYM (8) Nhn c 2 v ca h phng trnh (8) vi T dn n:

0uMYkYcYM TTTT (9) Do tnh cht trc giao ca ma trn dng dao ng ring v cc ma trn [M] v [k] l cc

ma trn i xng dng, [c] l ma trn cn truyn thng [9] nn cc ma trn MT , cT v kT ch l cc ma trn ng cho. V d MT tr thnh:

n

T

m

mm

0000...00000000

2

1

M (10)

Trong :

n

jiiji mm

1

2 , i = 1, 2, ..., n.

H phng trnh vi phn (9) s bao gm n phng trnh vi phn c lp nh sau:

i

Ti

iiiiii muYYY 022 m (11)

Trong : i = 1, 2, ..., n; inii

Ti ...21 - vc-t dng dao ng ca dng th i;

nT mmm ...21m - vc-t khi lng tp trung ti cc tng;

ii

iii m

c

2

- h s cn dao ng tng ng vi dng dao ng th i;

i tn s ring th i ca h. Phng trnh (11), tng ng vi dng dao ng th i, c th vit di dng sau:

0

1

2

122 um

mYYY n

jijj

n

jjij

iiiiii

(12)

H phng trnh vi phn dao ng ca h n bc t do (6b) s tng ng vi n phng trnh vi phn c lp dng (12) tng ng vi n dng dao ng ring ca h (i =1, 2, ..., n).

Phng trnh (12) tng ng vi dng dao ng ring th i, ging nh phng trnh (1c) i vi h 1 bc t do. y l phng trnh vi phn tuyn tnh nn ph gia tc ca )(tYi s l:

maxi

Y )(

1

2

1ian

lill

n

llil

Sm

m

(13)

Cng thc (7) v quan h gia {u} v {Y}, vit di dng ma trn y s nh sau:

nnnnn

n

n

n Y

YY

u

uu

......

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

...2

1

21

22221

11211

2

1

= n

nn

n

n

i

i

i

i

nn

YYYY

......

......

......2

1

2

2

1

2

2

22

12

1

1

21

11

(14)

Nh vy, s tham gia ca cc dng dao ng trong dao ng tng th ca h s l:

nnn

nn

nn

ii

ii

ii

nn

n

ii

n Y

YY

Y

YY

Y

YY

Y

YY

u

uu

......

......

.........2

1

2

2

1

22

222

212

11

121

111

1

2

1

u (15)

Trong : iniiT

i uuu ...21u (16) Gia tc ti cao trnh im j ca dng dao ng th i s xc nh nh sau: iijij Yu (do

jiij ) (17) Thay (13) vo (17), dn n:

)(

1

2

1maxmax ian

lill

n

llilij

iijij Sm

mYu

(18)

V lc ng t tc dng ti cao trnh im j ca dng dao ng i s l:

jiaijjij mSumF )(max

n

lill

n

llilij

m

m

1

2

1

(19)

Lc ng t Fij, xc nh theo cng thc (19), cn c vit di dng sau: a. Theo dng cng thc s dng trong SNiP II-7-81*:

ijjiaij mSF )( (20)

Trong :

n

lill

n

llilij

ij

m

m

1

2

1

(21)

ij c gi l h s dng dao ng. b. Theo dng cng thc s dng trong TCXDVN 375:2006 hay UBC:1997:

n

lill

n

llil

n

llil

ijjiaij

m

m

m

mSF

1

2

2

1

1

)(

= in

llil

ijjia M

m

mS

1

)(

(22)

Hay:

n

llil

ijjbin

llil

ijjiiaij

m

mF

m

mMSF

11

)(

(23)

Trong :

n

lill

n

llil

i

m

mM

1

2

2

1

(24)

iiabi MSF )( = iia WgTS

)( (25)

Trong cc cng thc (24) v (25), Mi v Wi c gi l khi lng v trng lng hu hiu ca h tng ng vi dng dao ng th i, Fbi l lc ct y ng vi dng dao ng th

i. Do tnh cht trc giao ca cc dng dao ng nn:

n

iiMM

1

v

n

iiWW

1

, trong M v

W l khi lng v trng lng ca h. Lc ct y Fbi xc nh theo cng thc (25) cng da trn ph phn ng ca h 1 bc t

do nhng ng vi chu k dao ng ring Ti. Sau khi bit cc lc ng t Fij tc dng ln cao trnh th j ca dng dao ng th i, h

qu tc ng ng t Ei (ni lc: m-ment, lc dc, lc ct trong cc cu kin, chuyn v, vng v.v.) c th xc nh theo cc phng php ca c hc kt cu i vi bi ton tnh hc thng thng.

Phng php trnh by trn c gi l phng php ph phn ng nhiu dng dao ng. 4. T hp cc dng dao ng

Do ph phn ng (hay nh) ca cc dng dao ng th i (i = 1, 2, ..., n) khng xy ra ng thi nn vic xc nh ph phn ng tng th ca h kt cu nhiu bc t do c nhiu cch gn ng khc nhau.

Cch n gin nht l cng cc gi tr tuyt i ca h qu tc ng ng t Ei (ng vi dng th i) ca tt c cc dng dao ng li:

Emax =

n

iiE

1max (26)

y chnh l cc gi tr trn ca t hp cc dng dao ng cn xt. T hp ny gi l t hp tng cc gi tr tuyt i hay thng gi l phng php ABSSUM (the absolute sum of modal combination rule [9]). T hp tng cc gi tr tuyt i ABSSUM thng qu thin v an ton.

Phng php t hp th hai l phng php ly cn bc hai cc tng bnh phng ca cc h qu tc ng hay cn gi l phng php SRSS (the square-root-of-sum-of-squares rules):

Emax =

k

iiE

1

2 (27)

Phng php ny do E. Rosenblueth [15] kin ngh trong lun n tin s (Ph.D. thesis) ca mnh nm 1951. Phng php SRSS c s dng trong TCXDVN 375:2006, Eurocode 8, UBC:1997 v SNiP II-7-81* khi phn ng ca hai dng dao ng i v j l c lp vi nhau.

Phn ng ca hai dng dao ng i v j c xem l c lp vi nhau (ngc li l ph thuc ln nhau) nu cc chu k Ti v Tj tha mn cc iu kin sau [5, 7]:

Ti /Tj < 0.9 hoc Ti /Tj > 1 / 0.9 (28) Trong trng hp phn ng ca hai dng dao ng i v j l ph thuc ln nhau (cc chu

k Ti v Tj l rt gn nhau), th gi tr ln nht ca h qu ca tc ng ng t EE s ly bng:

EE =

k

i

k

jjiij EEr

1 1 (29)

Trong cng thc (29), rij c xc nh nh sau:

222222

2/3

)(4)1(4)1(

.)(8

jiji

jijiijr

(30)

Trong : = Tj / Ti , i v j l h s cn nht ly bng 0.05 (5%). Phng php t hp dao ng ly theo cng thc (29) c gi l phng php t hp bnh phng y CQC (the complete quadratic combination). Phng php ny do Der Kiureghian [16] kin ngh nm 1981. 5. Phng php phn tch tnh lc ngang tng ng Tiu chun TCXDVN 375:2006 v UBC:1997 s dng phng php tnh lc ngang tng ng tnh ton ng t i vi h nhiu bc t do nhng hn ch i vi nh thp hn 20 tng. Mc ny s trnh by c s ca phng php ny. Trong h nhiu bc t do, tng lc ct y xt n nh hng ca tt c cc dng dao ng s nh hn tng lc ct y ly theo phng php t hp tng cc gi tr tuyt i ABSSUM:

n

ii

ian

ibib Wg

TSFF11

)( (31)

Trong : Wi - trng lng hu hiu ca ton h tng ng vi dng dao ng th i, tn s ring i c thay bng chu k dao ng ring th i l Ti. Theo [9], nu cc gi tr )( ia TS u bng nhau v bng )( 1TSa th gi tr tng lc ct y s xp x:

WgTSW

gTSW

gTSF a

n

ii

an

ii

ab

)()()( 11

1

1

1 (32)

Tiu chun M UBC:1997 s dng cng thc (32) cho phng php tnh lc ngang tng ng. Trong tiu chun chu u v TCXDVN 375:2006, gi tr W cng th (32) c nhn thm h s hiu chnh ( = 0.85 nu T1 2TC vi nh cao hn 2 tng hoc =1.0 vi

cc trng hp khc). i vi nh cao hn 20 tng, thng ly bng 1.0, nn cng thc (32) cng p dng cho loi nh ny trong Eurocode 8 hay TCXDVN 375:2006. Tuy nhin, trong cc nh cao tng ng vi dng dao ng ring th i ( i > 1) th Sa(Ti) lun ln hn Sa(T1). V vy, vic p dng phng php tnh lc ngang tng ng tnh ton ng t c nhng hn ch nht nh nh trnh by [1-3]. Phn b lc ng t Fk ln tng th k xc nh theo cng thc (33) vi gi thit dng dao ng c bn ly gn ng bng cc chuyn v ngang tng tuyn tnh dc theo chiu cao nh:

n

jjj

kkbk

Wz

WzFF

1

(33)

Trong : zk v zj l cao ca trng lng Wk v Wj so vi im t lc ct y Fb. Khi tnh ng t theo SNiP II-7-81*, t hp dao ng ly theo phng php SRSS. i vi nh c chu k T1 < 0.4 s, nu ch xt 1 dng dao ng c bn th lc ct y hay h qu tc ng ca h nhiu bc t do ly gn bng cc gi tr tng ng ca dng dao ng th nht:

WgTSEEEEE anE 111

222

21

)(... (34)

Trong W1 l trng lng hu hiu ca h ng vi dng dao ng th nht v lun nh hn tng trng lng ca h W. Trong cng thc (34), cc gi tr E2, E3... b qua v vi T1 < 0.4s, theo SNiP nh hng ca cc gi tr ny n phn ng tng th ca h b.

T (32) v (34), c th thy rng tnh ton ng t s dng phng php tnh lc ngang tng ng ch k n 1 dng dao ng ring theo tiu chun M v Nga c s khc nhau. Lc ng t tnh theo (32) lun ln hn (34) v trong (32) xt ton b trng lng ca h. 6. So snh gia hai phng php tnh lc ngang tng ng v ph phn ng nhiu dng

dao ng Phng php tnh lc ngang tng ng trong TCXDVN 375:2006 c th p dng i

vi nh cao di 20 tng nhng phi tha mn cc tiu ch v tnh u n theo chiu cao, ngc li phi p dng phng ph phn ng nhiu dng dao ng khi tnh ton ng t. V vy, mc ny s trnh by cc v d tnh ton ng t i vi nh cao tng c tnh u n theo chiu cao ( cng phn b tng i u theo chiu cao nh, khi lng cc tng xem nh xp x bng nhau) theo phng php tnh lc ngang tng ng v phng php ph phn ng nhiu dng dao ng. Cc so snh v nhn xt v cc kt qu tnh ton theo 2 phng php cng c trnh by trong mc ny.

Cc thng s u vo v kt qu ra ca cc v d tnh ton ng t nh sau: - S tng N = 20, 30 v 40 tng trong tr s 40 tng l s tng ln nht c th p dng

ng cong ph gia tc thit k trong TCXDVN 375:2006, tr s 20 tng l s tng cho php chp nhn trong tiu chun i vi phng php tnh lc ngang tng ng;

- Tiu chun p dng: TCXDVN 375:2006; - Tng trng lng cng trnh: W (vi gi thit khi lng tp trung ti cc tng xp x

bng nhau). n gin, xem cng (EI) ca nh khng i theo chiu cao; - Chiu cao tng: h, v d nh c 30 tng th chiu cao nh H = 30 * h; - nh gia tc nn thit k: ag (gia tc nn ch theo phng x hay u); - H s ng x kt cu q = 3.9 ng vi h kt cu b tng c do trung bnh (Ductility

class medium DCM) v l h khung-li-vch nhiu tng, nhiu nhp, h khung kp - Chu k dao ng ring xc nh nh sau (theo phng php gii tch v kim chng li

bng my tnh i vi dao ng ca thanh consol chiu cao H, cng EI v khi lng tp trung ti cc tng bng nhau): T1 = 0.1n, T2 = 0.160T1, T3 = 0.057T1, T4=0.0291T1, T5 = 0.0118T1 v T6 = 0.0084T1;

- Cc dng dao ng ring c xc nh chnh xc bng chng trnh my tnh;

- Phng php phn tch: SRSS phng php ph phn ng nhiu dng dao ng t hp ly cn bc hai cc tng bnh phng ca cc h qu tc ng, SEM phng php tnh lc ngang tng ng (SEM Static equivalent method), SEM_MODIFIED - phng php tnh lc ngang tng ng c ci tin;

- S dng dao ng xt trong tnh ton: 6 dng dao ng, tng trng lng hu hiu xp x 95% tng lng ca kt cu;

- Kt qu ra l: lc ct y v lc ct ti cc tng, m men y v m men ti cc tng. Phng php tnh lc ngang tng ng c ci tin y l phng php tnh lc ngang tng ng trong TCXDVN 375:2006 vi phn b lc ng t ln cc cao trnh tng xc nh vi gi thit dng dao ng c bn ly gn ng bng cc chuyn v ngang tng theo hm bc 2 dc theo chiu cao nh gn ging nh khuyn ngh trong tiu chun M ASCE 7-05 [17] v dng phn b ny thch hp vi ng x ca nh cao tng hn v thin v an ton hn so vi dng phn b tuyn tch:

n

jjj

kkbk

Wz

WzFF

1

2

2

(35)

Biu m-men (M), lc ct (V) ti cc tng ca cc nh 20, 30 v 40 tng cho trong cc hnh 7, 8 v 9. n gin, biu lc ct trong cc hnh ny c v theo ng cong trn dc theo chiu cao nh ly theo gi tr lc ct ti cc tng. Trc honh trong cc hnh 7-9 l gi tr khng th nguyn M /( W h)*(ag/g) v V/W*(ag/g), trc tung l cao trnh cc tng.

Bending moment in 20 story building (q=3.9, ground type B)

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M/(W*h)*(ag/g)

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y le

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SRSSSEMSEM_NEW

M - bending momentW - total weight of buildingh - story height

(a)

Shear in 20 story building (q=3.9, ground type B)

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V/W*(ag/g)

stor

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(b)

Hnh 7. Nh 20 tng: (a) m-men ti cc tng, (b) lc ct ti cc tng Bending moment in 30 story building (q=3.9, ground type B)

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101112131415161718192021222324252627282930

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17M/(W*h)*(ag/g)

Stor

y le

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SRSSSEMSEM_MODIFIED

M - momentW - weighth - story height

(a)

Shear in 30 story building (q=3.9, ground type B)

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22V/W*(ag/g)

stor

y le

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SRSSSEMSEM_MODIFIED

(b)

Hnh 8. Nh 30 tng: (a) m-men ti cc tng, (b) lc ct ti cc tng

Bending moment in 40 story (q =3.9, ground type B)

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M/(W*h)*(ag/g)

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y le

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M - bending momentW - building weighth - story height

(a)

Shear in 40 story building (q=3.9, fround type B)

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

V/W * (ag/g)

Stor

y le

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SRSSSEMSEM_MODIFIED

(b)

Hnh 9. Nh 40 tng: (a) m-men ti cc tng, (b) lc ct ti cc tng Kt qu tnh ton cho thy, khong t 1/2 n 2/3 chiu cao nh xung mng, m-men v

lc ct ti cc tng tnh theo phng php tnh lc ngang tng ng ln hn so vi kt qu tnh theo phng php ph phn ng nhiu dng dao ng, trong m-men ti di chn cng trnh ln hn khong 40%. Ngc li, t 1/3 chiu cao nh ln ti nh, lc ct v m-men tnh theo phng php ph phn ng nhiu dng dao ng ln hn so vi phng php tnh lc ngang tng ng. ng x ca nh 20, 30 v 40 tng i vi 2 phng php ny l tng i nh nhau.

Tnh ton theo phng php tnh lc ngang tng ng ci tin cho kt qu an ton hn so vi phng php tnh lc ngang tng ng v phng php ph phn ng nhiu dng dao ng. Phn ng ca kt cu ti khu vc 1/3 chiu cao tnh t nh nh st vi phng php ph phn ng nhiu dng dao ng hn so vi phng php tnh lc ngang tng ng. 7. Kt lun v kin ngh Bi bo trnh by c s l thuyt ca phng php ph phn ng nhiu dng dao ng p dng trong tiu chun TCXDVN 375:2006 hay UBC:1997. C s a ra cc cng thc xc nh tng khi lng hay tng trng lng hu hiu ca kt cu ng vi cc dng dao ng ring v t hp cc dng dao ng khi thit k khng chn cng c trnh by c th. Ngi c c th d dng nm c bn cht ca phng php ph phn ng nhiu dng dao ng. Bi bo cng trnh by r, phng php tnh ton ng t trong tiu chun Nga SNiP II-7-81* v mt phng php lun (l thuyt) cng tng t nh phng php ph phn ng nhiu dng dao ng s dng trong cc tiu chun u, M. Ngoi ra, bi bo cng gii thch c s ca phng php tnh lc ngang tng ng p dng trong cc tiu chun u-M. Cc v d tnh ton ng t theo TCXDVN 375:2006 i vi cc nh cao tng c tnh u n theo chiu cao vi s tng 20, 30 v 40 tng c thc hin theo phng php tnh lc ngang tng ng, phng php ph phn ng nhiu dng dao ng v phng php tnh lc ngang tng ng c ci tin. Cc nhn xt v so snh v lc ct, m-men ti cc cao trnh tng cho thy phng php tnh lc ngang tng ng cho cc kt qu thin v an ton so vi phng php ph phn ng i vi c m-men v lc ct tng (bao gm c lc ct y) khu vc khong 1/2 chiu cao nh tr xung (mng). T khu vc 1/3 chiu cao nh tr ln (nh), chnh lch v m-men ti cc tng t, nhng lc ct tnh theo phng php tnh lc ngang tng ng nh hn so vi phng php ph phn ng. iu ny xy ra vi c nh 20 tng l nh m phng php tnh lc ngang tng ng c php p dng trong TCXDVN 375:2006 v nh 30 v 40 tng

(cc nh khng c php p dng). Cn c vo cc kt qu tnh ton, c th s dng c phng php tnh lc ngang trong tnh ton ng t i vi nh cao tng, trong khu vc pha trn (1/3 nh) c kh nng nguy him v lc ct so vi tnh theo phng php ph phn ng nhiu dng dao ng thng c b li i vi trng hp ti trng khc hoc nn xem xt b li bng cu to khi thit k (do lc ct khu vc b ny thng nh). Bi bo cng kin ngh phng php tnh lc ngang tng ng c ci tin i vi nh cao t 20 tng tr ln (n 40 tng) vi phn b lc ng t ln cc cao trnh tng xc nh vi gi thit dng dao ng c bn ly gn ng bng cc chuyn v ngang tng theo hm bc 2 dc theo chiu cao nh do dng phn b ny thch hp vi ng x ca nh cao tng hn so vi dng tuyn tnh. Kt qu tnh ton so snh gia phng php ph phn ng nhiu dng dao ng, phng php tnh lc ngang tng ng v phng php tnh lc ngang tng ng c ci tin cho thy phng php tnh lc ngang tng ng c ci tin cho kt qu an ton nht trong 3 phng php v phn ng ca cng trnh ti khu vc pha trn 1/3 chiu cao nh st vi phng php ph phn ng nhiu dng dao ng. Cc kt qu tnh ton ng t vi cc loi t nn khc nhau, h s ng x khc nhau c thc hin bi tc gi cng cho cc ng x tng t (do hn ch v di ca bi nn khng trnh by trong bi bo ny). V vy, i vi nh cao hn 20 tng c th kin ngh phng php tnh lc ngang tng ng c ci tin trong tnh ton ng t nu khng p dng phng php ph phn ng nhiu dng dao ng. Cui cng, trong tnh ton ng t i vi nh cao tng mc d thc hin theo phng php ph phn ng nhiu dng dao ng theo quy nh ca TCXDVN 375:2006, cn thit phi kim tra li theo phng php tnh lc ngang tng ng c bit i vi phn nn-mng (do ti tc dng ln cc nh hng do m-men un ti chn nh ln), cc kt cu v cu kin cc tng t 1/2 chiu cao nh tr xung. TI LIU THAM KHO 1. TCXDVN 375:2006. Thit k kt cu chu ng t, Nh xut bn Xy dng, H Ni,

2006. 2. BS EN 1998-1:2004. (Eurocode 8) Design of structures for earthquake resistance. British

Standard institution, April, UK, 2005, 229 p. 3. UBC:1997. Uniform Building Code, Vol. 2. International Conference of Building

Officials, Whittier, CA, USA. 4. NGUYN I MINH v NGUYN HONG ANH. Xc nh ti trng ng t tc dng

ln cng trnh theo TCXDVN 375:2006: Quy trnh n gin, Tp ch KHCN Xy dng, Vin KHCN Xy dng, H Ni, 2008.

5. Vin KHCN Xy dng. Hng dn thit k nh cao tng bng b tng ct thp chu ng t theo tiu chun TCXDVN 375:2006, Nh xut bn Xy dng, H Ni, 2008.

6. SNiP II-7-81*. Xy dng trong vng c ng t (ting Nga), Nh xut bn Stroizdat, Moscow, 2001.

7. FARDIS, M. CARVALHO, E., FACCIOLI, E., PINTO P. and PLUMIER, A. Designers guide to EN 1998-1 and EN 1998-5 Eurocode 8: Design of structures for earthquake resistance General rules, seismic actions, design rules for buildings, foundations and retaining structures, ThomasTelford, UK, 279 p.

8. PINHO, R. and CROWLEY, H. Revisiting eurocode 8 formulae for periods of vibration and their employment in linear seismic analysis, Proc. of Eurocode 8 perspectives from Italian standpoint workshop, E. Cosenza (ed.), Napoli, Italy, 2009, pp. 95-108.

9. CHOPRA, A. K. Dynamic of structures, Prentice Hall International, US, 2001, 844 p. 10. CLOUGH, R. W. and PENZIEN, J. Dynamics of structures, Computers & Structures Inc.,

USA, 2003, 730 p. 11. KEY, D. Thc hnh thit k chng ng t cho cng trnh xy dng, Nh xut bn Xy

dng, H Ni, 1997, 266 trang. 12. NGUYN L NINH. ng t v thit k cng trnh chu ng t, Nh xut bn xy

dng, H Ni, 2007, 513 trang.

13. PENELIS, G. G. and KAPPOS, A. J. Earthquake-resistant concrete structures, E & FN Spon, An Imprint of Chapman & Hall, London, UK, 1997, 572 p.

14. BUNGALE, S. T. Wind and earthquake resistant buildings Structural analysis and design, Marcel Dekker, USA, 2005, 892 p.

15. ROSENBLUETH, E. A basis for aseismic design, Ph.D. thesis, University of Illinois at Urbana, USA, 1951.

16. DER KIUREGHIAN, A. A response spectrum method for randam vibration analysis of MDF system, Earthquake Engineering and Structural Dynamics, 9, 1981, pp. 419-435.

17. ASCE/SEI 7-05. Minimum design loads for buildings and other structures, published by American Society of Civil Engineers, Virginia, USA, 2006, 338 p.

Ngy nhn bi: 12/10/2010.