DIEN DAN KHOA HOC CONG NGHE
TINH D O TIN CAY C U A KET C A U GIAN THEP BANG M O P H O N G MONTE-CARLO
CALCULATING RELIABILITY OF STEEL TRUSS STRUCTURES BASED MONTE-CARLO SIMULATION PGS. T S . BUI DUfC NANG - Vifin Ky thuat Cfing trinh flac bigt, Hgc vien KTQS
Email: [email protected] ThS. HOANG VAN AN - Cong ty Cd phin Hoa Dt/dng 3k Ninh
T6in tk: Vi€c tinh to^n k^t cau cfing trinh theo Qq tin cay \k rk ckn thilt. Tuy nhien cdc phiTdng phdp giSi tfch 6in\\ gid do tin cSy ciJa ket cku gap r^ nhiiu kh() khan. Mfi phfing Monte-Cailo Id phifcfng phdp so QMOc ddnh gid la hifu qud trong viec gidi cac bdl todn ngu trgn. Bdi bao trinh bdy each tinh da tin cdy ciJa ket c^u gidn th^p loai d^m bang st/ k^ hdp gida hai^udt todn Id phifdng phdp phan 11} hOu han vd mfi phdng Monte-Cario. K6t qud cho ^dy bdng each ndy dd cho ph€p t^o ra cCng cii s6 hOli hieu trong phan tich, ddnh gid dO tin cay ket cdu cong trinh noi ehung vd k^t cau gidn tiidp ndi riSng.
^ TH khoa. 66 tin c$y, kit du gian, md phdng, Monte-Carlo, xAc suit
Abstract: The reliabili^ calculation of construction sti^uctijres is essential. However, reliability analysis metiiods of sti'uc- tui^s, that based analytical mechanic, encountered many difficulties. Monte-Cario simulation mettiod is considered the effec- tiveness in addressing the above problems. This paper presents the reliability calculation of steel girder fruss by the combi- nation between two algoritiims are finite element meUiod and Monte-cario simulation. The results showed that in tiiis way has allowed creation of an effective tool in reliability assessment and analysis of construction sti-uctures and of steel fruss sti'uctures in particular.
Keywords: Reliability, Truss Structures, Simulation, Monte-Cario, Probability
I . D a l v a n d l
Qui trinh khao Scit, thi4t k§, thi cong cac cong trinh chijng ta vin thufmg xuy§n ti4p xijc vci c^c dai luCfng ngau nhien v4 vat lieu, hinh hoc kit clu vk tai trpng.
Trong cdc phuong phap tign djnh, de dem gian hod qua trinh ttnh toan vk thien v§ an todn, chtling ta vin bd qua tinh nglu nhign ciJa ehung vk diia vdo cdc he sd an toan.
Ly thuygt dO tin cdy co nhl^m vtj nghidn ctJu djiih lir^g cdc chi tieu chit lucmg cua sdn pham (kgt cdu cong trinh), sir biln doi theo thd^ gian ciJa cdc chi tidu chit lugng vd tu6i thp ct!ia sdn pham. Phuong phap do tin cdy cho ph6p xem xet todn dien hon st; ldm viec ciia kdt clu khi xdt ddn tinh bit dinh ciJa cac biln thilt k l va coi chting la cac dai lupng ngdu nhidn. Nhir vay 1;^ thuylt dd tin cay c6 y ngtiTa to Idn.
Hien nay, tfnh todn kdt cdu cac bd phdn cdng trtnh 6 nudc ta vdn chu ylu sii dijng cac phuong phdp tiln (flnh. Cdc nghidn cOfu, tt'nh toan theo hudng dp tin cdy c6n rdt ft.
Trong thuc t l , do tinh don gidn cua cdc cdu trtJc gidn ndn chiing duoc sit dtjng rdng rai trong xay dimg cdng trinh giao thdng, dan dung vd cdng nghidp... Do vgy, vide danh gid cac clu trtlc nay di/a trdn do tin c|y Id dilu cdn thidt d l xdc dinh dd an toan oOa ehiing.
Chua k l ddn viec ddnh gid dt^a trdn dd tin cay cung cd the duoc siJr dung d l tdi uit hda chi phf bao tri vd sCfa ehua cac clu triie nay.
2. Ctf sd ly thuyet tinh kit clu theo do tin cdy va phi/tfng phdp md phong Monte-Carlo [2]
2.1. Ccf sd ly thuyit tfnh kit ciu theo dd tin cay
Didu kien an toan v l kha ndng chju lire tai tiet dien dang xdt Id:
To£T„ . . . (^'
trong dd: To - gid trj ndi li/c bdt Ipfi nhdt cd the phdt sinh trdn tilt dien du'di tac ddng cua ngoai luc;
T,(, - khd ndnp chju li/c cua tilt dien dang xdt.
Vi TQ vd T„ diu Id hdm phu thudc vdo cac thdng sd ngdu nhien nen khdng the khdng djnh dugc (1) iudn thda mdn. Vi vdy de do miic dp thoa mdn ciJa (1) phdi tfnh xac suit:
Prob(T„-ToSO) (2) D l tfnh xde suit ndy, cd the dijng mdt trong cdc
phuong phdp sau: Tuyln tfnh hda de tfnh chi sd dp tin eay, tfnh theo phi/ong phdp l$p, tfnh theo phuong phdp tdch biln hoac tfnh true tilp tii hdm mdt dd ciJa ly thuylt xdc sudt. Cdeh tfnh cdn tuy thupc vdo ti^mg bdl toan CIJ the,
Ddi vdi bai toan kiem tra, IIJC ndy cdc thdng sd ngdu nhien vd hinh hpc, vat lieu, tai trpng coi nhu da bilt, edn tfnh xac suit theo (2).
Cac phuong phap giai tfch ddnh gid dd tin cdy (thdng qua xdc sudt khdng hdng) cua kit clu la phuong phap chfnh xac nhong gap nhidu khd khan v l mat toan hpc lidn quan din vlec tfnh cdc tfch phan chUa ede ham phdn phdi xdc suit vd mat dd xae suit, dac biet ddi vdi edc bdi toan nhidu biln vd cdc biln la qua trinh nglu nhien. Trong cdc trudng hop phtSc tgp nhuvay thi phuong phdp sd Id phuong tien duy nhat d l giai cac bai todn ddt ra. Mdt trong cac phuong phdp sd cd hidu qud de danh gid dp tin cay cua kit cdu Id phuong phap md phdng Monte-Carlo.
PHUCHUNG A '•ings NGIfdl XAY DI/NG s 6 THANG 3 & 4 • 2016
TiNH DO TIN CAY CUA KET CAU GIAN THEP...
2.2. Phuang phap md phong Monte-Cario Npi dung cua phuong phap md phong Monte-Carlo gdm 3 glai doan:
1' Md hinh hoa cac biin ngiu nhien ddu vao tU eae ham mat dp hoac hdm phan phdi xdc s u i t cho tri/dc cua Chung;
2- Tinh toin tiin dmh theo cdc the hien ddu vao d l nhan cdc the hien ddu ra;
3- Xd ly thing ke cac the hien ddu ra de tim cac dac trung xac s u i t ciJa nd va kiem tra cac gid t h i l t t h i n g ke. N I U sd the hien (phdp thCO duoc tao ra eang Idn thi ket qua cang tin cdy.
D l cho don gian, ta gia t h i l t rdng cac b i l n co ban Xi, i = 1 , . . . , n la ddc lap thdng ke va cd cdc ham phan phdi da b i l t . Phuong phap Monte-Cario nhdm tao ra tap cac gia tn the hidn ddc ldp xi cho mdi b i l n co ban vd tii do xac dinh eae gia tti the hien tuong img cua quang an toan M:
m = f{x^,x^,...,xj^f{x) (3) Bang each tao ra cac sd ngdu nhien, qua trinh ndy duoc lap lai nhidu ldn de nhan duoc mdt tap ldn cac gia tri m; ti^r dd cd t h i md phdng dang phdn phdi xae s u i t cua dai luong M. Ndi ehung, dang phan phdi xdc sudt chinh xdc ciJa dai lupng M thu&ng khdng theo mdt tidu chuan ndo, nhung nd cd the duoc q u y l t djnh bcrt dang phan phdi cua b i l n co ban noi trdi nhdt.
Xac s u i t pha huy cd the dupc danh gia theo hai each. ThU nhdt, vi M < 0 umg vdl m i l n pha hCty, nen xac s u i t phd huy Pf dupc v i l t thanh:
P . = F ( M < 0 ) = l i m - (4) trong dd n la tdng sd phep thu^ k Id sd phep thCf ma
f(x) <0.
Tuy nhien, ty sd k/n la mdt dai lupng thdng ke, ndn phan phdi va dac bidt Id phuong sai cua no se phu thude vao sd luwig phdp thtJ". Ddi vdl tru'dng hpp xac s u i t phd ht!iy t h i p hoac sd phep thCr n Id nhd thi vlec danh gid P, qua k/n cd the se cd tfnh bdt djnh.
Cach thtj" hai Id tCr eae gia tri the hien m, ta xdc djnh ham phan phdi phu hop M bdng cdc phep kiem nghidm luat phan phdi. Khi dd xac s u i t pha huy gdn dung bdng:
I /w('"W'"
(5)Trong dd PM(m) Id ham mat do xac suat eua quang an todn M.
Cach nay duoc dp ditng khi sd luong phep thuf la nhd.
3. Bii toan tfnh phin tfch tTnh kit ciu giin thep theo tiin djnh
Trong bai todn t h i l t k l thdng thudng theo tieu chuan hidn hdnh (TCVN 5572-2012), mot k i t cdu gidn dupc tfnh todn theo eae budc sau:
- Gia ^ n h t i l t dien.
- T f n h toan npi luc.
- C h o n so bd t i l t dien.
- K i l m tra didu kien bdn va dieu kien dp etJfng.
- Chpn lai tilt didn n l u kiem tra khdng dat hole qua thifa.
- Kiem tra lai.
Budc chon t i l t dien va kiem tra ed the lap lai nhigf ldn cho tdi khi kiem tra dat yeu cdu va khdng qud thife thi dimg lai.
D i l u kidn b i n va didu k i | n dp cufng ddi vcfi cac phdn tit gidn khi tfnh toan t h i l t k l dupc xae t^nh nhi/
sau [3]:
- Tinh thanh keo dUng tdm:
C7--<R (6) N A
Tinh thanh nen dung tam :
(7) - Tfnh theo dd manh gidi han [X].
T i l t dien ehpn nhd nhdt va bdo dam cdc ban kinh quan tfnh yeu cdu :
r =-L ;r =-^ (8)
' [Z]' ' [A]
Trong cac cdng thtjfc (5), (6), (7), eae dal Iirong duoc gidi thfeh nhu sau: c - irng s u i t (keo, ndn) xuat hien trong thanh gian ; N - luc dpe true trong thanh ; A - didn tfch t i l t dien thanh ; R - cudng dd tfnh todn cila thep ; tp - hd sd udn dpc, phu thudc dp manh (tra bang lap s d n ) ; Ix - chidu dai tfnh toan cua thanh gian trong mat phang; ly - chidu ddi tinh toan cua thanh gidn ngodi mat phdng ; m - he sd khi xet d i n cac trucmg hpp cdu tao cua thanh ndn dung tam.
Ngoai cac d i l u kien ddi vdi tCmg phdn tCr nhu trdn, phai kiem tra d i l u kien rang bupc v l dp cumg cua todn hd gian thdng qua ehuyen vj cho phdp ldn nhdt []. Dfii vdl gidn dam, dieu kien rang bupc c h u y i n vi tai mfii nhjp gian vdi kfeh thudc L duoe xac djnh:
S^^<[S] = — (9)
" " ^ -" 600 ^ Nhuvay, k i c d trong bai toan t h i l t k l eung nhubdl
toan k i l m tra k i t c l u gian, edn phai thuc hidn phdn tfch ndi luc de kiem tra cac d i l u kidn bdn va ciJng cua k i t c l u . D l Idm d i l u nay phu hpp vd'i s i ; k i t hop mfi phong Monte-Cario. edn phdi dp dung phuong phap phdn tit hull han.
Tren co sd ly t h u y l t vd phdn td hCtii han hd gidn [1], tac gia da xay dimg chuong trinh phdn tfeh tmh kit cdu hd gian theo phuong phap phdn ti!r hOii han trong mdi trudng Matiab. Chuong trinh cd ten FEMTRUSS_AN. Trong bai nay eh! tap trung eho he gian phang loai gian ddm.
De ddnh gia dp tin cay cCia chuong trinh da i^p, tiln hdnh phdn tfch hai vf du vd so sanh vdl k i t qua tfnh toan tU phdn mdm SAP2000. Ai sd tronp hai vf du nay 6 mute dd max « 2%. K i t qua eho thdy chucftig trinh da Idp^ cd du dp tin cdy de su' dung.
4. S o d d t i n h d o t i n cay k i t cau gian d i m [4]
N G U d l X A Y D U N G S O T H A N G 3 & 4 - 2 0 1 6
TINH DO TIN CAY CUA KET CAU GIAN THEP..
4.1. Ket ciu gian dam tinh djnh
Ddi vdi k i t c l u gian tTnh dinh, chi cdn mdt thanh bj pha hoai thi k i t cdu se bi b i l n hlnh va ddn tdi sup d l . Do dd, k i t c l u gian ttnh djnh c d the duoc m d phdng thanh s o dd ghdp ndi tilp tdt ca cdc phdn ti!!r ciJa nd.
V i du xdt gidn tmh dinh cd s o dd k i t c l u (a) n h u sau (hlnh 1):
Hinh 1. Stf tfo kit cau giin tinh dinh Ket cau gian trdn bao gdm 17 phdn tCr thanh chiu luc dpc true ed lien k i t hai ddu Id khdp. Chi cdn 1 thanh b i t ky hdng la k i t e l u hdng. Vi vdy, cd the md phdng nd thdnh he m i c ndi tilp nhu sau (hinh 2):
b)
HInli 2. Sd dd md hinh tinh BTC hS (a) hlnh 1 Xdc suit khdng hdng eua hd (a) qua so dd (b) duoe xae djnh:
P^PrP2-Pj6-Pn=Y.P. (10) Trong dd P, (1=1-^17) - xac suat khdng hdng ei!ia thanh gian thi^ I trong he dang xet.
4.2. Ket cau gian dim sidu tTnh a/ Mat cat chuyen thinh "khdp"
Trdn mdt mat cat, n l u mpt hoac mpt sd thanh bj roi vdo trang thdi m i t an todn (hdng), ehi cdn lai hai thanh, thi mat edt tuong duong vdi mdt "khdp". Vj trf
"khdp" tai giao diem cua hai thanh nay. Nhu vay, mot mat cdt gidn c h u y i n thdnh "khdp" khi tren mat cdt dd ehi edn lai hai thanh lam vi^c.
N I U tren mat edt ed n thanh thi sd kha nang tao
Hinti 3. Sd dd kit cau gian dim sidu dnh vi sd dd dien mo phdng khi nang hda khdp cda nd.
"khdp" se Id mdt to hgp chdp 2 cua n thanh: C ^ . Trdn hinh 3:
- Mat cat tTnh djnh: Id mat cat gian cd 3 thanh n h u so dd k i t c l u (c). S o dd dien md phong kha ndng hda
" k h d p " c i j a n d Id (d).
- Mat cat sidu tTnh: Id mat cdt gian cd 4 thanh n h u so dd k i t cdu (e). So dd S\en md phong cdc kha nang hda "khdp" ci^a nd Id (f).
b/Xic dmh kha nang tao thinh caciu cda giin Can ctjf gia tri ting s u i t trong cac thanh se xac djnh duoc sd luong mat c i t cd nguy co tao "khdp". Day Id eo s d de tfnh dd tin cay.
Vdi gidn sidu tTnh nhidu nhjp, viec xdc djnh s d t l hpp "khdp" tao thanh eo c l u , cd the duoc xdt thdng qua so dd d i m lien ttJC tucng duong.
Ndi Chung, vdi gidn lidn tuc ed n nhjp ehiu tai trpng thi d i m tuong duong ed bac sieu tTnh Id (n-1). D i l u kien hinh thdnh co c l u t6ng t h i Id trdn he c d n t i l t dien hda "khdp". Didu kidn hinh thanh eo c l u cue bp Id cd ba "khdp" l i l n k l nhau duoc tao thdnh.
Trong thuc hdnh tfnh todn, tdy theo tai trpng tac dung len tren gian, se xac dinh cu the tilt didn cd nguy CO hda "khdp". Khi do, sdp x l p thU t y ting sudt trong mat cat tii ldn d i n nho ta se xdc dinh dupc khd ndng hlnh thanh c o cdu tong the theo thtjr t\i uu tien, cung nhu khd ndng hlnh thdnh co cdu cue bd. Vide tfnh todn dp tin cay cua he ed the thtJC hien b i n g tay hay t i / ddng hda.
5. Xdy dirng chuong trinh tfnh dd tin cay k i t c l u gian theo mo phong Monte-Carlo
Chuong trinh tfnh dd tin edy k i t edu gidn theo md phdng Monte-Carlo dupc xdy dung dua tren co s d ket hpp hai thuat toan:
- Thudt toan phdn tir huu han phdn tfch tTnh k i t c l u hd thanh (dupc trinh bay d muc 3).
- Thuat todn md phdng Monte-Cario (duoe trinh bay d mue 2).
S o d d khdi ctia chuong trinh duoc t h i hien tren hlnh 4.
Tren co sd so dd khdi va chuong trinh FEMTRUSS- AN, phdt t r i l n thdnh ehuong trinh tfnh d d tin cay k i t c l u gian theo md phdng Monte-Carlo trong mdi trudng MATU^B. Chuong trinh duoe ddt tdn RES- TRUSS. Cdc phep tfnh ma trdn vd vecto trong chucmg trinh cung nhu tao phat cdc the hien eua ede b i l n ngdu nhidn ddu vao duoe thdc hien bdng cdc ham cd sdn ciia b d t h u vidn Matrix VB dUOc v i l t bdl MathWorks Ltd. C l u true cua chuong trinh gdm cac md dun chfnh: md dun nhdp sd lidu, md dun tao phdt cac the hipn cua b i l n n g l u nhien ddu vao, md dun tfnh k i t e l u theo quan niem tiln djnh, md dun xir ly ket qua.
Ngoai ra cdn cd eae hdm vd thu tue con 6\iac gpi bcri edc md dun ehfnh cua chuong trinh.
Chuong trinh cho phdp tfnh xac s u i t khdng hdng cua k i t c l u hd thanh cd k l d i n cac y l u td ngdu nhien v l vat lieu, hinh hoe k i t cdu vd tdi trpng.
Trong bdi bdo nay se sir dung cac phuong phap v d cac gia t h i l t dudi day d l tinh todn do tin edy ddi vdi N G U d l X A Y D U N G S O T H A N G 3 & 4 • 2 0 1 6
TiNH DO TIN CAY CUA KET CAU GIAN THEP...
Ttiu n^u$m (TN) = 0
M6 pli6ng sd c ^ b i ^ r)g3u l A I ^ ccr ban ( d ^ via): V l hinh
hfn; V l v§t G&i: V l tai trpng
" T "
Tirdi n$i Krc, chuyin vi k4t c^u d6l vat C ^ BNN ccr ban da dv^rc MPS Iheo quan dilm tiln
djnh t ^ l=ENfmUSS_AN
ix:
nnhXSlchanghww:
Tlwo ^ u l^en ® ben + Theo iSlu tdan (ffi cirng
Hinh 4. Sd do khdi cua chddng trinh dnh xac suat ididng hdng kit {^ugiin
k i t c l u gian thep.
- DCing phuong phdp tinh theo trang thai gidi han tiiiJr n h i t (gidi hetn ben), de tfnh todn ket cdu gidn thdp.
- Cac b i l n n g l u nhien cd ham phan phdi mc s u i t ia ham phan phdi c h u i n .
6. Vl d u s d 6.7. Bai toin 1
Xet gian cd so dd nhu hlnh 5 va dupc lam bdng thep cd mddun dan hdi vol ky vpng !a E = 2,1.10*
kN/em^ dd Idch ehuan cua nd la 1,05.10" kN/em=. IJfng s u i t ehju kdo, ndn cho phdp cd ky vpng Id [o] = 21 kN/cm^ vd dp Iech chuan Id 1,05 kN/cm^ Cdc tilt dien thanh cd ky vong ldn luot la A l = 54,60cm^ (2 thep gdc L l 40x140x10); Ag = 38,40cm= (2 thep gdc L100 x 100 xlO); A3 = 23,00em* (2 thep gdc L75x75x8) va he sd b i l n sai bdng 0,01. Cdc tai trpng ntJt cd ky vpng ldn lupt Id P, = 45kN; Pj = 60 kN; P3 = 90kN, hd sd b i l n sai bang 0 , 1 .
A, ^ ^ A, ^
A^^-4 ^ ^ ^ 4 ^ 5 ^ ^ J^^^
^ ^ ^ ^ ^ ^ ^^'^
.A T I
4 - -+- -4-
Hinh 5. Sd dd hinh hgc va tii dong bii toan vidul - din dim Snh dinh
^
Bang 1 . Ong suit trong t^c phan tiy ffianh giin ttia toin 1 tfnh theo tien dinh Phan 41
IJianti 1 2 3 4 5 6 7 3 9
Jngsu^ trong ttianh (N/mm^
-70,3125 .71,7391 -39,1304 -71,7391 -70,3125 0,0000 117,1875 117,1875 0,0000
Phan tit thanh
10 11 12 13 14 15 16 17
tifng suit tnmg Ihanh (tfmnfl -117,1875 -109.8901 -109,8901 -117,1875 92,1457 72,9153 72,9153 92,1457 [ol - 210 kidn bdn.
+ Theo didu kien (9) d i u y l n vj cho phep ciJa he I&
600 = 2cm
D I thdy do tfnh ddi xtjfng, chuyen v\ ldn nhdt cua he se la chuyen vj t ^ nut 5 va nijt 6. K i t qua do ctiucng trinh FEMTRUSS_AN tfnh ( ^ u y l n vj Idn tihll cua he tai nut 5 Id 1,99 cm va tai nut 6 ta 2,00 cm. Nhi/
vdy hd da t h i l t k l bdo ddm didu kidn c h u y i n vi cho phdp.
b/. Tfnh toan dd tin ciy cda he idii xet den cac bk dmh cua vat lieu, hinh hgc cua kit ciu i/id tUtrgrtg:
Khi cac y l u td vdt lidu, hinh hpc cua k i t c ^ vatS trpng dupc xem xdt Id cdc b i l n ngdu nhidn vdf cdc <&:
trung S i l n g ke da cho, s& dung chuWig trinh RES- TRUSS de tfnh todn d d tin cdy ci^a hd gidn.
Bang 2. Kit qua tfnh dd tin ciy cua hd gian BTl S6 lin mO-nghi$m: 10.000
6. Sd do nut vi phin tii bii toin 1 trong FEUmUSSJN a/. Kiem tra thiet kd theo tidn djnh:
Sii dung etiUOng trinh FEMTRUSS_AN tfnh k i l m tra d i l u kidn bdn va chuyen vi cua thanh.
+ Theo d i l u kien bdn, cdc gid trj tjng s u i t trong thanh cd k i t qua tfnh nhu trong bdng 1.
Nhuvay edc thanh trong he gian ddu dam bao d i l u
Q I NGUdl XAY DUNG S 6 T H A N G 3 & 4 - 2 0 1 6
fiatindyveii^n Piiinlir
thanh 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
S i i i n M g s u ^ >[a]
3 3 0 5 5 0 145 141 0 166 109 103 130 25 7 10 34
Xac suit hong{%) 0,03 0,03 0 0,05 0.05 0 1.45 1.41 0 1.66 1.09 1.03 1,3 0.25 0,07 0,1 0,34
fiptJnc%vddaGdtig NIK
1 2 3 4 5 6 7 8 9 10
S6 lin chuyin vtdlJng >[S]
0 0 7 19 4372 4913 16 22 0 0
Xac suit hing(%) 0 0 0,07 0,19 43,72 49,13 0,16 0,22 0 0 M tin cay vSlAi ciia hS theo
(10): = 91,47*
Sd tin cly vS chuy^ vi cDa li^:
=50,87%
TINH BO TIN CAY CUA KET CAU GIAN THEP.., Kit qud tfnh todn duoc trinh bdy trong bSng 2,
trong dd cd cdc thdng tin vd kit qui s6 ldn hdng (pha huy) cCia tCmg thanh gidn, xac suit khdng hdng cua timg phdn tCr vd cua todn he theo dp bdn; sd ldn chuyin vi niit vuot qua gid trj cho phdp va xdc suit khdng hdng cOa he theo rdng buOc v l chuyen vj.
* Nhan xet: H^ cd do tin cay vd chuyin vi khd thip, Id do khi thilt k l theo tidn d\nh he da cd chuyen vj Idn nhit sdt vdi gid tri chuyen vj cho phdp. Do do chuyen vi not rit d l ddng vuot qua ngudng an todn khi cd nliCmg biln ddng ngdu nhidn v l vdt li^u, hlnh hpc cua kit cau va tdi trpng.
6.2. Bai toin 2
Xdt gian cd so dd nhu hinh 7 vd duoc lam bdng thdp CO modun ddn hdi vdi ky vpng E = 2,1.10*
kN/cm*. do lech chuan cOa nd la 1,05.10* kN/cm*. ting suit chju kdo, ndn cho phdp cd ky vpng Id [a] = 21 kN/cm' va d0 l$ch chuan Id 1,05 kN/cm^ Cae tilt dien thanh cd ky vong ldn luot id A,= 39,40em' (2 thdp gdc L125x125x8); Ag = 19,18cm* (2 thep gdc L100x63x6 ghdp canh ldn); A3 = 23,00 cm* (2 thdp gdc L70x45x5 ghdp canh Idn) va he sd biln sai bang 0,01. Cdc tai tnpng cd kJ vpng ldn luot Id P, = 45kN; Pg = 60 kN; P3
= 90 kN, he s6 biln sai bdng 0,1.
8. ^ddnutva pfm ^bii loan 2 bong FEMTBUSS-AN
a/. Kiem tra thiit ki theo tien dfnh:
Sii dung chuong trinh FEMTRUSS-AN tfnh kilm tra dilu kien bin va chuyin vi cua thanh.
•1- Theo didu kidn bdn, kit qud tfnh cac gid trj limg suit trong thanh duoc dira ra trong bdng 3.
Bdng 3. Ung suit trong cic phan td thanh giin bii toin 2 tinh theo tiin dinh
Phin til Uianh 1 2 3 4 5 6 7 8 9 10 11
l^ng suit Irong Ihanh (N/mmO -78,9135
-7,2077 -11,9896 -7,2077 -78.9135 123.7163 133.6537 133,6537 123,7163 -110,9031 -132,8437
PhintH thinh
12 13 14 15 16 17 18 19 20 21
|}ng suit trong Ihanh (K/mm^
-132,8437 -110,9031 -67,3340 60,3603 -76,5980 73,4065 73,4065 -76,5980 60,3603 -67,3340 H = 210
Nhirvdy cdc thanh trong he gian diu dam bao dilu kien bin.
+ IQem tra v l dilu ki^n chuyen vi:
Vdn do tinh ddi xung, chuyen vj Idn nhit cua hd se Id chuyen vj tai nut 5 vd ni3t 6. Kit qua do ehuong trinh FEMTRUSS_AN tfnh chuyen vj Idn nhit ciJa he tai nut 5 Id 1,99 cm vd tai nut 6 la 2,00 cm. Nhuvay hd da thilt k l hko dam dilu ki$n ehuyen vj cho phep.
tl/. Tfnh toin dd tin cay cOa he khi xdt din cic bit dinh ciJa vit Udu, hinh hgc cua kit ciu vi tii trgng:
Tuong tir nhu da trinh bdy dli vd! bdi todn 1, kit qua tfnh toan duoc trinh bay trong bang 4.
Bang 4. Kit qua tfnh dd tin ciy eOa hd giin BT2 So lin thi>nghiSm: 10.000
Ddtinc4yvlblnPhinti Ihanh 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
S6 lin Ihig
suit>|ol
0 0 0 0 0 20 52 50 18 10 34 30 12 0 0 0 0 0 0 0 0Xac suit hang (%) 0 0 0 0 0 0,20 0,52 0,50 0,18 0,10 0,34 0,30 0,12 0 0 0 0 0 0 0 0
f)6tinc$yvilldcang Nut
1 2 3 4 5 6 7 8 9 10
S6 lin chuyin v|iIiDig>[5]
0 0 0 0 2320 2513 0 0 0 0
Xdc suit hSng (%) 0 0 0 0 23,20 25,13 0 0 0 0 Do tin cly ve chuyen vi cua hfi; P^ = i r a n p^'.p^ = 74,87%
Dp tin cay vd bin cua tie xet ttieo dilu l<ign l<ha nang tioa "I<ti6p" tren c^c mat cat gi&n. Do tinti cti^t ddi xijmg cua so dd l<gt c^u va tii tronp, ctii din ti'nti ctio 1/2 gian tito la ctii tinli v6i 2 mat cat gian:
(1). Mat cat I (qua cSc ttianh 6, io. 14.15) Vol mat ckl gian c6 4 thanh se x4y ra 3 tnifmg hdp.
tucmg ilng c6 3 xac suit:
P, =(i-PfPf )(^-Pf Pf}
P. '(I-P/Pf }(l-P/Pf j
„/-3 / i „6 „l5\/'i „I0 „14'l P, =[l-Pf.Pf }[l-Pf .Pf }
Xkc suit an toan {khdng hda "khdp") cua mdt cdt!
Trdn mgt cdt I, kit quk bdng sd nhusau:
NGUdl XAY DUNG SO THANG 3 & 4 - 2016
TJNH BO TIN CAY CUA KET CAU GIAN THEP..
Phin til thanh (1)
6 10 14 16
Xac suit pha huy p'f
(%)
0.20 0,10 0 0
Xac suit an lean cua m ^ cit P' = 99,98%
P- =100%
/ - I P' = 100%
' ' " = 99,98%
(2). Mat cat II (qua cac thanh 7 . 1 1 , 1 6 . 1 7 ) : Tuong 111 tren. co cac tni&ng hop xac s u i t : P " = ( 1 - P i P V X I -P'r'.pn
p r = (1 - p;.pi')(i - pv.p?) p r ' = ( i , - p i . p i ' ) ( i - p ; ' . p i ' )
Xac suat an toan (khong hoa "khdp'O cua mat d t I 14:
Tren mat d t I, k i t qua bdng sd nhu sau:
Gian cd mdt nhjp se hlnh thanh co e l u khi cd mot trong 4 mat cat hda "khdp" tuong dng so dd mdc ndi t i l p cua 4 mat c i t gidn. Nhu vdy, xac s u i t an todn Chung ciJa k i t edu gidn la:
P,= p^.p:.p'^.p?
Do tfnh ddi ximg eiJa so dd k i t c l u va tdi trpng, ta cd: Ps= P™ va p^ = p'^
Nhuvay: P^ = (p^.p^)^= 99,8032%
Phin til thanh (i) 7 11 16 17
Xic suit pha huy p'j
(*l
0.52 0,34 0 0Xac suit an loan cua n d t c l l ^ o-i ~ P' = 99,823211.
P- = 100%
P- = 1 0 0 * , u
P' =99,8232%
7. Ket ludn
- Vide k i t hop giOa hai phuong phap phdn tir hOu han vd md phdng Monte-Cario cho phdp tao ra cdrw cu sd hOu hidu trong phdn tfch, danh gid dd tin cdy k i c l u cxing trinh ndi ehung va k i t c l u gidn thdp ndi ridng.
- Qua hai vf du sd, cho thdy k i t cdu gidn thep dang d i m cd xdc s u i t an toan cao v l c^lu kidn bdn, uilp v l d i l u kien do etjng ( c h u y i n vj) cho phep.a
lai lieu tham kttao:
1. Nguyen Qu6c %io. Tr4n Nhit Oung [2002). f^iUdng phip i ^ t&hdu han. ly thuyit vi lip trinh. Nxb Kiioa hoc va ky thu|t Hi Noi.
2. Phan Van Khoi {2001). Cd sd dinh gii dd bn ciy N)ffl Khoa hoc va ky thuit Ka Npi.
3. Ooan Dinh Kiin vi cgng su (2005). Kit du thdp. WS ¥im hoc va ky thuSt Ha Ngi.
4. Le TO (2003). Kit hdp do bn cay bong Unh biin t^'dddao dim. Luan v3n Ttiac si ky thuat TniOng Oai hgc Xay di/ng Ha NSL
X A C D I N H KHOANG C A C H CUA...
(Tiep bieo trang 58)
2000 ) la IAB
i^B = L A B . ( 1 / M ) (19)
= 994,061.(1/10 000)
= 0,099 406 m
= 99,4 mm 7. K i t luan
Trong ddn gian chi cd mdt khdi niem duy nhdt vd khoang cdch cua hai (Bem A vd B, dd Id khoang each thang theo dudng chim bay tnrt: t i l p tir A d i n B.
Nhung trong ngdnh t r i e dja bdn dd, khoang each cua hai diem lai Id mot khai niem rat phong phu, da dang.
Cdn phai xdc dinh thdt chfnh xdc:
1. Khodng each cua hai diim nio?.
2. Khoang each gi?.
2 . 1 . Khodng each nghieng (thuc) cua hai diem A, B (d trong khdng gian).
2.2. Khoang each ngang eua hai diem A, B (d tren mat phdng ndm ngang cua thtic dja).
2.3.Khoang cdch tiing cua hai diem A, B (d tren mat elipxoit tron xoay trai ddt).
2.4. Khoang cdch io ciia hai diem A, B (dtren mat phdng c h i l u hinh ban dd UTM-VN-2000).
2.5. Khoang each giiy ciia hai diem A, B (dtrento' ban dd dja hinh ty le 1/M kieu VN-2 000).
3. Cdng trinh tdn tai trong khdng gian thuc. Na Chung, cdng trinh thu&ng duoe cSnh vi tren mdt mat plnang ndm ngang cu t t i l n h i t djnh ndo dd. Nhung cac sd Iidu t r i e dia ban dd nha nudc (nhu tpa do VMf 000, chidu ddi canh lud^ khdng c h l trdc dia ban &
nha nudc...) lai tdn tai trong khdng gian do cua p h ^ c h i l u ban dd UTM-VN-2 000. Bdi vay khi sif dung chiing trong t r i e dja xdy dtmg cdng trinh thi cac so lieu trdc (Ba bdn dd nha nudc nay d i u n h i t thilt phai duoc tfnh toan c h u y i n doi v l khdng gian thuc cua cong trinh se duoc xay d t m g . a
TAI LIEU THAM KHAO:
1. So tay cua ngiiSi ky sir trie dja. Chii bign VO.Son -sa H»p.
G.RLep-tnic.nh^ mk lun 'nhe flra'.Mat-sco-va nam 1966.
2. BD dac xay dung c6ng trinh. PGS.TS. Pham Van Chuyfin M XuSt ban XSy difng. Ha Ngi n3m 2014.
Bja chi tdc gia : Pham Van Chuygn
Nha sd 10, Day A, Khu Dai hoc Xay dimg Ngo 194, Di/omg Giai Phdng Quan Thanh X u i n -TR Ha Ndi DT: 093 606 9858 N G U d l X A Y D U N G S O T H A N G 3 & 4 • 2 0 1 6
