163440776 Cot Lech Tam Xien

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  • 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.

  • Lun vn tt nghip Trang 6 Chng I: Tng quan

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

    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

  • Lun vn tt nghip Trang 7 Chng I: Tng quan

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

    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.

  • Lun vn tt nghip Trang 8 Chng I: Tng quan

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

    - 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

  • Lun vn tt nghip Trang 9 Chng I: Tng quan

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

    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

  • Lun vn tt nghip Trang 10 Chng I: Tng quan

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

    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

  • Lun vn tt nghip Trang 11 Chng I: Tng quan

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

    - 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)

  • Lun vn tt nghip Trang 12 Chng I: Tng quan

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

    + 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

  • Lun vn tt nghip Trang 13 Chng I: Tng quan

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

    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.

  • Lun vn tt nghip Trang 14 Chng I: Tng quan

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

    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

  • Lun vn tt nghip Trang 15 Chng I: Tng quan

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

    + 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

  • Lun vn tt nghip Trang 17 Chng I: Tng quan

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

    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)

  • Lun vn tt nghip Trang 18 Chng I: Tng quan

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

    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 t...