CH DN TNH TON BN HAI PHNG

THEO ACI318-02

TS. Nghim Mnh Hin

Bng 18-1: Chiu dy ti thiu ca bn hai phng (ct thp mc 60)

B tr ct thp trong sn khng dm

PHNG PHP KHUNG TNG NG

(Dch t tiu chun ACI318-02, chng 20)

Cc vn chung

Phn tch theo phng php khung tng ng l chuyn i t h khung ba

chiu vi sn hai phng (sn bn k, tc gi) sang cc khung hai chiu (sn-dm v

ct), vi mi khung c ko n ton b chiu cao ca nh nh hnh v 1. Chiu rng

ca khung tng ng ko n trung bnh nhp gia cc trc ct. Phn tch hon chnh

cho cc bn hai phng ca mt cng trnh bao gm phn tch mt lot cc khung tng

ng bin v gia theo trc dc v trc ngang ca nh. Vi ti trng bn thn, sn-dm

ti mi mc sn hoc mi c th phn tch ring bit vi u khng lin kt ca ct vi

sn-dm ang tnh c coi l ngm.

Phng php phn tch n hi khung tng ng c ng dng cho cc cng

trnh vi cc ct c b tr trn li trc giao, cc trc ct theo phng dc v ngang

nh. Phng php ny c th p dng cho cc sn c dm hoc khng dm.

Phng php khung tng ng c th s dng phn tch ti trng ngang nu

cng ca cc phn t khung c iu chnh khi k n vt nt v cc yu t lin

quan khc. Xem tho lun ti 13.3.1.2 phn 8.

Thit k s b

Trc khi thc hin phn tch khung tng ng, chiu dy s b ca sn h

hn ch chuyn v, theo yu cu v chiu dy ti thiu ti muc 9.5.3. Bng 18-1 v hnh

18-3 c th dc s dng n gin ha vic tnh ton chiu dy sn. i vi sn

khng dm, khi thit k cn kim tra cng chu ct ca sn ti vng ln cn ct v

cc gi ta khc, theo cc quy nh cho sn ti mc 11.12. Xem tho lun ti mc

13.5.4 phn 18.

13.7.2 Khung tng ng

p dng nh ngha khung ti cc mc 13.7.2, 13.2.1, v 13.2.2 c th hin

trong hnh 20-1 v 20-2. Mt s iu chnh c yu cu khi p dng nh ngha cho

trong 13.2.1 i vi h sn c cc nhp khc nhau dc theo di thit k. Cc phn t ca

khung tng ng l sn-dm, phn t chu xon (phn t trc giao nm ngang) c

bng ct (phn t ng). Phn t chu xon mang m men chuyn gia sn-dm v

ct. Cc phn t ca khung tng ng th hin trong hnh 20-3. Bc u tin ca

vic phn tch khung l cc thnh phn cng un ca cc phn t khung cn c

xc nh.

Hnh 20-1: Khung tng ng cho nh 5 tng

13.7.3 Sn-dm

Dng chung ca h sn c hoc khng dm gia cc gi ta c th hin trong

hnh 20-4 v 20-5. Mt ct ngang xc nh cng ca phn t sn-dm, sbK gia

cc trc gi ta c th hin cho mi dng. Biu cng tng ng sn dm c

th c s dng xc nh hng s phn phi m men v m men u ngm cho

phn tch khung tng ng.

Vic tnh ton cng tng ng ca sn-dm da trn cc vn sau:

- M men qun tnh ti cc mt ca gi ta da trn mt ct ngang nguyn ca

b tng. S bin i m men qun tnh dc theo trc ca sn-dm gia cc gi

ta cn c k n.

- Gi ta l ct, m ct, vm hoc tng. Dm khng c coi l gi ta trong

khung tng ng.

- M men qun tnh ca sn dm t mt gi ta n trc gi ta c gi thit

l bng m men qun tnh ca sn-dm ti mt gi ta chia cho mt lng

bng ( )22 2c l (13.7.3.3) 1H s ( 22 21 c l ) c p dng cho m men qun tnh ti mt gi ta v tm gi

ta, vi nh hng, t nht l to phn t vm cho sn-dm trong khong chiu di ca

n. Do , cng, cc h s v m men u ngm da trn gi thit thng dng l

phn t lng tr u khng th p dng cho phn t sn-dm.

Hnh 20-2: Di thit k ca khung tng ng

Hnh 20-3: Cc phn t ca khung tng ng

Hnh 20-4: Cc dng mt ct tnh cng Sn-Dm sbK

Hnh 20-5: Cc dng mt ct tnh cng Sn-Dm

13.7.4 Ct

Dng chung cc iu kin bin ca ct nh trn hnh 20-6. cng ca ct da

trn chiu cao ct l tnh t tm sn pha trn n tm sn pha di. th cng ca

ct c th c dng xc nh cng ngang ca ct, . th cng da trn

cc vn sau:

c

cK

- M men qun tnh ca ct ngoi nt sn-dm da trn din tch mt ct

ngang nguyn ca b tng. S bin i ca m men qun tnh gia cc

nt sn-dm cn c k n. Vi ct c m, m men qun tnh c

coi l bin thin tuyn tnh t y m ct n y sn dm.

- M men qun tnh gi thit l bng v cng t y sn dm n nt.

Cng nh cc phn t sn dm, h s cng, cK khng th da trn

gi thit phn t lng tr u.

Bng A7 trong ph lc A20A c th c s dng xc nh cng thc t

ca ct v h s chuyn i.

Hnh 20-6: Cc dng mt ct tnh cng ca ct cK

Phn t chu xon

Phn t chu xon ca cc nt sn-dm thng thng c th hin trong hnh

20-7. Mt ct ngang ca phn t xon l gi tr ln nht trong s nhng gi tr c

nh ngha theo ba iu kin trong 13.7.5.1. cc iu kin a, b, c c th hin trong

hnh 20-7.

cng ca phn t chu xon c tnh ton theo biu thc sau y: tK

( )cs

32 2 2

9E1t

CKl c l

=

Trong tng c thc hin vi tt c cc phn t xon lin kt vi nt: 2 i

vi khung trong v 1 i vi khung bin.

Thnh phn l m men qun tnh xon ca cc phn t chu xon lin kt vi

nt.

C

3

1 0.633

x x yCy

= Trong x l cnh ngn v y l cnh di ca phn mt ct ch nht ca phn t

xon. Gi tr c tnh ton bng cch chia mt ct ngang ca phn t chu xon C

thnh cc phn c dng ch nht v tnh tng cc gi tr ca cc phn ch nht .

Nn chia sao cho gi tr C cui cng tnh c l ln nht. p dng ca biu thc tnh

c th hin trong hnh 20-8.

C

C

Hnh 20-7: Cc phn t chu xon

Nu dm ni vo nt theo hng m cn xc nh m men th cng xon cn

tng ln nh sau:

t sbta

s

K IKI

=

Trong : l cng tng ln do dm song song (nh hnh 20.3); taK sI l m

men qun tnh ca bn c chiu rng l : 2l 32 12sI l h= ; sbI l m men qun tnh ca tit din ch T bao gm c dm song song v bn nh trn.

Hnh 20-8: Cc phn t chu xon

Ct tng ng (R13.7.4)

cng tng ng ca ct c vit di dng nghc o nh sau: 1 1 1

ec c tK K= +

K Tnh ton m men

Theo ch dn ca ACI318-02, phn tnh ton m men ca khung tng ng

c tnh cho mt sn theo phng php phn phi m men. Phng php ny mt kh

nhiu thi gian tnh ton. rt ngn thi gian tnh ton, c th s dng phn mm

tnh ton.

M men m

M men m thit k nn ly ti mt ca gi ta nhng khng qu 0.175 tnh t

tm gi ta. Gi tr ny l mt gii hn i vi gi ta hp v di. Gi ta c th l ct,

m ct, tng. Gi ta khng c dng ch nht c a v dng hnh vung c cng

din tch mt ct ngang. Ch i vi sn c dm, mt dm khng c k n trong

1l

vic xc nh v tr mt gi ta. V tr ca mt ct ti hn cho cc dng gi ta khac

nhau c th hin trong hnh 20-11.

Hnh 20-11: Mt ct ti hn tnh m men m

Phn phi m men trong di ct v di gia

Phn phi m men cho di ct:

M men m ti gi ca nhp gia di ct c cc h s phn phi tnh theo phn

trm nh sau:

M men m ti gi ca nhp bin di ct c cc h s phn phi tnh theo phn

trm nh sau:

M men dng ti nhp ca nhp bin v nhp gia di ct c cc h s phn phi

tnh theo phn trm nh sau:

M men ca di gia l phn trm cn li ca tng m men sau khi tr i m

men do di ct chu

V d tnh ton

V d 1 (V d ACI20-1): S dng phng php khung tng ng xc nh m

men theo phng tnh ton nh hnh v, sn ti ch.

Chiu cao tng: 9 ft (2.74 m)

Kch thc ct: 16x16 in (0.41x0,41 m)

Kt cu chu ti trng ngang l vch cng

Khng c dm bin

Tnh ti: 20 psf (97.7 kg/m2)

Hot ti: 40 psf (195.4 kg/m2)

4000cf = psi (281.5 kg/cm2) cho sn, b tng thng 6000cf = psi (422.2 kg/cm2) cho ct, b tng thng 60000yf = psi (4222 2 kg/cm2)

Tnh ton v tho lun

1. La chn s b chiu dy sn:

Theo iu kin bin dng:

i vi h sn phng, chiu dy ti thiu vi ct thp mc 60 l: 200 6.67

30 30nlh = = = in (17 cm)

V khng nh hn 5 in (12.7 cm)

Vi l nhp thng thy in (5.08 m) nl 18x12-16=200nl =Chn sn c chiu dy 7 in (17.78 cm)

Theo iu kin chc thng (theo tiu chun Vit Nam):

2. Cc phn t ca khung tng ng

a. cng un ca sn dm ti hai u, sbK :

1

1

16 0.07418x12

Ncl

= = ; 22

16 0.114x12

Ncl

= =

Vi v 1Nc c= 1F 2F2Nc c= , tra bng A1 ph lc 20A v ni suy: 4.13NF FNk k= =

cng ca sn l: s s1 1

4.13c s c ssb NFE I E IK kl l

= =

Trong :

M men qun tnh ca sn: 3 3

2 14 12x7 480212 12sl h xI = = = in4 (199874.33 cm4)

M un n hi ca b tng sn: psi (253332.5 kg/cm2) 6csE 3.6x10= Nh vy, gi tr cng ca sn l:

6331x10sbK = lb/in (592x105 kg/cm) b. cng ca phn t ct ti hai u, : cK

Tham kho bng A7, ph lc 20A, 3.5at = in, 3.5bt = in 9x12=108H = in (2.74 m); 108-7=101cH = in (2.57 m); 1a bt t = ; 1.07cH H =

Tm c bng ni suy 4.74AB BAk k= =6cc4.74E 1059x10cc

c

IKl

= = lb/in

Trong :

M men qun tnh ca ct: 4 416 5461

12 12ccI = = = in4 (227304 cm4)

M un n hi b tng ct: psi (311036 kg/cm2) 6ccE 4.42x10=Chiu di ct: in (2.74 m) 9 12 108cl x= =

c. cng xon ca cc phn t xon, tK

( )6cs

32 2 2

9E 3.45x101

tCK

l c l= =

lb/in (632740 kg/cm)

Trong : 3 37 7 161 0.63 1 0.63 13253 16 3

x x yCy

= = = in4 (55151 cm4)

in v 2 16c = 2 14 12 168l = = in

Mt ct ngang ca phn t chu xon

d. cng tng ng ca ct, ecK

( )( )( ) ( ) 6

2 1059 2 345520 10

2 1059 2 345c t

ecc t

K KK

K K = = =+ +

lb/in

3. Tnh ton khung tng ng bng phn mm:

tnh ton bng phn mm th cng ca sn v ct phi nhn vi chiu di

tng ng ca sn v ct.

cng ca sn s l: 6 61 331 10 216 71496 10sb sbK K l= = = lb/in cng ca ct: 6 6520 10 108 56160 10c c cK K l= = = lb/in Tng ti trng phn b u l: 0.193 14 2.702q = = kips/ft Kt qu phn tch bng phn mm KCW2010V5 kt qu nh sau:

Nt 5 6 7 8

Phn t 1 1 2 2 3 3

ACI318-02 Gi -46.5 -84 -76.3 -76.3 -84 -46.5

Nhp 44.2 33.1 44.2

KCW Gi -45.9 -82.8 -75.3 -75.3 -82.8 -45.9

Nhp 45 34.1 45

Phn phi m men n di ct v hai na di gia

V tr Di ct Hai na di gia

Nhp bin

Gi bin 100 0

Nhp 60 17.7

Gi gia 75 16.7

Nhp bin

Gi 75 15.2

Nhp 60 13.2

V d 2 (ACI318-02 20-2): Bn hai phng c dm phn tch bng phng php khung

tng ng.

Chiu cao tng: 12 ft (3.66 m)

Kch thc ct: 18x18 in (0.46x0.46 m)

Kch thc dm bin: 14x27 in (0.36x0.69 m)

Kch thc dm gia: 14x20 in (0.36x0.51 m)

Hot ti: 100 psf (488.7 kg/m2)

4000cf = psi (281.5 kg/cm2) cho tt c cc cu kin, b tng thng 60000yf = psi (4222 2 kg/cm2)

Tnh ton v tho lun

1. La chn s b chiu dy sn:

Theo iu kin bin dng:

Chn sn c chiu dy 6 in (15.24 cm)

Theo iu kin chc thng (theo tiu chun Vit Nam):

2. Cc phn t ca khung tng ng

a. cng un ca sn dm ti hai u, sbK :

1

1

16 0.0857 0.117.5x12

Ncl

= = ; 22

18 0.068222x12

Ncl

= =

Vi v 1Nc c= 1F 2F2Nc c= , tra bng A1 ph lc 20A v ni suy: 4.11NF FNk k= =

cng ca sn l: c c1 1

25387E4.11 4.11 497E17.5 12

c sb c sbsb NF

E I E IK kl l

= = = =

Trong :

M men qun tnh ca sn-dm: 314 202.72 25387

12sbI = = in4 (1056687 cm4)

b. cng ca phn t ct ti hai u, : cK

Ct gia:

Tham kho bng A7, ph lc 20A, 17at = in, 3bt = in 12x12=144H = in (3.66 m); 144-17-3=124cH = in (3.15 m); 5.67a bt t = ; 1.16cH H =

Tm c ; bng ni suy 6.82ABk = 4.99BAk =c

c6.82E 414Ecct

c

IKl

= = ; c c4.99E 303Eccbc

IKl

= =

Ct bin:

Tham kho bng A7, ph lc 20A, 24at = in, 3bt = in

12x12=144H = in (3.66 m); 144-24-3=117cH = in (2.97 m); 8a bt t = ; 1.23cH H = Tm c ; bng ni suy 8.57ABk = 5.31BAk =

cc

8.57E 512Ecctc

IKl

= = ; c c5.31E 323Eccbc

IKl

= =

Trong :

M men qun tnh ca ct: 4 418 8748

12 12ccI = = = in4 (364119 cm4)

M un n hi b tng ct: psi (311036 kg/cm2) 6ccE 4.42x10=Chiu di ct: in (3.66 m) 12 12 144cl = =

c. cng xon ca cc phn t xon, tK

( )6cs

32 2 2

9E 3.45x101

tCK

l c l= =

lb/in (632740 kg/cm)

Trong : 3

1 0.633

x x yCy

= in v 2 18c = 2 22 12 264l = = in i vi ct gia:

c493EtK = Trong : C c ly t gi tr ln nht trong hai ct trong bng sau:

Mt ct ngang ca phn t chu xon ti ct gia

i vi ct gia:

c752EtK = Trong : C c ly t gi tr ln nht trong hai ct trong bng sau:

Mt ct ngang ca phn t chu xon ti ct bin

d. Tng cng chng xon do dm song song

i vi ct gia:

cc

493E 25387 2634E4752

t sbta

s

K IKI

= = =

i vi ct bin:

c c752E 25387 4017E

4752t sb

tas

K IKI

= = =

Trong : 314 202.72 25387

12sbI = = in4 (1056687 cm4)

3264 6 475212s

I = = in4 (197793 cm4)

Phn t dm song song

d. cng tng ng ca ct, ecK

Ct gia:

( )( )( ) ( )c c c cc c c

303E 414E 2 2643E631E

303E 414E 2 2643Ec ta

ecc ta

K KK

K K+ = = =+ + +

Ct bin:

( )( )( ) ( )c c c cc c c

323E 521E 2 4017E764E

323E 521E 2 4017Ec ta

ecc ta

K KK

K K+ = = =+ + +

3. Tnh ton khung tng ng bng phn mm:

tnh ton bng phn mm th cng ca sn-dm v ct phi nhn vi chiu

di tng ng ca sn-dm v ct.

cng ca sn-dm: 1 c497 17.5 8697.5Esb sb cK K l E= = = cng ca ct gia: c c631E 12 7572Ec c cK K l= = = cng ca ct bin: c c764E 12 9168Ec c cK K l= = = Tng ti trng phn b u l: 0.261 22 5.742q = = kips/ft

Phn phi m men n di ct v hai na di gia

V tr Di ct Hai na di gia

Nhp bin

Gi bin 75 25

Nhp 67 33

Gi gia 67 33

Nhp gia

Gi 67 33

Nhp 67 33

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Title: Tnh bn hai phng theo phng php khung tng tng Subject: Author: Hien Nghiem Keywords: Comments: Creation Date: 1/13/2011 8:39:00 AM Change Number: 121 Last Saved On: 6/28/2013 8:55:00 AM Last Saved By: ASUS Total Editing Time: 3,843 Minutes Last Printed On: 6/28/2013 11:39:00 AM As of Last Complete Printing Number of Pages: 21 Number of Words: 2,529 Number of Characters: 8,954