Dao động của nhà và công trình khi có động đất

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DIEN

DAN KHOA H O C

CONG NGHE

^ DAO D O N G CUA NHA VA

C O N G T R I N H KHI C O D O N G DAT

(Tiep theo)

5. Dao dong ci/dng biPc

Dao ddng cadng bac Id chi loai dao ddng sinh ra
dadi tdc dpng ciia mdt lac kich thich ben ngodi lien tuc
len vat the'. Trong ky thuat cdng trinh, ta thadng gap
loai dao dpng dd. Vi du, dao ddng cadng bde ciia mdt
gian xadng cd the' sinh ra dadi anh hadng ciia sa van
hanh mdy mdc ddt trong dd; bdi Id mdy mdc khi quay
khdng the tuydt ddi khdng cd dp lech tdm; ma saquay
ciia khdi lapng lech tdm dd se sinh ra lac qudn tinh; td
dd, lam cho kdt cau chiu tdc dpng ciia lac kich thich
cd tinh chu ky cadng bde kdt cdu sinh ra dao ddng
theo quy luat ciia lac kich thich.

Trong thdi gian ngdn ddu tien ciia dao ddng cadng
bde cua he ket cdu, tdn tai ddng thdi dao ddng gdy
nen bdi lac kich thich va dao dpng ta do ciia he. Kdt
qua ciia sa hpp thdnh ciia hai dang dao ddng ndi tren
Id rdt phdc tap. Nhung do cd tdc ddng cua lac cdn, sau
mdt thdi gian nhdt dinh (thdng thadng thi khodng thdi
gian ndy rdt ngan), dao dpng ta do hodn todn tdt hdn
ma dat tdi trang thdi on dinh, chi bidn doi theo quy luat
cua lac kich thich. Khi lac kich thich bidn thien theo

quy luat didu hda thi dao ddng cadng bde trong trang
thdi on dinh dd Id dao ddng didu hda. Ndu ta diing B
va phdn biet bie'u thi bien dp vd tdn sd ciia nd, thi
phaong trinh dao ddng cua dao ddng cadng bde trong
trang thdi on dinh dd cd the bieu dat thanh.

X = Bcos et (20) 
Tan sd cua dao ddng nay la tan sd ciia lac kich

thich khdng cd quan he ndo vdi tdn sd dao ddng ridng
ciia he cd. Dp Idn ciia bidn dp B ciia dao ddng cadng
bde cd quan he vdi tan sd dao ddng rieng ciia he, lac
can tdn sd ciia lac kich thich va tri sd cue dai ciia lac
kich thich. Qua dien todn, ta thu daoc:

N G U Y E N H O N G HIEP

mco

1 e

CO

2 \

4n'd

2z52

(21)

a>

Trong dd:

P- Ld tri sd cac dai cua Igc kich thich
n- Ld he sd phan dnh dp Idn ciia lac can.

Kdt qud cua thac nghiem vd nghidn ciru vd ly
thuydt da chdng niinh: khi tdn sd ciia lac cadng bde Id
chenh lech rdt nhidu vdi tdn sd ciia dao ddng ridng thi
bien dp ciia dao dpng cadng bde rdt nhd. Khi 6 tidp
can vdi , thi bien dp B tang rdt nhanh. Khi tdn sd ciia
kich thich 0 chenh rdt it va xdp xi bdng tdn sd dao
ddng rieng , thi bien dp cua dao ddng cadng bde dat
ddn tri s6 cdc dai.

Hinh 12

Khi dd, dao
ddng trd ndn dd
dpi nhdt. Hidn
tapng nay gpi la
cdng hadng. Hinh
12 tren day bieu thj
dadng cong bien
thien ciia bien dd
dao ddng cadng
bde theo bien thidn
cua tdn sd cua lac
kich thich, dapc
gpi la dadng cong
cdng hadng.

taong ong vdi dao
Trong hinh 12, dadng cong

dpng cadng bde khdng cd lac cdn, dadng cong td (2)
den (5) Idn lapt bieu thi mot sd tradng hpp tang to len
ciia lac cdn. Td tren bieu dd, ta thdy rd: lac cdn cdng
nhd, khi cdng hadng thi bidn dp cdng to. Ndu lac can
rat nhd thi trong dieu kien cdng hadng, trade khi dao
ddng dat ddn trang thai on dinh thi he kdt cdu da cd
the' bi pha hoai bdi le dao ddng qua dd dpi.

Khi cd ddng ddt, nha vd cdng trinh chiu tac ddng
ciia lac quan tinh do ddng dat sinh ra ma tao ndn dao
ddng cadng bde. Vi thdi gian dpng ddt rdt ngdn, thanh
phan dao ddng ta do chaa kip tat, cho nen khi nghien
cdu dao ddng do ddng dat gay nen ddi vdi nhd va
cdng trinh, ta phai ddng thdi xet den ca dao ddng ta
do vd dao ddng cadng bde.

6. Khai niem ve dang dao dong

Tren ddy, ta da thao ludn vd dao ddng ciia he ket
cdu cd bac ta do don, chi cd mdt tdn sd dao ddng
rieng. Taong dng vdi loai tdn sd ndy, chi cd mdt dang
dao ddng nha hinh 13 bieu thi.

Dao dpng cua he cd nhieu bac
ta do phdc tap hon dao ddng cua
he cd bac ta do don rdt nhidu, Ket

qua nghien ciru da chimg minh:
trong he ed nhidu bac ta do, tdn tai
nhieu tdn sd dao ddng rieng. Sd
tdn sd dao ddng rieng ciia he bdng
sd bac ta do ciia he. Vi du, trong he
cd n bde ta do, tdn tai n tan sd dao
ddng ridng dapc xdp theo thdta Idn
nhd theo hang dadi day:

CJ < CO2 < . . . < CO, < . . . < OJn

Trong dd, mdt tdn sd nhd nhdt
gpi la tdn sd thd nhdt hoac tdn sd
Hinh 13 cobdn. Cdc tdn sd khdc theo thdta

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gpi Id tdn sd tha 2... tha i,.. thd n - gpi chung Id tdn sd
cao. Tong hpp ciia tdt cd cdc tan sd sdp hdng theo thd
ta Idn nhd dapc gpi Id pho tdn sd dao ddng rieng.

Ket qua nghien ciru cung da chdng minh: taong
dng vdi mdt tan sd co, nao dd, gida cac chuyen vi dao
ddng ciia nhung chat diem ciia he deu tdn tai mdi
quan he ty Id xdc dinh; do dd hinh thdnh mdt dang dao
ddng khdng doi taong img vdi tdn sd co, gpi Id dang
dao ddng. He cd n bac ta do thi cd n tan sd dao ddng
rieng vd tacmg img se cd n dang dao ddng. Dao ddng
thac te ciia he Id dao ddng phdc hpp hinh thanh bang
each cdng n dang dao
dpng dd.

Hinh 14 dadi day Id
so dd dao ddng ciia he
cd 2 bac ta do.

Hinh 15 dadi day la
so dd dao ddng cua he
cd 3 bde ta do.

Dang dao ddng la
chi kieu ddng dao ddng
eua he, khdng cd quan
he gi vdi dp Icfm cua
chuyd'n vi ciia dao
ddng.

Hinh 14

Khi he dao ddng, chuyen vi dao ddng ciia chdt
diem bien thien theo thdi gian. Khi chuyen vi ciia
nhCmg chdt die'm tang hoac gidm deu mdt bdi sd ndo
dd, dang dao ddng ciia nd khdng doi md chi cd mdt
dang dao ddng xdc dinh.

Bdi le trong ket cau thac td khdng trdnh khdi satdn
tai ciia lac cdn, dang dao ddng cao taong ung vdi tdn
sd cao va tat rdt nhanh; ngodi ra bidn dp ciia dang dao
ddng cao lai rdt nhd nen thac sa cd gid tri dng dung
chi Id mdt vdi dang dao ddng phia trade ma thdi. Do
dd, ddi vdi cdc kdt cdu cdng trinh ndi chung, ta chi cdn
xet dang dao ddng thd nhdt Id cd the thda man dp

chinh xdc trong tinh todn rdi. Ddi vcfri mdt sd kdt cdu
cdng trinh quan trpng hoac cao, mdm, ta mdi cdn xet
den dang dao ddng thd 2 vd thd 3.

7. Ap dung phuong phap gdn dung de tinh 
toan chu ky co ban cua he co nhidu bac t a do

Chu ky dao dpng ridng cua kdt cdu phdn anh ddc
trung ddng lac vdn cd ciia nd. Khi xdy ra ddng ddt, dp

\dn eiia lac ddng ddt md kdt cdu phai chiu cd quan he 
vd\ chu ky dao ddng rieng cua nd. Khi tinh todn dao 
ddng eiia kdt cdu, trade tidn ta phdi tinh ra chu ky dao
ddng rieng ciia nd. Ddi vdi he cd bac ta do dan. vide 
tinh toan chu ky dao ddng rieng khdng khd khdn vd
cd the tien hdnh bang each trac tiep dung bieu thdc td
(15) den (18). Nhung trong thac td, kdt cdu cdng trinh
ddu la nhdng he ed nhieu bde ta do hoac bac ta do vd
han, vide tinh toan chinh xac chu ky dao ddng rieng
ciia nd Id rdt phae tap.

Dd' tien tinh todn trong thidt kd cdng trinh vdi muc
dich thac dung, ta thadng dimg nhung phaong phap
gan dimg. 0 ddy, chiing tdi se gidi thieu hai phucjng 
phdp gdn dung de' tinh chu ky co ban ciia dao ddng
ridng ciia ket cdu,

(1). Phuang phap nang luqng

Trdn day da ndi khi he dao ddng ta do, ndu khdng

xet den tae ddng ciia lac cdn, thi ndng lacpng ciia he
khdng bi tieu hao. Trong qud trinh dao ddng, ddng
nang vd thd nang ciia he chuyen hda lan nhau va
tong gid tri ciia nang laong ciia nd khdng doi, tdc la tai
mdt thdi diem bat ky, tong ciia ddng nang U va the
ndng ciia he la mdt bang sd:

U -I- n = constant = hang sd

Khi he dao ddng den vi tri can bang, vi du nha vi
tri C trong hinh 16, he chaa cd bidn dang nen thd
nang ciia nd bang 0; nhung khi dd, van tdc chuyen
ddng ciia chat die'm Id \qn nhdt, vi vay ddng nang ciia 
nd dat tdi gid tri cac dai \J^^. Cdn khi he dao ddng ddn 
vi tri cd chuyen vi cue dai, vi du nha cdc vi tri B vd D
trong hinh 16, van tdc ciia chdt die'm bdng 0; do dd,
ddng nang ciia nd cung bang 0. Nhung khi dd, bidn
dang ciia he Id Idn nhdt; do dd, thd ndng ciia nd dat
tdi gia tri cue dai

Flmax-Td dd ta cd:

U„,ax = n „ ^ (22)

Tdc Id, ddng nang cac dai ciia he dao ddng tai vi
tri can bang bang thd nang cue dai khi he ndm tai vi
tri cd chuyd'n vi cue dai. Can cd vdo ly le dd, ta cd the
tinh ra tdn sd co bdn vd chu ky co ban ciia he. Od
chinh Id phacmg phdp ndng lacpng.

Ddi vdi he cd bac ta do don nhu hinh 16 bieu thi,
gia sd khdi lapng ciia chdt diem la m, td cac bieu thdc
(10) va (11), ta cd chuyen vi dao ddng x,,, va van tdc
v„) bdng:

x„) = A cos tot
V|„ = - coA sin cot

Tri so cac dai ciia chuyd'n vi vd tri
sd cac dai ciia van tdc lan lacpt Id:

X - A
Vmax = WA

Td mdn vat ly ta bidt, dpng ndng
bang 1/2 tich ciia khdi lapng nhdn
vdi binh phaong ciia van tdc; do dd,
ta thu dapc tri sd cue dai ciia ddng
ndng bang:

1 ,

U„

-

—mv_

=

—m

[coAf

Hinh 16

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T d mdn ca hpc kdt cdu ta lai bidt, thd nang ciia he
bdng cdng dapc sinh ra la do tdi trpng tac ddng len kdt
cdu Idm tren chuyen vi tTnh hpc tao nen. Ndu ta cho
rang bidn dp dao dpng khi he dao dpng la chuyen vi

tinh hpc sinh ra ha\ trpng lapng W cua chdt diem thi tri 
sd cac dai cua the nang Id:

n.

\mgA

Thd vdo bieu thire (22) ta c6

— micoAY =

-2 ^ ^ -2

-m{coAy = —mgA

Vdy: 0) =

(24)

(25)

(26)

Ddy chinh la cdng thdc tinh todn tdn sd vd chu ky
dao dpng ridng ciia he cd bac ta do den ma ta da riit
ra bdng phaong phdp ndng lapng. Do dd trong bieu
thdc trdn, A chinh Id chuyen vi tTnh hpc A,;„f, do trpng
lapng ciia chdt die'm sinh ra, ndn bieu thdc tren day
thac chat Id bieu thac (18) trong bdi dd ddng trong sd
tap chi thdng trade.

Tidp sau ddy, ta lai dung phaong phdp ndng lapng
de' riit ra cdng thdc tinh todn tan sd vd chu ky dao
ddng rieng cua he cd nhidu bac ta do.

Hinh 17 dadi day bieu thi mdt he ddn hdi cd n chat
diem. Ta dung m;, x,,^,,, x, Idn lapt bieu thi khdi lapng,

chuyen vi dao ddng vd bidn dp dao ddng ciia chdt
die'm thd i. Gid thidt khi mdi bdt ddu dao ddng, cac chat
diem deu d vi tri khdi ddu cua bien dp ciia chiing, van
tdc ban ddu Id 0 vd cdc chdt diem ddu thac hidn dao
ddng didu hda vdi tdn sd thi phaong trinh dao ddng va
van tdc ciia khdi lapng thd i cd the bieu thi nha sau:

Xi(Mj=XiCOS0)t 
'i(M) = HoXiSin (ot

Can cd cdc bi§u thdc (23), (24) ta cd ddng nang

cue dai ciia chdt diem thd i la —m, (cxc,) , thd nang

cue dai Id ~\tn^g)x^. Odng nang cue dai U^^vk thd 
nang cue dai U^^ phan biet la tdng ciia dpng nang 
cue dai vd thd nang cue dai ciia chdt diem, tdc la:

(27)

(28)

Cho hai bi^u thdc trSn bang nhau, ta thu dapc tdn

s6 dao dpng ri§ng cua hd Id:

CO =

IgYjn^

I.m,x^

hoac CO = (29)

Chu ky dao ddng ridng co b^n Id:

T. = In,

(30a)

Day chinh la cdng thdc tinh tan sd
dao ddng ridng thd nhat hoac chu ky
dao ddng ridng ca ban ciia he nhieu
bac ta do; trong dd, Wj la trong lapng
ciia chdt die'm thd i. Khi dung phaong
i , phdp nang lapng de tinh chu ky dao
I T ddng rieng, ta can phai cd bien dp

ciia cac diem, tdc la phai cd dadng
cong dang dao ddng ciia he mdi cd
the' sd dung cdng thdc (30a). Oieu dd
ddi hdi phdi trade tien gia dinh dacbng
cong dao ddng rdi mdi tinh toan. Kinh
nghiem thac tien chi ra rang: khi tinh
chu ky CO ban ciia dao ddng rieng
CLia he, chi cdn dadng cong dang
dao ddng gid dinh cd the thda man dieu kien rang
budc ciia diem mut thi hinh dang ciia nd dai the gan
xdp xi vdi dang dao ddng thap nhdt ciia he, dp chinh
xac ciia chu ky dao ddng ridng tinh dapc bang phaong
phap nang lapng kha cao, hoan toan cd the thda man
nhu cau thiet ke ddi vdi cdc cdng trinh thac te. Khi dd,
ta thadng lay dadng cong chuyd'n vi ngang ciia cac
chat die'm dadi tdc dpng nam ngang ciia trpng lacpng

de' Idm dUdng cong ciia dang dao dpng. Nha vay, bieu
thdc (30a) cd the vidt thanh:

Hinh 17

V w,A';. (Zw A'

gSw,.A,

Zw,A_

(30b)
Trong dd:

V\/|: La trpng lapng cua chat diem thd i.

A,: Chuyd'n vi ngang ciia chat diem thd i khi gia
thiet cdc lac nam ngang ciia nhdng W, tac dpng len
cdc chat diem tac?ng dng.

(2). Phuang phap khdi luqng quy ddi

Dimg phaong phdp khdi lapng quy doi de tinh chu
ky CO ban ciia ket cdu Id mdt phaong phap tinh toan
gan diing hay dapc dp dung khac. Khdi niem co ban
ciia nd la: khi tinh toan chu ky co ban ciia dao ddng
rieng ciia mdt he nhieu bac ta do, ta dung mpt he cd
bac ta do don de thay thd, lam cho chu ky dao ddng
rieng cua he cd bac ta do don nay bang hoac xap xi
nhdt vdi chu ky co ban ciia dao ddng ridng ciia he ban
ddu. Khdi lapng ciia he cd bac ta do dem ndy dapc gpi
la khdi lacpng quy ddi (hoac khdi lapng laong daong,
khdi lapng thay the') dimg M^,;; bieu thi. He cd bac ta do
don ndy vd he ban dau gidng nhau hoan toan vd hinh

thdc ket cdu, didu kien rang budc va dd cdng... chi cd
mdt didu Id khdng trpng lapng. Nd Id mdt he chat diem
don cd khdi lapng quy ddi.

Tri sd Mqj cua khdi lapng quy ddi cd quan he vdi vi
tri ciia nd. Ndu vi tri tren he ciia nd dd daoc xac dinh
thi tri sd taong img ciia M^j se dapc xdc dmh theo.
Theo kinh nghidm, tdt nhdt nen ddt khdi lapng quy ddi

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tai diem cd chuyd'n vi cac dai khi dao ddng thi se

thuan Ipi nhdt.

Tri sd cua khdi lacing quy ddi M^^ tinh dapc daa

theo quan diem ndng lapng khdng ddi; tac Id ddng

nang cac dai ciia he cd bde ta do don thay the he ban

dau khi dao ddng bdng ddng ndng cue dai ciia he ban

ddu.

Vi du, khi tinh chu ky co ban ciia he nhidu bde ta

do trong hinh 17, ta cd the thay thd bdng he cd bac ta

do don bid'u thi trong hinh 16; he ndy cd khdi lacing

quy ddi M^^, cdc yeu td khdc gidng hodn todn nha he

ban ddu. Can cd vdo ddng ndng cac dai ciia hai he

[(xem bieu thdc (23) va bieu thdc (27)] bdng nhau, ta

cd the thu dapc bieu thdc dadi day:

Vdy: M

qd

I.m,xf

(31)

Trong dd x^,: Chuyen vi cue dai ciia vi tri khdi

lapng quy ddi.

C6 dapc khfli lapng quy ddi rdi, thi ta c6 t h i tinh

chu ky CO ban cua no theo he cd bac ta do dan,

nghTa la:

T = ITT^JM^ (32)

Vidu 1: Cd mpt thanh cdng son ddng chdt vdi tidt

didn ddu khdng ddi bilu thi trong hinh 18a. Chidu ddi

thanh Id I; dd cdng khdng udn Id EJ; trpng lapng tren

mpt don vi chidu dai la q (khdi lapng tren mpt don vi

chidu ddi Id —).

g

Tinh chu ky dao dpng rieng T.

^f

9

- 1 °

.?5^ •-12

T

(^')

(b)

(c)

Hinh 18

Giai. Phdn deu thanh cdng son ra 5 doan. Td dd,

ta thay thd thanh cd bac ta do vd han ban ddu thdnh

mdt he cd nhieu bac ta do vciri 5 khdi lacpng tap trung

nha hinh 18b bieu thi. Nay ta Idn lapt tinh chu ky dao

ddng ridng ciia nd theo phaong phap ndng lapng vd

phaong phdp khdi lapng quy ddi nha sau:

Trpng lapng ciia mdi chat diem Id W^ --qt.

Ta l^y dutfng cong dfl v5ng cua thanh cflng son

chiu tdc ddng ciia trpng lapng ban thdn phdn bo d^u

Idm dudng cong dang dao ddng tuc Id:

qi

4 f

8EJ

3t 3e' e

i \

Bi^u thue tr§n Id dadng cong dp vong ciia thanh

cdng son dudi tdc ddng ciia trpng lutmg ban thdn

phSn b6 d^u - Cd th^ tra cdu trong mfln Sdc b4n vdt

Ii3u ciia chudng trinh dai hpc. Ta Idn lutJt mang cdc

1 3 5/" 7 9

tri s6 V = —L — L — , — (.vk —(. th6 vdo bigu

10 10 10 10 10

thuc tr§n, thi ta c6 th^ tinh ducc ehuydn vi ciia cdc

ch4t diem nha sau:

r i V

^ =

qt

8EJ

qt

SEJ

qt

ll_Li _l|i

3U0J 3U0^

+ 2 —

" i r ^ y _ 4 r 3 V

loj 3

-I-SEJ

[0,0187]

+ 2

10 8E/

1 ^

8£y

1 ^

8£/

If 5

3110

V i O y

4 r 5

10 SEJ

[0,1468]

-I-A <; -I-A

+ 2

vlOy

SEJ

[0,332]

'\(

31

' 7 ^

loj

'

'i

3I

/ v V

+ :

)

UO

<7>

,10;

3

-1-8EJ

[0,532]

" i r 9 ^

3I10;

.2(1

' 4f9^

3I1O;

T

3

+

SEJ

[0,933]

- Niu ta dung phuong phap nang luqng de tinh

toan, trade tien phdi tinh ra:

l^.x!=-ql

'ql^^

SEJ

(0,0187)'+(0,1468)'+'

+ (0,332)'+(0,532)' +

+ (0,933)'

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Y^w,x^=~qi

'qt^

f „D^ \

qi

SEJ

\SEJ

[1,9625]

0,0187 + 0,1468 +

+ 0,332 + 0,532 + 0,933

Mang cdc ket qua tren day thd vdo bieu thdc
(30a), ta cd:

T^ln.

In

TW,:

gTW,x,

2n

1,282

l,9625g

^qt_^

ySEJj

n952t

3,5 V EJ

So vdi tri s6 chinh xdc

2n

3,515

m

— = 1,7987^'

EJ

thi sai sd

Id 0,43%.

- Niu ta diing phuang phap khdi luqng quy dd'i de 
tinh toan, trade tien ta phai tinh ra khdi lapng quy ddi 
Mqj. Gid sd khdi lapng quy ddi dapc bd tri tai ddu miit
tren cua cdu kien nha hinh 18c bid'u thi, chuyen vi tai
ddu mut tren Id:

" SEJ

Vay ta co:

id 2

4 > ^

mi

q£

SEJ

[1,282]

^SEJ J

= 0,256mi = -mi

4

Trong do, m la khdi lapng ciia mpt dtjn vi dai cau
kien.

1 e'

Vay: T =

ITTJM.S

=

2nJ-m£-= 2;r.j~t

2n

3,47

£'

r = i 811^^

—

So sdnh vdi tri sd chinh xdc thi sai sd Id 1,28%.
Mdt didu quan trpng cdn ghi nhd Id vide tinh todn
vi du tren ddy theo phaong phdp khdi lapng quy ddi de
giai thich rang: Ddi vdi nhd mpt tdng cd khdi Iddng
phdn bd taong ddi ddu theo chidu cao, ndu dd la mdt
ngdi nhd trdng ben trong hoac nhd cdng nghiep mdt
tdng thi khi tinh todn chu ky dao dpng rieng ciia he kdt
cdu, ta cd the' mang 1/4 tdng khdi lapng ciia nd dat tai
diem mut tren dinh cot vd tinh todn theo he cd chdt
diem don Id dapc.

' i k

c it

'W//

»l.io

M 
yi dy 2. Cd m0t thanh cdng son ddi I, khdng 
trpng lacpng; dp cimg khdng udn cua tidt didn thanh

Id EJ. Tai didm C cdch ddu mut ngdm Id — ^ , cd mdt

5

khdi lapng tap trung m. Tinh khdi lapng quy ddi tai
ddu milt A ciia thanh cdng son (Xem hinh 19)

Giai: Dadng 
cong dan hdi ciia
thanh cdng son khi
cd mdt don vi lac
ndm ngang tac
dpng tai ddu miit
cdng son - dapc
Idy lam dadng
cong dang dao
ddng, tdc la gia

thidt: (UJ (1^)

X =

W-/)

Hinh 19

6EJ

Thi chuyen vi tai ddu miit tren la:

3EJ

Chuyen vi ciia die'm C la:

X , = •

6EJ

f,

3e -i

\-1/

5

J

6EJ

48 64

25 125

e =

1

- X 1

6EJ 125

The vao bieu thdc (31), ta thu daoc:

i

^ . . -

Z-,-f

m

1 176

6EJ 125

^ ^ 3 ^

3EJ

176

250 m = 0,496w « 0,5w.

Vi du ndy giai thich rdng: khi ddm cdu true ciia
. 4

nhd cdng nghidp mdt tdng d vi tri gdn - chidu cao

ciia cdt, thi ta cd thd Idy tdp trung - khdi lapng ciia
cdu trgc dat tai dinh cdt; rdi lai cdng vdi khdi laong
ciia mdi de tinh chu ky dao ddng rieng ciia nd nhu

hd cd bac t a d o don,

Tavide phdn tich hai vi du trdn day, ta cd the biet
rang: khdi lacpng quy ddi Id khdi lapng ciia he ban ddu
nhan vdi mdt he sd mdi thu dapc. He sd nay goi la he
sd quy ddi taong daong ddng lac ciia he lan lapt cd gia
tri bdng 0,25 vd 0,5.0

</div>

Dao động của nhà và công trình khi có động đất

<b>DIEN</b>

<b> DAN KHOA H O C</b>

<b> CONG NGHE </b>

<b>^ DAO D O N G CUA NHA VA </b>

<b>C O N G T R I N H KHI C O D O N G DAT </b>

<b>N G U Y E N H O N G HIEP </b>

<i>mco </i>

1

<i><b>e </b></i>

<i>4n'd </i>

<i>a> </i>

<b>1 , </b>

<i><b>U„ </b></i>

<i><b><sub> —mv_ </sub></b></i>

<i><b><sub> —m </sub></b></i>

<i>[coAf </i>

<b>n. </b>

<i>\mgA </i>

<i>— micoAY = </i>

-2 ^ ^ -2

<i>-m{coAy = —mgA </i>

<i>IgYjn^ </i>

<i>I.m,x^ </i>

<i>T. = In, </i>

<b>V w,A';. (Zw A' </b>

gSw,.A,

Zw,A_

tai diem cd chuyd'n vi cac dai khi dao ddng thi se

thuan Ipi nhdt.

Tri sd cua khdi lacing quy ddi M^^ tinh dapc daa

theo quan diem ndng lapng khdng ddi; tac Id ddng

nang cac dai ciia he cd bde ta do don thay the he ban

dau khi dao ddng bdng ddng ndng cue dai ciia he ban

ddu.

Vi du, khi tinh chu ky co ban ciia he nhidu bde ta

do trong hinh 17, ta cd the thay thd bdng he cd bac ta

do don bid'u thi trong hinh 16; he ndy cd khdi lacing

quy ddi M^^, cdc yeu td khdc gidng hodn todn nha he

ban ddu. Can cd vdo ddng ndng cac dai ciia hai he

[(xem bieu thdc (23) va bieu thdc (27)] bdng nhau, ta

<i>cd the thu dapc bieu thdc dadi day: </i>

<i>Vdy: M </i>

<i>I.m,xf </i>

Trong dd x^,: Chuyen vi cue dai ciia vi tri khdi

lapng quy ddi.

C6 dapc khfli lapng quy ddi rdi, thi ta c6 t h i tinh

chu ky CO ban cua no theo he cd bac ta do dan,

nghTa la:

<i>T = ITT^JM^ (32) </i>

<i>Vidu 1: Cd mpt thanh cdng son ddng chdt vdi tidt </i>

didn ddu khdng ddi bilu thi trong hinh 18a. Chidu ddi

thanh Id I; dd cdng khdng udn Id EJ; trpng lapng tren

mpt don vi chidu dai la q (khdi lapng tren mpt don vi

chidu ddi Id —).

<i>g </i>

Tinh chu ky dao dpng rieng T.

<i>^f </i>

9

<sub>T </sub>

<i>(^') </i>

<i><b>(b) </b></i>

<i>(c) </i>

<i>Giai. Phdn deu thanh cdng son ra 5 doan. Td dd, </i>