QUYTRlNHDANHGIAfiOTINCAY CUA KET CAU THEO MO HINH MOf
DUNG CHO NHA CHUNG CU*
Nguyin Hiing Tuan Le Xuan Huynh
ABSTRACT
This article presents "Fuzzy regression anal- ysis by quadratic programming reflecting central tendency"algorithm and analysis methods to evaluate quality based fuzzy model. Hence, proposes procedure to asssess safe level of buiding structures.
Th.S Nguyen Hiing Tuan SdXaydimgHaNpi GS. TSLe Xuan Huynh TrUofng Dai hoc Xay di/ng 55 Giai Phong, Hai Ba TnAig, Ha Noi
1. Dat van de
Danh gia chat iQpng nha chung cQ, dac biet la danh gia mQc dp an toan cua ket ca'u trQdc khi dQa edng trinh vao sQ dung la mdt van de bQc thie't, de dam bao lpi ich cua cdng ddng, tranh lang phi cua cai xa hdi.
Tren thQc te, trong ket eau nha ehung cQ, phan Idn cac dai iQpng dQpc dQa vao trong tinh toan deu khdng the 6ugc xac djnh mdt each chinh xac hoan toan. Ngoai ra, trong qua trinh thie't ke phai sQ dung cac gia thie't de don gian hoa tinh toan.
NhQng gia thiet nay thQdng khdng phan anh het nhQng tinh hudng xay ra trong thuc te, vi ve ban chat, cac sU kien, hien tQpng deu cd chQa nhQng yeu td khdng ehinh xac hay mo hd nhu dja chat cdng trinh, tai trpng gid, ddng dat..., ben canh dd edn phai ke den eae sai lech cua dung cu thi nghiem, kiem djnh, han ehe trong tri thQc cua ngQdi thiet ke.
Bai nay gidi thieu mdt quy trinh danh gia mQc dp an toan eua ke't ca'u ndi chung va ap dung eho nha ehung cUxay mdi vdi quan niem gia tdc nen, he sd tam quan trpng va CQdng dp be tdng la cac dai iQpng md, nhQng dai iQpng khae dQpc xem la td. Vi du minh hpa viec ap dung phUPng phap do tae gia de xua't danh gia mQc dp an toan cua ket ca'u dang khung edng trinh nha chung eu 9 tang d Ha Npi.
2. Xay diTng quy trinh danh gia 2.1.Nguyen tae chung
Mpi phep danh gia ke't cau deu la cae phep so sanh giQa 2 tap sd : tap kha nang va tap trang thai eua ke't eau. Ne'u d md hinh tien djnh, phep so sanh nay dQpc thQc hien tren cO sd eae sd lieu la eae bie'n sd cd gia trj xac djnh thi d md hinh md, eae sd lieu nay la cac tap sd cd mQc dp phu thudc vao trj sd "tin tudng". De Qng dung ly thuyet md danh gia mQc dp an toan, cd hai ndi dung cP ban can giai quye't la : xay dung tap md kha nang va trang thai tren eo sd eae dQ lieu dau vao - dau ra; iQa chpn cdng thQc de xay dQng phQong phap danh gia chat lUpng cdng trinh theo md hinh md de ap dung trong thUc te. Trong bai nay, tae gia de xua't phuong phap xay dUng tap md va mdt phuong phap danh gia chat luong ke't eau edng trlnh theo md hinh md, tQ dd xay dQng quy trinh danh gia mQc dp an toan tQOng tQ nhQ dp tin cay trong md hinh ngau nhien ddi vdi ke't cau nha chung cQ.
2.2. Cac gia thiet va quan diem tinh toan
- Cac hieu Qng tai trpng va kha nang ket eau dupe xem la nhQng sd mdtam giac can.
- Cae dai iQpng md ed tinh chat ddc lap, khdng tQPng tae vdi nhau.
- MQc dp an toan cua ket ca'u dupe danh gia thdng qua mQc dp an toan cua cac bd phan ket cau cd nghi ngd ve chat lUpng (cae thdng tin thu dupe ve kha nang cua bd phan dd la khdng day du do viee lay mau vat lieu khdng tuan thu theo tieu ehuan
^ B i l i n S l .12.2009 57
thi cdng nghiem thu, hoae ket qua nhan dQpc khdng dap Qng dQpc ly thuyet thdng ke do dp sai lech vQpt qua sai lech cho phep).
2.3. Phan tich mdt sd phuong phap va lUa chpn cdng thQc danh gia theo md hinh md
Oe danh gia mQc dp an toan cua ke't eau theo md hinh md, cd mpt sd phuong phap da dUpc de xuat, vi du: phuong phap lat eat a, phQOng phap dp tin cay bae nhat md (FFORM), phQOng phap ty sd giao hdi, phQong phap ty sd dien tich khoang an toan md.
PhQOng phap lat eat a [11] chi dQa ra each tinh trung binh gan dung va chQa xet de'n anh hQdng dp rdng eua hai tap trang thai Q va kha nang R. Phuong phap dp tin cay bac nha't md [7] dQpc xay dQng kha edng phu dQa tren eo sd ham mat dp xac sua't f(x) va ham phan phdi xac sua't F(x) deu la nhQng tap md, tuy nhien trong thUc hanh tinh toan vdi nganh xay dung se khdng thuan tien do ed khdi lupng tinh toan ldn.
Phuong phap ty sd giao hdi [2]
dupc xay dUng tren co sd phep giao (theo luat min) va phep hpp (theo luat max) hai tap md trang thai Q va kha nang R, sau dd danh gia mQc dp pha hoai bang ty sd ke't qua eua phep giao vdi ke't qua phep hdi trong dieu kien an toan chac chan { R > Q). Phuong phap nay da xet den anh hudng dp rdng eua hai tap Q va R. Tuy nhien, trong edng thQc xae dinh can tim tung dp h, giao giQa Q va R. Oieu nay se khdng thUe hien dupe khi 2 tap md Q va R eat nhau nhieu hPn mdt diem.
Oe khac phuc dupe viee tim giao diem giQa Q va R, cd the ap dung edng thQc danh gia chat iQpng trong [1], de xuat edng thQc danh gia mQc dp an toan, xet trQc tie'p khoang an toan md:
M = R - Q, vdi edng thQc danh gia sau day (hinh 1):
MQe dp pha hoai:
FP = i j , / (u),-hw^) (1) Va mQc dp an toan:
SP= w2/(ijjl-1-0)2) (2) Cd the thay cdng thQc ty sd dien
tich khoang an toan md de ap dung
trong thQc te vi khdng can tinh giao diem cua tap trang thai Q va tap kha nang R. Cdng thQc tinh toan tQOng tQ vdi edng thQc tinh dp tin cay (sQ dung ham mat dp xac suat quang an toan trong md hinh ngau nhien). Vi vay, ed the xem mQc dp an toan SP tinh theo (2) la tQOng dQong vdi dp tin eay P^ va FP tinh theo (1) la tQOng dQOng vdi dp khdng tin cay P, theo djnh nghTa d md hinh ngau nhien.
DQdi day se sQ dung khai niem tQOng dQOng nay.
2.4. Thuat toan hdi quy bang quy hoaeh bac 2 xet anh hQdng xu hQdng hQdng tam:
Trong bai toan danh gia dp tin cay theo md hinh md cua ket cau, ta thQdng gap trQdng hpp cac dQ lieu dau vao - dau ra la cae bd sd da bie't (x., y.) trong dd xi la cac dQ lieu dau vao - ddi vdi viee xae lap ham trang thai la eae dQ lieu ve tai trpng tae ddng, dp cQng eua ket eau, dac trQng eo ly eua vat lieu, ddi vdi viec xac lap ham kha nang la cac dQ lieu ve vat lieu, kich thudc hinh hpe eua ke't eau; y. la eae dQ lieu dau ra (ddi vdi ham trang thai thQdng la ndi iQc: Qng sua't, mdmen..., chuyen vj, ddi vdi ham kha nang la dp ben ve vat lieu, mdmen kha nang... cua ke't eau). Thuat toan phan tieh hdi quy cho phep vdi sd iQpng nhd eua tap dQ lieu (x., y.) cua hien tQpng khdng rd rang va bat djnh, xae djnh cac ham thude eua bien dau ra Y, sao eho dp lech trong viec Qdc iQpng eae gia trj dau ra yi tQ gia trj dau ra y. eho trQdc la nhd nha't.
Theo [9], thuattoan hdi quy bang quy hoach bae 2 xet anh hudng xu hudng hQdng tam dQpc thQc hien theo 5 bQde nhQ sau :
BQde1 :
Md hinh hdi quy md dupe viet dudi dang:
Y(x) = (a„, ejL + (a,, e,),x, + ... +
(a„,e„),x„=(a'x,e'|x|), (3) vdi|x| = ( l , | x j |xj)',a = (a^
a )', c = (c ,... ,c )• va a'x va c'lxi la gia trj trung tam va dp rdng cua sd md dau ra Y(x).
Xae dinh A =(a, e) trong md hinh
I * r i' - '
(3) thdng qua viec giai bai toan quy
hoach sau:
Ham muc tieu:
minJ = k,a' ^ x ^ x ) a-2k,^yjX|a-i-
' p_ ^ _p_
-nkjC
Z
l II I' 1 V ^ 2hlhl c+k,Xyj
V j=i J j=i
trong dd k^, k^ la cac trpng sd.
Cae dieu kien rang bude:
a'x - c'lx I < y a'x. + c'|x,| s y 1
BQde 2: SQ du'n^ c^a^ gia til ^. =(1,!
c) tim dupc d bQde 1, giai bai toan quy hoach tuyen tinh :
p
maxJ = V h i
vdi cac rang budc dau ra y thudc tap mQc h cua sd md dau ra Y.
BQde 3 va budc 4 : Sap xep hj theo thQ tQ tang dan h, < ... < h,^ <
... < h , tinh gia sd (^^ xac djnh bdi (j)i^ = h|^ - h|^,. Tim gia trj dau tien hk thoa man dieu kien (|)k > w vdi w la dung sai gidi han quyet djnh bdi ngQdi quan sat. Tat ca cac mau cd h^,...,h|^, thude nhdm duRG (remain- ing group), cac mau edn lai thupc nhdm djnh vj trung tam CLG (center located group).
Bude 5: Giai bai toan quy hoach bac 2 xae djnh eae he sd md A. =(a., c.), i = 0,...,n, va E=(0,e)|^ nhU sau:
minJ:
a,c,e
= k,Z(yr a\f
i-k^c' kae^
Cae dieu kien rang bude:
y £[a'x-(1-h)c•|xj|,a'x-^(1- e'|x|] vdi,j e CLG
y^ e [a'x. - (1 - h)e' |x.
a'x -H(1-h)e'|xJ -i-(l
( 1 - h h)e];j eRG Trong do: k^, k^, k^ la cac trpng sd, h dupe gpi la mQc m d .
SQ dung md hinh xap xi tren chQa dQng tat ca cac quan sat de tinh toan:
Y"(x) = A -i-A xl -I-...-I-A X +E = Ax
o 1 n n
-I- E = (a'x, c'x-i-e),^ (7) 2.5. Xay dUng quy trinh danh
gia dp tin cay eua ke't ca'u nha chung eU
Oanh gia dp tin eay cua ke't cau nha ehung eu dQpc thue hien theo cac budc, the hien tren so dd sau:
(6)
58 SiE^niiiSil . 12.2009
3.Viduminhhoa 3.1.0at bai toan
Cdng trinh nha ehung C[J 9 tang cd mat bang ket eau dien hinh va ehi tiet cot nhu hinh ve. Cdng trinh dupe xay chen, dja hinh dang C (dja hinh bj ehe chan manh).Tac ddng eua gid dQpc tinh toan tQ tang 6 trd len.
Cdng trinh dQpc thiet ke vdi nen dat loai C, gia tdc nen a = 0,1486 m/s^ (theo cae sd lieu ed trong [3]).
Tuy nhien, tren thuc te cac sd lieu gia toe nen do dQpc tai dja diem xay dQng ed gia trj nhd nhat va ldn nhat lan iQpt la 0,1281 m/s^va 0,1516 m/
s^. Cdng trinh dQpc tinh toan chju ddng dat vdi mQc dp quan trpng la mQc 11, he sd tam quan trpng tUOng Qng Y, = 1,0. Tuy nhien, viec phan loai mQc dp quan trpng theo [3] dUa tren nhQng tieu chi khdng that sU rd rang, nha't la ddi vdi cac edng trinh cd chQc nang hon hpp (vi du vQa nha d ke't hpp van phdng eho thue, nha tre..), va dac biet sU chuyen ddi dot ngdt gia trj Y, giu'a cac mQc dp quan trpng lien ke nhau khdng ed sU giai thich thda dang .
Cap dp ben chju nen eua be tdng theo yeu eau thiet ke la B 20 (tuong Qng vdi be tdng M 250#).
Phan tieh cac dQ lieu dau vao:
- Cae vung, ca'u kien nghi n g d can danh gia;
- Md ta sQ bat dinh (md hda dQ lieu)
Xae djnh ndi iQc va eae tie't dien nguy hiem (bang p h u o n g
I
phap PTHH - sQ d u n g chuong trinh Etabs de t i n h toan) Xay dQng cac sd m d trang thai tai cac tiet dien nguy hiem
I
(bang thuat toan hdi quy m d - s Q d u n g chQOng trinh Matlabs de t i n h toan)
Xay dQng cac sd m d kha nang tai cac tie't dien nguy hiem
I
(bang thuat toan hdi quy m d - sQ dung ehuong trinh Matlabs de t i n h toan)
Tinh dp tin eay eua eae eau kien (bang phQpng phap phan tich
I
ty sd dien tieh khoang an toan m d - sQ dung chuong trinh Matlabs de tinh toan)
Tinh dp tin eay eua ke't ca'u :
I
- Phan tieh kha nang hinh thanh co eau - O p tin eay eua ket ca'u
Danh gia dp tin eay
I
(so sanh vdi dp tin eay eho phep theo tieu ehuan chau Au)
M(a,.) t
Hinh 1
0,1281 Hinh 2.Tap mda
0,1486 0,1516 a (m/sO
^(1)
205 252 281 R„(KG/cm^
Hinh3.TapmdR Hinh 4. Cac tap md cua mdc dp quan trpng cua cdng trinh
^l^niEiSl ,12.2009 59
Bang 1. Ndi iQc nguy hiem va mdmen quy doi cua cdt C2-A Vj tri cdt
(phantQ) C2-A( C9) C2-A( C9) C2-A( C9) C2-A( C9) C2-A( C9) C2-A( C9) C2-A( C9) C2-A( C9) C2-A( C9)
3gr
(m/s^) 0,1486 0,1486 0,1486 0,1281 0,1281 0,1281 0,1516 0,1516 0,1516
Yl
1,0 0,75 1,25 1,0 0,75 1,25 1,0 0,75 1,25
Mdmen M2 (Tm) -47,2815 -38,1613 -59,64281
-42,2494 -34,39 -50,1099 -48,0162 -38,7157 -57,317
Mdmen M3 (Tm) -3,57081 -1,78382 -10,9014 -2,58481 -1,04487 -4,12498 -3,71476 -1,89245 -5,53715
Mdmen quy ddi (Tm) 50,34 39,69 68,67 44,47 35,28 53,63 51,20 40,34 62,01 Bang 2. Dp tin cay Ps cua cdt C2-A
MQc md h 0 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00
A trang thai [51,2519,7,2827]
[51,3131; 10,6528]
[51,2694; 12,5010]
[51,0827;15,1574]
[50,9044; 19,1522]
[ 50,7700; 25,9667]
[ 50,7700; 38,9500]
[ 50,7700; 77,9000]
[52,4081; 2.248,6]
A kha nang [76,6797;10,2358]
[77,2814;15,1615]
[77,2814;17,6884]
[77,2814;21,2260]
[77,2814; 26,5325]
[77,2814; 35,3767]
[77,2814; 53,0651]
[77,2814; 106,1302]
[71,9502; 27.200]
Dp tin cay Ps 1,0000 1,00000 0,99040 0,96080 0,91070 0,83880 0,74660 0,63370 0,50070
Trong qua trlnh thi edng, don vj thi edng lay mau be tdng cac cdt tang 1 tai true 3 thi nghiem nen mau thu dupe cae ke't qua tuong Qng cua 1 td mau la 205, 270, 281 KG/cml Ke't qua nay cho thay be tdng khdng dap Qng dQpc tieu ehuan thie't ke ( xac suat vUpt qua mac thiet ke nhd hon 95%), va tieu chuan nghiem thu (chenh lech cQdng dp be tdng eae mau qua 15%).
Yeu eau: danh gia mQc dp an toan cua ket ca'u nha ehung eu tren.
3.2.Giai bai toan theo quy trinh de xuat
Degiai bai toan, ta thuc hien theo quy trinh de xua't trong muc 2.5.
3.2.1.Xacdjnh cac vung, eau kien ed nghi ngd can danh gia, phan tich eae dae tinh cae dQ lieu dau vao de dUa ra phuong phap md ta sQ bat djnh (bQde 1):
3.2.1.1. Xac djnh eae vung, cau kien ed nghi ngd can danh gia
Theo cac dQ lieu bai toan, vung ed nghi ngd ve chat lUpng can danh gia la eae cdt true 3, bao gdm : 2 cdt C2 va 1 cdt C4 do cUdng dp be tdng eua vung nay khdng dap Qng dQpc tieu ehuan thie't ke, va tieu ehuan nghiem t h u .
3.2.1.2. Phan tich cae dae tinh eae dQ lieu dau vao de dua ra phQOng phap md ta sQ bat djnh
Cac dai iQpng md trong bai toan la : gia tdc nen a r va he sd tam quan trpng Y,, eUdng dp chju nen cua be tdng R^. Cac dai iQpng nay dQpc bieu dien tren eae hinh 2, 3 va 4.
3.2.2. Xae djnh npi luc eua eae eau kien va cae tiet dien nguy hiem (bude 2):
SQ dung chQPng trlnh Etabs ver- sion 9.2.0 de xae dinh cac tiet dien
nguy hiem va ndi iQe eua eae eau kien, sau dd quy ddi cdt chju nen lech tam xien ve cdt chju nen lech tam theo mdt phuong theo [4] (trang 193, 194). Mdmen quy ddi chinh la dau ra trang thai. Ke't qua tinh toan cua cdt C2-A (C9) the hien d bang 1.
3.2.3. Xay dQng sd md trang thai, sd md kha nang eua cac cau kien tai cac tie't dien nguy hiem (bUdc 3 va bude 4), tinh dp tin eay cua eae eau kien (bUde 5)
SQ dung thuat toan phan tich hdi quy md bang quy hoaeh bac 2 xet anh hUdng xu hudng hUdng tam trinh bay tai 2.4 xay dQng sd md trang thai, sd md kha nang cua cac eau kien; tinh dp tin cay cua eae eau kien theo cdng thQc (2). Ket qua tinh toan eua cdt C2-A dQpc the hien d Bang 2 vdi cac mQc md thay ddi tQ 0 de'n 1.
e o ^ i g n i i i ^ i . 12.2009
SP, k
_ _ J - , 1
1 1 1 1 1 1 1 1 1 0 0,05
-J. _ 1
I 1 1 1 1 1 1 0,10
_ c~ r
1
0,20
~J - 1
1 1 1 1 1 1 1 1 I 0,30
0,99999
X"
1
r
1 1 1 1 1 1 1 1 0,40
0,99995
• " T - -
- n
1 1 1 1 1 1 1 1 1 0,50
0.9932
_ _ j - - - 1 1 1 1 1 1 I 1 1 0,60
0,99588
1 1 1 1 1 1 1 1 1 1 0,70
'o,98378
1 ^
1 1 1 t I 1 1 1 0,80
CO
1 l \
0,90 0,95
S
^,8
1,00 "
Hinh 5. f)6 thj quan he gida mdc md h va dp tin cay cua ket cau 3.2.4.Tinh dp tin eay eua ke't eau
(budc 6), danh gia dp tin eay (bQde 7)
Ve ly thuyet, viee danh gia dp tin cay eua ket eau ed the thQc hien theo phQPng phap danh gia can hoae phQOng phap so dd dang maeh dien. Trong trQdng hpp ket eau khung, phan tQ nguy hiem la cdt C2-A, VI vay sQ dung so do dang song song vdi 3 phan tQ cdt ciJng tang 1 la phu hpp.
Xae djnh dp tin eay eua he theo he
'P^^?"Tl(1-F^,)
Vdi mQc md h=0,5J=' thay sd ta dQOc:P ,. = 0,99995.
s he
Theo tieu chuan trong [10], Qng vdi trang thai gidi han eudi cung [P^]
= 723x10' ta dugc [PJ = 0,9999277.
Nhan tha'y P^^. = 0,999950 > [PJ
= 0,9999277 => dam bao an toan.
3.2.5. Khao sat dp tin cay cua ke't cau theo phQong phap ty sd dien tieh khoang an toan md vdi cac mQc mdh e [0,1]
Trong vi du neu tren, mQc md h dQpc lay d gia trj trung tam bang 0,5.
Oe thay rd vai trd eua h, tQsd lieu tinh toan d Bang 2, ed do thj tren hinh 5.
Nhan xet: TQ cac ket qua tinh toan va dd thj, nhan tha'y khi mQc md h tang thi dp rdng ei eua cae sd md trang thai va kha nang tang, va dp rdng eang tang nhanh khi mQc md h tien dan tdi 1. Viec tang eua dp lech dan den viec giam dp tin cay P^, va ndi suy ta dQpc Pj=[P3]
khi h = 0,596453 . Nghia la khi mQc md h tang, ndi each khae la iQpng thdng tin thu dupe cang khdng day du, khdng chinh xac thi dp tin cay cang tha'p, va khi h eang dan tien tdi
1 (lupng thdng tin thu dQpc hoan toan khdng ehinh xac) dp tin cay P^
cua eae eau kien va he ke't eau giam eang nhanh.
4. Thaoluan
-Mdhinh mdcho phep phan anh ban chat eua nhQng ye'u td khdng ehac chan, khdng day du, khdng chinh xac tdn tai ca ben trong cung nhu tac dpng ben ngoai ket cau, thdng qua viec md ta tinh lien tue tQ trang thai nguyen ven sang trang thai hu hdng (khai niem dp thudc), sU dan xen, Idng nhau giQa cac cap dp, eae phan tQ eua tap tham chieu.
- Phuong phap de xuat kha don gian, ed tinh thQc tien eao do ehi can xay dung hai sdmdtrang thai Qvasd md kha nang R. Khi sd md trang thai Q va sd md kha nang R la eae sd md tam giae, ed the xay dUng ehuong trinh con trong Matlab, nhap cac gia trj trung tam ai va dp rdng c. cua eae sd md tam giac nay de tU ddng xae djnh dp tin eay md eua eau kien.
- Thuat toan hdi quy bang quy hoaeh bae 2 xet anh hUdng eua xu hQdng hQdng tam la phQPng phap thieh hpp de xay dUng sd md do sQ dung eae ket qua ed dupe tQ phQOng phap sd eua co hpc ke't eau va ham thude da xet den dung sai gidi han quye't djnh bdi ngQdi quan sat (ehuyen gia). Thuat toan nay thich hop hon thuat toan hdi quy bang quy hoach tuyen tinh vi da xet den anh hudng ddng thdi eua gia trj trung tam va dp rdng sd md trong ham muc tieu can tdi Uu, do dd trong tinh toan it gap trQdng hpp he sd dp rdng bang 0 hon so vdi khi sQ dung thuat toan hdi quy tuyen tinh.
- Trong bai toan danh gia, viee
xac djnh dai lUpng de lam dau ra trang thai mang mdt y nghTa quan trpng. Ddi vdi trudng hpp khi sd md trang thai va kha nang cd dang tdng quat, dan den sd md quang an toan phQc tap va khdng phai dang tam giae, thl each tinh theo (1) va (2) van ed y nghTa.
- Viec iQa chpn mQc md h thich hpp de tinh toan trong thUe te tuy thude vao sU nhan djnh ve sd lUpng thdng tin ve ddi tQpng nghien cQu, cac nhan td anh hQdng de'n ket qua quan sat d dau vao, dau ra, tam quan trpng eua ddi tUpng, dae trQng cac tac ddng len ddi tQpng nghien cQu ma cac ehuyen gia iQa chpn mdt
mQc md h hpp ly. • TAI UEU THAM KHAO
1. Le Xuan Huynh, Kha nang dng dung ly thuyet md danh gia chat lifpng cdng trinh xay dpng. Tap chi Khoa hpc cdng nghe xay dpng - sd 1/2007 TrPdng Bai hpc xay dpng.
2. Le Xuan Huynh, Le Cdng Duy, Phuong phapty sd giao hpi trong trudng hpp hieu dng tai trpng va sdc ben la hai tap md tong quat. Tuyen tap bao cao hpi nghi co hpc toan qudc lan thd VIII, Ha Ndi ngay 6-7/12/2007.
3. TCXDVN 375:2006 Thiet ke cdng trinh chju dpng dat.
4. TS.Nguyen Trung Hoa, Ket cau be tdng cdt thep theo quy pham Hoa Ky. Nha xuat ban Xay dpng.
Ha Npi 2003.
5. Nguyen Hung Tuan, U'ng dung ly thuyet tap md danh gia mdc dp an toan cua ket cau nha chung as.
Luan van thac sy ky thuat Ha Npi nam 2009.
6. Hd so hoan cdng cdng trinh Nha chung cP9 tang.
7. Bernd Mdller, Wolfgang Graf, Michael Beer and Jan - Uwe Sickert, Fuzzy Randomness - Towards a new Modeling of Uncertainty,Vienna 2002.
8. Bernd Mdller - Michael Beer, Fuzzy Random- ness - Uncertainty in Civil Engineering and Com- putational Mechanics. Springer, Dresden 2003.
9. Fuzzy regression analysis by quadratic pro- gramming reflecting central tendency. Hae- kwan Lee and Hideo Tanaka. Behaviormetrika, 25(1998)65-80.
10. ENV 1991 -1 :1993 Basis of design and ac- tions on structures. CEN, Brussels,1993.
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Icossar'89, The 5th International Conference on Structural Safety and Reliability.
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