Bai Giang BTCT 8 2013

Bi ging kt cu b tng ct thp 08/2013 www.bmketcau.net

B mn Kt cu Khoa Cng trnh H GTVT 1

KT CU B TNG CT THP ( THEO TIU CHUN 22TCN272-05)

Mc lc

1 KHI NIM CHUNG V KT CU B TNG CT THP .......................................... 4

1.1 C IM CHUNG CA KT CU B TNG CT THP .................................. 4

1.1.1 B tng ct thp...................................................................................................... 4

1.1.2 B tng ct thp d ng lc (DL) ....................................................................... 5

1.2 C IM CHUNG V CU TO V CH TO KT CU B TNG CT

THP 7

1.2.1 c im cu to : .................................................................................................. 7

1.2.2 c im ch to: ................................................................................................... 9

2 VT LIU DNG TRONG B TNG CT THP ........................................................ 14

2.1 B TNG .................................................................................................................... 14

2.1.1. Phn loi b tng .................................................................................................. 14

2.1.2. Cc thuc tnh ngn hn ca b tng cng ........................................................... 15

2.1.3. Cc thuc tnh di hn ca b tng cng ............................................................. 22

2.2 CT THP .................................................................................................................. 29

2.2.1. Ct thp thng .................................................................................................... 29

2.2.2. Ct thp d ng lc .............................................................................................. 31

2.3 B TNG CT THP ................................................................................................ 36

2.3.1. Khi nim v dnh bm gia b tng v ct thp ................................................. 36

2.3.2. Chiu di pht trin lc ........................................................................................ 37

2.3.3. Cc dng ph hoi v h hng ca b tng ct thp ............................................ 38

3 NGUYN L THIT K THEO TIU CHUN 22TCN272-05 ................................... 40

3.1 QUAN IM CHUNG V THIT K ...................................................................... 40

3.2 S PHT TRIN CA QU TRNH THIT K .................................................... 40

3.2.1. Thit k theo ng sut cho php (ASD)-Allowable Stress Design ...................... 40

3.2.2. Thit k theo h s ti trng v sc khng (LRFD-Load and Resistance Factors

Design) 41

3.3 NGUYN TC C BN CA TIU CHUN 22TCN 272-05 ............................... 42

3.3.1. Tng qut.............................................................................................................. 42

3.3.2. Khi nim v tnh do, tnh d v tm quan trng trong khai thc ...................... 43

3.3.3. Cc trng thi gii hn ......................................................................................... 44

3.4 TI TRNG V H S TI TRONG THEO 22TCN 272-01 ................................ 46

4.4.1. Ti trng v tn ti trng- Cc t hp ti trng .................................................... 47

4 CU KIN CHU UN .................................................................................................... 51



4.1 C IM CU TO ............................................................................................... 51

4.1.1 Cu to ca bn v dm........................................................................................ 51

4.1.2 Tiu chun la chn t l chiu di chiu cao nhp .......................................... 54

4.1.3 Chiu dy lp b tng bo v ............................................................................... 54

4.1.4 C li ct thp ........................................................................................................ 55

4.1.5 Trin khai ct thp chu un ................................................................................. 57

4.2 C IM CHU LC , CC GI THIT C BN .............................................. 58

4.2.1 c im lm vic ................................................................................................ 58

4.2.2 Cc gi thit c bn .............................................................................................. 61

4.2.3 Gi thit phn b ng sut khi ch nht ............................................................. 62

4.3 TNH TON TIT DIN BTCT THNG THEO TTGH CNG ................ 62

4.3.1 Tnh ton tit din ch nht ct thp n ............................................................. 62

4.3.2 Tnh ton tit din ch nht ct thp kp: ............................................................ 68

4.3.3 Tnh ton tit din ch T ...................................................................................... 73

4.4 TNH TON THIT K CHU CT ......................................................................... 80

4.4.1 M hnh chng v ging ( Strut And Tie Models) ............................................... 80

4.4.1.1 Nguyn l chung v phm vi p dng : ......................................................... 81

4.4.1.2 Phn chia kt cu thnh cc vng B v D: .................................................... 82

4.4.1.3 Mt s m hnh tiu biu. .............................................................................. 85

4.4.2 Cc b phn ca m hnh chng v ging :.......................................................... 89

4.4.3 Cc phng php thit k, cc yu cu chung ..................................................... 91

4.4.3.1 Cc phng php thit k .............................................................................. 91

4.4.3.2 Cc yu cu chung ......................................................................................... 91

4.4.4 M hnh thit k mt ct ....................................................................................... 94

4.4.4.1 Sc khng ct danh nh ................................................................................ 94

4.4.4.2 Thit k chu lc ct cu kin BTCT thng ................................................ 95

4.5 TNH TON KT CU BTCT THEO TRNG THI GII HN S DNG V

TRNG THI GII HN MI ............................................................................................. 102

4.5.1 Trng thi gii hn s dng ............................................................................... 102

4.5.1.1 Nt v Qu trnh hnh thnh v m rng vt nt ......................................... 102

4.5.1.2 Kim sot nt ca dm BTCT thng chu un (A5.7.3.4) ....................... 103

4.5.1.3 Khng ch bin dng (A5.7.3.6) .................................................................. 105

4.5.1.4 Phn tch ng sut trong BT, CT ca dm BTCT thng chu un ............ 106

5 CU KIN CHU LC DC TRC ............................................................................. 115

5.1 C IM CU TO ............................................................................................. 115

5.1.1 Hnh dng mt ct: ............................................................................................. 115

5.1.2 Vt liu: .............................................................................................................. 115

5.2 C IM CHU LC V GI THIT TNH TON ......................................... 118

5.2.1 Phn loi ct- theo tnh cht chu lc: ................................................................ 118

5.2.2 Cc gi thit tnh ton: ....................................................................................... 122



5.3 TNH TON CC LOI CT ................................................................................. 123

5.3.1 Kh nng chu lc ca ct ngn: ........................................................................ 123

5.3.2 Tnh ton ct mnh ............................................................................................. 135

5.3.3 Tnh ton ct chu nn lch tm theo hai phng .............................................. 138

6 KT CU B TNG CT THP D NG LC ........................................................ 145

6.1 KHI NIM CHUNG ............................................................................................... 145

6.1.1 Gii thiu ............................................................................................................ 145

6.1.2 Trng thi ng sut dm b tng d ng lc...................................................... 145

6.2 PHN LOI B TNG CT THP D NG LC ............................................. 146

6.2.1 Theo v tr ca lc cng ...................................................................................... 146

6.2.2 Theo thi im cng ........................................................................................... 147

6.2.3 Theo hnh dng cp d ng lc .......................................................................... 148

6.2.4 Theo mc hn ch ng sut ko trong trong b tng .................................... 148

6.2.5 Theo mc dnh bm ca thp d ng lc v b tng .................................... 148

6.3 CC CH DN V CU TO ................................................................................ 148

6.3.1 Thit b cho cu kin BTCT DL ..................................................................... 148

6.3.2 Vt liu dng trong BTCT DL ........................................................................ 151

6.3.3 B tr ct thp ..................................................................................................... 153

6.4 CC CH DN V TNH TON ............................................................................ 153

6.4.1 Tr s ng sut trc trong ct thp v b tng ................................................. 154

6.4.2 Mt mt ng sut trc trong ct thp ............................................................... 154

6.4.2.1 Tng mt mt ng sut trc ...................................................................... 154

6.4.2.2 Cc mt mt ng sut tc thi ..................................................................... 154

6.4.2.3 Cc mt mt ng sut theo thi gian ............................................................ 157

6.4.3 Ch dn tnh ton theo trng thi gii hn s dng ............................................ 158

6.4.3.1 Gii hn ng sut i vi b tng ti thi im truyn lc cng - cc cu kin

d ng lc ton phn ........................................................................................................... 159

6.4.3.2 Gii hn ng sut i vi b tng giai on s dng - cc cu kin d ng

lc ton phn 160

6.4.3.3 Cc gii hn ng sut i vi ct thp d ng lc ...................................... 162

6.4.4 Ch dn tnh ton chu un theo trng thi gii hn cng ........................... 163

6.4.4.1 Chiu cao trc trung ho ca dm c ct thp dnh bm ............................. 163

6.4.4.2 V tr trc trung ho i vi dm c ct thp khng dnh bmh .................. 166

6.4.4.3 Sc khng un .............................................................................................. 169

6.4.4.4 Cc gii hn v ct thp ............................................................................... 169

6.4.5 Thit k chu lc ct cu kin BTCT D ng lc ............................................. 174

TI LIU THAM KHO ....................................................................................................... 178



1 KHI NIM CHUNG V KT CU B TNG CT THP

1.1 C IM CHUNG CA KT CU B TNG CT THP

1.1.1 B tng ct thp

B tng ct thp l mt loi vt liu xy dng hn hp do hai vt liu thnh phn c tnh cht

c hc khc nhau l b tng v thp cng cng tc chu lc vi nhau mt cch hp l v kinh t.

B tng l mt loi nhn to thnh phn bao gm ct liu (ct, ) v cht kt dnh ( xi

mng, nc...). B tng c kh nng chu nn tt, kh nng chu ko rt km .

Thp l vt liu chu ko hoc chu nn u tt. Do vy ngi ta thng t ct thp vo trong

b tng tng cng kh nng chu lc cho kt cu t sn sinh ra b tng ct thp.

thy c s cng tc chu lc gia b tng v ct thp ta xem cc th nghim sau:

Un mt dm b tng nh trn hnh 1.1a, trn dm chia thnh hai vng r rt l vng ko v

vng nn. Khi ng sut ko trong b tng fct vt qu cng chu ko ca b tng th vt nt

s xut hin, vt nt di nhanh ln pha trn v dm b gy t ngt, khi ng sut trong b tng

vng nn cn kh nh so vi cng chu nn ca b tng. Dm b tng cha khai thc ht

c kh nng chu nn tt ca b tng, kh nng chu m men ca dm nh.

Vi mt dm nh trn c t mt lng ct thp hp l vo vng b tng chu ko hnh

1.1b, khi ng sut ko fct vt qu cng chu ko ca b tng th vt nt cng s xut hin.

Nhng lc ny dm cha b ph hoi, ti tit din c vt nt lc ko hon ton do ct thp chu,

chnh v vy ta c th tng ti trng cho ti khi ng sut trong ct thp t ti gii hn chy hoc

b tng vng nn b nn v.

f

f

ct

cc

ccf

fs

(a)

(b)

P P

P P

As Hnh 1.1 Dm b tng v b tng ct thp

Dm BTCT khai thc ht kh nng chu nn tt ca b tng v kh nng chu ko tt ca thp.

Nh vy kh nng chu m men hay sc khng un ln hn hng chc ln so vi dm b tng c

cng kch thc.



Ct thp chu chu ko v nn u tt nn n cn c t vo trong cc cu kin chu ko,

chu nn, cu kin chu un xon tng kh nng chu lc gim kch thc tit din v chu lc

ko xut hin do ngu nhin.

B tng v thp c th cng cng tc chu lc l do:

Trn b mt tip xc gia b tng v thp c Lc dnh bm kh ln nn lc c th

truyn t b tng sang thp v ngc li. Lc dnh bm c tm rt quan trng i vi

BTCT. Nh c lc dnh bm m cng ca ct thp mi c khai thc, b rng

vt nt trong vng ko mi c hn ch. Do vy ngi ta pho tm mi cch tng

cng lc dnh bm gia b tng v ct thp.

Gia b tng v ct thp khng xy ra phn ng ho hc, b tng cn bo v cho ct

thp chng li tc dng n mn ca mi trng.

H s gin n di v nhit ca b tng v ct thp l xp x bng nhau ( b tng

c=10,8.10-6/oC , thp s=12.10-6/oC ). Do khi nghit thay i trong phm vi

thng thng (di 100oC) ni ng sut xut hin khng ng k, khng lm ph hoi

lc dnh bm gia b tng v ct thp.

u nhc im ca b tng ct thp:

u im:

C kh nng s dng cc vt liu a phng .

C kh nng chu lc ln hn so vi kt cu gch v g .BTCT chu cc ti trng

ng tt ,k c ti trng ng t. BTCT chu la tt.

Gi thnh h hn, chi ph duy tu bo dng t.

C th c thnh hnh dng kt cu khc nhau dp ng cc yu cu cu to, kin

trc v yu cu s dng.

Khuyt im:

C trng lng bn thn ln.

Kim tra cht lng kh khn, tn thi gian thi cng. Sa cha thay th kh khn.

Thng hay xut hin khe nt nh hng n cht lng s dng v tui th ca kt

cu.

1.1.2 B tng ct thp d ng lc (DL)

Khi s dng BTCT ngi ta thy xut hin cc nhc im:

Nt sm gii hn chng nt thp

Khng cho php s dng hp l ct thp cng cao. Khi ng sut trong ct thp

chu ko fs=20-30 MPa cc khe nt u tin trong b tng s xut hin. Khi dng thp

cng cao ng sut trong ct thp chu ko c th t 1000-1200 MPa hoc ln hn

iu lm xut hin cc khe nt rt ln vt qu tr s gii hn cho php.

khc phc hai nhc im trn ngi ta a ra kt cu BTCT d ng lc (BTCTDL).

Hai nhc im trn u xut pht t kh nng chu ko km ca b tng. Trc khi chu lc nh

hnh 1.1b ngi ta to ra trong cu kin mt trng thi ng sut ban u ngc vi trng thi ng



sut khi chu ti, ta s c biu ng sut nh hnh 1.2 v s c kt cu nt nh ( fct nh )

hoc khng nt ( fct=0).

Khi nim kt cu d ng lc: kt cu d ng lc l loi kt cu m khi ch to chng ngi

ta to ra mt trng thi ng sut ban u ngc vi trng thi ng sut do ti trng khi s dng,

nhm mc ch hn ch cc yu t c hi n tnh hnh chu lc ca kt cu do tnh cht chu lc

km ca vt liu.

Hnh 1.2 ng sut trong cu kin BTCT d ng lc

Vi b tng ct thp, ch yu ngi ta to ra ng sut nn trc cho nhng vng ca tit din

m sau ny di tc dng ca ti trng khi s dng s pht sinh ng sut ko. ng sut nn trc

ny c tc dng lm gim hoc trit tiu ng sut ko do ti trng s dng sinh ra. Nh vy m

cu kin nt c th nh hoc khng nt.

Ta c th to ra cc trng thi ng sut ban u khc nhau bng hai cch: Thay i v tr lc

nn trc, thay i tr s lc nn trc. Nh vy c th to ra cc kt cu ti u v mt chu lc

cng nh gi thnh.

u im ca kt cu BTCTDL so vi BTCT hay tc dng chnh ca d ng lc:

Nng cao gii hn chng nt do c tnh chng thm cao.

Cho php s dng hp l ct thp cng cao, b tng cng cao

cng tng ln nn vng gim ,vt c nhp ln hn so vi BTCT thng.

Chu ti i du tt hn nn sc khng mi tt.

Nh c ng sut trc m phm vi s dng ca kt cu b tng ct thp lp ghp, phn

on m rng ra nhiu. Ngi ta c th s dng bin php ng lc ni cc cu kin

c sn li vi nhau thnh mt kt cu.

Nhc im ca kt cu BTCTDL so vi BTCT thng:

ng lc trc khng nhng gy ra ng sut nn m cn c th gy ra ng sut ko

pha i din lm cho b tng c th b nt.

Ch to phc tp hn yu cu kim sot cht ch v k thut c th t cht lng

nh thit k ra.



1.2 C IM CHUNG V CU TO V CH TO KT CU B

TNG CT THP

1.2.1 c im cu to :

Trong b tng ct thp vn gii quyt cu to sao cho hp l l rt quan trng. Hp l v

mt chon vt liu (Mc b tng hay cp b tng, nhm thp hay loi thp ), hp l v chon dng

tit din v kch thc tit din, hp l v vic b tr ct thp. Gii quyt cc lin kt gia cc b

phn, chn gii php bo v kt cu chng xm thc ,tnh c th thi cng c ( tnh kh thi).

Dng tit din v s b tr ct thp ph thuc vo trng thi ng sut trn tit din. Trong

cu kin chu un trng thi ng sut trn tit din c vng ko c vng nn th tit din thng

c m rng vng nn( nh ch T). Vi cu kin ch chu lc dc trc trn tit din ng sut

gn nh phn b u dng tit din thng c chon l i xng nh vung, trn, ch nht.

a/-B tng ct thp thng:

Ct thp c t vo trong cu kin b tng ct thp : chu ng sut ko, chu ng sut

nn, nh v cc ct thp khc. S lng do tnh ton nh ra nhng cng phi tho mn cc

yu cu cu to.

Ct thp chu ng sut ko do nhiu nguyn nhn gy ra: M men un, lc ct, lc dc trc,

m men xon, ti cc b.

Ct thp chu ko mmen un gy ra l cc ct thp dc ch t vng chu ko ca cu

kin, t theo s xut hin ca biu m men hnh 1.3, t cng xa trc trung ho cng tt.

Ct thp chu ko do lc ct gy ra d l cc ct thp ai (ct ngang ) c t theo s xut

hin ca biu lc ct hnh 1.4

Ct thp chu ng sut nn: l cc ct dc chu nn trong dm, ct, cc ct thp ny cng

tham gia chu nn vi b tng.

Ct thp nh v cc ct thp khc trong thi cng.

Ct thp kim sot nt b mt phn b gn b mt cu kin lm nhim v chu ng sut d co

ngt , thay i nhit , cc ct dc v ct thp ngang l mt phn ca ct thp kim sot nt b

mt.

Hnh 1.3 Biu m men v cch t ct thp



A

A

A-A

Hnh 1.4 Biu lc ct v b tr ct ai

Trong cu kin chu un khi ch c ct dc chu ko th c gi l tit din t ct thp n,

cn khi c c ct thp dc chu ko v ct dc chu nn th c gi l tit din t ct kp.

S b tr ct thp trong cu kin chu nn lch tm ln, chu ko lch tm ln gn ging

nh trong cu kin chu un.

Trong cu kin ch chu lc dc trc trn tit din cc ct thp dc thng c bt tr i

xng.

Kch thc tit din do tnh ton nh ra nhng phi tho mn cc yu cu cu to, kin trc,

kh nng b tr ct thp v k thut thi cng.

Ngoi ra cn phi ch n quy nh v b dy lp b tng bo v ct thp, khong cch

trng gia cc ct thp. Cc quy nh ny c quy nh trong cc tiu chun ngnh.

b-B tng ct thp d ng lc .

Trong cu kin BTCTDL gm hai loi ct thp: Ct thp thng ( hay ct thp khng ko

cng) v ct thp D ng lc ( ct thp ko cng ). Ct thp thng lm nhim v v c b tr

ging nh cu kin b tng ct thp thng.

Ct thp DL c nhim v to ra ng sut nn trc trong b tng. Ct thp d ng lc c

th t theo ng thng hoc ng cong hoc thng v cong, hnh 1.5.

Hnh 1.5 S b tr ct thp DL



Ti ch un cong thng c ni lc tip tuyn ln nn cn gia cng cho b tng ti bng

cc li ct thp gia cng.

Ti u neo lin kt s xut hin lc tp trung ln cng cn phi gia cng cho b tng ti cc

v tr ny bng cc ct thp gia cng hoc bn phn b.

1.2.2 c im ch to:

a-Phn loi theo phng php thi cng : 3 loi

ti ch ( kt cu ton khi )

Lp ghp

Bn lp ghp

b-Phn loi theo trng thi ng sut khi ch to v s dng :

B tng ct thp thng

B tng ct thp d ng lc ( b tng ng sut trc )

c-Phn loi BTCTDL theo phng php to d ng lc :

Cu kin thi cng ko trc ( phng php cng ct thp trn b) : Hnh 1.5

Ct thp d ng lc c neo mt u c nh vo b cn u kia c ko ra vi lc ko N.

Di tc dng ca lc ko N ct thp c ko trong gii hn n hi s gin di ra mt on l

tng ng vi ng sut ko thit k xut hin trong ct thp. Sau ngi ta c nh u ny ca

ct thp vo b. Tip theo ta t ct thp thng v b tng cu kin. Khi b tng cu kin

cng cn thit, ngi ta tin hnh bung ct thp. Lc ny ct thp d ng lc c xu hng

co li khi phc chiu di ban u v sinh ra nn b tng .

Hnh 1.5 S phng php thi cng ko trc

tng thm dnh bm gia b tng v ct thp DL ngi ta thng dng ct thp DL l

ct thp c g, hoc ct thp trn c xon li, hoc to mu neo c bit hai u .

Phm vi p dng: Dng cho cc cu kin thng c nhp ngn v va, c bit hiu qu vi cc

cu kin sn xut hng lot xng.



Cu kin thi cng ko sau: Hnh 1.6

Trc tin ngi ta lp dng vn khun, ct thp thng v t cc ng to rnh (trong c

th t trc ct thp DL hoc lun sau) bng tn , km hoc vt liu khc .Sau b tng

cu kin, khi b tng cu kin cng ta tin hnh lun ct thp v ko cng n ng sut

thit k. Sau khi cng xong ct thp DL c neo cht vo u cu kin.Thng qua cc neo cu

kin s b nn bng lc ko cng trong ct thp. Tip ngi ta bm va xi mng vo trong ng

rnh bo v ct thp khi b n mn v to ra lc dnh bm gia b tng vi ct thp. Nhng

cng c trng hp ct thp c bo v trong ng rnh bng m chng g, trng hp ny c

gi l cu kin DL khng dnh bm.

Phng php ny lun phi c neo, khi ko t mt u th u kia l neo cht ( neo sn mt

u nh : neo mc cu, neo kiu mi bi, kiu thng lng ).

Phm vi p dng ca phng php ny: dng ko cng cc b si hoc dy cp t theo

ng thng hoc cong, dng cho cc cu kin chu lc ln nh kt cu cu. Phng php ny

thng oc thc hin ti cng trng.

Hnh 1.6 S phng php thi cng ko sau



2 VT LIU DNG TRONG B TNG CT THP

2.1 B TNG

2.1.1. Phn loi b tng

1. Theo thnh phn ca b tng ti (hn hp b tng)

B tng l mt loi nhn to c to thnh t cc vt liu thnh phn, bao gm: dm,

si (ct liu ln); ct (ct liu nh); xi mng (cht kt dnh), nc v ph gia (nu c). Cc vt

liu ny sau khi nho trn u vi nhau s ng cng v c hnh dng theo khun c. T l ca

cc vt liu thnh phn trong hn hp s c nh hng n thuc tnh ca b tng sau khi ng

cng (b tng). Trong phn ln cc trng hp, ngi k s cu s chn cp b tng c th t

mt lot hn hp thit k th, trn c s cng chu nn mong mun tui 28 ngy 'cf .

c trng tiu biu i vi cc cp b tng khc nhau c cho trong bng 2.1 nh sau:

Bng 2.1 - Cc c trng trn ca b tng theo cp

Cp b

tng

Lng xi mng ti thiu

kg/m3

T l nc/xi mng ln nht

kg/kg

cha kh

%

Kch thc ct liu theo AASHTO M43

Kch thc l vung sng (mm)

Cng chu nn 28 ngy tui

MPa

A 362 0.49 - 25 n 4.75 28 A (AE) 362 0.45 6.0 1.5 25 n 4.75 28

B 307 0.58 5.0 1.5 50 n 4.75 17

B (AE) 307 0.55 - 50 n 4.75 17 C 390 0.49 7.0 1.5 12.5 n 4.75 28

C (AE) 390 0.45 - 12.5 n 4.75 28 P 334 0.49 Nh quy

nh ch khc

25 n 4.75 hoc 19 n 4.75

Nh quy nh ch khc

S 390 0.58 25 n 4.75 T trng

thp 334 Nh quy nh trong h s hp ng

Cp b tng A ni chung c s dng i vi tt c cc cu kin ca kt cu v c

bit i vi b tng lm vic trong mi trng nc mn.

Cp b tng B c s dng trong mng, b mng, thn tr v tng chu lc.

Cp b tng C c s dng trong cc chi tit c b dy di 100 mm nh tay vn cu

thang v cc bn sn t li thp.

Cp b tng P c s dng khi cng c yu cu ln hn 28 MPa. i vi b

tng d ng lc, phi ch rng, kch thc ct liu khng c ln hn 20 mm.

B tng loi S c dng cho b tng di nc bt y chng thm nc trong cc

khung vy.

T l nc/xi mng (W/C) theo trng lng l thng s quan trng nht nh hng n cng

b tng. T l W/C cng gn mc ti thiu th cng cng ln. Hin nhin l, i vi mt



lng nc cho trong hn hp, vic tng hm lng xi mng s lm tng cng b tng.

i vi mi cp b tng u c quy nh r lng xi mng ti thiu tnh bng kG/m3. Khi tng

lng xi mng trn mc ti thiu ny, c th tng lng nc v vn gi nguyn t l W/C. S

tng lng nc c th khng tt v lng nc tha, khng cn thit cho phn ng ho hc vi

xi mng v v lm t b mt ct liu, khi bc hi s gy ra hin tng co ngt, lm b tng km

c chc. Do vy, Tiu chun quy nh lng xi mng ti a l 475 kG/m3 hn ch lng

nc ca hn hp.

B tng AE (b tng bt) pht huy c bn lu di khi lm vic trong cc mi trng

lnh. B tng bt c ch to bng cch thm vo hn hp mt ph gia do to ra s phn b

u cc l rng rt nh. S phn b u cc l rng nh ny trong b tng trnh hnh thnh cc l

rng ln v ct t ng mao dn t mt ngoi vo ct thp.

t c cht lng ca b tng l bn lu di v chu lc tt, cn phi hn ch hm

lng nc. Nhng nc lm tng lu ng ca hn hp b tng, c bit lm cho b tng

c trong khun. ci thin tnh cng tc ca hn hp b tng m khng phi tng lng nc,

ngi ta a vo cc ph gia ho hc. Cc ph gia ny c gi l ph gia gim nc mnh (ph

gia siu do), rt c hiu qu trong vic ci thin thuc tnh ca c b tng t v b tng

ng rn. Cc ph gia ny phi c s dng rt thn trng v nht thit phi c ch dn ca nh

sn xut v chng c th c nhng nh hng khng mong mun nh lm rt ngn thi gian

ng kt. V vy trc khi s dng cn lm cc th nghim xc minh cht lng ca c b

tng t ln b tng cng.

Trong vi nm gn y, ngi ta ch to c b tng c cng rt cao, cng chu

nn c th ti 200MPa. Mu cht ca vic t cng ny cng nh chc chn l m bo

cp phi tt nht, sao cho tt c cc l rng u c lp y bng cc ht mn cho n khi

khng cn l rng na. Trc y ngi ta ch ch ti cp phi tt nht ca ct liu ln v ct

liu nh l v ct. Vic lp y cc khe h gia cc ht nh c th l cc ht xi mng Poc

lng, m sau ny phn ng vi nc s to lc dnh v gn kt thnh khi. Trong b tng CC

v rt cao, ngi ta cn tin thm mt bc na l chn thm vo khe h gia cc ht xi mng

Poc lng. Cc loi vt liu mn chn ny c th l t Puzolan ht nh, tro bay, mui silc,...

Chng c th thay th mt phn cho XM v vn gi nguyn lng XM ti thiu v t l W/C.

2. Theo t trng ca b tng:

Theo t trng, b tng c phn thnh

B tng t trng thng: L BT c t trng trong khong 2150 2500kG/m3.

B tng t trng thp: L BT c cha cp phi nh v c t trng khi kh khng vt

qu 1925kG/m3.

2.1.2. Cc thuc tnh ngn hn ca b tng cng

Cc thuc tnh ca b tng c xc nh t mt chng trnh th nghim phn nh s lm

vic chu lc ngn hn v cc th nghim ny thng c thc hin trong vng vi pht, trong

khi thi gian ti trng tc dng ln b tng trong kt cu l nhiu thng, thm ch nhiu nm. Cc

thuc tnh ngn hn ny rt hu dng trong nh gi cht lng ca b tng v s lm vic chu

lc ngn hn nh di hot ti xe c. Tuy nhin, nhng thuc tnh ny phi c iu chnh khi



chng c s dng nh gi s lm vic di ti trng tc dng lu di nh trng lng bn

thn ca dm, ca bn v lan can.

1/Cng chu nn

Cng chu nn ca b tng 'cf tui 28 ngy thng c xc nh bng th nghim

ph hoi mu th hnh tr ng knh 150 mm, chiu cao 300 mm di tc dng ca lc dc

trc.

4/'

2maxmax

d

P

A

Pf c

Hnh 2.1 biu din ng cong ng sut-bin dng in hnh ca mu th hnh tr khi chu

nn dc trc khng c kim ch (khng c cn tr bin dng ngang). Bin dng ti nh ng sut

nn 'cf xp x bng 0,002 v bin dng c th ln nht vo khong 0,003. Mt quan h n

gin i vi b tng c cng nh hn 40 MPa c a ra di mt hm bc hai nh sau:

2

''

' 2c

c

c

c

cc ff

(2.1)

Trong 'cf l cng chu nn tng ng vi bin dng '' , cc f l nh ng sut

t th nghim khi tr v 'c l bin dng ng vi ng sut 'cf . Quy c du y l ng

sut nn v bin dng nn mang gi tr m.

Hnh 2.1 ng cong ng sut-bin dng parabol in hnh i vi b tng chu nn khng

c kim ch

M un n hi (Ec):

M un n hi c cho i vi b tng trong AASHTO c nh gi bng dc ca

ng thng i t gc to qua im ca ng cong c ng sut bng '4,0 cf . M un ct

tuyn cE (tnh bng MPa) ny c biu din trn hnh 2.1 v c tnh bi hm s m sau:

'5,1.043,0 ccc fE (2.2)



trong c l khi lng ring ca b tng tnh bng kg/m3 v

'

cf l gi tr tuyt i ca

cng chu nn danh nh ca b tng tnh bng MPa. i vi c = 2300 kg/m3 v

MPafc 28'

1,5 ' '0,043. 2300 . 4800. 4800. 28 25c c cE f f GPa

Trong AASHTO, cng chu nn tui 28 ngy ti thiu l 16 MPa c khuyn co i

vi tt c cc b phn ca kt cu v cng chu nn ti a c quy nh l 70 MPa, tr khi

c nhng th nghim b sung. Cc bn trong cu phi c cng chu nn tui 28 ngy ti

thiu l 28 MPa t c bn thch hp.

Gi tr trung bnh v gi tr c trng ca cng :

Tin hnh th nghim n mu th ca cng mt loi b tng, ta thu c cc gi tr cng

ca cc mu th l: ''2'1 .,..,, cncc fff . Cc gi tr cng ca cc mu th thu c l mt i

lng ngu nhin phn b chun. Gi tr trung bnh cng ca cc mu th k hiu l

'cmf hay cn gi l cng trung bnh ( gi tr trung bnh ca phn b) c tnh nh sau:

n

f

f

n

ici

cm

1

'

' (2.3)

lch tiu chun ca cng k hiu l ( khi n30):tnh theo cng thc (2.4)

1

2''

n

ff cmci (MPa) (2.4)

i vi cng mt gi tr trung bnh 'cmf gi tr cng nh th kim sot cht lng ca b

tng cng tt (hnh 2.1a).

H s bin ng ca cng k hiu l v : tnh theo cng thc (2.5)

%100'

cmfv

(2.5)

Gi tr c trng ca cng ( hay cn gi l cng dc trng) k hiu 'cf : tnh theo

cng thc (2.6)

kff cmc ''

(2.6)

Trong k l xc xut m bo, khi xc sut m bo 95% th k=1,64, cc gi tr khc ca k

tham kho bng ca ACI 214R-02 nh sau:



Hnh 2.1a Cc ng cong tun sut chun i vi 3 phn phi khc nhau c gi tr trung

bnh ging nhau nhng bin thin khc nhau.

Cng chu nn trung bnh yu cu nh nht k hiu l 'crf c tnh theo cng thc

(2.7) nh sau:

kff ccr '' (2.7)

Theo ACI-318R-08, cng nn trung bnh yu cu c s dng lm c s la chn ca

cc t l pha trn b tng c xc nh t bng 2.2 v 2.3.



Bng 2.2: Cng trung bnh yu cu khi c cc d liu th nghim xc nh

Cng chu nn c trng

(MPa)

Cng chu nn trung bnh yu cu

(MPa)

MPafc 35' 5,333,2;34,1max ''' cccr fff

MPafc 35' 33,29,0;34,1max ''' cccr fff

Bng 2.3: Gi tr cng trung bnh yu cu nh nht khi khng cc d liu thng k

Cng chu nn c trng

(MPa)

Cng chu nn trung bnh yu cu

(MPa)

MPafc 21'

MPaff ccr 9,6

''

MPafMPa c 3521'

MPaff ccr 3,8

''

MPafc 35' MPaff ccr 8,41,1

''

Theo ACI-318R-08 h s iu chnh lch tiu chun khi s mu th nh hn 30 nh sau:

S mu th H s iu chnh



Trong th nghim ch khi tr [hnh 2.2(c)], khi tr tiu chun c t nm v chu ti trng

ng phn b u. ng sut ko gn nh u xut hin vung gc vi ng sut nn sinh ra bi

ti trng ng. Khi cc ng sut ko ny t ti gii hn cng , khi tr b ch lm i dc

theo mt chu ti. Theo mt l thuyt v s lm vic n hi (Timoshenko v Goodier, 1951),

cng thc tnh ng sut ko ch spf c a ra nh sau:

D

LPf crsp

/.2 (2.9)

trong Pcr l ton b ti trng gy ch khi tr, L l chiu di ca khi tr v D l ng

knh ca khi tr.

C hai gi tr ng sut ko un rf v ng sut ko ch spf u c xc nh ln hn so

vi ng sut ko dc trc crf c xc nh trong th nghim ko trc tip [hnh 2.2(a)]. Cc

tc gi Collins v Mitchell (1991) v Hsu (1993) a ra cng thc xc nh cng chu ko

trc tip crf nh sau:

'.33,0 ccr ff (2.10)

Hnh 2.2 Th nghim ko b tng trc tip v gin tip

a)Th nghim ko trc tip

b)Th nghim ph hoi dm

c)Th nghim ch khi tr

ng cong ng sut bin dng ko trc tip ( hnh 2.3)gi thuyt tuyn tnh cho n ng sut

fcr c cng dc Ec nh trong phng trnh (2.2).Sau khi nt , nu c ct thp , ng sut ko

gim nhng khng v khng, ni lin kt ga cc ht cn tn ti v c th truyn lc ko qua vt



nt. Hin tng ny rt quan trng khi d tnh ng sut ko trong ct thp v sc khng ct ca

dm BTCT.

Collins v Mitchell (1991) cho biu thc sau y v ng cong ng sut bin dng ko

trc tip trn hnh 2.3

Nhnh i ln: ( 1 cr = fcr/Ec)

11 cEf

Trong f1 l ng sut ko trung bnh v 1 l bin dng ko trung bnh ca b tng .

Nhnh xung : (1>cr)

1

211

5001

cr

ff

Trong : 1 L h s xt n c trung dnh kt ca ct thp :

1=1,0 cho ct thp c g

1=0,70 cho ct thp trn trn , si v tao thp c dnh bm

1=0 cho ct thp khng dnh bm

2 -H s xt n ti trng thng xuyn hay lp

2 =1,0 i vi ti ngn hn

2 =0,70 vi ti thng xuyn hoc ti trng lp.

0.001 0.002 0.003 0.004

crf

f'cf =0,33cr

1 2

1f =1,0 +

f cr

1

Bin dng trung bnh , 1

0

ng

sut

trun

g b

nh ,

f 1

Ec

Hnh 2.3 : ng sut trung bnh theo bin dng trung bnh ca b tng chu ko

Nu khng c ct thp s khng c nhnh xung , v ng sut ko ca b tng sau nt bng

khng . Tuy nhin nu b tng c dnh bm vi ct thp , ng sut ko ca b tng cn tn ti

.Mt ln na cho thy r tnh cht ca BTCT khc b tng .

M un n hi ca b tng khi chu ko c th c ly nh khi chu nn.

3. H s gin n nhit

H s gin n nhit nn xc nh bng th nghim trong phng theo loi b tng c cp phi

c em dng.

Trong trng hp thiu cc s liu chnh xc, h s gin n nhit c th ly nh sau :



B tng c t trng thng thng: 10,8 x 10-6/ oC , v

B tng c t trng thp : 9,0 x 10-6/ oC

4. H s Poisson

Tr trng hp c xc nh bng th nghim vt l, h s Poisson c th ly bng 0.2. i vi

cu kin cho php xut hin nt, c th khng xt n hiu ng Poisson .

2.1.3. Cc thuc tnh di hn ca b tng cng

1/Cng chu nn ca b tng theo thi gian

Ni chung, cng chu nn ca b tng tng theo tui ca n. C cc phng php khng

ph hu xc nh cng chu nn, thng bng con ng gin tip thng qua vic xc

nh trc ht m un n hi ri tnh ngc tr li tm cng chu nn. Theo mt phng

php khc, ngi ta o ny ln ca mt vin bi bng thp, vin bi ny c nh kch thc

da vo ny trn b tng bit cng chu nn.y chnh l nguyn l ch to sng bn

b tng xc nh cng .

Tnh cht ca BT c c trng bi cng chu nn c trng tui 28 ngy 'cf . Tuy nhin trong mt s trng hp, nh i vi BTCT DUL th ta cn phi bit cng chu nn

'cif v ciE ca b tng thi im cng ct thp DUL, cng nh cc thi im khc trong

lch s chu ti ca kt cu.

Thng thng, cng chu nn ca BT c xu hng tng theo thi gian v ph thuc vo

nhiu tham s nh loi XM, iu kin bo dng,... C cc phng php khng ph hu xc

nh cng chu nn, thng bng con ng gin tip thng qua vic xc nh trc ht m

un n hi ri tnh ngc tr li tm cng chu nn. Theo mt phng php khc, ngi

ta o ny ln ca mt vin bi bng thp, vin bi ny c nh kch thc da vo ny

trn b tng bit cng chu nn. Hip hi quc t BTCT DUL (FIP) kin ngh xc nh

cng chu nn ca BT theo thi gian theo biu c dng nh sau:

0,0

0,5

1,0

1,5

3 7 14 28 56 90 180 360 t (ngy)

cf /f'c BTXM PL thng BTXM PL ng cng nhanh

+ Theo Branson (1977) th biu thc xc nh cng chu nn ca BT theo thi gian c

dng nh sau:

,..

cci ft

tf

Trong :

t = thi gian tnh theo ngy;



, = l h s ph thuc vo loi XM v iu kin bo dng. i vi XM loi I, iu kin

bo dng m th = 4,0; = 0,85. Khi :

,..85,00,4

cci ft

tf

Tiu chun ASTM (C150) quy nh c 5 lai XM c bn c sn xut nh sau:

XM loi I: L loi chun, c s dng trong cc cng trnh bnh thng, ni khng cn phi

c cc thuc tnh c bit.

Loi II: L loi c bin i, nhit thy ha thp hn lai I, loi ny thng c s

dng ni chu nh hng va phi ca s n mn do sunfat hoc ni mong mun c nhit

thy ha va phi.

Loi III: L loi c CC sm, c s dng khi mong mun BT t CC sm, nhit thy

ha cao hn nhiu so vi lai I.

loi IV: L loi ta nhit thp, c s dng trong cc p BT khi ln v cc kt cu khc

m nhit thy ha gim chm.

Loi V: l loi chu c sunfat, thng c s dng trong cc mng, tng hm, cng

rnh,..., ni tip xc vi t cha sunfat.

2/Co ngt ca b tng

Co ngt ca b tng l s gim th tch di nhit khng i do mt m sau khi b tng

ng cng.

Co ngt c c im l y l loi bin dng th tch, bin dng theo mi phng.

Cc yu t nh hng n co ngt:

- Lng xi mng v hot tnh ca xi mng nh hng ti co ngt, dng nhiu xi

mng co ngt s ln

- Co ngt ph thuc vo t l nc trn xi mng (W/C), vi W/C ln th co ngt ln.

- Co ngt ph thuc vo m ca mi trng (H), H cao th co ngt sh

s nh

- Co ngt ph thuc vo t s th tch trn din tch b mt ca cu kin (V/A)

nh hng ca co ngt n s lm vic ca kt cu:

- Co ngt gy ra cc bin dng trong kt cu, c th sinh ra cc vt nt do co ngt khng

u.

- Trong cu kin BTCTDUL co ngt sinh ra hin tng mt mt ng sut trc trong

ct thp ko cng, do lm gim ng sut nn trc trong b tng.

Bin php lm gim co ngt v khc phc tc hi:

- Chn thnh phn cp phi b tng thch hp, hn ch lng nc trn, m cht b

tng v gi cho b tng thng xuyn m t trong giai on u.

- khc phc tc hi ca co ngt ta c th dng cc bin php cu to nh lm khe co

trong kt cu, t ct thp nhng ni cn thit.



Trong AASHTO, mt biu thc thc nghim c xy dng bi Collins v Mitchell (1991)

c s dng nh gi bin dng co ngt sh da trn thi gian kh, m tng i v t s

gia th tch v din tch b mt. (shrinkage)

310.51,0.35

..

t

tkk

hssh (2.11)

Trong t l thi gian kh tnh bng ngy, sk l mt h s kch thc c tra t hnh 2.4

hoc tnh theo cng thc 2.12 v hk l h s m c ly theo bng 2.2.

923

3.70(V/S)-1064

45

26 )/(0142.0

t

t

te

t

kSV

s (2.12)

Hnh 2.4 H s sk i vi t s th tch/din tch b mt

Bng 2.4 H s hk i vi m tng i H

m tng i

trung bnh ca mi

trng H (%)

hk

40

50

60

70

80

90

100

1,43

1,29

1,14

1,00

0,86

0,43

0,00

Thi gian kh (ngy)



V d 2.1

Hy xc nh bin dng co ngt trong mt bn b tng cu dy 200 mm vi mt trn v mt

di c lm kh trong khng kh c m tng i 70%. T s gia th tch v din tch b

mt i vi 1 mm2 din tch bn l

th tch 200(1)(1)

100 mmdin tch b mt 2(1)(1)

T hnh 2.4 i vi thi gian t = 5 nm ( 2000 ngy), ks = 0,73, v t bng 2.2 i vi H =

70% ta c kh = 1,0. T , biu thc 2.11 c vit nh sau:

32000

0,73 . 1,0 . .0,51.10 0,0003735 2000

sh

trong , du m biu th s co ngn li.

S ph thuc ca bin dng co ngt vo thi gian kh i vi cc iu kin ny c biu

din trn hnh 2.5. V cng thc thc nghim ny khng bao gm tt c cc yu t nh hng n

co ngt, AASHTO ch thch rng, cc kt qu c th tng gim khong 50% v co ngt thc

t c th ln hn -0,0008. Ngay c khi cc gi tr ny khng chnh xc th khuynh hng tc

co ngt gim khi thi gian kh tng ln vn ng. Khi khng c cc thng s c trng v b

tng v cc iu kin ni khai thc, AASHTO khuyn co s dng cc gi tr bin dng co ngt

l 0,0002 sau 28 ngy v 0,0005 sau 1 nm ng cng.

Hnh 2.5 Bin dng co ngt theo thi gian. V d 2.1.

3/T bin ca b tng

Di tc dng ca ti trng di hn bin dng ca b tng tng theo thi gian. T bin l hin

tng bin dng tng theo thi gian trong khi ng sut khng i.

T bin trong b tng c gn vi s thay i bin dng theo thi gian ti nhng vng ca

dm v ct chu ng sut nn thng xuyn.

Cc yu t nh hng n t bin:

- T bin ph thuc vo tr s ca ng sut v thi gian tc dng ca ng sut.



- T bin ph thuc vo t l nc trn xi mng (W/C), vi W/C ln th bin dng do t

bin ln.

- T bin ph thuc vo m ca mi trng (H), H cao th cR s nh

- T bin ph thuc vo cng ca b tng, 'cf cao th cR s nh

- T bin ph thuc vo t s th tch trn din tch b mt ca cu kin (V/A)

nh hng ca t bin n s lm vic ca kt cu:

- T bin l cho vng dn tng v vt nt ngy mt m rng.

- Vi cc cu kin chu nn lch tm c mnh ln, t bin lm tng un dc.

- Trong cu kin BTCTDUL t bin sinh ra hin tng mt mt ng sut trc trong ct

thp ko cng, do lm gim ng sut nn trc trong b tng.

- Trong cc kt cu siu tnh, t bin lm phn phi li ni lc.

Bin dng t bin cR

c tnh bng tch s ca bin dng nn n hi tc thi do ti trng

thng xuyn ci v h s t bin :

ciittittCR .

,, (2.13)

trong t l tui ca b tng tnh bng ngy k t thi im b tng v ti l tui ca b

tng tnh bng ngy k t khi ti trng thng xuyn tc dng. AASHTO s dng mt cng thc

thc nghim xc nh h s t bin, c xy dng bi Collins v Mitchell (1991), nh sau:

6,0

6,0

118,0

,10120

58,1..5,3i

i

fcitt tt

ttt

Hkk (2.14)

Trong H l m tng i (%), kc l mt h s iu chnh i vi nh hng ca t s

gia th tch v din tch b mt, c ly theo hnh 2.6 hoc tnh theo biu thc 2.15 v

'42

62

c

ff

k

(2.15)

y, fc l gi tr tuyt i ca cng chu nn c trng tui 28 ngy ca b tng

(MPa).

2.587

1.77e+1.80

t45

t

t26e

t

ck

)0.0213(V/S-)0.0142(V/S

(2.16)



Hnh 2.6- H s kc i vi t s th tch/din tch b mt

V d 2.2

Hy xc nh bin dng t bin trong bn b tng cu v d 2.1 sau mt nm nu ng sut

nn do ti trng di hn l 10 MPa, cng chu nn c trng tui 28 ngy l 31 MPa v ti =

15 ngy. M un n hi theo cng thc 2.2 l

1,5

0, 043 2300 31 26, 4 GPacE v bin dng nn tc thi c tnh nh sau

10

0,0003826400

cuci

c

f

E i vi mt t s th tch/ din tch b mt bng 100 mm v (t - ti) = (365 - 15) = 350 ngy,

hnh 2.6 cho mt h s iu chnh kc = 0,68. H s cng ca b tng kf c tnh theo biu

thc 2.15 nh sau:

62 420,85

31fk

H s t bin trong mt mi trng c m H = 70% c tnh theo biu thc 2.14:

0,60,118

0,6

70 350365;15 3,5 0,68 0,85 1,58 15 1,13

120 10 350 T , bin dng t bin sau mt nm c xc nh theo biu thc 2.13 nh sau:

365;15 1,13 0,00038 0, 00043CR Bin dng ny cng c ln tng ng so vi bin dng co ngt. y, vic xc nh ny

cng c th sai lch ti 50%. i vi cng cc iu kin nh v d ny, s thay i ca tng

bin dng nn theo thi gian sau khi t ti trng di hn c biu din trn hnh 2.7. Bin dng

nn ton phn c(t,ti) l tng ca bin dng n hi tc thi v bin dng t bin, ng thi mc

tng bin dng gim dn theo thi gian. Bin dng tng cng c th c tnh nh sau:

ciittittCRciittc ,,, 1 (2.17) i vi v d ny, bin dng nn tng cng sau mt nm l

365;15 1 1,13 0, 00038 0, 00081c bng hai ln so vi bin dng n hi.



Hnh 2.7 - Bin dng t bin theo thi gian. V d 2.2.

Cng c th lm gim bin dng t bin bng cc bin php nh lm gim co ngt, tc l

gim thnh phn nc trong hn hp b tng v gi cho nhit tng i thp. Bin dng t

bin cng c th c gim bt nh vic b tr ct thp vng chu nn v phn ni lc nn m

ct thp chu khng lin quan n t bin. Trng hp ti trng di hn tc dng tui b tng

ln, bin dng t bin s gim i do b tng tr nn kh hn v bin dng t hn. iu ny c

phn nh trong biu thc 2.9, y gi tr ln hn ti i vi tui b tng cho t lm gim h s

t bin (t,ti).

Cui cng, khng phi tt c cc nh hng ca bin dng t bin u l c hi. Khi c s ln

khc nhau xy ra trong mt cu BTCT, c tnh t bin ca b tng lm cho ng sut trong cc

cu kin gim r rt so vi gi tr d on bng phn tch n hi.

4/M un n hi i vi ti trng di hn

tnh ton i vi s tng bin dng do t bin di ti trng di hn, mt m un n hi

di hn c chit gim Ec,LT c th c nh ngha nh sau:

,

1 ,1 ,ci ci

c LT

ii i

f EE

t tt t

trong , Eci l m un n hi ti thi im ti. Gi thit rng Eci c th c biu din bng

m un n hi Ec t biu thc 2 .2 th ta c:

itt

c

LTc

EE

,

,1

(2.18)

Khi tnh i cc c trng mt ct ca thp thnh cc c trng tng ng ca b tng i

vi cc TTGH s dng, ngi ta dng t s m un n, c nh ngha nh sau:

c

s

E

En (2.19)

T s m un di hn nLT i vi ti trng thng xuyn c th c nh ngha tng t, gi

thit rng ct thp khng c t bin:

ittLTc

S

LT nE

En ,

,

1 (2.20)



V d 2.3

i vi cc d kin ca v d 2.2, hy xc nh h s m un di hn nLT vi t = 5 nm.

T hnh 2.6, i vi (t - ti) = 5.(365) 15 = 1810 ngy, ta c kc = 0,75. T :

0,60,118

0,6

70 18101825;15 3,5 0,75 0,85 1,58 15 1,45

120 10 1810

v

2, 45LTn n

Bin dng ca b tng theo thi gian di ng sut nn khng i:

2.2 CT THP

Ct thp c t trong cu kin nhng ni c th pht huy tc dng ln nht. Ct thp

thng c tnh n chu lc ko, tuy nhin n cng c b tr chu lc nn. TTGH v

ct trong dm, phi b tr ct thp dc v ct thp ngang chu ng sut ko xin.

S lm vic ca ct thp khng d ng lc thng c c trng bi quan h ng sut bin

dng i vi cc thanh ct thp trn. S lm vic ca ct thp d ng lc l khc nhau i vi b

cp c dnh bm v khng c dnh bm, iu ny khin chng ta phi xem xt li s lm vic ca

ct thp khng d ng lc c bao bc bi b tng.

2.2.1. Ct thp thng

Theo ASTM A615 v A706 Ct thp thng phn thnh 3 loi chnh: Grade 40 (cp 40);

Grade 60 (cp 60) ; Grade 75 (cp 75)

Cc ng cong ng sut bin dng in hnh i vi ct thp trn c biu din trn

hnh 2.8 i vi cp ct thp 280, 420 v 520. S lm vic ca ct thp trn c th c chia

thnh ba giai on, n hi, do v cng ho bin dng. on n hi AB ca biu gn ging

nh mt on thng vi m un n hi khng i Es = 200 000 MPa cho ti gii hn bin dng

n hi s

yE

f . on chy BC c c trng bi thm chy ti ng sut khng i fy cho

Cht ti khng i D ti

elastic(Phc hi n hi)

(Phc

hi t

bin) T

bin

Bin dng n

hi elastic

Bin dng d

Thi gian



ti lc bt u cng ho. di ca thm chy l thc o tnh do v c phn bit vi cc

cp thp khc nhau. on cng ho bin dng CDE bt u bin dng h

v t ti ng sut

ln nht u

f ti bin dng u

trc khi gim nh bin dng ph hoi b

. Ba on ca ng

cong ng sut - bin dng i vi ct thp trn c th c m t c trng bng nhng quan h

sau

on n hi AB

fs = s . Es vi 0 s y (2.21)

on chy BC

fs = fy vi y s h (2.22)

on cng ho bin dng CDE

1 1 exp 1-s h u s hs y h s bu h y u h

ff f

f (2.23)

Bng 2.5 Cc gi tr gii hn danh nh i vi cc ng cong ng sut-bin dng ca ct

thp thanh

Cp thp fymin

(MPa)

fu

(MPa)

y h u b

Cp 40

Cp 60

Cp 75

280

420

520

550

730

900

0,00138

0,00207

0,00259

0,0230

0,0060

0,0027

0,140

0,087

0,073

0,200

0,136

0,115

Hnh 2.8- Cc ng cong ng sut-bin dng ca ct thp trn dng thanh

Khi cc thanh ct thp c t trong b tng, s lm vic ca chng khc vi cc thanh ct

thp trn. S khc bit ny l do b tng c mt cng chu ko nht nh d kh nh. iu



ny c tha nhn sm, ngay t khi pht trin c hc BTCT nh trong kin sau y ca

Morsch (1908):

Do lc ma st i vi ct thp v do cng chu ko ca b tng tn ti trong nhng on

cu kin nm gia cc vt nt, b tng ngay c khi nt vn lm gim mt phn gin ca ct

thp.

Phn b tng dnh bm vi ct thp v khng b nt lm gim bin dng ko trong ct

thp.Hin tng ny gi l tng cng ko .

Hiu ng tng cng ko ny xut hin khi ng sut trung bnh ca thp tng i nh . Vi

bin dng ln hn , s tham gia ca b tng chu ko gim v ng x ca ct thp chn trong b

tng theo on ho cng ca ng cong US-BD ca thp trn .

2.2.2. Ct thp d ng lc

Thp d ng lc c th di dng si , tao v thanh .Tao gm mt s si xon li vi nhau gi

l tao cp .Theo AASHTO thng dng ba loi thp cng cao :



Thp si khng bc kh ng sut d hoc t chng thp;

Tao cp khng bc kh ng sut d hoc chng thp;

Thp thanh cng cao khng bc;

Thp d ng lc thng thng nht l tao thp by si, loi ny c kh ng sut v c

chng thp. Khi ch to cc tao thp, thanh thp cc-bon cao c ko lin tc qua cc khun

ko si c ng knh nh lin tc nhm sp xp cc phn t thp theo mt hng v lm tng

cng ca si thp ti trn 1700 MPa. Ri 6 si c t bao quanh mt si gia theo kiu

xon c. S ko ngui v xon cc si to ra ng sut d trong tao thp. Cc ng sut d ny l

nguyn nhn khin cho biu ng sut bin dng trn hn v gii hn chy thp hn. Gii

hn chy ny c th c nng cao bng cch lm nng cc tao thp ti 350oC v chng ngui

dn. Bin php ci thin hn na i vi s chng ca thp c thc hin bng cch ko cc tao

thp trong chu trnh nng, lnh. Qu trnh ny c gi l s ti thp v a ra sn phm l cc

tao thp c chng thp. Hnh 2.9 so snh quan h ng sut bin dng ca tao thp 7 si c

sn xut theo cc qu trnh khc nhau.

Cc thanh ct thp do cng cao cng c s dng lm ct thp d ng lc. Cng

chu ko ln nht ca cc thanh ct thp ny vo khong 1000 MPa.

c trng tiu biu i vi cc thuc tnh ca cc tao cp v thanh thp d ng lc c cho

trong bng 2.4. Cc gi tr khuyn co i vi m un n hi ca thp d ng lc, p

E , l

197 000 MPa i vi tao cp v 207 000 MPa i vi thanh thp.

Bin dng trong ct thp d ng lc ps c th c xc nh mt mc ti trng no t

bin dng trong b tng bao quanh cp nh sau

pecpps (2.24)

trong cp l bin dng ca b tng cng mt v tr vi ct thp d ng lc v pe

thng c tnh gn ng nh sau:

/pe pe pf E

Trong trng hp ct thp khng dnh bm, s trt xy ra gia ct thp v b tng xung

quanh v bin dng trong ct thp tr nn u n trong on nm gia cc im neo. Bin dng

di tng cng ca ct thp lc ny phi bng bin dng di tng cng ca b tng trong on ni

trn, tc l

pecpps

(2.25)

y, cp

l bin dng trung bnh ca b tng ti v tr ct thp d ng lc, c tnh trung

bnh trong khong cch gia cc neo ca ct thp khng c dnh bm.



Hnh 2.9 Quan h ng sut-bin dng ca tao thp 7 si c sn xut theo cc qu trnh

khc nhau

Bng 2.4 Cc thuc tnh ca tao thp v thanh thp d ng lc

Vt liu Cp hoc kiu ng knh (mm)

Cng chu ko fpu

(MPa)

Gii hn chy fpy (MPa)

Tao cp 1725 MPa (cp 250) 1860 MPa (cp 270)

6,35-15,24 10,53-15,24

1725 1860

80% ca fpu hay 90% ca

fpu i vi tao thp t chng

Thp thanh

Kiu 1, trn Kiu 2, c g

19-25 15-36

1035 1035

85% ca fpu 80% ca fpu

Cc ng cong ng sut-bin dng in hnh i vi thp d ng lc c cho trn hnh

2.10. Cc ng cong ny c th c tnh gn ng bng cc cng thc sau:

i vi cp 250:

197000 i vi 0,008

0,41710 < 0,98 i vi 0,008

0,006

ps ps

pspu ps

ps

ff

(2.26)

i vi cp 270:

197000 i vi 0,008

0,5171848 < 0,98 i vi 0,008

0,0065

ps ps

pspu ps

ps

ff

(2.27)

i vi thp thanh

207000 i vi 0,004

0,1921020 < 0,98 i vi 0,004

0,003

ps ps

pspu ps

ps

ff

(2.28)



Hnh 2.10 Cc ng cong ng sut-bin dng in hnh i vi thp d ng lc

Cc loi tao cp d ng lc, 7 si khng sn ph, c kh ng sut, hoc c t chng

thp, hoc cc thanh thp khng sn ph cng cao, trn hay c g, phi ph hp vi tiu

chun vt liu quy nh trong Tiu chun thi cng cu:

AASHTO M203M (ASTM A416M) - Tao thp 7 si d ng lc khng sn ph, c kh ng

sut cho b tng d ng lc hoc

AASHTO M275M (ASTM A722) - Thp thanh cng cao khng sn ph dng cho b

tng d ng lc.

Nu trong h s thu c cc chi tit v d ng lc th phi ch r kch thc v mc hoc loi

thp. Nu trong h s ch quy nh lc ko d ng lc v v tr t th vic chn kch c thp v

loi thp do nh thu la chn v k s gim st duyt.

1/ M un n hi

Nu khng c cc s liu chnh xc hn, m un n hi ca thp d ng lc, da trn

din tch mt ct ngang danh nh ca thp, c th ly nh sau :

i vi tao thp : Ep = 197 000 MPa v

i vi thanh : Ep = 207 000 MPa

2/Neo d ng lc ko sau v ni cp

Neo v mi ni cp phi c cu to theo cc yu cu ca cc Tiu chun tng ng.

Phi tin hnh bo v chng g cho cp, neo, cc u neo v cc mi ni cp.



3/ ng bc cp

ng bc cho cp phi l loi cng hoc loi na cng bng thp m km hoc bng nha hoc

to l trong b tng bng li ly ra c.

Bn knh cong ca ng bc khng c nh hn 6000 mm, tr vng neo c th cho

php nh ti 3600 mm.

Khng c dng ng bc bng nha khi bn knh cong nh hn 9000 mm.

Khi dng ng bc bng nha cho loi cp c dnh bm th phi xem xt c tnh dnh bm

ca ng nha vi b tng v va.

Hiu qu p lc ca va ln ng bc v vng b tng xung quanh phi c kim tra.

C ly ln nht gia cc im k c nh ng bc trong khi thi cng phi c quy nh trong

h s thu.

4/Kch thc ca ng bc cp

ng knh trong ca ng bc t nht phi ln hn ng knh ca thanh thp d ng lc

n hay b cp d ng lc 6 mm. i vi loi thp d ng lc nhiu thanh v b cp d ng lc

th din tch mt ct ca ng bc t nht phi ln hn 2 ln din tch tnh ca mt ct b thp d

ng lc, khi lp t b cp bng phng php ko sau th din tch mt ct ca ng bc phi gp

2,5 ln din tch mt ct ca b cp.

Kch thc ca ng bc khng c vt qu 0,4 ln b dy b tng nguyn nh nht ti v tr

t ng bc.

ng bc ti v tr neo chuyn hng

ng bc v tr chuyn hng phi l ng thp m ph hp vi tiu chun ca ASTM

A53, loi E, cp B. dy danh nh ca thnh ng khng c nh hn 3 mm.



2.3 B TNG CT THP

2.3.1. Khi nim v dnh bm gia b tng v ct thp

2.3.1.1. Khi nim

Lc dnh bm gia b tng v ct thp l yu t c bn m bo s lm vic chung ca

hai loi vt liu, lm cho b tng v ct thp c cng bin dng vi nhau v c s truyn lc qua

li gia chng.

2.3.1.2. Th nghim xc nh lc dnh bm

Ch to mu bng cch b tng m ly on ct thp. Th nghim bng cch ko hoc

nn cho cho ct thp tt khi b tng (hnh 2.10). Cng trung bnh ca lc dnh c xc

nh theo cng thc:

P

l

(2-24)

Trong : P Lc ko (hoc nn) lm ct thp tt khi b tng

- ng knh ct thp

l Chiu di on ct thp chon trong b tng

Hnh 2.10: Th nghim xc nh lc dnh

th nghim lm ct thp tt khi b tng th chiu di on l phi c hn ch trong

mt phm vi no . Nu l qu ln th khi th nghim ct thp c th b ko hoc nn qu gii

hn chy (thm ch c th b ko t) m khng b tt. Kt qu th nghim cho thy s phn b

lc dnh dc theo on ct thp l khng u, n bng khng ti hai u mt v t gi tr max

ni cch tit din u tin mt khong C

1 1

4 3C l

v axm hoc maxP

l

(2-25)

Trong : - h s hon chnh biu lc dnh, < 1



2.3.1.2. Cc yu t to nn lc dnh bm

Lc dnh bm c to ra nh cc yu t chnh sau :

- S dnh bm ho hc,

- Ma st,

- S tng tc c hc gia ct thp v b tng.

c c thanh ct thp trn trn, hai yu t u tin ng vai tr quan trng nht trong vic to

ra lc dnh bm. Trong khi , ct thp c g th s tng tc ci kho gia b tng vi cc g

ct thp li ng vai tr quyt nh. V vy, cc yu t chnh c nh hng n s dnh bm gia

ct thp v b tng l :

- Din tch g tnh i ca ct thp,

- Cng v thnh phn ca b tng,

- B dy lp b tng bo v,

- ng knh ct thp,

- V tr ct thp khi b tng.

2.3.2. Chiu di pht trin lc

Lc cn thit ko mt thanh ct thp ra khi mt khi b tng s tng ln khi chiu di

chn ca thanh ny tng ln (Hnh 2.11). Khi chiu di chn tr nn ln, thanh thp s b chy

do trc khi b ko ra khi k hi b tng. Chiu di chn ti thiu cn thit pht trin lc

chy do ca thanh ct thp c gi l chiu di pht trin lc. Chiu di pht trin lc dl , c

s dng nh l mt gi tr ch th v c trng dnh bm ca cc thanh ct thp.

Tiu chun ACI gi thit rng, chiu di pht trin lc c s cn thit phng nga s v

ch (split), ,db sp , l hm ca din tch thanh ct thp trong khi chiu di cn thit phng nga s

ko tut (pull out) ,db po l hm ca ng knh thanh thp. Cng thc tnh chiu di pht

trin lc c s ny nh sau: i vi thanh s hiu 35 v cc thanh nh hn:

, 0,02 mm, MPadb sp b y cA f f (2.29)

, 0,375 mm, MPadb sp b y cd f f (2.30)

Cc cng thc (2.29) v (2.30) ch ra rng, khi cng ca b tng tng, chiu di pht trin

lc s nh i. Tuy nhin, khng cho php chiu di pht trin lc gim hn na khi cng b

tng ln hn 70 MPa v v vy, thnh phn cf khng c ly ln hn 8,37 MPa.



Hnh 2.11 Khi nim v chiu di pht trin lc

Hnh 2.12Vng ng sut ko trong b tng cn bng vi thnh phn ly tm ca lc nn

nghing

2.3.3. Cc dng ph hoi v h hng ca b tng ct thp

2.3.3.1. Ph hoi do chu lc

B tng v ct thp lm vic vi nhau cho n khi b ph hoi. Vi thanh chu ko, sau

kho b tng b nt ct thp chu ton b lc ko v n b xem l bt u ph hoi khi ng sut

trong ct thp t n gii hn chy. Vi ct chu nn s ph hoi bt u khi ng sut nn trong

b tng t n gii hn cng chu nn, b tng b nn v. S ph hoi ca cu kin chu

un c th bt u t vng chu ko hoc chu nn. Khi ct thp chu ko l va phi th s ph

hoi l bt u t vng chu ko vi vic ct thp t n gii hn chy, c bin dng ln, vt

nt m rng. Khi ct thp kh nhiu th s ph hoi bt u t vng nn vi vic ng sut trong

b tng t n gii hn cng , vng nn b nn v.

2.3.3.2. Ph hoi do bin dng cng bc

Bin dng cng bc gy ra do chuyn v ca cc lin kt, do thay i nhit , do co

ngt ca b tngTrong kt cu tnh nh bin dng cng bc khng gy ra ni lc. Trong kt

cu siu tnh bin dng cng bc thng b ngn cn, lm pht sinh ni lc v c th lm kt

cu b h hng hoc ph hoi. S h hng th hin ch b tng b nt, v. S ph hoi xy ra

ging nh khi ph hoi do chu lc.

2.3.3.2. H hng do tc dng ca mi trng

Di tc ng ca mi trng b tng ct thp c th b h hng do tc dng c, l, ha,

sinh vt.

V c hc v vt l, b tng c th b bo mn do ma, dng chy, b hun nng do mt

tri hoc cc ngun nhit. i vi cc cng trnh chu lnh, ng v tan bng c th gy h hng

cu trc ca b tng.

Chiu di chn

Chiu di chn

Chiu di chn=Chiu

di pht trin lc

b yP A f

Gi

tr

t

i

a c

a

l

c

P



V ha hc, b tng b xm thc do cc cht ha hc (axit, baz, mui) c trong mi

trng. Cc cht ny c phn ng ha hc vi cc thnh phn ca xi mng to ra cc cht ha

tan hoc lm gim cng , ph hng s lin kt (b tng b mn).

Ct thp c th b xm thc do tc dng ha hc v in phn ca mi trng. Khi ct

thp b g th tch lp g tng ln nhiu ln so vi th tch kim loi ban u chn p vo b tng

lm cho lp b tng bn ngoi b nt, v. S m rng vt nt trong b tng lm cho ct thp d

b g hn. Trong mi trng c hi nc mn, mi trng c nhit v m cao ct thp b

g nhiu hn. ng sut trong ct thp cng cao v s gia cng ngui ct thp cng lm cho ct

thp d b g hn.

V sinh vt, cc loi rong ru, h, nhng vi khun sng bin cng gy tc dng lm h

hng b mt b tng do tc dng ca nhng cht ha hc chng tit ra.

V tc dng thi gian, trong vi nm u b tng c tng cng (trong mi trng

thun li). Tuy vy sau vi chc nm b tng s b gi lo v cng c th b gim dn.



3 NGUYN L THIT K THEO TIU CHUN 22TCN272-05

3.1 QUAN IM CHUNG V THIT K

Trong thit k cc k s phi kim tra an ton v n nh ca phng n kh thi c

chn .Cng tc thit k bao gm vic tnh ton nhm chng minh cho nhng ngi c trch

nhim thy rng mi tiu chun tnh ton v cu to u c tho mn .

iu kin m bo an ton ca mt cng trnh l :

Sc khng ca vt liu Hiu ng ca ti trng

R Q (3.1)

iu kin trn phi c xt trn tt c cc b phn ca kt cu .

Khi ni v sc khng ca vt liu ta xt kh nng lm vic ti a ca vt liu m ta gi l

trng thi gii hn(TTGH).

Mt trng thi gii hn l mt trng thi m vt qua n th kt cu hay mt b phn no

khng hon thnh mc tiu thit k ra .

Mc tiu l khng vt qu TTGH, tuy nhin khng phi l mc tiu duy nht , m cn xt

n cc mc ch quan trng khc , nh chc nng , m quan , tc ng n mi trng v yu t

kinh t.S l khng kinh t nu thit k mt cu m chng c b phn no, chng bao gi b h

hng.Do cn phi xc nh u l gii hn chp nhn c trong ri ro ca xc sut ph hu .

Vic xc nh mt min an ton chp nhn c ( cng ln hn bao nhiu so vi hiu ng

ca ti trng )khng da trn kin ch quan ca mt c nhn no m da trn kinh nghim ca

mt tp th.Tiu chun 22TCN272-05 c th p ng c .

3.2 S PHT TRIN CA QU TRNH THIT K

3.2.1. Thit k theo ng sut cho php (ASD)-Allowable Stress Design

an ton c xc nh bng cch cho rng hiu ng ca ti trng s gy ra ng sut

ch bng mt phn ca ng sut gy ph hoi (ng sut ph hoi l cng gii hn ca b

tng hoc gii hn chy ca thp) ,

H s an ton (F)= Cng ca vt liu(R) / hiu ng ti trng(Q)

sc khng,

2hiu ng ti trng, 0,5

y

y

fRF

Q f

V phng php thit k ny t ra gii hn v ng sut nn c bit n vi tn gi thit

k theo ng sut cho php (Allowable Stress Design, ASD).

Phng php ny c nhiu nhc im nh :

- Quan im v bn da trn s lm vic n hi ca vt liu ng hng,ng

nht .

- Khng biu hin c mt cch hp l v cng gii hn l ch tiu c bn v

kh nng chu lc hn l ng sut cho php

- H s an ton ch p dng ring cho cng , cha xt n s bin i ca ti

trng



- Vic chn h s an ton da trn kin ch quan v khng c c s tin cy v xc

sut h hng.

khc phc thiu st ny cn mt phng php thit k c th :

- Da trn c s cng gii hn ca vt liu

- Xt n s thay i tnh cht c hc ca vt liu v s bin i ca ti trng

- nh gi an ton lin quan n xc sut ph hoi .

Phng php khc phc cc thiu st trn l AASHTO-LRFD 1998 v n c chn lm

c s bin son tiu chun thit k cu 22TCN272-05.

3.2.2. Thit k theo h s ti trng v sc khng (LRFD-Load and Resistance Factors

Design)

xt n s thay i c hai pha ca bt ng thc trong phng trnh 3.1 .Pha sc

khng c nhn vi mt h s sc khng da trn c s thng k (Pha ti trng c

nhn ln vi h s ti trng da trn c s thng k ti trng, thng ln hn 1.V hiu ng

ti trong trng thi gii hn bao gm mt t hp ca nhiu loi ti trng (Qi) nhiu mc

khc nhau ca s d tnh nn pha ti trng c biu hin l tng ca cc gi tr i Qi .Nu sc

khng danh nh l Rn , tiu chun an ton s l :

Rn Hiu ng ca i Qi (3.2)

V phng trnh 3.2 cha c h s ti trng v h s sc khng nn phng php thit k c

gi l thit k theo h s ti trng v sc khng ( LRFD).

H s sc khng cho trng thi gii hn cn xt ti tnh phn tn ca :

- Tnh cht vt liu

- Phng trnh d tnh cng

- Tay ngh cng nhn

- Kim sot cht lng

- Tnh hung h hng

H s ti trng i dng cho cc ti trng cn xt ti phn tn ca :

- ln ca ti trng

- S sp xp ca ti trng

- T hp ti trng c th xy ra

u im ca LRFD:

- C xt n s bin i c v sc khng v ti trng

- t c mc an ton ng u cho cc TTGH khc nhau v cc loi cu m

khng cn phn tch xc sut v thng k phc tp.

- Phng php thit k thch hp

Nhc im ca LRFD:

- Yu cu thay i t duy thit k ( so vi tiu chun c )

- Yu cu hiu bit c bn v l thuyt xc sut v thng k



- Yu cu c cc s liu y v thng k v thut ton tnh xc sut chnh l h s

sc khng trong trng hp c bit.

3.3 NGUYN TC C BN CA TIU CHUN 22TCN 272-05

Bn Tiu chun thit k cu mi 22 TCN 272-05 (lc ra i, nm 2001, mang k hiu 22 TCN

272-01) c bin son nh mt phn cng vic ca d n ca B giao thng vn ti mang

tn D n pht trin cc Tiu chun cu v ng b .

Kt qu ca vic nghin cu tham kho a n kt lun rng, h thng Tiu chun

AASHTO ca Hip hi cu ng M l thch hp nht c chp thun p dng Vit nam.

l mt h thng Tiu chun hon thin v thng nht, c th c ci bin ph hp vi cc

iu kin thc t nc ta. Ngn ng ca ti liu ny cng nh cc ti liu tham chiu ca n

u l ting Anh, l ngn ng k thut thng dng nht trn th gii v cng l ngn ng th hai

ph bin nht Vit nam. Hn na, h thng Tiu chun AASHTO c nh hng rt ln trong

cc nc thuc khi ASEAN m Vit nam l mt thnh vin.

Tiu chun thit k cu mi c da trn Tiu chun thit k cu AASHTO LRFD, ln xut

bn th hai (1998), theo h n v o quc t SI. Tiu chun LRFD ra i nm 1994, c sa

i v xut bn ln th hai nm 1998. Tiu chun ny c son tho da trn nhng kin

thc phong ph tch ly t nhiu ngun khc nhau trn khp th gii nn c th c coi l i

din cho trnh hin i trong hu ht cc lnh vc thit k cu vo thi im hin nay.

Cc ti liu Vit nam c lit k di y c tham kho hoc l ngun gc ca cc d

liu th hin cc iu kin thc t Vit nam:

- Tiu chun v thit k cu 22 TCN 181979

- Tiu chun v ti trng gi TCVN 2737 1995

- Tiu chun v ti trng do nhit TCVN 4088 1985

- Tiu chun v thit k chng ng t 22 TCN 221 1995

- Tiu chun v giao thng ng thy TCVN 5664 1992

Cc quy nh ca b Tiu chun thit k cu mi ny nhm s dng cho cc cng tc thit k,

nh gi v khi phc cc cu c nh v cu di ng trn tuyn ng b. Cc iu khon s

khng lin quan n cu ng st, xe in hoc cc phng tin cng cng khc. Cc yu cu

thit k i vi cu ng st d kin s c ban hnh nh mt ph bn trong tng lai.

3.3.1. Tng qut

Cu phi c thit k t c cc mc tiu: thi cng c, an ton v s dng c, c

xt n cc yu t: kh nng d kim tra, tnh kinh t, m quan. Khi thit k cu, t c

nhng mc tiu ny, cn phi tha mn cc trng thi gii hn. Kt cu thit k phi c

do, phi c nhiu ng truyn lc (c tnh d) v tm quan trng ca n trong khai thc phi

c xt n.

Mi cu kin v lin kt phi tha mn phng trnh 3.3 i vi tt c trng thi gii hn.

rniiiRRQ (3.3)

Trong :



Qi Hiu ng ti trng (ni lc do ti hoc cc tc ng bn ngoi sinh ra)

i h s ti trng: h s nhn da trn thng k dng cho cc lc

Rn sc khng danh nh

h s sc khng: h s nhn da trn thng k dng cho sc khng danh nh

i vi cc trng thi gii hn s dng v trng thi gii hn c bit, h s sc khng c

ly bng 1,0

Rr sc khng tnh ton, Rr = . Rn

i h s iu chnh ti trng, xt n tnh do, tnh d v tm quan trng trong khai thc

0,95i D R I i vi ti trng dng gi tr max

1

1, 0iR D l

i vi ti trng dng gi tr min

D = h s lin quan n tnh do

R = h s lin quan n tnh d

I = h s lin quan n tm quan trng trong khai thc

Hai h s u c lin quan n cng ca cu, h s th ba xt n s lm vic ca

cu trng thi s dng.

Tr trng thi gii hn cng , i vi tt c cc TTGH khc , D = R = 1,0.

3.3.2. Khi nim v tnh do, tnh d v tm quan trng trong khai thc

1/ H s xt n tnh do D

Tnh do l mt yu t quan trng i vi s an ton ca cu. Nh tnh do, cc b phn chu

lc ln ca kt cu c th phn phi li ti trng sang nhng b phn khc c d tr v cng .

S phn phi li ny ph thuc vo kh nng bin dng ca b phn chu lc ln v lin quan

n s pht trin bin dng do m khng xy ra ph hoi.

H kt cu ca cu phi c nh kch thc v cu to m bo s pht trin ng k v

c th nhn thy c ca cc bin dng khng n hi trng thi gii hn cng v trng

thi gii hn c bit trc khi ph hoi.

Nu mt cu kin ca cu c thit k sao cho bin dng do c th xut hin th s c d

bo khi cu kin b qu ti. Nu l kt cu BTCT th vt nt s pht trin v cu kin c xem l

vo tnh trng nguy him. Phi trnh s lm vic gin v n dn n s mt kh nng chu lc

t ngt khi vt qu gii hn n hi. Cc cu kin v lin kt trong BTCT c th lm vic do

khi hn ch hm lng ct thp chu un v khi b tr ct ai kim ch bin dng. Ct thp c

th c b tr i xng chu un, iu ny cho php xy ra s lm vic do. Ni tm li, nu

trong thit k, cc quy nh ca Tiu chun c tun theo th thc nghim cho thy rng, cc

cu kin s c tnh do cn thit.

i vi trng thi gii hn cng , h s lin quan n tnh do c quy nh nh sau:

D 1,05 i vi cc cu kin v lin kt khng do

D = 1,0 i vi cc thit k thng thng v cc chi tit theo ng Tiu chun ny

D 0,95 i vi cc cu kin v lin kt c cc bin php tng thm tnh do vt

qu nhng yu cu ca Tiu chun ny



2/ H s xt n tnh d R

Tnh d c tm quan trng c bit to ln i vi khong an ton ca kt cu cu. Mt kt cu

siu tnh l d v n c nhiu lin kt hn s lin kt cn thit m bo khng bin dng hnh

hc. V d, mt dm cu lin tc ba nhp l kt cu siu tnh bc hai. Mt t hp hai lin kt n,

hoc hai lin kt chng quay, hoc mt lin kt n v mt lin kt chng quay c th b mt i

m khng dn ti hnh thnh khp do ngay lp tc v ti trng tc dng c th tm c cc con

ng khc truyn xung t. Khi nim nhiu ng truyn lc l tng ng vi tnh d.

Cc ng truyn lc n hay cc kt cu cu khng d c khuyn co khng nn s dng.

Tnh d trong kt cu cu lm tng khong an ton ca chng v iu ny c phn nh

trng thi gii hn cng qua h s xt n tnh d R, c quy nh trong Tiu chun 22

TCN 272-05 nh sau:

R 1,05 i vi cc cu kin khng d

R = 1,0 i vi cc cu kin c mc d thng thng

R 0,95 i vi cc cu kin c mc d c bit

3/ H s xt n tm quan trng trong khai thc I

Cc cu c th c xem l c tm quan trng trong khai thc nu chng nm trn con ng

ni gia cc khu dn c v bnh vin hoc trng hc, hay l con ng dnh cho lc lng

cng an, cu ha v cc phng tin gii cu i vi nh , c quan v cc khu cng nghip.

Cu cng c th c coi l quan trng nu chng gip gii quyt tnh trng i vng do tc

ng, gip tit kim thi gian v xng du cho ngi lao ng khi i lm v tr v nh. Ni tm

li, kh c th tm thy tnh hung m cu khng c coi l quan trng trong khai thc. Mt v

d v cu khng quan trng l cu trn ng ph dn ti mt vng ho lnh c s dng

khng phi quanh nm.

Khi c s c ng t, iu quan trng l tt c cc con ng huyt mch, nh cc cng trnh

cu, vn phi thng. V vy, cc yu cu sau y c t ra i vi trng thi gii hn c bit

cng nh i vi trng thi gii hn cng :

I 1,05 i vi cc cu quan trng

I = 1,0 i vi cc cu in hnh

I 0,95 i vi cc cu t quan trng

i vi cc trng thi gii hn khc:

I = 1,0

3.3.3. Cc trng thi gii hn

1 .Trng thi gii hn s dng

Trng thi gii hn s dng phi xt n nh mt bin php nhm hn ch i vi ng sut,

bin dng v vt nt di iu kin s dng bnh thng. 2. Trng thi gii hn mi v ph hoi gin

Trng thi gii hn mi phi c xt n trong tnh ton nh mt bin php nhm hn ch

v bin ng sut do mt xe ti thit k gy ra vi s chu k bin ng sut d kin.



Trng thi gii hn ph hoi gin phi c xt n nh mt s yu cu v tnh bn ca vt

liu theo Tiu chun vt liu. 3. Trng thi gii hn cng

Trng thi gii hn cng phi c xt n m bo cng v s n nh cc b v

n nh tng th c d phng chu c cc t hp ti trng quan trng theo thng k c

nh ra cu chu c trong phm vi tui th thit k ca n.

Trng thi gii hn cng I: T hp ti trng c bn lin quan n vic s dng cho xe tiu

chun ca cu khng xt n gi

Trng thi gii hn cng II: T hp ti trng lin quan n cu chu gi vi vn tc vt

qu 25m/s

Trng thi gii hn cng III: T hp ti trng lin quan n vic s dng xe tiu chun

ca cu vi gi c vn tc 25m/s TTGH cng l mt TTGH c quyt nh bi cng tnh ca vt liu ti mt mt ct

c vt nt cho. C 3 t hp ti trng cng khc nhau c quy nh trong bng 1.1. i

vi mt b phn ring bit ca kt cu cu, ch mt hoc c th hai trong s cc t hp ti trng

ny cn c xt n. S khc bit trong cc t hp ti trng cng ch yu lin quan n cc

h s ti trng c quy nh i vi hot ti. T hp ti trng sinh ra hiu ng lc ln nht c

so snh vi cng hoc sc khng ca mt ct ngang ca cu kin.

Trong tnh ton sc khng i vi hiu ng ti trng nhn h s nh lc dc trc, lc un,

lc ct hoc xon, s khng chc chn c biu th qua h s gim cng hay h s sc

khng .. H s l h s nhn ca sc khng danh nh Rn v iu kin an ton l tho mn

phng trnh tng qut 3.3.

Trong cc cu kin BTCT, c nhng yu t khng m bo c chnh xc nh cht lng

vt liu, kch thc mt ct ngang, vic t ct thp v nhng cng thc c dng tnh sc

khng.

Mt s m hnh ph hoi c th c a ra vi chnh xc cao hn cc m hnh khc v

hu qu do s c ca chng l t nguy him. Chng hn, dm chu un thng c thit k

tng i t ct thp, do ph hoi xy ra do s chy t t ca ct thp chu ko, trong khi cc

ct chu nn thng b ph hoi t ngt khng c bo trc. M hnh ph hoi do ct thng t

c hiu bit v n l s kt hp ca m hnh ph hoi do ko v do nn. Do vy, h s trong

trng hp ny phi nm trong khong gia h s ca dm chu un v ca ct chu nn. Hu

qu s ph hoi ca ct l nghim trng hn ca dm v mt ct b ph hoi s ko theo s sp

ca mt s dm, do , d tr trong thit k ct cn phi ln hn. Tt c cc l do trn cng

nh cc nguyn nhn khc c phn nh trong h s sc khng, c quy nh bi AASHTO

v c gii thiu trong bng sau

i vi trng hp un v nn kt hp, h s trong trng hp nn c th c ly tng ln

tuyn tnh t gi tr 0,75 lc dc trc nh cho ti h s i vi un thun tu lc dc bng

khng. Mt lc dc nh c nh ngha l 0,10.fc.Ag vi fc l cng chu nn 28 ngy ca

b tng v Ag l din tch mt ct ngang nguyn ca cu kin chu nn.



i vi cc dm chu ko hoc khng chu ko c t ct thp thng v ct thp d ng

lc hn hp, h s ph thuc vo t l d ng lc b phn (PPR) v c tnh bng cng thc

sau:

= 0,90 + 0,10.(PPR)

trong :

( )ps py

ps py s y

A fPPR

A f A f

vi

Aps = din tch ct thp d ng lc,

fpy = gii hn chy ca ct thp d ng lc,

As = din tch ct thp thng,

fy = gii hn chy ca ct thp thng.

Bng 3.1-H s sc khng i vi cc kt cu thng thng

Trng thi gii hn cng H s i vi un v ko B tng ct thp B tng ct thp d ng lc

0,90 1,00

i vi ct v xon B tng c trng lng trung bnh B tng nh

0,90 0,70

i vi nn dc trc c ct thp xon, tr trng hp ng t vng 3 v 4

0,75

i vi b phn ta trn b tng 0,70 i vi nn trong m hnh chng v ging 0,70 i vi nn ti vng neo B tng c trng lng trung bnh B tng nh

0,80 0,65

i vi ko trong ct thp ti vng neo 1,00

4. Trng thi gii hn c bit

Trng thi gii hn c bit phi c xt n m bo s tn ti ca cu khi ng t

hoc l ln hoc khi b tu thu, xe c va, c th c trong iu kin b xi l.

Trong tiu chun chu u v tiu chun Vit nam TCXDVN356-2005 ngi ta xp thnh 2

nhm trng thi gii hn l trng thi gii hn s dng (SLS) v trng thi gii hn cc hn

(ULS)

3.4 TI TRNG V H S TI TRONG THEO 22TCN 272-01

Ti trng c phn loi theo nhiu cch. Theo tnh cht ca ti ngi ta chia ra thnh hai

loi:

Ti trng thng xuyn (Tnh ti): l ti trng khng thay i phng chiu, tr s trong sut

qu trnh s dng nh trng lng bn thn kt cu, trng lng lp ph mt ng

Ti trng tm thi ( Hot ti): l ti trng thay i phng chiu tr s trong qu trnh s dng

nh hot ti xe c, hot ti ngi i b, hot ti gi



4.4.1. Ti trng v tn ti trng- Cc t hp ti trng

Ti trng thng xuyn

DD = ti trng ko xung (xt hin tng ma st m)

DC = ti trng bn thn ca cc b phn kt cu v thit b ph phi kt cu

DW = ti trng bn thn ca lp ph mt v cc tin ch cng cng

EH = ti trng p lc t nm ngang

EL = cc hiu ng b hm tch lu do phng php thi cng.

ES = ti trng t cht thm

EV = p lc thng ng do t trng t p.

Ti trng tm thi

BR = lc hm xe

CE = lc ly tm

CR = t bin

CT = lc va xe

CV =lc va tu

EQ = ng t

FR = ma st

IM = lc xung kch (lc ng ) ca xe

LL = hot ti xe

LS = hot ti cht thm

PL = ti trng ngi i

SE = ln

SH = co ngt

TG = gradien nhit

TU = nhit u

WA = ti trng nc v p lc dng chy

WL = gi trn hot ti

WS = ti trng gi trn kt cu

Tiu chun AASHTO LRFD quy nh xt 11 t hp ti trng.

Trong Tiu chun 22TCN 272-05, vic t hp ti trng c n gin ha ph hp vi

iu kin Vit nam. C 6 t hp ti trng c quy nh nh trong bng 3.2.

Bng 3.2 Cc t hp ti trng theo Tiu chun 22TCN 272-05

T hp ti

trng Trng thi

gii hn

DC DD DW EH EV ES

LL IM CE BR PL LS EL

WA

WS

WL

FR

TU CR SH

TG

SE

Cng mt lc ch dng mt trong cc ti

trng

EQ CT CV

Cng I p 1,75 1,00 - - 1,00 0,5/1.20 TG SE - - - Cng II p - 1,00 1,40 - 1,00 0,5/1.20 TG SE - - - Cng III p 1,35 1,00 0.4 1,00 1,00 0,5/1.20 TG SE - - - c bit p 0,50 1,00 - - 1,00 - - - 1,00 1,00 1,00 S dng 1.0 1,00 1,00 0,30 1,00 1,00 1,0/1,20 TG SE - - - Mi ch c LL, IM & CE

- 0,75 - - - - - - - - - -

1. Khi phi kim tra cu dng cho xe c bit do Ch u t quy nh hoc xe c giy php thng qua cu th h s ti trng ca hot ti trong t hp cng I c th gim xung cn 1,35.



2. Cc cu c t l tnh ti trn hot ti rt cao (tc l cu nhp ln) cn kim tra t hp khng c hot ti, nhng vi h s ti trng bng 1,50 cho tt c cc kin chu ti trng thng xuyn.

3. i vi cu vt sng cc trng thi gii hn cng v trng thi s dng phi xt n hu qu ca nhng thay i v mng do l thit k xi cu.

4. i vi cc cu vt sng, khi kim tra cc hiu ng ti EQ, CT v CV trng thi gii hn c bit th ti trng nc (WA) v chiu su xi c th da trn l trung bnh hng nm. Tuy nhin kt cu phi c kim tra v v nhng hu qu do cc thay i do l, phi kim tra xi nhng trng thi gii hn c bit vi ti trng nc tng ng (WA) nhng khng c cc ti trng EQ, CT hoc CV tc dng.

5. kim tra chiu rng vt nt trong kt cu b tng ct thp d ng lc trng thi gii hn s dng, c th gim h s ti trng ca hot ti xung 0,08.

6. kim tra kt cu thp trng thi gii hn s dng th h s ti trng ca hot ti phi tng ln 1,30.

H s ti trng tnh cho gradien nhit TG v ln SE cn c xc nh trn c s mt

n c th ring. Nu khng c thng tin ring c th ly TG bng:

0,0 cc trng thi gii hn cng v c bit

1,0 trng thi gii hn s dng khi khng xt hot ti, v

0,50 trng thi gii hn s dng khi xt hot ti

Bng 3.3 H s ti trng dng cho ti trng thng xuyn, p

Loi ti trng H s ti trng

Ln nht Nh nht

DC: Cu kin v cc thit b ph 1,25 0,90

DW: Lp ph mt cu v cc tin ch 1,50 0,65

2/ Hot ti xe thit k

a/ S ln xe thit k

B rng ln xe c ly bng 3500 mm ph hp vi quy nh ca Tiu chun thit

k ng t. S ln xe thit k c xc nh bi phn nguyn ca t s w/3500, trong w l

b rng khong trng ca lng ng gia hai va hoc hai ro chn, tnh bng mm.

b/ H s ln xe

H s ln xe c quy nh trong bng 3.4

Bng 3.4 H s ln xe m

S ln cht ti H s ln

1 1,20

2 1,00

3 0,85

>3 0,65

c/ Hot ti xe t thit k



Hot ti xe t trn mt cu hay cc kt cu ph tr c k hiu l HL-93, l mt t hp

ca xe ti thit k hoc xe hai trc thit k v ti trng ln thit k (hnh 1.2).

Xe ti thit k

Trng lng, khong cch cc trc v khong cch cc bnh xe ca xe ti thit k c

cho trn hnh 1.1. Lc xung kch c ly theo bng 1.4.

C ly gia hai trc sau ca xe phi c thay i gia 4300 mm v 9000 mm gy ra

ng lc ln nht.

i vi cc cu trn cc tuyn ng cp IV v thp hn, ch u t c th xc nh ti

trng trc thp hn ti trng cho trn hnh 1.1 bi cc h s chit gim 0,50 hoc 0,65.

Xe hai trc thit k

Xe hai trc gm mt cp trc 110.000 N cch nhau 1200 mm. Khong cch theo chiu

ngang ca cc bnh xe bng 1800 mm.

Lc xung kch c ly theo bng 1.4.

i vi cc cu trn cc tuyn ng cp IV v thp hn, ch u t c th xc nh ti

trng hai trc thp hn ti trng ni trn bi cc h s chit gim 0,50 hoc 0,65.

Ti trng ln thit k

Ti trng ln thit k l ti trng c cng 9,3 N/mm phn b u theo chiu dc

cu. Theo chiu ngang cu, ti trng c gi thit l phn b u trn b rng 3000 mm. Khi

tnh ni lc do ti trng ln thit k, khng xt tc ng xung kch. ng thi, khi gim ti trng

thit k cho cc tuyn ng cp IV v thp hn, ti trng ln vn gi nguyn gi tr 9,3 N/mm,

khng nhn vi cc h s (0,50 hay 0,65).

Lc xung kch

Tc ng tnh hc ca xe ti thit k hoc xe hai trc thit k phi c ly tng thm

mt t l phn trm cho tc ng xung kch IM, c quy nh trong bng 3.5.

Hnh 3.1 c trng ca xe ti thit k



Hnh 3.2 Hot ti thit k theo Tiu chun 22 TCN 272-05 v AASHTO LRFD

(1998)

Bng 3.5 Lc xung kch IM

Cu kin IM

Mi ni bn mt cu, i vi tt c cc trng thi

gii hn

75%

Tt c cc cu kin khc

Trng thi gii hn mi

Cc trng thi gii hn khc

15%

25%

3/ Ti trng mi

35 KN 145 KN 145 KN

4300 mm 9000 mm

Hnh 3.2a Xe t i thit k mi

Lc xung kch l 15% v h s ti trng l 0,75.

V sc khng mi ph thuc vo chu k ng sut , do vy cn bit chu k ca ti trng

mi .



4 CU KIN CHU UN

4.1 C IM CU TO

4.1.1 Cu to ca bn v dm

1/ Cu to ca bn

Bn l mt kt cu phng c chiu dy kh nh so vi chiu di v chiu rng. Chiu dy ca

bn thng t 60-200 mm tu theo loi kt cu. Vi bn mt cu yu cu b tng c fc28MPa.

Ct thp trong bn gm ct thp chu lc v ct thp phn b .Ct thp chu lc c t

trong vng chu ko do m men gy ra. S lng ct thp chu lc do tnh ton nh ra. Ct thp

phn b t thng gc vi ct thp chu lc v gn trc trung ho hn so vi ct thp chu lc.

Hnh 4.1 Cu to ca bn

Theo s lm vic ca bn c cc loi bn : Bn kiu dm ( k trn hai cnh song song ) ,

bn k bn cnh, bn hng, bn kiu dm hai u ngm, bn 4 cnh ngm .

Theo 22TCN272-05: Ct thp phi t cng gn cc mt ngoi cng tt nhng phi tho mn

cc i hi v lp bo v cho php. Ct thp phi c t trong mi mt ca bn vi lp ngoi

cng t theo phng ca chiu di hu hiu. S lng ct thp ti thiu bng 0,570 mm2/mm

thp cho mi lp y v 0,380 mm2/mm thp cho mi lp nh. C ly ct thp khng c vt

qu 450 mm. Ct thp cp 400 hoc hn. Ton b ct thp l cc thanh thng, tr cc mc cc

ch c yu cu. Ch c dng mi ni chp u.

Ct thp phi c b tr hng ph di y bn bng t l phn trm ca ct thp

hng chnh chu m men dng di y:

cho ct thp hng chnh song song vi ln xe: %50S/1750

cho ct thp chnh vung gc vi ln xe: %673840 S

y:

S = chiu di nhp hu hiu ly bng chiu di hu hiu iu 9.7.2.3 (mm)

Kch thc tit din ph thuc vo tnh ton , t s chiu cao vi chiu rng ca tit din (

h/b) thng t 2-4.



Hnh 4.2: Cc loi bn

(Bn cngxxon; bn k hai cnh; bn ngm hai cnh; bn k 4 cnh; bn ngm 4 cnh)

Hnh 4.3: S tnh v neo ct thp

Tnh ton bn c th theo m hnh n hi hoc m hnh ng chy do ( Theo 4.4 ca

22TCN272-05 Cc phng php phn tch kt cu c chp nhn).

Tnh ton bn mt cu khi s dng cc phng php phn tch gn ng cn tun th iu

4.6.2.1 ca 22TCN272-05. Tnh ton bn theo tit din ch nht.

2/ Cu to ca dm

Dng tit din :

Ch nht , ch T, ch I , hnh thang , hp .Hay gp nht vi dm nhp gin n l tit din

ch T, I .Trong cc cu nhp lin tc , kt cu cu khung tit din thng c dng hp.

Kch thc tit din :



Chiu cao h thng c chn trong khong 1/8 n 1/20 chiu di nhp dm.

Khi chn kch thc tit din cn phi xem xt n yu cu kin trc v vic nh hnh ho

vn khun.

Hnh 4.4: Cc loi mt ct dm

Hnh 4.5: Cc loi ct thp trong dm

Ct thp trong dm :

Ct thp ch yu trong dm gm ct thp dc chu lc, ct dc phn b, ct thp ai v ct

thp xin.

Ct thp dc chu lc t vng chu ko ca dm, s lng do tnh ton nh ra. Ct thp t

cng xa trc trung ho cng tt. Ct dc chu lc c th t ri, t chng, hoc b, cn phi tun

th yu cu cu to ca quy trnh v c li, chiu dy lp b tng bo v.

Ct thp dc phn b (hay ct dc cu to) nh v tr ct ai, cng vi cc ct thp khc to

nn khung cng trong khi thi cng .N c nhim v chu cc ng sut do co ngt, v th

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