Tong Hop Bai Giang

TRC A

(GEODESY)

GV: o Hu S

Khoa Xy dng

[email protected]

TRC A

(GEODESY)

GV: o Hu S

Khoa Xy dng

[email protected]

[email protected]

Huy 0909559196

NI DUNG CC CHNG MC:

Chng 1. Tri t v cch biu th mt t Chng 2. Sai s trong o c Chng 3. Dng c v cc phng php o trong trc a

Chng 4. Li khng ch trc a Chng 5. o v s dng bn a hnh Chng 6. B tr cng trnh Chng 7. Quan trc cng trnh

Kim tra, bi tp

Thi cui k

TI LIU THAM KHO:

Trc a i cng Tc gi: Nguyn Tn Lc- NXB: i hc Quc gia Tp.HCM

Trc a xy dng thc hnh Tc gi: V Thng NXB: Xy dng.

TCXDVN 309 2004 Cng tc trc a trong xy dng Yu cu chung

K hiu bn a hnh ca Tng cc a chnh (Nay l B Ti nguyn v Mi Trng),

Internet

Trc a (Geodesy) l mt ngnh khoa hc chuyn

nghin cu v hnh dng, kch thc v b mt t nhin ca

Tri t.

Bn (Map) l hnh nh thu nh ca b mt tri t

c biu din ln mt phng theo mt quy lut ton hc

nht nh.

1. KHI NIM

Trc a: - Thut ng trc a hm phn chia t ai

- Ngnh khoa hc trc a c t lu i, n sinh ra do nhu

cu ca i sng x hi loi ngi: nh vic i li, qun

l t ai, giao thng bun bn, thm him, qun s... - Trong qu trnh pht trin, Trc a c phn ra

lm nhiu phn ngnh chuyn mn hp nh: + Trc a cao cp + Trc a nh + Trc a cng trnh + Bn hc . . .

2. LCH S PHT TRIN

Trc a, bn c vai tr quan trng trong cc ngnh

kinh t quc dn nh:

Nng - lm nghip,

Giao thng vn ti, thy li,

Quy hoch - Xy dng,

Quc phng (bn l con mt ca qun i)

Trc a cn thit trong tt c cc giai on: quy hoch,

kho st, thit k, thi cng, nghim thu qun l v s dng

cng trnh.

3. VAI TR

Ngy nay nh cng ngh pht trin m trc a

pht trin ln tm cao mi:

- Cng ngh nh vin thm, cho php con ngi c

th xc nh nhng v tr, thnh lp bn nhng khu

vc nguy him hoc khu vc khng th tip cn

- Cng ngh nh v ton cu GPS (NAVigation

System with Time And Ranging Global Positioning

System) vic xc nh v tr nhanh chng v cho kt qu

vi chnh xc cao

LCH S GPS:

n c hnh thnh vo u thp nin 60

V tinh u tin c phng vo qu o nm 1973

c B Quc phng M vn hnh v khai thc.

Hin ti c tng cng 30 v tinh ang hot ng

CU TRC GPS:

S lng v tinh GPS quan st c

GV: o Hu S

Khoa Xy dng

Chng 1:

TRI T V CCH BIU TH

MT T

NI DUNG CHNG 1

Hnh dng - kch thc tri t v cch biu th

mt t

Cc h ta - cao

Khi nim v bn

Phn mnh v nh s hiu bn

1.1 HNH DNG V KCH THC

TRI T 1.1.1 Hnh dng

B mt tri t c din tch S 510,2 triu km2. Trong

: i dng chim 71%

Lc a chim 29%

L mt g gh, li lm; ch cao nht +8882m (nh

Hymalaya), ch thp nht -11032m (h Marian Thi

Bnh Dng, gn Philippines)

u th k 20 (Listinger c), a ra khi nim

mt Geoid v dng mt ny biu th b mt tri t

Mt Geoid : l mt nc bin trung bnh yn tnh, ko

di xuyn sut qua cc lc a hi o to thnh mt mt

cong khp kn (Mt Geoid cn c gi l mt thy

chun lc a, hay mt nc gc tri t)

Hnh nh tri t chp t v tinh

Mt Geoid c dng lm mt quy chiu ca h thng

cao

Mt Geoid c c tnh:

+ Mt Geoid khng phi l mt ton hc

+ Ti mi im trn mt Geoid u vung gc vi

phng ca ng dy di ti im .

1.1.2 Kch thc.

Do mt Geoid khng phi l mt ton hc, nn khi

tnh ton - biu din kch thc Tri t chng ta phi

dng b mt khc gn trng vi Geoid v phi l mt

ton hc, l mt Ellipsoid tri t (Gi tt l

Ellipsoid), cn tho mn:

- Tm Ellipsoid trng vi tm Geoid

- Mt phng xch o Ellipsoid trng vi mt phng

xch o Geoid

- Th tch Ellipsoid tri t = th tch Geoid

- Tng bnh phng chnh cao t mt Ellipsoid ti

mt Geoid l nh nht ([h2] =min)

c im ca Ellipsoid:

- Ellipsoid l mt mt biu din c bng phng

trnh ton hc v hu ht mi tnh ton Trc a thc

hin trn mt ny (gi l Mt quy chiu)

- Ti mi im, b mt Ellipsoid lun vung gc vi

phng php tuyn.

c trng cho Ellipsoid

+ Bn trc ln (bn knh ln): a

+ Bn trc nh (bn knh nh): b

+ dt a

ba

2 2 2

2 2 2

Ph.trnh:

1.X Y Z

a a b

Geoid

Ellipsoid

O

b a

Tc gi

(Ellipsoid)

Quc

gia

Nm Bn trc ln a (m)

Bn trc nh b (m)

dt

Delambre Php 1800 6.375.653 6.356.564 1:334,0

Everest Anh 1830 6.377.276 6.356.075 1:300,8

Bessel c 1841 6.377.397 6.356.079 1:299,2

Clark Anh 1980 6.378.249 6.356.515 1:293,5

Krasovski Nga 1940 6.378.388 6.356.863 1:298,3

WGS84 M 1984 6.378.137 6.356.752,3 1:298,257

Mt s Ellipsoid tri t

1.2.1 Khi nim

Trong trc a,

tin cho vic thit k

k thut, ngi ta

tm cch biu din b

mt tri t ln mt

phng. Phng php

ny cho php chng

ta thu nh b mt tri

t vi chnh xc

cn thit.

1.2 CCH BIU TH MT T

V b mt tri t l b mt t nhin v cng phc

tp, v vy biu din ln mt phng ta phi chiu b

mt tri t ln mt Ellipsoid hoc mt cu ri thu nh

mt cu tri t theo t l mong mun. Bng php chiu

xuyn tm ngi ta tip tc chiu hnh cu tri t ln

mt tr, mt nn, theo cc phng php khc nhau.

Sau ct mt tr, mt nn, theo mt ng sinh c

chn trc v tri ra mt phng.

Phng php chiu ny lm cho b mt qu t b

bin dng. S bin dng ph thuc vo im chiu v cc

im trn mt t cng nh phng php chiu.

1.2.2 nh v cc im trn mt t

V tr khng gian cc im trn mt t c xc nh

bng 2 yu t:

1. To a l (, ) hoc to vung gc phng (x, y) trn mt quy chiu Ellipsoid

2. cao ca im so vi mt Geoid

xc nh v tr cc im A,B,C trong khng gian ta

chiu chng xung mt Geoid theo phng dy di ta

c cc im a, b, c.

Trong trng hp biu din b mt tri t trong mt

phm vi khng ln, vi yu cu chnh xc khng cao

chng ta coi b mt tri t c chiu trc tip ln mt

phng

B

A

C

c

b

a

P

1.3 H TO A L Trong ton hc cng nh trong trc a, xc nh to

ca mt im, chng ta cn xc nh quan h gia im

vi mt h trc c chn lm gc.

P

P1

O M

M

Q Q1

xc nh to a l ca mt im trn b mt

tri t, Gi s phng php tuyn trng vi phng dy

di v mt Geoid trng vi mt Ellipsoid trn xoay ca

tri t.

Cc yu t c chn lm gc trong h to a l

nh sau:

- Tm O ca tri t c chn lm gc to

- Hai mt phng gc l mt phng kinh tuyn gc v mt

phng xch o

T hnh v:

- P, P1: l cc Bc v cc Nam ca tri t

- PP1: trc xoay ca tri t

- Q, Q1: l cc Ty v cc ng ca tri t

- G (Greenwich): V tr i thin vn Greenwich ngoi

Lun n

hiu r h to a l, chng ta c mt s khi

nim sau:

- Mt phng kinh tuyn l mt phng i qua trc xoay PP1

ca tri t

- Mt phng v tuyn l mt phng vung gc vi trc xoay

PP1

- ng kinh tuyn l giao tuyn ca mt phng kinh tuyn

vi mt cu tri t

- ng v tuyn l giao tuyn ca mt phng v tuyn vi

mt cu tri t

- Mt phng kinh tuyn gc l mt phng kinh tuyn i qua

G (Mt phng kinh tuyn gc chia tri t ra lm hai na

ng bn cu v Nam bn cu)

- Mt phng xch o l mt phng v tuyn i qua tm O

ca tri t

To a l ca im M(M ,M)

M (v ): l gc hp bi mt phng xch o v ng

dy di qua M

M (kinh ): l gc hp bi mt phng kinh tuyn gc v

mt phng kinh tuyn i qua im M

Trn xch o =0, trn kinh tuyn gc =0

Thng quy c:

M t xch o ln gi l v Bc (00 900)

M t xch o xung gi l gi l v Nam (00 900)

M t kinh tuyn gc G sang ng gi l kinh ng (00

1800)

M t kinh tuyn gc G sang Ty gi l kinh Ty (00

1800)

1.4 H TO VUNG GC KHNG GIAN

OXYZ (H T. A TM)

H ta vung gc khng gian: l h thng gm

im gc to v 3 trc to X, Y, Z xc nh

trong khng gian Euclide 3 chiu: h quy chiu ny

c s dng trong o c v tinh v nhng bi ton

trc a ton cu.

1.5 H TO VUNG GC PHNG Trong trc a h to vung gc phng ngc vi h

to vung gc cc; trc X theo phng ng, trc

Y theo phng ngang

Qua nhiu thi k khc nhau th c nhng h to cng

khc nhau (ngay c Vit nam cng nh th gii)

y

x

O

th hin mt khu vc trn b mt tri t ln mt

phng ngi ta phi s dng cc php bn . Thng qua

cc php chiu bn nh ngha cc h ta vung gc trc a

Cc li chiu bn thng dng:

- Hnh tr ngang,

- Hnh tr ng,

- Hnh nn,

- Phng v,

1.5.1 Php chiu Gauss, H to vung gc phng

Gauss Kruger

Php chiu ny s dng Ellipsoid Krasovski vi cc

thng s

a= 6.378.245 m , b= 6.356.863 m, = 1/298,3

Php chiu Gauss l php chiu hnh tr ngang ng gc.

Trong php chiu ny tri t c chia thnh 60 mi

chiu 60 v c nh s tng ng t 1 60 bt u t

kinh tuyn gc Greenwich (00) sang ng vng qua Ty

ri tr v knh tuyn gc.

Mi mi chiu c gii hn bi kinh tuyn ty - bn

tri v kinh tuyn ng - bn phi (2 kinh tuyn bin). V

kinh tuyn gia ca mi chiu c gi l kinh tuyn

trc, i xng vi 2 kinh tuyn bin.

T=60(n-1), G=6

0.n-30, P=60 .n

Vi n l s th t ca mi chiu

GP'

O

P

Sau khi chia ra tng mi chiu v xc nh kinh tuyn

trc ca mi mi chng ta cho qu cu tri t tip xc

vi mt trong ca mt hnh tr ngang theo ng kinh

tuyn trc.

Ly tm chiu O l tm tri t ln lt chiu cc mi ln

mt tr tng mi mt, sau va xoay va tnh tin hnh

cu n mi s 2 tng ng vi on chn cung trn xch

o

v tip tc cho n ht

Sau ct mt tr theo hai ng sinh KK ri tri ra mt

phng ta c nh hnh sau

kmR

L 84,666180

6..0

0

x

y

K

K'

c im ca mi mi chiu:

- Bo ton v gc

- Xch o c chiu thnh ng thng v lm trc Y

- Kinh tuyn trc (gia) c chiu thnh on thng v

chn lm trc X; X Y

- Kinh tuyn trc khng b bin dng sau khi chiu

- Cc kinh tuyn v v tuyn khc b thay i sau khi chiu

- Cng xa kinh tuyn trc bin dng cng ln

to Y lun dng ngi ta di kinh tuyn trc v

pha Ty 500km, X dng di X v Nam 10000km

Vit Nam h to Gauss c thnh lp nm 1972

gi l h to HN72, chn Ellipsoid quy chiu Kraxosky

gc t ti i thin vn Punkv (Lin X c) truyn to

ti Vit Nam thng qua h to quc gia Trung Quc.

1.5.2 Php chiu v h to vung gc phng UTM

(Universal Transverse Mercator)

500 km

x

xch ao

cat tuyen

kinh tuyen truc

y

Php chiu UTM s dng Ellipsoid WGS 84

Thng s Ellipsoid WGS 84

Bn trc ln a = 6.378.137 m

Bn trc nh b = 6.356.752,3 m

dt cc = 1 / 298,257

Php chiu UTM cng l php chiu hnh tr ngang

ng gc nhng mt tr khng tip xc vi mt Ellipsoid

ti kinh tuyn trc m ct mt Ellipsoid ti 2 ct tuyn

cch kinh tuyn trc 180km

c im ca mi mi chiu.

- Bo ton v gc (ng dng)

- Xch o thnh ng thng ngang kinh tuyn trc

- Hai ct tuyn h s bin dng m = 1 (khng bin dng)

- Kinh tuyn trc m = 0,9996

Vng trong ct tuyn m < 1 (bin dng m)

Vng ngoi ct tuyn m > 1 (bin dng dng)

K t ngy 12/08/2000 Vit Nam s dng thng nht

trn phm vi ton quc h to vung gc UTM gi l

VN2000, chn Ellipsoid quy chiu WGS 84, im gc to

l im gc ca li GPS cp 0 ti H Ni.

1.5.3 H ta c lp (t do)

Y

X

O

1.6 H CAO Mt Geoid c chn lm mt quy chiu cho cao.

cao ca mt im l khong cch tnh theo phng

dy di t im ti mt Geoid

A

B

H

H

g g

A

B

Mat thuy chuan gia nh

Geoid (mat thuy chuan goc)

Ellipsoid trai at

- Nu mt chun gc (l mt Geoid), ta c cao tuyt i

- Nu mt thy chun l mt gi nh ta c cao gi nh

- Khong cch t mt im ti mt Ellipsoid theo phng php

tuyn gi l cao trc a

- Hiu s cao gia 2 im (chnh cao) l khong cch theo

phng dy di gia 2 mt thy chun i qua 2 im .

Trong trc a khng o c cao trc tip m ch o

c chnh cao gia cc im.

Trc 1975, Bc Vit Nam mt thy chun gc c chn i

qua trm Nghim triu Hn du Sn Hi Phng.

Nam Vit Nam chn mt thy chun gc Mi Nai H Tin

Sau 1975, Vit Nam mt thy chun gc c chn i qua

trm Nghim triu Hn du Sn Hi Phng

HH.Dau = HM.Nai + 0,167 m

T 2001, thng nht trn lnh th VN ch s dng cao HD

CC H TA C TI VIT NAM

Thi Php thuc: Ellipsoid Clark (Anh), im gc ti H

ni, php chiu Bonne v h thng im to ph trm

ng dng; lm c s cho lp bn 1/100.000 v

1/200.000 khu vc ng Dng.

Min Nam VN t 1954-1975: h Indian 54 vi Ellipsoid

Everest (Anh), im gc ti n , php chiu UTM v

h thng im to ph trm Nam Vit Nam, h cao

Mi Nai, H Tin;

Min Bc t 1959 bt u xy dng h thng li Trc a

v h quy chiu v kt thc nm 1972 => h HN-72 vi

Ellipsoid Krasovski , im gc ti Punkovo chuyn v VN

ti i thin vn Lng HN (thng qua im Ng Lnh

Trung Quc), php chiu Gauss- Kruger, h cao Hn

du, Hi phng

Quan h gia cao Hn du v cao Mi nai

HH = HM + 0,167 m

T 1992-1994: nh v li Ellipsoid Krasovski ph hp

Vit Nam.

T 1996-2000: Xy dng h VN-2000 vI Ellipsoid

WGS-84 c nh v ph hp vi lnh th Vit nam,

im gc to N00 t ti Vin nghin cu a

chnh, ng Hong Quc Vit, H ni; php chiu

UTM, h cao Hn du - Hi phng.

H Quy chiu WGS 84

1.7 KHI NIM BN .

1.7.1 nh ngha bn Bn l hnh v thu nh trn giy cc hnh chiu bng

ca nhng phn b mt tri t, c k n s bin dng

do nh hng ca cong tri t, theo mt quy lut ton

hc no .

Bn l biu hin thu nh ca b mt tri t ln mt phng theo mt quy lut ton hc xc nh, th hin bng

cc k hiu quy c c bit; trn trng thi, s phn

b v mi quan h gia cc hin tng t nhin, kinh t,

vn ha, x hi c chn lc v khi qut ha ph hp

vi mc ch s dng c th ca bn

1.7.2 Phn loi bn :

a. Phn loi theo mc ch: Ph thng, chuyn ngnh

b. Phn loi theo ni dung

* Bn a l chung: Bn a hnh, Bn a hnh

khi qut, Bn Khi qut.

* Bn a l chuyn (gi tt l bn chuyn ):

Cng nghip, Nng nghip, Du lch, a cht, Thy vn,

Kh hu, Th nhng, Thc vt, ng vt

c. Phn loi theo t l

Bn t l ln, trung bnh, nh

d. Phn loi theo phm vi din tch

Ton cu, i dng, lc a, chu lc, quc gia, tnh,

huyn, x

1.7.3 T l bn a) nh ngha:

T l bn l t s gia chiu di ca mt on thng

trn bn vi chiu di nm ngang tng ng ca n

ngoi thc a (thc t).

T l bn k hiu 1:M hoc

T l bn l mt phn s c t s l n v, cn mu

s thng l nhng s trn trm, trn nghn,..

b) Phn loi bn a hnh theo t l

- T l ln:

- T l trung bnh:

- T l nh:

;5000

1;

2000

1;

1000

1;

500

1

;000.50

1;

000.25

1;

000.10

1

1.000.000

1;

500.000

1;

250.000

1;

100.000

1

tt

bd

SM

1 S

c. chnh xc (sai s) ca t l bn

t = 0,1xM (mm)

M: Mu s t l bn

t: sai s c bn quy ra thc t

1.7.4 Thc t l c gi tr chiu di on thng ngoi thc a tng

ng biu din trn bn mt t l no c nhanh

chng v d dng, ngi ta dng thc t l:

C hai loi thc t l:

+ Thc t l thng

+ Thc t l xin (cho chnh xc cao hn)

1.7.5 Biu din a vt trn bn . - K hiu theo t l

- K hiu phi t l

- K hiu na t l

- K hiu ch gii

1.7.6 Biu din a hnh trn bn . - Phi cnh, t bng (t s dng)

- Ghi cao v ng bnh (phng php ph bin)

1.7.7 Bn s. D liu c lu tr di dng file v hin th trn cc

thit b in t.

u im:

chnh xc, lu tr, cp nht x l thng tin, tt hn

hn so vi bn giy

1.8 CHIA MNH V NH S HIU BN .

Bn a hnh ni ring cng nh cc loi bn khc

c biu din nhiu loi t l khc nhau.

Mc ch ca chia mnh v nh s hiu tin cho qun

l v s dng bn .

S hiu bn cn gi l danh php bn (hay

phin hiu bn ).

Trn th gii v Vit nam tng tn ti nhiu kiu t

danh php bn khc nhau.

Lu : mi loi bn c cc quy nh v t l v cch

chia mnh nh s hiu khc nhau

Di y trnh by cch chia mnh v phin hiu

(danh php) bn a hnh theo kiu hin nay ang

c s dng Vit Nam

T bn a hnh c bn c t l 1:1.000.000, trn

c s t bn ny tin hnh chia mnh v nh s hiu

cho cc t bn t l ln hn (theo s chia mnh

trang tip sau)

T bn t l 1:1.000.000 c hnh thnh theo

php chiu hnh nn, c dng hnh thang (l giao ca

hng v ct) nh sau:

- Theo v tuyn t xch o v hai cc Bc, Nam ta

chia ra cc di 40 v t tn bng cc ch ci Latin:

A,B,C, . . . (b ch ci I v O)

- Theo kinh tuyn chia tri t ra cc mi 60 (nh

vy c 60 mi) v nh s t 1 60.

nh s th t t Ty sang ng (bt u t kinh tuyn

1800)

Mi s 1 nm gia kinh tuyn 1800 v 1740T

Mi s 2 nm gia kinh tuyn 1740T v 1680T

Nu kinh tuyn nh s lin tc t 0 3600, th mi 1? mi 2?

Ch : Mi bn khc mi chiu. S th t mi chiu

c nh s bt u t kinh tuyn gc Greenwich (00)

v ng sang Ty. Cn mi bn c nh s t

kinh tuyn 1800 v Ty sang ng. Nh vy s hiu

mi chiu v s th t ct ca t bn 1:1.000.000 lch

nhau 30 n v.

V d: = 1050 ng, tc mi chiu th 18 ct ca t bn 1:1.000.000 l 18 + 30 = 48.

1.8.1. Phin hiu bn a hnh t l 1:1.000.000

giao nhau gia hng v ct ni trn s c biu din

thnh 1 t bn t l 1:1.000.000

Tn ca t bn ny ghp t k hiu Hng s hiu

Ct

S chia mnh sau th hin cch chia mnh v nh s

hiu cc t bn t l khc nhau.

3 x 3 = 9

c, d

1, 2

3, 4

a, b

A, B

C, D

3, 4

1, 2

C, D

A, B

25.000

10.000

1

III, IV

I, II

2 x 2 = 4

2 x 2 = 4

1

1.000

5.000

2.000

1

1

2 x 2 = 4

2 x 2 = 4

50.000

250.000

500.000

1.000.000

1

1

1

2 x 2 = 4

1

2 x 2 = 4

1

8 x 12 = 96

100.000

1

241, 242,. . .256

1, 2 , . . . 16

13, 14, 15, 16

1, 2 , 3, 4

.

.

.

4 x 4 = 16

500

1

g, h, k

.

.

.

a, b, c

.

.

.

85, 86, . . . 96

1, 2 , . . . 12

.

.

.

16 x 16 = 256

1.8.2 Phin hiu bn a hnh t l 1:500.000

T mnh bn 1:1.000.000 c chia ra thnh 2x2 = 4

mnh bn t l 1:500.000, v ghi k hiu A, B, C, D

theo nguyn tc t tri qua phi t trn xung di.

Tn: ghp t tn t c s chia ra n k hiu

BA

C D

F-48

(1:1.000.000)

F-48-D

(1:500.000)

1.8.3 Phin hiu bn a hnh t l 1:250.000

T mnh bn 1:500.000 chia ra thnh 2x2 = 4 mnh

bn t l 1:250.000 v nh s 1, 2, 3, 4 theo nguyn

tc t tri qua phi t trn xung di.

F-48-D

(1:500.000)

3

1

F-48-D-4

(1:250.000)

4

2

1.8.4 Phin hiu mnh bn t l 1:100.000

T mnh bn t l 1:1.000.000 chia ra thnh 8x12 =

96 mnh bn t l 1:100.000, v nh s t 1, 2, ,

95, 96 theo nguyn tc t tri qua phi t trn xung di

F-48-96

(1:100.000)

F-48

(1:1.000.000)

1 2 3 4 5 6 7 8 9 10 11 12

13 24

969785


T mnh bn 1:100.000 chia ra thnh 2x2 = 4 mnh

bn t l 1:50.000 v nh s 1, 2, 3, 4

F-48-96-D

(1:50.000)D

B

F-48-96

(1:100.000)

C

A


T mnh bn t l 1:50.000 chia ra thnh 2x2 = 4

mnh bn t l 1:25.000 v nh k hiu a, b, c, d

F-48-96-D

(1:50.000)

c

a

d

b

F-48-96-D-d

(1:25.000)


T mnh bn 1:25.000 c chia ra thnh 2x2 = 4

mnh bn t l 1:10.000 v nh s 1, 2, 3, 4

F-48-96-D-d-4 (1:10.000)

F-48-96-D-d (1:25.000)

3

1

4

2


T mnh bn t l 1:100.000 c chia ra thnh

16x16 = 256 mnh bn t l 1:5.000 v nh s t 1,

2, , 255, 256

32

122

17

1 43

F-48-96

(1:100.000)

65 87 109 11

F-48-96(256)

(1:5.000)

13 14 15 16

256255241

240


T mnh bn t l 1:5.000 c chia ra thnh 3x3 = 9

mnh bn t l 1:2.000 v nh k hiu a, b, c, d, e, f,

g, h, k

F-48-96(256-k)

(1:2.000)

F-48-96(256)

(1:5.000)

g

a

d

h

e

b

k

c

f


T mnh bn t l 1:2.000 c chia ra thnh 2x2 = 4

mnh bn t l 1:1.000 v nh s I, II, III, IV

F-48-96(256-k-IV)

(1:1.000)

F-48-96(256-k)

(1:2.000)

III

I

IV

II

1.8.11 Phin hiu mnh bn a hnh t l 1:500

T mnh bn t l 1:2.000 c chia ra thnh 4x4 =

16 mnh bn t l 1:500 v nh s 1, 2, , 15, 16

F-48-96(256-k)

(1:2.000)

9

1

12

4

F-48-96(256-k-16)

(1:500)

2 3

8765

10 11

13 14 15 16

Cch chia mnh v nh s hiu theo quc t

(SV tm c trong cc ti liu)

GV: o Hu S

Khoa Xy dng

Chng 2:

SAI S TRONG O C

NI DUNG CHNG 2

Khi nim v php o

Phn loi sai s trong kt qu o

Cc tiu chun nh gi sai s

Sai s trung phng hm tr o v sai s trung phng trung bnh

nh gi chnh xc theo Bessen

Cc n v hay dng trong trc a v nguyn tc lm trn s

2.1 KHI NIM PHP O

2.1.1 nh ngha php o

Php o l em so snh i lng cn o vi i lng

cng loi c chn lm n v.

Trong o di chn n v l: mt.

Trong o gc n v l: ( ; pht; giy), grat ( grat,

pht grat, giy grat)

2.1.2 Phn loi php o

Trong o c c o trc tip v o gin tip

- o trc tip: l nhng i lng nhn c sau php so

snh trc tip

- o gin tip: l nhng i lng c tnh ra t cc i

lng o trc tip thng qua mi quan h ton hc.

Theo chnh xc c:

- o cng chnh xc (o cng iu kin o)

- o khng cng chnh xc (o khng cng iu kin)

iu kin o: Dng c, con ngi, ngoi cnh

Kt qu o cn thit (o ) v o tha (o d):

- Kt qu o cn thit k l s lng kt qu o ti thiu

xc nh i lng cn xc nh.

- Kt qu o tha l n-k kt qu o cn li. (n>k)

o tha l cn thit trong trc a. V n gip ta kim tra

c cc kt qu o vi nhau v tng chnh xc.

2.2 PHN LOI SAI S O C

Mt i lng c o nhiu ln, d cn thn kt qu

vn khc nhau. iu chng t trong kt qu o lun c

sai s:

Cng thc:

Trong : i : l sai s thc ca ln o th i

li : kt qu o ln th i

X : tr s thc ca i lng cn xc nh

Cn c vo tnh cht ca sai s i (nguyn nhn xut hin

sai s) ngi ta phn lm 3 loi sai s sau:

2.2.1 Sai s do sai lm

L sai s gy nn do s thiu cn thn, nhm ln trong

khi o, khi ghi s, khi tnh (c sai, ghi sai,..). Thng sai

s do sai lm c tr s ln d pht hin.

Khc phc: o nhiu ln (o lp)

(2.1) Xlii

2.2.2 Sai s h thng

L sai s nh hng n kt qu o c tnh cht h thng

trong cng iu kin o nht nh.

- Sai s h thng c th do tt ca ngi o, dng c o,

ngoi cnh thay i

- Sai s h thng c tnh cht: c tr s v du thng

khng i, mang tnh tch lu

- Sai s h thng c th loi b hoc hn ch bng cch

kim nghim, iu chnh dng c o, s dng phng

php o thch hp. Tnh s hiu chnh vo kt qu o.

2.2.3 Sai s ngu nhin

L sai s nh hng ln kt qu o theo tnh cht ngu

nhin, kt qu ca ln o sau khng ph thuc vo ln o

trc .

Sai s ngu nhin c c im:

- Sai s ngu nhin c du v tr tuyt i thay i.

- Sai s ngu nhin khng mang tnh tch lu m mang

tnh b tr.

- Sai s ngu nhin khng kh c m ch hn ch.

Sai s ngu nhin c 4 tnh cht sau:

- Tnh gii hn: Trong cc iu kin c th tr s tuyt i

ca sai s ngu nhin khng vt qu mt gii hn nht

nh.

- Tnh tp trung: sai s c tr tuyt i cng nh s ln

xut hin cng ln.

- Tnh i xng: sai s ngu nhin dng v m vi tr

tuyt i nh c s ln xut hin gn bng nhau.

- Tnh b tr: Khi s ln o tin ti v cng th tr trung

bnh cng ca cc sai s ngu nhin tin ti khng 0.

(n l s ln o; i l sai s thc)

0lim

nn

2.3 CC TIU CHUN NH GI CHNH

XC KT QU O CNG CHNH XC.

2.3.1 Sai s trung bnh:

Trong :

i = li - X l sai s thc ca ln o th i

li : kt qu o ln th i

X: tr thc ca i lng cn xc nh

n : s ln o

(2.2) 1 || ||

nn

n

ii

2.3.2 Sai s trung phng mt ln o

Cng thc Gauss: Tnh sai s trung phng theo sai s

thc

Sai s trung phng c nh ngha

Trong : i _l sai s thc ca ln o th i

i = li-X

n _s ln o

(2.3) 2

n

m

2.3.3 Sai s gii hn: l hn sai ca sai s

Theo tnh cht ca sai s ngu nhin trong iu kin o

nht nh tr tuyt i ca sai s ngu nhin khng vt

qu mt gii hn nht nh.

Thc nghim cho thy: gh = 2 3m

Trong trc a ly gh = 2m

m: l sai s trung phng.

Sai s gii hn c quy nh trong cc tiu chun, quy

phm; lm c s so snh xc nh s liu o t yu

cu hay cha?

2.3.4 Sai s trung phng tng i:

L t s gia sai s trung phng vi gi tr ln

ca i lng o:

Trong : mX _l sai s trung phng ca i lng o

X _l tr ln ca i lng o

Lu : kt qu tnh SSTPT lun th hin dng phn s m

c t l 1

(2.4)1

X

X

m

T X

2.4 SAI S TRUNG PHNG HM TR O V SAI

S TRUNG PHNG CA TR TRUNG BNH

2.4.1 Sai s trung phng hm

C hm F = f(x,y,,t)

x, y,..., t l cc bin s o c lp c o trc tip tng ng

c sai s trung phng mx, my , , mt

(2.5) ..... 22

2

2

txF mt

Fm

x

Fm

Trong : l cc o hm

ring phn ca hm F theo bin x, y,,t

(2.5) l cng thc tng qut tnh sai s trung phng

hm tr o (i lng o gin tip) thng qua cc i

lng o trc tip

t

F

y

F

x

F

; ... ; ;

2.4.2 Sai s trung phng trung bnh

o i lng X trong n ln o c l1, , ln 1 = l1 X

+ :

n = ln X

[]= [l] nX

Vi phn 2 v (2.6) chuyn qua sai s trung phng ta c

n

l

nn

lX

nn

lX

nn

][lim)

][][(lim

][][

(2.6) 1

...1][

1 nln

lnn

lX

(2.7) 1

...1 2

2

2

1

2

2

nXm

nm

nm

Nu coi cc tr o cng chnh xc: m1 = m2 = = mn Tac c:

Trong : mX : Sai s trung phng tr trung bnh

m : Sai s trung phng tr o (1 ln o)

n : S ln o

22

2 mn

nm

X(2.8)

n

mm

X

2.5 CNG THC BESSEN

Tnh sai s trung phng theo sai s xc sut nht

(s hiu chnh).

Nhn xt: tnh c sai s trung phng theo cng thc

Gauss th ta phi tnh c sai s thc i = li X ngha

l ta phi bit c tr thc X ca i lng cn o.

V vy cng thc Gauss (2.3) ch mang tnh thc nghim.

V nh trc a Bessen a ra cng thc tnh sai s

trung phng theo sai s xc sut nht nh sau:

(2.9) 2

1-n

v

m

T (2.8) v (2.9) ta c cng thc tnh sai s trung phng

trung bnh cng:

Trong : : l sai s xc sut nht (s hiu chnh)

li : kt qu o c ln th i

: s trung bnh ca kt qu o (tr xc

sut nht)

n : s ln o

(2.10)

)1(

nn

vv

n

mm

X

Xlv ii

n

lX

2.6 N V DNG TRONG TRC A V NGUYN

TC LM TRN S

2.6.1 n v thng dng

a) o di: mm, cm, dm, m, km

1m = 1.650.763,73 Kr86 Kr86 : Bc sng truyn trong chn khng ca nguyn t

Kripton 86 trong vng quang ph nht nh

b) Din tch: mm2, cm2, dm2, m2, km2, ha

cng, mu, 1 mu = 10 cng, 1cng = 1000 m2

c) o gc:

* , pht, giy

10=60=3600

* grat, pht grat, giy grat

2 =4000G, 10G=100G, 1G=100G

d) n v chuyn i

=1800 0=180/ = 5703 = 0x60 = 3438

= x60 = 206265

2.6.2 Nguyn tc lm trn s trong trc a

Cc s t 0 4 b V d: 3.34 = 3.3

Cc s t 6 9 lm trn ln 1 V d: 3.36 = 3.4

Vi s 5;

- nu trc n l s chn b V d: 5.25 = 5.2

- nu trc n l s l th lm trn ln 1. V d: 5.35 = 5.4

Vi hm lng gic khi tnh ton, hn ch sai s lm

trn phi ly n 6 s l thp phn

BI TP 1: Cho bit s liu o c nhiu ln mt on thng nh sau:

Tnh: 1. Tr trung bnh ca on thng

2. Sai s trung phng m (Gi s coi tr thc bng tr tb)

3. Sai s trung phng ca s trung bnh cng

4. Sai s trung phng tng i (1/T) ca on thng

trung bnh

STT Tr o

li (m)

TBinh

L (m)

Vi =li-L(m) Vi2 (m2)

1 120.55 0.00 0

2 120.57 0.02 0.0004

3 120.53 120.55 -0.02 0.0004

4 120.56 0.01 0.0001

5 120.54 -0.01 0.0001

0.00 0.0010

BI TP 2: Dng thc thp o din tch hnh ch nht c chiu di a=50m, b = 40m vi sai s trung phng tng ng ma= mb = 5mm.

Hy tnh:

1. Sai s trung phng xc nh din tch

2. Sai s trung phng tng i xc nh cnh a, b, v din tch

Gii:

2 2

2 2 2

S a b

2 2 2 2 2 2 2 2 2 2

S a b a a a

2 2 2 2 2

S a

2

S

a

a

b

b

S S1. Dien tch S a.b m m m

a b

m b m a m (b a )m (v m m )

m m (b a ) 0,005 40 50 (m )

m 0,320(m )

2. Saiso trung phng tng oi

m1 0,005 1

T a 50 10.000

m1 0,

T b

S

S

005 1

40 8.000

m1 0,320 1

T S 2000 6250

BI TP 3: o bn knh ca mt vng trn c R =

45,3cm 0,4cm. Tnh chu vi/din tch vng trn, sai s

trung phng v sai s tng i ca chu vi/din tch

Gii

C

C

: C 2 .R 2 .45,3 284,6 cm

m 2 . 2 .0,4( )

m 2.5( )

1 2,5 1

284,6 114

R

C

C

m cm

cm

m

T C

Chu vi vong tron

Sai so trung phng xac nh chu vi

Sai so trung phng tng oi cua chu vi

BI TP 5: o 1 gc 4 ln c cc tr s o

9002130 , 9002115 , 9002108, 9002140

1. Tnh tr trung bnh cng

2. Sai s trung phng mt ln o

3. Sai s trung phng ca s trung bnh cng (coi cc ln o c cng chnh

xc)

BI TP 6: Tnh mh khi h = S.tgV + i - l

S = 100m 0,05 m

V = 10020 0, 5

i = 130cm 7 cm 1,3 m 0,07

l = 125 cm 2 cm 1,25 m 0,02

BI TP 4: Hnh bnh hnh ABCD o cnh a=

AB=40,00 m, cnh b=AD=50,00 m. V sai s

trung phng tng i cnh a l 1/Ta=1/4000 ,

cnh b l 1/Tb = 1/5000, Gc A = 6000000 vi

sai s mA=0,5

1. Xc nh din tch hnh bnh hnh ABCD

2. Tnh sai s trung phng tng i xc nh

din tch hnh bnh hnh

B

a

A b D

C

GV: o Hu S

Khoa Xy dng

Chng 3:

DNG C V PHNG PHP

O TRONG TRC A

NI DUNG CHNG 3

Dng c v phng php o gc

- Cc loi gc c th o

- Thit b v phng php dng o gc

Dng c v phng php o di

- Cc loi chiu di

- Thit b v phng php dng o di

Dng c v phng php o cao

- Cc loi cao

- Thit b v phng php dng o cao

3.1 DNG C O GC 3.1.1 KHI NIM V CC LOI GC

3.1.1.1 Gc bng

Gc bng hp bi hai hng OA v OB l gc hp bi 2 mt phng thng ng cha hai hng y (Hay gc gia hai hng

OA v OB l gc to bi hnh chiu vung gc ca chng trn mt

phng nm ngang).

3.1.1.2 Gc ng V Gc ng V ca hng ngm OM l gc to bi hng ngm

vi mt phng ngang

VOM = 00 900

VOM = -VMO

3.1.1.3 Gc thin nh Z L gc hp bi hng thin nh vi hng ngm.

Z = 0 1800 Quan h gia V v Z:

Z + V= 900

P

O

M

M'V

Z

Z V

M

3.1.2 CU TO MY KINH V (THEODOLITE)_

THIT B O GC

My kinh v u tin c ch to Anh vo nm 1730 My kinh v l dng c o gc bng v gc ng. Ngoi ra n cn c

th dng o di, o cao vi chnh xc thp.

3.1.2.1 Nguyn l cu to My kinh v no cng c cu to vi 3 b phn chnh:

- B phn ngm (ng knh)

- B phn nh tm cn bng my: di tm (dy+qu di, ng di tm);

ng thng bng trn, thng bng di; 3 c cn

- B phn c s (bn ngang, bn ng)

3.1.2.2 Phn loi my kinh v a) Theo chnh xc

- My kinh v chnh xc cao, c sai s trung phng o gc: m=

0.51.5 - My kinh v chnh xc trung bnh: m = 210 - My kinh v chnh xc thp: m = 1530 b) Theo cu to

- My kinh v c hc (kim loi): C bn ngang, ng c cu

to bng kim loi, c s trc tip bng mt thng hoc knh lp

- My kinh v quang hc (*): C b phn s, c s: lm bng hp

cht trong sut. c s bng b phn knh khuych i (knh hin

vi).

- My kinh v in t:

Cc bn ngang +ng, lm bng hp cht trong sut

Bn c khc bng m vch

c s trc tip trn mn hnh

C th c b nh lu s liu

3.1.2.3 Cu to my kinh v k thut (quang hc)

y ta xt cho my kinh v k thut (my c chnh xc thp)

Cu to ca my c 3 b phn chnh:

- B phn ngm: ng knh

- B phn c s: bn ngang + ng

- B phn nh tm cn bng my: ng nh tm (ng di tm),

ng thy,

c cn.

a) Cu to ng knh: Gm 4 thnh phn

- Knh vt

- Knh mt

- c iu quang

- H li ch

* Trc ngm: l trc i qua quang tm knh vt v giao im h li

ch ngm.

* Trc quang hc: ng ni quang tm knh vt v knh mt

* Trc hnh hc: l trc i xng ca ng kim loi.

phng i ng knh: : VX = / = fV/fM Trong : , _ l gc nhn qua ng knh, gc nhn bng mt thng

ca cng mt vt.

Lu : Mt ngi bnh thng, khong cch ti thiu nhn r mt

vt l 25cm, gc nhn 60.

Oc ieu quangKnh mat

He thau knh

phan ky

Knh vat Li ch

b) Cu to b phn c s.

Bn ngang: - ng yn khi my xoay quanh

trc ng

- Khc vch t 00 3600 theo chiu kim ng h

Bn ng: - Chuyn ng cng ng knh quang

trc ngang

- Khc vch i xng qua tm (00 900) hoc lin tc (t 00 3600)

Thng b phn c s c thang chnh (chia n ) thang ph (chia

n pht)

chnh xc c s: ph thuc vo sai s c lng

B phn c s ca my kinh v 3T5K khi nhn qua

knh hin vi

V tr thun knh (bn ng bn tri ng knh)

S c bn ng: -20 13,2

S c bn ngang: 320 05,3

V tr o knh (bn ng bn phi ng knh)

S c bn ng: 60 35,2

S c bn ngang: 1230 19,3

c) Cu to b phn nh tm cn bng my

* B phn nh tm: c th l

Dy + qu di Mc ch a trc quay ca

ng di tm quang hc my trng vi tm mc

Tia laser

* B phn cn bng

- ng thy trn: Dng cn bng s b

Mc ch a trc quay ca my vo phng thng ng

- ng thy di: Dng cn bng chnh xc

Mc ch a bn ngang trng vi mt phng ngang

3.1.3 CC IU KIN HNH HC CA MY

m bo gc c o chnh xc th cc iu kin hnh hc

c bn ca my phi hon chnh. Tuy nhin thc t khng c

nh vy Cn kim tra v hiu chnh.

3.1.3.1 Trc ng thy di VV1 trn bn ngang phi vung gc

vi trc quay thng ng ca my LL1.

- t ng thy di song song vi 2 c cn, xoay 2 c cn ngc

chiu a bt nc vo gia. Quay my 900 xoay c cn th 3 a

bt nc vo gia. Quay my 1800 kim tra

nu khng lch khi v tr cn bng th my

n nh, nn lch ln hn vch khong

chia th phi hiu chnh

- Hiu chnh: hng kim tra (1800)

Dng vt iu chnh ng thy di a

bt nc vo khong lch, dng c cn

cn li a bt nc vo gia.

Tip tc kim tra v hiu chnh n khi t.

3.1.3.2 Trc ngm ca ng knh CC1 phi vung gc vi trc

quay nm ngang HH1 ca ng knh (sai s 2C)

ng knh nm ngang, Nhn mt vt A (cao ngang my) r nt

c 2 v tr bn Tri v Phi ta c:

M=T- C

M= P+ C

(3.1)

Nu C gii hn: my n nh

C > gii hn: my khng

n nh, phi hiu chnh

2

180)( 0

PTC

3.1.3.3 Trc quay nm ngang HH1 ca ng knh phi vung gc

vi trc thng ng LL1 ca my (sai s 2i).

a ng knh ln 40500 ngm im M cch my 10m, xong a ng knh v nm ngang nh du c hnh chiu MT(m1) ca

M. o knh ngm M xong a ng knh nm ngang nh du

c MP(m2) ca M: Nu MT = MP my tt

Nu MT MP nhiu a my vo xng sa cha.

3.1.3.4 Sai s MO (Sai s ch tiu ca bn ng)

xng oi khaco banvi

2

Tr -PhMO MO PhV

2

PhTrV MO TrV

3.1.3.5 Trc ng di tm quang hc K1K2 phi trng vi trc

xoay LL1 ca my

Xoay my di tm 3 v tr cch u mt gc 600 kim tra

3.1.3.6 Kim tra ch ng ca h li ch

So trng bng cch ngm si dy di

3.1.3.7 Kim tra sai s khc vch bn ngang

o cng mt gc cc vng bn khc nhau

3.1.4 O GC BNG

Nguyn l:

Gi s cn o gc AOB

H: mt phng nm ngang;

Mt phng trn N (bn ngang)//H

S (tm bn ngang) l giao ca

OO vi N

Hnh chiu ca OA, OB trn H l

OA , OB v trn N l Sa1, Sb1 gc bng AOB = AOB=a1Sb1

xc nh gc bng AOB, i xc

nh a1 v b1 trn N khi my ngm A

v B

Khi AOB = b1 a1 + (0 hoc 3600)

Thao tc ti mi trm o gm: * nh tm cn bng my

- nh tm (=dy di, di quang hc, laser): a trc ng ca

my i qua nh ca gc cn o

- Cn bng my: a trc ng ca my vung gc vi mt

phng ngang

* Ngm mc tiu

- Bt mc tiu s b: Nhn qua b phn ngm s b

- Bt mc tiu chnh xc: Dng c vi ng ngang v vi ng

ng thch hp a tm mng dy ch thp vo ng mc

tiu

* t tr s hng ban u (nu gc o nhiu ln)

Tr s hng ban u thng t 00 00 00 hoc 1800/n. Vi n

l s vng o

C hai phng php o gc bng:

3.1.4.1 Phng php o n (o gc n): trm ch o hai hng

t my ti O (nh tm, cn bng)

* Na ln o thun knh (bn ng bn tri)

Ngm A c c tr s hng trn bn ngang l a1 Quay my theo chiu kim ng h ngm B c c tr s hng

trn bn ngang l b1 Ta c: Gc na ln o thun knh T = b1 - a1 T = b1 - a1+360

0 (nu b1 < a1)

* Na ln o o knh (bn ng bn phi)

Sau khi o na ln o thun xong, o knh ngm B c c b2 Quay my cng chiu kim ng h ngm A c c a2 Ta c: Gc na ln o o knh P = b2 - a2 P = b2 a2+360

0 (nu b2 < a2)

Nu |P T| gii hn th tnh = (P+ T)/2

V d: Mu s o + ghi chp+ tnh ton gc o n bng my 3T5K

Trm

o

V tr bn

ng

im

ngm

S c trn

bn ngang

Tr s gc

na ln o

Tr s gc

mt ln o

B

Tri

(Thun knh)

A 920 10,5 1730 1012

1730 0954 C 2650 20,7

Phi

(o knh)

C 850 20,5 1730 0936

A 2720 10,9

C

Tri

(Thun knh)

B 3580 00,4 500 2224

500 2203 D 480 22,8

Phi

(o knh)

D 2280 23,2 500 2148

B 1780 01,4

3.1.4.2 Phng php o ton vng

(ti trm o 3 hng ngm)

Thng chn hng no xa nht lm hng khi

* o thun knh (na vng o thun knh)

Ngm A c c a1 Quay my theo chiu kim ng h ngm B c c b1 C c1 A a1 * o o knh (na vng o o knh)

Sau khi o xong na vng o thun knh, o knh

Ngm A c c a2 Quay my ngc chiu kim ng h ngm C c c c2

B b2 A a2

A

B

O

C

3.1.4.3 chnh xc o gc bng

Trong kt qu o gc bng lun c cha sai s. Cc nguyn nhn sai

s nh sau:

a) Sai s do mi trng

Do hin tng khc x ngang

Do s chuyn ng i lu ca lp khng kh

Do sng m, bi,

Hn ch : Chn thi im o thch hp

2

22

2

2

22

2

'

221

'

11

3

22112

'

222

'

111

1

caa

caa

AOC

bcbcCOB

aab

aab

BOA

b) Sai s do my mc thit b

Sai s do trc ngm khng vung gc vi trc quay nm ngang ca

ng knh

Sai s do trc quay nm ngang ca ng knh khng vung gc vi

trc ng ca my.

Sai s do trc ng ca my khng tht thng ng

Sai s do lch tm gia bn ngang v vng chun ngang

Sai s do khc vch trn vnh ngang khng u

Khc phc (hn ch): o thun v o knh, gia n vng o t tr s

hng khi l 1800/n

c) Sai s do con ngi

Sai s do nh tm my cha chnh xc

Sai s do nh tm tiu ngm sai

Sai s do ngm

Sai s do c s

Hn ch: Cn thn trong qu trnh o

3.1.5 O GC NG

o gc ng ca hng ngm n im M

* Thun knh: Ngm M, c trn bn ng c s c VT * o knh: Ngm M, c trn bn ng c s c VP

Gc ng V = (VT + VP)/2

Gc thin nh Z = 900- V (3.2)

Sai s Mo = (VT - VP)/2

Z V

M

3.2 DNG C V PHNG PHP O DI 3.2.1 KHI NIM o di l xc nh khong cch ca mt on thng no

xc nh v tr khng gian ca n trn mt t t nhin

C hai loi khong cch: Ngang: gi s k hiu S

Nghing: gi s k hiu D

chuyn t khong cch nghing D v khong cch ngang S,

ta phi o c gc nghing ca on thng hoc chnh cao

V d: on thng DAB nghing so vi mt phng nm ngang mt

gc AB

C 3 phng php o khong cch ph bin:

- o trc tip bng thc dy (thc vi hoc thc thp)

- o bng my c dy th c (kinh v quang hc, thy bnh quang hc)

- o bng thit b in t (my o xa in t, my ton c in t,..)

A

ABB'

DAB

AB

h AB

22

.

ABABAB

AB

hDS

cos D SABAB

3.2.1.1 Phn loi o di theo chnh xc

a) chnh xc cao:

b) chnh xc va:

c) chnh xc thp

3.2.1.2 Phn loi theo dng c o

a) My kinh v quang hc c chnh xc:

b) Thc vi, thc thp c chnh xc thp:

c) Thc thp chnh xc cao:

d) My in quang hoc ton c in t.

000.5

1

200

11

000.10

1

000.5

11

000.000.1

1

000.10

11

T

T

T

000.100

1

000.10

1

000.5

1

2500

1

000.1

1

800

1

500

1

300

1

3.2.2 O DI BNG THC THP 3.2.2.1 Dng c

Thc thp c lm bng thp mng ~ 0,4mm, rng 1525 mm, chiu di thc 20m, 30m, 50m. Trn thc c chia n dm, cm,

mm.

3.2.2.2 nh hng ng thng.

Thc t c nhng on thng cn o vi chiu di ln hn

chiu di ca thc. V vy c th o c khong cch on

chnh xc ta phi dng hng.

- C th dng hng bng mt thng: chnh xc thp.

- C th dng hng bng my: chnh xc cao.

A B D

C

C'

a) nh hng thng khi A thy B

Ti A v B t 2 so tiu.

Ngi th nht ng cch tiu ti A mt khong iu chnh ngi

th 2 cm so tiu di chuyn n khi no tiu A C B trng

nhau th cm tiu xung, v c th tip tc cm tiu tip theo.

b) nh hng thng khi A khng nhn thy B

nh hng theo phng php nhch dn

3.2.2.3 Phng php o

Vic o cn t nht c 2 ngi ( 1 trc, 1 sau)

Ngi sau cm u vch "0" ca thc, ngi trc cm u

thc c vch chn chc mt ko cng thc nm ngang ri cm

tiu. Ngi sau nh tiu ti A ri c 2 cng tin v pha B, tip tc

o cho n on cui cng. on cui thng khng chn mt nn

ngi trc cn phi c s l cn thn.

Sau khi o i t A B xong phi o v (bt buc) t B v A.

3.2.2.4 Tnh ton.

Ty c/x yu cu ta phi o gc nghing (AB) hoc chnh

cao gia hai im A v B (hAB) tnh chuyn v khong cch

ngang:

Sau khi o i v o v, tnh c S= SAB - SBA

Nu th ly kt qu trung bnh S = (SAB + SBA)/2

Ngc li nu phi o li

A

ABB'

DAB

AB

hAB22

cos.

ABABAB

ABABAB

hDS

DS

ghTS

S

1

ghTS

S

1

3.2.2.5 chnh xc o di bng thc thp

- Sai s do kim nghim thc.

- Sai s do thc gin n v nhit

- Sai s do t thc lch hng ng thng.

- Sai s do thc b cong trn mt phng nm ngang

- Sai s do lc cng khng u.

- Sai s do khng tnh hiu chnh dc,

3.2.3 O DI BNG MY C DY TH C (CH

LNG C) Hin nay cc loi my kinh v (Theodolite), my thu bnh

(Nivo) u c dy th c o khong cch. Trong h ch ch thp

c 2 ch trn v di nm i xng v song song vi vch ngang

(ch gia) ca mng dy ch thp.

Mia thng c lm bng g thng, di 3m, khc vch n

cm.

3.2.3.1 Trng hp tia ngm nm ngang

S

f

A

p

T'

D'

n

DE

B

T

t

d

F

A: My

B: Mia

S: di t my n mia

f: tiu c knh vt

E: di ngang t tiu im knh vt ti mia

: di ngang t knh vt ti trc chnh ca my

p: l khong cch ca 2 ch lng c

n: khong chn trn mia gia 2 ch lng c

T hnh v ta c : S = E + f+

Xt tam gic ng dng ta c:

k = f/p: l h s o di (thng k=100)

C = f+: hng s o di

S = k.n + C

Thng C nh c th b qua S = k.n (3.3)

n l hiu ca ch trn tr () ch di

np

fE

n

E

p

f

3.2.3.2 Trng hp tia ngm nm

nghing.

D=k.n = k.n.cosV

S = D.cosV = k.n.cos2V (3.4)

May

V

V

Mia

S

D

V

A B

C

n/2

n/2

n'/2

n.cosv'

n cosv

2

n

2

'n

3.2.4. O DI BNG THIT B IN T Cc thit b dng o: My + Gng phn x.

My c th l:

- My ring l

- B phn gn vo my kinh v quang hc

- My ton c in t

Cc thit b ny s dng sng v tuyn bc sng ngn hoc sng

nh sng.

Khong cch:

S=V.T/2

V: Vn tc nh sng

T: thi gian lan truyn sng t my ti gng v ngc li

Gng phn x +..

3.3 DNG C V CC PHNG PHP O CAO 3.3.1 KHI NIM CHUNG

o cao l mt trong nhng yu t xc nh v tr khng gian ca

mt im trn mt t.

cao H ca mt im l khong cch theo phng dy di t

im ti mt thy chun (Mt Geoid). Thc t khng o c

trc tip cao m ch o c chnh cao gia cc im ri cn c

vo im bit tnh ra cao ca im kia.

V d: HB = HA + hAB

hAB _ l chnh cao gia im A v B

HA, HB _ l cao ca im A, B so vi mt Geoid

Ty theo dng c v phng php o ta chia thnh cc loi sau:

A

A

H B

AB

mat Geoid

- o cao hnh hc

- o cao lng gic

- o cao kh p: chnh xc thp, sai s: 2 3m - o cao thy tnh: sai s 0.2mm/16m di - o cao bng my bay: sai s 5 10 m - o cao bng nh lp th.

3.3.2 CU TO MY NIVO (hay my thu bnh, thu chun)

Gm cc b phn chnh

- ng knh

- ng thy trn, thy di

- Cc c khng ch chuyn ng: c ni (lin kt) my v chn, 3 c

cn my, c kho ngang, c vi ng ngang.

3.3.2.1 ng knh

C 2 loi: ng knh cho nh thun

ng knh cho nh ngc

3.3.2.2 ng thy

- Thy trn: c cu to l dng chm cu, dng cn bng my s

b

- Thy di: c cu to l mt phn cung trn, dng cn bng chnh

xc.

3.3.2.3 Cc c khng ch chuyn ng

- c ni: gn cht my vi chn my

- 3 c cn: dng cn bng my (a trc ng thy trn v thng

ng hoc a trc ng thy di v nm ngang.

- c kho ngang: dng hm hay m cho ng knh quay ngang.

- c vi ng ngang: dng y cho ng knh quay ngang mt cht

(phi hm c kho ngang mi dng c c vi ng)

- c kch nng: dng chnh ng knh (trc ngm) ngc ln cao

hay chc xung thp mt cht

3.3.3 CU TO MIA O CAO

- Mia thng: thng c lm bng g, di 3m c khong chia

nh nht n cm, c hai mt en . C loi di 3m 7m gp

hoc rt (mia nhm), c khong chia nh nht n cm hoc cm.

Gia mt en v mt thng chnh nhau mt hng s 4475

hoc 4575 v hng s ca mt cp mia thng l 100.

- Mia c chnh xc cao: Mia Inva, l loi mia chnh xc nht,

c di inva gia; hai thang chnh ph hai bn.

- Ngoi ra cn c mia m vch dng cho cc my thy chun

in t.

.

00

01

02

03

04

05

25

26

27

28

29

45

46

47

48

49

71

72

73

74

mia mia

50

69

70

3.3.4 KIM NGHIM V IU CHNH MY NIVO

3.3.4.1 Kim nghim v iu chnh ng thy di

Trc ca ng thy di phi vung gc vi trc quay thng ng

ca my.

Kim nghim: t ng thy di song song vi 2 c cn, vn 2 c

ngc chiu nhau a bt nc vo gia. Quay my 900 dng

c cn th 3 iu chnh a bt nc vo gia. Quay my 1800 nu

bt nc lch khi v tr gia (v tr cn bng) th phi iu chnh.

iu chnh: Dng c hiu chnh bt nc iu chnh bt nc

chy ngc li cung lch, na cung lch cn li th dng c cn

my th 3 hiu chnh a bt nc vo gia. Sau quay my

i 1800 kim tra nu vn cn lch tip tc hiu chnh n khi t

yu cu.

3.3.4.2 Kim nghim v iu chnh mng dy ch thp

* Kim nghim: Chn ni khut gi, dng si ch buc qu di 1 u,

u kia buc ln trn ngay pha trc bc tng. t my cch

tng 25 30m, cn bng my chnh xc. 1 u vch ng ca dy ch thp trng vi dy di, nhn xem u kia c trng khng.

Nu lch qu 0,5mm phi iu chnh mng dy ch thp.

* iu chnh: Vn lng cc c iu chnh ca ring mng dy ch

thp, xoay nh b phn ny cho vch ng du ch thp trng kht

vi dy di ri vn cht cc c c nh mng du ch thp li

3.3.4.3 Kim nghim v iu chnh gc i

t 2 mia trn 2 cc st A v B. A v B cch nhau 50m

t my ti I (IA = IB) cn bng my c c ti mia A, B l a1, b1

t my ti II (IIA = AB/10) cn bng my c c ti mia A, B l

a2, b2

a2

5m

II

a1

A

25m

i"

25m

i"

I

i"

b1

B

b2

t 2 mia trn 2 cc st A v B. A v B cch nhau 50m

t my ti I (IA = IB) cn bng my c c ti mia A, B l a1, b1

t my ti II (IIA = AB) cn bng my c c ti mia A, B l a2,

b2

Gc i c tnh:

Trong : h = (b1 a1) + (a2 b2)

D: l khong cch gia A v B

= 206265

Ty theo yu cu cp hng o m ta c igh.

Nu i < igh th my t yu cu

Nu i > igh th hiu chnh nh sau:

nguyn my ti II, chnh mng dy ch thp cho s c trn mia B

l b2 = b2 + 1,1 h.

Sau kim tra li gc i nu vn cha t th tip tc hiu chnh.

Lu : kh sai s gc i, ti mi trm o lun t my v tr gia.

hD

i "

3.3.5 PHNG PHP O CAO HNH HC

Nguyn l ca phng php o cao hnh hc l da vo tia

ngm nm ngang (ngha l song song vi mt thy chun v vung

gc vi phng dy di) xc nh chnh cao gia 2 im. Dng

c o l my v mia thy chun

3.3.5.1 o cao t gia

00

01

02

03

04

05

mia

B

A

a b

h AB

00

01

02

03

04

mia

B C

NA

a b

hAB

Trng hp on AN phi chia thnh nhiu on o, ta tin hnh o

chnh cao tng on

hAN = hAB + hBC + hCN

B, C l cc im trung gian

3.3.5.2 o cao pha trc

Trng hp my thy chun t ti im M bit cao,

xc nh cao ca cc im ln cn, chng hn N.

t my ti im M cn bng, o chiu cao my i, c s ch

gia trn mia dng N l b, ta c

hMN = i - b

HN = HM + hMN = HM + i b

3.3.5.3 Cc ngun sai s trong o cao hnh hc

Trong o cao hnh hc c cc ngun sai s sau:

a) Sai s do trc ngm b nghing (trc ngm khng song song vi

trc ng thy di)

Hn ch: + Hn ch khong cch t my n mia

+ t my cch u 2 mia

b) Sai s do my v mia b ln theo thi gian

Hn ch: + Thao tc ti mi trm o phi nhanh v o theo quy

trnh: Sau Trc Trc Sau.

+ o i v o v ly tr trung bnh

c) Sai s do cong ca tri t v khc x nh sng.

Tia ngm b khc x do i qua cc lp khng kh c chit xut

khc nhau.

Hn ch: t my chnh gia 2 mia

d) Sai s do nh hng ca hin tng chit quang ng.

Hn ch: + Tia ngm cch mt t > 0.5m

+ o i v v hai bui khc nhau, ly kt qu trung

bnh

e) Sai s do mia:

- Do mia khng thng ng: Hn ch bng cch gn bt thy

- Do mia b mn: Hn ch bng cch b tr s trm o chn trn

mt on o.

- Do di mia thay i: Kim nghim ri hiu chnh vo kt qu

o.

f) Sai s khc

Sai s do c c

Sai s do lm trn s

Sai s do nhit , nh sng,

3.3.6 O CAO LNG GIC o cao hnh hc cho ta kt qu chnh xc cao nhng tn nhiu

cng sc v thi gian. Khi phi o nhiu, nhanh v chnh xc

i hi khng cao lm th ta p dng phng php o cao lng

gic.

Nguyn l ca o cao lng gic l da vo mi tng quan

hm lng gic trong tam gic to bi tia ngm nghing, khong

cch gia hai im v v phng dy di i qua im cn xc nh

cao. Dng c o l my c bn ng (my kinh v, my ton

c) v mia

o cao lng gic l o gc ng v cnh nm ngang gia 2

im. Phng php ny c p dng o chi tit bn a

hnh

xc nh chnh cao hAB

t my ti A, mia ti B

T hnh bn ta c: hAB +l = iA +h

hAB = iA +h l

trong h= S. tgV

m S = kn.cos2V

h = kn.cos2V.tgV = kn.cosV.sinV = kn.sin2V

hAB = kn.sin2V + iA l (3.5)

khi V = 0, ta c: hAB = iA l

iA

V

AB

lh'

hB

D

S

Bi tp: Bit rng chng ta c my kinh v v mia. Hi c xc nh

c chiu cao ca cy nh hnh di khng? Nu c, cch xc

nh nh th no?

h?

BA

GV: o Hu S

Khoa Xy dng

Chng 4:

LI KHNG CH TRC A

NI DUNG CHNG 4

Khi nim v gc phng v

Cc bi ton c bn v gc phng v ta

Li khng mt bng Phng php thnh lp v

tnh ton

Li khng cao Phng php thnh lp v

tnh ton

4.1 GC NH HNG V GC PHNG V

4.1.1 nh hng ng thng nh hng mt ng thng no l xc nh gc hp bi ng

vi mt ng khc c chn lm gc.

Trong trc a, hng gc c chn c th l: Kinh tuyn thc, kinh

tuyn t, kinh tuyn trc ca mi. Tng ng c cc khi nim gc phng

v thc, phng v t, gc nh hng.

4.1.2 Gc phng v a) Gc phng v thc

Gc phng v thc Ath ca mt ng ti

mt im l gc phng tnh t hng Bc

ca kinh tuyn thc (cn gi l kinh tuyn

a l) theo chiu kim ng h n hng

ng thng. (Ath: 00 3600)

Hng Bc ca kinh thc ti mt im c

xc nh bng o thin vn

A

B

Ath

b) Gc phng v t

Gc phng v t At l gc phng tnh t hng Bc ca kinh tuyn t

theo chiu kim ng h n hng ng thng. (At = 00 3600)

Hng bc kinh tuyn t c xc nh bng la bn, chnh xc thp

B

A

At

AA

B

tA

th

Ti mi im thng kinh tuyn t khng trng vi kinh tuyn thc

m lch mt gc (gi l lch t)

lch t c th mang du m (+) nu lch v pha ng (bn

phi) kinh tuyn thc, du (-) nu lch v pha ty (bn tri) kinh tuyn

thc.

mi ni khc nhau lch t cng khc nhau, v lch t bin

i theo thi gian nn ti mi im lch t cng khc nhau nhng

thi im khc nhau.

Cng thc tnh gn ng th hin mi quan h gia gc phng v thc

(Ath) v gc phng v t At.

Ath = At +

c. Gc nh hng (phng v ta )

Gc nh hng ca mt ng thng l gc phng tnh t hng Bc ng song song vi kinh tuyn trc trn mt chiu theo chiu kim ng

h n ng thng . ( = 00 3600)

A

AB B

Ti mi im trn cng ng thng

gc nh hng khng thay i.

Ti mi im thng kinh tuyn trc khng trng vi kinh tuyn thc m

lch mt gc (gc hi t kinh tuyn)

=Ath +

m Ath = At + = At + +

Gc hi t kinh tuyn ca mt on thng AB c xc nh theo cng

thc

AB = ABsin

Trong : AB = B - A v trung bnh cnh AB.

4.2 CC BI TON C BN V GC NH HNG

4.2.1 Tnh gc bng khi bit gc nh hng

(Tnh gc bng hp bi 2 ng thng bit gc nh hng)

Bit gc nh hng ca hai cnh OA, OB l OA, OB nh hnh v. Xc

nh =AOB?

= OB - OA

Tng qut:

AOB= OB - OA + (0 hoc 3600)

BOA= OA - OB + (0 hoc 3600)

O

B

AO

A

O

B

4.2.2 Tnh chuyn gc nh hng

Gi s bit AB , gc = ABC. Tnh BC

BC = AB + T 1800 (ABC = T , gc bng bn tri ng tnh)

BC = AB - P + 1800 (CBA = P , gc bng bn phi ng tnh)

A

ABB

BC

P

C

4.2.3 Bi ton thun: Chuyn t to cc sang to vung gc

Gi s bit: A(xA, yA), SAB, AB. Tnh B(xB, yB) ?

xB = xA + SAB*cos AB yB = yA + SAB*sin AB

A

XAB

0

x

YAB

ABSAB

B

y

B'

4.2.4 Bi ton ngc: Chuyn to vung gc sang to cc

Bit A(xA, yA), B(xB, yB). Tnh SAB, AB?

* Tnh SAB

* Tnh AB Xt tam gic ABB, c

Gi tr gc nh hng AB ph thuc vo du ca x, y c th nh

bng sau:

22 ABAB yyxx SAB

tgAB B A

AB

AB B A

y y y

x x x

0 at ABAB

AB

yarctg

x

Du x Du y Gi tr AB = V tr

+ + Gc phn t th 1

- + 1800 - Gc phn t th 2

- - 1800 + Gc phn t th 3

+ - 3600 - Gc phn t th 4

0

AB0

AB0

AB

0

AB

4.2.5 Bi ton to cc

Bi ton ny c ng dng xc nh im chi tit khi o v bn ,

kim tra ta ,

Bit A(xA, yA), AB; o c gc cc j, cnh cc Sj . Xc nh ta ca

j (xj, yj)?

tnh ta ca im no : tm cch chuyn v dng bi ton thun.

X.nh ta ca j, tm cch a v dng bi ton thun gia 2 im A v j

xj = xA + Sj .cos(AB+ j)

yj = yA + Sj .sin(AB+ j)

A

j

Sj

j

B

4.3 LI KHNG CH MT BNG

4.3.1 Khi nim Li khng ch trc a l mt h thng (tp hp) nhng im

ngoi thc a c to (x, y, H) c xc nh vi chnh xc cn thit

lm c s cho o v bn , b tr cng trnh,

Theo bn cht, li khng ch trc a c chia ra lm: li khng

ch mt bng (nu cc im ch c to x,y) v li khng ch cao

(nu cc im ch c cao H)

C hai phng php chnh xy dng li khng ch mt bng l li

tam gic v li ng chuyn.

Ngoi ra, c th ng dng GPS xy dng li khng ch .

Vi li tam gic: hoc o tt c cc gc, hoc o tt c cc cnh, hoc

o cnh ln gc

Vi li ng chuyn phi o tt c cc gc v cnh trong li

- A, B, C, D, M, N, S, T: l cc im gc bit ta

- K1, K2,.. T1, : l cc im cn xc nh ta

Lu : Khng o cnh gc

D

N

B

A

M

S

T

C

K1

K7 K4

K5 K2

K3 K6

T1

T2

T3

4.3.2 Phn loi Theo quy m v chnh xc gim dn, li khng ch mt bng c

chia ra:

- Li khng ch ta GPS cp O

- Li khng ch nh nc (hng I, II, III, IV)

- Li khng ch khu vc (li khng ch a phng): cp 1 & 2

- Li khng ch o v.

V nguyn tc pht trin li: T chnh xc cao xung chnh xc thp.

S lng im khng ch ta trn lnh th VN:

- Cp O: 71im

- Hng I: 328 im

- 1.177 im hng II, 160 im ng chuyn hng II

- Hng III: 12.658 im

4.3.3 NG CHUYN KINH V

4.3.3.1 Thit k: - ng chuyn kinh v l loi li khng ch o v mt bng, c pht

trin t li cp trn c chnh xc cao hn. Trong trng hp c bit

c th c xy dng li ng chuyn kinh v c lp.

- Phi o tt c cc cnh, gc ni v gc ngot ca li

- C 3 loi ng chuyn:

+ Ph hp (h)

+ Khp kn

+ Treo (nhnh)

Cc ch tiu k thut c trng ca ng chuyn kinh v

- Chiu di cnh ca li Si 20m Si 400m

- T s chiu di 2 cnh lin k khng vt qu 1,5 ln

- Sai s khp gc f:

- chnh xc o cnh

S= Si Sv

S= (Si + Sv )/2

- Sai s khp tng i ng chuyn:

[S]: tng chiu di cc cch o trong li

Trong : n l s gc o ca li ng chuyn kinh v

nui vung

bang ong vung

n

n

"60

"40

S

fS

nui vung

1000

1

bang ong vung

2000

1

nui vung1

bang ong vung

1000

2000

1

S

S

4.3.3.2 Cc bc thnh lp ng chuyn kinh v

a) Kho st chn im

- Tm hiu mc ch, nhim v, yu cu,

- Tnh hnh c im khu o: ng bng, vng ni, , tnh hnh giao thng?

- Thu thp t liu trc a c ca khu o.

- Chn im nhng v tr c nh c tm nhn bao qut nhiu nht, nhn

thy im trc im sau n v di cnh trong quy nh.

- D kin trc phng n o, dng c o.

- Cc im chn m bo khng ch ton b khu o.

- im khng ch c nh du bng cc b tng, cc g,n nh v tn

ti trong thi gian yu cu.

b) o gc, cnh ng chuyn.

* o gc:

Cc gc c o bng my kinh v k thut c chnh xc m =

30. V ch o 1 ln o (o thun + o knh)

- o gc ni (li ph thuc); o gc nh hng (li c lp), c

th dng la bn xc nh gc phng v t v coi l gc nh hng.

- o cc gc ngot trong li

* o cnh: o bng thc thp hoc my o di in quang, ton c in

t.

- o bng thc thp: o 2 ln ly trung bnh, vi yu cu sai s o

cnh:

- o bng my o di in quang: o 2 ln ring bit, sai s 2a

a: hng s ca my ly t cng thc: mS = a + b/1km

khan) kho hnha hoacli) thuan hnha (1000

1(

2000

1

S

S

C) TNH TON BNH SAI NG CHUYN KINH V (BNH SAI

GN NG)

* S li

* Tnh sai s khp gc

N: l tng s gc trong li ng chuyn ph hp

Nu f > f g.hn kim tra s liu, tnh ton Nu f f g.hn Tnh:

A

B

1

2

3

C

D

n 1

0

o lt i cuoi au

1

f - N.180

-

i

i

f

So hieu chnh goc : -

Goc sau hieu chnh :

VN

V

'i i

* Tnh chuyn gc nh hng theo gc hiu chnh

* Tnh s gia ta Xi, i+1 = Si, i+1.cosi, i+1 Yi, i+1 = Si, i+1.sini, i+1

* Tnh sai s khp ta

0

i, i 1 i 1, i i ' 180

j

n

x o lt j cuoi auj 1

n

y o lt cuoi auj 1

2 2

S x y

2 2

x y

gii han

f X - X X - X

f Y - Y Y -Y

f f f Sai so khep tuyet oi

f f

Sai so khep tng o

S

S S

X

Y

f f

S S

i

* Nu

Tnh:

S S

gioihan

f f

S S

Xi,i 1 i, i 1

Y i, i 1 i, i 1

'

i, i 1 i, i 1 Xi, i 1

'

i, i 1 i, i 1 Yi, i 1

- SS

- SS

V

V

x

y

fV

fV

X X

Y Y

So hieu chnh so gia toa o

So gia toa o sau hieu chnh

*

'

1 i 1, i

'

1 i 1, i

i i

i i

X X X

Y Y Y

Toa o sau bnh sai

A (100m,100m)

B (150m,150m)

C (100m,300m)

D (150m,350m)

B1 =61.145 m

12 = 74.894m

2C = 79.320 m

1. Hay bnh sai li kinh v tren.

BAI TAP1: Bnh sai ng chuyen phu hp

Cho li kinh v nh hnh ve vi A, B, C, D la cac iem goc; 1, 2 la iem can xac nh.

Toa o :

Canh o:

2. Biet SSTP o canh B1 la 5mm, SSTP o goc B la 10"va coi cac iem goc khong co sai

so. Tnh sai so trung phng xac nh iem 1

B

A

1

2

C

d) VI NG CHUYN KHP KN

Tnh ton tng t nh ng

chuyn ph hp trong ch khc:

f = [] 1800 (n-2)

fx = [X] fy = [Y]

1

2

3

4

A

BI TP 2: Li ng chuyn kinh v khp kn nh hnh v ( khu

vc ng bng), o tt c cc cnh, cc gc ca li v AB = 15402100.

Bit A(X=1000,000m; Y=1000,000m). S liu o trong bng sau:

S hiu im Tr gc o Tr cnh o

(m)

A

73.180

B

450 23 05

75.960

C 29501450

640 45 10 57.600

A 690 51 00

Hy bnh sai li ng chuyn kinh v khp kn trn.

A

C

B

AB

4.4 LI KHNG CH CAO

4.4.1 Khi nim:

Li khng ch cao l tp hp nhng im c nh ngoi thc a c

cao H c xc nh chnh xc, n l c s nghin cu khoa hc, o

v bn , b tr cng trnh,

He thong co iem nut

M

N

P

Q

III

K

1

1

1

2

3

2

3

4

2

3

4

5

67

8

ng khep kn

ng n

4.4.2 Phn loi

Theo quy m v chnh xc gim dn, li khng ch c cao c chia

ra:

- Li cao nh nc hng I, II, III, IV

- Li cao k thut (li cao khu vc)

- Li cao o v

V hnh dng ( hnh) li khng ch cao c cc dng ng n,

khp kn, h thng mt hay nhiu im nt.

S lng im khng ch cao trn lnh th VN:

Hng I: 1.176 im,

Hng II: 1.114 im,

Hng III: 2.334 im

(S liu thng k ngy 30/04/2007 ca B TNMT)

4.4.3 LI CAO K THUT

4.4.3.1 Thit k

Li cao k thut l li khng ch cao khu vc, lm c s v cao cho li o v. N c xy dng pht trin t cc im cao nh nc (hng I, II, III, IV). Trong trng hp c bit n c xy dng c lp.

Li cao k thut c b tr di dng ng n hoc h thng c mt hay nhiu im nt, gi u t nht ln hai im hng cao.

Trong trng hp c bit c th b tr di dng ng khp kn. Chiu di ng chuyn khp kn khng vt qu 50% chiu di ng n.

Ph thuc vo khong cao u ng ng mc m chiu di cho php cc ng cao k thut c quy nh trong bng sau:

4.4.3.2 o li

Li cao k thut c o bng my NIVO c h s phng i ng

knh Vx > 20x; nhy ng thy < 45; mia mt mt hoc mia hai mt.

My v mia phi c kim nghim trc khi o.

Li cao k thut ch phi o mt chiu.

Dng ng li khng ch

cao k thut

Khong cao u o v bn (m)

0.25 0.5 1 2 5

1. ng n 2 km 8 km 16 km

2. Gia im gc v im nt 1.5 km 6 km 12 km

3. Gia hai im nt 1 km 4 km 8 km

Trnh t thao tc o ti mt trm my:

* Khi s dng mia hai mt en

- Mia sau: c mt en

- Mia trc: c mt en

* Khi s dng mia mt mt

- c mia sau, mia trc

- Thay i chiu cao my 10cm, c mia trc, mia sau.

Khong cch t my ti mia: trung bnh 120m, max = 200m

Chnh khong cch trc sau: (S1-S2) 5m

S2S1

Chnh lch cao ti mi trm theo hai mt mia hay theo hai cao my

khng c vt qu 5mm

h1 - h2 5mm

Sai s khp cho php:

Trong : L (n v km) _ l chiu di ng o

ni c dc ln c s trm o 25 trm/1km th

Trong : N_ l s trm o trn ng o.

4.4.3.3 Quy trnh bnh sai li cao k thut.

Li cao k thut c bnh sai theo phng php gn ng.

a) S li

(*) (mm) L 50 hf

(**) (mm) N 01 hf

2

1

3

h1 h2h3

h4

l1 l2 l3

l4A

B

b) Tnh sai s khp chnh cao

fh = [h]o- [h]lt = [h]cng chiu (Hcui Hu) vi ng n

fh = [h] o vi ng khp kn

Lu : Khi tnh [h], cc chnh cao phi cng chiu

L(km) =[ l ]; li l chiu di on o th i

N=[n] ; ni l s trm o trn on o th i

Nu fh > fhgh kim tra li s liu, tnh ton

Nu fh fhgh -> tnh qua bc c

c) Tnh s hiu chnh chnh cao

( )

( )

50 ( ) *

10 ( ) **

gh

gh

h

h

f L mm

f N mm

( )

i,i 11

( )

i,i 11

h

h

*

**

h

i,i

h

i,i

fV l

L

fV n

N

d) Tnh chnh cao, cao cc mc sau bnh sai

Chnh cao sau binh sai hi, i+1, = hi, i+1 + vh i, i+1

cao bnh sai Hi = Hi-1 + hi-1, i

V d

o thu chun hnh hc, li cao k thut. S liu o c th hin trn s

tuyn o (nh hnh v). Trong : A, B l hai im gc, li l chiu di

on o, hi l chnh cao on o.

Hy xc nh gi tr cao xc sut nht ca im 1 v 2 ?

h 2 = -0.766m

l 2 = 420m

H A = 5.450m

A

l 1 = 459m

h 1 = -1.234m

1

3

l 3 = 660m 2

B

H B = 5.500m

S

hiu

im

di

li (m)

Chnh

cao o

hi (m)

S h.chnh

chnh cao

Vhi (mm)

C.cao

h.chnh

h'i (m)

cao

Hi (m)

A 5,450

459 -1,234 -11 -1,245

1 4,205

420 0,766 -10 0,756

2 4,961

660 0,555 -16 0,539

B 5,500

1539 0,087 -37

L

lifVh

mmLf

mmHHhfh

hi

gh

AB

62539,15050

37)54505500(87)(

4.4.4 LI CAO O V

Li cao o v l cp pht trin cui cng.

N c xy dng pht trin t im cao k thut tr ln hoc c

xy dng c lp

Li cao o v c o bng phng php o cao hnh hc (my Nivo

hoc my kinh v c gn ng thy di trn ng knh) hoc bng phng

php o cao lng gic.

4.4.4.1 Tiu chun li cao o v khi c lp bng o cao hnh hc

- Khong cch t my ti mia 200m

- Chiu di ng chuyn khng qu 2km hoc 4km (khi o v bn

vi khong cao u 0,5 ; 1,0m)

- Sai s khp gii hn: Trong L(km) l chiu di tuyn o

)(100 mmLfgh

4.4.4.2 Tiu chun li cao o v khi c lp bng o cao lng gic:

p dng khi o v bn a hnh vng ni vi khong cao u 2m.

C s pht trin li cao lng gic l cc im cao k thut tr

ln.

- ng o cao lng gic c th b tr trng vi li ng chuyn cp

1&2, ng chuyn kinh v, ng chuyn ton c.

- Gc ng trong li ng chuyn cp 1, cp 2, kinh v, v ton c

c o cng lc vi o gc bng.

Sai s khp gii hn:

Trong : n _ s lng cnh trong li

S = [S]/n chiu di cnh trung bnh, n v l m

Phan c hng: CT09A. Cm thi

)( 4,0 mmnSfgh

GV: o Hu S

Khoa Xy dng

Chng 5:

O V V S DNG BN

A HNH

NI DUNG CHNG 5

Cc PP thnh lp bn a hnh

Cc PP xc nh im chi tit khi o v bn

o v mt ct a hnh

Xc nh khong cch, ta , din tch

ng bnh v ng dng

- dc v gc dc a hnh

- Mt ct,

5.1 KHI NIM V NI DUNG

O V BN A HNH

5.1.1 Khi nim

o v bn a hnh gm cc cng on: Thit k lp li khng

ch to , cao; o v chi tit a hnh; tnh ton v v bn .

Bn a hnh th hin a vt v dng t cao thp khc nhau

C 3 phng php o v chnh:

- Phng php o v ton c

- Phng php o v trn nh

- Phng php tng hp (tng hp c hai phng php trn)

Hin nay, c th dng cng ngh GPS thnh lp bn a hnh.

C s khng ch to v cao o v bn a hnh t l ln

khu cng nghip, thnh ph v khu kinh t trng im quy nh trong

bng sau:

Dien tch khu

vc o ve (km2)

Cc loi li khng ch phi c

Mat bang

o cao Nha nc

(hang)

Khu vc

(cp)

o v

200 v ln hn II, III, IV 1, 2 ng

chuyn

kinh v

(1,2)

Li

tam gic

nh

II, III, IV, k thut, o

v

T 50 n 200 III, IV 1, 2 II, III, IV, k thut, o

v

T 10 n 50 IV 1, 2 III, IV, k thut, o v

T 5 n 10 IV 1, 2 IV, k thut, o v

T 2.5 n 5 1, 2 IV, k thut, o v

T 1 n 2.5 1, 2 IV, k thut, o v

Nh hn 1 2 k thut, o v

Mt im khng ch mt bng ca li trc a nh nc v li tam gic gii tch cp 1, cp 2 hoc ng chuyn cp 1, cp 2 phi m bo t nht 4im/km2 vng thnh ph, khu cng nghip, khu xy dng

v 1im/km2 vng khng xy dng. 5.1.2 Ni dung o v bn a hnh (t l ln 1:5000 1:500):

- Cc im khng ch trc a, cc kin trc c lp, nh , cng trnh cng cng, cng trnh cng nghip v nng nghip, cng trnh dn dng

- ng thng tin lin lc, n bin bo, ct in, ct cy s

- ng st v cc cng trnh lin quan: ng ngm, sn ga,

- Cu ng: ng nha, ng t, cu cc loi

- H thng thy vn: sng sui, ao h, knh rch,

- H thc ph, cy c lp

- Phi o ht cc ng c trng ca dng t: nh ni, y lng cho, im un thay i dc, ng phn thy, ng t thy, ng mp cho, yn nga cao mc nc trong ao h, sng sui,

- Dng t c trng c biu th bng cc ng ng mc kt hp

vi k hiu, ghi ch cao.

- Phi ghi a danh chnh thc, nu c tn a danh c th tn c y

trong ngoc n.

Ai

Si

i

B

5.2 CC PHNG PHP O V CHI TIT.

o v chi tit l o a vt v dng t. o chi tit l xc nh v tr

tng i ca im chi tit vi im khng ch.

Trong bn a hnh, cc im chi tit c xc nh c v tr mt

bng (x, y) v cao H

5.2.1 Cc PP xc nh v tr mt bng ca cc im chi tit

a) Phng php to c cc

A, B: im gc; i cn xc nh

o gc cc v bn knh cc (, S)

b) Phng php h ng vung gc

T im chi tit M,

h ng vung gc vi cnh

khng ch AB ti M o

c c S v S

M'

B

A

S

S'

c) Phng php giao hi gc

A,B: im gc; N: im cn xc nh

Dng xc nh im xa hoc im m ta khng th n c.

Xc nh A, B

t my ti A nh hng v B, ngm N o c gc A=3600- A

t my ti B nh hng v A, ngm N o c gc B

A

N

BBA

cotg cotg ( )

Cong thc IUANG

cotg cotg

cotg cotg ( )

cotg cotg

A B B A B A

N

A B

A B B A B A

N

A B

X X Y YX

Y Y X XY

AC

BBA

SA SB

d)Phng php giao hi cnh

A, B: im gc, C: cn xc nh

o cnh AC v BC ta xc nh c C.

5.2.2 Xc nh cao H ca im chi tit

a) o cao lng gic (xem phng php o cao lng gic)

Trong o v bn a hnh, cao cc im chi tit thng c

xc nh bng phng php o cao lng gic. Trong phng php to

cc, ta o ng thi 3 yu t (S, , V): cnh cc, gc cc, gc ng;

b) o cao hnh hc

Khi yu cu cao c xc nh chnh xc cao th ta s dng

phng php o cao hnh hc.

Phng php ny t dng trong o chi tit v tn km thi gian v

cng sc.

5.3 O V BN A HNH (PHNG PHP TON C)

Trong phng php ny ta s dng my kinh v ton c o chi tit. V my ton c o c ng thi c 3 yu t: gc, chiu di, chnh cao

My ton c c 2 loi: Ton c quang hc v ton c in t.

5.3.1 Lp li khng ch mt bng v cao.

Vic o v chi tit bn a hnh c da vo tt c cc im khng ch trc a c trong khu vc

Khi mt im li khng ch o v cha th b tr tng dy bng ng chuyn ton c.

ng chuyn ton c c pht trin t cc im kinh v tr ln. V m bo cc yu cu trong bng sau:

V ng chuyn ton c tho iu kin:

- Sai s khp

- Sai s o cnh

TIU CHUN NG CHUYN TON C

Ty le ban

o

Chiu di ln nht

ca c ng

chuyn (m)

Chiu di ln

nht ca mt

cnh (m)

S cnh nhiu

nht trong ng

chuyn

1:5000 1200 300 10

1:2000 600 200 8

1:1000 300 150 6

1:500 200 100 4

)1.5("60 nf

phang bangVung

doc nui, oi Vung

400

1

300

1

S

S

- Sai s khp ca ng

- Khp chnh cao

Trong : n_ s cnh ng chuyn cao S = [S]/n chiu di cnh trung bnh, tnh theo n v m

Khi o v bn t l 1/500, cnh ng chuyn ton c phi o

bng thc thp v tho mn cc yu cu:

phang bangVung

doc nui, oi Vung

400

1

300

1

S

fS

)2.5()(4,0 mmnSfgh

h

1000

1

S

S

1000

1

][

S

fS

5.3.2 o v chi tit (phng php to cc)

o ng thi xc nh S, , V

My kinh v phi c kim tra sai s MO trc khi o.

Thao tc ti mt trm o nh sau:

- t my vo trm o A (nh tm, cn bng my)

- o chiu cao my iA (tnh t mt mc n trc quay nm ngang ca ng knh tm bn ng)

- Ngm chun B (t bn ngang = 00 00 00)

- o im chi tit (S, , V)

+ c ch trn ch di: ( + gc ng V xc nh S) + c ch gia xc nh chiu cao mia

+ c bn ngang xc nh

+ c bn ng xc nh V

- Khp chun ngm li B. Kim tra iu kin 130

Ngi i mia phi dng vo tt c cc im chi tit c trng ca a vt v dng t.

Khong cch gia im mia im mia v khong cch gia my mia c quy nh trong bng sau:

T l

bn

Khong

cao u

(m)

Khong cch ln nht

gia cc im mia

(m)

Khong cch ln nht t my

n mia khi o v (m)

Dng t a vt

1:500 0,5 15 100 60

1,0 15 150 60

1:1000 0,5 20 150 80

1 - 2 30 200 80

1:2000

0,5 40 200 100

1.0 40 250 100

2 - 5 50 250 100

1:5000

0,5 60 250 150

1,0 80 300 150

2,0 100 350 150

5,0 120 350 150

Nhng vn cn lu khi o chi tit:

- C s phi hp nhp nhng gia ngi o, ngi i mia v ghi s.

c s trn mia trc, khi ngi i mia di chuyn ti im khc ngi

ng my c , V

- Ch o mt v tr ng knh (thun knh), c n pht

- khu vc bng phng nn t V=0 tin cho vic tnh ton

- Phn chia ranh gii cho tng trm o, cn o ph mt vi im

cc trm k cn kim tra.

- Phi v s ho v ghi ch.

- Cc s liu phi ghi ngay vo s o.

5.3.3 Tnh ton

* Tnh ton bnh sai li khng ch

* Tnh ton cc s liu o chi tit

- Gc ng: Vj = VTj Mo

- Khong cch ngang:

Sj = K.nj.cos2Vj (5.3)

- cao im chi tit:

Ta c: iA+ h=hAj +l

iA+ S.tgV = Hj-HA+l

Hj = Hmy + imy + Sj.tgVj l (5.4)

Trong : VTj _Gc ng c v tr thun knh.

Mo _Sai s Mo = (VT+VP)/2

nj = ch trn - ch di)

Hmy _ cao im t my

imy _ Chiu cao my

l _ S c ch gia

iA

A

V

h

h'l

j

Aj

S

5.3.4 V bn

* Giy v: t co gin

* K li to vung (kch thc vung 10x10cm)

* Trin im khng ch trc a ln bn v theo phng php to

vung gc, v k hiu im khng ch; ghi s hiu im (t s) v

cao ca n (mu s).

V d:

* V im chi tit ln bn v theo phng php tng ng khi xc o

thc a bng thc chuyn dng, compa, v ghi cao ca n (

cao im chi tit ch ly n cm khi ghi ln bn c o v vi

hong cao u >1m).

Cc a vt c th v theo t l, v theo k hiu, kt hp vi ghi ch.

075,8

5KV

* V ng ng mc.

- Phng php gii tch

- Phng pho k tia

- Phng php ng song song

- Phng php c lng

5.4 O V MT CT A HNH

phc v cho cng tc thit k v thi cng cc cng trnh c dng

tuyn nh: ng st, ng t, knh o, ng hm ng ng,

phi tin hnh o v mt ct a hnh

Mt ct a hnh biu din hnh dng cao thp ca mt t t nhin

chy dc theo mt tuyn no .

Mt ct a hnh gm: mt ct dc v mt ct ngang

o v mt ct a hnh gm cc cng on chnh sau:

- Cm tuyn ra ngoi thc a (i vi cng trnh y/c chnh xc v

tr im cao)

- o mt ct dc

- o mt ct ngang

- o cao dc tuyn

- Tnh ton

- V mt ct a hnh

5.4.1 o mt ct

Tuyn mt ct dc v mt ct ngang vung gc vi nhau.

v c mt ct chng ta cn phi o c xc nh c v tr

cng nh cao ca cc im cn th hin trn th mt ct.

5.4.2 V mt ct

C cao v khong cch gia cc cc ta v c mt ct dc, mt

ct ngang.

Thng t l theo trc ng (th hin cao H) ln gp 10 ln t l

theo trc ngang (th hin khong cch S) i vi mt ct dc, v t l

trc ng: trc ngang l 1:1 i vi mt ct ngang.

Mt ct ngang (T l S:H =1:1)

Mt ct dc (T l S:H =10:1)

S(m)

300

17.42

14.94

13.52

9.90

8.08

H(m)

23148

Mat cat ngang

0 50

8.00

H(m)

S(m)

6.52

5.02

5.81

110 150 200

Mat cat doc

7.24

Minh ha cch dng im mt ct a hnh

xc nh im mt ct da vo khong cch S v cao H:

- T khong cch S, k ng // trc H

- T cao H, k ng // trc S

Giao hai ng k l im cn xc nh

ng ni cc im (ng gp khc) th hin mt ct a hnh

Ten coc

Khoang cach ngang (m)

o cao mat at (m)

25,7

8

24,2

5

24,0

0

23,2

8

24,4

0

24,3

0

28,0 42,5 42,0 15,0 27,6

Mat cat doc

Ty le ng 1:100

Ty le ngang 1:1000

AB

C1 C2 C3 C3

o thiet ke (m)

Chenh cao M-TK (m)

B?nh o tuyen

S DNG BN A HNH

5.5 NH HNG BN ( THC A)

5.5.1 nh hng bng a bn

t bn nm ngang trn mt t,

t a bn sao cho ng ni Bc Nam

trng vi trc X ca li to .

Xoay t bn cho n khi u Bc

kim nam chm ch hng trng vi

hng Bc Nam ca t bn .

5.5.2 nh hng da vo a vt

Ta da vo a vt hnh tuyn nh ng st, ng t, nh

hng bn . t bn nm ngang v xoay cho n khi phng ca

a vt hnh tuyn trn bn trng vi phng ca a vt hnh tuyn

ngoi thc a.

5.6 XC NH KHONG CCH GIA HAI IM

TRN BN

5.6.1 Xc nh on thng

a) Dng thc khc vch n mm

Mun xc nh khong cch gia hai im trn bn ta ch vic t

thc o khong cch gia hai im trn bn (c s n mm hoc

0,1 ca mm) ri nhn vi mu s t l bn M ta c khong cch

thc

Sthc t = Sb * M (5.5)

(M: Mu s t l bn )

b) Dng thc t l v compa

t hai u compa trng vi 2 im cn xc nh trn bn , gi

nguyn khu t compa ln thc t l, sao cho mt u trng vi

vch 0 ca thc, ri c s u kia ta c khong cch thc.

c) Da vo to phng (x,y)

Da vo li to ta xc nh c to im A(xA, yA),

B(xB, yB)

5.6.2 Xc nh chiu di ng cong

a) Chia ng cong thnh nhiu on nh

Dng compa m khu nh ( c xc nh chiu di theo

thc t l hoc thc mm) o m s on

Chiu di ng cong = s on x ln khu + phn l

b) Dng dng c o ng cong

2 2

(5.6) AB B A B A

S x x y y

5.6.3 Xc nh to vung gc.

xc nh ta vung gc ca im bt k trn bn ta da

vo li ta vung gc phng (li km)

Hoc:

1 1 1

1 1 1(5.7)

A i i i i i i

A i i i i i i

a bX X X X X X X

a b a b

c dY Y Y Y Y Y Y

c d c d

1

1

. .

. .

A i i

A i i

X X aM X bM

Y Y cM Y d M

5.7 O DIN TCH TRN BN

C th s dng mt trong cc phng php sau y:

5.7.1 Tnh din tch bng cch chia hnh tam gic (o

din tch a gic) tnh din tch mt hnh a gic, ta chia n thnh cc tam gic

ri sau o ng cnh y v chiu cao ca n ta tnh c din

tch ca tng tam gic

Pi = ai.hi Sai s gii hn:

Trong :

M _ mu s t l bn

P _ din tch hnh cn o, n v m2

2

1

3

45

n

i

iPP1

giac da

0,04.(5.8)

100

M

P P

5.7.2 o din tch bng li vung o mt khu t nh c ng bin l mt ng cong khp

kn dng phim k li vung 1x1 mm, 2x2 mm hoc 5x5 mm t ln

hnh cn o.

- u tin m s nguyn

- m s khuyt, c lng

Ty theo t l bn m ta tnh ra c 1 vung tng ng

vi bao nhiu m2 ngoi thc a.

Din tch ca khu t bng tng s nhn vi din tch ca 1

ngoi thc a.

tng chnh xc, ta xoay li vung theo hng khc v

ta tip tc m, tnh din tch ln th 2. Nu sai s nm trong gii hn

theo cng thc (6.4) th ly kt qu trung bnh.

5.7.3 Tnh din tch theo to vung gc. Khi a gic c cc nh bit to

Trong : i = 1, 2, 3,..., n l k hiu

s hiu nh ca a gic c nh s

tng theo chiu kim ng h.

1 1 1 1

1 1

1 1 (5.9)

2 2

n n

i i i i i iP x y y y x x

y

x

1

2

3

4

5.8 NG DNG CA NG NG MC TRN

BN

5.8.1 Khi nim ng ng mc

Trong gii hn hp c th coi ng ng mc l ng bnh

- ng bnh : l ng th hin cc im cng cao.

ng c s l ng 0 mt

- Khong cao u (E): l chnh cao gia 2 ng bnh lin

tip

- ng bnh m (ci): nt m

Thng 5 khong cao u c 1 bnh m; nn s l cc

ng 0m, 5E, 10E, 15E, 20E,

- ng bnh con: nt mnh

ng phn thy v t thy

Tm mi lin h thch hp Ghi ch cao, cha v bnh

5.8.2 Da vo ng ng mc xc nh cao

V d cn xc nh cao HN ca im N nh hnh v

V ng ngn nht qua N ct 2 ng bnh 2 bn, ri o a, b

Ta c:

Trong E l khong cao u (trong v d ny E = 30 - 28 = 2m)

1( ) 28 .2N i i ia a

H H H Ha b a b

5.8.3 Xc nh dc v gc dc

xc nh dc, gc dc gia hai im A v B ta phi xc nh

c HA, HB v SAB . Lm sao xc nh c HA, HB, SAB ?

Ta c hAB = HB - HA dc i

i tnh bng % hoc

Gc dc V

AB ABi tgV (5.10) AB

AB

h

S

AB

AB

AB

hV arctg (5.11)

S

5.8.4 V mt ct trn bn

Da vo ng ng mc trn bn ta c th v c mt ct dc

theo mt tuyn bt k

1

2

3

4

5 6

7

8

9

25

3035

40

40

35

30

25

S

H(m)

Chng 6:

CNG TC B TR CNG TRNH

GV: o Hu S

Khoa Xy dng

NI DUNG CHNG 6:

Khi nim v b tr cng trnh

B tr gc bng, chiu di, cao

Cc phng php b tr im

o kim tra cng trnh

6.1 KHI NIM B TR CNG TRNH

6.1.1 nh ngha

Tt c cc cng trnh xy dng u c thit k trn bn v. Khi thi

cng ta cn phi chuyn bn thit k ra thc a.

B tr cng trnh l tt c nhng cng tc trc a nhm xc nh v

tr mt bng v cao ca cc hng mc cng trnh ngoi thc a

theo ng thit k.

Nh vy, ngc li vi cng tc o v bn , trong b tr cng trnh

phi cn c vo bn thit k xc nh cc trc, cc im, v tnh

ton nhng s liu cn thit ri o c b tr cng trnh ngoi thc a

vi chnh xc theo yu cu ca thit k. Yu cu chnh xc trong

b tr cng trnh cao hn trong o v bn .

C s hnh hc chuyn bn v thit k ra thc a l cc trc dc,

trc ngang v cao ca mt quy c ca cng trnh. Tt c cc kch

thc thit k u c xc nh tng i so vi cc trc v cao y.

Cc trc ca cng trnh

- Trc chnh: Nu cng trnh c dng tuyn th trc chnh l trc dc

ca cng trnh. Trc chnh ca to nh l trc i xng (trc XX, YY)

hoc c th l trc tng bao.

- Trc c bn: l trc xc nh kch thc hnh dng c bn ca cng

trnh (trc 11, 22), n l trc ca cc b phn quan trng ca cng trnh

v thng c quan h cht ch vi nhau.

- Trc ph tr: l trc b tr cc phn chi tit ca cng trnh

2

21

1

Y

X

Y

6.1.2 Trnh t b tr cng trnh

Bn thit k

3. B tr: chi tit, cng ngh

1. Thit lp (th hin)

li khng ch trn TK

2. Trc (chnh, ph, chi

tit); mt cao quy

c

Xc nh

1. Xy dng li khng

ch

2. B tr c bn (trc chnh,

ph, mt cao quy c)

Thc a Bn v hon cng

cng trnh

o v cc

hng mc

Tin hnh

a) B tr li khng ch trc a (li khng ch cng trnh) lm c

s cho vic b tr cng trnh

Li khng ch cng trnh c cc dng: li tam gic, li a gic,

li ng chuyn, li vung,...

b) B tr c bn (b tr cc trc chnh, trc c bn ca cng trnh)

T li khng ch cng trnh b tr cc trc chnh b tr cc

trc c bn ca cng trnh

Hai trc ny c b tr vi chnh xc yu cu: 3 5 cm

c) B tr chi tit cng trnh

Da vo cc im ca trc chnh, trc c bn b tr cc trc dc,

trc ngang ca cc b phn ca cng trnh ng thi b tr cc im chi

tit c trng v mt phng theo cao thit k

Giai on ny nhm xc

Documents

Tong Hop Bai Giang