Illk ' KHOA HOC - CONG NGHE
ism DUNG MO HINH PHAN TUT HOU HAN MOl RONG TRONG PHAN TICH DANH GIA TiNH DUKET CAU CONG TRINH CAU
ThS. N G U Y E N VI^T HUY P G S . T S . T R A N DU'C NHIEM PGS.TS. N G U Y E N THj MINH N G H I A
Tdm tit: Bai bao gidi thi$u viec ung dyng mo hinh phan ti> hOv han md rgng trong vi$c cai tiin quy trinh tn/c tiep xac dinh /?# s6 tinh dw cho cic bo ph$n cua kit cau cdng trinh du. Quy trinh di ndi dw(?c minh hpa thong qua mot vi dy tinh toan cu the cho dim BTCT lien tyc hai nhjp.
Abstract: The paper introduces an application of embed-displacement finite element method in
"direct" procedure of determining the redundancy of bridge's stmcture. The proposed procedure is ^
applied for an example of two-span continuous reinforced concrete beam. : ^ ^ H
I.OATVANOe
Tinh d u trong ket d u cong trinh d u la mpt chu de du'pc quan tam nghien ci>u rat nhieu tren the gidi cOng n h u d Viet Nam, O Hoa Ky, viec danh gia tinh d u d u p c d u a vao tieu chuan thiet ke d u theo tieu chuan AASHTO ti> nhung phien ban dau tien (xem [1]) va lien tuc xudt hien trong nhOrtg phien ban cap nhat sau nay (xem [2]).
Song hanh vdi viec d u a ngi dung quy dinh ve tinh d u vao tieu chuan t h i l t k l , chu-ong trinh nghien c u u h g p tac quoc gia (NCHRP) cung CO nhung nghien c u u nen lang ve khai niem tinh d u , cac p h u a n g phap danh gia tinh d u va d u a ra quy trinh tryc t i l p xac dinh tinh d u cho ket cau phan tren va ket cau phan d u d i cua cdng trinh cau (xem [3], [4], [5]), 6 chau Au, khai mem tinh d u (redundancy) d u g c tiep can bang mpt khai mem co tinh t u a n g d u a n g nhung rdng h a n la dO kien c6 cua ket cau cdng trinh (robustness) va cac ket qua nghien c u u cung d u g c phan dnh trong cac tieu chuan t h i l t k l hien hanh (xem [6]. [7], [8]), Cf Viet Nam, khai niem ve tinh d u ciJa ket cau cong trinh cau cung da d u g c d u a vao tieu chuan t h i l t k l d u 22-TCN-272-05 cua Bo Giao thong van tai. Iheo dd he
mm
sd tinh d u phai d u g c xet den khi tien hanh tinh loan, thiet ke cac bp phan cua cong trinh cau (xem [9]).
Tuy nhien trong nhieu nam qua chua CO nhung nghien c u u c a ban de lam ro khai niem tinh d u , cac p h u a n g phap tinh loan tinh d u va quy trinh xac dinh tinh d u cho cac bp phan cue cdng trinh cau d Viet Nam Trong cac nghien c u u t r u d c day, chung loi da cdng bd nhung ket qua nghien c u u ve p h u a n g phap dp tin cay va cac trang thai gidi han t u a n g i>ng trong xac djnh tinh d u ket cau cau (xem [10]) va gidi thieu quy trinh cac b u d c de xac dinh true t i l p tinh d u cho ket d u cdng trinh (xem [11]), Mot vdn de gay kho khan cho viec xac dinh he so tinh d u cua ket c l u cdng trinh cau la quy trinh ti>ng b u d c danh gia tinh d u do cac tac gia de xudt t r u d c day la qua phuc tap va ddi hdi phan mem phan tich k i t cau chuyen dung (xem [3], [4]).
Theo do, quy trinh xac djnh he sd tinh d u cho k i t d u phan d u d i cua cong trinh cau bao gom 10 b u d c t u a n g dng vdi 3 trang thai gidi han khac nhau d n phai phan tich, tinh loan (xem [3]) la:
• TTGH c u d n g dp bp phan:
TTGH dng vdi tru'dng h g p mpt k i t cau chju (yc chinh bj pha hoai
T T G H s u dgng: U'ng vcri t r u d n g h g p k i t d u bj bien d a n g , chuyen vj qua miJc cho phep
T T G H c u d n g do l o n g the:
iJng vdi tru'dng hgp ket cau bj sap d d , xac dinh bdng each d d mpt bp phan chju lye chinh cua ket cau roi t i l p ti,ic gia tai d i n khi k i t d u con lai bj pha hoai.
Ddi vdi k i t cau phan tren cua cong trinh cau, quy trinh danh gia tinh d u theo de xual cua cac tac gia t r u d c day bao gdm 12 byoc t u a n g u n g vdi ba trang thai gicri han t u a n g t u n h u ddi vdi ket cau phan d u d i (xem [4]). Van de gay khd khan cho vipc tinh toan la trong cac quy trinh nay deu d6i hdi sau khi da xac djnh dugc bp phan k i t d u bj pha hoai thi phai lan l u g t t i l n - hanh bd cac bp phan bj pha hoat de tiep tuc tinh toan k i t d u (sau khi rd bo thanh phan bi pha hoai) n h u mdt ket d u mai den khi loan bd ket cau bi sup do (trang thai gidi han c u d n g dp cuoi cung), Quy trinh nay doi hdi phai tinh lap, ngoai ra khdng the phan tich d u g c hoan toan chinh xac si/
lam viec ciJa ket d u sau khi xuat hien phd hoai,
Trong bai bao nay, chung tdi gidi
S o i l nam 2015 I
KHOA HOC - CONG NGHf ,
iffilSilSHB
to. P/ia ho^i do uon vi phi ho^i do cit, u6n ddng thdi Hinh 1. Cic d^ng phi ho^i diin hinh trong idt du bd tong c6t thdp
11*^
a. Phi ho^i do ndn u6n ding thdi thiOu vipc ung dgng phuang phap phan tu hu-u han md rOng cho phep phan tich sy Idm viec cua kit d u cdng trinh d u sau khi mOt bO phdn cOa kit d u da bj phd hogi, do dd giOp trdnh viec tinh l^p trong quy trinh phdn tich tinh du vd giOp d i tiln quy trinh ddnh gid tfnh du trd nen dan gian vd rO rdng han. Quy trinh ddnh gid tinh du d i tiln dugc dp dgng de phdn tich cho mOt so vi dg kit d u eg the de ddnh gid kha nang ung dgng cOa quy trinh ndy trong vIOc tinh todn xdc djnh tinh du ket d u cdng trinh d u d Viet Nam.
2. Gib'l THIfU v e PHU'aNG P H A P P H A N TCP H U U M A N M d
RONG XET D^N P H A HOAI CMC BO TRONG KtJ CAU CdNG TRiNH
Doi vdi kit d u d n g trinh d u (dang cOL dam hoac thanh), d c dgng phd hoai diln hinh thudng thay Id;
• Phd hogi do keo, nen (gpi Chung Id pha hoai do tyc dpc trgc)
• Phd hogi do uon
• Phd hogi do d t
; Hope phd hopi do kit hgp cOa 2
I S o l i nam 2015
hope ca 3 thdnh phan nOi lye: nen uon dong thdi, keo udn dong thdi, cdt uon dong thdi.
Hinh 1 t h i hien mOt dgng pha hoai thudng gpp kit d u be tdng d t thep, dpng kit d u p h i biln trong cdng trinh d u
D l md phdng cac dang pha hopi ndy trong k i t cau, nhdm nghien cuu cOa Ibrahimbegovie da phat trien md hinh phan tu khung/dim truyln thong cua Timoshenko d l xet den sy Idm vipc ngodi miln ddn hoi cua d i m . dong thdi xdt den cac dang pha hoai cue bO do uon va cat (xem [12], [13], [14], [15]). Theo dd, cdc phd hopi
do u6n, cat duge xem nhu cae bude nhay khdng lien tue trong trudng chuyin vj; phd hopi uon duge hilu Id mOt budc nhay ve gdc xoay, phd hopi elt dugc hieu la budc nhay ve chuyin vi thing ddng (xem Hinh 2). Cae budc nhdy ndy dugc xem nhu cdc I n so chuyin vj b l sung (vao cac chuyin v| tgi nOt) tpi phan tu' dam xuat hien phd hopi va dugc dua vao phuang trinh x i p xf chuyin vj thdng qua hdm dpng Heaviside (COng thue 1).
TLP phuang trinh xap xi chuyen vj vd md hinh phi luyin v l u l n vd elt cho phin 10- d i m (xem Hinh 3) xdy dyng dugc phuang trinh ca ban cho phuang phdp phan tu hiJu han md rOng (Cdng thuc 2).
Hinh 2. Ham d^ng md ta phi ho^i cyc bQ do uon va dt trong
phin tw dim Timoshenko
/i V
m \
h \ . \ .
Hinh 3. Quan h^ mi-men tfg cong (M-Kj vi luc cSt - bien d^ng
truvt (V-y)
mm
m i l KHOA HOC - C O N G N G H E
Phifong trlnh xap xi cua chuyen vj:
u ' ( x ) . N d + a ( H ^ W - A ^ W ) ( 1 )
Phuang trinh phan ti> h&u h^n md r0ng:
ft[r»M»,r2«^]-A(cr-c«|
Trong 36:
Kf-/B^c:«B<fa
0
0
0
r _ _
H:i? = /G^Ci%,d:r (3)
0
Vdi K S * „ , vdK^'^ila cdc ma tr^n
tilp tuyIn t h i hipn quan hO 910*3 nOi lye tgi vj trf xay ra phd ho^i cgc bO vdi budc tang d a chuyin vj nut vd budc tdng d a "budc nhdy"
chuyin "A-
A<V,-KS!„,Ad«+KM„,Aa»(4)
v 4 C " f ' 1^ m6-aun tiep tuySn t h i hi$n quan h$ giua npi l^rc v^ biln d^ng cua dim tai thfri dilm dang x6t
AaE-Ci'A^W (5)
Md hinh phi tuyen md rOng ndy dugc cdc tdc gia Igp trinh thdnh d c phin ti> frong thu vi$c PTHH md cua phin mem phdn tfch kit d u FEAP (xem [16]) vd dugc Cmg dgng trong bdi bdo ndy.
3. (XHQ DMNG PHlfONG P H A P PHAN rCr HOXI HAN MCT RONG CHUY£N V| D£ CAI n^N QUY
T R I N H D A N H GlA TfNH DIT TRI/C T I 6 PPhuong phdp phin tu* huu h^n nrtd rOng chuyin \^ trinh bdy d phin 2 cho phdp xdc djnh sy Idm vi$c cOa
mx^
h | k^ d u edng trinh sau khi da xuit hipn mpt hay nhieu bO p h ^ bj phd hogi cgc bO- T r ^ co sd dd, d t h i d i ten quy trinh tn/c tilp xdc djnh tfnh du cOa cdng Irinh thdnh quy trinh don gidn gom 5 budc nhu sau:
1. Xic dinh ndi Iwc gidi h^n cOa kit ciu theo tidu chuin thiit ki- (PJ
2. Md hinh hda kit du. dit tii tr^ng thiit ki idn md hinh 3. Gia ting tai trgng thiit ki di
xic dinh hd so tii trong cua tii trgng thiit ki tucmg Ong vdi cic TTGH:
' TTGH vi m$t sir dyng: P^
• TTGH cwdng d0: P^
4. Xic dinh h$s6 tinh dw ung vdi cic TTGH. Hi s6 tinh dw ting thi ii h$ so tinh dwnhd nhit 5. Niu h$ s6 tlnh dw >1 thi du cd dw. Niu h$ so tinh dw nhd hem 1 thi du l&idng dw.
Trong quy trinh ddnh gid tfnh du d i tiln ndy, do da xdc djnh dugc tdi trpng cyc hgn culi cOng cua kit c l u md khdng d n phdi lin lugt dd bd d c bO phan kit d u bj phd ho^i nen kiln nghj gOp chung trgng tiidi gidi hpn cudng dp ban d i u vd b^ng thdi gidi hpn cudng dO ting the thanh chi mOt trpng thdi gidi hpn vd gpi Id trgng thdi gidi hgn cirdng dO, xdt d i n trgng thdi Idm vipc cyc hgn d a kit d u ting thi. Trgng thdi gidi hgn v l sCr dgng vin dugc xdt nhu trong quy trinh ddnh gid tinh du tn/c tilp trudc ddy (xem [3], [4], (IO]). TCr dd, quy trinh gom 10 budc (cho kit d u phin dudi) vd 12 budc (cho kit d u phan trdn) du^c d i tiln thdnh quy trtnh gIm 5 budc nhu da trinh bay.
4. Vf o g A P DgNG Q U Y TRINH
D A N H G I A TJNH DU TRl/C Tl6p
CAl TI^N VA MO HiNH P H A N Tl>HCru HAN M d R O N G C H U Y £ N
Vj XAC bjNH TfNH DU K^T CAU 4.1. Md ta bai toan
Xet dam lien tuc 2 nhjp cd mgt edt ngang va sa do chju lye nhu Hinh 4:
0.3m
4@12 J
) 0 O I 4D20
4D20
'
Mat cat ngang dam
Hinh 4. Dam lien tyc 2 nhip chju
tai trong thing duvg Dam chiu tai trgng thang dung tgi mgt cat gil>a nhjp thu 2, vj tri d|t tai dugc lya chpn de tgo ra mo men va dp vdng Idn nhat tren nhjp thu 2. Day la vj tri dgl tai gdy ra hipu ung tai trpng bat Igi nhit.
Cac dac trung vat lieu dam the hien d bang sau (Bang 1).
4.2. K i t qua phdn tfch sy Idm vipc cua dam dudi tdc dgng tang dan cua tai trpng K l l qua phan tich bang theo ly thuyet cho dudng cong lye - chuyen vj vd trang thdi dim khi pha hoai d Hinh 5.
Bing 1. D$c tnmg v$t li$u sw dyng dam lien tyc hai nhjp V$tli#ubSt6ng
M6 dun dan hii Cu6ng d9 chju n^n khi u l n
E, f .
26889.6 30
N/mm^
N/mm^
V f t l i f u t t i i p Gidfi h^n chiy
MS dun Sin h i i f „ E.
400 20000
N/mm^
N/mm'
S611 nam 2015 I
KHOA HOC-CONG NGH? t t t K K phd hogi: F = 229.78kN.r =
229.78/162/1.3=1.06 Trong dd, hO so 1.1 d budc 2 vd he sd 1.3 la hp s6 ti 1$ xdc djnh tu- ly thuylt dO tin d y theo nghien CU'U cua Ghosn cho kit d u phin tren d n g trinh d u (xem [3]).
Nhu vgy h^ s6 tinh du- cua k i t cau dam lidn tgc 2 nhjp trong v(
dv nay bang 1.06.
5. Ktl LUAN
Bai bdo da gidi thipu quy trinh cai tien giOp xac djnh tinh du eho k i t c l u edng trinh c l u bang
vipc dng dgng md hinh phan tO' hi>u hgn md rOng chuyen vj, cd xet d i n phd hogi cgc bO cua k i t d u do uon vd d t . Cung vdi dd cung dd t i l n hdnh ung dgng quy trinh cdi t i l n de tinh todn tinh du cho k i t cau dam lien tge 2 nhjp bdng be tdng elt thep. Quy trinh cai t i l n cho thiy dugc tinh dan gian, tryc quan vd cd t h i dp dgng tryc tiep vdo cdc bai todn phan tich thilt k l d u , phiJ hgp vdi yeu cau lieu chuan thiet k i t cau 22-TCN-272-05 cOa bp GTVT, Vipt Nam •
J Hinh 5. Su lam viec cua dam du'dl tac dyng cua tai trong
4.3. Xdc i^nh tinh du* cOa dam n^slien tgc hai nhjp theo Quy trinh ix^ tryc t i l p cai tien
(li^jTiJ' kit qud md hinh tren, cd I h l {ittcac djnh dugc hp s i tfnh du eua Qjiiijlm lien tge 2 nhjp theo d c budc '0fiua quy trinh tryc tilp nhu sau:
"j^^udc 1. Xac djnh tdi trpng phd ll"''*iogi theo phan tich ddn hoi cOa
l„^Nltkl:
j'l 'heo tidu chuin thiet k l , md-men
•^mHidi hgn cOa m^t d t dam bang jtki^'vq ~ IfilkNm. Ngogi lye tdc
gng gay ra md-men uon nay tren ' l m b l n g F ^ = 162kN I f V ^ 2. Xdc dinh hO so tinh du Jj,ing vdi TTGH su" dgng
Lye ngang u'ng vdi TTGH su dgng (gdy chuyin vj . bing L/1G0 = 5000mm/100 5 ^ = 50mm) bing F=210kN. HO
s i t i n h d u r f = (210/162)/1.1)
^ j ^ 3. Xdc djnh h | s i tinh du - ^ i g vdi TTGH cudng dO 0 Lye ngang O-ng vdi TTGH r - j ^ culi cung cho dilu kiOn
T A I L i f u THAM K H A O •'^^m [I] AASHTO, Standard specifications for highway bridges, Washington D.C:
American Association of State Highway and Transportation Officials, 1996.
[2] AASHTO-LRFD-2012, 'AASHTO LRFD Bridge Design Specifications,' Highway Subcommittee on Bridges and Structures, 2011.
[3] Ghosn; Moses, "NCHRP Report 406 "Redundancy in Highway Bridge Substructure",' Transportation Research Board, Washington DC, 2001 [4] Moses and Ghosn, "NCHRP Report 406 "Redundancy in Highway Bridge Supersfruclures", Transportation Research Board, Washington DC, 1998.
[5] Ghosn, M. and Yang, J, Bridge system Safety and Redundancy, NCHRP Report 776, 2014
[6] EN 1991-1-5, "Eurocode 1: Actions on slmdures - Part 1-5: General actions - Thermal actions", European Standard, 2003.
[7] EN 1993-1-2. "Eurocode 3. Design of steel stnjctures. Part 1.2: General rules. Structure fire design", European Standard, 2005.
[8] EN-1992-1-2, Eurooide 2: Design of Concrete Structure - Part 1-2:
General njles - Structural Fire Design., Eurocode, 2004.
[9] BO GTVT, "Ti&u chuin thilt k l c l u 22-TCN-272-05", NXB Giao Thdng V | n Tdi, 2005.
[10] Tran Due Nhipm, Nguyen Thj Minh NghTa, Nguyen Vilt Huy. "Gidi thi§u quy trlnh cac budc kiem tra linh du' ln,rc tiep", Vol. 4, 2014.
[ I I ] Trln Due Nhi#m, Nguyin Thj Minh NghTa, Nguyin Vilt Huy "Nghidn ci>u tinh du trong ket c l u b6n dudi cong trinh c l u , cdc TTGH vd dO tin cpy".
Vol. 3, 2014.
[12 V. Ngo, A. Ibrahimbegovie and D. Brancherie, "Model for localized failure with thermo-plastic coupling. Theoretical formulation and ED-FEM implementation", Computers and Stnjctures, Vol. 127, pp. 2-18.2013.
[13] B. Pham, L, Davenne, D. Brancherie and A. ibrahimbegovie, "Stress Resultant Model for Ultimate Load Design of Reinforced Concrete Frames:
Combined Axial Force and Bending Momenf, Computers and Concrete, pp.
303-315,2010.
[14] N. Bui, V. Ngo, D. Brancherie and A. Ibrahimbegovie. "Enriched Timoshenko beam finite element for modelling bending and shear failure of reinforced concrete frames". Computer and Structures, 2014.
[15] A, Ibrahimbegovie and E. Wilson, "A Modified Method of Incompatible Modes'. Communications in Applied Mechanics Methods, pp, 187-194,1991.
[16] R. Taylor, 'FEAP - A Finite Element Analysis Program. Version 7.5.
Prcigrammer Manual", 2004.
, l l 1 n S m 2 0 1 5 l * * ^
