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Full text of "tinh toan cot btct-Nguyen dinh cong"

GS. NGUYEN OINH CONG 




SACH XUAT BAN 



KY NIEM 40 NAM THANH LAP 

TRl/OfNG DAI HO C XAY DUNG 

1966-2006 



..lUTYIUVni 



i THI/vjus 

m £*»« 



NHA XUAT BAN XAY Dl/NG 

HA NOI - 2006 



LCJI NOI DAU 

Thidi ke kit cau betdng cot thep gom nhieu Cong doan irong do tinh todn del dien 
cdi Id mot phdn Ufaiig dot quan trong vd cluia diaig m6t so van de phtt'c tap nlu( cot chin 
nen lech lam xiin, c&l co ti£'t dien iron hodc chifT... Nhfcng van de do tuy co dicoc de 
cap tdi trong Tiiu chudn thiet ke'cung nine trong mot so gido trinh vd sdch tham khdo 
nhtmg ihicdng moi dtcac trinh bay a dang nguyen ly chung ma it duac chi nil hoa, cu the 
hoa de co die van dung trice tiep. Ngay meting hop don gidn la iWt dien chS nhdt chut 
nen lech (dm phdng. fuy ddduoc gi&i thieit 6 nhieu ids lieu, dadiwc cu the' hoa bang ede 
cong ihi'cc link wan nhimg cung con cluia diotg mot vat van de can /dm sang 16 lion. 

Trong kin thief ke ede cong winli, nhieu ky xif vd sinh vien thudng gap ede van de 
vita nen vd yen can tdc gid gidi dap. Dien do fhdi thde tdc g'td bien soan tdi lien nay 
iiham gidi linen mdt so van de ve tinh todn, hy vong co the cung' cap duqc ede fhdng tin 
vd plutong phdp can thiet cito ede can bd nghien ciixt vd thiet ke. 

Day fa tdi lieu tham khdo ma mot so not dung vupt ra ngodi cck gido trinh thon$ 
thudng d bde dai hoc. Nhfcng van de tinh todn chit yen thco $dt tiett chudn thiet ke hien 
lianh cua Viet Nam TCXDVN 356 : 2005. Ttty vdy co mot so van de dtfoc md rang, gidi 
tideit theo nhieu quan diem khdc nhau nlrdm gitip ddc gid hieu sdu va rong iujti ve ly 
thiiyet hitdng cot thep. 

Tiiu chudn TCXDVN 356 - 2005 duoc ban hdnh vd co hieu lire fft tiidng J I nam 
2005, dung de (hay the tiiu chudn TCVN 5574 • 199!. Trong qud trinh bien soan tdi 
lieu nay (2004 - 2005) tdc gid dd dim vdo ticu chudn TCVN 5574. Khi TCXDVN 356 
ditoc cdng b6 tin tdi lieu nay da die ban xong vd chudn bi dem in. Tdc gid da kip thai 
sua chila ban thdo theo not dung vd ky hieu ciia TCXDVN 356. Chdc chdn rdng nhimg 
van de quan trong vd co ban dd ditcc trinh bay theo TCXDVN 356. Tuy vdy co mot vdi 
vi du dung so lieu cu cua TCVN 5574 tdc gid van de nguyen. vi thd'y rang no khdng gdy 
ra nhdm Ian v4 niton thtic, khdng dull hitting den mite dd chink xdc cua tdi lieu. 

Nam 2006 Trifong Dqi hoc Xdy dtptg ky miim 40 nam thank lap vd 50 nam ddo too. 
Tdc gid viet tdi tiiu nay cung id degop phdn vdo leky niem dd. 

Vi tiictt giaa co han nen tdc gid chi mdi de cap den viec tinh todn mot sd'tiet dien cot 
md chua dua them ede van de khdc nhicxdc dinh noi hec, cdu tao chi net. Hy vong c6 the 
bo sung vd hodn cliiiih vdo dip khdc. 

Tdc gid xin hoan nghenh vd to long biei on ede ban doc chi ra, gap y kien cho nhCaxg 
sax sot cua tdi lieu de tdc gid co the hodn thien hon. 

Tac gia 

5 



Chircmg 1 
DAI Cl/ONG \i KHUNG VA COT BfiTONG COT THEP 



] . 1 . CAC BUOC THIET K£ KET CAU KHUKG 

Tliiet ke ket cSn belong cot thep noi chung va ket cau khung noi rieng ihuong theo 
[hu* lucac bade sau: 

i . G\6\ thieu, mo la ket cau. 

2. Lira chon phuefftg an. tap so 66 ket cau. 

3. Chon kich thtfox so bo cac tiet dien. chon vat lieu. 

4. Tfnh toan cac tai Irong, du kien cac lac dong 

5. Xac dinh not lire, to hop noi luc. 

6. Tinh loan lie! dien. kiem tra cac dieu kien sir dung. 

7. Thief ke'chi lie!, chon cau tuo. the" hien. 

Cac buoc tren duoc quy ve cac giai doan ihiei ke gom; Thiel ke co" so 1 (so bo), thiel 
k€ ky thuSi va ihi& k£ ban vc thi cong. 

Voi cac c6ng irinh Ion chie-'l ke theo ba giai doan trong 66 thiel ke cc sd gom n6i 
dung cac bifde 1, 2, 3; tbiet ke ky thuat gom noi dung cac buac 4, 5. 6 va thifil ke ban ve 
thi cong gom noi dung buoc 7. 

Vdi cong irinh viia va nho duel ke theo hai giai doan hoac mot giai doan (thiet ke' 
trite tiep ban ve thi cong) tuy v3y win thuc hi£n ca 7 buac trong do c6 mot so buoc co 
the lam gan dung, don gian hoa. 

Ho so thiet ke g6m co ban thuye't minh va cac ban ve. Nt>i dung cua cac hu6c co the 
duoc trinh bay trong ban tbuyet minh hoac trong die ban ve. 

buoc 1 can trinh bay ten goi cua ket cau. vi trf (tren mat bang ket ca'u cua cong 
trinh). nhiem vu, dac diem cua ket cau. 

Buoc 2 fa buoc kha quan trong trong do vide d£ xua't c3c phirong an, phan n'ch va so 
sanh de* chon dupe phutmg an hop ly co y nghla Ion den nhieu mat. Mot phuong an hop 
\f cua ket c3'u la dam bao duoc yeu ciu cua kien true (y£u cau ve su dung), bao dam do 
ben vung, sir dung tiet iti&n vat li£u va fhufln lien cho thi cdng. 



Vide 66 xua't cac phuong an c6 the* theo hai each: 

a) Dira iren nhiem vu, dac diem cua fc£l ca'u ma d£ ra cac phucmg an d6c lap nhau 
(do mot so nguoi hoac do mdt nguoi). 

b) Truoc lien dua ra mot phuong an, phan tich mi, nhupc diern cua phuong an do, 
tren co so 1 urn each khac phuc nhuoc diem ma 6& xua'i phuong an khac. 

Viae lap so do kel ca'u mot each diing dan la rat can thtet. D6'i voi ca ngoi nha th'i do 
la vi6c bo irf ket ca'u long ihe va ve mat bang kel ca'u. Doi voi ket ca'u khung thi do la 
xac dinh hinh dang, lien ket, cac kich ihtfoc co" ban. Khi \kp so 66 ket ca'u truoc h£'l can 
quan lam tdi on dinh t6ng the* cua chung, sau 66 moi xem xet den sir lam viec cua ttrng 
b6 phan. Trong viec lap so do khung thi van de khung phang hoac khung kh6ng gian la 
quan trong, van de" nay duoc de cap d muc 1.2. 

Mdt $6 van do ve 16 hop n&i lire va chpn kich thudc tiet dien duor trinh bay 6 muc 

1.3 va 1.4. 

Noi dung chinh cua tai li£u nay bao gom viec linn toan tiet dien theo hai dang bai 
loan: tinh loan col thep hoac kiem tra. 

Tinh loan cot thep la khi biet n6i luc va kich thuoc tiet dien can xac dinh lugng co'l 
thep can thiel, du kha nang chiu luc. 

Tinh roan kiem tra la khi da bie'i tiel dien va cot thep can kiem tra xem lie't dien co 
du kha nang chiu dugc nSi luc cbo truoc hay kh6ng. 

Viec chon kich truroc d budc 3 la so' bo, co the ia hop ly hoac chua. D6 danfi gia 
kich thuoc tiei dien da chpn la hop if hay khong can phai can ctx vao ket qua u'nh toan 
cot thep hoac ke"i qua kiem tra. Neu kfch Ihuoc da chon la qua bat hop ly (qua be hoac 
qua Ion) tm* can phai chon lai va tinh toan Lai. 

1.2. SO DO K^T CAU KHUNG 

Khung gSm co cac c6t, cac dam lien kel voi nhau va lien kel v6i mong. Trong so d6 
khung cac cot va dam duoc thay bang dtfdng true cua n6. 

Ve hinh hoc va su lam vide, phan bi£l khung phang va khung khong gian. 

Khung goi la phang khi true cac b6 phSn cua n6 cung nam trong mot mat phang va 
cac lai trong tac dung irong mat phang do. Mat phang do dugc goi la mai phang khung 
hoac mal phang u6n. 

Khung la khong gian khi true cac bO ph&n kh6ng cung nam trong mat phang hoac luy 
cung nam trong mdt mat phang nhung co chiu tai trong tic dung ngoai mat phang khung. 

Trong kel ca'u nha, khung thudng duoc ca'u tao thanh h£ khdng gian (kho'i khung). 
He khung khong gian co the* dugc xem la g6m cac khung phang lien ket vdi nhau bang 
cac dam, ngoai mal phang khung. 

6 



tift 



Tuy iheo phucmg an ke't ca'u chiu luc chinh cua nha ma ht khung co the thuoc v£ nha 
khung hoac nha ke't hop. 

Voi nha khung. he khung chiu roan b6 tai trong dung va .tai tcong ngang. 

V6i nha k£c hap (vcfi l$i cong, vach ctmg) khung chiu phda cat uoug durig true tid'p 
truyen vao no va chiu phan tai trong ngang duoc 
phan pho'i cho no. 

Tuy h£ khung la khong gian nhung v6 sir lam 
vi6c va ifnh loan co the theo so" do khOng gian ho&c 
theo so do phang tuy thuoc vao tai trong tac dung 
va muc do gan diing co ih£ chap nhan duoc. 

D6 phan bi£t truong hop lam viec cua khung la 
phang hay khftng gian. xct jruong hop he khung 
don gian gom 4 cot A, B, C, D va 4 dam li£n ke't 
cac d£u cot (hinh 1,1). Khao sat cac tafong hop 
khung chiu tai trong dung va ngang. 

a) Khung chiu tai irons dfaig 

Tai trong tren san truyen vao khung tuy thuoc vao ket ca'u s&n iheo cac trucmg 
hap sau: 

Trtf&ng hap I. San lap ghep dung panen d5t theo mdt phuong (hinh 1.2a), tai 
trong tir pancn chi truyen len hai khung phang song song, hai khung nay lam viec 
theo khung phdng, cac dam vuong gdc voi cac khung nay chi dong vai tto Hen ke't, 
khona chiu luc. 



SW 




Hinh I J. He khung denx gian 



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Hinh 1.2. Cac Irif&ig hap sun truyin idi trong dung vao khung. 



Trifdng hap 2. ¥Ju ban san la toan khoi ke" len 4 darn ma ty s6' giira cac canh ban 
■y- > 2 , xem gan. dung ban chiu uon m6t phuong, tad trpng tit ban truyln len hai khung 



661 di£n, m6i khung lam viftc theo khung phlng (hinh 1.2b). 

Truang hop 5. Ban ke len 4 dam ma ty so' canh ban — <2, ban chiu u6'n theo hai 

phuong, truyen tai trong len ca 4 dam, he khung lam viSc kh6ng gian (hinh Lie). 

Tncong hap 4. Khi dung them cac dam phu (ddm san) 6& da ban san, dam phii kd 
len dam khung. Tuy theo so* do bo' tri dam phu ma xet khung lam vide phang hofic 
kh6ng gian. 

b) Khung chut idi Trong ngang (gio) 

Tuy theo phuong cua tai trong. Khi xet tai trong gio theo phuong ngang (hinh 1.3a) 
thl cac khung AB Va DC lam vific theo kliung phang. Khi xet gio theo phuong doc (hinh 
1.3b) thi hai khung AD va BC lam vice theo khung phang, con khi xet gio theo phuong 
xien I hi he khung lam viec khong gian. Chii y rang khi \i\ tac dung cua gio nguoi ta 
xcm san la cling v6 cung trong mat phang cua no nen san lam dupe nhi£m vu truyen tai 
irons gio vao c&c khung. 

S t>) A B c) A B 





Hinh 13- Cue truong hop hi khung chiu tai trgng ngang 

V6i he khung cua toan nha cung tien hanh phan tich nhu tren de xem xet la khung 
lam vide theo phang hoac theo khong gian. Tu cho phan tich sir [am vifcc cua san d£ 
quye': dinh each truyen tai trong dung. Khi ma co the xem loan b& tai trpng dung tren 
san chi truyen len cac khung ngang (hoac khung doc) tin cac khung ay dupe xem la lam 
vi6c theo khung phang duai tac dung cua tai trpng dung. Nguoc lai thi pbai truyen tai 
trpng dung Idn ca cue khung doc va ngang va co khung khong gian. 

Voi tai trpng ngang, ihu&ng ngutri ta dua vao mSt bang ket c£u nh& 6t xet truong 
hop bat loi cua lai irong. Khi m&l bang nha hep ma dai, do cung ttSng the cua nha theo 
phuong ngang la kha be* so vdi phuong doc. Luc nay tac dung cua gio theo phuong 
ngang se bat loi hem do do chi xet gio theo phuong ngang (hinh 1.4a) va m6i khung 
ngang duoc ti'nh theo khung phang, chiu tac dung cua phan lai trpng gio phan pho'i 
cho no. 



8 



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Hinh 1,4. Cdc iru&ng hap 

bai loi a'ta gid doi voi 
ket can nha 



Khi miU bang ket csi'u nha co dang gan vu6ng, d6 ctmg t6ng the cua nha theo hai 
phucng gan bang nhau ihi phai xet lac dung ciia gio theo ba truir.ig hop: ngang, doc va 
xien (hinh 1.4b). V'di gio doc va agang nha cac khung lam vice phang con voi gio xien, 
khung lam viec khong gian. 

Tinh loan ao\ luc khung phang !a bai loan ket can thong thuimg, co the giai bang 
nhi£u phuong phap khae nhau.. Hien nay cdc biu toati khung phang chu y£u duoc giai. 
nha viec su dunj cdc ph;in m^m u'nh toan tr£n may tinh. 

Tinh toan noi luc khung kh6ng gian la kha phirc tap va thucmg chi co the* giai nhtf 
cac chuong trinh kha manh. Co the giai gan dung bai toan khung fcltdinj gian bang each 
dim ve bai toan phang iheo each phan cliia he kJiung thanh cac khung doc va khung 
ngang. iren in6: khung xe'p dat cac tinh mi va hoai tai tac dung leu khung do. Giai toan 
bo cac khung doc va khung ngang theo trirong hop khung phang. Noi lire uong dim ciia 
khung nao la cua dam do con nc)i lire trong c6t la bang long n6i luc trong cot a'y cua hai 
kJiung giao nhau. 

1.3. TO HOP NOI LUC KHUNG 

1.3.1. Dai cuxrng vc to hop noi lire 

Khi u'nh loan noi lire khung can tinh rieng noi luc do tai trons> thucmg xuyen (tTnh 
tai) va noi lire do cac trirang hop khae nhau cua tai trong lam then (hoat tai). Cuoi cung 
can td hop de' tim ra cdc gia tri nc/i luc ba't loi. 

Vol cdc khung phang thuoc ket c^u nha dan dung, trong t6 hop co* ban cin xel 6 
m/dng hop tai trong sau: 

1. Tai trong thiicmg xuyen (tinh tai) (hinh 1.5a). 

2. Tai trong tarn thoi each t£ng each nhip truong hop 1 (hinh 1.5b). 

3. Tai trong tarn thoi each ta^ig edeh nhjp latong hop 2 (hinh 15-c). 

4. Tai trong tam thai tren toan bo dam (hinh l,5d). 

5. Tai trong gio tu* trai sang (hinh 1.5c). 

6. Tai trong gio tCrphai sang (hinh 1.5g). 



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P3 Gatri Gtophai 

Hinh 1-5- Cac irtfmig hap ids trong link khung phang. 

Vol ket cau khung nha cong nghiep, Irong 16 hop co" ban con phai xet them lai trong 
do cau true (g6m lac dung lhang dung va tac dung ngang) lac dung 6" m6t phia hay hai 
phia cua efli dang xit. 

Tinh loan khung voi (6 hop dSc biet con can xet them ndi lire do cac tai trong dac 
biei (dona da't. chay no...). 

TO hap n6i lire la mot phep cpng co iya chon nham tirri ra nhung gia tri noi lire bat 
}&) de' iinh man cot ihep hohc de kiim Ira kbi nang chiu Jut. Vice 16 hcrp noi Jur fhoAc 16 
hop lai trong) duoc twin hanh theo cac tieu chuan thiet ke. Tieu chuan cua cac nu6c quy 
dinh each 16* hop co khac nhau. 

Tieu chuan Viet Nam TCVN 2737 -1995 ve Tai trong va tic dong quy dinh hai t6 
hop co ban To hop co ban J gom noi luc do iinh lai va noi lire do mot Irirotig hop cua 
hoat tai (co Ufa chon). To hop co ban hai gom noi luc do unh tai va not luc do fl nha'l 
hai hoal tai (co lira c'lipn trucmg hop bat lpi) trong do noi luc cua boat lai duoc nhan voi 
hfc so to hop 0,9. Khi Lrong 16 hop co xet den tai irpng cdu true thi con can chu y he so 
to hop khi xet sir boat dong dong thci cua mot, hai hay boh cau true, Trong moi :6 hop, 
tuy theo irang thai gioi han duoc dung de Iinh loan ma con dung hf so dp tin cay (he 
s6* Vtfrjt tai) cua tai trong. (Tai trong tinh loan bang tai Irpng tieu chuan nhan voi he so 
dp tin c&y). 

Tieu chuan thiet ke" cua Anh, Phap, My kh6ng dua rieng he so dp tin cay ma ghep 
chung vao he so l6 hop. Cac npi luc dupe x^c dinh theo tai trong tidu chuan, ky hieu 
nhu sau; 



JO 



G - noi lire do tai trong thirong xuyen, trong do mot vai tieu chuan ihiet ke con phiin 
bide G mas la tnrdng hop bat lot (gay ra tac dung cung da'u voi n6i luc do boat tii) va G ma 
la irucmg hop co loi (gay ra lac dung nguoc da'u voi ndi lire do hoat tai). 

P, (i = K 2. . .n) - n6i lire do cac hoat tai 

N6i lire to hop ky hieu la S duac tinh voi cac he so' to* hap khac nhau. 

Khi chi xet lac dung cua mol hoat tai san P k (nhu t6 hop ca ban I cua TCVN) thi cac 
h£ so' trong cac tieu chuan nhu 5au: 

Tieu chuan Phap BEAL - 99: 

S, = l,35G max + G min +l,5P k ' 
Tieu chuan Anh8S81iO: 

S v = 1,40^+0^+1^ 
Tieu chuan My - ACI 318: 

S, = l,4G+i.7P k 
Khj xet tac dung cua ca hoat tai san P k va hoat tai gio P w thi: 
Tifiu chuan Phdp: 

S,= I,35G + L5P k +P w 
Hoac: S 2 = G + 1 .5? w + 1 3 y P k 

i%=OJ7-0,9. 



Tjeu chuan Anh; 



Tieu chudn My: 



S2=1,2G+ !,2P k -f L2P V 



S 2 = 0,75(1.4G4-1.7P k ) + l,6P w 

Can chu y ring he so trong to hop ndi luc duoc lay cao bon chua ijhang dinh duac la 
do an toan ciia ket ca'u se cao hon vi ring do an to&n cdn phu thudc vao gia tri cuong do 
cua vat lieu duot dung trong tinh loan (hoac h£ so' do tin cay doi vdi cucmg do vat liSu). 
Cung m6t loat b£tdng va m&t loai thep thi cuong dd de* tinh toan ln?ng cac tieu chuiui c6 
gia tri khac nhau. Chfah vi di6u nay cac can bo thi& ke can luu y khi sir dung c£c tieu 
chu&V Da xac dinh noi luc theo tieu chudn nao thi phai lay cuong dp vAi li£u theo tieu 
chudn tuong ung de tinh loan, nfifu khong thi c6 the" g&p phai nhffng nham I5n dang tiec. 

1.3.2. To hop noi luc khung phing theo TCVN 

Vi£c 16 hop ndi luc co ban cua k& ca'u kbung phing duac giai thidu kha chi ti€t 
trong nhieu tai li£u vS giao trinh. day chi trinh b£y m6t s6 van $$ co ban. 



T6" hop ndi luc dupe l&p rieng cho cdt va d$m. Voi c6( can lien hanh t6 hop d6ng 
thai lire doc N va momen uo'n M cho ttmg tiet dien vi rang khi tinh toan c6\ thep can su 
dung cung Iric ca N va M. Vol mdmen M can quy dinh chteu duong va trong bang 16 
hop gid tn cua M duoc mang dau dai so. 

Trong m6i to hop, tai moi tie! dien can to hop de lim ra cac cap ndi lac: M max va N 
moTig uTig t M min (gia iri max theo chieu ngucc lai) va N tuong ring. N max va M tirong 
ung. Thi du v6 16 hopnOi luc cua m6t doan edi cua khung nha dan dung duoc trinh bay a 
bang l.J, con ihi dy ve to hop noi lite cua mot liel dien cot nha cong nghicp m6t tang co 
cau true duoc trinh bay a bang 1.2. 

Bang L.I. Bang lo hop noi luc cot khung nha dan dun" 



TiC'i 

di£n 

■ 


Noi 

luc 


Noi 
luc 
do 

iinh 
iai 


Noi luc do hoai tai 


N6i luc 

rto girt 


T6 hop co ban 1 To hop co ban 2 


THI 


TH2 


TH3 


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Phai 




M MM 




N 




1 


2 


*% 

j 


4 


5 ' 6 


7 


8 9-10 


ii 


12 


A 


M 

N 


27 
230 


21 

100 


-3 
39 


IS 
139 


-36 
-7 


38 
9 


65 
239 


-9 

223 


45 i 80 
369 32S 


-S 
259 


77.4 
363 


B 


M 


-14 

24: 


-10 

!■:■: 


2 
39 


139 


37 
-7.5 


-35 
6 


23 
232 


-49 

246 


-22 ' 21 -54.5 j -53 
379 268 i 335 | 370 



O A7: M^ = 27 + 38 = 65; N llf = 230 + 9 = 239 
A8: M min = 27 - 36 = -9; N,„ - 230 - 7 - 223 
A9: N^ = 230 + 139 = 369; M w = 27 + 18 = 45 
A10: M mx = 27 + 0,9 (21 + 38) = 80; N lu = 230 + 0.9 (100 + 9) = 328 
All; M mn) = 27 + 0.9 (-3 - 36 ) = -S; N l0 = 230 + 0.9 (39 - 7) = 259 
A12: N^ = 230 + 0.9 (139 +9) = 363; M lu = 27 + 0.9 (18 * 3Sj = 77.4 
B12: N^ = 240 +0,9 (139 +6) = 370; M w = -14 +0.9 (-8-35) = -53 

Bang 1.2. Bang'to hop n6i luc cot nha cons nghiep 



Titft 
dten 


N6i 
luc 


Noi 
luc 
do 
iinh 
tai 


Noi luc c 




.. 


Noi luc do cau true 


Noi 


luc 


O JlOai ai uidi 


Bfcn trai Ben phai 


do gio 


THI 


TH2 


TH3 


Do 


Do 


Do Do 

D ' T 

nut TT J I 


Tnii 


Phai 


1 


2 


3 


4 


5 6 


7 


8 


9 


10 


C 


N 


0,4 
118 


-0.5 
7 


0.6 

8 


0.1 
15 


-20 


i2 



25 
56 


t 




14 



-14 




12 



Tft hop co ban J 


To hop ca ban 2 


N 


Mo- 
ra 


M 


N 


N 


M 


11 


12 


n : 14 


15 


16 


1.7,8 

24,2 

165,6 


1,5.6 

-18,3 

15S 


1,5.6,7.8 
7.4 
190 


1,3,7,8,9 

35 
150.4 


1,2,5,6.10 

-29,5 

:61 


1.4,5.6,7,3,9 
19.4 

J 96.4 



Trong bang 1-2. hoat tai mai diroc xet 3 trucmg hop: trucmg hop I boat tai a phia ben 
trai: truong hap 2 hoat lai 6 phurben phai; irucmg hop 3 hoai lai 6 ca hai rxsn. 

Vdi ne)i lire do cau True lay he so 0,85 kbi xet hoat dong dong thai ciia 2 cau true va 
0.7 Jchi xet 4 cdu true. 

6 CI 1 : M max = 0.4 + 0,85 (25 +3) = 24.2 

N= 118 4-0,85x56-= 165,6 
CI 2: M mm = 0,4 + 0,85 (-20 -2) = -IS.3 

N= 118 + 0,85x47 = 158 
C13: N mjx = 118 + 0.7 (47 + 56) = 190 

M = 0,4 + 0.7 (-20 +2 + 25 + 3) = 7,4 
C34: M mas = 0.4 + 0,9 [0.6 + 0.85 (25+3) +14] = 35 

N = 1 18 + 0,9 [8+ 0.85 x56] = 150,4 
CI 5; U mili = 0.4 + 0.9 [-0,5 - 0,85(20+2) - 14] = -29,5 

N = 1 18 ^0.9 [7 + 0.S5 x47] = 16 1 
™* N mas = US + 0,9 \\5 + 0,7 (47 + 56)] = 196.4 

M = 0.4 + 0,9 [0.1 + 0,7 )-20 + 2 + 25 + 3) + 14] = 19,4 

Khi id hop nc)i luc c6l thuoog nguai ta chi chii trong den cac cap npi luc gom M va 
N lac dung dong th6i ma bo qua luc cil vai nhan xet la lire cit trong cot kha be, rieng 
belong du kha nang chiu ma khong can tinh loan cot thep ngang (de chiu lire cat). Voi 
ciet dien a chan cot con phai td* hop them luc eai de 7 co so lidu khi ti'nb mong. Voi nhiSng 
tiet dien khac. neu th£y rang lire cdt la dang ki, can phai ilnh toan cot thep ngang thi 
ciing can id hop thern luc cat. 

Vai darn khung, noi lire chu ye'u la rnornen uon M va luc cat Q, ngoai ra c6n co luc 
doc N (nen hoSc keo). Th6ng thuang dot vai diirn cd the bo qua anh huong cua lire nen 
neu N n < 0,1 R^bl^ va bo qua anh huang cua luc k6o N k neu N k £ 0,1 R bl blv, (R b va R bI 
la cuong 66 tinh toan cua betong ve nen va keo) va chi to hop n6i lire M va Q. Can to" 
hop rieng M va Q de ve bie'u 66 bao cua M va cua Q. Vai dam kh6ng to hap M va Q 

13 



tuong ung vi M va Q duoc dung rieng de tlnh toan cot thep doc va cot thep ngang 
(khong dung d6ng thai nhtf MvaNc* trong cot). To hop noi Luc cua mot doan darn 
khung duac truth bay a bang 13, 1.4 va trdn hlnh 1.6. 

Bang 1.3. To hop mom en cua dam khung 



Tiet 


NOi luc 


Noi luc do hoai tai san 


N6i lire do gi6 


TohopCBl 


To' hop CB2 


j-* 1 do 

, tinh tai 


TH1 


TH2 


TH3 


Trai 


Pha, ! M max 


M™ 


Mmax 


M min 


A 
B 

C 


-50 
40 


-25 
36 

22 


-20 
-JO 
-24 


-45 

26 

-46 


38 

3 
-37 


-32 

-4 
35 


-12 

76 

-2 J 


-95 
30 

-102 


75,1 


-119.3 

27.4 

-130,7 



Bang 1.4. To hop lire c&t cua dam khung 





Noi 


Noi luc do hoat tai 


Noi luc do gio 


T6hc<pCBl TohopCB2 


Tiel 
di£n 


luc do 
ilnii 

lai 


TH 1 


TH2 


TH3 


Trai 


Phai 


Q-u, 


xmn> "vrtw* 


Q™„ 


A 


34 


24 


-8 


16 


15 


-12 


58 


22 69.1 


16 


B 


-1 


2 


-8 


-10 


15 -12 


14 


-13 


-■':,? 


C 


-M> 


-M 


-8 


-28 15 -12 


-21 -64 -?: 



Gin chu y rang M max va M^ cung nhu Q max va Q ma duoc the hien \oi duu dai so va 
co the la khac dau hoac cung da'u. 

Hinh bao momen va hlnh bao luc cat cua doan dam duoc the hien tren hinh 1 6. 



119,3 



130.7 





Hinh 1.6. Hinh boo mdmen va Itfc cat cua dam khung 



Can chu y rang. d2 ve dugc hinh bao momen chtnh xac hern ihi can tinh ihem gia tri 
M maK , M ni0 cho m6t so tiet dien n&a o khoang gifla cua dim. Hlnh bao luc cat ve a hinh 
1.6b ung vcfi tmdng hop doan dim khong chiu lai trpng tap trung. Neu tren doan daVn co 
tai trpng tap trung (hi bie\» do luc cat co buoc nhay tai noi dat lire t&p trung, can xac dinh 

them Q^. Q min tai cac tiet dien do. 



14 



Trong tnrong hop n£u xet thay khong the bo qua lye doc N khi linh loan ddm thi cdn 
phai to hop momen M trong diim cung v6i luc dpc N nhu d<5i vol cflt. 

1.3.3. To hop noi lire khung khong gian 

So voi viec Id hop noi lire khung phang thi to* hop n6i Luc khung khong gian la phuc 
tap hem rat nhieu v\ phai xet d6ng thai den 6 Ihanh ph£n noi lire. 

2.3.3-2. To hop noi Utc dam 

Gan cac true Oxyz vao dam nhir Iren hinh 1 .7. Thong thudng cdn quan tam icri M v 
Q x la nOi lire tac dung trong mat phang xOz ma co the bo qua M yt Q y tac dung trong mat 
yOz. Tuy vdy voi khung kx)6ng gian con can chu y d£n momen xoan M, tac dung trong 
mat phang xOy (vuong goc vcri true dam). 

Khi xet thay khong the bo qua momen xoin Vl t thi c<Sn 16 hop no cung voi rnCrnen 
uo'n dt tinh toa"n hoSc kie'm tra cot thep chiu d6ng thoi uon va xoan. 

1,3.3.2. To hop noi luc cdt 

Gan true Oxyz vao cdt nhu irfin hinh 1.8. To' hop n6i lire can quan tarn gom luc doc 
N va cac momen M x . M y . Ngoai ra trong nhung trucmg hop cdn thiel con phai xet den 
luc cat Q s , Q v va momen xoan M,. 

De* xac dinh duoc cac gia tri bai loi cua M v M v va N cito phai chu y phan rich so 66 
khi tinh voi tai trong cfimg va tai trong ngang. 




Hinh 1.7. C6c mdmen 
irong dam khung khong gian 



V 


N 


K 






/ 


\ / 




X 


/ v 





/ , 






L 


z 






A 





Hinh 1.8. N6't luc chu yiu 
trong cdt khun% khdng gian 



a) Voi hoat tai dftng trin san 

Lay vi du mat bang k€t ca'u voi 2 san thudc hai ling lien tiep nhtr tren hinh 1,9. 
Tucmg tu nhu tnrdng hop xe'p hoat tai each ting each nhip a hinh 1.5b. c can xet 4 dang 



15 



chat tai: each ting each nhip theo phuong ngang va edeh tang each nhip theo phucmg 
doc. O cac gach cheo hai phuong duac chat 100% hoal tai con cac o gach cheo theo 
mdr phueffig duac chat 50% hoat tai. Tuy vfiy each chat tai nhu the' mdi tao ra su bat lai 
cho c6t con voi dim thi chua duac hoan toan. De* c6 dutfc gia tri bait lai nhat cua mdmen 
dirong 6 gii?a moi nhip dim thi can chal 100% hoat tai len cac 6 co gach cheo. Cbii y 
rang ne'u chat hoal tai nhir vua noi, khi to* hep n6i luc de" u'ob coi se co nhung 6 duac chat 
hoal lai gap doi, lam tang qua miic luc nen trong c6l. 





San 8rg K 



<t> 



HwhlS.S&dochat 

hoat idr dung len son 

de tinh not luc khung 

khong gian 




Wmw 

M 1 .',* -/if 1 ■T«.*Ot> /// 



San larc trfin va ojdr s&1 vOi K 




Ngoai 4 iruang hop chat hoat tai cich tang each nhip con xct them truong hop chat 
hoal lai len toan bo san. 

Trong nhung nha nhieu tang co tinh tai kha Ion so voi hoal tai (g > 2p vol g va p la 
tTnh lai va hoar lai tren dam) va cq chieu cao nha kha Ion (tren 40 me!) Thi momen trong 
dim va cot do hoat tai dung gay ra la kha be so vai momen do tinh tai va tai irons gio 
g3y ra. Luc nay co the tinh toan gin dung bang each bo qua cac truong hop xe'p hoat lai 
dung each ling each nhip ma gpp loan bo hoal tai san va tinh lai de tinh. 

To hop npi lire cho cot khung khong gian cin x6l cic truong hop sau: 

M, max ,M v vaN t 

M. 



y max' *^x va ™iuong ling- 



N , M v va M v 



mav 



16 



Trong qua trinh tinh toan n6i lire tin quy dinh dau cua M x , M y ; khi 16 hop cung phai 
chu y den dau. Tuy vay cot khung khong gian ihuong dirge bo' tri cot thep do'i ximg do 
do khi to" hop chi can tim M x max va My ^ la nhung m6men Ion nha't vi gii tri tuyet 
dot ma khong can tim gi£ tri Ion nha't ciia M dirong va M am. Neri co dir kien dat cot 
thep khong do'i ximg thi bat buOC phai to hop d£ tim dirge cac b6 ba ngi lire vdi M x , M y 
co gia tri ducmg Ion nh£t (max) v& gia tri am nho nha't (min - momen am co gia tri 
tuydt doi Ion nha't). 



1.4.DAICUDXGVECOT 

1.4.1. Chieu dai va chieu dai tinh loan 

Trong ket cau kJiung nha co th£ xem chi6u dai moi cot dirge tinh lu mii den roong. 
Tuy vay trong tinh io£n xem m6i c6t cht la doan c0t trong mdi tang. Chie^u dai th&t cua 
c6t ky htdu la / !a khoang each giua hai liSn ket (lidn ke'l co tac dung ngan can chuyen vi 
ngang cua c6t). 

Chieu dai tinh loan cua cot ky hieu la / . la chilu dai dirge xac djnh theo so do bien 
dang cua c6t. dirge Lay bang chie*u dai biroc song khi cdt bi rna't on dinh vi hi udn doc. 

'o = M>/ d-l) 

\\! - h£ so phu ttiuoc vao so do bien dang, cung tiic la phu Ihuoc vao lien ket 6 hai 
dau col. 

Voi cac so do ly ttfOng, lay y theo lunii 1.10. 



_ //s//// 



/////// 



V77P777 
3) 



/P77777 

W 
Hinh I JO. Cdc sa dd !y mang cua edi 



1 


Y/// 


,tfGTYTU 


if AN AM Lrv.Vj- 






:SS:<: 


..l&cMtf 


c 




. ■". 


.W 


///7/// 


///)/// 

y = 2 




) 




0j 



Can chu f rang trong so do LJ urong ngam la iifin kel can tro moi chuyen vi thing va 
xoay, khop la lien ke'l can ITO" chuyen vi thang (xoay diroc). Cac lien ket trong thuc le 
khdng giong hoan toan vol lien ket ly tuotig. Trong ket cau khung belong c6't thep toan 
kho'i, lien ket giCa dam va cot chi c6 th£ xem ta liftn k& cung ma khong phai la ngam vi 
nut khung co the co chuyen vi ngang vk chuySn vi xoay. 

Voi cac ket ciu there te, he so y dirge lay trftn co scV phan tich so d6 bien dang. 



17 



c. 



777777 777777 



-O 



777777 



77777 



¥ = 1,5 

Hinh Ml. Khung mdi idng rndf nhip 



;:: -r 



&z y 



, T ~777 



-V.- T 7 7''7 ~~77~; 






Hinh 1.12, Khung nhieu tang I nhip, 2 nhip 

a) Khung mot nhip. nhieu tang co Hen k6'i cung eiQa dam va c<M 
Khi s<in soan khoi: 

- Cot tang duoi ciing \y = 1. 

- Cot cac ling Lrfen v|» = 1 ,25. 
Khi san lap ghep: 

- C6t ling dudi cung vy = ) ,25. 

- Col cac lang tten >p = 1.5. 

b) Khung nhie\i lang co lien ket cimg giua dam va col, co hai nhip <ba col) ma long 
hai nhip B nho hem mot pha'n ba chieu cao H. 

He so v lft'y thco muc a nhan vai 0,85. 

c) Khung nhieu tang co lien ket ciing giua dam va cot co tif ba nhip (4 cot) tro len 
hoac co hai nhip ma t6ng hai nhip I6n hem 1/3 chieu cao loan khung: 

- Kht san roan khoi y = 0,7. 

- Khi sail lap ghep y = 1, 

d) Khung do cau true, khung nha cong nghiep mot ting co c6t lien kel khop voi ket 
ca"u mli ma m£i thi ciing trong mai phang cua no, c6 kha nang truyen tai trpng ngang, 
ltfy/ iheo bang 1.5. 



Bang 1.5. Chieu dai tinh loan /^ ciia cot nha mot tang 











Gia" irj / khi tmh trong mat phang 


DSc trurng 


Khung 

ngang 

hoac 

vuftng 

goc von 

iruc ciu 

can 


Vudng goc voi khung 

ngang hoac song song 

voi true cdu can khi 


Co Khong co 


Cac gjang trong mat ' 
phang cua hang cOt doc 
hoac cua cac go'i neo 


Nha co 
cSu iruc 




Phdn cot 


Khong tien luc 


1,5 H, 


o.8h, 


I.2H, 


Khi fce den 

lai trong 

do cau iruc 


duci d3m 
cati true 


Lifin me 


L2H, 


0,SH, 


O.SH; 


Phan cot 
rr£n dam 
cau (rue 


Khong lientuc 


2,0 H; 


l.5B> 


2.0H- 


Lien tuc 2,0 H 2 


1,5H ; 


L5H> 


Khi khOng 

ke den lai 

!rpng do 


Phan cc* 

ducti darn 

ctfu true 


Mdinhip 1.5 H 


0,8H, 


i,2H 


Nhieu nhjp 


J.2H 


O.SH, 


1.2H 

i 
| 


Phan col 


Khong lien mc 


2.5 H. 


1.5H : 


2. OH. ; 


ca*u (rue [ tren dam 
c&u true 


Lien tuc 


2.0 H; 


L5Hi 


L5FL 




Phancoi 


M6t nhip 


!..•>(( 


0.8H 


i.::-i 


Nha khong 
co cau true 


Cot bjc 


dirdi 


Nhieu nhjp 1,2 H 


0.8H 


1.2H 


Ph&n cor tren 


2,5 Hj 2.0H. 


2.5H 2 


Coc c6 uei difin khong 
doi 


Mot nhip 


(,5H 


0.8H 


1.2H 


Nhieu nhip 


1,2 H 


O.SH 


L2H 


G5u can 


Khi co dam cau iruc 


Khong lien luc 


2,0 H, 


0,811, 


1.5H, 


Lien tuc 


1.5 H, 


O.SH, 


LOH, 


Khi lien kei giffa cftr dd 


Khop 2,0H I. OH 


2.0H 


ducmg On a 


va nhjp 


Cfeg l,5H 0.7H 


1.5H 



Ky hie a: 

H - clueit cao toa/t bo cua eg! tinh lt( mat tren mang den kei can ngang (gt'an keo hoac 
lhanh xitn cua dam d$ vi keo) trong mat phang tsrong ii>ig; 

H, - chieu cao phan cot duoi (tinh sic mat tren cua mong den mat du&i dam can true). 

H 2 • ciuJu cao ptidn c6l tren (tinh tit mat tren cua bac cot deh kef cau ngang trong mat 
phutig tuong icng). 

Ghi chii: Neu co /sen kei den dinh cot trong nha co cau true, chieu cao tinh loan phan 
cdt irtin trong mat phang chua iruc hang cot doc fay bang H 2 . 



L9 



1.4.2. Tief dien cot 

Hinh d£ng tie't di6n c6i thuong la chu nhat, vuong, trdn. Cung co the 7 gap cOt c<5 tiel 
dien ch&T, chu* I hoac vong khuyen. 

Viec chon hinh dang, kich thuot liet dien col dira vao cac yeu c&u ve kien true, ket 
ca'u va ihi c6ng. 

V6 kitfn true, do ta cac yeu cdu ve tham my va yeu ca'u v6 sir dung khong gian. Vcri 
cac y£u cdu nay nguoi thiet ke kien true dinh ra hinh dajig va cac kich thtf6e toi da, td'i 
thie"u co the chap nhSn duoc, lhao lu&n vc*i nguoi thiel ke ket ca'u d£ so bo chon lua. 

Ve ke*t cau, kich thuoc tie! dien cot can bao dam dp b£n va do 6n dinh. Do ben se 
duoc tlnh loan hoac kiem Ira (day la n6i dung chuih cua tat lieu nay). 

Ve do on dinh, do la viec han che do manh X. 

i-^-sV " (1-2) 

Trong do: 

i - ban kinh quan tinh cua tj£i di£n. Vdi rie'l dien chu nhit canh b (hoac h) thi i = 
0.288b (0.288h). Voi iM dien tr&n duong kinh D thi i = 0.25D. 

?v h - 66 manh eio*i han. v6i c6i nha ). gh = iOO. 

Ve thi cbng, do la viec chon kich thuor liet dien cot thuSn tien cho viec lam Va lap 
dung van khuon, viec dat cot inep va d6 b&dng. Theo yeu cau nay kich Ihuoc liet dien 
nen chon la boi so cua 2: 5 ho&c 10cm. 

Viec chon kich thutfc cot theo do ben (ebon so bo) co the lien hanh bang each tham 
khao cac ket cau tuong ty (da dugc xay dung hoac thiel ke), theo kinh nghiem thiet ke 
hoac bang each linh toan gan dung. 

Dien tich liet dien cot la Aq xac dinh theo cdng thuc (1-3). 

Trong do: 

R b - cuong do tinh toan vi nen cua bet6ng. Xem phu luc 1; 2. 

N - lire nen. duoc tinh toan gan dung nhu sau; 

N = m,qF, (1-4) 

F s - dien tich mat san truydn tai trong len c6t dang xet; 

m^ • $6 san phia tren liet dien dang xet (ke ca mai); 

q - tai trong tuong durottg tinh tren moi m6t vu6ng mat san trong do gom tai uong 
thuong xuyen va tam then tren ban san, trong luong dam, tuong, cOi dem tinh ra phan b6' 
deu ir£n san. Gia tri q duoc lay theo kinh nghiem thiet ke. 

20 



Voi nha co be day san la be (10 -^14cm ke* ca cac lop ca'u tao mat san), co it urcmg, 
ki'ch thuoc cua dam va cot thudc loai be, q = 10 -?- 14kN/m 2 (1 + MT/m 2 ) 

Voi nha co be day san trung biiih (15 +■ 20cm), ludng, dsim, ctM la trung blnh h'oac 
ltfn,q = 15 - 18kN/m 2 . 

Vol nha co be day san kha Ion (tren 25cm). cot va d£m deu Ion thi q co the" den 
20kN/rn 2 hoac hon ntia. 

k, - he so xet den anh lurong khac nhtf momen uon, ham lupng c6't thep, d6 manh 
cua cot. Xet su anh huong nay theo su pban itch va kinh nghidm cua nguci ihiet ke\ 

r 

khi anh hudng cua momen la Ion. dp manh cdt Ion (/ Ion} thi iay k, \&n. vao khoang 
1.3+ 1,5. Khi anh hixongcua momen la be thi [tfyjc, = 1,1 ■*■ 1,2. 

Trirong hop ihiet k£ k£t ca'u chiu tai irpng d6ng da't thi kich thircrc cua cot c6n phai 

N 
man theo dieu kien ve han che ly so nen n c = — - . Ro rang la voi n c be thi can tang 

R b A U 

he so k r 

Sau khi so bo Unh dupt Aq thi lien hanh chon ki'ch chuoc ti£'t di&n c6t, Voi liel dien 
chiJ nhai ty le giua canh Ion va canh be khong qua 4 (neu ty !e Ion hon 4 thi phai xern la 
lam iirong). 

Ki'ch thuoc ti& dien cot duoc chpn so b6 co duoc xem la hop \y hay kh6ng ve mat 
chiu luc chi duoc danh gia sau khi da u'nh loan hoac bo tri cot thep va dua vao ty l£ phan 
tram cot thep. Neu phai hi&n dupe kich thtrdc da chpn la qua* bat hop ly (qua ]&n hoac 
qua be) :hi nen chpn Jai va ttnh lai. 

Trong nha nhieu ting, theo chieu cao nha lir m6ng dfih m£i luc nen trong cdt giam 
dan. D£ bao darn su hop ly vd su dung v&l Ii6u thi cang len cao ntn giam kha nang chiu 
luc cua cdt. Vi£c giam nay co the' ihuc hien hang: 

- Giam ki'ch thucrc tifi't dien cot. 

- Giam co't thep trong c6t. 

- Giam mac bet6ng. 

Trong ba each tren thi viec giam co'l Ch^p la don gian hon ca nhung pham vi dieu 
chinh khOng ton. Cach giam kich thudc tiel di£n la c6 ve hop ly hon ve mat chiu lire 
nhung lam phric tap cho thi cong va anh hudng khong :6\ den sir lam vide t6ng the" cua 
ngoi nha khi turn toan v& giao d6ng. Thdng thudng thi nen k^i hop ca ba edeh tren. 

1.4.3. Co't thep trong c6t 

Co't thep irong c6t g6m c6t thep doc chiu luc, co't thep doc ca'u tao va cot thep ngang. 

21 



2.4.3.1. Col thgp doc chiu luc 

D6 la cac co't tii6p duoc tinh loan hoSc duere kiem tra 66 chju noi luc trong cot- 
Thuxmg dung cac loai thep co cuong do tinh toan R s = 260 * 400MPa (2600 - 4000kG/cm 2 ), 
ducmg klnh thanh thep 12 ■+■ 40ram. Khi canh lifil di£n cOi Ion hem 200mm, duong kinh 
co't ihep phai tCr 16mm iro len (irir iruong hop co't thep tinh duoc qua be, chi can d&t theo 
yeu cau toi lliieu). 

Trong tiet di6n iron cot ihep duoc d5t deu theo chu vi (hinh 1.13a). Trong tie't didn 
vuong, chu nhat. chu T hofic chtr I c6 hai each dat: 

- Dat !heo chu vi (hinh 1.13b, c). 

- Dat lap trung tren canh vu6ng goc voi mat phang uon (canh h - hinh J . 1 3d, e). 






V 










m 




■ 




« 




■ 








(,> 


• 


• 


*f 


■ 


• 




• 


• 




■ 


• 




1- — "- 







Hinh LIS. Cac each ddi c6i ihep doc cftiu Sire 



Truong hop cGl viia chiu nen vua chiu uon trong m6t m3i phang do'i xung (nen 16ch 
tarn phang) (hi dai cot thep tap trung tren canh b la hop ly ve mat chiu lire vi cot ihep 
phat huy duoc toi da kha nang cua no. Dat cot thep theo chu vi thfch hop cho c<>t lam 
viec kh6ng gian (bi uon theo hai phuong - n£n 16ch tarn xien). Truong hop nen l£ch tarn 
phang cung co the" dat co't thep theo chu vi de thuan li£n cho thi cong va cung de khoi 
phai dat them cot thep c&u lao tren canh h (canh song song voi mat phang uon). 

Dat A sl - dien tich tiet dien loan bo cot thep chiu iuc. 



At. - dien tich tie't di£n belong 



u .s = 



Am 

A h 



» 100A «. 
hoacu s % = 



A, 



u. s - ly le cot thep. 
Difcu ki6n han ch£ la; 



(1-5) 



\i min - iy le cot thep lo'i thieu, thuong lay \x min = 0,005 = 0,5%. 

Pnwx " r y >£ c & 'hep i& d a - Trong m6t so lieu chuan ihiei ke' lay p mjx = 0.06 - 0,6%. 



22 



Khi bo tri cot thep doc can dam bao dieu kien ve chi£u day lop bao v£ va khoang ho 
giua cac thanh cot Ihep. Trong moi truong hop chi£u day lop bao v£ (c ) va khoang ho* 
giua cac thanh cot thep (Cq) khong duac nho hon duang kinh thanh {$) (hinh L14a). 
Ngoai ra voi col co chi^u cao tiel dien h tu 250mm tro 1 len thi cbieu day lop bao ve 
khdng nho hon 20mm. Vol co't thcp co vi tr£ dung khi do' be-iong khoang ha giua cac 
thanh khong nho hen 50mm. Trong dieu kien kich thuoc tiet di£n bi han che mk bu6c 
phai dai nhidu cot thcp ihi dirge phep dat ctfl thep ihanh doi, ghep sat vao nhau thco 
phucmg chuyen dong cua vtfa belong khi do, luc nay khe ha giua cac doi c6*t thep khong 
duoc nho hon 1.5 i£r\ duong kmh ihanh (hinh 1.14b). 



*! 


O 









T 


o 




0— 


k 


* 1 






1 


' 


o 


o~ 


f 




o 

1 




°i 






*Jc s 


'[k 


h 





w 



<. *% 




Hinh 1.14. Lop bao ve va khoang ltd cua cot thep 

1.4.3,2- Col thep doc cdu Cao 

Trong truong hop cot thep doc chiu lire duc/c ddi cSp trung tr£n canh b ma canh 
h > 500 mm thi doc theo canh h can dat cot thep doc cau tao co duong kuih tu 12 -^16mm. 
Khoang each giua cac true cac thanh cot thep do doc theo canh h la s khong duge Ian 

han 400mm. Dien tfch thanh cot doc cau tao kliong nho hon 0,00!sb ( vdt b( = min 
(0,5b va 200mm). 

a) 



Hinh U5. 
Cot i hep doc edit too 



500 < Jl< 850 





• 4 


• 
• 
• 

• 

T 




o 


s 


s 




850 <n< 1250 



1.4.3.3. Col thep ngang 

Cot thep ngang cua c6t khi dung khung co't bu6c la nhurig co't dai khep kin va nhung 
tlianh neo du*gc uon moc chuin hai dau. Cot thep ngang trong cot co nhiem vu lien ket 
voi cac cot ih£p doc thanh khung chic chan, giu dung vi tri co't thep khi thi cong, giu 6n 
djnh cho cot thep doc ch|u nen- Khi chiu nen, co't thep doc co the 7 bi cong, pha v& lop 
belong bao ye va bat ra khoi bet6ng. Cot dai giu cho co't doc khong bi cong va bat ra 
ngoai, luc nay co't thep dai chiu keo va n£u n6 khong duoc neo chac chan thi co the* bi 
bung ra hoac cot dai qua be thi co the bi keo diit. 



23 



Ducmg kinh cot thep dai ^ > 0,25^ mM (c6 lieu chudn quy dinh ^ £ 034> doc ). 

Bo td cot thep dai doc tbeo chieu cao c6t tuy thufic vao ke*i c£u c6 yeu c£u chd'ng 
dOng d£t (kh£ng chan) hay khong. 

V6i k£t cau bmh thtfdtig (kh6ng khang chaji) khoang each cua cot thep dai trong 
loan bo cot (trir doan noi buoc c6t thep doc) la a d < a d ^ c mm . Lay a<, = 15 khi ty s6 cot 
thep u« £ 0,03 va tt a = J 0, khi u; s > 0,03. dong tboti a rf £ AOOmra. 

Trong viing no'i cot thep doc ca"n phai dat cot thep dai day hen v6i khoang each 
khong qua J0^ oc m j n . Trong doan no'i bu6c cot thep doc phai co it nha't 4 co't dai 
(hinh 1.16a). 

Vcri ket ca'u co yeu c£u kha'ng chah cot thep dai Ccin duor dai day hem irong doan 
gan sat vcfi nut khung. Mtic 66 dat day ciia cot dai phu Ihuoc vao cap chong dong dat 
ciia c6ng irinh (hinh t . 1 6b). Ngoai ra con co yeu clu dat cot dai cho col a trong pham vi 
nut khung khi nul khung co dam lien ket til 3 mat ben ircf xuo'ng- 

Ve hinh dang. co't dai phai bao quanh loan b6 ciic co'l thep doc va it nhat each mot 
thanh cd't thep doc c6 m6t thanh dSt vao goc cua cot dai (hinh 1.16). Truotig hop canh 
b < 400mm ma tren do dat 4 thanh col Ihep doc thi co the kh6ng tufin theo quy dinh vua 
neu. (Tien chuan Phap BAEL quy dinh rooi ihanh col ihep doc co tjt £ 20 deu phai duoc 
aco git? b&ng c6t rhep dai d£ khdng the hi u6n cons b&t ra khot beions). 




b\ 



Z 



S3 




• • 




F : 
t : 






- :" ;.oo 



L_L^ 



Hinh 1.16. B6tri c6i ihep dai 

a) Trong edi bbth iJnrang; 

b) Trong cdt co yeu cau khong chan 



1 -: i'X 



I: ■:-;"o 



24 



Co't dai lam vific chiu keo do a*6 dau mut phai dupe neo chic chdn, thuotig lam moc 
neo gap a < 45° vrri doan thang 6in mut S > 3$ daj . Truong hop lam neo gap 90° thi doan 
thang S > Stjija, va c<£n dung day [hep buOc d&u miit vao voi ihanh cot dai, rranh cho khi 
cOt tfai chiu fce'o miic 63t ra ngoat (hxaft 2-17). Khi dtiag t/iaoh neo <fon, ftai ddu phai co 
moc neo tieu chuan voi S > 3<|) Ut ,. 








<r 



s> 



1,5. NOl LUC VA DO LECH TAM 

1.5,1. Nen dung turn va nen lech tam 

COt chiu lire nen N la chu yen. Ngoai ra cdt con co the bj utfn theo m<M phuong hoSc 
hai phirang. 

Khi cot chi chiu niot luc nen N dat dvng doc theo true ciia no, c6t chiu nen dting 
lam. Thuc ra nen dung tam chi II truong hop ly tuong. trong thuc te rat it khi gup. Kha 
nang chiu luc cua cor chiu nen dung tam la N duoc xac dinh theo cong thuc: 

N Q =<p(R b A b -hR sc A S i> d-6) 

R b , R sc - cuang d6 tt'nh loan chiu nen cua belong va cua cot thep. 
A b . A sl - dien tich tifft dien betong va cua ioan b6 cot thep doc. 

<p < 1 - ht so giam kha nang chiu luc do uon dpc (he so uon doc). Xac dinh cp 
theo cong thtic thuc nghiem (/.7), dung duoc khi I4<k< 104. 






cp = 1.028 -O.OO00288X 2 - 0,00 16A, 
- dp manh cua cot (xem cong thuc (1-2)). 



U-7) 



Khi X <14, bo qua anil huong uon doc, lay <j> = 1. 

C6t vua chiu nen N vua chiu uon M duoc doi thanh so do luc nen dat Ifch tam (hinh 

M 
1 . 1 S) va duoc goi la cot chiu nen lech tam. Gii tri e, = — dupe gpi la 66 Ifich tam tuih hoc. 



25 



Khi inomen uon M tac 
dung irong mat phang chi>a 
true dtfi xixng cua tifi't difin 
co trtfcmg hep nen lech t&m 
phing, khi M khong nam 
irong mai phing doi xung 
vu;a nSu, c6 iruong hop nen 
lech tarn xifin. 





A _ 




' 





e> N 



f/i«/* J. IS- So d6 cot chiu nen tech tarn 



1.5.2. D6 lech tam va lech t&m ngSu nhien 

M , 

Ngoai dd l£ch tam e, = — , irong u'nh loan con can ke den do lech lam ngau nhien 

e a 8*y ra b°*i nhung nhaJi \6 chua x6l de>i duerc nhu sai Ificb do thi cong. belong khong 
dong ahitt v.v.i. Quy dinh v£ vi£c x6i dd \tch (Am n^ku nhien c d iranz cac li&u chum 
thiet ke la khac nhau. 

a) Theo lieu chuSln Viet Nam TCVN 5574 • 1991. (lieu chuan cu) d6 lech lam ban 
dau ep 6t iinh loan la: 



Cri - Ci + e.. 



(1-3) 



Doi vol cac cau kien chiu nen co so do nnh dinh hoac la bo phan ciia kel cau sieu 
iTnh nhung chiu lire nen true tiep dat len no thl gia tri e y lay khong nho hem 1/25 chieu 
cao lidi difin va kh6ng nho hem cac iri $6 sau: 

20mm d6l vdi cdt va cac tam tuong co chieu day lif 250mm tro' len. 

15mm doi von cac tam co chi£u day 150 + 250 mm 

lOmin doi vol cac Um co cht£u day ducVi 150mm 

£>6'i vdi cic b6 phan cua ke't c&i sieu iinh khong chju lye nen true tiep cho ph6p bo 
qua dp I5ch tam ngSu nhien (e d = 0). 

b) Theo lieu chua'n TCXDVN 356 : 2005, do lech lam e a irong moi trtrcmg hop lay 
khong nho hem 1/600 chieu dat cau kien va 1/30 chieu cao life! dien. D6 lech iSm ban 
d£u e lay nhusau: 

- Vdi c&'u ki£n cua ke't ca'u sieu iinh; 

e = max(e, ; ej (1-9) 

- Vdi cS'u kien iinh dinh, x£c dinh e iheo cong ihiic (1-8). 

c) Tieu chuan Phap BAEL - 99 My e a = max (//250; 20mm) va iinh e theo (1-8), 

d) Tieu chuan Anh BS 81 10 quy dinh d6 lech tarn e khdng nho hem d6 lech tam loi 
ihieu bang gia iri Idn hon trong hai gia in 1/20 chieu cao ticl di£n va 20mm. 

26 



1.5.3. Anh hirong cua uon doc 

C6i co d6 manh Ion co ihe bi uon doc lam cho no bi cong (hinh 1.19). Luc nay lire 
nen N gay ra them mot women thti cap M 2 = Ne 2 v&i e 2 la chuyen vi tuong d6i cua Tie! 
dien dang xet so vcri vi tri dSt lire N, 

Mdmen u6n (u M tang len thanh 
M, = M + M 2 . Vi6c tang M nhir vSy 
la tuong duong vtfi vise lang do l£ch 
tSm tCr e thanh e' = e + e 2 . 

Tieu chuan thiet ke cua cac nude 
xet vice tang d6 lech tam nay theo cac 
each khac nhau. 

a) Tieu chuan cua Phap BAEL va 
cua Anh BS St 10 dua ra cdng ihuc 
tJiuc nghi£m xac dinh e 2 . 

Tieu chuan Phap: 

I 2 
e 7 =0,0003f- (2 + G t p,) 

h 

o, va p, la cac ht so' ke* den anh 
huong cua lac dung dai han va tCr bie'n 
cua bStong (a t = 0,7+1; p t = 2 +1.5) 





Hitth 1J9. Aiiit huoiig 
cua uon doc 



Tieu chuan Anh: e-> = 



200Q 



Kh 



4' 



k £ 1 he so phu thuOc muc $& chiu nen cua tier dien. 
c - canh be cua tiet dien. 
b) Tifiu chuan cua Nga, Trung Qu6'c, Viet Nam xet viec tang d6 lech tam theo he 



so nhan. 



e,, = e a + e-> = 



e 0/ 



e o = 7 l e o 



r| > 1 - he so xet d&n uon doc. 

Trong ty thuye't on dinh da chiing minh duoc cong thtic xac dinh n.; 

1 



1 = 



1- 



N 



N 



(1-10) 



(1-11) 



N cr - luc nen toi han. Cung Irong ly thuyel 6n dinh da chiing minh cong thuc Ole 
CEuIer) doi v&i ca'u kien bang vft li£u dan hdi, dong nhS"t: 



27 



7l 2 EJ 



N * = a 



« 



(1-12) 



E - modun dan h6i cua vat lifcu; 
J - momen quan tfnh cua tiet dien. 
EJ - d6 ciing chong uon cua tie! dien. 

De tinh loan ca'u kien b6t6ng cot th6p ngtfoi la kh6ng dung cong thuc (1-12) ma 
dung cac cdng thiic thirc nghidm. Co kha nhieu c6ng thifc nhix vfiy vol cac muc do gin 

dung kbac nhau trong 66 tinh loan N cr theo cudng d6 chiu nen R b hofic theo modun dan 

h6i E b cua belong, co k£ hoac khong ke* d£n do lech lam va sir co mat cua cot thep. 

Cong thurc theo cuong 66 chiu nen R b . 

4800RJ 400R.A h h : 



N. = 



b" _ 



b^b J 



<0 



A b = bh - dien lich tiftt dien chu nh&l. 
C6ng tbuc tinh theo modun dan hoi E b : 

2.5E b J 



N = 



A 3 



Cong thuc tinh theo R b co ki d6 Jech tam va cot ihep; 



(1-B) 



(1-14) 



N^C.R.A^ 



66000 
s ~R + 350 



/• 



^ + 0.16 
. h 



+ 200.u c 4l 



(1-15) 



Trong do: 

R - mac thift't kd cua betong theo circmg do chiu nen trung binh (kG/cm 2 ); 

^ s - ty It cdt thep. 
C6ng thiic tinh theo E b co ke den do lech tam, col thep va tac dung dai ban cua luc nen. 

6,4E b ' 



N = 



/; 



5 s 



V. - h£ so k6 cte'n do lech lam: 

0,1) 



v < = 



J t +cU 



+ 0.1 



(l-16a) 



<M7a) 



0,1 + 3L 
h 



28 



K d - he so ke den tac dung dai han cua lire nen: 



K d = l3*^£ (M7b) 

d M + Ny 

y - khoang each tCr irpng llim tiet dien den mep chiu keo (hoac chiu n£n it) cua 
tiet dien. 

M^, N dh - pha*n ndi lire do tai trong dai haa gay ra. 
a s - - JL v<Si E s la modun dan hdi cua cot thep. 

J s - oiomen quart linn cua tiet dien cot thep. 

Tieu chuan TCXDVN 356 - 2005 cho c6ng ihixc linh N cr tren ca so cua cong thuc 
(] -16a) voi cac he so chi tie^t hon. 





N„ 


C h E h 


J 


? — hOJ 


+a A 


Trons do; 


« 


Vi 



(I-16W 



e 
S. lay bang ty $6 — nhimg khdng oho hon 6 mjn 

h 

5 em]n =O.5-0,01^-O.OlR b (R & :MPa) 
ii 

* 

<p p - [it s6 xet den anh hudng cua co't thep iiog lye inroc den do ciing ciia csfu 
kien. (<p p > I - thi khong co cot thep i/ng lire true*; <p p = 1). 

C b - he so. Voi betong nang va belong hat nhd nh6m A lA'y C b = 6.4- 

Voi betong hat nho nhom B la"y C. = 5.6. 

tp/ - he so, xac dinh theo cong thuc: 

*-i+p§- 

p- he so, vcri betong nang |J = I; betong hat nho nhom A: [J = 1,3; nhom 8: J3 = 1,5. 

M - momen lay doi vdi mep tiet dien chiu keo hoic chiu nen it hem do t^c dung 
cua toan bo tai irong. 

Mj - Nhu tren, do tai trong throng xuyen va tai trong ram thoi dai han. 

Tieu chuan cua Trung Quoc GBJ10 - 98 tuy cung xet sir tang d6 16ch t2m bang hd so' 
nhSn r| nhung khong dung cong thifc (I-1I) ma xac dinh r| bang cong thtic thirc nghifim: 



29 



T| = l + 



I 







1400-^ h> 
ho 



^2 



; i =M|^;; 2 = U5-0.04 

N h 

A b - dien tfch tiet difen. 

Voi Tihtfng c6( ngan, c6 66 manh be, X = -7- < 14 . co* the bo qua anh hiring ciia uon 

i 

doc, 12y e 2 = hoac r| = 1. 

Qu3 irinh xet su tang do tech lam the' hifen tren hinh 1.20. 



■V 




Hinh 1.20. Sttrang do fcch tarn 

Gia iri r| n'nh theo cong thtrc (1-11) la doi voj net dien co chuyen vj Ion nhil. 

Tuy theo vi tn lie* dien tinh loan ma co Ihe lay gia iri t| titcrng tmg. 

Tren hinh 1.19a gia iri e^ Ion nhat ogiOacol con iren hinh 1.19b, c co e-> 16n obat 6 
chan cot, lai dinh cot e 2 = tuong ung voi n, = I. 

Trong tinh lo£n thuc te. de thien ve an loan co the xem gan dung r\ la hang so irong 
toan cot. Tuy vay neu muo'n U'nh loan chinh xac hon tha can dua vao so do bien dang biCl 
loi »ua cOl 6i lay gia tri r\ umg voi tCmg ttei diSn. 

Sau khi ke den do lech tarn ng&c nhien e a va anh huong cua uon doc r\ ihi momen 
uon da tif gia tri ban dau la M tang fen thanh M* 

M*^Nr|e (1-18) 

1,6. SULAM VlfiC COA TifT DlfiN C<>T 

1.6.1. f)ieu kien ve do ben 

Tilth loan tiet dien c6t theo phuongphap irang thai gidi hart, Dieu ki£n ca ban dam 
bao do ben khi tinh theo trang thai gidi han vi khi nang chiu luc la: 



Mj 






(1-19) 
(1-20) 



N - lire nen duoc xac dinh theo id hop npi luc. 

N gh - kha nang chiu nen cua tie't di6n. 

M u = Ne u . Mdmen uon do luc nen N dat lech tarn gay ra do'i vol true U (khong 
nim trong mat phang uon). 

e u - kboang each tu diem d2i luc ISch lam N den true U da chon (e„ > 0). 

M ch - kha n3ng chiu uon cua tie't di6n lay dtfi vai true U da chon. 

Xac dinh N^ h , M ob dua vao su lam viec a trang thai gicn nan v6 kha nang chiu luc. 
Trang thai nay duoc thie't l&p tr£n ccr so phan tich cac k& qua nghien cun thirc nghiem. 
di/a tren cac quy lu$t chi pho'i sir lam vi€c va cac gia thie't duoc de" xua't. Ttr do lap ra cac 
bieu thuc loan hoc de tmh toan. 

Trong bai loan u'nh cot thep hoSc bai loan kie*m Ira can thoa man ca hai di£u kien 
neu tr6n irong do co the 7 iay m<M dieu kien iheo dau dang thirc (=) con difeu kj£n kia theo 

dau quy dinh (<). Trucmg hop nen dung tarn chi can rndt dieu ki£n (i- 19) trong do N^ = N 
tinh theo cong ihiic (1-6). 

1.6.2. Cac ket qua thi/c nghiem 

1.6,2.2. Quart he ttrng sudt bien dang 

Ret qua quan trong nha't cua thuc nghiem la quan h6 gitfa ting sua't o va bien dang ty 
do'i £ cua vat iieu duoc gioi thieu tren hinh 1.21. 




3) 




Hinh 121. Quan he giua 
ting sudt <7 eciia vai lieu: 
a) Befdng; b) Cd't thep dip. 



Hinh 122. Quan hi 

<r- sdung trong tilth toan. 

a) Belong; b) Cd't thep. 



31 



De" dung vao tinh loan, cac quan he tren da duoc don gian boa va sau khi da dira vao 
cac he so' de xei den do an toan (dd tin c&y) thi bie"u do ting suae bien dang duoc lay theo 
hinh 1.22, trong do: 

R b , R< - cuong do linh toan cua bft&ng (vi nen) va cua c6l thep (ve keo); 
%, 8, - bien dang cua betong va cot ihep a trans thai gidi han; 

e t = — - gici han bien dang dan h6i cua cOt thep, irong do E, la modun dan hoi. 



Vai bft6ng, khi chiu nen dung tarn ngtrdi ta cho rang khong nen d6 cho b&tdng c6 
bier dang qua 2%o va nhu v3y lay £ c = 2%o.. Khi tren lift didn co mOt vung chiu keo m&t 
viing chiu nen, kha nang bien dang cua betong a mep chiu nen tang len, lieu chuan cua 
Phap lay £ c = 3,5%o. con tieu chuan cua M? lay s c = 3%o. 

Vai c6J thep, bien dang cua c6'[ ihdp dco khi bi keo dut la kha Ion (0,1-^0.2). Tuy vay 
khi xet su lam vice cua kel cau belong cdl thep 6" trans, thai gidi han mot so tieu chuan 
co quy dtnh han che gia iri cua c a trong khoang 10%o. 

1.6.2.2. Sir lam viec cua cau kien 

Thirc nghi£m \>t six lam vi6c cua cau kidn chiu nen lech tain duoc lien hanh iheo so 
do tren hinh J. 23 vai lire nen N d2l each true moi doan e . Lam thi nghiem voi cac dp 
J6eh tarn e khac nhau va irong m6i Ian thi nghiem tang din lire N cho den khi cau kien 
bi pha hoai. 

Kft qua thuc nghi£m cho bie'l voi e 
be loan bo liel dien chiu nen va su pha 
hoai bai d£u tu betOng a mep chiu nen 

nhteu hen. Voi e Ion. mdt phan lift dien 
chiu nen, phan con lai chiu keo. belong 
chiu keo co the bi nui, su pha hoai co the 
bai ddu tu vung b£t6ng chiu nen hoac tii 
col ihepchju keo. 

Co hat quan diem ve ph£ hoai: ling 
suat va bien dang. 

Quan diem ve irng suat cho rang vat 
lieu se bi pha hoai khi ung sua'l trong no 
dal va vuert cuong 66 vat lieu. Theo 
quan diem nay bieu do ting suat dung 



M 



** 



O" 



i • i 






v- 



Hinh 1.23. Sodd iht/c nghiem 
can kien nen lech tarn 



32 



cho t f 11 h loan diroc ihie't I5p tCr ket qua (hire nghiem va khong can quan tarn den cac 
gia trj £ c , £ a . 

Quan diem ve bien dang cho rang &u phi hoai dtfoe quyet dinh boi bien dang cua v&t 
U6u. Theo quan diem nay xuar phat 6& lap so" do tinh toan la bien dang. Til $0 do bien 
dang, dung cac quan hd cf hinh 122 dt suy ra so do ung suae va dung so dd ung suit d£ 
Jap c6ng thuc. 

1.6.3. Gia rhiet tinh toan 

De 7 h)p cac cone ihuc ii'nh toan tic! dido belong cot thep nguoi la dung quy fuat ve" 
can bang luc. ngoat ra 6& don gian h6a cong vice ti'nh toan nguoi ta cbn dung gia thie't 
bo qua su Lam vice cua betong chiu keo. Ri£ng voi quan di6*m v6 bien dang con dung 
them gia thiet tie! dien phang va gia thiet b£t6ng, c6i thep co cung bien dang (tai moi 
vi tri). 

1.6.4. So" do ling sua! bet6ng vung nen 

Tuy xuat phat cua hai quan diem co khac nhau nhimg so 66 ung suat trong betong 
vung nen duoc lay gio'ng nhau va do la mot duong cong nhu tren hwh L23c. Duong 
cong do c6 dang cua dudng cong tren hinh 
V .2 1 hoac 1 .22. Can chu <t rang h\nt\ 1 .11 ibt 
hien quan he c-e theo hai true vuong goc con 
hinh 1.24b va 1. 24c the hien quan he o - s 
theo hai true song song. True trung hda each 
mep chiu nen ra<M doan x$, tai do co s = va 
a = 0. trong doan z < 2%o, quan h£ a- s Ja 
duong cong. trong doan e > 2%o, co a la 
hang so, bang R^ (doan AB tren bieu 66). 

Nham don gian hda vi£c tinh loan nguoi 
ta da thay bie'u do co mot doan cong OA va 
mot doan thang AB tr£n hinh 1.23c voi chieu 
cao vung nen thuc x bang bie'u 66 hinh, chir 
nhat voi chieu cao vung nen tinh 66i x va 
ling suat tinh d6i R' b . Xac djnh x va R'^ dira 
vao hai didu kidn: gia tri cua hop lire D b va 

diem dat cua D b trong hai bieu dd la trung Hin(t l - 24 - &*£ suat trong betong vung nen. 

r,i™». t\„ l .". i-- l- i_-.i_- - a)Sod6 ndi tuc; b)Bieud6 bWndane; 

nhau. Truotig hop tiet dien chu nhat be rong '\ _.> :, ; '., , ,'«,., " 5 

c) Bieu dStfng suat thac;d) Bieu dd 



^ 



i, 



o) 



a 



*i 




"mn 



■p- 



* 



t 


f i 

1 


t 


- 


Q» 


C: 




X 





R' 



b thi hai phuong trinh d£ xac dinh x va R' b 



don gian hda. 



23 



v 

la: D b = R* b bx va c b = — (xem hinh 1.24} trong do D b va C b da duoc xac dinh iheo R b 

va x . Trong truong hop chung co the bi£u dien x thco *q va R' b iheo R b nhir sau: 

x = 9x c vaR , b = 3 b R b (1-21) 

Gia iri cua 9 va fi b phu lhu6c hinh dang viing bet6ng chiu nen va e c . Voi ti£t dien 
chu rtot co the lay J3 b = 1 va 9 = 0,8 + 0,85 khi e c = 3%o. + 3,5% . V6i liet dien chu T co 
canh trong vung nen lay f* b = 1 va 9 = 0,82 * 0,88 vdi tid't dien iron P b = 0,9 -5- 0,95 va 
0=0,8-0,85. 

Gia iri 8 nhir vira neu dung 6*cong thtfc (1-21) chi dung khi x^ <h. Tnrcmg hop nen lech 
tarn ma loan bo tiet dien chiu nen thi true trung hoa nam ngoai ti£t dien, x > h va Xy co the' 
tang den v6 cung irong luc gioi nan cua x chi c6 the* dai den UK da la bang h. Khi ma x > h 
va 9 = 0.85 co the dung luong qua giua x va x theo bieu ibuc (1-22) sau day: 

X s>-°- 85h)h 0-22) 

x -0,8235h 

1.6.5. tjng susft trong cot thep 

1.6.5.1. Theo quart diem itng sudt 

Vdi truong hop cot Ihep duoc dat lap irung tren cac canh \ uong goc vdi mat phang 
iion !a A,, (chiu keo hoac nen ft hon) va K\ (chiu nen nhieu hon) thl cac ung sua'i tuong 
irrig la o\ va a\ dupe lay theo kfe'i qua thuc nghiem nhu sau (hinh 1 .25). 

a) Vdi col thep A,. Khi A., chiu keo, a s . dat gia Iri Ion kht cot thep dal xa true trung 

Y 

hoa va nguoc \ai. Khoang each \& A ( den uuc trung hoa la v a = h - x =■ h - — . Gia iri 

Jon nhtfi ma <j s co the' dat den theo quy udc unh loan la R s . Di dat duoc di£u nay thl v a 
phai lcwi hon mot ph£n nao d<5 cua h^ tarn dal la a,li . 

V 

v * = h o-£- a i h o n3tra x^(l-« l )0h =^ R h, J 

V&y di£u kten de* o~ s dai deh R; la: 
x<^ R ho 

Ngir&i ta xac djnh gia iri 4r bang thuc nghi6m, tha'y rang £ R phu thu6c vao R s va R b . 
Da c<5 nhimg cong thCrc thuc nghi£m de t£nh toan £ R nhimg thirong co the tra bang 6 phu 
luc 4. 

Khi x > £ R ho thi c\> chiu keo chua dal R, hoac khi x tang den mdt miic nao do thi a, 
chuyen thanh chiu ndn. Tieu chuan TCXDVN 356 : 2005 dua ra cong thtrc thuc nghtem 
xic dinh o* q : 

34 



<T.. = 



r 2 iz±iK_; 



i-k 



R 



R. 



1-23) 



Cong thuc (1-23) duoc dung cho betong co cap bang hoac nJio hem B30, cot thep 
nhom CI, AI, CII. All. CHI, AflL (R s < 400) va chip nh|n duoc khi x < h a con khi 
x > h thi lay o% = -R v Cong thtfc (l-23a) do Idc gja d£ xuat cho ket qua dung duoc khi 
^ho < x < h va R, < 400. 



o, = 



I 2(x-4 R h 



R 



(l-23a) 



Trong hai cong thuc tren tinh duoc cj s > la ung suat keo con a s < la img SU& nen. 

b) Voi col thep A^ . Vdl cot chiu net lech tarn col thep A^luon luon la chiu nen. Ung 
sua! trong A{ la o\ se Ion khi khoang each tir A' s den true trung hoa la v^ = x -a' kha 
Ion va nguoe Iai. Gia tri Ion nha't ma crj co the dal l6i la R^ . D6 dat duoc dieu nay thi 
v^ phai Ion hon md£ so' Ian nao day ciia a' , duoc dat la y,a' : 

V L =^o- a ' = ~- a '^Y^' 
Rutra: x> (1 -;- y, )0a' = 5 t a' 

Phan Tich ket qua thuc nghiem tha'y rang 6, phu thuoc vao R, c va thay ddi trong 
khoang l,5-r2 (6, tang l£n khi R w tang). De don gian hoa, chap nhan gia tri 6, = 2 cho 
moi loai co"t thep (vdi R^ c < 400MPa), 



Nhu vav dieu kien de" o*' dat den 



R st la: 



x > 2a' 



Khi x < 2a' xem la <j' % chua dat den 
R^ : Dieu kien x > 2a' duoc lay tjieo tieu 

chuin TCVN 5574 - 1991. Tieu chuin 
TCXDVN 356 - 2005 khong dua ra dieu 
kien cho o\ , Trong tai lieu nay tac gia 

van giu* Iai dieu kien x > 2a 1 nhu la mot 
tSiin ki£n de phan bi£i cac iru&ng hop 
tinh todn. Vi£c nay chi co loi la lam ro 
rang hon sii lam viec cua tiet dien va 
edeh tinh loan. 





\ 














* 










c^ s 


IL_ 




i 








* 


t>„| 




■Eft 




X 




a 




i 




r ^r~ 






h 


— 1 





















Hinh 1.25. &ng sua! 
trong cot thep a s , G' & 



35 



V6i c6i thep co R, < 400MPa lay R sc = R,.. 

Vdi c6t thep c6 Ri cao hon 400MPa thl trong mat stf tifeu chuan rhie't k€ cung chi lay 
R K < 400MPa. Ly do la khi chiu nen dung lam lay bien dang gidi han ciia belong s c = 

2%o va bien dang cua cot thep chiu nen t6'i da cung bang khoang a'y. Vol bien dang do 
ung suat trong c6'( th£p (c6 cuong d6 kha cao) khong vuoi qua gia trj. 

<y' c = Gf E t = 0,002 X200.000 = 400MPA 

(Lay modun dan hoi cua thep E, = 200.000MPa). 

Voi cot thep citong do kha cao (AV, AVI, AVIII) TCXDVN 356 - 2005 cho phep 
lay R sc = 500MPa irong mflt so' iruong hop dac bi$l. 

1.6.5.2. Theo quan diem bien dang 

Xua't phai tir bien dang cua belong tai mep vung nen da diroc quy dinh. dung gia 
ihiel tiel di£n phing, khi bid'i vi iri iruc trung hda (biel x ) va vi in cua thanh hodc hang 
cot thep thtf i (h p |) se tinh ra ducc bi£n dang cua no la t- t (hinh 1.26). 



Hinh 1.26. Ifng sud'i 
trong cdi (hep <r f dime 
tittfi f/iet? bien dang s t 





_Jx_ 


A. 


A; 




2 






Ate 




K, 








l>* 






\i 


















pAi 


£A 


°A 


c.A 



B-i-ZSL. 



(1-24) 



Khi: 



£j >e T thi o, = R S 
|e.|<e T th\Cj = s<E< 



Cl-25a) 
(l-25b) 



36 



p 

Trong do: e T = — - 

Kbi tinK dtrac e, > 0, a, la ung suae keo, khi e, < co ung sua't nen. 
Theo quan diem bien dang, de cho a t chiu keo dat gi£ tri R s thi: 

- - h ci- X r >f ^^ 

e. 



^T 



-* 



(I -26b) 



Voi x = Gx thi dieu kten de a, dai R s la: 

x<Pih in (!-27a) 

ft=«h- o- 27b > 

Di£u kien (i-2?a) la lifong tydieu ki£n x < 4r ho da trinh bay Irong muc 1.6.5.1. 
vdi h„j = h (xern hinh 1.25. 1.26V 

Vot cot thep chiu nen. de cho ung suai c t dai gia tri cutrng do ti'nh loan ve nen 



i i ^n'h-M -. R 



sc 



x E< 



Rutra: x > ^-h^ 



t. 



va: x>6 2 h oj (l-2Sa) 

8 3 =-^ (l-28b) 

Dieu kien (l-28a) la tirong tu didu kiSn x > 2a' Irong muc 1.6.5. 1 (hinh 1,26 va 1.25 
cho tha'y h^ = a'). 

1.6.6ft Cac trtfong hop tfnh loan 

Tir phan tfch su lam viec cua tiet dieji chju nen I6ch tam ngu&i la dua ra cac truong 
hop ti'nh toan. Trong viec nay cQng co cac quan die*m khac ohau. 

37 



M6t so nucfc Au My phan chia ra hai iruong hop dura vao vung chiu nen: Tie'i di6n 
chiu nen loan bo va tiet dien chiu nen m6t phan. 

Tieu chua'n thiet ke cua Nga, Thing Quoc, Viet Nam phan chia ra hai truong hop 
nen ISch tarn 36n va nen lech tam be dua vao sur lam viec cua cot thep A s . cGog tire la dua 
vao gia tri cua chieu cao vung nen x. Khi x < ^ R h cd't thep A s chiu keo, ung sua'i cr R dat 
den R s , xay ra su pha hoai deo, co trudng hop nen Itch tarn Ion. Khi x > ^h^, cot thep A s 
co the chiu keo hoile nen ma ung sua'i trong n6 chua dat den Rj. hoSc R„. sir pha hoai bat 
dau lis betong vung nen, c6 iruong hop nen lech tam be. Tie'l di£n lam viec iheo trucmg 
hop nao la phy Ihu6c vao tuong quan giua M ( N vdi kich thuoc tie! dien va su bo' In cot 
thep. Khi M tuong do'i Ion tiet di£n lam vific gan vdi trucmg hop chiu uon. co vung nen 
va vung keo t6 r£t. Neu c<5t thep chiu keo A, kh6ng qua Jon thi su pha hoai se bat d£u lu 
vung keo. co truong hop nen l6ch lam Ion. 

Khi N tuong do'i Ion, phUn Ion lie't di£n chiu nen. su pha hoai bfa dau tir betong phfa 
bi nen nhieu, co trucmg hop nen lech tarn be. 

Can iuu y rang irong ilnh toan (hue hanh dieu kifin de phan bidi cac trucmg hop nen 
ldch tarn chi la tuong do'i. C6 mOl so' trucmg hop. voi tiet dien va diem dat luc N da cho, 
khi thay doi cot thep c6 the' chuyen su lam vi£c cua tiet di&n tu nen lech tarn loti sang 
nen lech tarn be va ngtfoc lai. Khi chuyen nhu v£y tbl gia tri luc doc gioi nan ma lie'l 
dien chiu duot N fh thay do'i theo. 



5! 



\ 



t» 



A', 



\ 



A". 



—\ 

Hinh 1.27. Thi da ve cac trudng hap nen lech tarn 

Lay thi du nhu iren hinh 1.27. 

hmh 1.27a. d6 lech t£n? cua luc doc e^ tuong doi be. ihucmg Sa truong hop nen 
lech tarn be v6i kha nang chiu lire N, . Neu giarn col thep \ tiet di£n co the" chuye'n sang 
lam vice tbeo n£n I6ch tarn lort v6i kha nang N 2 < N,. 

6 hinh 1.27b, 66 l£ch tarn e tuong doi Ion, thifcfng tiet dien lam vide iheo nen lech 
tarn 1cm. Tuy vky neu tang co'l Ihep A s thi den m6t ldc nao do tiet dien se chuye'n sang 
lam viftc theo nen Ifich 13m be (vl ung su^l o s trong A s giarn XUong khiA, lang) va luc 
doc N tiet dien chiu duoc se cao hen. 

Viec phan biei trucmg hop nen lech tam Ion hay be chu yeu dua vao gia tri chi£u cao 
vimg nen x, chi khi kh6ng c6 each nao 66 xac dinh dupe x thi m6i dung dieu kifen bo trg, 

can cts vao dp lfech iSm e . 



38 



Chtrong 2 
TIET DltN CHtf NHAT CHIU NEN LfiCH TAM PHANG 



2. 1 . SO Dd VA CONG THOC CO BAN 

2. LI. So do va ky hieu 

Xet ti£! di&n chu nhat co cac canh b, h. 

b - chieu cao tict di£n, la canh song song vdi'mat phang ud'n. 
b- be rong, la canh vuong goc mat phang urfn. 

Trong nhCmg truong hop thong thuang cot thep doc cniu lire dtfot dat tap trung theo 
canh b va ky hieu la A A , Aj . 

A^ - dien tich tiet dien cot thep 6 phia gan vdi luc doc dat lech tarn N, trong 
vung bi nen nhi^u- 

A^ - dien tich tiel dien cot thep 6" phia doi dien vol A[, cot thep A s c6 the bi keo 
hoac nen it. 

a, a" khoang each iu trong tam A s , A* den mep tiet dien gun nhat. 

h = h - a - chieu cao iam vice cua tiet dien. 

Z t = h - a' - khoang each giua Irpng lam A s va A^ . 

x - chie*u cao vung nen tinh d6i, gpi tat la chi<5u cao vung nen; 

R b - cuong do tinh toan ve nen cua belong. Gla tri R b duoc lay tlieo phu luc 2 
nhan vdi he so dieu kien lam vice y^ cho a phu luc 1. 

a si a[ - ung sua't trong eft Thep A s v& A^ . 

R^, R M - cuong dc) tinh loan ve keo va, nen cua cot thep. lay theo phu luc 3. 

£ R - h6 s6 tinh roan gicfi nan vung nen. lay theo phu luc 4. 

So do lire lac dung the hien tren hiah 2.1a va 2.1b, vdi true U 6i lay rnorrten la true 
di qua trong tam cua A s hoac A^ . Nhir vSy gia tri e u duac lay bang e hoac e' (xem cong 

thuc 1-20). 

e~ khoang each tu diem dat luc doc N den trong tam cot thep A v 

39 



e = iie +0,5h-a (2-1) 

r| > 1 - he so' xet den anh huong uon doc, xac dinh theo cong thtic (1-11). V6i 

Mi dien chii nh§t khi X h = — < 8 co the bd qua u6n doc, r| = 1 . 

h 

e' - khoang each tit diem dat lire N d6n trong tfcm A'^ . Tuy trirong hap diem dat N 
d khoang gitfa bay b ben ngoai A s A^ ma co each tinh khac nhau. 



t; 





e ' , 






fca 


N 






i 






\ 


4 


.K. 




fr- 

i 

e 




1 ne 




! r 


s' L 




,r 


K\ 


_JL : 


-a; 








' 


■^ 








— i 
i 


t 

i 


Y/////& 




t> 




a 








•'•• 




h 





a.b - sodd htc idc dung; c - so do ling sua); d- (set dteit 

2.1.2. Dieu ki&n va edng thurc co* ban 

Dieu kien ve do ben la cac dieu ki£n (l-)a) va (1-20) trong do iruc cu ban de" lay 
mdmen di qua trong tarn cot (h6p A h va nhu vay M„ = Ne. dieu kien (1-20) difoc viei thanh: 

Ne<M lgh (2-2) 

Ttong mot so' trirang hap dac bi§t true lay momesi duoc cho di qua tron£ tarn A^ Va 
dieu ki6n se la; 



NV^M 



2gh 



(2-3) 



Mj gh - m6men gioi han the" hien kha nang chiu luc cua liet dien lay doi vdi true 
di qua trong tarn cot thep A r 



M 1|h =R b bx h -- -f C ; A ;z 



(2-4) 



40 



M 2s ji • momen kha nang chiu luc cua liet dien lay doi voi true di qua irong tam 
A' s (luy truong hop n'nh loan se lap cong (hire sau). 

Kha nang chiu nen cua tiet di6n M gh duec xac dinh bang long hinh chieu cac luc; 

N gh = R,bx + <7;A;-a,A s (2-5) 

Trong cong (hue (2-4) va (2-5) tinh loan vtfi gia tri tuyet doi cua a s va o' s theo chieu 

da ghi tren hinh 2.1c. N6'u cr s la nen thi a cong ihiic (2-5) lay da'u c^ng truot o,A r 
Twang hap a; diroc tfnh theo c6ng tbut vdi da'u dai $6, quy trac inig suit keo la duong 
thl van gift nguyen dau cua cong (hue (2-5) vi luc a 3 ia nen se mang da'u am. Gia tri cua 
<j[ va a s lay theo muc 1 .6.5, cu the ta: 

Khi : x>2a' thi <=R W (2-6a) 

Khi : x < ^ho thi a s = R, (2-6b) 

Nhu v^y die'u ki6n de" dung net kha nang chju luc cua col thep la: 

2a'<x<4 R h a (2-6c) 

Tfnh loan cot thep hoac kiem Ira kha nana chiu luc tlurang diroc tieri hanh theo dieu 
kien (2-2) vc*i M lf , h theo (2-4) trong do x duoc xac dinh tir die'u ki£n N = N gh . Vol gia 
thiet la dieu kien (2-6c) duexe thoa man thi co phuong trinh (2-7a): 

N=N^R,bx + R $c A;-RA (Z-7a) 

Khi xa*y ra x > ^hg. gap uuong hop nen l£ch tarn be (mac nhien c6ng nhftn x > 2a 1 
do do &.. = R. it ). di xac dinh x can giai dong thai hai phuang trinh. Phuang trinh thu 
nhat ia dieu kien can bang luc nen: 

N = N gh = R B bx+R w A; -a fi A s (2-7b) 

Phuong trinh thir hat la quan h£ gitJa ung su^'t c? s va chieu cao vung nen x. lay theo 
m6t trong cac cong Ifauc (1-23) hoac (1-25). 

Can chu y la chi c6 the" giai hd hai phuong trinh vua neu khi da biet cot thep A s , A' s 
(hai todn kiem era) hoac bi£'t quan ht gitra A s va A^ (i£nh loan cot thep doi xung). Khi 
chua bie't A s va A^ (bai loan tinh ctft ihep khong doi xung) co the x4c dinh x bang cong 
(hue there nghiern, gin dung. 

Titiu chua'n thi£t ke TCVN 5574 -1991 co dua ra cac cong ihuc sau: 

Khi e < 0.2ho, tJnh x theo cong thirc (2.8a): 

41 



\ = h- 



W+^-L^L 



Khi 0,2h < &q Z e op . tinh x theo (2-8b): 

x=l,8(e op -e ) + £ R h 
Trong do: e op = 0,4(l > 25h ■ ^h,,) 

Khi e > e op lay x = ^ 

Ngoai cac cong (hue (2-8) cung con c6 m6t s6'c6ng thtic kh&c: 



X = 



^R + 



1 + 50e 



j 



= [4 R +{l-3e )(l-^)lh, 



(2-8a) 

•: 

(2-8b) 

(2-9) 

(2-8c) 



(2-10) 



Trong hai c6ng thtfc tren ihi £ = — . Cdng thuc (2-10) diing cho mpi e^ con cong 

h 

thuc (2-11) chl dung diroc khi s < -, khi e a > — thi lay x = £ R hQ. 

Can chtf ^ rang gia tri gan dung cua x xac dinh iheo cac cong inure (2-8a) den i2-ll) 
chi duoc dem dung de* n'nh M,_ h theo (2-4) ma khong diing de xic dinh gia iri o. theo 
cac cong thuc (1-23) hoac (1-25). 

Khi xiy ra x < 2a' dung dicu kien (2-3) dti tinh loan se thuan loi hoti (x < 2a m£c 
nhien cong nhAn x < c, k \\q do d6 cx^ = R s ). Tinh M 2c . h : 



M,„u=RAZ, + R.bx a'-- 



l 2«h 



•v *s 



(2-12a) 



Nh&n xei r5ng thanh phan thu 1 hai irong c6ng chiic la kha be; va neu bo qua ihi vifcc 
tinh toan thien ve an loan hern, vi vay thitang ngiroi ta bo qua de linh toan dem gian. 

M 2gll =R s A 5 Z a <M2b) 

Gap truang hop a' kha I6n, vifcc bo qua lhanh phan thtr hai o cong thirc (2-1 2a) dan 
den vice gtam dang ke* M 2gh hoac tang d&ng ke c6l (hdp A^ thi trong tinh toan co the bo 
qua cot thep A^ hoac ke* them thanh ph^n inti hai. 

Chi chu quan trong: Cac bieu thtic da lap di xdc dinh M,^,: M 2 ^ va 'V cf " c6 8 ia lr \ 
{duoc chap nhqn ta diing) khi dien licit cot thep A s . A[ deu duang. Khi dung ede cong thuc da 
lap ma tinh duoc c&'i thep dm thi chicd thek$'t ludn Id khong can den cot thep theo tinh loan (dat 
thep theo can too) con cac ke) qua tinh loan (trutig gian hoac cud'i cun$) Id kitdttg phan dnh 
dung thuc te. 



42 



2.2. TRn~H to An cot thep doi xumg 

Bie'l kich thudc liet dien t>. h, chieu dal tinh loan l , noi lire M, N. chung loai vAl 
lieu. Yeu cau tinh loan cot thep doi xung A s = A\ . 

2.2 J. Chuan bi so' lieu 

- Xac dinh cucmg do linh loan chiu nen cua b6t6ng R b iheo phu luc 2 va khi can thi 
ke ihem djeu kien lam vide y b ihco phu luc 1 . Xac dinh modun dan Iigl E b . 

- Tim ci/ong d<> linh loan R^; R lfi cua col thep theo phu luc 3. 

- Tim h£ soc R iheo phu luc 4. 

- Gia thiei cac dai luong a. a' de tmh ho = h - a; Z a = l>> - a'. 

- Xet anh hutms cua uoii doc. khi — < 4 lav r\ = I , khi — > 4 cin linh N rr va n iheo 

h ' i h ' 

chi dan 6 muc 1.5.2. Tmcmg hgp linh loan N CI theo (1-16) ihi con can phai biet cac gia 
in M d]1 , N dh de xac dinh he so <j> ; va gia thiet dien iich cot thep hoac ty ]e eo't thep de tinh 

J v . Trong cinh loan thirc i£ co th£* bo qua anh hutmg u6n doc khi — < 8 . 

h 

- Xet 66 Iich lam ngau nhi£n e r linh e, , e,, va e theoeong thue (2-1). 
Tinh loan cot ihep bat din iu" viec xac dinh chie*u cao vung nen x. 

2.2.2. Xac dinh so bp chieu cao vung nen x 3 

Truce he! can xac dinh so bp chieu cao vung nen roi can cu vao do de phan biet cac 
iruong hop u'nh loan. 

2.2.2.1. Xac dinh x, khi R x = R s 

Voi nhieu loai coi thep thirong dung co R % < 4CX)MPa va nhir vSy R K = R s . Gia thifit 
o*i£u ki£n (2-6c) dugc thoa man, co the* xac dinh x theo cOng thi^c (2-13) nit ra tir dieu 
ki£n(2-7a) vadatlax,. 

*'!& (2 " 13) 

2.2.2.2. Xac dinh x, khi R 5C # R s 

Trtfbng phiii Au My khong phan biet gia tri cirdng do tinh loin cua cot thep khi nen 
va khi keo vl vay kh6ng co trucmg hop R sc t= R s . Trucmg ph^i Nga va mot stf nutic khac 

c6 phan biet va khi R s kha cao thi R x < R s . 

43 



De tinh loan so bo chieu cao ciing nen Xj cung tarn gia thie't x thoa man di£u kien 
(2-6c). Lay gia tri N o cong thuc (2-7a) lhay vao dieu ki£n (2-2) vdi da'u bang va dung 
bicu thiic M lgh d cong ihiic (2-4) vdi <jj = R sc nit ra duoc phuong trinh bac hai cua x. 

x 2 -2(h !) + t s )x + -^-(e-t 5 > = 

s R 5 -R K 

Giai phuong trinh bac hai, lay nghiem co nghla la x,. 
2.2.3. Cac truong hop tinh toan 

Gia tri X| vira linh loan duac clii m6i ia so b6. Can dua vao x ( de phan biel cac 
truong hop linh loan la nen lech tam Ion thong thiiong. nen lech tarn be hay ia trudng 
hop dac biet. 

2.2.3.1. Nen lech tam l&n thong thuang 

Khi ma 2a f <x, <£ R h d"ieu kien gia tftiet (a dung. Luc nay lay x = x t vi o\ = R st 

lhay vao cong thuc (2-4), ket hop dieu kien (2-2) va chu y rang N = R fc bx rul ra duac 
cong thtrc linh A^. 

N(e + 0.5x-h ) 

r;z, 

c6i thcp d6i xung. iSfy A 5 = A^ . 

2.2.3.2. Nen leek torn be. Kki x f > q R h 

Khdng dung duac gia tri X) vi ichong phu hop vdi dieu kifin gia thi£l. Luc nay de lim 
x can phai giai dong thai ba phuong trinh: phuong trinh (2-7b) vdi A s - K- phucmg 

trinh quan he giua o s va x lay theo mot trong'cac c6ng thuc (1-23) hoac (1-25) va phuong 
trinh (2-2) ke't hop (2-4). Kfit qua riit gpn lai duoc mCl phuong trinh bac ba cua x. 



Jt 



3 , . 2 



a 3 x + a,x+ ao = (2-15a) 



Dem dat 4 = — . d" 3 phuong trinh v£ dang kh6ng ihu nguyen: 
h 

S 3 + k 3 c/ + k J i + + K o = (2-15b) 

Cac he so" k->, k,, ko duac xac dinh phu thudc vao phuong trinh quan b£ giua a s va_ x, 
duac cho trong bang sau: 

44 



. Phucmg trinh 

k-, 

a v -x 


ki 


ko 


(1-23) | -(4r+2) 


2(1 +(jKj+n6-2q>) 


2n (2pe • y<p - s) 


{I -23a) -«r+2) 


2(nE + 5 R ) + r(2-y-£ R ) 


-n[y{2-y-5 R ) + 2sc R )] 1 


(l-25b> i< y -),7p H -l) 


ifi»(l + 1,2ft J]+ ft, -Bf 


-inp a s 


N e 


7 ? F 

■r - 1 . - n e * -r-ns n ^° 


nm W e -K' V M1 W 


' h '"* 1.2R, 


■' f i 



Giai phucmg trinh b&c ba co the bang each gan/hing vol chii y dd bien thien cua £ 
trong khoang giua c,r v a 1* co Ih6 dung phucmg ph&p d6 thi hoac co tliti (ham khao each 
giai 6'phu luc 5. 

Theo v nshla vat ly ihi £ chi bien thien irong khoang ^ R < ^ < — . Tuy vay vdi six 

h o 

can than can thiet c6 the" han eh£' £, irong khoang sau: 

5 R S*<1 (2-16) 

Trong cac phucmg trinh quan he C\. - x da co dung mot vai dieu gan dung, den gian 
hoa do do co mot so truong hop giai phucmg irinh (2-15) duoc nghidm khftng n3m trong 
gicri han da neu (khi n vat; deu kha be ibudng tim ducc £, > 1), luc nay can dung &iiu 
kien (2-16) de xac dinh c^. 

Sau khi co I. cCnh x = £ho- 

De tranh vide phai lap va giai phucmg trinh b3c ba qua" phuc tap ma ket qua cung 
chua bao dam dung hoan toan, irong tinh toan thuc te co th£ dung cong thuc thuc 
nghiem (2-8): (2-10) ho&c (2-11) de xac dinh x. Sai s6 giua cac cong thuc gan diing voi 
nhau va vcri nghiem cua phucmg trinh (1-15) la binh trurcmg, co mot vai truotig hop hoi 
Icm, tuy vay ket qua cot thep ti'nh duoc chenh lech khong dang ke* va van dam bao dieu 
kien an toan. 

Vdi x da co, dung dieu kien <2-2) ket hop vdi cong thuc (2-4) nit ra cong thirc tthh A' . 



A , = Ne_-R b bx(h -x/2) 



*,A 



(2-17) 



cot rhep doi xung lay A s = A' . 



2.2.5 J. Truong hap dqc biet. Kki x t < 2a' 

Khi jtfty ra \j < 2a* thi gia thje't de* tinh Xj khdng c6n dung do 66 cung khdng dung 
duoc. Luc nay neu linh loan chuih xac thi se duo*c x > x, tuy vay x van con nho hon 2a'. 
D£ tinh loan cot (hep dung dieu kien (2-3) ket hop cdng (hue (2-12b), rut ra: 

45 



A = 



Ne' N(e^Z a ) 



R.Z. 



R*z a 



(2-18) 



OS thep doi xung lay A| = A,. 

Khi a' la kha ldn c6 the dfcng cong thi'rc (2-26) $£ tinh A B . 

2.2.4. Stf do tinh cot thep doi xung 

Bai toan linb c«5t thep doi xtfrig cau kien chiu nen lech lam, del dien chu* nh&i, co co'i 
thep dat tap trung iheo canh b duoc sa dd hoa nhir tren hlnh 2.2. 



x = x, 



1 



A,*A',*(Mfl) 



S6 lieu tfio Inrfrc: b, h. / , M. N. e a 
Cfcfing toai v|l lieu: b* tbng, cot thep 



Chuan bj s6 lieu li'nh loan: 

Tim R b , E(„ Rj. R^ , Ej, he $6 ^ (iheo cac phu luc) 

Giathi^i3,a'.Tinhh 0( z a 

Ttnhe v e ,e 




K t = {2-13) 



Up va giii ptwong trinh 
Unix, 





Xac djnh x b^ng each gi3i 
phjonj trinh (2-55) hoac dung 
cfingihfltgar dting (2-8K2-10) 



A'^A,= (M8) jA' t »V<M7j 



OAihgiS.x&lykgtflua 



ifinA 2.2. So dd tinh cd't ihep d6i ximg 



46 



2.2.5. Danh gia va xu ly ket qua tinh toan 

Theo cac cong thtfc da Up co the 7 tinh loan duoc A SJ A^ la duong hoac am. Khi tirth 
duoc A^ = A[ < chihig to kich (hudc tiet dt£n qua Ion, khong can den cot thep. Luc 

nay neu co the diroc ihi nit bot kich thuac tiet di£n (hoSc dung loai v3t lieu cd cuong do 
thA'p hon) de tinh lai. Khi khong the nil box nhif vira neu thi can chon dat cd't thep theo 
yeu cau idi thieu. goi la dat cot thep theo y$u cau ca'u tao. 

Chu y rang khi tinh toan duoc A 5 , A^ am thi cac ke't qua trung gian ti'nh duoc hoac 

duoc chap nhan (chieu cao viing nen x 3 ; uog suai trong betdng va trong col thep...) la 
khong ehi'nh xac, cluing chi co tac dung ohu la dieu kjdn d& tinh toan chu khdng phan 
anh dung sir lam viec thuc tc'cua tidt difin. 

Khi tinh duoc cot thep dirong, tinh ty te cot thep: 

A,+A; _ lOOtA+A'j 

Uv = — hoac u,% = *~ 

bho °n 

Kiem tra dieu ki£n (1-5): u mm < u< < u ma3E 

Khi u. s < u m!JI chung to kich rhucrc tier dien la hoi Icm, can xu ly nhir khi tinh dura 
cot thep am. 

Khi \i s > p^ chung to kich thuoc tiet dien qua be, cdn phai tang kich thuoc tiet 
dien hoac dung vat lieu co cuong d6 cao hon (hoac dung ca hai bien phap) roi tinh toan 
lai de thoa man u s < p ma?l . 

Chon va bo' tri cot thep can tuan theo quy dinh ve crufiu day lop bao vi va khoang ha 
giua cac cot thep. Sau khi bo tri cot thep can xac dinh gia tri a, a" tinh lai h , Z 3 , so sanh 
chung v6i gia tri da duoc dung trong tinh toan trirot d&y. Khi gia tri h va Z a vira tinh 
toan dtroc ia* idn hon ho&c bhag cdc gia tri cfa dtroc dung thi k£t qua la tiuen ve an roan. 
N£u gia tri ho va Zj vira tCnh toan duoc be hon cac gia tri da dugc dung Ihi ket qua 
nghieng ve phia thieu an toan. can co xir ly thich dang. Khi mux: dp be hon la khong 
dang ki thi chi can chon cd't thep tang len so vcn ket qua tinh duoc (mile tang len c6 thi 
bang hoac Ion hon mtfc giam cua Zj. Neu muc dp be hern la dang ke thi can gia thiet lai 
a va linh toan lai. 

Mot van de rat quan trong trong khi dung cac cong thtic de tinh toan la viec thong 
nhat don vj. Khi dung don vi cua cuong do v|t lieu la MPa = N/mm thi can doi don vi 
chieu diti (b, h^, Z a ...) thanh milimet va don vi cua n6i luc LaNiuton, Niuton^mm (ky 
hieu la Niu va Nmm de tranh nhaVn ISn vcn N da dung de 7 kj hit u luc nen). Khi s6 lieu 
d^u vao duoc cho theo don vi khac (vi du kich thutfc tiet di^n theo cm, n6L luc theo kN, 
kNni) can dung he s6 chuyen d*Si don vi thich hop, iranh su: nh&m lan lam sai ket qua. 

47 



2.2.6. Thi du 

Thi du 1. GM tang 5 cua khung nha m6t nhip, san toan khtfi, chi£u dai col / = 3,8m, 
tie! dien chtf nhAt b - 25cm; h = 40cm. bei6ng mac 300 (theo tieu chua'n cu) c6\ ihep 
nhdm CQ. Yeu cau tlnh toan c6't thep dd'i xvhig. Khi c6t chiu cap n6i luc M = 138kNm; 
N = 650kN, trong do noi luc do tai trong thuong xuyen va tai trong tam thai dai hart gfly 
ra la M dh = 80; N dh = 500. 

Khung mdt nhip, tang trtn f = 1,25/ - 1,25x3,8 = 4,75m. 

B£l6ng m£c 300, khi kh6ng xdl he s6 di£u kien lam viec co: 

R b = 13MPa, E b = 29000MPa. Cot thep CTL co R sc = R s = 2S0MPa 

Voi R b = 13; R B = 280 c6 ^ R = 0,608 (phu luc 2, 3, 4) 

Gia thie'l a = a' = 4cm; h^ = 40 - 4 = 36cm = 360mm; Z a = 320. 

Xec uon doc: -& - — — = 1 1, 8 > 8 . Gin xei u6'n doc. 
h 0.4 

D6 lech lam tlnh hoc e, = — = 0.212m = 212rnm. 

N 650 



l ■ 

Do lech i&rn ngiu nhi£n e, > max I , — 

.600 30, 



= 1 3. 3mm. 



Do lech tarn ban dau e = max(e,, e a ) = 212mm. 

Xac dinh he so r\ theo cong thue (1-1 1) irong dd K cr theo (1.16b). 

Gia thiet ty 16 cot thep p s = 1,5% =0.015. 

J i -(A l -fA;)(0,5h-a) 2 =u s bh (0,5h-a) 2 
= 0,015x25Ox360(2O0-40) 2 =34.56xlO 6 mm 4 

•■ ^ = 2100O0 =7 ^^250,400^ 1333xlo6mm , 

E b 29000 12 12 

5 = 0,5-0,01 ^-0 ( 01R h =0,5-0,01-^^-0,01x13 = 0.251. 
Cmi0 h 400 

e 212 

5 c ^-2. = = 0,53>5 C . ; <p p = l (kh6ngcoimgluc truox) 

<p, = 1 + (3— l - . Betong nang p = 1. Trong cong thuc tlnh <p, thi M va M, duoc lay doi 
M 

voi mep tie't di6n chju keo: 
48 



M = 138 + 650x^ = 268 

2 

M,=80 + 500x — = 180 



( p =1+ -1,67 

1 268 



N cr 


6.4E, 


r j 


( 0.1 1 


% 


0,1 + -^ 

I % 



-0.1 



Ws 



6,4x290.000 



1333x10' 



4750 2 

= 3873 100 = 38?3kN. 

1 I 



167 



0,11 



0,1 + 0.53 



+ 0.1 



7.24x34,56x10' 



l- 



N_ 



1- 



650^ 

3873 



= 1.18 



e = iie + — a = 1,18x212+- 40 -410mm 



N 650x1000 „ n 
x, = = = 200mm 



R b b 13x250 



x, < § R ho = 0,608 x 360 = 218mm. D6ng thoi x, > 2a' = 80. 



, _N(e + Q,5x-U )_65Q>aQ 3 (410 + 100-360)^ 



A - 



!-'- 



R^ 280x320 



1088mm 2 



hli 



250x360 



(ij. ihuc tS" Ion hon tri so' da gia tbiet de tinli N cr 

Chon cot thep: m<5i 6£n dung 3<|>22 co dien tfch; 1 140 mm 2 . Bo tri nliir tren hinh 2.3. 



Lay chieu dav lop bao v£ 25mm {> ^) linh dtfoc chi£u day I6p dem a= 25 + — -36 mm 

h = 400 - 36 - 364mm, lorn hon gia tri dung irong tinh toan la 360mm. 
Khoang ho gitia hai cot thep; 

250-2 x 25 — 34»22 



<o=* 



- 67mm > 50 , dat yeu c£u. 



49 



52? 



O 

ft 



J2 
a 



C 



CT 







'a 



K 






/fi/j/r 2.3. 7V' dfaw C<5f • ih't du /. 



J^22 







1 






V 


a 


1 


- 


o 

























f 




ifcj 
1 


4 r J0 




25 





C6t thep dai Irong c6l chpn <(>6 > 1/4^^ ^j.. 

Khoang c^ch co'i dai ^ = 250 < 15(fij pcmm = 330. 

7"/!)" tfw 2 Col cua nha cong nghidp mOt tang. Tinh loan cho phan coi duoi cau iruc 
vdi chieu cao H| = 6.4m. dam cau true khong lien luc. Tiet diea chtf jihat b = 40cm; 
h = 80cm, betong c6 cap 66 ben 25. col ihep loai RB40Q. Yeu cau linh cot ihep doi xirns 
chiu cap not luc M = 480k>im. N = 500kN. 

Chieu dai linh loan / p = 1.5H f = 1,5x6.4 = 9,6m. 

Belong cap 25 co R h = l4,5MPa. E h = 30000MPa. 

Col iheo R&400 co R sr = R. = 365MP* . 

He .so I,, = 0.558. 

Gia lhiel a = a' = 5cm: h c - 80 - 5 ~ 75cm = 750mm; Z a = 700mm. 

Xci uo'n doc: 

i = *± = 12>S 
h (U 



J = 



bh J 400KSOO' 1 



12 



12 



^17060xlO*mm J 



J5-- 



2.5E.J 2, 5 x 30.000 xl 7060 x J0° 



/; 



N cr =138SOkN. 

i 



) 



n= 



l- 



N 



N 



I- 



:i00 



9600" 



= 1.04 



= 13880000Niu 



_M s 



480 



N 500 



13880 
= 0.96 = 960mm 



50 



Do lech tarn nsau nhien e, £ max 



f h > 

- 1 — va — 1 = 27rnni 
,600 WJ 



Tmh loan cot nhu call ki£n tinh dinh. 

ey = e 5 -f e a = 960 + 27 = 987mm. 
h . „. ™ 800 



= Wq +T~ a = 104x987 + 50 = 1377mm 



Xi = - — - = 86mm < 2a = lOO 

1 R.b 14.5x400 

Tinh toan theo trucms hop d&c biet: 

K = a, . BlzM m 500000(^76-700) = a 

RZ, ^65x700 

bh. 400x750 

Chon cot thep: moi ben dat 3i|>25, chon chieu day lop bao vc 35mm: a = 35 + tJ>/2 = 
4Smm (hinh 2.4a>: 

x, = 90,6 < 2a' = 96, 

Ghi chii. Gin ihii nhucho/t lop bao re 25mm. a = a' = 25 + fll-SHnun. x t =86> 2a = 76mm 

Tinu Uii col thep theo cong thiic khac vai hf> = 762. Z. f = 724. 

. N(e + 0.5x-ho) 500000(1376 + 43-762) _„ i 
A =A < = - ii- = - = 1243mm 

R,Z, 365x724 

Tin du 3. COt co chi^u dai linh loan / n = 2.8m. ti£t dien ch& nfi£t b - 30cm; 
h = 50cm, batons cap do ben 20. cot thep nhom CI1. Noi luc tinh toan g6m N - 1320kN. 
M = 218kNm. Yeii cau tinh toan cot thep d6"i xtfns. 

Betong cap 20 co R b = I l,5MPa. E b = 27000; col ihep CII c6 R sc = R s = 280. H6 s6 

£,, = 0.61. 

Gia thiet a = a' = 4cm; h<, = 50 - 4 = 46cm = 460mm; Z a = 460 - 40 - 420mm. 

/ ? H 

-2. = — ^5.6<8.boquauondoc. n = 1. 

h 0,5 






e, = — = = 0. 165m = E65mm; 



Do lech lam ngau nhidn Cj > max 



'2800 . 500 



va— =17mm 



. 600 30 

51 



Q'u kien thuSc kfit ca'u si€u tinh: 

e = max (e,, c a ) = 165mm. 

500 

e = l65 + 40 = 375mm 

2 



N 1320x1000 



Xi - 



R b b 



11x300 



= 400mm 



^R^o = 0-6 x 460 = 276 < x,. Tinh toan iheo irucmg hop nen ISch tarn be. Dung cong 

thifc g£n dung de' xac dinh x. He so e fl = -& = = 0.33 

h 500 



x = 



■?* 









h = 0,6 



0,4 



1+50x0,33'/ 



T 460 = 304 



A. =A' = 



_ A , _ Ne+R b b x(h -x/2) _ 1320000x373 -J 1.5x300x304(460- 152) 
'~l, ™ 280x420 

.2 



= 1462mm' 
A. +A.' 1462x2 



K = 



bb 300x460 



= 0,0247 = 2,479$ 



« 



Chpn cox (hep: inoi ben chon 4(^22 (hinh 2.4b) 
6^25 



31.J 



2*14 



35 ! 



Til 



soc 



8 



55 



M 



5M 



ii 

250 o 
8 



£fi/?Jt 2.4. Ttc'i dim c&i ihi da 2 va 3 



Ghi chit. Twig ihi du 3 neu muon tinh loan x bang each lap \>a gidi phid/tig trinh Ihi. 

375 



<p = 0.5(1 -£ R ) = 0,2: £= — = - — = 0,815 



h 460 

k, = 2<p-3 = -2.6 



\ 460 
N 



1320000 



R b bh 11.5x300x460 



^0,8696. 



51 



k, = 2(1 + w + ne- 2cp) = 2(1 4- 0,2 x 0,913 +■ O.S696 x 0,8 15 - 0.4) = 2,9826. 
k = 2n(2<pe + y<p-e) = 2x 0,8696(2x0.2x0,815 -0.913x0,2-0,815)= -1,168. 
Phuang trinh se la: 

^ J -2.6c 2 -i- 2.98264- 1-168 = 

Gia duct c = 0.71: x = 0,71 x 460 = 326. 

,, 1320000x37.*) -11.5x300x326(460- 163) ,_ , 
A, = - = 1368mnr . 

280x420 

2 3. TINH TOA\ COT THEP KHONG DOI XUNG 

Trong ihirc te cht co m6t so' it iruong hop ngudi la moi dat ctfi ihep kh6ng doi xung 
A v * A[ . Voi mot cap npi fuc M. N cho trudc ihi iinh loan col Ihep khong doi xung cho 

long luong cot ihep A s + A{ be hort iruong hop cot ihep doi xung (dac biei la khi nen 

lech tarn be). Tuy vdy khi cau kien chiu M d6i duu ma gia tri tuyet doi gan bdng nhau thi 
tdng luong coi thep trong iruotig hop dat doi xung va khong doi xung clienli nhau khong 
dang ke. Col ihep khong doi xung thai sir co hicu qua ve tie! kiem vat lieu chi khi tiet 
dien chiu momen khong doi dau hoac momcn theo chieu nay kha Ion hoti rno men theo 
chieu nguoc lai Tiucmg hop dac biei cua col ihep khong doi xung la chi n'nh loan coi 
thtfp o mot phia. pliia kia khong dal col ihep hoac chi dat iheo cau lao (khong ke den 
trong linh loan). 

De linh loan col ihep khong doi xung truric tien cung c3n chu&n bi so lieu giong nhu 
da lam 6 muc 2.2.1 doi voi c6"f ihep doi xung. 

2.3.1. Trtfbng hop tinh loan 

Khi dal coi rhep khong doi xung. ban dau chira co each gi xac dinh duoc x de dita 
vao dd ma phan biei iruong hop n'nh toan. Luc nay co the dira vao do lech tain: 

Khj r\t^ > e^ - n'nh iheo nen lech lam Ion 

x\Cy < Cy - tinh theo nen I6ch lam be. 

Tieu chuan TCVN 5574 cho cong (hue (hue nghiem e Cf> = 0.4 (1.25h - £, R hJ c6 the 
lay gdn dung e op = 0,3h o . 

2.3.2. Nen lech lam Ion 

Oieu kien de linh loan la r)e.j > e^ va chieu cao vung nen x thoa man dieu Jcien 
(2-6e). Luc nay co hai phucmg trinh la (2-2) va (2-7a) de' xac dinh ba an so la x, A s va 
A!.. Day la bai loan co nhiiu nghiem. Trong thuc te khong can tim duoc ta*t ca cic 

53 



nghiem ma chi can moi nghifetn hop 1J 14 duoc. $)& giai baj toan co* the cho trade mOt gi£» 
tri ciia mot trong ba an s5 roi lim hai an con lai. Chu y rang cac an So x, A 5 , All chi bien 

ihien trong mot khoang nhat dinh, tuong doi hep nen gia tri cho tnrdc hop \y phai nam 
irong khoang xac dinh vua n£u. Trong ba an thi khoang bien thien cua x la ro rang hon 
ca (2a' < x < ^rig) vl vay cho x m6i gi£ iri de ttnh A s , A, la thuSn lai hon. Cung cd xh£ 

cho trudc A^ de* tinh x va A,, hoac cho Wiidc A^ de tinh x va A^ . Tuy vay vi khoang bien 

Ihien cua A^ Ja kha be va khd du doan nen Irong thuc te linh toan it dung each cho trirdc 
A,, ma thong thuong chi cho trirdc x hofic A[ . 

2.3.2 J. Chon x, tilth A' t vaA, 

Cho x m6i gia irj luy J trong khoang 2a <x ^rV 

Thay x da co vao bieu ihuc (2-4) va dung dieu kien (2-2) vdi chu y o\ - R st se rut 
ra cong thtrc de ijnh A^. . Do la cong thuc da duoc lap (2-17). Viet lai: 

Ne-R b bx(h -0.5x) 

Cong Ihuc (2-37} va (2-19) co dang hoan loan giong nhau, cai khac chu yeu la gia 
iri cua x. 

Khi tinh duoc A^ > 0, dem x va A^ thay vao phuong irinh (2-7a) rui ra cong thuc 
linh A v : 

A= R b bx + R, e A;-N (2 _ 20) 

R s 

Uhg vdi m6i gia tri cua x cd A^ va A^ tirong ung tuy vAy tong lircmg cot ihep A+A 
thay dOi khong Ion. vi khi lang x ihi A^ giam con A s tang. Co the chung minh diroc 

bang loan hoc khi x = x A = — Ihi l6ng cot thep A N + A^ la be nhat. Trong mot so 

lili lieu ngudi la khuyen lay x = c^Jiq de tinh loan vdi y nghla sir dung h& kha nan* vung 
belong chiu nen va co duoc long A,. + A^ gan vdi gia tri be iiha'l. 

Trucmg hop tfnh loan dupe A^ < thi chon lai x be hon roi tinh lai. Khi da chon x 
be nha't bang 2a' ma van tinh duoc A^ < thi chon A^ theo ca'u tao va tinh A y theo cong 
thuc (2-26). 

2.3.2.2. Chon A' s tinh x vd A s 

Khi biet irudc hoac chon trade A' s can tinh x iu dieu kien (2-2) vdi dau bang; 

54 



Ne = R b bx 



>°-h 



+KKZ* 



(2-21) 



De' tninh vice giai phuong irinh b3c hat, dem dai £ = — .a^ =£(l-0,5£)lhay vao 

tin 



(2-21) rut ra: 



a m = 



Ne-R VC A;2, 



(2-22) 
(2-23) 



^=i-Vr^a 

Hoac iCr a m tra ra ^ rheo bang a phu lye 6. 

Tinh x = cho va kiern tra dieu kien 2a' < x < £ R ho {£ < £r) Khi thoa man dieu kien 
vCra neu thi lhay .x va A' vao cong thtic (2-20) de n'nh A<. 

Khi ^ > 4r chiing lo A^ da biei la chifa du. can tang A^ roi tmh lai hoac xac dinh 
a; theoc6nsih.trc{2-19). 

Khi x = z\\q < 2a, ke ca trudng hop a m < 0, chirng to A^ La qua Ion, neu co the 
duot thi giiim boi A^ roi tinh lai. Neu van siu nguyen A^ thi tinh A,, theo trirdng hop 
diic hiet o muc 2.3.2.4. 

23.2 J. TVwctog /*#; AJ = 

Do la truong hop dac biet khi khong can den c6t thep A^ (tinh duoc A[ < 0, khong 
d&l cO'i thep chiu ncn hoac chi dat theo caii lao voi A^ >0.0005bh , khOng ke* vao irong 

tinh toan). 

Luc nay tinh a ro theo cong thuc (2-22) (rong do cho A^ = 0. Carth tay d6n npi 
luc la Z v 

x 



; = l-0,5£ = 0.5(i + ^l-2a m ) 



(2-24) 
(2-25) 



Dien t/ch col ihep A s c6 th£ dupe tinh iheo cong chiic (2-20) irong do cho a; = 
hoac ifnh theo cong Ihirc (2-26); 

N( e-Z„) 

•A, 



A > = R..Z, 



(2-26) 



55 



2.3.2.4. Tru&ng hap doc biit x < 2a' 

Khi bi£t iriftk A' s , tinh cx m , ^ ma x = £flo < 2a'. ke ca trtfong hap a m < thi khong 
the 1 dung x 6i tinh tiep. Luc nay tinh A R iheo c6ng ihurc (2-18). 

Truong hop a' fa kha I6n, dung (2-18) se tinh duoc A s kha" 16n. Co the* s£ ti£t kifim 
hem neu bo qua A^ trong tinh toan va luc nay khong can dieu kien x £ 2a'. Tinh loan A s 
iheo cong thtfc (2-26). 

Ket hop cong thuc (2-18) va (2-26) cd the viet thanh: 

A. = *^ (2-27) 

Trong do: Z = max (Z d ; Z b ). 

2.3.2.5. Chon A s tinh x va A' s 

Co the* chon trucrc cot thep chiu keo A s de tinh toan. Ltic nay rut A^ iu bieu ihuc 
(2.7a) roi dem lhay vao (2-4) se dira ve dtrot mot phuong trinh chua x: 

= R s A,Z a -N(e-Z;> 



R b bx 



,2 



Cung c6 [he lap duoc phuong trinh tren day bang each lay rnomen cac lire doi vdi 
true di qua trong tarn cot thep A^ va vuong goc vdi mat phiing uon. 

Giai phuong trinh, tim duoe x, khi x thoa man dieu kien han che (2a* < x < c, R h ) thi 
lhay x vao cong ihiic (2-19) di tinh a; . N£u lirn dtroe x khdng thoa man dieu ki£n han 

che chung to gia tri A v da chon la khong hop ly. can chon iai. 

Nlw <& nhftn x.€\ q phSn diu cua mv*c 2.3.2, vice cho wuoc \ de \'\w\\ w>ftn mans 
nang tinh cha'l ly thuyei, lime le ft dung den. 

2.3.3. Nen lech lam be 

Dieu kien de tinh loan la ne f) < e^. Gicfi han cua chieu cao vung nen x la l^, < \ < h. 

Nen lech tarn be khi thoa man dieu kien (2-28) thi xem la rieng belong du kha nang 
chju luc, c6't thep hoan loan dat iheo cau tao. 

N<N a = R b b(h-2iie ) (2-28) 

Khi N > N B can tinh loan- Liic nay co 4 an so can xac djnh la A v A[ . x va o s (rong 
luc chi c6 ba phuong trinh. Do la phuong trinh (2-2) kei hop cong ihuc (2-4), phuong 
trinh (2-7b) va mot trong cac phuong trinh quan he giua o 5 va x. 

56 



Day la bai loan co nhieu nghiem. tuy v&y trong thiet ke' thuc le chi can mot nghiem 
hop !y la duc/c. De llm diroc nghiem. ve nguyen tac co the cho trudc gia tri cua mot an 
so' bai ky r6i aiai he phuong trinh de liin ba an con iai- Chii y rang cac an so x, A s , \ f 5 . 

o\ chi bien ihien irong mot khoang xac dinh kha hep, nghiem t'irn duc/c chi hap ly khi 
cho trirac un so mol gia tri phu hop. Trong cac an ihl khoang bien ihien cua x la kha ro 
rang vi vay ihuong nguoi la chon truce x de linh cac In con lai. Tuy v3y cung co the 
chon trudc A x de u'tih toan. Khong dat van de chon Iruoc <7 S hoac A^ vi kiio du* doan 

khoang bien Ihien hop ly cua chung. neu chon truac mot gia tri khong phu hop se co kel 
qua khong hop ly va phai iinh lai mot so la'n. 

2.3.3 J. Chon truac x delink toan 

Ve nguyen lac loan hoc co the chon tnroc cho x m6t gia lrj tuy y trong khoang xac 
dinh ch < x < h. Tuy vay nen xac dinh x theo cong thuc thuc nghiem (2-8) hoac (2-10). 
Tinh loan cot thep A^ theo cong thiic (2-17). 

Ve ph irong dien ly thuyet. khi da co x va A^ thi co the tinh a s va lir (2-7b) nit ra 
cong thuc tinh A s : 

R b bx + R, C A;-N 



A. - 



(J. 



(2-29a) 



Gia tri o\ tinh theo cong thuc 1.1 -23a) hoac ( 1-231, 

Tuy vay chi nen dung cong thiic (2-29a) khi o\ fa wong do'i Ion con khi a s kha be 
ihl kha nang pham sai so trong tinh loan (a Ion vi rang cac cong thuc xac dinh x va c s 
deu la cong thuc thuc nghiem. gan dung. Hern nCfa khi do lech tarn e t ia kha be, cot thep 
A s chiu nen thi viec tang dp lech tarn lue, lhanh ne se lam giam dien iicb ,\. Luc nay 
>>t la bat Ic/i cho A s neu giam d6 lech tarn. Vi nhting ly do tren, ngoui yeu cau ve dieu 
kien cau tao. cot ihep A s cua ciu kien chiu nen lech tarn be con can thoa man dieu 
ktfn(2-29b)$au: 

a A;^A % <A; (2-29b) 

Yeu cau A, <A^ la de phong khi tinh duoc a, qua be, theo (2-28a) co the tinh ra A, 

qua Ion, khong dung voi thuc te. Yeu cau A, £ &, Aj. la de phong khi do l£ch tarn qua be, 

ket qua tinh theo (2-29a) duoc tinh vdi do tech tarn Ion hefn se chua du an toan. Hfi so 4 
lay iheo bang sau: 



cfio | 


0.02 


G,04 


0.06 


0.03 


0.10 


0.12 


SO. 15 


K 


i 


0,94 


0.36 


0.78 


0.70 


0.60 


0.50 


0,30 



57 



2.3.3.2. Chpn trade A 8 detinh todn 

Nen Idch tarn be* c6 the* chpn trudrc c6'( ihep A & theo ca'u tao. Luc nay c6 ba phirang 
irinh de* xac dinh ba an stf. Sau khi Ihuc hten rnOt s6 bieh ddi can thie'i dua v£ m6i 
phuemg nlnh chtia x: 

0,5R h bdx 2 + (2R s A s Z a - R b bda')x - (Ned + tR AZJ = & 
Trong do: 

d = h - 4 R h a ; I = h + $ R ho ; e = Z a - e. 

Giai phuong trinh. kie*m tra dieu ki£n cua x, dem x thay vao cong thiic (2- 17) de tfnh 
A[ . Nd'u x khong ihoa man dieu kifen han che' da neu chung 16 gia in A, da chpn la 
khong hop ly. 



2.3.3.3. Trit&ng hop ddc biet A s <=0 

Nen lech tam be vtji n,e < e op co (he 
ihiei ke voi A s = 0. Luc nay can tinh loan 
de* bei6ng va cot ihcp A^ chiu loan bo 

noi lire. VI kh6ng co col ihep A s , khong 
c6 di£u ki£n gi cho o* s nen cung khong 
ciin dieu kien x > 4r^)- Ch' °^ n dieu * £ '? n 
2a' <x <h. 

Lap phtfong irinh de* xac dinh x bang 
d\£u kitn (2-3), lay mdmen 661 vdi true 
di qua trong lam Aj. (hlnh 2.5). 



1 in 


e' 


3" 




i 








l 

i 

i 




A' 






•M^IMMff 




<— K 


r 








X. 




ft 





Hinh 2-5. Sadd tftih wan khi A=0 



Ne' = M, fh =R*bxlf-a'] 

e' = 0,5h-r|e -a' 
Dieu kidn ve khi nang chiu luc Ik: 

N<N gh = R b bx + R;A; 
De don gian viae giai phuong trinh (2-30) dat; 



(2-30) 



(2-31) 



a a =-; T^O.^-l). 
a 



Rut ra: 



T = 



Ne' 



R b ba' 2 



(2-32a) 



58 



a a =*lWl + 2T (2-32b) 

Hoflc lir T ira a a 6 bang cua phu luc 6, 



x =0^3 



Oi8u kien la x < h 

Neu tinh dirot x > h thl bat buoc phai dat col thep A,, khong the' bo dura. 

Sau khi co X. dem thay vac (2-31) njl ra cong tbtrc finh A^ : 

*."-*& (2-33) 

Khi can dat cot thep A^ Theo cau tao thi lay A, £ 0.0005bhg. 

2.3.4. Da nh gia va xu ly ket qua 

Ket qua tinh cot thep khong doi xtmg co the duortg hoSc am. Viec xu ly ii£n hanh 
theo muc 2.2.5 nhudoi vol Iruorighopdai cot thep doi xung. 

Trircmg hop nen lech ia.m be. neoi can tinh cot thep khong d&\ xung thl cung chi nen 
lien hanh khi do lech tarn e^ > 0.15l\j- Voi do lech tarn be hen. toan bo tiet dien chiu 
nen. chi tiftn dat co'l thep doi xung. 

Khi dat coi thep khong doi xung, truong hop nen lech tdm be Iu6n xay ra A^ > A x 

con irucmg hop nen lech turn Ion thi A\ co the' Ion hon hoac nho hon A,. Khi ma R b bx < N 

thi A[ Ion hon A { va nguoc lai. 

2.3.5. Thi du 

Tlii du t. Theo so lieu cua thi du 1 a muc 2.2.6, yeu cau tinh cot thep khong doi 
xung. So lieu (da cho va da tinh dirac): 

b = 250; h = 400; a = a' = 40; Uq = 360; Z a = 320mm. 

R b = 13, R; = R s = 280 MPa; ^ =0.608; 

N = 650RN; M = 138 kNm; e = 212mm; r\ = 1,18; 
e = 410mm; c R ho = 2 16mm. 
Tinh tie'p: 

e op = 0,4 {l,25h-5 R ho) = 0.4(1,25 * 400-216) = L14mm 
r\e - 1,18x212 = 250 >e op = 114. 

59 



Tfnh thco nen tech tarn Ion. 
Chpn x - ^r^o - 2J6mm. 

Ne-R b bx(h -0,5x) 

A , 650000x410-13x250x216(360-108) lfW1 , 
A, = = 1000mm" 



A = 



280x320 
_ R b bx + RX-N _ 13x250x216 + 280x1000-650000 



BL 



280 



= 1186mm' 



T6ng luong col ihep A s + K\ - 1186 + 1000 * 2186mm 2 . 

Ket qua gan bang khi linh Iheo doi xung. 

Chu thick. T/ong ihi du fren. ueii chpn x ktiac di ciiiig dime, tyd si'f chon x — ) '50mm (2a' = 
SO < .v < crIii, = 2l6h Iffl .v = 150 linh duac A' = }42$mm~; A, = 8-i3tnm~. rong iKtfitg cot 

ihep id; A % + A^ = 2266uinf . Ket qua gdn bang vrfl cac tritetoig hep da /iith. 

Tin du 2. Col tiet dien chfl nhai b = 40cm; h = 60cm, chieu daj linh loan / = 3.6m; 
belong mac 250 (cu) col thep RB400W. Noi lux linh loan gom N = 2200kN. 
M = 352kNm. Yen can linh col Ihep khong doi xutig. 

So lieu: R h = 1 1.5. £ b = 27000: R^ = R\ = 365 MPa. ^ R = 0.5S5. Gja thiei a = a' = 4cm: 
h = 56cm - 560mm; Z^ = 520mm. 

Xet uon doc: -& = -^ = 6 < 8. Bo qua uon doc, r\ = 1 , 
' h 0,6 



- — - — Z- = 0,1 6m = 160mm:e., = 20mm 



N 2200 
e ( , =160;e = 1604 



600 



-40 = 420mm. 



e (5rt =0.4(l,25b-; R h fl )^ 0,4(1.25x600-0,585x560) = 177 
rfe - 160< ft— =* 177. Tmh loan iheo nen lech lam be. 



e 160 



e.=-^ = ^0,267 

h 600 



x = 



\-i 



?R 



~>R 



\+50t:, 



"0 = 



0.585 + 



0,4]5 



l + 50x0.267-J 



1560 = 364mm 



A> 



Ne-R h bx(h n -0 t 5x.) 2200000x420-11.5x400x364(560-182) 



^ 



U 



365x520 



= 1 802mm ■ 



60 



Tinh o\ theo c6ng thuc (1-23): 






R = 



1 364 

2^SSL-1 

1-0,585 



365 = 250MPa 



A = 



_R b bx+R iC A' s -N __ 11x400x364 + 365x1302-2200000 _ 



a. 



250 



68mm 



h 600 



DiduJddnchon A,: A^>- 



0,0Q25bh o =560mirr 
4 A; ^0.3xi802=600mnr 



Ul'v A s theo gia iri l&i hon trong 3 gia tri o tren, A s = 600. 
A s + A; = 600+1802^2402 

2402 



^ = 



400x560 



= 0,0107 = 1.07% 



Cung vol bai loan tren thu giai voi (nrdng hq> A^ = 0. (Thuc t£ chpn A s theo cau lao 
loi thieu A s = 0.0005 x 400 x 560 = 1 I2rnm : va khong kc vao iinh toan). 

e' = 0.5U - r^e - a = 300 - 160 - 40 - 100mm 

T _ Ne' 3200.000x100 _ 3I , 5 

R h ba' 2 Il,5x400x40 2 



a d = lWl+2T = 1 + ^1 + 62,5=8.97 
x = a a' = 8,97x40 = 359mm 



A , N-R b bx 2200.000-11x400x359 m 2 
A, = — — *— = rr: * I324mm :i 



R 



sc 



36i 



A s + A; =112 + 1824 = 1936mm 2 

2.4. TINH TOAN KHA NANG CHfU LUC 
2.4.1. Cac loai bai toan 

Khi da bte't kich thtfc*c ciet dien va ca'u tao cot thep c6 th£ tfah loan kha nang chitt 
luc theo mot so bai toan khic nhau: 

- Kiem Ira xem tiet diiti cd du kha n&ng chiu dutfc mfct cap nOi luc M, N hay Jch6ng. 

61 



- Voi lire nen N cho trirac tfnh xem liel dien chiu duac mdt momen M bans bao nhieu. 

- Vdi do lech tarn Cq cho trudc tinh xem liel di£n chiu duoc lire nen N bang bao nhiSu. 

- Voi M cho truoc ttnh xem ti€\ dien chiu duoc N bane bao nhieu. 

24.2. Kiem tra kha nang chiu cap noi lire M. N 

Theo chieu lac dung cua M di xac dinh vi trf va iri so cua A c , A' ( (truefng hop cot 

thep doi xung thi khong can). Chuan bi cac so lieu nhir trong muc 2.2.1. Chu y rang 6 
day khong gia thiet a, a' ina xac dinh true tiep iu so' lieu cau tao. 

De biet duoc trucmg hop tinh loan c&n llm gia tri cua chieu cao vimg nen x. Trudc 
net gia thiet dieu kien (2-6c) duoc Ihoa man de iu phuong trinh <2-7a) nil ra x va dat 
la x-.. 

R.h 

Dua vao gia tri x 2 de phan biet cac irucmg hop. 

2.4.2 .1. Nen lech tarn l&n thong t hi f&vg 

Khi x 2 nam trong pham vi 2a' < x ? < vRh , kci qua dung vdi gw Thiet. lay ,\ = x 2 tfiay 

vao cons thuc (2-4) vdi c' = R' de tinh M. k va kiem ira iheo diet* kien (2-2). 

2.4.2.2. Nen tech tarn be 

Khi tinh duoc x^ > ^h^ khong dung duoc gia tri x-, vi gia thiet khong dung. Luc nav 
phai giai dong ihdi hai phuong trinh de xac dinh x. Phuong trinh thu nha'l la difcu kien 
can b5ng lire <2-7b). phuong trinh thu hai la quan h£ giua a s va x (1-23) hoSc < I -25). 

Khi dung phuong trinh f l-23a) ket hop(2-7b) rut ra duoc: 

R h b(h-^b n )-i-2RA 

Dieu kien cua x la c„\\r, < x <h 

Sau khi c6 dirge x dem thay vao c6ng thuc (2-4) vfli o\ - R 3C de u'nh M lgh va kiem 
ira dieu kien (2-2). 

2.4.2.3. Trtfo'tig hop dgc biet 

Khi linh duoc x 2 < 2a' cung khdng dung duoc gia tri x 2 . Luc nay can tien hanh kiem 
tra theo dieu kien (2-3) voi M 2g h xac dinh theo (2- 12b). 

62 



2..-4J.4. Kiem tra su chiti nin ngoai mat phang uon 

Ngoa! vice kiem tta vet cap npi luc M. N. khl b < h con can kiem ira slt chiu Luc 
theo phuong ngoai mat phang uon. Dieu kien kiem tra la N < N v6i N la kha nang chiu 
nen dung tSm. xac dinh Iheo cong thiic (1-6). 

2.4.3. Xac djnh M khi cho Iruoc N 

Tien hanh iheo cac budc nhu da lap trong muc 2.4.2. de xac djnh M, gh . Thay bleu 
ihCrc cua e vao dieu kien (2-2^ tinh dupe c^. 

e!= M, ell -N(0. 5 h- a) - (236i 

t] is- 

Tu e va do lech ifim ngau nliien e^ linn ra dd l£ch lain e,: 

M = Ne, (2-37) 

Khi xac djnh M can chu y den da'u (chi^u tac dung). Dua Wlo d£u cua M de biei cot 
(hep nao la A s . j\[ . Ncu khong quy dinh truoc da'u ciia M thi khi cot tbep khong dot 

xirng ac xac dinh dupe 2 gia irj cila M iheo hai chieu Lmg voi cot ihep A v 6 ben trai hoac 
ben phai. 

2.4.4. Xac dinh N khi bict c„ 

Cho Crude do lech lam e co ngiua la cho truoc diem dai cua N. Dua vao diem dat do 
de phan dinh cot thep A s , A' s ( Aj. dat gan N hen). Gia ihi£t di£u kien x > 2a' dupe ihoa 

man. dem lhay bieu thifc cua N (2-51 vai o[ = R sc vao dieu kien (2-21 rut ra phuong 
Irinh de xac dinh x; 



2(c-iu)x, 2,R ^ e '- g - A - e ^ 



x--t-2(e-h )x-K * N '—^^0 (2-38) 

R b b 

Cung co" the lip dupe phuong irinh (3-8) bang each lay long momen cac luc doi v6i 
true di qua diern dat cua N. 

Gia thiei tiep la x < £ R ho d£ Uy o\ - R^ thay vao phuong trinh, giai ra, lay nghiem 
co nghia va dat lax 3 ; 



X3 = (ho-e) + )(h -^ + ^^^i2 (2 . 38a) 



Trong nay e' = e - 2^ dupe lay iheo da'u dai. so* d& tinh. 
Dua vao x 3 fim dupe di phan biei cac tmong hop. 



63 



2-4.4.1. Nen lech tarn Ion thong thaong 

Khi thoa man ca hai gia thiet 2a' < x 3 :* £ R h(, !hi lay x = x 3 thay vao cong thuc (2-7a) 

de tmhN. 

2.4.4.2. Nen lech tarn be 

Khi x 3 > ^pho, phai tinh lai x. 

Liic nay can giai dong then hai phuong irlnh de tim x va o%. Phuong trinh thir nha't la 
phtrcmg trinh (3-38), phuong trinh thu hai la quaa h£ o\ va x, co the' chpn m<5t irong cac 
c6ng xMc da lap (1 -23); (1 -23a) hoac 0-25). 

Sau khi tim duoc x, dem thay vao cong thuc (2-4) vcii o^ =R K de u'nh M )gh . Tir 
dieu kien (2-2) riit ra: 



. N = M '«" = R b bx(h n -x/2)-rR sC A:Z i< 



(2-39) 
e e 

2.4.4.3. Truong hop dac biet 

Khi tfnh duoc x 3 < 2a' (ke* ca tardng hop x 5 < 0) can dung dieu kien (2-3) va c6ng 
tburc (2-l2b) 6i xac dinh N; 

M M= R i AA (2 .39a) 

e' (e-ZJ 

2.4.4.4. Gia" thiet trtfoc 7} 

Trong bteu thiic xac dinh e c6 he so rj chua tinh duc/c, vay ban dau phai gia thiet 
m6t gia tri r\ > \ 6i tinh toan. Sau khi co duoc N thi tinh lai n. so sanh vdi gia tri da gia 
thiet. neu hai gia tri la gan bang nhau thi chap nhan duoc. 

2.4.4.5. Kiem tra ngoai m&t ph&ng 

Gia iri N tinh duoc con can thoa man dieu kien N < N nliir da trinh bay uong muc 2.4.2.4. 

2.4.5. Xac dinh N khi cho trtioc M 

2.4.5.1. Tinh loan M theo tm&ng hop chiu uon 

Dua vao chieu cua momen 66 dinh vi cot thep chiu keo A s . Tinh toan M la m6mcn 
uon tiet dien chiu diroc khi N - 0. 

TCr phuong trinh (2.7a) khi N = rut ra x va dat la x 4 : 

R.A -R_A' 



(2-40) 



*<= bR 



64 



Khi 2a' < % A < £ R h ( , fay x = x 4 de* tinh M . 

Mo =R b bx(h a -a5xHR iC A;z a (2-41) 

Cong thuc (2-41) tuong tit nhu c6ng ihuc (2-4). 
Khi x 4 > ^. R ho vd.n dCtftg cdug thtic (2-4 i) trong do x = 4ft^o 
Khi x 4 < 2a' (k£ ca khi x 4 < 0) tinh M Iheo (2-42): 

Mb = 8, Aft (2-42) 

2.4.5.1. Truang hop M > M & 

Khi M > \L) ca"n xac dinh hai gla tri N, va N> img voi trifong hap nen tech tarn Ion 
va nen lech cam be. 

Gia (hiei dieu kien x > 2a' diroc thoa man {o\ = R NC ). Thay bie'u thuc e vao bieu thuc 
(2-S\ vao dijii kien (2-2) cut ra. phusng Vfinh bic 2 cua x. 

R b bx 2 -R b bhx-R sc A;(h-2a')-a s A s (h-2a)+2TiM = (2-43) 

Tarn gia thiei n. di tinh (oiln nhir 6 muc trirdc. 

Glu thiel liep x < ^Iiq de co o\ = R y Thay o\ = R x vao phuang irinh (2-43) tim duot 
hai nghicm x a . x b . Uhg vdi m5i nghi&n co iighTa ifnh dirge gia iri N lucmg tbig. 

Voi x ihoa man didu kidn gia thic't 2a' < x < c K h D thi thay x vao cong thiic (2-7a) de 
tinh K. 

Voi x > Cftlia can giai dong thdi hai phuong trinh dfi' xac dinh a. t va x. Phirong trinh 
(2-43) va moi trong cac phuang irinh quan he <r s va x. Co x se tuih ditoc N. 

Voi x < 2a'. bang each bien doi dieu kien (2-3) rut ra: 

„ llM-RAZ, 

N= 0,5h-.' ^ 

2.4.5.2. Tru&ng hopM< Mo 

Luc nay xay ra nen 16ch tam be va chi co mot gia tri N. Tjnh loan bang each giai 
d6ng thai hai phuong trinh di tim x va cr, sau do tu x xac dinh N, 

2.4.5.3. KiemtraN 

Gia tri N tinh diroc trong muc 2.4.5 deu khong duoc lay ion hon gia tri N tinh theo 
cong thuc (1-6). 

65 



2.5. BIEU DO TUONG TAC 

2.5.1. Khai niem ve bieu do tuong tac 

Tuong tac 6 day la tuong tac gtua kha nang chiu rnomen uo'n M va kha nang chiu 
iuc nen M 

V6i m6i net dien co cd't thep da bie't bieu do tuone tac the hi£n loan bC kha nang 
chiu Iuc cua no ung vai moi gia tri cua M va N. 

Nhu da rrinh bay trong muc 2.4 ung vai root gia trj N tim duoc m6t gia tri M, ung 
vai m6i gia tri e^ tim duoc rnot gia trj N hoac ung \*6i m6i gia tri M tim duoc mot hoac 
hai gia tri N. Lap bieu do v6i hai true la M va N. Moi cap gia tri nhu vua neu cho mot 
diem. Tap hop tat ca cac dieYn co duoc bieu do tuong tac Khi dat cot thep dot xung bieu 
do co dang nhu tren hinh 2.6. Trong hai true co the lay true dung de* bieu dien M hoac N 
ttjy theo syihuan loi khi the hien va khi diing. 

Hmb 2.6 the hien bieu do khi momen M theo moi chieu. Khi xet jM iheo hai chisu 
(duong va am) thi bieu do duoc phat trien theo ca hai phia nhu tren hinh 2.7. 





Hinh 2.6. Bieu do tinxitg tac the hien 
theo hai each v&i M theo I chieu 




C_N 




Hinh 2.7. Bieu do tuong tac vcri M has chieu 

Khi xet ca N theo hai chi£u (ndn va keo) thi bieu 66 duoc ph£i then thanh dang khep 
kin nhu tren hinh 2.8. 



66 




Hinh 2.8. Bicif dd itt'&ng lac \ai M va N ihco hai clticit. 

Xel riens goo mpt phan lu vdi N nen. tren bieu do cd ba diem dac biet. Diem D ting 
vol N = va M ; fcong thtrc 2-4 1 , 2-42). Diem C ung vdi M = va N . Gia tri N xac 
dinh iheo cong [hire ( 1-6). Diem B img vdi M mM va N B . Co the chung minh diroc rang 



khi a = a', diein B ung vdi uudng hop x = x R = 



tin 



= 0.5h. Vdi «ia tri nav ctia x. neu 



cfrth toan cot thep khong doi xung se cd dupe (6ng Iircmg cot thep A N + A^ la oho nhai. 

Bieu do luong lac chia mat phang lain hai mien: ben trong va ben ngoai. Vdi mpi 
cap npi luc M. N cho tnfdc co mpt diem trong mat phing. Khi diem do thuoc mien irong 
(diem I) tier dien dii kha nang chiu luc. iNe'u diem da ihitoc mi£n ngoai (diem K) tiet 
dien khong dii kha nang chiu lire (hinh 2.9). 

Tren bieu do. vung Ian can diem B co (he lu nen lech lam Idn hoac be. phan con |ai 
nong dean DB tuong ung vdi nen lech lam Idn. irong doan BC - nttn lech lain be. 

Vdi cac diem nam ngay Iren bieu do (diem P) kha nang chiu luc vim dung bang npi 
luc ma tiet dien phai chiu. Khi diem do nam tren doan BC ihi mpi trong hai npi luc M 
hoac N giam xiidng se lam tang do an toan va nguoc iai. Neu diem dd nam tren doan DB 
(hi khi M giam se tang an loan 
con N giam se nguy hiem. Trong 
doan M > M ung vdi moi gia iri 
ciia M co hai luc N t va N> Khi N 
thay ddi irong khoang tren N t <N 
< N 2 ihj cd duoc an toan (gia ihie'i 
N-i > N|) con neu N vorot ra ngoai 
pham vi tren la nguy hiem. 



Di^m B ung vdi M 



TT.-:<. 



Vdi 



momen nay tiet diSn chi du kha 
nang chiu luc khi N vira bang 
dung N„ con neu N tang len Viay 
giam xutfng tiet dien deu bi nguy 




Hinh 2.9. Bi/it do vd ede cap ndi lire 



hiem. Voi nhfin xet nay, khi thiel ke" khong nen vi muc di'ch liet kiem cot thep ma cho 
tie! dien lam vjec 6" diem B neu chua co dupe do tin cay can thiel cua M va N. 

2.5.2. Bi&u 66 tuong t£c vol A s khac A' s 

Voi liet dien dat col thep kh6ng doi xung, dac biet la khi A s va A^ khac nhau nhieu 

th) bieu d6 tucmg tac co m6t doan lui hoi khac so voi cac bieu do da ve cho tie! dien dat 
cot thep doi xung. Di xem xet van de nay trade he'l c£n ban ve trpng tarn hinh hoc va 
trpng tam vat lieu cua tietdi£n. 

Trpng tam hlnh hoc O cua 
liet dien chu" nhSit each 66u cac 
canh. la giao diem cua hai duong 
cheo. Trong lam v&i h£u cua tte't 
dien, ky hieu O v dirac xic dinh 
co ki den su khac nhau vg kba 
nang bien dang cua betdng va 
cua col Ihep thong qua gia Iri 
mddun dan hoi cua chung. 

Mot each khac. trpng tarn 
vai lieu O v la trpng tam cua lie't 
dien luxmg duong irong do da 
quy d6i di£n tich cot thep ra 
dien lich belong tuong duong. 
He so' quy doi la ty scV cua 

modun dan hoi n, = — *- 



K/ 



K 



I 



;.5- 



A 



o,5n 



Hinh 2.10, Trpng torn hinh hoc 
vd trong ram vqi ttfai O v cua ttf't dien. 



A r . 



Lay true di qua mep tie's di£n phi'a co Aj. lam chuan, khoang each tir 0, den true 
chuan la y v duor xac dinh nhtr sail: 



_ 0,5bh 2 + n s (AJi +A;a'? 
Yv " bh + n,(A s +A;) 



(2-45) 



V6i tiei dien c6 co'i thep do'i xung (hi y v = 0.5h, diem O v trung voi O. 

Khi lap so 66 linh loan chung ta lay true di qua trpng tam O di xac dinh d& I6ch 
tam e va linh M = Ne . Nhung ne'u lay true di qua trpng tam O v th'i momen M v se la 
(hlnh 2.11a). 

M v = N(e - d J = M- Nd v (2-46) 

Trong do: a\. - khoang each giua va O v ; d v = 0.5h - y v . 

6S 



NhGng nghien cltu ve su lam vite cua tie't di£n b6t6ng col thep cho rang n'nh loan 
voi true qua Y la dung hon, tuy vay trong nhieu trucmg hop d6 sai lech khOng dang kC 
nen dugc bo qua. Nguoi ta chi neu ra van de nay khi muon the hi£n that chinh x&c (theo 
ly ihuySi) bieu dd tuong i3c. 

W M 





W, N, 



H'inh 2.1S. So do va bteu do itfong tac khi A[ > A, 



Nhu* vay khi lire N dal dung vao O v tid't didn moi thiic sir chiu nen trung lam va chiu 
duac lire nen Ion nhat N L = K . Tuy v4y neu so vdi true qua ihi luc nay tiet dien van 
con chiu mot momen M = M L = Nd v . Khi vj tri dSt lire N ndm giua O va O v ihi thuc 
chut, so voi % . VI da doi chie'u. Tren bieu do co mot doan lui tir L (hinh 2.1 lb). 

Khi A x > A \. diem O v gan voi A< hon, so do va bieudonrong tac nhu tren hinh 2.12. 



\ 





i. , 


*c 


N 




1 






1 

— 


o v 
* 




A 






















/&/»& 272. Sfft/o va brat <M ttrtwg /tfr Jt/j/ /* s > Aj 

2.5.3. CAe phirong phiip v£ bi£u d6 lirong tic 

Bieu d6 tuang Uc duoc tfnh toan iheo t&ng die'm, ni5i ede didm lai thanh ducmg hen 
luc. Di xac dinh cpa do tung diem co the dung mot trong nhCmg each da trlnh bay 6 ede 
muc 2.4.3. den 2.4.5; Cho N tim M, cho M Urn N bote cho t^ tim N. Dung bai loan 
biel n.e u'nh N trong viec v6 bie"u d6 tuong tic c6 nghla la ttr goc toa do ke ducmg xien 



69 



lap v&i true N mOl goc <p ma tg<p = r|e . Diem can tim nam tren duong xien do (khi da 
iinh, duoc N). Co the va nen dung k€i hop cac phuomg phap vi moi phuong phap co cho 
manh va ch6 yeu cua no. Ba pturong phap da trlnh bay la vm m6t gia tn da biet cua dai 
luang nay tim gia tri tuong ling cua dai lupng kia. De" ve bieu d<5 thl chiing ta tu cho dai 
iuong nay cac gia iri khac nhau de tim cac gia tri tuong ting ciia dai luong kia va c<5 
duoc mot so diem. 

Trong cac phuong phap da biet phuong phap nao cung phai tinh toan thong qua m6t 
bien trung gian la x. VSy co the xem x la bien doc lap de lir do xac dinh cac gia tri cua 
M va N. Ve phucmg diin vat ly, cho x bien doi co nghla la sir dung thay d6t mtic do chiu 
nen cua bet6ng tir 66 ma xac dinh kha nang chju nen ma kha nang chin momen cua tie! 
dien. Vd mat thuc hanh lay x lam bien so' la don gian hem ca. 

Truac net linh x A theo cong thifc (2-40). 

Khi x 4 £ 2a' thl lay x bien thien trong khoang x 4 <x< h. 

Khi x 4 < 2a' (ke* ca khi x 4 < 0) lay 2a' < x < h. 

Nh5n xet rang, khi tinh loan tiei dien. neu ke den do lech tarn ngau nhien e a va anh 

huong cua uo'n doc r\ thl momen lit M lang ien lhanh M = Nrje^ - xem cong thuc (1-18). 
Trong tinh loan thuc hanh. 6" true momen nguoi ta khdng dai gia tri M ma dat gia Iri M*. 
lam nhu vay viec lap va sir dung bieu do don gian hon. 

Voi cac gia tri cua x trong khoang 2a' < x < £ R h tl tinh si5 tri N theo cong ihiie (2-7a). 
tinh M|,,|, iheocong ihtrc (2-4) irong do g[ - R SL va tinh Nt)^ theo cong thuc (2-47) rtki 
ra tir dien kien (2-2). 

M" = Nrie {1 =M ]Eh -N{0,5h-a) (2-47) 

Voi cac gia tri x trong khoang c, R hQ < x < h. dung cong thuc (l-23a) xac djnh o\. dung 
cong ihuc (2-7b) iinh N. dung c6ng thuc (2-4) iinh M lch va xac djnh Ni)e theo (2-47). 

2.5.4. Nhan xet ve bieu do tuong tac 

Bi£u <i6 iuong tac cua tiei dien dSt cot rhep doi xung co hinh dang nhu hinh 2.6. va 
2.9. Khi dung bieu do nay de xem xet kha nang chiu luc cua tiet dien co mot so nhan xet 
nhtr sau (hinh 2. 1 3): 

- Diem I nam ben trong mien chiu luc v6l M,, Nj. Cac diem K|, K 2 , K 3 nam ben 
ngoai rnifen chju luc thl hoac la ca M^:, N Kl d£u \&n hon M )? Nj, hoic it nhat cung c6 m&i 
trong hai dai lucmg Ion hon M|, N,. D6 la trong dai the. 

- Trong vung Ian can doan DB itnh hinh co khac. Mot diem Q 6 mien trong vdi Mq\ 
Nq. M61 di^m R 6 mien ngoai trong luc do M R < Mq va N R < Nq. Nhu vay tiel dien 

70 



chiu dugc mot cap noi lire Mq, Nq trong liic khong chiu duoc cap M R , N R deu co gia tri 

M 

nho hen. Tuy v&y cap noi lire Mr, N r co dp lech tam e - — Ion hon. Di2u nh$n x6i 

vira rdi nhu la mot nghich ly. no duac giai ihich bang each phan tich sir lam viec cua iitt 
dien belong cot thep chiu nen lech tfim Ion, su* phi hoai bit dau ilt vung keo. Khi M 
va N d^u giam nhirng N T giam nhieu hon thi lire keo trong cot thep se tang len. Cong 
ihuc (2-20) cho thay. khi N Icm thi cot thep chiu keo A s se be htm. 




Hinh 2.13. Nftan xif ve bieu do tuojig tac 

Hinh dang duotig cong ciia bieu do tuong lac phu thuQc vao gia tri luyet doi va ty Id 

v 

giua col ihep 6 hai phia. vao sia tri tuong doi ciia x 4 la ■*, = — . 

h 

Xet tiet dien dal cot ihep a phta b£n inii la A p ben phai la A p . Cho A p mc)t gia tri c6 
dinh vao muc irung binh. cho A, ihay d6i tir den mdt gia tri kha ion. Ve cac bieu dd 
voi cd m6men duong (A, chju keo) va mornen am (A p chiu keo). Hinh dang cac bi£u dd 
thay doi nhu the hien tren hinh 2.14. 

Xet rieng pha'n bieu dd ung vol m6men duong (A t chiu keo) thay nhu sau: 

Khi A, = co duong I, diem D s trung gdc toa d?. Tuy A ( = nhung khi tang lire nen 
N khu nang chiu momen ting cho d£n die"m B| . 

Tang A, nhimg A t < A p , co duong 2. Bte'u d6co diem lui Lj o phia tren. Khi A ( = A p , 
c6 duong 3, doi xims. 

71 




Hinh 2,14. Cac dang dtrvtsg cong ciio bieu do itfang tac 

Tang A, > A p nhimg van giu cho ^ = — < ^ R (xem x 4 6 cong ihuc 2-40), co duong 

n o 

4 vol diem lui L 4 nam a phia duai. Khi gia tri ^ cang lang len ihi doan DB cang giam. 
Tang A, ddri mtic £4 > £ R , doan DB bien mat (ducmg 5). 

2.5.5. Bieu do tircmg tac khong thtf nguyen 

Lap bieu 65 vai ki'ch (huoc lie'i di£n va col ihep da bie'i nhir phan ir6n da irinh bay 
chi Ihfch hop cho mot trudng hop cu ihi nao do \vi vjec van dung bi han elie. Lap bieu 
do vdi cac thong so khong thu' nguyen, dac biet la lap cac ho bieu do sc co diroc su van 
dung r6ng rai hem. 

Xel tiet di6n dfil cd't (hep do'i xung \= A[ va thoa man di£u kien R s = R^. . 



Dul 



-\ 



M 



n = 



R b bh 



in - 



Nt)e 



R b bh* R b bh£ 



5 = jUJL ; %m ± 

h h h 



72 



a = 



R b bh R b bh 



Cdng thifc (2.7b) bie'n ddi thanh: 

n = | + a(l-(p s ) 

Trong do ip s = — . Khi % < c R ihi ^ = 1 va n = £. 

Vol 1 > £r va khi dung cong thdc ( I -23a) de xac dinh o\ se co duor: 

R N l+a-$ R 



(2-48) 



(4-49) 



(2-50) 



Bien ddi cong ihire (2-47) inanh: 

m=yi-0,5c) + (l-S)(cc-O,5n} . (2-21) 

0£ lap mot bieu do. cho 5, £ R va a moi gid tri chon san, cbo c lhay doi se tinh ra cac 
gia iri n va m. M6i cap n. m cho mot diem cua bieu do. Lay £ lhay doi lit O den ^r. sau 
do tu4i? ^ en h. 

Voi 6, £ K chon san. lai cho a iliay doi (ct,. a-... a^) se co dirac moi ho bieu do. Nhir 
vay mot ho bieu d6 ling vol mdt gia in 8. z R . nhieu gia iri a. Cho (S (hay ddi se co nhifeu 
ho bieu do v<Ji cac 6. a khac nhau. Hmh 2.15 ve mot ho bi&a do nhu vay. 




0.2 0.4 0.6 0.8 1.0 1.2 1,4 1.6 1.8 2.0 
Hinh 2.15. Ho bieu do tUffng t6c khong fhiinguyen 



73 



Khj vc bi£u do cho moi lie't di£n cu ihe* vdi chie'u dai u'nh loan / cho irirdc, da xei 
dirge anh huong cua uo'n doc theo phuortg yeu nhat (he so' uon doc p) de linh gia tri N 
(kha nang chiu nen dung lam. khi M = 0). Khi lap bie*u dd khong ihu nguyen crura xet 
dugc dieu vira trinh bay v] vay gia tri n ung vdi m = chi moi the hien kha nang chiu 
nen Ion nhai luc chua k£ u6'n doc. 

2.5.6. Dung bieu do lucrrig lac 

Bieu do tuong lac cua liet di6n moi cau kten cu the dirge dung chu yeu de kiem Ira 
kha nang chiu luc theo cac bai toan trong muc 2.4. 

De kiem ira kha n5ng chiu cSp n6i lire M, N thi irudc hd'i linh e D , v, va M = Nr|e y . 
Voi M* va N co dugc moi diem I. Khi diem do nam 6 mien Irong cua bieu do thi liel 
di£n du kha nang chju luc. 

De" xac dinh M khi fcie't N thi lir N lim dugc diem P la giao cua ducmg giong tir N vdi 
bieu 66. Tu P Tim ra M*. linh duoc e^ va M 

De xac dinh N khi bie't e , gia ihie'l he so r|. Ke dudng xien co goc ma tg 6 = ne . 
Duong nay c£t bieu do iaj di^m Pj. Tu*P| lim ra gia tri N (hinh 2.16). Chii y ig0 6 day co 
don vi chidu dai. phai rihh toan iheo ty Id tren bai true cua bieu 66. 



W-tifi 




li'mh 2.16, Dim§ bieu do tit&ng tuc de xac dinh kha /ting chiu hrc 

Ho bieu 66 khong thu nguyen, ngoai viftc dung de kiem ira kha nang chiu lire nhu 
tren (chi dung mo( duong irng vdi a da biei) con diing d6 linh loan co'i ihep mdl each 
rihanh chong. 

Tu C$C S<5 lieu M, N, b, h, R s , R b da cho, gia ihiel a de tfnh h va 6 = — Tinh n. 

h o 

nef>. m. Dung ho duong cong vdi 5 va * R thich hop se tu m, n lim dugc a va : 

7-i 



Thi da. Lay so lidu a thi 4u 3 rrtuc 2,2.6: b = 300, h ^ 500rnrn; l = 2,8m; R b = 11 ,5; 

37 

R, = 280MPa; N = I320kN; M = 218kN. Gia* thief a * 37, h^> = 463, a = = 0,08; 

463 

c R =0.61. 

Da ifrih toan dirac c = 165mm: rj = I . 

N 1320x1000 ■ rt _. 

n = * = 0,864 

R b bh, v U5* 300x463 

m= i^, n n£l = .S64 1^^0.308 
R b bh,i h () 463 

Voi n = 0.864 va m = 0,308 Tim tr£n ho bitiu &6 c6 diem K nam giffa hai duong cong 
ung vol a = 0.2 va 0,3. Noi suy co daoc a = 0,28 (gSn dung). 

t 0.23x11.5x300x467 _ rrt 2 
A, = 1610mm 



2S0 



2.5.7. Tin du vd bieu do lixong fac 

7"V^/ tfy A Gio lifii dicn nhir ir£n hinh 2.4b vdi / = 2.8m; b = 30cm, h = 50cm. 
A s ~ A> 2622 + 2<t»25 = (7.4cm\ a = a = 3.75cm, lay iron a = a' = 4cm. R b = fl, 

R,. - 260MPa: i ?v = 0.64. Tinh loan vk ve bleu do wcmg tic. 

ho = 50 - 4 = 46cm = 460mm; Z a = 420mm. 

ra-R.a; 

R b b 

Mq = R^ A,. Z a = 260x 1740 x420 = 190* 10 6 N in mm = I90kNro. 

N = <p(RbA b + R S AJ (cong thiic 1-6). 

A s , = A, ■ + a;= 17,4 x2 = 34 ( 8cm 2 = 3430mm 3 

A b = 300x500 -3480 = 146500mm 2 . 
i =. 0,2S8b = 0,288x300 = 8,6 

X = ^ =|^ = 32,4 > 28 , can xet u6n doc 
i 86,4 

75 



<!> = 1 ,028 - O,O0O0288x32.4 2 - 0,0016 x32.4 = 0.94 
M^ = 0,94 ( 1 1 x 146500 +260 x3480) = 2365000Niu. 
N = 2365kN 

Cho x bie'n thjen irong khoang 2a' = 80 < x < £ R h<, = 276 

Lay x = 80; 

N = R b bx + R s a; - R<A S = 1 1 x 300 x 80 + (0) = 264000 Niu = 264 kN 

M,^ = R b bx(ho-0,5x)+R iC A;Z a 

= 1 1 x300x80(460-40)+260x 1740x420 = 300,9 x]0 6 Niu mm = 300.9kNm- 
M* = M lgh - N (0,5h - a) = 300.9 - 264 (0,5 * 0.5 - 0.04) = 245.4 kNm. 

Tiep iuc lay cac gia' iri khac cua x bang 120, 160, 200, 230. 250. 276. tinh duoc ket 
qua ghi irong bang: 



x (mm) 


N(JcN) 


M lph <kNm) 


M* (kNm) 


120 


396 


348,4 


265.2 


160 


528 


390.6 


279.7 


200 


660 


-127.6 


289 


230 


759 


451.8 


292.4 


250 


825 


466,4 


293,2 


276 


9) 


483,3 


207 



Tiep iuc cho x bifc'n thi&i trong khoang c> R h < x < h = 500. vdi x = 300. (dung cong 
ihirc 1.23a itnh a J: 



: 



o. = 



1- 



2(x-$ R h 



K^IL 



R. = 



1- 



2(300-276) 
500-276 



260 = 204.3MPa 



N = R b bx+R sC A;-CT,A,. 

= 11 x300 x 300 + 260 xl740 - 204.3 xI740= 108~xlQ^Niu. 
M ieh = R b bx{h -0,5x)+R 5L A;2; 

=11 x300x300(460- 150)+260xl740x420 = 496.9xlO ,, Nmm. 

M* = 496.9 - 1087 (0.5 x5 - 0.04) = 268.6. 
Tie'p iuc tinh toan vai cac gia tri cua x bang 350, 400, 450. 480. Ket qua ghi 6 



,6s 7. 



bang sau: 



76 



x (mm) 


ct s <MPa> 


N (kiNiu) 


M Igh (kNm) 


M* (kNm) 


300 


204.3 


1087 


497 


269 


350 


88,2 


1454 


519 


214 


400 


-27,8 


1820 


533 


151 


450 


-144 


2L88 


539 


80 


480 


-213,6 


2407 


- 


- 



Luc nen loi da cot chiu duoc N - 2365 kN. khi tfnh vol x = 480 co N = 2407 > N , 
dung ttnh loan. Kfi'l qua d6 ve bicu do ghi trong bang sau: 



N 


| 396 52S 


6^0 


759 | 825 | 911 


1087 


1454 1820 


?''.< 


2365 


M* 


190 1 265,2 i 279.7 


289 292.4 


293 292 j 269 


214 151 


539 






Thi du 2. Ve b\i\x d6 tuong tdc khong thii nguyen. cot (hep doi xuog voi 5 = — = 0. 08 



A 



Ty 16 coi thep u = — ^ = 0,01, R s = 260; R b = 13; ^ R = 0,6 



bh 



a = A^ = .01^ = 0,2 
R b bh 13 

Trong plum vi < £, < £ R = 0.6 co n = £. 

Khi ; = 0; n = 0; rn = (1-6) (a - 0.5n) = 0,92 *0,2 = 0,184 

vdi £ = 25 = 0,16; n = 0,16 

m = ^(l - 0,5c) + (1-8) (a -0.5n) = 0.16 (1-0,08) + 0,92 (0.2 -0,08) 
m = 0,2576. 

Vai cac gid tri khac cua i £ £ R = 0.6, kei qua ghi trong bang sau: 



s 


0.2 


0.3 


0A 


0,5 


O.o 


n 


0.2 


0,3 


0,4 


0.5 


0,6 


m 0.272 


0,301 


0.32 


0.329 


0.328 



V6i£ R <^< 1+5= 1,08. 

1+S-4 R 0.24 

n = q + a(l-(p)=4 + 0^(l-<p s ) 
m = § (1 - 0,5£> + (1 - 8) (a - 0,5n) =4 (I ■ - OSp + 0,92 (0,2 - 0.5n) 



77 



4 


0.7 


0,8 


0,9 


1,0 


1.08 


<Ps 


0.583 


0.167 


-0.25 


■0.667 


-1.0 


n 


0.7R3 


0,967 


1.15 


1,33 


1.48 


m 


0.28 


0.23 0.15 0.07 


tl ° 



Kel qua de ve bie*u dd tirang lac lay theo hai bang Iren. Khi cho a thay ddi se c6 m6t 
ho bieu (36. Hlnh 2.15 thd hifin ho bieu do voi cac gia tri a = 0,2; 0.3; 0,4 va 0,5. Chii y 
rang ho bie'u d6 a hinh 2.15 mang tinh chai tucmg trimg, duac the' h'ien chua that chfnb 
xac do do chua dung duac d£ thie't ke' thuc i£. De' dung cho thuc tcco the iham khao cac 
bieu dd d phu luc. Theo nguyen tac va thi du da neu, m6i co quan ihie't ke'nen tu lap cho 
ni'inh nipt so" bieu do mau de dung. 

2.6. TINH TOAN VCJI NHIEU CAP N0l LIT 
2.6.1. Chon cac cap n6i lire de'tmh loan 

Khi to hop noi luc de tinh loan cdl (xem muc 13) thong thuefng moi col duoc xei ii 
nhat hai tie't di£n. mdi lie't di£n c6 6 cap nc)i luc trong hai to hop co ban, nhu vay mdi col 
co ft nhai 12 cap npi luc ca ban. Ngoai ra con co \ht co cac cap n6i luc cua id hop dac 
biel. Theo nguyen lac thi liel dien can phai du kha nang chiu tat ca cac cap noi luc co the 
xay ra. Khi dung bieu do tuong tac de ii'nh loan cot ihep hoac kicm tea thi vice n'nh voi 
moi so Ian ccic cap noi luc khong co g*t la phiic tap. Tuy vay. khi dung eong thuc de n'nh 
loan ihi khoi iuong Cong vice tang len nhi^u. De giam nhe khoi luong nguoi ta iim each 
bo bet mot so cap. chi chon ra ni6t so cap thuoc loai bat lei nhai de tinh loan (can nhieu 
cot thep hon). Khi ii£\ dien co du kha nang chiu duac cac cap thuoc loai bat loi nhai thi 
no cung du kha nang chiu cac cap con lai. 

Dieu 3.21 cua TCVN 5574 - 1991 quy dinh: Chon cac cap noi luc M. N bat loi trong 
do ngoai gia iri tuyet doi cua momen con can xei den chieu cua no. Voi moi luc nen N 
da chon. de tinh loan can lay M co gia tri tuong ung Ion nhat. Con neu voi M da chon dc 
tinh loan ma H tucmg ling co kha nang thay d6i thi can xei den ca gi£ tri N be nhat va N 
Ion nhat. 

r 

Trong cac cap npi luc ciia bang to hop thi ca M va N deu thay ddi do do kho chon ra 
mot cap nao do la bat toi nhat ma ihuong phai chon ra mdl so cap dang nghi ngc ihuoc 
ioai ba'i loi nhat, trong 66 neu dat co't Ihep doi xung thi khong can chu y den chieu cua 
m6men con neu dai cot thep khong do'i xung thi phai chu y ca den chieu cua momen (M 
dtftfng, M amj. Ca*c cap ihu6c foai bat jpi nhat fa cac cap: 

- Cap co gia trj tuy6t doi rn6men Icm nhat, 

- Cap co luc n^n ion nhai. 

78 



- Cap co do lech tam e lcrn nha't. 

- Cap c6 M va. N d£u rhudc loai Icm. 

- Cap co M va do lech lam e deu thuoc toai I6o. 

Viec chon bao nhieu c3p de* tinh toan khong co quy dinh cu the\ co ihe* la 2, 3, 4 
hoac nhieu hem tuy ihuoc vao su phan rich cua ngiroi thi£t ke'. Noi chung dung cang 
nhieu cap de ifnh loan th: d0 tin cay cang cao. 

2.6.2. Tinh toan cot thep voi nhieu cap noi luc 
2.6.2 J. Nguyen tdc chung 

Khi da chon diroc mot so* cap noi lire, neu tfnh cot thep doi xung thi tien hanh tinh 
cho tat ca cac cap roi lay gia Iri Ion nha't de bo In. 

Khi dai c6i ih.6p khong doi xung voi muc dich ti£t ki£m col thep thi viec ifnh loan se 
irer nen phiic tap hem vl tmg voi mot cap noi luc thuong phai tinh mot so Ian. cij sau moi 
Ian lai so sanh ket qua cua cac cap khac nhau de dieu chinh nham dat duoc viec su dung 
col ihep lhat hop ly, tie't ki£m. De ii£n theo doi chung ta danh so cac cap noi luc ia i = a. 
b. c... goi cot thep phia ben Trai la A,, ben phai fa A p , thutucac Idn tinh la j = 1,2... Ky 
hieu cua mot cot ehep irong qua trinh tinh toan la A u : ho£c A ; =. Trong truong hop can 
phan biet ro rang cot thep chiu keo hoac chju nen thi co the' them da'u phiy cho col thep 
chju nen. ihi du. neu ky hieu A' ihi da co ngu y c6'l ihep do ch£c chan la chiu nen con 

neu ky hieu A tJJ la chung chung. Hlnh 2. 17 neu mdl thi du tiei dten duac tinh voi hai cap 
noi luc a, bo hai Ian tinh. Khi can phan bi£i ro rang su chiu lire cua cot ihep co the ky 
hieu A^ va A' b . 

Viec tinh loan phu ihu6c vao cac cap mdmen la cung chieu hay khac chi£u. tinh 
Eoan iheo nen lech lam Ion hav lech tarn be. 



A. 



^[> 'A 



A. 



A* 



sj^t 



A* 



*.. 



-i 



*m 




LanJ 



Aus 



\» 



^ Un 2 



Hink 2.17. Sodd dtit t4n cot ihep c6c \6n tinh 



79 



2.6.2.2. Tru&ng hop cdc cap momen cung chieu 

Tuih loan cot thep khong doi ximg v6i c5c cap noi luc cd m6men cung chieu, trutfc 
net tuih cho tal ca cac cap va so sanh ket qua. Khi co m6t cap nao do cho A, va A p deu 
Ion nha't thi dung vific tinh loan va lay ke'l qua 66 de* chon ihep. 

Trixong hop co cap a cho A ul Ion nha't con mot cap khac, vi du cap b. cho A pbl Ion 
nhal (trong so cac A pM ) thi liep tuc tinh vdi hai cap do, sau se xlt ly vdi cac cap con )ai. 
Hai cap duoc xel thudng co it nhfl't mdt cap duoc tinh iheo nen 16ch tarn Ion. 

De de theo doi, cho rang ca hai cap deu chiu momen duong, A p dong vai tro col chiu nen 
A'. A, chiu keo (hoac nen it). Ke"t qua tinh Ian ihii nha't cho A ul > A, b , va A^, < A' pbl 

(them dau pha'y vao A p de" ndi rang do la cot Ihep luon luon chiu nen). 

a ) Irubtxg hop c&p a nen lech lam be 

Cot ihep cua cap a kh6ng the' thay d6i. chi co the thay d6i c6'i thep cap b (nen I6ch 
tarn lori). Xem tai khi tinh c2p b da dung x bang bao nht6u. Khi da lAy x = c^h thi 
ngung tinh loan va diing ngay A^j va A' pb | de chon cot thep. Neu da lay x < ^r^i 'h' 

xoa bo ket qua, tinh lai cap b nhtfng van xem nhirtinh Ian thu* nhai, vdi x = ^h , hie nay 
Alj. van ldn nhal in! ngung linh loan, con neu lai phut hien co cap c nao do ma AL| la 

Ion hon ihi itep tuc xlt ly vdi cSp c nhu da lam vdi cap b. 

b) Tnidng hap cd has cdp a, h deu nen lech lam Ion. 
Tinh Ian thir nhat co k XiS > A, bl va Aj^, < A' pb) . 

Tinh cap a Ian thu* hai vca A' pa 2 = A pbl se duoc gia tri A u2 < A laJ . So sanh A U)2 voi 

A, cua cac cap con lai. neu A la2 vfin ion nhal thi dung tinh loan va chon col ihep Iheo 
A l:i 2 va Apy->. Neu phal hien thay co mot cap c nao do ma A IC) > A,^ thi liep luc linh loan 
vdi cap c nhu da" lam vdi cap a. 

2.6.2.3. Trrt&ng hop cdc cap momen khdc chieu 

Tinh toa'n co'i ihep khong doi xung cho nhieu cSp n6i luc co mOmen khac chieu, 
truo'c het can tinh toan c6'e thep kh6ng doi xung cho lat ca cac cap. 

Khi co mot cap nao do ma ca A, va A p deu Ion nha't thi dung linh loan. Neu khong 
co cap nao nhu the' thi trong cac c5p m6men cung chieu chon ra mot cap dai dien de so 
sanh. Thi du chon duoc cap a chiu momen duong. cap c chiu momen Am. Khi ma ca A t 
va A p cua cap nay deu ion hon cap kia thi loai bo cap co cot thep be\ chon mfii cap khac 
co mdmen ciing chieu v6i cap co cb'l thep ion de linh toan iheo muc 2.6.2.2. 

80 



Klii ma rn6i cap co cot thep o mdl phia Ian hon cua cap kia ihi ifnh loan theo cac 
trucmg hop sau: 

a) Trucng hop ca hai cap deu nen lech tarn be thi dung tinh toan, moi phia chpn theo 
cot thep loti nha't ciia phia do. 

b) Trucmg hap mot cap nen lech lam Ion (thi du cap a), cap kia nen i£ch tam be. Chi 
co the thay doi cot rhep ciia nen lech tam ton- Khi cot thep chiu keo cua nen l£ch tam 
loti la be hon ma khi tinh to£n da 1 dung x = ^ R h ihi dung tinh toan. Neu Khi tinh loan 
dung x < £ R h ihi can tang x, tmh lai de' giam cot thep chiu nen va tang cot thep chiu 
keo. Tuy iheo k£'t qua tinh lai nay ma xu ly, dirng tint loan hoic ffnh v&\ cap khac. 

c) Trircmg hop mot cap nen Ifich lam Jon, cap kia nen 16ch iam be ma cot thep chiu 
keo ciia nen lech. tam Ion. lai Ion hem cot thep cuag phia cua nen lech tam bi ihi cin tfnh 
lai v6\ cap ntn lech tam Ion. 

Thi du cap a chiu momen duong, nen l^ch cam Ion, cap c chiu momen am nen lech 

tam be ma; 

A ul >A; tI con A p) <A pcI 

Tinh lai cap a [in ihu hai voi A^ 2 = ^V, se duoc A la2 < A ]aJ . Tuy iheo Icet qua tinh 

Ian hai ma xu Ly, khi A r .^ van la l&\ ahat ttong ede \ thi dung tinh toM. Neu co mdt 
c:)p d niko do ma A ld > A,^ thi lai dem cap ay ra de* so sanh va tinh lai. 

d) Trirong hop ca hai cap deu nen lech tam Ion. 

Luc nay cac \in tuih co the nhieu hon va tien hanh theo phuong phap tinh lap. 

2.6.2.4. Phuong phap tinh lap 

Phuong phap tinh lap (hoac tinh vong) cho hai cap a. c nen lech tam lem c6 momen 
khac chieu. cot thep khong ddi xung ma trong Ian tinh thu ni\& n\oi cap c6 cot thep o 
mot phia Ion hon cua cap kia. Cot thep o m6i phia la chiu nen cua cap nay va chiu keo 
ciia cap kia. Xel hai irudng hop sau: 

a) Trucrng hap !. Cot thep chiu nen lori hon. 

Luc nay can xem khi tinh toan da ItCy x nhu th£ nao. Neu da lay x - ^Rho thi dung 

iinh toan. Neu da lay x < £ R ho thi tang x den 4r"o r ^' ,,nn '^'- $% u ^hi l * nn ^ m ^ cot 
thep phia chiu nen van lot* hon thi dung tinh toan con neu xay ra col Ihep chiu keo Ion 
hon thi tinh tiep theo trucrng hop 2. 

b) Trucrng hap 2. Cot thep chiu keo IcTn hon. 

Thi du cap a chiu momen duong, A u chiu keo con cap c chiu momen 5m, A^ chiu 
keo. Xa'y ra: 



Tinh Ian ihuhai nen bal ddu bang capc6 cS't thep chiu keo Ion nha't (ihidu A^i > A^) 
va tinh col ihep chju keo (A^) khi da chon irudc col thep chiu nen A' 2 . Chon A' 2 

nhu sau: 

Ap.ii <A p 8 2^A pcl . Nen chon: A^* 0,5 (A'^, + A^,). Btei co't thep chiu nen 

Aj^j tinh ra col lliep chju keo A u? . Neu A u? < A[ c) ihi dung tinh loan. Viec tinh lap chi 

lien hanh khi A la2 > Aj c , . 

Tinh Ian hai cho cap c bang each chon iruoc col [hep chju nen A[ t , 7 ^ A^, linh 

duoc col ihcp chiu keo A^. So sanh A^ voi A^ 2 • So do linh loan moi vong the; hjen 

lien hinh 2.18. 

,N, n. 




_!_ 



'A 



-. 



\ 



A. 



*; 



Tinh rii/OC 
A* 



Cflon A" , 



Tinh ducc 



SO S3 -i.l 



LiyA'^ 1 ^ 



//in/f 2./#. 5#tfc> pjw/ i Ohp thili !dp 

Khi say ra A p:2 - A' -> ihi dung. 

Neu A^ > Aj^ 2 liep luc linh loan Ian ihii ba voi Aj^ duoc chon irudc trong 
khoang A' , < A' , < A^ 2 - v <* A' 3 da chon liep tuc tinh toan mot vong rndi cho den 
khi tim duoc A j 6i so sanh v6i A' ? . Neu kei qua chua duoc nhu mon° muo'n Ihi linh 

liep vong intf 4, ihu 5. Ttnh nhu the den vong ihur k {co the k = 2: 3 la du) khi A^ co gia 

iri gan bins A fc ihi dung. 



S2 



2.6.3. Nhan xet ve phuong phap tfnh 

Khi can tinh loan cot thep cho m6t lififi di£n chiu nhieu cap npi luc khac nhau thi 
dung phuong phap linh cot (hep doi xung la dcm gian hem. Cans don gian lion nua n£u 
dung dude ho bieu do tutmg tic khong ihii nguyen. 

Vide tfnh cot thep khong doi xtfng voi nhi^u cap nfii !uc nham six dung col thep mot 
each tiet ki£m, hop ly trong nhieu truong hop la kha phut tap va mang ttnh ly thuyet 
nhteu hon. De cd the van dung (rang (hire te^nen va can lap cac chuong trinh phan mem, 
six dung may tinh. 

2.7. TlPlT DIEN CO COT THEP DAT THEO CHU VI 

2.7.1. Dai etrong ve viec dat cot thep thco chu vi 

Trong nliung phdn triroc day da trinh bay each tinh loan cho trudng hop cot thep 
chiu lye ditc/c dat tap [rung iheo canh b co dien [fch A^ , A[ (hoac A t , A ). Khi canh h [a 

kha Ion. iheo yeu cdu ca'u tao, doc theo canh h can dat them cot thep doc nhung cht xem 
la cot cau tao ma khong ke vao irons tinh loan. 

Tiet dien co col thep dal theo chu 
vi la khi cot thep chiu lire duoc dat 
ph&n ra tuong doi deu tren ca canh b 
va canh h va ihuong dat doi xung iheo 
hai iruc (hinh 2.19). Goi s, va s : ia 
khoang each giifti cac true thanii col 
thep iheo canh b vh canh h- Khi dung 
cac thaoli cung duong kfnh fy va s, - s 2 
co trudng hop dat cot ihcp deu Iheo 
chu vi. 

Thucmg chi co (hti dat cot Ihep deu 
trong ijfii di£n hinh vuong hoac tiet 

dien chu nhat ma b,, h, la boi so' eua khoang each s. Khi dai khong deu ihi nen lao ra 
mat d6 cot ihep iheo canh b ion hem theo canh h bang each dung s, < S2 hoac chon 
dudng kinh cot ihep dat theo canh b Ion hem. 

Xet ve mat chiu luc, khi nen lech lam phang [hi viec dat thep theo chu vi ft hieu qua 
hon so vdi viec dat thep tap iruns doc canh b. Tuy va_v khi kich thuoe tiet dien kha Ion, 
so luong col Ihep kha nhieu thi vific d5t cot thep iheo chu vi lam cho (hi cong don gian 
hon va khong can dal them cot thep ca'u tao. Hon nfia khi cot co the bi uo'n theo hai 
phuong tht viec dal thep theo chu vi trd n£n cin thie"t. 









• 

1 




H 


I 


• 




1 

is, 

t 


b, 




1 
.3, 




» 
[a, 








h 


* 


a 


Si 


s 3 i s, 


! s, 


i= 


tit thep 








h; 






h 








Hit 


h 2.19. Tie) rfit'ii c 
dat iheo chu v 







S3 



2.7.2. So do cot thep va so 66 umg su£t 

Tie't di£n co kich thuac b * h trong do h la canh song song vai mat phing uo'n. Co'l 
thep ducc bo' in thanh timg 16p vuong goc vai canh h Ian luat co dien tich la A, , A 2 >- - A n 
irong do A, va A„ la hai lap ngoai cung dat theo canh b vai A) la cot thep chiu keo hoac 
nen fl hon, A n la cot thep chiu nen nhieu. Khoang each lir Irong tam cac lap co'l thep den 
trong tim lift dien la y r Lay da'u cua y ( la duemg khi co'l thep 6* khac phia vai Luc nen N dai 
16ch tfim, y- t la 3m khi a cung phia (so vai trong tarn tiet dien). Goi h oi la khoang each lir 
trong iam cot thep lop ihu i den mep vung nen. Moi h rt deu diiong (hinh 2.20). 

De I4p so do" trrg suat, dung cac co* sa va gia thlei da neu o muc 1 .6. Se la ihufin ti£n 
hon khi theo quan diem bte'n dang, dung gia thie't liei dien phang de xac dinh bie'n dang 
Ej cua cac lop cot (hep. lir z-, suy ra una suat o,. 

Goi x - khoang each tu true irung hda den mep chiu nen; 

x- chieu cao vung nen linh doi. 
Khi tift dien co rn6t phiin chiu keo Xq < h, lay x = Gh (6 = 7 85). 

Khi Eoan bo tie't di£n chiu nen, x > h. lay x theo cong thiic (j-22)c6ih£n'nh loan Ej 
va Oj theo cac cong ihtfc (1-24) va (1-25). 

Tieu chuan TCXDVN 356 - 2005 dua ra cong thiic ihuc nghiem de xac dinh c t : 



o\. .. . co 



> 



LI 
o sp} - irng suat taroc trong cot thep. voi cot thep thuong c Npi = 0. 

o\c.u • ung suat gidi han cda cot thep a vung chiu nen, voi cau kien lam Ctr belong 
n.lng. b£tong hat nho. bei6ng nhe gia tri c v duac lay nhu sau: 

- Voi lat trong a muc 2a cua phu luc 1 lay c SCM - 50MPa 

- Vai tai trong a muc 2b. lay o SQM = 400MPa. 

co = a - 0.0CSR b 

Lay a = 0.85 doi vai betong nans, a = 0.8+0,75 ddi vai belong hat nho (xem phu 
iuc4). 

V 

4j = — • Chie*u cao tuong ddi vung chiu nen cua belong. 
K 

Theo c6ng ihiic (2-54) tfnh daoc a, > la ung sua't keo, o t < !a tfng suat nen. Gia 
tri cua u, duoc lay trong gioi han - R sC < o, < R,. 

84 



Theo TCXDVN 356 : 2005 ne'u gia tri a, ti'nh theo c6ng ihuc (2-54) d6'i v6i col ihep 
nh6m CIV, AIV. AV, AVI. AT V[[ mk virqt qua PR (i thi phai tinh !ai iheo chi dan cua 
lieu chuan (cong ihirc 68, di£u 6.2.2. 19). 

! 



ne, 



<jA 



$2*1 



^TWY] 



II Iff* 



<*A 



a)*** 




* a 




■^r - 








,K -<^ 












£ 




/fiflA 2-20. Str do t'fng sua), bien dang va liit diin cd c6t thep dot theo chit vi 



85 



2.7.3. Cong thuc linh loan cc ban 

So d& dug sua't da JAp 6* hinh 2. IS la long quat do do khong can phan biet nen lech 
tam la Ion hay be, khong can cac didu kien x < c^h^ va x > 2a' nhir khi tlnh vdi tie't dien 
ihOng thucmg c6 cot thep dat lip trung theo canh fa- 
Lap cong thuc hinh chien: 

N = R b bx~Io,Aj (2-55) 

C6ng ihuc momen: 

M* = NTie = 0,5 R b bx(h - x> +Io, Aj)', (2-56) 

Hai phuong irinh (2-55) va (2-56) duoc dung d6ng thcri vol phuong trinh (2-54). 

Viec van dung cac cong Ihuc. phuong trinh vua neu de tinh co'l thep la kha phiic tap 

v] phai chon truoc vj in' cac lop ecu thep de xac djnh y,. h^. gia thie't quy lual pliaii ho' 

dien tich cac Idp col thep va thuong phai dung each tinh gan diiug dan. Oe' van dung 

trong thuc tc thi lSp va dung ho bieu do" tuons tac khong ihu nguyen la ihu&n loi lion ca. 

2.7.4. Lap bieu do tuong tac 

Ve nguyen i&c co the lap bieu do cho moi Irudng hop dat tot thep bat ky. tuy vay 
thong dung hon ca ia iruong hop cot thep doi xung theo hai true. Phuong phap dung bicn 
so Irung gian X la thuan loi. 

l_4p bieu do cho mot cau kien cu thi khi da biel kich thudc tiet dien va bo ifi col 
thep bang each cho x thay doi, ban d£u lay x = O.lh r6i lang dan tung cap cho d^n x = h. 
Vdi m6t gia tri x tim duoc m6t c3p N va M*. Vdi x kha be" co the tinh dirge N < 0, ung 
v&i truong hop keo lech t&m, khong dung cac gia tri do. Chi Ea'y so ii^u 6i v£ bieu 66 khi 

N>0. 

Tinh ihem mot gia tri ntfa vdi nen dung tarn (M* = 0). luc nay N = R,,bh +■ R xC lA r 
Khi co xei den uo'n doc din dua them hfi s6q < 1, 

Thi du. Ve bi£u d6 tuong tac cho tiel dien 6" hinh 2. IS vdi cac so lieu sau: 

b = 400; h = 800mm; / = 6m; belong co R b = 14,5MPa; c6i thep 16 * 22 co 
R s = 365MPa; E s = 210.000; a = 40mm. So lieu ve cot thep ghi 6 irong bang; 



Ky hieu 


A r 


A 2 


A3 


A 4 


A, 


A 6 


Dien tich (mm ) 


1520 


760 


760 


760 


760 


1520 


>'i (mm) 


360 


2)6 


72 


-72 


-216 


360 

1 


h,_. (mm) 


760 


616 


472 


328 


1S4 


40 



i>6 



Ti'nh a. theo cong thirc (2.54) trong do lay g <c u = 400MPa. 
a - a - 0,008 R b = 0,85 - 0,008 x (4.5 = 0,734. 



a - 



1- 



U) 



0> 



--1 



400 



1-- 



0,734 



0,734 



-1 



. St 



= 1202 



'0,734 _ 



1-1 1.1 

Dong thai - R w < o, < R„ nhir vay - 365 <o,< 365. 



1 

i x 


Kr- 


i 
760 | h,,, i 


\ 2 
= 616 


i 

A, 

h,„ = 472 


A, 
Ka - 328 


As 
IU=1S4 


A* 


: 


*■ 


1 * 


-, t2 


G? 


%> 


CT-i 


C4 Oi 


^ 


ffs 




<T* 


SO 


X 


365 


X 


365 


x | 365 


x | 365 


0.434 


565 


2 


X:5 


160 


< 


365 


365 


* 


365 


0,488 1 365 


0.86-) 


-186 


X 


-365 


240 


X 


365 x 


365 


0.50K 


365 


0.731 


5 


1.304 


-565 


X 


-365 


320 


0.421 


365 ; 0.519 


365 


0.678 


99 


0.975 


-297 


1.739 


j -365 


X 


-365 


400 


Co2c 


365 | 0,649 


| 157 


0.847 


-160 


1.219 


-365 


X 


1 -365 


X 


-365 


4Si: 


0.631 


196 


0.779 


-69 


1.017 


-33-1 


1.465 


-565 


X 


-365 


X 


"* 5 


560 


P.737 


-5 


0.909 


-231 


(.186 1 -365 


x -305 


X 


-565 


X 


-365 


540 


0.S42 


-154 j L03S 


-352 


x 065 




-365 


X 


-365 


X 


-365 


720 


0.94? 


-270 


1.(68 


-563 


x j -365 


X 


-565 


* 


-565 


X 


-565 ! 


8UU 


1.052 


-363 \ 1.298 

1 


-JOj 


X 


-365 


X 


-505 


X 


-J63 


K 


■JO J 


a 


tit thfch 


; Witting ocdi! 


jnh dan 


x khvng can lit 


A few f; ma c€ 


i/ie lay 


0; = R s iiogc a 


= ■**. 


X 


A,= 


1520 ' A ; = 
360 y,= 


760 
216 


A, = 760 
y>«72 


A,* 760 

y^-72 


A-i = 


760 
-216 




1520 
-360 


cA 
10' 


oAy 

10" 


oA 

io- n 


it Ay 
10" 


ctA 
10* 


<rAy 
10" 


tfA 

10' 


aAv 


ffA 
iO 1 


cAy 


oA 
10' 


©Ay j 

It/ 


80 


554 


199 


277 


59.S 


277 


19.9 


277 


-19.9 


277 


-59.8 


-554 


199 


160 


554 


199 


277 


59.8 


277 


19.9 


277 


-1 9*9 


-141 


30.4 


-554 


199 


2^0 


554 


199 


277 


59.8 


277 j 19.9 


4 


-0,3 


-277 


59,8 


-554 


199 


320 


554 


199 


277 


59,8 


75 \ 5.4 


-225 | 16.2 


-277 


59.8 


-554 


199 


400 


554 


159 119 


2x7 


-121 


-8.7 


-277 | 19.9 


-277 


yj.s 


-554 


199 


480 


293 


107 -52 


-11,2 


-253 | -18.2 


-277 j 19,9 


-277 


59,8 


-554 


199 ; 


560 


-7 


-2.5 


475 


-J7.S 


-27" 


-19.9 


-277 


19.9 


-277 


59,* 


-554 


199 


640 


234 


84 


-267 


-57.6 


-2^7 


-19,9 


-277 


19,9 


•277 


59,8 


-554 


199 


720 


-410 


147 


-277 


-59,8 


-277 


-19,9 


-277 


19.9 


-277 


59.8 


-554 


199 


800 


-551 


-198 


-277 


-59,8 


-277 


-19.9 


-277 


19.9 


-277 


59,8 


-554 


199 



87 



X 


R„bx 


I0 l 


iff* 


0-5R„bx(h-;i) 

10 6 


XoAy 
10* 


M' 
10* 


80 


464 


1108 


-644 


167 


398 


565 


J 60 


928 


967 


-39 


297 


4S8 


7S5 


240 


1392 


2*1 


1111 


389 


537 


926 


320 


1856 


-150 


2006 


445 


539 


984 


400 


2320 


556 


2876 


464 


495 


959 


480 


2784 


-1115 


3899 


460 


356 


816 


560 


3248 


-1567 


4815 


189 


218 


607 


640 


3712 


-1886 


5598 


297 


117 


414 


720 


4176 


-2072 


6248 


188 


52 




240 


800 


4640 


-2213 


6S53 





] 


3 



Vc* M = 0. c6r chiu nen dung tarn, luc nay phai ke" den uon doc theo phirong yeu njiai. 
Ban kinh quan linh be nhat i = 0.288 x400 = \ 1 5mm 

i = ^L = ^22. = 52,2 > 28 , can k£ uon doc 
i 115 

<p = 1 .028 - 0.000028S x52.2 2 - 0.0016 x52,2 = 0.S66 

Tinh Nf, iheo cong ihut (1-6): 

M u = <p(R b A b + R'A,,) = 0,866 (14.5 x 400 x §00 + 365 x 60S0) = 5940000 Niu. 

Lay gia !rj ciia N kh6ng qua 5940 kN. 

Trong ket qua linh loan co 1 so N < 0, ch|u keo lech tarn, bo cac so lieu do. Uhg voH 
N = linh duc/c M = 790 kNm. Ket qua de* ve bieu do ghi trong bang sau: 



N X ° 


111! 


2006 2876 


3S99 


48 15 5598 


5940 


M v 1 790 


926 


984 959 


816 


607 1 414 






2.7.5. Ho bieu do khong thur nguyen 

Ho bieu do duor lap cho liet. dien co kich thudc b. h bat ky va ty le cot thcp 



^ = 



bh 



ha"! ky voi A s , la dien tich loan bo cot thep doc. 



Tuy vfiy can du kien bo' iri cac (op col ihep de* xac dinh cac gia tri 

5 = _ ; y. =_ ol ; ^ = Zl , Di6n tich moi lop cot thep !a A s = k s A sl = |4jbh vdi yi, = k|U s . 
h h h 

4 
Nhu each the hien tren hinh2-18 thi A„ = 16$; A, = A 6 = 4ij)dod6k 1 = k 6 = -- = 0,25 

16 



A, ^ A 3 = A, = A 5 = 26; k : = k 3 = k 4 = k 5 = 0.125; 

N M* Nne 

DiU; n* ; m = 



R b bh ' R b bh 2 R & bh* 

x , x c 



a 



Dai p. = — !-. Dung cdng thurc (2-54) bicn d6i thanh: 
R b 

P(= _ ( T y.,[ ■ 



Rb 






R R 

Dons l hoi — — < p. < — - 

Dung cong ihirc (2-55) va (2-56) bie'n cI6i thanh: 

n = 4-Ip,Mi (2-5?) 

m = 0.5£(l-£)+Ip,^P 1 <2-58) 

Voi cac gia iri i kha be linh ra dirge n < 0. Bo qua cac gia tri do. Ohg vdi c = 1. iinh 

p 
iheo ncn dung liro. m - va n = i ^ — ^- u v . 

R i> 

Moi bie'u d6 dupe Lap vdi mot kieu bo iri cot thep the' hien qua cac he so k t va cac 
thong so 6; R s ; R b . Vdi 6 da co se tfnh ra cac gia iri y,; p r Vdi m6i gia tri u. s da chpn cho 
£ ihay ddi iCmg cap se iinh toan va ve duoc mO! bieu d6. Cho l^ cac gsa iri khac nhau se 
co rnpl ho bie'u do. Hinh 2.21 gidi ihieu rnOt ho bieu d6 nhu* vfiy. 

Van dung ho bleu 66 co (he' de kie'm Ira kha nang chiu lire hoSc de tinh toan cot 
ihep. Trong cac bai toan kiira tra thi khi bie't r|e$ can tim lire N la kha pho bicn trong 
vice linh toan cou ki£n chiu nen lech lam xien se irlnh bay crchircmg 5. Thi du theo hinh 

2.21. lie! dieti co u,. = 0.01 = 1%. Vol ige = ^- = 0,25 , tim N? 

h 

Ke duong xien goc ma tgG = 0.25 vdi chii y ty 16 tr€n hai iruc la khac nhau. Gii iri 
0.25 lu ly le giua tung do va hoanh d6. Dtrcmg xien cat bieu do cd u... = \% lai di£m P. 
gidng xuong tim thay n = 0,65 tu* d6 tinh duoc N = nR b bh. 

De linh toan cot Ihep, iCr n va m t\m dirot diem K nam giffa hai duong vdi u, h cho 
irudc. Noi suy duoc jj^cdn thie't va tinh: 

89 









V 


14^. 


















■ 
















r 


, 






? 


^ -- 


b 




* ' 











ri 15 




R,= 2cMPa 
R.= 9MPa 



Hinh 2.2J. Ho bteit do wang idc li:. ''i.v lh(( iigj/yeu 
a/a lief dipt co cot thi'p (fat tow elm vi 



A sl = mbh (2-59) 

Thidu. 

Tie'i di£n b = 400mm, h = 600mm, belong co R b = 9; cot thep co R N = 260MPa. 
N = 2000kN; M = 340 kNm. Chi£u dai linh loan cua col / = 5.4m. Yen cau unh loan 
col ihcp dal iheo chu vi, 

a 40 1 

Giathie't: a = 40mm, 8 = —= = — 

h 600 \5 

Xeiuondoc: i.^M =9 >S 
h 600 

. bh 3 4CH)x'600 3 „ m s 2 
J = = =72xJ0 mm 



12 12 

ting vdi R b = 9 co E b = 24000MPa. 



'0 



2.5EJ 2,5x24000x72x10' 



v _ 



5400- 



= 14800xl0 J Niu 



90 



N^ 14800 

e. = — = = 0.17m = 170mm. Do lech tarn ngiu nhiene,. 

1 N 2000 

e . > — — : = 20mm . Ca'u kjeo ihu&c k£t ca'u sieu linn e^ = max (e, , ej = 1 70mm. 

* K6Q0 30/ ' 

r)e = i, 1 5 x 0.17 = J95m = J 95mm 

N 2000xl0QQ 

n = = = 0, 926 

R & bh 9x400x600 

Nn.e 2000000x195 
m = — = — = 0, 5k) I 

R b bh" 9x4GQx60Q 2 

Du kien dung 14 thanh cot thep dat theo chu vi nhu tren hinh 2.21. Vdi 6 = — ; 

R x = 260; R,, = 9. tra bieu do vdi n = 0,926; m = 0.301 co duc/c diem K nam giua hai 
bieu do voi u. = 0.025 va 0.03. Noi suy co m, = 0.028. 

A M = 0,028 x 400 x 600 = 6720mm 2 

Bo tri 14 ihanh. dien tich m6\ thanh; = 480mm" . Chon dung cot ihep 4>25 co 

14 

dien lich 491mm 2 (hinh 2.23). 

Chu y rang ho bieu do a hinh 2.21 mang nhi£u tinh tuotig trimg, chua du do cbuih 
xac de dung cho ihiet ke ihtrc le. O phu luc 9 cho mol so bieu do co the dung duoc. 

2.7.6. Phinmg phap g£n diing xac dinh N 

Khi bie'i dd lech tarn t\&q can xac dinh N ma khdng co bieoi d6 tuotig tac phu hop de 
dung thi co the llnh toan nhu sau: 

Tfnh uoc chung chie'u cao vung nen x theo cong thirc (2-60): 



x=(a5h-ne )t/(0.5h-i,e ) i + - 8R ^^ h - 2a) (2-60) 

Lay hai gia tri x de tinh loan la x t va x 2 v<5i Xj = X + 0c,h; 

x 2 = x + a : h. Gia tri a, , 04 lay phu Ihudc vao ty s<5 x/h theo bang sau: 

91 



x/h 


<0,1 } 0,1 -0.2 


0.2*0,3 


0.3*0.410,4*0.5 


0.5*0.6 


0.6*0,7 


0,7*0,8 J0.S*0,9 >0,9 


a j 


0.1 


0,05 





-0,05 


-0.1 


-0.15 


-0.2 


-0,25 -0,3 | -0.35 


a 2 


0.25 


0,20 


0.15 


0.10 


0.05 





-0.05 


-0.10 


-0,15 | -0.2 



Cfrig vdi rn6i x da chon, linh loan a, cua cac lop cot thep theo cong thiic (2-54). Tir 
do ifnh hai gia iri cua N la N, va N 2 . Tinh N, iheo cong ihuc (2-55) da lap: 

Nj = R b bx - Eo,A f 
Tinh N 2 theo cong ihuc (2-61) rut ra tir (2-56): 

N _M' _ 0,5R b bx(h-x)^Vg,\y, 

Voi hai gia iri x urn duoc hai cap N,. N 2 nhu viy. Ghi ket qua vao bang sau: 



(2-61) 



X 


X, x 3 


Nj 


Nn ' N l2 


N 2 


N 2 t M fi 



Co the xac dinh N gan dung bang do thi hoac bang unh loan. Vc do thi N, va N 2 
iheo x. Oiem ck\ nhau cua hai do thi cho btet gia iri cua X (hmh 2.22). 

Voi hai gia Iri cua x nhu da 
chon kha nang hai do thi N ( va N? 
cat nhau la rfit Ion. N£"u chiing vao 
chua cat nhau Ilia can phan dodn de 
chon them mot gia iri x mcu' ngoai 
hai gia in da co. 

Cling co the iap cong ihiic de 

linh io£n N dua ir£n cac s6' Jieu Nj. 

• 

N; da co. Truck; hel can biet khoang 
Xj. x k ma trong khoang do hai do thi 
cdi nhau. Tieu chi de nMn bi£i la : 
N 2 : < N,: irong khi N ?k < N, k (ho5c 
ngucc lai). 





N..N, 




N. 












N r 










/ N, i 
/ 1 


N 






N. 












Mj. 


■ 







ffiri/i 2.22. 06 thi xac dmh gia rri N 






(2-62) 



92 



Thirc chat eua phuong phap vua irinh bay cung la phucng phap ve bleu 66 tirong tac 
nhimg khong ve loan b6 bieu do rna chi linh loan cho mot doan vcfi hai diem. Tuih chat 

gan dung acong thut (2-62) la xem a irong doan dang xet sit thay doi cua N, va N 2 theo 
quy luAt dirong thjing. 

Thi ihi. Lay ket qua cua thf du 6 muc 2.7.5. Yfiu cjSu xac djnh lye N khi cho r|e = 
195mm: R b = 9: R s = 260MPa. 

Tifit dien lhe hien iren hinh 2.23. Cac so lieu ve col thep dung de" iinh (oan ghi 
buns sau: 



Ky hieu 


Oi'u iao 


Dien lich 


s 


Zr 


A, 


4*25 


1964 


260 


560 


*2 


2*25 


982 


130 


430 


A 3 


2<t>25 


982 





300 


*4 


2^25 


982 


-130 


170 


As 


4<j>25 


3964 


-260 


40 



A, = EA,= 



25=6874mnr. 



i/«i/j 2.23. 7"te/ d/en 
t/fvr //?^p iheo chu vi 



14 4>2S 






z.= 560 



y430 



: 



* : 300 



170 



i_t 



40 



130 13fl 



•260 



2S3 



60C 



40 



Tfnh x cheo cong (hue (2-60): 



x = (300 - 195) +■ /(3G0- 195)* + 
V 



1 0.8x260x6874x520 



9x400 



= 570mm 



— = -0,95. La"v hai gia tri cuax la x, va x- 

h 600 .■*■■- i 



93 



x, = x + a,h v6i a, = - 0.35; x, = 570 - 035 x 600 = 360mm 
x 2 = x + ct^h = 570 - O r 2 * 600 = 450mm 
Tinh <Tj theo c6ng thurc (2.54) vcri o = 0.85 - 0,008x9 = 0,778 



a , = 



^CU 



1- 



to 

1.1 



CO 



A 



-1 



400 



i- 



0.778 
1.1 



'0.778 



, 4, 



-1 



= 1366 



0,778 



1 



4| = — ■ Dons thai - R, < o s < R v , lire la: - 260 < C7, < 260. 
h... 



L,6p coi ihep 


x,= 


360 


x 7 = 450 


t 
^i 


o, 


*?i 


<*> 


A,.h (M = 560 


0.643 


260 


0.803 


-42 j 


A 2 ,h 02 = 43O 


0.837 


-97 


L.046 


-260 


A v h 0? = 300 


1.0 


-260 


1.433 


-260 ! 


A j. h Q4 = 1 70 


2.11 


-260 


2.53 


-260 


A v h 05 = 40 


9.0 


-260 


10.75 


-260 



Kei qua u'nli loan v£ lire: 



-\ 


A.!* I%4 
y. = 260 


A 2 = 982 A»=0B2 A. = 9S2 A<=i%4 
y 2 =130 y v =0 v. = -130 y, = -260 


aA 

10 1 


oAy 

10" 


cA 

!()■' 


oAy 
10" 


aA 

Mr 


aAy aA 

10" iC 


aAy | a.A oAy 
\0'' I0 1 10' 


360 


:m0 


132.6 


-9? 


-12.3 


-255 


1 -255 


33.1 510 ! 132,6 


450 


-S2.s 


-21.4 


-255 


-33.1 


-255 


■ -255 


33,1 | -510 


132.6 



N^R^x-Sa.Aj, 

. M' _ 0.5R b bx(b-x^yo,A i y l 



N«- 



Wo 



ne. 



x N, j N 2 


360 0) 1901 2264 


450 (K) 2977 1193 



N N, j (N, K -N 3j )-N 2j (N, K -N, J ) 
N|j^N 2K -N, r N IK 



94 



xt - 19 01(1 193 -2264)- 2264(2977-1901) = 1Qr ^ 
1901^1193-2264-2977 

Ghi chit: Tru&itg hap co bieu d6 nrong idc Ihi viic xac dtnh N sedfffi .pan Ii&n, Bieu do piu't 
hop co cac thong sd'sati: R& = 9. 

R s = 260 VlPa; — = = — - . c6"t thep gom 14$ duoc bo tri iha&h 5 hang vong <36 

h 600 15 

hang ihu nhai (A,) va hang thii 5 fA 5 ) co 4 $, cac hang khac co 2o. Ho bieu d6 o hinh 
2.2! co cac thong so phu hop nhu vay. 

Gia ihur bieu do 6 limh 2.2 i co dircc do chi'nh xac can ihiet fhi each lim gia Iri N 
iihu sati: 

Tinh A vi - L4425 = 68?4mm : : 

K = — * 68>4 = 0. 0286 = 2- $6% 
bh 400x600 

h 600 

Kc dudng xien goc v<jj (g0 = 0.325 gap cac bi£u 66: 

V6i ^i, = 0.025 tim duoc n - 0.S7 

u., = 0.030 Um duoc n = 0.98 

Nai suy. vtfi f^ = 0.0286 co n = 0.94 

N = n.R b bh = 0.94 x 9 x 400 x 600 = 2030000 

N = 2030kN 

KA qua co sai .SO' so voi tinh toan (sai &o do tinh, todr. g&t dung va do do chrnh xac 
ciia bieu do). 



95 



Chuong 3 
TIET DlfeN CB0T VA CHtfl 



3. \ . DAI CUDNG VE TIET DlfeN CHUT 

- Tie't dien ch& T gotn co canh va sudn (hinh 3.1) vol ki hieu cac kfch thuoc nhi/ treu 
lilnh ve. 



!i 



b - be rdng stffrn.; 

B - be rong canh: 

c - be day (chieu cao) canh; 

h - chi£u cao tie't dien (trong 
pbuong mat pbang uon); 

A w . A c - dien ti'ch cot thep dat 
i$p trung d phiin siron (theo canh b) 
va a phan canh (iheo canh B); 

a, v , a c - khoang each tir trpng 
tfim col thep A w , A c den mep li6'i 
dien gan nhat. 

Z a = h - a w - a c - khoang each 
giua trong tarn A w va A c . 

I - di£m giGa cua i\6\ dien, each 
deu hai mep mot doan 0.5h; 

G - trpng ram hinh hoc cua tier didn. 

Tie't dien co m6t true d6i ximg. Momen uo'n lac dung trong mat phang chiia iruc dot 
xung do. 

Tie* didn chu T thircmg gap la net dien cua vom v6\ c£nh la phan vo due lien kho'i 
vdi suon. Trong khung cua kel cau nha, cot co lie! dien chO* T c<5 ih£ gap trong mot so 
twang bop dSc bi£t, ho&c la c6i d6c i&p khi can mo rong ra hai ben. hoac col duoc due 
lien vdi ttf&ng cua vach cung, loi cting. 

Tarcmg hop cot doc lap !hi be rong B dtrtfc cau tao trong m6l pham vi giai han nao 
66 con khi cot diroc due \\&n vdi tudng thi be rOng cua lucrng cd the la kha Loti, luc nay 
de lay B dua vao trong li'nh toan can co mot han chc nao do. 















i 

ir 
\ _ 


b A*." 


4 ■ 


i 


[ 


i 

v- 1. 




0J5h 


i 

• 




t 

!> 
i 




6 




.. '- . 






b 


y e 




i 





Hinh 3 J. Tie'i dien chti T 



% 



B = b -r 2v 

Vtft dsum tie'i dien ehu T da. co nhimg quy dinh ve do vuan cua canh v dirac ghi rrong 
cac lieu chuan thie't k£ Doi vrii cot co ti& (lien chu T cac ti£u chuin con it de c3p den. 
Suu day dua ra mot vai gioi ban co tfnh chat tham ichao. do tac gia de nghi. 

Lay v < — chi<!u cao ciia cot, d6ng thai: 
8 

Khi * c>0,[5hlayv<4c. 

0. 1 h < c < 0. J 5h iay v < 3c. 

0,05h<c<G.Jhlayv£2c. 

c<0.05hlay v <c. 
Dien tich tid't dien cliff T la A T ; 

A T = bh + (B - b) c 

Trong tarn hinh hoc cua tiet dien O each mep canh inOt doan y c va each mep si/cm 
mot doan v^..- 



.' w 



0.5bh-+O,5(B-b)c : 
y v = (3-1) 

Trong cam G each diein giura ciia tiet ditin I mot doan la d: 

d = 0.5h-y c (3-2) 

Momeii quan (inh cua tie"! dien lay doi voi true di qua trong tarn G va vu6ng goc voi 



canh h la: 



J-T<y^yc) + (B ,? >C + (B-bjc(y c -0.5cj 2 (3-3) 



3 " ^ 12 

Ban kinh quan (inh i va d6 manh %'. 

i= iJ ;X =T (3 - 4) 

3.2. NOI LUC VA D1EU KJEN TINH TOAK 

3.2.1. Noi Itxc 

Noi iuc de tinn toan tret dien chu T cung g6m \yc nen N va momen uO'n M nhimg d 
day can chu y momen M da diroc ia'y theo true nao, true di qua diem I hay true di qua 
diem G (hinh 3.2). 

97 



Gpi M| - mOmen uon doi vai true qua I. 
Mq - mdrnen udn doi v6i true qua G. 
Mc = M, ± Nd 



Q.5h I 0.5H. 






m 



"if - 



♦ Aid 



— * — t 



/4yM e =M,-Nd 



->* 



Hinh 3.2: Ndi tucderinh lie: dieu cfv7T 



(3-5) 



Trong cong ihuc (3-5) lay dau (+) khi momen lam cho canh chiu keo. dau (-) 
khi momen lam cho canh chiu nen. 

Trong khj tfnh toan ket cau va lo hop noi luc can chu y la ciic momen da dude linh 
iheo iruc qua I hoac qua G. 

Khi chuyen m6men iCi Mj sang M^, ihl c6 ihe' Nay ra la M, va M c cuns chieu hoac 
khac chieu (M| la duong nhung M Cl la am). Thong thuotig. khi M, va M (; cung chieu ihl 
irong imh loan, du linn vco M ( hay M G cung khor.g co p khac biei. cln can linh dung gia 
irj do lech lam e va e" (e va e" kh6ng lhay doi khi n'nh vai M i hoac M G >. Khi M ( va M <; 
khac chieu ihl phai dao nguoe phep linh vi neu lay iheo chieu M| (gia tbu* la momen 
duong) ihj canh chiu nen con iheo chi£u M G (momen am) canh ircV ihanh chiu keo. 

N 



Do lech lam imh hoc: 



e, = 



(3-6a) 



Do lech lam ban dau e n : 

cau kien linh dinh: 
cau kien sieu linh; 



e o= e ! +e ; 



e rt = ma.\(e i .ej 



(3-6b) 



Vci e u la do lech tarn ng&u nhien (xcm muc 1-5.2}. 

Khi xei anh huong cua ud'n doc, do lech tarn iu e c tang len lhanh qc v6i r\ £ 1 duoc 
xac dinh iheo muc 1-5-3. 

Khi X = s- < 28 bo qua uon doc. lay r\ = 1 . Vdi >. > 28 can tfnh J iheo cong thtfc (3- 

L 

3)iinhN (ll lheoc6nglhi>c(l.l4)ho5c(1.16}irnhritheo(l-ll). 
98 



3.2.2. Cae trirdTig hop linh loan 

Tinh loan liet dien chir T duoc phdn Thanh hai truong hop chlnh tuy theo chieu cua 
M lam clio eanh bi nen hoac bi keo. Trong moi trucng hop chinh lai phan ihanh cac 
[rirong hap nen 16ch lum be, nen l#ch Kim Ian va iruong hop dac biel. De tinh loan col 
ibep con phan biet c6i thep do'i xiing hoflc khong do'i xung. 

So do phat trien cua bai loan the' hien 6 hinh 3.3. 

Tren hinh 3.3 da phan bi£t ra 14 truong hop tinh loan khac nhau. cuy viy van ia chua 
du. Khi canh chu T nam trong vung ehiu nen con can phan biet trtrong hop true trung 
hoa nam trong canh hoac cat qua sticm. 



Chuan to s6 iisg *x~ i-.vC. wi lieu 




ffin/r J.3. Scf do hai toast tilth n'e't dien chit T 



99 



3.2.3. Dieu kien tinh toan 

Tinh toan tje't di§n bfitdng c6't thep iheo trang thai gici nan ve kha nang chiu lac ciSn 
tu&n theo cac d'teu kl&n vi do ben a (1.19) va (1.20) va eic chS din b muc 1.6. J . Tuttig ty 
nhtf d<5i v6i tiet didn chir nhSt. true U de lay mo men thuong du<x chpn di qua irong tarn 
cO't thep A w hoac A^, va nhir v&y }\ = Ne hofic Ne'. E>i£u kien { 1 .20) duoc cu xhi hoa thanh: 



Ne<M 



ign 



Ne'^M 



2gh 



(3-7) 

(3-8) 



Trong do: 

e - khoang each tir diem dat luc l&ch lam N den irong lam cot thep chiu keo 
(hoac nen it); 

e' - khoang each tCr diem dat lire l&ch tam N den trong tam cot thep chiu nen 
(hoac nen nhi&j). 

3.3. TIET DIEN C6 CANH BI NEN 

PhSn bict truong hop canh bi nen hay bi keo dua vao chifiu tac dung cua mo men M G . 
3.3.1. Cac trircmg hop tinh toan (hinh 3.4) 



a) 



J& 



^7 



i>) 


U- 




« 




1 
1 

I 




i. *** . 




e i 


e', 




III 




i 


il 






y. 


' * 







ft. 



c) 


e 


N 


e' 




i 


• 


1 


•. 




i 






e , 



Li *. 



: wmw, 



(*>£A 



worn 



Hinh 3.4, Cue frtt&ng http canh bi nen 



100 



Tuy theo tirong quan ciia vung chiu nen mil co the xay ra: 

a) Nen lech tarn ton khi x < c^h oy rrong d6 con co cac crtfdttg hop cfac bict x < c 
(true tung lioa n3rn trong canh va x < 2a,. (a. ddng vui trd a' ia khoang each lir irong tarn 
cot thep chiu nen den inep chiu nen cua tier di£n). 

b) N r en l£ch [am be khi x > t K h v6\ hai tri/ong hop: tier dien co mot phan Ion chiu 
nen (phan nho chiu keo) (hlnh 3.4c) va toan bo tiet dien chiu nen (hlnh 3.^d). 

3.3.2. Cong thik co ban 

Trireme hop chung ifnh to;tn dya \ : ao dieu kien [3-7). truong hop dac biec. dung dieu 
kien (3-8) trang do: 

e = T]e i ,+y ll -a sx (3-9) 

Khi luc doc dai ra ngoai tiei dien thi: 

e '=e-Za =1^ + ^-3^ (3-10) 

33.2.1. Tnr&ng hop trite trung hoa qua canh 

M,, h =R,Bxih i> -0.5x) + o; A,z, (3-11) 

N = N d] = R.Bx-a; A. ~o\A.. v (3-12) 

Oieu kien la \<c. 

3.3.2.2. Truung hop true (rung had qua suifu 

M fBh =R f) bx(h il -0.5x)'R t> (B'b)c(h iJ ^0,5cV-^G7; A,z rt (3-13) 

.N* ( . n ^R b tHc + R,lB-b)c+a; A L -o\A w (3-14) 

3.3.2.3. Gia Iri cua <x 5 va a[ 

Khi thoa man x < lRh thi o, = R,.: 
Khi Thoa man x > ?.a c thi cr^ = R vC : 

Khi dOng Ihoi Thoa man: 2a c < x <£ ft h di6u kiSn (3-14) rrath.vin!i.<3-15): 

N = R b bx^-R b (B-b)c-R sc A c -RAv (3-15) 

33.2.4. Qid tri <r 4 vtf x khi nen lech lam be 

Khi x > q K h xay ra nen lech tarn be. o s < R s va co the la keo hoac ncn. Luc nay. de 
xac dinh x co the dung phirong trinh (3-14) irong do lay quan he cua x va o\ theo cong 
thu-c (1.23) hoac (1.23a), viet lai dirdiday (3-16). 

101 



o\. = 



c, - 



1- 



2(x-^ R h p ) 

n^ R h 



R. 



> 



' 2 l-x/h ) N 



l-^R 



R. 



(3-16) (l-23a) 
(3-16) (1.23) 



/ 



Cung co the dung cojig thiic thuc n°hiem de xac dinh x: 

Cl-4 R )C0.Sy c -c o ) 



x = 



3= 



O.Sv. 



(3-17) 



Khie >0Jiy t layx = * R h o 

3.33. Trutmg hop dac biet 

Nen lech tarn Ian. khi xay ra x < 2a c (ih$c nliien cong nhan x < ^ R h de co cr v = R N ) 
Luc nay d&flg di£u kien (3-8) de n'nh loan, tron£ do: 



Mj»'MA+Mi 



(>!S> 



Trong do: My - momen cua n6i lire irony b£ i6ng viing nen. Twang hop iruc (rung 
hort 11am irong canh. >. £ c. linn M B iheo (3- 18); 



M H =0.8R b Bx 



x 
a. — - 



(>J.s;i. 



Tuy vay irong iihieu iruons hop, de* don gian hoa n'nh loan va ihien ve an loan co llie 
lay M B = vl kha be. 

3.3.4. Tilth toan cot Ihep doi xung 

Biel ki'ch thircfc liel dien. cbieu dai n'nh loan I c , noi lire gom N va M (co chieu gay 
cho canh chiu mn). Bsei dac irung cua vai lieu (R h . £ h , R s , R v _) h£ so i%. Gin linh loan 

cot (hep doi xi'mg A % = A c . 

3.3.4.2. Chudn bi so lieu 

Gia ihiel a tt .. a e dc linh h = h - a u . va Z a = h u - a,.. 

Tinh y pi y w , J; i. >.. xet anh buong uo'n doc. xac dinh v\. 

Khi X*^-<28 c6Theb6quau6ndoc.Ti = l. 
i 

KhiX>28.n'nb*N lh .n 



102 



Tinh G] =— : e 

Khi tfoh dp lech tarn tinh hoc c } can chii y la gia til momen M da dutrc lay do'i v6i 
true qua trong tam G. t>T£u M da biet duoc lay do'i voi true qua [rung diem O thi can tinh 
Mq iheo cong Thuc (3-5). 

Tinh do lech tam e theo cong [hue (3-9). 

3.3.4.2. Lap cong ihuc tinh todn theo cac trtf&ng hop voi R s , = R^ 

Voi A s = A, va R xc = R s , gia thw't x thoa man dieu kien 2a c < x < %%h n tir dieu ki£n 
(3-15) rut ia bicu ihuc tinh x va tam dat la X|- 

x, = ^ u -^J 

R b b 

Dua vac x, de phan biet cac irudng hop tinh toan. 

a) Truong hop I. Khi \ > c dong ihoi x, > 2a c . Dung d*eu ki.;''. '3-7) trong do iM.,. ; 
theo '3-13) voi o>R sC . 

^ ^ Ne-R h bX:h,-0.Jx)-R^B-bic(h o -n.x) 

R sc Z :i 

Trong do: khi \, < c R h u - nen icch tam Ion. lay x = \ ]m 

Khi Xj > ; R h„ - nen lech tarn be. c6 the* lay x theo cong thuc thirc nghiem (3-16) 
hoac lap va giai he* phuong rrinh uuong tir nhir dot voi tiet dien chir nhat) de dong then 
xac dinh x v& o\ Cdt tbep doi xuns. lay A, v = A c . 

b} Trudng hop 2. Khi x ( >cma\|< 2a c (mac rxliien cong nhan x <^h u ). Dung cong 
ihuc cua dieu kien dac biet (3-8) va (3-17) trong do dung x = c de' tinh M. B iheo (3- 18): 

A N*'-Mp N(«-Z,)-M. 

" RA R«z, 

Coi ihep do'i xtmg, lay A c = A. A . 

c) Truons hop 3. Khi x, < c. Can u'nh gia iri x theo cong thuc (3-22) rut ia tir (3-12) 
voi o\A c =ov-V v : 

N 
X=-— (3-22) 



R,B 



103 



Dieu kien la x < c. 

Khi x > 2a c tinh col thep iheo cong thtic (3-23) duoc rut ra lis diSu ki£n (3-7) va 
cong thuc (3-11) voi a{ ^ R^ : ' 

Ne-R,Bx(h c -0.3x) 
Khi X <2a c .linhA„ iheo c6ng thu-c (3-24) rut lit cong thirc (3-2i)v6i M E = 0. 

Z = max (Z d = h - a. va Z, = h fl - 0.5c) 

3.3.5. Tinh toan cot (hep khong C(i\ xirn« 

So' lieu da biet va chuan bi so' lieu de linh toan nfui irong m tic 3.3 4. 1. 

De phun hiet uucnxg hop oca lech lam la Lon hay be, lav r.itfang hap phau gidi 
x h = ^^h© ^m c huari. Tim vi irf irong lam vune nen Q, co khoang each den rnep cua 
canb la Vq. Vdi x R > c co: 



Cs bSn *Q.3(B-M c-' 
bx R -*-(B-bic 



}g= T-* ,.. . - tf-25J 



Khoang each Ut Q den irong iam G cua lie! dien ia d f : 

d,=y c -y Q (3-26) 

Xem la nm lech lam Ion khi Tie,, > l.25d, va nguoc lai. 

3.3.5.1. ;\en lech lam ton 

Khi xay ra rte (i > l,25d ( , u'nh toan iheo nen iech lam Ion. Luc nay co hai phucmg 

frinh (3-13), (3-15) de xac dinli 3 an so' la A„. A_ va x. Co the giai bang each chon iruoc 
x hoac A c (col thep chiu nen). 

a) Chon tiuoc x. Co Hie tu chon m6t eia tri x dong then ihoa man cac dieu kien: 
x < ^ R h. (1 ; x > c ; x > 2a t . tinh duoc A c theo c6ng ibtfc (3-20). 

Kbi A c > 0, tur (3-15) rut ra cong ihiic A w : 

K = R h bx*R,(B-h)c + R u .A c -N p27) 

104 



Khi Tinh dvqc A, < thi hoac la giam x de tfnh lai hoac la chon A c iheo caii tao de 
tfnh theo muc b. Co the giam \ din gia iri nho nhat bang max (c va 2a c ). 

b) Chon [rude A c . Co the biei inroc A c bang each chon dat theo cau tao hoac v) mot 
li do nao do ma da co sfln cm ihep clai trong phan canh. COng co the xem A^ = (thi 
xem la ceit thep cau tao. khone ke vao Uona Cinh loan). Luc nay can xac dinh vj iri true 
trung hoa b3ng each tinh M c . 

M L =R b Ec(h ll ^0,5c) + R, t A c Z J (3-28) 

Truftng hop I . Khi Ne > \\. true trung hoa qua sudn. 

Tfnh: M b = R s (B-b)clh (1 -0.5c; Z^A.Z U (3-29) 

^=^% !3-30> 



4=1-^1-2^ 

\ = l\u (3-3!) 

Dieu kicn la x <£ l7 h () (c < 1^\ dong ihdi x > c va x > 2a'. Thay gia iq x va A c vao 
eong ilurc i3-27i de iinh A w . 

Truonu hop 2. Khi Ne < M._ True trung hoa qua canh (x < c). 

R b Bh; 



4 = l-^l-2ct n .( : x=4h„ C3-3U) 

Khi x > 2a.. tfnh A. A . theo cons thuc (3-32): 

R s 

Khi x < 2a £ . ke" ca khi ct_,, < 0. linn A. A iheo ccVig thixc (3-24) ihuoc truing hop 
dac biei. 

33.5.2. N4n tech tarn be 

Khi xay ra r\t it < l,25d,. tinh loan theo nen l£ch lam be. Tinh x tjifta c6ng chut 

(hire ngliiem (3-16). Kie'm tra dieu kien x > c. Tinh cot thep A c (heo cone thuc (3-2U). 
Chon A vv theo dieu kien: 

A w > max «X0025bh o va C A C ) 

105 



Gia In O c lay phu rhuoc vao ti so e|/d,. 



e,/d, 





0,2 0.4 


0,6 


0.8 1 


1,1 


1,25 


6c 


1 


0.85 


0.70 


0.55 


0.4 1 0.30 

i 


0.34 


0.40 



Truong hop dac bi£(. Voi nen lech tarn be, Jchi thoa man dicii kien 0.2y c < t\c 

< 0.8y c co the* tinh loan voi gia thiet A w = (xem cd'( ihep 6 phfa chiu keo hoac nen it la 
hoar> toan dai theo call iao. khdng ke vao irong tinh loan). Luc nay ket hop phuong trinh 
(3-7) vm phuong trinh (3-14) trong do M uh lay theo (3-13), cho A w ~ va o^ = R sc dua 
ve mot phucmg irinh b&c hai cua x: 



R b bx 



= N(Z 3 ~e)-R b (B~b)cf|-a c 



(3-33) 



V2 f 

Cung co the dal duc*c phircmg trinh (3-33) bang each lay m6men cac luc doi vol true 
di qua Irong tarn A c . 

De tranh vice giai phirong irinh bac hai, dem dal a a =— : T = a il (0.5a. l -1). 

a 



Tinh diroc: 



T = 



N(Z.. -e)-R h (B-b)c(0.5c-a.) 



* K 



(3-34) 



ct 



= ]Wl+2T 



x = o,a t 
Dieu kien cua x la: c < x < h. 
Co dirge x. dem fliay vao cons thiic (3-35) de (inh A c : 
N~R b nx-R b (B-b)c 



A_ = 



R- 



(3-35) 



Ne'u tinh diroc x > h thi khong the' ho qua A w . 

3.3.6. Danh gia va xtr li ket qua 

Col ihcp tinh dupe theo cac cong thuc da lap co ths" ia duong hoac am, 16n hoac be. 



Danh gia sir hop U bang each tinh li 1£ cOt thep: 
106 



' ^ te ^ = M^,G0% 



bh. 



bh. 



Dieu kien la: u^ <u s <u M . 

Ne'u iinh diroc u^qua be. tham chi col thep am chung 16 kich thuoc qua Ion va 
ngircfc iai. 

Sau khi da chon va bo tri cot thep can xae dinh cac tri so a w , a,, tmli lai h va Z a . Khi 
1\, vi Zj tinh duor rheo cau tao thue te ciia cot thep deu Ion hem cac giii tri da dung dt 
ti'nh roan fa w va a_ iheo gia thiet) la co kcl qua thieri \i an loan. 

3.3.7. Kiem tra kha nang chiu lire 

Biet kich ihuoc liet dien va cau tao co'i thep. / . Yeu cau kiem tn xem tiei dien co du 
kha nang chju cap noi luc M. N hay khong. trong do M duexe lay doi vcfi trong tam G cua 
net dien va co chieu lam cho canh chiu oen. 

3.3.7.1. Chudn bi so lieu 

Voi cd'f thep da bier, xac dinh A w , A c . a w , a c , u'nh h , Z,. Tra cac so lieu R,,, E^, R,. 
R H .» £, R . Tinh loan y c « y^, J. Xet anh huenvg uon doc, xac dinh ti. tinh toan do !6cK tan* 

e l ,e .e. 

3.3.7.2. Lap cang thitc tinh todit cho cac tnrong h<Xp 

Truoc net tam gia thiol trudne hop non lech tain Ion co true (rung hoa di qua sudn: 
x < 4k '\j : x - c d6ng that x > 2j c . Tinh x iheo cong (hire (3-36) nit ra tu cici: .'uen (3- 15) 

vadat la x>. 

^ N , RA . Rb(B . bic -R A 

R„b 

Dira vao gia tri x, d£ phan dinh cac trudng hop. 

a) Truong hop 1. Khi ihoa man cac dieu kien da neu ra iron;: «ia *hiei 
(x 2 -4ft n o ; x 3 > cdongihoi x-. > 2a c ) tht la"y x = x-^ vii a' = R\ thay vao cong thuc (3-13) 

de tinh M, gh , kiem tra iheo dieu kien (3-7). 

b) Truotig hop 2. Khi x, ££#h a \ x 2 £ c njiimg x 2 < 2a^.. Tinh toan kiem tra iheo 

truong hop dac biet, ti'nh M :gtl theo c6ng thuc (3-17) trong do lay x = c dc tinh M n theo 
cons thuc (3-18). Kiem ira theo dieu kien (3-8). 

c) Truong hop 3. Khi x-> < c (mac nhien xem x < cr!i ) can tinh £ Iheo cong ihuc 
(3-37a) nit ra tu (3-12). 

R b B 

107 



KM x > 2a', tinh M lp ^ theo cong thtic (3-11) vdi o\ = R u . va kiem ira theo dieu 
kien (3-7). 

Khi x < 2a 1 linh M 2gh tlieo cong thiic (3-17) irong do lay M B = 0. kie"m ira theo dieu 
ki£n (2-8). 

d) Trucmg hop 4. Khi x 2 > £ R h„. Can xac dinh lai x. 

Tir hai phircmg lnrili(3-14) va (3-16) nil rac6og ihurc tinh x: 

Dieu kien la c, R h„ < x < h . 

Co duoc x. dem ihay vao cong thtic (3-13) veVi a[ = R^. de* linh M,„ h va kiem ira 
theo dieu kien (3-7). 

3.3.8. Bieu do tucmg tac 

De vc bicu do tuong [ac cua lie! dien chu T co canh trong vung nen cung tien hanh 
nhir doi v&i u€l dien Chi? nhftl, co the* dung mot so phuons phap kliac nhau. trong do 
phuong phap dung bie'n so iron* gian x Va thuan loi hon ca. Dau tien linh \6t N = 0, tim 
gta in x 5 theo cong ihuc Q-3&) (la cong thiic 3.36 voi N = 0j. 

_ RA,-MB-b)c-RA 
x,- — (3-38) 

Khi x 3 < s R li lt ddng thai x 3 > c; x 3 > 2a,. tinh M theo cong thuc (3-39) trong rid lay 
x = x. v 

M (l =R l% bx(h i) -O.5x>-R ? (B-b)cih 1 -0,5c)-rR^.A^Z J (3-39) 

Khi x > c ma x < 2a_ (mac nhien xem x <i R h ) : 

M„ = M w Z*+Mb (3-40) 

Trong do M 3 tinh theo (3-J8) v-6i x = c. 

Khi X-, < c. true irung hoa ndm Irong canh. (bao gom ca trifdng hop x^ < 0), tinh x c 
theo cong ihuc (3-41): 

R.A.-R.A 

R b B 

Khi x v . > 2a 1 .:::!. M e theo (3-42). 
108 



M = R b Bx,(h o -0.5x i: ) + R w A c Z J (3-42) 

KM x, < 2\ tinh M ibeo c6ng thu-c (3-43); 

M -R S AZ (3-43) 

Trong do; Z = max (Z ;i : Z c = h - 0,5c) 

K.hi x 3 > £Rh n u'nh M thco c6ng ihuc (3-39) trong do lay x = c R h u . 

Tinh tifi'p vcri cac gia tri khac cua x; x = x 3 + Ax. Uhg vai moi gia iri cua x fun duc/c 
NvaM". 

3.4. TIE! DlENCQ CANH BI KEO 

3.4.1. Cac Iruonj* hop tinh loan 

Dim v«ao chieu cua momen M = .M de biel duac trucmg liap canh hi keo do tac dung 
cua momen uon (khi ke" ca lye nen N thi canh co rhe bi k£o hoAc bi nen it hem). Luc nay 
col ihep dal phfa sucm A w la chiu nen. cot thep dat phfa canh A c chiu keo hoac nen ft hen. 
Dira vao gia iri ehieu cao vung nen x d£ phan biei nen lech tain Ion (x < £ ft h„) va nen 

lech lam be {x >c R h it ). 

Tn&tig hap J. Khi .\ < h - c. Toan bd canh chiu keo (hinh 3.5a). Bo qua sit lam vice 
cua belong phan canh. Lap cong ihuc linh toan nhu d<5i voi tiei dien chu nhai bxh. col 
ihep A, = A c ; A', = A„, 



,' 



. *% J 



4 




3.i 






■■■ 






K\ 




Hinh 35: Cac tnfertig hap canh hi keo 



109 



Trudng hap 2. Khi x > h — c, canh co mot phan hoac loan bo chiu nen, Ihucrng chi co 
the xay ra vol trirdng hop nen lech tarn rat be. 

3.4.2. Dieu kien tinh toan, c6ng thirc ccr ban 

Dieu kien tfnb toan la dieu ki6n chung (3-7). trong d<5: 

e = n«„ + y c - a c < 3 " 44 ) 

Truoiig hop dac biet dung dieu kien (3-8). 

Cong thifc tinh M|„ h , M 2 g h duac thanh lap my thco gia tri cua x. 

3.4.2.1- Trtf&ng hop cdnh chiu keo toan bo 

Khi canh chiu keo toan b6; x < h - c: xac dinh M lfh theo cong thirc (2-4). vol cac 
chi dan ve xac dmh x ibeo muc 2. J. 2. Truane hop dac bifit, khi x < 2a„ tinh M 2ch theo 
cong thuc (2- J 2). 

3.4.2.2. Trttfrng hop cdnh c6 mot phan chiu nen 

Nen lech tam be. khi tinh duac x > h - c thi canh cd mot phan chiu nen. Dai x c = x 
+ c-h la clueu cao phan chiu nen cua canh. Tinh kha nana chiu lire iheo cong thuc (3-45): 

M Jr ^R h bxfh o -^;M).8R b iB-blx,(c- il(: -0.5x^ + R,A tt 2, (3-45) 
N = N gh = R b b * + 0.8R b (B - b)x c t R s: A„ - o\A c (3-45u) 

3.4.3. Tinh loan cd't thep doi xirng 

Dieu kien va chuan bi so li£u giona nhu 6 ede muc 2.2.1 va 3.3.5.1. Chu y rnomen 
M duac fay doi vefl true qua trong lam G va co chieu lam cho canh bi keo. 

Trirac hoi linh Xj theo c6iig thuc (2-13) vict hi (hanh (3-46): 

X]=— (3-46) (2-13) 

R fc b 

Dua vao %\i tri cua k, de phfcn biel cac uucmg hop tinh toan. 

3.4. 3 J. Nen lech tarn l&n thong thuong 

Khi x 3 < 4 R h a dong thai x, 2 2a tt (2a) lay x = x- thay vao cong (hue (3-47), viet lai 
tu cong thuc (2-14) dc linh A w . Cot ihep doi xung lay A c = A n . 



A<rg N( e + 0.5x-h o j (3.47)(2-14» 

110 



Rs t z. 



3.4.3.2. i\'en lech lain l&n, ddc biet 

Khi x | < 2a, . dun* cong thtfc (3-48) de tinh A c , lay A w = A c . 

A ^ = N (c-ZJ (3-48) (2- IS) 

3.4.33, Nen lech tarn be thong thicang 

Khi x, > S^h , can xac dinh x iheo cac chi dan 6* muc 2.2.3.2. bang each giai phiiong 
irinh (2-15). pbucmg irinh buc ba ciia x hoac co the dung cong thiic gdn dung (2-10)- Khi 
co duoe x < h - c dung cong thiic (3-49) viet 3ai tt/cong ihirc (2-17) de tinti i\ s . 



A,, = 



= Nc-R v bx(h p -0,5x) (3-49X2-17) 



RA 



Cot thep do'i xung lily A c = A H . 

3.4.3.4. Nen tech tarn be d&c biet 

Khi tfnh ducc x > h - c. true [rung hoa nam trong canh, canh co mot phan chiu nen. 
co truemg hop d5c biet. phai u'nh lai x iheo each khac. 

Kel hop pbu'cmg irinh can bang lire, phticng trinh (3-16) quan he giua x va c\ co 
<liroe phuong irinh bac ha ciia x: 

x ; -h o (2-r^ R )x--Dx-E = (3-50) 

D = |^ + 2§ R h-+Z,(h-4 R h ) + (h-c)(c+h-2a)[ l~ 



R-o " ^ " \ B 



E = -^ae4 R h t , + hZ J -c R h,Z :i )^(h-c)(£ R h <> c + hZ a ) 



B 



Giai phirong trinh (3-46) Urn x. Dieu kicn la h - c < x < h. Dem x thay vao cong 
thurc (3-45) rut ra cong thuc tinh A„.- 

_ Ne-R h bx(h fl -x/2)-0,SR^B-b)x c (c-a,-0.5x c ) 

A w - — — (JO I) 

Troag do x c = x + c — h. 

Celt thep dtii xihig tay A c = A w . 

3-4.4. Tinh toan col Ihep khong doi xtrng 

Lay trirong hop phan giai cua vung nen. x =£ R b„, tinh khoang each d-> tu trong tarn 
vung nen ciia Inrcmg hop nay den trong tarn G cua tiet dten. 

Ill 



d 2 = y w -0,5^h o (3-52) 

So sanh dp lech tarn r|e \*6i d 2 dz phan bifet tnrong bop tinh todn. 

3.4.4.1. Nen lech tdm l&n 

Tinh loan iheo nen l£ch tam Ion kh! r\z > 1.25d 2 . 

Luc nay co th£ tinh loan bang each clio trade x ho5c A w (A' t ). 

a) Cho tnrcc x, Co th£ chon mot gia iri x ihoa man cac dieu kien 2a^ < x < £ R h„. 
thay'vao cong thuc (3-49) de* tinh A^,.. 

Khi A w . > thl thay A w , va x vao cong thuc (3-53) de tinh cot thep chiu keo A c : 

Ac= R,b S + R w A.-N (3-53) (2-20) 

Neu tfnh dupe A ft < thi giarn x de tfnh lai hoac chuyen sans tinh loan theo truong 
hop b. 

b) Chpn truoc coi (hep chiu nen A„.. 

Co Ihe chon trade hoac biet trtfoc A„. linh A.. Dung cong thuc (2-22) va (2-23) de 
linh o m va t. Tinh .x = £h„va Idem ira dieu kien: 2a tt < x S ^h,,- Khi dieu kien ve x 

dupe ihoa man ihi dung cong ihuc (2-20) de" tinh A c . 

Khi x > £ph„ chung to A w da biet Ja qua be, can tang len hoac tinh iheo muc a. 

Khi x < 2a w , ke ca truxmg hop a m < 0, tinh A c theo trifotig hop dac biet. dung cong 
thuc (3-48). 

3.4.4.2. Nen lech tam be thong thu&ng 

Khi nje n < l,25d 2 tinh toan theo nen l£ch tarn be. 

Xac djnh x ibeo cong thuc [hire nshiem (2-JO) hoac (2-11). Khi ihoa man dieu kien 
c R h„ < x < h - c, dung cong thuc (3-49) de' tinh cot thep chiu nen nhieu A w . Cot thep A c 
ducc chon theo ca'u lao iheo dieu ben (2-28). 

3.4.4.3. Nen lech lam be dac biet 

Khi tinh dupe x > h - c. co truong hop dac biet. Luc nay neu T)e„ < 0.4d 2 nen tinh 
loan va ca'u tao cot thep doi ximg. Khi 0,4d 2 < ne,, < l,2d 2 . chon dat A c theo ca'u tao. 
tfnh x iCr phuong trinh (3-54): 

x 2 -2a c x + F = (3-543 

312 



_ 2N(e-Z,) , < bl 

F = l! -^(h-c){c + h-2Z 1 -2a.)| 1 — 

Dieu ki6n la h - c £ x < h. 

Co dirge x dem (hay vao c6ng shut (3-47) &£ ilnli A tt . 

3.4.5. Danh gia va xii" li ket qua 

Vice danh gia va xu li ket qua tmh col thep trirong hop khong ddi xung cung tien 
hanh nhu trirong hap do'i ximg da irinh bay a mue 3.37. 

3.4-6. Kietn ira kha nang chiu lire 

Vtii [Lei di<*n da bt£'L ki6m tra xcm co du kha nang chiu cap not luc M. N irong do M 
duoc lay doi vch true qua irong tarn G cua lie! dien (M = Mq) va tiic dung cua M lam 
cho canh bi keo. Luc nay eoi thep \ v 6 irong stron la col thep chiu nen. 

Triroc her gia ihiet truong hop chiu nen i£ch tam Ion thong rhuong, ihoa man dieu 
kien 2a ta s xS ^aA, ■ 'Hnh x 2 theo cona ihut (3-55). chep lai lir (2-34). 

R h b 
Dira vao \^ de phan biet cac irirdng hop u'nh loan 

3.4.6 .1. Sen lech lam l&n thong thit&ng 

Khi thoa man dieu kien 2a,,. < x-, < ^Rh ()> lay x - x 2 thay vao con<r thixc (3-56) 
de u'nh M !nh . 

M lL , K =R b bxJ'h J -^R, c A w Z ;i <3o6)(2-4) 

Dung dieu kien (3-7) de' kiem ira. Irong do u'nh e theo (3-44). 

3.4.6.2. Nen tech (dm lo'n dac biet 

Khi xay ra x : < 2a c , cd iruong hop dac bi£i. Tfnh M 2gtl iheo cong thuc (3-57) chep 
laiiir(2-12b). 

M 2gh = R,A c Z a (3-57) (2- 12b) 

Va kie'm ira iheo dieu kien (3-S) voi c' = e - Z r 

3.4.6.3. Nen lech tarn be tilting thu&ng 

Tinh chieu cao vung nen iheo c6ng thdc (3-58) chep iai til (2-35): 

113 



^. (N-RgA^h-JUhJ + RACb + W n 58) (2 35) 

R b b(h-4 R h )-r2R s A c 

Didu kien cua x la ^ R h < x < h - c 

Vol x thoa mail dieu kien tren day. thay x vao cong thuc (3-56) de' linh M )& h va 
kiem tra theo dieu kien (3-7). 

3-4.6.4. Nen lech tarn be dac biet 

Khi xay ra x > h - c, co trudng hop dac biet. Tinh ]ai gia tri cua x: 

;c _ <N»R h <B-bKh-c>-R < A.(h-5 K h,)rR.A c <hHRh.) n 59) 

RB(h-^ R h ) + 2R t A c 

Dieu kien la h - c < x < h. Ti'nh x c = x + c — h. 

Thay x va x. vao coiig thuc (3-45) de tj'nh M Jch . Kiem tra theo dieu kien (3-7) trong 
doe tinh theo (3-44). 

3.4.7. tficu do tiron" lac 

De lap l>icu do tuong lac cho lie'i dien chu T co canh irong viing keo (hoac nen it luni). 
dung x lam bieb so irung sum. 1 rtroc bet cho \ hieii thien irong khoang < x < h - c va 
itnh loan nhu do'i voi net dien chu nhai b * h cd coi thep chju keo A s = A., cot ihep chin 
nen A' v - A u , da duoc icinh bay trong myc 2.5.3 va 2.5.7. Tiep den cho x bien thien 
trong jthoang tiep theo )i - c < x <: h. Dung cons thuc (3-16) de tinh o\ (vol x > srX )■ 

Tinh N theo cong thiic (3-45a). ti'nh M Iph theo cons thuc (3-45). Ttr M, Jh tinh ra duoc 
M = Nne p vol chu y M, gh = Ne = N (n^ c * >'- - a c ). 

3.5. HNK TIET DIEN CHU" T V'Ol NHIEU CAP NO[ LUC 

Viec tinh loan voi nhieu cap noi lire cho liei dien chu nhAl da irmh bay trong muc 

2.6. Tinh loan tie'l dien chu Tcung lucrng ty nhu vay. 

Khi dal cot thep doi xung. chi viec tinh cot thep cho til ca cac cap ro*i chon lay nia 
tri Ion nhat. 

Khi dat cot thep khong doi xung vdi muc dich dung hop if va tie: kiem c6l thep thi 
viec ifnh toan tra nen kha phuc tap, nhat la Khi tinh vcVi cac cap co mo men ngiroc chieu 
\a chiu nen lech i3m Ion. Viec Up va dung bie'u d6 lucmg tac cung tuong doi phiic tap 
hoti so v6\ iiel dien chu nhat vi rnoi tie! dien can lap hai bieu <\6 tuong tac ibeo hai chieu 
cua m6 m*ft. Tuv vSy khi da lap duoc bieu d6 tuong tac ihi cd the dung dd kiem tra kha 
nang chiu lire cua rat nhidu cap noi Juc m6t each nhanh chong. 

114 



3.6. TINH TOAN TIET DIEN CHI* I 
3.6.1. Dai euwig ve tiet dien chu I 

Tiet dien chir I g6m co phan sumi va hai canh, ihong thuong Ja do"i xung qua hai true 
(hinh 3.6). Cot tie! dien chu I thuong gap la cac cor idp ghep trong cac nha cong nghicp. 
Trong nha dan dung ii gap cot del dien chO I. 

Cau cao col thep trong tier dien co hai each: 

a) Dat cot ihep chiu luc tap trung trong phan canh. trong plum sucm chi dfit cot thep 
cau tao (hi lib 3.6a). 

b) Dai coi ihep dim iuc gom hai phan. mot phan tap trung irony hai canh. phan con 
lai dat doc theo sudn (hinh 3.6b). 

COt theo cau 133 _ 

fil 



• 


! 






k 






• 




T 


* 


i 




* 






• 



* 1 



;6t ihep tfnu ijc 



Wfji/i J.6. 7" ft 1 : ti&fl dull 

3.6.2. Tinh toan trirung hap dat col Ihep tap trunt* 

Col thep doc chiu Luc duyc dat tap trung o hai phia nhu tren hinh 3.6a. Luc nay luon 
luon co mot canh chiu nen nhieu (canh kia chiu keo hoac chiu nen it lion). Bo qua sir 
linn vice cua be long trong canh chiu 3ceo (hoac nen it hen). Tin h loan tiet dien chu I 
theo nuong hop liet dien chuTcocanh chju nen. 

3.6.3. Tinh toan truxmg hop co col thep chiu life dat theo suxm 

De \ikp cong thuc itnh toan cho trucmg hop nay co the iheo phirong phap da trinh bay 
trong inuc 2.7 vci tiet dien chir nhat co cot thep d3t theo chu vi. Tlieo phuong phap nay 
can Idp biou do bien dang cua tiet dien. xac dinh bien dang va ung suat irong tung thanh 
coi ihep. ttr do lap ra c6ng thuc tfnh toan. dung dieu kien can bung lire. 

Caen r in h gan dung la phan chia tie* dien lam hai phan nhir tren hinh 3.7. Phan tiet 
dien chO" 1 voi cot thep dat tap trung 6* hai pht'a. chiu cap noi lux; M. N; phan tiet dien chi 
gom cac cot thep da! trong st/dn (khong co betong) chiu cap not luc M v ; N v . 

Theo Quy pham ihiet ke ket cau be tOng cua Trung Quoc GB500IO - 2002 klii dung 
cot thep co gidi han chay ro ring (R v < 400 fMPa) gia tri N v , M v duoc tfnh toan theo cac 
cong Ehtic sau: 



115 



r 



V 



I * 



\ -^ 









N. 





















\\K) 



: K//-#^ 






*T 



* t ' * ] 



JftnA 3.7: Stf do fifth tie) dien cint I co cd! (hep chnt hfC dgi fheo sit&a 



N v = 



M v = 



R.A, 



0,5- 



0.4«o ..' 
'£-0.8 



, O.to J _ 



RAh, 



Trong do: 

A v - dien tich tier dicn loan bo c6l ihep dar doc iheo siicm: 
h v - chi£u dai doan dat A v ; 

1 = — - - chieu cao lirong doi cua vuna nen; 

' K 
K 



(3-60) 



<3-6l> 



116 



Viec linh toan lien hanh iheo each gun dting dun. D;iu u6n gia thiet bo iri co» thep 
trong suon, gia thiet £j de ttnh N v . M v . Tier dien chiu cap noi luc M|. N,. 

Tinh phan r\6i lire M = M, - M v ; N ^ N, - N v . 

Dung cap noi lire M va N de tuth loan cot thep dut tap trung trong pham vi canh va 

x . - 

tinh di/ac x. Tinh lai gia tri ^ = — va tinh lai M V( N v - Tinh toan mot so I5n cho den krij 

K 

gia tri 4 dung de tinh va thu duoc sau khi linh gan bang nhau la duoc. 

3.7. THlDLTrfNH TOAN 

Tin du I . Cho lie! dien chu T co b = 40cm: h = 80cm; 

6 = 160; c = I Gem. Chicu cao cot H - 6m; chieti dai u'nh toan f = 4,2m. Be tony co 
R h = 9; E b = 24000 MPa; cot thep R s = R sC = 260MPa. Luc nen N = 2000 kN, mumen 
duoc linh vdi true di qua trung diem M| = 800 IcNm co chieu fam cho canh tiet dien chiu 
ncr). Do Ifich tarn ngdu nhien e^ = 4cm. Yeu cau linh c6*t thep <5oi Kung. 

Kiem tra cau tao cua tie'i dien: 

Do vucfn ciia canh; 

6-b 160-40 „ 
v = = = 60cm 

2 2 

c - 16cm > 0,1 5h = 12cm; v < 4c - 64cm -Thoa man. 

v = 60cm<-H = -x600 = 75crn. 
8 8 

Dien tfch tiet dien: 

A T = bh + <B - b) c = 40 x SO +■ (160 - 40)16 = 5 120 cm 2 

Toado trong tarn: 

0,5bh 2 +0.5(B-b)c ? 



y.: - 



A 



T 



0.5x40x30- +0,5x 20xl6 3 _ 
y,. = = 28cm = 280mm 

5120 

y w = h - y c = 300 - 280 = 520mm 
Khoang each tu trung diem O den trong tarn G; 
. d = 0.5h - y c = 400 - 280 - 120mm 



17 



Momen quan rinh J: 



40„„i „i. l2GxJ6 3 



J = ^i(28 3 -r52 3 ) + + 120*16(28-3) 2 = 2,976*10 6 cm 4 



Baa kinh quan n'nh i: 



i^= J =24. lcm = 241mm 

V 5120 

i 241 

Bo qua anh huong uon doc, tj - 1 . 

MOmen da cho la o*6i voi true qua diem giiia O. Tinh jn6men doi vol iruc qua trpng 
iam G. 

M G = M, ± Nd = 800 - 2000 x 0,1-1 = 560 kNm 
Gia Ihiel a w = a c = 50mm; h c = 800 - 50 = 750; Z a = 700mm. 

Doldehtam e, =- — = 0. 28m = 280mm 
1 2000 

c. ( = e, + e o = 280 + 40 = 320mm 

e = ne ( , + y w - a w = 1 x 320 + 520 - 50 = 790mm 

He so ; R . Voi R s = 260: R h = 9 co £ R = 0.64. 
= R h o = 0,64x 750 -480mm. 

Tinh toan cot ihep doi xiing. canh trong vung nen; 

N~R h (B-bte 2000 * 1 ? - 9(1 600 -400) 1 60 __ 
1 R b b 9x400 

X] < c = 160. Can linh hi x. 

N 2000x1000 _„_ 
X = = = 1 39mm < c ~ 1 60 

R n B 9*1600 
Ddng ihoi x > 2a. = 100. 

Ne~R u Bx(h -0,5x) 2000000-9x160x139(750-69,5) ,_„ 2 

A e ' ■ = i2Ut)mm 

R..-2. 260x700 



Co'i thep doi ximg lay A w - A c = 1200mm' 

2 x 1 200 

a = -— = 0,008 = 0.8^ 

400x750 



.8 



Thi dtt 2. Theo so lieu cua thi du I . yeu cau u'nh cot thep khbng d<3i xutis. 
Da ti'nb diroc: h c = 750: 2 a = 700mm; x R = g B h ri = 480 

e = 790 ;ric = 320mm. 
Tfnh y Q iheocong thuc (3-25): 

0.5b\J + 0.5(B~b)c 3 0.5x400x465 : +0.5* 1200* 160 2 .,. 
v = -j> = . _ — = 10 limn 

2 bx ft + (B - b )c 400 x 465 + ] 200 x 1 60 

<*] =y c -y = 280-161= 1 19mm 

r|e o =320> 1.25 d, = 1.25 x 119= 143mm. 
Tinh loan iheo nen lech tan) Icm, 
Chon x = 300inm < ; R h = 480; x > c = 160 : 

x > 2a_ = 100. 
Tinh Ac iteo cong ihuc (3-20)' 

A _ Ne-R.,bx(h, -0,5x)-R b (B-b)c(h -0,5c) 

20!)i"J(y':: .v7vO-^-<400x300t?50-i50i * 1200 < 160(75;.. - SO: 

A . = — < U 

200 x 700 

Tinh duoc A v 3m. chpu iheo cau iao: 

A. c > 0,0025 x 400 x 750 = 750 moT 
Chon A c = 3 4> 18 = 763 mm 2 . 

M c = R h Be(h d -0 ( Sc}+K w .A.Z jl 

M c = 9 x J600 x J60 1750 - SO) 4- 260 x 763 x 700 = 1682 x (0°. 
Ne = 2000.000 x 790 = 1580 x 10 6 < M c . 
True (rung hoa qua canh: 

tte-R^Z, 1580x10* -260x763x700 _ r __ 
R b Bh- 9xl600x750 2 



q = l~ 1 j'l-2a m[ =1-71-2x0,178 =0.1974 

x= 0,1974 x 750= 148mm <c = 160; x> 2^ = 100. 

Tmh A w theo cOng rhuc (3-32): 

_ R,,Bx + R vC A c -N _ 9x1600x148 + 260x763-200000 
A "~~ R. = ~ 260 



119 



A w = 1267mm* 

763 + 1^ 7 = 06?% 

s 400x750 

Thfdu 3. Cho ti£t dien aha hinh ve. 

Chieu diii linh loan t = 5,3m. Be tfing c6 R b 
= 1 3 MPa c6i thep co R, = R„ = 340 MPa. Cap 
noi lire K = 1600 KN, M = 519,2 kNm. Moment 
lay doi vdi true qua irojig tarn G va lam cho 
canh bi nen. Bo qua do lech tarn ngau nhien. 
Yeu cau tinh loan col thep cI6i xihig. 

So lieu: h - 300: h = 600: B = 700; c = 120mm. 

R b = 13: £ b = 29000; R N = R AC = 340MPa; 4 R =0.58 

Kiem tra kfch ihuoc canh: v = = 200mm. 

2 

c = 120 > 0.13h = 0.15 x 600 = 90; v < 4c = 480. Dat yeu cau. 

Dien u'ch: A T = 300 x 600 + (700 - 300) 120 = 22S0OO mm 2 




>'c = 



0.5x300x600^0,5x400x120' 



228000 
\\, = 600 - 249.5 = 350,5mm. 



= 249,5mm 



300 3 . ^ ,3, . 400xl2 : 



J=— ^^•^SO^-'- 
^SBx 10*mm 4 



12 



+ 400x120(249.5-60)" 



Ban kinh quan tinh i = 



7813x30' 



V 228000 



= 185 mm 



X = ^- = — - = 28.6 > 28 . Can ke* den u6a doc 
i IS5 



N ^2 1 ^ = 2,5x29000x7S13x l 0^ 2016xjQ6Niu 



'•* 



530fr 



N^ 20160 kN. 



120 



fcr ih 20160 

Gia thiet a, v = a c = 40mm; h = 560; Z a = 520mm- 

M il9 2 
e, = — = — = 0.3245m = 324, 5mm 

e a = 0: c c = e, + e a = 324,5cm. 

* = ne Q ■+ y w - a tt = 1.086x324 J + 350.5 -40 = 66 1.6mm 

N"-R h (B-b)c 1600000-9(700-300)120 nc „ 

x, = £ = = 250mm 

1 R b b 9x300 

4 R h = 0.58 x 560 = 308mm: x, = 250 < ; R h G 
Dong thai: x, > c = 120; x, > 2a* = 80. Lay x = x, = 250. 
Tinh A c iheo cong thifc (3-201: 

_ Nc-R b bx(h o -0.5x)-R,(B-b)c{h o -0.5c) 

M* 

1600000x661.6 -13k 300x250(560 -125) -13x400x? 20(560-60) (ani 

A = _ = f g24 

340x520 
Cot ihep doi xiJiig. idy A w = A c = 1824mm": 

2x1824 

M = = 0.0217^2.17%. 

300x560 



121 



Chircmg 4 
TIET DI$N TRON VA VONG KHUYEN 

4. ] . DAI CUDNG Vl C6T CO Tl£T Dl£N TRON VA VONG KHUYEN 
4.1.1. Hinh dang va cau tao 

Cot co tie! dien iron thirong duxfc dung trong cac nha dan dung va cong cong ihec 
yeu cau cua kifin true. Khi chju u6n va nen lech tarn tie't dien tron lam vice it hi£u qua 
lion so v<ji net dien chu nbat vi trong net dien iroixphan IoTi vat lieu tap trung gan true 
Irung hoa. Tuy vay liel dien Iron co tai diem la doi xung v<5i moi true qua Irong tam, do 
ltiaiih bang nhau theo moi phirong va trong ti'nh toan khong can phan biet nen lech turn 
phang hoac n£n lech tarn xien. 

C6i net di£n iron duoc dftt cot thep deu theo chu vt va thudng co so luong lu 6 ihanh 
tro len. Tuy vay vol nhCmg cot co duong kinh be (duoi 25cm) co the chi can dat ■* thanh 
hoiic 3 th4nh fneu chi dut theo cau iao) 

C6r co tie'i difcn vdng khuyen (hinh 4.2) ihuong la cac coi lip ghep duoc che iao san 
bang phuong phap li lam. CQng co the gap cac cot do tai cho a mot so cong irinh cong 
cong, d\nh chka, col do bHv ihip nude, ong khoi. . . 




* 





•; 




Hinh 4.L Ttti dtf-n iron 



Hinh 4.2. Tie) dien von? Ihmai 



Ve phirang dien chju lur net dien vdng khuyen hop !i hon net dien tron. nhuitg thi 
cong phur tap hon. 

Tie't di£n vong khuyen thuong duoc cau tao vol chicu day S < — D (D - duong kinh 

nsoai), ctft thep diroc dat theo chu vi voi so luong ttf 6 thanh tro len. Vc/i ciet dien viia 
phai va sd' luong cot thep khong nhieu ihi cot thep chi dal mot !6p. tren m6i vong tron 



122 



duong kinh D Jt Voi tiet di£n Ion. so tucmg col ihep nhiOu. co the* da( cot thep thanh hai 
lap (hinh 4.2a) voi duong kinh [rung birth D d . Trucmg hop d5c biet khi D kha be co the 

cau tao tiet di£n voi 5 > — D va s6' lirong cot thep it hon 6 thanh (hina 4.2c). 
Voi iiet dien iron: 
Dien lich lie! dien A b = ~ rrD* = m~ 

ivldmen uuan tinh J = — :iD"* = — txt 
64 4 

4.1.2, Gia thief ve cot thep 

Trong lie! dien ir6n va voog khuyen co cot thep dat diu iheo chu vi, de ihuan lien 
cho vice lap cong there tinh toan ngudi ta gia thiet cot thep duoc phan bo deu iren vong 

A 

iron duong kinh D 3 voi mat do la A = — — . tinh tren cung I radian. A sl la didn ifch toan 

2~ 

bo cot thep doc. D a = D - 2a voi a ta khoang each tu tarn ctft thep dfih mep ngoai tiet 

di£n. Khi bo tri cot (hep tren hai v6ng iron (hinh 4.2a) ma a m6i vong so c6t thep bang 

nhau ihi Dj la duong kinh trung binh ciia hai vong do. Chinh vi mud'n dung gia thiet nay 

ma co ydu cau so luong cot ihep khong it hon 6 thanh. Neii so lhanh col thep it hem 6 ihi 

khdng dung duoc gia Ihiet nay. 





Hinh ~f-3. So do tinh roai\ cua tiet dien 



4.1.3. Sit do ling sual 

Trong trucmg hop thong thirong, khi chiu nen lech tarn tie'i di£n duoc chia thanh 
hai vung: nen va keo. True trung hoa each me'p chju nen mot khoang x . Cung gidng 
nhu trong tiet dien chir nh&t. lay chieu cao tinh dot ciia vung nen la x (x < x c ) va xem 
rang irong pham vi dd ting suae trong belong vung nen phan bo de'u, bang cuong do 
tinh loan R b . 

123 



Gidi han cua viing nen la ir»6t 
dudng thang vu6ng goc voi mat phing 
uon va mep vung nen duoc chin boi 
goc 2<p (hinh 4,4). 

Xem rang col ihep chiu nen cung 
duoc gidi han trong pham vi g6c 2cp va 
ung sua't phan bo deV, dat gia iri cuong 
do tiiih toan R NC . 

Trong vung k£o, bo qua sir chiu luc 
cua belong va chi ke den sir lam vifcc 
cua col Ihep chiu keo irong pham vi 

goc 2q>|. Bo qua su chiu Luc cua col 
ihep Irong pham vi goc <p?, irong pham 
vi d6 mcM phan col ihep chiu keo, m6i 
phan chiu nen va ling sua'l deu ra'l be. 

(P,= 7t-(p-<p 2 . 

Tren bieu do bien dang, the hien e c 
[a bien dang Ion nhaj cua mep belong 
vung nen, e s Ik bien dang /on jilidc cua 
col ihep chiu keo. 




Hinh 4.4. So do t'ntg sua't ti/ih wan 



De don gian hoa viec li'nh loan gia ihiei irong pham vi cung 2<f>| ung sua't trong col 
Ihep chiu keo phan bo deu, co gia in R s . 

051 <j> 2 = V ?<P 'hi cpj = rc-(l+v 2 )cp. Gia iri v-, phu rhur)c vao goc cp. Khi <p la kha be 

v 2 > * v & 8'^™ xudag nhanh chong khi <j> lang len. Voi cac gia in irung blnh. ihucrng gap 
cua q> bang (0.3 ■*■ 0.6)ti ihl Vj (hay doi irons khoang 0,6 den 0.45. Thee lieu chuan 
TCXDVN 356 thi lay v, = 0.5 + 6R 5 10". 

4.1.4. Dieu kifcn li'nh loan, cong Ihtic co ban 
4 A '.4.1. N6i lire t'tnh toan 

Noi luc cinh loan g6m momen M va Juc doc N duoc dua ve thanh luc N dai each true 
cau kien m6i doan T|e voi n, > 1 la hs so' xei den uon doc. xac dinh iheo cong ihtfc (1.11), 

4.1.4.2. Dieu kien ve do ben 

D£ dam bao 66 b£n can thoa man cac didu ki£n chung (J.I 9), (1.20). Voi liet dien 
iron va vong khuyen. iruc de lay momen M u va M fh la duong [Jiang vuong goc voi mat 
phang uon va di qua irong tarn cua tid'i dien. DiSu kien ben duoc viei thanh: 



124 



N=N fih *N B + N; V -N A (4-1) 

Nne <M gh = M B ^M' A +M A (4-2) 

N B , N A . N A - hinh chicfu cua noi lire trong belong vung nen. etfi thep chiu nen va 
col ihcp chiu keo len phuong true ca'u kidn. 

M B . M A . M A - momen cua cac Lire ke iren lay doi vci true di qua trpng tarn cua 
tieC dien. 

4,1.4.3, Not life trong cot thep 

Trong ciei dien tron va vong 
khuyen. noi iuc N A . N. v M A . M A 

duo'c linh loan along nhau. Cho khac 
nhau giua hai tiet dien la each xac djnh 
N B va M B . 

Cot thep vung nen duoc gioi han 

boi goc 2<o. dien lien se fa 

A A 

A'=— ^2(&-— ^q>. G5t ihep vung 

27T 71 

keo se la A A = — — (p l . 




dA = AjOf i 



~Z. -r.cosu 



Hinh 4.5. Satlotinh not h(c 
irong co'( iiicp 



N A =^R,.p,:N A =^-R^ 

7? 71 



(4-3) 



Momcn =M A , M A diroc xac djnh theo phircmg phap itch phan. Lay bien so la goc a 

A 
nhu* iren hinh 4.5 vdi vi phan da. Vi phan cua dien tich cot thep la dA = A do = — — da . 

M A = 2j^XdAZ !1 = ^R^£cosadcc ^^k^simp (4-4a) 

7T 7* 






sin<j>, 



(4-4b) 



TCXDVN 356 - 2005 dat <p N = -^- va dua ra cong thtfc thuc nshiem: 

n 

(p^ = <0| - G> 2 ^ von 4 = — ■ 



a 



«i =l ir-^ : co 2 =(0,5; 



!25 



5=] +v 2 = ],5 + 6RJ(r. 

r| r - h£ so', la*y tuy thuoc vao loai col thep. Vdi cot (hep co gioi han chay thuc le (CI, 
CII. CI1I) lay n r = 1. Voi col thep co gioi han chay quy uoc (CIV, AIV...) lay ri f = 1.1. 

a sp - ung suat rrong c6x thep Lrng lire tnrdc. V6i cac c6i bang be t6ng cot thep thirong 
thi o\ p = 0. 

Vdi cac cot bang BTCT thong thirdng dung cac cot thep co gioi han chay thl: 

N A =AAcp s (4-3a) 

TCXDVN 356 trinh bay each tioh M A tneo cong ihiic (4-5): 

M A - N A Z S = AJ^ft?, (4-5) 

Z, - khoang each lii diem d5i N. den irong tam liet dien; Z s = — - 

TCXDVN 356 - 2005 dtfa ra cong ihite (hue nghiem xac dinh 2,: 

Z, = (0.2 +U£X (4-6) 

4.1.4.4. Cac truang hop tinh todn 

o 
TCXDVN 356 - 2005 dua ra hai irircfna hop tinh loan phu ihupc vao c = — . Khi c > 

0.15 ihi irong cong thuc (4-3a)dung <p, = <o, - m 2 l. 
Khi ^ < 0.15 thi lay £ = 0. I5de xac dinh ip,. vaZ,. 
Trong cac irucmg hop, khi u'nh dirge cp^ < Ehi )ay cp,. - va irong cac cong thuc IfL'y 

U| = G>2 - 0. 

4.2. TINH TOAN TIET DIEN TRON 

4.2.1. N6i luc Irong belong viing nen 

Dung phirong phap lay tfch prian. Bien so la goc a va da nhir uen hinh 4.6. Vi phan 
dien ttch viing nen la dB. 

dB = bdZ: b = 2rsina : Z - rcosa ; dZ = rsinada. 

N B = CR.dB = 2R b r 2 £W ada = *£*[» -^] (4-7) 

M B = J o X<*BZ = 2R b r 3 JW acosada = ^R b r 3 (sin<j>) 3 



126 



. T 



Trong Cong thurc (4-7) da dung A b = rcr" , nhu vSy r = — ^ . 

71 



(4-8) 



not htc Wong be idng 



4.2.2. Cong thuc ca ban 




Tinh toan can (uan Iheo dien kien (4-i), (4-2) trong do" cac ihanh phan cua N oh va 
M^ dupe xac djnh theo cong thurc {-1-3), (4-4). (4-5), (4-7), (4-8). Kit qua ia: 



2 R \ 

* 3:r 7t 



** it I. 2 



It 



(4-9) 
(4-10) 



4.2.3. Bai toan hiem tra kha nan" chiu lire 



Bie^t kich ihuoc tie! dien va coi thep. chieu dai tinh toan / , kiem Ira xem lie"t dien co 
du kha nang chiu cap n6i luc M. N. 

Tra cac so lieu R b ; E b ; R v 

Xac dinh a iheo cau tao. tinh r. r = r - a: dien u'ch tict dien A. dien lien toan bo cfl'r. 
lhepA S[ . 

Xet anh huong cua uo'n doc. \ D =— . KhiX$<l lay t\ = 1. KIu X D > 7 tinh J, N^ van;. 

M 

Tinh e, = — . Xet d6 lech lam neau nhien e... 
i N - • s 

voi kel cau linh dinh e = e t +- e r 
voi ket cau sjeu tinh e = max (cj, e a ). 

M*=Nne - 
Gia ihietco £ = — >0,I5. QioN=N atl = (4-IO), vdi<p, = co, -co^rutfaphuongtrinh: 



127 



Ti(N + RA<o>.) + 0.5R b Asin2 t p 
R b A+A SI (R, c +G> 2 Rj 

Neu tinh duoc ip = — <0,15 thi l£y I = 0.15 6i iinh <p s va Z 5 va xac dinh <p iheo 

7t 



phuong tcinh (4-12). 



7i(NRA,^)^Q-5R h A 5 in2<p 
R K A + R,„A. 



Giai phuong irinh sieu viet (4-1 1) hoftc (4-12) co the dung chuong trinh may iinh, 
dung phuong phap d6 thi hoac gaYi dung d£n. 

Co duo? cp diin° cong thirc (4-9) de xac dinh M E(1 va kiem tra theo dieu kien (4-2). 
4.2.4. Tinh loan cot thep 

Biet kich thudc nei dien, chieu daj itnh toan Z^. yeu ca"u iinh toan cot ihep A st dti de 
chiu cap n6ii luc M. N. 

Chuan bi c&c so lieu R^. E h , R s . Gia ihiei chieUi day lop dem a, tinh r. r a , dien tfch 

tiej di£n A. 

Xei anh huong uon doc, xac dinh r|: tfnh e y va M = Nne y . 

Hien lai chua co phuong phap tfnh iruc licp ra duoc A st mi ihuong phat dung each 
unh gan diing. dan va roi nhat ia lap chuong irinh cho may iinh. Co the lap chuong irinh 
tmh iheo phuong phap so gia gioi not nhu sau: 

Chon m6i gi& iri m a dc* bat dau tinh loan: 



<P = <P< = 



AR, 



co the' lay <J> i( - 1,5 + 2,5 va 4<j> = 0.08 + 0.12. 

Tfnh simp, sin V sin2<p va ru dieoj ki£n Nr|e = M"„ h = (4-a) rut ra: 

jsn,^,- — R^Arsh^c 

A, =- ^ (4-13) 

-R NC r a sin? + R^Z N 

Vai Ajh va <j> da co. u'nh gia trj N nh iheo cong thiic (4-10) 

So sanh N ah vira Tinh duoc vai N. Khi ma K rn < N thi uep tuc tinh vai gia tri moi ctia 
cp = tp, + A<p cho den khi dat duoc N p |, "2. N. 

Gia tri cin thi fit cua A v , ung vai trirong hop N 1 = N ffl . 
128 



Truong hop khdng co die*u kien Up va sir dung chirong irinh may rinh thi cung co 
the theo phuong phap tren de" imh bang lay va 6i giam nhe khdi lucmg linh loan thi sau 
rn<5i Ian cfrih can, phan lich kec qua nhan diroc de' chon Acp thich hap. 

4.2-5. Thi du ti'nh toan 

Thi dit I: Qio c<M iron thudc ket ca'u sieu imh dtfdng ktnli D = 40cm, Wtong cap 
cuong do 25. chieu dai rfnh toan f = 3m; cot Ihep dat deu theo chu vi 84*20 loai ihep 
RB400. Yeu cau fciem tra xcm col co du kha nang chiu cap npi lire N = SCO kN; 
M= [76kNm. 

So lieu: cap cuong do 25 co cuotig do tinh loan goc 14,5 MPa; E b = 30000 MPa. Cot 
Ihep RB 400. 

C6R,= RV=365MPa, 

Lop bao ve 3cm; a = 3 + <j>/2 - 4cm. 

r = 0.5D = 20cm = 200mm: r, = 160mm 

A = nr 2 = 3.14 x 200 : = 125600mm 2 ; A s[ = 8^20 = 2510mm* 

Xei uon doc; X n = — = = 7, 5 > 1 

° D 400 

J = — =— x4Q0~ = 12.566x10* mm J 
64 64 

N jjE^J M 2.5x30000x 12.566xl0^ |Q470QQQN . u " 

lh / 2 3OO0 2 

H lh = (0470kN 

N th 10470 

e, = — = - 0.22m ~ 220mm: Do lech lam n^Au nhien e„ = 20rnm 

1 N 800 ° a 

e = max (e, , e a ) = 220m. 

Nne - 800 x 1,08 x 0,22 = 190,08 kNm 

Theo phuong phap gan dung dan, gia thiet <p a Imh sin2(p J , linh lai tp b theo (4- 1 3a), so 
sanh q> b va <p a . 

Cot thep RB400 c6 gidi hanchay, lay co, = 1; 6= L5 + 6RJV* = 1,72. 
to 3 = co, 5 = 1 ,72. Theo (4-1 1) co: 

129 



_ 3.1416(800000 + 365x2510) + 0,5x34,5xl25600sin2<p 

i4,5xl25600 + (365 + 1.72x365)2510 

(p= 1,25 + 0.211 simp. 

Giai phuang irinh bang phuang phap gdn dung dan. 

Gia thiet <p a = 1,5 ; sin2(p a -0,1412. 

q) b = 1-25 + 0,211 x 0,1412= l^.Nhohorxp^ 1.5 da gia (hie't. 

Lay q>j = 1 .35; .$in2<p a = 0,42738: tinh lai duoc <p b = 1,34. 

Lay tp a = 1 ,343 n'nh racj> b = 1 .3428. Chap nhan (p = 1 ,343. 

i= *=i^2 = 0.4275>O.I5. 

71 3.14 

sing - 0.9"U : sinV - 0.924: sia2o = 0.44. 
Xacdinh M* h lheo<4-9): 

M h = ^R b ArsinV + — A^smcp+R^A^Z, 

Trong do ^^(0,-0)^ = 1 - 172;= 1 - 1,72x0.4275 = 0.2647 
Z, (0.2 -^ 1.3;)r, = ro.2 + 1,3 * 0.4275)160 = 121mm. 

M„ h = — x 14.5 x 125600^200x0,924-- x 365 x 2510 * 160x0.974 + 

3-1 7i 

+ 365 x 25 10 x 0,2647 x 121 = 146,2 x 10* 

Ni)e c = 190.08 > M ch . Tiet dien chua du k)ia nans chin lite. 

Thi du 2. Voi so lidu nhu ihi du I nhung clii/a co co'i (hep. Yeu cau n'nh loan cfil 
ihep can thiet. 

Gia ihiei a = 40mcn: r, = 160mm. n'nh loan theo phucvm? phap gan dung dan 

Tinh A vl theoi4-J3) irons do o>, = 1:6= 1-5+ 6RJO" 5 = 1.72: <o 2 = to ,6 = 1.72 

«\ = o>, - w,c =1-1 .72c = 1 - 0.5475© 
Z v = (0.2 * 1.3?)r = (0,2 + 041380 160 



Nn^-^R.Arsin'cp 19G.08xl0 6 --~- x 14.5x1 25600* 200xsin 5 <p 



A., = 



3* 



- R^r siti(p+R v cp^Z s -x365xl60xsintp4-365tp v Z % 

71 7? 



_ 090.08 -77, 294 sir 1 <p)K?' 
s5 " lS,59sinq)+O.M3<p t Z, 



130 



rv- . ,.. 2,5N 2.5x800000 , t D .. 
Dau Lien lav <p = -■ — = J. t Radian ; 

R b A 14,5x125600 

£ = - = - : — =0,35 >Q45; sirup = 0,3912; sin 2(0 = 0.8085; 
- 7C 3-14 K 

sur> = 0.7078; <f\ = \ -0,5475<p = 0.39?75 ; 
Z, = (0.2^0.413Scp)160 = l04.Smm 

(109.08-77,294x0.7078)10-" 

A,. = = 42d8 mm _ 

SL 18.59x0.5912 + 0,365x0.39775x104.8 

Tinh N„ h iheo cong ihuc (4- 10): 

^=-^^-0.55in2 ( p) + -^^<p-RA.^ 

Nj,, - 579700 (<p - 0.5sin2<p) + (1 16.1 Sep - 365<p,.)A s( . 
Vdi cp = l.l; .sin2t» = 0,8085; tp, = 0,39775 linh diroc N fih = 329000. 
Giu in N gh tinh ouac Mia be so v6i N = 300000. 

Lav rp = 1,3; I = - = 0. 4 182: tmh ducc <p s = 0.2887: Z, = ilSrnm; simp = 0.963558: 

sin'V = 0,8946: sin 2<p = 0.5155. Tinh duvc A„, = 3985. Vdi A,, = 3955 va rp = 13 rihh !ai 
dune N„ h = 786 1 70; giin vert N = 800000. Lay <p = 1 ,35 u'nh diroc A sl = 3989 va N = 905000. 



tp — 1.3 


A„ = 3985 N = 786 170 

s ' i 


<p=L35 A sl = 39S9 


N= 905000 



Suy ra vol N = 800000. lay <p = 1.31 va A* = 3986 mm 1 ; u\ - 3.1<&. 

4.2.6. Ddrih gia va xir li kct qua 

Cd'l (hep U'nh duoc co did !a dircrng hoac &m. Khi u'nh duyc A SI > nCn tfnh li Ic col 
thep ja, *^. Dieu ki£n u min < u, < M™*- ™°ng lhird ng M™ = 0,005 va 

u m;w = O 1 06(6%). 

Klu |a s qua be hoAc A,,, £ chung to kich thudc liet dien qua I6n, neu co the ihi nen 
giam kich thirdc tie! dien va tinh Lai. neii kh6ng. can dar ctfi tliep ther; yeu cau loi thieu. 
Khi co \x s qua Ion chiing to kich thiroc tiet di£n qua be, can tang kich thudc hoac tang 
mac belong (hoac tang ca hai). 

131 



4.2.7. Bieu do tutmg tac 



Vi£c tinh loan cot thep hoac kiSm tra kha nang chiu life se tro nen don gian hon rift 
nhieu kht lap duc/c ho bie'u 66 tuong lac khong thu" nguyen. 

42.7-1. Lap ho bieu do 

Bieu do dupe lap voi hai true bie'u di£n thong so n, m: 

N 

(4-14) 

(4-15) 

(4-16) 







u — « * 
R b A 






R b Ar 






R„A 


Chon thong so P., 


r 





Voi cac: loai col thep co gicti han chay va R, < 400MPa co R sC = E s va co, = I . 

6 = 1,5 + 6R«10"' ; <p s = 1 - 6; ; Khi % < thi lay <p, = 0. 

2 S = (0.2 + 1.34>r a = p., (0.: + 1 .34) r 
Bicn doi cong ihiic (4-9) va (4-10) thanh: 

11=4 (I + a>-CU59sin&p-CWFs 

m = 0.2122 sm 3 tf> + OJlf^asimp + (5,09,(0.2 -+■ 1,3c) 



(4-17) 
(4-18) 



Uhg voi m6i gia tri R s va a chon nude, cho 4 (hay doi. Voi rnoi gia iri cua 4 l 'm 
cUroc mot cap gia tri cua n va m. Tap hop cac gia tri cua n va m c6 duqc m6t bieu 66 irng 
vdi a. Cho a nhieu gia tri khac nhau se co difoe mot ho bieu do. Khi ve bieu 0*6 can loai 
bo cac cap co n < 0. 

Tiif du ve bieu do luong tac voi p a = -^ = 0.9 :R^ = 280MPa. 

r 

Tiiih loan: 6 = 1.5 + 6R V 10^ = 1.66S. 

(p s = I - 04 = 1 - 1,668c : Lay a = 0.20. 
Cho 4 lhay doi. ke't qua tinh loan ghi trong bang. 



1 0.12 1 02 [ 0.26 036 ( u 


0.52 1 6C C.fifi ere 


0.8i 092 1.0 


o=:r t 0.3770 


0.6283 ! 05756 j t.1310 | 1.3823 1 1.6335 | 16350 


21383 : 23876 


2.6393 | 1890C | 3.K16 


-- ,., 


.' ■;.■:■' 


B»Y7 


C.7705 | 0.9045 I O.S623, 1 Qft& 1 &.95W 


CftMl J 0.684S 


D4BIS i A24H 1 0.00 


Wftfl 


1. ."O 


O.2030 


' ^;= g;mo^ 


0.947* 1 ::.S940 


C-flSCO 


0.tj006 j 0.3208 1 o.nw 


0.0SS4 1 050 


iirrip 


■ ..~J 


owo 


0.9623 ( G.T3G4 


CJ6ffif / -£. I2SJ 


-c.sev 


-0.9X7 ', -ZSm -0.6450 


-0.4r.20 | 0.00 


Or 


c ???e 


6664 


D5233 


G,3£95 


C.2£fi: 


:i i;« 


coo 


OCC 


:i.oo 


0.02 


0X0 1 


n 


0.1.246 


-C.0445C 


0.0732. 


0.22S6 


r.Jie; 


55:3? 


09135 


0.5600 


'.070 


VM20 


'.ISO 1 1.20 


ni Cu'X 


"2^ 


Q.1952 


0.2S69 


0.2942 ' 5 28/5 


0.2-tS ! 1760 


1703 1 0.0513 


0.O17C | C.00 



132 



Hint) 4.7 gidi thi£u mot ho bie'u 66 vai a = 0,1 + 0,6. Tuy tren hinh co ghi day du 
cac so fieu nhimg mang tinh tuong (rung la chu y£'u, chua du dp chinh xac dfi* dung cho 
ihiet ke Ihirc te. phu juc 10 co cho m6t so bicu do co rh£ dung <5t ihiet ke. 




0.1 0,2 3 0.4 0,5 

Hinh 4.7. Thi du ve ho hid'u do ii&tig iuc i\£'l dic'n iron 

4.2.7 X Cdeh d&ng bleu dd 

Ho bidu do tucng tac khong Ihu nguyen cua tiet dien tron cung duoc dung tuong ttr 
nhu doi vol Tiet dien chu nhat da trinh bay 6 muc 2.5.6. 

D£ linh loan co'i thep can gia ihie't a, tinh P d =— chon dung ho bieu d6 vai p u va R s 

ihi'ch hop. Tinh cilc gia iri n, m va tra bi£u do, dm duoc gia iri a can chifit. Thong Ihuong 
d£ co ducrc a can phai nOi suy. PiCn tich toan b6 co'i thep A M tinh iheo cOng thuc (4-19): 

ceRkA 



A R, 



(4-19) 
133 



De kiern Era kha nang chju lire khi da biet ca'u lao cua col thep, dung cong thuc 
(4-16) tinh ra a. Tir ho bieu do trich ra bi£u do ling voi a da biet. Ti'nh gia tri n. m va 
co diroc m6l diem. Khi diem do nam o mien trong cua bieu 66 thi tiel dien du kha 
nang chiu lire. 

4.3. CAU KJEN C6 C6r DM LO XO 
4.3.1. Dae diem cau rao 

Col dai !6 xo dirge u6n thanh cac vong iron lien iuc tir cac soj thep kha dai. Duong 
ki'nh soi ihep 5 ■*■ 8mm. co ihe den 10mm. Goi D la ducmg kinh cua vong iron tinh den 
true col (hep id xo va s ia buck: 16 xo (la khoing each cua cac co'i dai). 






Hinh 4.8, Can ktrji co col dm Id xo 



Ngoai cac quy dinh dol vdi col ihep dai irong cau kien chiu n^n Ihi buoc cua 16 xo 



duoc gioi han trong khoang s = 



4 ' S 



£> . Nen chon s < - D (hinh 4.6). 



Col dai 16 xo 6m lay loan b6 c6't thep doc duoc d5i phan deu iren moi vong Iron. 
Tiei dien cua ca'u kien co the' la tr6n hoac da siac deu. 

4.3.2. Sir lam viec cua cau kien 

Khi bj nen. batons ngoai bien dang co ngan con bi no ngang. Thuc nghiem cho biet 
iieu han che dirge sir no ngang cua belong se lam lang duoc mot each dang ke kha nang 
chiu nen cung nhir bien dang doc cue han cua no. 

Dung coi thep dai 16 xo la nham muc dich tren. 

Goi phan betong nam ben trong cot dai 16 xo la loi. phan nam ben ngoai la lop bao ve. 

Thi nghiem nen ca'u kien cho den lilc lop belong bao ve bi pha vS hoan toan th'i phan 
loi van chua bi pha hoai va con tie'p iuc chiu ctuoc lire nen tang ihem nua. C6r dai 16 xo 
da co tac dung can Ira bien dang no* ngang cua belong phan loi va khi cau kiSn chju nen 
ihi cot dai 16 xo chju keo. Loi bi pha hoai khi ung suai keo trong cot dai 16 xo dat den 



i:>4 



gioi han chay. col dai co bien dang Eon, kh6ng du kha nang ngan can bien dang ngang 
cua berong loi. 

4.3.3. Dieu kien sur dung, cong thifc tinh toan 

C&t c6 cot dai 16 xo duoc sir dung dc tang khu n3ng chin nen. Jam giam boi kich 
rtiLftfc tiet dien col. Thong thuotig chi ncn dung cho cue col ngan (khOng bi uon doc) va 
chiu nen diing lam hoac nen Ifich tAm vol do lech Jam rat be (e < 0,1 D ). Khi c6t co do 
manh ion (bi anh huong dang k$ ciia uon doc) hoac chiu nen l£ch tdm Ian ihi dung c6t 
dai 16 xo khong co hieu qua. 

Tinh loan kha nang chiu nen ciia cot nguoi la chi ke den sir lam viec cua belong 
phan loi. cua cot [hep doc va anh hirong cua cot dai 16 xo ma bo qua lop betong bao vc. 

Tinh toan call kie-n chiu nen dung tam. khong bi uon doc duoc tien hanti theo dieu 
ki£n<4-20): 



N<N ah =(R b A L+ R NC A, l + 2R v A lx ) 



(4-20) 



1 



Trong do: A L = — ^D^ - dien rich lieE dien loi; 



A u - dien rich loan b6 cot thep doc: 

R^ - cirong dd tinh loan ve kco ciia col dai id xo: 

A: v - dien tfch u'nh doi cua cot dai 16 xo: 



a lx - dien tich tiet dien ngang ciia cot dai !6 xo. 



I 



Tinh toan cau kien nen l£ch tarn khi do manh ca'u ki6n k--^ < 35 dirge tien hanh 

i 

theo tiet dien iron dutmg kinh D ol trong do thay gui tri R b bang R blc la cucmg d6 b6 i6ng 

da duoc tang cao nho 1 tac dung cua cot 16 xo. 



(4-21) 



R bIC =R b +2p lx R s 


v D J 


, - 4a " 





Trong tinh toan chi ke den tac dung cua c6t thep 16 xo khi ma ke den no se lam tang 
kha nang chiu lire (hoic giam duoc cot thep A sl ). Neu ke 7 deh col 16 xo ma khong dat 
hieu qua nhu vCra neu thl tmh toan theo tiet dien nguydn, dirfrng kinh D, khdng kfe den 
cot 16 xo. 

135 



4.4. TIET DIEN VONG KHUYEN 

4.4.1. So lieu ve tie't dien 

Tie't dien vong khuyen co cac kfch (huac nhu sau: 
X[ - bin kinh irong: 
r, - ban kinh ngoai 
r = 0.5 (r, + r,) - ban kinh [rung binh; 

6 = r 2 — r, - chieu day. Thong ihuong co 6 < C'.5r 2 (hoac rj > 0.5r 2 ). 
A - dien Iich cua tie'i dien bStone: 

J - momen quan linji cua liei dien: 
i - bar. kinh quail ti'nh: 

,= VX v r - +Ti 

A v] - dien n'ch loan bo col [hep doc. 

t d - ban kinh vong col thep. 

Trtforig hop so lupng col ihep khong qua nhieu iti- tal ca cac llianh dupe dal Iren root 
vong iron dudng kinh D a = 2r a . Khi liei dien kh£ Ion. so' lugng co'i ibep nhidu Ihi c6 ih£ 

ho in eOi th6p iren hai vong, co difin rich bang nhau. luc do r, la ban kinh irung binh cua 
hai vong cot ihep (hlnh 4.2). 

4.4.2. Oieu kien va gia (hiet 

NOi lire linh loan soni lire nen N. momen uon M. Dp manh ?«. = — . Khi X > 28 can 

i 

,\et dexi uon doc, u'nh N 1h iheo cons rhur (1 -14) va he so q iheo (!.] 1). Op b£n dupe lay 

iheo dieu ki£n (4-1) va (4-2). Noi lire irong cot thep N A . N' A . M A , M' A dirpc lay theo 

muc 4. 1 .4.3. gio'ng nhu Irong liei dien iron. 

Npi luc irong belong vung nen dupe xac dinh ven gia ibiei ung suui phan bo deu. dai 
gia trj R b . Thyc te vung nen dupe gioi han bai root ducmg lhane nhung de don gian hoa 
vice lap cong thuc chap nh&n gia ihiet vung nen dupe gioi han bed hai ban kinh lap lhanh 
goc 6 lam 2ip (vi dung gia ihiel nay ma can dieu kien 6„ < 0,5r ? ). 

136 




Hinh4'9.$ffda 

tilth fowi net dien 
yd fig khu\en 



4.4,3. Cong ttuic cu ban 

De Jap cong thtfe. dung bien so goc a va v[ phan da. Vi phan cua dien iich vung nen 

!adB, 



dB = 6,.r da 
N6i lut ciia vung bctong chiu nen la Ng va Mg. 



RkA 



N fi -2 ;R b dB-2R b 6 rc , P = -^P 



- 



M D =2rR & dBZ = 2R b 5 r 2 £cosada 



R.A 



ft 
K€i hap vdi noi lire irong cO'i ihep da lap ducfc, cuoi cung co: 

Nne D < M rt = -(R„Ar a ■* w A ll r,)sinq>+R Ai^Z,. 



N = N Eh =^(R b A+R K A u )-R s A fl 9 s 



(4-22) 

(4-23) 
(4-24) 



4.4.4. Ki&n ira hha tiang chiu Hie 

Biei kich thirot tiet dien va cau tao cot thep, chieu dai tfnh loan / G , yeu cau kiein tra 
xem tiet dien co du Kha nang chiu cap n6i luc M, N. 



137 



Chuan bi so lieu: R b , E b . R s , R 5C , xac dinh a theo cau tao cot thep, cac ban kfnh r Jt 

r 2' r o' r a = T 2 ™ a - Tinh dien ifcb tiet dien A, dien tlch cot thep A sl . Xet anh hirong uon 
doc, xac dinh J; N„,; r\, Tinh d6 l£ch lam e,, e ol Tfe c . 

a) Gia ihie'l £ > 0,15. Tir di£u Ki£n N = N gh = (4-24) va\ ^ = ca, - &> ? £ ma 4 - — , 
lap duoc c6ng thtic tinh <p: 

,. <"+»>*,«>,>» (4 , 25) 

R b A + (R sc+M ,R s )A N1 
Khi £, = — > 0, 15 thi tinh <p s , Z s theo c va u'nh M^ theo cong ihiic (4-23). 

b) Khi mil £ < 0, 15 thi lay c = 0. 15 de liiih cp s va Z v . 
Tinh <p iheo cong thuc (4-26): 

y - (N ^" (4^26= 

R b A-rR,A„ 

Tinh M^lhco (4-23). 

4,4.5. Tinh loan col thep 

Biet kich ihirdc tic! dien, cap noi lire M. N. Yeu cau tinh loan cot thep. Truck het can 
chuan bi so lieu nhu 6' bat loan kiem tra. xac dinh duoc A. r . r]c . 

Gia thiet chieu day 16p dem a, tinh r a = r 2 - a. 

De tinh du*c/c c6t thep can giai dong thoi hai phuong trinh (4-23) (4-24 trong do co 
mot phuong trinh lirong gi&c. Th6ng thudng giai theo each g&n dung dan. 

Truac he"! chon mpi gia in <j>, tinh 4-~' lmn <P< va ^ s (Neu c < 0.15 thi dung <; = ■ 

it 

0. 1 5 de tinh <p s va Z s ). Tir dieu kien (4-23) u'nh duoc: 

= 7rNT^ -R b Ar siR<p (42?) 

R^sinqs + jHp.Z^ 



Dem gia iri q> va A sl lim duoc vao cong [hue (4-24) de* imh N^,: 

N f) ,=-i(R t> A + R K A sl )-RA,(?, 

So sanh N gh voi N. Dua vao ke'i qua so s«Snh ma chon lai <p. Gia tri A sl va <j> duoc 
chap nhSn vc*i dieu kien N = N-j,. 

138 



4.4.6. Bieu do tirong tac 

Vol tie! dien co kich thudc va cot thep da biet (nhu Irong b5i loan kiim tra kha nang 
chju Iltc) can ve bieu do tucmg tie vai hai mic la N g>1 va M gh = N^e r 

Chon bien trung gian va dOc 13p !a cp. Cho 9 thay doi trong khoaog (p., den n. 

3R,A S . 
tp b =- 



R„A*2,5R,A M 

Lay gia so Acp = 0. 1 ■*■ 0.25 hcac co the" Jan hon. 



Tu q> t in h c = — . <p<. 2, , sin<?. 
71 



Vai mdi gia iri cua <p linn dircc m6t cap N r ?h va M gh theo cdng thuc (4-23), (4-24). tu 
do ve bieu do ruons tac. 



De I5p bieu do khong thirngu\en. dot: 






n= : oi= ' p ; 

R»A R,Ar 


P a 





Voi cac loai cot chep co gioi han chay (CI, CII. CIII, RB300. RB400: RB500) va co" 
R, C = R, <400MPa. liyco, = I; 6 = 1.5 + 6RJCT; 

(p, = (Oj - Ovi = 1 ~ 8£. 

Z v = (0,2-l.^y a = (0.2^i.3£)(S a i o 

R b A 
Dung cong thiie (4-23) va (4-24) bien doi thanh: 

n = £(l4-a)-a^ (4-28) 

m = -(1 4-a{5 a )sina + ap, 9,(0,2 + 1,3^) (4-29) 

Moi bieu do dtfe/c l&p theo ba thong so p a , R^ va a khi cho bien so 4 thay ddi. Kht 
lip bie'u d6 can Loai 06 cac cap gia tri ting vai N < (keo l£ch cam). 

Cho a (hay ddi se co mot ho bteu do vai hai thong so' 3 a va R s . 5u* lhay ddi cua bie'u 
do theo R s la rift it vi vhy c6 the ve chung iren mdt bieu d6 v6i cac R Ti khac nhau. 

phu luc 1 1 cho mot vai ho bieu do nhir vay. Cach dung ho bie'u d6 cua iter dicn 
vong khuyen cung gio'ng nhu doi voi net dien tron (xem muc 4.2.7.2). 

139 



4.5. TIET DIEN TR&N VA VONG KHUYEN BAC BIET 

4.5.1. Tiet dien tron dac biet 

Khi cot chiu luc tucmg do'i be nhung theo y£u cau ve kien true hoac ve nan che do 
m&nh ma phai chon dutmg kinh D tuong ddi Ion so vdi dieu kien bao dam do bdn th] col 
thep A s , linh dugc thuong kha be hoac khong can :hiet. Luc nay khi ma D < 400mm. neu 
chon bo in col thep theo yeu cau tot thieu thong thuong la 6 <j» 16 (hi nhieu khi luong col 
thep dugc dung Ion gap nhieu Ian gia tri A k , tthh duefc. Trong irudng hop nay de tiet 
kiem col thep co the Wiong can luan theo cac quy dinh ve so Jutmg thanh loi thieu va 
dudng kinh <f> vo*i chu y rang quy dinh so thanh cot thep khong it hon 6 la riham llioa 
man gia thifl tinh toan chir khong phai do yen cau chiu )yc. 

Khi tinh dugc A s , qua be hoac am can chon dien tich ihco yeu cau loi thieu A mu = 
lW vdi m„„„ - 0.005. 

Klu ma D < 400 va A mm £ I.5A,., co the* bo tri 4 <p 16 6 4 goc cua hinh vuong- Neu 
A SI < co the bo tri 4 4 J 2. 

Khi ma D < 250 va A mn > 2A M co the bo in* 3 tji 16 3 goc cua tarn giac deu. Neu 
A v( <0c6ihcchidal3s>)2. 

4.5.2. Tiet dien vnng khuyen dac biet 

Khi ban kinh ngoili r 2 la kha be net dien co the rai vao truong hop dac bisi. khong 
ihoa man cac yeu cau cau tao th6ng thuong: hoSc la 5 > 0.5r 2 hoac 3a so luong rhanh 
cot thep doc i'i hem 6. Cbii y rang cac yeu cau cau tao noi tren chi nham de tlioa man cac 
gia th Lei tinh toan chu khong phai do yeu cau chiu lire. Vi vay van co the tinh loan cac 
net dien d&c bi£t nhu vua neu. nhung khong dung ducc cac gia thie't tuong irng. 



i40 



Chircma 5 



Tl£T DIEN CHtTNHAT NEiN l£ch TAM xi£n 



5. 1 . DAI Ct'ONG VE NEN LECH TAM XIEN 

Nen lech lam xien xay ra khi mas phang uon khohg chiia true doi xting cua lies dien. 

Goi hai true doi xting cua net di6n la ox va oy. Goc gitto mat phang uon va true ox la 
a. fhinh 5.1a). Co the phan momen uon M thanh hai thanh phan tac dung rrong hai mat 
phang chtia true ox va oy la, M x va. N-l s . 

M, = Mcosa,, ; M y = Msina (5-1) 

3) 










\/ 


/ 


**■<«* V 




//tn/r 5J. 5f «W /re* fwr /je;> iecii Sam. xien 

Truoiig hop khi tinh loan noi luc da xac dinh va 16 hop rieng M x va M v theo hai 
phuong thl rnomen long M se la: 



m = JmJ + m* 



(5-2) 



Goc lap boi vecto cua momen long M va true ox la a ma tga = — - . 

Cot chju nen ldch tarn xien ihucmg gap Trong cic khung klii xet sir lain viec cua cot 
d6ng thai chiu uon theo ca hat phuong. 

Tiet dicn chti nhkt chiu nen lech lam xten co cac canh la c x . c y , cot ihcp thi/ong dicac 
dat theo chu vi va doi xung qua hai true (hinh 5.2). Trircmg hop M x va M v co gia iri gin 
bang nhau nen 3am ii£i di£n vu6ng. 

Tiet dien tron va v6ng khuyen khong co truoog hop nen tech tarn xien. 



\4\ 





c, 










r 




M, 


X 


ri 


*py w 







c, 










• 


• • 


• 


t 


• 
• 




• 
• 




C > 


• 


v • 


• 







Hmh 5.2. Jtei dicit chm iwn ti-ch ram xicn 

5.2. N0I LUC NEN LECH TAM Xl£N 

Noi lire 6i n'nh loan nen lech tam siftn duac lay iir ke'E qua 10 hap irong do can chu y 
cac bo ba noi luc sau: 

- Co N fon nhai va M x , M v tuong ung; 

- Co M x 16*n nhai, N. M v luong unc: 

- Co Mv Ion nhai. N. M x luong ung: 

- Co M x va M v deu Ion; 

M My 

- Co do lech tarn e., - — -hoace ,= — - Ion. 

'Prong moi bo ba noi luc can xei den do lech lain ngau nhien e iheo moi phuong vu 
anh huong cua uon doc iheo tirng phirong. He so xci anh huens uo'n doc theo moi 
phuong r\ j dupe tinh theo c6ns thtic (1. 1 1) trons do momen quan imh J r chieu dai linh 
toan / or luc doc ioi nan N r , hl duoc tinh riens biei theo itmg phirong o = *• y). 

So do noi luc tinh loan dirac dira ve Thanh luc N dat tai diem E co toa do la T^e^ va 
Ti^e^. (hinh 5.3). Diem £ cd the* nam ben irong hoac ben ngoai lie'i dien. 6 vao goc phan 
\u nao la tuy ihiiGe vao chieu iac dung ciia M v va M v . 

Sau khi xet dp lech tarn ngau nhien va uon doc ihi momen uic dung iheo hat phuonc 
duoc tans leu thanh M . M.. . 



e. 



ne. 



U— 










V* r 




1.V 


, F 









/Ji«A 5 J. &' rftf «£/ /wc JW tffl /cc/; j<hm 



142 



5 3. Sl/LAM VIEC NEN LECH TAM XfEN 

Voi ca"u kien lam bang vat Ucu dan hoi va dcng chat chiu nen I£ch lam xien co the 
dung phuong phap cong tac dungdel tinh uno suau 



a - 



J. 



x + 



^v+* 



(5-3) 



Dieu kien ben la han che tins sua'i a khong vuyt qua img suae cho phep hoac cuong 
do tinh toan cua vat lieu. 

Khi tmh roan c;Vu kien belong col thep theo trang thai gioi han khong the dung 
phiinng phap cong tac dung nhu a cong thuc (5-3) vi khong the" tinh ricng urng suit do 
tiling noi luc gay ra. De tfnh toan cot rhep ciing nlitr d6 kiem tra kha niing chiu luc phai 
set tac dung d6ng thai cua bu noi lye N, M v M y 

Khi chiu nen lech utm xien. luy theo vi id di£m dat luc cung nhu luong quan giua 
cue noi !uc voi ki'ch ihuoc tidi dien va bri rri co't thep ma c6 the 1 xya ra truong hop loan b$ 
tiet dien bi n4n hay mot phan bj nen. mdt phan bi keo. 

Voi liei daen toun bo chiu nen. co mot dinh chiu nen nhieu nhat (dinh a gan diem 
dat lire E) con dinh phia kia cua dudng cheo chiu nen ft hem. 

Voi tiet dien co mot phan chiu nen (hi viing n£n co the la mot trong bon dang nhu 
trcn hinh 5.4. Luc nay. cung giong nhu twang huf> nen lech tarn phftng. can phan bi£t 
true trung hoa va gioi han cua viing ncrt (xern muc 1.6.4). True trung hoa each dinh chiu 
nen Ion nhat mot doan x va do la chieu cao thuc cua vung nen. Gioi han (mdp) cua vting 

nen ifnh d6i each dinh vua noi rn6t doan x = 9x (9 = 0.8 ^0.85). Trong tinh toan, virng 
betong chin nen dvoc lay theo gioi han nay. 






/> 



s 



* *<x 


f^ 






^ 




\\\^ 




iHS 


•\\^ 





Hinh 5.4. Cdc dang cua viitig nen 



143 



D6n trang th2i gic?i han tmg sua\'t trong bfcidng vung nen duoc xem la phan bo de"u va 
dat gia tri R b . Ohg sufi'i trong nhtfng c6t thep a xa true irung hoa c6 the" dat den gia tri R s , 
R sc trong khi do 6" nhfing co't thep gin true trung ho& ling sua*: be htm. 

Goi thu" tir (hoac dat ten) cac thanh cot thep la i = 1,2,..- n. Pien tich liet dien moa 
thanh )a a,, ung suit trong thanh thep la a Tuy theo quan diem tfnh toan (xem muc 
1.6.5) ma co the* xac dinh a, phu ihubc vao bien dang cua thanh cot thep s, hoac phu 
thuoc vao khoang each ttr diem dat co't thep den gidi han viing nen 




Hinh 5.5. So do link toon cua li& ditn 



Tir lam cua co't ihep chiu kdo xa nha't va lir dinh chiu nen Ion nha't ke cue true U-U 
va V-V song song vdi mep vung nen (trie la cung song song vdi true trung hoa). 

Goi h^ - khoang each lir cot thep thu i den true V-V. 

Wj - khoang each tir cot thep thu i den true U-U. 



W; 



n oi ~ "QflUX 



(hinh 5.5). 



144 



TrenhlnhJ.ocoh^^h^. 

Bien dang E t duoc xac dinh dua vao gia Ibiet tiet dien phang; 



15-4) 



Gia tri a, duoc xac dinh iheo cong ihuc (1.25), khi e, > co a, !a ting suit keo, c6n 
khi Ej < co a, !a irng suat nen. 

Tieu chua'n thiet ke TCVN 5574-1991 dtra ra c6ng thtrc rhuc nghiem -\uc dinh o t 
nhu sou: 

V#i cot thep chiu keo: 

Khi h fll >0.6(h o ^-x)ihla, = R s 



R 



^<\, :1 ^> " 



h Q <0J(h^-x>th](j ] = 

Voi cot thep chiunen: 
Khi h O] >0>6xchi g\=K 

h <0,6x«hia,=-^R; 
Tieu chuSn TCXDV^ 356 - 2005 dua ra cac cong thiJC sau; 



a - 



v,- t 



1 



1.] 






Trong do: 
4-^ 



(5-5) 



a^ u - ling sua'i gidi han cua cot thep vung chiu nen. Trong truong hop btnh 
thucrng lay o SCiU = 400MPa (xem phu luc 4). 

to = a - 0,008R b 

a - h£ s6' phu thuoc toai b&Qng. V6v belong nto3 tl\6n§ thvibng lay a = 0,85. 

Theo cdng thuc (5-5) tinh duoc a t > la irng suat keo va nguoc lai. Gia iri <jj duoc 
han cM khong Ion hon curing d6 linh toa*n cua co't thep (v6i <s x > neu tinh duoc a- > R s 
thi lay <y- i = R s , voi a; < 0, ncu tinh duoc u- < - R sc thl lay a- = - R, c ). 

145 



5.4. CONG THUC VA Dlfej KI$N TONG QUAT 

Dieu kien d6 ben cua nen lech tam xien cung la cac dieu kien (1.19) va. (1.20). Tieu 
chuan thist ke'TCXDVN 356 - 2005 quy dinh lay true chua"n la ducmg thang U-U di qua 
trpng lam thanh cot thep xa nhat (so voi diem da? lire E) vk song song v6i mep vung nen. 

Dieu ki6n duoc vie! thanh: 

Ne<M £h =R b S,-Xcr 1 S si (5-6) 

N = N ph = R b A b -I<7,a l (5-7) 

Trong do; 

e - khoang each tiidiem dat luc den true chuan U-U; 

S b - m6men ilnh cua dien tich tie'l dien be tone vung nen lay 66\ vcfi true U-U. 

S^ = AhW b 
S,.; - momen nnh cua dien lich thanh cot thep doc thu i doi voi true noi tren. 

S,i = a r w i 
a, - dien lich tie'l dien lhanh cot Ihep thiii; 
w ( - khoang each lir irong lam a, den true chuan U-U. 
A & - dien ti'ch betong vung nen; 
\V b - khoang each \ii trong lam A b (diem Ci den true chuan. 

Hmh dang cua belong vung ncrt diroc xac dinii lii dieu kidn sau; Diem dat ciia lire 
doc (diem E). diem d&T cua hop lire cua belong v& cua co't tbep vung nen. diem da: cua 
hop lire cac cd'l thep chiu keo phai cimg nam tren mot dirdng Ihang. Dung ra thi duong 
thine qua 3 diem vua neu phai nam trong mat pbaiig uon. tuy vSy voi muc do gan dung 
chap nhan duoc chi can ba diem Ihang hang. Trong tinh loan thuc le de dai diroc ba diem 
lining hang la luong doi kho. phai linh nhi6u Ian. vl vay cd the' chap nhan die'u kien la ba 
diem gan th^ng hang. Lay ducmg ihang qua diem dat luc nen (E) va hop luc cua c6i ihep 
chiu keo (K) lam ducmg moc, diem dat ciia belong va cot thep vung nen co the l&ch voi 

dudng moc nay voi sai so cho phep — h olliax ■ 

Diem dat ciia lire N va cua cac hop lire noi iren diroc xac dinh bang loa dc) cua chiing. 
Lay hai true ox va oy. Toa do cua diem dat luc dS duoc xac dinh bang hai do lech 
lam e ox , c ov hoac khi kc den uon doc la r^e^, 7i v e ov (hmh 5.3). 

Goi toa d6 cua cac thanh col Ihep la Xj, yj va hop lire cua co'l ihep vung keo dai lai 
die\n K co toa dd x K , y K , hop lire cua cac cot thep Wing nen dai tai diem G c6 toa d6 x G , 
y Cr (hmh 5.6) chi: 

J 46 



x„ = 



T*tVt&\ , .. ...IXsr.yi 



Tmh x K , y K khi lay tong cac cot thep chiu kco. Tuong tu linh x G , y G khi U'y t6ng cac 
cot thepchiu nen. 

Diem d&i hop luc belong vung nen la C co toa d6 x c , y c . Xac dinh x c . y c phu thuoc 
vao hlnh dang vung nen la iam giac, hinh thang hoac ngu giac (hinh 5.4) vai dang vung 
nen la hinh thang voi cac canh day (,, t 2 , chieu cao C y nhir tren hinh 5.6 thl: 

A b = 0.5 (i,+i 2 )C y 

1 



v„ = 



_^< t - t ^ c ;_(i ] -i 2 )c ) . 



A, 



6(1, *-t,) 



x c = 0,5C x - 



tf +t; + t,u 



3(t,+t 2 ) 

Vdi cac dang khac cua vung nen cung theo nguyen tac thong ihirong 66 lim loa dd 
irong cam x c , v c . 

Hop luc cua belong va ciia cot thep vung nen dai tai diem D. nam vao kiioang giuii 
diem C va G. 




Hinh 5.6. S&d6xac dink diem dat kcrp h/c 



147 



Xn = 






„ _ R bA n y c + Ip,a,x, 

Lay tong cac cOi thep irong vung nen. Tnuir' Long ihu'c tinh x^, y R cac ung suai <j, 
lay iheo gia tri tuy6i d6'i (hoac xem ung sua'i nen la duong de phu hop vol viec lay R b 
duong). Neu lay o, nen la am ihi R b cung lay gia tri am. 

Duong Thing KE di qua diem dat hop lire edi thep vung keo va diem dat lire nen co 
phirongtunh: 

y = ax + b 

a = = ;b = y K -ax K = ri v e ov -aii x e llN 

Khi ba diem K. D, E thang hang (hi loa do X&. y^ phai nghiern dung phi/ong trinh 
duong lhang. Neu diem D 6 ngoai duong lhang thi dp lech A bang: 

. _ yn-<ax +b) 

H — 
Va' + l 

Mire do cho phep cua do lech la A < — h„_.,, 

Truong hop loan bo tie"! dien chiu nen thi die*m 6U cua hop lire belong va c6't thep 
phai trung vdi diem dai cua lire nen (diem D trung voi diem E). 

5.5. MAT BIEU DO TUONG TAC 

Vm nen tech tarn xidn kha nang chiu lire duc/c bieu difcn thanh mai bieu do luong 
lac. Do la mot mat cong the hi£n iheo ba true cxyz. True dung oz the" hien gia trj lire nen 

N ph . Cac true ngang ox va oy the" hien momen M x = Nn,e )W ; M v = Nile,* - Moi djern 

tren mat bieu do duc/c xac dinh bdi ba toa do x. y, z the hien cac npi luc ttfong ung (hinh 
5.7). Ki hieu C. D x . D v la giao diem cac true vcfi mat bieu do. Duong net each O k D Kx 
D Kv la giao luyen cua m6l mii phang ngang (song song vdi mAl soy) voi mat phang loa 
d6 va mat cua bie'u d6. Duong cong CD Ka D a la giao tuyen cua mat phang dung chua 
true oz voi mas bieu do. 

MS 



Hinh 5.7. Mai hii'n do 
iiiaixo uic 



5.5.1. Xac dinh toa do ciia mat bieu do 




Xct mot lie! dien vdi kfch Chirot va bo tri co't (hep da biet. Yen cau tinh toan xac 
djnii toa do cac diiim cua mat bieu do ti/ong tic. 

De don gian hoa van d& ma van du mire do khai qudt chung ta chi xct 6 phain vi goc 
mot phan tu. \0i mot dinh liet dien chiu nen Ion niiiti. 

De tin!) coin, dung bien so doc lap la hinh dang va kicji thirdsc vung belong chiu nen. 
Ve hinh dang cd 5 tnro'ng hop: 4 ^riromg bop nhir tren blnh 5.4 va irirong hop toan bo tiet 
dien chiu nen. true Erung hoa nam ngoai tiet dien. M6i mdt trirong hop trong 5 trirong 
hop deu c6 the bieu dien vung nen bang hai bien so: t ( , £?; U|, u 2 hoac t\ r U\', ^ u?. Trong 

do i la kfch thudc tren canh C x (iheo ph irons: true ox), u la kfch thudc tren canh C y . Chi 
so 1 gan vdi canh ke sal dinh chiu nen Idn nhat (hinh 5.S). Ka htdu giai nan vung nen 
bang doan PQ va true trung hoa la P Q Q . uhg vdi moi vung nen cho trudc (cho trirdc 
diem P va Q hoac cho imdc gi;i tri t, u) se tinh toan diroc dien tich vung nen A c , ting suit 

trong tung lhanh cot thep a,. Tu do xac dinh dugc diem dat hop lire belong va cot thep 
vung nen D. diem dat hop lire cot thep chiu keo K. Cung xac dinh diroc true chuan U-U 
va tinh cac gia iri W C1 W r 

Tinh gia tri N sh theo c6ng (hue (5-7). 

Tinh gia tri M* va M' bang each lay momen do'i vdi true oy va ox cua cac hop lire 
trong be long va Irong cot thep. 

Ml =R b A b x c -ScT i a i x L 

149 



■ • 
*- 



0.0 <2 





/ft/*fc 5.8. Dang \a krch ilntoc viittg nen 



Cung co the u'nh M va M theo mot each khac nhu sau: Theo cong thut (5-6) tinh 



duoc M gh . Tinh do lech tarn e = 



M 



?h 



K 



£''■ 



Noi diem K voi diem D va keo dai. Diem dat luc E nam tren duong lhang KD va 
each true cbuan U-U m6i khoang bang e. Xac djnh duoc vi in difem E se co toa dp cua 

no la nj^e^ va n^e m . Tir do tinh duoc M x va M v ta co duoc 3 toa do can fim. 

Ifng v6i m6i vi tri cua PQ co duoc mot diem. Cho P. Q ibay d6i (cung nhir cho t. u 
ihay d6i) se fim duoc mpi diem cua mat bieu do. Cho y rang voi moi vi irf P co nhieu vi 

iri luong ung cua Q. Trong so" do linh loan voi t, va l 2 phai thoa man l 2 £ l(- Trong so do 

linh voi U| va u ? ihi u 2 £ u ( . 

Viec linh va ve mat bieu do tuan« tac mang nang tinh chat If Ihuye'l. ihuc tecon it 
duoc sir dung vi viec linh toan qua phu*c tap Co the lap chirang trinh may tinh di giam 
nhe cong viec linh toan. 

5.S.2. Cac hinh cat cua mat bieu do 
5.5.2.1. Cat bang mat phang dung 

Ck mat bieu do bang mat phang dans xoz se co diruc duong coiig CD„- Do la bieu 
do tuong tac ung voi. hai noi luc N va M x con M v = (hinh 5.8a*}. 

Cal bang mat phang yoz co ducrng cong CD y la bieu do theo N va M y con M x = 
(hliih5.S*b>. 

Cac ducmg CD^ va CD V la b\i\i do tuong iac cua nen lech tarn phang iheo hai 
phuong ox va oy. 



150 



Cat bang mat phang aoz lap vdi mSi phung xoz mot goc a , co duong cong CD C£ . do 
la bieu do luong tac cua neti lech lam xien ung vdi N va momen M - JM^ + Mj vdi 

M 

M, = Mcosa. M v = Msinu ; tga = — - 

M. 






o, .. . 



*-a 



Hinh 5.5*.* Bii'H do UKwq 'oc aio nett fech tdm pitting \a xidit 

5-5.2.2. Cat bang mat phang Jigang 

Dung mai phang ngaiig song song vai mat xoy lam mat cat. Mat phing nay cdt iruc 
oz uii diem 0^ una vdi gja tri N^- Giao luyen cua mat cai va mul bieu 66 la duong cong 
D K , D Kv (hinh 5.9a). Do la bieu do tuong lac cua n£n l£ch (am xien ung vdi (uc nen N K 
h&ng so. 

Duong cong D V D V tren mat phing xoy la trudng hop dac bi£t irng vdi N - 0. do la 
bieu do iuong rac cua truong hop uo'n <cien (hinh 5.9b). 

Duong cong D^ D^ co dang g3n gio'ng vdi duong cong D X D„ vdi muc dc) rang hep 

c6 khac nhau luy thucic vao gia (ri N K . Hinh dang cua cac duong cong vua noi phu Ihuoc 
vao each chuc bo* tri c6'i ihep tren tiet di£n. Vdi ite'i di£n co co'l thep dsU deu theo chu vi 
va ddi xung qua hai true, duong cong thirong co dang loi (duong A hinh 5.9c) vdi 
phuong trinh; 



Khi xem duong cong la enlip (hi n = 2, con xem la duong thang thl n = 1. 



151 



a} o< 



\ 


D 


^* 










'l>* 



*) 




D. 



y v 

/foiA 5.P. C<5r w*tf/ />]/« do bang mat phang ngang 




Ve* ban chat p x = M ox ; q v = M la kha nang chiu momen ung vol tniong hop nen 
lech lam phang va x = M^; y = M* la kha nang chiu mornen cua irucmg hop nen lech 



lam xien Ihi: 






r M^ 



v M oy, 



= 1 



(5-S) 



Trong tfnh loan thuc hanh lay n phu ihuoc vao gia tri luong doi ciia N. 

Trucmg hop dat cot ihep khong deu. tap irung nhieu vao giua cac canh ma dal 11 lion 
6 cac goc ihi duong cong co the co phan 16m nhu duong B 6 hmh 5.9c. Trong thiet ke 
ihuc t£ nen iianh irucmg hop nhu the nay vj bat loi cho sir lam vice chiu nen lech Jam 
xien. Dhi cc>t ihep nhieu hon 6' cac goc ihi do loi cua duong cone se Ion hem, hieu qua sir 
dung vai Ii6u se cao hon. 

De co duoc bieu do nhu* Iren hinh 5.8* va 5.9 khong nhat thiet phai cal ra lir mat 
bieu do o hmh 5.7 ma hoan loan co the ve rieng. De ve bieu do hinh 5.8*3 va 5.8*b can 
n'nh roan rheo truong hop nen iech lam phang da (rioh bay trong chirong 2 (niuc 2.5 va 
2.7.4). Bieu 66 6* hinh 3.9b la irucmg hop u6'n xien. cac gia iri urng vfli D x va D v duoc xac 
djoh iheo irucmg hop uon phang fheo hai phurmg. can tim them mot so gia in D {1 ihi se 
ve duoc bieu do. 

bieu do hmh 5.9a cac diem D Kx va D Kv duoc xac djnh lit bieu do 5.8*a va 5.8*b 
khi da co diem K (biet luc nen r%). Diem D Kn co the' duoc noi suy khi chap nhan gia 
ilnei duong cong D Kx D K) c6 cung dang voi duong D x D y . Suy ra: 



O k Dk« 



I; 



\ 



K D Ko = 



Z~% |- i -O K D Kj a 



(t. 



^ 



-0D (( 



:::;::: \-- a<f j+OD y a 



Khi da co duoc doan K D KO ting vai gia tri N K (diem O k ) ihi se suy ra duoc bie'u do 
6hinh5.8*c. 

152 



5.6. PHUONG PHAP GAN DUNG TfNH COT THEP 

5.6.1. Tinh toan Met dien chtfnhat 

Phuong phap gin dung dua itin viae bi&i doi truong bop nen lech tam xien thanh 
nen l£eh i&m phang tuemg dirong de tinh cot the*p. Nguyen lac cua phuong phap nay 
duoc Irinh bay crong tieu chua'n cua nuac Anh BS8I10 va cua My ACI 31$, lac gia da 
dua vao nguyen cac do de lap ra cac c6ng thuc va dieu kien tinh loan phu hop voi lieu 
diuan Viet Nam TCXDVN 356 - 2005. 

Xel tiei di£n co canh C r C v . Dieu Jci£n de ap dung phuong phap gan diing la: 

C 

0.5 < — -< 2. c6t thep duoc dat iheo chu vi, phdn bo deu hoSc mat d6 c6t thep tren canh 

b co the Ion han (canh b duac giai thfch 6 bang ve mo hinh tinh). 

Tie! ditn chiu lire nen N. momen uo'n M x , M v , do lech tam ngau nhien e JX , e av . Sau 
klii xet upn doc iheo hai phuong. ti'nh duoc he $6 n, x . v\ y . M6mcn da gia tang M x[ \ M y| . 

M xl = nxMx- M yt = T lyM y £5-9) 

Tuy iheo tuong quan giua gia iri M Nt , M y , voi ki'ch thuoc cac canh ma dua ve mot 
uong hai mo hinh tinh toan (iheo phuong x hoik: y). Dieu ki£n va ki hi£u tbeo bang sau: 



i\ Id (fifth 


Theo phuong x 


Iheo phtwng y 


Dic'u ki£n 


C C 




Ki'hjiu 


h = C,; b = C y 
e 3 = e ax x0.2e dY 


h = C v ; b = C x 
M I =M, I :.M, = M X| 



Gia thiet chieu day lop dern a. tinh h = h - a; Z = h - 2a chuan bi cac so lieu R b . 
R.. R^ , c R nhudo'i voi truong hop nen lech uim phang. 

TiS'n hanh tfnh toan theo iruong hop dai cot ihep del xung: 

N 



X, = 



1 R»b 



(5-10) 



Hd .so chuyen doi m . 



Khi x | < h ihi n^ = 1 - 



0.6x 



x, > h ihi m = 0,4. 



153 



Tinh momen tucmg duong (ddi nen I6ch lam xien ra nen lech tam phang). 

M = M,+m oM ^ (5-U) 

" 2 b 

Do lech lam c> = — ; Vcfj ket cau tlah dinh: e A = e. +c. 

■ . N ■ o I a 

e«e +«a (5-12) 

Tinh toan do manh theo hai phiwng % =■ — ; X y , 

X - max (X s : a v ) 
Dira vao do lech lam e va gia tn x, de phan biet cac irirong hop tinh loan. 

a) Titfdng hop L Nen lech tam ra'i be khi e = — <0.30 tinh toan g£n nhu nen 

ciiing tam. 

He so' anh huong d6 lech tam y c : 

y c = ' (5-J2) 

(0.5-z)(2 + z) 
I-Je <i6 uon Joe phu them khi set nen dung tam: 

<P C =. + ^ (5-13) 

Khi X < 14 lay <p = 1; jchi 14 < X < 104 lay <p theo cong there (1 .7) vjei lai durca day: 

(f> = l .028 - 0,0000288/. 2 - 0.00 1 6a. 
DiOn tfch toan bO c6i thep doc A sl : 

Cot thep duoc chon dat dcu iheo chu vi (mat do col thep tren canh b co the' Ion hem 
xem muc 2.7.1). 

b) Trucmg hap 2. Khi e = — > 0. 30 d6ng thai x, > 4 K h c . Tinh loan theo irucmg hop 

h 

nen lech tam be. Xac dinh chie'u cao vung nen x theo cac chi dan cua muc 2.2.3-2. V<fc 
muc d6 °5n dung, co the tinh x theo c6ng Ihtie (2-10) duoc viei lai sau day: 

154 



X = 


,' R t+3to*) 


s o = 


% 



Dien tich loin bo cot thep A s[ Unh theo cong thiic (5-15): 

Nc-R^bx(h n -.V2) 



•% = 



kR.„Z 



(5-15) 



Cone ihtic (5-15) ia viet lai cong (hue (2-17) trorsg do (2-17) chi ifnh cot thep A',, da* 
6 mot phia con (5- 15) tinh loan cot ihep toan bo. He so k < 0,5 la de xel den van de vira 
neu. Quy dinh lay k = 0,4. 

c\ Tnr&ug hap 3. Khi e = — >0.30 d<5n« ihoi Xj < 4 R h . Tinh loan iheo truong 

h c 

hop nen lech tarn Ion. Tinh A, t theo cong thuc (5-16) suy ra tu cdng (hire (2-14) voi 
he so" k ^ 0.4. 



A„ = 



N(e-0,5x 1 -h n ) 



kR .Z 



(5-m 



Cot thep duoc dal iheo clui vi crong do col ihep dat thco canh b co mat do Ion hon 
hoftc bang mat (16 iheo canh h. 

5.6.2. Tinh toan tiet dien vuong 

Tier di£n vu6ng chiu nen lech Earn xien co the dtroc tinh toan nhu doi vd"i tiet dien 
chfr nh^t da trinh bay irons muc 5.6.1. 

RLeng vdj tiet dien vuong co col thep dat deu iheo chu vi voi so lupng lu* 12 thanh 
ird ien (12; 16: 20. ..) co the dirge tinh loan g£n dung bang each quy vc tiftf di£n tron co 

duong kjnh D= 1.05 C v Tinh voi lire nen N va momen tong M = JM^ + My .Tinh toan 
iheo tiet dien Iron cot ihep A*,, chon va bo tri cot thep cho tiet dien vuong. 

5.6.3, Danh gia va xu* If ket qua 

Gia tri A sl tinh dirge theo cac cong thuc da Up co the la dirong, am. Ion hoac be. 

A 
Danh gia muc dd hop li bang li It: cot thep u s = — — voi A = C x C y - bh. 

Tuy theo ket qua finh dirge ma co each danh gia va xu li nhu d6i voi tnrcmg hop n£n 
lech lam phdng. 

155 



5.6.4. Thi du tinh toan 

Tin du L Cho li£t dj6n chu nhat co cac canh C A = 60cm, C v = 40cm; chiiu dai linh 
loan ! ox = / 0¥ = 4m. Luc nen tinh loan N - UOOkN: M, = 300 kNm; $6 lech tarn ng&u 
nhien e dK = 3cm; M y = 150 kNm; e ay ^ 2cm. Be tone co R b = 1 3 MPa; E b = 29000 MPa. 
Yeu cau linh loan cot ihep bang thep co R s = R SN - 260MPa . 

Chuan bi so lieu: £ R = 0,60. 



i v 0,2S8x60 



/ lx= _^o^ =M7 

5 i y 0,288x40 

?, = max (X x , A v >- 34,7 
Xet u6n doc: Z, = 23. 15 < 28 lay n, = 1. 
/v ; . =5 34.7 > 28 can linh r| y . 

60x4tf =32000()cmJ ^ 32xl0 « mm , 
■ 12 

2.5E b J 2. 5 x 29000 x 32x10 s , , . 

( \ lh = — 2"^- = - Z5 --1.9^x10 Niuum 

N (h = 19500 kN 



/* 4000 ; 



N th 19500 



M A . = i)M x = 300 : M vj = r\M y = 1 .065 x 150 = 159.8 



= 399 



C x 0,6 
M VJ _ 159,8 

M M v , 

Co lru£jn£ hop —JU- > — =*- . Tinh iheo phuoag x. 

h = C x = 600mm; b =. C v = 400mm 
Gia ihi£t a = 50mm; h = 550; Z = 500mm. 



156 



M, = M,, = 300kNm: M 2 = M,,, = 159,8 
Dd lech tarn ngdu nhien e a = e ax + 02c ay = 30 + 0,2 x 20 = 34mm. 
N 1200*1000 



x, - 



R b b 13x400 



= 23tofi<li„~5SO 



h„ 550 

M-M, +m M. - = 300+0, 784xl59,Sx — = 483,2 
1 ° 2 b 400 

VI 483 ? 
e, = tt ^ -tit- = 0,403m = 403mm 



N 1200 
V<ft ketctfu tlnh dinh: 



e = e. +- e a = 403 + 34 = 437 mm 



437 






= 0.785 > 0,3 



K 550 

^h = 0-6 x550 = 330mm 

x, = 231 < E^h^ Tinh theo miong hop Ifech \Srn 16n: 

h ri 600 .. ,<„ 
e - e, - — a = 4j7h d0 = 687mm 

11 : 2 



A S1 = 


N(e + 0.5x, 


-K) 




0.4R V 2 






1200 


< 1000(68? *■ 


116- 


550} 



Ti lecd'tth£p m = 



I). 4x260x500 

5838 



= 5838mm' 



= 0,0243=2,43^. 



600x400 
Chon dung 16 $ 22 - 16 x 380 = 6080 mm' 



Hink 510. Tier Jip\ 

cot cila tin du I 









:fio<2 






i 








. 1 










a 


* 




s 


-i 




"IT' 


• 


1 


M. 


130 


130 


I 
130 




600 





157 



Kiirn Ira; Chon lop bao v£ c„ = 30mm; a=C„ + -:= 30+— = 4i 

h Q = 600 - 41 = 559mm > 550 da dung de luih toan. 

Thi dtt 2: Vdj ki'ch ihuoc va v£t lieu nhu a tin du 1 ., yeu cau tfnti cot thep di chiu 
bo ba aoi lite g6m N = 230QKN; M x = 142 kNm; M y = 120 kNm. 

Cot thu6c ket cau sieu tinh. 

8d lieu: C K = 600; C y = 400mm; l m ^ l oy - 4000; 

R b = 33; Et, = 29000, R s = R; = 260 MPa; £, R ~ 0,60. 

?. X = 23J5; ?- y = 34.7; I = 34.7. 
Xet uo'n doc: r», = 1; N (h> . = 19500 kN. 

19500 
M xl = 142; M y , = 1.13 x 120 - 135.6 k>Jm. 

M xl 142 M vl |35,6 , 

C y 0.6 C, 0.4 

Tmh theo phucms >\ 

h = Cy = 400mm: b = C s = 600mm. 
Gia thiet a = 45mm; h = 400 - 45 = 355mm: Z = 310. 

M t = M yl = 135,6 ■ M 2 = M X = J 42. 

N 2300x1000 __ . ... 

x, ^ = = 295mm < h. =r 35:> 

1 R h b 13x600 

M=M l +m n M^ = 135,6 + 0,5xi42x^ = i83kMm 
1 ° 2 b 600 

183 
1 2300 

K£'t cau sieu t&ih: e = max (e ]( eJ^SQmm 

e ^ = i°_, a 225<0,3. 

h„ 355 



158 



Tinh toan iheo tnrdng hop nen l£cft lam rat be: 

I 1 



r e = 



= 1,634 



(0,5^£)(2 + c) (0,5-0,225)12 + 0,225) 

cp = 1 .028 - 0.0000283/. 2 - 0.0016 k 
= 1.028 - 0,0000288 k 34.7 2 - 0,0016 x 34.7 = 0.938 



0,3 



0,3 



-R b bh -13*600x400 



K. = 



<P e 



0,984 



R,-Rb 



A, = 2811 mm 2 . ja, = 



2811 



600x400 



260-13 



= 0.0118 = 1,18% 



Bo tn 14«(>16. co A s[ = 2834 mm" 



■-c :5 




JjTiirA 5.//. 7"r# t/wf r<if 
Cf/a /Af du 2 



Thi du 3: Cho C, = 800; C y = 600; ! m = / , = 3600mm; R b = 9; R, t = K = 340 MPa; 
N = 2700 kN. M x = 560 ; M y = 330 kNm. Yeu cau unh col thep. 

So lieu: t; R = 0.56. 

360Q 



A x = 



X = 



0.288x800 

3600 

0.288x600 



= 15.6 < 28 , bo qua anh hucmg uon doc 



- 20. 8 < 28 , bo qua uon doc, r\ = 1 . 



. M xl _560_ 



M XJ =M, = 560; C( Qg 

M vl =M=330;^U^ 
yi y C v 0,6 



= 700 



= 550 



159 



Co — — > — — . Tlrih Iheo phirang x. 
C x C 



h = q = 800; b = C y = 600;Gia thi& a = 40. 
h = 760; Z = 720mm; £ R h = 0,56 x 760 ^ 426 mm 
M, = M s1 = 560 ; M 2 = M yl = 330 
IN- 2700x1000 



>: - 



R,b 9x600 



= 500mrn<h =760 



m = 1-0,6^ = 0,605 

M = 560 + 0.605 x 300 x — = 794, 5kNm 

600 

794 5 

e, = = 0,295m = 295mm 

' 2700 

K£l c^'u sieu ilnh : e = max (e,, cj, e (1 * 295mm. 

e ^95 
£ = ^- = ^— *=O.388>0.3. 
h e 760 

Dong ihdi x , = 500 > 4 R h = 426. 

Tinh toan rheo iruang hop nen I6ch l&ni be: 



x = 






K vffii^^fiLfc — *&37 

° h 800 



.\ = 



0.56 + 



0.44 



A s .= 



H50x0.37 2 
Ne-R b 6x(h. Q -x/2) 



760 = 486mm 



**** 



e = e n - 1 - — a * 295 + 400-40 = 655mm 

2 

27O0xl00Ox655-9x6O0«468C760-234) 

A . = ■ — = 4485mm" 

sl 0,4x340x720 

W du 4. Tiet dien vudng canh C = C v = 500mm; /^ * / oy = 3200. 



160 



Be tons; co R b - 16,5, efli ihep co R, = R, c = 400MPa. Lire nen tinh loan N = 1600 kN, 
M x = 400loNm: M v = 200 kNm. 

B6 qua do lech tarn rtglu nhien. 
Yeu edit tinh cot thep. 

So lieu; R b = 16.5: R s -R 4C = 4Q0MPa; t R = 0,53- 

3200 






= 22. 2 < 28 - Bo qua uo'n doc, n. = 1 . 



0.2SSx500 

Gia ihid'c a = 50, h = 450; Z = 400mm; b = 500. ' 

c R h = 0.53 x 450 = 23Smm 

N 1600x1000 lrti 
' R b b 16,5x500 " K ** 

i94 

m =l-0.6x = 0,741 

* 450 

M = 400 + 0.741 x 200 = 54S,2 kNm. 

5-kS ^ 
e, = ^-^ = 0.343™ = 343mm; e =343 
1600 ° 

e = e -r-^-a^ 343- 250-50 = 543mm 

e 34" 
6 =- -2~ = — - = 0.762 >0,3.Ddng thcxi x f < £ R h , tinh toan theo rien lech tarn Ion. 

* ? " 1600x1000(543 + 97-450) _„ 
A,. = ^— — = = 4750mm- 

0,4R (1 Z 0,4x400x400 

Tiep theo. thur dung phtxong phap quy doi thanh tiet diSn trdn ti/ong dirang dc 
tinh toan: 

D= 1,05x500 = 525 mm 

a = 50:r = 0,5D = 262;r a ~r-a = 212mm 

(3 =i- = — = 0,809 
3 r 262 

nD 2 3 ,UxS25 2 j 

A = = = 2 16500mm 

4 4 

161 



N 1600x1000 _ .._ 
n= = = 0,448 

R h A 16,5x2)6500 



M=^/M*+Mj = >/400 2 + 200 2 = 447.2kNm 

Bo qua uon doc ncn Nn,e = M ~ 447.2. 

ttfi^ 447.2*10* m 

R b A b r 16.5x216.100x262 

Vori n = 0.448; m = 0,478 ira bieu do. noi suy co dugc a = 0.54 (ung v<3i p u = 0,309 
vuR v =400.Phuluc 10). 

aR.A b 0.54x16.5x216500 , onn 

Aj = — t — 2- 4822mm" 

1 R, 400 

Kei quii aiin vol gia tri da tt'nh (itfOC 6 1 iren. 

Khi khong co bieu do phii hop co ih£ iinh loan iheo hucmg dan o inuc 4.2.5 va thco 
Ihidu2amuc4.2.6. 

5.7 TiKH TOAN K1EM TRA 

5.7.1. Nguyen tec ehung 

Tie'i d>en cho iruoc vol cue co'i ihep 6k duac bo in. Ycu cau kie'm ira xcm liei dien 
co du kha nans chiu dupe n.161 b6 bit noi luc 56m N\ M v M v . 

Theo nguyen lac, vice kiem ira can dira vao dieu kien (5-6) va (5-7) trong do co the: 

a) Tif dieu kifcn (5-7) ch.0 N ■ N„ h , xac dinh vung chiu nen. cac ung suai ctj. iinh loan 
M. ;b va duns dieu kien (5-6) Ne < M^ de kiem Ira. 

b> Vci iruong hop nen lech lam be co the lim each xac dinh N flh va kiem ira theo 
dieu kien N < N ph . 

Vjec iinh loan nhir iren la kha" phuc lap vi con phai Ihoa man dieu kien lhang hang 
cua ba diem dal lire. Cho den nay. irong nhieu iruong hop nguoi la van dung phuong 
phap can dung. Sau day irinh bay phuong phap g£n diing da dupe cong nhan fpng rai va 
cune da duac dua vao lieu chuan ihiei ke cua nhieu nude. 

De~ iinh loan chiu ra cac irudng hop pbu thu6c vao dp Ion cua lire nen. 

5.7.2, Truunjz hop Itfc nen kha Ion 

Luc ncn dugc xem ]a kha Ion khi Ihoa man dieu kien (5-17): 

162 



N>0.5 R b C,Q (5-17) 

Co the xern khi thoa man dichi kien (5-17) la trucmg hop nen lech tarn be. can kiem 
ira kha nana chiu lire nen. 

Kha nang chiu Urc nea la N^ duc/c xac dynh i\i phtf<mg iririh {5- LSI. 

1 J_ J I 



N 



•\h 



- N v N 



(5-18) 



Trong do: 

Ny - khu nang chiu nen diing tarn, xac dinh theo cong thuc (1.6) diroc chep lai 
s;iu day: 

N x - kha nang chiu nen iruong hop lech cam phang khi tmh loan theo phucmg x. 
Tinh N\ theo gia tri da bie't cua Hi hoac cua f\e os . 

N v - nhu triJn. theo phi/cng y. 

Khi da co bieu do tuong tac cua tier dien iheo hai phicong x \a y thi viec xac dinh N t 
va l^ diroc tien hanh mot each de dang (hmh 5.12). Luc N x duac xac djnh tu bieu do 
CD X (hlnh ?.Sa) vol tg|J, = n^.n hoac vol VI* = n v M v Luc N, iix bieu d6 CD V (hmh 

S.Hb) vdi igl% - tVV no '> c v< ^ ^C = ^j^V Chu <' rang iheo hai each (tgfr hoac M") co 

the xac dinh duac hai gia tri N khdc nhau, Trong tinh loan thtrc hanh chi can theo moi 
each con ncu iheo ca hai each Ihi co the lay gia iri N ton hem d£ finh loan tiep. 

Bieu do CD X va CD V duoc thUft lap tren ca so tinh loan nen Ifich tarn pbang theo hai 
phirong rieng biel (xem muc 2.5 va 2,7-5). Cung can chu y rang :sf> phai lay theo ti Ic 
cac true cua bieu do" {d day tgp co don vi la dp dai). 

H i 2 



n k ___^___: 





N ( «,_- 



M". 0, 



///nA 5-/2- So do. xac dinh N x 



163 



Trucmg h<?p khong co* bieu dd tirong tac thi co ib£ dung phuong phap linh loan da 
irinh bay trong muc 2.4.4; 2.4.5 hoac 2.7.6 de tinh loan N x , N v (luj 1 ihuoc vao each bo' tri 
cor thep). 

Phuong irinh (5-18) duoc Boris Bresler (My) 6i xua't nam 1960 tren co so g£n diing. 

thay dudng cong D Kx D Kv a hinh 5.9a bang duong lhang, lhay doan CD Ka a hinh 5.8c 
bang doan lhang. Vi each x6i gan dung, don eian hoa nhu v5y nen irong m6( so' truong 
hop co d6 an loan kha cao. 

Khi chpn va be' tri c6t thep (khdng tinh loan) thi can kiem tra dieu ki6n N < N gh . 

Khi da tinh toan col thep mot each dang tin cay theo muc 5.6 thi khong can linh 
loan N oll Iheo phuong irinh (5-18) va khong can kiem Ira theo dieu kien vua neu. Trong 
mdi so truong hap khi lay cot thep da tinh duac theo muc 5.6 d£ xae dinh N„ h thi co ihe 
xay ra N > N gh . Luc nay khong nen vpi ket lu&n la liet dien khong du kha nang chiu !uc 
hoac cot thep con thieu ma nen kiem (ra lai can than eac budc. dieu kien. cong ihtfc va 
so lieu da dung de" tinh loan. Neu vice tinh loan cot thep la dung dan thi ket qua van 
duoc chap nban. So dl xay ra N > N £h v) N gh da duoc linh toan gan dung, trong trtrong 
hop nay lai qua thien ve an toan nen gia tri tim duoc la kha be so vci kha nang ihuc cua 
liet dien. 

5.7.3. Trifong hop niomen Ian (luc nen be) 

V'6'i mot liet dien cho trudc kiem Ira kha nang chiu luc khi luc nen la luong doi be 
(N < 0.5 R h A b ). momen luong do'i Ian can lien hanh iheo dieu ki£n (5-19): 



V = 






M„ ) { K, 



(5-19) 



Trong do M ( „. M lrt la kha nang chiu momen uon duac xac dinh theo iruoitg hop 
nen lech lain phang theo hai phuong x va y ung voi lure nen N. Gia iti cua M^va M r 
duoc the hien bang doan K D Kv va O k D Kv tren hinh 5.9a. 

Dieu kien (5-19) la thi hien su van dung phuong irinh (5-S) da thicE lap dua tren 
phan tich su lam viec cua cau kien. 

Khi co bieu do tuong tac cua nen lech lam phajig theo hai phuong thi viec xac dinh 

M^va M* y la tucmg dpi dan gian iheo hinh 5. 13. Vdi gia tri N da bie't. lir bieu do CD X 

tim ra M^, x , tu CD y tim ra M* v . 
164 




I 



N. »■ , 







Htnh 5.13. St/ do xac dinh M m vh M ov 



-v 



Truong hop khong co bie'u do (ucnig lac co ihe u'nh loan MV, M^ mot each gan 
dung nhu sau: 

Tren bieu do CD X tfnh hai gia in rndmen ting voi hai diem: Diem D v (N == 0), 
momen M Ql la kJia nung chiu udn ph5ng iheo phirong x. Ditm B. v6i lire nen N^ va 
momen M Bv Diem B x diroe xac dinh tlseo tri/otig hap nen lech tarn phang vol chieu cao 
vung nen x = k v = 0.5C X (liic nay |i = C x ; b = C v ). V6i gia trj da biet cua x lien hanh tfnh 
ling suat o. cua cac lop col thep A, iheo ciic chi dan ciia muc 2.7.2 hoac ciia muc 5.3. 

N Ux = R h C r ^IcY\ (5-20) 

M Gx - D,5R b C y X x (C, - x,) * la^y, <>2U 

Aj - dien tieh tiet dtcn ciia cac lop cot thep. 

y, - khoang each tii trong cam ciia A, den true irung t;im cua ti£t di£n (hinh 
5.14a), Gia m ciia y ; diroc lay theo dau dai so. y, > khi cot thep 6 khac phia voi diem 
dat lire N (so vdi true di qua trong tam tiel dien), y ( < khi col thep acting phia. 

Ung sua't a, Ea dircrng khi chiu keo. am khi chju nen, 

Hai cons thuc (5-20) va (5-21) ta viet lai cac cOng there (2-55) va (2-56). 

Mornen M Da ducrc xac dinh theo truong hop uO'n phang {N = 0). Tir dteu ki6n N = 
lim dtroc chieu cao vung nen x ; tir x tfnh loan ra Kj va o s> dung cdng thuc (2-56) de ti'nh 
M D ,. Voi irudng hop dai cot rhep d6i xung thuong tfnh duoc x < 2a' v] vay nen nnh toan 
iheo truong hop dac biei. dung cong thurc gan dung (5-22) baog each lay momen doi vdi 
true di qua lop cot thep chiu nen ngoaicung (true B-B tren htnh5.14b) va xem s = 2a'. 

(5-22) 
165 



Mp^SRAr* 




5/ 



B 
1 



ffl 



h = C. 




A* 



a =a 



Aj 



Trong do (, ia khoang each lu lop col ihep ihii i den true BB (hinh 5. J 4b). Trong 
cong thixc (5-22) chl lay cac lop co'r ihep co I, > u - max (4a' va 0.3h) de n'nh loan. 

Gia iri M ori tXuoc tfnh theo c6ng ihuc (5-25). 

De tinh toan M* v can xac djoh M By , N Uv va M D( ung vol hai diem B > va D y tren 

hie'u <\6 CD V . Tfnh toan M BjM N Bv va M^ cung lien hinh luong tir nhu tren. into phuong 
y. iheocac ki liieu tren hinh 5.15 (luc nay h = C v ; b = C x ) Lay x v = 0.5h = 0»5C V . 

(5-23) 
M 8v = 0,5 R b C x x v (C, - x J + Ia 1 A l y 1 (5-24) 



N By = R b C K X y -I C r i A l 





Hinh 5.15. Sod6 tinh M Bv M Dx 



166 



Chi lay cac lop c6t thep c6 t; > t, = max (4a' va 0,3h) d£ iinh loan. 
Tinh gia fri M Q! ^ , M theo cong thue chung (5*25); 

N 1 



m;=m Dj +(m 8 . i -m Dj )^- 



N 



(5-25) 



ui 



j = x>y 



Thuc chat cua each tinh gan dung tren day la xac dinh hai diem cua bicu do urong 
lac va xem doan bieu do giCia hat diem la ihang d£ n<M suy. 

So inu n itong dieu kien (5-19) ahu da trinh bay 6 c6ng thuc (5-8) la: 1 < n < 2. Tieu 
chua'n thiel ke cua mot so nude Au My lay n iheo cong thuc thuc nghi£m sau: 



n- 



N -5N 
N -N 



(5-26; 



Vice kiem Tra theo dteu kien (5-19) la bat buoc doi voi trirong hop chon dat col thep 
rheo cau lao ho3c theo mot dir kien ;iao do ,Tia khong tinh loan. 

Khi dat col thep theo ket qua tinh tcin 6 muc 5.6 thi khons can kiem Ira lai theo 
dieu kien (5-19) vi irong mot so triicmg hep kei qua kiem Ira se khong dal yeu cau ma 

nguyen uhan chu y£u la do M." CK . My V d'Jcc tinh toan gan dung, co tn s6 be han kha 
nane thuc ce cua tiet dien. 



5.7.4. Trirong hop tiet dien vuong 

Tie-t dien vuong co so luong cot thep :ii 
12 ihanh ira ien co the diroc kieni ira barig 
each doi thanh tie! dien Iran luong duemg. 
duong kinh D = 1,05C (C; canh tiet diea 



vuong). Momen (inh toan M = yM x + M: . 

Voi tiet dien tron khong pban bie)t nen le)ch 
lam la xien hay phdng. 

5.7.5. Thi du tinh toan 

Thi du I. Dung so lieu cua thi du 1 muc 
2.76, col co tiet dien cho cr hinh 2.21, ve lai 
6 hinh 5, 16. Belong co R b = 9» E b = 24000 
MPa. cot thepco R s = R, c = 260MPa , 



14 25 



j 1 

• 


i 


i 

• 

* 


1 


i 






oi 






• 


















-i C 
















• 










• 










* 






oi 




1 














Ti._ _. 




4Cl 

~1 




6C 





40 





















Hinh 5J6. Hinh vectict (hi du I 



167 _ 



Yen can kiem tra liei di£n co du kha nang chiu b6 ba noi lire gom N = 1200 kN: 
M x = 234 kNm; M y = 120 kNcn. Bo qua dp lech tarn ng&u jihien. Chieu dai tinh loan 
L = >ov = 4m. 

So lieu: C, = 600: C y = 400: a = 40mm 

R b - 9; E b = 24000: R, = R^ = 260 MPa; 

Cot ihep 14 ty 25. A, = 6874mm 2 . 

= / 2iL = — 4000 — = 23 j < 28.B6quaurfndoc 
* i,. 0,288x600 

a„ = -^- = = 34, 7 > 28 . Can xet uon doc 

y i v 0.288x400 

Trudng hop iinli loan: 

0.5R h C x C y = 0,5 x 9 * 400 x 600 = 1080000 = 1080 kN 

N = 1200 > 1080. Tinh iheo truong hop luc nen Ion. dungphucmg irinh (5-1S) de 

?iiicdinhNp h . 

Tinh kha ruing chiu nen dung tam N : 
A = max (/.,.. ~L V ) = 34.7 

He so uon doc <p = i ,028 - 0.00002B8A 2 - 0.0016>. 

<p = 1.028 - 0.0000288 x 34.7 3 - 0.0016 x 34.7 = 0.938 

N = «p(R n A + R vc A tl ) vol A = 400 x 600 - 6874 = 233100mm 2 

N = 0,938(9 x 233 100 + 260 x 6874) = 3644000 = 3644 kN. 

Tinh yia iri N v 

Theo pliuoiig x co X x = 23.1: ho qua uo'n doc. r| = 1. 

M ^34 
e, = J- = - — = 0. 1 95m = 195m m 
K 1200 

n,e n = 195mm. 

Thi du c muc 2.7.6, vol r|e = 195mm da tinh duac N x = 2083 kN (da u'nh loan theo 
each gan dung hoac sir dung bieu do tuong tac). 

Tinh gia tri N v „ Tinh loan theo iruong hop nen lech lam phang veti b = C x = 600; 
h = C v = 400mm. Theo phucmg y c6't thep duac dal lhanh 4 hang: 

Aj = A 4 = 5 (J» 25 = 2455 mm 2 : 

A 2 = A^ = 2 4> 25 = 982 mnr; A, = EA, = 6874. 

J 68 



So do tinh loan ve iren binh 5.17. so lieu ghi o bang sau: 



Ki hieu 


Dien tich mm 2 


y,(inm) 


h oj (mm> 


A, 


2455 


160 


360 


Ai 


982 


53 


253 


A, 


9S2 


-53 


147 


A4 


2455 


-160 


40 



ISO , 160 




HiniiS.17. So do tilth N v 

Xei uon doc; X y = 34,7 > 28 can xet udn doc 

. bh 3 600x400' ,_ . o , 

J =— - = = 32x 10 mm 

12 12 

2.5EJ 2.5x24000x32x]0 ! 



N * = /2 



4000 2 



^12000x10 =12000kN 



n = 



1- 



N 



N 



1- 



ih 



1200 
12000 



= 1.11 



M v 120 






N 1200 



= 0.1m = 100mm 



He = 1,11 x 100= Ulnun. 



169 



Tihh ueVc chi/ng chieu cao vung nen theo cong thuc (2-60): 



x(0,5h-,e o ) + ) (0.5h-,e o )^3 8R A(h-2a> 



R b b 



x-(200- 1 ll)-^(200-n 1 )U - 8x260 ': 6874 / 400 - 80 U 393mm 



9x600 



x 393 



!i 400 



= 0,98 



De linh loan c, co the" theo mot irons hai each: Dung cong (hue thirc nghiem (2-54) 
cua TCXDVN 356 - 2005 hoSc dm vao bien dang e„ theo ccng Ihifc (1-24). (1-25). 6 
thi dy ciia muc 2-7-6. khi linh N x da dung cong ihur (2-54). Duoi day, de tinh N v « irtnh 
bay each linh iheo e,. 

Khao sal cua lac gia thay rSng kei qua N iheo hai each (inn la gan bane nhau. Vitc 
trinh bay ca hai each linh chi nh&m mcV rong pliuong phap. Trong linh loan lliuc hanh chi 
can dung moi trong hai phtrcmg phap la diroc. 

Lay hai gia m x de* tinh toan. K Qi =■ 350; x R2 = 300mm 

E, = 2l0000MPa; c T = — = 26 ° =0.001238 

1 E 210000 



Bien dang ciia belong E c = 0.003. 

h„, -x 



Vot: 



x o! = 350;c,=^ 



ri (36o^5maoo3 =OL0000857 



'•>1 



350 



a, = e,£ s = 0.0000857 x 260000 ^ 13 MPa fkeo) 

C253-350)0.003 



e, = 



£> = 



350 

(147-350)0,003 
350 



= -0.00083: c\ = -l/4 (nen) 
= -0.00l74>e T ; o.=-R;=-260 



Kel qua linh loan ve & ; va o, ghi irong bang sau: 



Lop cot iliep 


x„i = 


350 


-\: = 


300 




E . 


o. 


c. 


o, 


A,;h, M = 360 


0,0000857 


18 


0,0006 




126 


A,i h,,. = 253 


-0.00083 


- 174 


- 0.00047 




-99 


A.-,; 1^=147 


-0.00174 


-260 


-0.00153 




-260 


A,: h, u = 40 


x 


-260 


X 




- 260 



1/0 



Ket qua tlnh toan ve lye ghi trong bung sau 



x, 


A,= 


2455 
1 60 


A,= 


53 


A,= 

y: = 


9S2 
-53 


A 4 = 2455 
7, = -160 


aA 


crAy 
10* 


crA 


erAy 
10" 


ffA 
10 1 


cAy 

to" 


I0 3 


aAy 
10" 


350 


44.2 


7,07 


-10,7,8 


-5.7 


-255.3 


13,5 


-63$ 


102,1 


300 

„_ — 


309 


49.4 


-97.2 


-5.1 


-255.3 


13.5 


-63S 


J02J ! 



V6-i x,, = 350: x = 0.85x o = 0.85 x 350 = 298mm 
X, = R b bx - ScA 

Nj = 9 x 600 x 298 - [44200 - 107800 - 255300 - 6380001 = 2566000 
N, = 2566JcN 
N 0.5R i ,bxch-x)^Ig,A l y, 

Xa.A.y, =(7.07-5.7+ 13,5+ 102J)10 6 = U6.97x 10 6 



., 0.5x9x600x298(400-298)+ 1 16.97* 10* ,™^™ 

N, = = 1 /93000 

111 

Vd] x cl = 300; x = 0.S5 * 300 = 255mm 

N, = 9 x 60G x 255 - (309 - 97.2 - 255.3 - 638) 10" = 2058000 

.. _0.5^9x600x255(400-255)^-159.9xl0 6 „™ nn 



111 



Kei qua ti'nh loan ghi a bang sau; 





x, | x 


N, | 


J 


350 


29S 


2566 1793 


K 


300 


:>= 


2058 


2340 



6f- 



2566(2340 - 1 793) - 1793(2058 - 2566) 



2566 + 2340-1793-2050 



Tim duycN v = 2180 kR 



^ B h N s 



N, 



N. 



1 



1 



2083 2180 3644 



= 2180 



= 0,00067618 



171 



H * = 



] 



0,00067618 



^!479kN 



N=1200<N gh = 1479 
Thoa man di6u ki&i N < N gh . Tuy vay muc 66 chfenh lech la kha Ion: 

— '■ x 100% = 23% . De tiei kiem nen giam bor c6i th^p roi linh loan lai. 

1200 ' 

Thi du 2. Vai kfch ihude tiet dien va bo trf col thep nhtf a thi du 1 (huih 5.16). Yeu 
cau kiern ira kha nang chiu b6 ba n0i iuc gom N = 800 JcN; 

M,. = 238 kNm; M v = 1 80 kNm. 

Truong hop linh loan: 

O^R^C, = 0.5 x 90 x 600 x 400 = 1OS00OO = 1080 fcN 
N = 800 < 1080. Tmh ki£m ira theo dieu ki£n (5-19). 

a) Theo phucfng x. Lay x = x,. = 0.5 C v = 300mm 
300 



x c = 



= 353 . Tinh t, va <j, 

0.S5 



£, = "' X ° c c ; £ T =-2^ = 0.001238 



e, = 



£o = 



(56 0-353)0.003 

353 
! 43 -353)0, 003 

353~ 



= 0.00: 76 > St: cr, = R s =260 



= 0.000654 <s t 



a 2 =0.000654x210000 = 137 



e 3 = 



e.i = 



(300-353)0,003 

353 
(170-353)0,003 

353 



= -0,00045; c* -95 



-■■0.00155 : c - 260 



Kel qua linh loan ghi irong bang sau: 



C61 thep 



A*= 1964 



A-, = 982 



A,=9S3 



A, = 982 A,= 1964 



K, 


560 


■VM\ 


301' 


170 


4 


y, 


260 


130 





-130 


-260 


t, 


520 


390 


260 


L31- 





x = 300 
x* = 353 


£, 


0.00176 


0.000c 54 


- 0.00045 


-0.00 J 55 


x 


cr, 


260 


!37 


-95 


-260 


-260 


o,A,(10*) 


5 * 0.64 


134.53 


■ 93.29 


- 255.32 


-510,64 


oAv.dO 6 ) j 132.76 


17,489 





33.19 


132.76 


RAi,(10*) i 265.53 


99.57 


66.3S 


X 


X 



172 



i, = max (4a va0.3h) = mas (160 va 0.3h = ISO) = 180mm. 
Chi lay cac gia iri t, > 1 80 de tfnh loan: 

5-C r V= (5 10,64 + 134.53 - 93,29 - 255,32 - 510,64)10* = - 214 x iff 1 

E^Ajft = (132.76 + 17489 + 33.19+ 132.76)10* = 316.2 x 10* 

N Bx = R b CyX s - Ia,A, = 9 x 400 x 300 - (- 2 14000) = 1294000 = 1294 kN 

M B , = 0,5R b C y x x (C,-x,) T i:(T 1 A l y [ 

= 0.5 x 9 x 400 x 300 (600 - 300) + 316.2 x 10* * 478,2 x 10* 

M B , = 478.2 kNrn 

M Dx = lR,A,t, (265.53 + 99.57 + 66,38)10* = 431.5 x Uf 



Mp„=431.5kNm 



M;,=M 0x +{M Bx -M d ,) 



N 



N 



:k 



M" =431.5 + (478.2 -431.5)-^- =460.4 
» 1294 

b] Theo phiicmg y. Lay x = x > = 0.5 C y = 200mm 
200 



x„ = 



:-.ss 



= 235mm . Kel qua imh loan ghi Irong bang sau; 



Col thep 


A, = 5<j>25 = 2455 


A : = 2<t>25 = 982 


A, = 2*23 =982 


A, = 5<t>25 = 2455 


li„. 


360 


253 


147 


40 


y, 


160 


53 


-53 


-160 


t. 


320 


213 


107 





s. 


0.00159 


0.000229 


-0.001257 


x 


°. 


260 


48 


-260 


-260 


<X|A,<Mft 


638.3 


47.13 


- 255.32 


-638.3 


oAy.d^ 


102.13 


2.5 


13,53 


102.13 


RAt.ilO*) 


204.26 


54.3S 







I. = max (4a" = 160 va 0,3h = 120) = (60. 



M 1>v chi dugc n'nh voi A, va A-, co I > 160. 



M Djr = SR^Ajt, = (204,26 + 54,38)10* = 258.64 x 10* 
M Dy = 258,64 kNm 
N By = R b C v x y -ZaA 

= 9 x 600 x 200 - (47,13 - 255,32)10' = 1288 x 10' = 1288 kN 



173 



M % = 0,5R b C x x Y (C y - x v ) + ScAiy, 

= 0,5 x 9 x 600 x 200 (400 - 200) + <102,13 + 2,5 + 13,53 + 102,13)10* 
M By = 328,3 x 10 6 = 328,3 kNm. 

M^M^.+fM^M^.)-^ =258,64+{328,3-25g,64}i^ = 30J.9 

M* y =301.9 kNm 

c) Xac dinh Nrje^ va NV|e oy 
Thco pfiuong x bo qua anli hcrong uort doc ncn: 
Nrie^ = M x = 238 kNm 



Thco phircmg y co L h = -^ = 



L 4000 



C ; . 400 



= 30> 



fhoac A = -^ 



4tW 



- 34,7 > 28) 



0.288x400 

Cm x£i uon doc. Da linh duoc N th = 1 2000 kN (thi du 1 ) 
i 



T| = 



1~ 



800 



-1.07 



12000 
Bo gua do lech tam ngiu nhien nen: 

N^e (1> = iiM ; . * 1.07 x 180 * 192.6 kNm 
d) Tinh n va kiem tra 



n = 



n = 



»■•' = 






. 6 thi du 1 da linh duoc N„ = 3644. 



364 4 + 5x80 0^ 
3644 -r 800 

Nile 



0.5 



= 1.31 



." 



K 






* 



Ml, 



23S > 

460,4 



uj 



■+- 



192.6 
,301.9 



>ui 



^4213^0,555 = 0,9763 



\u = 0.9763 < 1. Thoa man dieu kien ki£m ira. 



174 



Phu luc 1 

HE SO DIEU KIEN LAM VIEC CUA BETONG 
(TRICH TCXDVN 356 : 2005) 



Cac veu to can ke den he so dieu kien lam vifcc cua be tong 



He s6 KDLV 
ciia be long 



. Tai tTong tup irung d6ngj 



KI hieu j Gia u i 
i 

Co quy 

dinh riena 



! 2. Ti'nh chai i.ic dung cua lai Irong: 

|a) Khi ke den (ai irons thuong xuyen. tai irong iam ihoi dai han va ngan 

! han ngoai (fir iai irong tac dung ngan han ma ions ihoi gian tac dung cua 

chiing croog ihoi gian S\i dung nho; cuns nhu khi ke* de"n tai irong dae 

biei gay bien dung lun khcng d^u v.v... 

al> Do'i veil be tong nang, b€ t6ng hai nho. be long nlie dong ran tu nhi<in 

va be tong duoc duong h6 nhiet trong die'ii kien mot iruong 

+ Dair bao cho be (dng dugc liep ttic rang cuang d6 iheo (hoi gian 
I + Khong dam bao cho be tong dtfoc ciep luc tang cuong do iheo thai gian 
ja2) Doi vol be long to ong. be tong rong, khong phu thuoc vaodicu kien: 

i sit dung 

i ■... . - - ■ 

! b» K.hi ke din lat irons lam ihoi ngiln han (tac duna ngan haoj irong to 

h$p dang \ei hay tai irons die biei" khong neu trong mac 2a, dot voi 

cac loai be i6n«* 



1,0 
0,9 
0.35 

1.10 



3. 06 be tdng iheo phtfong diing. moi iop day tren 1.5m doi voi: 
+■ Belong nang, be long nhe va be tong hat nho 
+ Be tong to ong va be tong rong 



']V 



4. Ann huong cua trans thai img suat hai true "nen - keo" den cuong do 
be i6ae 



0.85 
0.85 



5 Oo be ions cot iheo phirotig dung, kich thuoc Ion nhai ciia li.et dien 
cot nho han 30cm 



' fe 



O.to 



* Khi dua ihcm hd so' die'u kien iam vi£c oo sung irong truong hop ke' 

dfin tai irong dac bi£i iheo chi dan cua ligu chua'n mong Ling (vf du: khi 

ke den lai irong dong dal) thi lay y K = 1 . 

CM (Ai'cA: 

/. He so dieu kim titm viec /„, dtfgc dung khi nnh iheo do bin mot. hi s6 

Yw difoc dims de xdc djnh ctfdng do chin keo khi tinh loutt kiern tra dieu 

kien suduiig bhth ihv&ng (irwig thai gioi hats thirl}, 

2. Cac he stffij. fi,j. 'fa dung de xdc dinh cuong do tinh loan R H cua can 
kien be /ong cd't iliep ihu&ng (ngom irii ke't edit dung b£ tdn% id ong con 
phdi xii them dd am cua be (ong). 

3. Khi co dSng didi cac yen id can ke den he so dieu kien Jam viec (hi lay 
y ; , bang rich am cac he so n^ng bu'f. khong phu thuoc tan nhau. 



175 



Phu luc 2 

CU&NG DO TfNH TOAN 
VA MO DUN DAN HOI CUA BE TONG 



Circmg do linh loan cua be tong kf hieu ia R b diroc cho o bang cua phu luc. Khi co 
cac ye'u co kc den diiu kidn lam viec cua b£ long thi R b c&n duoc nhan voi he so didu 
kien lam viec y b (cho 6 phu luc f ). 

Gia in cua R b duoc Yiy phu thuoc vao mac hoic cap d6 ben cua be tOng. 

Theo lieu chain TCVN 5574 - 1991 (lieu chuan cu) thi mac la con so lay bang 
cuong dp chiu nen irung blnh cua mau ihir lieu chuan linh iheo don vi kG/cm . Ki hieu 
mac bangchirM. Be long co cac mac: M75;M)00; M150;M200... M800. 

Theo tieu chuan TCXDVN 356:2005 (lieu chuan hien hanh lhay the TCVN 5574 - 1991 ) 
thi cap do ben la con so* lay bang cuong d6 dac inms cua cac mlu ihir tieu chuan linh 
theo don vi MPa. Cuong dp dac trirng diroc xac dinh theo ti'nh loan thong ke voi xac sua'i 
bao dam khong duai 95%. Ki hieu cap do ben bang cliur B. Be long co cac cH'p d6 ben 
B5; B7.5; BIO: B12.5. B15... B60. 

Co the Jhiel lap luong quan giua B va M iheo bicu ihuc sau: 

a - he s6 chuyen doi do*n vi giira .MPa va kG/cm". (lay g£n dung IMPa = 
]0kC/cm\ ru do a =0.1). 

P - h£ so' xac djnh theo linh loan thong ke. Voi phan pho'j chuan va xac sua'l bao 
dam 95% thi p = 1 - 1,64 v irong do v la he so bien dOng. 

Vai be long co chat luong thi cong bao darn co the lay v = 0. ! 35. nhu vay (3 = 0.77S. 
Hang PL2a. Cuong do linh loan R b cua be tong (trieh TCXDVN 356 : 2005) 





Gia in K t * MPa ling voi cap do ben hoac mac cua be long 


Loai be i6ng 


B15 


B20 


B25 


B30 B35 


B40 ! B45 B50 


B55 | B60 




M2<i:.' 


M250 


M350 


M400 


M450 1 M500 ! M600 


M700 


M750 


M800 


He lOnc nanf 
Be iftng hat nho 


8.5 


n,s 


14.5 


I7.Q 


19.5 


i 

22.0 [ 25.0 


27,5 


30.0 


33.0 


Be i£ng nhe 8.5 


11.5 


14.5 


17.0 


19.5 ! 22,0 j 


- 


- 


- 



Chu ihick: Khi co cac yeu lokedeh siflam viec cua he long thi can nhan gid iri cua R n cho 
t'oag btifi£ voi he s& *f h & phu luc t . 

176 



Bang PL 2b. Modun dan hoi £ b cua be tong 
(theoTCXDVN 356: 2005) 



r— — — 




Cia" iri cua E h : 10'MPa tfng voi cap do ben va m^c cua belong 


Loai be sOng 


B15 


B20 


B25 


B30 


B35 


B40 


545 


B50 


B55 


B60 


M200 


B250 


M350 


M400 


M450 


M500 


M600 


M700 


M750 


MS00 


Betfing 
nang 


Dong ran 
[ir nhien 


23.0 


27,0 


30.0 


32,5 


34.5 


36.0 


37,5 


39 


39.5 


40.0 


DirSng ho 6 ap 
sua't khi quyen 


20,5 


24,0 


27,0 


29,0 


31,0 


32,5 


34.0 


35 


35.5 


36.0 


Chung ip 


RQ 


20,0 


22.5 


24,5 


26.0 


27.0 


28.0 


29 


29.5 


30.0 


hat nho 

ii horn A 


Dong ran 
Ctf nhien 


19.5 


22,0 


24.0 


26.0 


27,5 


28.5 


- 


■ 


- 


- 


Duong ho a ap 
suai khi quyC'n 


17,0 


20,0 


21,5 


23.0 


24,0 


24.5 


- 


- 


- 


- | 


Belong 
ha l alio 
nhom B 


Dong ran 
tu nhi^n 


17,0 


20.0 | 21.5 
i 


23,0 


- 


- 






- 


- 


Dirong ho tf ap 
suat khi quyCn 


15.5 


17.5 


19,0 


20.5 




- 


- 


- 


- 


- 



Chii thick: Be long hat nho nhom ,4. cot lieu cat co modun dd lot\ > 2- Bi tdng has nho 
nhom B, cot lieu cut co modun do Ian £2. 



177 



Phu luc 3 

CUC5NG do tinh to an va mO dun dan h6i cua cot thep 



Cuong d6 tj'nli toan cua col thep ve kco R s va ve nen R ec diroc lay theo nhom hoac 
loai c6i thep. 

Theo lieu chuan TCVN 1651 - J985 col thep can nong ducfc chia thanh cac nhom 

ci, en, an. civ. 

Theo lieu chuan TCVN 6285 - 1997 c6'i thcp ducc chia theo cac loai RB300; 
RB400; RB400W; RB500; RB500W (con so dang sau chu RB la gidi nan chay cua col 
thep v&t xic suat bao dam 95%, tinh bang MPa). 

Cot Ihcp AI. An... AVI la cdt thep cua N°a. 

Bang PL3a. Curing do tjnh roan cua cot thep thanh 



Nhom. loai cot thep 


Cucms do tinh loan - MPa 


Chiu keo R, 


Chin n?n K (L . 


C1.AI 

CIK All. RB300. 

AIIT co ducng ki'nh 6 ■*■ 8mm 

CHI, RB400. RB400W. AII1 co duong kinh 10 + 40mm 

RB5OO.RB5O0W 

CtV.AfV 

AV 

AVI 

A T VII 


225 
280 
355 
365 
400 
510 
680 
815 
980 


225 
280 
355 
365 

400 
400 (450) 
400 (500) 
400 (500) 
400(500) 



Chu thick: Cac sd'Iifu d6i v&i thep C! * CIV va Ai + A T VH dupe lay theo TO'N 356: 2005. 
Con s6 ghi t''ong ngoqc dot v&i R 1C : (450), (500> ditoc dung khi trong tinh loan ke den cac tat 
trong rime 2a cua PLl . 

Cac so lieu dor \vi cO'i tltep RB300 ^ RB5Q0 dim lay theo cac hat thep tuang duong 

Trong nhi/iig wrong hop can he den su lam nee cua cot thep thi R, va R iT pftdi dupe nhdn 
vol he sodieu kien /dm vtec cua cot thep y sr \'6i ket can dung be long /the, he long toong dung 
he so y t ~ y^. Voi ket can dung cot tficp c.U&ng do cao tir nhom CIV lid leu dung he so y^. Ket 
cc'iu chin mi trong rung ddng dung he so y s j. y^. Cac he sd nay dupe cho trong TCXDVN 356 . 
2005 diets 5.22.4. 

Voi cdr cluu nen dung be long /tang thong ihuong va dung cos thep co /?, <400 MPa not 
chung khdng can hi din he soy r 

Bang PL 3b. Modun dan hoi E s cua col thep 



Nhom. loai c6i thep 


CI. AI CII. AU. 

R?>300 


OH. Am. RB400, 
RB500 


CIV, AIV.AV.AVI, 
A T VII 


E.:MP a 


210000 1 200000 


190000 



17S 



Phu luc 4 

HE SO ^ DE PHAN BIET CHIEU CAO 
VUNG CKIU NEN CUA BE TONG 



Theo TCXDVN 356 : 2005 ht s6't yR dircrc xac dinh b^ng cong thuc thuc nghiem: 



SR 



1 + 



c 



SR 



a 



SC,U *■ 



u 



co - dac (rung vung chiu nen cua be long: <o = a — 0,008R & 
R b - ti'tih bang don vi MPa. He so ct lay nhu sau: 

Doi vdi b& tong nang : a = 0.85. 

Doi vol be Jong hat nho nhdm A: ci = 0.80 

Doi vol be tdng hat nho nhom B: a = 0,75 

Doi vdi be i6ug nhe: a =0,80 
a SR - ung su& trong co'i ihep (MPa) 
Doi vdi c6i thep co gidi han chdy ihirc tc" <R X < 4O0 MPa) 

Doi vdi coi ihep c6 gi6i han eMy guy u6c (CIV, AIV, AV, AVI, A T VII): 

a Sft = R, + 400-o %p -Aa ip 
o, p - img sua't trudc tcong col thep. Voi cac cot bang be long cot thep thuong thi 

*» = °- 

Ao\ p - gia s6 cua tfng sua't trudc irong cO't thep, phu thuOc vao phuong phap cang. 
Vdi cac cot thdng thudng Aa s _ = 0. 

c?j. c u - ilug suat gtdi han cua cot ihep 6 vung chju nen, duac 13'y nhu sau: 

Doi voi cac cau kien lam til be long nang, be long hat nho. be t6ng nhe, tuy thuoc 
vao cac yeu td neu irong bang phu luc I. 

- Vdi loai tai trong i*ic dung nhu tai muc 2a: a Kll = 500MPa 

- Vdi loai tai trong tac dung nhu tat muc 2b: a !CU = 400MPo. 



179 



Bang PL4. H£ so £ R dfi'i v6f ca'u kien lam tir be tdng nflng va c6't thep Ihuang 



RJMPa) 


Gia tri 4r frig v oi R& cua b£ t6ng 


3 


10 


12 


15 


17 


20 


22 


25 


28 


30 


225 


0.677 


0,658 


O.640 


0.613 


0,596 


0.570 


0.553 


0.532 


'"" " ~ — ^ 
0.503 


0.487 ; 


280 


0,655 


0.636 


0,6] 7 


-.590 


0,573 


0.S47 


0.530 


0,510 


0,480 


0,465 


365 


0,623 


0.604 


0,585 


0,558 


0,540 


0.510 


0,498 


0,479 


0.449 


0,433 


400 


0,611 


0,592 


0,573 


0,546 


0,528 


0.502 


0,485 


0.467 


0.437 


0,422 


510 


0,576 


0,556 


0,538 


0,510 


0,493 


0.467 j 0,451 


0.433 


0.404 


0,390 



Chit thick: Gia trj Rj, dung de xac dinh £ s duac tilth v&i he so y hV khdng ke den cac he so 

n, Mac. 



180 



PhuIucS 
CONG TttUC GIA1 PHLQNG TRIHH BAC BA 



Cho phuong trlah: x 3 +■ ax 2 + bx + c = 



Dai 



2 = x + — d6i thanh: z + otz + y = 

L a 2 2a 5 ab 

a = b ; y = + c 

3 27 3 



Dat 



K = y 2 +4 



f a tf 



Os 



Cic phirong trinh b&c 3 khi tfnh chieu cao vdng nen cua tiet dien belong cot thep 

:0. 

i 



ihdng thuong deu co K > 0. 



A - 



D = 



y+ 



7k ^ 



z = ~(A+D);x = z-- 

Thi da: pbucmg irinh x 3 - 3x 2 + 5x - 6 = 
a = b = > = 2 

y = A ( _ 3) 3_ 6 _il^) = _ 3 
27 3 



K = y 2 +4 



'a v 



,3; 



3 



-(-3) 2 +4J-| =10,185185 



A = 



D = 



y 



+7k 



-k/k 



\- / 



- 2 



■ — 

3 



3 



-3 + ^/10185185 



V 



=; 0,457427 



= -1,457427 



z = - <A + D) = - (0,457427 - 1,457427) = 1 
3 
5 



x =z — = l+~ = 2 



IS I 



Phu luc 6A 

BANG TRA CAC HE s6 ^ g, c^ 



«; = l-0.5S;<x m = 4C 1^-0,5 



l + ^-2«m) 



$ 


; 


«* 


0,01 


0.995 


0.01 


0.02 


r i. -.vo-:: 


0.02 


0.03 


0.985 


0.03 


0,04 


0.980 


0,039 


0.05 


0.97S 


0.049 


0.06 


0.970 


0.058 


0.07 


0.965 


< n-17 


0.08 


0.960 


0.077 


0.09 


0.955 


0.086 


0.10 


0.950 


0.095 


0,11 


0.945 


0.104 


0.E2 


<. /MO 


0.113 


0.:) 


0.935 


0.121 


0.14 


0.930 


0.130 


0.15 


0.925 


0.139 


0.16 


0,920 


0.147 


0.17 


0.915 


0.155 


0.18 


0.910 


0,104 


O.J 9 


0.905 


0.172 


0.20 


0.900 


0.180 


0.21 


0.&95 


0.188 _, 


0,22 


0.S9O 


<i.:9t 


0.23 


Q.88S 


0.203 


0.24 


0.SS0 


0.211 


025 


0.&75 


0,219 


0.26. 


0.870 


0,726 


0.27 


0.865 


0.234 


0.28 


C.S60 


0.241 


0.29 


0.855 


0.248 


u. ?;; 


0.S50 


0.255 


oj i 


0,S45 


0,262 


0.32 


0.840 


0.269 


0.33 


O.S35 


0.275 


0.34 


0.830 


0.2H: 



K 


L c 


On, 


0.35 


0.825 


0.289 


u..* 


0.820 


"0,295 


0,3? 


0,815 


0,301 


0.38 


0.S1O 


0.308 


0.39 


0,80.5 


0.314 


0.40 


o.soo 


0,320 


0.41 


0.795 


0.326 


0.42 


O.790 


0.332 


0A2 


0,783 


0037 


0,44 


0,780 


0.345 


0.45 


0,775 


0.349 


0.46 


0.770 


0.354 


0.47 


0.765 


0,559 


0.48 


0.760 


0.365 


0.49 


U.O- 


0.570 , 


0.50 


o.oo 


0,375 


0.5 i 


0.745 


0.380 


0.52 


0,740 


0.385 


0.53 


0,735 


0.390 


0.54 


0,730 


0.395 


0.55 


0,703 


0.400 


C.56 


0.720 


0.403 


0.57 


0,715 


0,407 


0.58 


0.710 


0.412 


0.59 


0,705 


0,416 


0.60 


0,700 


0.420 


Col 


0,695 


0.424 


0,62 


0.690 


0.428 


0.63 


0.685 


0.432 


0.64 


0.680 


0.435 


0.65 


0.675 


0,439 


0,66 


0.670 


0.442 


0.67 


0.665 


0.445 


0.6S 


0.660 


0.449 



182 



Phu luc 6B 

BANG TRA HE SO a,; T 



T = a 3 (0.5a a -1); a a =lWl + 2T 



a u 


T 


2.0 


o.co 


2.1 


0,105 


2.2 


0,220 


2.3 


0,345 


2.4 


0,480 


2.5 


0,625 j 


2.6 0,780 


2,7 J 0,945 


2.3 


1,120 


2.9 


1.305 


3,0 


1.500 


3.1 


1.705 


3.2 


1.93": 


J.3 


2.J45 i 


3,4 


2,330 


3.6 


2.880 ' 


3.7 


3,145 


3.8 


3.420 


V-< 


3,705 

i 


4.0 ' I 4.000 > 


4.1 j 4.305 


4.2 | 4,620 


4.3 | 4,945 


4.4 I 5,280 


4.5 .5.625 


4.6 


5,980 


4,7 


6.345 


4.S 


6.720 


4,9 


7,105 



«* 


T 


5.0 


7,500 


5,1 


7,905 


>2 


$.320 


5,i 


8.745 


5,4 


9, ISO 


5,5 


9.625 


5.6 


10.080 


5,7 


10.545 


5,8 


11.210 


5,9 


11,505 


6.0 12.000 

i : 


6.J 12,505 


:;.: 13,020 


n.3 


13.545 


6,5 


14,625 


6.6 


15.1 SO 


6.7 


15,745 


6.8 


16,320 


6.9 


16,905 


7.0 


17.50 


7.1 


18,10 


7.2" 


IS.72 


7.3 


19,34 


7.4 


19,98 


7.5 


20.62 


7.6 


21,28 


7.7 


21,94 


7.8 


22.62 


7.9 


23.30 



«, j * 


S.O 24.00 


8,1 


24.70 


S.2 


25,42 ' 


3.3 


26.14 


H.- 


26.88 


8.5 


27.62 


3.6 


2S.3S 


8.7 


29.14 


R.S 


29.92 


8,9 


30,70 


9.0 


31,50 


9.1 


32.30 ! 


s>.2 


33.12 | 


V..i 


33.94 


9.5 


35.62 


9.6 


36,48 j 


9.7 


37,34 


9.S 


38.22 


9,9 39.10 


1,0 ! 40.00 


10,1 


40,90 


10.2 


4I.S2 


10,3 


42,74 


10,4 


43.68 


10,5 


44,62 


10.5 


44,62 ; 


10,7 


i&.' : 


10.8 


47.52 


10.9 48,50 



183 



Phu lux 7 
BANG TRA D1EN T1CH VA TRONG LUtJNG COT THEP 



.mm 




Di6n tich li£'i di£n ngang. mm" - ling 


vol s6' thanh 




Trpng 
iuong Im 

<kG) 


) 


2 


3 


A 


5 


6 


7 


8 


9 


6 


28,3 


57 


85 


113 


142 


170 


198 


226 


255 


0,222 


8 


50,3 


100 


151 


201 


251 


302 


352 


402 


453 


0.395 


10 


78,5 


157 


236 


314 


392 


471 


550 


628 


707 


0,617 


12 


113. L 


226 


339 


452 


565 


679 


792 


905 


1018 


0,888 


14 


153.9 


308 


462 


616 


769 


923 


107? 


1231 


1385 


1.208 


16 


201. 1 


402 


603 


804 


1005 


1206 


1407 


1608 


1810 


1.578 


18 


245,5 


509 


763 


1018 


1272 


1527 


1781 


2036 


2290 


1,998 


20 


314.2 


628 


942 


1256 


1571 


1885 


2199 


2514 


2827 


2.466 


22 


380,1 


760 


1140 


1520 


1900 


2281 


2661 


3041 


3421 


2,984 


25 


490,9 


9S2 


11.73 


1963 


2454 


2945 


3436 


3927 


4418 


3,853 


28 


615.8 


12.>2 


1847 


2463 


3079 


3695 


4310 


4926 


5542 


4,834 


30 


707.0 


1414 


2120 


2827 


3534 


4241 


4948 


5655 


6362 


5,549 


32 


804.2 


IM>8 


2412 


3217 


402! 


4S25 


5630 


6434 


723S 


6,313 


36 


1018 


2036 


3054 


4072 


5090 


6108 


7126 


8144 


9162 


7,990 


40 


1256 


2512 


3768 


5024 


6280 


7536 


8792 


10040 


11300 


9.870 



184 



Phu luc 8A 



HO BIEU DO TUONG TAC 
T1ET DIEN CHCNHAT, COT THEP DOI XUNG, 5 = 0,05. 



2.4 



2,2 



i ■ 



K6 



1 4 



U 



1.0 



0.6 



Co 



G.4 



0.2 



V 1 






1 






a n *r 


1 

i 

b 

1 
_I_ 




\ i 
i 


$£\ 


8 = — = u.w 




**= 






1 \ 


A 






i * * 


3 


^=0.45- 


X 






a 


\ ^ 


% 


~ 












h 


n- N ! 




\c 














\*K 


V 


X 












■\ \ 




\ v 










RA 




\\- 




v 


V. \ 


% 


( 




X 


X 






x 


x 


I 


i 
i 
I 


\ \ 




1 N 


*» 


\ 


\ 


i 










, \ 


L "\ 


\ \ 
vv 

V. 

V-v 


X 








\ 


L \ 

\ 


^ 






\ 'X 

x 




V s 

\ 

1 


\\ 


\ \ 
s \ 

\ \ 




s \ 


\ \ 
V \ 

\ \ 
\ \ 
\ \ 
% \ 






1 ' 




\ " 






\ \ 

v H 

\ 1 

\ 1 

vl 






/ 


/ 


/ 1 


/ 

/ 


V 


/ 




* 


■" 


> 


s / 


s 


/ 


/ 





0.' 



0.2 



0,3 



G.J 



0,5 



3 



3.7 



m 



185 



Phu luc 8B 

HO BIEU D<5 TUONG TAC 
TIET DltN CHtf NHAT, C6T THEP £>0'l XtSNG, 5=0,1 




Phu luc 9 

Blfo d6 ttjonc tag cua 

TIET Dl£N CHCNHAT CO COT THEP DAT THEO CHU VI 



Bieu ct<5 loai nay phu thuoc kha nhieu thong stf. Trong phu luc nay chi gidi thiiu mdr 
vai bieu do lam dai dien, chua du miic pho bien. Cac co so* thiet ke co Ih6 theo hirong 
dan sau day de* lap ra cac ho bieu do phu hop vol thuc \£ ihifift ke" cua co set 

Lap bieu do cua mot tie't dien da cho: theo thi du ciia rnuc 2.7.4. 

Lap ho bieu do khdng thti nguyen iheo cac birdc sau (xem hlnh 2.18). 

1. Du kieh each bo iri coi (hep. biei long so thanh, tinh he so k, cua cac lop cot thep: 

A C 
k, = — L - — L . Trong do C ( la tdng so ihanh cot thep, Cj la so thanh a lop thu 1 i - cac 

thanh co cung duong kfnh <j>. Co A $l - C t f .. Chon ti so' co't thep ^ (u^ = 0,005 *■ 0,06). 

Tlieo ki hieu; u, = — — . 
v bh 

p 

2. Chon cueJng do linh loan cua be t6ng R b va cua cot thep R,.. Tinh p s = — - 

R b 

3. Chon ti so" 5 = - (thong thucmg 5 - 0,05 - 0, 12). 

h 

4. Tinh khoang each giua cac lop cot thep. Khi dat n lop cot thep thi khoang each 
h - 2a s 1 - 2o 



s = ; ct = — = • 

n -l h n -i. 

Tinh h oi cua cac lop co't thep; h oi = h - a - (i - 1 )s. 

r ( =^=t-a-(i-0o: o 
n 

5. Tinh khoang each lif true lie't dien den trong tarn cac top ccit thep y-: 

y i = h oi -0,5h;|3 i =^- = r i -0,5 

n 

6. Ttnh to theo chi dan 6 phu luc 4: to = a - 0,008 R b . Vai be t6ng nSng thdng 
thucmg a = 0,85. Gia tn R b theo don vi MPa. 



187 



7. Lap chuong trinh hoac cac bang tinh toin bang each cho gia tri 4 'bay doi *if 0,1 

V 

den 1 . Theo dinh nghia £ *• — - 

h 

Tinh cac gia iri p ( ting vdi i; va c<5t thdp A^: 

a 






SC.il 



1-^ 
1,1 



°-l 



Gia tri a SCAl lSty theo muc 2.7.2. hoSc theo phy luc 4: 
Thong thudng lay a SCM = 400 MPa. 



p, = 



sC.U 



Kh 1- 



co 



U> 



cry. 



-i 



p 
Dieu ki£n la: - p s < p, S p„ v6i p = — 



R, 



N£'u tinh dicoc p, > p s thi lay p t ^ Ps 

Pi < - p s thi lay ^ =- p 5 . 
Uhg vdi moi gia tri £ linh dupe m&t cap n va rn (xtm cOng ihiic (2.57), (2.58). 

m=0,5^1-y+ t i s Ik 1 p j B i 

8. Cho n* thay d6i s£ co duac m6t ho bieu d6. 



18$ 



Phu)uc9A 

BIEU DO TUDNG TAC TIET DT£N CH&NHAT COT THEP 
DAT THEO CHU VI (12<t>) VCJl R b = 1 1,5; R, = 280 MPa 




1-39 



Phu luc 9B 

Bl£u d6 Tl/ONG TAC Tl#T WEN CHtfNHAT COT THEP 
DAT THEO CHU VI (12*) VOl R b = 17; R, = 280 MPa 



*V = {4 * Z + 2 - 4H> = 12+ 



5= -0.05 



5 = 0.1 




0.05 0.1 



0.15 0.2 C.25 0,3 0,35 0.4 0,45 m 



190 



Phu luc 9C 



BIEU D6 TU3NG TAC TIET DIEN CHUNHAT C6*T THfr 
DAT THEO CHU VI ( l2 « V0I %, . - 17- R, = 400 MPa 



\ = (4*2 + 2*4fc*12$ 

R,*17.R,*400MR| 

5-f.= 0,05 



ft* 




191 



PhuIuc9D 

BEU D6 TIKJNG TAC TIET B1EN CHONHAT c6t THfeP 
DAT THEO CHU VI (]4<|>) V(3l R* = 14,5; R, = 365 MPa 



2.4 



T,l 



2.1 



1.8 



-.6 



i; 



'.2 



1.0 



o.e 



0,4 



0.2 

























b 




ft • • • 

• • 

• * 

T • ♦ T 




A„ = (4*2*2*4>i-=144» 
R^= 14.5; «V 365 MPa 


\ ^ 




«-g-0 


(tt 






















Rtbh 








I 
( 

■ 


N n e, 




V 


XN. 








o 


k \ 

v X 

X *" ' 
X * 
X i 


x\ 








V 


Not 

X -s 


\\ \ - \ \ 






^ 
\ 


L\ 


X \ 
X ^ 

\ V 

X. 1 


\ N \ ^ 
\ \ \ \ 

\ % \ N 






s 


V\ 

\v 

X, \ 
X "I 

"V v 

X \ 

X V 

". * 
\ v 


X \ 
X \ 
x ^ 
X \ 


^ \ '* 

\ \ «, 

\ \ \ 

V \ \ 

V v i 


\ \ 

\ V 
\ \ 
\ \ 


\ 
\ 


( 
\ 


^> 


\ s 


p 


\ v! \ \ 


K \ 
\ \ 


1 

i 

i 




V V- 


i 


\\ \ \ \ 


i 


\ \ 
\ \ 
\ \ 






■ ' 




i 

: 1 

i 

i 

1 / 


\ \ 


\ • 




1 
i 

i 


1 
\ 
1 






1 ! 
j I 


! I 




i 

i 
> 

i 
i 


1 
I 




J 


s / 
/ / 


/ / 

/ ' 

/ / 


/ 1 I 
/ I f 

1 ! / 
f / 
/ / 


// 


~ — 


'// 





0.1 



02 



C.3 



0.4 



0.S 



0,6 



192 



Phu luc 10A 
BI1EU DO TUDNG TAC TIET DIEN TRON V(5l (3 a = 0,9 






R t = flOO 



""lyf 







193 



Phu luc 10B 

BLEU DO TUDNG TAG TtfiT DI$N TR6N VCJI J», = 0,J 




r, = r-a 



Ay = Dien Uch loan b& 
cdllftep-dcc 



194 



Phu luc 11A 
Bl£U DO TUDNG TAC TIET DIEN V6^G KHUYEN V<3l p a = 1,1 




0.2 0.3 



195 



Phu luc 11B 

BIEU DO TUDNG TAC TIET DIEN VONG KHUYEN V(3l (}„ = 1 



1.8 



U> 



'.4 



5.0 



o.s 



cf 



04 



0.2 




196 



Phu luc 11C 
Bl£u DO TLtJNG TAC TIET DIEN V6NG KHUYEN VCtt p, = 0,9 



R =400 




197 



MUC LlIC 

Trang 

Ldi noi ddu 3 

Chtfong 1. Dai cirong ve" kimng va cot betong ceil thep 

1.1. C&c buck thiei k£ k£t ca'u khung 5 
\ .2. So do ket cau khung 6 

1.3. To hop noi luc khung 9 

1.4. Dai ctrong v£ col \~) 

1.5. JSJpj lire vh do lech lam 25 

1 .6. Sir Um viec cua tift difcn col 30 

Chixong 2, Tift dien chu: nhat chiu ticn lech lam phang 

2J . Sd do va c6ng thurc co ban 39 

2.2. Tinh loan col thep ddi xifng 43 

2.3. Tinh toan col thep khong do'i ximg 53 

2.4. Ti'nh toan kha nang chiu fuc 6 1 

2.5. Bi&i 6*6 tirong fie 66 

2.6. "JwiJi loan v6i nhieu cap n6i luc 7S 

2.7. Tie! difen c6 cdt thep d&t theo chu vi 33 

Chuang X Tiel dien chiJT va chif 1 

3. 1 . Dai cuong vi tiet dien chu T 96 

3.2. Noi luc va dieu ki§n tinh toan 97 

3.3. Tift dien c6 canh bi nen 100 

3.4. Tiet dien c6 canh bi keo 109 

3.5. Ti'nh liet dien chu" T vdi hhieo c%p noi Juc J 14 

3.6. Tinh loan liet dien chu I 1 15 

3.7. Thidu ti'nh toan 117 

Chtfffttg 4. Tiet dien Iron va vong khuven 

4.1. Dai cuong ve cot co tie*t di&n tron va vong khuven 122 

4.2. Tinh toan net dien iron 126 

4.3. Cau ki6n co cot dai 16 xo 134 

198 



4.4. Tiet dien vong khuyen 136 

4.5. Tiet dien Iron va vong khuyen dac biet 140 

Chuong 5. Tiet dien chu nhat nen lech tam xien 

5. 1. Dai cuorig ve nen lech tam xien 141 

5.2. Noi lire nen lech tam xien 142 

5.3. Sir lam viec nen lech lam xien 143 

5.4. Cdng ihiic va dieu kien long quat 146 

5.5. Mat bie'u do tucmg tac 148 

5.6. Phuong phap gan diing cuih cot thep „ 153 

5.7. Tinh loan Idem Era 162 
Phu luc I . He so die*u kien lam viec cua belong (trich TCXDVN 356 : 2005) 175 
Phu lye 2. Cixong do tinh loan va mo dun dan hoi cua be long 176 
Phil luc 3. Cirong d6 lijih toan va mo dun dan hoi cua c6'c thep 178 
Phu Luc 4. He so 4r de phan biel chieu cao viing chiu nen cua be lOng 179 
Phu luc 5. Cong thuc giai phuong trinh bac ba 18 1 
Phu luc 6A. Bang tra cac he so £, £ , o^ 182 

Phu toe 6B. Bang m \\t *>6 a a ; T \ S3 

Phu luc 7. Bang ira dien ti'ch va irong tucmg cot thep 184 

Phu luc 8A. Ho bie'u do luong tac tiet dien chu nhat. cot (hep doi xutig, 6 = 0.05 185 

Phu luc SB. Ho bieu d6 tucmg rac net dien chu nhat, co'tthep d6i xung, 5 =0.1 186 

Phu luc 9. Bieu d6 tucmg tac cua liel di£n chu nhat co cd't thep dat Iheo chu vi 187 
Phu luc 9A. Bie'u do luong tac tiet dien chu nhat co't thep dat Iheo chu vi 

(12<|>) v6i R h = 11.5: R, = 2S0 MPa 189 
Phu luc 9B. Bieu do tucmg tac tiet dien chir nhat cot thep dat theo chu vi 

(12*) voi R a ~17;R^ = 2S0MPa 190 
Phu luc 9C. Bifi'u d6 tuong tac tiet dien chu nhat cd't thep dat theo chu vi 

(12*) vol R h = 17; R, = 400 MPa 191 
Phu luc 9D. Bieu do luong tac tiet dien chu nh&t cot thep dat theo chu vi 

(14*) vc?i R b = 14,5; R s = 365 MPa 192 

Phu luc 10 A. Bieu do' tucmg tac tie! dien iron vol 0, = 0,9 193 

Phu luc 10B. Bieu do tuong tac tiet dien tron v6'i J3 a = 0,8 194 

Phu iuc 1 1A. Bieu d6 tuong uic lift dien v6ng khuyen voi P. = 1,1 195 

Phu luc LIB. Bieu do tuong tac tiet dien v6ng khuyen vdi (3 4 = 1 196 

Phu iuc 1 1C. Bie'u d6 tuong uic ufit dien vong khuyen vdi (3, = 0,9 197 



199 



TINH TO AN TB&T DD5N 
COT B&TONG COT THEP 



Chi 


if trdch nliitm xuds ban : 




BOlHUUHANH 


Bi£n sap . 


DiNTfBAOHANH 


Che ban ; 


LETHI HUONG 


Sua ban in : 


DINH BAO HANK 


Bia: 


vO BtNH MINK 



In 1000 cuon kh6 19 x 2?cm, tai Xucrtig in Nha xuac bin Xsy dung. G'&y chap nljikn dans ty fc£ 
hoach xuat ban stf H33/XB-QLXB-02. ngay 26/&2005. In xong ndp tuu chi&u ihang 5-2006.