tkmh - cau be tong 1 - 272-05_k46

Thit k mn hc Cu B Tng Ct Thp F1

Mc lcPhn 1: Ni dung thuyt minh1. Chn tit din mt ct dm ch

1.1 B tr chung mt ct ngang cu 1.2 Chn mt ct ngang dm ch. 2. Chiu cao kt cu nhp ti thiu (A2.5.2.6.3-1) 3. Xc nh chiu rng bn cnh hu hiu (A.4.6.2.6) 3.1 i vi dm gia 3.2 i vi dm bin 4. Tnh ton ni lc dm ch do tnh ti 4.1 Tnh ti ri u ln 1 dm ch 4.2 Cc h s cho tnh ti 4.3 Xc nh ni lc 5. Ni lc dm ch do hot ti 5.1. Tnh ton h s phn phi hot ti theo ln 5.2 Tnh ton h s phn phi ca ti trng ngi i b 5.3 Xc nh ni lc. 6. Cc c trng vt liu cho dm ch 6.1 Thp 6.2 Btng dsa 7. Chn v b tr cp d ng lc 7.1 Chn cp d ng lc 7.2 B tr cp d ng lc 7.3 Tnh ton cc c trng hnh hc 8. Tnh ton cc mt mt ng sut 8.1 Xc nh mt s thng s cho cc b cp Nguyn Vn B1p

(Bng A.3.4.1-2)

Lp : Cu Anh k46


8.2 Mt mt do ma st fpF 8.3 Mt mt do tt neo 8.4 Mt mt ng sut do co ngn n hi 8.5 Mt mt ng sut do co ngt (A.5.9.5.4.2) 8.6 Mt mt ng sut do t bin 8.7 Mt mt do do thp ng sut trc 9 Kim ton theo - Trng thi gii hn cng I 9.1 Kim ton Cng chu un 9.2 Kim tra hm lng ct thp ng sut trc 9.3 Tnh ct ai v kim ton ct theo trng thi gii hn C1 9.4 Kim ton dm theo trng thi gii hn s dng 10. Tnh vng cu 10.1 Tnh vng lc DL 10.2 Tnh vng do ti trng thng xuyn (tnh ti) 10.3 Tnh vng tc thi do hot ti c xt lc xung kch 11. Tnh ton dm ngang 11.1 Ni lc do ti trng cc b (hot ti) gy ra 11.2 Ni lc do ti trng phn b (tnh ti) 11.3 B tr ct thp 11.4 Duyt cng khng un 11.5 Duyt cng khng ct 12. Duyt dm ngang. 13. Vt liu cho dm

Phn 2: Bn v k thut(Bn v kh A0)Nguyn Vn B2

Lp : Cu Anh k46


Nhim v thit k Thit k 1 cu B tng ct thp DL1* Cc s liu cho trc: - Dm T, chiu di ton dm L=28m, kt cu ko sau - Kh cu K8+2 x1,5m --------> W=8+2x1,5+2x0.5=12m. - Ti trng thit k: HL93, Ngi - Tao cp DL: 15.2 mm. 2*Tiu chun thit k: - Quy trnh thit k : 22TCN 272 - 01 B Giao thng vn ti. - Ti trng thit k: HL93 , on Ngi i b. 3* Vt liu s dng: -Thp DL: .Cng quy nh ca thp ng sut trc fpu=1860 Mpa .Gii hn chy ca thp ng sut trc .ng sut cho php khi kch .Cng tnh ton khi ch to .Cng tnh ton khi s dng .Mun n hi -Vt liu btng: .Cng chu nn ca btng tui 28 ngy .Cng chu nn ca btng khi to ng sut trc Ma. .Mun n hi ca btng .Cng chu ko khi un 4* Yu cu: - Ni dung bn thuyt minh y r rngEc 0,043.1,5 c

fpy=0.9* fpu=1670Mpa fpj=0.8* fpu=1488 Mpa Rd1=13280 Kg/cm2 Rd2=12800 Kg/cm2 Et=197000Mpa

fc=45Mpa. fci=0,9.fc=40.5

f 'c

33914.98(MPa)

fr=0.63 fc' 4.23Mpa

Nguyn Vn B

3

Lp : Cu Anh k46


- Bn v th hin mt chnh dm, mt ct ngang, b tr ct thp ( bn v trn giy A1)Phn 1: Ni dung thuyt minh 1. Chn tit din mt ct dm ch

1.1 B tr chung mt ct ngang cu Tng chiu di ton dm l 38 mt, hai u dm mi bn 0,3mt k gi. Nh vy chiu di nhp tnh ton ca nhp cu l 37.4 mt. Cu gm 5 dm c mt ct ch T ch to bng btng c fc=45MPa. Lp ph mt cu c chiu dy trung bnh l 12(cm) gm c 2 lp: lp phng nc ,lp btng Asphalt trn cng. Lp to dc.53453

i=2% 100 150 1500 200195

i=2% 125 125 1500 150 1001000

125

125 7000/2 7000/2

600

1800

340

1100

2200

2200

850

2200

450

2200

1100

Khong cch gia cc dm ch S=2400 mm , dm bin l 1200 mm Gia phn xe chy v l ngi i phn cch bng gii phn cch cng kch thc theo phng ngang cu l 25 cm 1.2 Chn mt ct ngang dm ch. Dm ch c tit din hnh ch T vi cc kch thc sau: Chiu dy bn: Chiu cao ton dm: Chiu rng bu dm: Chiu cao bu dm: ts=20 cm H=180cm bb=60cm hb=34cm4

Nguyn Vn B

Lp : Cu Anh k46


-

Chiu dy bng: Chiu rng bn cnh: Rng vt cnh trn: Cao vt cnh trn: Rng vt bu: Cao vt bu:

bw=20cm b1=160cm 20cm 20cm 20cm 20cm

Cc kch thc khc nh hnh v:MT CT NGANG DAM CHUT L 1:100

1600 200 200

200

1600 200 200

600

Ti gi th m rng sn dm ra ht bu dm b tr neo d ng lc 3. Xc nh chiu rng bn cnh hu hiu (A.4.6.2.6) 3.1 i vi dm gia B rng bn cnh hu hiu c th ly gi tr nh nht ca + 1/4 chiu di nhp (=37400 4 9350 mm)

+ 12 ln dy trung bnh ca bn cng vi s ln nht ca b dy bn bng dm hoc 1/2 b rng bn cnh trn ca dm =12.200+max200 1600 / 2

= 2750mm

+ Khong cch trung bnh gia cc dm k nhau (S= 2200)->bi=2200mm 3.2 i vi dm bin B rng cnh dm hu hiu c th c ly bng 1/2 b rng hu hiu ca Nguyn Vn B5

Lp : Cu Anh k46


dm k trong(2200/2=1100) cng tr s nh nht ca + 1/8 chiu di nhp hu hiu(=37400 8 4675 mm)

+ 6 ln chiu dy trung bnh ca bn cng vi s ln hn gia 1/2 dy bn bng hoc 1/4 b rng bn cnh trn ca dm chnh =6.200+max200 / 2 1600 / 4

=1600 mm

+ B rng phn hng( =1100 mm) ->be=1100+1100=2200 mm Kt lun: B rng bn cnh dm hu hiu Dm gia (bi) Dm bin (be) 2200 mm 2200 mm Bng 3

4.Tnh ton bn mt cu 4.1 Phng php tnh ton ni lc bn mt cu p dng phng php tnh ton gn ng theo iu 4.6.2(AASHTO98). Mt cu c th phn tch nh mt dm lin tc trn cc gi n hi l cc dm ch. 4.2 Xc nh ni lc bn mt cu Theo iu (A.4.6.2.1) : Khi p dng theo phng php gii phi ly m men dng cc tr t ti cho tt c cc vng c m men dng, tng t i vi m men m do ta ch cn xc nh ni lc ln nht ca s . Trong dm lin tc ni lc ln nht ti gi v gia nhp. Do s tnh l dm lin tc 3 nhp i xng, v tr tnh ton ni lc l: a, b, c, d, e nh hnh v. Theo iu (A.4.6.2.1.6): Cc di phi c coi nh cc dm lin tc hoc dm gin n. chiu di nhp phi c ly bng khong cch tm n tm gia cc cu kin . Nhm xc nh hiu ng lc trong cc di , cc cu kin phi c gi thit l cng v hn . Cc ti trng bnh xe c th c m hnh ho nh ti trng tp trung hoc nh ti trng vt m chiu di dc theo nhp s l chiu di ca din tch tip xc c ch trong iu (A.3.6.1.2.5) cng vi chiu cao ca bn mt cu, n ny coi cc ti trng bnh xe nh ti trng tp trung. Nguyn Vn B6

Lp : Cu Anh k46


Chn kch thc ca bn mt cu pha trong: +Nhp tnh ton ca bn ly t hai tim cua dm: l=2400 mm +Chiu dy ca bn mt cu : h=200 mmS i vi phn hng pha ngoi : +Chiu di tnh ton: l=1200 mm

+Chiu dy ca bn mt cu h=200 mm Bn ta trn hai dm dc v cc dm ngang ,khong cch gia cc dm ngang l 5343mm, khong cch gia cc dm dc l 2200mm(b/a>2)=>tnh ton bn mt cu theo m hnh bn ngm hai cnh i vi phn pha trong tnh theo m hnh bn ngm hai cnh, phn pha ngoi tnh theo m hnh bn cnh hng. S tnh ton nh sau:

2400

S bn ngm 2 cnh

1200

S bn hng

4.1 Phng php tnh ton ni lc bn mt cu p dng phng php tnh ton gn ng theo iu 4.6.2(AASHTO98).

Nguyn Vn B

7

Lp : Cu Anh k46


Mt cu c th phn tch nh mt dm lin tc trn cc gi n hi l cc dm ch. 4.2 Xc nh ni lc bn mt cu do tnh ti S tnh v v tr tnh ni lc Theo iu (A.4.6.2.1) : Khi p dng theo phng php gii phi ly m men dng cc tr t ti cho tt c cc vng c m men dng, tng t i vi m men m do ta ch cn xc nh ni lc ln nht ca s . Trong dm lin tc ni lc ln nht ti gi v gia nhp. Do s tnh l dm lin tc 3 nhp i xng, v tr tnh ton ni lc l: a, b, c, d, e nh hnh v. Theo iu (A.4.6.2.1.6): Cc di phi c coi nh cc dm lin tc hoc dm gin n. chiu di nhp phi c ly bng khong cch tm n tm gia cc cu kin . Nhm xc nh hiu ng lc trong cc di , cc cu kin phi c gi thit l cng v hn . Cc ti trng bnh xe c th c m hnh ho nh ti trng tp trung hoc nh ti trng vt m chiu di dc theo nhp s l chiu di ca din tch tip xc c ch trong iu (A.3.6.1.2.5) cng vi chiu cao ca bn mt cu, n ny coi cc ti trng bnh xe nh ti trng tp trung. Xc nh ni lc do tnh ti T trng ca cc cu kin ly theo Bng (A.3.5.1.1) AASSHTO Tnh ti tc dng ln bn mt cu gm cc tnh ti ri u do TTBT ca bn mt cu, TTBT ca lp ph, lc tp trung do lan can tc dng ln phn hng. i vi tnh ti, ta tnh cho 1 mt di bn mt cu Thit k bn mt cu dy 200mm, tnh ti ri u do TTBT bn mt cu: gDC(bmc)=200.1800.24.10-6= 8,64 KN/m Thit k lp ph dy 74mm, tnh ti ri u do TTBT lp ph: gDW=74.2250.10-4=1,665 KN/m

Nguyn Vn B

8

Lp : Cu Anh k46


Ti trng do lan can cho phn hng: Thc cht lc tp trung quy i ca lan can khng t mp bn mt cu nhng n gin tnh ton v thin v an ton ta coi t mp. gDC(Lan can)= 1.13 KN/m + Cng thc xc nh ni lc tnh ton: MU= ( P.M DC1 +P

M DC2 +

P

M DW )

: H s lin quan n tnh do, tnh d, v s quan trng trong khai thc xc nh theo iu 1.3.2 = i. H s lin quan n tnh do H s lin quan n tnh dD. R

0,95

D

= 0,95 (theo iu 1.3.3)

R

= 0,95 (theo iu 1.3.4)i

H s lin quan n tm quan trng trong khai thc =>p:

= 1,05 (theo iu 1.3.5)

= 0,95

H s tnh ti (Bng A.3.4.1-2) Loi ti trng TTGH Cng 1 1,25/0,9 1,5/0,65 TTGH S dng

DC: Cu kin v cc thit b ph DW: Lp ph mt cu v cc tin ch 4.3 Ta tnh theo s hng (s 2) Mmen ti mt ct a l mmen phn hng. S tnh dng cng xon chu un

1 1

Nguyn Vn B

9

Lp : Cu Anh k46


Tnh ton tI trng : 1. TI trng bn thn : DC=hf* c =200*10-3*25=5 (KN/m). 2. TI trng do lp ph : DW=0.12* lp =0.12*23.5=2.82(KN/m) 3. TI trng do lan can + tay vn : DC2=0.7+0.43=1.13(KN/m). 4. TI trng ngi i b : PL=3 (KN/m) Tnh ton m men Ma=[. p . g DC (bmc) *1100 *1100 2.10p

6

p

*

g DW *1100 *1100p

g DC (lcncan) *1100 *1,25 *10

3

2.10

6

*

pL * 850 * 850 2.10 6

=

Trong THGH C1 Ma= 0,95.[1.25 *1.575 * 2.10 6

5 *1100 *1100 2.82 *1100 *1100 1.5 * 1.25 *1.13 *1100 *10 6 2.10 2.106 3 * 850 * 850

3

=-9.12 (KN.m)

Trong THGH SD Ma= 0,95.[1 * 7.297 (KN.m) 4.5 Tnh ton ct thp chiu lc + Lp bo v Theo bng (A.5.12.3-1) Nguyn Vn B Lp : Cu Anh k465 *1100 *1100 2.82 *1100 *1100 1* 1 *1.13 *1100 *10 6 2.10 2.1063

1.575 *

3 * 850 * 850 2.10 6

=-

10


Mp trn bn : a = 60 mm v bn chu mi mn ca vu lp xe Mp di bn : a= 25 mm + Sc khng un ca Bn Mr = .Mn : H s sc khng quy nh theo iu (A.5.5.4.2.1) ta c gii hn cng 1 (Cho BTCT thng) Mr : Sc khng un tnh ton Mn : sc khng un dang nh i vi cu kin chu un khi s phn b ng sut gn ng theo hnh ch nht nh quy nh ca iu 5.7.2.2 th Mn xc nh iu 5.7.3.2.3Mn a ps f ps d p a 2 As f y d s a 2 A' s f ' y d s' a 2 0.85 f c' (b bw ) 1hr a 2 hr 2

= 0,9 i vi trng thi

V khng c ct thp ng sut trc ,b=bW v coi As = 0 MnAs f y d s a 2

Trong : AS fy dS = = = Din tch ct thp chu ko khng ng sut trc (mm2) Gii hn chy qui nh ca ct thp (Mpa). Khong cch ti trng t th nn ngoi cng n trng tm ct thp chu ko khng ng sut trc (mm) A'S f'y d'p = = = Din tch ct thp chu nn (mm2) Gii hn chy qui nh ca ct thp chu nn (Mpa). Khong cch t th ngoi cng chu nn n trng tm ct thp

Nguyn Vn B

11

Lp : Cu Anh k46


chu nn (mm) f'c b bw1

= = = =

Cng chu nn qui nh ca b tng tui 28 ngy (Mpa) B rng ca mt chu nn ca cu kin (mm) Chiu dy ca bn bng hoc mt ct trn (mm) H s chuyn i biu ng sut qui nh trong iu (A.5.7.2.2)

h1 = Chiu dy cnh chu nn ca cu kin dm I hoc T(mm) a= c1

; chiu dy ca khi ng sut tng ng (mm) iu (A.5.7.2.2)Aps f ps1

a

c

As f y' c 1 w

Ac' f y' b1

As f y 0.85 f c' b

0.85 f

Theo trng thi gii hn cng I Ct thp phi b tr sao cho mt ct kh nng chu lc 4.5.1 B tr ct thp chu mmen m ca bn mt cu(cho 1 mt di bmc) v kim ton theo THGH Cng 1. + Khng xt n ct thp chu nn (s b tr cho mmen dng ca bn mt cu) + Mmen tnh ton cho mmen m ca bn mt cu Mu= 9.12 KNm (Bng 4.b) + Ta chn trc s thanh ri kim ton cng + B tr 6 thanh ct thp 16 => Din tch ct thp As=6.3,1416 .16 2 =1206,3744mm2 4

dp=ts- 60-

d0 16 = 200 - 60- =132 mm 2 2

1=0,85-(12/7)0,05=0,764

> 0.65 tho mn theo A5.7.2.2

Nguyn Vn B

12

Lp : Cu Anh k46


c

As f y 0.85 f' c 1 f

b

1206,374*420 = 8.27 mm 0,85*45*0, 728*2200

a= .c=0,728* 8.27 =6.02 mm Mn=As.fs.(dp- )=1206,374*420*(132a 2 6.02 )*10-6= 65.36 KNm 2

Mr= .Mn=0,9* 65.36 = 58.82 KNm > Mu=9.12 KNm => (Tho mn) Vy mt ct tho mn v cng . + Kim tra lng ct thp ti a (A.5.7.3.3.1) Phi tho mn iu kinc de 0.42

de = dP =132 mm (Do coi Aps = 0 (A.5.7.3.3.1-2)) c: khong cch t th chu nn ngoi cng n trc TH, c=18,2796 mmc 8.27 = = 0.06 < 0,42 => Tho mn d e 132

Vy mt ct gia nhp tho mn v hm lng thp ti a. + Lng ct thp ti thiu Phi tho mn Trong minmin 0.03 fc' fy

min

t l gia thp chu ko v din tch nguyn

1206,374 =0,00335 1800 * 200fc ' fy 0, 03 45 =0,03*0.107=0.003214 420 fc' fy

0,03

min

0,03

Nguyn Vn B

13

Lp : Cu Anh k46


Vy mt ct tho mn v hm lng thp ti thiu C ly ti a gia cc thanh ct thp Theo iu (A.5.10.3.2) Trong bn c ly gia cc ct thp khng c vt qu 1,5 chiu dy cu kin hoc 450mm Smax 1,5x200=300 (mm)

.4.5.4 B tr ct thp co ngt v nhit Theo iu A.5.10.8 ct thp cho cc ng sut co ngt v nhit phi c t gn b mt b tng l ra trc cc thay i nhit hng ngy. i vi cc cu kin mng hn 1200mm din tch ct thp mi hng khng c nh hn:AS 0,75 Ag fy

Ag = Tng din tch mt ct Chiu dy c hiu 200mm => Chiu dy thc =200+30 =230mm => Ag=230x1 = 230mm2AS 0, 75 Ag fy 0, 75 230 420 0.41mm2 / mm

Ct thp do co ngt v nhit khng c t rng hn hoc 3.0 ln chiu dy cu kin (3.200=600mm) hoc 450 mm. Ct thp co ngt v nhit theo phng dc cu 0.5AS =0.2065 S dng NO10 @450 c As=0,22mm2/mm 4.5.5 Kim tra bn mt cu theo trng thi gii hn s dng (kim ton nt) Theo iu A.5.5.2 cc vn phi kim tra theo trng thi gii hn s dng l nt , bin dng v ng sut trong b tng Do nhp ca bn nh v khng c thp d ng lc nn trong n ny ch kim ton nt i vi bn mt cu theo iu 5.7.3.4 Nguyn Vn B Lp : Cu Anh k46

14


Cc cu kin phi c cu to sao cho ng sut ko trong ct thp trng thi gii hn s dng fsa khng c vt qufs f sa Z 1/ 3 dc A 0,6 f

(A.5.7.3.4-1)

Trong : dc =chiu cao phn b tng tnh t th ngoi cng chu ko cho n tm ca

thanh hay si t gn nht ; nhm mc ch tnh ton phi ly chiu dy tnh ca lp b tng bo v dc khng ln hn 50 mm . Z = Thng s b rng vt nt (N/mm).

Ly Z= 23000 N/mm i vi cc cu kin trong mi trng khc nghit v khi thit k theo phng ngang +fsa +A = = ng sut ko trong ct thp trng thi gii hn s dng Din tch phn b tng c cng trng tm vi ct thp ch chu ko v

c bao bi cc mt ct cu mt ct ngang v ng thng song song vi trc trung ho, chia cho s lng ca cc thanh hay si (mm2)

4.5.5.2 Kim tra nt i vi m men m M men m ln nht l M= -9.12 KNm/m

Khong cch t TTH n mp trn ca mt ct: y=200-8.27=191.73 mm ng sut trong ct thp mp trn bn :fs n My I cr 200000 9.12*(191.73 68).105 33994, 48 10624750 62.4846Mpa

dc = 60 +16/2 = 68mm < 50 mm =>dC = 50 mm(theo iu trn) A=2.50.1800 =36000 mm2 5

Nguyn Vn B

15

Lp : Cu Anh k46


=> f sa

Z 1/ 3 dc A

23000 (50 x36000 )1 / 3

189 Mpa

0,6 f y

0.6 x 420

252 Mpa

do vy ly fsa=189 Mpa > fS =

62.4846 Mpa Tho mn

Vy bn mt cu tho mn iu kin kim ton nt trng thi gii hn s dng.

40

70

100

40

B tr ct thp bn mt cu5. Tnh ton ni lc dm ch do tnh ti Ti trng tc dng nn dm ch Tnh ti : Tnh ti giai on 1 DC1v tnh ti giai on 2 (DC2+ DW) Hot ti gm c lc xung kch(IL+IM) : Xe HL 93 Ni lc do cng cp ng sut trc Ngoi ra cn cc ti trng: Co ngt, t bin, nhit , ln, gi, ng t (khng xt).

5.1 Tnh ti ri u ln 1 dm chT trng ca cc cu kin ly theo bng (A.3.5.1.1) AASHTO,gi thuyt tnh tnh ti phn b u cho mi dm, ring lan can th mt mnh dm bin chu. + Ti trng bn thn dm DCdc Thnh phn tnh ti DC bn trn bao gm ton b tnh ti kt cu tr tnh ti lp mt hao mn d phng v ti trng d chuyn dng . Do mc ch thit k 2 phn ca tnh ti c nh ngha nh sau: Tnh ti ri u ln dm ch xut hin giai on cng ng sut trc. gDC1(dc) = .A.g

Nguyn Vn B

16

Lp : Cu Anh k46

150


Trong : - Trng lng ring ca dm, =24 KN/m3 A Din tch mt ct ngang ca dm khi cha m rng. Vi kch thc chn nh trn, ta tnh c A=7760 c m2. Do dm c m rng v 2 pha gi(xem bn v) nn tnh thm phn m rng ta c c trng lng bn thn ca dm ch gDC1(dc) = 18.624 KN/m

Mt ct ngang dam chuT l 1:100

1600 200 200 200 1600 200 200

600

+ Ti trng do dm ngang: DC1dn Cu to dm ngang nh hnh v,2000 200 200 1260 1260 200

450

200 200

Theo chiu dc cu b tr 7 dm ngang(xem bn v), theo chiu ngang cu b tr 4 dm ngang, suy ra tng s dm ngang = 4.7=28. Trng lng mt dm ngang: DC1dn= .Ag*l=24*(2000*1260-4*0.5*202)*200*10-9=12.09 ( KN) Tnh ti ri u ln 1 dm ch do dm ngang: gDC1(dn)=12 .092 * 28 =1.81 KN/m 37 ,4 * 5

Nguyn Vn B

17

Lp : Cu Anh k46


+ Ti trng do lan can +tay vn DC2 : Trng lng lan can xut hin giai on khai thc sau cc mt mt Ta s dng loi lan can theo tiu chun AASHTO50 70

110 50 70

175

25 20 20

30

30 cm

=> Tnh ti DC2 tc dng cho dm bin : lan can : =

25 * 20 * 10

* 1.10 * 20 * 25 37 ,4

6

0.7

KN/m TI trng g chn bnh bng b tng c kch thc nh hnh v =(0.20 0.25 ) * 0.30 * 38 * 25 2 * 37 ,4 * 5

1.72 KN/m

Tay vn bng hp kim nhm t trng bng 28 KN/m :=* (7 2 5 2 ) * 10 4 * 38 * 2 * 28 37 ,4

0.43 KN/m

+ Ti trng ca lp ph: B tng Asphalt dy 12 cm =>g3=0.12*11*23,5/5=6.204 KN/m Tng lp ph v tin ch cng cng : Dm ngoi(tnh cho c lan can v tay vn ) : DW=10.07 KN/m Dm trong : DW=7.92 KN/m

Ta c bng : Do ti trng bn thn dm ch Nguyn Vn B 18.62418

KN/m Lp : Cu Anh k46


Do ti trng bn thn dm ngang Do lp ph mt c u Do lan can Tay vn G chn bnh

1.81 6.2 0.7 0.43 1.72

KN/m KN/m KN/m KN/m KN/m

+H s ti trng cho tnh ti :

Loi ti trng DC:cu kin v thit b ph Lp ph v cc tin ch : 5.2 .Tnh ton h s phn b ngang.

TTGH cng 1 1,25/0.9 1,5/0,65

THGH s dng 1 1

Quy trnh AASHTO (1998) cp n phng php gn ng c dng phn b hot ti cho tng dm (AASHTO LRFD 4.6.2.2.2). Nhng kch thc lin quan : Chiu dy bn bng b=200 mm Khong cch ca cc dm: S=2200mm; Chiu di nhp: L=37400mm; Khong cch t tim ca dm bin n mp trong ca lan can: de=900 mm S dm Nb=5 dm ch Cc s liu trn tho mn iu kin p dng cng thc tnh phn b ngang theo cng thc sau a. H s phn phi hot ti theo ln i vi m men un i vi dm gia (AASHTO bng 4.6.2.2.2b-1): S=2200=> 1100g=0.38*0,447=0.17 c. H s phn phi ca ti trng ngi i b :0,6 de => e 3000 0,6 650 =0.38 3000

Nguyn Vn B

20

Lp : Cu Anh k46


1000

125 125

1500

150 100

2200

1100

1

1.05 1

Dng phng php n by tnh cho c m men v lc ct : Coi ti trng ngi l lc tp chung : g=1.05*1.5=1.575 Bng tng hp kt qu tnh h s phn b ti trng H s phn b hot ti Dm gia Dm trong Ngi i b 5.3 Xc nh ni lc Ta tnh ton ni lc dm ch ti 4 mt ct: Gi, L/2, L/4. xc nh ni lc, ta v ng nh hng cho cc mt ct cn tnh ri xp tnh ti ri u ln ng nh hng. Ni lc c xc nh theo cng thc: + Mmen: Mu= p. + Lc ct: Vu= ( p.+

Mmen 0,556 0.45 1.575

Lc ct 0,45 0.17 1.575

-. p. -)

Trong : - Din tch ng nh hng mmen ti mt ct ang xt+ +

-Din tch ng nh hng lc ct dng ti mt ct ang xt -Din tch ng nh hng lc ct m ti mt ct ang xt

5.3.1 Tnh Ni lc do hot ti cc mt ct c trng a. ng nh hng mmen mt ct gia nhp L/2

Do tnh ti -Do ti trng bn thn DC v lp ph + cc tin ch cng cng Mmen MDC=(1.25*DC+1.5*DW)*wm

Nguyn Vn B

21

Lp : Cu Anh k46


Dm trong =(1.25*(18.624+1.81)+1.5*7.92)*0.5*9.35*37.4=6543.14(KN) Dm ngoi =(1.25*(18.624+1.81)+1.5*10.07) )*0.5*9.35*37.4=7107.01(KN) Lc ct Vr=09.35

37.4

Do hot ti:0.3 1.2

0.75 0.75 4.3 4.3 PL=3KN/m 9.3kn/m

6.825

110

0.5 0.5

8.975

8.9

37.4

Nguyn Vn B

9.35

7.575

9.2

22

Lp : Cu Anh k46


1.2 110

110

4.3

4.3

PL=3KN/M 9.3KN/M

0.5 0.47 0.39 0.27 D.A.H V

0.5

37.4

M3 trc+lan = 1.75*93*wm+1.75*(1+IM)*gll*Pi*Yi =1.75*9.3*0.5*9.35*37.4+1.75*(1+0.25)*0.556*(145*7.58+145*8.98+35*6.83) = 6056.81(KNm) M2trc+lan = 1.75*93*wm+1.75*(1+IM)*gll*Pi*Yi =1.75*9.3*0.5*9.35*37.4+1.75*(1+0.25)*0.556*(110*8.9+110*9.2)=5267.156KNm V trc = 1.75*93*w+1.75*(1+IM)*gll*Pi*Yi =1.75*9.3*0.5*0.5*37.4+1.75*(1+0.25)*0.45*(145*0.5+145*0.39+35*0.27)=212.42 KN

V2rc = 1.75*93*w+1.75*(1+IM)*gll*Pi*Yi =1.75*9.3*0.5*0.5*37.4+1.75*(1+0.25)*0.45*(110*0.5+110*0.47)=181.12(KN)

-Do ngi: PL MPL=pl*1.5*g*w =0.5*9,35*37,4*3*1.575*1.5=1239.2 ( KN.m) VPL=0.5*0.5*37,4/2*3*1.575*1.5=33.13 KN Nguyn Vn B23

Lp : Cu Anh k46


Vy t hp ni lc ti mt ct gia nhp l: Dm trong : Mr=6543.14+6056.81+1239.2=13839.15 KNm Vr=0+212.42+33.13=245.55 KN Dm ngoi : Mr=7107.01+6056.81+1239.2=14403.02 KNm Vr=0+212.42+33.13=245.55 KN

b.Gi lm tng t i vi cc ti trng DC, DW, PL, W.Ch khi xp ti ca xe ti thit k tnh gi tr mmen phi tm ng v tr bt li nht .y s l v tr bt li nht vi xe ti hai trc v ba trc ti mt ct 3L/8 cc mt ct khc ch thay i bng cch tnh tin cc trc xeMt ct ti gi

1.2110

4.3

110

4.3 PL=3KN/m LL=9.3KN/m DW DC

0.968 0.885

1

0.77

37.4

37.4 d.a.h.m

.A.H.V

M3 trc = 0 M2trc = 0 V 3trc = 1.75*9.3*w+1.75*(1+IM)*gll*Pi*Yi+ pl*1.5*g*w+(1.25*DC+1.5*DW)*wv Dm trong :

=1.75*9.3*0.5*37.4+1.75*(1+0.25)*0.45*(145*1+145*0.89+35*0.77)+3*1.5*1.575*37. 4*0.5+1.25*(18.624+1.81)+1.5*7.92)*0.5*37.4=1432.26 KN Dm ngoi :

=1.75*9.3*0.5*0.5*37.4+1.75*(1+0.25)*0.45*(145*1+145*0.89+35*0.77)+3*1.5*1.575 *37.4*0.5+1.25*(18.624+1.81)+1.5*10.07)*0.5*37.4=1492.57 KN V2rc = 1.75*93*w+1.75*(1+IM)*gll*Pi*Yi+ pl*1.5*g*w+(1.25*DC+1.5*DW)*wv

Nguyn Vn B

24

Lp : Cu Anh k46


Dm trong : =1.75*9.3*0.5*37.4+1.75*(1+0.25)*0.45*(110*1+110*0.968)+ 3*1.5*1.575*37.4*0.5+(1.25*(18.624+1.81)+1.5*7.92)*0.5*37.4=1349.78(KN) Dm ngoi =1.75*9.3*0.5*37.4+1.75*(1+0.25)*0.45*(110*1+110*0.968)+ 3*1.5*1.575*37.4*0.5+(1.25*(18.624+1.81)+1.5*10.07)*0.5*37.4=1410.09(KN) Bng tng hp ni lc trng thI gii hn cng 1

Mt ct M men Mr:(KN.m): Dm trong: Dm ngoi : Lc ct Vr:(KN): Dm trong : Dm ngoi :

L/2 13839.15 14403 245.55 245.55

Gi 0 0 1432.26 1462.57

Trng thi gii hn s dng :Mt ct gia nhp: Do ti trng bn thn (DC) v lp ph + cc tin ch cng cng

Mmen MDC=(DC+1.5*DW)*wm Dm trong =(18.624+1.81)+1.5*7.92)*0.5*9.35*37.4=5649.94(KN)

Dm ngoi =(18.624+1.81)+1.5*10.07) )*0.5*9.35*37.4=6213.82(KN) Lc ct Vr=0 M3 trc = 93*wm+*gll*Pi*Yi =9.3*0.5*9.35*37.4+0.556*(145*7.58+145*8.98+35*6.83) = 3094.04(KNm) M2trc = 93*wm+gll*Pi*Yi

Nguyn Vn B

25

Lp : Cu Anh k46


=9.3*0.5*9.35*37.4+0.556*(110*8.9+110*9.2)=2733.05 KNm V trc = 93*w+gll*Pi*Yi =9.3*0.5*0.5*37.4+0.45*(145*0.5+145*0.39+35*0.27)= 149.28KN

V2rc = 1.75*93*w+1.75*(1+IM)*gll*Pi*Yi =9.3*0.5*0.5*37.4+0.45*(110*0.5+110*0.47)=134.97(KN) -Do ngi: PL MPL=pl*1.5*g*w =0.5*9,35*37,4*3*1.575*1.5=1239.2 ( KN.m) VPL=0.5*0.5*37,4/2*3*1.575*1.5=33.13 KN Vy t hp ni lc ti mt ct gia nhp l: Dm trong : Mr=5649.94+3094.04+1239.2=9983.18 KNm Vr=0+149.28+33.13=182.41KN Dm ngoi : Mr=6213.82+3094.04+1239.2=10547.1 KNm Vr=0+149.28+33.13=182.41KN Bng tng hp ni lc trng thi gii hn s dng: Mt ct M men Mr:(KN.m): Dm trong: Dm ngoi : Lc ct Vr:(KN): Dm trong : 182.41 10547.1 L/2 9983.18 Gi 0

0 1046. 17

Nguyn Vn B

26

Lp : Cu Anh k46


Dm ngoi : 6.3.3 T hp ni lc

182.41

1019. 52

* T hp theo trng thi gii hn cng I + T hp M men theo trng thi gii hn cng I(iu 3.4.1.1) MU= ( P.M DC1 +P

M DC2 +

P

M DW +1.75MLL+IM +1.75*MLP )

+ T hp Lc ct theo trng thi gii hn cng I(iu 3.4.1.1) VU= (P

V DC1 +

P

V DC2 +

P V DW

+1.75VLL+IM +1.75 VLP)

Trong : MLL: Mmen do hot ti tc dng ln 1 dm ch ( tnh h s phn b ngang) MU VUP

: M men tnh ton theo trng thi gii hn cng I ca dm gia : Lc ct tnh ton theo trng thi gii hn cng I ca dm gia : Xc nh mc1.3.2 : H s lin quan n tnh do, tnh d, v s quan trng trong khai thc xc

nh theo iu 1.3 = H s lin quan n tnh do H s lin quan n tnh di D R

0.95

D

= 0.95 (theo iu 1.3.3)

R

= 0.95(theo iu 1.3.4)i

H s lin quan n tm quan trng trong khai thc = 0,95 IM

= 1.05 (theo iu 1.3.5)

= H s xung kch IM = 25% Theo iu 3.4.1-1.

Nguyn Vn B

27

Lp : Cu Anh k46


* H s ti trng v t hp theo trng thi gii hn s dng I MU=M DC1 + M DC2 + 1.5M DW +MLL+IM + MDN VU= VDC1 + V DC2 + V DW +VLL+IM + VDN Bng ni lc do hot ti (TruckLoad+PeopleLoad+LaneLoad) Bng tng hp ni lc trng thI gii hn cng 1 : MU=Mr* VU=Vr* Vi =0.95 Mt ct M men :(KN.m): Dm trong: Dm ngoi : Lc ct:(KN): Dm trong : Dm ngoi :233.2725 1389.4415 233.2725 1360.647 13682.85 0 13147.1925 0

L/2

Gi

Bng tng hp ni lc trng thI gii hn s dng : Mt ct M men :(KN.m): Dm trong: Dm ngoi : Lc ct:(KN): Dm trong : Nguyn Vn B173.2895 993.8615 10019.75 0 9484.021 0

L/2

Gi

28

Lp : Cu Anh k46


Dm ngoi :173.2895 968.544

7. Cc c trng vt liu cho dm ch. 7.1 Thp 7.1.1 Thp ng sut trc. S dng tao thp 15.2. Din tch mi tao tra bng vt liu 140 mm2 Cng ko quy nh ca thp ng sut trc : f pu Gii hn chy ca thp ng sut trc : f py Mdun n hi ca thp ng sut trc : E p0.9. f pu 1860 MPa (A.5.4.4.1) 1670 MPa (A.5.4.4.1)

197000 MPa

S dng thp thng VSL: ASTM A416 Grade 270. H s ma st = 0,20,8. f pu 1488 MPa

ng sut trong thp ng sut khi kch f pj -H s quy i ng sut =0.9

7.1.2 Thp thng:G60

-

Gii hn chy ti thiu ca ct thp thanh: f y Mdun n hi : E s 200000 MPa

420 MPa

7.2 Btng

-

T trng ca btng:

c

24 KN / m 3

Cng chu nn ca btng quy nh tui 28 ngy f ' c

45 MPa

Cng chu nn ca btng lc bt u t ti hoc to ng sut trc :f ' ci 0,9 f ' c 40 ,5MPa

Nguyn Vn B

29

Lp : Cu Anh k46


-

Mdun n hi ca btng lm dm : Ec

0,043.

1,5 c

f 'c

33914.98 MPa

Mdun n hi ca btng lm dm lc cng ko:E ci 0,85 E c 0,85 * 33914.98=28827.73 MPa

-

H s quy i hnh khi ng sut (5.7.2.2): Cng chu ko khi un: f r0,63 f 'c

1

0,85 0,05

f ' c 28 7

0.7286

4,23MPa (A.5.4.2.6)

8. Chn v b tr cp d ng lc 8.1 Chn cp d ng lc Chn cp d ng lc theo cc n in hnh b tr mt cc hp l v mt chu lc v khng tn km vt liu 8.2 B tr cp d ng lc B tr cp d ng lc phi tun theo cc khong cch ti thiu quy nh trong quy trnh, l khong cch ti thiu gia cc ng cp d ng lc vi nhau l 40 mm, kch thc ca ng bc cp phi ln hn 2.5 ln din tch b cp, khng ln hn 0,4 ln b dy b tng nguyn nh nht, khong cch gia tim cc ng cp khng nh hn 1,33 ln kch c ln nht ca cc ht ct liu ln nht,c ly tim n tim khng nh hn 44 mm, b dy lp b tng bo v khng nh hn 1/2 ng knh ng bc=>chn chiu dy lp b tng bo v l 50 mm, ng bc cp c ng knh l 60mm Cc b cp d ng lc c b tr theo phng trnh c to ca cc ng cp tho mn sao cho trong cp d ng lc ch c lc dc trc m khng c mmen un,hay l cho tr s m men un nh nht trong cp ta b tr cp theo phng trnh ging phng trnh ca vm y=4 f ( L x) x L2

Nguyn Vn B

Trong :30

Lp : Cu Anh k46


f: chiu di ng tn L:chiu di theo phng nm ngang X to theo phng ngang Y to theo phng thng ng + B tr trong mt phng ng: Ta b tr cc b cp ti mt ct ti gi v mt ct gia nhp nh sau:

72.572.572.5

7*657*65

72.572.5

mt ct l/2

72.5

7*65

72.5

Theo phng dc cc b cp c b tr nh sau

Nguyn Vn B

60

4*55

60

60

60

60

60

4*55

60 60 60

60

60

60

31

Lp : Cu Anh k46


mt ct gi

8*12572.572.5

7*657*65

72.572.5

Khong cch t trng tm ct thp chu ko xung y dm : Vi mt ct ti L/2 Y=8*6 8*11.5 8*17 8*22.5 8*28 6*34 4*40 2*46 32 21.85 (cm)

Vi mt ct ti gi :Y 6*6 6*11.5 6*17 6* 22.5 6* 28 2*34 2* 49.7 2*65.4 2 *81.1 52 2*96.8 2*112.5 2*128.2 2*143.9 2*159.6 2*157.3 2*191 52

60

4*55

60

60

36076

51.02(cm)

+ Khong cch t trng tm ct thp chu ko (DUL)n th chu nn ngoi cng : Dp =h-y Mt ct L/2: dp=180-21.85=158.15(cm) Mt ct gi : dp=180-51.02=128.98(cm) + Khong cch t trng tm mt ct ti trng tm ct thp chu ko ; Mt ct L/2: eCL=Yd-y=494.02-218.5=275.52 (mm) Mt ct gi : eCL= Yd-y=508.2355-510.02=-1.964(mm) Nguyn Vn B32

Lp : Cu Anh k46


8.2 Ta c mt ct tnh i ;1600 228.6

200 1800

368.6

600

Ta tnh c cc c trng hnh hc : Din tch mt ct qui i (Ag) M men qun tnh ca mt ct qui i (S0) Yd= Ig=419494.5 8255.6

Cm2

Cm3 cm cm4

107.830318096

8.3 Tnh ton cc c trng hnh hc mt ct tnh i. H s tnh i t thp sang btng. n=Eathep Ebetong 197000 33914.98 5.809

cho nhanh chng v chnh xc, khng phi tnh i di dng v fc tp ta tnh cc c trng hnh hc bng cng c t ng ho tnh c Nguyn Vn B33

Lp : Cu Anh k46


trng hnh hc trong Autocad bng cch to min v tnh c trng hnh hc bng lnh massprop, v din tch ca ct thp d ng lc l rt nh so vi din tch ca b tng ti cc mt ct coi l gn ng khng quan tm n din tch ca ct thp d ng lc khi tnh ton c trng hnh hc ca b tng Ti mi mt ct ta dng cc cng thc c kim chng trong mng sc bn vt liu +Cc c trng St=Sc+n*Ss trong : Sc l c trng hnh hc ca b tng n l h s tnh i t thp ra b tng Ss l c trng hnh hc ca thp T ta c c: Vi mt ct gia nhp : +Xc nh din tch mt ct tnh i Atd Atd =A0+n.APS =825560+5.809*7280=867846.9(mm2) M men tnh ca mt ct tnh i : Std=S0+APS*n*YPS=419494500+7280*5.809*218.5=428734760 (mm3) Xc nh trng tm ca mt ct tnh i ytd ytd=S td 428734760 = 494.0212(mm) 867846.9 Atd

+Xc nh Itd :Mmen qun tnh ca met ct tnh i Itd= Ic+n*APS*( ytd-YPS )2=30318096*104+5.809*7280*(494.02-218.5)2=3.06*1010(mm4) i vi cc mt ct khc (mt ct gi) cng lm tng t. Kt qu tnh ton th hion bng sau:

c trng A S

Mt ct gia 867846.9428734760

Mt ct gi 867846.9441070613

n v Mm2 Mm3

Nguyn Vn B

34

Lp : Cu Anh k46


Yd Yt=h-Yd

494.0212

508.2355

Mm Mm Mm4

1800-494.0212= 1305.979 3.06*1010

1291.76 3.03*1010

Ig

9. Tnh ton cc mt mt ng suti vi dm T ko trc ta c cc mt mt sau: {A.5.9.5}f pt f pES

fPsr+

fPCR+

fPR

Ti mt ct gia nhp : 9.1.Mt mt do ma st=0 9.2 Mt mt do co ngn n hi Kt cu ko trc ; fPes= Trong fcpg=tng ng sut btng trng tm ca cc b thp ng sut do d ng lc khi truyn v t trng ca b phn cc mt ct mme gia dm (Mpa) EP=Mun n hi ca thp d ng lc.(Mpa) Eci= mun n hi ca btng lc truyn lc(Mpa) fcgp=F:Fi Ag Fi 2 ecl IG M dg ecl IgEP fcgp E Ci

{ A.5.9.5.2.3.a}

lc nn ca b tng do cp d ng lc

Fi=0.7*fPU*APS=0.7*1860*7280=9478560(N)=9478.56(KN) Ag=867846.9 mm2: Ep=197000 Mpa Mdg=7107.01(KN.m) Eci=28827.73 Mpa Nguyn Vn B Lp : Cu Anh k46 Din tch mt ct nguyn ca b tng

35


lch tm e=Yd-y=494.02-218.5=275.52mm Y:l khong cch t trng tm ct thp chu ko xung y dm Vy ta c : fcgp=V fPes=9478 .56 867846 .9 9478 .56 * 275 .52 2 3.06 *10 10 7107 .01 * 275 .52 =-29.56(MPa) 3.06 *10 10

EP 197000 fcgp= *29.56=202.0041(MPa) E Ci 28827.73

9.3 Co ngt B tng ko trc :f pSP 117 1.03 H

H: l m tng i=700/0 vi mi trng Vit Namf pSP 117 1.03 * 70 44 .9MPa

9.4 T binf pCR 12 * f cgp 7 * f cdp =12*29.56-7*8.8=293.12 MPa

fcdp: thay i ng sut trong b tng ti trng tm ct thp d ng lc do ti trn thng xuyn tr ti trng tc ng vo lc thc hin d ng lc 9.5 Mt mt do trng ct thp a.Lc truyn lc.f pR1 log( 24t ) f pi ( 40.0 f py 0,55) f pi

t:thi gian gi nh t lc cng n lc ct ct thp = 4 ngy fpi: ng sut ban u trong b ct thp cui giai on cng. lp ln u : fpj=0.74*fpu - fpES=0.74*1860-202.004=1174.396(MPa) fpy=0.9*1860=1674 Mpaf pR1 log(24 * 4) 1174.396 ( 0,55) *1174.396 8.82( MPa) 40.0 1674

Tnh li Pj v Nguyn Vn B36

Lp : Cu Anh k46


fpj=1174.396-8.82=1165.58

f pR1

log( 24 * 4) 1165.58 ( 0,55) *1165.58 8.45(MPa) 40.0 1674

Lp ln 2: fpj=0.74*fpu ( fpES+ fpR1 =0.74*1860-(202.004+8.45)= 1165.95(MPa) Fi=7280*1165.95=8488.116(KN) fcgp=33.19 (MPa) fpES=197000 *33.19=226.81(MPa) 28827.73

fpj=0.74*fpu ( fpES+ fpR1 =0.74*1860-(226.81+8.45)= 1141.14(MPa)f pR1 log( 24 * 4) 1141.14 ( 0,55) *1141.14 7.45( MPa) 40.0 1674

9.6 Tnh gn ng tng mt mt theo thi gian:fp=230*(1-0.15*

f ' 41 )+41*PPR 41

Trong PPR=1 t l do d ng lc mt phnfp=230*(1-0.15*

f ' 41 )+41*PPR 41

=230*(1-0.15*

45 41 )+41*1=267.634(MPa) 41

i vi tao cp c t trng thpfp=267.634-41=226.634(MPa)

9.7 Tng mt mt ti mt ct gia nhp:fp=(mt

mt ban u )+(mt mt theo thi gian)

=(202.004+44.9+293.12+7.45)+ 226.634=774.108(MPa)

Ti mt ct gi :

Nguyn Vn B

37

Lp : Cu Anh k46


9.1.Mt mt do ma st=0 9.2 Mt mt do co ngn n hi Kt cu ko trc ; fPes= Trong fcpg=tng ng sut btng trng tm ca cc b thp ng sut do d ng lc khi truyn v t trng ca b phn cc mt ct mme gia dm (Mpa) EP=Mun n hi ca thp d ng lc.(Mpa) Eci= mun n hi ca btng lc truyn lc(Mpa) fcgp=F:Fi Ag Fi 2 ecl IG M dg ecl IgEP fcgp E Ci

{ A.5.9.5.2.3.a}

lc nn ca b tng do cp d ng lc

Fi=0.7*fPU*APS=0.7*1860*7280=9478560(N)=9478.56(KN) Ag=867846.9 mm2: Ep=197000 Mpa Mdg=7107.01(KN.m) Eci=28827.73 Mpa lch tm e=Yd-y=508.2355-510.02=-1.964mm Y:l khong cch t trng tm ct thp chu ko xung y dm Vy ta c : fcgp=V 9.3 Co ngt B tng ko trc :f pSP 117 1.03 H

Din tch mt ct nguyn ca b tng

9478 .56 *10 6 867846 .9

9478 .56 *1.964 2 *10 6 3.06 *10 10

7107 .01 *1.964 *10 6 =-10.92(MPa) 3.06 *10 10

fPes=

EP 197000 fcgp= *10.92=74.62(MPa) E Ci 28827.73

H: l m tng Nguyn Vn B38

i=700/0 vi mi trng Vit Nam Lp : Cu Anh k46


f pSP

117 1.03 * 70

44 .9MPa

9.4 T binf pCR 12 * f cgp 7 * f cdp =12*29.56-7*8.8=293.12 MPa

fcdp: thay i ng sut trong b tng ti trng tm ct thp d ng lc do ti trn thng xuyn tr ti trng tc ng vo lc thc hin d ng lc 9.5 Mt mt do trng ct thp a.Lc truyn lc.f pR1 log( 24t ) f pi ( 40.0 f py 0,55) f pi

t:thi gian gi nh t lc cng n lc ct ct thp = 4 ngy fpi: ng sut ban u trong b ct thp cui giai on cng. lp ln u : fpj=0.74*fpu - fpES=0.74*1860-74.62=1301.78(MPa) fpy=0.9*1860=1674 Mpaf pR1 log( 24 * 4) 1301.78 ( 0,55) *1301.78 14.69( MPa) 40.0 1674

Tnh li Pj v fpj=1301.78-14.69=1287.09

f pR1

log(24 * 4) 1287.09 ( 0,55) *1287.09 13.96( MPa) 40.0 1674

Lp ln 2: fpj=0.74*fpu ( fpES+ fpR1 =0.74*1860-(74.62+13.96)= 1287.82(MPa) Fi=7280*1287.82= 9375.33(KN) fcgp=33.19 (MPa) fpES=197000 *33.19=226.81(MPa) 28827.73

fpj=0.74*fpu Nguyn Vn B39

( fpES+ fpR1 =0.74*1860-(226.81+13.96)= Lp : Cu Anh k46


1135.63(MPa)f pR1 log(24 * 4) 1135.63 ( 0,55) *1135.63 7.23( MPa) 40.0 1674

9.6 Tnh gn ng tng mt mt theo thi gian:fp=230*(1-0.15*

f ' 41 )+41*PPR 41

Trong PPR=1 t l do d ng lc mt phnfp=230*(1-0.15*

f ' 41 )+41*PPR 41

=230*(1-0.15*

45 41 )+41*1=267.634(MPa) 41

i vi tao cp c t trng thpfp=267.634-41=226.634(MPa)

9.7 Tng mt mt ti mt ct Gi:fp=(mt

mt ban u )+(mt mt theo thi gian)

=(74.62+44.9+293.12+7.23)+ 226.634= 646.504(MPa)

10. Kim ton theo - Trng thi gii hn cng ITrng thi gii hn cng phi c xem xt n m bo cng v s n nh c v cc b v ton th c d phng chu c cc t hp ti trng quan trng theo thng k c nh ra cu chu c trong tui th thit k ca n. 10.1 Kim ton Cng chu un Quy trnh AASHTO[4] qui nh i vi trng thi gii hn cng 1:Mu Mn

M men tnh ton (Mu) Trng thi gii hn cng I Mu =iMi

Kt qu (Mu) ca dm gia c tnh ton bng trn

Nguyn Vn B

40

Lp : Cu Anh k46


Sc khng un tnh ton Trong :

Mr

Mn

: l h s khng un c quy nh iu A.5.5.4.2, dng cho un v ko b tng ct thp ng sut trc = 1,0 Mn : Sc khng un danh nh Tnh ton sc khng un danh nh (A.5.7.3.2) Phn b ng sut theo hnh ch nht (A.5.7.2.2) Quan h t nhin gia ng sut b tng chu nn v ng bin c th coi nh mt khi hnh ch nht tng ng bng 0,85f'c phn b trn mt gii hn bi mt ngoi cng chu nn ca mt ct v ng thng song song vi trc trung ho cch th chu nn ngoi cng mt khong cch a = 1c . Khong cch c phi tnh vung gc vi trc trung ho. H s 1ly bng 0,85 i vi b tng c cng khng ln hn 28 Mpa.Vi b tng c cng ln hn 28 Mpa , h s 1 gim theo t l 0,05 cho tng 7 Mpa vt qu 28 Mpa, nhng khng nh hn tr s 0,65 . Cng thc tnh ton sc khng un (A.5.7.3.2.2.1)hc

bc

0.85f'c 0.85 f'c(bc -b) A'sf'y

a

d's

b

A's 0.85 f'cbhcde

ds dp

Aps Apsfps Asfy As

Mn

Aps f ps d p

a 2

As f y d s

a 2

As ' f y ' d s '

a 2

0,85. f c ' (b bw ) 1h f

a 2

hf 2

Coi mt ct ch c ct thp ng sut trc chu lc khi :Mn Aps f ps d p a 2 0,85. f c ' (b bw ) 1h f a 2 hf 2

Trong : Nguyn Vn B41

Lp : Cu Anh k46


Aps

=

Din tch thp ng sut trc (mm2)

fps = ng sut trung bnh trong thp ng sut trc sc khng un danh nh ,tnh theo phng trnh 5.7.3.1-1(Mpa) dp = khong cch t th nn ngoi cng n trng tm ct thp chu ko khng ng sut trc (mm) As = fy = Din tch ct thp chu ko khng ng sut trc (mm2) Gii hn chy qui nh ca ct thp (Mpa).

ds = Khong cch ti trng t th nn ngoi cng n trng tm ct thp chu ko khng ng sut trc (mm) A's f'y = = Din tch ct thp chu nn (mm2)

Gii hn chy qui nh ca ct thp chu nn (Mpa).

d'p= Khong cch t th ngoi cng chu nn n trng tm ct thp chu nn (mm) f'c = bc= bw =1=

Cng chu nn qui nh ca b tng tui 28 ngy (Mpa) B rng ca mt chu nn ca cu kin (mm) Chiu dy ca bn bng (mm) H s chuyn i biu ng sut qui nh trong iu 5.7.2.2 > 0,65

1=0,85-(12/7)0,05=0,764

h1 = c = a =

Chiu dy cnh chu nn ca cu kin dm I hoc T(mm) Khong cch t trc trung ho n mt chu nn (mm) c.1

; chiu dy ca khi ng sut tng ng (mm)

Tnh ton ng sut trong thp ng sut trc mc sc khng un danh nh (A.5.7.3.1) i vi ct thp ng sut trc dnh bm mt ct hnh ch T chu un quanh mt trc, c ng sut phn b nh quy nh ca iu 5.7.2.2v fPe(ng sut c hiu cn li trong thp ng sut trc) = 0,7428fPu M =0.95*14403.02=13682.87(KN.m) Tho mn iu kin v cng 10.2 Kim tra hm lng ct thp ng sut trc + Lng ct thp ti a (A.5.7.3.3.1) Phi tho mn iu kinc de 0.42

Suy ra

Nguyn Vn B

44

Lp : Cu Anh k46


de: Khong cch t th ngoi cng chu nn n trng tm lc ko ca ct thp chu ko de = thng c: khong cch t th chu nn ngoi cng n trc TH Vy :c de 212 .7 1581 .5 0.135 0.42

Aps . f ps d p Aps . f ps

As f y d s As f y

=dp =1581.5 b qua ct thp

tho mn

+ Lng ct thp ti thiu Mr > min ( 1,2Mcr, 1,33Mu) (iu A,5.7.3.3.2)(bng 23 v 24) Trong : Mcr : Mmen nt c xc nh trn c s phn b phn b ng sut n hi Mcr=Ig yt

fr

yt:khong cch t th chu ko ngoi cng n trc trung ho.

fr: cng chu ko khi un fr 0.5 f c' (A.5.4.2.6) yt=h-c=1800-212.7=1587.3(mm) Ig= Mcr= 3.06*1010(mm4) m men qun tnh ca tit din nguyn.3.06 * 10 10 4.23*103=950.60(KN.m) 158 .73

min ( 1,2Mcr, 1,33Mu)=min(1.2*950.60;1.33*13682.87) =18198.22(KN.m) Vy ta c :Mn=20366.38*0.9=18329.74> min ( 1,2Mcr, 1,33Mu)= 18198.22(KN.m) Tho mn v hm lng Nguyn Vn B45

ct thp ti thiu ti mt ct gia nhp . Lp : Cu Anh k46


10.3 Tnh ct ai v kim ton ct theo trng thi gii hn C1: 10.3.1 Ti on dm gn gi Cng thc tnh sc khng ct Vr 0 nu ngc chiu lc ct (N) Vp=(Pe)sin (gc hp bi phng nm ngang

v hng cp ),Vp s = min( bv ; 0,8dv ) 600 mm

Chn s=150 mm ti gia Av:Din tch ct thp chu ct trong c ly S (mm2).Av =2.As (ai 2 nhnh ) AV=2*3.14*1.42=12.3(cm2) =2 H s ch kh nng ca b tng b nt cho truyn lc ko tra bng 5.8.3.4.2 =45 =gc nghing ca ng sut nn cho c xc nh trong iu 5.8.3.4 ( Tuy nhin trong khun kh ca n TKMH c th cho lun =2, =45o) +Xc nh Vp: Vp=Acable.fp13

sini 1

i

Nguyn Vn B

47

Lp : Cu Anh k46


Trong Acable:din tch cc tao cp=140 cm2 Fp:ng sut trong cp sau khi mt mt, gi tr ng vi mi mt ct. Pj=Aps.(0,8fpya.Tnh Vp: Bng tnh gc lch ca cp I so vi phng ngang : M B1(sin t ct G i L/2 0.051 0.039 4 0.061 0.061 0.063 0.061 0.076 2 0.061 0.061 0.088 4 0.061 0.100 5 0.061 0.112 0.124 0.061 ) B2(sin ) B3(sin ) B4(sin ) B5(sin ) B6(sin ) B7(sin ) B8(sin )f pT )

Mt ct Gi L/2

Tng (sin) 0.56 0.28

Mt ct Aps fp in s Vp

L/2 72.80 895.892 0.28 18.26186

Gi 72.8 1023.496 0.56 41.72588

n v cm4 MPa

kN

Nguyn Vn B

48

Lp : Cu Anh k46


Mt ct Vu Vp bv dv 0.25*fC*bv*dv b.Tnh VS Mt ct ti gia nhp :A *f * dv * cot g s

L/2 233.27 0.90 18261.86 20 129.6 2916.0

Gi 1389.44 0.90 41725.88 20 150.408 3384.18

n v kN

kN cm cm (KN)

VS=

v

y

=

12 .3 *10

2

*1670 *129 .6 *10 2 cot g 45 0 15 *10 2

=1774.74(KN) Mt ct ti gi :A *f * dv * cot g s12 .3 *102

VS= =2059.69(KN)

v

y

=

*1670 *150 .408 *10 2 cot g 45 0 15 *10 2

c. Tnh Vc: Vc=0.083f c' bvdv45 *20*129.6*10 =28.93(KN)45 *20*150.408*10 =33.57(KN)-2 -2

Mt ct L/2: Vc=0.0832*2* Mt ct gi : Vc=0.0832*2* Bng duyt :

Nguyn Vn B

49

Lp : Cu Anh k46


m/c L/2

VP(KN)

VC

0.25*fC*bv*dv 2916.0

VS 1774.74

Vn 1 1821. 93

Vn2 2934. 26 3425. 91

18.26186 28.93

Gi

41.72588 33.57

3384.18

2059.69

2134. 99

Min(VN 1; Vn2)1821.932 2134.986

0.9* Min(VN 1; Vn2)1639.739 1921.487

Vr 245.55 1462.57

Kt lun

t t

10.4 Kim ton dm theo trng thi gii hn s dng Cc vn phi kim tra theo trng thi gii hn s dng ca b tng ng sut trc l ng sut trong b tng(5.9.4), bin dng( vng). 10.4.1 Cc gii hn ng sut trong b tng: a. Trng hp ng sut trong btng do tnh tI v DUL: ng sut nn trong b tng :ft = F A Fe yt I M TTBT yt I 0.45 f c '

ng sut ko trong b tng fb=

F A

Fe yt I

M TTBT yb I

0.5 f c '

Trong :

F : tng lc ko trong cc b thp d ng lc tr i mt mt tc thi F=APS*(0.8*fPU-Tng mt mt) APS=7280(mm2); fPU=1860(MPa) MTTBT:mmen do trng lng bn thn dm A:din tch mt ct dm I:mmen qun tnh ca tit din dm e: lch tm ca trng tm cc b thp d ng lc n Nguyn Vn B50

Lp : Cu Anh k46


trc trung ho yt:khong cch t trc trung ho n th trn cng ca tit din yb:khong cch t trc trung ho n th di cng chu ko ca tit din

Tham s Mat cat A F fci' fc I Mttbt e yt yb ft 0.45fc Kt lun fb 0.5 (fc')

L/2 7.7 5.197134 40.5 45 30318096 7107.01 27.55 21.27 158.73 6.79838 20.25 t -6.798 3.35410197 t

Gi 7.7 6.12 40.5 45 30318096 0 -1.96 14.94 165.06 7.948111 20.25 t -7.948 3.354102 t MPa cm2 MN MPa MPa cm4 KN.m cm cm cm MPa MPa

Kt lun

b. Tnh cho trng hp ng sut trong btng do hot ti +DL + Tnh ti : ng sut nn trong b tng :ft = M1 yt I F A Fe yt I M TTBT yt I 0.6 f c '

ng sut ko trong b tng 51

Nguyn Vn B

Lp : Cu Anh k46


fb=

M1 yt I

F A

Fe yt I

M TTBT yt I

0.5 f c '

M1 : l m men ln nht do hot ti gy ra :

Mt ct Tham s As M1 F fci' fc I Mttbt e yt yb ft 0.6 (fc') Kt lun fb 0.5 (fc') L/2 7.7 6056.81 5.197134 40.5 45 Gi 7.7 0 6.12 40.5 45 MN MPa MPa cm4 KN.m cm cm cm MPa MPa n v cm2

30318096 30318096 7107.01 27.55 21.27 158.73 0 -1.96 14.94 165.06

6.840872 7.948111 27 t 27 t

0.665818 0.7947993.354102 3.354102

Kt lun

t

t

c. Trng hp ng sut do hot ti +0.5*(DL+Tnh ti ): ng sut nn trong b tng :fC-3=M1 yt I 0.5*( F A Fe yt I M TTBT yt ) 0.4* f c ' I

Nguyn Vn B

52

Lp : Cu Anh k46


Mt ct Tham s As M1 F fci' fc Ac I Mttbt e yt yb fc3 0.4fc Kt lun 30318096 30318096 7107.01 27.55 21.27 158.73 0 -1.96 14.94 165.06 L/2 7.7 6056.81 5.197134 40.5 45 Gi 7.7 0 6.12 40.5 45 MN MPa MPa m2 cm4 KN.m cm cm cm MPa MPa n v cm2

3.441682 3.974056 18 t 18 t

11.Bin dng: Gii hn v vng: +Ti trng xe tiu chun :f L 1 800

+Ti trng xe tiu chun v ngi i b Cng thc tnh ton vng ca kt cu f=

f L

1 1000

5 Pl 4 . 384 0.84Eb I

Nguyn Vn B

53

Lp : Cu Anh k46


Tnh vng tc thi vi vic dng cc tr s m un n hi ca b tng quy nh iu 5.4.2.4 v dng mmen qun tnh hoc vi gi tr nguyn Ig, hoc mmen qun tnh hu hiu Ie tnh theo cng thc:M cr Ie= Ma0.3

Ig

1

M cr Ma

0.3

I cr

Ig

Vi Mcr=fr Trong : Mcr:mmen nt fr:cng chu ko un

Ig yt

yt:khong cch t trc trung ho n th chu ko ngoi cng Ma: mmen ln nht trong cu kin giai on ang tnh bin dng Kim ton ti mt ct L/2 c vng ln nht Ig=17029775.03 cm4 Ec=31975 Mpa q=17.1875+15.9=34.085kN m

5 * 34.085 *10 * 28002 L 384 =>f= =1.96 cm < => t 2 1000 0.84 * 31975*10 *17029775.03

Nguyn Vn B

54

Lp : Cu Anh k46


Dm ch chu

Dm ngang chu

2250

6800

6800

0.0175 2250 6800

1

2275

2275

0.0175

14.1 Tnh ton ct thp chu lc +Lp bo v Theo bng 5.12.3-1 Mp trn bn : a= 25mm Mp di bn : a=25 mm +Sc khng un ca bn Mr= Mn :H s sc khng quy nh theo iu 5.5.4.2.1 thi gii hn cng 1 Mr:Sc khng un tnh ton Mn:Sc khng un danh nh i vi cu kin chu un khi s phn b ng sut gn ng theo hnh ch nht nh quy nh ca iu 5.7.2.2 thi M n xc nh iu 5.7.3.2.3 =0,9 i vi trng

Nguyn Vn B

55

Lp : Cu Anh k46


Mn= a ps f ps d p

a 2

As f y d s

a 2

A' S f ' y d ' s

a 2

0,85 f 'c b bw

1 r

h

a 2

hr 2

V khng c ct thp ng sut truc ,b=bw v coi As=0 Mn= As f y d s Trong AS= din tch ct thp chu ko khng ng sut trc. fy= gii hn chy quy nh ca ct thp(Mpa) ds= khong cch ti trng t th nn ngoi cng n trng tm ct thp chu ko khng ng sut trc (mm) As= din tch ct thp chu nn fy= gii hn chy quy nh ca ct thp chu nn (Mpa) dp= khong cch t th ngoi cng chu nn n trng tm ct thp chu nn (mm) fc= cng chu nn quy nh ca btng tui 28 ngy (MPa) b= b rng ca mt chu nn ca cu kin (mm) bw= chiu dy ca bn bng hoc mt ct trn1

a 2

= h s chuyn i biu ng sut quy nh trong iu 5.7.2.2

h1= chiu dy cnh chu nn ca cu kin dm I hoc T (mm) a= c.1

chiu dy ca khi ng sut tng dng (mm) xem iu 5.7.2.2

a

c

Aps f ps1

As f y

A'c f ' y1 w

As f y1

0,85 f 'c

b

0,85 f 'c b

Theo trng thi gii hn cng 1 ct thp phi b tr sao cho mt ct kh nng chu lc Ta chn trc s thanh ri kim ton cng +Tnh ton b tr ct thp chu mmen dng: B tr 8 thanh ct thp 18

Nguyn Vn B

56

Lp : Cu Anh k46


-> din tch ct thp As= 8

3,1416 .18 2 4

2035 ,757 mm 2

dp=h-25-5.18=1150-25-90=1035 mm1

=0,85-(12/7).0,05=0,764>0,65AS f y 0,85. f c 1b f1

c

2035,757.420 164,578mm 0,85.40.0,764.200

a=

.c=0,764.164,578=125,74 mm125,74 ).10 6 =831,2 KNm 2

Mn=As.fs(dp-a/2)=2035,757.420.(1035-

Mr= .Mn=0,9.831,2=748 KNm>Mu=156,845 KNm Vy mt ct tho mn v cng +Kim tra lng ct thp ti a (A.5.7.3.3.1) Phi tho mn iu kinc de 0,42

Tho mn

de=dp =1035 mm (Do coi Aps=0(a5.7.3.3.1-2)) c:khong cch t th ngoi cng n TTH , c=164,578 mmc de 164,578 1035 0,156 0,42

Tho mn

Vy mt ct gia nhp tho mn hm lng thp ti a. +Kim ton hm lng thp ti thiu: Vi bn khng c thp DL ta c cng thc kim tra l : theo iu 5.7.3.3.2min

0,03

f 'c fy

Trong : fc= sc khng btng quy nh (Mpa) fy= sc khng chy do ca ct thp chu keo (Mpa) Pmin= t l gia thep chu ko v din tch nguyn Nguyn Vn B57

Lp : Cu Anh k46


Pmin=

AS b.d S

2035 ,758 200 .103540 420

0,00983

0,03

f 'C f 'Y

0,03

0,0286

Vy tho mn +Tnh ton b tr ct thp chu mmen m Mmen tnh ton :M=137,372 KNm Tnh ton v b tr tng t vi ct thp chu mmen dng ta cng c lng ct thp cn thit l 8 thanh 18 .

Nguyn Vn B

58

Lp : Cu Anh k46

tkmh - cau be tong 1 - 272-05_k46

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