Mot vai nhan xet ve van de tinh toan san thep trong do an ket cau thep 1 cua sinh vien nganh Xay dung
ThS. Nguyen Thanh Tung T o m tat
S ^ thep la mgt trong cac cau kien ccf ban thildng gap trong ket cSu thep, tuy nhien cac cdng thufc tinh toan trong cac giio trinh hien hanh cdn khd hi^u do khdng difcfc dien giai cu the, vi vay muc dich cua bai vi^t n i y nham lam sing to C0 sd ly thuyet, dUa ra nhan xet mgt so cong thdc trong giio trinh hien hanh. Ngoii ra, bai viet difa ra nghidm cua phifdng trinh giai a de c6 th^ uCng dyng trong l i p trinh tinh t o i n thiet ke.
Abstract Steel deck is one of the basic elments found in steel structure. But some fomulae in current text books are still difficult lo understand due to no detail explainations. In this paper, the author make it clearly to understand by describing theory foundations behind some fomulae in current text-books, induce comments. In addition, exact form of a solution is found to help engineers easier to apply for programming in practical design.
Ths. Nguyen Thanh TUng BQ mon Icet cdu Thep - Go. Khoa Xdy dipig.
DT: 0912 634 901
1. C a s d \)i thuyet bai toan s i n chiu uon San Ihep thdng thudng lam viic Iheo 1 phuang, do dd cd t h i d t 1 dai ban ra d l tinh, cd I h l coi nhu mgt dam ed modun dan hdi qui ddi Ei=E/(l-v^) [2]
Thdng thudng cd trgng thai gidl hgn 1 (vdng) x i y ra Inrdc Irang t h i i gidi hgn 2(ben). han nua chilu d i y s i n Ihep rit mdng so vdi nhjp do dd khic vdi d i m , san thep can phai k l d i n i n h hudng cua dg vdng tdi lyc cang Irong s i n de t i l l kigm v i s i t thuc t l khi tinh toin. T u g i i thiel nay, ed I h l Ihiit l i p dugc he cdng thuc linh loan cho s i n Ihep.
Day l i b i i toin phi tuyen hinh hgc, sieu ITnh bgc 1 vi cdn I n sd l i lyc cang H chua bilt, do dd phii can ed them vao phuang Irinh bien dang d l tim duac lyc cing H. Dudi d i y trinh b i y c i c thilt lap ly thuyet d l dua ra cdng thdc tinh t o i n san
G i i thilt dd vdng l i nhd, phuang trinh vi phin dam chju udn theo sire ben vgt ligu:
y"(z)=-M(z)/(E,J) (1)
t u dd ta cd.M(z)=-E:Jy-(z) (2)
Mgt khic, mdmen M(z) bing mdmen cCia d i m dan gian khdng ke den lye cang (MO(z)) tru" di mdmen do lyc cing g i y ra: IVI(z)=Mo(z)-H.y(z), thay v i o phuang trinh tren dugc phuang trinh vi phin cap 2Mo(z)-Hy(z)=-EiJy-(z)
Hay viet Igry(z) EJ EJ
Cd the gial tryc tiep phuang trinh vi phan (9) bang ly thuylt phuang Irinh vi phin, tuy nhiin cd H i l g i i i g i n diing bang each gia su hinh dgng cua ham dg vdng, sau dd thay vao phuang trinh vl phin trin d l lim c i c thdng sd (cich lam n i y khiln cho nghiem lim dugc dan gian, d§ dung frong khi sal sd khdng cao va dugc sd dung phd bien [3], [4]). G l i t h i l l h i m y(z) cd dang sau:
y{z) - A.sin-
(4) Trong dd A l i dg vdng Idn n h i tGgi dd vdng ban dau (chua k l den anh hudng cua luc cang) cua d i m dan giin l i AQ, dgt yo bing.
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KHOA HOC & CONG NGHE
y,(z) = AaSm— (5)
Trong do, AQ duge Unh Iheo cdng thdc dd vdng cua dam dan giin:
\ = -^— (6)
384 E,J
Tlieo (2) Mo(z)=-E,Jyo"(z), thay gia tri nay va (4),(5) vSo ptiifong trinii vi piian(3) cr tren co;
Bd qua c i c vd eung be bgc cao ta co:
" (>''(^)) , thay v i o cdng thiJc
Vi+(y(2)r-i
(10) d Iren cd:
(.y\z)f (z = /+- E.JA -^ sin — = E.JAn -^r'
1 , ! I 1 0 ,2Tiiay quan tie y(z) = A . s i n -
-Hy(z)
v i ya(z) = AQ s i n — ngugc lgi vao phuang trinh trin dugc
E,Jyy(z) = E,J-p-y,(z)-Hy(z)
l^=\ds = y \ + (,y\z)fdz = \\ +
I 0 0 - thay vao cdng thuc tinh H (9)cd:
H = ^^E,S^ (11)
Vgy tinh dugc ^ dya v i o c i n bang H tinh theo dtnh nghTa (8) d trin va cdng thdc vua t h i l l Igp(ll):
H=—^E,S. n'EJ ir'E.S',
P \2V
-a (12) Ttiay A = — — (8) vao ptllfongtrinh (12)vanjtgpn ta di/cyc: 1 + cc
TO" 66 giai ra Q\300 y(z) ia- y«(z)
y(z)--
El$t:
H
(7)a(\ + aY
(13)Vai tai trpng tinh to^n, Co hS s6 Vli-at t3i id 7Q (giS tiiiet bo qua trpng itppng ban than), v | y iiFc H (Ju-pc tinh tiiso c6ng thCpc;
,_H_.p ^ n-E,J i-
4 I'
H = Ya^^E,S, (14)
du'pc c6ng thCpc sau,
M l + a ' \ + a ' I' a (8)
Trong cong thirc tren, iuc H van chua biet, tuy nhien n6 c6 quan h0 voi do gran dai i<hi d i m vong. Coi lire cang\h d i u tren todn bo chieu dai d i m , iirc cang H diroc tinh b*i:
H = Al,.F = ME,lt, (9)
Trong dd, A / ia dp gian dai dupc tinh theo djnh nghTa
Al = t,-I
Khi biet dugc h i sd a l u phuang trinh (13) cd I h l tinh toin duac dg vdng eiia s i n theo (8) A = v i kilm tra dieu kien dd vdng theo cdng thde ^ "•" ^
Khi b i l l dugc lyc c i n g H cd t h i kilm tra dieu kign bin theo cdng thdc
„=K^IL<fy^ „7)
W, A, ^''
Trong dd M =-,—'— xac d|nh Iheo (8), Ws, A, iin
l + a
i,: dp dan dai Ithi vong cua dam dupc tinh theo tich lupt ia momen i<hang uon va di#n lich tie! dipn cua mpt ph§n dud-ng dai ban dupc cat ra tinh lo^n (dSi don vj).
/ 2. iVlpt s6 nhan xet v l cac cong thijc t h i l t i<l s i n 'i =\ds = \-i\-^(y' (zyf dz (10) Thong thupng aeui<i$n ben (17) se dupc thoa man vl Khai Wen IhSnh chuli iuy thCa ham duoi d i u tich ^'^ f " <19 ^ ^ . '\ h ' ^ i ^ i S ' ' l ^ S ' = i'',';*"^ '^'^
phan tai ian can z cd; t h i x i y r a d l n g t h p i c i h a i d * u ki|n (16)va (17).
Cdng lhi>c linh H; theo (14),(15) bo qua h§ so vupt ISi
74
TAP CHi KHOA HOC K I ^ N T R U C - X A Y D U N GT
„ . " ' " " U . _ ,
3=
Hinh 1 . Sd do tinh toan cua bai toan
san mong co ke den bien dang Hinh 2. Dd thj he so a theo ti so -
cua tai trgng ban t h i n vi g i i djnh lai trgng ban than nhd, luy nhien n l u lai trong ban t h i n Idn Ihi cdng thuc se khdng chinh x i c . Cdng thirc (14) va (15) cd dgng sau frong cae giio Irinh k i t cau tliep la:
--ro m E.S^ (18)
H=^^—a (19)
Nhgn thiy cdng thdc (18) khic so vdi cdng thde thiet lgp td ly lhuylt{14) vi — ?i — nhung vi — < — n i n cdng thuc (18) Itilen v l an t o i n v i dan g i i n Irong tinh toan vi khdng phii linh A, va dieu kign ben khdng phai dieu kign quyit djnh. Tuy nhien g i i tri H theo edng thdc n i y se l i cd djnh khdng phy thugc lai trgng.
Cdngthuc(19)khacsovdicdngthucthilt l i p t d l y thuylt (15) vi thilu he sdyn, do dd neu tinh H Iheo (19) se cho kit qua nhd han so vdi (18) vi(14),(15)cd t h i day la sai sdt do in an nen tac gia kien nghj higu dinh lai cdng Ihuc Irong cac giio trinh d l k i t qua dugc chinh x i c han.
Bing dudi day trinh b i y khao sat 1 trudng hgp tinh toin va so s i n h k l l qua theo c i c cdng thuc (14),(15) vdi (18) v i (19) vdi c i c Ihdng s6 s i n : E=2.1x}(f daN/cm^ ,yQ=h2. t=l cm, l,=100 cm
Bang 1. So sinh k i t qua tinh toan theo cac cdng thdc khac nhau
Plc (KN/m^)
10 15 20
Hlheo (14) 129.627 200.249 265.412
Htheo (15) 129.627 200.249 265 412
Htheo (18) 282.38 282.38 282.38
OhSnh lech H Iheo (18) so VPi
(14),(15)%
117.840419 41.01443703 6.393079439
Hlheo (19) 108.023 166.875 221.177
Chenh Ipch H theo (19) so vd'i
(14),(15)%
-16.66628094 -16 66625052 -16.66654108 Cdng Ihuc (13) la phuang Irinh bac cao, do vay Irong do an, sinh vien can phai giai nghipm cua phupng Irinh nay bang phupng phap thir d i n . D l lien ipi Irong viec lap Irinh bang tinh EXCEL, cd I h l dung cdng thirc tinh a thu dupc UP nghi$m cua phuong trinh(13);
-2 + -
81A„'// 12 + 1,'' + | V A O ' ' , ' ( 8 1 A „ ' - I - 4 ; / ) 1
fglAo'// 12 + 1," + | V A O ' ' / ( 8 1 A „ ' - I - 4 / / )
(20)
(xem tiep trang 81) S6 20-2015 / 3
^ ' ^^' ^'^"^ ^' '^' ^ ^ ngudn ban d i u . dung thdi diem ma cdn thu dugc hinh anh v l su phin t i n ning luong (focal mechanism) giong nhu ngudn dgng d i t md hinh m i ta sd dyng ban d i u .
7. K i t lugn v i k i l n nghj
Nhu vgy khi i p dyng phuang phip DNTG ddi vdi sdng dja c h i n la thu dugc sg hpi ty cua sdng ddng d i l dung v| tri, dung Ihdi diem cung nhu viic lim lai dugc cie dang phin l i n nang lugng cua c i c ngudn ddng d i t md hinh khac nhau hay ndi c i c h khic l i la hoin toan cd
the lim lai dugc hinh i n h cua ngudn ddng d i t ao bang phuang phip dao ngugc thdi gian. Tuy nhiin d d i y l i e gia chi mdi ddng Ipi nghien cdu ngudn ddng d i t md hinh vdi cae dpng phin l i n n i n g lugng khac nhau, trong khi dd t i e g i i cung chua d l c i p den anh hudng cua eua c i c yeu id khic vf du nhu sd lugng trgm thu, vj tri c i c trpm thu,... den vipc ap dyng phuang phip DNTG va k i t q u i md hinh hda c i c ngudn dgng d i l va vipc dua v i o i p dung phuong phip nay cho eae d y liiu Ihu dugc I d cac dpng d i l ttiuc te./.
Phan bien: TS. Tran Thi/dng Binh TAi Mu tham khdo
/ . A. Derode. A.lburin. andM Finh. Time reversal in multtj^
scattering media. Ultrasonics 36 (1998). no 1-5. 443-447.
i. A. M. Dziiewonsh and D. L, Anderson, Preliminary r^erence earth models, Phys. Earth Planet Inl. 25 (1981), 297-356.
3. FA.DahlenandJ. Tromp, Theoretical Global Seismology, Princeton University Press, I99S
4. F. Gilbert and A M Daewonsfd. An application of normal made theory to the retrieval of structural parameters and source mechanisms Jmm seismic spectra, PhiL Thins. Roy SocLondon Series A 278 (1975). vol 278,187-269.
3. H. Kmvakastu and J.-P Montagner, Time reversal seisnuc source and moment-tensor inverson, Geophys. J. Inl 175 (2008). 686-688.
o. H. Phung, Imaging of seismic source raid hum scaate by time reversal methods, PhD. Thesis, Univenily Paris 7 - Dems Diderot. 2010
7. J. Tromp and C. Tape and Q. Liu, Seismic tomography adjoint methods, time reversal and banana- doughnut kernels, Geophys. J. Inl 160 (2005), 195-216.
e. K-Ah and P. G Richards, QuanliUUive seismology Theory and Methods, vol I.W.H Freeman and company. New-York, 1980 r. M, Fmk. Time reversal in acoustics. Contempory Physics 37
(1996). no 2, 95-107
11. Phung Thi Hoai Huong, Hiidi dnh cua d^ng dot bang phuang phdp ddo ng^^ thai gian. Ky yeu hgi nghi khoa hoc Vdlb?u.
Kei cau vd Cong nghf x^ dung 2012. Trudng Dgi hgc Hen true Hd ngi, 11/2012, 431-439
12. g. A. Phinney and R. Bumdge, Representation of the Elastic- Gravttationnol Excitation of Spherical Earth Model by Generalized Spherical Harmonics, Geophys. J. R, Aslr. Soc 34 (1973). 451-487
Mgt vai nhan xet ve van de tinh toan san thep..
(tiSp tlieo trang 75)
Td cdng thuc (20) cd I h l ve dugc dd thj quan hp giua a theo ti sd — ^ nhu hinh 2.
Dga v i o do Ihj Hinh 2 cd the Ihay khi If sd gida dg vdng ban d i u cua s i n / chieu d i y c i n g Idn thi h i so a cing Km, h i s6 a n i y lang nhanh khi nam faxing phgm vi I d 0-»5 ( l i pham vi thudng gip%ong thyc l l ) . Thdng t h u d n g « n i m trong phpm vi t u 0-+3.5. Hieu
dng phi tuyen hinh hpc l i m giam md men v i d$ vdng l u I —14.6 so vdi b i i loan dam ddi vdi c i c so lipu thdng dyng cua kfch thudc va t i i trgng cua s i n . T u dd thiy rang anh hudng cua hipu ung phi luyen hinh hpc d i n md men v i d$ vdng cda s i n la k h i Idn nen vipc thiet k l k l tdi hipu dng phi luyen hinh hpc niy l i hoin t o i n phCi hgp vdi Ihuc I I v i khiln cho s i n tilt kipm hon.
3. K i t lu|n
B i i viel d i khao s i l co sd ly thuylt c^a b i i loan s i n d l tim hilu sau hon ve ban chit v i i c t h i l l k l s i n . ddng thdi kiln nghj hipu dinh mpt cdng thuc bong c i e tai lipu hipn hanh khien cho viic tinh l o i n cd t h i bj sai lich v l mgl k i t qua. Ngoii ra b i i viet dua ra nghiem d l lim a giiip cho d l d i n g ung dung v i o l i p trinh tinh toin./.
TAi l i * u t h a m k i a o
I TCVN .1 JA' -;W" ^^' ' ^ *«P - Tliu chudn duet k£ Nhd xudt bdnXdydUnt: 2iX)5
ph^m van Hdi (chu hlln). Kit cdu thip- C&iki(ncilbdn.Nh^
xudi hdn Khoa hgc kf OiudlJOOe
Phan bien: PGS.TS. Phgm Minh H i 3. S.R Timodienko, I.M. Gere 6n dinh ddn hdi. Nhi xudt ban
Khoa hgc vi l^ ihudt, 1976.
4. SP. Timoshenko, J M Gere. Ly Oiuyit Idm, vd. Nhi xuit bdn Khoa hgcviKy thuit. 1976
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