Nghien CLFU, tinh toan v6 conoid du'O'i tac dung cua ap ILPC thuy tinh va ap ILPC dat
Ngay nhan bai: 15/7/2014 Ngay sirS bai: 5/8/2014 Ngay chap nhan dang: 10/8/2014
TOM TAT:
V6 conoid bi tdng c6t thep la loai v6 c6 ba bien thing va m6t bien cong. Dp cong ciia v6 tang dan tii bien thang trd xuong, khien cho idia nang chiu lUc cua v6 tang dan theo phucfng nay. Viec iing dung dac diem nay cho cac ket cau chiu ap lUc thuy tinh hay ap lUc dat {nhflng ap luc co dang phan bo hinh tam giac, gia t n tang theo do sau) nhif dap thiiy dien, be chUa chat long, silo, tudng chan dat c6 the tan dung dUOc Uu diem ciia loai v6 conoid, khien cho iing suat tren be mat v6 ddng deu hon, giiip tiet kiem vat lieu, thep chiu lUc dvtac bo tri deu hon, de dang hOn trong thi cong.
ABSTRACT
Reinforced concrete conoidal shell is the shell type has three straight edges and a curved edge. The curvature of the sheU increases gradually from the straight edge downward, leading to the bearing capacity of the shell increases gradually according to this direction. The application of this feature to the structures bearing hydrostatic pressure or earth pressure (triangular distribution pressure types, the value increases according to the depth) such as hydroelectric dam, fluid reservoir, silo, retaining wall can take advantage of the strengths of this type of conoidal shell, causing stress on the shell surface more evenly, saving material, bearing steel will be arranged more evenly and easily in construction.
PGS. TS Le Thanh Huan Tnidng Dai hoc Kien triic Ha Noi Th.S TrSn Anh Tii
Cong ty CPTM Cong nghe va Xay difng TRATECHCOM
Le Thanh H u a n , Tran Anh Tu
l.DktvSnai
Ket cau v6 mong be tong cot thSp (BTCT) eo Uu diem noi bat so vdi cac k^t eau ban phang cung loai la phkt huy toi da khd nang chiu nen tot, khac phuc nhuoc diem chju keo kem cua be tong do do wuot duoc nhjp Idn va tiet kiem vat lieu.
V6 conoid la loai v6 eo do cong thay doi, duoe tao bdi mot dUdng smh 1^ dudng thang chuyen dong song song vdi mot mat phang co dmh.
Dudng t h i n g nay ludn luon tUa tren hai dUdng chuan; mot dudng t h ^ n g va mot dudng eong (hinh 1). Dudng chuan cong cd dang doi xiing qua true cua no, cd the la mot dudng parabol, mot cung trdn hoac mot dUdng day xich.
!
a) b) Hinhl a-Sodovoconoiddangnimngang; b-Sudovoconoiddangdiing
Vd conoid cd do eong tang dan tU bien t h i n g xuong theo phUcmg true y, khien cho kha nang chiu luc cua vd tang dan theo phuong nay.
Viec Ung dung dac diem nay cho cac ket cau chiu ap lUC nUde hay ap lUC dat (nhu'ng ap lUc ed dang phan bo hinh tam giae, ap lUc tang theo d d sau) n h u d a p thuy dien, bechUa chat Idng, silo, tudng chSn dat cd the tan d y n g dUoc het uu diem cua loai v6 conoid, khien cho Ung suat tren be mat v6 dong deu hon, giup tiet kiem vat lieu, t h e p chju lUe dUoc bo tri deu hon, de dang hon trong thi cong.
Ket cau vd cong trong cac cong trinh thiiy dien hay be chUa da duoc Ung dung tU lau. Cdng trinh dap thuy dien cd the ke den dap Hover d Nevada, Hoa Ky (hinh 2a)hay dap Xiluodo 6 Van Nam, Trung Qudc (hinh 2b).
Xiluodo -Van Nam, Tmng Oufic
Cdng trinh dap XilucKto cd dang v6 tru ngan, day la dang vd chiu lUe t o t de thi edng, tuy nhien loai vd nay cd d d cong khong doi, khi chiu ap lUc nudcse xuat hien noi lUc Idn dchan cdng trinh.Dap Hoover eua Hoa Ky, dUoe thiet ke khoa hoc hon. da Ung dung viec tang dan dp cong vd theo phUcJng (lUngtC/trgnxudng(taangtUnhuvd conoid). Dang vd neiy la mdt phan eua vd ndn cut. Tuy nhien neu mudn lien ket nhieu v6 tao thanh mot bUc tUdng ch3n Idn til nhieu vd nhd x^p thSng hang thi dang vd nay khd dap Ung dugc Vdi ckc bien t h i n g , vd conoid hoan toan cd the giai quyet dUCJC viec nay, nhSm lam giam chieu dai nhip.
Cdng trinh be ehUa Ung dung ket cau vd eong ed the ke den be chUa dung tfch rat Idn, len den aOOOm^ dugc xay dung tai Ph^p nam 1952 (hinh 3 ) . Be chUa nay dugc cau tao thanh 2 ldp, hop ly ve mat chiu, nhUng vd tru phia trong van cd m o t sd yeu t d khdng hgp ly khi chju ap luc thijy tinh. Ngoai ra, lien ket thanh be va mai cung phUe tap hon, do bien cong cua v6 tru gay nen, oen khd cd the dung loai mai dang vdm de tan dung khci nang chiu lUc
quat ma eae tae gia ndi tren da lay d o lam CO sd de xay dUng cac Idi gik\ eho bai toan v d conoid.
Trong do, A.M.Haas va W.FIugge da giai true tiep he phuong trinh tren bSng each si!t d u n g ly thuyet dac trUng (theory of charatenst). Ldi giai cua W.FIugge chl ap dung eho v6 conoid trdn, vdi v i e c o n g v i e t lai phuong trinh mat vd theo he toa do eUc. Trong mdt sd nghien cUu khkc, M.Soare va Ramaswamy da sU dung ham Ung suat de gian tiep giai he phUdng trinh tren. M.Soare da ap dung m o t sd ham Ung suat dang da thUc de giai bai toan vd conoid t o n g quat trong khi Ramaswamy sU dung ham Ung suat dang chuoi de giai bai toan vd conoid dang parabol da duge viet lai phuong trinh mat v6.
3. Phan tich t r a n g t h a i Ung suat, b i e n d a n g cua v 6 c o n o i d dUdi t i c d u n g ciia t i i t r o n g p h a n b o d a n g t a m giac bSng phUtfng p h a p p h i n tiir h u l l h a n :
Nam 2013, eac tac g\k Le Thanh Huan vk Tran Anh Tu da nghien cUu mai vd conoid chiu tai trong phan bd dang tam giae bSng p h u o n g phap PTHH nhd sUdung phSn mem SAP2000. Nghien eUu ap dung vdi nhieu loai lien ket bien va hai trudng hop chieu day vd (ehieu day khong d6\ vk chieu day tang dan t U t r ^ n xudng). Dudi day xin neu ket quk khko sat v6 cd ehieu day khong doi {toan vd day 30em), kieh thude 30x16m, do vong 5m, vat lieu be tong c^p d o ben B40, cd 4 eanh lien ket khdp, chiu ap lUe thuy tinh (hinh 4).
Kinh 3: Bechi}a2%dungt[chS0OI}ni tai Phap a) Mat bdng IK, b) Mat cat be; c) Chi tiet c3t ngang 2 lap be 2. T6ng q u a n v e t i n h h i n h n g h i e n ciJTu ly t h u y e t t i n h t o a n v 6 m d n g :
DUa tren co sd iy thuyet ve vd thok\, ldi gicii cho bai toan v6 conoid dugc cac nha khoa hpe bSt dSu nghien cUu vao cuoi nhUng nam 50, dau nam 60 cUa the ky XX, trong do phk\ ke den eae tae g\k tieu bieu n h u MSoare, W.FIugge, A.IW.Haas, Ramaswamy... Vd conoid la m o t trudng hop rieng cua v6 cong hai ehieu dUong, nen ta hoan toan co the sUdung he phuong trinh can bSng tdng quat eija vd cong hai ehieu dUOng d^lcim CO sd tinh toan:
3N. ^ dx dy
o Q . ^ , dx dy
= 0; aN„ 5N.
dx dy
• k N + k X - H 2 k „ N „
Doi vdi vi6c ti'nh toan v6 theo 1^ thuyet phi md men thi he phuong trinh can bSng tr^n dugc don giSndi rat nhieu:
dy
5y
^p, sh(^5 ^k^^'^4'^&?
(2) being tdng
Hinh 5. Mo hinh li'nh to^n vi conoid lien ket khdp, do day khong doi trong SflP2000
TUcac hinh 7-10 ed the nhan thay Ung suat o_
bien thien theo dang parabol doc theo p h u o n g Oy, chu yeu la Ung suat nen, phan b d kha dong deu. Gia t n o_, Idn nhat xuat hien tren dUdng OA, (dudng giUa vd), tai vi t r i diem M ed t u n g d o
yM = - L . Cung theo p h u o n g nay, Ung suat giar dan v4 phia hai bien tren vk dUdi. Tai vi trf 2 bie nay, Ung suat rSt nhd, xap xi bSng khdng. Gia t o^tai cac bien BC Vci DE rat nhd, day la do die kien bien da chon. K h i nang truot dugc the phuong X cua cac khdp tren 2 bien nay khie cho Ung lUe tai bien gan nhu bkng khdng, do I nguyen nhan lam giSm Ung suat tai day. SUphSi bd Ung suat va gia trj Ung suat kh^e nhau, tu nhien ve t i n h todn so b d c6 nhieu Uu diem, Gi tri Ung suat nen Idn nhat cda vd o „3,= 1628,7(T m'), be t d n g B40 dang dCing cd R^ = 2200 [Vm hoan toan d u k h ^ nang chju lUc
iJng suat o^ vk Ung luc N^ bien ddi rat phii tap, chu yeu la Ung suat nen. Lien ket khdp trUc hoan toan triet ti&u Ung suat tai bien t h i n g CDv bien cong BA E.Tai hai bien nay, Ung suat xap) bang khdng. Vung cd Ung suat nen Idn xuat hiei tai vi trf gan tam vd vci gan bien BC, DE Ve ma gia tri, Ung suat nen Idn nhat van nhd han nhiei so vdi Ung suat theo phUOng ngang, nhUva d u o n g nhien be tdng van dCi khci nang ehju li/c.
Hinh 6 VUng cd dng su3t Mo - do cong Gausses am Tren vd t o n tai mdt vCing cd Ung suat o_, va t la Ung suat keo cd gici trj nhd, chinh la vung cd 3 cong Causes am (hinh 6). Tuy nhien vung nay ri nho, gia t n Ong sucit k6o cung rat nhd.
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Hinh B: - Ung suat theo phuong diing phan bo tren mattrung iih(Jiavfi(donviT/m')
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Trang thdi Ung s u ^ bien dang cua vd conoid dudi tac dung cua tk'i trong phan b d deu da dugc cac tac gia A.IW.Haas, W.FIugge, M.Soare va Ramaswamy nghien cUu, tuy nhien chua ed tdc gid nao de cap den trUdng hgp vd conoid chju tai trong phan bd dang tam giac. Mat khac, Idi giai gidi tich cua cdc tae gia eon mdt sd han che nhat djnh nhU. ehi p h i i hop vdi vUng cd 36 cong Idn gan bien eong. Cang tien tdi gan bien t h i n g , khi do cong tien tdi khdng (R—•") thi ket qud nhan dugc khdng con ehi'nh xae. Oieu nay da duge eac tac gid thUa nhan, va cd dUa ra gidi phap n h u huy bd bJen thang (de v6 bien thanh vd conoid cut). Dieu nay khien cho loi the ve mat lien ket cilia bien thSng vd vdi eac c^u kien khac da khdng cdn. Ngoai ra, cae loi gidi gidi tich cua nhUng tac gid tren, neu sU dyng vao viee gia! bai todn vd conoid chiu tSi trong phan b d dang tam giac cung gap khdng ft khd khan ve mat todn hoc cung n h u ve mat cau tao hinh dang v6. Cac tae gia Le Thanh Huan va Tran Anh Tu [5] da nhan duoc mdt sd ket qua trong qud trinh t i m Idi g i i i bai toan vd conoid dUdi tac dyng eua tdi trong phan bd dang tam giac bang each sU dyng ham Ung suat, cd tham khao dang ham Ung suat cda Ramaswamy cung mot sd tac gia khac, ket hop vdi phuong phap diem. Day la mdt phUOng phdp dugc nghien cUu bdi Le Thanh Huan [1], sUdung ham Ung suat ket hap vdi viee khao sdt cac diem dac biet tren vd de dUa ra cdc gia tri ndi lUc trong v6 dudi dang cac ham sd. Ham Ung suat (p(x,y) duoc chgn can thoa man dieu kien biSn va tuan thCi theo cac mdi lien he:
N = dy'- 5x' N „
Oxyz z = f l i b '
Cdc do cong cda mat vo:
dx8y L b '
HinhIO N -Onn luc •''^ophiffng ddng cua v6 (don viT/m) 4 Phan'ticht g thai limg suat, bien dang cOa vd conoid ciuc. tac d^rtg cAa t i i trong p h i n b6 d-':.v - ' - ^ '^"^ ' » * " 3 phuong p h i p g i i i tich:
= 0
Phuong trinh can bang theo thuyet phi m o m e n :
KK + 2k„N., + K^, = pX + qY - Z (7) Trong dd:
Hmh 11: So do mat vd chm tac dung ciia tai trong phan bo dang tam giac
Do tai trgng theo phUOng X, Y r^t nhd, cd the coi gan dung X = 0, Y = 0.
T^i trgng theo phuong z:
Z - p - H)
(9)(10)
(3) Khi do viee t i m leri giai cua chung bSng cdch dua vao he phuang trinh can bang (2), ta se tim dugc cac he sd a' cua ham thong qua vi^c giai he p h u o n g trinh vdi toa do x, y cua cae diem cho trudc.
Phuang trinh mat vd viet cho he true toa do
Oieu kien bi§n cho vd cd hen ket khdp trugt n h u t r o n g muc 3:
x = ± b ; N . = 0 ; N j = 0 ; N , , ^ O l y = + a ; N , - 0 ; N , = 0 ; N ^ 5 ^ 0 j De thda man dieu kien bien (10), sau khi da thU rat nhieu ham Ung suat d l chon ra ham phu hgp, tdc gid da chgn ham ijmg suat cd dang dUdi day:
<p(x,y)=a, ( x ' - 6 b ' x ' + 5 b ' ) ( y " - 6 a V + 5 a ' ^ ( 8 1t,_2 6 ?,-4 . V -1 ^ 2 2 r 4 \
^ 3 , | ^ x ' - - b V ^ - b x J ( y - 6 a y - . 5 a ) ( ^ ^ j Cung vdi vi§c xet 2 diem A(0,—) va B(^—,0) tren mat vd t i m dUOc:
Cdc bieu thUc ndi luc;
32p
(4) De thuan tien cho viec tinh toan, chgn hdm Ung suat, cdc tdc gid dd rdi gdc toa do vao tam mat bang vd, goi la he true O, x, y, z, [hinh 11).
Khi do, phuang trinh mat vd t r d thanh:
(x' -6bV +5b')(y' -a')^
+ 1 , 7 3 0 4 - E ^ f «• - - b ' x ' + - b ' x ' V y " - a " ) a V f l , 5 3 J ^ ' N = i . ^ ^ ( x - - b " Y y ' - 6 a y + 5 a ' V
' a ' 195a'b"f'- • ^ '
+l,7304-5-(2x' -3b'x' +b'x'')(y' - 6 a y +5a a b r^ ^^
a > _ 128p
exdy~ 585a'tff (x=-3b'xXy'-3a'>
- 0 , 2 4 7 2 -2 - P _ f 8 x ' - ? l b V 3 b ' x = V y ' - 3 a ' ' a ' b ' f l 5 3 J * - ' • Cac bi^u 06 noi luc cho m o t so mat c3t tren v6 duoc trinh bay tren hinh 1 2 v a h i n h 1 3 v 6 i c a c gia trj cu the: p = 16(T/m"), a = 8 m , b = 15m, f
= 5m.
^ ^ — : , ":iiX'
, , \ . ^ , - - Mi • - -
-^
Hinhl5:K6ilil(N_taimattstcdtpadoy=0
Tinh theo phu'ong phap phan tithiiu ban (SAP2000) Tfnh theo phuvng phap gi^i tieh (phuong ph^p di^m)
Hlnh14:M6ilUcN,taimatcSt cdtoa d6K=7m
Tinh theo phuWig ph^p phan tiyhQu han (SAPIOOO)
Tinh theo phuang phapgiai tich (phirong ph^p diem)
5. Ket l u i n .
1. Nhu'ng ldi giai trUdc day cua vo conoid chi p h i i hap eho eae ket eau mai eong trinh ehju tai trgng th^ng dUng phdn bd deu, khong thich hop vdi nhUng ket cau vo conoid hay vd tru trong eae edng trinh dap chan nUde, tUdng chan dat, dUdi tac dung ciia dp luc thuy tinh hay ap lUe dat va can cd nhUng nghien cUu rieng.
2. Trong nghien eUu cua minh, cac tdc gia da dat dugc nhUng ket qud ban dau ve trang thai Ung suat trong vd thoai conoid chiu tac ddng ciia dp lUc thuy tmh hay dp luc dat, cd 3 bien thang, 1 bien cong nhd viec Ung dung phan mem SAP2000 vd cac idi giai giai tfch theo ly thuyet phi momen.
NhijTig ket qua bang s6 nhan dugc da chUng t d vd conoid BTCT ba bien t h i n g cd nhieu Uu viet khi chiu dp lUe thuy tinh hay dp lUc dat, cd the sUdung trong cdc cong trinh dap chkn nudc hay tUdng chan dat cd khau do vd chieu cao Idn.
3. Ket eau vd conoid thoai cd do vdng hoan toan cd the sU dung cac phutfng trinh giai theo 1:^ thuyet phi mdmen bang phuong phap diem la phuang phdp dOn gian, cho ket qua nhanh vd ed do tin cay nhU eac phuong phap khac, so ca vdi phan mem SAP2000. Phuong phap nay cdn CO loi the ddi vd\ loai vd cd do cong thay doi.
4. De ed the dua vao Ung dung thUe te can cd nhUng nghien cUu tiep theo nhat Id bang thuc nghiem tren m o hinh.
TAI LIEU THAIM KHAO:
1. PGS. TS. Le Thanh Huan (2008), Ket du diuyen dung be tong col thep, N«b Xay di/ng. Ha Noi.
2. PGS. TS L" Thanh HuEn (1981), KOt cEu m.i va mang b- t«ng eet tht)p, Nxb X©y dimg, Kp Nei
3 X RTimosenb,X.Voinopxki (1971), Pham Hong Giang, Vu ThJnh Hai, Nguyen Khai, €oan HOii Quang dich, Ta'm va vo, Nxb Khoa hoc Ky thuat. Ha Noi
4. PGS. TS Le Thanh Hua'n, ThS 06 fliic Duy (2001), Nghien cdu trang thai dng suat bien dang cua ket cau mai vd mdng be tong edt Ihep dang conoid chiu tac flgng ciia tai trong va su thay doi nhiet do trong dieu kien khi hau Viet Nam Tn/cmg Dai hoc Kien tnic Ha Noi, Ha Ndi.
5 PGS. TS Le Thanh Huan, ThS Tran Anh Tii (2013), Nghien ciiij tfnh toan v6 conoid dudi tac dung ciia ap \\sc thiiy tfnh va ap luc dat TnrangOai hoc Kien triic Ha Noi, Ha Noi.
6 Arend Maarten Haas (1962), Design of thin - concrete
shells Voll Positive cuvature index, JohnWeily and sons.
7. Wilhelm Flugge (1962), Stresses in shells, Springer - Verlag.
8. 6.S Ramaswamy (1968), Design and construction of Concrete shell roofs, McGraw Hill, NewVorit
9. MSoare (1958), Menbrane Theory of Conoid shells, Cement and Concrete Association