Huong Dan Tinh Toan San (So Do Tinh Theo Tung o San Doc Lap)

Nguyn Thc V - Khoa XD DD&CN Trang 1/12

CHNG 1: TNH TON SN. 1. B TR H LI DM : Da vo bn v kin trc + h li ct b tr h li dm theo cc yu cu:

- m bo tnh m thut. - m bo tnh hp l v mt kt cu: cc dm nn b tr sao cho nhanh truyn lc

xung t, khng nn ri rm v mt kt cu (VD: Dm D1 gc ln dm D2; dm D2 gc ln dm khung DK; ).

- Kch thc sn khng qu nh cng khng qu ln (tr trng hp yu cu v kin trc phi thit k sn ln).

Vi h li dm b tr, mt bng sn c chia thnh cc sn. Ta quan nim cc sn lm vic c lp vi nhau: ti trng tc dng ln sn ny khng gy ra ni lc trong cc sn ln cn (quan nim ny khng c chnh xc nhng c p dng v cch tnh n gin, nu khng: cn tnh v t hp ni lc trong sn - xem thm gio trnh KC BTCT).

V quan nim rng cc sn lm vic c lp nn ta xt ring tng sn tnh. Tin hnh nh s th t cc sn tin tnh ton (cc sn cng loi: cng kch thc;

cng ti trng, cng s lin kt th nh s trng nhau). Cc s tnh ton sn xem gio trnh KCBTCT trang 327.

2. XC NH TI TRNG TC DNG LN SN : 2.1. Tnh ti : Da vo cu to kin trc mt ct sn xc nh tnh ti tc dng ln sn.

S b chn chiu dy bn sn:

lmDhb .= hb: ly chn cm.

+ Bn loi dm: m = 30 35. + Bn k 4 cnh: m = 40 45. + Bn console: m = 10 18. D = 0,8 1,4 ph thuc ti trng, ti trng ln th ly D ln. l = l1: kch thc cnh ngn ca bn.

Trng lng ring vt liu: ly theo thc t hoc cc s tay kt cu. VD: BTCT: g = 25 KN/m3. Va XM: g = 16 KN/m3. Gch hoa XM ( 20020020 ): 0,45 KN/m2. Gch men ly g = 22 KN/m3 hoc 0,17 KN/m2. Khi xy gch c: g = 18 KN/m3. Khi xy gch ng: g = 15 KN/m3. BT gch v: g = 16 KN/m3. Ca knh khung g: 0,25 KN/m2. Ca knh khung thp: 0,4 KN/m2.


Ca knh khung nhm: 0,15 KN/m2. mi : g = 20 KN/m3.

H s vt ti n: Tra bng 1 trang 10 TCVN 2737 - 1995. Xc nh ti trng: g = . .n g d ( n v KN/m2 )

n : h s vt ti. g : trng lng ring. d : chiu dy lp vt liu.

Trng hp c tng hoc ca xy trc tip trn sn tnh ti trng n v ca tng (KN/m2), din tch tng, din tch ca ... tng trng lng ca tng + ca. Sau chia cho din tch sn g phn b (xem gn ng phn b u trn ton sn).

2.2. Hot ti: Ly theo TCVN 2737 - 1995 (Bng 3 trang 12). H s vt ti n ly theo mc 4.3.3 trang 15 - TCVN 2737 - 1995. Xem thm mc 4.4 trang 16 xc nh cng trnh c thuc mc ny hay khng? Hot ti k hiu l: p (kN/m2).

3. XC NH NI LC : Ni lc trong sn c xc nh theo s N HI ( khc vi n BTCT1 ). Gi l1: kch thc cnh ngn ca sn.

l2: kch thc cnh di ca sn. (Do s n hi nn kch thc ny ly theo tim dm).

Da vo t s l2/l1 ngi ta phn ra 2 loi bn sn : + l2/l1 2 : sn lm vic theo 2 phng sn bn k 4 cnh. + l2/l1 > 2 : sn lm vic theo 1 phng sn bn dm.

Da vo lin kt sn vi dm: c 3 loi lin kt C nhiu quan nim v kin kt sn vi dm:

+ Quan nim 1: Nu sn lin kt vi dm bin th xem l lin kt khp. Nu sn lin kt vi dm gia th xem l lin kt ngm, nu di sn khng c dm th xem l t do. + Quan nim 2: Nu dm bin m l dm khung th xem l ngm, dm ph (dm dc) th xem l khp. Cc dm gia xem l lin kt ngm. + Quan nim 3: Dm bin xem l khp hay ngm ph thuc vo t s cng ca sn v dm bin. Nu dm bin cng lin kt ngm, nu khng cng lin kt khp.

Cc quan nim ny cng ch l gn ng v thc t lin kt sn vo dm l lin kt c cng hu hn (m khp th c cng = 0, ngm c cng = ), khi cn tnh chnh xc th phi dng s tnh gm c sn v dm lin kt vi nhau.

lin kt gi

t do

lin kt ngm


Nu thin v an ton: quan nim sn lin kt vo dm bin l lin kt khp xc nh ni lc trong sn. Khi b tr thp th dng thp ti bin ngm i din b tr cho bin khp.

VD:

3.1. Xc nh ni lc trong sn bn dm : Ct di bn rng 1m theo phng cnh ngn (vung gc cnh di) v xem nh 1 dm. Ti trng phn b u tc dng ln dm: q = (p + g) * 1m (KN/m) Tu lin kt cnh bn m c 3 s tnh i vi dm :

3.2. Xc nh ni lc trong sn bn k 4 cnh :

Da vo lin kt cnh bn c 9 s :

S 1 S 2 S 3

l

1m

1

Tnh ni lc xem l bin khp: M bin = 0 B tr ct thp: dng ct thp bin ngm b tr

q

M = max

ql8

2

l1

q

minM = 1- ql

8

2 3/8l

maxM = 1

29ql128

l112

minM = - ql

12

q

maxM = 1

2ql24

M = - qlmin 12

211

l1

(a) (b) (c)


S 4 S 5 S 6

S 7 S 8 S 9 Xt tng bn: C 6 moment

Momen theo phng cnh ngn Momen theo phng cnh di

M1, MI, MI : dng tnh ct thp t dc cnh ngn (MI = 0 nu l bin khp, MI = MI nu l bin ngm).

M2, MII, MII : dng tnh ct thp t dc cnh di. (MII = 0 nu l bin khp, MII = MII nu l bin ngm).

M 'II

M 2 l 2

l1

M 1M I M 'I

M II

IDung M ' e tnh

1Dung M e tnh

Dung M e tnhI

Dung M ' e tnhII

Dung M e tnh2

Dung M e tnhII


Vi M1 = a1. (g + p).l1.l2 MI = -b1. (g + p).l1.l2 M2 = a2. (g + p).l1.l2 MII = -b2. (g + p).l1.l2 ( n v ca Moment : kN.m/m ). a1, a2, b1, b2 : h s ph thuc s lin kt 4 bin v t s l1/l2, xc nh bng cch tra Ph lc ca gio trnh KCBTCT hoc cc s tay kt cu, nu l1/l2 l s l th cn phi ni suy. VD: l1/l2 = 1,78 th ni suy t 2 gi tr l1/l2 = 1,75 v l1/l2 = 1,8.

4. TNH TON CT THP : - Tnh thp bn nh cu kin chu un c b rng b = 1m = 1000mm, chiu cao h = chiu dy

sn (mm). ( i n v M t KN.m N.mm : nhn vi 1000000 )

- Xc nh 2. .M b o

MR b h

a = ( kim tra iu kin aM aR ).

Nu aM > aR: tng chiu dy hoc tng cp bn b tng. + Rb: cng chu nn ca b tng, tra Ph lc ca gio trnh KCBTCT, ph thuc cp bn b tng, n v MPa (#N/mm2). + ho: chiu cao tnh ton ca tit din (mm). ho = h a. (xem mc 5.1 bn di) + aR: xc nh bng cch tra Ph lc ca gio trnh KCBTCT ph thuc nhm ct thp v cp bn b tng, ng vi gb2 = 1. - Sau khi tnh aM v tho mn aM aR:

1 1 2.

2Maz

+ - =

. .TTS

S o

MAR hz

= (mm2)

+ RS: cng chu ko ca ct thp, tra Ph lc ca gio trnh KCBTCT, ph thuc nhm thp, n v MPa (#N/mm2) Xc nh din tch ct thp tng ng vi cc ni lc ti gi v nhp ca sn. VD: dng M1 tnh AS1 dng M2 tnh AS2

dien tch cac cay theptrong 1m = Fa1

1m

1m

F 2aAS1 AS2


- Din tch ct thp TTSA c xc nh trn xem nh b tr cho 1 m chiu di bn. Khi thit

k ct thp sn ta thng chn ng knh v tnh ton khong cch cc thanh thp. Chn ng knh thp: chn 6; 8; 10; ng thi tha mn iu kin h/10.

T ng thc : 1000

TTS s

TT

A amm s

=

+ aS: din tch 1 thanh thp (mm2) + sTT: khong cch ct thp theo tnh ton (mm)

.1000TT S TTS

asA

= .

- Tnh hm lng ct thp : % .100%1000.

TTS

o

Ah

m = .

- Trong sn = 0,3% 0,9% l hp l v > min = 0,05% (thng ly min = 0,1% ).

- Vic b tr ct thp cn phi phi hp ct thp gia cc sn vi nhau, khong cch ct thp b tr sBT sTT. Tnh li din tch ct thp b tr AS theo khong cch sBT:

ASb tr .1000S

BTa

s=

- Kt qu tnh ton ni lc v thp trong sn nn lp thnh bng tin theo di, kim tra. 5. YU CU CU TO SN :

5.1. Khong cch lp bo v : abv = khong cch t mp BT n y ct thp. abv = 10 mm i vi h 100 mm. abv = 15 mm i vi h > 100 mm.

Khong cch t mp btng n trng tm ct thp a:

21daa bv += hoc 2

21

ddaa bv ++=

Ch : i vi ct thp chu momen dng th a ca 2 phng khc nhau. Do momen theo phng cnh ngn thng ln hn momen theo phng cnh di nn ngi ta thng t thp cnh ngn nm di tng ho.

5.2. Khong cch ca ct thp : - Khong cch gia cc ct thp chu lc a = 70 200 mm. - Khi chiu dy bn h 80mm nn dng cc thanh thp un t xen k nhau, im un cch mp gi = l/6, gc un = 30o khi h 100mm, = 45o khi h > 100mm (iu ny khng

d (ng knh lp tren)2

d (ng knh lp tren)1


bt buc). S thp sau khi un c neo vo gi 13 S

A gia nhp v khng t hn 3

thanh/1m di. - Ct thp phn b (ct thp t theo phng cnh di i vi sn bn dm) khng t hn 10% ct chu lc nu l2/l1 3; khng t hn 20% ct chu lc nu l2/l1 < 3. Khong cch cc thanh 350mm, ng knh ct thp phn b ng knh ct thp chu lc. Ct phn b c tc dng : + Chng nt do btng co ngt. + C nh ct chu lc. + Truyn ti sang vng xung quanh trnh tp trung ng sut. + Chu ng sut nhit. + Cn tr s m rng khe nt.

5.3. Chiu di thp m :

Ti vng giao nhau tit kim c th t 50% AS ca mi phng nhng khng t hn 3 thanh/1m di ( an ton th khng p dng).

5.4. Phi hp ct thp : Do quan nim tnh ton cc sn c lp nhau (iu ny trnh by trn) nn thng xy ra hin tng: ti 2 bn ca 1 dm, cc sn c moment gi khc nhau. VD: MII(1) : momen gi ca (1). MII(2) : momen gi ca (2). MII(1) MII(2)

iu ny khng ng vi thc t v cc dm c kh nng b xon do phn phi li

moment trong sn, nn cc momen trong hai sn hai bn dm thng = nhau. S d kt qu 2 momen khng bng nhau do quan nim tnh ton cha chnh xc (thc

t cc sn khng c lp nhau, ti trng tc dng ln ny c th gy ra ni lc trong cc khc).

l /41

1l /4

l 1

(1)

(3) (4)

(2)MII(1) (2)

IIM


Biu moment theo quan nim tnh ton Biu moment thc t n gin v thin v an ton ta ly momen ln nht b tr ct thp cho c 2 bn gi. VD: B tr i vi ct thp chu moment dng th khng nht thit phi thc hin nh trn, nhng

c th thun tin thi cng ta b tr ct thp cc sn ln cn nhau cng mt loi thp nu din tch ct thp tnh ton cc sn chnh lch nhau khng nhiu.

6. V D :

Tnh ton ni lc v b tr ct thp sn. 6.1. Mt bng sn :

1, 2, 3, 4 : phng hc. 5 : hnh lang.

6.2. Mt ct cu to sn: S b chn chiu dy sn phng hc:

075,03401

=== lmDh m.

chn hb = 80mm. Sn hnh lang c th chn chiu dy nh hn

nhng thun tin thi cng ta cng chn hb = 80mm

(1)IIM

(2)MII

F = f8/120a aF = f8/150 f8/120

1500

3000

3000

4000 4000 4000

(1) (2) (1)

(3) (4) (3)

(5) (5) (5)

- gch ceramic

- va xm lt dy 20, mc 50

- sn btct dy 80, mc 200

- va xm trt trn dy 15, mc 50


6.3. Xc nh ti trng : 6.3.1. Tnh ti : ( ca sn phng hc, sn hnh lang).

Lp vt liu Ch.dy (m)

Tr.lng ring (KN/m3)

gtc (KN/m2)

H s vt ti n

gtt (KN/m2)

- Gch ceramic - Va XM lt - BTCT - Va trt

0,02 0,08 0,015

16 25 16

0,17 0,32 2,00 0,24

1,1 1,3 1,1 1,3

0,187 0,416 0,220 0,312

Tng tnh ti tnh ton : Sgtt = 0,3115 kN/m2.

6.3.2. Hot ti :

Loi phng ptc (KN/m2) H s vt ti n ptt (KN/m2) - Phng hc - Hnh lang

2,00 4,00

1,2 1,2

2,40 4,80

6.4. Tnh ton ni lc v ct thp bn :

6.4.1. Bn (1) : S tnh : l2/l1 = 4/3 < 2 bn k 4 cnh (thuc s 6). T s l2/l1 = 1,333 ni suy xc nh : Trong bng tra c : + l2/l1 = 1,3: + l2/l1 = 1,35: a1 = 0,0319 a1 = 0,0320

a2 = 0,0188 a2 = 0,0176 b1 = 0,0711 b1 = 0,0711 b2 = 0,0421 b2 = 0,0391

a1 = 031967,0)0319,0032,0(3,135,13,1333,10319,0 =-

--

+

a2 = 018,0)0188,00176,0(3,135,13,1333,10188,0 =-

--

+

b1 = 0711,0)0711,00711,0(3,135,13,1333,10711,0 =-

--

+

b2 = 0401,0)0421,00391,0(3,135,13,1333,10421,0 =-

--

+

M1 = 0,031967 (3,115 + 2,40) 3 4 = 2,1156 KN.m M2 = 0,018 (3,115 + 2,40) 3 4 = 1,1912 KN.m

l = 3m1

2l = 4m

g = 311,5p = 240

g=3,115 p=2,4


MI = -0,0711 (3,115 + 2,40) 3 4 = -4,7054 KN.m MII = -0,0401 (3,115 + 2,40) 3 4 = -2,6538 KN.m

* Tnh ton ct thp : Thp AI c RS = RSC = 225MPa; B tng B15 Rb = 8,5 MPa - Ct thp chu momen dng theo phng cnh ngn (ly a = 15mm ho1 = 65mm).

6

12 21

2,1156.10 0,059 0,446. . 8,5 1000 65M Rb o

MR b h

a a= = = < =

1 1 2 1 1 2 0,059 0,97

2 2Maz

+ - + - = = =

6

1 2,1156.10 149. . 0,97 225 65

TTS

S o

MAR hg

= = =

mm2.

Chn thp 6 aS = 28,3mm2 1000. 1000 28,3 170

149TT S

TTS

asA

= = = mm.

- Tng t i vi ct chu lc khc Sau khi tnh ton c khong cch ct thp tng , u tin ta v mt bng sn b tr thp

theo tnh ton. Thp di (chu moment dng)

Khi l2/l1 < 3 ly 20% AS chu lc ca cnh ngn, khi l2/l1 > 3 ly 10% AS chu lc ca cnh ngn

f6/290 f6/

210

f6/280 f6/

170

f6/

170

f6/280

f6/440 f6/

270

f6/460 f6/

240

f6/

240

f6/460

C.T f6

f6

f6

300

300

300

C.T C.T


Thp m (chu moment m)

T y ta quyt nh phng n b tr ct thp trong sn. Phng n 1 : B tr ct thp st vi tnh ton.

a170

a200 f6

f6 f

620

0

f6

200

f6a200

f6a150

f6a200

f6a130

f6a130

f6a150

a150

f6

a130 f8

a180 f8

f6

a200

f6

a170

f6a150

f6a150

f6a150

f6a150

f6a200

f6a200

f6a200

f6a200

f6

a150

f6

a170

a200 f8

f6

a150

f6

a130

a180 f8

f6

Cu tao : bin nay la khp nn c.thep t theo cu tao : khng phai ly theo momen m tai gi nhng an toan th co th b tr bng thep chu momen m tai gi i din

f6/140 f

8/13

0C.T

C.T

f8/

170

C.T

C.T

f8/

130 f6/130

f6/130 C.T

f6/140

C.T f6/250 f6/210 f6/210 f6/250

C.T

f8/

180

f8/

200

f8/

180

f8/

200

f8/

180

f8/

180

C.T C.T C.T C.T

C.T

C.T

C.T

f6/

160

f6/

160

f6/

160


Phng n 2 : B tr ct thp thin v an ton v n gin khi thi cng.

f6 f6 a1

70

a200

f6a200

f6a130

f6a200

f6a130

f6a130

f6a130

a130

f8

a130 f8

a130 f8

f6

a170

f6

a170

f6a130

f6a130

f6a130

f6a130

f6a150

f6a150

f6a150

f6a150

f6

a130

f8

a130

a130 f8

f6

a130

f8

a130

a130 f8

f6

f8

f8

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Huong Dan Tinh Toan San (So Do Tinh Theo Tung o San Doc Lap)