Danh gia do tin cay ket cau khung be tong cot thep vo'i tham so dau vao khong chac chan dang khoang (Reliability assessment of the reinforced concrete frame with uncertain input paramaters formed interval numbers)
Ngay nhan bai: 25/12/2015 Ngay sij-a bai: 20/02/2016 Ngay chap nhan dang: 12/03/2016
TOIHTAT
Do tin c^y ciia k^t cSu la van de dac biet dtldc quan tam trong cong tac tiiiet ke tinh toan ket cau c6ng trinli. Noi dung bai bao lien quan den hai noi dung cua m o hinh danh gia do tin cay, do la p h a n tich trang thai ket c§[u v^ d a n h gid d6 tin c | y cua ket can khung be tong cot thep troiig tritdng h o p xet d f o tinh kli6ng chac chan ciia cac so tham so dau vao diicii dang so khoang la tai trong tac dung va dac triing vat lieu.
ABSTRACT
The rehabihty of structures is a problem particularly interested in design work building structure. Contents of the article relating to the two contents of assessment reliability model, which is analyzing the state of structure and evaluate the reliability of the reinforced concrete frame structure in the case of considering the uncertainty of the number of input parameters formed interval numbers as the static load and character of material Key words: Inetrval numbers, Interval analysis. Interval rehability of structures.
Reliability of structures. Structural system.
TS.Le Cong Duy
Khoa Xay difng - DEU Hoc Duy Tan KS.Nguy^n Xuan Hoang
Hoc vien cao hoc KIO - Dai Hoc Duy TSn
1 . Dat van 3e.
Trong tinh toan ket cau thifdng gap nhClng dai laong dau vao thuoc ve ket cau va tac dong ham chiJa cac thong t i n ngau nhi^n, khong ro rang, cac dai lifong do diJoc gpi la cac dai luong khong chac chan. TCJ trUdc Sen nay ta t h a d n g tinh toan ket cau cong trinh theo iJng suat cho phep va theo trang thai gi6i han. Tinh toan theo cac phitong phap nay chUa phan anh dUoc toan di&n sU lam viec ciia ket cau va chu^ ke den sU cinh hUdng cCia cac yeu t o mang tinh chat ngau nhien. mang tinh khfing ro rang hay noi each k h i c la chUa k^
d^n cac y^u t d mang tinh ch^t kh6ng ch3c chan t&c dflng d^n ket c^u, cho nen nhieu tru&ng hop trong thuc te cong trinh van x i y ra h u hong mac d i i khi tinh toan ket cau cong trinh v6i he so an toan tUUng doi I6n.
De m o ta nhuing dai lUOng khong chac chan, ngU6i ta djjng so khoang, dai lUOng ngau nhien, so mcf, dai luong ngau nhien-md.
NhQng dai lu'ong khong chac chan dUoc bieu d i l n du'di dang dai luong ngau nhien dUoc tinh toan theo mo hinh n g i u nhien. Phan tich danh gia ket cau theo m o hinh ngau nhien bang ly thuyet do tin cay da co nhi^u nghiSn cu'u. Trong trUdng hop cac dai luong khong chac chan mo ta du6i dang so k h o i n g , viec phan tich danh gia phai thUc hien theo m o hinh k h o i n g . M6 hinh nay trong iinh vUc xay dung da cd nhu'ng ket quS bUdc dau nghien cilu. Tuy vay, do tinh chat va hinh thiJc m d t i dai ludng khong chac chan rat g^n v6i thUc t ^ nen hien nay m o hlnh nay duoc cac nha nghien ciJu quan tam phat trien. Noi d u n g bai bao lien quan den hai noi dung ciDa m o hinh nay, do la phan tfch trang thai ket cau va d i n h gia dd t i n cay cua ket cau trong trudng hc(p m o t so dai lUOng khong chac chan 6 dau vao cLia bai toan dupc m o ta du6i dang cac sd khoang.
SI g S^
I 1 r Qi—
Le Cong Duy, Nguyin Xuan Hoang
2. Cong thuTc d a n h gia.
2.1. Salvtdc vesokhodng IWdt khoang thi/c la m o t t i p hop khong r6ng CLiacacsdthUc:
X = [ X , X ] = { X E R | X < X < X }
trong do x va x la c i n dUdi va can tr^n cua k h o i n g x , x ia m d t phan trong khoangx, Ria tap so thuc.
Bon phep t i n h cO ban cua s6 thiTc la (+,- ,x,-^) CO the m d rdng cho cac so k h o i n g . Mat phep tinh bat ky oe(+,-'X,-^) tren cac khoang duoc dinh nghia n h u sau:
x o y = { x o y | x e x , y e y }
Tap hpp cac ket qua cua phep,,toin doi vd!
X£ X va y e y tao thanh m o t k h o i n g ddng [ neu 0 khong nam dudi mau sd) vdi cac can cua cac khoang dUPcxac d m h n h u sau:
X o y = [min(xo y), max(xo y )] vdi oe(+,- ,X,-r).
C i n dudi v i c i n tr6n cda phep toan x o y dUOc xac dinh tCl bori cap sd x o y , x o y , x o y , x o y .
2.2. Cdng thurc"Ty so khodng"
Cong thilc danh gia do t m cay" T f so' khoang" da du'pc trinh bay chi tiet trong [l].' Cdng thilc dupc thiet lap de d i n h gia do tin c i y cua t d n g phan t i l va cho c i h& ket cau trong trUdng hop cac t h a m so cila b i i toan danh gia la cac t h a m so k h o i n g . Tren cO sd so sanh tap trang thai cua ket cau 5 vdi tap k h i nang cila ket c i u R, dp t i n cay khoang cila phan t i l ket c i u dupc xac dinh b i n g each xet tap M, = R|-S, la tap khoang an toan. Tiiy thudc vao khoang gia tri cila cac tap so khoang R|Va Q, cd Xhi x i y ra ba trUdng hop n h u tren Hinh 1
Hinh ^. Cdc tri/dng hdp tap khoang an toan M,
6S|I
Trong 66: - Ivlu = min(Riu- Siu, Rig- S,i, Rir Si„, Ru- Sii).
- Mm = niax(R™- 5 „ , fii„- Sii, Ri- S™, Ru- &i).
Trgn Hinh 1 a ta cd sfi khoang cila t i p M, nhm h o i n toan ben t r i i tmc tung nen do Widng tin cay cCia nd l i Pi=1 hay d6 tin cay P(=0
Tren Hinh l b so k h o i n g ciia tap IWl, nSm hoan toSn ben p h i i true t u n g nen do khdng tin cay cua no la P(=0 hay do tin cay Pi =1
Trifdng h o p t o n g q u i t nhif Hinh I c , s6 khoang cila t i p M, c6 mot phan ben t r i i va mdt p h i n bSn phai true t u n g , do khong tin cay cua ket cau dupc x i c dinh:
0 - M „ _ |M„|
M . - M , i M „ , - M , , (1)
Dp tin c^y Pi cda p h i n t i i b i n g x i c s u i t khdng hdng cda p h i n tCr diiOc tinh theo cdng thilc:
M, - M , ,
= 1 n h u trong dinh nghia dd tin c i y theo md hinh Ta t h a y :
ngau nhien.
Sau khi x i c dinh duBc do tin cay cae phan cua he ket c i u ta co t h ^ xac djnh dd tin c i y cCia he ket cau theo khoing nhif cdng thde sau:
f J P ^ ^ P , 5mln(PJ,P,^...,P;) = P > !3) 3. Qng dung danh gi^ do tin cay cho ket cau khung phang be tdng cot th^p
3.1.Bdt bdi todn:
IVldt k i t cau khung phltng chju t i i trong n h u hinh 2. Dam duoc bo tri h i m luong cdt thep gidng nhau 6 tai g 6 i v a nhip vdi m a t c S t l - 1 v i 2 - 2 n h u dudi. Cdt thep cot dupc bd tri n h u c i c mat c i t 3-3 va 4-4 . Cac thanh co cCing cap dd ben B20, cac dai luong kich thudc tiet dien tfch la cac sd t d , c^c dai lUOng md dun d i n hdi E , tai trpng p , q la c i c sd k h o i n g vdi cac g i i tri c i n dudi va can tr^n cila cac dai luong duoc cho n h u ben dUdi. Bii t o i n yeu cau xac dinh ndi lUc v i danh gia d d tin c i y cila ket cau theo dieu ki&n ve dp ben.
H = 3.6 m = 360 cm; I = 5.4 m = 540 cm;
C = b . x h c = 2 0 x 2 5 c m ; D = bdXhd = 2 0 x 5 0 c m ; q = (qL, qH) = (o.l 8,0.22) k N / c m , p = {pL, pu) = (22.5, 27.5) k N ;
E HB-, E^=(2385,2.915)10' kN/cm'- md dun d i n hdi cila be tdng Rb = (Rh"-, Rb") = (1.035,1.265) k N / c m ' - cUdng do nen be t d n g ; R, =(R,'-,R,^) .28) kN/cm^- cudng dd chju k^o cdt thep;
HHIIQJ rra im.
Hlnh 2. Sadd kit clu iihung phSng
3.2. Phdn tich ket cdu theo phifiOig phdp PTHH khodng[2]
Danh sd phan tCf ket cSu va so chuydn vj ndt nhU hinh 3.
Qua trinh phan tich k^t c i u khung theo phUdng phap phan tCr hCru han cd tham sd k h o i n g dUdc lap trong phan mem IWaple 13 theo thuat g i i i trong [2], xac dinh dupc ket qua c h u y i n vi tai cac nilt cda he ket cau n h u B i n g 1,
9 a , .
=^ G )
Qy
? > ' •
•y cs
9 [
o "
Ce)
a>
,,^y ®
? 1 0? = • '
^.y (S>
Q.
O"
o ^ HinhB.SddDphantifketdukh
Bang 1 .K^t q u i tinh toan chuyen vi nilt he ket cau khung.
Chuyen vi k h o i n g P i
^ i q , (xoay)
^ 4
^s q j (xoay)
^ 7 qa q , (xoay) qio
^11 q,! (xoay)
G i i t n chuyen vi k h o i n g (cm).
q^CandUdi) 0 9972 -0.0281 -0.0026 0.9971 -0.0453 -0.0001 1.7698 -0.0437 -0.0024 1.7661 -0.0662 0.0009
q'^fTrunq tam) 1 2189 -0.0216 -0.0021 1,2187 -0.0371 0.0003 2,1631 -0.0339 -0.0020 2.1588 -0.0541 0.0011
q''(Can tr§n) 1.4899 -0.0163 -0.0017 1.4895 -0.0303 0.0006 2,6438 -0.0259 -0.0016 2.6387 -0.0443 0.0015 Bang 2.Ket qua noi lUC cda phan t i l dam khung
Phan t i l D i m 3 Dam 6
Momen Idn nhat tronq dam M (kN.cm) [11391.222,13922.605]
[9368.535,11450.432]
Banq 3,Ket qua ndi lUc cila phan t i l cdt khunq Phin t i l
C d t l Cdt 2 Cdt 4 Cdt 5
Ndi lUc chan cdt dang khoang IVIdmen M (kN.cm)
[2690 577,3492.145]
[3604.138,4405.057]
[281.729,1015.372]
[3299.614,4032.861]
LUc doc N (kN) [65.821 ,93.127]
[122.873,150.178]
[39.056,51.591]
[56.409,68.944]
Ket q u i c i c chuyen vj cd gia tri am nghia l i cac chuyen vj d d cd chieu chuydn vi ngupc lai vdi chieu qui udc ban dau cila he ket cau.
3.3. Ddnh gid dp tin cdy cho ket cau theo cdng thu'c "T^ so khodng"
3.3.1. Xac dinh ndi lUc c i c p h i n tCfdam cdt cila he ket cau TCr ket q u i tfnh toan chuyen vj ndt, x i c dinh k i t q u i ndi lUc cho cac phan t d d i m , cdt cila ket cau khung dang xet. De d i n h gia do tin cay cho ket cau theo dieu kien ben thi doi vdi phan t i l dam can xac d|nh g i i tri md men Idn n h i t trong dam, con doi vdi phan tif cdt c i n x i c djnh ddng thdi gia tri mo men v i lUc dpc d tiet dien chan cdt cila moi tang Ket q u i npi lUc ciia tilng phan tCf ket c i u khung dUpc the h i f n n h u trong B i n g 2& 3.
69
Trong b i n g tren, g i i tri momen dupc the hien gia trj dUang de de t i n h t o i n , tuy nhien tat c i mdmen nay deu lam c i n g t h d tr&n cila dam(m6men tai g6i).
Trong bSng t r i n , gia trj luc dpc ph^n tif cot duoc t h i hien g i i trj d u o n g de de t i n h t o i n dd tin c i y , tuy nhien cac cdt deu chiu nen(theo qui Udc la g i i tri am).
3,3.2. Xac dinh k h i n i n g chiu lUc c i c phan t d d a m cot cila h i ket cau T i l so lieu dau vao cila ket cau khung vdi tiet dien v i cdt th4p bd t r i trong dam, cdt i p dung cdng thilc tinh toan kha nang chju lUc cCia tiet dien dam, cdt theo cac cdng thilc trong [4].
3.3.2.1. X i c djnh k h i n i n g cda tiet dien phan t i l d i m chju uon Biet kich thudc tiet dien v i c l u tao cda cdt thep trong d i m , xac dinh mo men gidi han cua tiet dien Mqu theo cdng thde trong {4]:
Mgh=RsA^ah„ (4) 7 = 1-0.5-
Rgbh, Trong d d :
- R, cUdng d p ehju keo cila cot thep - A I dien tich tiet dien ngang cot t h e p chju keo - Rb cUdng dp chju nen eila be tdng - b b l rdng cda t i l t dien - h c h i l u cao cda t i ^ t d i § n
• a khoang each t d mep chiu keo eila tiet dien d i n trpng tam cdt t h i p chiu k l o .
3.3.2.1. Xae dinh k h i nang cCia tiet dien phan 111 cot chju nin-uon Bilt kieh thudc tiet dien bxh, c h i l u dai t i n h toan lo v i cSu tao eila cot t h i p trong cdt, xae djnh k h i n i n g chju lUe eua tiet dien [Ne]gh theo cdng thilc trong [4]:
Tinh chieu eao viing nen khi cdt thep dat doi xung trong tiet dien c o t N + R s A . - R ^ A ^
R.b (5)
TrUdng hop 1: khi 2a's x s £,^\ lay x thay v i o cdng thilc (6) de tinh
[Ne]g(,= R „ b x [ h „ - - ] - i - R , , A X (6) TrUdng hop 2: khi x s 2a' tinh [Nelgn theo cdng thde (7):
[Neigh=R,A5Z, (7) TrUdng hop 3: khi ^^h^ s x lilc nay tinh lai x theo edng thilc [8) v i
tinh [Nelah theo cdng thu'c (9):
^ ( N - R ^ A ' J t l - ^ , ) h „ + R , A , ( l - i - i ^ „ ) h „
'^'^ Rbb(1-§„)h„+2R,A, (8)
[Nelsh=R„bx h „ — +R«A,Z, (9)
v6i:Qd=Mna.;Rd=IVIgh
Dp tin cay cua phan t d cot theo dieu k i l n ben:
N e s (Neigh hay Q i S R t ^11) vdi;Qc=Ne;Rc=[Ne]gh
Trong do: -N iUc doc tai tiet d i l n dang xet
-e l i do leeh tam tinh toan x i c dinh theo cdng tfidc trong [4]
Khi c i c tham sd dau v i o cd dang so khoang thi d i l u k i l n ben cila phan t i l dam, cdt cd dang nhU dUdi:
Q , S R . ( " ) D o tin c i y cda phan t d he ket cau n h u trong Bang 4& 5
Bang 4.Ket q u i t i n h do tin cay ph^n tCf dam k i t cau ) Phan t i l
K h i n i n g tiet d i l n R„i (kNcm) [12913,464, 13668.080]
(12913.464, 13668.080]
Trang t h i i tiet d i l n (kNcm) [11391.222, 13922.605]
[9368.535, 11450.432]
Dp tin Ciy theo'TJ^sd k h o i n g "
Trong d d :
- 1 ^ la he so han c h l e h i l u eao vdng nen tra b i n g phu thudc vao cap d d ben cOa be tdng
- RK cudng dp ehiu keo cila cdt thep vting nen - A,c dien tfch t i l t dien ngang cdt thep vung n^n
- a' k h o i n g c i c h t i l mep ehiu n^n cua tiet dien den trong t i m edt t h i p viing nen
- Z i k h o i n g c i c h t d trpng tam cdt t h ^ p vung keo den trpng t i m cdt t h ^ p viing nen
3.3.3. D i n h gia do tin cay eua he ket cau
Oe d i n h gia do tin c i y eua he ket cau, can tinh do tin cay cua tdng p h i n t i l ket cau theo cong thde 'Ty so khoang" va sau dd tinh toan dp tin c i y cho toan bd ket cau theo cdng thde (3),
Dd tin cay cua phan t d dam theo d i l u k i l n ben:
M™,slvigh hay QdSRd (10) B i n q 5.Klt quS t i n h do tin cay p
Phan t d C6t1 Cot 2 Cdt 4 Cdt 5
K h i nang t i l t d i | n R,i (kNcm) [6266,938, 6393,542]
[6266.938, 6393.542]
[5135.851, 5239.605]
[5135.851, 5239.605]
i 3 n cdt k i t cau Trang t h i l t i l t dien
Qj, (kNcm) [3440.2359, 4682.8053]
[5059.2047, 6426.2816]
[609.6471 , 1525.0790]
[3980.4716, 5028.970]
Dp tin c i y theo'T:^sd' k h o i n q "
1.000000 >' 0.893322 1.000000 1.000000 D6 tin cay cOa he ket cau duoc danh gia theo c6ng thilc [3):
n":-
in(P,',P^..,P') = p5n (3)Vay d d tin cay k h o i n g cda he k i t e a u : 0.61898 < P,< 0.692897 4. Ket lu^n chUOng
Bai b i o trinh b i y mdt dng dung tinh t o i n phan tich x i c djnh trang thai ndi lUe eila h& cua k i t c i u khung phSng be tong cdt thep trong trudng hop xet den "tinh khoing" cda c i c tham sd t^i trpng va eda dac truTig v3t lied tren cd sd vSn dung phupng p h i p p h i n t d hdu han khoing. Tif dd i p dyng edng thde 'Ty sd khoing" de danh g i i dp tin c i y cho tdng phSn t i l k i t ciu v i cho e i he ket cau lam cO sd cho vifc d l x u i t g i i i p h i p eii tao va bio ducftig tang eudng kha nang ehiu lUe cho he ket cau.
TAIU|»THAMKHAO
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[3]. Le Xuiin Hu^nh, Le Cong Duy, Bo t i n cay Ciia k^t du khung co tham so dSu v^o dang s^ mb, Tuyen tap cong trinh Hgi nghl cdliacloan quoclan thi) iX, Ha NOI, 12/2012.
[4] Plian Quan Mmh, Ngo The Phong, Nguyen Binh Cong, Ket cau be tong cot t h f p - Phan cau kien CO b^n, Nha xuat ban Khoa hoc va Ky that, 2010.
[51. Bend Moller, Wolfgang Graf, Michael Beer, Safe^ Assesanait of Stnictuie in Ifiew of Fuzzy Randomness. Institute of Stmctural Analsis, [Aesden Universrty ofTedinolDgy, Dresden Gennany,20a3.
[6].Kwan-Ling-Lai, Fuzzy Based Structural Reliabllily Assessment, Strudure Dept, China Engineering Consultants, Inc, Taipei 1990.
[7].Zhipin9 QIU, DI Yang, Isaac Elishakoff, Probabilitisc interval reliability of structural systems.
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