Vẽ Kỹ Thuật Xây Dựng (NXB Giáo Dục 2003) - Nguyễn Quang Cự, 219 Trang

Rieng cac tieu chuan lien quan den vi~c thiet l~p cac ban ve xay dl,ingC* dttQc in Trong qua trl.nh su d1,mg, nhieu tieu chuan da duQc soat xet, bO sung, sua doi hoi;ic each chia d6i kh6

TR UNG T AM

TH ONG T I N -TH U ' Y I ;:N

HT

E>OAN NHU' KIM - DU'dNG TIEN THQ

eoAN NHU' KIM (chu bien)

• (£)§ dLtQ'C h(>i d6ng man hQC cua 89 Giao dl:JC va f)ao t~o thong qua

(Taiban Ja'n thti sau)

NHA XUAT BAN GIAO Dl)C

Sll LL9t08L :

LCH NOI DAU

Giao trznh "VE Ki THUAT ~AY DlfNG" duqc bien soqn theo chuang

trznh cdi each giao dlfc cila B¢ Giao dtf-c ua Dao tqo ua dZ!a tren co sa

cila giao trznh "VE Ki THUAT XAY DlfNG" duqc xuat ban tan dau

nam 1970 (do Doan Nhu Kim, Nguyen Quang Cf!,, Duong Tie'n Tlu; ua

Vu Tr9ng' Hung<•) bien soqn)

Giao tr'inh nay duqc dung lam tai li~u gidng dqy ua h9c tqp cho sinh

uien cac nganh c6ng trznh

Sach gom hai nl)i dung chinh :

1 - Nliung khai ni~m co bdn ue ve ki thuqt

2 - ve xaydZ!ng

Cac n¢i dung tr'inh bay trong chuang 5 (H'inh bie"u dien noi tren bdn

ue xay dZ!ng) ua chuang 12 (Bdn ue c6ng trznh dat) ci'in duqc lZ!a chQn

de gidng dqy cho phil hqp uoi chuyen nganh dao tgo

Trong Zan tai bdn nay, cac Tieu chuan moi c6 lien quan toi bdn

ue ki thuqt deu duqc chung toi xem xet ua trinh bay lgi cho phil hqp

uoi Tieu chuan da duqc UBKHNN ban hanh

Trong qua trinh bien soqn ua chinh li chung t6i da nhqn duqc

nhi'eu y kien nhqn xet quy bliu cila cac dong nghi~p Chung t6i xin

chan thanh cam an ua mong tilp tlfc nhqn duqc nhieu y kien cua cac

bqn d9c de giao trinh duqc hoan thi~n han trong Zan tai ban sau

Cac tac gU1

(•) j Vu Tn;mg Hung j

MO DAU

Nha nhfrng ban ve nay nguai can b(i

kl: thu~t the hi~n duqc cac y do thiet ke

cua minh len to giay ve va tu do se dU<;Ic

Hinh ve da co tu rat lau, dung de mo

con nguai (H 0-1) V oi sv ph at trie n cua

cong trinh xay d1,1ng, may moe ngay cang

trie'n do yeu ciiu cua san xu at va tren co

SO CUa nhitrig thank tlf,U ve cac phuong

phap bie"u dien

Hi~n nay tat ca cac cong trinh, may

moe du to, du nho, truoc khi thi cong,

che t~o deu duqc ngucri ta ve va tfnh toan

vi~c ap d1,mg no ngay cang sau r(ing trong

den S\1 thay d6i to l{!n ve cac phUong

Ve may la to hqp cac phuong ti~n va

phuong phap dam bao tlf, d¢ng h6a qua

trinh xu li va luu trit th6ng tin ve Mng

may tinh di~n tzi Hien nhien ve may la

( •) Computer <~ided design viet tM Iii CAD

HiNI-1 0-L Hinh ve nhli sim vii dmh danh trong tren trong d6ng NgQc Lii each day glin 3000 nam

thong tt;t d(>ng hoa thiet ke va no tra thanh doi tugng ap dl,mg va nghien cuu cua nhung

thu~t nhu· chua TMin Quang (Keo), Van Miet1, thap c6 chua·Tuc M:;~.c Cac c6ng trl.nh

hinh thuc khac rihau de thiet 1:1lp cac ban ve

HiNH 0-2

· Canh Thang Long ·the ki ihu XVII· ·

~huan Ve ban Ve Cd khf dttc;1C in chung VaO m(it t~p '·' ·r · · 1 · , ·" ' • ,

Cac tieu chuan ve ve xAy

rieng "Ban ve xAy dl,trig"

Vi~c nuoc ta tro thanh

thanh vien chinh thuc ctia

Ban thuong tn;cc ve tieu

chuan hoa thu¢c H¢i dong

tuCing trq kinh te (C3B) nam

T6ng C\J.C Tieu chuan do luang

· chat luqng nuoc ta duqc cong

nh~n la thanh vien chinh

thuc ctia T6 chuc quae te ve

tieu chuan hoa (I.S.O) la

nhung nhAn to gmp cho

phat trien tot

HINH 0-3 B:'m d6 tinh Bien Hoa

mon ve xAy dl,tng co lien quan ch?t che voi man Hinh h9c h9a hinh Cimg voi man h9c

chuan bj cho sinh vien h9c tot cac man h9c chuyen nganh, va nguqc l~i cac man chuyen

d~ng va cau t~o ctia v~t the

Phctn I : Nhung khai ni~m cCI ban ve Ve ki thu~t, trong do trQng tAm neu len nhung

PhCtn II: Ve xay dljng, trong do neu len cac quy d!nh ve ve cac ket

true, cau duang, thuy lqi va cong trinh dat)

dao t:;to ki su, kien true su trong

vi~n thiet ke, cac b(> mon ve ki

thu~t cua cac truang d:;ti h<;>c da bat dau nghien cuu ve ve may

va ap dl,lng cac b(> chuong trinh

gilmg d:;ty, nham chuB:n bj cho sinh vien kha nang di vao tv d(>ng hoa

(TDHTK - CT)

Trang cong tac thiet ke, ho:;tt d(>ng ve cliiem tu 30 den 70% sue

vi~c nghien cuu cac phuong phap

thiet ke

Thiet ke va ve bang MTDT cho

ki thu~t, danh gia cac ket qua thiet

ke, stta d6i nhanh va chfnh xac, giai

·!?, ::r:: [ l'

1 ~2.4 H()p compa

2 - Compa do ;

3 - Compa quay vong tron nhO ; '

4 - Compa do chfnh xac ;

7 - Dau mvc cua compa ;

sao ~ho no nam trong m~t phling thling

dung, bUt hC1i nghieng ve phfa chuyen d(>ng

cua but

but nay co the dung de ve cac net thling,

ThOng thttong ngttoi ta dung cac bUt kim s6

phling to giay ve (H 1-12) Khi ve cac vong tron co dttong kfnh Ion he1n 150mm thl

dung can n6i de keo dai nhanh compa mang dau chi (hay mvc) ·

12

lliNl-1 I-Re HlNH 1-9

-~ ~~ -- ~ - HINI-1 1-10

HiNH 1-11

- Compa quay vong tron nh6 : (H 1-14) khi quay dung ba ngon tay, ngon tro an

1.2.5 Thu:oc cong (H 1-15) dung de to d~m cac duong cong kh6ng ve duqc bang

compa

HiNH 1-14

1.2.6 Thu:<lc 16 (H 1-16), de nang cao

thuoc lo de viE'h chu, ve m<?t so duong cong nhu

(da tieu chwin hoa) ho:;tc cac lo tron, lo elfp v.v voi nhieu ca khac nhau Khi dung

1.3 CACH TO D!M BAN VE

TrE:m blm ve, trudc tien cac hinh ve duQc ve mo bang but chi cllng Sau khi kiem tra

ban ve

a - Cac duong tr1,1c, duong tam ;

b - Cac duong baa quanh thay, t6 thea ·thll tv

- Cac duong tron va cung tron ;

- Cac cung luQn ;

- Cac duong bang : to tti !ren xuong dudi ;

d - Cac duong giong va duong ghi kich thudc ;

g - Khung ban ve va khung ten

h - Tay xoa cac net thtia va xen ria to giay ve

- Neu ban ve can to mau ma net ve l1;1i can to mljc, thi phai to mau trudc khi to net ve

CHUONG 2

NHUNG TlEU CHUAN CO BAN

d!nh nay duqc Nha nude thOng qua va ban hanh gQi la cac tieu chuan nha mtdcC*)

(*) • Tieu chu~n Nha nuflc du<;c ki hi~u bilng cac chl! TCVN (viet t~t cua chfl Tieu chu&n Vi~t Nam) kem theo d6 ghi .so tieu chu&n vii nam ban hilnh tieu chu&n d6

Rieng cac tieu chuan lien quan den vi~c thiet l~p cac ban ve xay dl,ingC*) dttQc in

Trong qua trl.nh su d1,mg, nhieu tieu chuan da duQc soat xet, bO sung, sua doi hoi;ic

each chia d6i kh6

Ion hon ke voi no

bang each d9c d6i

Khung ban ve : Moi Mn ve deu phai co khung, do la m9t hl.nh chf:t nh~t ve bang

t.rai, khung ban ve each mep to giay 25mm hoi;ic 30mm CH.2-2a)

( •) Trong phiin II

Khung ten : Moi ban ve phai co m¢t khung

ten, d6la m¢t hlnh chli nh?t ve bang net Win·

cua ban ve, sat vai khung ten N¢i dung va

kich thuac cua khung ten do tung co quan thiet

ke quy dinh

dung trong nha t.ru0ng (H.2-2b)

J- ghi ten him ve -1- <.:hlr ki ,cllil ngLitli kit111 lra

2- ghi tri sri <.:lti ti It; dLing tr"t'n h::m vc 'i- ghi len tn1<1ng l<'lp v:·, ien ngLirli vc

3- ghi ng;:,y vc xong 1,- ghi s(i thtl tV ct:w h:?m ve

di~n do

di~n trong cac day sau :

(I : 40)

I : 10°

100 : l

A

T L 2 : 1

tren hl.nh ve tach

- Doi khi m(>t so hl.nh kh6ng the ve theo

dinh tan tren ket diu thep Khi do cho phep

vegan dung

B A Tren hl.nh 2-4 la m(>t thuoc ti 1$ chinh

vi do, phan ben trai diem 0 ve cac duong xien, dau mut cua chung each nhau 1/10

987651;3210 2 don vi do Trong tam giac vu6ng OAB,

HlNH 2-4

Thtt<'lc ti It;: chinh x{tc Ben tr{Ji diCm 0 Ia thiiy co cac dtfdng xien ; ti:t cac tam gi{tc

d6ng d<:~rig AOB, A10Bt, A20B2 ta th:l'y day cua m(it ·tam giac

' 1

ruto do khac day etta tam giac kt'! tit'!p m(it do;,m bang 100 do;,m

I d<ln vi vi dav AB ctta tam gi{tc lrln nhiit chi bAng- c(ta docm lO

d<ln vj Mu6n do m<)t dn::m tren hirih hitu di0n, dtmg compa do

!{iy do::m d<'1 d:)t len tren thti<'lc ti 1¢ dQc then m(it dtlflng nAm

ngang s:tn cho 111(11 d::iu kim nAm tren 111(11 Lhiflng th?.ng d[tng

ben ph;ti diCm 0 c(m dilu kia n:'im tren 111(11 dttilng xien Tren

hinh 2-4 dn,m MN e<i chit''ti d~ti 1::1 1.74m n6.t do:.m eel sc'l 01

c~nh goc vu6ng AB dai bang l/10 don vi

do Do tinh chat cua cac tam giac dong

9/10 AB (tuc 9/100 don vi do), 8/10 AB

la 1/100 don vi

2.3 CAC NET VE

dang va cong dt,mg khac nhau Vi$c quy d!nh cac lo;;ti net ve nham lam cho cac hinh

TCVN 8 -1993

Bdng 2-1

Al Cc~nh thiiy dl!Clng bao thiiy

A3 Khung t:i:in ve, khung ten

Bl DLIClng dong lhiClng d~n, lhiClng kich thl!dc

B Net

B3 DliClng gl;lch g<Kh tren mi;it dt

134 OLIClng chiin rcn thily

-c Net dLII - - - - C~;~nh khwit, dLIClng b;;o khu&t

-02 Dlldng tam CUa vong tron

E Net dt , Danh ct&u vj tri CLICJ mi;it ph~ng dt

~

FJ DLIClng dt lla hinh bieu ctien

F Net IL!<:Jn s6ng ~ F2 chieu khi kh6ng dung DLIClng phan each gill;; hinh cih va hinh tr~1c d6i x(tng lam

dlldng phan each

G Net dich d~c DLIClng dt lla dili hinh bieu lMn

¥

HI DL!Clng bao CLia b(l ph:;in ru1m phi;; trlldc

H Net g~ICh h;;i ch&m manh mi;it ph~ng dt

HZ Out1ng tr0 ng tam H3 OLtClng bao cu;; chi tiet tru6c khi hinh thimh

va lay trong day kich thuoc sau : 0,18 ; 0,25 ; 0,35 ; 0,5 ; 0,7 ; 1 ; 1,4 va 2mm

~ Khi hai hay nhieu net khac lo~i trimg nhau thl phai ve theo thu tl,i uu tien nhu sau:

lien manh (H 2-6)

lo~i net nay bang m(lt g~ch ngan, manh ;

bieu dien ChO g:;ip nhau cua hai net dut phai ve cac

net g~ch cat nhau Neu net dut Ia phan keo dai cua net

de M (H 2-7)

- Duong dan lien quan den m(lt phan tu nao do duc;1c

- Rieng tren cac ban ve cong trl.nh, cac duong bao

thay nam phfa SaU m:;it phang cat duc;1c ve bang net lien

d~nh de cho de dQC, d~p mat va tranh nham Ian

Co hai kieu chu chfrih :

2.4.1 Chu ki thu~t

nghieng 75° ho?.c thling dung

- Kho chu va chu so duqc gQi theo chieu cao (h) cua chu hoa Co cac kho chu sau

14 ; 10 ; 7 ; 5 ; 3,5 va 2,5 (mm)

- Chieu r(>ng cua chu hoa va chu so noi chung bang 6/10h

- Chieu r(>ng cua chu thubng noi chung bang 5/10h

_;

tren cac hEm ve xay dl,ing (theo TCVN 2233 - 77)

a) Kie'u chu gay

net dqm (H.2-11)

chu nay la chu viet

dvng, deu net Be

r(>ng cua chu va so

chieu cao chu Kieu

chu nay dung de ghi

ten cac ban ve, cac de

b) Kie'u chil mi thuqt (H.2-12) D~c diem cua kieu chu nay la chu viet dvng, co net

HiNU 2-12

N goai ra kie u chu nay con duqc dung de viet cac con so kich thtiC:Jc, viet thuyet minh

ki thu~t Khi do chu dti<;1C viet deu net (net cua ngoi

2.5 GHI KICH THU'OC

ban ve dtt<;Jc de dang, tranh m9i nham Ian

'·

2.5.1 Nhung quy djnh chung

- Khi ghi kich thuoc tr€m hinh bieu dien, noi chung phai tien hanh nhu sau :

• Ve duang dong kich thuoc

• Ve duang kich thuoc

• Ghi con so kich thuoc

- Moi kich thu6'c chi ghi m(>t Ian tren ban ve Doi v6'i ban ve xay dt.mg cho phep ghi l~p l~i m(>t so kich thu6'c khi can thiet

Neu ban ve dung don v! d(> dai khac thi phai ghi chu(')

so kich thu6'c

Du6'i day trinh bay cac quy d!nh co lien quan den duong dong, duong ghi kich thu6'c

va cac con so kich thu6'c

2.5.2 Dl1ong dong va dlt(mg kich thl1dC

(•) · Xem cite ha~ ve thLIY l<1i, chL!dng I I

hinh bieu dien No du<;Jc ve bang net lien manh va

t.hfmg du<;Jc ve vuong goc voi duong kfch thuoc (H 2-13) Duong dong cua kich thuoc cung tron du<;JC ve VUong goc VOi day cung chan cung tron

Hi.NH 2-14

do (H.2-14a) Dt:tong dong cua kich tht:toc goc la dt:tong 25

keo dai hai c:;mh cua goc do (H 2-14b) Cho phep dung

dt:tong dong Mui ten phai thuon, nh9n, dai khoang

- Khi dt:tong kich tht:toc qua ngan, kh6ng du eM ve mui ten thl cho phep dt:ta cac

hl.nh cat va hl.nh chieu thl dttong kfch thttoc dtiQC ke qua tr\].C doi xung CUa hl.nh mQt

( •) Khi d6 tren tn,1c d6i xiing ngUdi ta thUdng ve them hai dm;~n th~ng nho song song va vuong g6c v6i tnfc

nay, (H 2-18)

HiNH 2-20

- Trang truong hqp hinh ve du(;!c cat lia thi duong kich thuC1c v:in duqc ve lien net va so do kich thudc la so do toan b(> chieu dai (H 2-20)

- Neu duong baa cat ngang qua mui

- Tren ban ve xay dl,ing cho phep thay mui ten bang cac do;;tn g;;tch xien 45° va

HINH 2-21

2.5.3 Con so kich thuoc:Dung de bieu th!

gia tr! thvc cua kich thudc, no kh6ng_ ph\1 thu(>c

- Con so kich thuC1c luon duqc ghi phia tren,

vao khoang giUa cua duong kich thudc

Doi vC1i kich thuC1c chi d9 dai, huC1ng ghi con

so ph\1 thu(>c vao d9 nghieng cua duong kich

thuC1c so vC1i huC1ng nam ngang cua ban ve (H

2-22) Cac ducmg kich thuC1c co d9 nghieng

HiNH 2-22

con so kich thuC1c duqc viet ngang nho m(>t duong dong g:iy khuc

"')

HINI 1 2-23

2Lf00

"1 ' ghi cac con so kfch thuC1c dai

- Doi Vdi cac kfch thudc goc, huC1ng ghi con so · kich thuC1c chinh la huC1ng ghi cua con so kich thuC1c dai co duong k.lch thudc vuong goc vC1i phan giac cua goc can ghi kich thudc (H 2-24)

I-fiNI-1 2-2-+

- Khong cho phep bat ki duong net nao

cua ban ve cat qua con s6 kfch thuoc

(H 2-25)

- Cac con s6 kfch th uoc cua cac kfch

- D6i voi cac phan tli gi6ng nhau va

thuoc cua chung nhu tren hl.nh 2-26

hinh 2-28 ·

HiNII 2-28

b) Ban kinh : Doi vi'Ji cac cung trcm co goc C1 tam nho bon 180° thl ghi kich thui'Jc

c.ua ban kinh Trtti'Jc con so kich thui'Jc cua ban kinh co ghi chu R (chu hoa) Duong

vao cung trcm do (H 2-29a)

so kich thui'Jc C1 ngoai, (H2-29b,c)

- Neu cung tron co ban kinh Ion va tam nam ngoai giiri

lam- duong kich thui'Jc (H 2-30) Khi do tam cua cung tron

Ia gia d!nh

c) Hinh vuong : Trtti'Jc con so kfch thui'Jc canh cua hl.nh

De phan bi~t phan m:;it phling vi'Ji m:;it cong, thuong dung

ve chan doc (H 2-33a,b) ;

Khi ghi d¢ cao tren m?t bang cua cong trlnh, con so chi d¢ cao duqc d?t trong m¢t

2.5.5 Truong hqp d;;tc bi~t

- Tren cac b:'m ve SCI do ket cau xay dl,tng (thep, go ) va tren hinh ve tach cac c;.ot

thep cua ban ve ket cau be tong cot thep, cho phep kh6rig ve duC:Ing dong va duC:Ing kich thuoc rna chi can ghi con so kich thuoc chi chieu dai cua cac thanh, (H 2-36)

220

lliNII 2-.\IJ

- De bieu th~ be day cac lop v~t li$u

tren mllJ.t cat, nguC:Ii ta ghi kich thuCJc nhti

li$u gi, tren b:'m ve nguC:Ii ta dung cac ki IIi NI-l 2-37

hi$u v~t li$u Cac kf hi$u nay thubng ve

tren mllJ.t cat, doi khi ve tren mllJ.t dung cua cong trlnh Hinh 2-38 gioi tlii$u m¢t so kf hi$u v~t li$u ~e tren mllJ.t cat, duqc quy d~nh trong TCVN 7-1993

r 7// /// /// /// ///' Dfit thien nhien G6

hinh '2-39 ;

ngat quang va nghieng m(>t goc thkh h<;Jp, tot nhat la 45° voi dtiong baa quanh chinh

ho~c voi trtJC doi xung cua m~t cat (H 2-40) ;

nhau thi phai de m9t khe ha kho:ri.g nhO han

li~u chua duqc quy d~nh trong tieu chwin

phtJ va phai ghi chu bang chu (H 2-43)

ae TONG G1CH vri

\

IIINI·l 2-43

CHUONG 3

VE HINH HOC

don gilm tai phuc t1;1p, vi d\1 chia m9t da1;1n thAng thanh cac phan thea m9t ti I$ cha truoc, chia duong trcm thanh cac phan bang nhau, ve cac duong cang hinh hQc, ve n6i

b)

HiNH 3-1

Ung d1,lng phep dl;tng hl.nh nay ta co the chia m9t da1;1n thAng thanh nhieu phan bang nhau

5 phan bang nhau

d) Chia lam 5 phan (H.3-5)

< ~

HINH 3-2

- Xac d!nh ,diem giua K

cua do~n OA;

duqc cac diem 2 va 3 thu(>c

th:ing 12 va 13 la hai qnh

tiep dubng tron

pha.n bang nhau

each chia dubng

bang nhau ·

Ve

dubng

hai kfnh·

vuong goc nhau

- Noi E va F voi cac digm chia le 1, 3, 5 (ho:;tc voi cac diem chia chan ·2, 4, 6) va

tren dubng tron ·chia dubng tron do lam 7 phan bang nhau

- 2R ~ · ·

+Phuong ph6p tin(~ toan : Dung cong thuc a = ~sin1800 trong do a la chieu dai

c~nh cua da giac deu n c~nh n(>i tiep duCing tron ban kfnh R

S6 qnh ctlii d;, giac deu (n) Chieu dili c<:~nh ciw d;, giac (")

3.1.3 Ve du<mg thling_ co de? doc ch_o trurlc

BC

AC

- Qua M ve m9t dubng th:ing nam ngang va

- Tu B ke duCing th:ing vuong goc voi

3.2 VE NOI TlEP HAl DUONG

kh6ng co s\j giiy khuc

Trong khi dl,ing hlnh bieu di€\n cua cac

trtidng hc;1p ve noi tiep duai day

tuyen vai duCing tron qua m(>t diem cho

t.ruac), CI:I.3-9)

OM r6i ve duCing tron duong kinh

OM

duCing tron vua ve vai duCing tron

da cho

3.2.2 Noi tiep hai dttang trim

tiep tuyen chung cua hai duCing

tron)

a) Truong hqp n6i tie'p ngocl-i

(H.3-10a) Cach ve nhu sau

(OI;Rl-R2);

tron ·nay (each lam nhtt tren hlnh

3-9)

b) Truong hqp n6i tie'p tron;g (H.3-10b)

Dttoi day Ia m<)t so trttbng hQp noi tiep hai dttbng cho trttoc bang cung trim Khi do

tron noi tiep

3.2.3 Noi tiep hai dubng thtmg bang mc)t cung trim

Bai toan : N oi tiep hai dttbng th:lng I va m bang cung tron ban kfnh R '(H 3-11)

lliNH ~-II

3.2.4 Noi tiep dubng thtmg vOi cung trim bang mc)t cung trim

Bai toan : Noi tiep dttbng thling d voi cung tron tam 01 ; ban kfnh R1 bang ·cung

HiNH 3-12

tron da cho

- Ve ducrng th:ing d' // d va each d m(>t khoang bang R va ve ducrng tron tam 0 1 ban kinh R

b) Truong hqp n6i tiep trong (H.3-12b) : Cung tron n6i tiep tiep xuc trong voi duang

tron dii cho

Tam 0 cua cung tron n6i tiep dUQC xac dtnh bang giao diem cua d' voi duang tron (0

Bai toa.n: N6i t.iep cac cung tron tam 0 1 ban kinh R1 va tam 02 ban kinh R2 bang cung tron ban kinh R (H.3-13)

HiNil 3-13

a) Truong hqp n6i tiep ngoa,i (H.3-13a.)

0 cua cung tron n6i tiep

cuilg tron dii cho

b) Truong hqp n6i tiep trong (H.3-13b) :

Tam 0 cua cung tron n6i tiep la giao cua cac cung tron (0

hinh, co nhung duong cong co the ve duqc bang compa, co nhung duong cong kh6ng the

ve duqc bang compa, rna phai d1,1ng tungdiem, sau do noi ohung lai bang m(>t duon?i cong tron va to d:Itm bang thuoc cong

3.3.1 Cac duong cong b:Itc hai

di~n bang phuong tdnh d~i so b:;tc hai Duong

cong b:;tc hai kh6ng suy bien gom co : eHp,

hypecb6n, parab6n;

HINII 3-15

3.3.1.1 Elip

dtnh cua ml\it phang do bang hang so, (H.3-' 15)

b) Ve elip theo hai dztang kinh lien hqp Phuong phap hinh binh hanh (H 3-17)

HINH 3-17

Cho hai duCing kinh lien hQp AB va CD cua m(>t eHp(*)

- Ve hinh binh hanh EFGH co cac c;:tnh tung doi ni(>t song song voi AB va CD

- Ve cung tron tam C, ban kinh CI Cung tron nay cat c;:tnh EF t;:ti K va L

- Qua K va L ke cac duCing thang song song voi CD Cac duCing nay cat hai duCing cheo EG va FH cua hinh binh hanh t;:ti M, N, P va Q EHp can d\fng di qua 8 diem A,

chieu trl,lC do cua cac dUCing tron

(•) H:;i dlti'lng kinh Iien h<:Jp ctla 111(11 elip Iii hinh chit\u song song CLI<~ h:;i dlti'lng kinh vutmg goc nh:;u cti<~

dltdng tn)n c<i hinh chiCu song song 1:1 clip d<i

c) ve elip gan dung f;ia.ng compa

3:3:1.2 Parab6n : Parab6n la t.$-p hc;1p cac diem t.hu(>c m(>t m~t ph:ing each deu m(>t

(H.3-20)

- Xac dinh dinh A cua parabon (diem gifla cua

do~n OF) ;

- Tren m1a duong th:i.ng Ax lay m(>t diem N tuy

chuan d;

- Ve cung tron (F, ON), n6 cat duong th:ing n vua

n6 (H.3-21)

Jl

lliNII 3-21

Gia stt cho biet tr1,1c Ax, dinh A va m<)t diem M cua parab6n Xac d~nh cac diem khac cua parabon nhu sau :

- Qua M ve duong th:ing song song

m<)t s6 phan bang nhau ;

- Noi cac diem chia nhu chi ro tren

hlnh ve ;

., Noi cac giao diem cua tttng c;:i.p

duong th:ing tuong ung bang duong cong

tron deu, ta duqc m<)t ntta parabon can

se nh~n duqc Iittljl con l~;ti

3.3.1.3 Hypecb6n : Hypecb6n la t~p

hqp nhftng diem thu¢c m<)t m;:i.t ph:ing co

hi~m khoang each tdi hai diem co d~nh

cua m;:i.t phang do bang m<)t hang so

(H.3-22)

MF2 - MF1 = A1A2 ::::: 2a

Duong thang noi hai tieu diem g9i la

trl,l.C cua hypecb6il Cach ve hypecb6n khi

biet hai tieu diem va hai dinh cua no nhu

sau (H.3-23)

- Tren tr1,1c di qua hai tieu qiem lay

diem M va M' thu<)c hypecbon can ve

Cac diem khac cua hypecb6n duqc ve

tuong tv

3.3.2 Duong xoitn oc

1-!INH 3-22

HiNH 3-23

m<)t ntta duong th:ing, khi ntta duong th:ing nay quay quanh dau mut cua no

3.3.2.1 Duong xoan 6c Acsimet : La duong cong ph:ing dttqc t~;to thanh boi m<)t diem chuyen d¢ng deu tren m<)t ntta duong th:ing, trong khi ntta duong th:ing nay quay deu trong m(lt m;:i.t ph:ing quanh dau mrit cua no D¢ doi cua diem tren ntta duong th:ing khi ntta duong th:ing quay m(lt goc 360° g9i la buoc cua duong xoan oc Ve duong xoan 6c Acsimet khi biet buoc a cua no nhu sau, (H.3-24)

- Ve dubng trcm tam 0, ban kfnh OA = a ;

- Chia deu dubng tr<m va ban kinh OA ra

cung m(it so phan nhu nhau bang cac diem chia

1; 2, 3 va 1', 2', 3'

- Ve cac cung trcm tam 0, ban kfnh lan luQt

02', 03' la cac diem thu(ic dubng xoan 6c

Acsimet N6i cac diem vi:ta nMn duqc bang dubng

cong tron deu

3.3.2.2 Duong xofm 6c nhieu tam : Ngubi

taco the dung compa de ve cac dubng cong co

d~ng giong nhu dubng xoan oc Co thf>' dung

hai, ba, bon hay nhieu tam

lay 0

3

1-IiNH 3-25

Hl.nh 3-26 ve Ctubng xoan oc ba tam

Hl.'nh 3-27 ve dubng xoan 6c bOn tam

Hl.nh 3-28 ve dubng xoan 6c I -6-nkh Ta

Truoc tien ve · dubng tron "mat", trong do xac

H.3-28a) Lay diem 1 lam tam, ve cung xoan oc

AB co ban kfnh bang 9 li:ln ban kinh dubng tron

"mat" Tiep t1,1c ve cung BC, tam la diem 2, ban

true Nguyen tac ve cac dubng cong nay chu yeu la dl,ia tren each ve nol tiep hl.nh hQc