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 th[r]
Trang 1^ 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
NGUdi XAY DUNG SO THANG 5 • 2011
Trang 2gpi 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 ,
Hinh 16
NGUdl XAY DUNG SO T H A N G S • 2011
Trang 3T 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:
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^
Chu ky dao ddng ridng co b^n Id:
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
NGUdi XAY D U N G S O T H A N G 5 - 2011
Trang 4tai 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 I.m,xf
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
k!
- 1 °
(^') (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
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)'
NGUdi X A Y Dl/NG S6 T H A N G 5 • 2011
Trang 5Y^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,:
1,282 l,9625g
^qt_^
ySEJj
n952t
3,5 V EJ
So vdi tri s6 chinh xdc
2n
3,515
m
— = 1,7987^'
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
4
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
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
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
NGUdi X A Y D U N G S 6 T H A N G 5 • 2011