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n Thit k Cu dm BTCT nhp gin n

S liu u vo

Chiu di dm L 15.7m:= Ltt 15.7m 2 0.3 m:= h 1.2m:=

Ltt 15.1 m= Nhp tnh ton Chiu cao dm

S dm n 6:= Khong cch gia cc dm S 2.44m:= Tng b rng cu B 14.42m:=

Bxc 13.42m:= Blc 2 0.5 m:=

B rng phn xe chy

B rng lan can

Mt ct ngang cu

S ho dm ch

Chiu dy lp ph mt cu: 75mm

Vt liu: f'c 30MPa:= B tng dm Thp fy 400MPa:= Trng lng ring:

- B tng: 2400kg/m3

- Lp ph: 2250kg/m3 Chi tit lan can

Phn 1: THIt K Bn Mt Cu

1.1 Chn chiu dy bn [A9.7.1.1]

S 2440:= hmin

S 3000+30

:= mm( )

hmin 181.333= hmin 175> mm OK

Vy chn chiu dy bn mt cu hs 200mm:= 1.2. Trng lng cc b phn 1Kg = 9.81N

Lan can c mt ct ngang nh hnh v trn, din tch 326510mm2, trng lng lan can coi nh mt ti trng tp trung

Nmm

Pb 2400 109 9.81 326510:=

Nkg

kg

mm3

Pb 7.687= mm2

Lp ph mt cu dy 75mm (Dead load of Wearing surface)

N

mm2 WDW 2250 10

9 9.81 75:= WDW 1.655 10 3=

Bn chu lc dy 200mmN

mm2 Ws 2400 10

9 9.81 200:= Ws 4.709 10 3=

1.3. Tnh ton ni lc bn mt cu

Tnh ton ni lc cho 1mm bn theo phng dc cu. Tnh ton bn mt cu theo cc giai on lm vic: - Trc khi b tng mi ni bn phn bn ng cng: + S : mt tha (cnh ca dm ch T). + Ti trng: trng lng bn thn ca bn (k c trng lng mi ni) - Sau khi b tng mi ni ng cng. Dng phng php di bn. Coi bn nh mt dm lin tc k trn cc gi cng l cc dm ch. Ni lc c tnh bng cch xp ti ln cc ng nh hng (dah) ni lc. Trong v d ny, do mt ct ngang cu c 6 dm nn c th s dng tung dah trong ph lc A - "Cu BTCT trn ng t", L nh Tm, 2005. Dng ah m men ti tit din 200, 204, 205, 300 v ah lc ct ti gi 200 nh trang sau. Trong v d ny ch tnh ni lc cho tit din 200, 204, 300. + S : dm lin tc k trn gi cng + Ti trng: Lp ph mt cu, lan can, hot ti

Trc khi b tng mi ni ng cng

Sau khi b tng mi ni ng cng

1.3.1 Do trng lng bn thn bn: (tc dng ln s hng) N

mm Ws 4.709 10

3= S 2440=

R200_WS WsS2

:= Nmm

R200_WS 5.7=

Nmmmm

M200_WS Ws S2S4

:= M200_WS 3504.3=

M204_WS Ws 244 2442

:= Nmmmm

M204_WS 140.2=

Nmmmm

M300_WS M200_WS:= M300_WS 3504.3=

1.3.2. Do lan can (barrier), tc dng ln s dm lin tc

Ti trng lan can coi nh mt lc tp trung c gi tr Pb=7.68N/mm t ti trng tm ca lan can. Xp ti ln dah tm tung dah tng ng. Tra bng vi:

L 1110 193:= L 917= mm

R200 = Pb*tung ah

R200_b Pb 1 1.270LS+

:= N

mm R200_b 11.356=

M200 = Pb*tung dah * L Nmmmm

M200_b Pb 1.000( ) L:= M200_b 7049.3=


M204_b Pb 0.4920( ) L:= M204_b 3468.3=


M300_b Pb 0.27( ) L:= M300_b 1903.3= 1.3.3. Do lp ph mt ng dy 75mm (Dead load of Wearing):

WDW 1.655 103= L 1110 500:= L 610= Dng bng tra vi:

R200 = WDW * [(din tch dah on hng)*L+(din tch dah khng hng)*S]

R200_DW WDW 1.0 0.635+( ) LS

L 0.3928( ) + S

:= N

mm R200_DW 1.999=

M200 = WDW * [(din tch dah on hng)*L^2

M200_DW WDW 0.500( ) L2:= Nmmmm

M200_DW 307.994=

M204 = WDW * [(din tch dah on hng)*L^2+(din tch dah khng hng)*S^2

M204_DW WDW 0.2460( ) L2 0.0772( ) 2+ S := Nmmmm

M204_DW 609.336=

M300 = WDW * [(din tch dah on hng)*L^2+(din tch dah khng hng)*S^2

M W 0.135( ) L2 0.1071( ) 2+300_DW DW S := M300_DW 1138.7=

Nmmmm

1.3.4. Xc nh ni lc do hot ti

Cc ti trng trc thit k l 145kN gm 2 bnh xe v t cch nhau 1800mm theo phng ngang cu. Tim bnh xe cch 600mm t mp ln thit k. Khi tnh phn bn hng, tim bnh xe s t cch mp lan can mt on l 300mm. Khong cch t bnh xe n tim gi:

X 310:= mm Chiu rng c hiu ca bn chu ti trng bnh xe ca bn mt cu ti ch

Khi tnh bn hng SW 1140 0.833 X+:= SW 1398= mm SW 660 0.55 S+:= SW 2002= Khi tnh m men dng mm

Khi tnh m men m SW 1220 0.25 S+:= SW 1830= mm

S ln xe thit k = phn nguyn (b rng phn xe chy / 3500mm)

NL134203500

:= NL 3.834= NL 3:= vy s ln

H s ln xe cho mt ln xem 1.2

cho hai ln xe m 1

cho ba ln xem 0.85

a. M men m ti tit din 200 do hot ti trn phn hng

Chiu rng lm vic ca di bn SW=1398 mm

Ch xp mt ln xe m 1.2

M200_LL1.2 72500 310

1398:= Nmm

mm M200_LL 19291.8=

b. Mmen dng ln nht do hot ti ti v tr 204


Cht ti 1 ln xe: H s ln xe: m 1.2:=

M204_LL_1 1.2 0.2040 0.0195( ) 2440 725002002:= Nmmmm

M204_LL_1 19563.3=

m 1:= Cht ti 2 ln xe: H s ln xe:

M204_LL_2 1 0.2040 0.0195 0.0086+ 0.0016( ) 2440 725002002:= Nmmmm

M204_LL_2 16921.3=

M204_LL max M204_LL_1 M204_LL_2,( ):= M204_LL 19563.3=

Nmmmm

Trng hp mt ln xe khng ch

c. Mmen m ln nht ti gi 300 trong do hot ti.


Cht ti 1 ln xe bt li hn: H s ln xe: 1.2

M300_LL 1.2 0.1007 0.0781( ) 2440 725001830:= Nmmmm

M300_LL 20741=

1.3.5 T hp ti trng

Cng thc tng qut tnh hiu ng do ti trng gy ra

Ru i Qi Trng thi gii hn cng I:

1:= DC 1.25:= DW 1.5:= LL 1.75:=

IM 25%:=

M men m ti gi 200

M200 1.25 M200_WS M200_b+( ) 1.5 M200_DW+1.75 1 IM+( ) M200_LL+

...

:=

M200 55.8 kN mm:= Nmmmm

M200 55855=

M men dng ti v tr 204: do trng lng bn thn ca bn v trng lng lan can gy ra m men m lm gim hiu ng bt li ca m men dng ti v tr 204 nn ly vi h s 0.9

M204 0.9 M204_WS M204_b+( ) 1.5 M204_DW+1.75 1 IM+( ) M204_LL+

...

:=

M204 40461=Nmmmm

M204 40.5kN m

m:=

M men m ti v tr 300: do trng lng lan can gy ra m men dng lm gim hiu ng bt li ca m men m ti v tr 300 nn ly vi h s 0.9

M300 1.25 M300_WS 0.9 M300_b( )+ 1.5 M300_DW+1.75 1 IM+( ) M300_LL+

...

:=

M300 49.75 kN mm:= Nmmmm

M300 49746=

1.4 Tnh ton ct thp chu mmen dng - Kim tra TTGH Cng 1

1.4.1 B tr ct thp

Gi thit s dng thp s No.15

Ab 200mm2:= db 16mm:= fy 400 MPa=

Chiu cao c hiu ca bn mt cu

Chiu cao c hiu ca bn ti tit din gia nhp chu m men dng:

dduong 200mm 25mmdb2

:= dduong 167 mm=

0.9:= H s khng un

Mu M204:= Mmen dng ln nht (TTGH cng I):

Mu 40.5kN m

m=

Khong cch t trng tm min chu nn ca b tng n trng tm ct thp chu ko trong b tng thng (ly gn ng):

jd 0.9 dduong:= jd 150.3mm=

S b chn din tch ct thp chu ko

As

Mu

fy jd

:= As 0.749 mm2

mm=

Tra ph lc B, bng B4, "Cu BTCT trn ng t", L nh Tm, chn No.15@225mm

As 0.889mm2

mm= As

Ab225mm

:= Din tch ct thp thc:

S 5.7.3.3.2 Kim tra din tch ct thp ti thiu yu cu trn mt n v chiu rng bn:

minAs 0.03f'cfy

1( ) dduong:=

As 0.889mm2

mm= minAs 0.376 mm

2

mm= OK >

S 5.7.3.3.1 Kim tra lng ct thp ln nht c gii hn theo yu cu v tnh do:

S 5.7.2.2Vi gi thit phn b ng sut nn theo hnh ch nht:

Chiu cao khi ng sut hnh ch nhtvng nn:

aAs fy

0.85 f'c 1:= a 13.943mm=

1 0.85 f'c 28MPaif

max 0.85f'c 28MPa

7MPa0.05 0.65,

otherwise

:= 1 0.836=

ca

1:=

OK c 16.684mm= 0.42 dduong 70.14mm= Vy < 1.4.2 Kim tra cng tit din (TTGH cng I):

Sc khng un ca tit din

Mn As fy dduong a2

:= Mn 51.209 kN m

m= M204 40.5 kN mm

OK = >

1.5 Tnh ton ct thp chu mmen m - Kim tra TTGH Cng 1

1.5.1 B tr ct thp

Gi thit s dng thp s No.15

Ab 200mm2:= db 16mm:= fy 400 MPa=

Chiu cao c hiu ca bn mt cu

Chiu cao c hiu ca bn ti tit din gia nhp chu m men dng:

dam 200mm 60mmdb2

:= dam 132 mm=

0.9:= H s khng un

Mmen dng ln nht (TTGH cng I): Mu M300:=

Mu 49.82kN m

m:=

Khong cch t trng tm min chu nn ca b tng n trng tm ct thp chu ko trong b tng thng (ly gn ng):

jd 0.9 dam:= jd 118.8mm=

S b chn din tch ct thp chu ko

As

Mu

fy jd

:= As 1.165 mm2

mm=

Tra ph lc B, bng B4, "Cu BTCT trn ng t", L nh Tm, chn No.15@150mm

A's 1.333mm2

mm= A's

Ab150mm

:= Din tch ct thp thc:

S 5.7.3.3.2 Kim tra din tch ct thp ti thiu yu cu trn mt n v chiu rng bn(1mm):

0.03

f'cfy

minAs 1( ) dam :=

A's 1.333mm2

mm= minAs 0.297 mm

2

mm= OK >

S 5.7.3.3.1Kim tra lng ct thp ln nht c gii hn theo yu cu v tnh do:

Vi gi thit phn b ng sut nn theo hnh ch nht:

S 5.7.2.2

Chiu cao khi ng sut hnh ch nht vng nn:

aA's fy

0.85 f'c 1:= a 20.915mm=

1 0.85 f'c 28MPaif

max 0.85f'c 28MPa

7MPa0.05 0.65,

otherwise

:= 1 0.836=

ca

1:=

OK

1.6 Kim tra nt th di theo cc trng thi gii hn s dng.

1= i 1:= IM 25%:=

cho c tnh ti v hot ti

Kim tra nt ti tit din 204, m men ti tit din ny tnh theo TTGH s dng:

M204 1 M204_WS M204_b+( ) 1 M204_DW( )+1 1 IM+( ) M204_LL+

...

:=

Nmmmm

M204 2.145 104=

Tit din bn bao gm ct thp v b tng c a v tit din b tng tng ng. Din tch ct thp c chuyn i thnh din tch b tng tng ng bng cch nhn vi t s modul n hi n, c trng tm trng vi trng tm ct thp

nEsEb

:=

Trong :

Ec 0.043 Wc1.5 f'c:= Mun n hi ca b tng: S 5.4.2.4

Wc 2400kg

m3:= f'c 30MPa= T trng b tng:

EcEc 2.769 10

4 MPa= Mun n hi ca thp:

Es 200000MPa:=

T s modul n hi:

nEsEc

:= Lyn 7.222= n 7:=

Tit din b tng tng ng Tit din bn

V lp b tng bo v pha trn bn mt cu kh ln (60mm) nn gi thit trc trung ha nmtrn ct thp chu nn A's, chiu cao min chu nn l: x < 68mm

Ly tng m men tnh i vi trc trung ha ta c:

0.5 b x2 n A's d' x( ) n As d x( )+= vi b 1mm:= d' 68mm:= d 167mm:=

As 0.889mm2:= A's 1.333mm2:=

Gii phng trnh bc hai i vi x, thu c:

xn As n A's n As n A's+( )2 2 b n As d n A's d'+( )++

b:=

< Vy trc trung ha ng nh gi thitx 44.358mm= 68mm

Mmen qun tnh ca tit din n hi chuyn i:

Icrb x3

3n A's d' x( )2+ n As d x( )2+:=

Icr 1.279 105 mm4=

fs nM204 d x( )

Icr:= ng sut trong ct thp chu ko As:

M204 22330N mm:=

fs nM204 d x( )

Icr:= fs 149.873MPa=

Nt c kim tra bng cch gii hn ng sut ko trong b tng (A5.7.3.4-1)

f f Zs sadc A( )

1

3

0.6f y

dc = chiu cao phn b tng tnh t th chu ko ngoi cng cho ntm ca thanh hay si t gn nht; nhm mc ch tnh ton phily chiu dy tnh ca lp b tng bo v dc khng c ln hn 50mm.

A = din tch phn b tng c cng trng tm vi ct thp ch chu ko v c bao bi cc mt ca mt ct ngang v ng thng songsong vi trc trung ho, chia cho s lng ca cc thanh hay si(mm2); nhm mc ch tnh ton, phi ly chiu dy tnh ca lpb tng bo v khng c ln hn 50 mm.

Z = thng s b rng vt nt (N/mm).

Chiu dy lp bo v tnh t th chu ko xa nht n trng tm ca thanh gn nht (nhng khng qu 50mm):

dc min 33mm 50mm,( ):= dc 33mm=

Tham s chiu rng vt nt ly trong iu kin mi trng khc nghit:

Z 23000N

mm:=

Din tch b tng c cng trng tm vi ct thp chu ko chnh chia cho s thanh. Dng thanh s No.15 cch nhau t tim n tim 225mm

A 1.485 104 mm2= A 2 33mm( ) 225mm( ):=

fsaZ

dc A( )1

3

:= Ta c: fsa 291.73MPa=

Kim tra:

1.7 Kim tra nt th trn theo cc trng thi gii hn s dng.

Kim tra nt ti tit din 200 hoc 300, m men ti cc tit din ny tnh theo TTGH s dng:

1= IM 25%:= M200 1 M200_WS M200_b+( ) 1 M200_DW( )+

1 1 IM+( ) M200_LL+...

:=

M200 3.498 104= Nmmmm

M300 1 M300_WS M300_b+( ) 1 M300_DW( )+1 1 IM+( ) M300_LL+

...

:=

Nmmmm

M300 2.867 104=

V tit din 200 v 300 b tr b tng v ct thp ging nhau, v do M200 > M300 nn s kim ton nt ti tit din 200

Tit din bn bao gm ct thp v b tng c a v tit din b tng tng ng. Din tch ct thp c chuyn i thnh din tch b tng tng ng bng cch nhn vi t s modul n hi n, c trng tm trng vi trng tm ct thp

n 7=

Tit din bn Tit din b tng tng ng

Ti v tr 200, ct thp pha di chu nn k hiu l A's, ct thp pha trn bn chu ko k hiu l A. Gi thit trc trung ha nm trn ct thp chu nn A's nh hnh v, tc l chiu cao min chu nn by gi x > 33mm

Ly tng m men tnh i vi trc trung ha ta c:

0.5 b x2 n 1( )A's x d'( )+ n As d x( )= b 1mm:= d' 33mm:= d 132mm:= vi

A's 0.889mm2:= As 1.333mm2:=

Gii phng trnh bc hai i vi x, thu c:

xn As n 1( ) A's n As n 1( ) A's+ 2 2 b n As d n 1( ) A's d'+ ++

b:=

x 40.385mm= > Vy trc trung ha ng nh gi thit 33mm

Mmen qun tnh ca tit din n hi chuyn i:

Icrb x3

3n 1( ) A's x d'( )2+ n As d x( )2+:=

Icr 1.006 105 mm4=

fs nM200 d x( )

Icr:= ng sut trong ct thp chu ko As:

M200 34370N mm:=

fs nM200 d x( )

Icr:= fs 219.18MPa=

Nt c kim tra bng cch gii hn ng sut ko trong b tng (A5.7.3.4-1)

fs fsa Z

dc A( )1

3

0.6fy

Din tch b tng c cng trng tm vi ct thp chu ko chnh chia cho s thanh. Thp chu ko ti v tr 200 l thanh s No.15 cch nhau t tim n tim 150mm

A 1.5 104 mm2= A 2 50mm( ) 150mm( ):= Tham s chiu rng vt nt ly trong iu kin mi trng khc nghit:

Z 23000N

mm:=

Chiu dy lp bo v tnh t th chu ko xa nht n trng tm ca thanh gn nht (nhng khng qu 50mm):

dc min 68mm 50mm,( ):= dc 50mm=

fsaZ

dc A( )1

3

:= Ta c: fsa 253.148MPa=

fs 219.18MPa= fsa 253.148MPa= Kim tra: < OK

1.9 Ct thp chng co ngt

Lng ct thp ti thiu theo mi phng {A5.10.8.2}

minAs 0.75Agfy

:=

Ag - din tch tit din nguyn. Vi bn cao 200mm, rng 1mm

mm2 Ag 200= Ag 200 1:=

fy 400 MPa=

minAs 0.75Agfy

:= = 0.375mm2/mm

Ct thp chng co ngt phi b tr chia u cho c hai mt trn v di. Nh vy hm lng thp phn b mi phng l 0.19mm2/mm. Ngoi ra khong cch ln nht ca ct thp ny khng vt qu 3 ln chiu dy bn hoc 450mm. Pha di c thp phn b ( tnh ton trn). Vy chn thp chng co ngt pha trn No10@450, c As=0.222mm2/mm.

1.10 S ha cu to thp bn (khng th hin ct thp dm)

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