163440776 Cot Lech Tam Xien

Lun vn tt nghip Trang 5 Chng I: Tng quan

Gio vin hng dn: Gs. Ts. Nguyn nh Cng Hc vin: Nguyn Phan c Hng

CHNG I: TNG QUAN 1.1. Khi nim nn lch tm xin: - Nn lch tm xin l trng hp nn lch tm m mt phng un khng

cha trc i xng ca tit din. - Thc t thng gp tit din hnh ch nht c hai trc i xng (tit

din trn khng xy ra nn lch tm xin). - Gi hai trc i xng ca tit din l Ox v Oy. Gc gia mt phng un

v trc Ox l o.

N

Mo o

NMx

yM

Hnh 1.1. S ni lc nn lch tm xin

- C th phn mmen un M thnh hai thnh phn tc dng trong hai mt phng cha trc Ox v Oy l Mx v My (Xem hnh v 1.1)

Mx = M.cos

My = M.sin - Trng hp khi tnh ton ni lc xc nh v t hp ring Mx v My

theo hai phng th mmen tng M l:

M = 22 yx MM

- Gc hp bi vct ca mmen tng M v trc Ox (gc ) c xc nh

bi: tgo = x

y

MM

- Ct chu nn lch tm xin thng gp trong cc khung khi xt s lm vic ca ct ng thi chu un theo hai phng.

- Tit din ch nht chu nn lch tm xin th ct thp thng t theo chu vi v i xng qua hai trc. Trng hp Mx My th nn lm ct vung.



1.2. Ni lc tnh tan nn lch tm xin: - Ni lc tnh tan nn lch tm xin c ly t kt qu t hp ti

trng, trong cn ch n cc b ba ni lc (N, Mx, My) sau: Nmax v Mx, My tng ng Mxmax v N, My tng ng Mymax v N, Mx tng ng Mx&My u ln v N tng ng

C lch tm e1x = NM x hoc e2x = N

M y ln.

- Trong mi b ba ni lc, cn xt n lch tm ngu nhin ea theo mi phng v nh hng un dc theo tng phng. H s un dc theo tng phng i c tnh theo cng thc sau:

i =

thiNN

1

1 ;

Vi vt liu n hi, Nthi = 22

oi

i

lEJ . Vi b tng ct thp , Nth tnh theo cng

thc thc nghim. - S ni lc tnh tnh ton c a v thnh lc N t ti im D c

to l xeox v yeoy (Hnh 1.2). im E c th nm bn trong hoc bn ngoi tit din, gc phn t no l ph thuc vo chiu tc dng ca Mx v My.

- Sau khi xt lch tm ngu nhin v un dc th mmen tc dng theo 2 phng c tng ln thnh *xM v *yM :

*xM = Nxeox ; *yM = Nyeoy .

xeox

oyey

x

y

Cx

yC Cy

xC

y

x

yeoy

oxex

EE

Hnh 1.2. S ni lc vi lch tm



1.3. S lm vic nn lch tm xin: - Vi cu kin lm bng vt liu n hi v ng nht chu nn lch tm

xin, c th dng phng php cng tc dng tnh ng sut:

= FNy

JM

xJM

y

y

x

x

iu kin bn l hn ch ng sut khng c vt qu ng sut cho php hoc cng tnh ton ca vt liu.

- Khi tnh theo trng thi gii hn, do khng th tnh ring ng sut ca tng loi ni lc nn khng th dng phng php cng tc dng m phi xt tc dng ng thi ca N, Mx , My.

- Khi chu nn lch tm xin, tu theo v tr im t lc cng nh tng quan gia ni lc & kch thc tit din v cch b tr ct thp m c th xy ra trng hp ton b tit din chu nn hoc mt phn tit din chu nn & mt phn tit din chu ko.

- Vi tit din c mt phn chu nn th vng nn c th 1 trong 4 dng (Hnh 1.3). Trong :

Trc trung ho l trc cch nh chu nn ln nht mt on xo Gii hn vng nn l ng thng cch nh chu nn ln nht mt

on x=xo ( = 0.80.85): y l vng b tng chu nn.

X

Xo

Vng nn tnh i

X

Xo

X

Xo

X

Xo

Hnh 1.3. Cc dng ca vng nn

- n trng thi gii hn, ng sut trong b tng c xem l phn b u v t n gi tr Rb. ng sut trong nhng ct thp xa trc trung ho c th t n Rs (ko) hoc Rsc (nn), trong khi nhng ct thp gn trc trung ho ng sut b hn.



- Tu theo quan im tnh ton m cc tiu chun cc nc a ra cc cch tnh ng sut trong thanh thp i khc nhau.

1.4. ng sut trong ct thp: 1.4.1 Theo quan im ng sut: a) Vi ct thp chu ko (hoc chu nn t hn) As: Tiu chun TCXDVN 356:2005 a ra

cng thc thc nghim xc nh s:

s = sR

Rhx

11

/12 0

; trong R

l h s thc nghim. Cng thc ny dng cho b tng c cp

bng hoc nh hn B30, ct thp nhm CI, AI, CII, AII, CIII, AIII (Rs 400) v chp nhn khi x ho. Khi x > ho th ly s = -Rs.

Tc gi Nguyn nh Cng [5], xut cng thc dng trong trng hp Rh0 x h v Rs 400 nh sau:

s = sR

R Rhhhx

0

0 )(21 ;

b) Vi ct thp chu nn nhiu hn As: iu kin 's t n Rsc l: x 1a

Phn tch kt qu thc nghim thy rng 1 ph thuc vo Rsc v thay i trong khong 1,52 (1 tng khi Rsc tng). n gin ho, chp nhn gi tr 1 = 2 cho mi loi ct thp (vi Rsc 400Mpa)

1.4.2 Theo quan im bin dng: Xut pht t bin dng ca b tng ti mp vng

nn c quy nh, dng gi thit tit din phng, khi bit v tr trc trung ha (bit x0) v v tr ca thanh hoc hng ct thp th i (h0i) s tnh ra c bin dng ca n l i (xem hnh 1.5)

sA'As

o

bD s' A's

sAs

x

N

a'

h

h

4A43A32A21A1

c4

321

0x

04

03

02

h

h

h

h01

N

sA A's

Hnh 1.5. ng sut trong ct thp i c tnh theo bin dng i.

Hnh 1.4. ng sut trong ct thp i v i



i = coi xxh

0

0

Khi i T th i = Rs

i < T th i = iRs , vi T = s

s

ER

Vi ct thp chu ko: iu kin i = Rs l:

x ih0i (Vi i = iT, T =

s

sc

c

ER

)

i vi ct thp chu nn: iu kin 'i = Rsc l:

x 2h0i (Vi 2 =

s

scc

c

ER

)

1.5. Cc trng hp tnh ton nn lch tm T phn tch cc trng hp nn lch tm, ngi ta a ra cc trng hp

tnh ton. Trong vic ny cng c nhng quan im khc nhau. Mt s nc u M phn chia ra hai trng hp da vo vng chu nn:

tit din chu nn ton b v tit din chu nn mt phn. Tiu chun thit k ca Nga, Trung Quc, Vit Nam phn chia ra hai trng

hp: nn lch tm ln v nn lch tm b da vo s lm vic ca ct thp As, cng tc l da vo gi tr ca chiu cao vng nn x.

Khi x < Rh0: ct thp As chu ko, ng sut s t ti Rs, xy ra ph hoi do trng hp nn lch tm ln.

Khi x Rh0: ct thp As c th chu nn hoc ko m ng sut trong n cha t n Rs hoc Rsc, s ph hoi bt u t b tng vng nn (ph hoi gin) trng hp nn lch tm b.

Tit din lm vic theo trng hp no l ph thuc vo tng quan gia M, N vi kch thc tit din v s b tr ct thp. Khi M tng i ln, tit din lm vic gn vi trng hp chu un, c vng nn v vng ko r rt. Nu ct thp chu ko As khng qu ln th s ph hoi s bt u t vng ko, ta c trng hp nn lch tm ln. Ngc li, khi N tng i ln, phn ln tit din chu nn, s ph hoi bt u t b tng pha b nn nhiu, c trng hp nn lch tm b.

Tuy nhin, trong tnh ton thc hnh, iu kin phn bit cc trng hp nn lch tm ch l tng i. C mt s trng hp, vi tit din v im t



lc N cho, khi thay i ct thp c th chuyn s lm vic ca tit din t nn lch tm ln sang nn lch tm b v ngc li. Khi chuyn nh vy th gi tr lc dc ti hn m tit din chu c Ngh thay i theo.

1.6. Theo tiu chun Vit Nam TCXDVN 356:2005 [2] Theo tiu chun TCXDVN 356:2005 [2], vic tnh ton tit din tng qut

cn kim tra t iu kin:

M (RbSb - siSsi) Trong : - M: mmen trong cu kin chu nn lch tm, l mmen do lc dc N i

vi trc song song vi ng thng gii hn vng chu nn v i qua trng tm tit din cc thanh ct thp dc chu ko nhiu nht hoc chu nn t nht khi cu kin chu nn lch tm.

- Sb: mmen tnh ca tit din vng b tng chu nn i vi trc - Ssi: mmen tnh ca din tch thanh ct thp dc th i i vi trc

- si: ng sut trong thanh ct thp dc th i

Chiu cao vng chu nn x v ng sut si c xc nh t vic gii ng thi cc phng trnh:

RbAb - siAsi N = 0

si =

1

1.11

,

i

usc

ng sut si km theo du c tnh ton theo cc cng thc trn, khi a vo tnh ton cn tho mn iu kin:

Rsi si Rsci (Rsci: mang du m) Ngoi ra, xc nh v tr bin vng chu nn khi ung xin, phi tun theo

iu kin b sung v s song song ca mt phng tc dng ca mmen do ni lc v ngoi lc, cn khi nn v ko lch tm xin, phi tun th thm iu kin: cc im t ca ngoi lc tc dng dc trc, ca hp lc nn trong b tng v ct thp chu nn, v ca hp lc trong ct thp chu ko (hoc ngoi lc tc dng dc trc, hp lc nn trong b tng v hp lc trong ton b ct thp) phi nm trn mt ng thng (Hnh 1.6).

Vi: - Asi: din tch tit din thanh ct thp dc th i



- i: chiu cao tng i vng chu nn ca b tng, i = ih

x0

, trong h0i

l khong cch t trng tm ct thp th i n trc i qua im xa nht ca vng chu nn song song vi ng thng gii hn vng chu nn (Hnh 1.6).

- : t trng vng b tng chu nn, c xc nh theo cng thc:

= - 0.008Rb ( = 0.85 i vi vi b tng nng) - ch s i l s th t ca thanh ct thp ang xt (i = 1,2,...,n).

R

As5 s5 As6 s6

As7 s7

As4 s4

As8 s8Ab b

As3 s3

As2 s2s1s1A

C

B

A

I

I

05

06

07

04

08

03

02

hh

hh

hh

h

01h

56

74

8

3

2

1

Hnh 1.6. S ni lc v biu ng sut trn tit din thng gc vi trc dc

cu kin b tng ct thp trong trng hp tng qut tnh ton tit din theo bn (Trong :

I-I: l mt phng song song vi mt phng tc dng ca mmen un, hoc mt phng i qua im t ca lc dc v hp ca cc ni lc ko, nn

A: im t hp lc trong ct thp chu nn v trong b tng vng chu nn B: im t ca hp lc trong ct thp chu ko C: im t ngoi lc)

1.7. Theo tiu chun Vit Nam TCVN 5574-1991 [1] Tiu chun Vit Nam TCVN 5574-1991 [1] chia ra 2 trng hp lch tm

tnh ton. - Trng hp lch tm ln:

+ iu kin lch tm ln: khi chiu cao vng nn x 0h0B (Vi 0 = 0.4 0.62 ph thuc cng tnh ton v ko ca ct thp v mc chu nn ca b tng nng)



+ Cu kin c tnh ton theo 2 iu kin: M RnFbZb + aiZaifai - aiZaifai

RnFb + aifai - aifai N = 0 Vi M l mmen ca lc dc t lch tm N ly i vi trc bin, trc ny

song song vi ng thng gii hn vng nn v i qua trng tm ct thp chu ko xa nht.

Ngoi 2 iu kin trn th vic b tr ct thp, hnh dng v kch thc hnh vng b tng chu nn c xc lp t iu kin sau: im t lc dc lch tm N, im t hp lc vng nn v im t hp lc ct thp vng ko phi nm trn mt ng thng - Cc im N, B, A trn hnh 1.7 (Ging TCXDVN 356:2005).

fai

aif '

ai

bZ

11

aiA

B

N

Z' h

Zx

0B

t't

ii

Trc bin

Hnh 1.7. S tnh ton ct chu nn xin (TCVN 5574-1991).

Trong :

0: tng t khi tnh cu kin chu un phng, c tra bng ph thuc vo mc b tng v cng tnh ton v ko ca ct thp.

h0B: khong cch t im xa nht ca vng ko n trc bin Zb: khong cch t trng tm din tch vng b tng chu lc nn Fb n

trc bin Zai v Zai: khong cch t ct thp chu ko v chu nn th i n trc

bin

ng sut trong ct thp chu ko ai v trong ct thp chu nn ai ly ph thuc khong cch ti, ti tnh t trng tm ca mi ct thp n ng thng gii hn ca vng nn.

Vi ct thp chu ko:

+ Khi ti 0.6(h0B x) th ai = Ra

+ Khi ti 0.6(h0B x) th ai = aBi R

xht

'06.0



Vi ct thp chu nn:

+ Khi ti 0.6x th ai = Ra

+ Khi ti 0.6x th ai = ai Rxt

'6.0'

- Trng hp lch tm b: Cu kin chu nn lch tm xin trng hp lch tm b vi tit din c 2

trc i xng x v y c tnh ton kim tra theo iu kin:

N

0

1111

NNN yx

Trong : N: lc dc tnh ton khi tng hp tt c cc yu t tc ng Nx, Ny: kh nng chu lc ca tit din khi xt ring v nn lch tm trong

phng x v y (nn lch tm phng) N0: kh nng chu lc khi nn ng tm 1.8. Theo tiu chun Anh BS 8110-1997 [9] (Tnh ton theo trng thi gii hn ca bin dng)

fcu0.67 m

m5,5 cu

f

ng cong parabolic

fcu2,4.10 m

-4 0,0035 Bin dng

ng

su

t

Ghi ch 1: 0.67 l h s tnh n quan h gia bn khi vung v bn khi

un trong cu kin chu un. H s ny cha c h s an ton ring.

Ghi ch 2: fcu: bn khi vung tnh bng N/mm2, m: h s an ton ring. Hnh 1.8. ng cong ng sut bin dng ngn hn dng cho thit k i vi b

tng thng thng.



xc nh kh nng chu lc ca tit din, phi s dng gi thit sau y: + S phn b ca bin dng trong vng b tng chu nn v bin dng

trong ct thp chu ko hoc nn c xc nh t gi thit tit din phng

+ ng sut trong b tng khi nn c th xc nh t ng cong ng sut bin dng trn hnh 1.8 vi h s an ton ring i vi bn ca vt liu m = 1.5

+ bn ca b tng chu ko c b qua + ng sut trong ct thp xc nh t ng cong ng sut bin dng

trn hnh 4 vi h s an ton ring i vi bn ca vt liu m = 1.05

T cc gi thit trn, ta tnh c bin dng ca tit din, t bin dng ta xc nh c ng sut trong ct thp v b tng.

myf

ng

su

t

Bin dang

Nen

Keo

2

fym

200 kN/mm

Ghi ch: fy tnh bng N/mm2 Hnh 1.9. ng cong ng sut bin dng

ngn hn dng cho thit k i vi ct thp

Trong tiu chun Anh BS 8110-1997 [9] c a ra cch tnh gn ng nh sau:

- Tnh ton theo un phng, b tr thp vi mmen tng thm:

+ Khi 'h

M x 'b

M y tnh ct thp theo

Mx = Mx + yMbh''

Mx

yM

y

y

xxh'h

b'

b

Hnh 1.10. Ct chu un theo 2 phng



+ Khi 'h

M x 0.4 th = 100000

400003.1 '

y

gc

u fAf

P 0.5

Trong : Pu: lc dc tnh ton, lb Mu: mmen un tnh ton, lb.in ex, ey, e0x: lch tm ca lc dc, in fc: bn nn ca b tng, psi fy: gii hn chy ca ct thp, psi Ag: din tch ca ton b tit din, in2 x,y: kch thc cc cnh ca tit din ch nht, in

- Nu phng trnh x

ex y

e y khng tho mn cc gi tr x v y, ex v ey

trong biu thc (*) c thay th cho nhau tng ng. Quy trnh ny ch c dng trong trng hp tit din ct i xng theo

hai phng v t l kch thc ca tit din yx nm trong khong t 0.52.0. Ct

thp dc trong ct b tr trn c 4 mt ct.

1.9.2 Phng php ng bao ti trng:

nynxnP - M -MMt cong tung tc

ng bao ti trngMx0

My0nMt phng P

nP

(b)

(c)

(a)

y

xM

M

P

Hnh 1.12. Mt cong tng tc Pn Mnx Mny v im mmen tnh ton

Quy trnh ny dng phng php ng bao ti trng tnh ton ct chu nn lch tm xin. Theo , mt phng trung gian lm thnh mt gc vi mt phng POMx, ct mt cong tng tc Pn Mnx Mny ti ng cong (c). Mt



phng l mt phng ph hoi v (c) l ng ph hoi i vi ct chu nn ng thi vi mmen un.

= arctgy

x

ee = arctg

nx

ny

MM

ng bao ti trng l ng to thnh giao din gia mt phng Mnx Mny ti cao Pn v mt cong tng tc. Khi , phng trnh tng tc ca ng bao ti trng nh sau:

12

0

1

0

ny

ny

nx

nx

MM

MM

Trong : Mnx = Pney (un phng) v Mnx0 = Mnx khi Mny = 0 (nn lch tm phng) Mny = Pnex (un phng) v Mny0 = Mny khi Mnx = 0 (nn lch tm phng)

Gi tr 1 v 2 ph thuc vo kch thc ct, ng knh v s phn b ct thp ct, c trng ng sut bin dng ca vt liu thp v b tng, chiu dy lp b tng bo v, kch c v loi ct thp ai.

Khi 1 = 2 = , phng trnh trn c vit thnh:

100

ny

ny

nx

nx

MM

MM

Theo cc kt qu nghin cu ca Bresler, gi tr = 1.15 1.55 i vi tit din ch nht, gi tr cng gn vi gi tr thp th cng an ton.

1.9.3 Phng php dng phng trnh tng tc Bresler: bn ca ct chu nn lch tm xin c th tnh ton v kim tra theo

phng trnh:

0

1111

nnynxu PPPP

Trong : Pu: lc dc tnh ton

Pnx: bn thit k theo lc nn dc trc tng ng vi lch tm ex (vi ey = 0)

Pny: bn thit k theo lc nn dc trc tng ng vi lch tm ey (vi ex = 0)



Pn0: bn thit k theo lc nn dc trc tng ng vi lch tm ey = 0 v lch tm ey = 0

Phng trnh ny cng tng t nh tnh ton i vi cu kin lch tm b trong TCVN 5574-1991, v tiu chun Trung Quc GB 50010-2002.

1.10. Theo tiu chun c AS 3600-2001 [11] Tiu chun c AS 3600-2001 [11] cng dng phng php ng bao ti

trng tnh ton v kim tra cho ct chu nn lch tm xin (tng t nh trong ACI 318-99).

Phng trnh tng tc:

0.1**

nn

uy

y

ux

x

MM

MM

Trong :

*xM , *yM : mmen un tnh ton tch ring theo tng trc x,y

Mux, Muy: kh nng chu mmen un ca ct quanh trc X v Y vi lc nn N v c tnh ton ring bit.

n: h s ph thuc ti trng tc dng dc trc, kch thc ct, t l phn trm ct thp, quan h ng sut bin dng ca thp v b tng.

Theo AS 3600-2001, n c xc nh nh sau:

n = 0.7 + 1.70

*

6.0 uNN

v phi nm trong gii hn: 1 n 2 (so vi ACI 318-99 th = 1.15 1.55)

Vi N* l lc tc dng ln ct v Nu0 l kh nng chu nn ng tm ca ct Theo AS 3600-2001, cc trng hp sau ct chu nn lch tm c tnh

theo lch tm theo mt phng khi im t lc dc ri vo vng gii hn bi cc ng nh hnh v - vng gch cho (hnh 1.13):

Vng khng phi tnh ton lch tm xin

Vng phi tnh ton lch tm xin

0,1D

0,1b

0,2b

0,2D b

D

Hnh 1.13. Xc nh vng gii hn khng phi tnh ton lch tm xin



1.11. Theo tiu chun GB 50010-2002 ca Trung Quc [12]

iye

iye

y

y

1

2 : Khu vc chu p lc nn: im t lc

2

1a x

0h

ay 0b

bx

h

y

xO

Cu kin chu nn lch tm theo 2 hng vung gc nhau theo trc i

xng. Kh nng chu lc ca cu kin c tnh theo 2 cng thc di y: 1). Theo phng php tnh ton ca ph lc F, th lc ny Mx, My trong

cng thc F.0.1-7 v F.0.1-8 c thay th bi ln lt Nxeix v Nyeiy. Trong khong cch lch tm ban u c tnh nh sau:

eix = e0x + eax eiy = e0y + eay Trong cng thc trn, e0x, e0y l cc khong cch lch tm theo trc x, trc y

ca p lc quanh trc i i vi trng tm ca mt ct, c tnh nh sau:

e0x = NM x0 ; e0y = N

M y0

M0x, M0y l gi tr thit k ca m men un ca p lc quanh trc trn 2 trc x v y khi cha tnh n m men un ph thm.

eax, eay: khong cch lch tm ph thm trn 2 hng trc x v trc y, ly gi tr ln hn ca 2 gi tr 20mm v 1/30 kch thc tit din ln lt theo phng y, x.

x, y: h s khuch i (un dc) ca khong cch lch tm trn 2 hng trc x v trc y.

Di y l ni dung ca ph lc F:



(c)(b)(a)

sj A sjpkApk

fc

h 01

slsj

pku

ci

cuc

Or

ciA

Apk

sjA

y

x

Hnh 1.14: Cch tnh ton kh nng chu lc ca cu kin c tit din tu . (a) Tit din chu lc; (b) S phn b bin dng; (c) Phn b ng sut

Kh nng chu lc ca tit din c tnh ton da theo cc cng thc sau y:

l

i

m

j

n

kpkpksjsjcici AAAN

1 1 1 (F.0.1-6)

l

i

m

j

n

kpkpkpksjsjsjcicicix xAxAxAM

1 1 1 (F.0.1-7)

pk

l

i

m

j

n

kpkpksjsjsjciciciy yAyAyAM

1 1 1

(F.0.1-8)

N: gi tr thit k ca lc nn Mx, My: m men un theo phng x v phng y Cc ch s ci, si, pk ln lt dng cho cc phn t n v ca b tng th i,

ct thp thng th i v ct thp ng sut trc th k. A: din tch n v 2). Di y l cng thc tnh tng t:

0

1111

uuyux NNN

N

Trong : Nu0: gi tr thit k ca p lc ti tm trc ca mt ct cu kin (gi tr thit

k ca p lc nn ng tm) Nux: gi tr thit k ca lc nn lch tm quanh trc x, c tnh trn ton b

ct thp dc sau khi tnh n xeix, x tnh theo cc cng thc sau:

212

0

0/140011

hl

hei



N

Afc5,01

hl0

2 01,015,1

Nuy: tng t theo phng y. Gi tr thit k Nu0 (p lc ti tm trc ca mt ct cu kin) c th dng

cng thc mc 7.3.1 { 0,9N(fcA+fyAy) } nhng thay bng du = , N c thay th bi Nu0 v khng tnh n h s n nh v h s 0,9.

1.12. Cc nghin cu khc v ct chu nn lch tm xin [5] Gs. Ts. Nguyn nh Cng trng i hc Xy dng c rt nhiu

nghin cu v tnh ton cu kin chu nn lch tm xin. Trong nhng nm qua, Gs. Ts. Nguyn nh Cng cng hng dn nhiu hc vin lm lun vn cao hc v vn ny.

Lun vn thc s ca Phm Th Hu (do Gs. Nguyn nh Cng v Pgs. V Vn Tho hng dn) da vo TCVN 5574-1991 kt hp vi lp trnh a ra bi ton kim tra cu kin chu nn lch tm xin.

Lun vn thc s ca Nguyn Danh Thng (do Pgs. Bi Quang Trng hng dn) xy dng ng cong tng tc ca cu kin chu un xin da trn gi thit tit din phng.

Lun vn thc s ca L Hong Sn (do Gs. Nguyn nh Cng hng dn) kt hp vi lp trnh xy dng ng cong tng tc theo tiu chun Vit Nam TCXDVN 356:2005, xy dng v kim tra cc cng thc gn ng tnh ton cu kin nn lch tm xin.

1.13. V lun vn thc s ca tc gi L Hong Sn [13] Tm tt ni dung lun vn: - Nghin cu xy dng mt biu tng tc theo tiu chun Vit Nam

TCXDVN 356:2005. Xy dng chng trnh tnh theo 5 dng vng nn, v ng gii hn vng nn c xc nh bi ng thng y = kx+ v v tr ca ng gii hn vng nn c xc nh theo 2 bin k v

- Lp chng trnh my tnh xy dng mt biu tng tc - Xy dng cng thc gn ng tnh ct thp b tr u theo chu vi

bng cch tham kho cc cng thc tnh gn ng trong tiu chun Anh, M v ph hp vi tiu chun xy dng Vit Nam TCXDVN 356:2005.



- So snh v nh gi cng thc gn ng v a ra cc nhn xt v h s k trong cc cng thc gn ng.

1.14. Cng thc gn ng tnh ton cu kin BTCT chu nn lch tm xin [5], [13], [14]

Phng php gn ng da trn vic bin i trng hp nn lch tm xin thnh nn lch tm phng tng ng tnh ct thp. Nguyn tc ca phng php ny c trnh by trong tiu chun thit k ca nc Anh BS:8110 v ca M ACI:318, da vo nguyn tc lp ra cc cng thc v iu kin tnh ton ph hp vi tiu chun Vit Nam TCXDVN 356:2005.

Xt tit din c cnh Cx, Cy. iu kin p dng phng php gn ng

l: 0.5y

x

CC

2, ct thp c t theo chu vi, phn b u hoc mt ct thp

trn cnh b c th ln hn (cnh b c gii thch bng v m hnh tnh).

Ooxe

eoy

Cx

Cy

y

x

My

xM

Tit din chu lc nn N, moment un Mx, My, lch tm ngu nhin eax,

eay. Sau khi xt un dc theo hai phng, tnh c h s x, y. Moment gia tng Mx1; My1.

Mx1= ye0yN ; My1= xe0xN

Ty theo tng quan gia hai gi tr Mx1, My1 vi kch thc cc cnh m a v mt trong hai m hnh tnh ton (theo phng x hoc y). iu kin v k hiu theo bng sau:

Hnh 1.15: S tnh ton ct chu nn lch tm xin



M hnh Theo phng Mx Theo phng My

iu kin y

x

CM 1 >

x

y

CM 1

x

y

CM 1 >

y

x

CM 1

K hiu h=Cy; b=Cx

M1= Mx1; M2= My1 ea= eax+0.2eay

h= Cx; b= Cy M1= My1; M2= Mx1

ea= eay+0.2eax

Gi thit chiu dy lp m a, tnh h0= ha; Z = h2a; chun b cc s liu Rb; Rs; Rs; R nh i vi trng hp nn lch tm phng.

Tin hnh tnh ton theo trng hp t ct thp i xng:

x1 = bRNb

H s chuyn i m0

Khi:

x1 h th m0 = 1 hx7,0

x1 > h th m0 = 0.3

Tnh mmen tng ng (i nn lch tm xin ra nn lch tm phng)

M= M1+ m0M2bh

lch tm:

e1= NM ; e0= e1+ea

e= e0+ 2h a

Tnh ton mnh theo hai phng:

x=x

x

il0 ; y=

y

y

il0

= max(x;y)

Da vo lch tm e0 v gi tr x1 phn bit cc trng hp tnh ton.

a) Trng hp 1: Nn lch tm rt b khi =0

0

he

0.3, tnh ton gn nh



nn ng tm.

H s nh hng lch tm

e = )2)(5.0(1

H s un dc ph thm khi xt nn ng tm:

e = + 3.0)1(

Khi 14 ly = 1

Khi 14 < < 104 ly theo cng thc sau:

= 1.028 0.00002882 0.0016

Din tch ton b ct thp dc As:

Ast bs

be

RR

bhRN

Ct thp c chn t u theo chu vi (mt ct thp trn cnh b c th ln hn).

b) Trng hp 2: Khi x1> Rh, tnh ton theo trng hp nn lch tm b.

Ta phi lp chng trnh xc nh chiu cao vng nn x.

T 2 iu kin cn bng, kt hp vi phng trnh tnh s i vi b tng c cp bn B30, ct thp Rs 365 MPa, ta c phng trnh bc 3 xc nh x.

x3 + a2x2 + a1x + a0 = 0

Trong :

a2 = -(2+R)h0

a1 = ZhhbRNe

RRb

020 12

2

a0 =

bRhZeN

b

RR 0)1(2

Gii phng trnh bc 3 tm x, theo [14], nu tnh ra c x > h0 c ngha l s = -Rs

Khi tnh li x bng cch gii h gm 3 phng trnh (gm 2 phng trnh cn bng v phng trnh s = -Rs), tm c:



x =

e

bRNhhb

8

21 2 vi iu kin h0 < x h

Din tch ct thp As tnh theo cng thc:

Ast= zkR

xhbxRNe

sc

b )2( 0

H s k < 0.5 l h s xt n vn t ct thp phn b theo chu vi cho ton b tit din. Quy nh ly k=0.4.

c) Trng hp 3: Khi x1 Rh0, tnh ton theo trng hp nn lch tm ln.

Khi 2a x1 Rh0, ly x = x1 v tnh As theo cng thc sau:

Ast = ZkR

xhbxRNe

sc

b

20

Trng hp Rs = Rsc, dng cng thc:

Ast= ZkRhxeN

s

)5.0( 01

Khi xy ra x1 < 2a, gi thit tnh x1 l khng ng, khng th dng gi tr x1, s dng cng thc:

Ast = ZkRZeN

ZkRNe

ss

)('

Ct thp c t theo chu vi, trong ct thp t theo cnh b c mt ln hn hoc bng mt theo cnh h.

1.15. Cc yu cu t ra i vi vn tnh ton cu kin BTCT chu

nn lch tm xin: - Phi c s kim tra li i vi chng trnh xy dng mt biu tng

tc. Trong ti lun vn ny, ng li kim tra l cng xy dng mt biu tng tc nhng i theo mt hng khc trong vic nh ra cc bin t xc nh vng chu nn.

- Xy dng s khi chng trnh tnh gn ng ct thp c th p dng trong tnh ton thc hnh, t c th xy dng c mt chng trnh my tnh mang tnh ng dng cao hn (c th tnh gn ng ct thp v sau c th kim tra li ct thp b tr bng cc biu tng tc c v ra bi chng trnh my tnh).



- Mt s xut gp v cc h s hiu chnh trong cng thc gn ng c th p dng trong thc t tnh ton cu kin b tng ct thp chu nn lch tm xin.

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163440776 Cot Lech Tam Xien